Comprehensive Inorganic Chemistry III, Third Edition (Comprehensive Inorganic Chemistry, 3) [9, 1 ed.] 0128231440, 9780128231449

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COMPREHENSIVE INORGANIC CHEMISTRY III

COMPREHENSIVE INORGANIC CHEMISTRY III EDITORS IN CHIEF

Jan Reedijk Leiden Institute of Chemistry, Leiden University, Leiden, the Netherlands

Kenneth R. Poeppelmeier Department of Chemistry, Northwestern University, Evanston, IL, United States

VOLUME 9

NMR of Inorganic Nuclei VOLUME EDITOR

David L. Bryce Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, ON, Canada

Amsterdam • Boston • Heidelberg • London • New York • Oxford Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo

Elsevier Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom 50 Hampshire Street, 5th Floor, Cambridge MA 02139, United States Copyright Ó 2023 Elsevier Ltd. All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions. This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein). Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary. Practitioners and researchers may always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein. In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility. To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein. Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library ISBN 978-0-12-823144-9

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CONTENTS OF VOLUME 9 Editor Biographies

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Volume Editors

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Contributors to Volume 9

xv

Preface

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9.01

Introduction: NMR of inorganic nuclei David L Bryce

1

9.02

Nitrogen-14 NMR spectroscopy Diego Carnevale

4

9.03

19

F NMR on polymers Ulrich Scheler

26

9.04

Applications of 17O and 51V NMR in inorganic and bioinorganic chemistry Jianqin Zhuang, Qian Wang, and Rupal Gupta

35

9.05

NMR of carboranes David Ellis

62

9.06

Applications of silicon-29 NMR spectroscopy Darren H Brouwer

107

9.07

High field solid-state nmr of challenging nuclei in inorganic systems Frédéric A Perras and Alexander L Paterson

138

9.08

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry Hellmut Eckert

178

9.09

Solution NMR spectroscopy of single-molecule magnets Markus Enders

209

9.10

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements Yuji Furukawa

230

9.11

Solid-state nmr studies of halide perovskite materials with photoconversion potential Guy M Bernard, Abhoy Karmakar, and Vladimir K Michaelis

261

9.12

Solid-state NMR of energy storage materials Kent J Griffith and John M Griffin

282

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Contents of Volume 9

9.13

A review of exotic quadrupolar metal nmr in mofs Bryan EG Lucier, Wanli Zhang, Andre Sutrisno, and Yining Huang

330

9.14

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants Daniel Jardón-Álvarez and Michal Leskes

366

9.15

NMR of nanoparticles Cory M Widdifield and Navjot Kaur

398

9.16

NMR studies of 2D and pseudo-2D systems Kristopher J Harris

450

9.17

NMR of catalytic sites Kuizhi Chen, Yuting Sun, and Guangjin Hou

471

9.18

The expanding frontier between mechanochemistry & solid state NMR: Special focus on inorganic components of materials César Leroy, Thomas-Xavier Métro, and Danielle Laurencin

514

9.19

Advances in the characterization of inorganic solids using NMR correlation experiments Andrew GM Rankin, Frédérique Pourpoint, Nghia Tuan Duong, Laurent Delevoye, Jean-Paul Amoureux, and Olivier Lafon

534

9.20

Solid-state nmr of glasses Mattias Edén

583

9.21

Solution NMR of transition metal complexes Zi-Ling Xue and Tabitha M Cook

660

9.22

Transition metal nmr thermometry Ökten Üngör, Tyler M Ozvat, Josef V Grundy, and Joseph M Zadrozny

745

9.23

Gas-phase NMR of nuclei other than 1H and Piotr Garbacz and Włodzimierz Makulski

771

9.24

Applications of NMR spectroscopy in cultural heritage science Molly Wagner, Jaclyn Catalano, Valeria Di Tullio, Roberta Pigliapochi, Nicholas Zumbulyadis, Silvia A Centeno, and Cecil Dybowski

788

9.25

Advances in the computation of nmr parameters for inorganic nuclides Sean T Holmes, Fahri Alkan, and Cecil Dybowski

837

13

C

EDITOR BIOGRAPHIES Editors in Chief Jan Reedijk Jan Reedijk (1943) studied chemistry at Leiden University where he completed his Ph.D. (1968). After a few years in a junior lecturer position at Leiden University, he accepted a readership at Delft University of Technology in 1972. In 1979 he accepted a call for Professor of Chemistry at Leiden University. After 30 years of service, he retired from teaching in 2009 and remained as an emeritus research professor at Leiden University. In Leiden he has acted as Chair of the Department of Chemistry, and in 1993 he became the Founding Director of the Leiden Institute of Chemistry. His major research activities have been in Coordination Chemistry and Bioinorganic Chemistry, focusing on biomimetic catalysis, molecular materials, and medicinal inorganic chemistry. Jan Reedijk was elected member of the Royal Netherlands Academy of Sciences in 1996 and he was knighted by the Queen of the Netherlands to the order of the Dutch Lion (2008). He is also lifetime member of the Finnish Academy of Sciences and Letters and of Academia Europaea. He has held visiting professorships in Cambridge (UK), Strasbourg (France), Münster (Germany), Riyadh (Saudi Arabia), Louvain-la-Neuve (Belgium), Dunedin (New Zealand), and Torun (Poland). In 1990 he served as President of the Royal Netherlands Chemical Society. He has acted as the Executive Secretary of the International Conferences of Coordination Chemistry (1988–2012) and served IUPAC in the Division of Inorganic Chemistry, first as a member and later as (vice/past) president between 2005 and 2018. After his university retirement he remained active as research consultant and in IUPAC activities, as well as in several editorial jobs. For Elsevier, he acted as Editor-in-Chief of the Reference Collection in Chemistry (2013–2019), and together with Kenneth R. Poeppelmeier for Comprehensive Inorganic Chemistry II (2008–2013) and Comprehensive Inorganic Chemistry III (2019-present). From 2018 to 2020, he co-chaired the worldwide celebrations of the International Year of the Periodic Table 2019. Jan Reedijk has published over 1200 papers (1965–2022; cited over 58000 times; h ¼ 96). He has supervised 90 Ph.D. students, over 100 postdocs, and over 250 MSc research students. Kenneth R. Poeppelmeier Kenneth R. Poeppelmeier (1949) completed his undergraduate studies in chemistry at the University of Missouri (1971) and then volunteered as an instructor at Samoa CollegedUnited States Peace Corps in Western Samoa (1971–1974). He completed his Ph.D. (1978) in Inorganic Chemistry with John Corbett at Iowa State University (1978). He joined the catalysis research group headed by John Longo at Exxon Research and Engineering Company, Corporate Research–Science Laboratories (1978–1984), where he collaborated with the reforming science group and Exxon Chemicals to develop the first zeolite-based light naphtha reforming catalyst. In 1984 he joined the Chemistry Department at Northwestern University and the recently formed Center for Catalysis and Surface Science (CCSS). He is the Charles E. and Emma H. Morrison Professor of Chemistry at Northwestern University and a NAISE Fellow joint with Northwestern University and the Chemical Sciences and Engineering Division, Argonne National Laboratory. Leadership positions held include Director, CCSS, Northwestern University; Associate Division Director for Science, Chemical Sciences and Engineering Division, Argonne National Laboratory; President of the Chicago Area Catalysis Club; Associate Director, NSF Science and Technology Center for Superconductivity; and Chairman of the ACS Solid State Subdivision of the Division of Inorganic Chemistry. His major research activities have been in Solid State and Inorganic Materials Chemistry focusing on heterogeneous catalysis, solid state chemistry, and materials chemistry. His awards include National Science Council of Taiwan Lecturer (1991); Dow Professor of Chemistry (1992–1994); AAAS Fellow, the American Association for the Advancement of Science (1993); JSPS Fellow, Japan Society for the Promotion of Science (1997); Natural Science Foundation of China Lecturer (1999); National Science Foundation Creativity Extension Award (2000

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and 2022); Institut Universitaire de France Professor (2003); Chemistry Week in China Lecturer (2004); Lecturer in Solid State Chemistry, China (2005); Visitantes Distinguidos, Universid Complutenses Madrid (2008); Visiting Professor, Chinese Academy of Sciences (2011); 20 years of Service and Dedication Award to Inorganic Chemistry (2013); Elected foreign member of Spanish National Academy: Real Academia de Ciencia, Exactas, Fisicas y Naturales (2017); Elected Honorary Member of the Royal Society of Chemistry of Spain (RSEQ) (2018); and the TianShan Award, Xinjiang Uygur Autonomous Region of China (2021). He has organized and was Chairman of the Chicago Great Lakes Regional ACS Symposium on Synthesis and Processing of Advanced Solid State Materials (1987), the New Orleans National ACS Symposium on Solid State Chemistry of Heterogeneous Oxide Catalysis, Including New Microporous Solids (1987), the Gordon Conference on Solid State Chemistry (1994) and the First European Gordon Conference on Solid State Chemistry (1995), the Spring Materials Research Society Symposium on Environmental Chemistry (1995), the Advisory Committee of Intense Pulsed Neutron Source (IPNS) Program (1996–1998), the Spring Materials Research Society Symposium on Perovskite Materials (2003), the 4th International Conference on Inorganic Materials, University of Antwerp (2004), and the Philadelphia National ACS Symposium on Homogeneous and Heterogeneous Oxidation Catalysis (2004). He has served on numerous Editorial Boards, including Chemistry of Materials, Journal of Alloys and Compounds, Solid State Sciences, Solid State Chemistry, and Science China Materials, and has been a co-Editor for Structure and Bonding, an Associate Editor for Inorganic Chemistry, and co-Editor-in-Chief with Jan Reedijk for Comprehensive Inorganic Chemistry II (published 2013) and Comprehensive Inorganic Chemistry III (to be published in 2023). In addition, he has served on various Scientific Advisory Boards including for the World Premier International Research Center Initiative and Institute for Integrated Cell-Material Sciences Kyoto University, the European Center SOPRANO on Functional Electronic Metal Oxides, the Kyoto University Mixed-Anion Project, and the Dresden Max Planck Institute for Chemistry and Physics. Kenneth Poeppelmeier has published over 500 papers (1971–2022) and cited over 28000 times (h-index ¼ 84). He has supervised over 200 undergraduates, Ph.D. students, postdocs, and visiting scholars in research.

VOLUME EDITORS Risto S. Laitinen Risto S. Laitinen is Professor Emeritus of Chemistry at the University of Oulu, Finland. He received the M.Sc and Ph.D. degrees from Helsinki University of Technology (currently Aalto University). His research interests are directed to synthetic, structural, and computational chemistry of chalcogen compounds focusing on selenium and tellurium. He has published 250 peer-reviewed articles and 15 book chapters and has edited 2 books: Selenium and Tellurium Reagents: In Chemistry and Materials Science with Raija Oilunkaniemi (Walther de Gruyter, 2019) and Selenium and Tellurium Chemistry: From Small Molecules to Biomolecules and Materials with Derek Woollins (Springer, 2011). He has also written 30 professional and popular articles in chemistry. He is the Secretary of the Division of Chemical Nomenclature and Structure Representation, International Union of Pure and Applied Chemistry, for the term 2016–2023. He served as Chair of the Board of Union of Finnish University Professors in 2007–2010. In 2017, Finnish Cultural Foundation (North Ostrobothnia regional fund) gave him an award for excellence in his activities for science and music. He has been a member of Finnish Academy of Science and Letters since 2003.

Vincent L. Pecoraro Professor Vincent L. Pecoraro is a major contributor in the fields of inorganic, bioinorganic, and supramolecular chemistries. He has risen to the upper echelons of these disciplines with over 300 publications (an h-index of 92), 4 book editorships, and 5 patents. He has served the community in many ways including as an Associate Editor of Inorganic Chemistry for 20 years and now is President of the Society of Biological Inorganic Chemistry. Internationally, he has received a Le Studium Professorship, Blaise Pascal International Chair for Research, the Alexander von Humboldt Stiftung, and an Honorary PhD from Aix-Maseille University. His many US distinctions include the 2016 ACS Award for Distinguished Service in the Advancement of Inorganic Chemistry, the 2021 ACS/SCF FrancoAmerican Lectureship Prize, and being elected a Fellow of the ACS and AAAS. He also recently cofounded a Biomedical Imaging company, VIEWaves. In 2022, he was ranked as one of the world’s top 1000 most influential chemists.

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Zijian Guo Professor Zijian Guo received his Ph.D. from the University of Padova and worked as a postdoctoral research fellow at Birkbeck College, the University of London. He also worked as a research associate at the University of Edinburgh. His research focuses on the chemical biology of metals and metallodrugs and has authored or co-authored more than 400 peer-reviewed articles on basic and applied research topics. He was awarded the First Prize in Natural Sciences from Ministry of Education of China in 2015, the Luigi Sacconi Medal from the Italian Chemical Society in 2016, and the Outstanding Achievement Award from the Society of the Asian Biological Inorganic Chemistry in 2020. He founded Chemistry and Biomedicine Innovation Center (ChemBIC) in Nanjing University in 2019, and is serving as the Director of ChemBIC since then. He was elected to the Fellow of the Chinese Academy of Sciences in 2017. He served as Associated Editor of Coord. Chem. Rev and an editorial board member of several other journals.

Daniel C. Fredrickson Daniel C. Fredrickson is a Professor in the Department of Chemistry at the University of WisconsinMadison. He completed his BS in Biochemistry at the University of Washington in 2000, where he gained his first experiences with research and crystals in the laboratory of Prof. Bart Kahr. At Cornell University, he then pursued theoretical investigations of bonding in intermetallic compounds, the vast family of solid state compounds based on metallic elements, under the mentorship of Profs. Stephen Lee and Roald Hoffmann, earning his Ph.D. in 2005. Interested in the experimental and crystallographic aspects of complex intermetallics, he then carried out postdoctoral research from 2005 to 2008 with Prof. Sven Lidin at Stockholm University. Since starting at UW-Madison in 2009, his research group has created theory-driven approaches to the synthesis and discovery of new intermetallic phases and understanding the origins of their structural features. Some of his key research contributions are the development of the DFT-Chemical Pressure Method, the discovery of isolobal bonds for the generalization of the 18 electron rule to intermetallic phases, models for the emergence of incommensurate modulations in these compounds, and various design strategies for guiding complexity in solid state structures.

Patrick M. Woodward Professor Patrick M. Woodward received BS degrees in Chemistry and General Engineering from Idaho State University in 1991, an MS in Materials Science, and a Ph.D. in Chemistry from Oregon State University (1996) under the supervision of Art Sleight. After a postdoctoral appointment in the Physics Department at Brookhaven National Laboratory (1996–1998), he joined the faculty at Ohio State University in 1998, where he holds the rank of Professor in the Department of Chemistry and Biochemistry. He is a Fellow of the American Chemical Society (2020) and a recipient of an Alfred P. Sloan Fellowship (2004) and an NSF Career Award (2001). He has co-authored two textbooks: Solid State Materials Chemistry and the popular general chemistry textbook, Chemistry: The Central Science. His research interests revolve around the discovery of new materials and understanding links between the composition, structure, and properties of extended inorganic and hybrid solids.

Volume Editors

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P. Shiv Halasyamani Professor P. Shiv Halasyamani earned his BS in Chemistry from the University of Chicago (1992) and his Ph.D. in Chemistry under the supervision of Prof. Kenneth R. Poeppelmeier at Northwestern University (1996). He was a Postdoctoral Fellow and Junior Research Fellow at Christ Church College, Oxford University, from 1997 to 1999. He began his independent academic career in the Department of Chemistry at the University of Houston in 1999 and has been a Full Professor since 2010. He was elected as a Fellow of the American Association for the Advancement of Science (AAAS) in 2019 and is currently an Associate Editor of the ACS journals Inorganic Chemistry and ACS Organic & Inorganic Au. His research interests involve the design, synthesis, crystal growth, and characterization of new functional inorganic materials.

Ram Seshadri Ram Seshadri received his Ph.D. in Solid State Chemistry from the Indian Institute of Science (IISc), Bangalore, working under the guidance of Professor C. N. R. Rao FRS. After some years as a Postdoctoral Fellow in Europe, he returned to IISc as an Assistant Professor in 1999. He moved to the Materials Department (College of Engineering) at UC Santa Barbara in 2002. He was recently promoted to the rank of Distinguished Professor in the Materials Department and the Department of Chemistry and Biochemistry in 2020. He is also the Fred and Linda R. Wudl Professor of Materials Science and Director of the Materials Research Laboratory: A National Science Foundation Materials Research Science and Engineering Center (NSF-MRSEC). His work broadly addresses the topic of structure–composition– property relations in crystalline inorganic and hybrid materials, with a focus on magnetic materials and materials for energy conversion and storage. He is Fellow of the Royal Society of Chemistry, the American Physical Society, and the American Association for the Advancement of Science. He serves as Associate Editor of the journals, Annual Reviews of Materials Research and Chemistry of Materials.

Serena Cussen Serena Cussen née Corr studied chemistry at Trinity College Dublin, completing her doctoral work under Yurii Gun’ko. She then joined the University of California, Santa Barbara, working with Ram Seshadri as a postdoctoral researcher. She joined the University of Kent as a lecturer in 2009. She moved to the University of Glasgow in 2013 and was made Professor in 2018. She moved to the University of Sheffield as a Chair in Functional Materials and Professor in Chemical and Biological Engineering in 2018, where she now serves as Department Head. She works on next-generation battery materials and advanced characterization techniques for the structure and properties of nanomaterials. Serena is the recipient of several awards including the Journal of Materials Chemistry Lectureship of the Royal Society of Chemistry. She previously served as Associate Editor of Royal Society of Chemistry journal Nanoscale and currently serves as Associate Editor for the Institute of Physics journal Progress in Energy.

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Rutger A. van Santen Rutger A. van Santen received his Ph.D. in 1971 in Theoretical Chemistry from the University of Leiden, The Netherlands. In the period 1972–1988, he became involved with catalysis research when employed by Shell Research in Amsterdam and Shell Development Company in Houston. In 1988, he became Full Professor of Catalysis at the Technical University Eindhoven. From 2010 till now he is Emeritus Professor and Honorary Institute Professor at Technical University Eindhoven. He is a member of Royal Dutch Academy of Sciences and Arts and Foreign Associate of the United States National Academy of Engineering (NAE). He has received several prestigious awards: the 1981 golden medal of the Royal Dutch Chemical Society; in 1992, the F.G. Chiappetta award of the North American Catalysis Society; in 1997, the Spinoza Award from the Dutch Foundation for Pure and Applied Research; and in 2001, the Alwin Mittasch Medal Dechema, Germany, among others. His main research interests are computational heterogeneous catalysis and complex chemical systems theory. He has published over 700 papers, 16 books, and 22 patents.

Emiel J. M. Hensen Emiel J. M. Hensen received his Ph.D. in Catalysis in 2000 from Eindhoven University of Technology, The Netherlands. Between 2000 and 2008, he worked at the University of Amsterdam, Shell Research in Amsterdam, and Eindhoven University of Technology on several topics in the field of heterogeneous catalysis. Since July 2009, he is Full Professor of Inorganic Materials and Catalysis at TU/e. He was a visiting professor at the Katholieke Universiteit Leuven (Belgium, 2001–2016) and at Hokkaido University (Japan, 2016). He is principal investigator and management team member of the gravitation program Multiscale Catalytic Energy Conversion, elected member of the Advanced Research Center Chemical Building Blocks Consortium, and chairman of the Netherlands Institute for Catalysis Research (NIOK). Hensen was Head of the Department of Chemical Engineering and Chemistry of Eindhoven University of Technology from 2016 to 2020. Hensen received Veni, Vidi, Vici, and Casmir grant awards from the Netherlands Organisation for Scientific Research. His main interests are in mechanism of heterogeneous catalysis combining experimental and computation studies. He has published over 600 papers, 20 book chapters, and 7 patents.

Artem M. Abakumov Artem M. Abakumov graduated from the Department of Chemistry at Moscow State University in 1993, received his Ph.D. in Chemistry from the same University in 1997, and then continued working as a Researcher and Vice-Chair of Inorganic Chemistry Department. He spent about 3 years as a postdoctoral fellow and invited professor in the Electron Microscopy for Materials Research (EMAT) laboratory at the University of Antwerp and joined EMAT as a research leader in 2008. Since 2015 he holds a Full Professor position at Skolkovo Institute of Science and Technology (Skoltech) in Moscow, leading Skoltech Center for Energy Science and Technology as a Director. His research interests span over a wide range of subjects, from inorganic chemistry, solid state chemistry, and crystallography to battery materials and transmission electron microscopy. He has extended experience in characterization of metal-ion battery electrodes and electrocatalysts with advanced TEM techniques that has led to a better understanding of charge–discharge mechanisms, redox reactions, and associated structural transformations in various classes of cathode materials on different spatial scales. He has published over 350 papers, 5 book chapters, and 12 patents.

Volume Editors

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Keith J. Stevenson Keith J. Stevenson received his Ph.D. in 1997 from the University of Utah under the supervision of Prof. Henry White. Subsequently, he held a postdoctoral appointment at Northwestern University (1997– 2000) and a tenured faculty appointment (2000–2015) at the University of Texas at Austin. At present, he is leading the development of a new graduate level university (Skolkovo Institute for Science and Technology) in Moscow, Russia, where he is Provost and the former Director of the Center for Energy Science and Technology (CEST). To date he has published over 325 peer-reviewed publications, 14 patents, and 6 book chapters in this field. He is a recipient of Society of Electroanalytical Chemistry Charles N. Reilley Award (2021).

Evgeny V. Antipov Evgeny V. Antipov graduated from the Department of Chemistry at Moscow State University in 1981, received his Ph.D. in Chemistry in 1986, DSc degree in Chemistry in 1998, and then continued working at the same University as a Researcher, Head of the Laboratory of Inorganic Crystal Chemistry, Professor, Head of Laboratory of fundamental research on aluminum production, and Head of the Department of Electrochemistry. Since 2018 he also holds a professor position at Skolkovo Institute of Science and Technology (Skoltech) in Moscow. Currently his research interests are mainly focused on inorganic materials for application in batteries and fuel cells. He has published more than 400 scientific articles and 14 patents.

Vivian W.W. Yam Professor Vivian W.W. Yam is the Chair Professor of Chemistry and Philip Wong Wilson Wong Professor in Chemistry and Energy at The University of Hong Kong. She received both her B.Sc (Hons) and Ph.D. from The University of Hong Kong. She was elected to Member of Chinese Academy of Sciences, International Member (Foreign Associate) of US National Academy of Sciences, Foreign Member of Academia Europaea, Fellow of TWAS, and Founding Member of Hong Kong Academy of Sciences. She was Laureate of 2011 L’Oréal-UNESCO For Women in Science Award. Her research interests include inorganic and organometallic chemistry, supramolecular chemistry, photophysics and photochemistry, and metal-based molecular functional materials for sensing, organic optoelectronics, and energy research. Also see: https://chemistry.hku.hk/wwyam.

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Volume Editors

David L. Bryce David L. Bryce (B.Sc (Hons), 1998, Queen’s University; Ph.D., 2002, Dalhousie University; postdoctoral fellow, 2003–04, NIDDK/NIH) is Full Professor and University Research Chair in Nuclear Magnetic Resonance at the University of Ottawa in Canada. He is the past Chair of the Department of Chemistry and Biomolecular Sciences, a Fellow of the Royal Society of Chemistry, and an elected Fellow of the Royal Society of Canada. His research interests include solid-state NMR of low-frequency quadrupolar nuclei, NMR studies of materials, NMR crystallography, halogen bonding, mechanochemistry, and quantum chemical interpretation of NMR interaction tensors. He is the author of approximately 200 scientific publications and co-author of 1 book. He is the Editor-in-Chief of Solid State Nuclear Magnetic Resonance and Section Editor (Magnetic Resonance and Molecular Spectroscopy) for the Canadian Journal of Chemistry. He has served as the Chair of Canada’s National Ultrahigh-Field NMR Facility for Solids and is a past co-chair of the International Society for Magnetic Resonance conference and of the Rocky Mountain Conference on Magnetic Resonance Solid-State NMR Symposium. His work has been recognized with the Canadian Society for Chemistry Keith Laidler Award and with the Gerhard Herzberg Award of the Canadian Association of Analytical Sciences and Spectroscopy.

Paul R. Raithby Paul R. Raithby obtained his B.Sc (1973) and Ph.D. (1976) from Queen Mary College, University of London, working for his Ph.D. in structural inorganic chemistry. He moved to the University of Cambridge in 1976, initially as a postdoctoral researcher and then as a faculty member. In 2000, he moved to the University of Bath to take up the Chair of Inorganic Chemistry when he remains to the present day, having been awarded an Emeritus Professorship in 2022. His research interests have spanned the chemistry of transition metal cluster compounds, platinum acetylide complexes and oligomers, and lanthanide complexes, and he uses laboratory and synchrotron-based X-ray crystallographic techniques to determine the structures of the complexes and to study their dynamics using time-resolved photocrystallographic methods.

Angus P. Wilkinson

Angus P. Wilkinson completed his bachelors (1988) and doctoral (1992) degrees in chemistry at Oxford University in the United Kingdom. He spent a postdoctoral period in the Materials Research Laboratory, University of California, Santa Barbara, prior to joining the faculty at the Georgia Institute of Technology as an assistant professor in 1993. He is currently a Professor in both the Schools of Chemistry and Biochemistry, and Materials Science and Engineering, at the Georgia Institute of Technology. His research in the general area of inorganic materials chemistry makes use of synchrotron X-ray and neutron scattering to better understand materials synthesis and properties.

CONTRIBUTORS TO VOLUME 9 Fahri Alkan Department of Nanotechnology Engineering, Abdullah Gül University, Kayseri, Turkey

Valeria Di Tullio “Segre-Capitani” Nuclear Magnetic Resonance Laboratory, ISB-CNR, Rome, Italy

Jean-Paul Amoureux Univ Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181 e UCCS e Unité de Catalyse et Chimie du Solide, Lille, France; and Bruker Biospin, Wissembourg, France

Nghia Tuan Duong Aix Marseille Univ. CNRS, ICR, Marseille, France

Guy M Bernard Gunning-Lemieux Chemistry Centre, University of Alberta, Edmonton, AB, Canada Darren H Brouwer Department of Chemistry, Redeemer University, Hamilton, ON, Canada David L Bryce Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, ON, Canada Diego Carnevale Département de chimie, Laboratoire des biomolécules, LBM, École Normale Supérieure, PSL University, Paris, France Jaclyn Catalano Department of Chemistry and Biochemistry, Montclair State University, Montclair, NJ, United States Silvia A Centeno Department of Scientific Research, The Metropolitan Museum of Art, New York, NY, United States Kuizhi Chen State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China Tabitha M Cook Department of Chemistry and Biochemistry, Berry College, Mount Berry, GA, United States Laurent Delevoye Univ. Lille, CNRS, INRAE, Centrale Lille, Univ Artois e IMEC, Lille, France

Cecil Dybowski Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, United States Hellmut Eckert Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil; and Institut für Physikalische Chemie, WWU Münster, Münster, Germany Mattias Edén Department of Materials and Environmental Chemistry, Stockholm University, Stockholm, Sweden David Ellis Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, United Kingdom Markus Enders Anorganisch-Chemisches Institut, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany Yuji Furukawa Ames Laboratory, US DOE, Ames, IA, United States; and Department of Physics and Astronomy, Iowa State University, Ames, IA, United States Piotr Garbacz University of Warsaw, Warsaw, Poland John M Griffin Department of Chemistry, Lancaster University, Lancaster, United Kingdom Kent J Griffith Department of Chemistry, Northwestern University, Evanston, IL, United States Josef V Grundy Department of Chemistry, Colorado State University, Fort Collins, CO, United States

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Rupal Gupta Department of Chemistry, College of Staten Island, City University of New York, New York, NY, United States; and Ph.D. Programs in Biochemistry and Chemistry, The Graduate Center of the City University of New York, New York, NY, United States Kristopher J Harris Department of Chemistry, Louisiana Tech University, Ruston, LA, United States Sean T Holmes Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, FL, United States; and National High Magnetic Field Laboratory, Tallahassee, FL, United States Guangjin Hou State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

Thomas-Xavier Métro IBMM, University of Montpellier, CNRS, ENSCM, Montpellier, France Vladimir K Michaelis Gunning-Lemieux Chemistry Centre, University of Alberta, Edmonton, AB, Canada Tyler M Ozvat Department of Chemistry, Colorado State University, Fort Collins, CO, United States Alexander L Paterson US DOE Ames Laboratory, Ames, IA, United States Frédéric A Perras US DOE Ames Laboratory, Ames, IA, United States Roberta Pigliapochi Department of Scientific Research, The Metropolitan Museum of Art, New York, NY, United States

Yining Huang Department of Chemistry, The University of Western Ontario, London, ON, Canada

Frédérique Pourpoint Univ Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181 e UCCS e Unité de Catalyse et Chimie du Solide, Lille, France

Daniel Jardón-Álvarez Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot, Israel

Andrew GM Rankin Univ. Lille, CNRS, INRAE, Centrale Lille, Univ Artois e IMEC, Lille, France

Abhoy Karmakar Gunning-Lemieux Chemistry Centre, University of Alberta, Edmonton, AB, Canada

Ulrich Scheler Leibniz-Institut für Polymerforschung Dresden e.V., Dresden, Germany

Navjot Kaur Department of Chemistry & Biochemistry, University of Regina, Regina, SK, Canada

Yuting Sun State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

Olivier Lafon Univ Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181 e UCCS e Unité de Catalyse et Chimie du Solide, Lille, France Danielle Laurencin ICGM, University of Montpellier, CNRS, ENSCM, Montpellier, France César Leroy ICGM, University of Montpellier, CNRS, ENSCM, Montpellier, France Michal Leskes Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot, Israel Bryan EG Lucier Department of Chemistry, The University of Western Ontario, London, ON, Canada W1odzimierz Makulski University of Warsaw, Warsaw, Poland

Andre Sutrisno NMR/EPR Laboratory, School of Chemical Sciences, University of Illinois at Urbana-Champaign, Urbana, IL, United States Ökten Üngör Department of Chemistry, Colorado State University, Fort Collins, CO, United States Molly Wagner Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, United States Qian Wang Department of Chemistry, College of Staten Island, City University of New York, New York, NY, United States Cory M Widdifield Department of Chemistry & Biochemistry, University of Regina, Regina, SK, Canada

Contributors to Volume 9

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Zi-Ling Xue Department of Chemistry, University of Tennessee, Knoxville, TN, United States

Jianqin Zhuang Department of Chemistry, College of Staten Island, City University of New York, New York, NY, United States

Joseph M Zadrozny Department of Chemistry, Colorado State University, Fort Collins, CO, United States

Nicholas Zumbulyadis Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, United States; and Independent Researcher, Rochester, NY, United States

Wanli Zhang Department of Chemistry, The University of Western Ontario, London, ON, Canada

PREFACE Comprehensive Inorganic Chemistry III is a new multi-reference work covering the broad area of Inorganic Chemistry. The work is available both in print and in electronic format. The 10 Volumes review significant advances and examines topics of relevance to today’s inorganic chemists with a focus on topics and results after 2012. The work is focusing on new developments, including interdisciplinary and high-impact areas. Comprehensive Inorganic Chemistry III, specifically focuses on main group chemistry, biological inorganic chemistry, solid state and materials chemistry, catalysis and new developments in electrochemistry and photochemistry, as well as on NMR methods and diffractions methods to study inorganic compounds. The work continues our 2013 work Comprehensive Inorganic Chemistry II, but at the same time adds new volumes on emerging research areas and techniques used to study inorganic compounds. The new work is also highly complementary to other recent Elsevier works in Coordination Chemistry and Organometallic Chemistry thereby forming a trio of works covering the whole of modern inorganic chemistry, most recently COMC-4 and CCC-3. The rapid pace of developments in recent years in all areas of chemistry, particularly inorganic chemistry, has again created many challenges to provide a contemporary up-to-date series. As is typically the challenge for Multireference Works (MRWs), the chapters are designed to provide a valuable long-standing scientific resource for both advanced students new to an area as well as researchers who need further background or answers to a particular problem on the elements, their compounds, or applications. Chapters are written by teams of leading experts, under the guidance of the Volume Editors and the Editors-inChief. The articles are written at a level that allows undergraduate students to understand the material, while providing active researchers with a ready reference resource for information in the field. The chapters are not intended to provide basic data on the elements, which are available from many sources including the original CIC-I, over 50-years-old by now, but instead concentrate on applications of the elements and their compounds and on high-level techniques to study inorganic compounds. Vol. 1: Synthesis, Structure, and Bonding in Inorganic Molecular Systems; Risto S. Laitinen In this Volume the editor presents an historic overview of Inorganic Chemistry starting with the birth of inorganic chemistry after Berzelius, and a focus on the 20th century including an overview of “inorganic” Nobel Prizes and major discoveries, like inert gas compounds. The most important trends in the field are discussed in an historic context. The bulk of the Volume consists of 3 parts, i.e., (1) Structure, bonding, and reactivity in inorganic molecular systems; (2) Intermolecular interactions, and (3) Inorganic Chains, rings, and cages. The volume contains 23 chapters. Part 1 contains chapters dealing with compounds in which the heavy p-block atom acts as a central atom. Some chapters deal with the rich synthetic and structural chemistry of noble gas compounds, low-coordinate p-block elements, biradicals, iron-only hydrogenase mimics, and macrocyclic selenoethers. Finally, the chemistry and application of weakly coordinating anions, the synthesis, structures, and reactivity of carbenes containing non-innocent ligands, frustrated Lewis pairs in metal-free catalysis are discussed. Part 2 discusses secondary bonding interactions that play an important role in the properties of bulk materials. It includes a chapter on the general theoretical considerations of secondary bonding interactions, including halogen and chalcogen bonding. This section is concluded by the update of the host-guest chemistry of the molecules of p-block elements and by a comprehensive review of closed-shell metallophilic interactions. The third part of the Volume is dedicated to chain, ring and cage (or cluster) compounds in molecular inorganic chemistry. Separate

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chapters describe the recent chemistry of boron clusters, as well as the chain, ring, and cage compounds of Group13 and 15, and 16 elements. Also, aromatic compounds bearing heavy Group 14 atoms, polyhalogenide anions and Zintl-clusters are presented. Vol. 2: Bioinorganic Chemistry and Homogeneous Biomimetic Inorganic Catalysis; Vincent L. Pecoraro and Zijian Guo In this Volume, the editors have brought together 26 chapters providing a broad coverage of many of the important areas involving metal compounds in biology and medicine. Readers interested in fundamental biochemistry that is assisted by metal ion catalysis, or in uncovering the latest developments in diagnostics or therapeutics using metal-based probes or agents, will find high-level contributions from top scientists. In the first part of the Volume topics dealing with metals interacting with proteins and nucleic acids are presented (e.g., siderophores, metallophores, homeostasis, biomineralization, metal-DNA and metal-RNA interactions, but also with zinc and cobalt enzymes). Topics dealing with iron-sulfur clusters and heme-containing proteins, enzymes dealing with dinitrogen fixation, dihydrogen and dioxygen production by photosynthesis will also be discussed, including bioinspired model systems. In the second part of the Volume the focus is on applications of inorganic chemistry in the field of medicine: e.g., clinical diagnosis, curing diseases and drug targeting. Platinum, gold and other metal compounds and their mechanism of action will be discussed in several chapters. Supramolecular coordination compounds, metal organic frameworks and targeted modifications of higher molecular weight will also be shown to be important for current and future therapy and diagnosis. Vol. 3: Theory and Bonding of Inorganic Non-molecular Systems; Daniel C. Fredrickson This volume consists of 15 chapters that build on symmetry-based expressions for the wavefunctions of extended structures toward models for bonding in solid state materials and their surfaces, algorithms for the prediction of crystal structures, tools for the analysis of bonding, and theories for the unique properties and phenomena that arise in these systems. The volume is divided into four parts along these lines, based on major themes in each of the chapters. These are: Part 1: Models for extended inorganic structures, Part 2: Tools for electronic structure analysis, Part 3: Predictive exploration of new structures, and Part 4: Properties and phenomena. Vol. 4: Solid State Inorganic Chemistry; P. Shiv Halasyamani and Patrick M. Woodward In a broad sense the field of inorganic chemistry can be broken down into substances that are based on molecules and those that are based on extended arrays linked by metallic, covalent, polar covalent, or ionic bonds (i.e., extended solids). The field of solid-state inorganic chemistry is largely concerned with elements and compounds that fall into the latter group. This volume contains nineteen chapters covering a wide variety of solid-state inorganic materials. These chapters largely focus on materials with properties that underpin modern technology. Smart phones, solid state lighting, batteries, computers, and many other devices that we take for granted would not be possible without these materials. Improvements in the performance of these and many other technologies are closely tied to the discovery of new materials or advances in our ability to synthesize high quality samples. The organization of most chapters is purposefully designed to emphasize how the exceptional physical properties of modern materials arise from the interplay of composition, structure, and bonding. Not surprisingly this volume has considerable overlap with both Volume 3 (Theory and Bonding of Inorganic NonMolecular Systems) and Volume 5 (Inorganic Materials Chemistry). We anticipate that readers who are interested in this volume will find much of interest in those volumes and vice versa Vol. 5: Inorganic Materials Chemistry; Ram Seshadri and Serena Cussen This volume has adopted the broad title of Inorganic Materials Chemistry, but as readers would note, the title could readily befit articles in other volumes as well. In order to distinguish contributions in this volume from

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those in other volumes, the editors have chosen to use as the organizing principle, the role of synthesis in developing materials, reflected by several of the contributions carrying the terms “synthesis” or “preparation” in the title. It should also be noted that the subset of inorganic materials that are the focus of this volume are what are generally referred to as functional materials, i.e., materials that carry out a function usually through the way they respond to an external stimulus such as light, or thermal gradients, or a magnetic field.

Vol. 6: Heterogeneous Inorganic Catalysis; Rutger A. van Santen and Emiel J. M. Hensen This Volume starts with an introductory chapter providing an excellent discussion of single sites in metal catalysis. This chapter is followed by 18 chapters covering a large part of the field. These chapters have been written with a focus on the synthesis and characterization of catalytic complexity and its relationship with the molecular chemistry of the catalytic reaction. In the 1950s with the growth of molecular inorganic chemistry, coordination chemistry and organometallic chemistry started to influence the development of heterogeneous catalysis. A host of new reactions and processes originate from that time. In this Volume chapters on major topics, like promoted Fischer-Tropsch catalysts, structure sensitivity of well-defined alloy surfaces in the context of oxidation catalysis and electrocatalytic reactions, illustrate the broadness of the field. Molecular heterogeneous catalysts rapidly grew after high-surface synthetic of zeolites were introduced; so, synthesis, structure and nanopore chemistry in zeolites is presented in a number of chapters. Also, topics like nanocluster activation of zeolites and supported zeolites are discussed. Mechanistically important chapters deal with imaging of single atom catalysts. An important development is the use of reducible supports, such as CeO2 or Fe2O3 where the interaction between the metal and support is playing a crucial role.

Vol. 7: Inorganic Electrochemistry; Keith J. Stevenson, Evgeny V. Antipov and Artem M. Abakumov This volume bridges several fields across chemistry, physics and material science. Perhaps this topic is best associated with the book “Inorganic Electrochemistry: Theory, Practice and Applications” by Piero Zanello that was intended to introduce inorganic chemists to electrochemical methods for study of primarily molecular systems, including metallocenes, organometallic and coordination complexes, metal complexes of redox active ligands, metal-carbonyl clusters, and proteins. The emphasis in this Volume of CIC III is on the impact of inorganic chemistry on the field of material science, which has opened the gateway for inorganic chemists to use more applied methods to the broad areas of electrochemical energy storage and conversion, electrocatalysis, electroanalysis, and electrosynthesis. In recognition of this decisive impact, the Nobel Prize in Chemistry of 2019 was awarded to John B. Goodenough, M. Stanley Whittingham, and Akira Yoshino for the development of the lithium-ion battery.

Vol. 8: Inorganic Photochemistry; Vivian W. W. Yam In this Volume the editor has compiled 19 chapters discussing recent developments in a variety of developments in the field. The introductory chapter overviews the several topics, including photoactivation and imaging reagents. The first chapters include a discussion of using luminescent coordination and organometallic compounds for organic light-emitting diodes (OLEDs) and applications to highlight the importance of developing future highly efficient luminescent transition metal compounds. The use of metal compounds in photo-induced bond activation and catalysis is highlighted by non-sacrificial photocatalysis and redox photocatalysis, which is another fundamental area of immense research interest and development. This work facilitates applications like biological probes, drug delivery and imaging reagents. Photochemical CO2 reduction and water oxidation catalysis has been addressed in several chapters. Use of such inorganic compounds in solar fuels and photocatalysis remains crucial for a sustainable environment. Finally, the photophysics and photochemistry of lanthanoid compounds is discussed, with their potential use of doped lanthanoids in luminescence imaging reagents.

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Vol. 9: NMR of Inorganic Nuclei; David L. Bryce Nuclear magnetic resonance (NMR) spectroscopy has long been established as one of the most important analytical tools at the disposal of the experimental chemist. The isotope-specific nature of the technique can provide unparalleled insights into local structure and dynamics. As seen in the various contributions to this Volume, applications of NMR spectroscopy to inorganic systems span the gas phase, liquid phase, and solid state. The nature of the systems discussed covers a very wide range, including glasses, single-molecule magnets, energy storage materials, bioinorganic systems, nanoparticles, catalysts, and more. The focus is largely on isotopes other than 1H and 13C, although there are clearly many applications of NMR of these nuclides to the study of inorganic compounds and materials. The value of solid-state NMR in studying the large percentage of nuclides which are quadrupolar (spin I > ½) is apparent in the various contributions. This is perhaps to be expected given that rapid quadrupolar relaxation can often obfuscate the observation of these resonances in solution. Vol. 10: X-ray, Neutron and Electron Scattering Methods in Inorganic Chemistry; Angus P. Wilkinson and Paul R. Raithby In this Volume the editors start with an introduction on the recent history and improvements of the instrumentation, source technology and user accessibility of synchrotron and neutron facilities worldwide, and they explain how these techniques work. The modern facilities now allow inorganic chemists to carry out a wide variety of complex experiments, almost on a day-to-day basis, that were not possible in the recent past. Past editions of Comprehensive Inorganic Chemistry have included many examples of successful synchrotron or neutron studies, but the increased importance of such experiments to inorganic chemists motivated us to produce a separate volume in CIC III dedicated to the methodology developed and the results obtained. The introduction chapter is followed by 15 chapters describing the developments in the field. Several chapters are presented covering recent examples of state-of-the-art experiments and refer to some of the pioneering work leading to the current state of the science in this exciting area. The editors have recognized the importance of complementary techniques by including chapters on electron crystallography and synchrotron radiation sources. Chapters are present on applications of the techniques in e.g., spin-crossover materials and catalytic materials, and in the use of time-resolved studies on molecular materials. A chapter on the worldwide frequently used structure visualization of crystal structures, using PLATON/PLUTON, is also included. Finally, some more specialized studies, like Panoramic (in beam) studies of materials synthesis and high-pressure synthesis are present. Direct observation of transient species and chemical reactions in a pore observed by synchrotron radiation and X-ray transient absorption spectroscopies in the study of excited state structures, and ab initio structure solution using synchrotron powder diffraction, as well as local structure determination using total scattering data, are impossible and unthinkable without these modern diffraction techniques. Jan Reedijk, Leiden, The Netherlands Kenneth R. Poeppelmeier, Illinois, United States March 2023

9.01

Introduction: NMR of inorganic nuclei

David L. Bryce, Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, ON, Canada. © 2023 Elsevier Ltd. All rights reserved.

Abstract Nuclear magnetic resonance (NMR) spectroscopy has long been established as one of the most important analytical tools at the disposal of the experimental chemist. The isotope-specific nature of the technique can provide unparalleled insights into local structure and dynamics. As seen in the various contributions to this Volume, applications of NMR spectroscopy to inorganic systems span the gas phase, liquid phase, and solid state. The nature of the systems discussed covers a very wide range, including glasses, single-molecule magnets, energy storage materials, bioinorganic systems, nanoparticles, catalysts, and more. The focus is largely on isotopes other than 1H and 13C, although there are clearly many applications of NMR of these nuclides to the study of inorganic compounds and materials. The value of solid-state NMR in particular in studying the large percentage of nuclides which are quadrupolar (spin I > ½) is apparent in the various contributions to this chapter. This is perhaps to be expected given that rapid quadrupolar relaxation can often obfuscate the observation of these resonances in solution.

Nuclear magnetic resonance (NMR) spectroscopy has long been established as one of the most important analytical tools at the disposal of the experimental chemist. The isotope-specific nature of the technique can provide unparalleled insights into local structure and dynamics. As seen in the various contributions to this Volume, applications of NMR spectroscopy to inorganic systems span the gas phase, liquid phase, and solid state. The nature of the systems discussed covers a very wide range, including glasses, single-molecule magnets, energy storage materials, bioinorganic systems, nanoparticles, catalysts, and more. The focus is largely on isotopes other than 1H and 13C, although there are clearly many applications of NMR of these nuclides to the study of inorganic compounds and materials. The value of solid-state NMR in particular in studying the large percentage of nuclides which are quadrupolar (spin I > ½) is apparent in the various contributions to this chapter. This is perhaps to be expected given that rapid quadrupolar relaxation can often obfuscate the observation of these resonances in solution. Several chapters are focussed on NMR studies of a particular isotope or isotopes. Carnevale offers an overview of applications of 14 N NMR spectroscopy (see chapter 9.02). While most important recent developments and applications are in the area of solid-state NMR, the utility of 14N solution NMR is also discussed. Given the ubiquity of nitrogen in inorganic systems and materials, and the high natural abundance of the 14N isotope (99.6%), the practicing chemist is well advised to consider using 14N NMR spectroscopy to their advantage. Scheler reports on 19F NMR studies of polymers (see chapter 9.03). While solution NMR is limited to those polymers which are soluble, solid-state NMR using fast magic-angle spinning can be used to great advantage. Information obtained includes the relative populations of polymer end groups and side groups. Furthermore, relaxation measurements can be employed to understand molecular mobility in semicrystalline polymers. Gupta and colleagues report on applications of 17O and 51V NMR in inorganic and bioinorganic chemistry (see chapter 9.04). Oxygen-17 is clearly a very important isotope and several advances have been made in recent years to overcome the sensitivity challenges posed by this quadrupolar nucleus with a very low natural abundance. Vanadium-51, another quadrupolar nucleus, benefits from favorable NMR properties and has been employed to understand a variety of inorganic and bioinorganic systems. A comprehensive survey of the NMR literature pertaining to carboranes as well as some metallaboranes and metallacarboranes, is provided by Ellis (see chapter 9.05). Information available from 11B, 10B, 13C, 1H, and 19F isotopes is surveyed and tabulated. Various relevant one and two-dimensional NMR methods are presented, and applications to the study of dynamics and of aromaticity are discussed. Brouwer presents an excellent overview of applications of 29Si NMR spectroscopy, both in solution and in the solid state (see chapter 9.06). A wide range of materials are covered, including siloxane polymers, silicates, functionalized silica, porous materials, zeolites, and glasses. This contribution also very nicely highlights the value of two-dimensional 29Si NMR experiments and touches on various signal enhancement strategies, including dynamic nuclear polarization. Perras and Paterson provide a thorough account of high field solid-state NMR of challenging nuclei in inorganic systems (see chapter 9.07) . Here, challenging nuclei include those that are dilute, that have low resonance frequencies, and/or have large nuclear electric quadrupole moments. Their contribution focusses on the benefits achieved from using very high applied magnetic fields to study challenging nuclei in inorganic compounds and materials, and provides a survey of available data for several isotopes. Eckert’s contribution on NMR spectroscopy of the rare earth nuclei explores some of the farther reaches of periodic table (see chapter 9.08). In addition to the fundamentally interesting aspects of developing the spectroscopy of various exotic isotopes of lutetium, praseodymium, and samarium, for example, developments related to the more common 45Sc, 139La, and 89Y are covered. Part of the motivation for this work stems from the usage of rare-earth compounds and materials for the development of novel optical, electronic, and magnetic devices.

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This Volume includes two contributions specifically aimed at understanding magnetic materials using NMR spectroscopy. Enders elegantly explains the information available from solution NMR spectroscopy when characterizing molecular magnets (see chapter 9.09). Such information includes the magnetic anisotropy, details on delocalization of unpaired electron density onto the ligand framework, and the ligand field energy splitting. The issues arising when treating the solution NMR spectra of paramagnetic single molecule magnet systems are discussed in detail. In a separate chapter, Furukawa describes the determination of magnetic structures using on-site NMR measurements. Chapter 9.10 describes how the magnitude and direction of the electronic magnetic moments in magnetically ordered states can be measured. Thus this contribution elucidates nicely the role that NMR can play in nanomagnetic and antiferromagnetic materials. NMR spectroscopy plays an important role in the development and understanding of next-generation optical, electrical, and energy-storage materials. Michaelis and coworkers describe solid-state NMR studies of halide perovskite materials with photoconversion potential (see chapter 9.11). The power of a multinuclear approach to understanding structure and dynamics in these systems is well-demonstrated. Griffith and Griffin recount the current state-of-the-art in NMR studies of energy materials, including lithium battery cathodes, anodes, solid electrolytes, interfaces, and supercapacitors (see chapter 9.12). The special steps needed to study such systems in situ or in operando are evident. The unique role of magnetic resonance in shedding light on local structure, heterogeneity, defects, and dynamics is highlighted, as such information is often difficult to obtain by other experimental techniques. Metal-organic frameworks are by now well-established materials with a variety of potential applications including carbon capture, gas storage, and catalysis. Solid-state NMR has an important role to play in understanding the structure of MOFs and in particular how and where guest species interact with the metal centers. Huang and coworkers review the information available from solid-state NMR studies of a range of ‘exotic’ nuclei in MOFs. NMR crystallographic approaches, where NMR data are combined with diffraction data and density functional theory modelling, are particularly relevant in providing a complete molecular-level picture of adsorption and of dynamics in such systems (see chapter 9.13). The Achilles’ Heel of NMR is sensitivity. Dynamic nuclear polarization, whereby the higher polarization of unpaired electrons is transferred to nuclear spins, has gained traction as a game-changing sensitivity enhancement technique in recent years. JardonAlvarez and Leskes describe DNP advances specifically in inorganic solids, where paramagnetic metal ion dopants can be used as sources of electron spin polarization (see chapter 9.14). In this approach, the radical source is endogenous, rather and exogenous, and the various practicalities associated with each approach are compared. The limitations and potential advantages of metal ionbased DNP (MIDNP) are discussed; in particular, in this approach every sample presents its own unique set of conditions which may need to be optimized differently. The method could hold particular promise for systems where a small pore size precludes the use of exogenous radicals. Widdifield and Kaur report on the most recent advances in NMR studies of nanoparticles (see chapter 9.15). A variety of techniques are described and applications to a wide range of materials including metal and metal/metalloid oxide nanoparticles, carbon nanoparticles, semiconducting nanoparticles, core@shell nanoparticles, alloyed nanoparticles, doped/lithiated nanoparticles, nanocomposites, molecular organic and polymeric nanoparticles, nanocrystalline inorganic compounds, nanocrystalline cellulose, and nano-sized metal-organics. A significant number of NMR-active isotopes are shown to be useful probes of such systems. Two-dimensional and pseudo-two-dimensional materials are another area of intense research interest, spurred on in part by the discovery of graphene and its properties. Harris reports on NMR methods for studying graphene and carbon nanotubes as well as their modified or doped analogs, phosphorenes, hexagonal boron nitride sheets, silicate sheets, and MXenes (see chapter 9.16). A focus of this chapter is on the information available from NMR experiments which is not available via other methods. The exquisite sensitivity of NMR observables, such as chemical shifts, to changes in chemical bonding is apparent. NMR spectroscopy has long played an indispensable role in understanding catalytic processes. In their chapter (9.17), Chen, Sun, and Hou describe the NMR theory and a range of experimental methods for characterizing solid catalysts. The chapter aims to demonstrate how modern solid-state NMR techniques are imperative in solving real catalytic problems. The use of in-situ NMR methods is highlighted with this in mind. The authors conclude that very strong magnetic fields, very fast magic-angle spinning, and dynamic nuclear polarization are likely to be critical in pushing forward the characterization of heterogeneous catalysts in the future. Mechanochemistry is an ancient topic which continues to see a resurgence in recent years. Perhaps surprisingly, solid-state NMR spectroscopy is somewhat underused to study and understand mechanochemical reactions and solid-solid transformations. Leroy, Métro, and Laurencin present an excellent and insightful chapter (see chapter 9.18) describing the constructive confluence of research in the areas of mechanochemistry and solid-state NMR spectroscopy. NMR is a valuable tool for understanding structure and morphology of solid materials, and can also provide unique insights into mechanochemical reactivity via in situ and ex situ analyses. Already, a large number of isotopes have been probed using NMR spectroscopy to understand mechanochemical transformations. Isotopic enrichment via mechanochemical routes, particularly using 17O, holds significant value in studying mechanisms and structure in a range of inorganic materials including oxides, metal-organic frameworks, and zeolites. Many advanced applications of NMR spectroscopy rely on multidimensional correlation experiments. Such experiments are diverse and can provide extensive information on chemical bonding, local structure, and non-covalent interactions. Lafon and colleagues provide a thorough overview of modern correlation methods used in solid-state NMR spectroscopy and describe many applications to a range of inorganic systems (see chapter 9.19). The development of novel and improved radiofrequency pulse sequences to observe specific internuclear correlations is an active area of research with a strong potential for enabling breakthroughs in understanding molecular structure in otherwise difficult-to-characterize systems.

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One of the strengths of NMR is its ability to probe matter in many different forms. In the solid state, a crystalline sample is not required. The study of glassy or disordered materials is an area where diffraction methods may not be apposite or sufficient, but where NMR can offer key information. Eden contributes a comprehensive overview of the utility of carrying out multinuclear magnetic resonance experiments on glasses (see chapter 9.20). Xue and Cook present an authoritative account of the state-of-the-art in solution NMR of transition metal complexes (see chapter 9.21). In addition to providing a systematic survey of transition metal NMR of groups 3 through 12 of the periodic table, several important and unusual NMR methods are highlighted and their utility discussed. These include e.g., diffusion measurements, dynamic and variable temperature NMR, high-pressure NMR, and NMR studies using parahydrogen for signal enhancement. The authors conclude by noting a select few transition metal isotopes for which solution NMR data are sparse or completely absent from the literature. Zadrozny and coworkers discuss the temperature dependence of NMR properties, and in particular the potential applications of these effects. Transition metal NMR thermometry is proposed as a promising non-invasive tool with potential applications in disease monitoring and treatment. Chapter 9.22 provides a highly useful pedagogical overview of the origins of the temperature dependence of the chemical shift and presents a survey of literature data for several transition metal isotopes as well as some lighter isotopes. Recent work has shown a temperature dependence of the 59Co chemical shift on the order of 150 ppm  C 1 for a select few Co complexes. The field of transition metal NMR thermometry is underdeveloped and appears to offer fertile ground for several new lines of research. While most applications of NMR spectroscopy are on solutions or on powdered solids, NMR of gaseous samples can provide highly valuable information as well. Garbacz and Makulski describe the basics of gas-phase NMR spectroscopy and explain how precise information on nuclear shielding constants, spin-spin coupling constants, and relaxation time constants can be obtained (see chapter 9.23). Such information is invaluable in determining nuclear magnetic moments and in understanding isotope effects on NMR parameters. Gas-phase NMR provides essential experimental information for the establishment of absolute shielding scales for a long list of isotopes. Dybowski and coworkers report on fascinating applications of NMR spectroscopy in the area of cultural heritage science (see chapter 9.24). The unique perspectives furnished by NMR are described, and a number of interesting examples are discussed. These include NMR studies of musical instruments, paper artifacts, biological remains and materials, paints and paintings, and stone and ceramic materials. The use of unilateral magnetic resonance sensors to study objects such as frescoes suggests an important opportunity for ongoing and future work. Computational chemistry, and density functional theory methods in particular, continue to play an increasingly important role in understanding and interpreting experimental NMR data. In addition to adding to our fundamental understanding of the relationship between NMR observables and the local molecular and electronic structure, NMR crystallography is another area of research where computational methods are critically important. Holmes and coworkers report on advances in the computation of NMR parameters for inorganic nuclides. Their focus is more specifically on understanding nuclear magnetic shielding tensors in solids, and the impact of coordination geometry, oxidation state, relativistic effects, and density functional approximations on the results obtained. Chapter 9.25 largely focusses on fluorine, cadmium, tin, tellurium, mercury, lead, and platinum. All in all, the contents of this Volume demonstrate how innovations in pulse sequence development, instrumentation, theory, and computational chemistry have all helped to advance NMR spectroscopy as a premier tool for understanding inorganic molecules and materials. These developments often translate into improved spectral sensitivity, new or unique chemical and structural information, or an improved understanding of the connection between what one records in an NMR experiment and the nature of the sample under study. It is hoped that this Volume serves as a useful state-of-the-art guide to NMR in inorganic chemistry to routine users and advanced practitioners alike.

9.02

Nitrogen-14 NMR spectroscopy

Diego Carnevale, Département de chimie, Laboratoire des biomolécules, LBM, École Normale Supérieure, PSL University, Paris, France © 2023 Elsevier Ltd. All rights reserved.

9.02.1 9.02.2 9.02.3 9.02.4 9.02.4.1 9.02.4.2 9.02.4.3 9.02.5 References

Introduction Quadrupolar interaction 14 N in solution NMR 14 N in solid-state NMR Direct detection Indirect detection Structural insights obtained by Outlook

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4 5 8 9 9 11 15 19 22

N NMR

Abbreviations CP Cross polarization CSA Chemical shift anisotropy CT Central transition DCP Double cross polarization DFT Density functional theory DQ Double quantum EFG Electric field gradient HMQC Heteronuclear multiple quantum correlation HSQC Heteronuclear single quantum correlation MAS Magic angle spinning SDA Structure directing agent SQ Single quantum ST Satellite transition

Abstract Nitrogen-14 is a ubiquitous and high-abundance isotope that offers great potentialities for NMR spectroscopy in structural characterizations of a wide variety of chemical systems, including organic, inorganic, or hybrid materials. In spite of its high abundance, nitrogen-14 is a low-g quadrupolar spin with I ¼ 1, and is therefore very difficult to detect due to the absence of the central transition which instead characterizes half-integer spins with I > 1. The only available satellite transitions can be severely broadened by the quadrupolar interaction and are therefore very difficult to excite uniformly and detect. This Chapter describes the challenges associated with the acquisition of NMR spectra of this nucleus and the main possible experimental approaches that have been developed over the years to tackle this isotope.

9.02.1

Introduction

Solid-State NMR is an invaluable tool for structural studies of materials. The anisotropic or orientation-dependent interactions that affect the NMR lineshapes in the solid state are very sensitive to nuclear local environments and offer a means to probe structural details with atomic-scale resolution. This capability renders solid-state NMR an ideal complementary approach to diffraction techniques. In fact, single-crystal diffraction studies often require large crystals and, more generally, samples characterized by long-range order. In contrast, NMR may be applied to any type of sample, including amorphous materials or heterogeneous systems. Information such as the number of crystallographically-distinct sites or molecules in the asymmetric unit cell can be readily obtained by this spectroscopic technique and can greatly help and assist structure refinement of diffraction data. Inhomogeneous interactions such as chemical shift anisotropy (CSA), dipolar, or first-order quadrupolar couplings may severely broaden NMR lineshapes in the solid state.1 This ultimately reduces resolution and sensitivity. The use of magic-angle spinning (MAS) can greatly help to circumvent these hurdles. If the frequency nR of the mechanical rotation – about an axis at an angle

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b ¼ 54.736 with respect to the external B0 field – is larger than the anisotropic interaction that one wishes to average out, highresolution isotropic peaks can be obtained. However, in cases where the quadrupolar interaction is large, MAS cannot be used to completely remove the broadening and a second-order description of the lineshape is required. This is due to the more complex orientation dependence of this interaction. Additionally, when any of the above mentioned inhomogeneities is considerably larger than the available spinning rate nR, a manifold of spinning sidebands spaced by the spinning frequency is obtained. Besides being a fundamental atom present in all essential biomolecules such as RNA/DNA and proteins, nitrogen is commonly found in a wide variety of chemical compounds, from substantially any drug class, to organic linkers2 or templates3 utilized in the synthesis of porous materials. From an NMR point of view, the isotope nitrogen-14 is particularly interesting thanks to its favorable high natural abundance of 99.6%. However, being a low-g spin (g(14N)/g(1H) ¼ 0.07), 14N NMR is characterized by an intrinsic low sensitivity. Furthermore, nitrogen-14 is a quadrupolar spin with I ¼ 1. This means that this isotope does not feature the central transition (CT; m1 ¼ þ 1/2 4 m1 ¼  1/2) found in half-integer spins I > 1 which is broadened only to second order by usually a few kHz. The only available single-quantum (SQ) transitions for 14N are the satellite transitions (STs; m1 ¼  1 4 m1 ¼ 0), which are also broadened to first order by a few MHz. Therefore, the lack of a CT greatly limits the sensitivity of 14N NMR. As the available rf-field strengths are much smaller than quadrupolar couplings (n1 < < CQ) a uniform excitation of the STs – or, of all crystallite orientations – is usually not possible. Furthermore, the available methods developed for half-integer I > 1 spins to refocus second-order broadenings by correlating different transitions or coherence orders – namely, satellite transition magic-angle spinning (STMAS)4 and multiple quantum magic-angle spinning (MQMAS)5 experiments – are not applicable to I ¼ 1 spins. Aside from highly symmetric environments such as tetrahedral cations, nitrogen-14 lineshapes are therefore difficult to acquire via either static or MAS NMR spectroscopy. This Chapter presents a brief overview of the challenges connected with the detection of 14N NMR spectra and the current methods of choice that have been developed to circumvent the hurdles associated with this nucleus. Section 9.02.2 describes the main source of broadening that affects nitrogen-14 lineshapes and that renders them challenging to acquire, i.e., the quadrupolar interaction. Section 9.02.3 discusses the limitations encountered in solution NMR studies exploiting 14N. Section 9.02.4 deals with NMR methods that have been developed for the direct detection of nitrogen-14, the techniques utilized for the indirect detection by means of 2D correlation experiments, and examples of structural details that may be obtained in a range of chemical systems by the acquisition of spectra of this isotope. Section 9.02.5 briefly summarizes the future perspectives of 14N NMR. Excellent reviews can be found in the literature about the topics herein overviewed.6–10

9.02.2

Quadrupolar interaction

The main difficulties in acquiring nitrogen-14 NMR spectra arise from the quadrupolar coupling between the electric quadrupole moment of the nucleus and the electric field gradient (EFG) given by the surrounding charges. This section briefly summarizes this interaction. Quadrupolar nuclei are characterized by a non-spherical nuclear charge distribution. This gives rise to an electric quadrupole moment eQ that can couple with the EFG at the nucleus and results in anisotropic splitting of the NMR transitions in 2I þ 1 lines. The orientation-dependent series of multiplets associated with a polycrystalline powder results in the typical second-order quadrupolar lineshapes. The quadrupolar Hamiltonian in a uniform space is11,12: HQ ¼

eQ I,V,I 2Ið2I  1ÞZ 0

Vxx
B eQ ¼ Ix Iy Iz B @ Vyx 2Ið2I  1ÞZ Vzx

Vxy Vyy Vzy

10 1 Vxz Ix CB C B Iy C; Vyx C A@ A Vzz Ix

where V is the EFG tensor. In a principal axis system P where V is diagonal, the 0 Vxx 0 B B
eQ Ix Iy Iz B HQ ¼ B 0 Vyy 2Ið2I  1ÞZ @ 0 0

¼

(1)

expression simplifies to: 10 1 Ix 0 CB C CB C B C 0 C CB Iy C A@ A Ix Vzz

 i eQV zz h 2 3Iz  IðI þ 1Þ þ hQ Ix2  Iy2 : 4Ið2I  1ÞZ

(2)

6

Nitrogen-14 NMR spectroscopy

As V is traceless in P, only two parameters are ultimately required to describe the quadrupolar coupling, i.e., the quadrupolar coupling constant CQ and the asymmetry hQ: CQ ¼

eQV zz e2 qQ ¼ h h

(3)

Vxx  Vyy ; Vzz

(4)

hQ ¼

where the convention for the three main components | Vzz | > |Vxx | > |Vyy | is assumed. CQ determines the size of the linewidth whereas hQ determines the features of the second-order lineshape. For most practical cases such as static or MAS NMR experiments conducted at high B0 field, one utilizes the truncated Hamiltonian as expressed in the Zeeman frame13:

   1
1  HQ ¼ uQ;0 ðt Þ pffiffiffi 3Iz2  I2 þ uQ;2 ðt ÞuQ;2 ðt Þ 2I2  2Iz2  1 Iz þ uQ;1 ðt ÞuQ;1 ðt Þ 4I2  8Iz2  1 Iz : 2u0 6

(5)

The first term of Eq. (5) is the first-order quadrupolar correction to the Zeeman levels whereas the second term, proportional to u0 1, is the second-order one. The former has an orientation dependence which is proportional to the 3cos2q  1 Legendre factor that can be averaged to zero by MAS. The latter, in contrast, has a more complex orientation dependence and is not fully removed by MAS, regardless of the spinning rate.12 The corresponding energy levels for one spin I ¼ 1 are shown in Fig. 1. It is worth noting that the double-quantum transition m1 ¼ 1 4 m1 ¼  1 is not perturbed by first-order terms. The anisotropic time-dependent coefficients can be conveniently expressed as a Fourier series: 2 X

uQ;m0 ðt Þ ¼

ðmÞ

uQ;m0 eimuR t

(6)

m¼2

i

hQ h ð2Þ ðmÞ ð2Þ ð2Þ ð2Þ p ffiffiffi D ðU Þ  ðU Þ þ D ðU Þ dm;m0 ðbRL Þ; (7) uQ;m0 ¼ uQ D PR PR PR 0;m 2;m 2;m aniso 6 pffiffiffi (2) (2) where uR/2p ¼ nR, uQ aniso ¼ 2p 6CQ =ð4Ið2I  1ÞÞ, and the second-rank Wigner (D ) and reduced Wigner (d ) rotation matrices describe the orientation dependence of the frequency coefficients. The Euler angles UPR relate the quadrupolar coupling tensor as expressed in P to a rotor frame R, and are those considered for powder averaging. One additional required transformation to the lab frame L is described by URL ¼ (aRL bLR gRL) ¼ (uRt bLR 0), with bLR being the magic angle. The R / L transformation is implicit in Eqs. (6), (7) in this formalism. It is worth noting that, in cases where more than one interaction or spin is considered, an additional crystal frame C is required so as to relate all tensors to a single common frame: ð2Þ

Dm0 ;m ðUPR Þ ¼

2 X m00 ¼2

ð2Þ

ð2Þ

Dm0 ;m00 ðUPC ÞDm00 ;m ðUCR Þ:

(8)

In this case, the overall series of changes of frame of reference is therefore P / C / R / L. The second-order correction of the quadrupolar interaction contains an isotropic term12 that, in analogy with the isotropic part of the shielding interaction, simply shifts the first moment of the anisotropic lineshape within the spectrum. This isotropic part, for the m1 ¼  1 4 m1 ¼ 0 ST of a spin I ¼ 1 such as nitrogen-14, can be expressed in Hz as14–16:

(A)

(B)

(C)

|1, –1 Z0

Z0 + 3/2ZQ,0

Z0 + 3/2ZQ,0 +

Z0

Z0 –

Z0 –

ZQ,2ZQ,–2 – ZQ,1ZQ,–1 2Z0

|1, 0 3/2ZQ,0

3/2ZQ,0 +

ZQ,2ZQ,–2 – ZQ,1ZQ,–1 2Z0

|1, 1 Zeeman

Quadrupole 1st order

Quadrupole 2st order

Fig. 1 Energy level diagram for a spin I ¼ 1 nucleus in a high magnetic field B0 as affected by the Zeeman (A), first- (B) and second-order (C) quadrupolar interactions. The m1 ¼ þ 1 4 m1 ¼ 1 DQ transition is not affected by first-order broadenings.

Nitrogen-14 NMR spectroscopy

ðQÞ

niso ¼

2  3 CQ 1 1 þ h2Q : 40 n0 3

7

(9)

For large values of coupling constant CQ and low Larmor frequencies (n0 ¼ u0/2p) such as for 14N, the isotropic shift due to the quadrupolar interaction can greatly exceed in size the isotropic chemical shift. In other words, the position of the inhomogeneous lineshape within the acquired bandwidth can be largely determined by the quadrupolar interaction rather than by the chemical shift. A series of 14N NMR spectra simulated with SIMPSON13 at B0 ¼ 18.8 T under various static and spinning conditions with inclusion of the second-order quadrupolar interaction as described above is shown in Fig. 2. It is worth noting that a coupling constant CQ ¼ 3 MHz results in an inhomogeneous lineshape due to the first-order interaction that spans over 4 MHz. In contrast, the second-order anisotropic broadening evident in Fig. 2D is only a few kHz in size. The isotropic part of the second-order inhomogeneity niso(Q) of Eq. (9) evaluates to 11.67 kHz in these simulations. Fig. 2D also shows an important technical feature that can be

(A)

(B)

(C)

2

1

0

–1

–2

Vrf (MHz)

(D)

40

20

0

–20

–40

Vrf (kHz) Fig. 2 Numerical simulations of 14N NMR spectra for a single spin with parameters CQ ¼ 3.0 MHz, hQ ¼ 0.0, and quadrupolar interaction described to second order in a B0 ¼ 18.8 T. (A) Spectrum of a single crystal with bPR ¼ 90 . (B) Powder pattern resulting from a polycrystalline sample. (C) Spinning sideband pattern for a spinning rate nR ¼ 100 kHz. (D) Spectrum analogous to (C) acquired with rotor-synchronized sampling of data points. The isotropic shift due to the second-order quadrupolar interaction niso(Q) affects all spectra and is highlighted by a red line in (D). An ideal initial state r(0) ¼ Ix was assumed in all cases. The crystallite orientations considered for powder averaging were 28,656 in (B) and 986  45 (C,D) sampled with the ZCW scheme.17–19 A line broadening of 200, 20,000, 1000 and 100 Hz was applied from top to bottom, respectively. Spectra were normalized in height for clarity.

8

Nitrogen-14 NMR spectroscopy

employed when dealing with the ST of quadrupolar nuclei under MAS conditions, i.e., rotor-synchronization for either direct or indirect acquisition.20 By setting the dwell time between each acquired data point that constitutes the FID to be equal to the rotor period sR ¼ 1/nR, one can achieve aliasing of all excited spinning sidebands onto a single centerband thus removing the first-order quadrupolar interaction and improving the signal-to-noise ratio of the resulting spectrum. Rotor-synchronization is usually crucial for the indirect detection of 14N in 2D NMR experiments. One strict requirement for the implementation of this technical feature is that the magic angle needs to be adjusted very carefully in order to remove first-order broadenings.21

9.02.3

14

N in solution NMR

The inhomogeneous features that affect lineshapes such as that shown in Fig. 2B are generally not observed in solution. This is due to the very fast longitudinal (and hence transverse) relaxation that usually affects quadrupolar nuclei and that results in linewidths that can easily reach a few kHz. More specifically, if the molecule under investigation is assumed to undergo fast isotropic tumbling, the anisotropic part of interactions such as quadrupolar couplings is averaged to zero. In spite of this simplification, however, highresolution isotropic peaks for nitrogen-14 are observed in solution only for tetrahedral chemical environments, for R4Nþ sites, or for R4–xNHxþ species when chemical exchange of the protons is either absent or slow on the NMR time scale. This is due to the fact that the fast isotropic reorientation of the EFG in the external B0 field caused by the fast isotropic molecular tumbling results in fluctuations of the quadrupolar coupling interaction that can act as a very efficient source of relaxation. Fig. 3A shows the solution 14N NMR spectrum of bis-diazabicyclooctane-butane in D2O with the addition of two equivalents of Hþ.3 The peak at 47.7 ppm is ascribed to the R4Nþ site, for which the highly symmetric tetrahedral geometry results in a linewidth of 13 Hz. Fig. 3B shows a vertical expansion of the spectrum of (a), where one can identify a second much broader peak ascribed to the

(A)

+

N

+

N

+

N

N H

R 4N +

(B) R 4N + R3NH+/R3N

43

90

80

70

60 14N

50

40

30

20

10

Giso (ppm)

Fig. 3 (A) Solution 14N NMR spectrum of bis-diazabicyclooctane-butane (structure given in the inset) in D2O with the addition of two equivalents of Hþ. (B) Vertical expansion of the spectrum of (A) where a second broader peak assigned to the apical R3N site in fast exchange with its protonated form can be identified. A numerical fit of this latter lineshape results in a line broadening of 723 Hz and isotropic shift diso ¼ 33.1 ppm. Adapted with permission from Ref. Castro, M.; Seymour, V. R.; Carnevale, D.; Griffin, J. M.; Ashbrook, S. E.; Wright, P. A.; Apperley, D. C.; Parker, J. E.; Thompson, S. P.; Fecant, A.; Bats, N. Molecular Modeling, Multinuclear NMR, and Diffraction Studies in the Templated Synthesis and Characterization of the Aluminophosphate Molecular Sieve STA-2. J. Phys. Chem. C 2010, 114(29), 12698–12710, https://doi.org/10.1021/jp104120y.

Nitrogen-14 NMR spectroscopy

9

apical R3N in fast exchange with its protonated R3NHþ form. A numerical fit of this latter lineshape yields an isotropic shift of 33.1 ppm and a linewidth of 723 Hz. The acidification of the solution was necessary in order to shift the equilibrium of the R3N apical nitrogen, characterized by a large CQ value and thus substantially unidentifiable, toward its protonated R3NHþ form, with a much smaller CQ value due to the tetrahedral nitrogen environment. In the slow-exchange limit, the R3NHþ and R4Nþ peaks are expected to have comparable linewidths. For small molecules in non-viscous solutions, when the extreme narrowing limit applies, i.e., u0sc < < 1, the longitudinal and transverse relaxation rates coincide, and can be expressed as22,23: ! 2 h2Q 1 1 3 2I þ 1 e2 Qq ¼ ¼ sc ; (10) 1þ 2 T1 T2 40 I ð2I  1Þ Z 3 where the correlation time sc characterizes the isotropic tumbling rate and is defined as the average time it takes for a molecule to rotate about one rad, and e2Qq/Z is the quadrupolar coupling constant CQ expressed in rad/s. Eq. (10) shows that asymmetric geometries characterized by large EFGs (large CQ values) and high molecular-weight compounds characterized by long correlation times result in very short relaxation time constants and hence, very broad NMR lineshapes. The resulting linewidths are usually much larger than scalar couplings with neighboring nuclei so that fine structures due to J-coupling interactions are rarely observed. Fig. 3 represents an example of typical 14N lineshapes in solution NMR of small molecules. Unless tetrahedral cationic nitrogen environments are present, linewidths can vary between several tens of Hz, to hundreds of Hz, depending, besides the EFG size, on the molecular weight, viscosity of the solvent, and pH, with those on the order of kHz being difficult to identify in the spectrum. Table 1 presents typical values of full width at half height for 14N lineshapes of small molecules in solution NMR. Further reading about general aspects of 14N solution NMR and relaxation data may be found in the literature.25,26

9.02.4

14

N in solid-state NMR

The isotropic tumbling that generally characterizes molecular dynamics in solutions is absent in the solid state. In such cases, the anisotropic part of the quadrupolar interaction is not averaged to zero, and 14N lineshapes present inhomogeneous features as shown in Fig. 2, for either static or MAS spectra. Therefore, in the solid state, the precious structural information carried by the EFG tensor can be directly measured from the analysis of the NMR lineshapes. The following paragraphs describe the two main strategies developed over the years to acquire such 14N NMR spectra, i.e., either direct or indirect detection methods.

9.02.4.1

Direct detection

The simulations of Fig. 2 show that 14N lineshapes can easily reach several MHz in width. These broad lineshapes represent a challenge for NMR as the rf-field strengths n1 available with most probes are usually much smaller than the quadrupolar interaction. This is particularly true for low-g nuclei, for which acoustic ringing represents an additional problem. The MAS frequencies nR available are also much smaller than first-order broadenings. Therefore, a uniform excitation of the whole lineshape – or alternatively, of all crystallite orientations – is not possible, whether in static or spinning samples. Furthermore, the first-order anisotropies that affect 14 N nuclei largely exceed the bandwidth of the probes so that multiple acquisitions by stepping the carrier frequency nrf – and tuning adjustment – over the lineshape would be required for the accurate reconstruction of the full spectrum. Such a ‘piecewise’ approach was demonstrated by Hill and Yesinowski27 for the acquisition of the powder pattern of 14N in potassium nitrate by means of the QCPMG technique,28 that allows for a gain in sensitivity for each acquired subspectrum.29 The train of echoes produced by this experiment results, upon Fourier transform, in a manifold of spikelets that mimics the first-order powder pattern. Alternatively, all echoes can be coadded so as to result in a conventional spectrum, as shown in Fig. 4 for KNO3. This piecewise method for

Table 1

Examples of full width at half height values for

14

N lineshapes in solution NMR of small molecules.

Compound

Molecular Weight

Solvent

Width at half height (Hz)

References

Pyrrole

67.09 117.15

Gly Ala Pro Glu His

75.07 89.10 115.13 147.13 154.16

172  5 50  5 40  5 730  30 380  30 55  3 71  4 87  4 146  7 169  8

24

Indole

Neat Dioxane (1:1) Methanol (1:1) Dioxane (satd) Methanol (satd) Water (0.1 M, pH ¼ 0.5)

25

10

Nitrogen-14 NMR spectroscopy

Fig. 4 Static 14N NMR spectrum of powdered KNO3 at B0 ¼ 7.05 T resulting from a piecewise acquisition with the QCPMG method where all echoes were coadded. A theoretical lineshape is shown by a dotted line. Adapted with permission from Ref. Hill, E. A.; Yesinowski, J. P. Wide-Line 14N NMR in Solids and Reorientation-Induced Redistribution of Isochromats. J. Am. Chem. Soc. 1996, 118(28), 6798–6799, https://doi.org/10.1021/ ja960757j.

the acquisition of ultra-wide powder patterns was further developed by the incorporation of WURST pulses.30,31 O’Dell and Schurko implemented these frequency-swept pulses with the QCPMG technique.32 The WURST-QCPMG approach has been successfully utilized for the acquisition of 14N spectra of static powders of KNO3 and various amino acids.33,34 In this work, they also demonstrated a mechanism of signal enhancement that stems from the increase in population difference across one ST transition while the other one is swept across by the irradiating carrier frequency nrf. The effects of relaxation and dynamics on 14 N WURST-QCPMG spectra of static powders of deuterated urea35 and melamine36 were also investigated. More specifically, different nitrogen environments with different transverse relaxation rates can be discerned by the QCPMG train of echoes. Fig. 5 shows 14N spectra of a powdered sample of imidazole acquired with this method at B0 ¼ 21.1 T. Veinberg et al. have utilized this technique to distinguish polymorphs of glycine by an accurate measurement of quadrupolar parameters and transverse relaxation rates.37 These frequency-swept pulses were also employed in the acquisition of nitrogen-14 spectra by means of crosspolarization (CP) experiments.38 For nitrogen sites characterized by high symmetry and therefore small CQ values, i.e., up to ca. 1 MHz, a common approach based on direct detection under MAS conditions can be utilized.39–43 An example is given by the MAS spectrum of KNO3 acquired in a B0 ¼ 14.1 T field spinning speed nR ¼ 6 kHz, as shown in Fig. 6. For such relatively small quadrupolar coupling constants the manifold of spinning sidebands does not exceed dramatically the bandwidth of most probes and first-order envelopes can be fully characterized by means of small flip-angle rf pulses. Nonetheless, as shown by Jakobsen et al.,41 second-order broadenings are clearly visible on each spinning sideband. Furthermore, CSA and second-order cross-terms need to be taken into account in order to interpret the inhomogeneous spectral features. Schemes of rf pulses for CP specifically designed for I ¼ 1 spins were also developed and applied to nitrogen-14.44 Another experimental approach for the observation of 14N spins in NMR is that given by overtone spectroscopy. This methodology is based upon the excitation and observation of the m1 ¼ þ 1 4 m1 ¼  1 transition, which is not affected by the quadrupolar interaction to first order and thus results in lineshapes which are broadened only to second order by a few kHz. In contrast to double-quantum excitations, which are induced by irradiation with the carrier nrf sitting at the Larmor frequency n0 and cannot be directly observed, overtone NMR requires an irradiation frequency at nrf ¼ 2n0 (neglecting chemical shift and isotropic quadrupolar shift) and can be observed directly. As shown by Bloom and LeGros,45 this Dm1 ¼ 2 overtone transition is partly allowed when the size of the quadrupolar coupling is comparable with the Zeeman interaction. In these cases, the quantization axis is not aligned with the external field B0 and the non-secular terms of the quadrupolar interaction need to be retained, so that the high-field approximation does not apply. Initially applied only to static single crystals46 or, less often, to powdered samples,47 overtone 14N NMR has been more recently extended to MAS conditions. Following theoretical investigations of overtone NMR under sample rotation by Marinelli et al.,48 the first experimental 14N overtone MAS spectra were reported by O’Dell and Ratcliffe on a sample of powdered glycine spinning at nR ¼ 10 kHz.49 Subsequent studies have highlighted that, in a spinning sample, the overtone signal is split into sidebands at 0,  nR and  2nR with respect to the static lineshape, with the condition at þ 2nR showing the highest signal intensity in a powder.50 The þ 2nR overtone sideband also showed the highest nutation rate for a given rf-field strength when compared to the other sidebands.51 Frequency-swept WURST pulses were also utilized to excite 14N overtone transitions under MAS in a powdered sample of histidine.50 The resulting spectrum with numerical simulations is shown in Fig. 7. Methods to enhance the polarization of overtone 14N NMR were investigated by Tycko and Opella in their early work.52,53 By means of Jeener-Broekaert and adiabatic demagnetization in the rotating frame experiments they achieved polarization transfer from the dipolar order of the proton bath to nitrogen-14 nuclei, obtaining an enhancement of ca. 6. Under MAS conditions, and with the boost in sensitivity granted by dynamic nuclear polarization (DNP),54–56 Rossini et al. have performed direct CP from protons to the þ 2nR overtone sideband

Nitrogen-14 NMR spectroscopy

11

(A)

N1 N2

(B)

N1 (C)

N2

(D)

3

2

1

0

–1

–2

–3

vrf (MHz) Fig. 5 (A) 14N NMR spectrum of imidazole resulting from the first echo of a WURST-QCPMG experiment. (B) Numerical simulation of the spectrum of (A). The individual lineshapes for the two nitrogen sites are shown in (C). (D) Spectrum obtained by coadding all echoes of the QCPMG train. An imidazole molecule is shown in the left-top inset. Adapted with permission from Ref. O’Dell, L. A.; Schurko, R. W.; Harris, K. J.; Autschbach, J.; Ratcliffe, C. I. Interaction Tensors and Local Dynamics in Common Structural Motifs of Nitrogen: A Solid-State 14N NMR and DFT Study. J. Am. Chem. Soc. 2011, 133(3), 527–546. https://doi.org/10.1021/ja108181y.

in a series of amino acids (Fig. 8).57 An alternative approach to gain sensitivity of nitrogen-14 overtone NMR has been taken by Haies et al.,58 who used symmetry-based dipolar recoupling schemes of rf pulses – namely, PRESTO59 – to achieve 1H / 14N polarization transfer.

9.02.4.2

Indirect detection

The indirect detection of 14N signal relies on ‘spy’ nuclei, such as 1H or 13C (via CP from 1H), that are in spatial proximity with the nitrogen sites. These neighboring I ¼ 1/2 spins supply the initial source of polarization as well as the single-quantum coherence which is finally detected within the NMR experiment. This represents an advantage in terms of sensitivity as 1H has a much higher gyromagnetic ratio than nitrogen-14. The spatial proximity between 14N and, say, 1H nuclei, implies that they are coupled to one another – either via dipolar or scalar interaction. These couplings allow for coherence transfer from the ‘spy’ nuclei to the nitrogen ones via a suitable scheme of rf pulses or periods of free evolution. Once the transfer has occurred, 14N coherence is allowed to evolve for a time interval t1 of a 2D experiment and then transferred back to the ‘spy’ nuclei for detection. The subsequent Fourier transform of the data set unveils nitrogen-14 resonances in the indirect dimension u1 of the resulting spectrum. This experimental approach was introduced independently by Gan60 and Cavadini et al.61 in 2006 (Fig. 9). In both these studies a 1H / 13C CP step was followed by a 13Ce14N HMQC block, with MAS rates of 25 and 30 kHz, respectively. Immediately after the CP transfer, carbon13 SQ coherence was allowed to evolve under 13Ce14N scalar J-couplings and/or ‘residual dipolar splittings.’ The latter represent second-order cross terms between the quadrupolar and dipolar interactions that are not completely removed by MAS. By virtue of these couplings, two-spin anti-phase coherences are created according to Cx / sin(pJs)2CyNz, so that magnetization is transferred

12

Nitrogen-14 NMR spectroscopy

(A)

500 400 300 200 100

0

–100 –200 –300 –400

(B)

(C)

279

277

275

273

271

269

ν rf (kHz) Fig. 6 (A) 14N MAS NMR spectrum of KNO3 acquired at nR ¼ 6 kHz in a B0 ¼ 14.1 T magnet. A small flip-angle (b ¼ 14.3 ) pulse sp ¼ 1 ms was utilized (n1 ¼ 40 kHz), with 4 s recycling delay and 30,000 scans. The isotropic shift is marked by an asterisk. (B,C) Numerical simulations and experimental spectrum of (A), respectively, expanded over three spinning sidebands at ca. 270 kHz from the carrier frequency nrf. Adapted with permission from Ref. Jakobsen, H. J.; Bildsøe, H.; Skibsted, J.; Giavani, T. 14N MAS NMR Spectroscopy: The Nitrate Ion. J. Am. Chem. Soc. American Chemical Society 2001, 5098–5099, https://doi.org/10.1021/ja0100118.

to the 14N nuclei. An rf pulse on the nitrogen-14 channel acting on such two-spin state can create both SQ or DQ 14N coherences (Fig. 10) that can be selected for the t1 period of free evolution via phase cycling.62 It is worth noting that indirect detection methods for nitrogen-14 NMR based on the HSQC experiment have been investigated and compared to HMQC ones.6,63 However, this latter type of experiment has found a wider utilization in the NMR community. Cavadini et al. also introduced the 1He14N HMQC approach, which can grant for higher sensitivity thanks to proton detection, particularly at faster spinning rates (with smaller rotor sizes) or when 13C enrichment is not available.64,65 The general pulse sequences for HMQC-type experiments for the indirect detection of 14N nuclei are depicted in Fig. 11. The subsequent development of these indirect techniques involved the use of recoupling schemes (in place of the simpler free evolution) to facilitate magnetization transfer from the X ‘spy’ nuclei to nitrogen. This approach implies the recoupling of the dipolar interactions (much larger than J-coupling and residual dipolar splittings) that would be otherwise averaged out by MAS and is based on the use of rf irradiation schemes on the X spins such as rotary resonance66–68 or symmetry-based techniques.69,70 Replacing the free evolution period for coherence transfer with a dipolar recoupling scheme also allows to minimize the deleterious effect of homogeneous losses due to the extended 1H dipolar network.71 In this respect, the extension of the transverse relaxation times of protons can be also achieved by very fast MAS rates.72 Further studies have been conducted to improve the efficiency of the rf-driven conversion of the two-spin state of the type 2XyNz into SQ or DQ nitrogen coherences via irradiation of the N spins. In this regard, rotor-synchronized trains of short rf pulses in the manner of DANTE73–77 have been explored in 1He14N HMQC experiments.78,79 Another strategy involved the implementation of rectangular centerband-

Nitrogen-14 NMR spectroscopy

13

(A)

130

110

90

70

50

30

110

90 70 ν rf (kHz)

50

30

(B)

130

Fig. 7 (A) Numerical simulations of an overtone 14N MAS NMR spectrum in a B0 ¼ 11.7 T and nR ¼ 22 kHz, assuming a WURST excitation pulse and quadrupolar parameters for the orthorhombic L-histidine. (B) Corresponding experimental spectrum. Adapted with permission from Ref. O’Dell, L. A.; Brinkmann, A. 14 N Overtone NMR Spectra under Magic Angle Spinning: Experiments and Numerically Exact Simulations. J. Chem. Phys. 2013, 138(6), 064201, https://doi.org/10.1063/1.4775592.

(A)

14

NOT CP Pw on

(B)

Pw off

(C)

Simulation

40

35

25

30

20

15

vrf (kHz) Fig. 8 (A) Overtone 14N spectrum of glycine enhanced by DNP by means of CP from 1H and acquired at T ¼ 107 K, in a field B0 ¼ 9.4 T at nR ¼ 10 kHz spinning rate. (B) Analogous spectrum without microwave irradiation. (C) Numerical simulation of the spectrum of (A). Adapted with permission from Ref. Rossini, A. J.; Emsley, L.; O’Dell, L. A. Dynamic Nuclear Polarisation Enhanced 14N Overtone MAS NMR Spectroscopy. Phys. Chem. Chem. Phys. 2014, 16(25), 12890–12899, https://doi.org/10.1039/c4cp00590b.

selective rf pulses several tens of ms in length with n1 ¼ 30 or 40 kHz.80,81 Furthermore, the use of long rectangular pulses on the ms timescale with relatively low rf-field strengths (30–70 kHz) without irradiation on the ‘spy’ spins have been proposed.82,83 An interesting variation has been proposed by Gan,84 who replaced the two 14N rf pulses with a single one, with carrier frequency stepped over the first-order pattern in an indirect continuous-wave 2D experiment. Hung et al. have shown that, by irradiation of the 14N spins with rf pulses longer than a rotor period, spectra free of spinning sidebands can be generated.85 Wijesekara et al. have shown that by selective excitation and detection of 1H magnetization one can shorten considerably the recycling delay, thus providing

Nitrogen-14 NMR spectroscopy

Gly3

Ala1 Gly2

Ala1

Gly2

Gly3

15N

0

200 iso

200 GQ

14N

(ppm)

0

(ppm)

14

400

600

CO 176

Cα 172 Ala1

168

48

Gly2

Gly3

44

40

O H NH2 CH C N C CH2 OH N CH2 C CH3 H O O

200

160

120 80 13C (ppm)

40

0

Fig. 9 13Ce14N HMQC spectrum of the AlaGlyGly tripeptide at natural abundance acquired in a field B0 ¼ 14.1 T with spinning rate nR ¼ 25 kHz. Vertical brackets indicate the second-order quadrupolar shifts as measured from 15N MAS spectra. Reprinted with permission from Ref. Gan, Z. Measuring Amide Nitrogen Quadrupolar Coupling by High-Resolution 14N/13C NMR Correlation under Magic-Angle Spinning. J. Am. Chem. Soc. 2006, 128(18), 6040–6041, https://doi.org/10.1021/ja0578597.

a gain in sensitivity per unit time.86 The overtone approach has also been implemented by Nishiyama et al. in HMQC experiments under very fast MAS conditions (nR ¼ 90 kHz).87 O’Dell et al. further developed this latter strategy by means of WURST pulses (Fig. 12).51 DNP under MAS conditions has been also utilized to boost the sensitivity of these indirect-detection methods for 14 N NMR.57,88,89 As discussed above, and similarly to overtone spectroscopy, also DQ coherences offer a means to get rid of the first-order quadrupolar broadening. However, the excitation of these multiple-quantum coherences is usually inefficient when compared to SQ ones. The development of new schemes of rf pulses to improve the efficiency of DQ excitation has been recently considered by Aleksis and Pell in a theoretical framework based on average Hamiltonian theory.90 DQ coherences have been exploited in 3D 14N/1H(DQ)/1H(SQ) HMQC experiments at nR ¼ 70 kHz so as to probe simultaneously 1He1H and 1He14N spatial proximities.91,92 By comparing 14N SQ and DQ linewidths as a function of the temperature, Cavadini et al. have utilized the 1He14N HMQC experiment to investigate motion and dynamics in the AAG tripeptide.93 Other structural studies that have utilized this indirect approach include investigations of nucleosides self-assemblies,94,95 azo-hydrazo tautomerism in dyes,96 as well as pharmaceutical polymorphs, cocrystals and amorphous dispersions.97–101 An alternative method for the indirect detection of 14N NMR spectra was introduced in 2017.102 This experiment is based on 1 a H / 14N / 1H double cross polarization (DCP) transfer and is particularly straightforward to implement as it requires an optimization of parameters that is completely analogous to that of a conventional 1H / 13C 1D CP spectrum. A scheme depicting the pulse sequence is shown in Fig. 13. The DCP technique has been tested by the authors at nR ¼ 62.5 kHz in B0 fields of 9.4 and 18.8 T, and nR ¼ 100 kHz at B0 ¼ 20.0 T.16,102,103 The rf match conditions for the CP steps were found to be very similar in all these fields and spinning rates. More specifically, the rf-field strengths optimized experimentally for the CP contacts were n1(1H)  50 and n1(14N)  80 kHz. One-bond correlation 2D spectra could be obtained with contact times for the CP steps between 100 and 200 ms. Long-range correlations were instead obtained with contact pulses of ca. 600 ms. Dipolar couplings in a powdered sample of cyclosporine were probed by means of this technique (Fig. 14).16 A long-range 1He14N correlation spectrum highlighted heteronuclear

Nitrogen-14 NMR spectroscopy

(A)

L-leu (I)

60

(I)

15

58

(II)

56 54 52 G (ppm)

50

48

(B)

(II)

0

50

14N

100 4 150

Z1/2S (kHz)

G1 (ppm)

2

6

SQ

G1 (ppm)

(C)

60

58

56

54

52

50

48

0

100

2

150

4

200

6

14N

Z1/2S (kHz)

200

DQ 60

58

56 54 52 G2 (ppm)

50

48

13C

Fig. 10 (A) 13C CP MAS spectrum of L-leucine 13C-enriched in the Ca position acquired in a B0 ¼ 14.1 T field with spinning rate nR ¼ 20 kHz. Two crystallographically-distinct sites are indicated by (I) and (II). (B,C) SQ and DQ 13Ce14N HMQC spectra, respectively. Left and right inner projections refer to sites (I) and (II), respectively. Outer projections were obtained by numerical simulations. Adapted with permission from Ref. Cavadini, S.; Antonijevic, S.; Lupulescu, A.; Bodenhausen, G. Indirect Detection of Nitrogen-14 in Solid-State NMR Spectroscopy. ChemPhysChem 2007, 8(9), 1363–1374, https://doi.org/10.1002/cphc.200700049.

spatial proximities within 3.3 Å. In another study, the DCP method was utilized to investigate stacking interactions in guanine quartets.103 Intra- and inter-plane dipolar contacts could be identified by comparing short- and long-range correlation experiments. Sajith et al. recently presented a theoretical analysis of the spin dynamics involved in the 1H / 14N / 1H DCP process.104

9.02.4.3

Structural insights obtained by

14

N NMR

Nitrogen-14 NMR is extremely sensitive to chemical environments on the atomic scale, with 2nd-order anisotropic lineshapes that can vary dramatically with changes in the local structure. As discussed in the previous paragraphs, this is due to the quadrupolar interaction, i.e., the coupling between the electric quadrupole moment of the nucleus at hand and the EFG generated by the neighboring sites. Different nuclear arrangements around the quadrupolar spin, or different geometries characterized by different symmetries, can alter the inhomogeneous 14N lineshapes significantly.

16

Nitrogen-14 NMR spectroscopy

(A)

S/2 1H

Heteronuclear Decoupling

CP

S S (13C)

τexc

CP

τ rec

t2

τ rec

t2

τp

τp l (14N) t1

(B)

S/2 S (1H)

S

τ exc

Wp

Wp

l (14N) t1 (C)

p s pl +1 +2 +1 +1 +1 0 +1 –1 +1 –2 0 +2 0 +1 0 0 0 –1 0 –2 –1 +2 –1 +1 –1 0 –1 –1 –1 –2

Fig. 11 (A) Pulse sequence for the 13Ce14N HMQC experiment. (B) Pulse sequence analogous to that of (A) for 1He14N correlation experiments. (C) Coherence transfer pathway for SQ and DQ coherence selection, in black and red, respectively. Rotor-synchronization of the free evolution period t1 is required when SQ is selected in F1. Adapted with permission from Ref. Cavadini, S.; Abraham, A.; Bodenhausen, G. Proton-Detected Nitrogen-14 NMR by Recoupling of Heteronuclear Dipolar Interactions Using Symmetry-Based Sequences. Chem. Phys. Lett. 2007, 445(1–3), 1–5. https://doi.org/ 10.1016/j.cplett.2007.07.060.

The use of density functional theory (DFT) methods for calculations of NMR parameters105–107 has found considerable applications in structural studies of a variety of chemical systems. Parameters such as CSA, EFG tensors, scalar or dipolar couplings, are nowadays routinely investigated by DFT methods in NMR studies. In particular, the possibility to compute NMR observables in solid-state systems has been revolutionized by the introduction of the gauge-included projection augmented wave (GIPAW) method,108,109 that enabled calculations of magnetic shieldings in periodic systems in a planewave-pseudopotential formalism. Such methods, based on periodic boundary conditions, can also be implemented to mimic both positional and compositional disorder.110 Alternatively, an approach based on atom-centered basis sets such as the gauge-independent atomic orbital (GIAO) method111,112 may be utilized. This latter strategy implies the use of an isolated cluster of atoms or molecules to model the solid sample, be it ordered or disordered, and requires some care to ensure that electronic effects of the ‘fictitious surface’ do not affect significantly the NMR parameters of the nuclei of interest.106,113,114

Nitrogen-14 NMR spectroscopy

17

NOT / kHz

150

14

140

130

(A)

20

0 1

H / ppm

NOT / kHz

180

14

170

160

(B)

0

20 1

H / ppm

Fig. 12 (A) 1He14N HMQC spectrum of L-histidine hydrochloride monohydrate utilizing WURST pulses on the 14N channel, at B0 ¼ 11.7 T and spinning rate nR ¼ 62.5 kHz. (B) Spectrum analogous to that of (A) on a sample of N-acetyl-D,L-valine. Adapted with permission from Ref. O’Dell, L. A.; He, R.; Pandohee, J. Identifying H-N Proximities in Solid-State NMR Using 14N Overtone Irradiation under Fast MAS. CrystEngComm 2013, 15(43), 8657–8667, https://doi.org/10.1039/c3ce40967h.

The computational prediction of NMR observables can greatly help spectral interpretation and assignment. This is particularly useful when dealing with low-g and low-abundant nuclei, most often encountered in inorganic materials, when relatively little NMR information might be present in the literature. Furthermore, the previous knowledge of the inhomogeneous interactions that affect challenging nuclei as obtained in silico, can greatly help the experimental acquisition of NMR data by guiding the often tedious procedure of optimization of experimental parameters such as rf-field strengths or flip angles. In general, when different structural hypotheses need to be considered, in cases such as, say, assisting in the refinement of diffraction data, the discrimination of different polymorphs or the effect of atom substitutions, DFT methods have so far proven to be an extremely precious tool for NMR spectroscopists. Given the great utilization for structural determinations and/or model refinements, the combination of solidstate NMR and computational methods has emerged in recent years as a new field termed ‘NMR crystallography.’115–117 In this context, all methods developed to acquire 14N NMR spectra, allowing for the experimental measurement of parameters such as CQ and hQ, can further expand the ensemble of possible nuclei to exploit in NMR crystallography studies. The following paragraph presents a brief review of the main classes of compounds that have been investigated by 14N NMR spectroscopy. Nitrides, nitrates, and ammonium cations are characterized by relatively small CQ values that usually allow for a direct detection by means MAS in simple 1D spectra. Examples of typical quadrupolar parameters for these chemicals are given in Table 2. Various nitrides such as BN,39,118 AlN40,118 and GaN119,126,127 have been investigated by 14N MAS NMR thanks to favorable CQ

18

Nitrogen-14 NMR spectroscopy

(S/2)y

1

H

(TCP)x

(TCP)x t2

(TCP)M 14

14

N

(TCP)M

N

t1 = nWR

+1 =0 –1

Fig. 13 Pulse sequence for the 1H / 14N / 1H DCP experiment with coherence transfer pathway. The following phase cycling is applied: f ¼ x, x, x, x, f’ ¼ x, x, x, x, frec ¼ x, x, x, x. Adapted with permission from Ref. Carnevale, D.; Ji, X.; Bodenhausen, G. Double Cross Polarization for the Indirect Detection of Nitrogen-14 Nuclei in Magic Angle Spinning NMR Spectroscopy. J. Chem. Phys. 2017, 147(18), 184201, https://doi.org/10.1063/1.5000689.

250

Sar3 Leu4

Val5

Ala7 (HE)3 J (H )3 Ala8 NCH3

300

Abu2

Ala8 Ala7

Val11 EJ (H )n Bmt1 Abu2

Val5

350

14

HD

N G1 (ppm)

NH

400

10

8

6 1H

4

2

0

G2 (ppm)

Fig. 14 1He14N DCP experiment for a sample of the undecapeptide cyclosporin at B0 ¼ 20.0 T and nR ¼ 100 kHz. A contact time sCP ¼ 60 sR ¼ 600 ms was used. The most intense one-bond correlations are highlighted by red dashed rectangles. Long-range correlations are highlighted by magenta rectangles. Printed with permission from Ref. Carnevale, D.; Grosjean, B.; Bodenhausen, G. Dipolar Couplings in Solid Polypeptides Probed by 14N NMR Spectroscopy. Commun. Chem. 2018, 1(1), 1–9, https://doi.org/10.1038/s42004-018-0072-5.

values below 150 kHz. Knowledge of these quadrupolar parameters has allowed the identification of AlN impurities in b-SiAlON ceramic phases.40 Oxynitride environments were detected in studies of the oxygen-nitrogen substitution in BaTiO3.128 The ionicity of TaeN bonds in perovskite oxynitrides ATaO2N (A ¼ Ca, Sr, Ba) was investigated by means of 1D MAS 14N NMR spectra.129 Nitrates are characterized by CQ values usually smaller than 1 MHz, and have been chosen to investigate, by means of numerical simulations, the effects of quadrupolar–CSA second-order cross terms on 14N spinning sideband patterns.41,130 The phase transition between the IV and III forms in NH4NO3 was monitored thanks to differences in the asymmetry parameter hQ in the nitrogen environments.42 Thanks to their highly symmetric tetrahedral geometries, ammonium cations are generally characterized by CQ values smaller than 1 MHz, and can be therefore easily characterized by direct acquisition of 1D MAS 14N NMR spectra. The mobility of

Nitrogen-14 NMR spectroscopy Table 2

19

Examples of isotropic shift and quadrupolar parameters for nitrogen-14 in the solid state for nitrides, nitrates, ammonium salts, alkylammonium salts and organic molecular crystals.

Compound

diso (ppm)

CQ (kHz)

hQ

References

BN cubic BN hexagonal AlN GaN LiNO3 NaNO3 RbNO3 MgNO3 NH4Cl NH4H2PO4 (NH4)2MoO4 site 1 (NH4)2MoO4 site 2 (NH4)2WS4 site 1 (NH4)2WS4 site 2 (CH3)3NHCl (CH3)4NCl (CH3)4NBr (CH3)4NI Hydrazine$2HCl Imidazole N1 Imidazole N2 Urea-d4

 17.6 63 n.a.  301.0 282.0 337.8 337.0 293.0 0.0  16.1  17.9  16.2  12.7  8.5  141.0 n.a. n.a. n.a. n.a. n.a. n.a. n.a.

< 10 140 n.a. 0 993 740 743 877 0 24 252 217 129 48 1500 17 27 31 3820 1430 3250 3470

n.a 0.00 n.a. 0.00 n.a. 0.01 n.a. n.a. 0.00 0.03 0.91 0.84 0.18 0.12 0.02 0.00 0.00 0.00 0.00 0.98 0.15 0.31

39 118 119 120 41 120 – 121 122 123 124 125 36

NH4þ cations and dynamics in letovicite (NH4)3H(SO4)2 have been probed by variable temperature MAS 1H and static 14N NMR, highlighting changes in spectral features near the phase transition.131 Quadrupolar and shift parameters have been accurately measured in a series of ammonium molybdates by means of 14N MAS NMR,122 showing that nitrogen-14 spinning sideband patterns, mainly determined by the quadrupolar interaction, can serve as a tool to fingerprint subtle differences in crystal structures. These simple techniques also allowed to identify site preferences of NH4þ in solid solutions of Cs2WS4 and Rb2WS4.123 Compounds containing ammonia might require more advanced NMR methods due to lower-symmetry environments. The WURST-QCPMG technique was utilized to characterize square-plane platinum complexes, namely, cis-PtCl2(NH3)2 (cisplatin), trans-PtCl2(NH3)2 (transplatin), and [C4H6(CO2)2]Pt(NH3)2 (carboplatin).132 The corresponding 14N static NMR spectra, acquired in a matter of hours, are shown in Fig. 15. In this latter study, DFT calculations of the EFG tensors were employed to rationalize the experimental evidence. In particular, the orientation of the main component of the EFG, i.e., Vzz, was found to be roughly aligned with the PteN bond. Subsequently, Lucier et al. utilized 14N NMR, in combination with diffraction techniques and DFT methods, to elucidate the previously unknown structure of Magnus’ pink salt [Pt(NH3)4][PtCl4].133 Similarly to ammonium cations, tetra-alkylammonium species are also characterized by highly symmetric chemical environments that result in small CQ values (from tens to few hundreds of kHz) that allow for a straightforward direct acquisition of nitrogen-14 NMR spectra. These molecules are often utilized as templates in the synthesis of porous materials such as zeolites. In these cases, 14N NMR can be utilized to probe structural details related to the organic-inorganic interface, the crystallization process as well as the mobility of the SDA species within the pores of the materials. Generally, highly mobile cations result in narrow isotropic lineshapes whereas less mobile species result in broader signals. In cases when mobility is highly restrained, quadrupolar features may also be observed in static lineshapes, or as spinning sideband patterns in MAS spectra. A typical example is given by the study of Fyfe et al., who showed how the increase in anisotropy in 14N MAS spectra of the tetra-propylammonium SDA can be used to follow the crystallization process in the clear solution synthesis of the MFI zeolite (Fig. 16).134 Dib et al. utilized nitrogen-14 MAS spectra of the same SDA to monitor local order in silicalite-1 zeolites.135 They showed that materials obtained by synthetic route utilizing F anions result in 14N spinning sideband patterns where well defined quadrupolar features can be easily discerned. This is indicative of order for the nitrogen environments in the sample. In contrast, when OH are used, a featureless Gaussian envelope of spinning sidebands is obtained, indicating a distribution of quadrupolar parameters and hence, local disorder (Fig. 17). By analyzing such broad distributions of 14N quadrupolar parameters, Mineva et al. were able to distinguish between lamellar, hexagonal and cubic mesostructured silica templated by the hexadecyltrimethylammonium SDA.136

9.02.5

Outlook

This Chapter has presented a brief overview of 14N NMR spectroscopy, the difficulties encountered when dealing with this highlyabundant low-g I ¼ 1 spin, a discussion about the typical lineshapes obtained for small molecules in solution, and the experimental

20

Nitrogen-14 NMR spectroscopy

(A)

(B)

(C)

800 (D)

600

400

V22

0

200

(E)

–200

–400

–600

–800

kHz

(F)

V33 V33 V33 V11 V22 Fig. 15 (A–C) Static WURST-CPMG 14N spectra of cisplatin, transplatin and carboplatin, respectively. Simulated lineshapes are shown in red. (D–F) Vii components of the EFG tensors for the compounds corresponding to (A–C) as calculated with DFT methods. Adapted with permission from Ref. Lucier, B. E. G.; Reidel, A. R.; Schurko, R. W. Multinuclear Solid-State NMR of Square-Planar Platinum Complexes Cisplatin and Related Systems. Can. J. Chem. 2011, 89(7), 919–937, https://doi.org/10.1139/v11-033.

methods that have been developed over the years to acquire nitrogen-14 spectra in the solid state. A series of strategies have been adopted in this respect, ranging from piecewise acquisition of ultra-wide static lineshapes, frequency-swept excitation pulses, overtone spectroscopy, to indirect detection via 2D correlation experiments. Research is currently conducted to improve these methods by designing more efficient schemes of rf pulses, including the process of polarization transfer from the high-g and highly-abundant proton bath. Examples were given about the structural details that can be obtained by nitrogen-14 NMR in a wide range of chemical systems. The implementation of DNP techniques offers a further venue to greatly boost the sensitivity of 14N NMR spectroscopy. Numerical investigations of all the spin dynamics involved in these different experiments can further improve the state-of-the-art and guide the development of new strategies. It is worth noting that DFT calculations of NMR parameters such as the CSA or EFG tensors are expected to become more and more utilized for the interpretation and assignment of the 14N lineshapes that one can experimentally acquire by means of the methods discussed in this Chapter. Besides the main components of the various tensors, the Euler angles relating different interactions for a given spin (or a given interaction for different spins, or, more generally, different interactions for different spins), are another precious structural information that can be obtained by means of DFT methods and that may be required in order to interpret correctly the experimental spectral features.28,36,137–139 Opensource software that can easily extract such tensorial orientations is available, e.g., EFGShield140 or MagresView.141

Nitrogen-14 NMR spectroscopy

21

Fig. 16 Time evolution of 14N MAS spectra of the tetrapropylammonium template as used in the clear solution synthesis of the silicalite-1 zeolite. Reprinted with permission from Ref. Fyfe, C. A.; Darton, R. J.; Schneider, C.; Scheffler, F. Solid-State NMR Investigation of the Possible Existence of “Nanoblocks” in the Clear Solution Synthesis of MFI Materials. J. Phys. Chem. C 2008, 112(1), 80–88, https://doi.org/10.1021/jp7095955.

(A)

(B)

Experiment

Model

Difference

70

0 G(14N) / kHz

–70

70

0 G(14N) / kHz

–70

Fig. 17 (A) 14N MAS NMR spectrum of the tetrapropylammonium SDA in the silicalite-1 zeolite when F anions are utilized as structure directing agents. The spinning sideband pattern reveals quadrupolar features that indicate local order in the nitrogen environments. (B) Spectrum analogous to that of (A) when OH anions are utilized in the synthesis. The featureless Gaussian-like envelope of spinning sideband pattern is indicative of a distribution of quadrupolar parameters and, hence, of local disorder in the sample. Reprinted with permission from Ref. Dib, E.; Mineva, T.; Gaveau, P.; Alonso, B. 14N Solid-State NMR: A Sensitive Probe of the Local Order in Zeolites. Phys. Chem. Chem. Phys. 2013, 15(42), 18349–18352, https://doi.org/10.1039/c3cp51845k.

22

Nitrogen-14 NMR spectroscopy

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111. Zeroka, D.; Hameka, H. F. Calculation of Magnetic Shielding Constants of Diatomic Molecules. I. General Theory and Application to HF Molecule. J. Chem. Phys. 1966, 45 (1), 300–311. https://doi.org/10.1063/1.1727325. 112. Ditchfield, R. Molecular Orbital Theory of Magnetic Shielding and Magnetic Susceptibility. J. Chem. Phys. 1972, 56 (11), 5688–5691. https://doi.org/10.1063/1.1677088. 113. Carnevale, D.; Mouchaham, G.; Wang, S.; Baudin, M.; Serre, C.; Bodenhausen, G.; Abergel, D. Natural Abundance Oxygen-17 Solid-State NMR of Metal Organic Frameworks Enhanced by Dynamic Nuclear Polarization. Phys. Chem. Chem. Phys. 2021, 23 (3). https://doi.org/10.1039/d0cp06064j. 114. Banach, E.; Invernizzi, C.; Baudin, M.; Neier, R.; Carnevale, D. Columnar Self-Assembly of: N, N 0 , N 00 -Trihexylbenzene-1,3,5-Tricarboxamides Investigated by Means of NMR Spectroscopy and Computational Methods in Solution and the Solid State. Phys. Chem. Chem. Phys. 2017, 19 (7), 5525–5539. https://doi.org/10.1039/c6cp05598b. 115. Harris, R. K.; Wasylishen, R. E.; Duer, M. J. NMR Crystallography, Wiley, 2009. 116. Martineau, C.; Senker, J.; Taulelle, F. NMR Crystallography. Annu. Rep. NMR Spectrosc. 2014, 1–57. https://doi.org/10.1016/B978-0-12-800184-4.00001-1. 117. Hodgkinson, P. NMR Crystallography of Molecular Organics. Prog. Nucl. Magn. Reson. Spectrosc. 2020, 118–119, 10–53. https://doi.org/10.1016/j.pnmrs.2020.03.001. 118. Bastow, T. J.; Massiot, D.; Coutures, J. P. 14N NMR in AlN and BN. Solid State Nucl. Magn. Reson. 1998, 10 (4), 241–245. https://doi.org/10.1016/S0926-2040(97) 00106-9. 119. Yesinowski, J. P. 69,71 Ga and 14 N High-Field NMR of Gallium Nitride Films. Phys. Status Solidi. 2005, 2 (7), 2399–2402. https://doi.org/10.1002/pssc.200461334. 120. Marburger, S. P.; Fung, B. M.; Khitrin, A. K. 14N Chemical Shifts and Quadrupole Coupling Constants of Inorganic Nitrates. J. Magn. Reson. 2002, 154 (2), 205–209. https:// doi.org/10.1006/jmre.2001.2490. 121. Jakobsen, H. J.; Hove, A. R.; Hazell, R. G.; Bildsøe, H.; Skibsted, J. Solid-State14N MAS NMR of Ammonium Ions as a Spy to Structural Insights for Ammonium Salts. Magn. Reson. Chem. 2006, 44 (3), 348–356. https://doi.org/10.1002/mrc.1772. 122. Hove, A. R.; Bildsøe, H.; Skibsted, J.; Brorson, M.; Jakobsen, H. J. Probing Crystal Structures and Transformation Reactions of Ammonium Molybdates by 14N MAS NMR Spectroscopy. Inorg. Chem. 2006, 45 (26), 10873–10881. https://doi.org/10.1021/ic061197k. 123. Jakobsen, H. J.; Bildsøe, H.; Skibsted, J.; Hansen, M. R.; Brorson, M.; Srinivasan, B. R.; Bensch, W. Site Preferences of NH þ4 in Its Solid Solutions with Cs2WS4 and Rb2WS4 from Multinuclear Solid-State MAS NMR. Inorg. Chem. 2009, 48 (5), 1787–1789. https://doi.org/10.1021/ic8023937. 124. Penner, G. H.; Webber, R.; O’Dell, L. A. A Multinuclear NMR and Quantum Chemical Study of Solid Trimethylammonium Chloride. Can. J. Chem. 2011, 89 (9), 1036–1046. https://doi.org/10.1139/v11-034. 125. Pratum, T. K.; Klein, M. P. A 14N NMR Study of Tetraalkylammonium Compounds in the Solid State. J. Magn. Reson. 1983, 53 (3), 473–485. https://doi.org/10.1016/00222364(83)90218-4. 126. Yesinowski, J. P.; Purdy, A. P. Defect Dynamics Observed by NMR of Quadrupolar Nuclei in Gallium Nitride. J. Am. Chem. Soc. 2004, 126 (30), 9166–9167. https://doi.org/ 10.1021/ja049603r. 127. Purdy, A. P.; Yesinowski, J. P.; Hanbicki, A. T. Synthesis, Solid-State NMR, and Magnetic Characterization of H-GaN Containing Magnetic Ions. Phys. status solidi 2005, 2 (7), 2437–2440. https://doi.org/10.1002/pssc.200461495. 128. Bräuniger, T.; Müller, T.; Pampel, A.; Abicht, H. P. Study of Oxygen - Nitrogen Replacement in BaTiO3 by 14N Solid-State Nuclear Magnetic Resonance. Chem. Mater. 2005, 17 (16), 4114–4117. https://doi.org/10.1021/cm050411k. 129. Kim, Y. I.; Paik, Y. Bond Covalency in Perovskite Oxynitrides ATaO 2N (A ¼ Ca, Sr, Ba) Studied by 14N NMR Spectroscopy. Solid State Sci. 2012, 14 (5), 580–582. https:// doi.org/10.1016/j.solidstatesciences.2012.02.007. 130. Giavani, T.; Bildsøe, H.; Skibsted, J.; Jakobsen, H. J. Determination of Nitrogen Chemical Shift Anisotropy from the Second-Order Cross-Term in 14N MAS NMR Spectroscopy. Chem. Phys. Lett. 2003, 377 (3–4), 426–432. https://doi.org/10.1016/S0009-2614(03)01140-0. 131. Fechtelkord, M.; Engelhardt, A.; Buhl, J. C.; Schwalowsky, L.; Bismayer, U. Proton Dynamics in Letovicite, (NH4)3H(SO4)2: A 1H and 14N NMR Spectroscopic Study. Solid State Nucl. Magn. Reson. 2000, 17 (1–4), 76–88. https://doi.org/10.1006/snmr.2000.0006. 132. Lucier, B. E. G.; Reidel, A. R.; Schurko, R. W. Multinuclear Solid-State NMR of Square-Planar Platinum Complexes Cisplatin and Related Systems. Can. J. Chem. 2011, 89 (7), 919–937. https://doi.org/10.1139/v11-033. 133. Lucier, B. E. G.; Johnston, K. E.; Xu, W.; Hanson, J. C.; Senanayake, S. D.; Yao, S.; Bourassa, M. W.; Srebro, M.; Autschbach, J.; Schurko, R. W. Unravelling the Structure of Magnus’ Pink Salt. J. Am. Chem. Soc. 2014, 136 (4), 1333–1351. https://doi.org/10.1021/ja4076277. 134. Fyfe, C. A.; Darton, R. J.; Schneider, C.; Scheffler, F. Solid-State NMR Investigation of the Possible Existence of “Nanoblocks” in the Clear Solution Synthesis of MFI Materials. J. Phys. Chem. C 2008, 112 (1), 80–88. https://doi.org/10.1021/jp7095955. 135. Dib, E.; Mineva, T.; Gaveau, P.; Alonso, B. 14N Solid-State NMR: A Sensitive Probe of the Local Order in Zeolites. Phys. Chem. Chem. Phys. 2013, 15 (42), 18349–18352. https://doi.org/10.1039/c3cp51845k. 136. Mineva, T.; Gaveau, P.; Galarneau, A.; Massiot, D.; Alonso, B. 14N: A Sensitive NMR Probe for the Study of Surfactant-Oxide Interfaces. J. Phys. Chem. C 2011, 115 (39), 19293–19302. https://doi.org/10.1021/jp206567q. 137. Carnevale, D.; Ashbrook, S. E.; Bodenhausen, G. Solid-State NMR Measurements and DFT Calculations of the Magnetic Shielding Tensors of Protons of Water Trapped in Barium Chlorate Monohydrate. RSC Adv. 2014, 4 (99), 56248–56258. https://doi.org/10.1039/C4RA09992C. 138. Carnevale, D.; Pelupessy, P.; Bodenhausen, G. Cross-Term Splittings Due to the Orientational Inequivalence of Proton Magnetic Shielding Tensors: Do Water Molecules Trapped in Crystals Hop or Tunnel? J. Phys. Chem. Lett. 2019, 10 (12), 3224–3231 https://doi.org/10.1021/acs.jpclett.9b00914. 139. Carnevale, D.; Marhabaie, S.; Pelupessy, P.; Bodenhausen, G. Orientation-Dependent Proton Relaxation of Water Molecules Trapped in Solids: Crystallites with Long-Lived Magnetization. J. Phys. Chem. A 2019, 123 (45), 9763–9769. https://doi.org/10.1021/acs.jpca.9b07303. 140. Adiga, S.; Aebi, D.; Bryce, D. L. EFGShield d A Program for Parsing and Summarizing the Results of Electric Field Gradient and Nuclear Magnetic Shielding Tensor Calculations. Can. J. Chem. 2007, 85 (7–8), 496–505. https://doi.org/10.1139/v07-069. 141. Sturniolo, S.; Green, T. F. G.; Hanson, R. M.; Zilka, M.; Refson, K.; Hodgkinson, P.; Brown, S. P.; Yates, J. R. Visualization and Processing of Computed Solid-State NMR Parameters: MagresView and MagresPython. Solid State Nucl. Magn. Reson. 2016, 78, 64–70. https://doi.org/10.1016/j.ssnmr.2016.05.004.

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9.03

F NMR on polymers

Ulrich Scheler, Leibniz-Institut für Polymerforschung Dresden e.V., Dresden, Germany © 2023 Elsevier Ltd. All rights reserved.

9.03.1 9.03.2 9.03.3 9.03.4 9.03.5 9.03.6 References

Introduction Experimental considerations Liquid-state NMR Radiation chemistry of fluoropolymers NMR relaxation Semicrystallinity

26 27 28 29 31 32 34

Abbreviations FEP Fluoro-ethylene-propylene; poly(tetrafluoroethylene-co-hexafluoropropylene) MAS Magic angle sample spinning NMR Nuclear magnetic resonance PTFE Poly(tetrafluoroethylene) PVDF Poly(vinylidenedifluoride) THV Poly(tetrafluroroethylene-ter-hexafluoroprpylene-ter-vinylidendifluoride)

Abstract NMR is an ideal method for the characterization of polymers because of the local nature of the interactions that determine the spectrum. 19F as a probe nucleus combines high receptivity with a wide range of chemical shifts meaning the line position in the spectrum strongly depends on the chemical environment. Experimental challenges for 19F NMR are discussed. Liquid state NMR, being limited to soluble polymers, provides detailed insight into structure and microstructure. The resolution that can be achieved in various types of experiments is compared. In the solid state the line broadening from orientation dependent interactions like chemical shift anisotropy and dipolar coupling, both homonuclear and heteronuclear, need to be averaged; this is most effectively done by fast magic angle spinning (MAS). Together with the quantitative information in NMR this is used to characterize the structure and conformation of fluoropolymers and to follow their radiation chemistry. Information on molecular mobility contained in NMR relaxation measurements is utilized for characterizing semicrystalline polymers.

9.03.1

Introduction

Polymers play an important role in practical applications because of their mechanical properties, light weight, and in general their machinability. Fluoropolymers are characterized by high chemical and thermal stability and unique surface properties. The most popular fluoropolymer is poly(tetrafluoroethylene) (PTFE), which cannot be melt processed. Melt processing is possible only for copolymers containing either perfluorinated or partially fluorinated comonomers. 19 F is an ideal probe nucleus for NMR. It combines high receptivity with a wide chemical shift range. On the other hand as a spin ½ nucleus it is accessible for rather simple and widespread NMR experiments. The receptivity results from the natural abundance of 100% of the NMR-active isotope 19F and the gyromagnetic ratio just 6% lower than that of the protons, the highest for all stable isotopes. The chemical shift range for 19F is about 2000 ppm in general; for fluorinated organic materials it is about 400 ppm. For an illustration, a trifluoromethyl group (CF3) has a chemical shift of 83 ppm as an end group of a perfluorinated polymer while it resonates at 72 ppm as a side group on the same polymer. The difference of 11 ppm almost spans the entire chemical shift range for protons. This implies great resolution of chemical structures in the NMR spectrum, and therefore for molecules containing fluorine, 19F NMR is the method of choice for any characterization. NMR because of its local nature, is particularly suited for materials of low long-range order or entirely disordered materials as is common for polymers. In particular when the repetition time of the NMR experiment is adjusted to be sufficiently long, i.e. three to five times longer than the longitudinal relaxation time, the spectra provide direct quantitative information.

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9.03.2

F NMR on polymers

27

Experimental considerations

The Larmor frequency of 19F is just 6% lower than that of 1H. Historically NMR spectrometers and probeheads have been designed for one high-frequency channel for 1H and one or more low-frequency channels capable for frequencies of so-called heteronuclei with Larmor frequencies nearly a factor of three lower like 31P and lower. To filter out noise the bandwidth of the high-frequency channel of both the spectrometer and in particular the probehead often does not accommodate the Larmor frequency of 19F. It is less a problem for modern spectrometers, however probeheads often need special attention to perform well for 19F. If the interest of the experiment is solely on 19F, the resonance frequency of the probehead can be adjusted (retuned) to the Larmor frequency of 19F by any skilled experimentalist. More challenging is a situation in which both 1H and 19F are involved in the NMR experiment.1,2 At low and nowadays intermediate field strengths and resulting frequencies, overcoupling of the highfrequency channel allows for splitting the initial proton channel into a proton-fluorine channel.3 At higher frequencies, dedicated transmission-line probes become the method of choice. Interesting experimental approaches become feasible for proton-fluorine double resonance. On the other hand, the high natural abundance in conjunction with the large gyromagnetic ratio results in strong dipolar couplings, both homonuclear and heteronuclear, in particular with protons. This becomes a severe obstacle for NMR studies of solid fluorine-containing polymers. With the advent of fast magic-angle spinning (MAS) spectroscopy of materials containing 19F in high abundance became feasible because fast MAS is capable of averaging the anisotropic interactions leading to the significantly broadened lines in the solid state.4 The large range of chemical shifts is accompanied by a strong orientation dependence of the chemical shift meaning a large chemical shift anisotropy. The high gyromagnetic ratio in conjunction with the natural abundance of the NMR-active isotope leads to strong homonuclear dipolar couplings next to those of protons. Under MAS both chemical shift anisotropy and dipolar coupling lead to spinning sidebands in the spectrum separated by the sample spinning frequency.5 The anisotropy of the chemical shift represents an inhomogeneous broadening and thus the resulting spinning sidebands are narrow even at low spinning speed as it is well known for 13 C. In contrast those originating from the incomplete averaging of the dipolar coupling as a homogeneous multispin interaction, as is common for protons, are significantly broader and reduce their linewidth with increasing spinning speed; the resolution in the spectrum improves with increasing spinning speed. In general MAS NMR spectra of 19F exhibit spinning sidebands which become narrower with increasing sample spinning frequency as seen in Fig. 1. The extent to which the line narrowing can be achieved depends on the density of fluorine nuclei in the sample and thus the strength of the dipolar coupling. Heteronuclear dipolar coupling to protons also contributes to the line broadening and would be averaged by MAS as well. However with a double-resonance probehead it is more efficiently suppressed by high-power proton decoupling.6 When such a probehead is available, cross polarization from 1H to 19F is often applied even when the interest is in 19F only because the longitudinal relaxation time is generally significantly shorter than that of 19F. It often helps for the suppression of background signals because many materials in probeheads contain either protons or fluorine and will thus not contribute to a signal generated by a magnetization transfer from protons to fluorine.

7 kHz 7 kHz

14 kHz 14 kHz

21 kHz 21 kHz

28 kHz 28 kHz

35 kHz

35 kHz

CF2 CF3

CF2

CF

-115 0

-100 δ F(ppm)

-200

-120

-125 δ F(ppm)

Fig. 1 A series of 19F MAS NMR spectra of FEP acquired at different MAS sample spinning frequencies. Left: full spectrum with dashed lines indicating the spinning sidebands moving out with increasing MAS frequency. Right: zoom on the CF2 centerband indicating the line narrowing with increasing MAS frequency. From Scheler, U., Bull. Magn. Reson. 1999, 19, 52.

28

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F NMR on polymers

As an alternative to MAS, the homonuclear dipolar coupling can be averaged by multipulse sequences.7 Good resolution is then achieved when the chemical shift anisotropy is averaged by slow MAS, which is named ‘combined rotation and multipulse spectroscopy’ (CRAMPS).8 This method works in principle for 19F but requires intense short radio-frequency pulses and multipulse cycles to enable a sufficiently wide spectral window for the chemical shift range of 19F and is thus practically limited to low or intermediate field strengths. CRAMPS is possible even in a proton-fluorine double resonance experiment. It has been shown as proton CRAMPS with fluorine decoupling by synchronized p pulses on 19F7 and later the same concept has been applied to 19F CRAMPS with heteronuclear proton decoupling.9 The static multipulse experiment has been demonstrated to be a rare possibility to measure a 19F chemical shift anisotropy powder pattern directly. It should be noted that the bandwidth may be a problem for applications on high-field instruments. Despite the mentioned positive properties of 19F as a probe nucleus for NMR in materials which are partially fluorinated only, the method may only provide fairly limited information. For such polymers 13C becomes the probe nucleus of choice.10 In the solid state, recording 13C spectra is nonetheless significantly more challenging as high-power decoupling is required on two channels which are as mentioned separated by only 6% in frequency.11

9.03.3

Liquid-state NMR

While diffusion-ordered spectroscopy (DOSY) has become standard for the study of mixtures of materials with different molecular weights,12 the above mentioned special NMR properties of 19F requires extra attention for DOSY experiments as well. Rinaldi and coworkers have taken that challenge and developed dedicated versions of the DOSY pulse sequence accommodating the wide range of isotropic chemical shifts and large J couplings in particular.13 These modifications and the resulting distortion-free lineshapes finally permitted the DOSY derived size analysis of the some partially fluorinated polymers like poly(VDF-ter-TFE-ter-HFP) and poly(chlorotrifluoroethylene-co-vinylidene chloride). Some co- and terpolymers, in particular those involving hexafluoropropylene and vinylidenefluoride, combine the stability and inertness of PTFE with some degree of thermal processability. The large chemical shift range of 19F in organic materials enables relatively easy assignments of signals from different comonomers which are directly quantified from the spectral integrals. Naturally there is an interest in the backbone structure and the comonomer sequence. To determine those, multidimensional NMR experiments are utilized.14 To determine the tacticity of poly(vinylfluoride) even three-dimensional triple-resonance 1He13Ce19F experiments have been applied as depicted in Fig. 2.15 The solubility of some co and terpolymers like tetrafluoroethylene (TFE), hexafluoropropylene (HFP), and vinylidene fluoride (VDF), known as THV, enables direct multi-dimensional solution NMR characterization to establish the microstructure.16 In general solution-state NMR is limited to a small fraction of fluoropolymers because of solubility issues. The great advantage of chemical inertness implies low solubility, most fluoropolymers are insoluble in particular those of high molecular weight which are those of practical relevance. Some of the copolymers of tetrafluoroethylene and polymers of lower molecular weight are soluble. Thus solid-state NMR opens a window to understand fluorinated polymers in a wider sense. In addition any information on phase separation, packing, etc. is inherently lost in the solution, which means despite the experimental obstacles there is a significant interest in solid-state NMR of fluorinated polymers. In many cases there remains a desire for improved resolution in the spectra beyond what is achievable at fast MAS. Supercritical (sc) CO2 offers the possibility of dissolving otherwise hard to dissolve materials which in parts have been utilized for 19F NMR.17,18 Again the dissolution of high-molecular weight polymers has proven to be difficult. In one approach, the achievable resolution between fast MAS NMR, NMR in the melt state and dissolution of the polymer in supercritical CO2 has been compared for the

Fig. 2 Schematic of the three-dimensional triple-resonance NMR spectrum and 1He13C planes thereof at different 19F chemical shifts. The planes show couplings of non-equivalent protons indicating mm triads. From Li, L.; Zhang, B.; Wyzgoski, F.; Li, X.; McCord, E. F.; Rinaldi, P. L., ACS Macro. Lett. 2013, 2(2), 141–145.

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F NMR on polymers

29

same polymer: a terpolymer of tetrafluoroethylene, hexafluoropropylene and vinylidene difluoride. For fluoropolymers of high molecular weight all three approaches have proven to be difficult. The inherently disordered nature of the polymers, may these be fluorinated or not, leads to inhomogeneous broadening of the lines in the NMR spectra because of the variations in the local environment due to conformation and packing. Part of that is overcome when the experiments are performed in the melt when motional averaging sets in. Apparently for most fluorinated and in particular perfluorinated polymers the melt temperature is only slightly lower than the start of the thermal degradation of these materials. Just above the melt temperature the viscosity of high-molecular-weight polymer is relatively high which limits the effect of motional averaging of the anisotropic interactions and thus the line narrowing. Unfortunately for such a characterization where thermal degradation sets in at temperatures not far above the melting point, the temperature cannot simply be increased for the NMR measurements besides possible limitations imposed by the equipment available. So the natural thought is dissolving the material. The choice of solvents for perfluorinated polymers is limited to some fluorinated solvents which would because of their additional solvent signal complicate the analysis anyway. Using solvents with an NMR inactive fluorine isotope would be prohibitively expensive. The only remaining solvent is supercritical CO2. The solubility of fluoropolymers of high molecular weight even in supercritical CO2 is low. It may be facilitated by enhanced temperatures again which is understood to be due to entanglements of the polymer chains.19 In general, comparable resolution is achieved as can be seen in Fig. 3. However the best resolution is obtained in the solution in sc CO2. This has been used as well in two-dimensional experiments like NOESY to improve the peak assignment according to the fine structure.

9.03.4

Radiation chemistry of fluoropolymers

A special focus over several years had been on radiation chemistry of fluoropolymers.20 The fact that fluoropolymers are chemically inert opened them a variety of application possibilities in aviation and space instrumentation. In those applications radiation damage is a major issue. For the investigation of radiation chemistry of fluoropolymers, 19F solid-state NMR played a major role contributing significantly to the understanding of the radiation chemistry of perfluorinated polymers.21 Oxidative processes play an important role in the degradation of such perfluorinated polymers, but often chain scission is the dominating process.22 Oxidative degradation can form additional reactive species which even enable the formation of composites of polyamide with radiation-modified PTFE.23 Only if the irradiation is performed under the exclusion of oxygen,24 i.e. in vacuum, and at higher temperatures close to the melt a different mechanism has been observed. There is a dominance of chain scission but branching may occur under certain conditions in particular for copolymers of PTFE.24 Under loss of fluorine from the system, crosslinking of the polymer chains may occur. Fast MAS 19F solid-state NMR provided clear evidence for that. Fig. 4 shows the 19F MAS spectrum of PTFE that has been irradiated by high-energy electrons in the vacuum at high temperature. A variety of structures are identified and can be quantified directly by integrating the peaks in the spectrum. The only kind of end group found in this particular case is CF3. Evaluating the molar content of CF-branches taking side groups etc. into account shows that the polymer contains significantly more branches than end groups what implies that some branches end in other branches which means there are crosslinks between polymer chains. In fact that is one of the rare cases where crosslinking of polymer has been shown directly from the structure rather indirectly from reduction of the molecular mobility.25 Investigating the spectra as a function of radiation dose and other parameters the relative content of crosslinks, branches and side groups has been determined. Radiochemical yields and G values for the various reactions have been determined.26

sc CO2 480K

melt 460K

MAS 33kHz -40

-60

-80

-100

-120

-140

-160

-180

δF(ppm)

Fig. 3 19F NMR spectra of THV-200 under fast MAS, in the melt, and dissolved in supercritical CO2 at elevated temperatures. From Salim Ok, U. S., Polymer Preprints 2008, 49, 734.

30

19

F NMR on polymers ~CF -CF -CF ~ ~CF -CF-CF ~ CF ~CF -CF

~

~CF -CF ~ ~

~

CF-CF ~CF

>CF-CF
Solids, Academic Press: Orlando, 1985. 9. Scheler, U.; Harris, R. K. Chem. Phys. Lett. 1996, 262, 137–141. 10. Lan Li, P. L. R. Macromolecules 1996, 29, 4808–4810. 11. Holstein, P.; Scheler, U.; Harris, R. K. Magn. Reson. Chem. 1997, 35, 647–649. 12. Morris, K. F.; Johnson, C. S. J. Am. Chem. Soc. 2002, 114 (8), 3139–3141. 13. Xu, C.; Wan, Y.; Chen, D.; Gao, C.; Yin, H.; Fetherston, D.; Kupce, E.; Lopez, G.; Ameduri, B.; Twum, E. B.; Wyzgoski, F. J.; Li, X.; McCord, E. F.; Rinaldi, P. L. Magn. Reson. Chem. 2017, 55 (5), 472–484. 14. Twum, E. B.; McCord, E. F.; Fox, P. A.; Lyons, D. F.; Rinaldi, P. L. Macromolecules 2013, 46 (12), 4892–4908. 15. Li, L.; Zhang, B.; Wyzgoski, F.; Li, X.; McCord, E. F.; Rinaldi, P. L. ACS Macro Lett. 2013, 2 (2), 141–145. 16. Ok, S. Magn. Reson. Chem. 2015, 53 (2), 130–134. 17. Takehiko Tsukahara, Y. K.; Kayaki, Y.; Ikariya, T.; Ikeda, Y. J. Phys. Chem. B 2008, 112, 16445–16454. 18. Mitsuhiro Kanakubo, T. U.; Raveendran, P.; Ebina, T.; Ikushima, Y. J. Solution Chem. 2004, 33, 863. 19. Salim, O. K.; Scheler, U. Polymer Preprints 2008, 49, 734. 20. Forsythe, J. S.; Hill, D. J. T. Prog. Polym. Sci. 2000, 25, 101–136. 21. Lunkwitz, K.; Lappan, U.; Scheler, U. J. Fluorine Chem. 2004, 125 (6), 863–873. 22. Dargaville, T. R.; George, G. A.; Hill, D. J. T.; Scheler, U.; Whittaker, A. K. Macromolecules 2002, 35, 5544–5549. 23. Lehmann, D.; Hupfer, B.; Lappan, U.; Pompe, G.; Häußler, L.; Jehnichen, D.; Janke, A.; Geißler, U.; Reinhardt, R.; Lunkwitz, K.; Franke, R.; Kunze, K. Des. Monomers Polym. 2012, 5 (2–3), 317–324. 24. Forsythe, J. S.; Hill, D. J. T.; Logothetis, A. L.; Seguchi, T.; Whittaker, A. K. Macromolecules 1997, 30, 8101–8108. 25. Fuchs, B.; Scheler, U. Macromolecules 2000, 33, 120–124. 26. Beate Fuchs, U. L.; Lunkwitz, K.; Scheler, U. Macromolecules 2002, 35, 9079–9082. 27. Bennett, A. E.; Griffiths, J. M.; Zhen, W.; Lansbury, P. T., Jr.; Griffin, R. G. J. Chem. Phys. 1998, 108, 9463–9479. 28. Lappan, U.; Fuchs, B.; Geißler, U.; Scheler, U.; Lunkwitz, K. Polymer 2002, 42, 4325–4330. 29. Lappan, U.; Geißler, U.; Häußler, L.; Pompe, G.; Scheler, U. Macromol. Mater. Eng. 2004, 289 (5), 420–425. 30. Schierholz, K.; Lunkwitz, K. Nucl. Instrum. Methods Phys. Res. B 1999, 151, 232–237. 31. Fuchs, B.; Scheler, U. Applied Magnetic Resonance 2004, 27, 435–442. 32. Fedotov, V. D. NMR Basic Principles and Progress; vol. 21; Springer: Heidelberg, 1989. 33. Geschke, D.; Holstein, P. Prog. Colloid Polymer Sci. 1989, 80, 71–77. 34. Geschke, D.; Holstein, P.; Mendler, M. Acta Polymerica 1988, 39, 206–207. 35. Holstein, P.; Scheler, U.; Harris, R. K. Polymer 1998, 39, 4937–4941. 36. Zumbulyadis, N. Phys. Rev. B 1986, 33, 6495–6496. 37. Scheler, U.; Harris, R. K. Solid State Nucl. Magn. Reson. 1996, 7, 11–16. 38. Ando, S.; Harris, R. K.; Hazendonk, P.; Wormald, P. Macromol. Rapid Commun. 2005, 26 (5), 345–356.

Applications of 17O and 51V NMR in inorganic and bioinorganic chemistry

9.04

Jianqin Zhuanga, Qian Wanga, and Rupal Guptaa,b, a Department of Chemistry, College of Staten Island, City University of New York, New York, NY, United States; and b Ph.D. Programs in Biochemistry and Chemistry, The Graduate Center of the City University of New York, New York, NY, United States © 2023 Elsevier Ltd. All rights reserved.

9.04.1 9.04.1.1 9.04.2 9.04.2.1 9.04.2.2 9.04.2.2.1 9.04.2.3 9.04.3 9.04.3.1 9.04.3.1.1 9.04.3.2 9.04.3.2.1 9.04.3.2.2 9.04.3.2.3 9.04.3.3 9.04.3.4 9.04.3.5 9.04.3.6 9.04.3.7 9.04.4 9.04.4.1 9.04.4.2 9.04.4.3 9.04.4.4 9.04.5 References

Introduction: Vanadium and oxygen centers in inorganic and bioinorganic complexes 17 O and 51V solid state NMR measurements Practical considerations for 17O and 51V NMR Sample preparation and challenges Background and common techniques 51 V solid state NMR Calculations of NMR parameters Applications of 17O NMR Conductors Structure Zeolites Structure Bronsted acid Adsorption and reaction mechanism Nanocrystalline oxides Metal-organic frameworks Glasses Biological systems Dynamic nuclear polarization Application of 51V NMR Bioinorganic and inorganic complexes Biological systems Inorganic materials NMR measurements of internuclear metal-to-ligand distances involving vanadium centers Conclusions

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Abstract Vanadium and oxygen centers are prevalent in a plethora of inorganic complexes ranging from functional materials to biological systems and pharmaceutical agents. Nuclear magnetic resonance (NMR) spectroscopy can provide a detailed characterization of electronic and coordination environments of vanadium and oxygen centers. Compared to the more common and relatively well-studied NMR nuclei such as 1H, 13C, 15N and 31P, 17O, and 51V NMR studies often suffer from sensitivity and resolution challenges owing to their unique nuclear properties. Despite these limitations, several detailed studies undertaken in the literature illustrate that extensive characterization of these centers can be performed by NMR, particularly in the solid state, leading to critical evaluation of the properties of the system under consideration. These studies underscore the development in NMR methodologies and hardware, which has allowed for 17O and 51V NMR measurements to become more widely available to researchers. In this chapter, we present an overview of the recent applications of 17O and 51 V solid state NMR spectroscopy to investigate oxygen and vanadium centers in inorganic complexes relevant to materials and biological systems.

9.04.1

Introduction: Vanadium and oxygen centers in inorganic and bioinorganic complexes

Bonding and electronic properties of oxygen in oxide-based materials, bioinorganic complexes, catalysts and ceramics dictates the functional properties of many inorganic complexes. Contributing to
50% of the planet Earth’s weight, oxygen centers are also abundant in biological molecules and play critical roles in various biological processes. For example, oxygen centers form hydrogen bonds and provide structural integrity and functionality to biomolecules, allow for the formation of metal ligand bonds in metalloproteins via backbone or sidechain carbonyl groups, and assist in a plethora of chemical reactions by natural and synthetic metalloenzymes via highly catalytic metal-oxo moieties. Therefore, detailed atomic-level characterization of oxygen centers is key to

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understanding the chemical properties of inorganic complexes, biological processes and for the development of function technological materials and catalysts, including those inspired by biomolecules. Furthermore, oxygen centers are often present in multiple chemical forms within a complex of interest and site-specific detection of these multiple sites is needed for complete characterization of the chemical properties of such complexes. Vanadium containing compounds are critical in materials science, industrial applications, and biological systems. While vanadium metalloenzymes such as vanadium haloperoxidases and nitrogenases are well characterized, vanadium-based materials also have various applications in non-biological systems. For example, vanadium oxides and coordination compounds catalyze numerous types of chemical reactions, including aerobic alcohol oxidation,1 non-oxidative CeO bond cleavage,2 oxo-transfer reaction,3 aerobic cleavage of CeC and CeH bonds,4,5 and selective epoxidation of olefins.6,7 Solid vanadium oxides are also used in rechargeable battery materials. The diamagnetic d0 electronic configuration of V5þ, however, leaves this oxidation state of the element spectroscopically silent as V5þ is not amenable to UV-Vis or electron paramagnetic resonance (EPR) spectroscopies. NMR spectroscopy, particularly solid-state NMR, offers a unique probe to characterize diamagnetic vanadium (bio)inorganic complexes and materials. In this chapter, we will discuss recent applications of solid-state NMR spectroscopy to investigate oxygen and vanadium centers with a focus on studies reported in the past decade. Due to the recent developments in solid-state NMR methodologies, coupled with computational studies, a wealth of information can be obtained for oxygen and vanadium centers with a wide range of nuclear and electronic environments.

9.04.1.1

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V solid state NMR measurements

The two naturally occurring nuclei of vanadium, 50V and 51V are both NMR active. At 99.8% natural abundance and with a nuclear quantum spin, I, of 7/2, 51V is easily amenable to NMR. The relatively high gyromagnetic ratio of this nucleus (g ¼ 7.049  107 rad T 1 s 1) and small quadrupole moment ( 0.052  10 28 V/m2) makes detection of 51V NMR signals easily achievable. Furthermore, due to its high natural abundance, enrichment of samples is not required. Among the three stable isotopes of oxygen (16O, 17O and 18O), 17O is amenable to NMR with non-zero nuclear quantum spin (I ¼ 5/2). Found only at 0.038%, this NMR active isotope has the lowest non-zero natural abundance in the periodic table. The low natural abundance of 17O poses sensitivity challenges for comprehensive NMR characterization using direct detection methodologies. Enrichment is often desired and necessary for detection and some enrichment schemes are discussed below. Compared to routine NMR active nuclei, the gyromagnetic ratio of 17O is fairly low (g ¼  3.63  107 rad T 1 s 1).8 The small gyromagnetic ratios and low natural abundances of these nuclei give rise to their overall small receptivity values. Receptivity values provide an estimate of relative ease with which an NMR signal of one nucleus can be detected compared to another. Relative to 13C, the receptivity value of 17O is 6.5  10 2. These factors, in conjunction with broad spectral densities induced due to anisotropic spectral broadening originating from non-uniform charge distribution within the nucleus (vide infra) give rise to sensitivity challenges for 17O solid state spectroscopy. Under NMR conditions, the complete nuclear Hamiltonian is composed of the Zeeman, the radio frequency, and dipolar interaction terms, along with the quadrupolar and the chemical shift anisotropy (CSA) interactions and can be described as: H ¼ HZeeman þ HRF þ HDIP þ HQ þ HCSA The degeneracy of magnetic spin levels is removed in the presence of a magnetic field due to its interaction with the magnetic spin moment, resulting in Zeeman energy levels. For a I ¼ 5/2 nuclear spin, six (or 2I þ 1) Zeeman energy levels give rise to five (or 2I) single quantum transitions (Fig. 1). The central transition refers to the Eþ 1/2 4 E 1/2 transition, while other single quantum transitions are called the satellite transitions. I > ½ nuclei also bear an electric quadrupole moment, eQ, originating from nonspherical electrical charge distribution at the nucleus, which interacts with the electric field gradient (EFG) at the nucleus to perturb the Zeeman energy levels. Quadrupolar interactions can affect the resonances of both central and satellite transitions. At moderate magnetic fields, the Zeeman term is larger than the quadrupolar interaction and the effect of the latter on the energies of the mI states can be considered using the first and the second order perturbations to the total energy Hamiltonian (in the high-field limit) and is defined in spherical tensor notation using the spatial (Rmn) and the spin (Tmn) variables as: ð1Þ

HQ ¼


eQ $RQ T S ¼ uQ 3Iz2  IðI þ 1Þ 4Sð2I  1Þ 20 20 ð2Þ

HQ ¼

C2 Q X R2m R2m ½T2m ; T2m  u0 ms0 2m

where HQ(1) and HQ(2) are the first- and second-order quadrupolar Hamiltonians. By defining the EFG in its principal axis system (PAS), which allows one to represent this tensor interaction by three principal components (Vxx, Vyy and Vzz), the quadrupolar coupling tensor (c) is given by: cii ¼ eQVii =h Vii is a second rank traceless tensor in its PAS: Vxx þ Vyy þ Vzz ¼ 0 and |Vzz |  |Vyy |  |Vxx |. Typically, the quadrupolar coupling constant (CQ ¼ eQVzz/h), which relates to the largest component of the EFG tensor and its asymmetry parameter (h ¼ [Vxx  Vyy]/Vzz)

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Fig. 1 Energy level diagram of an I ¼ 5/2 nucleus showing splittings due to the Zeeman interaction and perturbations from first- and second order quadrupolar interactions.

are reported to described the EFG tensor. Since the EFG tensor is traceless, CQ and h can be used to determine the three components of the tensor. The perturbations introduced by quadrupolar interaction to the Zeeman energy are shown in Fig. 1 for h ¼ 0. For nuclei with symmetric EFG tensors, the first order correction to the energies of all mI levels is proportional to CQ and (3cos2q  1). As expected, measurements on solid samples with multiple crystallite orientations will exhibit magnitude of CQ dependent spectral broadening. However, to the first order, the frequency of the central transition remains unchanged. For nuclei with large EFG tensors, second order perturbations need to be considered for accurate description of magnetic levels. As shown in Fig. 1, the perturbation introduced by the second order correction terms not only bear a quadratic dependence on CQ, but also have a complex dependence on crystallite orientation.9 While all magnetic levels are affected similarly via first order perturbation, second order quadrupolar interactions (HQ(2)) shift the frequency of the central transition. The CSA interaction can be expressed in terms of an irreducible rank 2 tensor in the high-field limit with the isotropic and anisotropic components as described below:    iso  S CS S aniso HCSA ¼  g RCS Iz 00 T00 þ R20 T20 ¼ uCS þ uCS The principal components of the CSA tensor can be described using the Haeberlen-Mehring-Spiess convention10–12: ds ¼ dzz  diso ; hs ¼

dyy  dxx dxx þ dyy þ dzz ; diso ¼ dzz  diso 3

where diso is the isotropic chemical shift; dxx, dyy, and dzz are the principal components of the CSA tensor. The reduced anisotropy of the CSA tensor is ds and hs is the asymmetry parameter. The Euler angles (a, b, g) are used to describe the orientation between the EFG and the CSA tensors. Taking the CSA and EFG tensors into consideration, solid state 51V and 17O NMR spectra are described by eight parameters: CQ, hQ, diso, ds, hs, a, b, g. Similar to the first order quadrupolar interaction, the Legendre polynomials describing the spatial component of the CSA interactions also bear a dependence of (3cos2q  1) with respect to the static magnetic field. Therefore, spinning a sample at the magic (1) angle (54.74 ) renders a spinning sideband pattern originating from the averaging of the second-rank tensorial components of H(Q) and HCSA. The anisotropic terms associated with the first and second order quadrupolar interactions in nuclei with large CQ manifest themselves in wide spectral envelopes and often cause satellite transitions to be broadened beyond detection. The shape and the width of the central transition, which in most cases can be observed, depends on anisotropic quadrupolar interactions, while the frequency of

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the transition itself is dependent on second order quadrupolar interactions. Magic angle spinning (MAS) at sufficiently fast rates can improve resolution by eliminating the orientation dependence of anisotropic terms, including CSA and dipolar interactions and first order quadrupolar interactions. But due to partial narrowing of second order quadrupolar interactions and numerous spinning sidebands, in the cases with large CSA or CQ, low resolution NMR spectra are obtained. Several examples of 17O and 51V MAS spectra suffering from low resolution due to large magnitudes of CSA and CQ can be observed in the literature.

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Practical considerations for

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Due to advances in instrument hardware, sample preparation schemes, and NMR methodologies, 17O and 51V NMR have become amenable to NMR spectroscopists interested in investigating these nuclei. Various applications of 17O and 51V NMR can be found in the literature demonstrating that detailed characterization of electronic, nuclear and structural properties of these nuclei can be performed by utilizing NMR spectroscopy.

9.04.2.1

Sample preparation and challenges

Due to the low receptivity of 17O, enrichment even at low levels can improve sensitivity and allow for detailed NMR characterization. However, 17O isotope labeling can be cost prohibitive and often poses challenges during sample preparation. Common isotope labeled 17O precursors include 17O2 and 17OH2. Approximately 20–30 atomic percent enrichment of oxygen containing compounds allows for 1D NMR measurements with reasonable sensitivity. However, synthesis schemes with enriched O2 and H2O precursors may be limited, result in low yields, or prohibit isotope labeling. Some common strategies include: hydrolysis of reaction precursors (such as chlorides and alkoxides)13 and initiating the reaction with pre-enriched oxides. Enrichment of oxides, including ceramic superconductors and zeolites often utilize gas exchange methodology. In this approach, a sample is heated under vacuum to evaporate oxygen. The sample chamber is cooled down to room temperature after back filling with 17 O2 gas. Targeted enrichment schemes have also been proposed for specific classes of compounds. For example, phosphate compounds including complex sodium niobiophosphate glasses were enriched by heating under 17O enriched water vapor14 and cost-effective synthesis using microliter amounts of enriched water has been proposed for 17O enriched aluminosilicate and aluminophosphate zeolites by ionothermal-based methods.15 Recently, Métro et al. have proposed a mechanochemistry based method that may offer an efficient, environment friendly and cost-effective approach to generate 17O enriched organic and inorganic compounds. In this work, a few hundred microliters of enriched precursors were added during ball milling, which induces reactions by mechanical forces enabling reduced particle sizes and increases reaction efficiencies.16 These advances in sample preparation can help eliminate major hurdles in the application of 17O NMR as a mainstream technique to characterize oxygen centers. Given the naturally high abundance of the 51V isotope, enrichment is not needed for 51V NMR measurements.

9.04.2.2

Background and common techniques

Several examples of characterization of oxygen and vanadium centers have been reported in the literature. A complete characterization of the NMR parameters of quadrupolar nuclei involves determination of eight independent parameters: CQ, hQ, diso, ds, hs, a, b and g. a, b and g are the Euler angles that define the relative orientation between the CSA and EFG tensors. Detailed and exhaustive characterization of these centers often requires advanced NMR methodologies complemented with computational approaches. Although 17O has the lowest natural abundance in the periodic table, advancements in instrumentation, NMR and computational methodologies have enabled 17O NMR spectroscopy to bed used fairly routinely on variety of oxygen containing compounds and materials ranging from small molecules to large biomacromolecules. 51V NMR, on the other hand, has been widely utilized for a variety of vanadium-based complexes in the context of biological, energy and pharmaceutical applications.

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V solid state NMR

Vanadium centers can bear oxidation states from  3 to þ 5. In its þ 3 (d8),  1 (d6) and þ 5 (d0) oxidations states, the vanadium ion is diamagnetic, making is easily amenable to NMR spectroscopy. 51V NMR chemical shifts are usually externally referenced to neat VOCl3 (diso ¼ 0 ppm). While near-complete spectral manifolds can be obtained for 51V nuclei with moderate CSA and quadrupolar tensors, usually only the central transition is observed for vanadium centers bearing large magnitudes of CQ, which broadens the signals from the satellite transitions. Most fundamental NMR measurements of vanadium centers include static and MAS spectra. MAS eliminates terms in the nuclear Hamiltonian with dependence on (3cos2q  1). These include the CSA, dipolar and first order quadrupolar interactions. However, the second order quadrupolar interactions, which has a more complex dependence on the crystallite orientations cannot be completely removed by MAS. The second order quadrupolar interaction renders a distinct shape to the NMR spectra that depends both on the magnitude of CQ and its anisotropy and Fig. 2 shows the effect of these parameters on the lineshapes of static and MAS NMR spectra.17 For vanadium centers with quadrupolar coupling constants of moderate magnitude, the eight NMR parameters described above can be extracted using magic angle spinning satellite transition spectroscopy (SATRAS) by numerical grid search of spectral parameters alongside least-square fitting to optimize the spinning sideband intensity or integrated intensities of the calculated spectra.18–25 The magnitude of CSA and quadrupolar interactions can give rise to wide spectral widths making the detection of even the central

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Fig. 2 Second-order quadrupolar lineshapes for different spinning angles and anisotropies. The frequencies are displayed in units of (uQ2/2pu0) [I(I þ 1)3/4]. Reprinted with permission from reference Jerschow, A. From Nuclear Structure to the Quadrupolar NMR Interaction and HighResolution Spectroscopy. Prog. Nucl. Magn. Reson. Spectrosc. 2005, 46, 63–78.

transition challenging. Two problems are typically encountered: (i) probe ringing can cause spectral distortion and; (ii) the breadth of the central transition may exceed the rf pulse excitation profile. Under these circumstances, variable offset cumulative spectroscopy can be used (VOCS).26 In this methodology, several frequency stepped spectra are collected by varying the offset frequency of the transmitter in steps to excite different regions of the spectra. An accurate powder lineshape can be obtained by addition of these subspectra. In general, it is advisable to record spectra at two different magnetic field strengths. This is because the CSA and the second order quadrupolar tensor have different dependences on the static magnetic field. While CSA scales directly with the applied magnetic field, second order quadrupolar broadening is inversely proportional to it. Measurements at two magnetic fields ensure accurate determination of CSA and EFG tensors. Quadrupolar interactions in vanadium centers have also been estimated by nutation spectroscopy.9,22,27–29 In this approach, the length of the excitation pulse is exploited to modulate the extent of excitation of the satellite transitions. Overall signal intensities, which incorporate the contributions of the satellite transitions depend on the length of the excitation pulse. Nutation profiles that depend on the quadrupolar frequency and radio frequency can be used to estimate quadrupolar coupling constants. Generally, this methodology is not widely used due to its poor accuracy often originating from weak signal intensities. If more than one non-equivalent site is present, 2D multiple-quantum MAS (MQMAS) experiments can be performed (Fig. 3).30–32 By correlating multiple-quantum coherence with single-quantum coherence associated with the CT, a highresolution spectrum composed of isotropic and anisotropic dimensions can be obtained. These 2D spectra allow for the determination of the quadrupolar coupling constants and isotropic chemical shifts. Furthermore, a multiple-quantum experiment under static conditions that correlates the highest  I / þ I transition to the central transition can be used along with MQMAS to determine second order quadrupolar interactions and CSA.33 While MQMAS can be highly beneficial when multiple non-equivalent sites are present, this technique is restricted to systems with moderate to large CQ and small ds,33 making its application limited in vanadium compounds. 9.04.2.2.1.1 17O NMR methodologies Given the prevalence of oxygen centers in chemical compounds, 17O NMR studies are now routinely performed. 17O NMR spectra are typically referenced to water at 0 ppm. Similar to 67Zn, static and MAS measurements can allow for the determination of the nuclear parameters of 17O spins. Both CSA and quadrupolar interactions dominate the linewidth of 17O NMR spectra. Consequently, the central transition of MAS spectra can be severely affected by CSA and second order quadrupolar interaction. In addition to these standard methodologies, below we describe few common approaches used to investigate oxygen centers. As more than one

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Fig. 3 (A) 51V 3QMAS sheared spectrum of AlVO4 obtained at 9.4 T. (B) 51V STMAS sheared spectrum of LaVO4 showing different correlations. CT is the autocorrelation of the central transition, ST1 correlates the central transition with the 1/2 4 3/2 satellite transition, and ST2 correlates the central transition with the 3/2 4 5/2 satellite transition. The experiment has been recorded at 9.4 T using 10 kHz MAS. Reprinted with permission from Lapina, O.; Khabibulin, D.; Shubin, A.; Terskikh, V. Practical Aspects of 51V and 93Nb Solid-State NMR Spectroscopy and Applications to Oxide Materials. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 3, 128–191.

type of oxygen center is routinely observed in samples of interest, these techniques were developed to resolve multiple sites and provide resolution enhancement. Multiple-quantum MAS (MQMAS) or satellite transition MAS (STMAS) are two dimensional techniques where isotropic 2D signals can be achieved upon elimination of anisotropic quadrupolar broadening by correlation of the central transition with either a symmetric multiple quantum transition or a single quantum satellite transition. For 17O, typically 3Q or 5Q transitions are observed but 5QMAS measurements often suffer from low sensitivity. 1D projections of MQMAS spectra in the F1 dimension represent the isotropic component, while the F2 dimension provides the quadrupolar patterns for each isotropic site. For instance, Chien et al. performed 17O MQMAS measurements on complex oxides with apparent composition of NaxSr1  xSiO3  0.5x that have potential application as solid-state oxide-ion electrolytes. With these measurements, six unique sites were resolved and the results of the spectral analysis were consistent with density functional theory (DFT) calculations (Fig. 4).34 While MQMAS measurements can help resolve multiple 17O species, they do suffer from low signal-to-noise ratios. The sensitivity challenges are further exacerbated in systems with large CQ. Several approaches have been proposed to overcome the sensitivity of 17O MQMAS experiments. These include rotation induced adiabatic coherence transfer (RIACT),35,36 double frequency sweep (DFS),37 fast amplitude modulation (FAM),38 rotor assisted population transfer (RAPT)39 and soft pulse added mixing (SPAM).40 Additionally, nonlinear sampling methods can be combined with MQMAS experiments to reduce data acquisition time. For instance, Rovnyak et al. demonstrated improved sensitivity and resolution for MQMAS experiments by applying nonlinear sampling in the indirect dimension and employing maximum entropy reconstruction.41 They demonstrated their methodology, which afforded two- to fourfold timesavings, on various oxygen centers including ammonium dihydrogen phosphate (NH4H2P17O4) and lithium sulfate monohydrate (LiSO4-H217O). Dynamic angle spinning (DAS)42 and double rotation (DOR)43 enable averaging of the second order quadrupolar interaction by mechanical spinning at two different angles (typically 54.76 and 30.12 ). The sample is spun at different angles sequentially in DAS and simultaneously in DOR. Dupree and coworkers reported 1H-decoupled DOR studies of various amino acids demonstrating 40-fold resolution enhancements with
1 ppm linewidth spectra.44 High quality NMR spectra were obtained for amino acids showing a wide range of NMR tensorial parameters, from CQ varying between 6.4 and 8.6 MHz and diso between 83 and 353 ppm (Fig. 5). Wu and coworkers observed four distinct NMR peaks with integrated intensity ratios of 1:2:1:2, consistent with six crystallographic ally unique CO groups in a-Al(acac)3 by DOR measurements at 14.1 and 18.8 T (Fig. 5).45

9.04.2.3

Calculations of NMR parameters

Eight independent NMR parameters, which include quadrupolar coupling constant CQ, asymmetry of the quadrupolar tensor hQ, isotropic chemical shift diso, chemical shift anisotropy ds, asymmetry of the chemical shift tensor hs and the Euler angles a, b, g, describe the quadrupolar and chemical shift anisotropy interactions. These parameters reflect important structural and dynamic features of the nuclei of interest. A general simulation tool is then required to extract those NMR parameters from experimental spectra. Various computer fitting programs have been developed, including SIMPSON,46 ANTIOPE,47 GAMMA,48 STARS,49 QUASAR,50 SPINEVOLUTION51 and Spinach.52 SIMPSON is one of the most popular and widely used NMR simulation packages. Many of these programs employ the density operator formalism using the Liouville-von-Neumann equation: d/dt r(t) ¼  i [H(t),r(t)] for single crystals, static powders, oriented samples, rotating powder samples, as well as liquid state NMR experiments. Here, r(t) is the reduced density matrix representing the state of the spin system. H(t) represents the time-dependent Hamiltonian, which describes the relevant nuclear spin interactions and the external operations. Depending on the input information, the

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Fig. 4 17O multiple-quantum magic-angle spinning (MQMAS) NMR of 17O isotope-enriched SNS45. The 1D quadrupolar patterns, labeled with (A– F), are cross sections from the 2D spectrum taken at the positions marked with dashed lines. Simulated patterns are overlapped with the cross sections. The purple dashed lines represent the sum of all simulated quadrupolar patterns for each spectrum in (A–F). The spectra on the top (red) and left (blue) of the 2D MQMAS spectrum are projections of the respective dimensions. The projection on the left (blue) is a sum of the isotropic spectra of various O sites and the simulated spectrum of each O site is also displayed (dotted lines under the projection spectrum). The projection (red) on the top of the 2D spectrum is overlapped with the regular MAS spectrum obtained at the same spinning speed as the MQMAS, i.e., 10 kHz MAS. Reprinted with permission from Chien, P.-H.; Jee, Y.; Huang, C.; Dervisoglu, R.; Hung, I.; Gan, Z.; Huang, K.; Hu, Y.-Y. On the Origin of High Ionic Conductivity in Na-Doped SrSiO3. Chem. Sci. 2016, 7, 3667–3675.

structural and dynamic parameters about quadrupolar and chemical shift anisotropy interactions can be extracted through leastsquares iterative fitting of experimental spectra to numerical spectra. Density functional theory (DFT) calculations provide complementary information to the experimental NMR analysis by providing computed values for various nuclear parameters.53–55 Generally, a structural model of the system of interest is first established based on the X-ray measurements or previous computational predictions. The geometry of the structure is optimized to achieve the ground state energy and structure and minimize the stress in the molecule. Once the appropriate geometry of the structure is chosen, NMR parameters, such as shielding tensors, J-coupling tensor, and electric field gradient tensors, can be computed by DFT calculations. Various DFT based methods are available to predict nuclear parameters. The local density approximation (LDA) approach can be used to obtain the shielding tensor. Linear augmented planewave method (LAPW) is widely used to predict EFG tensors in the solid state, which also can be obtained with the projector augmented wave method (PAW) approach.56 Considering the gage origin problem, several methods have been developed, such as gage including projector augmented wave (GIPAW) and gage-including atomic orbitals (GIAO). GIPAW is the most popular approach to calculate NMR tensors. It has been extensively used to predict the NMR parameters in organic, inorganic, polymer, catalysis, biomaterial and nanomaterial fields.53

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9.04.3.1

Conductors

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O NMR

Inorganic ion conductors have gained interest for their potential applications in solid oxide fuel cells (SOFC), oxygen sensors, membrane separation and batteries. Compared to currently used liquid electrolytes in batteries, solid ion conductors as electrolytes have advantages of high energy density, safety, and environmental friendliness.57 Higher ionic conductivity is desired for materials to be employed as potential electrolytes. Ionic transport in the solid ion conductors is critically dependent on the structure and composition of the materials. Even within the same class of the materials, modification could result in significant differences in ionic conductivity. Therefore, it is essential to understand the conduction mechanism in the solid at an atomic level, then establish the correlation between the structure and ion transport, which would guide solid conductors design to achieve higher ionic conductivity.

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Fig. 5 (A) (a) 17O MAS NMR spectrum of L-alanine hydrochloride together with simulation, (b) MAS NMR spectrum of L-alanine together with simulation, and (c) DOR spectrum of L-alanine, outer rotor speed 1800 Hz. (B) 17O NMR (14.1 T) spectra from D-glutamic acid hydrochloride: (a) MAS together with simulation of the center band and (b) DOR, outer rotor speed 1800 Hz. (C) 17O DOR spectra of a-Al(acac)3 obtained at (a) 14.1 T and (b) 18.8 T. The isotropic peak is marked by *. The outer rotor spinning frequency was 1305 and 1330 Hz for (a) and (b), respectively. (c) The experimental (lower trace) and best-fitted (upper trace) “total 17O DOR line shapes” of a-Al(acac)3. The experimental “total DOR line shape” was obtained by summing up all sidebands onto the isotropic peak shown in (b). D Molecular structure of Al(acac)3. Reprinted with permission from Pike, K. J.; Lemaître, V.; Kukol, A.; Anupold, T.; Samoson, A.; Howes, A. P.; Watts, A.; Smith, M. E.; Dupree, R. Solid-state 17O NMR of amino acids. J. Phys. Chem. B 2004, 108, 9256–9263, Wong, A.; Smith, M. E.; Terskikh, V.; Wu, G. (2011) Obtaining accurate chemical shifts for all magnetic nuclei (1H, 13C, 17O, and 27Al) in tris(2,4-pentanedionato-O,O0 ) aluminium(III)dA solid-state NMR case study. Can. J. Chem. 2011, 89, 1087–1094.

9.04.3.1.1

Structure

X-ray and neutron diffraction are usually used to characterize solid structures. However, crystal structures rely on long-range order. 17 O NMR is highly sensitive to the oxygen local environment of the structure due to the wide range of chemical shift. 17O NMR spectra are sensitive probes of local ordering and differences in the coordinated environment of the oxygen centers in oxide conductors. Therefore, 17O NMR has been used to detect the interfacial structure, local distortions, defects, and disordering of the structure, phase transitions and magnetic behavior of conductors.58–62 For example, oxides with the general formula A3 þ2B4þ2O7 show excellent oxygen ion conductivity and have been suggested as potential electrode materials.58 Based on the composition and size of the cation A and B, this material has two different structures. One is the pyrochlore structure, in which cations A are in eight-coordinate sites, and cations B are in octahedral sites. When the size of cation B matches to cation A, the structure of the oxide transfers from the pyrochlore to the fluorite phase, resulting in mixing and disorder at the A and B sites. This transition enhances the ion conductivity. Comparing the different compositions of Y2(B1  xB0 x)2O7 oxides, Grey and coworkers have investigated different oxygen local environments in pyrochlore and fluorite phases using 1D 17O MAS NMR.58 Based on 17O chemical shift differences, two oxygen sites in the structure of Y2Sn2O7 and Y2Ti2O7 with pyrochlore structure were identified (Fig. 6). The chemical shift at 385 ppm was attributed to the O2 site of O2Y4, which is independent of the cation B. The resonances at 165 ppm and 457 ppm are related to the tetrahedrally coordinated O1 site of O1Y2Sn2 in Y2Sn2O7 and O1Y2Ti2 in Y2Ti2O7, respectively. Except for the resonances related to O2Y4, O1Y2Sn2 and O1Y2Ti2, a new peak centered at 290 ppm appears in the 17O NMR spectrum of Y2(Sn0.4Ti0.6)2O7, which was assigned to OY2SnTi. The chemical shift of this oxygen site is affected by the surrounding Sn and Ti cations, which can be predicted by the chemical shift of O1Y2Sn2 and O1Y2Ti2 based on the composition. Large chemical shift difference for local oxygens was observed when Y ions were replaced by Sn or Ti cations, suggesting that 17O chemical shifts are very sensitive to the local coordination environment of the oxygen centers. Similar results were also obtained with a sample of Y2(ZrxTi1  x)2O7. Besides 17O chemical shift analysis, the EFG tensors also provide useful information on the local structure.63 In inorganic oxides, CQ is known to be related to the bond distance and angles of bridging oxygen atoms. Small magnitude of CQ indicates ionic character of the MeO bond and larger CQ are suggestive of greater covalency in the MeO bond. Comparing the Sn/Ti series, the line broadening and smaller quadrupolar couplings in the 17O spectra of Y2(ZrxTi1  x)2O7 indicate a disordered structure and greater ionic bond character of the ZreO bond, which is consistent with its higher conductivity. In addition, 2D 17O MQMAS has also been used to identify the distribution of local oxygen sites of the oxide conductor from overlapping signals resulting from the second order quadrupolar effect.64 In addition to the quadrupolar interaction, electron nuclear spin interaction in paramagnetic materials could result in the line broadening and Fermi contact shift, which influences the resolution and complicates resonance assignment. In such cases, the observed

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Fig. 6 (A) The effect of the x-parameter on the OA2B2 local environment. The arrow represents the direction of oxygen atom movement in the tetrahedron as x increases. (B) 17O MAS NMR spectra of (a) Y2(Zr0.3Ti0.7)2O7, (b) Y2(Zr0.8Ti0.2)2O7, and (c) Y2Zr2O7. The spectra were acquired with Hahn echo pulse at 14.1T with spinning speeds of 15 kHz. Isotropic resonances are marked with arrows and sidebands are marked with asterisks. Dashed lines indicate positions for the different local environments. In the case of the OZrxY4  x environments with x ¼ 1, 3, and 4, these are estimated based on the shifts of the x ¼ 0 and 2 environments. Reprinted with permission from Kim, N.; Grey, C. P. 17O MAS NMR Study of the Oxygen Local Environments in the Anionic Conductors Y2(B1  xB0 x)2O7 (B, B0 ¼ Sn, Ti, Zr). J. Solid State Chem. 2003, 175, 110–115.

linewidth might be much larger than the magic angle spinning frequency. Furthermore, the effect of these anisotropic interactions may not be mitigated by employing fast MAS frequencies. With magic angle turning and phase adjusted sideband separation (MATPASS), five Oax sites in La2NiO4 þ d mixed ionic electronic conductor could be identified by separating spinning sidebands.65 Additionally, 1H-17O HETCOR and 17O/51V TRAPDOR double resonance experiments were used to investigate the internuclear distance between the oxygen and other nuclei.66 9.04.3.1.1.1 Dynamics Oxygen ion hopping between different lattice sites is key for high conductivity of oxide conductors when utilized as electrolytes. Besides characterization of the structure of oxide conductors, 17O NMR has also been applied to directly probe the mobility of oxygen ions.59,66 Oxygen ion transport processes can be detected through variable temperature NMR. With increased temperature, 17 O signals start to broaden and eventually coalesce to one peak. The linewidth broadening in 17O NMR spectra indicates the exchange between the local oxygen sites, from which the hopping rate can be deduced. More detailed characterization of the oxygen transfer process can be performed by carrying out spin-lattice relaxation (T1) measurements at variable temperatures. These measurements allow for the determination of the activation energy and correlation time of oxygen hopping between different sites, which are related to the conductivity of the oxide conductor. For instance, Heinmaa et al. investigated the oxygen ion dynamics in La doped CeO2 by measuring T1 values at different temperatures.67 Based on the temperature dependence of T1, two different dynamic processes of oxygen in La doped CeO2 were identified. At lower temperature, the process is related to oxygen hopping in the lattice between different oxygen sites with the activation energy of 0.45 eV. At higher temperature, oxygen ions jump between occupied and vacant sites with the activation energy between 0.45 and 0.96 eV. This motion can also be probed by transverse relaxation (T2) measurement. Grey et al. compared the T2 values of oxygen sites on bulk CeO2 and at the interface in CeO2-SrTiO3 vertically aligned nanocomposite (VAN) films at different temperatures.60 They found that the T2 values of oxygen on the interface are temperature dependent. At higher temperature, T2 is shorter (0.4  0.1 ms) than at lower temperature (1.0  0.3 ms), which indicates that the exchange takes place in the slow-motion regime. Generally, the T2 temperature dependence for 17O ions on the interface provides strong evidence that the oxygen motion is on the kHz timescale and indicates significant oxygen mobility. They concluded that the interface makes a significant contribution to the increased oxide ion conductivity of CeO2-STO VAN films. 2D exchange spectroscopy is usually applied to detect the slow exchange process. The appearance of cross peaks indicates exchange between different oxygen sites. By varying the temperature and mixing time, slow exchange between tungsten and bismuth oxide layers as well as within tungsten oxide layer was detected.64 These motions were not observed in 1D 17O NMR spectra under the same conditions. The correlation time of oxygen hopping within the tungsten oxide layers is in the range of hundreds of microseconds. The exchange between bismuth and tungsten oxide layers is around several milliseconds at high temperature. In addition to variable temperature NMR, relaxation measurement and 2D exchange sequences, the TRAPDOR experiment has also been utilized to gain insights into oxygen motion between the crystallographic sites in conductors.66

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Zeolites

Zeolites are microporous, aluminosilicate materials with special channels and cavities, widely used in adsorption, separation, and heterogeneous catalysis. The size and the channels of the zeolite structure plays an important role in catalytic activity, selectivity, and adsorption ability. An understanding of the relationship between the zeolite structure and activity may be helpful to optimize the performance of these materials as catalysts. NMR methodologies are excellent tools to detect the local environment of the zeolite. 29 Si and 27Al MAS NMR measurements are normally conducted to identify the framework structure of zeolites, providing information on different coordinated species.68 The Si/Al ratio can also be extracted from the intensity of different Si species in 29Si MAS NMR spectra.69 Oxygen is one of the major elements in the framework of zeolite and is related to adsorption and binding in catalytic processes carried out by these materials. 17O NMR spectra are highly sensitive to the local zeolite environment, from which structural information can be extracted via isotropic chemical shift and quadrupolar tensor parameters. However, 17O NMR investigation is limited by the low natural abundance and relatively large electric field gradient of this nucleus. Therefore, several 17O enrichment methods have been developed, such as heating the dehydrated sample in 17O2 gas or H217O steam.70–72 Both methods are carried out at high temperature, which might result in the degradation or dealumination of the framework. Ionothermal synthesis is another method to label zeolites with 17O, in which ionic liquids are needed as solvents.73 Recently, Pugh et al. developed a new approach for 17O enrichment of zeolites by hydration with H217O (l) at room temperature.74 Using this technique, rapid enrichment of framework oxygen species was observed. The oxygen sites in Si-O-Al species were isotopically labeled much faster than in Si-O-Si linkages. Enrichment of the framework of Si-O-Si oxygen species took longer (less than 24 h).

9.04.3.2.1

Structure

Due to the low resolution and line broadening, only limited information can be extracted from 1D 17O static or MAS NMR experiments. Double angle rotation (DOR), multiple quantum (MQMAS), dynamic angle spinning (DAS) and satellite transition MAS (STMAS)75 have been developed to overcome these issues and probe the local 17O environment in zeolites. By employing 2D experiments, the isotropic chemical shift, quadrupole coupling constant and the asymmetry parameter h, can be extracted. These NMR parameters are sensitive to the local zeolite structure. In aluminosilicates, the CQ of 17O in SieOeSi bonds (5–6 MHz) is larger than that in SieOeAl bonds (3–4 MHz), allowing for the separation of the signals from Si-O-Si and Si-O-Al.76,77 In order to assign distinct oxygen species in an 17O NMR spectrum, ab initio calculations,78 first principle calculations,79 and semiempirical correlations between isotropic chemical shifts and SieOeT bond angles have been performed.80 Considering the correlations between chemical shifts of 29Si81 and 27Al82 and the TeOeT bond angle, Pingel et al. established the relationship between the chemical shift and SieOeT bond angle by 17O MQMAS and DOR NMR experiments on NaA and NaLSX zeolite.83 They found that the 17O isotropic chemical shift decreases with increasing bond angle (Fig. 7). However, Bull et al. suggested that there is no simple relationship between the TeOeT bond angle and 17O NMR parameters by investigating siliceous faujasite and ferrierite.78,84 Other reports demonstrated that the 17O isotropic chemical shift is influenced not only by T-O-T angle, but also by the hydration level and nature of the charge balancing cations85 as well as extra framework species in the zeolite.86 Freude et al. investigated 17O NMR spectra of zeolites A and LSX.87 Four and three individual crystallographically distinct oxygen species in zeolites LSX and A were distinguished, respectively. They confirmed that the isotropic chemical shift of 17O decreases with increasing TeOeT bond angle. The linear correlation between the chemical shift and the TeOeT bond angle only appeared in the sodium and potassium forms of the hydrated zeolites (Fig. 7). Dehydration and cation exchange in the zeolite resulted in changes in the 17O chemical shift, which showed a strong dependence on the radius of the cation (Fig. 7). When the lithium cation was replaced by cesium, a 10 ppm downfield

Fig. 7 (A) Correlation of 17O chemical shift d with the SiOAl bond angle 4. The points represent the experimentally obtained values, whereas the best fit is given by the straight line. (B) Correlation between the isotropic chemical shift of the 17O DOR NMR and the s-character of the oxygen hybrid orbitals for the oxygen sites of the zeolites Na–A (circles) and Na,K–LSX (rectangles).The straight line represents the best linear fit. (C) Plot of the centers of gravities of the isotropic chemical shifts (17O 3QMAS NMR) of the hydrated zeolites A (circles) and LSX (rectangles) against the ionic 17 radius of the cation. Reprinted with permission from Freude, D.; Loeser, T.; Michel, D.; Pingel, U.; Prochnow, D. ONMR Studies of Low Silicate Zeolites Solid State Nucl. Magn. Reson. 2001, 20, 46–60, Pingel, U.-T.; Amoureux, J.-P.; Anupold, T.; Bauer, F.; Ernst, H.; Fernandez, C.; Freude, D.; Samoson, A. High-field 17O NMR studies of the SiOAl bond in solids. Chem. Phys. Lett. 1998, 294, 345–350.

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shift in 17O signal was observed for zeolite LSX. An approximate 34 ppm shift difference for the O3 signal was observed when sodium was substituted by thallium in the zeolite A. With increasing ionic radius, the distance between oxygen and cation decreases which results in the deshielding of the oxygen nucleus, causing the 17O chemical shifts to increase. This trend also appeared when the ion is replaced with divalent cations.88

9.04.3.2.2

Bronsted acid

The amount and strength of the acidic sites could influence the catalyst activity and product distribution during the catalytic process, making acidity a critical property determining zeolite functionality. Various methods have been developed and applied to characterize the acidity of zeolites, such as titration, NH3-TPD, and infrared spectroscopy.89 NMR is certainly one of those useful methods to probe the acidity, either by detecting 1H or 27Al directly or 31P and 13C after adsorbing organic phosphine and acetone.89 Different acidic sites and acid strength can be identified quantitatively. In zeolites, the Bronsted acid sites are usually located in the Si-(OH)-Al framework. Probing oxygen in Si-O-Al bridges and measuring the distance between oxygen and hydrogen can provide direct information on acidity of zeolites. However, due to low natural 17O abundance and the limited concentration of acidic sites, particularly in high Si/Al ratio samples, 17O NMR spectroscopy has not been widely used in probing the acidity of zeolites. Grey and co-workers were first to detected the Bronsted acid sites though oxygen NMR signals in the zeolite enriched by heating the dehydrated sample in 17O2 gas.71 Although 17O NMR signals in the zeolite can be detected by simple single pulse experiments, the 17O signals from the Bronsted acid sites were buried in the broad signal belonging mostly to the framework oxygens of the zeolite (Si-O-Si). Therefore, 17O signals from the Bronsted acid sites were undetectable. To overcome this, 1 H-17O cross polarization (CP) and 17O-1H rotational echo double resonance (REDOR) experiments were used to enhance the signals in close proximity to protons.90,91 Bronsted acid sites can be observed and distinguished from the Si-O-Si or Si-O-Al species. By optimizing the contact time, the O-H distance, related to the acidity strength, can also be extracted based on the dipolar interaction between proton and oxygen.90 By utilizing these strategies, Peng et al. measured the OeH bond distance in HY zeolite to be in the range of 0.98–1.01 Å at room temperature. This bond distance is longer than the bond length determined by ab-initio calculations or that from neutron diffraction experiments.90 Considering the restricted motions and their effect on dipolar coupling, they measured the OeH bond distance in HY zeolite at low temperature.91 It was found that the bond distance between hydrogen and oxygen is shorter (0.0975  0.025 Å) at low temperature than that at room temperature, which is much closer to the results from the calculations. In zeolite structures, Bronsted acid sites could be in different cages or locations. For example, two Bronsted acid sites in HY zeolite are in the supercages and sodalite cages, respectively. Due to the dipolar interaction and line broadening, 1H-17O CP MAS cannot separate different Bronsted acid sites. Grey and co-workers applied 2D 1H-17O heteronuclear correlation (HETCOR) experiments to distinguish between various Bronsted acid sites in zeolites.90,92 Two 1H signals at 3.7 and 4.4 ppm were identified in 1H dimension slices extracted from the 2D 1H-17O HETCOR spectrum of HY zeolite, corresponding to the acid sites Si-(OH)-Al in the supercages and sodalites, respectively.90 By changing the contact time in 2D HETCOR spectra, different Bronsted acid sites were identified in zeolite H-Mordenite (Fig. 8). The 1H signal at 4.8 ppm was extracted from the major signal at 4.0 ppm in a 1H MAS NMR spectrum, indicating that the second component was buried under the 4.0 ppm resonance. Comparing the intensity of the signals, the intensity of the 4.8 ppm resonance in the long contact time spectrum was larger than that in the short contact time spectrum, indicating that the OeH bond distance in the Bronsted acid sites might be longer compared to the resonance at 4.0 ppm. These studies demonstrate that 17O NMR spectroscopy can be successfully implemented to directly probe the Bronsted acidic sites and acid strength.

9.04.3.2.3

Adsorption and reaction mechanism

With the high sensitivity of 17O chemical shift to the local environment, gas binding or cation interaction is expected to change the chemical shift, which provides an opportunity to detect the interaction of adsorbent or reactant with the zeolite. For example, by adsorbing nitrogen and oxygen to the zeolite Li-LSX, Readman distinguished and assigned the oxygen species in different cages.88 Since the b-cage in the zeolite cannot accommodate small molecules, adsorbed nitrogen and oxygen only enter the supercage, where O(1) and O(4) species are located. With loading of oxygen, 17O chemical shift of O(1) and O(4) centers shifted to higher frequency (from 25 to 30 ppm). Only small 17O chemical shift differences were observed for the O(2) and O(3) centers, which are located in the b-cage of the zeolite. This result demonstrated the sensitivity of the 17O chemical shift towards the local environment and confirmed the assignment of distinct oxygen species in zeolite LSX.88 In addition to absorbent, the interaction of supported catalyst and the silica carrier has also been investigated by 17O NMR.93 NMR spectroscopy can provide unprecedented quantitative information about grafted catalyst and silica carrier bonding situations and allow for the monitoring of structural variations at the molecular level as well. Mono and bis-grafted systems and metal-coordinated siloxane bridges were distinguished by 17O NMR spectroscopy, and cannot be observed by other methods.93 In catalytic processes, investigation of reaction mechanism is of interest to researchers. Understanding the mechanism during the reaction can help optimize the catalyst and the reaction conditions. Chen et al. detected the H217O involvement in the crystallization of molecular sieve AlPO4-11 by 17O NMR.72 17O MAS NMR and 17O {27Al}, 17O{31P} double resonance experiments were carried out at different stages during the zeolite formation. These experiments revealed that water vapor exchanged with those bound to the AlPO first, then incorporated in both P-O-H and P-O-Al units in the layered intermediate, preferentially over the P(2) and P(3) sites in AlPO4-11.72 This approach might provide a way to probe the crystallization kinetics and the mechanism of zeolites. The Bao group probed the adsorption site and investigated the interaction between framework oxygen in silver catalysts and the adsorbed molecules by 17O NMR.94 Although active 17O species were not directly detected, the peaks at 41 ppm and 2 ppm attributed to Si-17O-Si and Si-17OH in zeolite, indicated the exchange between

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Fig. 8 1H-17O HETCOR NMR at 17.6 T of (A) dry H-MOR, contact time, 70 ms; (B) dry H-MOR, contact time, 100 ms; and (C) H-MOR containing a trace amount of H2O, contact time, 120 ms. Recycle delay ¼ 1 s. 64 points were acquired on the first dimension with (A, C) 7200 and (B) 4000 scans per time increment; the full 2D spectra took (A, C) 5 days þ 8 h each and (B) 3 days to acquire. Reprinted with permission from reference Huo, H.; Peng, L.; Gan, Z.; Grey, C. P. Solid-State MAS NMR Studies of Brønsted Acid Sites in Zeolite H-Mordenite. J. Am. Chem. Soc. 2012, 134, 9708–9720. 17

O2 and the framework oxygen atoms of the support. Silver nanoparticles on the support promote the activation of 17O2 gas molecules, then facilitate the exchange between 17O2 gas and the framework oxygen in zeolite. The exchange rate is related to the size of silver nanoparticle. Such studies can inform on the design of more efficient catalysts for oxygen activation.

9.04.3.3

Nanocrystalline oxides

Oxides, such as MgO, g-Al2O3, ZrO2 and TiO2 are efficient catalysts or catalyst carriers, and widely used in industry for this purpose. Many studies in the literature have investigated structures of oxides by various 17O NMR methodologies. 17O enriched oxide can be easily obtained through heating the sample in 17O2 gas or synthesis in H217O environment.77,95 Different species, different coordination environments, and oxide phases can be distinguished by changes in 17O chemical shift.94,96 Oxygen dynamics in different phases can also be characterized by 2D exchange experiments.97 Recently, Deng and coworkers have investigated the distribution of various oxygen species including surface hydroxyl groups and (sub)surface oxygen species in g-Al2O3 by 2D 17O 3QMAS NMR, 2D 17 O DQ-SQ NMR and 2D 1H{17O} HMQC at high magnetic field. These studies provide a feasible method to locate the oxygen species on oxide surface.98 Due to their large surface area and better catalytic activities, nanocrystalline oxides are getting more and more attention. In addition to having higher surface area to volume ratio and smaller particle size, the structure of oxide nanocrystals is also different from the bulk solids, resulting in different catalytic activity. By detecting the 17O NMR spectra of MgO samples of different size, it was found that the observed 17O signals were related to the crystallite size of MgO nanophase.99 Only one sharp 17O signal at 47 ppm was observed in 35 nm MgO, which is expected from bulk polycrystalline MgO. For a 5 nm sample, a second sharp peak around 41 ppm was observed, which might be related to the bulk-like MgO connecting with H or CH3 at the third-nearestneighbor level MgOMgOMgOR (R ¼ CH3 or H). With the decrease in the crystallite size of MgO, broadening of 17O signals at 45 ppm from surface layer was observed. As the size decreases, the surface area increases resulting in more oxygen associated with the surface. The Peng group has investigated the nanostructure of ZrO2, TiO2, Ta2O5 and CeO2 using 17O NMR.100–104 They found that lower coordinated surface oxygen species exhibit higher 17O chemical shifts. For example, in 17O spectra of ZrO2 nanoparticles, the chemical shifts of 426, 402 and 325 ppm are related to O2c, O3c and O4c, respectively.101 Meanwhile, they took advantage of the priority exchange of H2O with the surface oxygen ions to develop a selective isotopic enrichment oxygen method and distinguish oxygen species on different surface facets and surface layers from the bulk oxygen signals (Fig. 9). When the ceria nanoparticle sample was treated with 17O2 gas, most of oxygen species on the surface and bulk are enriched non-selectively. The dominant species is located in bulk sites (877 ppm). Additionally, a small amount of the oxygen ions (1040, 920 and 825 ppm) on the surface can also be detected.100 When non-labeled ceria nanoparticles adsorbed H217O at room temperature, there

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(B) (A)

Fig. 9 17O NMR spectrum, calculated 17O NMR shifts and the structure model of ceria NCs-17O2. (A) The summarized 17O NMR shifts (dCGs) predicted for the CeO4-t model with two H2O molecules dissociatively adsorbed on each surface unit (M2); (B) the hydrated CeO4-t model used in the DFT calculations with NMR shifts (dCGs) for oxygen ions and the layer number shown on the right. Red, off-white, and white balls represent bulk oxygen, cerium, and hydrogen ions, respectively. Surface oxygen ions with different shifts are shown in different colors. Reprinted with permissions from Chen, J.; Wu, X.-P.; Hope, M. A.; Qian, K.; Halat, D. M.; Liu, T.; Li, Y.; Shen, L.; Ke, X.; Wen, Y. Polar Surface Structure of Oxide Nanocrystals Revealed With Solid-State NMR Spectroscopy. Nat. Commun. 2019, 10, 1–10.

were two dominant signals at 1040 and 270 ppm. The oxygen signal at 270 ppm is related to the hydroxyl group on the surface, which was confirmed by 17O-1H REDOR, and 1H-17O CP MAS, and 1H-17O TRAPDOR spectra. The signal at 1040 ppm is attributed to the oxygen species on the first layer of the surface, which is more easily to exchange with adsorbed H217O. Meanwhile, small amounts of signals at 920 and 825 ppm can also be detected, which are related to the surface oxygen ions on the second and third layers. By increasing the treatment temperature after adsorption, the signals from surface are disappeared gradually. Correspondingly, the intensity of bulk oxygen species at 877 ppm increases. This indicates that the oxygen ions on the surface can exchange with the oxygen ions in the bulk at high temperature. By controlling the temperature, 17O can be selectively enriched in different layers on the surface of nano oxide, which is very important to identify the most active species and probe the activity in chemical processes.

9.04.3.4

Metal-organic frameworks

Metal-organic frameworks (MOFs) are a class of organic-inorganic hybrid porous materials in which metal ions are coordinated to organic linker.105 With the unique features of high surface areas, high thermal stability and a porous structure, these materials can be potentially applied in gas adsorption and storage, catalysis, drug delivery and biomedicine.106 Structural characterizations of MOFs are usually done by X-ray diffraction (XRD) based methods. One of the limitations of XRD is the requirement for single crystals of MOFs, which limits its application, especially in activation/desolvation samples with lower crystallinity. 1H, 13C and 129Xe solid state NMR studies have been used to detect the organic linkers and the porosity in MOF frameworks.107–109 Although oxygen is an essential element in the functional groups of MOFs and plays a critical role in adsorption and phase transitions,110 17O NMR spectroscopy has not been widely applied to investigate MOFs. This is due to challenges with 17O enrichment of MOFs and the low sensitivity posed by the properties of this quadrupolar nucleus. Based on the different types of MOFs, He et al. prepared 17 O enriched MOF samples with various cost-effective methods, including ionothermal synthesis, dry gel conversion (DGC) and the 17O enriched water exchange method.111 Key oxygen species in MOF structures were distinguished by 17O MAS or CP/MAS NMR spectra. Ashbrook and co-workers obtained critical information about the final composition of the mixed metal MOFs and their unusual breathing behavior by this method.112 More recently, due to the availability of an ultrahigh magnetic field (35.2 T), higher resolution and sensitivity of 17O signals can be achieved.113,114 Vinicius et al. successfully identified all chemically and crystallographically inequivalent oxygen sites in different MIL-53(Al) phases by 2D 3Q MAS and 1D MAS NMR. In the framework of MIL-53(Al), there are two types of oxygen species, namely the carboxylate group (-COO) and m2-hydroxyl group, which can be probed by 17O NMR spectroscopy at lower magnetic field (Fig. 10).111 At higher magnetic fields, 17O NMR spectra provide more detailed MOF structural information.113 Different crystallographically inequivalent carboxylate oxygen sites were resolved in various phases: two sites in MIL-53(Al) as-made phase, one site in large pore phase, and four sites in narrow pore phase, indicating

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Fig. 10 Illustrations of the frameworks of MIL-53(Al)-lp (top left) and MIL-53(Al)-np (top middle), the metal coordination environment (top right), and 17O NMR spectra of MIL-53(Al). #: unreacted 1,4-benzenedicarboxylic acid. *: spinning sidebands. Reprinted with permission from He, P.; Xu, J.; Terskikh, V. V.; Sutrisno, A.; Nie, H.-Y.; Huang, Y. Identification of Nonequivalent Framework Oxygen Species in Metal–Organic Frameworks by 17 O Solid-State NMR. J. Phys. Chem. C 2013, 117, 16953–16960.

the structure changes related to the phase transition. In addition to detecting oxygen in the framework of MOFs to obtain the MOF structure and host-guest interaction information,114 17O enriched guest gas has been investigated to study the dynamics of the gas adsorbed in MOFs.115 Wang et al. detected the 17O signals of C17O2 adsorbed in CPO-27(Mg/Zn) at different temperatures.115 Based on simulations, localized wobbling and nonlocalized hopping parameters defining CO2 motion in MOFs were extracted, which is helpful for understanding adsorbent dynamics in MOFs as well as the adsorption mechanism.

9.04.3.5

Glasses

Silicate glasses are very useful materials and widely utilized in many industrial applications. They are used as optical fibers, sealing materials, for sequestering radioactive waste, and even in the bottles and windows which can be seen everywhere in our daily lives. Different from the crystal structure of silica (SiO2), in which oxygen atoms are primarily coordinated with two silicon atoms (Si-OSi linkages) to form the network of corner-sharing SiO4 tetrahedra, additional network-modifier cations to depolymerize the silica network and balance the charges are present in glass systems. Here, the Si-O-Si linkages are termed as bridging oxygen (BO). The oxygen atoms with one silica and network modifying cation to form Si-O-M linkages are designated as nonbridging oxygen atoms (NBO). The content of NBO in the system influences the viscosity, conductivity, diffusivity, structural disorder, and thermal expansion of the glasses.116,117 17O NMR methodologies including MAS, MQMAS and DAS have been utilized to identify the structure of various glasses.118–121 BO and NBO species can be easily distinguished based on their differences in the chemical shifts. Various types of BO, such as Si-O-B, B-O-B, Si-O-Si in borosilicate glasses or Si-O-Al, Al-O-Al in aluminosilicate glasses, can also be identified by 3Q MAS NMR (Fig. 11).119,122 Other NMR techniques, like 17O-11B rotational echo double resonance (REDOR)122 and

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O{27Al} transfer of populations in double resonance (TRAPDOR) NMR,123 can help to verify the peaks assignment. The size and charge of the network modifier cations will strongly influence the chemical shift of the NBO, which in turn indicates the type and number of coordination cations (Fig. 11).122,124–126 With higher charge and field strengths of the modifier cations, the decrease in 17 O shielding results in shifts of NBO resonances to high frequencies.118,122 Although the interaction between the modifier cations and BO is not as strong as that for NBO, they can also affect the chemical shift of BO.126 Like in binary sodium silicate glasses (Na2O-k(SiO2)), the 17O isotropic chemical shifts and quadrupolar coupling parameters of both BO and NBO increased with an increasing ratio of Na2O to SiO2, which indicates a relatively homogeneous distribution of Na in the glasses and that the modifier cation Na interacts not only with NBO but with BO as well.119 In general, the distribution of modifier cations in the glasses might be homogeneous or clustered with either random or nonrandom mixing. Comparing 17O NMR parameters derived from 17 O 3Q MAS NMR spectra with model calculations, the network cation coordination and mixing behavior can be obtained.127 For example, potassium cations prefer to mix with the avoidance of linkages between tetrahedral aluminum and tetrahedral boron groups, while calcium cations favor random mixing of Si, B and Al atoms in aluminoborosilicate glasses.127 In the more complex borosilicate glasses with mixed alkali, the isotropic chemical shift value of NBO in LK-BS glass is much closer to that of pure Li glass instead of K glass, which indicates Li prefers to interact with NBO, rather than mixing randomly.126 They found that the smaller cations with higher cation field strength are more likely to form NBO than are the larger cations. The fraction of various types of BO and NBO can be measured by direct integration of single pulse or 2D 17O MAS spectra or fitting the isotropic projections of 17 O 3Q MAS NMR spectra. Due to the difference in excitation and reconversion efficiencies for oxygen species with different quadrupole coupling constants, it is worth noting that the relative intensities deduced from 3Q MAS NMR spectra need to be calibrated before further analysis. By measuring the fraction of NBO and BO species, the degree of melt polymerization can be directly determined.119,128,129 As the NBO fraction decreases, the degree of polymerization increases. Meanwhile, the heterogeneity of the glasses can also be probed through the fraction of BO.124 Among alkali borosilicate glasses, the fraction of BO (Si-O-B) varies as Li < Na < K, which indicates the order of decreasing heterogeneity.126 Li-containing glasses have the highest degree of heterogeneity among alkali borosilicate glasses. In addition to the chemical shift and peak intensity, other 17O NMR parameters, including the quadrupolar coupling constant and linewidth, also provide structural information, such as the chemical and topological disorder environment, bond angle and bond length distribution in the network. As described previously, the TeOeT bond angle in zeolite is related

Fig. 11 (A) 17O sheared 3QMAS contour plots of (a) CBS-2–0.5 and (b) CBS-2–1.5. The contour lines are evenly spaced between 9% and 100%. (B) (a) 17O plot of the centers-of-mass in the MAS and isotropic dimensions of BO 17O species for several borosilicate glasses along with those of CBS-2–0.5. (b) 3QMAS center-of-mass plot of known NBO species in borosilicate glasses with different charge modifying cations along with that of CBS-2–1.5. The black line represents the slope of constant CQ. Reprinted with permission from Aguiar, P. M.; Michaelis, V. K.; McKinley, C. M.; Kroeker, S. Network Connectivity in Cesium Borosilicate Glasses: 17O Multiple-Quantum MAS and Double-Resonance NMR. J. Non Cryst. Solids 2013, 363, 50–56.

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to the 17O NMR parameters. Isotropic chemical shift and quadrupolar couplings are correlated to the local short to medium range coordination environment around oxygen, which is sensitive to bond angle and bond length. Although there’s no simple and accurate relationships between NMR parameters and the local coordination environment,128 the relationship of 17O NMR parameters with bond angle and bond distance has been established with ab initio calculation,130–133 in which the linear correlation between the Si-BO (M-NBO) average bond length and the chemical shift of BO (NBO) has been found.

9.04.3.6

Biological systems

In biological systems, metal ions play an essential role in either the structural or catalytic functions. Often, oxygen atom(s) are the bridge to connect the metal center with organic ligands. 17O solid state NMR is a powerful tool to directly probe the molecular interactions of the oxygen ligand with metal ions.134 17O NMR parameters, like quadrupolar coupling and CSA, can provide insights into the local chemical environment and bonding information, such as bond angles and bond distances. Kong et al. investigated the interaction of transition metal Pt(II) with the carboxylate oxygen in two platinum anticancer drugs, carboplatin and oxaliplatin.135 By measuring the 17O MAS and 17O static NMR spectra acquired at multiple magnetic fields, 17O nuclear parameters were derived. It was observed that 17O CSA and quadrupolar coupling tensors of carboxylate oxygen atoms are sensitive to the coordination with Pt(II). The isotropic chemical shift of the oxygen atom which is directly bonded to Pt(II) shifted to higher field by 200 ppm than that of the non-Pt-coordinated oxygen in the carboxylate group. Based on the analysis of 17O CSA tensor components and DFT calculations, it was deduced that the electron lone pair from oxygen nonbonding orbital donates to the Pt(II) empty dyz orbital, which causes the large energy difference between s(Pt-O) and unoccupied orbitals, thereby increasing the shielding along the direction perpendicular to the OePt bond. Gupta et al. also investigated the electronic structure of the peroxo ligand in a bioinorganic V(V) complex and its interaction with the metal ion by 17O solid state NMR and density functional theory calculations.136 They found the largest chemical shift tensor component (1288 ppm) is oriented along the VeO bond. Similar to the results in Kong’s platinum carboxylate complexes study, the lone electron pair of oxygen on the peroxide ligand is polarized by the electronic spin on vanadium d-orbitals, which results in the magnetic shielding of the ligand. These studies demonstrate that 17O NMR studied when combined with DFT calculation can provide invaluable information about bonding and structure of metal ligand complexes. 17 O NMR has also been used to investigate dynamics of biomaterials. Kong et al. first reported on the dynamics of sulfonate groups in organic solids by variable temperature 17O NMR.137 In their study, three 17O labeled crystalline amino sulfonic acids (taurine, homotaurine and ABSA) with zwitterionic structures ðNH3 þ  R  SO3  Þ were measured under both static and MAS conditions at variable temperatures. Due to the rotational dynamics of the SO3  group about the CeS bond, the lineshape of the 17O signal is strongly related to the temperature. Based on the changes of powder lineshapes and with the assistance of DFT calculations, the jump rates and the geometry of the SO3  group reorientation was extracted. They found that the SO3  groups in these solids undergo a threefold rotational jump mechanism. The jump rate is in the range of 102–105 s 1. The activation energies (Ea) were also determined with Ea ¼ 48  7, 42  3, and 45  1 kJ/mol for taurine, homotaurine and ABSA, respectively, which can be used to estimate the total hydrogen bond energies for each SO3  group in the solids quantitatively. Their studies demonstrate the potential application of solid state 17O NMR in probing the dynamic processes of oxygen centers in crystalline solids or biomaterials. Recently, Mn(II) complexes have been proposed as potential contrast agents (CAs) in magnetic resonance imaging (MRI) because of the efficient dipolar interaction between the unpaired Mn(II) electrons and protons in water. The contrast enhancement efficiency of a CA is related to the exchange rate between the water directly coordinated to the metal and the bulk water.138 Thus, understanding of the hydration state of metal ion in solution and its exchange dynamic properties is essential for developing efficient Mn(II) based contrast agents. Rolla and Gale investigated the hydration state of various Mn (II) complexes by measuring 17O linewidths.139,140 These studies revealed that the H2O line broadening induced by Mn(II) is mainly because of the coordinated water exchange with bulk water. The transverse 17O relaxivity is directly related to the hydration number q.140 The number of water molecules coordinated to the metal center can be obtained by H2O linewidth measurements at variable temperature. Gale et al suggested that this method can be applied to investigate metalloproteins or complex:protein interactions. The authors examined 12 Mn(II) complexes to estimate that the q value is within the range of  0.2 water molecules.140 By measuring the linewidth of the H217O signal, Rolla et al. investigated the hydration state of Mn(II) complexes with cyclen-based ligands.139 They found the number of inner sphere water ligands of the Mn(II) complex with the heptadentate ligands DO2A and 1,7-DO2A are 0, while one coordinated water molecule is present with ligands 1, 4-DOA2 and DO1A. Combined with computational studies, the 17O hyperfine coupling constants and the water exchange rate can also be estimated.

9.04.3.7

Dynamic nuclear polarization

Sensitivity enhancement is a major challenge often faced by NMR spectroscopists especially when investigating quadrupolar nuclei and the nuclei with low natural abundance or gyromagnetic ratio. Numerous strategies, including increasing the magnetic field strengths, using a cryoprobe, enriching the sample or designing sensitivity enhancing pulse sequences, are typically employed to improve signal-to-noise ratios. Various NMR methodologies such as double rotation (DOR), dynamic-angle spinning (DAS) and multiple-quantum magic angle spinning (MQMAS) are employed to overcome the sensitivity challenges encountered due to the low natural abundance (0.037%) and quadrupolar interaction in 17O nuclei. In 2012, Griffin and co-workers first employed

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dynamic nuclear polarization (DNP) for 17O detection.141 Using the TOTAPOL biradical as the polarizing agent, the 17O signal intensity of water/glycerol glass can be enhanced by 80-fold with DNP. The sensitivity enhancements achieved by DNP-based measurements afford dramatic time savings and allow for the characterization of minority species. In a typical DNP experiment, the polarization is directly transferred from unpaired electrons on the radicals to protons via microwave irradiation. Then, regular cross-polarization (CP), and/or echo, Carr-Purcell-Meiboom-Gill (CPMG) and spin-echo double resonance (SEDOR) pulse sequences are used to transfer the enhanced 1H polarization to 17O atoms. Since proton nuclei are required to achieve the transfer, this indirect DNP method is limited to detect samples containing protons, such as the surface hydroxyl groups in mesoporous silica nanoparticle samples.142 Later, Griffin and co-workers reported that the 17O signal enhancement can also be obtained by direct transfer of electron polarization to 17O nuclei.143 Different polarizing agents, such as biradical TOTAPOL, monoradicals trityl and SA-BDPA, were tested in this study. The radical selection was shown to be important for the enhancement of the signal. The trityl (OX063) radical exhibited the best polarizing efficiency in direct DNP experiments, which enhances the intensity of the 17 O signal in water/glycerol system by approximately 100-fold. Less than a 10-fold gain was obtained when using other polarizing agents. These studies extended the applicability of DNP based methodologies for the detection of samples without 1H nuclei in the vicinity. With enhancements introduced by DNP, 17O signals from natural abundance oxides can be easily detected within several minutes without enrichment.144 Grey et al. applied direct and indirect DNP based methodologies to investigate CeO2 nanoparticles, with TEKPol biradical in TCE as the polarizing agent.145 With indirect DNP NMR, only terminal Ce-OH and water adsorbed on the surface was observed. Due to the absence of nearby protons on the surface and bulk sites, efficient transfer of polarization from protons to oxygen does not take place resulting in no detection of surface or bulk sites by indirect DNP. Oxygen in different layers of CeO2 nanoparticles can be distinguished by the chemical shift. With direct DNP NMR, the authors found that the polarization efficiencies are not identical for oxygen atoms located in different layers. The surface sites or subsurface sites are much closer to the polarizing agents and can be selectively polarized by radicals. Through slow spin diffusion of oxygen polarization, the intensity enhancement of the oxygen on the bulk sites can be built up, while more slowly than surface sites (see Fig. 12). Therefore, using TEKPol biradical as polarization agent, the DNP can selectively improve the signals on the surface. This methodology is also referred to

Fig. 12 A (a) 17O NMR (14.1 T) spectra of 17O enriched CeO2 nano particles mixed with the TEKPol radical in TCE, with and without microwave irradiation, using a presaturated Hahn echo experiment. The spectra were recorded at 95 K. The OFF spectrum was recorded at 12.5 kHz MAS, whereas the ON spectrum was recorded at 10 kHz in order to separate the spinning sidebands from the signal arising from the first layer. Spinning sidebands are labeled according to the layer of the signal from which they arise. (b) The 17O saturation recovery build up curves for the different environments in CeO2 nanoparticles and the fitted stretched exponentials. The intensity is determined by deconvoluting the isotropic peaks. (B) Pulse sequences to acquire natural abundance 17O NMR spectra with DNP: (a) CP-QCPMG (b) PRESTO-QCPMG and (c) PRESTO-QCPMG-HETCOR. Reprinted with permission from Hope, M. A.; Halat, D. M.; Magusin, P. C.; Paul, S.; Peng, L.; Grey, C. P. Surface-selective direct 17O DNP NMR of CeO2 nanoparticles. Chem. Commun. 2017, 53, 2142–2145, Perras, F. A.; Kobayashi, T.; Pruski, M. Natural abundance 17O DNP two-dimensional and surface-enhanced NMR spectroscopy. J. Am. Chem. Soc. 2015, 137, 8336–8339.

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as surface-enhanced NMR spectroscopy (SENS). Investigation of bulk micron-sized inorganic particles is of interest to researchers developing functional materials. Although nitroxide biradicals are usually applied as polarizing agents, the signal enhancement is mostly obtained for the surface and subsurface layers. Wolf et al. developed an efficient approach to obtain the hyperpolarization in the bulk sites.146 Mn(II) ions were doped into the solid sample and the paramagnetic metal ions acted as endogenous polarization sources to achieve the polarization transfer. These studies demonstrated that Mn(II) dopants exhibit remarkable efficacy as endogenous polarization agents in DNP NMR. This metal-ion-based (MI) DNP NMR methodology can enhance the signal efficiently. Leskes et al. investigated 17O (MI) DNP NMR spectra of Fe(III) doped Li4Ti5O12 conductor.147 Interestingly, they found that the polarization buildup was through the paramagnetic coupling instead of spin diffusion. Fe(III) as a polarization agent was the predominant source of nuclear relaxation, which could spread the hyperpolarization throughout the entire bulk of the sample. The polarization enhancement was independent of the distance between the polarization agent and the nucleus. Thus, it provides a strategy to detect low sensitivity nuclei that are inaccessible through spin diffusion. Considering the lineshape distortions caused by spin dynamics during spin lock and cross polarization under MAS conditions, Pruski et al. developed a phase-shifted recoupling effects a smooth transfer of order (PRESTO) pulse sequence instead of using conventional cross polarization to achieve polarization transfer to the 17O nucleus148 (Fig. 12). In this pulse sequence, they replaced the 17O spin locking pulse with a symmetry-based single quantum heteronuclear recoupling to 1H and a simple Hahn echo applied at the 17O frequency (Fig. 12B). Compared to regular CP, the sensitivity of the 17O signal can be enhanced five times by applying PRESTO sequence. Combining PRESTO with quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) and HETCOR pulse sequences, Pruski et al. probed hydrogen bonding and detected Bronsted acidity on the surface hydroxyls in nature abundance silica materials by 17O DNP SENS.142,149 Based on the distance of OeH bond deduced from NMR results, hydroxyl groups on the surface with different acidic strengths can be identified.

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V NMR has been extensively utilized to characterize a plethora of multidentate ligands bearing a coordination number of four to eight. The presence of biological vanadium cofactors exhibiting catalytic and pharmaceutical properties has fueled extensive research on inorganic and biomimetic vanadium complexes.150–152 Biologically, vanadium cofactors are found in vanadiumdependent haloperoxidases (VHPOs) and nitrogenases.153,154 In addition to exhibiting phosphatase activity, VHPOs are the most efficient oxidants of halides known.155 Owing to the large amounts of VHPOs in seaweeds, fungi and lichens, vanadium is the second most abundant metal in the ocean. Among living species, the highest concentration of vanadium is nature is found in Amanita muscaria mushrooms that contain vanadium-based natural product called amavadin.150,156–158 Due to the rich chemistry exhibited by biological vanadium centers, a plethora of synthetic complexes with diverse chemical and catalytic properties have been synthesized. 51V NMR, particularly in MAS NMR has been instrumental in the characterization of coordination environment and geometry of these complexes.

9.04.4.1

Bioinorganic and inorganic complexes

A large number of vanadium complexes have been synthesized and characterized by NMR spectroscopy with an aim to recapitulate the structure and functions of biological vanadium centers. The isotropic chemical shifts in these complexes typically range from  300 to  700 ppm and generally a good correlation can be observed between diso measured in solids compared to the solution state. Generally, ligands bearing soft substituents (for instance, S2, Br and Cl) reduce magnetic shielding favoring chemical shifts at lower fields while hard substituents like O2, OH and F promote shielding and give rise to shifts to higher fields. Large deviations from this typically observed range of chemical shifts have been reported. For instance, [VSe4]3 exhibits diso of þ 2570 ppm159 and positive diso for vanadium complexes of non-innocent ligands is observed.160,161 High-resolution MAS NMR spectra of inorganic vanadium complexes have been reported for a large repertoire of compounds. For instance, Pooransingh et al. reported 51V MAS NMR spectra of a series of active site mimics of VHPOs modeled utilizing aminato and zonato based ligands.22 A wide range of NMR parameters were observed in this study including ds from  340 to  730 ppm and CQ from 3 to 7 MHz. Subsequent characterization of other inorganic complexes with different ligands and coordination number yielded a similar broad range of NMR parameters. It is both tempting and rational to speculate that a simple association between the observed NMR parameters and ligand coordination to the vanadium center may exist. However, while the eight nuclear parameters typically extracted from 51V MAS NMR spectra (CQ, hQ, diso, ds, hs, a, b, g) bear rich information about the coordination environment of the metal center, a clear correlation between ligand properties and NMR parameters does not exist. For example, correlation between CQ and ds was evaluated for complexes bearing coordination numbers of five to eight.162 Some clustering for six- and seven-coordinate complexes containing non-redox active ligands was observed, but no clear correlation could be identified. The majority of these complexes exhibited negative CSA and small CQ values. However, complexes with redox active, noninnocent ligands fall out of this cluster with higher CQ and distinctly small CSA values. These observations clearly demonstrate the complexity of utilizing 51V NMR as a probe for structure and coordination environment of the vanadium center: while NMR parameters are highly sensitive not only to the primary coordination sphere, they also carry information regarding the secondary coordination environment. However, a straightforward correlation between the ligand properties and NMR parameters does not exist. A successful approach that has evolved from numerous studies on 51V and other NMR active nuclei involves utilizing computational

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methodologies such as DFT calculations to guide and interpret NMR observables. The wealth of information embedded in solid state NMR parameters, when combined with computational studies has been demonstrated to provide detailed insights in to the structural and electronic properties of these complexes. Vanadium centers discussed here have oxidation state of þ 5 yielding a diamagnetic electronic spin for these complexes. However, non-spherical coordination environment in vanadium complexes gives rise to unpaired electron density in the metal d-orbitals, resulting in large distribution in the electronic charge around the nucleus. This charge distribution yields large magnitudes of CQ and ds observed in several vanadium complexes. In the context of biomimetic complexes for VHPOs, in addition to the mimics for the resting states of the enzymes, a peroxo complex, modeled after the peroxo intermediate detected in these enzymes has been synthesized and characterized by 51V MAS NMR.22 The NMR parameters of this peroxo complex were clearly distinct from the models of the resting state. For instance, compared to a series of active site models investigated, the peroxo complex exhibited larger CQ and ds. These studies demonstrated that NMR parameters are sensitive indicator of the coordination environment of the metal center and that similar differences can be expected between the resting state and reaction intermediates in the reaction cycles of VHPOs. Vanadium centers with dipicolinate ligands exhibit insulin-enhancing properties.156,163–166 Due to their potential application for treatment of diabetes, a series of seven coordinate hydroxylamido V(V) dipicolinate complexes with substitutions either on the hydroxylamido or on dipicolinate ligands were characterized using 51V NMR spectroscopy and X-ray crystallography.167 In a subsequent study, pentacoordinate vanadium(V) dioxo dicpicolinate complexes with substitutions on the dicpicolinate ligand were also analyzed 51V MAS NMR by the same laboratory.168 These two studies offer very interesting insights into the effect of primary coordination sphere substitutions on NMR observables. More importantly, these studies demonstrated that a comprehensive understanding of influence of the coordination and electronic environment on vanadium NMR parameters can be gained by DFT calculations. Contrary to expected, for the mono-oxo complexes, across the series minor variations in quadrupolar coupling constants were observed (3.0–3.9 MHz). This suggested that the substitutions did not significantly affect the quadrupolar couplings. However, the chemical shift, particularly its anisotropic component, exhibited significant sensitivity to the ligand substitutions. DFT calculations were used to gain a deeper understanding of these observations. DFT computed electrostatic surface potentials (ESP) exhibited distorted trigonal prism or capped square-planar geometry in the immediate vicinity of the metal ion. Although not perfectly octahedral, such charge distribution is expected to yield small quadrupolar couplings. Therefore, DFT calculations were pivotal in explaining small CQ values originating from these complexes for which large magnitudes would have been otherwise predicted. The dioxo series yielded larger CQ values and greater variations compared to the mono-oxo counterparts (5.8– 8.3 MHz). DFT calculations revealed that the electrostatic potential was dominated by the oxygen atoms with minor contributions from the nitrogen atoms of the ligands. Computed ESP surfaces indicated that the observed variations in the EFG tensors may arise from long-range effects such as changes in the dipicolinate rings and the counterion positions rather than the functionalization of the ligand ring. Molecular orbital analysis provided information regarding the nature and the symmetry of the d-orbitals contributing to paramagnetic shielding and the CSA. Redox active, non-innocent ligands can introduce significant changes to the electronic properties of the metal center and consequently affect its reactivity. Isotropic chemical shifts of vanadium complexes of catechol ligands fall outside the typical range of  300 to  700 ppm.160,169 Therefore, vanadium chemical shift tensors may be used as a probe for the reactivity of redox active ligands. DFT calculations offer insights into the influence of non-innocent ligands and their substitutions on NMR parameters. It was shown that the HOMO-LUMO gap increases with substitutions of electron-donating groups on the catechol ring, resulting in an upfield shift in the 51V frequency. Amavadin, a naturally occurring complex found in Amanita muscaria mushroom and responsible for its vanadium accumulation is an interesting compound given its coordination number of eight at the vanadium center. An oxidized derivative of amavadin exhibits isotropic 51V chemical shifts of  220 and  228 ppm.170 Compared to other vanadium complexes, these eight coordinate compounds are less shielded, which may be a consequence of the high coordination number or the lack of oxido ligand. DFT calculations were performed to investigate the origin of deviation of the isotropic chemical shifts from the usual range. However, although the EFG tensor could be predicted with a reasonable accuracy, the DFT computed CSA tensor did not agree with the experimental measurements. The origin of this discrepancy and the unusual chemical shift is not understood. Given that 51V NMR parameters are sensitive reporters of the metal coordination environment and its geometry, vanadium substituted polyoxometalate solids are well suited for their characterization by MAS NMR spectroscopy. The catalytic potential of vanadium substituted polyoxoanionic complexes has been utilized towards oxidation of NADH, selective epoxidation of alkenes and alkenols with H2O2, aerobic oxidation of alkyl aromatic compounds, benzene hydroxylation with H2O2, toluene and nitrobenzene oxidation with H2O2.171 Vanadium substituted Lindqvist, Keggin and Wells-Dawson polyoxotungstate solids have been investigated by MAS NMR spectroscopy. These studies highlighted the strength and applicability of this methodology to characterize complex, multicentered vanadium complexes.24,25,172 For example, CSA tensors were found to report on the cationic environments in oxotungstates upon substitution with one, two or three vanadium centers. However, the quadrupolar tensors in these complexes did not show any effect from the nature of the counterions. In di- and tri- substituted Wells-Dawson polyoxotungstates, both the quadrupolar and chemical shift anisotropy tensors were sensitive to the position and the degree of the vanadium substitution into the oxoanion core.173

9.04.4.2

Biological systems

While a large number of small molecules have been investigated in great detail by 51V MAS NMR, demonstrating the advancement of NMR methodologies and hardware, utilizing MAS NMR to characterize vanadium centers in large biological systems poses

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additional problems. In high molecular weight proteins containing one or two vanadium centers, the effective concentration of 51V spins is low giving rise to poor sensitivity. Despite low sensitivity, vanadium centers in VHPOs have been investigated by NMR spectroscopy. 51V MAS NMR studies were first reported for vanadium chloroperoxidase (VCPO), a 67.5 kDa member of the VHPO family that contains one vanadium atom per protein molecule.23Due to the expected low sensitivity and large quadrupolar coupling, complete 51V spectral manifolds representing both the central and satellite transitions could not be reported. But sufficient quality MAS NMR spectra were obtained at 14.1 T within 5–7 days. The authors demonstrated that despite of lack of resonances from the satellite transitions, the magnitude of CQ can be extracted from the contribution of the second-order quadrupolar interaction to the central transition lineshapes. This, in part, was because the resting state of the enzyme exhibited remarkably large CQ of 10.5 MHz. Lower CQ values observed for several biomimetic complexes of these proteins suggest that both the primary and secondary coordination environment of the protein influences the quadrupolar tensor. In large molecular weight proteins, the precise location of protons cannot be determined by X-ray crystallography. In VCPO, the knowledge of the protonation state of the vanadate cofactor is critical for the understanding of the reaction catalysis performed by this class of enzymes. However, this information cannot be easily determined. With the aid of DFT calculations performed on a series of vanadate cofactor models, the protonation of this cofactor in the protein at neutral pH was predicted. More recently, in a more detailed study that utilized fast MAS of 40 kHz, protonation states of the vanadate cofactor in VCPO were elucidated as a function of pH.174 This NMR crystallography based approach utilized fast spinning frequencies to enhance signal-to-noise ratios and DFT calculations of large active site models accounting for hydrogen bounds originating from the secondary and tertiary coordination sphere to explain the observed reactivity and its correlation to the location and number of protons on the catalytic vanadate center of the enzyme. These studies established the feasibility of investigating large macromolecules that suffer from limited sensitivity and demonstrate that detailed spectroscopic characterization of vanadium sites in dilute environment can be performed with MAS NMR methodologies.

9.04.4.3

Inorganic materials

In addition to bioinorganic vanadium centers, several laboratories have utilized 51V MAS NMR spectroscopy to characterize vanadium centers in nanoparticles, inorganic catalysts and battery materials. Complete spectral manifolds containing both central and satellite transitions for vanadia-titania model catalysts and industrial vanadia-based DeNOx catalysts were first reported by Nielsen et. al.175 51V nuclear parameters revealed that vanadium centers on the surface of the catalysts exist in a distorted octahedral oxygen coordination environment. Multinuclear NMR spectroscopy was utilized to investigate vanadium and phosphorus substituted bismuth oxide materials.176 Variable temperature 51V NMR spectra, used to characterize the VO4 environment, revealed high rates of tetrahedral rotation at room temperature, which increased with heating. Increasing vanadium doping resulted in two different local VO4 environments with differing rates of local ionic motions that interfere with the three-dimensional oxide-ion conduction network. This work demonstrates that multinuclear NMR spectroscopy, including 51V MAS NMR measurements, can yield complementary information regarding local dynamics of ionic complexes, which may provide rational design for conducting materials. In another interesting application, real time solution and solid state 51V NMR measurements were used to monitor the formation of nanosheets of V2O5$nH2O from VO2 and V2O5 in aqueous dispersion (Fig. 13).177 Weight normalized MAS NMR measurements, along with EPR and solution NMR experiments allowed the authors to propose a mechanism of assembly of nanosheets that involves first the formation and then assembly of [V4þO$5H2O]2þ cations or intercalation of [V4þO$5H2O]2þ between the layers of V2O5. 51 V MAS NMR characterization of vanadium containing MCM-41 catalyst has provided insights into the structures of various VOx species present in these materials and the influence of specific catalyst preparation schemes.178 Large dispersion of vanadia active species on high surface area mesoporous MCM-41 molecular sieve support plays a crucial role in selectivity of various chemical reactions such as the direct oxidation of methane to formaldehyde. MAS NMR studies revealed the presence of mixed vanadium oxide environments consisting of dimeric species, oligomeric chains and isolated trigonal pyramidal units in hydrated catalysts. Highly distorted VOx species were largely present upon dehydration. This distorted species was mainly present in oligomeric form in samples prepared either by co-condensation or grafting. Isolated VOx species were only detected in samples prepared by co-condensation. These results demonstrated that well dispersed monomeric VOx species that correlate with higher catalytic activity are generated by the co-condensation preparation scheme. Development of Mg ion batteries (MIBs) has gained interest due to their potential to offer improved energy density and cost efficiency. VS4 is proposed as a potential candidate for cathode material in MIBs. Vanadium and [S2]2 ions in VS4 form linear chains with large spacings that could allow for reversible Mg insertion and therefore reversible Mg intercalation needed for an efficient cathode. In a recent study by Dey et al., a combination of experimental and theoretical methodologies, along with 51V MAS NMR, were utilized to demonstrate the presence of a metastable intermediate in VS4 MIB electrode.179 To detect multiple vanadium based species during the electrochemical pathway, faster MAS speeds (50 kHz) were employed to increase the effective spectral distance between the sidebands (Fig. 14). 50 kHz MAS allowed for the detection of additional board signals at 1.1 V, which were not resolved while spinning at lower speeds of 25 kHz. However, the resonances associated with the new intermediate species were obscured by spinning sidebands even when spinning at 50 kHz. To overcome this issue, the authors employed magic angle turning and phase adjusted sideband separation (MATPASS)65,180 to clearly detect the broad resonance originating from intermediate species when VS4 was discharged to 1.1 V. V4þ (d1) center in VS4 exhibits diso at 163 ppm and the intermediate was detected with a wide feature between
300 and 1300 ppm. This new species was assigned to originate from diamagnetic (V5þ) centers, consistent with the 51V chemical shift of K3VS4 (1375 ppm). This study, with the aid of 51V MAS NMR, demonstrated that VS4 is

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Fig. 13 (A) Low-flip-angle direct excitation (a) and Hahn echo (b) MAS ss-NMR spectra at 70  C for the VO2/V2O5 mass ratio of 1:4 extracted from real-time experiments at time ¼ 0 (black trace) and time ¼ 38 h (red trace). (c) Normalized 51V integrals vs. time for reactions with aged VO2 (blue) or fresh VO2 (Hahn echo red; direct excitation gray) in the reaction mixture. The black curve is a repetition using a Hahn echo. (B) Proposed reaction pathways occurring during the synthesis of V2O5$nH2O nanosheets. Reprinted with permission from Etman, A. S.; Pell, A. J.; Svedlindh, P.; Hedin, N.; Zou, X.; Sun, J.; Bernin, D. Insights Into the Exfoliation Process of V2O5$nH2O Nanosheet Formation Using Real-Time 51V NMR. ACS Omega 2019, 4, 10899–10905.

a viable candidate for MIB electrodes and laid the ground work for the potential intermediates that should be taken into consideration during electrochemical reaction pathways.

9.04.4.4

NMR measurements of internuclear metal-to-ligand distances involving vanadium centers

Determination of internuclear distances is of great interest to NMR spectroscopists, particularly for the characterization of noncrystalline materials or in situ investigations. While many pulse sequences have been developed and modified for quantitative measurements of distances between two I ¼ ½ spins, reliable determination of internuclear separations between spin >½ and a spin ¼ ½ is more complicated due to the quadrupolar interaction. Recent efforts by various laboratories have yielded promising results suggesting that accurate determination of nuclear distances between I >½ is viable. Here we briefly discuss some examples involving 51V centers. Distance measurement in NMR relies on the quantification of the dipolar interaction, which is proportional to the inverse cube, r 3, of the distance between two nuclei of interest. Internuclear 31P (I ¼ ½) and 51V separation in vanadium substituted Keggin and Wells-Dawson polyoxoanionic solids was accurately measured by using rotational echo adiabatic passage double resonance (REAPDOR) experiments. In these complexes, with 51V nuclei exhibiting lower magnitudes of CQ (0.88– 1.73 MHz), distances up to 6.9 Å could be measured within  4% uncertainty.181 The measured distances agreed well with X-ray structures of other closely related complexes. Furthermore, the measured distances were sensitive to the positional disorder at the substitution sites, which is critical for polyoxoanionic solids. Although the REAPDOR pulse sequence has been successfully employed on various quadrupolar nuclei, this methodology is limited to relatively small quadrupolar coupling constants. A modification of this sequence was developed by Nimerovsky et al. in the form of low-alpha/low-amplitude REDOR (LA-REDOR) and phase-modulated LA-REDOR pulse sequences which were utilized to determine the 51V-15N distance in VO15NGlySalbz with a 51V CQ of 3.7 MHz.182 While distance measurements between 51V and 31P or 15N nuclei have been reported, determination of 51V-13C dipolar coupling is challenging because of small difference in their Larmor frequencies. Typical NMR spectrometers cannot simultaneously be tuned to two close frequencies on two independent radio frequency channels, which is a requirement for most pulse sequences utilizing dipolar coupling measurements. To overcome this issue, Pourpoint et al. utilized a frequency splitter which allows tuning and matching of a single RF channel to two close resonance frequencies.183 Using this methodology, 51V-13C dipolar couplings in an inorganic vanadium complex, salicylaldehyde[(benzylmercapto)-thiocarbonyl]hydrazine oxovanadium(V), were reported using the rotational-echo saturation-pulse double-resonance (RESPDOR)184–187 dipolar recoupling sequence.

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Fig. 14 (a) Hahn echo 51V NMR spectra of VS4 at various states of discharge and charge. Spectra are acquired at 11.7 T at a MAS rate of 50 kHz. The isotropic shift of VS4 (163 ppm) is marked by a dashed red vertical line. Asterisks denote spinning sidebands. The blue shaded area highlights the appearance of an additional broad resonance in sample B (1.1 V discharge) and sample F (1.8 V charge), as indicated by the arrow. Spectra recorded at a MAS speed of 25 kHz. (b) MATPASS NMR spectra of VS4 and samples B and F. (c) Analysis of structural transformation of VS4 to Mg3V2S8. (A) Initial insertion of Mg in VS4 (blue arrows) leads to disruption of the VS V chains, requiring S migration and expansion in the b direction. (B) Mg insertion sites in VS4 that are the most similar to Mg sites in Mg3V2S8 as calculated by using a Voronoi tessellation-based similarity metric. The majority of these sites occur within the VS4 chains, rather than between the layers, supporting the assertion in panel A that incoming Mg ions insert between V–V dimers, leading to S migration. (C) Final Mg3V2S8 structure. The green outlines in panels A and C emphasize the Mg insertion between V V dimers, as well as the resulting additional zigzag distortion of the chains compared to the pristine VS4 structure. Reprinted with permission from Dey, S.; Lee, J.; Britto, S.; Stratford, J. M.; Keyzer, E. N.; Dunstan, M. T.; Cibin, G.; Cassidy, S. J.; Elgaml, M.; Grey, C. P. Exploring Cation–Anion Redox Processes in One-Dimensional Linear Chain Vanadium Tetrasulfide Rechargeable Magnesium Ion Cathodes. J. Am. Chem. Soc. 2020, 142, 19588–19601.

9.04.5

Conclusions

Advancements in NMR hardware and methodology have allowed researchers to routinely undertake challenging and complicated systems in the past decade. These studies have put NMR, particularly solid-state NMR spectroscopy, at the forefront of characterization of complex (bio)inorganic systems. With the development of NMR methodologies and accurate determination of NMR parameters, 17O and 51V NMR can be easily employed for a plethora of materials, and inorganic and biological samples. With improved hardware, availability of high magnetic field strengths, and the advancement of computational methodologies, we expect that detailed characterization of more challenging and complex systems will be possible using 17O and 51V NMR spectroscopy.

References 1. Hanson, S. K.; Baker, R. T.; Gordon, J. C.; Scott, B. L.; Silks, L. P.; Thorn, D. L. Mechanism of Alcohol Oxidation by Dipicolinate Vanadium(V): Unexpected Role of Pyridine. J. Am. Chem. Soc. 2010, 132, 17804–17816. 2. Wu, A.; Patrick, B. O.; Chung, E.; James, B. R. Hydrogenolysis of b-O-4 Lignin Model Dimers by a Ruthenium-Xantphos Catalyst. Dalton Trans. 2012, 41, 11093–11106. 3. Hanson, S. K.; Baker, R. T.; Gordon, J. C.; Scott, B. L.; Sutton, A. D.; Thorn, D. L. Aerobic Oxidation of Pinacol by Vanadium(V) Dipicolinate Complexes: Evidence for Reduction to Vanadium(III). J. Am. Chem. Soc. 2009, 131, 428–429.

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D.; Lucier, B. E.; Terskikh, V. V.; Wang, W.; Huang, Y. Wobbling and Hopping: Studying Dynamics of CO2 Adsorbed in Metal–Organic Frameworks via 17O SolidState NMR. J. Phys. Chem. Lett. 2014, 5, 3360–3365. 116. Richet, P.; Bouhifd, M. A.; Courtial, P.; Téqui, C. Configurational Heat Capacity and Entropy of Borosilicate Melts. J. Non Cryst. Solids 1997, 211, 271–280. 117. Edén, M. NMR Studies of Oxide-Based Glasses. Annu. Rep. Sect. C (Phys. Chem.) 2012, 108, 177–221. 118. Stebbins, J.; Oglesby, J.; Xu, Z. Disorder Among Network-Modifier Cations in Silicate Glasses: New Constraints From Triple-Quantum 17O NMR. Am. Mineral. 1997, 82, 1116–1124. 119. Lee, S. K.; Stebbins, J. F. Effects of the Degree of Polymerization on the Structure of Sodium Silicate and Aluminosilicate Glasses and Melts: An 17O NMR Study. Geochim. Cosmochim. Acta 2009, 73, 1109–1119. 120. Nasikas, N.; Edwards, T.; Sen, S.; Papatheodorou, G. 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A.; Platas-Iglesias, C.; Botta, M.; Tei, L.; Helm, L. 1H and 17O NMR Relaxometric and Computational Study on Macrocyclic Mn(II) Complexes. Inorg. Chem. 2013, 52, 3268–3279. 140. Gale, E. M.; Zhu, J.; Caravan, P. Direct Measurement of the Mn(II) Hydration State in Metal Complexes and Metalloproteins Through 17O NMR Line Widths. J. Am. Chem. Soc. 2013, 135, 18600–18608. 141. Michaelis, V. K.; Markhasin, E.; Daviso, E.; Herzfeld, J.; Griffin, R. G. Dynamic Nuclear Polarization of Oxygen-17. J. Phys. Chem. Lett. 2012, 3, 2030–2034. 142. Perras, F. A.; Chaudhary, U.; Slowing, I. I.; Pruski, M. Probing Surface Hydrogen Bonding and Dynamics by Natural Abundance, Multidimensional, 17O DNP-NMR Spectroscopy. J. Phys. Chem. C 2016, 120, 11535–11544. 143. Michaelis, V. K.; Corzilius, B. R.; Smith, A. A.; Griffin, R. G. Dynamic Nuclear Polarization of 17O: Direct Polarization. J. Phys. Chem. B. 2013, 117, 14894–14906. 144. Blanc, F.; Sperrin, L.; Jefferson, D. A.; Pawsey, S.; Rosay, M.; Grey, C. P. Dynamic Nuclear Polarization Enhanced Natural Abundance 17O Spectroscopy. J. Am. Chem. Soc. 2013, 135, 2975–2978. 145. Hope, M. A.; Halat, D. M.; Magusin, P. C.; Paul, S.; Peng, L.; Grey, C. P. Surface-Selective Direct 17O DNP NMR of CeO2 Nanoparticles. Chem. Commun. 2017, 53, 2142–2145. 146. Wolf, T.; Kumar, S.; Singh, H.; Chakrabarty, T.; Aussenac, F.; Frenkel, A. I.; Major, D. T.; Leskes, M. Endogenous Dynamic Nuclear Polarization for Natural Abundance 17O and Lithium NMR in the Bulk of Inorganic Solids. J. Am. Chem. Soc. 2018, 141, 451–462. 147. Jardón-Álvarez, D.; Reuveni, G.; Harchol, A.; Leskes, M. Enabling Natural Abundance 17O Solid-State NMR by Direct Polarization From Paramagnetic Metal Ions. J. Phys. Chem. Lett. 2020, 11, 5439–5445. 148. Perras, F. A.; Kobayashi, T.; Pruski, M. Natural Abundance 17O DNP Two-Dimensional and Surface-Enhanced NMR Spectroscopy. J. Am. Chem. Soc. 2015, 137, 8336–8339. 149. Perras, F. A.; Wang, Z.; Naik, P.; Slowing, I. I.; Pruski, M. 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Towards Hydroperoxovanadium Complexes: The X-ray Crystal Structure of A Peroxovanadium(V) Complex Containing a V(O2)(RCO2H)(H2O)2 Cluster With Hydrogen Bond Inter-Linkages. Chem. Commun. 2001, 921–922. 164. Gätjens, J.; Meier, B.; Adachi, Y.; Sakurai, H.; Rehder, D. Characterization and Insulin-Mimetic Potential of Oxidovanadium(IV) Complexes Derived From Monoesters andCarboxylates of 2, 5-Dipicolinic Acid. Eur. J. Inorg. Chem. 2006, 18, 3575–3585. 165. Parajón-Costa, B. S.; Piro, O. E.; Pis-Diez, R.; Castellano, E. E.; González-Baró, A. C. Crystal Structures, Spectroscopic Characterization and Theoretical Calculations of the Guanidinium and Ammonium Salts of the Insulin-Enhancing Anion [VO2(dipic)]. Polyhedron 2006, 25, 2920–2928. 166. Gonzalez-Baró, A.; Castellano, E.; Piro, O.; Parajón-Costa, B. S. Synthesis, Crystal Structure and Spectroscopic Characterization of a Novel Bis (Oxo-Bridged) Dinuclear Vanadium(V)–Dipicolinic Acid Complex. Polyhedron 2005, 24, 49–55. 167. Ooms, K. J.; Bolte, S. E.; Smee, J. J.; Baruah, B.; Crans, D. C.; Polenova, T. Investigating the Vanadium Environments in Hydroxylamido V(V) Dipicolinate Complexes Using 51V NMR Spectroscopy and Density Functional Theory. Inorg. Chem. 2007, 46, 9285–9293. 168. Bolte, S. E.; Ooms, K. J.; Polenova, T.; Baruah, B.; Crans, D. C.; Smee, J. J. 51V Solid-State NMR and Density Functional Theory Studies of Vanadium Environments in V(V)O2 Dipicolinic Acid Complexes. J. Chem. Phys. 2008, 128, 052317. 169. Goncharova-Zapata, O.; Chatterjee, P. B.; Hou, G.; Quinn, L. L.; Li, M.; Yehl, J.; Crans, D. C.; Polenova, T. Effect of Ancillary Ligand on Electronic Structure as Probed by 51 V Solid-State NMR Spectroscopy for Vanadium–O-Dioxolene Complexes. CrstEngComm 2013, 15, 8776–8783.

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170. Ooms, K. J.; Bolte, S. E.; Baruah, B.; Choudhary, M. A.; Crans, D. C.; Polenova, T. 51V Solid-State NMR and Density Functional Theory Studies of Eight-Coordinate Non-Oxo Vanadium Complexes: Oxidized Amavadin. Dalton Trans. 2009, 3262–3269. 171. Briand, L. E.; Baronetti, G. T.; Thomas, H. J. The State of the Art on Wells–Dawson Heteropoly-Compounds: A Review of Their Properties and Applications. Appl. Catal. Gen. 2003, 256, 37–50. 172. Parker, W. O., Jr.; Cavani, F. Stable Pervanadyl Cation Encapsulated in Silica: Frivolous Vanadium in the H4PVMo11O40 Keggin. J. Phys. Chem. C 2015, 119, 24003–24015. 173. Gupta, R.; Huang, W.; Francesconi, L. C.; Polenova, T. Effect of Positional Isomerism and Vanadium Substitution on 51V Magic Angle Spinning NMR Spectra of Wells-Dawson Polyoxotungstates. Solid State Nucl. Magn. Reson. 2017, 84, 28–33. 174. Gupta, R.; Hou, G.; Renirie, R.; Wever, R.; Polenova, T. 51V NMR Crystallography of Vanadium Chloroperoxidase and Its Directed Evolution P395D/L241V/T343A Mutant: Protonation Environments of the Active Site. J. Am. Chem. Soc. 2015, 137, 5618–5628. 175. Nielsen, U. G.; Topsøe, N.-Y.; Brorson, M.; Skibsted, J.; Jakobsen, H. J. The Complete 51V MAS NMR Spectrum of Surface Vanadia Nanoparticles on Anatase (TiO2): Vanadia Surface Structure of a DeNOx Catalyst. J. Am. Chem. Soc. 2004, 126, 4926–4933. 176. Dunstan, M. T.; Halat, D. M.; Tate, M. L.; Evans, I. R.; Grey, C. P. Variable-Temperature Multinuclear Solid-State NMR Study of Oxide Ion Dynamics in Fluorite-Type Bismuth Vanadate and Phosphate Solid Electrolytes. Chem. Mater. 2019, 31, 1704–1714. 177. Etman, A. S.; Pell, A. J.; Svedlindh, P.; Hedin, N.; Zou, X.; Sun, J.; Bernin, D. Insights Into the Exfoliation Process of V2O5$nH2O Nanosheet Formation Using Real-Time 51V NMR. ACS Omega 2019, 4, 10899–10905. 178. de Oliveira, M.; Seeburg, D.; Weiß, J.; Wohlrab, S.; Buntkowsky, G.; Bentrup, U.; Gutmann, T. Structural Characterization of Vanadium Environments in MCM-41 Molecular Sieve Catalysts by Solid State 51V NMR. Cat. Sci. Technol. 2019, 9, 6180–6190. 179. Dey, S.; Lee, J.; Britto, S.; Stratford, J. M.; Keyzer, E. N.; Dunstan, M. T.; Cibin, G.; Cassidy, S. J.; Elgaml, M.; Grey, C. P. Exploring Cation–Anion Redox Processes in OneDimensional Linear Chain Vanadium Tetrasulfide Rechargeable Magnesium Ion Cathodes. J. Am. Chem. Soc. 2020, 142, 19588–19601. 180. Hung, I.; Zhou, L.; Pourpoint, F.; Grey, C. P.; Gan, Z. Isotropic High Field NMR Spectra of Li-Ion Battery Materials With Anisotropy > 1 MHz. J. Am. Chem. Soc. 2012, 134, 1898–1901. 181. Huang, W.; Vega, A. J.; Gullion, T.; Polenova, T. Internuclear 31P51V Distance Measurements in Polyoxoanionic Solids Using Rotational Echo Adiabatic Passage Double Resonance NMR Spectroscopy. J. Am. Chem. Soc. 2007, 129, 13027–13034. 182. Nimerovsky, E.; Goldbourt, A. Efficient Rotational Echo Double Resonance Recoupling of a Spin-1/2 and a Quadrupolar Spin at High Spinning Rates and Weak Irradiation Fields. J. Magn. Reson. 2010, 206, 52–58. 183. Pourpoint, F.; Yehl, J.; Li, M.; Gupta, R.; Trebosc, J.; Lafon, O.; Amoureux, J. P.; Polenova, T. NMR Crystallography of an Oxovanadium (V) Complex by an Approach Combining Multinuclear Magic Angle Spinning NMR, DFT, and Spin Dynamics Simulations. ChemPhysChem 2015, 1619–1626. 184. Chen, L.; Lu, X.; Wang, Q.; Lafon, O.; Trébosc, J.; Deng, F.; Amoureux, J.-P. Distance Measurement Between a Spin-1/2 and a Half-Integer Quadrupolar Nuclei by Solid-State NMR Using Exact Analytical Expressions. J. Magn. Reson. 2010, 206, 269–273. 185. Chen, L.; Wang, Q.; Hu, B.; Lafon, O.; Trebosc, J.; Deng, F.; Amoureux, J.-P. Measurement of Hetero-Nuclear Distances Using a Symmetry-Based Pulse Sequence in SolidState NMR. Phys. Chem. Chem. Phys. 2010, 12, 9395–9405. 186. Gan, Z. Measuring Multiple Carbon–Nitrogen Distances in Natural Abundant Solids Using R-RESPDOR NMR. Chem. Commun. 2006, 4712–4714. 187. Lu, X.; Lafon, O.; Trébosc, J.; Amoureux, J.-P. Detailed Analysis of the S-RESPDOR Solid-State NMR Method for Inter-Nuclear Distance Measurement Between Spin-1/2 and Quadrupolar Nuclei. J. Magn. Reson. 2012, 215, 34–49.

9.05

NMR of carboranes

David Ellis, Institute of Chemical Sciences, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, United Kingdom. © 2023 Elsevier Ltd. All rights reserved.

9.05.1 9.05.2 9.05.2.1 9.05.2.1.1 9.05.2.1.2 9.05.2.1.3 9.05.2.2 9.05.2.2.1 9.05.3 9.05.4 9.05.5 9.05.6 9.05.7 9.05.8 9.05.8.1 9.05.8.1.1 9.05.8.1.2 9.05.8.1.3 9.05.8.2 9.05.8.3 9.05.8.3.1 9.05.8.3.2 9.05.8.4 9.05.8.5 9.05.9 References

Introduction 11 B NMR spectroscopy The chemical shift Introduction Computational studies Antipodal effect J-coupling B-B coupling and relaxation 10 B NMR spectroscopy 13 C NMR 1 H NMR 19 F NMR Nucleus independent chemical shift (NICS) Experimental techniques Spin-decoupling experiments 11 1 B{ H} experiments 1 11 H{ B} experiments 13 11 C{ B, 1H) experiments 11 11 B- B COSY NMR spectroscopy Heteronuclear correlation spectroscopy 11 1 B- H correlation spectroscopy 11 19 B- F correlation spectroscopy Solid state NMR spectroscopy Dynamic NMR spectroscopy Conclusion

62 63 63 63 64 69 71 71 75 77 84 88 89 95 96 96 96 96 97 98 98 99 99 101 103 103

Abstract This contribution presents a survey of the literature on the NMR of carboranes from the early years of study to the present day. Following an introduction to the subject, subsequent sections deal with the principal nuclei concerned, namely the isotopes of boron, (overwhelmingly 11B), 1H, 13C and 19F (the latter as there are many examples of clusters where terminal B-Hs are substituted by B-F units, fluorine may therefore be regarded as a significant tool in the field). Despite the title, some literature on boron clusters (carbon-free) is included where it is felt they can illuminate the topic, also metallaboranes and metallacarboranes, with similar justification. Many journal articles describing synthetic and structural studies of carboranes will heavily feature NMR as a technique of characterization. Reference to these is limited, attention being focussed on work where novel or pioneering NMR concepts and discoveries are described. Significant attention is paid to computational methods, especially in relation to 11B NMR, and to the Antipodal Effect, a rich area of study over many years, both computationally and spectroscopically. The utility of NICS (nucleus-independent chemical shift) values in assessing three-dimensional aromaticity of some carboranes, is covered, including comparison with more conventional organic aromatics. Finally, there is included a relatively brief survey of instrumental methods, including 2D techniques, solid-state, and dynamic NMR spectroscopy. There is a vast literature on the NMR of carboranes and this chapter can only be a portal into that space, the reader is directed to the many relevant reviews, referenced in this work, for further information.

9.05.1

Introduction

Carboranes were first prepared in the 1950s but not declassified and published in the open press until 1962–63. Defined as polyhedral cluster compounds of boron and carbon, comprising delocalised, multi-center bonding, these compounds are well-suited to study by NMR spectroscopy, containing a series of NMR-active nuclei, the insensitive and challenging 13C, the quadrupolar and yet relatively straightforward boron (two isotopes, 11B and 10B) and, in the majority of cases, 1H, the most receptive of the common nuclei. In addition, derivatives incorporating other NMR-active nuclei either within the cluster (heterocarboranes) or as exo-bound

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moieties may be amenable to study. Neutral carboranes and metallacarboranes are generally highly soluble in common deuterated solvents, e.g., d-chloroform, while ionic forms of the clusters dissolve in more polar varieties, e.g., d6-acetone. Achieving samples of the required concentration is rarely an issue. The first NMR studies of carboranes date from the 1960s utilizing early spectrometers of low field strength and poor resolution. As technology advanced into the 1970s, the introduction of reliable superconducting magnets combined with the parallel improvement in computing enhanced the value of the technique. Today, high resolution capability and access to sophisticated multidimensional experiments ensure that NMR is a key tool, both for the analysis of carboranes and the study of other aspects of their chemistry including reactivity, dynamics and fluxionality.

9.05.2

11

B NMR spectroscopy

The three principal nuclei available for studying carboranes are 1H, 13C and 11B, with 19F where available. 1H and 13C are generally the most studied nuclei of all, due to their preponderance in organic systems. There is much information on their properties from standard textbooks, these also acting as excellent general introductions to NMR spectroscopy e.g.,1,2 Boron exists as two isotopes, 10 B and 11B and both are, in principle, available for study by NMR. Table 1 presents the key NMR parameters of these two nuclei. Both boron isotopes are quadrupolar and therefore present somewhat broadened lines in their spectra, though this property also enables short recycle times during acquisition, thereby allowing short accumulation times for relatively large numbers of scans. The natural abundance of 11B (80%) leads to it being the isotope of choice for general NMR characterization, this, together with good sensitivity (754 vs. 13C), and the short relaxation times (T1 and T2 have values typically 10-200 ms) ensures that high quality spectra can now be obtained in a few minutes in automation. Linewidths are significant but not unworkable (normally < 100 Hz) due in part to a relatively small contribution from electric quadrupole effects, in comparison with other quadrupolar nuclei.3 11 B NMR began to be used in the study of carboranes in the early 1960s. In 1963, Schroeder et al.4 published an 11B spectrum of carborane, formulated as B10H10C2H2 (the 1,2-isomer). The incompletely resolved spectrum, acquired at 19.3 Mc/s (19.3 MHz), shows two doublets suggesting spin coupling to terminal hydrogen atoms, an observation supported by the collapse of these to singlets on reaction with gaseous chlorine. A number of review articles have been published on the efficacy of 11B NMR spectroscopy in structural elucidation, including those by Todd and Siedle,5 Wrackmeyer6 and Siedle.7

9.05.2.1 9.05.2.1.1

The chemical shift Introduction

The accepted reference for the calibration of 11B (and 10B) shifts is Et2O.BF3. Fig. 1 shows the chemical shift range for 11B for the more common environments. 11 B chemical shift values for the carboranes typically fall in the range þ 75 to  60 ppm. Closo-carboranes typically present spectra with signals covering a relatively narrow chemical shift range, e.g., 1,2- or o-C2B10H12, by far the most studied of the carboranes, the structure of which is shown in Fig. 2, gives the 11B NMR spectrum reproduced in Fig. 3. The symmetry of the cluster (point group C2v) is reflected in the appearance of the spectrum, with all boron atoms represented as symmetry-equivalent pairs. The relatively narrow chemical shift dispersion of 11B signals of closo-carboranes, combined with lines broadened through quadrupolar relaxation can lead to significant and problematic signal overlap. It is often the case that useful structural information is not forthcoming by simple inspection of the one-dimensional spectrum. This is not necessarily true for nido- and arachno-forms, where the reduced symmetry of the clusters and specifically the presence of boron atoms incorporated into open faces can lead to greater signal-spread, though in the absence of labeling, unequivocal signal assignments may still be challenging without further information, possibly from 2D NMR (see also Section 9.05.8). The structure of the nido-carborane anion, [7-8-C2B9H12] is shown in Fig. 4, and in Fig. 5 the associated 11B NMR spectrum. Fig. 5 reveals the distinctive resonances arising from B1 and B10 in the open cluster at  37.2 and  32.5 ppm respectively, shifted to low frequency, with that from B(10) displaying the characteristic line-broadening resulting from 1J coupling to the endo-hydrogen atom (see also Fig. 4). Heteroatoms within the cage perturb the electron density of the cluster and can reduce symmetry and electronics, consequently leading to disruption of the characteristically tight profile of carborane 11B spectra into more complex patterns. Fig. 6 shows the structure of the 13-vertex species, 4-Cp-4,1,12-closo-CoC2B10H1212 and Fig. 7, the associated 11B spectrum. The symmetry of the Table 1

Key NMR parameters of the isotopes of boron.

Isotope

Natural abundance

Nuclear spin, I

Receptivity, Dc, (13C ¼ 1)

10

19.9 80.1

3 3/2

22.1 754

B B

11

Magnetogyric ratio, (g)  107 rad T 1 s 1 2.8740 8.5794

64

NMR of carboranes

Fig. 1

11

B Chemical Shift ranges for various boron atom environments.

cluster (point group C1) rendering all boron atoms in unique environments. The 11B spectrum therefore comprises 10 individual signals.

9.05.2.1.2

Computational studies

Chemical shift values for individual boron sites within carborane clusters depend on a number of factors including co-ordination number, the presence or absence of bridging hydrogens and endo/exo substituents, the shape of the cluster and the nature of atoms antipodal to the boron in question. Computational methods enabling the determination of NMR chemical shifts and other parameters are now near routine, and various general methods are available for ADF,13 Gaussian,14 and Dirac15,16 approaches.

Fig. 2 The structure of 1,2-carborane showing atom numbering (numbering schemes for carboranes are detailed elsewhere and will not be discussed here8).

NMR of carboranes

65

Fig. 3 The 11B NMR spectrum of 1,2-carborane, showing signal assignments.9,10 This spectrum was acquired from a 10 mg (ca. 0.7 mmols) sample dissolved in d-chloroform (0.5 mL). Number of scans ¼ 1024, relaxation delay ¼ 10 ms, experiment time ¼ 2.5 min. Note the obvious doublet splitting from 1J spin-spin coupling to terminal hydrogen atoms in the cluster.

The pivotal assignment of the 11B spectrum of 1,2-carborane was achieved by Lipscomb et al. and published in 196617,18 together with calculations that attempted to apply the current thinking on wave functions for boron-hydrides19 to carboranes. The ordering of the signal assignment for 1,2-carborane (see Fig. 5) is not consistent with an approach that considers a purely diamagnetic shielding contribution, sd, to the 11B chemical shifts; therefore a significant effect from the paramagnetic shielding term sP is implied. Lipscomb computed the paramagnetic contributions to the 11B shifts, concluding that this term was largely responsible for the detail of the observed chemical shifts.18 This issue was also addressed by Oliva,20 when calculating the 11B and 13C chemical shifts of 1,2-carborane, and of the substituted derivative, 1-2 (SH)-1,2-C2B10H10 using a DFTdGIAO (Gauge Independent Atomic Orbital21) model. The authors note that there is a difference of approximately 2–4 ppm between experiment and calculation, the latter values being upfield compared to the former, a discrepancy ascribed to use of a finite basis set, approximation of the exchange-correlation functional and the omission of solvent effects in the calculations. These results indicate that the paramagnetic contribution to the 11B shifts in the SH substituted carborane is more substantial than for 1,2-carborane, this being rationalized by the presence of the lone pairs of electrons associated with the sulfur atoms in the former. A series of empirical rules to predict the 11B chemical shifts for closo-boranes and closo-heteroboranes were devised by Teixidor et al.22 The aim was to utilize symmetry factors, which strongly influence the paramagnetic term, to obtain both the spectral pattern

Fig. 4

The Structure of the nido-carborane anion [7,8-C2B9H12] showing atom numbering, (see also Section 9.05.2.1.2).

66

NMR of carboranes

Fig. 5

The 11B NMR spectrum, recorded in d6-acetone, of the anion [7,8-C2B9H12] showing signal assignments.11

and the order of the shifts. This was more ambitious than earlier predictive studies of nido-boranes which focussed on the nature of any bridging hydrogens present and their subsequent tautomerism.23 Work by Wrackmeyer24 utilized CNDO/S calculations to derive charge densities at boron together with BeH bond orders, thereby demonstrating that 11B chemical shifts in carboranes can be interpretable on the basis of density matrix changes. In 1992, Her mánek published an early review describing the various shielding and deshielding effects influencing 11B chemical shifts.25 In this work, the author again exemplified the significance of the paramagnetic shielding component, sP within the overall nuclear screening expression. The Average Excitation Energy Method can be used to obtain the value of the paramagnetic term:

Fig. 6 The structure of 4-Cp-4,1,12-closo-CoC2B10H12. Burke, A.; McIntosh, R.; Ellis, D.; Rosair, G.; Welch, A. Collect. Czech. Chem. Commun., 2002, 67, 991–1006.

NMR of carboranes

67

Fig. 7 The 11B NMR spectrum, recorded in d-chloroform, of 4-Cp-4,1,12-closo-CoC2B10H12. All boron atoms in the cluster occupy unique environments, additional complexity in this spectrum results from the presence of 11B-1H coupling.

m e2 h 2 sLpðAÞ ¼  e 2 < r 3 >2p Pu 6pm DE where DE is the average excitation energy, < r 3 >2p is the size of the 2p orbital (orbital expansion term) and Pu the elements of the bond-order matrix. The negative sign within the formula determines that an increase in the size of the paramagnetic shielding term leads to a decrease in nuclear shielding and a consequent shift of the signal to higher frequency. Buhl and Schleyer26 used IGLO methodology (Individual Gauge for Localized Orbitals) to calculate 11B chemical shifts in boranes and carboranes, employing three sets of ab-initio geometries, 3-21G, 6-31-G* and MP2/6-31G*, it being observed that agreement between experimental and computed 11B shifts was significantly better for the MP2/6-31G* geometries, than for the IGLO shifts. 11B shift computations at a correlated (GIAO-MP2/TZP’, GIAO ¼ Gauge Including Atomic Orbitals) level of ab initio theory was assessed by Schleyer et al.,27 this approach performing better for specific “strained” molecules, e.g., 1,5-C2B3H5, than did some earlier work involving uncorrelated wave functions, though for many species, no significant improvement was noted. The authors argued that the superior results garnered for this protocol arose from the previous omission of correlation effects detrimentally affecting agreement with experiment for specific cases where these may be significant. The suggestion was made that “small, strained carboranes” require a high level of correlated theory to accurately account for geometries and chemical shifts.26 Schleyer28 has also used ab-initio/IGLO, GIAO/NMR calculations to challenge 11B (and 13C) NMR assignments of the postulated closocarborane structure of 3-Me2-1,2-C2B3H3. Rearrangement to a more stable 1,5-C2B3H3 form was noted to involve only a modest energy barrier. This isomer also is consistent with the known observed structural patterns of closo-carboranes, viz., the carbon atoms occupy the sites of lowest co-ordination and prefer to be non-adjacent in the thermodynamically more stable structures. IGLO calculations of the 11B shifts of the C-monosubstituted carborane, 1-Ph-1,2-closo-C2B10H11 were carried out by Welch et al. and published in 1996.29 These reproduced well the experimental values with the exception of those associated with B(9, 12) which were slightly overestimated. Onak and Barfield30 studied per B-Cl derivatives of C2B4H6 utilizing ab-initio IGLO 11B and 35Cl NMR calculations, predicting, by comparison with experimental data, that the structures of the compounds were more likely to be of a “classical” non-polyhedral type, rather than “carborane-like.” Other work on the IGLO/NMR approach to 11B shifts for hexaboranes and carbapentaboranes was carried out by Onak31 in 1998, a key conclusion being that tautomerism involving the incipient bridging hydrogen atom in these species, appeared more facile in the case of the borane clusters, than for the carborane. Spencer et al.32 examined the effects of paramagnetic samarium (II) ions on both neutral and anionic carborane (and borane) clusters while Schleyer et al.33 calculated 11B shifts for a 2,4-dicarba-hexaborane using the GIAO method. This cluster had previously been claimed as the first nido-2-pentaborane derivative but the observed chemical shifts were more consistent with the new and modified proposed structure, indicating the power of computational NMR methods in structure determination. The GIAO approach was also used by Maguire, in calculating11B chemical shifts for lithium and sodium derivatives of nido-[2,4(SiMe3)2-2,4-C2B4H4]2, in addition to other related closo- and nido-carboranes.34 The authors found that an approach at either the HF/6-311G** or the B3LYP/6-311G** level of theory provided good agreement in all cases, with recourse to the latter required for subjects where electron correlation effects were considered to be important, e.g., for 1,5-C2B3H5. In this case, the DFT results were far superior to those acquired using the Hartree-Fock model. Computation of 11B (and 1H and 13C) chemical shifts, and their applications in structure elucidation was the subject of a review by Her mánek,35 published in 1999. This work is a comprehensive overview of the contemporary knowledge of borane and carborane NMR spectroscopy, including discussion of empirical rules allowing

68

NMR of carboranes

signal assignment (BH vertex connectivity, “hydrogen-bridge” rule, “Edge” rule, antipodal effect (see also Section 9.05.2.1.3), trans effect and the b Effect). The aforementioned nido-[7,8-C2B9H12] anion was the subject of further study by Onak,36 site-specific deuteration studies confirming that, in the deboronation reaction converting the closo-C2B10H12 species to the anion, the boron lost is that adjacent to the two carbon atoms within the cluster (B(6) in Fig. 2). There had been some debate over the precise structure of [7,8-C2B9H12], specifically whether to formulate the “second” hydrogen associated with the B(10)H2 fragment as bridging37 or terminal (endo). Calculations by Onak36 to determine 11B chemical shifts (GIAO) and 1J(11B-1H) coupling constants (FTP-INDO) for (B10)H2 appeared to support a bridging mode in solution phase, with possible tautomerism between the B(10)-(B9) and B(9)-B(11) positions. The structure depicted in Fig. 4,11 indicating the presence of a terminal hydrogen, was determined by X-ray crystallography and therefore assumed to be the favored solid-state structure. Investigations on substituted nido-dicarbahexaboranes, carried out by Maguire and Hosmane38 involved GIAO computation of the 11B shifts of a series of B-alkylated derivatives. Teixidor39 presented a synthetic and computational study of the halo-substituted carborane, 3-I-1,2-closo-C2B10H12, and revisited the topic of the paramagnetic shielding contribution to 11B shifts more generally. For 1,2-C2B10H12, the authors rationalize the strength of the sP term by invoking strong overlap between low-lying unoccupied pꓕ orbitals and appropriate energy-rich occupied orbitals (Fig. 8). Perpendicularly placed s/pꓕ combinations produce deshielding contributions, perpendicular to the s/pꓕ plane, with the magnitude of the specific paramagnetic effects dependent on the electron density in the BeH bond in question. The order of this is BH(9,12) > BH(8,10) > BH(4,5,7,11) > BH(3,6). Therefore the largest single sP relates to BH(9,12) and the smallest to BH(3,6), reflecting the order of the 11B shifts presented in Fig. 3. Turning to 3-I-1,2-closo-C2B10H11, it is noted that the substituted boron atom B(3) displays an 11B shift some 14 ppm upfield, compared to that in the unsubstituted cluster. This is rationalized in terms of the lone pairs on the iodine interacting with the cluster pꓕ orbitals, increasing the electron density at B(3), thus augmenting the shielding term sd and shifting the resonance upfield. The calculations demonstrated that agreement with experimental chemical shift of the B(3) cage boron atom was imperfect in the iodosubstituted cluster, the discrepancy being ascribed to possible solvent effects influencing the experimental values. Rankin et al.,40 determined accurate molecular structures of the three isomeric icosahedral carboranes, 1,2-, 1,7- and 1, 12carborane from gas-phase electron diffraction, and then used the GED geometries to calculate NMR shifts at the GIAO-B3LYP/6311G* level. As with other studies, good agreement with experiment was reported, though the author notes that, despite the gas-phase structures being retained in solution, solvent effects would be expected in the latter medium. B-ethynyl substituted monocarba-closo-dodecaborates41 and dicarba-closo-dodecaboranes42 were the subject of a studies by Finze; experimental chemical shifts and coupling constants were well reproduced by GIAO methods at the B3LYP-6-311 þþG(2d,p) level of theory. The arachno nine-vertex species, 4,6-(CH2)2 B7H9 and 4,6-S2B7H9 were the focus of study for Wann and Maguire,43 calculations at the GIAO-MP2 level establishing reasonable agreement between theory and experiment for 11B chemical shifts of the compounds studied. In an attempt to ascertain whether the putative cationic closo-carborane family of clusters, [C3Bn  3Hn]þ might be accessible, Hnyk44 carried out a computational study (11B and 13C chemical shifts) on these currently unknown species, again, utilizing the GIAO-MP2 approach, concluding that they were potentially viable compounds. NICS studies (see also Section 9.05.7) indicated these species to be three-dimensional aromatics, in most cases displaying NICS values not dissimilar from those of classical closo-borane anions [BnHn]2. NMR shift calculations (including for 11B and 77Se) were also part of a study by Wrackmeyer45 in

Fig. 8 Perpendicular disposition of the occupied sBH and the Atomic pꓕ orbitals in 1,2-C2B10H12. Not all orbitals are shown. Reproduced from reference Vi nas, C.; Barberà, G.; Oliva, J.; Teixidor, F.; Welch, A.; Rosair, G. Inorg. Chem. 2001, 40, 6555–6562.

NMR of carboranes

69

2013, on a dicarba-closo-dodecaborane annelated 1,3,2-diselenaphospholane, these being carried out using the Gaussian 09 package with optimized geometries at the B3LYP/6-311 þ G9(d,p) level. The same author46 applied the DFT methods, B3LYP/6-311 þ G(d,p) and B3LYP/6-31þ G9(d) in the computation of 11B shifts and a range of coupling constants (including 13C-1H and 11B-1H) for the carborane, hexaethyl-2,4-dicarba-nido-borane and deprotonated derivatives. The calculated chemical shifts show good agreement with experimental results. A combined electron diffraction and computational study of the disubstituted carborane, closo-9,12-I2-1,2-C2B10H10 was carried out by Mitzel, Hnyk and Wann.47 Shielding tensors were calculated using the GIAO-MP2 level applying the ZORA (zeroth-order regular approximation). Despite use of the latter correction, agreement with experimental 11B shifts for the substituted boron atoms, B(9,12) proved unsatisfactory. Adoption of a level of theory that accounting for relativistic spin-orbit (SO) coupling significantly improved the results, most dramatically for these iodine-substituted boron atoms. Additional magnetically induced current field calculations for this species supported the existence of strong spin-orbit coupling via the HALA (heavy atom-light atom mechanism).48 Hnyk49 had established the existence of a similar phenomenon during the investigation of the mono-B-iodinated clusters, [12-I-1-CB11H11] and [7-I-1-CB11H11] where SO coupling was found to strongly influence the 11B shifts of the iodosubstituted boron atoms. Similarly, the 10-vertex, X-nido-5,6-C2B6H11 (X ¼ Br, I)50 displays computed SO influence on the 11B shifts of the heavy-halogen-substituted boron atoms. GIAO-MP2/II calculations where the relativistic two-component ZORA protocols (designed to take account of SO coupling) are omitted show particularly large discrepancies for the Br/I-substituted sites. 2,5-Bridged-1-carba-arachno-pentaborane derivatives were synthesized by Wrackmeyer51 et al. 11B shifts, computed by DFT at the B3LYP/6-311 þ G(d,p) level of theory, showed good agreement with experiment. Similar calculations were carried out for hexaethyl-2,3,5 tricarba-nido-hexaborane(7), together with the corresponding monoanion and gold and rhodium complexes.52 A recent approach from Yu applied the GIAO method to a series of boron-containing molecules.53 The use of linear regression correlating calculated isotropic shielding constants with experimentally determined NMR chemical shifts was shown to give improved predictability of 11B shift values. The calculations were carried out across eight different levels of theory to determine the best approach. Stibr has used an Alpha Shift Correlation technique to assess 11B NMR shielding effects in exo-halogen substituted boranes54 and carborane derivatives.55 The ASC approach arises from the notion that a substituent attached at a site in any boron cluster induces a significant NMR shift at that site (alpha or a shift) whose magnitude depends on the nature of both substituent and parent molecule. Other positions in the cluster will also be affected, the size of these changes being related to that of the a-shift in a linear fashion. In this contribution a range of substituted carboranes were examined. The graphical treatment demonstrated allows extraction of a “g” factors, parameters which reflect the sensitivity of specific positions, in a given structure, to substituent changes. The ASC method is described as an important tool for quantitative analysis of substituent NMR effects in exo-substituted boron clusters. The traditional GIAO approach to 11B shift calculations was compared to GIPAW (Gauge Included Projector-Augmented Wave) by Hillebrecht56 in the computation of isotropic 11B NMR shifts in a range of boron-based clusters. The icosahedral 1,2-,1,7- and 1,12-carboranes were examined, together with other heteroboranes, including structurally analogous phosphaboranes. Compared to earlier work40 using hybrid functionals (B3LYP) and working from GED geometries, higher deviations were obtained with the conservative conversion (dref). Application of hybrid functionals to the new approach reduced the deviations in these cases.

9.05.2.1.3

Antipodal effect

The antipodal effect represents a significant influence on the observed chemical shifts of skeletal cluster atoms in polyhedral heteroboranes. For clusters containing a heterovertex, E, the “A” effect moves the signal of the antipodal boron to higher or lower field (compared to E ¼ BH) depending on the electron density on E. Cages containing B-X (rather than B-H) vertices shifts the antipodal 11 B signal to higher field by 1-15 ppm (e.g., X ¼ I, Br, Cl, SR, F or OR). The phenomenon is not restricted to boron-boron transmission but can be delivered to or from boron to any antipodal atom-vertex or even between heteroatoms (e.g., 13C). Such an effect has been observed in basal boron substituted-B5H9 derivatives,57 -decahydrodecaborates,58 -carba-hexaboranes,59 -dicarbaheptaboranes60 and thia-closo-dodecaborane.61 Todd et al.62,63 reported a similar observation in the icosahedral carboranes, noting that in the 11B NMR spectrum of 9,10-I2-1,7C2B10H10, the signal arising from B(2,3), is shielded by some 4.8 ppm compared to that arising from the equivalent positions in the parent (Fig. 9). As a similar effect was observed in the analogous 9,10-Cl2-derivatives, the author postulated that it may stem from a perturbation of the shielding of the nucleus antipodal to the point of halogen substitution. Further studies on the antipodal effect as applied to substituted dicarba-closo-carboranes were described by Stibr and Plesek.64 In this work, the impact on chemical shift of antipodally disposed atoms, as a result of bromine substitution at various sites in the icosahedron was analyzed. Her mánek et al.65 drew an analogy between the antipodal effect in polyhedral heteroboranes and a parallelism in organic pelectron systems. It is argued that the order of the magnitude of the antipodal effect, increasing through the series of substituents, SH < I < Br < Cl < OR < F, suggest that the degree of electron donation is the predominant factor, drawing comparison with the mesomeric effect, well-established for aromatic ring systems. However, the authors emphasize caution in the analogy, the p-aromaticity of benzenes necessarily being distinct from the so-called pseudoaromaticity of three-dimensional polyhedral boron clusters. The same author66 has undertaken a more rigorous computational approach to the subject. Utilizing CNDO/2 and extended Hϋckel-type calculations, it was shown that, for two series of modified boron cages, EB11H11 and EB9H9 (Fig. 11) where E was a hetero-vertex; decreasing electron density on this vertex led to a fall in the electron density in the px/py orbitals associated with

70

NMR of carboranes

Fig. 9

The icosahedral disubstituted carborane, 9,10-I2-1,7-C2B10H10, highlighting the atoms antipodal to the halogenated vertices.

the antipodal atom, and an increase in the pz orbital. Table 2 indicates the consequences of these effects on the boron chemical shifts, for a series of E-substituted clusters within the two families. Good linear, correlations were identified between the antipodal 11B shift and the px/py electron density, and with an inverse slope, the pz electron density. The implication, through progressive low-field shift of the 11B resonance with decreasing electron density on E, is that the effect transmitted via px/py is key to rationalizing the NMR observations since, in turn, this factor dominates the paramagnetic shielding term sP (see also Section 9.05.2.1.2). Fehlner and Fenske71 used Fenske-Hall MO methodology combined with the Ramsey sum-over-states (SOS) approximation to investigate the shielding of 11B nuclei in boron-containing clusters, previously, this approach had proven successful in determining the paramagnetic component in the shielding of 13C nuclei. It was concluded that this methodology was more successful when considering restricted groups of compounds, somewhat more accurate correlations with observed shifts being obtained for broader groups of boranes with the IGLO method.72 The carborane series, 2-X-1,6-C2B4H5 (X ¼ Cl, Br, I and Me) was investigated in detail with the authors arguing, on the basis of a cluster MO description, that the magnitude of the antipodal effect is related to the strength of the interaction of the substituent with the cage. The latter, calculated from the results of photoelectron spectroscopy decreases in the order Cl > Br > I, matching the order of the calculated magnitudes of the antipodal effect. Complementing earlier work,66 Schleyer73 carried out studies on the 10-vertex heteroborane series, closo-EB9H9 (E ¼ BH2, AlH, CH, SiH, N, P, NH, PH, O or S) (Fig. 10). The authors conclude that increased paramagnetic contributions arising from lower DE(HOMO-LUMO) and a larger antipodal B2p character of the HOMO may rationalize the computed trends of 11B shifts for the antipodal boron, B(10) across the series. In the 10-vertex set, this “polarization” of the HOMO appears to be significant in determining the magnitude of the antipodal effect, being especially notable for more electronegative first row heteroatoms. It is also noted that, more generally, the antipodal effect is especially pronounced in 10-vertex clusters. Fox and Wade74 report on structural and NMR studies on substituted 1,2-carborane derivatives 1-X-2-R-1,2-C2B10H10 (R ¼ Ph, Me) where X ¼ NO, N ¼ NR0 or NHR0 . In such compounds the antipodal shift of B(12) increases as the degree of p-bonding from the substituent increases. The authors propose that the 11B shifts can therefore be used as an indicator of the scale of exo p-bonding in complexes of this nature.

Table 2 Nature of E S CH BH2 AlMe2

The antipodal effect expressed in the cluster families EB9H9 and EB11H11. Shift in signal for antipodal boron in EB11H11 ppm 67

34.0 8.468 0 10.270

See Hermánek, S.; Hnyk, D.; Havlas, Z. J. Chem. Soc. Chem. Commun. 1989, 1859–1861.

Shift in signal for antipodal boron in EB9H9 ppm 73.5 6169 31.8 0

NMR of carboranes

71

Fig. 10 Closo-EB9H9, indicating the position of B(10) antipodal to the hetero-vertex. Reproduced from Bϋhl, M.; Schleyer, P.v.R.; Havlas, D.; Hnyk, Inorg. Chem. 1991, 30, 3107–3111.

9.05.2.2

J-coupling

Much of the work previously referenced in Section 9.05.2.1 also relates to J-coupling.26,34,39,41,44,51,52 The following section focusses on further specific research concerned with this topic.

9.05.2.2.1

B-B coupling and relaxation

With a nuclear spin quantum number of 3/2, 11B is classified as a quadrupolar nucleus (spin value, I > 1/2). Routine 11B NMR spectra of carboranes generally do not show observable 11B-11B coupling, the value of 1J(11B-11B) being typically 14–28 Hz,75–77 smaller than the spectral linewidths and so special techniques are generally required to extract the experimental values, though, as will be described below and as with chemical shifts, these parameters can be derived by computational means. In the section below, reference is made to work on boranes in addition to that on carboranes. Some of the findings from the former work may be of interest to students of the latter. Allerhand78 had noted in 1969, that the 11B NMR spectra of pentaborane-9 and hexaborane-10 did not display the expected fine structure from the anticipated B-B coupling. Following the measurement of the spin-lattice relaxation times (T1) and subsequent comparison of 10B and 11B relaxation rates, it was concluded that the major contribution to T1 was a quadrupolar mechanism. Evaluation of the quadrupole coupling constant for triethylborane at 5.0 MHz implied that electric-field gradients at the boron centers were relatively small in these boron hydrides suggesting that rapid quadrupolar relaxation may not be responsible for linebroadening in the spectra of B2H6 and B5H9 (the line widths of 11B lines in these compounds is predicted to be < 10 Hz), their appearance instead being down to unresolved small couplings. The number of such individual coupling relationships can become significant for quadrupolar nuclei, and especially for those with nuclear spin quantum numbers, I, greater than one, this arising from the nE ¼ 2I þ 1 rule, where nE is the number of levels in the Zeeman manifold. This can be conveniently illustrated in an energy level/transition diagram79 (reproduced in Fig. 11). Odom and Ellis80 went on to further examine the 11B spectrum of pentaborane (structure presented in Fig. 12) at relatively high resolution (32.1 MHz). Through the application of 11B-1H decoupling, they were able to expose the 11B-11B coupling between the basal and apical boron atom, the former showing a well-defined quartet with a measurable 1J(11B,11B) ¼ 19.4 Hz (Fig. 13). This was the first direct observation of 11B-11B coupling. The transmission of BB coupling through bridging B-H-B units was compared to that in other bonding situations by Odom and Ellis.80 Through use of double and triple resonance techniques, they were able to show that the presence of B-H-B bridges led to significant reductions in the magnitude of the coupling constants in boranes where this mode of bonding was extensive, e.g., B4H10 (upper limit 0.3 Hz) and B2H6 (upper limit 1.1 Hz). A different approach to the determination of BB coupling constants was also published by Odom and Ellis in a separate contribution.77 For Lorentzian lines, the linewidth at half-peak-height (Dn1/2) ¼ 1/pT2* where T2* includes an expression taking into account magnetic field inhomogeneity (gDHo/2). Assuming the extreme narrowing limit (uo2sc 2 < < 1, where uo ¼ transition frequency and sc ¼ rotational correlation time) then T1 ¼ T2. Therefore, determination of the spin-lattice relaxation times will provide idealized values for natural line-widths. For 11B isotopically enriched B4H10 (Fig. 14), values of T1 for B(1,3) and B(2,4)

72

Fig. 11 2370.

NMR of carboranes

Energy levels and transitions for two coupled spin 3/2 nuclei. Reproduced from Sprecher, R.; Carter, J.; J. Am. Chem. Soc. 1973, 95, 2369–

were measured at  20  C at 62.6 and 13.1 ms respectively, translating to Dn1/2 of 5.1 and 24.4 Hz respectively. Through simulation of the lineshapes, it was possible to extract upper limit values for 1J(B(1),B(2)) of 1.0 Hz, again significantly reduced for this B-H-B bridged unit and experimentally unresolved. Simplistically yet intuitively, the values of BB coupling constants are greater for bonds where electron density between the interacting centers is highest. CNDO/S calculations were applied by Wrackmeyer24 to the evaluation of J(11B,11B) coupling constants in boron hydrides, demonstrating a correlation between the reduced coupling constant 1K(11B, 11B) and the corresponding element of the charge density bond order matrix, thereby demonstrating that the value of J(11B,11B) is related to the fractional s character in the bonding orbitals. Grimes81 carried out measurements of spin-lattice relaxation times for 11B atoms in carboranes. For nuclei possessing spin > 1/2, T1 is dominated by quadrupolar interactions rather than internuclear couplings, a hypothesis supported by the similarity between T1 values measured with and without proton decoupling, consequently, the experimental values of T1 in such cases represent an accurate measure of the true parameter. Trends observed include longer T1 values for the apical boron atoms in those polyhedra where such distinctions exist (e.g., pentagonal pyramidal/bipyramidal structures). These and other observations may be explained on the basis of variations in local field gradients (lower for apical boron atoms, hence a longer T1), or correlation times, sc related to motional effects (T1 shortened by the substitution of a boron vertex with a metal-ligand unit, increasing molecular size, therefore raising sc). It is argued that T1 measurements are a valid tool for spectral assignment and structure determination in carboranes. Grimes published further contributions to the topic of B-B coupling in boron hydrides.82 In this work, the notion of broadened lines in the spectra being the result of unresolved couplings was disputed. “Multiplet Collapse,” the degree of which is determined by the size of the parameter 2pJT1 can lead to various line shapes, including a single line where this value is less than one. Scalar relaxation is also associated with 2pJT1 < 1, in such cases the rapid changes in the spin state of the quadrupolar nucleus creates a local, fluctuating magnetic field which may act as a vector for efficient relaxation, again, a single line may then result.

Fig. 12

The Structure of B5H9. Reproduced from Odom, J.; Ellis, P.; Walsh, H.; J. Am. Chem. Soc. 1971, 93, 3529–3530.

NMR of carboranes

73

Fig. 13 Experimental 11B spectrum of a 40% solution of pentaborane in hexafluorobenzene. The signal due to the basal boron atoms is on the left. Reproduced from Odom, J.; Ellis, P.; Walsh, H.; J. Am. Chem. Soc. 1971, 93, 3529–3530.

Fig. 14

Structure of tetraborane, B4H10.

Direct BB coupling is able to be observed in linked boron and carborane cages where the clusters are connected by a boron-boron single bond. Sneddon et al.83,84 prepared such linked clusters, including 1,50 -(2,4-C2B4H6)2 where the connection between the two carborane units is via boron atoms B1 and B50 (Fig. 15). The proton-decoupled 11B spectrum of this compound clearly displays the

Fig. 15 The structure of 1,50 -(2,4-C2B4H6)2 and the 11B{1H} spectrum showing the quartet from direct B-B coupling. Reproduced from Astheimer, R.; Plotkin, J.; Sneddon, L.; J. Chem. Soc. Chem. Commun. 1979, 1108b–1109.

74

NMR of carboranes

expected four-line signal for B1, indicating coupling through the 2c–2e bond to B50 . The value of 1J(11B,11B) is 109 Hz, significantly greater than that reported for boron-boron coupling in the delocalised framework of the cluster. Sneddon85 went on to explore this topic in greater detail, determining the estimated value of 1J(10B,11B) (26.6 Hz) for the coupling between the linking boron atoms in 2:20 -[B5H8]2, again a 2c–2e bond. It proved possible to use Wrackmeyer’s24 findings that the size of the B-B coupling constants in boranes are related to the degree of s-orbital hybridisation in the bonding to calculate the latter parameter. It is to be expected that the value of 1J(11B,11B) will be greater for boron atoms involved in 2c–2e bonding than for those in delocalised cluster bonding networks where the s-orbital character is reduced. Leffler86 sought to determine the quadrupolar coupling constants of the icosahedral carboranes, 1,2-, 1,7- and 1,12-C2B10H12. These were derived from experimental T1 values for 11B and 13C, applying a series of assumptions and using a simple ratio method, the asymmetry parameter for 11B being ignored. The results showed a decrease in the weighted average on moving from the 1,2(1077 kHz, a similar value had been previously determined87) to the 1,12-isomer (887 kHz). The values displayed poor agreement with those calculated, a discrepancy arising from the difficulty of partitioning atomic charges and deriving accurate field gradients from the calculations. Galasso and Fronzoni88 used ab-initio methods, coupled Hartree-Fock (CHF) and equations-of-motion (EOM) to compute nuclear boron-boron spin-spin coupling constants for a series of boranes, the calculations indicated that for a 2c–2e bond the coupling constant should be considered positive, also that the Fermi contact term dominates in 1J(11B, 11B) (and 1J(11B,1H) irrespective of the nature of the bonding, the remaining electron-nucleus spin perturbations included in Ramsey’s original theory89 (orbital-diamagnetic, orbital-paramagnetic and spin-dipolar) are less significant in these cases. Application of DFT to the calculations of B-B (and other) coupling constants was explored by Onak and Barfield.90 The sensitivity of the dominant Fermi-contact term to electron correlation effects restricts the ab-initio approach described above to small clusters, DFT is more suited to the treatment of these effects. A large number of polyhedral boranes and carboranes were subject to study and the results are good in most cases, there being a linear correlation between the calculated Fermi terms and experimental values. Further studies on the 11B-11B (and 11B-1H) coupling constants were carried out by Wrackmeyer in 2004.91 These DFT calculations considered contributions from FC but also from SO (spin-orbital) and SD (spin-dipole terms) and showed good agreement with experimental data. This work included treatment of highly fluxional clusters (e.g., [B3H8]) where the NMR parameters were calculated on the basis of optimized geometries, regarded as minima on the potential energy surface. Compounds that had not been synthesized, including B3H7 and B4H8 were also the subject of computational study. Wrackmeyer92 carried out calculations to extract 11B-11B coupling constants for some five- to seven-vertex carboranes, again using the DFT approach, computed values showing good agreement with experiment. In this study It proved possible to use the calculated values to inform on the nature of the cluster bonding. It is noted that the 11B-11B coupling in the tetragonal plane of the six-vertex clusters, 1,2-C2B4H6 (Fig. 16) is unexpectedly strong. This arises from a significant s-orbital contribution to the bonding involved, an observation correlated to a negative 13C-13C coupling constant, in turn reflecting a low s-element to the CeC bond. Much of the s electron pool from the C-C connectivity is lost to the cluster, reinforcing 11B-11B and 11B-13C spinspin interactions. In contrast, the 11B-11B values for the boron atoms within the trigonal planes of the bipyramidal clusters 1,5-C2B3H5 and [1CB4H5] are small and possibly negative. Examination of a possible antipodal effect on spin-spin coupling constants suggests a dominant influence from direct bonding with non-contact contributions to the J values now non-trivial, the trends in these terms being opposite for 1J and antipodal 2J values. 1 11 11 J( B, B) and 1J(11B,13C) for derivatives of hexaethyl-2,4-dicarbahexaborane and hexaethyl-2,3,5-tricarba-nido-hexaborane were calculated by Wrackmeyer et al.52 The structures of the clusters are shown in Fig. 17. The B-B coupling constants involving the apical, formally six-co-ordinate B(1) are computed to be small (1.5–17.9 Hz) and of either sign. Computed B-B coupling constants for derivatives of a series of peralkylated tetracarba-nido-boranes showed good agreement with experimental values, where these were available.93 In the case of the cluster shown in Fig. 18, 2D COSY NMR (See also Section 9.05.8.2)

Fig. 16

The structure of the six-vertex carborane, 1,2-C2B4H6. Reproduced and modified from Wrackmeyer, B.; Z. Naturforsch. B 2005, 60, 955–961.

NMR of carboranes

75

Fig. 17 The structure of the six-vertex carboranes, hexaethyl-2,4-dicarbahexaborane (1) and hexaethyl-2,3,5-tricarba-hexaborane (2). Reproduced from Wrackmeyer, B.; Schanz, H-J.; Milius, W.; Veith, M., Eur. J. Inorg. Chem. 2015, 4101–4107.

is unable to establish unambiguous B-B connectivities in most cases, the calculated values for 1J couplings between boron atoms in the upper and lower belts are small and negative. Further structural information is available from 11B-13C interactions (see also Section 9.05.4).

9.05.3

10

B NMR spectroscopy

The less abundant, yet still NMR active isotope of boron, 10B is also quadrupolar (I ¼ 3), therefore displaying similar features to that of 11B, namely broadened resonances and poorly resolved couplings to some nuclei. The value of I results in higher multiplicities than for 11B. The resonance of a spin-1/2 nucleus e.g., 19F, coupled to 10B would be expected to show a seven-line spectrum from the

76

NMR of carboranes

Fig. 18 Structure of 1,2,3,4,5,6,7,8,9,10-R-2,6,8,10-tetracarba-nido-decaborane (R ¼ Me or Et). Reproduced from Wrackmeyer, B.; Schanz, H-J.; J. Organomet. Chem. 2015, 798, 268–273.

2nI þ 1 relationship. The natural abundance of 10B is substantial at 20% therefore distinct signals arising from coupling to the two isotopes may be visible in spectra of nuclei where there is coupling to boron, e.g., the 19F spectrum of BF4 displays both four- and seven-line multiplets associated with the 11B and 10B isotopomers, the distinct signal groups arising from the isotopic shift associate with the two nuclides. However, there appears to be no record of any studies of this effect in the field of carboranes. Much work has been carried out on boron hydride clusters and diborane and some of this is described below, with the hope that it will contribute to an appreciation of the situation for carboranes. Ellis and Odom94 make reference to an isotopic effect in 11B-11B/11B-10B resonances in pentaborane. In the proton-decoupled 11 B spectrum the expected 1:1:1:1 quartet resulting from 11B-11B coupling between basal and the apical boron atom is distorted, possibly due to interference from a slightly offset 1:1:1:1:1:1:1 septet from 11B-10B coupling. In extremis, the presence of unresolved 11 10 B- B coupling in some boron hydride clusters poses difficulties in attempting to measure 11B-11B coupling constants accurately, isotopically enriched samples being desirable for these studies.82 In diborane, the two boron atoms become equivalent by NMR in the presence of proton decoupling, in this case 11B10B coupling can be observed and an upper limit for the value of 1J(B,B) determined at 1.1 Hz.77 This is significantly different from a value (5  2 Hz) derived from computer simulation of NMR lineshapes obtained from a 50% 10B enriched sample 50%11B:50%10BD6 derivative, with deuterium decoupling during acquisition. Other work by Farrar et al. had obtained an upper limit value of 3 Hz for 1J(11B, 10B) in a similarly enriched sample.95 The work of Allerhand78 has been referred to previously in connection with the relaxation of 11B nuclei in diborane and pentaborane. In this paper, the relaxation times of 10B nuclei were reported and the ratio of 10B T1/11B T1 determined at 1.5–1.7 for the boron atoms of B5H9, close to the value of 1.534, characteristic for a quadrupolar-dominated relaxation mechanism. Direct measurement of the 11B-10B coupling constant in diborane was achieved by Farrar,96 using high resolution NMR observation (at 21.40 MHz). Direct analysis of the 10B spectrum, gathered with proton decoupling during acquisition reveals 1 10 11 J( B, B) ¼ 1.3 Hz, similar to the above value determined by Odom and Ellis.77 Wrackmeyer97 examined the 10B spectra of tetrachlorotetraborane. At 20  C, the resonance representing the four boron atoms appears as a single line. Under the same conditions, the rate of quadrupolar relaxation (TQ) of the 11B nucleus was found to be 10 ms, not especially rapid, and therefore not accounting for the lack of observable 10B-11B coupling. Increasing the temperature of the sample led to an increase in the line-width indicating the presence of unresolved 11B-10B interactions which did not completely average at the higher temperature. The lack of observable coupling allowed the authors to estimate a value for 1 11 10 J( B, B) at 1.0–2.5 Hz. Boron Neutron Capture Therapy (BNCT)98 constitutes a significant area of interest for boron cluster chemists and has been regarded as a promising binary treatment for certain cancers, particularly those deep-lying, e.g., in the brain, head or neck. This process, where tumors are specifically targeted with boron containing drugs and then exposed to a flux of neutrons of the required energy, requires the enrichment of compounds in 10B as this isotope alone will fragment in collision with thermal neutrons to produce the excited 4He2þ and 7Li3þ nuclides which can destroy the malignant cells. Though carboranes, due to their relatively high boron content, have been one of the compound groups investigated for possible BNCT application, there is little evidence in the literature of extensive use of 10B NMR in this research, much of the work has concentrated on non-enriched surrogate compounds, characterized by 11B NMR.99 Crescenzi100 applied 10B NMR Spectroscopy to evaluation of the boron content in the conjugate HApCB, comprised of an npropyl carborane unit linked to hyaluronan, a glycosaminoglycan. A review of the role that NMR has played more generally in BNCT is available.101

NMR of carboranes

9.05.4

13

77

C NMR

13

C NMR is less routinely carried out as part of carborane characterization than 11B or 1H. Though a spin-1/2 nucleus like 1H and unlike 11B, 13C has a natural abundance of only 1.1% and is significantly less sensitive than either of the other nuclei (approximately 6000 times less sensitive than 1H, DP(13C) ¼ 1.7  10 4 where DP(1H) ¼ 1). The chemical shifts of carbon signals in icosahedral carboranes appear close to the region associated with carbon resonances of alkynes, (d ¼ 50–80 ppm), but resonances may exhibit very different shifts in other carborane types (see also Table 3). Fast quadrupolar relaxation of the 11B nuclei can result in significant line broadening of signals from interacting 13C nuclei, exemplified by the 13C{1H} NMR spectrum of 1,2-carborane, presented in Fig. 19 (n1/2 ¼ 9.3 Hz). The precise lineshapes and observed multiplicities of 13C resonances in boranes and carboranes vary, depending on the local environment and the rapidity of spin-lattice relaxation. C-H coupling in those cases where there is a direct C-H bond is observable in non-decoupled experiments with 1J(13C,1H) ¼ 190–200 Hz. An early review covering aspects of the 13C NMR spectroscopy of carboranes was published by Wrackmeyer in 1979.109 The excellent review by Her mánek35 also includes a section on 13C NMR spectroscopy of carboranes and Table 3, reproduced and edited from this work provides a guide to indicative 13C chemical shifts for some representative examples. Her mánek notes a number of trends relating to nuclear magnetic shielding of the carbon vertex. This increases as follows:

1. With increasing connectivity of the carbon atom62 (1,5-C2B3H5 102.4 ppm; 1,6-C2B4H6 77.2 ppm; 1,12-C2B10H12 63.5 ppm). 2. With increasing presumed electron density of the neighbor vertex (1,2-CAsB10H11 70.0 ppm; 1,2-CPB10H11 68.4 ppm; 1,2C2B10H12 55.5; [1-CB11H12] 52.5 ppm). 3. With increasing electron density of the antipodal vertex E (As< P < CH- 1,7 > 1,6 > 1,2 > 1,5 > 1,3-isomer) does not correlate with the order of stability (1,7 > 1,2 > 1,6 > 1,3 > 1,5 > 3,4), an observation that reinforces evidence from some other studies.159–161 These data suggest that stability is not necessarily determined by the degree of aromaticity, other factors such as connectivity and topological charge distribution may be significant. Magnetic

90

NMR of carboranes

Fig. 33 Example of a carborane-appended 1,3,5-phenylene (carborane is the 1,2-isomer). The 1H NMR spectra of the 1,2- and 1,7-derivatives appear similar, that of the 1,12-species is somewhat different. Reproduced from Dash, B.; Satapathy, R.; Gaillard, E.; Norton, K.; Maguire, J.; Chug, N., Hosmane, N. Inorg. Chem. 2011, 50, 5485–5493.

susceptibilities (c), largely determined by the number of atoms and groups within the molecule and less dependent on connectivity, would be expected to reflect the trends observed in NICS values. Determination of the NICS values for the clusters 1,5-E2B3Y3 where E ¼ N, CH, P or SiH and Y ¼ H, CH3 or NH2 led to the conclusion that these too present significant delocalisation.162 The values vary with the vertex atom/group but show a trend to more positive values along the series Y ¼ H> CH3 > NH2. Calculations by Jemmis et al.163 on the dehydrogeno-forms of 1,2-carboranes (C2BnHn, n ¼ 4, 5, 8, 10, called carborynes) indicate, that according to the NICS values, the presence of the exopolyhedral double bond does not influence the three-dimensional aromaticity of the clusters. Zdetsis164 has introduced a “replacement rule” whereby hypothetical silicon-carbon clusters SinC2H2 are derived from isovalent closo carboranes C2BnH2n þ 2 (n ¼ 1–5). NICS calculations on the silicon clusters confirm them to be aromatic, values ranging from  7.2 ppm (Si3C2H2) to  13.8 ppm (Si4C2H2). No clear trend is noted in the magnitudes as n is varied, instead there being an “odd-even” pattern, with the values for clusters with odd numbers of silicon atoms being lower (more negative) than those where n is even. Kefalidis and Lavallo165 found that the presumed highly substitutionally inert chlorinated cluster HCB11H11 undergoes base induced cycloaddition reactions with organic azides, leading to selective C and B functionalisation (Fig. 36). NICS values suggest that both the carborane and the fused five-membered heterocycle have appreciable aromatic character. For the heterocycle, the NICS(0) (calculated at the center of the ring) ¼  7.8 ppm, NICS(1) (calculated at a point 1 Å above the ring) ¼  8.8 ppm, NICS(1)zz (calculated along the z axis) ¼  19.3 ppm. The carborane retains its three-dimensional aromaticity (NICS ¼  30.8 ppm). Further work in this field has been published by Xie,166 in which calculations, at the B3LYP/6-311 þþG(d,p) level of theory were carried out on a different range of carborane fused heterocycles (Table 6). Again, the values support the presence of significant aromatic character. DFT calculations suggesting significant conjugation between the 3D cage and the 2D p system.

NMR of carboranes

91

Fig. 34 Ethynylmonocarba-closo-decaborates. 1. [12-HCC-closo-CB11H11] and 2. [7, 12-(HCC)2-closo-CB11H10]. Reproduced from Himmelspach, A.; Finze, M. J. Organomet. Chem. 2010, 695, 1337–1345.

Replacement of one of the boron atoms in the macro polyhedral borane, B21H18, with carbon creates a series of isomeric possibilities for the neutral carborane CB20H18.167 The isomer presented in Fig. 37 is found to be the most stable. NICS calculations were carried out at three positions in the cluster, at the center of the face-sharing atoms ( 61.42 ppm), center of the first cage ( 18.40 ppm) and center of the second, carbon-containing cage ( 22.01 ppm). It is noted that the cage containing the carbon atom exhibits greater aromaticity according to this method, carbon being more electronegative than boron will create an environment of higher electron density for the associated cage. The cationic di-carboranes C2B19H18þ similarly show aromatic character through negative NICS values. A group of halogenated closo-borates were examined by Schulz.168 The NICS for silylated and protonated forms of these clusters are all negative, indicating aromaticity. More negative values are associated with higher symmetry and greater number of halogen atoms (example data {[CHB11(CH3)11]}  25.1 ppm; [CHB11H5F6]  34.8 ppm). A series of correlations between NICS and 13C chemical shifts were observed e.g., fluorinated carborates possess the smallest NICS values of those studied whilst presenting the most high-field shifted 13C signals. The concept of the “shielding cone” has been used to understand the behavior of planar aromatics e.g., benzene. MuñozCastro169 has extended this idea to three dimensional aromatics, e.g., [CHB11H11] and “mixture” compounds of combined 2D/3D aromatics, e.g., [PhCB11H11]. The planar species yield a shielding cone, only when the applied field is oriented perpendicular to the ring (Bzind), the spherical monocarborane, by contrast, can sustain a shielding cone under different orientations of the ind field. For the planar-spherical [PhCB11H11], the shielding isosurface for Biso (an isotropic representation of the field, averaging different orientations, therefore resembling random tumbling redolent of the solution state) resembles benzene and [CHB11H11], indicating that both components remain as independent circuits. A similar situation is found to exist for the two neighbor spherical

92

Fig. 35

NMR of carboranes

Structure of the fluorinated anion [1-H2N-CB11F11]. Reproduced from Finze, M.; Reiss, G.; Zähres, M. Inorg. Chem. 2007, 46, 9873–9883. Table 5

NICS values for a series of carboranes.

Compound

NICS value ppm

References

CB5H7 1-Me-CB5H6 1,2-C2B4H6 1,2-C2B4H6 1,6-C2B4H6 1,6-C2B4H6 1,7-C2B6H8 1,2-C2B6H8 1,6-C2B6H8 1,3-C2B6H8 1,5-C2B6H8 3,4-C2B6H8 1,12-C2B10H12 1,7-C2B10H12 1,2-C2B10H12

33.04 33.31 34.86 34.92 34.89 36.01 24.01 21.17 22.68 15.90 17.18 24.40 35.40 34.19 34.10

31a 31a 31a 158b 31a 158b 158b 158b 158b 158b 158b 158b 158b 158b 158b

a

Calculated at the 6-31G*//6-31G* level of theory. Calculated at the GIAO-SCF/6-31G*//MPs(fc)6-31G8 level of theory. Featuring data from Jaballas, A., Onak, T. J. Organomet. Chem. 1998, 550, 101–109, and Schleyer, P.v.R.; Najafian, K. Inorg. Chem. 1998, 37, 3454–3470. b

NMR of carboranes

93

Fig. 36 A carborane fused heterocycle synthesized by base induced cycloaddition of HCB11H11 with organic azide, (R ¼ Ph, 4-FC6H4, 4-MeOC6H4, 2-MeC6H4, mesityl, n-C4H9 or adamantyl). Reproduced from Wright III, J.; Kefalidis, C.; Tham, F.; Maron, L.; Lavallo, V. Inorg. Chem. 2013, 52, 6223– 6229.

Table 6

NICS values for a series of carborane-fused carborand heterocycles.

X

NICS value ppm

CH2 CH NH O S

5.8 9.9 9.6 9.3 9.0

Reproduced from Chan, T.; Xie, Z. Chem. Sci. 2018, 9, 2284–2289.

94

NMR of carboranes

Fig. 37 4-CB20H18, the most stable isomer of the hypothetical carborane CB20H18. Reproduced from Vidya, K.; Jemmis, E. J. Organomet. Chem. 2015, 798, 91–98.

Fig. 38 The 1H (11B-coupled) spectrum of 1,2-C2B10H12, showing the region containing the signals from the terminal B-H hydrogen atoms. The sharper resonance at d3.5 is due to the cluster C-H.

NMR of carboranes

95

Fig. 39 1H spectrum of 1,2-C2B10H12, with broadband 11B decoupling applied, showing the region containing resonances due to the B-H hydrogen atoms. These are significantly sharpened compared to their appearance in the 1H-coupled spectrum (Fig. 38).

aromatics, [CB11H11]22 but when the field is applied along the z or y axis, (Bzind and Byind) the two independent shielding cones from each cluster add, resulting in a common shielding and complementary deshielding surface. NICS values, calculated for the cage-dimers indicate aromatic character in these species ( 24.0 ppm and  24.1 ppm at the TZ2P/PBE0 level of theory for [PhCB11H11] and [CB11H11]22 respectively).

9.05.8

Experimental techniques

One dimensional 11B NMR spectroscopy is straightforward to execute, and good-quality datasets may be acquired within a few minutes. It should be noted, however that there may be interference in the 1D spectra from the presence of amorphous boron environments in the borosilicate glass from which many NMR tubes are constructed. Signal from this may appear as a broad, featureless

Fig. 40 A 2,5-bridged 1 carba-arachno-pentaborane derivative. Wrackmeyer51 has used 13C{11B,1H} decoupling in spectral assignment. Reproduced from Wrackmeyer, B.; Schanz, H-J., Z. Naturforsch B, 2015, 70, 741-745.

96

NMR of carboranes

“hump” in the sample spectrum on which authentic signals are superimposed. If the sample solution is particularly dilute, this feature may dominate. Simple pulse-acquire 11B sequences will show 1J (11B,1H) of typically 100–190 Hz for directly attached, and less than 80 Hz for bridging hydrogens.170 Coupling to more distant hydrogens can generally be ignored as can direct 11B-11B coupling, the value of 1 11 11 J( B, B) at 14–28 Hz, being smaller than the 11B linewidths, in the absence of resolution enhancement (see also Section 9.05.2.2.1). Some structural information can be gleaned from 1D 11B and 1H spectra, e.g., the presence of bridging hydrogens, co-ordination numbers of the boron atoms, also the presence or absence of terminal groups/atoms other than hydrogen may be detected by the absence of observable 1J(11B,1H) coupling. The assignment of the signals to specific boron sites in the cluster is not always straightforward, however. Simple electronegativity-chemical shift correlations that apply in e.g., 1H NMR are far less reliable in 11B spectra (see also Section 9.05.2.1.2), and the profiles are often congested, adding to the difficulty of interpretation. Recourse to additional NMR experiments is often required to achieve satisfactory assignment of the signals.

9.05.8.1

Spin-decoupling experiments

9.05.8.1.1

11

9.05.8.1.2

1

9.05.8.1.3

13

B{1H} experiments

Acquisition of the 11B spectra of carboranes will show those boron resonances representing B-H groups as doublets, this coupling may be suppressed by the application of broadband 1H decoupling using standard sequences. Pioneering experiments carried out by Vickers171 and published in 1966 demonstrated the feasibility of this technique for the three isotopes of C2B10H12, and it is now routine when carrying out 11B spectroscopy.

H{11B} experiments

As has been previously referenced, the 1H NMR spectra of carborane clusters generally show very broad, poorly resolved envelopes for the B-H protons (Fig. 38). Application of broadband 11B decoupling to the 1H spectra can result in significant sharpening of the B-H resonances, in Fig. 39 the 1H{11B} spectrum of 1,2-C2B10H12 reveals more detail in the B-H region, enabling precise chemical shift values to be extracted. Selective 1H{11B} experiments have also been carried out, e.g., Kennedy,172 in studies of diphosphine derivatives of decaborane, Janousek et al. when looking at N-alkyl derivatives of azadicarbaboranes,173 and Wrackmeyer, to help extract the values of 1 11 1 J( B, H) in carborane-fused diselenacyclopentanes.174 Kennedy utilized an 11B{1H} probehead in inverse mode for some observations and a retuned {1H} channel for others. Today such experiments are straightforward to install in standard hardware.

C{11B, 1H) experiments

More sophisticated multiple heteronuclear decoupling experiments have also been carried out. Wrackmeyer51 has applied 13C(11B, 1 H} sequences to assign the B(2,5)Et and B(3,4)Et groups in the 2,5-bridged 1-carba-arachno-pentaborane(10) derivative shown as Fig. 40. The same author used the same experimental sequence to assign the carbon atoms in the cluster 1,2,3,4-tetraethyl-5,6,7,8tetracarba-nido-octaborane(8).93

Fig. 41

11

B-11B COSY spectrum, with assignments according to the structure depicted in Fig. 4, of the carborane anion, [7,8-C2B9H12].

NMR of carboranes

Fig. 42

9.05.8.2

97

The Structure of 1,7-C2B10H12. 11

B-11B COSY NMR spectroscopy

Two-dimensional boron-boron correlation spectroscopy is a useful method of establishing connectivity within the carborane cluster. Strong correlations are normally observed between directly connected boron atom sites and if there is an easily identifiable entry point (e.g., a unique single boron environment, identifiable by the absence of 1J(B-H) coupling in a cluster B-X unit), the cage connections may be mapped, yielding a full assignment. Grimes et al.175 reported, in 1982, the first use of a homonuclear 11B-11B 2-D sequence to reveal direct bonding interactions in a range of boranes and heteroboranes. This experiment, the first demonstration of a COSY sequence applied to quadrupolar nuclei, utilized Jeener’s original 2D NMR176 concept, applied to 11B. The resulting contour spectrum follows the pattern familiar from other COSYlike experiments, a two-dimensional matrix with a diagonal, shown running bottom left to top right, representing the onedimensional 11B spectrum. Off-diagonals, or cross-peaks, arising from the evolution of multiple-quantum coherence from 11B-11B coupling, correlate the on-diagonal signals involved in a J-coupling relationship. As has been previously described, the values of 1 11 11 J( B, B) are small and generally unresolved in the one-dimensional spectra (2pJT1 < 1) yet are large enough to produce significant cross-peaks in the COSY spectra. Clearly, if the spectrum is crowded, with signal overlap, the effectiveness of the experiment is compromised, but for the structural analysis of compounds giving well-resolved spectra where the identification of the cross-peaks is not ambiguous, B-B COSY can be a powerful tool. It also finds application in the study of mixtures, where the cross-peak connectivity patterns from the different components can elucidate both the number of species present, and possibly their identities. Cross-peaks are produced by coupling between adjacent boron atoms within the cluster, those separated by bridging hydrogen atoms (m-H) do not normally display correlations.177 In Grimes’ original paper, the efficacy of the technique was demonstrated for a metalloborane, 6-(C5Me5)CoB9H13, the onedimensional spectrum of which displays six 11B environments 2:2:2:1:1:1, all of which may be assigned from the COSY experiment. Today, high-quality 11B-11B COSY spectra can be acquired in minutes, conventionally accompanied by simultaneous protondecoupling (correctly described as 11B{1H}-11B{1H} COSY). In Fig. 41 is shown the 11B-11B COSY spectrum of the [7,8-C2B9H12]– anion11 together with signal assignments (see Fig. 4 for the molecular structure). Grimes10 published a more detailed addition in this field in 1984, extending the application of B-B COSY experiments, to boron hydrides, other metallacarboranes, and carboranes themselves, including the ubiquitous isomers of C2B10H12. As mentioned above, data from COSY experiments alone may not be capable of providing unambiguous assignments of such high symmetry species, recourse to isotopic labeling experiments being required. In the case of 1,7-C2B10H12 (Fig. 42), identification of B(5,12) and B(9,10) was not achieved in Grimes’ study. Grimes10 also addresses theoretical aspects of the experiment in this contribution. Notably, it is pointed out that the short T1 values associated with 11B nuclides does not preclude COSY being achievable. Despite the presumption that T1 values, short compared to the reciprocal of the coupling constant (i.e., 2pJT1 < < 1) can be problematic for the generation of significant coupling-derived cross-peaks, the proven contribution of residual unresolved coupling to the observed line-widths of 11B resonances would indicate, correctly that the sequence is capable of generating well-defined off-diagonals. There are abundant further examples in the literature illustrating the use and power of BB COSY, including in studies of the [B9H12] anion,177 structural analysis of pentaborane based systems,178 products arising from the deboronation of

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Fig. 43 The 11B-1H correlation spectrum for the anion, with assignments according to the structure depicted in Fig. 4, of the carborane anion, [7,8C2B9H12].

1,7-carboranes with fluoride ion,147 products of fluorination of borane and carborane anions with N-fluoro reagents,148 assignment of boron atoms within the [1-NC-closo-1-CB11F11] anion,153 and the ethynylmonocarba-closo-dodecaborate anions.41 The work by Spencer178 on the application of B-B COSY to the analysis of a series of pentaborane derivatives addressed some issues surrounding the experiment itself. Two principal factors affect the generation of cross-peaks within the 2D matrix, values of the aforementioned T1 time constants, and the build-up of electron density between the “coupling” boron atoms. In this study, through the calculation of relevant relaxation times, the authors were able to show that “missing” cross-peaks in the spectrum of the anion [m-P(C6H5)2B5H7]. were associated with unusually short T1 values. Furthermore, it was concluded that, for the compounds involved in this study, coupled boron atoms giving MNDO-calculated bond orders of below 0.27 did not show observable cross-peaks in the 2D spectra. The previously mentioned absence of cross-peaks arising from B(m-H)B units is also associated with the lack of electron density between the two boron atoms. Spencer178 demonstrates the use of the INADEQUATE experiment, more familiar from 13C-13C systems, in 11B NMR. In these experiments, multiple quantum coherences arising from 11B-11B coupling are the only frequency responses from the acquisition. The conventional chemical shifts are displayed along the f2 (direct) dimension while double quantum frequencies, developing from two coupled atoms at n1 þ n2, occupy the f1 (indirect) dimension. From a known starting point it is possible to map out the molecular connectivity through these coupling relationships. Possibly because of the accessibility of the B-B COSY experiment (unlike the 13C analog), this 11B INADEQUATE sequence has not found widespread use.

9.05.8.3

Heteronuclear correlation spectroscopy

A suite of 2D correlation experiments is available in which boron frequencies occupy one dimension and a second nuclide occupies the other. The most widely used of these, unsurprisingly in view of the preponderance of B-H connectivity in borane and carborane clusters, is the 11B-1H sequence.

9.05.8.3.1

179

11

B-1H correlation spectroscopy

Grimes demonstrated the successful operation of the 11B-1H correlation sequence in 1980. The pulse sequence and technical details are included in the original paper, and the power of the experiment is exemplified through spectral analysis of the carborane 2,4-C2B5H7. The x-axis contains the 1H chemical shifts and the y-axis those of 11B with the latter fulfilling the role of “less sensitive” nucleus in the sequence and therefore, occupying the indirect dimension. The 2D matrix now shows responses arising from 11B-1H coupling, allowing 1H chemical shifts to be mapped onto those of 11B, rather in the fashion of the more familiar 13C-1H (C-H correlation) experiments, commonly used in organic chemistry.180 As both 1D 11B and 1H spectra of carboranes often contain overlapping signals (and 1H spectra are often not resolved in the absence of heteronuclear broadband 11B decoupling), these experiments furnish useful means for resolution of the 11B and 1H chemical shifts in different dimensions. Fig. 43 shows the 11B-1H correlation spectrum for the anion [7,8-C2B9H12]. McFarlane applied this new technique to the spectral analysis of decaborane, introducing heteronuclear decoupling in both dimensions as a modification to the original sequence. It was noted that the application of the 11B-1H correlation approach enabled the mapping of signals from bridging hydrogen atoms onto specific boron sites in decaborane, for the first time.181 11B-1H

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correlation experiments have been used extensively in structure determination studies of carboranes and other boron clusters. For a representative recent example of such work, that also embraces other multidimensional NMR techniques, the reader is referred to a contribution by Musah,182 focussing on the spectral characterization of 2-amino-3-(1,7-dicarba-closo-dodecacarboranyl-1-thio) propionic acid.

9.05.8.3.2

11

B-19F correlation spectroscopy

F- F COSY experiments were carried out by Finze152 within a study of the fluorinated carbadodecaborate anion [1-H2N-closoCB11F11] (Fig. 35) but the abundance of cross-peaks relating most of the 19F environments (due to large 4J and weaker 3J and 5J couplings between 19F) did not lead to unequivocal assignments. Application of 11B{19F}-11B{19F} and 11B{19F}-19F{11B} experiments were used to remove ambiguity. Finze went on to use 11B-19F correlation NMR spectroscopy in other work, e.g., the characterization of [1-NC-closo-1-CB11F11].153 19

19

9.05.8.4

Solid state NMR spectroscopy

Solid-state NMR offers another tool for the investigation of carboranes. Clearly this is less straightforward or accessible than solution-phase work but there are a number of papers reporting in this field. Direct analogs of conventional solution phase sequences are not always practical and so different experiments have been introduced, some of these are described below. Solid samples are generally packed into small cylinders of 4 mm diameter (called rotors, often made of zirconia) and are subject to rapid rotation (in the kHz range) in the probe whilst held at an angle of 540440 to the direction of the external magnetic field Bo, (the so-called magic angle).183 In solution phase NMR, rapid molecular tumbling averages out potentially problematic anisotropic interactions (dipolar, chemical shift anisotropy and quadrupolar), generating the familiar narrow resonances. This is not the case in the solid-state where these interactions, unless suppressed, lead to profound line-broadening. Examination of the quantummechanical description of these properties indicates that, through a combination of fast spinning and magic angle orientation of the sample, the terms representing these anisotropic interactions become zero, though it should be noted that only first-order and not second-order quadrupolar coupling is removed by this technique. Spin-1/2 nuclei of relatively low sensitivity (e.g., 13C) are often studied by cross-polarization experiments in the solid state (CPMAS),184 where the intensity of the resonances can be enhanced by polarization transfer from nearby protons, or other more sensitive spins. The study of quadrupolar nuclei (including the two isomers of boron, 10B and 11B) is more challenging due to the line-broadening arising from the second-order quadrupolar coupling.185 Quadrupolar interactions also modify the nuclear energy levels so that the transitions (2I transitions for a nucleus with spin I) are no longer degenerate, in contrast with solution phase behavior. This latter effect results in profound changes to the appearance of the spectra, where multiple resonances can represent each unique atomic environment. Solid-state NMR spectroscopy of 10B is particularly troublesome and has barely been reported in the context of carboranes, due to its low sensitivity and lack of a central transition (arising from its whole-integer spin). Multiple-Quantum Magic Angle Spinning (MQ-MAS) is an experiment designed to produce high-resolution NMR spectra of half integer quadrupolar nuclei (I > 1/2).185 It is not appropriate to discuss the technique in detail here, much information is available elsewhere (e.g., see Ref. 185), essentially the two-dimensional sequence eliminates second order line-broadening by allowing the spin, I, to evolve under the effects of two transitions, m1 and m2, during consecutive time periods, t1 and t2. An isotropic echo is created during time t2. In practice, a spectrum is produced where the f1 axis contains high resolution 11B chemical shift information and the f2 axis, the quadrupolar induced shift. Modifications of the basic MQ-MAS sequence have also been developed including 3Q-MAS and ST-MAS185 but will not be discussed here. Solid-state NMR spectroscopy has been used to probe the dynamics of carboranes and interesting information on the temperature- dependent phase behavior of the clusters has been unearthed. An early motional study of 1,2-carborane was carried out by Reynhardt.186 Due to the strong quadrupolar interactions between boron nuclei in the solid-state, and the consequential obscuring of dipolar coupling, interpretation of the second moments provided little information on the re-orientations of the icosahedron above and below the phase transition. The author notes that the equivalent values for 13C would be expected to be more sensitive to such reorientations.

Fig. 44 Example of a carborane-based hybrid class II material based on a Si-O-Si network. Reproduced from Gonzáles-Campo, A.; Nunez, R.; Viñas, C.; Boury, B. New J. Chem. 2006, 30, 546–553.

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NMR of carboranes

In a publication by Baughman187 from 1970, proton resonance absorption curves were obtained for microcrystalline 1, 2- and 1,7-carborane. These curves were used to calculate experimental line second moments that showed, by comparison with calculated values, that the icosahedral clusters rotate about the twofold molecular axis at the temperatures studied (non-room temperature measurements were garnered for only the 1,2-isomer). As the temperature is decreased the line second moment increases at around 193 K. At 175 K, the lowest temperature measurement recorded, molecular reorientation, in the case of the 1,2-isomer is still rapid enough to significantly narrow the resonance line. Early efforts at solid-state T1 measurements of the three isomers of C2B10H12 were executed by Beckman et al.188,189 High resolution solid-state 11B and 13C spectra of 1,2-, 1,7- and 1,12-carborane were reported by Harris et al. in 1988103 (see also Table 3). It is reported that linewidths within these spectra are comparable to those in the solution spectra and are similar when recorded at different magnetic field strengths (96 and 64 MHz), the dominant relaxation mechanism for 11B being quadrupolar. The value for T1 for 13C (at 298 K) in the 1,12-isomer is an order of magnitude smaller than for 1,2- and 1,7-clusters, an observation associated, by the authors, to the higher phase transition temperature for the former, in turn related to stronger intermolecular dipolar CH interactions. Examination of the spectra of substituted 1,2-carboranes revealed little effect on the linewidth on methylation, but significant broadening on introduction of a bulky phenyl group (1-Ph-1,2-C2B10H11). The phase properties of 1,7-carborane were also investigated by Winterlich et al.190 Again, the large change in magnitude of the spin-lattice relaxation time (T1), in this case of deuterium, in the C-deuterated cluster is highlighted as an indicator of a phase transition. In the case of 1,7-carborane, three phases are identified, an orientationally disordered orthorhombic phase that transforms into an ordered monoclinic phase at 170 K and to a higher temperature quasi-isotropic cubic phase at 280 K. The nature of the motion in the orthorhombic phase is described as composite, involving rotation about the molecular pseudo-C3 axis. This work was expanded191 by extension to the 1,2-isomer and the development of stochastic modeling to inform on the nature of the molecular re-orientation processes in a higher temperature disordered phase. A “tilt-jump” motion is discussed, involving a sequence of four, small-angle tilts about locally preferred axes accompanied by symmetry adapted threefold jumps. Ando et al.192 have used solid-state 11B MQ-MAS and 13C and 29Si CP-MAS to investigate the structure of hybrid diethynylbenzene-silylene polymers incorporating 1,7-C2B10H12 carborane units. A series of findings resulted, including information around the construction of the three-dimensional polymer networks and linking structural changes of the material with characteristics such as heat deflection temperature and flexural strength. This work marks a significant beacon for the application of solid-state multinuclear NMR spectroscopy to complex carborane-containing structures. A contribution describing solid-state

Fig. 45 Organometallic complexes of 1,2-carborane (1 is a 16-electron complex, 2 an 18-electron complex). Reproduced from Barry, N.; Kemp, T.; Sadler, P.; Hanna, J. Dalton Trans. 2014, 43, 4945–4949.

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 ez et al.193, these being Si-O-Si (Fig. 44) NMR analysis of hybrid organic-inorganic hybrid class II materials was described by N un and Si–N]C]N based networks. In this case, solid-state NMR characterization was carried out through 29Si CP-MAS and 13C CP-MAS experiments, no equivalent 11 B data is reported. Similarly, 13C and 29Si CP-MAS were used by Keller et al.194 to assist characterization of hybrid poly(carboranesiloxane-arylacetylene) structural isomers. Wimperis et al.195,196 has combined the study of molecular dynamics with the application of MQ-MAS multiple-quantum 11B measurements. Measurement of isotropic 11B shifts of 1,2-carborane over a range of temperatures (223–293 K) yields information on the tumbling dynamics of the cluster.195 The magnitude of the quadrupolar product, PQ, calculated from the measured isotropic quadrupolar shift in the single-quantum d2 and triple-quantum d1 dimensions can provide useful information when plotted against temperature. 1. The value of PQ decreases with temperature, indicating increasing molecular motion. 2. The large spread of PQ values representing different boron sites suggests that even at the lowest temperature recorded (223 K), molecular motion has not been frozen out and remains approximately on the timescale of the Larmor precession. 3. At the highest temperature measured (253 K), PQ is zero for the boron sites, B9 and B12 (see Fig. 2 for atom numbering) but non-zero for the others, indicating anisotropic motion. Different NMR experiments, carried out above 253 K, point to a high temperature phase where the motion is isotropic and fast on the NMR timescale. A further contribution by Wimperis,196 extending to the three isomers of C2B10H12, included determination of 11B spin-lattice relaxation times at various temperatures. On increasing the temperature, discontinuities of the measurements were identified, conforming phase changes referred to earlier. Again, the value of the quadrupolar product, PQ, was used to confirm an anisotropic molecular re-orientation around different symmetry axes for each isomer, at low temperature. Rotational correlation times (sc) obtained from molecular dynamics calculations support a quasi-isotropic rotation at high temperatures. Paquette et al.197 has used a series of MAS experiments to examine an intermediate in the plasma-induced chemical vapor deposition mediated conversion of 1,2-carborane to a thin-film amorphous hydrogenated boron carbide. It was determined that the structure of the intermediate is dominated by hydrogenated carborane icosahedra cross-linked via nonhydrogenated intraicosahedral boron atoms, either directly through BeB bonds or through extraicosahedral hydrocarbon chains. Solid-state 11B{1H} CPMAS spectroscopy was utilized by Vinas198 in order to probe the structure of radiopaque cements for vertebroplasty.one of the formulations comprising iodine as a constituent in the tetraiodocarborane 8,9,10,12-I4-1,2-closoC2B10H8 precursor. The solid-state spectra, processed with deconvolution, of the product IC-microsphere and IC-cement displayed signals in the same chemical shift region as the starting I4C2B10H8, indicating the presence of the latter in the new materials. Direct functionalisation of graphene with 1,2-C2B10H12 was studied by Rendina and Choucair199 and 11B MAS NMR spectroscopy was able to identify the presence of the bound cluster within the graphene surface. Line broadening of the trapped cluster signals was attributed to reduced rotational motions and reduced symmetry of the cluster. Sadler and Hanna200 have used solid-state MAS NMR to study the difference between 16- and 18-electron organometallic carborane clusters (Fig. 45). The 13C MAS resonances due to the carborane appear at 100 ppm for the 16-electron complex (1 in Fig. 45), and at 126.5 ppm for the 18-electron complex (2 in Fig. 45). This shift is related to the loss of pseudo-aromaticity on moving from 16- to 18-electrons and the accompanying extension of the CeS bonds.11B MQ-MAS results also show significant differences between the two complex types. For the 1, single broadened resonances at  9 ppm and  10 ppm are observed. For 2, three signals are seen. The lower resolution in the spectrum of the 16-electron complex is rationalized through motional averaging from some rotation of the carborane cage and the metallocene linker. Additional bulk arising from the presence of the PPh3 group in 2, would be expected to reduce the potential for this rotational freedom.

9.05.8.5

Dynamic NMR spectroscopy

NMR has been used extensively in the investigation of relatively high-energy molecular rearrangements in solution and an excellent text is available.201 Much of the emphasis has been directed toward organometallic and inorganic chemistry, where processes including pyramidal chalcogen inversion, ligand rotations and haptotropic shifts e.g.,202 have been examined. Molecules undergoing internal rearrangements will exhibit temperature dependent NMR spectra if the lifetimes of the individual conformers are similar to those of the excited spin states. At the low temperature limit, where the molecule is “static” on the NMR timescale, signals will represent all the conformers present, as the temperature of the sample is increased, these signals will broaden and coalesce to time-averaged profiles as the technique can no longer differentiate between the now, interconverting, forms. Computer programs are available, using a parametrisation approach203 for the simulation of the experimental data, as the lineshapes of the dynamic spectra are dependent, in part, on the rate constant(s) of exchange, the latter may be determined at the various temperatures studied. Two-dimensional EXchange SpectroscopY (EXSY)204 is another NMR tool for the study of solution dynamics. Based on the wellknown NOESY (Nuclear Overhauser Effect Spectroscopy) pulse sequence, this experiment generates a matrix where the 1D spectrum appears as a diagonal and the cross-peaks or off-diagonal signals now correlate the diagonal features undergoing chemical exchange. In principle, volume integrations of the off-diagonals vs. the diagonal signals may yield the rate constants of exchange directly.204

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NMR of carboranes

 Fig. 46 Suggested interconversion between the enantiomeric forms of arachno-4-CB8H13. Reproduced from Wille, A.; Plesek, J.; Holub, J.; Stíbr, B.; Carroll, P.; Sneddon, L. Inorg. Chem. 1996, 35, 5342–5346.

There are many examples of the application of dynamic NMR spectroscopy to the study of fluxional behavior of carboranes. There is only space here to point to some representative examples. Grimes et al. embarked on a major project to explore the synthesis, structure and reactivity of carbon-rich carboranes of the form R4C4B8H8 (R]CH3, C2H5, C3H7) and their derivatives, interesting manifestations of polyhedral cage fluxionality were observed during this study and has been reported e.g., Ref. 205–207. Additional contributions in this field were forthcoming from Hosmane, Maguire and Lipscomb e.g., Ref. 208. A full appreciation of the solution-state behavior of these species is complicated by the existence of multiple isomers, including “carbons-adjacent” and carbons apart’ forms, complementary computational efforts were published by King.209 The carborane, nido-4,5-C2B6H10 is believed to exist in a form featuring two asymmetrically arranged bridging hydrogens210 yet yields room temperature spectra indicating the presence of a mirror plane. A fluxional process interchanging the two possible enantiomers through rapid bridge-proton rearrangements would explain the spectra. This fluxion must have a very low energy barrier as it cannot be frozen out at 183 K. Another fluxional rearrangement driven by bridging proton movement was reported by Sneddon and  Stíbr, concerning the arachno-4-CB8H13 anion.211 The proposed process is shown as Fig. 46, it may be described as a simultaneous and rapid migration of two hydrogens between the two bridge and endo positions (B5-B6 and B6; B8 and B8-B9) and one hydrogen between two other bridging positions (B6-B7 and B7-B8).

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B NMR shifts can be calculated for the “static” structures and for those boron atoms that are rendered equivalent by the fluxional process (B2 and B3; B5 and B9; B6 and B8). Averaging these IGLO computed values produce shifts that agree well with the room temperature experimental results. 11

9.05.9

Conclusion

This contribution has demonstrated the great power of NMR spectroscopy in the study of carboranes, providing information on structure, bonding and dynamics both in the solid-state and in solution, helping us to understand more about their unique and fascinating character.

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104 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98. 99.

100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122.

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NMR of carboranes 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 185. 186. 187. 188. 189. 190. 191. 192. 193.

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9.06

Applications of silicon-29 NMR spectroscopy

Darren H. Brouwer, Department of Chemistry, Redeemer University, Hamilton, ON, Canada © 2023 Elsevier Ltd. All rights reserved.

9.06.1 9.06.2 9.06.2.1 9.06.2.2 9.06.2.3 9.06.3 9.06.3.1 9.06.3.2 9.06.4 9.06.4.1 9.06.4.2 9.06.4.3 9.06.4.4 9.06.4.5 9.06.5 9.06.5.1 9.06.5.2 9.06.5.3 9.06.6 9.06.6.1 9.06.6.2 9.06.6.3 9.06.7 References

Introduction General features of 29Si NMR The 29Si isotope 29 Si chemical shifts Solid-state 29Si NMR experiments 29 Si NMR of siloxanes and silicates 29 Si chemical shifts and notation for siloxanes 29 Si chemical shifts and notation for silicates and functionalized silica Solid-state 29Si NMR of zeolites 29 Si NMR of aluminosilicate zeolites 29 Si NMR of pure silica zeolites Two dimensional 29Si NMR of zeolites NMR crystallography of zeolites Locating guest species in zeolites Solid-state 29Si NMR of glasses Amorphous vs crystalline materials Bond angle distributions in silicate glasses Binary glasses Dynamic nuclear polarization 29Si NMR Dynamic nuclear polarization DNP-enhanced 29Si NMR of functionalized silica materials Other materials studied by DNP-enhanced 29Si NMR Conclusion

108 108 108 109 111 113 113 114 116 119 119 122 123 125 126 127 128 128 129 130 133 134 135 135

Abbreviations 1D One-dimensional 2D Two-dimensional COSY Correlation spectroscopy CP Cross polarization CSA Chemical shift anisotropy CW Continuous wave Dn Di-oxo silicon with n Si–O–Si linkages DFT Density functional theory DNP Dynamic nuclear polarization DP Direct polarization DQ Double quantum FID Free induction decay GIPAW Gauge-including projector augmented wave HETCOR Heteronuclear correlation INADEQUATE Incredible natural abundance double quantum experiment IZA International Zeolite Association J Through-bond scalar coupling Mn Mono-oxo silicon with n Si–O–Si linkages MAF Magic-angle flipping MAS Magic-angle spinning NMR Nuclear magnetic resonance ppm Parts per million Qn Quaternary silicon with n Si–O–Si linkages

Comprehensive Inorganic Chemistry III, Volume 9

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Applications of silicon-29 NMR spectroscopy

r.f. Radiofrequency REDOR Rotational echo double resonance SENS Surface-enhanced NMR spectroscopy SQ Single quantum T1 Spin-lattice relaxation time T2 Transverse relaxation time Tn Tri-oxo silicon with n Si-O-Si linkages TMS Tetramethylsilane g Magnetogyric ratio

Abstract This article provides an overview of a variety of applications of 29Si NMR to materials, with an emphasis on solid-state 29Si NMR of siloxane polymers, silicates, functionalized silica, porous materials, zeolites, and glasses. The unique features of the 29 Si isotope with respect to NMR spectroscopy and an overview of the 29Si chemical shift ranges of various structural environments in silicon-containing compounds and materials (in both solution and in solids) are presented. The main techniques of solid-state 29Si NMR spectroscopy are briefly described, including a number of important advanced twodimensional correlation techniques. A range of applications of 29Si NMR to siloxanes, silicates, functionalized silica, zeolites, and glasses are described. Finally, recent developments in dynamic nuclear polarization techniques that have led to remarkable increases in sensitivity and have enabled the application of 29Si NMR to new materials and new aspects of materials are outlined.

9.06.1

Introduction

Silicon-containing materials play a tremendously important role in our modern world. Our globalized digital age has been made possible by silicon-based semiconductor electronics and the fiber optic cables over which digital information ceaselessly and rapidly flows all over the world. The refining and separation of the petroleum products that provide the vast quantities of energy for society are carried out by silicon-containing porous zeolite catalyst materials. The cement that is a key ingredient in our main building material (concrete) is a vital silicon-containing material. Our present and future ability to convert the sun’s energy into electricity rests on silicon-containing materials. Silicon-bearing minerals are major components of the earth’s crust. The silicon-containing glasses we have been making for centuries from these minerals remain vitally important in our modern age. In addition, chemists have synthesized a vast array of organosilicon compounds, created valuable silicon-based polymers, and developed new porous materials, among many other important innovations. The ability to probe the structure of molecules and materials is a vital part of chemistry and materials science, as chemists pursue an understanding of how the properties and functions of materials are connected to the atomic/molecular level of organization of matter. While there are many tools available to the probe the structure of matter, nuclear magnetic resonance (NMR) spectroscopy is arguably one of the most important techniques available, due to its ability to probe the local structural environments surrounding NMR-active isotopes. Both solution-state and solid-state 29Si NMR spectroscopy have played important roles in the characterization of a wide range of silicon-containing molecules and materials. In fact, the very first article reporting 29Si NMR data, published in 1956,1 presented both solution-state and solid-state 29Si NMR results for a variety of materials. As Fig. 1 shows, the use of 29Si NMR spectroscopy really took off around 1980 and has steadily increased year-by-year to over 3500 citations per year. Interestingly, Fig. 1 also reveals that 29 Si NMR of the solid state is a more widespread application than 29Si NMR of liquids and solutions, likely a reflection of the importance and interest in silicon-based solid materials (minerals, zeolites, glasses, semiconductors, porous materials, polymers, etc.). The goal of this review is to give an overview of some of the main features and applications of 29Si NMR spectroscopy to several of the important classes of materials mentioned above. Obviously, a review of this field cannot be anywhere close to comprehensive with over 3500 citations per year! Much of the focus will be on solid-state 29Si NMR due to its prominence (see Fig. 1), the research interest and experience of the author, and the fact that solution-state 29Si NMR of organosilicon compounds has regularly been reviewed over the years.2–15

9.06.2 9.06.2.1

General features of The

29

29

Si NMR

Si isotope

There are three naturally-occurring stable isotopes of silicon: 28Si (92.191–92.318% abundant), 29Si (4.645–4.699% abundant), and 30Si (3.037–3.110% abundant),16 with only the 29Si isotope having the nuclear spin properties that allow it to be observed in NMR experiments.

Applications of silicon-29 NMR spectroscopy

109

Number of annual citations

4000 3500 3000 solution NMR

2500

29Si

2000 1500 1000

solid-state NMR

29 Si

500 0 1950

1960

1970

1980

1990

2000

2010

2020

Year 29

Fig. 1 Number of citations by year (according to Google Scholar) citing “ Si NMR” and “29Si solid-state NMR.” The former is presumed to capture publications reporting either solution or solid-state 29Si NMR, while the latter is presumed to capture publications reporting only solid-state 29Si NMR.

In many ways, 29Si NMR spectroscopy is quite comparable to 13C NMR spectroscopy due to the similarities of the isotopes (see Table 1). Like carbon-13, silicon-29 has a nuclear spin of 1/2 which simplifies the NMR spectra in contrast to majority of elements whose NMR-active nuclei are quadrupolar nuclei with spin
1. Both isotopes have a relatively low abundance of a few percent, yet are sufficiently abundant enough to usually be observed in NMR experiments at natural abundance levels. Although the magnetogyric ratios are opposite in sign, they are quite similar in magnitude, leading to comparable Larmor frequencies. The magnetogyric ratios of 13C and 29Si are approximately one-quarter and one-fifth that of 1H, respectively. On a 400 MHz NMR spectrometer with a magnetic field of 9.4 T, 13C would be observed at a Larmor frequency near 100 MHz and 29Si would be observed near 80 MHz. When the abundance and magnetogyric ratio are considered together to estimate the relative receptivity of nuclei, it can be seen that 13 C and 29Si are very comparable in terms of their sensitivity in NMR experiments. Finally, both nuclei have a similar sensitivity to their local electronic environments, with typical chemical shift ranges both on the order of 200 ppm.

9.06.2.2

29

Si chemical shifts

Compilations of 29Si chemical shifts of a wide variety of Si-containing compounds have been reported in many review articles over the years,2–15 primarily based on solution-state 29Si NMR. The objective here is to describe only the broad trends in 29Si chemical shifts, so the reader is directed to these review articles for references to original measurements, for more fine-grained dependence on local structure, for information about more exotic Si-containing compounds, and for detailed analysis and discussion of how 29Si chemical shifts depend on structure. The reader is also directed to a recent paper17 which reports a comprehensive and diverse set of 100 different Si-containing compounds with 146 experimentally measured 29Si chemical shifts, representative of the wide range of possible Si environments, which has been used for benchmarking the accuracy of quantum chemical calculations of 29Si chemical shifts. Fig. 2 is a summary of the ranges of chemical shifts expected for commonly occurring silicon environments, largely based on the most recent review articles by Marsmann11 and Uhlig.12 The majority of 29Si chemical shifts fall within the range þ 50 to  200 ppm, although 29Si chemical shifts as high as þ 828.6 ppm18 and as low as  400.3 ppm19 have been reported for Si(II) compounds (see Fig. 3), according to the recently reported benchmark set of Si-containing compounds.17

Table 1

Comparison of 1H, 13C, and 29Si NMR. 1

13

29

1/2 99.985 42.5775 5870 0–12 Tetramethylsilane

1/2 1.07 10.7074 1 0–220 Tetramethylsilane

1/2 4.68 8.465 2.16 200 to 50 Tetramethylsilane

H

Nuclear spin Natural abundance (%) Magnetogyric ratio (g/2p) (MHz/T) Relative receptivity Typical chemical shift range (ppm) Reference compound

C

Si

110

Applications of silicon-29 NMR spectroscopy

transition metal complexes

6-coordinate Si SiY

MSi= SiY5

Si=E bonds with main groups elements

5-coordinate Si R

SiI

R4- SiBr

silyl halides

R

SiCl R

trimethylsilyl derivatives

SiF

(CH ) SiY Si(Si–)4 RSi(Si–)

silanes

R Si(Si–) R Si(Si–) Si(O–)

silicates, siloxanes, silyl ethers

RSi(O–) R Si(O–) R Si(O–) R

Increasing deshielding

Increasing shielding

R Si (CH ) Si

300

silyl hydrides

SiH

50

0

tetramethylsilane (TMS) -50

-100

-150

-200

-350

Si chemical shift (ppm from TMS)

Fig. 2 Approximate 29Si NMR chemical shift ranges for silicon in different structural environments. The ranges reported here are based on summaries provided in Refs. 7, 11, 12.

Fig. 3

Silicon-containing compounds with the highest18 and lowest19 reported 29Si chemical shifts.

Tetramethylsilane, (CH3)4Si, is the chemical shift reference compound for 29Si NMR, with its chemical shift set to zero. All other Si chemical shifts are reported with respect to this value. This is noted as the line at 0 ppm at the bottom of Fig. 2. For a central Si with four Si–C bonds in an organosilicon compound (R4Si), the 29Si chemical shifts range from about þ 50 to  30 ppm,12 depending on the exact nature of the R group. The presence of Si–H bonds in silyl hydrides (R4  nSiHn) leads to increased shielding12 typically with more shielding with more hydrogens. The 29Si chemical shift of SiH4 is  93.1 ppm.17 For compounds with a single Si–O bond, such as silyl ethers R3Si(O–), the chemical shift range is similar to R4Si compounds. However, with additional Si–O bonds the 29Si chemical shift becomes increasingly shielded, to about  120 ppm in some silicates.12 A similar trend is seen for silanes, R4  nSi(Si–)n.12 The introduction of a single Si–Si bond leads to some shielding compared to R4Si compounds. However, with additional Si–Si bonds, the 29Si chemical shift becomes increasingly shielded to about  165 ppm in some Si(Si–)4 environments. Trimethylsilyl derivatives, (CH3)3SiY, have 29Si chemical shifts in the range of about þ 60 to  30 ppm, depending on which element Y that Si is bonded to.11 Fig. 4a shows the chemical shifts ranges for compounds with Y ¼ C, O, N, Si, P, or S.11 Fig. 4b shows how the 29Si chemical shift varies for trimethylsilyl derivatives of different oxygen-containing functional groups.20 Trimethylsilyl tagging of functional groups, and subsequent analysis by 29Si NMR is a useful technique for identifying functional groups in polyfunctional organic compounds, or their mixtures, such as saccharides, lignins, petroleum fractions, and coal products.20 29

Applications of silicon-29 NMR spectroscopy

111

(CH3)3Si-S

(A)

(CH3)3Si-P (CH3)3Si-Si (CH3)Si-C (CH3)Si-N (CH3)Si-O 2o 1

(B) Acids

o

3o

Alcohols Phenols Silicates

60

40

20 29

0

-20

Si chemical shift (ppm)

Fig. 4 29Si NMR chemical shift ranges for trimethylsilyl derivatives: (a) dependence of the trimethylsilyl 29Si chemical shift on the element to which Si is bonded (based on data in Ref. 11), (b) dependence of trimethylsilyl 29Si chemical shift on the type of oxygen to which the Si is bonded (based on data in Ref. 20).

Silyl halides show a very wide range of 29Si chemical shifts, depending on the identity of halogen and the number of halogens attached to the Si atom. Silyl iodides show the widest range of chemical shifts, with SiI4 having the most highly shielded chemical shift of silicon(IV) compounds at  350 ppm.5 Silicon nuclei in five-coordinate environments are more shielded compared to more typical four-coordinate environments, with 29 Si chemical shifts between about  60 and  160 ppm.7 Silicon nuclei in six-coordinate environments are even more shielded yet, with 29Si chemical shifts ranging from about  120 to  220 ppm.7 Silicon atoms with p bonds to various main-group elements are significantly deshielded, giving 29Si chemical shifts ranging from þ 280 to þ 15 ppm.11 Silicon involved in bonding with transition metals give a very wide range of chemical shifts,11 some of which are highly deshielded.

9.06.2.3

Solid-state

29

Si NMR experiments

In this section, a general overview of the types of 29Si NMR experiments typically performed on silicon-containing materials is provided. Since the applications of 29Si NMR presented in this article are mainly on solid silicon-containing materials, this section will focus on some of the basics of solid-state NMR. For further details on solid-state NMR spectroscopy, the reader is directed to a number of excellent books that have been published.21–24 This aim of this section is to only give a brief summary of the main 29Si solid-state NMR techniques which will be referred to later in the article, rather than provide comprehensive coverage of all the available techniques, of which there are many. In solids, NMR-active nuclei are restricted in their motions and cannot undergo the isotropic tumbling motions that lead to narrow, isotropically-averaged signals in solution-state NMR. As a consequence, the NMR-active nuclei in solids experience a variety of anisotropic (orientation-dependent) interactions such as chemical shift anisotropy, dipolar coupling, and the quadrupolar interaction (though not for 29Si) for which the observed frequencies depend on the orientations of nuclei and their surroundings with respect to the magnetic field. Since typical samples studied by solid-state NMR are powders consisting of crystallites with all possible orientations with respect to the magnetic field, these orientation-dependent interactions lead to signals that reflect the nature of these anisotropic interactions, but are typically broad and usually overlapping with each other. Solid-state NMR spectra (of nonspinning static samples) are inherently rich in information, but are typically poor in resolution. Magic-angle spinning (MAS) is perhaps the most important technique for typical solid-state NMR experiments, as it allows high resolution spectra to be obtained. By rotating a powdered solid around an axis oriented at the magic angle (54.74 ) with respect to the applied magnetic field at a sufficient frequency, most of the anisotropic interactions that lead to broad lines become timeaveraged to zero. As a result of this averaging, a typical 29Si MAS NMR spectrum will consist of a set of narrowed peaks, each at the isotropic chemical shift that is characteristic of the local structural environment surrounding the nucleus. Furthermore, the through-space dipolar couplings to surrounding NMR-active nuclei will typically be significantly reduced or completely averaged to zero under MAS conditions. In some cases, it may be necessary to further reduce the effects of dipolar couplings on the width of a peak by applying a decoupling radio frequency (r.f.) field, typically when there are protons in close spatial proximity to the 29 Si nuclei. Magic-angle spinning leads to a dramatic improvement in spectral resolution; however, it comes with the loss of the anisotropic interactions which can provide a great deal of information about structure. For example, dipolar couplings between nuclei are distance-dependent interactions and thus provide information about spatial proximities of nuclei. Chemical shift anisotropy can

112

Applications of silicon-29 NMR spectroscopy

provide detailed information about the local electronic structure around 29Si nuclei, such as the degree of distortion from tetrahedral geometry for a given Si site. As will be described below, these anisotropic interactions can be reintroduced or recoupled in MAS NMR experiments by applying sequences of r.f. pulses to the sample while magic-angle spinning is happening. After magic-angle spinning, the second most important technique for 29Si NMR spectroscopy of solids is probably cross polarization (CP). In a typical 29Si CP MAS NMR experiment, 1H nuclei are initially excited by a 90 pulse, then simultaneous 1H and 29Si r.f. fields are applied (with the appropriate strengths, or nutation frequencies). During this CP contact time, dipolar couplings between 1H and 29Si are recoupled and magnetization is transferred from the initially excited 1H nuclei to 29Si nuclei that are in close spatial proximity to the protons. The stronger the dipolar interactions between 1H and 29Si, the faster the magnetization is transferred from 1H to 29Si. In addition to potentially providing information about spatial proximities between 1H and 29Si nuclei, the CP MAS NMR experiment typically leads to a significant gain in sensitivity. The magnetization that is transferred from 1H to 29Si can be up to g1H/g29Si z 5 times as much as directly exciting 29Si with a 90 pulse. In addition, the experiment can be repeated when the 1H nuclei have returned to equilibrium magnetization (the rate of which is quantified by the T1 relaxation time). Since 1 H T1 relaxation times are typically much shorter than those of 29Si, more scans can be collected in a CP MAS NMR experiment for a given period of time, leading to increased signal averaging. It should be noted that the 29Si CP MAS NMR experiment can, in principle, be employed with nuclei other than 1H (e.g., 19F, 27Al). In addition to the cross polarization experiment, there are a number of other NMR experiments than can be used to probe dipolar interactions between heteronuclear pairs of nuclei (e.g., 1H/29Si, 13C/29Si, 19F/29Si, 27Al/29Si, etc.). A prominent experiment for probing spatial proximities between different nuclei is the “Rotational Echo Double Resonance” (REDOR) experiment.25 In the REDOR experiment, a series of carefully timed 180 pulses are applied to one of the nuclei, synchronized with the rotation of the sample around the magic-angle, such that the heteronuclear dipolar coupling interactions are prevented from being fully to zero by MAS. A typical REDOR experiment involves collecting a series of spectra as function of the number of rotor periods during which the recoupling pulses were applied. The spectra are analyzed to give REDOR curves, which are plots of the signal intensity of the peak(s) as a function of recouping time. When pairs of nuclei are sufficiently isolated from other nuclei of the same type, such a REDOR curve will have oscillations which reveal the dipolar coupling constant between the nuclei, which can be converted into an internuclear distance, thus revealing important structural information. Two-dimensional (2D) NMR experiments are also an important part of solid-state 29Si MAS NMR spectroscopy as they can provide a wealth of structural information beyond what is provided in a typical one-dimensional (1D) spectrum. With appropriately designed pulse sequences, it is possible to probe particular NMR interactions of interest which probe particular aspects of structure. In the context of heteronuclear dipolar couplings (e.g., between 1H and 29Si), it is possible to collect 2D heteronuclear correlation (HETCOR) spectra in which the 1H spectrum of a material is correlated to its 29Si spectrum. What this means is that the 2D spectrum will exhibit cross peaks or correlations between 1H and 29Si signals, the intensities of which are related to the spatial proximities (strengths of the dipolar couplings) between the 1H and 29Si nuclei contributing to the respective peaks in the 1D 1H and 29Si spectra. Such spectra can be very informative about the structure of materials. Again it is important to note that, in principle, any pair of nuclei (e.g., 19F/29Si, 27Al/29Si, etc.) could be investigated in this way. Furthermore, it is also possible to carry out 2D heteronuclear correlation experiment which probe the through-bond J-couplings, rather than the through-space dipolar couplings. It is also possible to probe the 29Si/29Si homonuclear interactions in solid-state 29Si NMR. These 2D NMR experiments are typically carried out via double quantum (DQ) correlation experiments in which a particular sequence of pulses is applied to excite DQ coherences between pairs of coupled 29Si nuclei. Depending on the pulse sequence used, the couplings between 29Si nuclei could arise via through-space 29Si/29Si dipolar couplings or via through-bond 29Si/29Si J-couplings. These DQ coherences evolve in the indirect dimension at the sum of the chemical shifts of the interacting 29Si nuclei before being converted through a sequence of pulses back into single quantum (SQ) signals which are observed in the direct dimension at each of their isotropic chemical shifts. The resulting 2D spectrum has a series of pairs of correlation peaks, one at each of the isotropic chemical shifts of the interacting 29Si nuclei in the direct SQ dimension and with a common frequency in the indirect DQ dimension at the sum of the isotropic chemical shifts of the interacting 29Si nuclei. These 2D experiments can provide a wealth of information about the spatial proximities and/or bonding networks between the Si atoms in materials. Another class of 2D experiments employed in 29Si solid-state NMR are those that correlate the anisotropy of the chemical shift interaction with the isotropic chemical shifts in the high-resolution MAS dimension. These spectra provide rich structural information in the form of the anisotropy of the chemical shift interaction while still maintaining resolution between the different 29Si environments in terms of their isotropic shifts. These experiments can be carried out using pulse sequences that recouple the chemical shift anisotropy or by rotating at different angles with respect to the magnetic field at different times in a pulse sequence. One of the challenges with NMR spectroscopy in general is that it is a relatively insensitive technique. Since the differences between the energy levels of nuclear spin states are small, the differences in the population of the different spin states is also small, as governed by the Boltzmann distribution. For 29Si NMR, additional challenges with respect to sensitivity arise from the typically long 29Si spin-lattice (T1) relaxation times and the relatively low natural abundance of the 29Si isotope. Materials that have long spin-lattice (T1) relaxation times typically also have long transverse (T2) relaxation times as well. This can be exploited in order to give quite large gains in sensitivity for 29Si solid-state NMR by acquiring the signal with a Carr-PurcellMeiboom-Gill (CPMG) pulse sequence.26 The CPMG sequence is a train of 180 pulses (usually rotor-synchronized in a MAS NMR experiment) that allow the transverse signal to continually refocus. Rather than collecting only a single free-induction decay (FID) in

Applications of silicon-29 NMR spectroscopy

113

each scan, the CPMG experiment essentially allows for multiple FIDs to be collected in a single scan which can be added together to give a substantial gain in sensitivity.27,28 Dynamic nuclear polarization (DNP) NMR has emerged as a powerful technique for enhancing the sensitivity of solid-state NMR experiments, including 29Si solid-state NMR. The details of DNP NMR will described later, but for now the basic principle can be described as a large polarization transfer from unpaired electrons in a biradical polarizing agent to NMR-active nuclei using microwave radiation, leading to significant gain in the NMR signal. In the context of 29Si NMR, the sensitivity enhancement of DNP has enabled solid-state NMR investigations of structure on the surfaces of silicon-based materials, so called surface enhanced NMR spectroscopy (SENS).29 Finally, it is worth very briefly mentioning the use of quantum chemical calculation methods for calculating NMR parameters. Grimme and coworkers have recently reported17 a comprehensive benchmark study of the calculation of 29Si NMR chemical shifts which includes 100 diverse silicon-containing compounds with 146 different 29Si chemical shifts experimentally measured by solution-state NMR. For solid-state NMR, plane-wave DFT methods are typically used to describe the electronic structure of periodic solids and the gauge-including projector augmented wave (GIPAW) method30,31 is used to calculate NMR parameters. Popular programs available to carry out these calculations include CASTEP32 and QuantumEspresso.33

9.06.3

29

9.06.3.1

29

Si NMR of siloxanes and silicates

Si chemical shifts and notation for siloxanes

One of the earliest applications of 29Si NMR spectroscopy was to the structural investigation of silicone (polysiloxane) polymers and related siloxane compounds.34,35 The 29Si chemical shift is very sensitive to the number of Si–O–Si linkages around a particular Si atom (see Fig. 5) and therefore provides important information about the relative proportions of end groups, chain groups and different types of branching groups. It is worth explaining the notation developed for polysiloxanes36 since this notation system is the basis for the notation commonly used for a wide variety of materials including silicone polymers, minerals, zeolites, glasses, functionalized silica, and others. As shown in Fig. 5a, the different types of Si environments in siloxanes are labeled as M, D, T, and Q based on the number of oxygen atoms bonded to the silicon (mono-, di-, tri-oxo and quarternary).36 Normally, the labels M, D, T, and Q on their own

Fig. 5 (a) Schematic drawing of the M, D, T, and Q building units in polysiloxanes. (b) 29Si chemical shift ranges of polysiloxane building units. Note that the M, D, T, and Q ranges highlighted by the light gray box refer specifically to building units with R ¼ CH3, whereas the other ranges refer to building units in which the methyl group has been substituted by one or more other groups. Adapted with permission from Williams, E. A. NMR Spectroscopy of Organosilicon Compounds. In The Chemistry of Organic Silicon Compounds; Patai, S., Rappoport, Z., Eds.; John Wiley & Sons, Ltd, 1989; pp 511–554. Copyright (1989) John Wiley & Sons.

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Applications of silicon-29 NMR spectroscopy

refer to methylated silicon atoms (R ¼ CH3). If the methyl group is substituted by another group, a superscript is used to indicate the functional group. For example DPh refers to a D unit in which one of the methyl groups has been replaced by a phenyl group, whereas DPh2 refers to a D unit in which both methyl groups have been replaced by phenyl groups. Fig. 5b summarizes the ranges of 29Si chemical shifts found for a variety of Si environments in siloxanes.7,11,15 The ranges for M, D, T, and Q units (when R ¼ CH3), highlighted in the light gray box, show that these different environments can be clearly distinguished from each other. The other chemical shift ranges show the effect that different functional groups other than methyl groups have on the 29Si chemical shifts. The ability to distinguish these different environments and quantify the relative proportions of these environments is important for structural characterization of materials containing these types of structural units. For example, Fig. 6 displays 29Si CP MAS NMR spectra of various solid organosilicon polymers34 in which the various Si environments are distinguished by the different 29Si chemical shifts. Fig. 7 displays a solid-state 29Si CP MAS NMR spectrum of octakis(trimethylsiloxy)silsesquioxane, also known as “Q8M8.” This structure consists of a central cube with a Q unit on each of the eight corners, each of which are linked to three other Q units of the cube and one terminating M unit. It is interesting to note that only two 29Si NMR signals would be expected in solution due to dynamics. However, in the solid-state in which dynamics are more limited, the Q8M8 molecules pack into a crystal structure37 such that the cube is slightly distorted, breaking the symmetry and leading to four inequivalent Q and M sites which can be seen in the 29Si CP MAS NMR spectrum38 (pairs of Si sites are related by inversion symmetry). This material is commonly used as a reference or set-up sample for solid-state 29Si NMR, being used to optimize 1H/29Si cross-polarization, 1H decoupling conditions, and the magnetic field homogeneity (shimming). It is often used as a secondary chemical shift reference by setting the most shielded signal to  109.7 ppm so that the 29Si chemical shift scale is with respect to tetramethylsilane at 0 ppm. Siloxane cages, such as the one found in Q8M8, can be functionalized with other groups and can be used as nanometer-scale building blocks in a wide range of polymeric materials, referred to as polyhedral oligosilsesquioxanes (POSS),39 and solid-state 29 Si NMR is a valuable tool in characterizing these materials.

9.06.3.2

29

Si chemical shifts and notation for silicates and functionalized silica

One way in which this M, D, T, Q notation system has been extended is for situations in which there is incomplete condensation of Si–O–Si linkages, where a superscripted integer is used to indicate the number of fully condensed Si–O–Si linkages around a Si atom (Fig. 8a). For example, a T unit normally has three Si–O–Si linkages and one R group connected via a Si–C bond, a situation which is labeled T3: “T” for three oxygens (trifunctional or trioxo) and “3” for three completed Si–O–Si linkages. If the silicon in a T unit is missing one Si–O–Si linkage, it is labeled T2 to indicate the presence of only two completed Si–O–Si linkages. When there is only one completed Si–O–Si linkage, the label T1 is used. Finally, if the T unit is completely unconnected, the label T0 applies. The

T T Methyl-silicone resin

(trisiloxane rings)

D

DPh,OH

T D

Methyl-phenylsilicone resin

TPh

DOH

MPh2,OH

T Q

QT-polymer

Q

Trimethyl- M silylated polysilicic acid 20

TOH

0

-20 29

-40

-60

-80

-100

-120

Si chemical shift (ppm)

Fig. 6 29Si CP MAS NMR spectra of a variety solid organosilicon polymers. See Fig. 5 for an explanation of the M, D, T, Q notation. Adapted with permission from Engelhardt, G.; Jancke, H.; Lippmaa, E.; Samoson, A. J. Organomet. Chem. 1981, 210, 295–301 Copyright (1981) Elsevier.

Applications of silicon-29 NMR spectroscopy

(A)

115

(B)

Q8M8

M

(C)

M Unit cell of Q8M8 crystal structure

-109.7 ppm

Q Q 13

12

20

0

−20

−108

−40

−109

−60

−80

-110

−100

−120

29

Si chemical shift (ppm)

Fig. 7 (a) Schematic drawing of the octakis(trimethylsiloxy)silsesquioxane (Q8M8) structure, (b) unit cell of the Q8M8 crystal structure,37 (c) 29Si CP MAS NMR spectrum of Q8M8.38

oxygens for which the Si–O–Si linkages are missing (the bolded oxygens in Fig. 8a) could be charged (–O), protonated (–OH), or could be a silyl ether (–OR). This notation system is used extensively for silicate materials (minerals, glasses, zeolites, etc.) in which each silicon has four Si–O bonds (Qn sites), but may have varying degrees of complete Si–O–Si condensation (n ¼ 0, 1, 2, 3, or 4). It is worth noting the equivalence of some of the labels between these two superscript methods described above when the functional group that replaces the methyl group is OH or OR. For example, a TOH unit in which one methyl group on a T unit is replaced with an OH (see Fig. 5) corresponds to a Q3 unit in the other notation (see Fig. 8). Similarly, DOH corresponds to T2 and MOH corresponds to D1. The 29Si chemical shift is sensitive not only to the type of site it is (M, D, T, or Q) and to the nature of the R group (Fig. 5), but also to the degree of condensation of each type of unit (Fig. 8). This makes 29Si NMR spectroscopy a powerful technique for probing the structures of materials having these types of structural units, such as organosilicon polymers, minerals, glasses, zeolites, layered silicates, functionalized silica, etc. Fig. 9 provides an example of 29Si MAS NMR spectra of a series of inorganic/organic hybrid materials synthesized via the sol-gel process from various mixtures of reaction precursors.41 These spectra clearly show the various Si environments in the materials, as well as their relative proportions, providing key information about the structures of these materials and insight into the sol-gel reaction process. Pruski and co-workers have employed 29Si solid-state NMR to study MCM-41 type mesoporous silica materials whose interior surfaces have been functionalized with various organic groups.28,42–48 Fig. 10 provides example 29Si NMR spectra of MCM-41 mesoporous silica materials with and without surface functionalization.42 The direct polarization (DP) spectra were collected with sufficiently long recycle delays and thus quantify the relative populations of different types of Qn and Tn silicon sites in the materials. Note how the DP spectrum of the unfunctionalized MCM-41 material reveals that it is mostly composed of silicons in Q3 and Q4 environments, while the DP spectrum of the functionalized material reveals the relative population of T2 and T3 silicons to which the organic group is connected. Since the cross-polarization (CP) process involves magnetization transfer from 1H to 29Si nuclei in close spatial proximity (via 1H/29Si dipolar couplings), the CP spectra show enhanced signals for the Q2, Q3, T2, and T3 sites that are close to silanol groups or close to the organic group. By combining fast MAS and CPMG acquisition, it has been possible to acquire two-dimensional 1H/29Si and 1H/13C CP HETCOR spectra which probe these proximities.28,43,44 Furthermore, remarkable gains in sensitivity have been achieved for these materials using dynamic nuclear polarization (DNP) methods (see later).45–48

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Applications of silicon-29 NMR spectroscopy

Fig. 8 (a) Schematic structural drawings and (b) approximate 29Si chemical shift ranges for Mn, Dn, Tn, Qn units where n represents the number of completed Si–O–Si linkages. The bolded oxygens could be O, OH, OR. (The Mn, Dn, and Tn ranges are based on data in Ref. 5 while the Qn ranges are based on data from Ref. 40.)

Another extension of the M, D, T, Q notation system that is widely used recognizes the effect of different elements in the coordination sphere of silicon, particularly the presence of aluminum in aluminosilicate minerals, zeolites, and related materials.40 As Fig. 11b shows, the 29Si chemical shift becomes increasingly deshielded as the number of nearest-neighbor Al atoms increases. For these situations, the labels for the various Si environments take the form of Qn(mAl) where n indicates the number of completed Si– O–Si or Si–O–Al linkages and m represents the number of Al atoms linked to the central Si atom (see Fig. 11a). Applications of 29Si NMR to zeolites will be expanded on in the following section, but for now it is worth presenting one set of 29 Si NMR spectra of zeolites which illustrates this dependence of the 29Si chemical shift on the number of neighboring aluminum atoms. Fig. 12 shows the range of possible 29Si NMR spectra for the same zeolite framework type (LTA) as the amount of aluminum in the framework changes. Zeolite A (Fig. 12a) has the maximum amount of Al in the framework (Si/Al ratio ¼ 1) with strict alternation of Si and Al atoms leading to a single type of Q4(4Al) environment for each 29Si nucleus.49 On the other hand, the very highly siliceous zeolite (Si/Al ratio of  2400) with LTA framework type has a negligible amount of Al in the framework such that every 29Si nucleus is in a Q4(0Al) environment (Fig. 12c).51 Fig. 12b presents a more typical 29Si NMR spectrum of an aluminosilicate zeolite with five peaks, reflecting a statistical distribution of the five possible coordination environments around Si. This spectrum is of the zeolite ZK-4 which also has the LTA framework type, but with a higher Si/Al ratio (lower amount of Al) than zeolite A.50 When properly acquired with sufficiently long recycle delays to allow for full relaxation, the integrated peak areas of these five peaks reveal the relative populations of each of these coordination environments and can be used to determine the Si/ Al ratio of the zeolite framework (see next section).

9.06.4

Solid-state

29

Si NMR of zeolites

Zeolites are microporous crystalline network materials with pores, channels, and cavities of molecular dimensions that have a wide variety of applications in catalysis, separations, and ion exchange. Zeolite frameworks are composed of corner-sharing tetrahedral

Applications of silicon-29 NMR spectroscopy CH3

–

EtO–Si–OEt

EtO–Si–OEt

EtO–Si–OEt

CH3

–

–

–

–

OEt

–

CH3

OEt

OEt

Dimethyldiethoxysilane (DMDEOS = D)

Methyltriethoxysilane (MTEOS = M)

Tetraethoxysilane (TEOS = T)

Ratio of reactants

Q3

D: M :T 0 : 0 : 100

117

Q4

Q2

D2 T2

23 : 21 : 56

T3

37 : 33 : 30 56 : 0 : 44 37 : 33 : 30 22 : 60 : 18 0 : 100 : 0

-20

0

-40 29

-60

-80

-100

-120

Si chemical shift (ppm)

Fig. 9 29Si direct polarization MAS NMR spectra of a series of tetraethoxysilane (TEOS) based multifunctional sol-gel materials synthesized with different proportions of DMDEOS (D), MDEOS (M), and TEOS (T) reactant precursors. See Fig. 8 for an explanation of the Dn, Tn, Qn notation. Adapted with permission from Glaser, R. H.; Wilkes, G. L.; Bronnimann, C. E. J. Non-Cryst. Solids 1989, 113, 73–87. Copyright (1989) Elsevier.

MCM-41

Q4 Q3 (B)

MCM-41 functionalized with

T2

Si

T3

Q2 29

Si DP

1

H/29Si CP

(A)

MCM-41 surfactant removed, unfunctionalized

29

Si DP

1

29

H/ Si CP

0

-20

-40

-60

-80

-100

-120

-140

-160

29

Si chemical shift (ppm)

Fig. 10 29Si direct polarization (DP) and 1H/29Si cross polarization (CP) MAS NMR spectra of MCM-41 mesoporous silica: (a) MCM-41 with surfactant removed and unfunctionalized, (b) surface-functionalized MCM-41 synthesized via a co-condensation method. See Fig. 8 for an explanation of the Dn, Tn, Qn notation. Adapted with permission from Huh, S.; Wiench, J. W.; Yoo, J. C.; Pruski, M.; Lin, V. S. Y. Chem. Mater. 2003, 15, 4247– 4256. Copyright (2003) American Chemical Society.

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Applications of silicon-29 NMR spectroscopy

Fig. 11 (a) Schematic structural drawings and (b) dependence of the 29Si chemical shift for Q4 and Q3 silicons on the number of Al atoms in the first coordination sphere. Adapted with permission from Engelhardt, G.; Koller, H. NMR Basic Princ. Prog. 1994, 31, 1–29. Copyright (1994) SpringerVerlag.

Fig. 12 29Si MAS NMR spectra of zeolites with the LTA framework topology with varying amounts of aluminum in the framework: (a) zeolite A (Si/ Al ¼ 1),49 (b) zeolite ZK-4 (Si/Al ¼ 2.3),50 (c) very high silica zeolite A (Si/Al z2400).51 Digitized versions of these spectra can be viewed online in the International Zeolite Association Database of Zeolite Structures.52,53

units, typically with Si or Al at the center of the tetrahedral unit with oxygen atoms linking the Si or Al atoms in neighboring tetrahedra. These tetrahedral units can assemble into an incredibly wide variety of network structures with differing sizes, shapes, and systems of channels and pores. The International Zeolite Association (IZA) currently has over 200 unique zeolite framework

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topologies catalogued in their Database of Zeolite Structures,52 with each zeolite framework type given a three-letter code. Many other elements such as B, P, Ge, Ga, Ti, Fe, Zn, Cr, Mn, etc. have also been incorporated into zeolite frameworks which can impart additional unique properties to the materials. While diffraction methods (particularly powder X-ray diffraction) play a very important role in the characterization of zeolite structures, solid-state NMR spectroscopy has developed into a very powerful complementary method for probing zeolite structures. The complementarity of solid-state NMR arises from the fact that it is particularly sensitive to the local structural environments around NMR-active nuclei, while diffraction methods probe the long-range periodic structure of the material. When combined, these two methods can provide a wealth of structural information on materials such as zeolites. The application of solid-state NMR to zeolites (using a wide variety of NMR-active nuclei beyond just 29Si) has been reviewed on many occasions.21,40,53–62 This section will only cover 29Si solid-state NMR of zeolites with a focus on recent developments in NMR crystallography of zeolites in which advanced 29Si solid-state NMR experiments have been used, in combination with diffraction methods and quantum-chemical calculation methods, to determine the crystal structures of zeolite frameworks and zeolite hostguest complexes.

9.06.4.1

29

Si NMR of aluminosilicate zeolites

Aluminosilicate zeolites are very important materials for catalysis, particularly in the petroleum industry. The presence of aluminum in the framework imparts negative charge to the framework, which is often balanced by protons (after ion exchange with NH4þ and removal of NH3 by heating). Such materials are outstanding acid catalysts with very high (internal) surface areas and the ability to carry out shape-selective catalysis based on the shape and size of the pores and channels. 29 Si solid-state NMR is an important tool for characterizing these aluminosilicate zeolites. For these materials, the 29Si chemical shift of each 29Si nucleus is mostly dependent on how many Al atoms are in its coordination sphere, as discussed earlier. Fig. 11 displays the chemical shift ranges for the possible coordination environments around a Si atom in an aluminosilicate zeolite framework (with 0, 1, 2, 3, or 4 Al neighboring atoms). Fig. 12 shows a series of 29Si MAS NMR spectra for the same zeolite framework type (LTA) as the amount of aluminum in the framework changes from the maximum amount (Fig. 12a) to a negligible amount (Fig. 12c). With intermediate amounts of Al, the 29Si NMR spectrum has up to five signals reflecting the five possible coordination environments (Fig. 12b). When properly acquired with sufficiently long recycle delays to allow for full relaxation, the integrated areas of these five peaks reveal the relative populations of each of these coordination environments. Because the 29Si NMR spectrum reflects the relative populations of the Si coordination environments, the set of integrated peak areas IQ4(mAl) with m ¼ 0–4 can be used to calculate the Si/ Al ratio of the zeolite framework according to the following equation: Si=Al ¼

4 X m¼0

IQ4 ðmAlÞ =

4   X m m¼0

4

IQ4 ðmAlÞ

Fig. 13 shows a series of 29Si NMR spectra of zeolites with the FAU framework type (zeolites X and Y) having a range of Si/Al ratios, clearly demonstrating how the spectrum reflects the relative populations of the various Si coordination environments as the amount of Al in the framework changes. These spectra were each fit with five peaks and the integrated peak areas were used to calculate the Si/Al ratio with the equation above. The NMR-determined Si/Al ratios were found to be within a few percent of ratios determined by X-ray fluorescence spectroscopy.63

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29

Si NMR of pure silica zeolites

Pure silica zeolite frameworks can also be prepared in which all tetrahedral sites in the framework are Si atoms. This can be done by dealuminating aluminosilicate zeolites64–66 via steam treatment or by reaction with SiCl4 vapor or by synthesizing the zeolite from a pure silica starting material (e.g., tetraethylorthosilicate), usually in the presence of fluoride ions.67–69 While not catalytically active like aluminosilicate zeolites, pure silica zeolites materials have interesting applications as absorbents and for separations. Solid-state 29Si NMR of pure silica zeolites reveals structural features of zeolite frameworks that are not accessible in aluminosilicate zeolites. Rather than the 29Si chemical shift being dependent on which elements are in the coordination environment of a 29Si nucleus as is the case for aluminosilicate zeolites (see above), for pure silica zeolites the 29Si chemical shift is dependent on the local structural geometry around the central Si atom. In particular, the 29Si chemical shift is strongly dependent on the four Si–O–Si bond angles that a particular Si atom is part of.53,64,70,71 Fig. 14 displays the 29Si NMR spectra of two zeolite samples with the OFF framework type.65 The aluminosilicate zeolite (Fig. 14a) shows the expected five signals arising from the number of Al in the coordination environment and can be analyzed to yield an estimate of the Si/Al ratio, as described above. Interestingly, upon dealumination of the zeolite framework, the spectrum does not simplify into a single Q4(0Al) peak (like highly siliceous LTA in Fig. 12c), but rather has two signals in a 2:1 ratio (Fig. 14b). As a consequence of the 29Si chemical shifts being primarily sensitive to the local geometry (when the effects of neighboring Al are no longer in play), the number of peaks in a 29Si NMR spectrum of a pure silica zeolite reveals the number of unique crystallographic sites in the crystal structure of the zeolite. Furthermore, the relative integrated areas of these peaks reflect the relative populations of these crystallographic sites. For example, the OFF framework is known to have two unique tetrahedral sites in its crystal

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Fig. 13 29Si MAS NMR spectra of aluminosilicate zeolites with the FAU framework topology with varying amounts of aluminum in the framework. Adapted with permission from Klinowski, J.; Ramdas, S.; Thomas, J. M.; Fyfe, C. A.; Hartman, J. S. J. Chem. Soc. Faraday Trans. 2 Mol. Chem. Phys. 1982, 78, 1025–1050. Copyright (1982) Royal Society of Chemistry.

Fig. 14 29Si MAS NMR spectra of offretite zeolite (OFF framework topology): (a) aluminosilicate zeolite with Si/Al ¼ 2.9 showing five signals depending on the number of Al in the first coordination shell, (b) dealuminated zeolite with Si/Al > 100 in which two distinct crystallographic Si sites are observed. Adapted with permission from Fyfe, C. A.; Gobbi, G. C.; Murphy, W. J.; Ozubko, R. S.; Slack, D. A. Chem. Lett. 1983, 12, 1547–1550. Copyright (1983) Chemistry Society of Japan.

structure with a relative population of 2:1 due to one of the sites being located on a higher symmetry position in the crystal structure. This explains the observation of two peaks having integrated peak areas in a ratio of 2:1 in the 29Si NMR spectrum of the dealuminated OFF zeolite shown in Fig. 14b. Such high-resolution 29Si NMR spectra can be said to have “crystallographic resolution.”

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A comprehensive collection53 of 29Si NMR spectra of pure silica zeolites having such crystallographic resolution has recently been compiled, digitized, analyzed, and incorporated into the International Zeolite Association online Database of Zeolite Structures,52 a valuable and highly-regarded source of information about zeolite structures. A few examples of these spectra are shown in Fig. 15.71–75 With such a comprehensive collection, it was possible to ascertain an empirical relationship between 29Si chemical shifts and geometric parameters describing the local structure around silicon atoms (Si–O distances and Si–O–Si angles) that can predict 29Si chemical shifts to within about 0.5 ppm.53 Resolving the crystallographic Si sites in pure silica zeolites by 29Si NMR can be useful in many ways. For the structure determination of new zeolites, this information informs the number of crystallographic Si sites in the structure and their relative populations. This information can also be useful for constraining the possible crystallographic space groups.

Fig. 15 Examples of 29Si MAS NMR spectra of pure silica zeolites showing crystallographic resolution: (a) ferrierite,71 (b) ITQ-4,72 (c) ZSM-12,73 (d) Sigma-2,74 (e) highly siliceous ZSM-5 at room temperature in its monoclinic phase,75 (f) ZSM-5 at high temperature in its orthorhombic phase,75 (g) ZSM-5 loaded with p-xylene (2 molecules per unit cell),75 and (h) ZSM-5 loaded with p-xylene (8 molecules per unit cell).76 Digitized versions of these spectra can be viewed online in the International Zeolite Association Database of Zeolite Structures.52,53

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For many pure zeolites, high-resolution 29Si NMR spectra have been used to monitor phase changes between different crystallographic space groups as a function of temperature or absorption of guest molecules into the zeolite pores.75,76 A classic example is the pure silica form of the zeolite ZSM-5 which gives a 29Si NMR spectrum at room temperature with 24 peaks (Fig. 15e), corresponding to a monoclinic space group with 24 unique Si sites in the crystal structure. When the temperature is raised above 85  C (Fig. 15f) or small molecules are absorbed in the pores (Fig. 15g), the 29Si NMR spectra undergoes a remarkable change to 12 peaks corresponding to an orthorhombic space group with 12 unique Si sites in the crystal structure. Surprisingly, further absorption of small molecules can lead to another change in the 29Si spectrum to 24 peaks (Fig. 15h) which corresponds to a different orthorhombic space group with a lower symmetry in which there are 24 unique Si sites.

9.06.4.3

Two dimensional

29

Si NMR of zeolites

Some of the powerful two-dimensional (2D) NMR techniques that have been developed for solution-state NMR of organic compounds to probe correlations between nuclei (e.g., COSY, INADEQUATE) have also been employed in 29Si solid-state NMR of pure silica zeolites to probe the correlations between 29Si nuclei, particularly between 29Si nuclei in the Si–O–Si linkages of the zeolite frameworks. For any of the 4.68% of silicon atoms in a tetrahedral node of a zeolite framework that are the NMR-active 29Si isotope, there is a 4  4.68% ¼ 17.84% chance of a pair of 29Si nuclei existing across a Si–O–Si linkage. The through-bond 2JSi–O–Si coupling constants in pure silica zeolites have been experimentally measured to range from about 6 to 25 Hz77 and demonstrated to depend primarily on the central Si–O–Si bond angle and secondarily on the other Si–O–Si bond angles around the Si atoms involved.78 The existence of pairs of J-coupled 29Si nuclei in pure silica zeolite frameworks means that various 2D NMR correlation experiments can be performed to probe the Si–O–Si bonding networks in zeolite frameworks. 29Si 2D COSY experiments were the first of these types to be applied79–82 due the simplicity of the experiment. However, the 29Si 2D INADEQUATE experiment was subsequently shown to be superior due to its ability to filter out the strong diagonal peaks which were present in COSY experiments. These 2D correlation spectra provide a wealth of structural information about the Si–O–Si bonding network in zeolite frameworks.57,76,81,83,84 One of the most important applications is the assignment of particular peaks in the 29Si NMR spectrum to particular Si sites in the crystal structure, a task that is made easier by framing the assignment problem in terms of graph theory (Fig. 16).85,86 Another approach to probing the Si–O–Si bonding network has been to employ solid-state NMR pulse sequences that reintroduce or recouple the through-space dipolar interaction between 29Si nuclei that is normally averaged to zero during magic-angle spinning.74 The Si–Si internuclear distances between Si atoms in a Si–O–Si linkage are about 3.1 Å which corresponds to a 29Si–29Si dipolar coupling constant of 160 Hz. By employing a sufficiently short recoupling time, it is possible to excite primarily only the dipolar double-quantum (DQ) correlations between the pairs of 29Si in close proximity across Si–O–Si linkages, generating 2D correlation spectra that map out the Si–O–Si bonding network. The main advantage of the through-space dipolar based

T3 T4 T6

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–112 29

Si chemical shift (ppm)

29

Fig. 16 Two-dimensional Si homonuclear correlation spectra of pure-silica zeolite ZSM-12 (MTW framework topology) probing the through-bond 29 Si–O–29Si J-couplings with (a) the COSY experiment and (b) the INADEQUATE experiment. Adapted with permission from Fyfe, C. A.; Feng, Y.; Gies, H.; Grondey, H.; Kokotailo, G. T. J. Am. Chem. Soc. 1990, 112, 3264–3270. Copyright (1990) American Chemical Society.

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correlation experiment is that it is possible to observe auto-correlations along the diagonal of the 2D spectrum arising from symmetry-related Si atoms of the same Si site type.74 These auto-correlations, which provide important structural information, are missing in the though-space J-coupling based INADEQUATE experiments, as shown in Fig. 17.

9.06.4.4

NMR crystallography of zeolites

NMR crystallography87–89 refers broadly to structure determination strategies that integrate complementary techniques (e.g., solidstate NMR, powder diffraction, quantum chemical calculations) with solid-state NMR playing a prominent role in solving and/or refining crystal structures. For materials that are difficult to obtain as suitably large crystals for single crystal X-ray diffraction (such as zeolites), or may not be fully crystalline, NMR crystallography approaches have been demonstrated to be very fruitful. The combination of diffraction (probing the long-range periodic order of materials) with solid-state NMR (sensitive to the local structure around NMR-active nuclei), accompanied by quantum chemical calculations (allowing for the validation and optimization of structural models) often yields structural models of materials that could not be obtained by any one method alone. The 2D 29Si double quantum (DQ) dipolar-recoupling experiments described above for probing the Si–O–Si bonding network (using short dipolar recoupling times) can be extended to probe longer-range Si–Si distances in the zeolite framework by collecting a series of 2D DQ correlation spectra as a function of the dipolar recoupling time.90 Pairs of correlation peaks in these spectra can be integrated and plotted as a function of the dipolar recoupling time, yielding a series of DQ buildup curves for each pair-wise combination of Si sites. Due to the favorable natural abundance of 29Si (4.68%), most DQ correlations will arise from isolated pairs of 29Si nuclei which vastly simplifies the calculation of DQ buildup curves from model structures.90 It has been shown that a combination of the unit cell and space group (obtained from powder XRD) with these 29Si DQ build-up curves can be used to solve the threedimensional structures of pure silica zeolite frameworks91 by systematically generating potential model structures and selecting only those structures for which the calculated and experimental DQ curves are in good agreement. Fig. 18 illustrates how the structure of the zeolite ITQ-4 (IFR framework type) was solved from 29Si solid-state NMR.91 The 1D 29 Si spectrum reveals that there are four unique Si sites in the structure with equal populations (Fig. 18a). The 2D 29Si DQ correlation spectrum reveals the nearest-neighbor Si–O–Si bonding network (Fig. 18b). After collecting a series of these 2D DQ correlation spectra as a function of the recoupling time, a set of experimental DQ build up curves were obtained (black circles in Fig. 18c). Then, a series of model structures of the zeolite framework were built and tested against these data until the best fit structure was found (red lines in Fig. 18c). The zeolite framework structure determined through this process is displayed in Fig. 18d and was found to be in excellent agreement with the structure determined by X-ray diffraction. Further developments in solving zeolite framework structures from 29Si DQ NMR experiments, employing a simulated annealing approach92 or a graph theory approach,93 have shown that zeolite frameworks can actually be solved from a single 2D correlation spectrum which provides information on the Si–O–Si bonding network (instead of full set of DQ build-up curves), even without diffraction information at all in some cases.94 In addition, this NMR crystallography strategy has also successfully been

Fig. 17 Two-dimensional 29Si homonulcear double-quantum correlation spectra of pure-silica zeolite Sigma-2 (SGT framework topology) probing (a) the through-space 29Si–29Si dipolar couplings with the SR26 dipolar recoupling sequence and (b) the through-bond 29Si–O–29Si J-coupling with the INADEQUATE experiment. Adapted with permission from Brouwer, D. H.; Kristiansen, P. E.; Fyfe, C. A.; Levitt, M. H. J. Am. Chem. Soc. 2005, 127, 542–543. Copyright (2005) American Chemical Society.

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Fig. 18 Summary of the NMR crystallography structure solution of the pure silica zeolite ITQ-4 (IFR framework topology): (a) 1D 29Si MAS NMR spectrum showing four Si sites with equal occupancies, (b) 2D 29Si DQ correlation spectrum showing the Si–O–Si bonding network, (c) 29Si DQ build-up curves showing the intensities of the correlation peaks as a function of dipolar recoupling time (black squares) along with calculated curves for the proposed structure (red lines), (d) framework structure of zeolite ITQ-4 determined from solid-state 29Si NMR data. Adapted with permission from Brouwer, D. H.; Darton, R. J.; Morris, R. E.; Levitt, M. H. J. Am. Chem. Soc. 2005, 127, 10365–10370. Copyright (2005) American Chemical Society.

applied to layered silicate materials which do not show full 3D crystallinity and are not amenable to full structural characterization by diffraction methods.95 The structural models of zeolite frameworks obtained from these NMR crystallography approaches described above can be further optimized or refined by incorporating 29Si chemical shift information in combination with quantum-chemical calculation methods. After adding oxygen atoms midway between the Si atoms and performing a simple preliminary geometry optimization based on expected Si–O, O–O, and Si–Si distances, the structural model for the zeolite framework can be further refined by carrying out a lattice energy minimization using quantum chemical calculation methods that employ periodic plane-wave density functional theory (DFT) methods (e.g., CASTEP32 or QuantumEspresso33). After such an optimization, the structure can be validated by calculating the 29Si chemical shifts for the energy-minimized structure and comparing to the experimentally measured 29Si chemical shifts. This validation is most rigorous when carried out on the principal components of 29Si chemical shift tensors rather than just isotropic 29Si chemical shifts.96,97 It has been shown that 29Si chemical shift tensors are best measured at high magnetic field strength with slow magic angle spinning or using a 2D experiment which provides high resolution in the direct dimension and recoupled chemical shift anisotropy patterns in the indirect dimension. For example, it has been possible to measure the chemical shift tensors for most of the Si sites in the monoclinic ZSM-5 structure with 24 signals in its 29Si NMR spectrum (Fig. 19) with a two-dimensional experiment which recouples the anisotropy of the chemical shift interaction under magic-angle spinning conditions.96 Furthermore, it has also been shown that structural models for the zeolite frameworks can be refined directly against 29Si chemical shift tensors, by adjusting atomic coordinates such that the differences are minimized between quantum-chemical calculated and experimentally measured principal components of 29Si chemical shift tensors.98,99 Zeolite framework structures solved and

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Fig. 19 (a) 1D 29Si MAS NMR spectrum of the room-temperature monoclinic phase of highly siliceous zeolite ZSM-5 (MFI framework topology) with 24 distinct crystallographic Si sites. (b) Experimental (solid lines) and best-fit calculated (dashed lines) chemical shift anisotropy (CSA) recoupled lineshapes extracted from the indirect dimension of a 2D CSA-recoupled spectrum. Reproduced with permission from Brouwer, D. H.; Enright, G. D. J. Am. Chem. Soc. 2008, 130, 3095–3105. Copyright (2008) American Chemical Society.

refined with these NMR crystallography strategies have been shown to be in excellent agreement with structures determined by single crystal XRD, with differences between atomic coordinates less than 0.05 Å.97,98

9.06.4.5

Locating guest species in zeolites

Another fruitful area of NMR crystallography of zeolites has been in determining the locations of ionic or molecular guest species within the pores of a zeolite framework, two examples of which will be briefly described here. In the synthesis of pure silica zeolites, it has been found that pairing complex tetraalkyl ammonium organic template cations (NR4þ) with fluoride ions by adding HF to the synthesis mixture has led to the discovery of many new zeolite framework types67–69 which often incorporate the fluoride ions into the as-synthesized zeolite structure. In order to gain a deeper understanding of the role of the fluoride ion as a structure directing agent, determining the location of fluoride ions in the zeolite structure has been important. For example, solid-state NMR experiments which employ heteronuclear 19F/29Si dipolar recoupling experiments100 were used to locate the fluoride ions in an as-synthesized zeolite with the MFI framework topology.101 First, the peaks in the 29Si spectrum were assigned with a 2D 29Si DQ correlation experiment, then by comparing 1H/29Si (Fig. 20a) and 19F/29Si (Fig. 20b) cross-polarization spectra, it was possible to identify a particular cage of the zeolite framework in which the fluoride ion was located (Fig. 20c). Furthermore, by carrying out 29Si{19F} rotational echo double resonance (REDOR) experiments, a set of F–Si distances were measured which allowed for a more precise location of the fluoride ion in the cage (Fig. 20d). Finally, because the peak that gave the greatest signal in the 19F/29Si CP spectrum (Si9) is very broad and at a chemical shift half-way between the shifts expected for four-coordinate SiO4 and five-coordinate SiO4F environments, it was proposed that the fluoride ion is dynamic and hops between adjacent Si9 sites (Fig. 20e). In other as-synthesized zeolites, the fluoride ion is not dynamic and it is possible to observe by 29Si NMR spectroscopy the presence of five-coordinate SiO4F sites102,103 with a chemical shift of about  150 ppm. It has also been possible to definitively demonstrate the covalent nature of the F–Si bond with solid-state NMR by observing and manipulating the through-bond 1JF–Si coupling.104 The second example of NMR crystallography applied to zeolite host-guest complexes involves determining the location and orientation of absorbed organic guest molecules in the channels of zeolites. In order to gain a deeper understanding of the interactions of zeolite frameworks with the organic molecules which can occupy the channels, pores, and cavities of zeolites, it is

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Fig. 20 Summary of the NMR crystallography approach used to locate the fluoride ion in as-synthesized silicalite (MFI framework topology): (a) 1 29 H/ Si CP MAS NMR spectrum showing 12 distinct crystallographic Si sites, (b) 19F/29Si CP MAS spectrum selectively enhancing only those Si sites in close proximity to the fluoride ion, (c) structure of the zeolite framework showing the tetrapropylammonium template cation along with the cage containing the fluoride ion highlighted in red, (d) location of the fluoride ion in the cage based on F–Si distances measured in a 29Si{19F} REDOR dipolar recoupling experiment, (e) proposed dynamic process in which the fluoride ion hops between Si9 sites related by mirror-symmetry, leading to a broad time-averaged signal halfway between 4-coordinate and 5-coordinate 29Si chemical shifts. Adapted with permission from Fyfe, C. A.; Brouwer, D. H.; Lewis, A. R.; Chézeau, J. M. J. Am. Chem. Soc. 2001, 123, 6882–6891. Copyright (2001) American Chemical Society.

important to have structures of these host-guest complexes. An NMR crystallography approach has been developed based on probing the spatial proximities between 1H nuclei of organic guest molecules and 29Si nuclei of the zeolite framework in a 1H/29Si cross-polarization (CP) NMR experiment.105–108 First the peaks in the 29Si MAS NMR spectrum (Fig. 21a) are assigned based on a 2D 29Si DQ correlation experiment. Then, a series of 1H/29Si cross-polarization spectra (Fig. 21b) are collected as a function of the CP contact time and the peak areas are integrated, yielding cross-polarization curves (integrated peak area vs contact time) for each resolved peak in the spectrum (Fig. 21c). These cross-polarization curves are then carefully analyzed109 to yield cross polarization transfer rates which are proportional to the spatial proximities of the 1H and 29Si nuclei involved. From these data, locations and orientations of guest molecules within the zeolite pores are evaluated and only those which show a strong linear correlation between the set of measured crosspolarization transfer rates and the calculated sum of squares of the 1H/29Si dipolar couplings for the corresponding crystallographic Si sites in the zeolite framework are selected (Fig. 21d). This NMR crystallography strategy has been applied to various organic guest molecules in the zeolite ZSM-5 (MFI framework topology) and has been shown to be in excellent agreement with those host guest structures that have been possible to be determined by diffraction methods.105–108

9.06.5

Solid-state

29

Si NMR of glasses

Solid-state 29Si NMR has played an important role in structural investigations of silicate glasses.110–116 The structures of glasses are inherently difficult to characterize since any description of their structure will be statistical in nature. Furthermore, glasses are

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Fig. 21 Summary of NMR crystallography approach to determine the location of p-dichlorobenzene guest molecules within the channels of highly siliceous ZSM-5 (MFI framework topology): (a) 29Si MAS NMR spectrum showing 12 distinct crystallographic Si sites with peak assignments based on a 2D DQ correlation experiment, (b) 1H/29Si CP MAS NMR spectrum in which signal intensities are related to the spatial proximity of 29Si nuclei to the protons of the guest molecule, (c) 1H/29Si cross polarization curves analyzed to quantify the relative strengths of 1H/29Si dipolar interactions between 1H of the guest molecules and 29Si of the zeolite framework, (d) location and orientation of the p-dichlorobenzene guest molecule giving best linear relationship between calculated 1H/29Si dipolar coupling constants and cross-polarization magnetization transfer rates. Adapted with permission from Fyfe, C. A.; Brouwer, D. H. J. Am. Chem. Soc. 2006, 128, 11860–11871. Copyright (2006) American Society.

difficult to characterize by diffraction methods due to their lack of periodic structural order. In this section, a few examples of the application of 29Si solid-state NMR to the structural characterization of glasses are described.

9.06.5.1

Amorphous vs crystalline materials

It is important to note how the structural differences between crystalline and amorphous materials are manifested in solid-state NMR spectra. Crystalline materials are highly ordered with well-defined structural environments throughout the entire structure. Since NMR spectroscopy is sensitive to the local structural environment around each NMR-active isotope, the structural order of a crystalline material leads to well-defined, sharp peaks in its NMR spectrum. As shown in Fig. 22, the solid-state 29Si NMR spectrum of highly crystalline quartz, for example, is a single narrow signal arising from the fact that every 29Si nucleus is located in the same structural environment throughout the entire material. Similar well-resolved 29Si NMR spectra with crystallographic resolution were described earlier in the section on pure silica zeolites (see Fig. 15). Although an amorphous material such as a silicate glass may have structural similarities to a crystalline silicate (e.g., being composed of a connected 3D network of corner-sharing SiO4 tetrahedral units), such materials fundamentally differ in that they lack the periodic structural order that crystalline materials have. Instead of having a finite set of well-defined local structural environments, an amorphous glass material has a distribution of structural environments. As shown in Fig. 22, the consequence of this

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Fig. 22 29Si MAS NMR spectra and schematic structures of (a) silica glass and (b) quartz (both with the composition SiO2), highlighting the differences in NMR spectra of amorphous and crystalline materials. Adapted with permission from Oestrike, R.; Yang, W.; Kirkpatrick, R. J.; Hervig, R. L.; Navrotsky, A.; Montez, B. Geochim. Cosmochim. Acta 1987, 51, 2199–2209. Copyright (1987) Elsevier.

for the solid-state 29Si NMR spectrum of a silicate glass is that there will be broad signals due to the distribution of chemical shifts which arise from the wide variety of possible structural environments around the 29Si nuclei throughout the material.

9.06.5.2

Bond angle distributions in silicate glasses

The lack of periodic structural order in amorphous materials means that diffraction methods provide very limited structural information and there is opportunity for solid-state NMR spectroscopy to provide important structural information. Even though the 29 Si NMR spectrum of a silicate glass is broad and seemingly featureless, the fact that the observed distribution of chemical shifts is somehow related to the distribution of structural environments means that structural information can still be gleaned from such NMR spectra. A number of attempts, starting with Dupree and Pettifer110 and reviewed by Malfait,115 have been made to invert the distribution of chemical shifts found in the 29Si NMR spectrum of glasses (Fig. 23a) into a Si–O–Si bond angle distribution (Fig. 23c), employing a model (Fig. 23b) for the relationship between the isotropic 29Si chemical shift and the average of the four Si–O–Si bond angles around a Si. More recently, Grandinetti and co-workers have carried out a sophisticated statistical analysis involving both distributions of 29Si isotropic chemical shifts as well as distributions of 2JSi–O–Si couplings to provide an improved distribution of Si–O–Si bond angles in silicate glass.117

9.06.5.3

Binary glasses

When an alkali or alkali earth cation is incorporated into a silicate glass (a so-called “binary glass”), the 3D network of connected SiO4 tetrahedral Q4 units becomes disrupted, with negatively charged non-bonding oxygens being formed to balance the charge of the incorporated cations, leading to Q3, Q2, and Q1 units. For such materials, solid-state 29Si NMR can provide valuable information about the relative populations of these Qn environments in these binary glass materials. For example, Fig. 24 shows a series of 29Si NMR spectra of the K2O–SiO2 binary glass system as a function of potassium content.118 The spectra clearly show that as potassium content increases, there is a depolymerization of the silicate network with fewer fully networked Q4 units and an increase in the lessconnected Q1 and Q2 units. Additionally, there is a downfield shift in the isotropic 29Si chemical shift of each Qn type as the potassium content increases. While the K2O–SiO2 binary glass example described above demonstrates that 29Si NMR spectroscopy can in principle resolve different Qn environments, due to the breadth of the individual peaks (arising from the distributions of chemical shifts which in turn arise from the distribution of bond angles), it is often difficult to sufficiently resolve the peaks to enable a reliable quantification of the relative populations of these different Qn environments. To solve this problem, Grandinetti and co-workers have devised a two-dimensional “magic-angle flipping” (MAF) NMR experiment to better distinguish these environments based on the anisotropy of the 29Si chemical shift interactions.119–122 As Fig. 25a shows, the different Qn environments have characteristic lineshapes

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Fig. 23 Determining bond-angle distributions in silicate glass: (a) 29Si MAS NMR spectrum of silicate glass, (b) two possible models that relate 29 Si chemical shifts to average Si–O–Si bond angles based on 29Si chemical shifts of silica polymorphs and zeolites, (c) resulting Si–O–Si bond angle distributions when the models in (b) are applied to the spectrum in (a). Reproduced with permission from Malfait, W. J.; Halter, W. E.; Verel, R. Chem. Geol. 2008, 256, 269–277. Copyright (2008) Elsevier.

when the sample is rotated about an axis at 90 with respect to the magnetic field (rather than being rotated around the “magic angle” of 54.74 with respect to the magnetic field). Under these conditions, the anisotropy of the chemical shift interaction is not completely averaged to zero, leading to these characteristic lineshapes. The MAF NMR experiment involves collecting the indirect dimension while the sample is being rotated at the magic angle, then flipping the rotation axis to being perpendicular to the magnetic field and then observing the direct dimension under these conditions. The result is a 2D correlation spectrum in which the high-resolution isotropic magic angle spectrum is correlated to the anisotropic 90 spectrum (Fig. 25b). By taking slices through this 2D spectrum and fitting these slices to the characteristic anisotropic lineshapes (Fig. 25c), it is possible to reliably identify and quantify the different Qn environments. From the spectra shown in Fig. 25, the relative populations were quantified to be 9.8% Q2, 83.0% Q3, and 7.2% Q4.121 Another class of advanced 29Si NMR experiments that can reveal structural features of binary glasses118,123,124 are twodimensional double quantum (DQ) correlation experiments which probe spatial proximities (via through-space 29Si–29Si dipolar couplings) or connectivities (via through-bond 29Si–O–29Si J couplings) between neighboring Si environments. Similar experiments were described earlier in the context of pure silica zeolites (see Figs. 16 and 17). For example, Jäger and co-workers 124 have reported 2D 29Si DQ correlation spectra of sodium-silicate binary glasses (see Fig. 26). Through the increased resolution afforded by a 2D spectrum, it is possible to distinguish (and quantify) different sub-types of Q3 and Q4 sites based on the number of neighboring Q3 and Q4 sites in the first coordination shell, providing much more structural information than just the 1D 29Si NMR spectrum alone.

9.06.6

Dynamic nuclear polarization

29

Si NMR

Some of the most exciting recent developments in solid-state 29Si NMR spectroscopy of materials have involved dynamic nuclear polarization (DNP) NMR experiments which have enabled remarkable increases in sensitivity. NMR spectroscopy is an inherently insensitive technique due to relatively small population differences in nuclear spin states at thermal equilibrium, as governed by the Boltzmann distribution. Furthermore, many nuclei (29Si included) have relatively low natural abundance and typically have long spin-lattice (T1) relaxation times, factors which further limit the sensitivity of NMR experiments. This poor sensitivity can be a significant barrier to studying some materials by NMR and can often limit the sophistication of the types of NMR experiments that can be

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Fig. 24 29Si MAS NMR spectra of potassium-containing binary silicate glasses. See Fig. 8 for an explanation of the Qn notation. Q20 represents Q2 units in three-membered rings. Reproduced with permission from Malfait, W. J.; Halter, W. E.; Morizet, Y.; Meier, B. H.; Verel, R. Geochim. Cosmochim. Acta 2007, 71, 6002–6018. Copyright (2007) Elsevier.

performed. This section will briefly describe the DNP NMR experiment and then provide a number of examples involving DNPenhanced 29Si NMR that have extended the capabilities of solid-state 29Si NMR to new materials, and new aspects of materials, through the remarkable gains in sensitivity that DNP NMR enables. For a thorough overview of the theory, instrumentation, and the wide range of applications (from structural biology to materials science) of DNP NMR, the reader is directed to a recent in-depth review125 and handbook126 on the topic. The reader is also directed to a number of recent reviews29,127–130 describing DNP NMR applications to a wide variety of materials, including DNP-enhanced 29 Si NMR of silicon-containing materials.

9.06.6.1

Dynamic nuclear polarization

At the heart of the DNP process is a transfer of spin polarization from unpaired electrons to nearby nuclear spins. For polarization transfer from unpaired electrons to protons, the signal enhancement (3 ) can be as high as 3 ¼ ge/g1H ¼ 658, although in practice signal enhancements of 10–200 are usually observed due to a wide variety of experimental factors. Nonetheless, such gains in sensitivity open up possibilities that could not be achieved under conventional conditions. For example, a gain in sensitivity of 3 ¼ 20 provides a 400-fold reduction in acquisition time, meaning an NMR experiment that would take 1 year to complete under conventional conditions could be carried out in only 1 day with DNP!130 Such gains in sensitivity enable NMR experiments that would never be possible with conventional NMR. A key aspect to any DNP NMR experiment is the presence of unpaired electrons. For most samples of interest, it is necessary to introduce an exogenous polarizing agent to the sample which has unpaired electrons providing the source of polarization. These polarization agents are typically organic nitroxide biradicals, examples of which include TOTAPOL, TEKPol, or AMUPol (see Fig. 27a). The design of organic radical exogenous polarizing agents for DNP NMR is a very active area of current research.

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Fig. 25 29Si 2D magic-angle flipping (MAF) NMR spectrum of a potassium-containing binary silicate glass: (a) expected lineshapes in the 90 dimension whose shapes depend on the chemical shift anisotropy of the various Qn sites. Adapted with permission from Zhang, P.; Grandinetti, P. J.; Stebbins, J. F. J. Phys. Chem. B 1997, 101, 4004–4008. Copyright (1997) American Chemical Society. (b) 2D 29Si MAF spectrum and (c) slices extracted from the 2D spectrum at the indicated 29Si chemical shifts, along with fits to the spectra. Reproduced with permission from Davis, M. C.; Kaseman, D. C.; Parvani, S. M.; Sanders, K. J.; Grandinetti, P. J.; Massiot, D.; Florian, P. J. Phys. Chem. A 2010, 114, 5503–5508. Copyright (2010) American Chemical Society.

The polarizing agents can be incorporated into the sample under investigation in a variety of ways (Fig. 27b). In biomolecular DNP NMR, the typical strategy is to dissolve or suspend the sample of interest (e.g., a protein) in a water/glycerol solution containing the polarizing agent. This solution or suspension is transferred to a MAS rotor then cooled to about 100 K, forming a glass-like solid with glycerol acting as a cryo-protectant. For mesoporous and particulate materials, a small amount of radical containing solution is added that is sufficient to fill the porous volume or uniformly wet the surfaces of the particles (see Fig. 27b). Rossini et al. report that typically only 10 mL of radical containing solution (with a concentration on the order of 10 mM) is required to impregnate and fully fill the porous volume of about 12 mg of a mesoporous silica sample.29 The transfer of spin polarization from the unpaired electrons of the polarizing agent to the nuclear spins of the sample of interest is induced by irradiating the sample with high power (> 10 W) continuous wave (CW) microwaves with frequencies of several hundred MHz. The microwave radiation is generated from a gyrotron source and directed to the sample in the NMR magnet via a waveguide transmission line. When the microwaves are turned on, spin polarization is transferred from unpaired electrons of the polarizing agent to nearby nuclear spins via a several possible mechanisms (solid effect, cross effect, Overhauser, thermal mixing) and the magnetization on the nuclear spins builds up over a period of time. The efficiency of DNP increases as the temperature is lowered, so most DNP NMR experiments are carried out at about 100 K, using cold nitrogen gas to cool and spin the sample for MAS. Fig. 28a provides a schematic diagram of how polarization is transferred from the unpaired electrons of the polarizing agent to the nuclear spins of interest. In an indirect DNP experiment, under microwave radiation (purple wave) the 1H nuclei nearest to the polarizing agent, usually protons in the surrounding solvent, are first polarized by DNP (dashed blue arrows). This polarization is subsequently distributed through the sample via a process called 1H spin diffusion (solid blue arrows). Protons on the surface of a particle or mesoporous material, for example silanols, organic molecules that have adsorbed or been grafted to the surface, or nearby solvent molecules, will eventually become polarized as well. This 1H magnetization can then be transferred via

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Fig. 26 (a) Two-dimensional 29Si double-quantum NMR correlation spectrum of 25Na2O $ 75SiO2 binary glass along with (b) deconvolution of 1D 29 Si MAS spectrum according to Q3,ijk and Q4,ijkl units. The ijk indices for Q3 and the ijkl indices for Q4 indicate the types of Qn in the first coordination shell of the central Q3 or Q4 unit. Adapted with permission from Olivier, L.; Yuan, X.; Cormack, A. N.; Jäger, C. J. Non Cryst. Solids 2001, 293–295, 53–66. Copyright (2001) Elsevier.

Fig. 27 (a) Common nitroxide biradical polarizing agents used in dynamic nuclear polarization NMR. (b) Schematic of sample preparation methods used to incorporate polarizing agents into various types of samples. Adapted with permission from Rossini, A. J.; Zagdoun, A.; Lelli, M.; Lesage, A.; Copéret, C.; Emsley, L. Acc. Chem. Res. 2013, 46, 1942–1951. Copyright (2013) American Chemical Society.

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Fig. 28 (a) Schematic representation of polarization transfer pathways in DNP-enhanced 29Si NMR. See text for more information. (b) Pulse sequence diagram for a DNP-enhanced 1H/29Si CP MAS NMR experiment. Adapted with permission from Rossini, A. J. J. Phys. Chem. Lett. 2018, 9, 5150–5159. Copyright (2018) American Chemical Society.

cross-polarization (solid red lines) to nearby nuclear spins on the surface, such as 13C or 29Si, that experience a dipolar coupling with the polarized protons. A schematic of the pulse sequence for indirect DNP is shown in Fig. 28b. In a direct DNP experiment, nuclear spins near to the polarizing agent are directly polarized (dashed red lines), although the time it takes for polarization to build up this way is typically much longer than in an indirect DNP experiment.131,132

9.06.6.2

DNP-enhanced

29

Si NMR of functionalized silica materials

The mechanism by which DNP operates, as well as the substantial gain in sensitivity it enables, makes DNP MAS NMR an ideal technique for structural characterization of surfaces.29,128,133,134 Emsley and co-workers introduced surface-enhanced NMR spectroscopy (SENS) in a pair of papers133,134 in which DNP-enhanced 13C and 29Si CP MAS NMR were used to study the surface species in functionalized mesoporous silica materials. One of samples studied was a mesoporous silica material having regular channels with a diameter of about 60 Å whose inner surfaces were functionalized with phenol (schematically depicted in Fig. 29). After impregnating channels with radical-containing solvent, indirect DNP-enhanced CP MAS NMR experiments were carried out with gains in sensitivity of 3 > 56 for 13C signals of the surface-bound phenols133 and 3 ¼ 21 for 29Si signals on the channel wall surfaces.134 Fig. 29 shows the 29Si CP MAS NMR spectra of this material with and without microwave radiation being applied, showing the remarkable gain in sensitivity achieved with DNP. This gain in sensitivity allowed the clear observation of signals arising from Tn sites on the surface which are present in quite low concentrations. In addition, the sensitivity gain allowed 1 H/13C and 1H/29Si 2D HETCOR experiments to be performed in just a few hours, revealing structural information in the form of spatial proximities between different environments.133,134 In a study of a polyethylsiloxane-functionalized silica nanoparticle material, De Paëpe and co-workers were able to achieve a sensitivity gain of 3 ¼ 23 for 29Si DNP CP MAS NMR, which allowed for the acquisition of through-space and through-bond

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Fig. 29 DNP-enhanced 29Si CP MAS NMR spectrum of a phenol-functionalized mesoporous silica material. Adapted with permission from Lelli, M.; Gajan, D.; Lesage, A.; Caporini, M. A.; Vitzthum, V.; Miéville, P.; Héroguel, F.; Rascón, F.; Roussey, A.; Thieuleux, C.; Boualleg, M.; Veyre, L.; Bodenhausen, G.; Copéret, C.; Emsley, L. J. Am. Chem. Soc. 2011, 133, 2104–2107. Copyright (2011) American Chemical Society.

2D 29Si DQ correlation experiments (see Fig. 30) in just a few hours (instead of months!), providing information about the interconnectivities between the organosiloxane polymer and the silica nanoparticle surface.135 Similar 2D DQ correlation experiments under DNP enhancement have been carried out by Pruski and co-workers on functionalized MCM-41 type mesoporous silica nanoparticles, revealing structural differences between surface functionalization achieved through co-condensation or post-synthesis grafting.47 Berruyer et al.136 have recently demonstrated that it is possible to determine the three-dimensional structure of an platinumcontaining organometallic complex on the surface of amorphous silica, a feat made possible by the signal enhancement enabled by dynamic nuclear polarization. In this study, an 15N-enriched organic ligand was bound to the silica surface during synthesis, followed by grafting (CD3)3Si groups to the silica surface and derivatization of the organic group with Pt(II). Under DNPenhancement conditions, 29Si{15N} and 13C{15N} REDOR experiments were carried to yield REDOR curves between two N sites of the organic ligand and three Si sites on the surface, as well as between the two N sites and the carbon site at the point of attachment to the surface. From these distance-dependent REDOR curves, ensembles of three-dimensional structures for the organometallic complex on the surface were proposed. The ability to determine three-dimensional structures of catalytically active sites on the surfaces of materials is very important step forward.

9.06.6.3

Other materials studied by DNP-enhanced

29

Si NMR

DNP-enhanced NMR has been applied to a variety of other materials beyond functionalized silica materials. A few of these recent applications are mentioned here. In a study of the complex structure of the zeolite SSZ-70, Smeets et al. employed DNPenhancement to obtain 2D 1H/29Si HETCOR and 2D 29Si DQ correlation spectra which revealed important information about connectivities between Q3 and Q4 sites.137 Using DNP-enhanced 29Si through-bond 2D DQ correlation experiments, Chemlka and coworkers were able to confirm the non-topotactic transformation of silicate nanolayers into a mesostructured zeolite through the observation of correlations between resonances of the nanolayers and the zeolite framework.138 Chmelka and co-workers also employed DNP-enhanced 13C, 29Si, and 31P CP MAS NMR, along with 2D HETCOR and REDOR experiments, to study the adsorption of organic molecules on the surfaces of silicate particles and establishing the molecular origins by which the organic adsorbates inhibit hydration, a process that is important for cement.139 Kumar et al. were able to use information from DNP-enhanced 1H and 29 Si MAS NMR experiments, including 1H/29Si 2D HETCOR and 29Si 2D DQ correlation spectra, to establish an atomic-level structural model for cementitious calcium silicate hydrate.140 Michaelis and co-workers studied silicon nanoparticles through indirect and direct DNP methods.141 They demonstrated that the relatively low sensitivity enhancement observed in indirect DNP experiments is likely to be attributed to the breakdown of exogenous radicals on the nanoparticle surface. However, they were able to observe better sensitivity enhancement in a direct DNP experiment which they attribute to polarization transfer from endogenous radicals arising from dangling bonds on the surface of the silicon nanoparticle. As dynamic nuclear polarization methods continue to improve, and instrumentation becomes more widely available, it is anticipated that DNP-enhanced 29Si NMR will find application to an increasingly wide variety of materials.

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Fig. 30 DNP-enhanced 29Si through-space dipolar-recoupling 2D DQ correlation NMR spectrum of a polyethylsiloxane-functionalized silica nanoparticle. Adapted with permission from Lee, D.; Monin, G.; Duong, N. T.; Lopez, I. Z.; Bardet, M.; Mareau, V.; Gonon, L.; De Paëpe, G. J. Am. Chem. Soc. 2014, 136, 13781–13788. Copyright (2013) American Chemical Society.

9.06.7

Conclusion

29

Si NMR spectroscopy is a powerful technique for probing the structural environments of silicon-containing materials and is a widely used technique, especially for the characterization of silicon-containing solid materials. 29Si chemical shifts are highly diagnostic of the variety of functional groups involving silicon in both solution and solid-state NMR. This review focused mainly on applications of solid-state 29Si NMR to materials like siloxane polymers, porous materials, functionalized silica, zeolites, and glasses, with an emphasis on advanced techniques used to enhance the sensitivity of 29Si NMR and to extract structural information beyond just chemical shifts. Techniques such as cross-polarization, CPMG acquisition, and dynamic nuclear polarization have led to substantial gains in sensitivity for 29Si. Various two-dimensional homonuclear and heteronuclear correlation experiments have enabled the investigation of spatial proximities and covalent bonding networks between 29Si spins and between 29Si and other nuclei, providing bonding and distance information that can be used to solve the three dimensional structures of materials. As sensitivity enhancement techniques and advanced pulse sequences continue to develop, the opportunities for 29Si NMR spectroscopy to probe the structure of matter will continue to expand.

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A.; Lee, J. S. J. J. Phys. Chem. C 2008, 112, 500–513. Fyfe, C. A.; Brouwer, D. H. Can. J. Chem. 2006, 84, 345–355. Fyfe, C. A.; Brouwer, D. H. J. Am. Chem. Soc. 2006, 128, 11860–11871. Fyfe, C. A.; Diaz, A. C.; Grondey, H.; Lewis, A. R.; Förster, H. J. Am. Chem. Soc. 2005, 127, 7543–7558. Fyfe, C. A.; Brouwer, D. H.; Tekely, P. J. Phys. Chem. A 2005, 109, 6187–6192. Dupree, E.; Pettifer, R. F. Nature 1984, 308, 523–525. Oestrike, R.; Yang, W.; Kirkpatrick, R. J.; Hervig, R. L.; Navrotsky, A.; Montez, B. Geochim. Cosmochim. Acta 1987, 51, 2199–2209. Eckert, H. Prog. Nucl. Magn. Reson. Spectrosc. 1992, 24, 159–293. Mauri, F.; Pasquarello, A.; Pfrommer, B. G.; Yoon, Y. G.; Louie, S. G. Phys. Rev. B 2000, 62, R4786–R4789. Eckert, H. Amorphous Materials. In Encyclopedia of Magnetic Resonance, John Wiley & Sons, Ltd, 2007. Malfait, W. J.; Halter, W. E.; Verel, R. Chem. Geol. 2008, 256, 269–277. Edén, M. Annu. Rep. Prog. Chem. Sect. C 2012, 108, 177–221. Srivastava, D. J.; Baltisberger, J. H.; Florian, P.; Fayon, F.; Shakhovoy, R. A.; Deschamps, M.; Sadiki, N.; Grandinetti, P. J. Phys. Rev. B 2018, 98, 134202. Malfait, W. J.; Halter, W. E.; Morizet, Y.; Meier, B. H.; Verel, R. Geochim. Cosmochim. Acta 2007, 71, 6002–6018. Zhang, P.; Dunlap, C.; Florian, P.; Grandinetti, P. J.; Farnan, I.; Stebbins, J. F. J. Non-Cryst. Solids 1996, 204, 294–300. Zhang, P.; Grandinetti, P. J.; Stebbins, J. F. J. Phys. Chem. B 1997, 101, 4004–4008. Davis, M. C.; Kaseman, D. C.; Parvani, S. M.; Sanders, K. J.; Grandinetti, P. J.; Massiot, D.; Florian, P. J. Phys. Chem. A 2010, 114, 5503–5508. Davis, M. C.; Sanders, K. J.; Grandinetti, P. J.; Gaudio, S. J.; Sen, S. J. Non-Cryst. Solids 2011, 357, 2787–2795. Glock, K.; Hirsch, O.; Rehak, P.; Thomas, B.; Jäger, C. J. Non-Cryst. Solids 1998, 232–234, 113–118. Olivier, L.; Yuan, X.; Cormack, A. N.; Jäger, C. J. Non-Cryst. Solids 2001, 293–295, 53–66. Lilly Thankamony, A. S.; Wittmann, J. J.; Kaushik, M.; Corzilius, B. Prog. Nucl. Magn. Reson. Spectrosc. 2017, 102–103, 120–195. Michaelis, V. K.; Griffin, R. G.; Corzilius, B.; Vega, S. Handbook of High Field Dynamic Nuclear Polarization, Wiley, 2020. Rossini, A. J. J. Phys. Chem. Lett. 2018, 9, 5150–5159. Liao, W. C.; Ghaffari, B.; Gordon, C. P.; Xu, J.; Copéret, C. Curr. Opin. Colloid Interface Sci. 2018, 33, 63–71. Rankin, A. G. M.; Trébosc, J.; Pourpoint, F.; Amoureux, J. P.; Lafon, O. Solid State Nucl. Magn. Reson. 2019, 101, 116–143. Hooper, R. W.; Klein, B. A.; Michaelis, V. K. Chem. Mater. 2020, 32, 4425–4430. Lafon, O.; Lilly Thankamony, A. S.; Rosay, M.; Aussenac, F.; Lu, X.; Trébosc, J.; Roumazeilles, V. B.; Vezine, H.; Amoureuxa, J. P. Chem. Commun. 2013, 49, 2864–2866. Lafon, O.; Rosay, M.; Aussenac, F.; Lu, X.; Trébosc, J.; Cristini, O.; Kinowski, C.; Touati, N.; Vezin, H.; Amoureux, J. P. Angew. Chem. Int. Ed. 2011, 50, 8367–8370. Lesage, A.; Lelli, M.; Gajan, D.; Caporini, M. A.; Vitzthum, V.; Miéville, P.; Alauzun, J.; Roussey, A.; Thieuleux, C.; Mehdi, A.; Bodenhausen, G.; Copéret, C.; Emsley, L. J. Am. Chem. Soc. 2010, 132, 15459–15461. Lelli, M.; Gajan, D.; Lesage, A.; Caporini, M. A.; Vitzthum, V.; Miéville, P.; Héroguel, F.; Rascón, F.; Roussey, A.; Thieuleux, C.; Boualleg, M.; Veyre, L.; Bodenhausen, G.; Copéret, C.; Emsley, L. J. Am. Chem. Soc. 2011, 133, 2104–2107. Lee, D.; Monin, G.; Duong, N. T.; Lopez, I. Z.; Bardet, M.; Mareau, V.; Gonon, L.; De Paëpe, G. J. Am. Chem. Soc. 2014, 136, 13781–13788. Berruyer, P.; Lelli, M.; Conley, M. P.; Silverio, D. L.; Widdifield, C. M.; Siddiqi, G.; Gajan, D.; Lesage, A.; Copéret, C.; Emsley, L. J. Am. Chem. Soc. 2017, 139, 849–855. Smeets, S.; Berkson, Z. J.; Xie, D.; Zones, S. I.; Wan, W.; Zou, X.; Hsieh, M. F.; Chmelka, B. F.; McCusker, L. B.; Baerlocher, C. J. Am. Chem. Soc. 2017, 139, 16803– 16812. Berkson, Z. J.; Messinger, R. J.; Na, K.; Seo, Y.; Ryoo, R.; Chmelka, B. F. Angew. Chem. Int. Ed. 2017, 56, 5164–5169. Sangodkar, R. P.; Smith, B. J.; Gajan, D.; Rossini, A. J.; Roberts, L. R.; Funkhouser, G. P.; Lesage, A.; Emsley, L.; Chmelka, B. F. J. Am. Chem. Soc. 2015, 137, 8096–8112. Kumar, A.; Walder, B. J.; Kunhi Mohamed, A.; Hofstetter, A.; Srinivasan, B.; Rossini, A. J.; Scrivener, K.; Emsley, L.; Bowen, P. J. Phys. Chem. C 2017, 121, 17188–17196. Ha, M.; Thiessen, A. N.; Sergeyev, I. V.; Veinot, J. G. C.; Michaelis, V. K. Solid State Nucl. Magn. Reson. 2019, 100, 77–84.

9.07

High field solid-state nmr of challenging nuclei in inorganic systems

Fre´de´ric A. Perras and Alexander L. Paterson, US DOE Ames Laboratory, Ames, IA, United States © 2023 Elsevier Ltd. All rights reserved.

9.07.1 9.07.1.1 9.07.1.2 9.07.1.2.1 9.07.1.2.2 9.07.1.2.3 9.07.2 9.07.2.1 9.07.2.2 9.07.2.3 9.07.2.4 9.07.3 9.07.3.1 9.07.3.2 9.07.3.3 9.07.3.4 9.07.3.5 9.07.3.6 9.07.3.7 9.07.4 9.07.4.1 9.07.4.2 9.07.4.3 9.07.4.4 9.07.4.5 9.07.4.6 9.07.4.7 9.07.4.8 9.07.4.9 9.07.4.10 9.07.4.11 9.07.4.12 9.07.4.13 9.07.4.14 9.07.4.15 9.07.4.16 9.07.4.17 9.07.4.18 9.07.4.19 9.07.4.20 9.07.4.21 9.07.4.22 9.07.4.23 9.07.4.24 9.07.4.25 9.07.4.26 9.07.4.27 9.07.4.28 9.07.4.29 9.07.4.30 9.07.4.31 9.07.4.32 9.07.4.33 9.07.4.34 9.07.4.35

138

Introduction Definitions and scope NMR interactions and their magnetic field dependence Magnetic shielding Electric quadrupolar interaction Paramagnetic interactions High field magnet development Conventional superconducting magnets Achieving fields > 23.5 T (1 GHz) Series-connected hybrid magnets Pulsed magnets Data acquisition methods Spin echoes (Q)CPMG Cross-polarization (CP) Variable offset cumulative spectrum acquisition Frequency-Swept pulses Fast MAS Dynamic nuclear polarization Applications of high field NMR 1 H 11 B 14 N 17 O 23 Na 25 Mg 27 Al 29 Si 33 S 35/37 Cl 39 K 43 Ca 47/49 Ti 55 Mn 59 Co 61 Ni 63/65 Cu 67 Zn 69/71 Ga 73 Ge 75 As 77 Se 79/81 Br 87 Rb 87 Sr 91 Zr 93 Nb 95/97 Mo 111/113 Cd 115 In 119 Sn 121/123 Sb 125 Te 127 I 135/137 Ba

Comprehensive Inorganic Chemistry III, Volume 9

139 139 139 140 141 144 145 145 145 146 147 147 147 148 148 149 149 150 151 152 152 153 153 153 155 156 158 160 160 162 163 163 165 165 165 165 165 166 166 167 167 167 167 168 168 168 169 169 169 170 170 171 171 171 171

https://doi.org/10.1016/B978-0-12-823144-9.00015-7

High field solid-state nmr of challenging nuclei in inorganic systems 9.07.4.36 9.07.4.37 9.07.4.38 9.07.4.39 9.07.5 References

139

La

185/187 207

Re

Pb Bi Conclusions and future outlook 209

139 171 171 172 173 173 173

Abstract Nuclear magnetic resonance (NMR) spectroscopy is a valuable technique for the study of inorganic systems such as organometallics, catalysts, semiconductor materials, battery materials, and surfaces. Experiments on most, though not all, of these systems benefit from being conducted at the highest magnetic field strengths. In this article we discuss the state-of-theart of “high field” solid-state NMR as it pertains to inorganic systems. The chapter will cover fundamental NMR interactions, and their relationship to the magnetic field strength, the development of high field NMR magnets, such as the recent integration of high temperature superconductive components, and a survey of data from “challenging nuclei” relevant to inorganic chemistry. This includes dilute, low-g, and high-Q nuclei, with a focus on the specific considerations involved with acquisition at high field.

9.07.1

Introduction

Nuclear magnetic resonance (NMR) spectroscopy can be used to gain precise structural insights into most materials, regardless of crystallinity or lack thereof, which makes it a particularly powerful tool in materials and inorganic chemistry. Given that NMR interactions are generally only sensitive to very short length scales, they can be used to gain unambiguous information into the coordination environment of a given atom as well as measure distances between it and its neighbors. In practice, however, many elements do not possess NMR-active isotopes with favorable NMR properties, which often prevents the use of NMR for addressing certain structural questions. The push towards higher magnetic fields has been the determining factor that has enabled the NMR investigation of a wider array of nuclides and materials. Increases in magnetic field strengths led to increased sensitivity and resolution which are crucial in studying many elements of interest that possess only quadrupolar NMR-active isotopes. Such efforts have been greatly expanded with the successful construction of hybrid, very high field, NMR magnets incorporating high-temperature superconducting or resistive components, with magnetic fields strengths as high as 36 T. The development of high field dynamic nuclear polarization (DNP) also promises to further enhance the study of rare or dilute nuclides, where high magnetic fields are required for resolution but alone may not provide the necessary sensitivity to enable detection. This article will cover basic topics including the various NMR interactions which impact solid-state NMR spectra, as well as their magnetic field dependence, and common data acquisition methods used to collect NMR data on some of the least sensitive NMRactive nuclides. The applications of high field NMR to various nuclides will then be reviewed to highlight the main points to consider when performing an NMR experiment on a given nucleus, as well as the type of information that can be expected from such an experiment.

9.07.1.1

Definitions and scope

A rigorous definition of “high field,” in the context of NMR, is elusive; as available field strengths have increased, the label of high field has drifted. For the purpose of this review, the term will be used to refer to magnetic fields of 18.8 T and above, which are often referred to as ultrahigh magnetic fields.

9.07.1.2

NMR interactions and their magnetic field dependence

In this section the various interactions impacting solid-state NMR spectra will be reviewed, in particular their field dependence and behavior at high field. On a basic level the overall sensitivity of a typical NMR experiment scales as B03/2, where B0 is the applied magnetic field strength. As such, an experiment carried out at 35 T should be approximately 7 times more sensitive than an experiment carried out at 9.4 T, with a 49-fold reduction in experimental time. In the case of the central transition of half-integer quadrupolar nuclei (nuclear spin I > ½) the sensitivity gain can be as high as B05/2, due to its narrowing at high fields, while in cases where the chemical shift anisotropy is the dominant broadening mechanism the benefits of high fields are much lower (on the order of B01/2) due to the proportional broadening of the powder pattern. The nuclear spin-spin coupling interactions (dipolar and J) are not discussed both due to their small size and field-independence. It is worth mentioning that high-resolution spectra of quadrupolar nuclei can be acquired at zero field via nuclear quadrupole resonance (NQR). This approach can be particularly useful when

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High field solid-state nmr of challenging nuclei in inorganic systems

the quadrupolar interaction is very large and the insights available from NMR are limited.1–3 As NQR is not performed at high fields, it will not be covered in this article.

9.07.1.2.1

Magnetic shielding

The interaction between a nuclear spin and a magnetic field B0 is known as the Zeeman interaction and is represented by the following Hamiltonian: HZ ¼  gZI$ð1  sÞ$B0

(1)

where Z is the reduced Planck constant and g is the gyromagnetic ratio of the nucleus. Note that italicized symbols are used to denote scalars while vectors and matrices are given in bold; for example, the magnetic field oriented in the z direction (the lab frame) B0 is equal to [0,0,B0]. The magnetic field experienced by the nucleus is altered by the nearby electrons whose interactions with the main magnetic field induce weak local fields. This magnetic shielding is represented by a second-rank tensor (s) with nine independent components: 2 1s 3 XX sXY sXZ 3 2 0 6 6 7 7 (2) HZ ¼  gZ½IX IY IZ $6 4 sYX 1  sYY sYZ 5$4 0 5; B0 sZX sZY 1  sZZ The antisymmetric terms, however, seldom impact the NMR spectra. As such we will focus solely on the symmetric part of the tensor, which can be diagonalized to obtain three principal components (eigenvalues: s11, s22, and s33), and their orientations (eigenvectors) relative to the molecule. Note that subscripts of X, Y, and Z are used when referring to a tensor component in the lab frame while 1, 2, and 3 are used when dealing with principal components. In the principal axis system (PAS) the two labeling schemes are equal. It is difficult to measure magnetic shielding directly, which is defined relative to the free atomic nucleus, and as such it is customary to instead use an external standard with a magnetic shielding constant of sref for reference purposes. The obtained chemical shift, d, is defined as: sref  s 1  sref

(3)

dzsref  s

(4)

n  nref nref

(5)

d¼

Experimentally, d is defined as d¼

where n is the observed frequency of the spin of interest in the sample and nref is that of a reference compound. There are two widely used notations for discussing s, or d, known as the Haeberlen and Maryland (or equivalently, HerzfeldBerger) conventions. In the Haeberlen convention, the principal components of the magnetic shielding and chemical shift tensors are ordered as: js33  siso j  js11  siso j  rs22  siso r;

(6)

jd33  diso j  jd11  diso j  rd22  diso r;

(7)

where siso ¼ 13 ðs11 þs22 þs33 Þ and diso ¼ 13 ðd11 þd22 þd33 Þ, are the isotropic parts of the tensors. The Haeberlen notation summarizes the anisotropic part of the tensor, known as the chemical shift anisotropy (CSA), with an anisotropy parameter 1 2

1 2

(8)

3ðd22  d11 Þ 3ðs11  s22 Þ z : 2Od 2Od

(9)

Dd ¼ d33  ðd11 þ d22 Þz ðs11 þ s22 Þ  s33 and an asymmetry parameter hCSA ¼

The Maryland convention instead orders the principal components as: s33  s22  s11 ;

(10)

d11  d22  d33 ;

(11)

and defines the anisotropy and asymmetry of the tensors with the span (U) and skew (k) U ¼ s33  s11 zd11  d33 ;

(12)

High field solid-state nmr of challenging nuclei in inorganic systems

k¼

3ðsiso  s22 Þ 3ðd22  diso Þ z : U U

141

(13)

Each convention has advantages and disadvantages.4–6 In a single crystal each crystallographically-unique site will give rise to a single resonance with a chemical shift value corresponding to the ZZ component of the tensor at that particular orientation, defined using two polar angles q and 4: dZZ ¼ d11 sin2 qcos2 4 þ d22 sin2 qsin2 4 þ d33 cos2 q:

(14)

In a powdered sample, however, the spectrum consists of the statistical distribution of possible dZZ values and a powder pattern is obtained (see Fig. 1) which ranges from d11 to d33. It is often convenient to separate the isotropic and anisotropic parts of dZZ. If the sample is spun rapidly about an angle of b with respect to the magnetic field, the anisotropic part (dani) is scaled by a factor of P2(cosb) ¼ (3cos2b  1)/2, where P2 is the second-order Legendre polynomial, such that dZZ ¼ diso þ P2 ðcosbÞdani ðq; 4; U; kÞ:

(15)

If b is chosen such that this scaling factor equals zero (b z 54.74 degrees, the magic angle), then the observed chemical shift corresponds to diso, regardless of the values of q and 4, and a high-resolution spectrum is obtained. This technique is known as magic angle spinning (MAS) and enables the acquisition of high-resolution NMR data from solids. If the spinning frequency (nR) is inferior to U, however, additional peaks will appear at diso  nnR, which are known as spinning sidebands. It is important to note that the shielding Hamiltonian is linearly dependent on B0 (Eq. 1). Hence, this interaction increases in magnitude at higher magnetic field strengths. For systems where the CSA is the dominant broadening mechanism (e.g., many heavy spin-1/2 nuclides such as 119Sn, 125Te, or 207Pb), this can lead to reduced gains in sensitivity from the higher fields and can complicate data acquisition. There is nevertheless tremendous value in the measurement of CSA which is facilitated at higher magnetic fields, particularly for cases where the interaction is weak or dominated by a stronger interaction such as the electric quadrupolar interaction; for examples see Section 4.28, Section 4.31, and Section 4.36.

9.07.1.2.2

Electric quadrupolar interaction

In addition to a magnetic dipole moment, all nuclides with spin I > ½ possess an electric quadrupole moment, Q: that is to say, the electric charge of the nucleus has a non-spherical spatial distribution. Approximately ¾ of NMR-active nuclei are quadrupolar. The quadrupole moment of the nucleus couples with the electric field gradient (EFG) at the nucleus which, due to the shared orientation of the nuclear magnetic dipole and electric quadrupole moments, leads to a perturbation of the Zeeman energy levels and the NMR resonance frequencies. This is represented by the following Hamiltonian: HQ ¼

eQ I$V$I 2Ið2I  1ÞZ

(16)

Fig. 1 Simulations of the 119Sn static (orange) and MAS (75 kHz, black) NMR spectra of SnO under various magnetic field strengths, plotted in ppm (left) and kHz (right). Parameters from Pöppler, A.-C.; Demers, J.-P.; Malon, M.; Singh, A. P.; Roesky, H. W.; Nishiyama, Y.; Lange, A. ChemPhysChem 2016, 17, 812–816.

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High field solid-state nmr of challenging nuclei in inorganic systems

where e is the fundamental charge and V is the traceless and symmetric EFG tensor with elements corresponding to the second spatial derivative of the electrostatic potential at the nucleus Vij ¼

v2 V : vxi vxj

(17)

The principal components of V are generally ordered by magnitude (|V33 |  | V22 |  |V11 |). The tensor has only two independent principal components, due to the Laplace equation (V11 þ V22 þ V33 ¼ 0), and as such is fully described in its PAS by the quadrupolar coupling constant (CQ) and quadrupolar asymmetry parameter (hQ) that ranges from 0, in axially symmetric cases, to 1. eQV33 ; h

(18)

V11  V22 : V33

(19)

CQ ¼ hQ ¼

The quadrupolar coupling constant is given in frequency units and is typically on the order of MHz. In a spherically symmetric site (e.g., tetrahedral, octahedral), there is no EFG at the nucleus, and the value of CQ is zero. The quadrupolar and Zeeman interactions do not share the same quantization axes (the Zeeman interaction aligning the spins with B0 and the quadrupolar interaction with V33 in the molecule frame) and as such the two interactions do not commute. A particularly useful approach to solving the combined Zeeman-quadrupolar Hamiltonian is to treat the quadrupolar interaction as a small perturbation to the Zeeman interaction. To first order, this Hamiltonian becomes ð1Þ

HQ ¼

  2 eQ 3IZ  I2 VZZ ðq; 4Þ 6Ið2I  1Þ

(20)

  2 eQ 3m  IðI þ 1Þ VZZ ðq; 4Þ 6Ið2I  1Þ

(21)

which has expectation values of ð1Þ

hmjHQ jmi ¼

where m is the magnetic quantum number which ranges from  I to I. There are 2I allowed NMR transitions with | Dm | ¼ 1. As can be seen in the above equation and Fig. 2, both the m ¼ 1/2 and the m ¼  1/2 states are shifted by the same amount and as such the central transition (CT, m ¼  1/2 to H1/2) is unaffected by the quadrupolar interaction to first order while the other transitions, known as satellite transitions (ST), are considerably broadened.7 Note that integer spin quadrupolar nuclei (such as 2H and 14N) do not have a CT, which can complicate their observation. Due to the size of the interaction, it is often necessary to consider higher orders of HQ, with the second-order perturbation usually being sufficient, although there are notable exceptions.8,9 The second-order perturbation (and CT linewidth) has the following dependence on the Larmor frequency (nL) ð2Þ

HQ f

C2Q nL

(22)

and as such is weakened at higher magnetic fields. In units of ppm, the enhancement in resolution has a B02 dependence! Typical lineshapes arising from the first and second-order quadrupolar interactions are shown in Fig. 3.

Fig. 2 The energy level diagram of a spin-5/2 system considering the cumulative effects of the Zeeman interaction (left), the first-order quadrupolar interaction (middle), and the second-order quadrupolar interaction (right). Figure adapted from MacKenzie, K. J.; Smith, M. E. Multinuclear Solid-State Nuclear Magnetic Resonance of Inorganic Materials; Elsevier, 2002; p. 54.

High field solid-state nmr of challenging nuclei in inorganic systems

143

Fig. 3 Satellite (A) and central (B) transitions arising from a 27Al environment with a CQ of 2.5 MHz and varying hQ as a function of external field; note the differences in the axes. In (B), spectra are plotted both under MAS (black) and static (orange) conditions.

The first-order quadrupolar interaction has the same orientational form as the CSA and as such can be averaged by sufficiently fast MAS. The second-order perturbation, however, depends on the zeroth-, second-, and fourth-order Legendre polynomials of cosb   (P0(cosb) ¼ 1; P4 ðcosbÞ ¼ 18 35cos4 b 30cos2 b þ3 ) and cannot be fully averaged by MAS, although MAS generally reduces central transition linewidths by  1/3. The second order perturbation is given by ð2Þ

Q Q S S S nQ ¼ AQ 0 C0 ðm1 ; m2 ÞP0 ðcosbÞ þ A2 ðq; 4ÞC2 ðm1 ; m2 ÞP2 ðcosbÞ þ A4 ðq; 4ÞC4 ðm1 ; m2 ÞP4 ðcosbÞ:

(23)

Here the spatial (AQi ) and spin (CSi ) parts are separated.10 Note that the first term is isotropic, meaning that the center of mass of the peak is shifted away from diso. This is known as the quadrupole-induced shift, which is given by: ! ð2Þ

dQ;iso ¼

3C2Q 1 þ 40nL

I2 ð2I 

h2Q 3

1Þ

2

½IðI þ 1Þ  9mðm  1Þ  3

106 ppm=MHz : nL

(24)

The two anisotropic terms can be removed, for instance, by spinning about two angles simultaneously to set P2(cosb) and P4(cosb) to zero, a technique known as double-rotation (DOR).11 Isotropic spectra may also be obtained in two-dimensional experiments either by changing b over two evolution periods t1 and t2 such that P2 ðcosb1 Þt1 ¼  P2 ðcosb2 Þt2 ;

(25)

P4 ðcosb1 Þt1 ¼  P4 ðcosb2 Þt2 ;

(26)

a technique known as dynamic angle spinning (DAS),

12

or by correlating two transitions under MAS such that   ¼ CS4 m01 ; m02 t2 ;

CS4 ðm1 ; m2 Þt1

(27)

which is known as multiple-quantum MAS (MQMAS) if m1 ¼  m2 and satellite transition MAS (STMAS) otherwise. Both MQMAS and STMAS can be performed on conventional MAS probes (Fig. 4).15 As it involves multiple-quantum coherences MQMAS is the least sensitive high-resolution technique, but is the easiest to perform since all the transitions involved are not 13

14

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Fig. 4 Comparison of 17O MAS, DOR, and MQMAS NMR spectra of monosodium L-glutamate monohydrate, which has eight crystallographically inequivalent oxygen sites. (A) MAS NMR spectrum at 14.1 T and 15 kHz MAS. (B) DOR NMR spectra at 14.1 T and 18.8 T. (C) 2D MQMAS NMR spectrum at 18.8 T; the isotropic projections at 14.1 T and 18.8 T are shown in (D). Modified from Wong, A.; Howes, A. P.; Yates, J. R.; Watts, A.; Anupõld, T.; Past, J.; Samoson, A.; Dupree, R. & Smith, M. E. Phys. Chem. Chem. Phys. 2011, 13, 12213. Published by the PCCP Owner Societies.

perturbed by the first-order quadrupolar interaction. Only DOR yields isotropic spectra in a single dimension, making it possible to perform high-resolution correlation spectroscopy between quadrupolar isotopes.16

9.07.1.2.3

Paramagnetic interactions

In systems containing unpaired electrons, the spin-spin coupling between the nucleus and the electrons, known as the hyperfine coupling, can be quite large. This interaction has a similar form as the nuclear spin-spin coupling Hamiltonian and is described by the hyperfine coupling tensor A. Note that for simplicity here A includes both through-space spin-dipolar terms as well as the isotropic Fermi contact terms.17 The hyperfine coupling Hamiltonian is given by A Hhyp ¼ I$A$S ¼ I$ $me : ge

(28)

In this expression S corresponds to the electron spin. Most often, however, the electron relaxation is fast on the NMR timescale and the nuclei only see the effective magnetic moment of the electrons, me ¼

m2B SðS þ 1Þ 2 g B0 ; 3kB T

(29)

which is non-zero due to the electron spins’ far greater Boltzmann polarizations. Here mB is the Bohr magneton, kB is the Boltzmann constant, T is temperature and g is the electron g tensor. In this regime, Hhyp takes a form akin to magnetic shielding:   m2 SðS þ 1Þ A 2 Hpara ¼ B $g $B0 (30) I$ 3kB T ge This interaction thus leads to shifts in the position of the resonances that are temperature-dependant, anisotropic, and scale linearly with B0. Like the CSA, there is thus little reason to perform paramagnetic NMR at high magnetic fields except for the measure  ment of the paramagnetic shift tensor gA $g2 , which can be most easily measured at high field, or if a secondary interaction such as e

the quadrupolar interaction is dominant. For this reason, most highly paramagnetic systems, such as battery materials, are studied at low fields where the interaction is weak. In metals, where the coupling is to conduction band elections, this interaction is known as

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the Knight shift. The effects of the paramagnetic interactions on NMR have been thoroughly and comprehensively reviewed by Pell, Pintacuda, and Grey, and we direct the reader there for additional details.18

9.07.2

High field magnet development

9.07.2.1

Conventional superconducting magnets

Early NMR experiments were conducted using iron-core resistive electromagnets, which quickly reached the practical upper limit of their field strength at 2.35 T. The first commercialized superconducting NMR spectrometer was reported in 1964 by Nelson and Weaver and produced by Varian Associates.19 This early superconducting magnet reached a field strength of 4.7 T, corresponding to a 1H nL of 200 MHz, with a magnet strongly resembling current superconducting magnets. At the time, the authors expected that 10 T was the practical upper limit in field strength achievable by superconducting magnets. These early superconducting magnets were produced using wires drawn from a NbZr alloy. Further experience led to a NbTi alloy being preferred due to its greater ductility. By embedding NiTi wires in a copper matrix and slightly twisting the overall wire, the superconducting coil became more resistant to flux jumps, a phenomenon which led to frequent quenching in early magnets.20 Copper-shunted NbTi wire was used to produce magnets with field strengths of 9.4 T in the late 1970s, which proved to be the upper limit of the material, due to its critical field of 11.7 T at 4.2 K. The critical field is the magnetic field above which superconductivity is suppressed and it is dependent on both temperature and pressure. The limitations of the critical field are a major driving force behind the development of new superconductors. To achieve fields greater than 9.4 T, magnet design turned to Nb3Sn. A Nb3Sn inner coil was placed within a NbTi outer coil, boosting the effective magnetic field. This required several advances in fabrication, in particular the “bronze process” for generating multi-filament Nb3Sn wires (as opposed to conventional Nb3Sn tape)21 and the development of compatible superconducting joints. Nb3Sn has a critical field of about 20 T at 4.2 K, and in the early 1980s 11.75 T magnets (1H nL of 500 MHz) became available. However, despite improvements in the physical properties of Nb3Sn from doping with titanium and tantalum,22 it is difficult to achieve fields greater than 17.6 T at 4.2 K due to practical limitations on the size of Nb3Sn magnets near their critical field.23 By reducing the temperature of the superconducting coil, the critical field of the material is increased by an additional 2–3 T. This sub-cooling of the coil, along with changes in the coil geometry to enable additional current, have led to the current state-of-the-art for low-temperature superconductors (LTS). Fields of 18.8 T, 19.97 T, and 21.15 T all became available during the 1990s.24 The highest field commercially available for conventional LTS is 23.5 T (1H nL of 1 GHz), designed and manufactured by Bruker and first available in 2009. Given the physical limitations of current LTS wires, it appears that 23.5 T may be the practical upper limit in magnetic field strength achievable by LTS alone; no new pure LTS magnet with higher field has become commercially available in the last 10 years. However, as we discuss below, new approaches to magnet design continue to push the limit of accessible magnetic fields for NMR spectroscopy.

9.07.2.2

Achieving fields > 23.5 T (1 GHz)

As discussed above, modern LTS appear to have hit their field strength ceiling at 23.5 T. Nevertheless, in 2018 Bruker released the first commercial 25.9 T magnet (1H nL of 1.1 GHz), and in 2020 delivered the first commercial 28.2 T magnet (1H nL of 1.2 GHz). The critical advance comes in the development of effective high-temperature superconductive (HTS) tape. Like the NbTi/Nb3Sn dual coil approach used to increase the field strength of LTS magnets, a triple coil approach can be used to break the 23.5 T limit. These new magnets use a HTS insert inside of a Nb3Sn coil, which in turn is contained within a NbTi coil (Fig. 5). The development of effective HTS magnet inserts required substantial advances in wire manufacturing: a HTS NMR magnet

Fig. 5 A schematic of a three-coil LTS-HTS hybrid magnet with 1H nL >1 GHz. The outer coil is made with NbTi wires, the middle with doped Nb3Sn wires, both of which are LTS. The inner coil is made of HTS tape, e.g., Bi-2223 or REBCO. Figure courtesy Bruker.

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High field solid-state nmr of challenging nuclei in inorganic systems

coil requires many hundreds of meters of wire,25 but most HTS are brittle ceramics (e.g., yttrium barium copper oxide (YBCO) or Bi2Sr2Ca2Cu3O10-x (Bi-2223)), and cannot be produced in the same manner as NbTi or Nb3Sn wires. There are ongoing efforts to increase the available field strength of LTS/HTS hybrid magnets. A team at the Francis Bitter Magnet Laboratory at the Massachusetts Institute of Technology (MIT) is actively developing at 30.5 T magnet (1H nL of 1.3 GHz) utilizing a rare-earth barium copper oxide (REBCO) insert with an 18.8 T magnetic field located in a LTS magnet with a 11.7 T magnetic field.26 However, recent reports show that further development is required to mitigate issues with quenching of the HTS component.27 The MIRAI program of the Japan Science and Technology Agency is currently actively developing superconductive joints for HTS wire, with the ultimate goal of constructing a 30.5 T magnet in 2024.25 The above approaches focus on the development of persistent magnets, i.e., those that do not require an active power supply. These magnets have advantages when it comes to power consumption, field stability, field homogeneity, and ease of use. However, higher magnetic fields can be achieved when working with resistive magnets, as will be outlined in the following sections.

9.07.2.3

Series-connected hybrid magnets

The highest field strengths accessible for high-resolution NMR spectroscopy at the time of writing come from the series-connected hybrid (SCH) magnet located at the United States National High Magnetic Field Laboratory (NHMFL). Commissioned in 2017, the SCH magnet is effectively an (unconventional) superconducting magnet boosted to ultra-high field by a resistive magnet insert (Fig. 6).28 This “magnet-in-magnet” approach is similar to magnet designs relying on HTS inserts, vide supra. While the earliest NMR spectrometers were constructed from resistive magnets, modern resistive magnets are not typically used for high field NMR. In principle resistive magnets can reach arbitrary field strengths, limited only by available power and magnet cooling, but the magnetic fields produced are typically insufficiently homogeneous over the sample space to allow for routine NMR investigation. In the SCH magnet the requisite field homogeneity is achieved by operating the superconducting magnet portion and the resistive magnet portion in electrical series. Both magnets are driven by the same power supply and are charged and discharged together. This requires a different approach to the construction of the superconducting coils as compared to those in conventional superconducting magnets: the requirement to frequently change the current in the superconducting coil of the hybrid magnet requires far greater tolerance to thermal fluctuations. The SCH superconducting wires are constructed in a style known as “cable-in-conduit conductor,” which results in superconductive wires with a substantial void space. During operation, supercritical helium is used to actively cool the superconductive wires, hence dramatically reducing the likelihood of a quench during routine operations. The series arrangement results in a dampening of high-frequency oscillations in the magnetic field that are frequently observed in resistive magnets. Low-frequency oscillations in the field are mitigated by a field-frequency lock system. The result is a magnetic field that can be regulated to a tolerance of 0.2 ppm, which is sufficient for most solid-state NMR experiments. The primary practical drawback to series-connected hybrid magnets is their intense power consumption, which can make continuous operation both cost- and resource-prohibitive.

Fig. 6 An example of the components involved in the SCH magnet, as well as a schematic of its design. (a) LTS wire. (b) A plate used for the resistive magnet component. (c) Length- and cross-section of the cable-in-conduit conductor. (d) The resistive coils of the SCH. (e) The superconducting coils of the SCH magnet. (f) The high-temperature superconducting junction between (d) and (e). (g) Cooling water feed. (h) Probe access. Modified from Gan, Z.; Hung, I.; Wang, X.; Paulino, J.; Wu, G.; Litvak, I. M.; Brey, P. L. G. W. W.; Lendi, P.; Schiano, J. L.; Bird, M. D.; Dixon, I. R.; Toth, J.; Boebinger, G. S.; Cross, T. A. J. Magn. Reson. 2017, 284, 125–136.

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147

Pulsed magnets

The highest magnetic fields achieved to date come from the use of pulsed magnets. Single-shot field strengths of up to 100 T have been achieved,29 and pulsed field strengths in the area of 50 T are relatively routine.30–32 However, NMR experiments are challenging to run on magnets with pulsed fields due to their poor magnetic field homogeneity over the sample volume, as well as the time-dependence of the magnetic field. Nevertheless, pulsed magnets have been used in solid-state NMR studies: for example, 11 B NMR spectra of the BO3 environment in magnetic SrCu2(BO3)2 were acquired at 54 T,30 and 27Al NMR spectra of Linde type-A zeolites at were acquired at a field of 55.7 T.33 There are ongoing efforts to improve the homogeneity of pulsed magnets, which if successful could expand the range of useful applications.34

9.07.3

Data acquisition methods

9.07.3.1

Spin echoes

The simplest NMR experiment, the Bloch decay, consists of a single 90 excitation pulse to tilt the magnetization into the transverse plane for detection by the probe coil. If the NMR line is broad, however (as is often the case when studying exotic nuclides), then the signal may significantly decay by the time the receiver is switched on, due to the need for a pre-acquisition delay to allow for the pulse to ring down. In such cases, echo sequences may be used to delay the start of the free induction decay. The simplest echo sequence to refocus the entirety of the signal, and the most frequently used, is the Hahn echo sequence (90-s-180-s-acq) (Fig. 7A). Here, the 180 pulse reverses the sense of the precession, leading to the return into phase of all signal contributions after s and the formation of a spin echo. Generally, low s values are preferred for sensitivity reasons, although whole echo acquisitions pffiffiffi (90-s1-180-s2-acq; s1 >> s2) are preferred if the spin-spin relaxation rate is low as these yield a 2 higher signal-to-noise ratio. s, or s1, need to be integer multiples of the rotor period in the case of MAS experiments. Echo sequences have the additional benefit of reducing the signal contributions from components situated outside the coil (e.g., probe background). In the case of spin-1 nuclei, echoes may be formed instead by using a quadrupolar echo (90-s-90-s-acq) where the second pulse is used to exchange the two single-quantum transitions that are mirror images of one another. Unlike the Hahn echo, this does not involve a change in coherence order. Half-integer quadrupolar nuclei have more complex spin dynamics. If excited alone, the central transition will nutate at an increased rate of (I þ 1/2)nrf which requires the use of shorter pulses than measured when using liquid or cubic samples where all transitions are excited simultaneously. In this CT-selective regime the central transition can be manipulated like a spin-1/2 nucleus and the Hahn echo experiment is able to produce an echo refocusing the majority of the NMR signal. In practice, there are many considerations which affect the optimal echo sequence. To obtain the highest quality lineshapes Bodart et al. have shown   that the radiofrequency field strength should be set to D= I þ12 (or slightly less), where here D is the breadth of the static central transition line (in Hz); the phase cycle should be set, depending on I, to a 6, 8, 10, or 12 scan sequence; and that while a 90-s-180-sacq sequence provides the best sensitivity, it may introduce unacceptable lineshape distortions.36 They find that a 90-s-90-s-acq

Fig. 7 (A) A Hahn echo pulse sequence. If s1 >>s2, the whole echo is acquired. (B) A CPMG pulse sequence with half-echo acquisition. sCPMG is defined by the length of the loop period. (C) A CP pulse sequence utilizing a ramped 1H spin locking pulse, which broadens the Hartmann-Hahn condition (D).35

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High field solid-state nmr of challenging nuclei in inorganic systems

sequence provides a reasonable compromise between sensitivity and lineshape fidelity. Note that this 90-s-90-s-acq sequence is commonly referred to as a solid echo. It is distinct from the quadrupolar echo mentioned above and can be effectively thought of as a Hahn echo where only half of the signal is refocused.

9.07.3.2

(Q)CPMG

If the refocusable decay rate (T2’) is significantly longer than the decay rate of the free induction decay (T2*), it becomes possible to acquire multiple echoes in sequence before needing to wait for spin-lattice relaxation. This is the general idea behind the CarrPurcell Meiboom-Gill (CPMG) sequence.37–40 Note that in the case of half-integer quadrupolar nuclei, CT-selective pulses must be used, and the sequence is referred to as the quadrupolar CPMG (QCPMG). The sensitivity enhancement from CPMG (3 CPMG), assuming a matched filter is applied,41 is equal to qffiffiffiffiffiffiffiffiffiffiffi  0 3 CPMG ¼ 2 T 2 T 2 nCPMG ; (31) where nCPMG is the frequency at which the echo pulses are applied, i.e., the CPMG frequency. The highest sensitivity enhancement pffiffiffiffiffiffiffiffiffiffiffiffiffi that can be obtained without truncation is 2 T 02 =T 2 and can be surprisingly large.42,43 The CPMG experiment is presented in Fig. 7B. In its simplest form, the experiment consists of a Hahn echo followed by a train of refocusing pulses. When the echo manifold is Fourier transformed, the resulting spectrum consists of a series of “spikelets” whose intensity reproduces the outline of the powder pattern (for examples, see Figs. 8, 22 and 27). The separations between the spikelets equals the frequency at which the refocusing pulses are applied and corresponds to the digital resolution when Fourier transforming a single echo. This variable is limited in the case of MAS since nCPMG must be a multiple of twice the MAS frequency. The echo spacing can be reduced to acquire a larger number of echoes, and in doing compressing the signal into fewer spikelets, thus enhancing the sensitivity at the expense of digital resolution. In a thorough study, Dey et al. determined that the optimal number of spikelets to maximize the information content in the presence of noise was in the range of 10.44 In the case of ultra-wide lines, using the widest spikelet separation possible is generally optimal.

9.07.3.3

Cross-polarization (CP)

The most commonly applied scheme for the excitation of a spin-1/2 nucleus is cross-polarization (CP).45,46 The CP pulse sequence (Fig. 7C) involves the initial excitation of a faster-relaxing, and ideally more magnetic, nuclide (most often 1H) after which its transverse magnetization is spin-locked with the application of an in-phase radiofrequency pulse. A radiofrequency pulse is then applied

Fig. 8 35Cl WCPMG NMR spectra of tetrachloroterephthalonitrile at 21.1 T (bottom) and 35.2 T (top). The two unique Cl sites are observable in both spectra. The VOCS subspectra are presented in color, while the overall spectra are presented in black. Modified from Szell, P. M. J.; Bryce, D. L. Concepts Magn. Reson. Part A 2016, 45A (6), e21412.

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149

to the nuclide of interest with a power satisfying the Hartmann-Hahn condition (gHB1(1H) ¼ gXB1(X), Fig. 7D). In doing so the precession frequency of the two nuclei is matched in the rotating frame, enabling for magnetization exchange between them. When the spin locking pulses are turned off, the X magnetization will begin to freely precess as though it had been excited by a 90 degrees pulse. CP experiments can then be repeated at the typically faster 1H relaxation rate and lead to the enhancement of X magnetization by a value nearing the ratio of their gyromagnetic ratios: (3 CP z gH/gX). CP is less effective in the case of quadrupolar nuclei which cannot be reliably spin locked under MAS47,48 and generally relax faster than the 1H spins.

9.07.3.4

Variable offset cumulative spectrum acquisition

Even with the highest magnetic field strengths available at the time of writing, many nuclei give rise to NMR spectra with linewidths that exceed the bandwidths of the pulses or even the probe. In such cases it is impossible to excite or detect the entirety of the spectrum at once. An effective method for acquiring such “ultra-wideline” spectra is to collect them via the variable offset cumulative spectrum (VOCS) acquisition method. In VOCS, the experiment is repeated at different transmitter offsets, and the spectra are then subsequently summed. To avoid distorting the powder pattern, the choice of frequency offset should be less than the observed effective excitation bandwidth of an individual experiment. Generally, incrementing the transmitter by < 1/3 the baseline-to-baseline width of a subspectrum produces relatively distortionless spectra. Additional care must be taken when using CPMG acquisition, where the transmitter offset must be stepped in an integer multiple of the CPMG spikelet separation. In the case of half-integer quadrupolar nuclei, the use of high magnetic fields enables a reduction in the number of sub-spectra that need to be acquired. For example, Szell and Bryce compared the 35Cl spectra of tetrachloroterephthalonitrile at 21.1 T and 35.2 T (Fig. 8).1,49 At the lower field, 20 sub-spectra were required to fully collect the powder pattern, while at the higher field only 14 sub-spectra were required. This is a significant difference to the user given that VOCS requires re-tuning of the probe at each frequency step, which typically precludes overnight acquisition unless the investigator is highly motivated (or sufficiently desperate). For instance, a 79/81Br NMR spectrum of CaBr2 acquired by Perras spanning over 20 MHz required the acquisition of a total of 167 sub-spectra.8 Pecher and coworkers have recently reported on the development of a tuning and matching robot which can be automatically controlled from the spectrometer terminal, allowing for frequent re-tuning without manual intervention.50 For resistive or hybrid magnets, an alternative option to stepping the transmitter for the acquisition of very broad spectra is to instead step the magnetic field.51,52 This has been demonstrated at high fields on a 25 T purely resistive magnet53 as well as at about 35.2 T on the SCH magnet.1 In the former case, a 35Cl VOCS spectrum of (C5H5)2ZrCl2 was collected in three VOCS sub-spectra, with the field stepped by 0.048 T (equivalent to a frequency step of 200 kHz). An advantage of field stepping is that it does not require access to the probe and can be done entirely remotely. Care must be taken, however, to ensure that the field dependence of the CSA and quadrupolar interactions are taken into account while processing field-stepped data.54 This requires the simulations of parts of the NMR spectrum as a function of the magnetic field, either continuously,55 or by replicating the VOCS procedure in silico.52

9.07.3.5

Frequency-Swept pulses

In 2007, Bhattacharyya and Frydman demonstrated that broader excitation bandwidths could be obtained by performing echo experiments with frequency-swept, or chirped, pulses as opposed to hard square pulses.56 This approach reduces the number of VOCS sub-spectra that need to be acquired and in doing so enhances the sensitivity of the experiment. To obtain a full echo, as is obtained for instance using a conventional Hahn echo sequence, the rate of the refocusing pulse needs to double that of the excitation pulse (Fig. 9A). Alternatively, if the rates of the two pulses are kept equal, a frequency-progressive echo is produced that mimics the shape of the NMR spectrum (Fig. 9B). Frequency-progressive echoes require second-order phase corrections to obtain in-phase spectra.59 O’Dell and Schurko later built on this concept, demonstrating that frequency-progressive echoes could be acquired in sequence à-la CPMG,57 an approach which currently provides the highest sensitivity per time in the acquisition of ultra-wideline NMR spectra (Fig. 9C). Note that wideband uniform rate and smooth truncation (WURST) pulses are most often used for this experiment, which is thus often referred to as WURST-(Q)CPMG or WCPMG, although other pulse shapes have been used.60 The practical aspects of acquiring WCPMG data have been described in detail by Hung and Gan and the reader is referred there for more details.59 Polarization transfer using CP can also be enhanced in bandwidth with the use of frequency-swept pulses. Unlike the echo and CPMG cases, here the swept pulse needs to be sufficiently long and powerful in order to result in the adiabatic inversion of the powder pattern. During this inversion the signal is spin locked to the effective field of the pulse and the higher magnetization from 1H spins can be transferred by CP. Enhanced longitudinal magnetization is produced which may then be excited and detected using WCPMG, for instance in the broadband adiabatic inversion (BRAIN) BRAIN-CP-WCPMG experiment (Fig. 9D).58 This approach has proved useful in the case of low-g nuclei which have low Boltzmann polarization and often have long relaxation times.58,61–64

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High field solid-state nmr of challenging nuclei in inorganic systems

Fig. 9 (A) A WURST-echo experiment with the rate of the refocusing pulse (P2) twice that of the excitation pulse (P1) thus generating a full echo. (B) A WURST-echo experiment with both pulses kept equal, thus generating a frequency-progressive echo (dashed line) which, when magnitude corrected, reproduces the shape of the NMR spectrum (solid line).56 (C) The WCPMG experiment.57 (D) The BRAIN-CP-WCPMG experiment.58 Arrows indicate the direction and rate of the frequency-sweep.

9.07.3.6

Fast MAS

The relative sensitivity of an NMR experiment depends on a number of factors, which include the gyromagnetic ratio of the excited (gexc) and detected (gdet) spins, the spin-lattice relaxation time of the excited spin (T1,exc), as well as the linewidth of the detected spin (Wdet), and the probe Q factor at the detected frequency (Qdet):65 3=2

S=Nf

1=2

gexc gdet Qdet 1=2 1=2 Wdet T1;exc

:

(32)

A cross-polarization experiment replaces gexc with the higher value from 1H spins as well as the typically smaller T1 value of 1H spins. Further gains in sensitivity can be obtained if 1H spins are detected in lieu of the lower-g nuclide, which also replaces gdet, along with Qdet, with the higher value; an approach known as indirect detection. Unfortunately, due to the numerous and strong 1 He1H homonuclear dipolar interactions found in most protonated materials, the proton linewidth (WH) is generally large and most of the sensitivity advantages are lost. In addition, the greater linewidth reduces the information content from the 1H dimension, making it difficult to justify the longer two-dimensional acquisition. The broadening caused by homonuclear dipolar interactions can, however, be mitigated by faster MAS:65–68 WH fn1 r :

(33) 69 1

With the development of MAS probes capable of spinning samples at frequencies surpassing 150 kHz, H detection has become the approach of choice for biomolecular solid-state NMR and has increasingly been used for the detection of exotic nuclei in inorganic systems.68,70–75 For most spin-1/2 nuclei, the most reliable approach to 1H detection is to use a double-CP sequence wherein magnetization is transferred to the desired nuclei for evolution during the t1 period of a two-dimensional experiment, the remaining 1H magnetization is purged with saturation pulses, and then the evolved magnetization of the heteronuclei is transferred back to 1H for detection (Fig. 10A). Venkatesh et al. have demonstrated that in the case of quadrupolar nuclei it is often best to directly excite the quadrupolar nucleus, due to its shorter T1 relaxation time, and transfer its magnetization to 1H for detection.76 This is most efficiently achieved with a dipolar-based insensitive nuclei enhanced by polarization transfer (D-INEPT) sequence due to the difficulty in spin locking quadrupolar nuclei (Fig. 10B).47 Otherwise, for heavy spin-1/2 nuclei with large CSA, where CP provides insufficient bandwidth, as well as some quadrupoles, a suitable replacement for the double-CP experiment is the dipolar heteronuclear multiple-quantum coherence (D-HMQC) experiment (Fig. 10C), which is less demanding on the heteronuclide. Infinite MAS spectra as well as STMAS spectra have also been 1H-detected with the use of D-HMQC.72,77 It is important to note, however, that achieving the greater MAS rates needed to perform 1H-detection requires the use of smaller rotors (diameters ranging

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Fig. 10 1H-detection sequences employing (A) double-CP, (B) D-INEPT, and (C) D-HMQC. Dec blocks indicate decoupling, while Rec blocks indicate recoupling. A directly detected 1He13C HETCOR spectrum of allyl-MCM silica, (D), is compared to a 1H-detected spectrum, (E). The 1Hdetected spectrum required 15 min while the 13C-detected spectrum was acquired in 15 h. Adapted with permission from Wiench, J. W.; Bronnimann, C. E.; Lin, V. S.-Y.; Pruski, M. J. Am. Chem. Soc. 2007, 129, 12076–12077. Copyright 2007 American Chemical Society.

from 1.6 to 0.5 mm) which dramatically reduces the sample sizes and per-rotor sensitivity. For this reason, sensitivity enhancements over conventional CPMAS with larger rotors are generally only obtained when studying low-g nuclei. At higher magnetic fields, fast MAS can be a necessity due to the scaling of the CSA which requires higher MAS rates to average.28,78,79

9.07.3.7

Dynamic nuclear polarization

Electron spins possess magnetic moments that far outclass those of nuclei (658 times larger than 1H). As such, it was recognized early on that the sensitivity of NMR would be dramatically enhanced if polarization transfer from unpaired electrons was used to polarize nuclei. This was originally postulated by Overhauser, and demonstrated experimentally by Slichter, in 1953 and became known as dynamic nuclear polarization (DNP).80,81 As magnetic field strengths increased, however, with the development of high field and high resolution NMR, the lack of availability of microwave sources capable of reaching the Larmor frequency of the electron spins at those fields hindered the development of high field DNP. Furthermore, a high-power microwave source (> 10 W) is required in order to successfully saturate the electron paramagnetic resonance (EPR) line and perform DNP. This status quo came to an end in 1993 when Griffin and co-workers introduced the gyrotron as a viable high power, and high frequency, microwave source for high field DNP.82 Initially produced for a 5 T NMR system, these successes led to the commercialization of MAS-DNP systems and the development of gyrotrons operating at ever higher frequencies. At the time of writing, MAS-DNP spectrometers with 1H Larmor frequencies of up to 900 MHz have been developed. The three most important DNP mechanisms are the solid-effect (SE), cross-effect (CE), and Overhauser effect (OE).83 The SE requires the saturation of zero or double-quantum electron-nuclear transitions that occur at frequencies of ne  nn, where ne is the electron Larmor frequency and nn is the nuclear Larmor frequency. The Overhauser effect involves the cross-relaxation of nuclei and electrons when the electron EPR transition is saturated. The same mechanism is responsible for the nuclear Overhauser effect commonly applied in solution NMR. Lastly, the cross-effect is a fundamentally-allowed 3-spin mechanism involving two electrons and a single nucleus when the difference in the resonance frequencies of the electron spins matches that of the nuclear spin. CE is responsible for most high field DNP investigations. With the introduction of 400 MHz MAS-DNP spectrometers, much success was obtained with the use of dinitroxide biradicals where the tethering of the two nitroxides facilitated the use of CE DNP.84 With two identical radicals, CE requires that the g anisotropy be greater than the nuclear Larmor frequency and as such narrow-line radicals would only operate through the less efficient SE. This is problematic for higher magnetic fields given that the g anisotropy increases in magnitude with B0 while the microwave powers are reduced at higher frequencies and dielectric sample heating becomes more severe. As such DNP enhancements with dinitroxides decrease far more steeply than the expected B0 1 relationship and are usually over an order of magnitude weaker at 18.8 T than they are at 9.4 T.85–87 The shortcomings of the dinitroxides motivated efforts by the groups of Griffin and Emsley to find alternative polarizing agents for very high field DNP. The two most successful candidates at the time of writing are the narrow-line monoradical BDPA, which is

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High field solid-state nmr of challenging nuclei in inorganic systems

able to polarize nuclei through the Overhauser effect with increasing efficiency as B0 is increased88 (although the mechanism is poorly understood and not agreed upon89) and asymmetric biradicals coupling a nitroxide center with a narrow line BDPA or trityl radical. In the second, the narrow-line radical can be efficiently saturated, even at high magnetic fields, and the large g anisotropy of the nitroxide center is able to satisfy the cross-effect condition, making CE DNP possible at field of 21.1 T, where comparable enhancements as obtained at 9.4 T can be observed in some samples (Fig. 11).85,90

9.07.4

Applications of high field NMR

Unless otherwise noted, gyromagnetic ratios and natural abundances are taken from the 2001 IUPAC Recommendations report,5 while quadrupolar moments are taken from the Year-2017 set compiled by Pyykkö.91

9.07.4.1

1

H

1 H has a high gyromagnetic ratio (g ¼ 26.75 107 rad s 1 T 1), near-total natural abundance (N.A. ¼ 99.99%), and is spin-½, making it the most receptive NMR active isotope. In solids, however, strong homonuclear dipolar interactions are a significant barrier to the use of 1H MAS NMR. This fact has been a strong driver for the pursuit for the faster MAS, due to the  nR 1 dependence of the linewidth. The resolution gains are further enhanced at high magnetic fields given that the linewidth is largely independent of magnetic field, in frequency units. Xu et al. used a combination of fast MAS (62.5 kHz), high field (21.1 T), and dilution with 2H to resolve closely-spaced 1H signals from the a-Mg3(HCOO)6 metal-organic framework (MOF).92 All three techniques are required to obtain adequate resolution between the six non-equivalent H sites, as the peaks span a range of only 0.59 ppm. The additional resolution also allowed for the acquisition of 2D 1He1H double-quantum-single-quantum (DQ/SQ) correlation spectra, and the unambiguous assignment of the spectral peaks to their crystallographic origins. Ducinskas et al. used 1H fast MAS (50 kHz) NMR at 21.1 T to probe the hydration of 1,4-phenylenedimethanammonium (PDMA) Dion-Jacobson layered lead perovskites.93 These 2D hybrid perovskites were expected to be more resistant to hydration as compared to their 3D analogues; however, solid-state NMR spectra confirmed their breakdown under sufficient humidity levels. Note that while the combination of fast MAS and high field allow for partial resolution of the multiple proton resonances, the overlapping PMDA resonances in the multi-phase hydrated sample could not be distinguished. Note that one of the greatest strengths of 1H fast MAS NMR is that it enables for the 1H-detection of the MAS spectra of challenging nuclei (see Section 3.6), most notably 14N.94,95 Examples of high field 1H detection of challenging nuclei will be described in their respective categories below.

Fig. 11 Left: 1H DNP enhancement from the HyTEK2 biradical (inset) at a field of 9.4 T (black squares) and 18.8 T (blue circles) as a function of MAS rate. Right: 27Al MAS DNP NMR spectra of amorphous silica-alumina collected at 18.8 T using the TEKPol radical (bottom, black) and the HyTEK2 radical (top, purple). The spectra were acquired using identical conditions and normalized to the mass of the sample. Right inset: a structural model of the aluminum layer on amorphous silica-alumina. Aluminum is in purple, silicon in yellow, oxygen in red, hydrogen in white. Modified from Wisser, D.; Karthikeyan, G.; Lund, A.; Casano, G.; Karoui, H.; Yulikov, M.; Menzildjian, G.; Pinon, A. C.; Purea, A.; Engelke, F.; Chaudhari, S. R.; Kubicki, D.; Rossini, A. J.; Moroz, I. B.; Gajan, D.; Copéret, C.; Jeschke, G.; Lelli, M.; Emsley, L.; Lesage, A.; Ouari, O. J. Am. Chem. Soc. 2018, 140 (41), 13340–13349. Copyright 2018 American Chemical Society.

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11

153

B

B (I ¼ 3/2) has a high gyromagnetic ratio (g ¼ 8.58 107 rad s 1 T 1), a high natural abundance (N.A. ¼ 80.1%), and one of the smallest quadrupole moments (Q ¼ 4.059(10) fm2), which together make it one of the more sensitive NMR-active nuclides. Due to being a relatively light element, it unfortunately has a narrow chemical shift range which spans about 100 ppm. While it is often possible to distinguish 3- and 4-coordinate species at magnetic fields greater than 11.7 T, distinguishing between subtly different species can be challenging. 10B (I ¼ 3), as an integer spin nucleus, is less commonly studied. Dorn et al. used 11B NMR at 35.2 T to probe the structure and connectivity of various three-coordinate boron species in boronnitride-based nanotube catalysts.96 In particular, the reduction in second-order quadrupolar broadening yielded nearly isotropic resolution. While the chemical shift resolution in the 1D spectrum is insufficient to resolve the different BN(3  x)Ox environments, the narrow isotropic peaks allow for the unambiguous determination of their connectivity by 11B DQ/SQ (Fig. 12). Zhou et al. used high field 11B NMR to resolve subtle chemical shift differences between conventional [BO4] units and consistently-distorted [OBO3] units in synthetic boracites, where the latter unit has one anomalously-long BeO bond.97 The difference in chemical shift between the two species was only resolvable using MQMAS at 21.1 T. In an earlier paper, 11B MAS NMR at 21.1 T also allowed the authors to resolve two BO3 sites in ulexite which were indistinguishable at 14.1 T.98

11

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14

N

Despite its low gyromagnetic ratio (g ¼ 1.93 107 rad s 1 T 1), 14N makes up 99.6% of natural nitrogen, and has a relatively small quadrupole moment (Q ¼ 2.044(3) fm2), making it at first glance an attractive NMR target. However, it has nuclear spin of I ¼ 1, and hence does not possess a central transition unaffected by the first-order quadrupolar interaction. 14N powder patterns are typically impractically broad for conventional spectral acquisition and are unaffected by the strength of the magnetic field. 15N NMR studies of inorganic materials are not commonly undertaken at high field due to 15N being a spin-1/2 nuclide. By far the most successful approach towards the acquisition of 14N NMR spectra has been indirect detection using a D-HMQC experiment under fast MAS.94,95 This experiment allows for the folding of the numerous spinning sidebands into a narrow centerband in the 14N dimension, yielding near-isotropic resolution. An alternative to indirect detection for obtaining high-resolution 14N NMR spectra is to observe the m ¼  1 / H1 overtone transition which, like the CT, is not affected by the quadrupolar interaction to first order.99 Despite the fact that the transition becomes increasingly forbidden as B0 is increased, the narrowing of the linewidth, increase in polarization, and increased rf efficiency lead to an overall linear improvement in sensitivity with B0 (Fig. 13).100 Resolution is, however, not improved at high magnetic fields given that the most important contribution to the shift is the second-order quadrupole-induced shift. 14N overtone NMR has even been performed at 36 T.101

9.07.4.4

17

O

O (I ¼ 5/2), the only NMR-active isotope of oxygen, has a moderate gyromagnetic ratio (g ¼  3.62 107 rad s 1 T 1) and quadrupole moment (Q ¼  2.558(22) fm2), neither of which present a significant challenge; but the natural abundance of 17O

17

Fig. 12 (A) 11B MAS echo spectra of spent hexagonal boron nitride nanotubes acquired at various field strengths. A spinning sideband is indicated with an asterisk. (B) 11B DQ/SQ spectrum of the same sample, acquired at 35.2 T. The solid lines indicate correlations between different boron sites. The diagonal dashed line indicates autocorrelation. Modified with permission from Dorn, R. W.; Cendejas, M. C.; Chen, K.; Hung, I.; Altvater, N. R.; McDermott, W. P.; Gan, Z.; Hermans, I.; Rossini, A. J. ACS Catal. 2020, 13852–13866. Copyright 2020 American Chemical Society.

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Fig. 13 (A) Simulated 14N overtone MAS spectra at multiple field strengths. A CQ ¼ 3 MHz site (left) and CQ ¼ 1 MHz site (right) are shown. The arrows to the left all span 400 ppm at each field strength. Note that the resolution in ppm does not improve with field strength. (B) Predicted signalto-noise ratios of both sites as a function of field strength. Black squares indicate the 1 MHz site, while red circles indicate the 3 MHz site. Modified from Brinkmann, A.; O’Dell, L. A. Solid State Nucl. Magn. Reson. 2017, 84, 34–40.

is particularly low, at 0.038%. NMR investigations of 17O have nearly universally relied upon isotope enrichment, which is a costly, and often synthetically-demanding, proposition: 70% H217O costs  1500 USD per gram, and 17O2 gas is approximately thrice that price. High fields, or DNP, can provide the sensitivity enhancements required to enable 17O NMR at lower or no enrichment. The enrichment of oxide materials typically involves the hydrolysis of a metal alkoxide or halide with labelled water. Enrichment can also be carried out by exchange of structural oxygen in network solids with 17O2 gas in a controlled atmosphere.102 Neither route is wholly satisfactory: the former requires a multi-step synthesis with potential products limited by available precursors; while the latter requires high temperatures, lengthy experimental times, and is not compatible with many species. Metal oxides and hydroxides can also be directly enriched via ball milling with a small amount of H217O (on the order of 1 mL mg 1).103 Ionothermal syntheses are a promising alternative, requiring only 50 mL of 35% 17O H2O to achieve a 4% enrichment in an aluminophosphate (AlPO) zeolite.104 Leveraging the ionothermal enrichment method, He et al. presented an early high field survey of 17O spectra of various MOF systems.105 Their results revealed both the power and limitations of 17O NMR: the sensitivity of various NMR parameters to local environment allowed for the straightforward separation and identification of the three distinct oxygen environments in the Zr-UiO66 MOF; but showed that even at a field of 21.1 T, not all of the carboxylate oxygen sites in the MIL-56(Al)-lp MOF could be resolved. Kong et al. used a combination of high field NMR (21.1 T) and fast MAS (50 kHz) to distinguish between extremely similar sites in oxygen-labelled oxaliplatin, an anti-cancer drug.106 The high field was required to provide adequate resolution between the two distinct carbonyl oxygen sites, as they differ in diso by only 7 ppm and in CQ by only 0.1 MHz. Romao et al. used 17O MAS NMR at 21.1 T to validate the structural model of the thermomiotic ZrMgMo3O12 material constructed via an NMR crystallography approach.107 The crystal structure of ZrMgMo3O12 had not been previously reported, and the large unit cell leads to a highly convoluted X-ray diffraction pattern. The authors postulated a structural motif using diffraction and proceeded to refine the atomic positions using the experimental and density-functional theory (DFT)-calculated EFG tensors directly. 17O diso and CQ parameters were used to independently cross-validate of the obtained crystal structure and were not included in the refinement. Collection at high fields was critical to allow for the determination of the diso and CQ values, given that no second-order lineshapes were observed. Kong et al. used 17O fast MAS NMR to probe the environments of oxygen bound directly to paramagnetic metal centers in several organometallic compounds.108 At a field of 21.1 T, the paramagnetic shift tensor was the dominant broadening interaction, and the resulting 17O NMR peaks resembled CSA patterns, rather than quadrupolar lineshapes (Fig. 14), see Section 1.2.3.17 Jakobsen et al. combined experiments at multiple high fields to extract a remarkably complete set of NMR parameters for sodium and potassium periodate.109 The spectra were influenced by quadrupolar coupling (CQ  11 MHz), CSA (Dd about 150 ppm), and J coupling to 127I (1J(17Oe127I) z þ 500 Hz). Many of the same authors had previously observed the coupling between 17O and 185/ 187 Re in ammonium and potassium perrhenates.110 Here, the 17O CQ values were much lower (about 1.3 MHz), such that the 1 17 J( Oe187Re) z  274 Hz dominates the lineshape. The J coupling is most apparent at low temperatures ( 138  C), where the 185/187 Re self-decoupling is mitigated. Sutrisno et al. used 17O MAS and MQMAS at 21.1 T to probe the structure of silicoaluminophosphates.111 The resolution at high field, combined with MQMAS, allowed for pairs of AleOeP and AleOeSi environments to be distinguished. Chen et al. conducted a multi-field study of the structural role of the 17O introduced via ball milling on a variety of s-, p-, and dblock oxides.103 Both one-dimensional and MQMAS 17O experiments at 35.2 T revealed that the milling process introduces 17O to Al2O3 as OAlx and AlxOH species, and not as bound water. Fast MAS (60 kHz) 1H{17O} J- and D-HMQC experiments carried out at 20.0 T confirmed the assignment of the AlxOH 17O peak, as well as indicating the close proximity of AlxOH and OAlx species. A

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Fig. 14 17O static (B and E) and MAS (C and F) spectra of the paramagnetic V([17O2]acac)3 (A) and K3V([17O4]oxalate)3$3H2O (D). The lineshapes are significantly distorted from the expected quadrupolar lineshapes due to the strong influence of paramagnetic interactions. Asterisks (*) in (F) indicate signal from satellite transitions. Reproduced with permission from Kong, X.; Terskikh, V. V.; Khade, R. L.; Yang, L.; Rorick, A.; Zhang, Y.; He, P.; Huang, Y.; Wu, G. Angew. Chem. Int. Ed. 2015, 54 (16), 4753–4757.

lengthy 27Al{17O} double-frequency sweep (DFS)-J-HMQC experiment showed that AlxOH environments were exclusively found as Al(VI). Shen et al. used the high resolution afforded by collection at 35.2 T to evaluate the surface structure of hydrated g-Al2O3 nanorods.112 The high field acquisition enabled them to distinguish between bare four-coordinated oxygen species and an environment tentatively assigned to three-coordinated oxygen. Martins et al. presented 17O NMR spectra of the microporous a-Mg3(HCOO)6 MOF collected at both 21.1 T and 35.2 T.113 a-Mg3(HCOO)6 was intentionally chosen as a challenging test sample, as it has 12 crystallographically-inequivalent oxygen environments which cannot be resolved at 21.1 T. At 35.2 T, the 1D resolution is improved, but is still insufficient to completely resolve the peaks. Through the use of both MQMAS (Fig. 15) and DFT calculations, the authors were able to identify most sites in the MOF and track the subtle changes caused by the activation of the sample by solvent evacuation. Subsequently, the authors tracked the changes in the inequivalent eCOO oxygen sites in a-Mg3(HCOO)6 as it transitions between the “as made” phase, the “large pore” phase resulting from the evacuation of the linker precursor, and the “narrow pore” phase resulting from the adsorption of water.114 Only half of the eCOO oxygen sites were found to be involved with the adsorption of water. Carnevale et al. applied 17O MAS DNP NMR to Zr carboxylate MOFs at 18.8 T using natural abundance samples.115 Despite the lack of isotopic enrichment, their 1He17O CPMAS spectra could be acquired in about 48 h, due to a 1H DNP enhancement factor of 3 ¼ 28, resulting in 800-fold time savings. The carboxylate, m2-OH, and m3-OH sites could all be identified.

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23

Na

Sodium is entirely composed of 23Na (N.A. ¼ 100%, I ¼ 3/2), which has a fairly high gyromagnetic ratio (g ¼ 7.08 107 rad s 1 T 1) and a moderate quadrupole moment (Q ¼ 10.4(1) fm2). It is quite receptive but suffers from a narrow chemical shift range, making acquisition straightforward but potentially complicating interpretation, particularly in amorphous environments. Greer and Kroeker made use of high field (21.1 T) 23Na MAS NMR to identify material crystallized from model nuclear waste glasses.116 These “yellow phase” materials (named for their yellow color originating from the presence of chromium) contained seven distinct resonances spread over a chemical shift range of 15 ppm. MQMAS acquired at 21.1 T, along with MAS at both

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Fig. 15 17O MQMAS spectra of 17O-enriched MIL-53, as-made (top) and activated (bottom), acquired at 35.2 T. Asterisks (*) indicate spinning sidebands. Reproduced with permission from Martins, V.; Xu, J.; Wang, X.; Chen, K.; Hung, I.; Gan, Z.; Gervais, C.; Bonhomme, C.; Jiang, S.; Zheng, A.; Lucier, B. E. G.; Huang, Y. J. Am. Chem. Soc. 2020, 142 (35), 14877–14889. Copyright 2020 American Chemical Society.

21.1 T and 14.1 T (Fig. 16), allowed for the identification of two environments, attributed to the formation of novel mixed-alkali molybdates. Mayen et al. used high field 23Na{31P} D-HMQC experiments to probe the sodium distribution in amorphous mixed-cation phosphates.117 They observed that sodium was equally likely to be associated with orthophosphate (PO43) and pyrophosphate (P2O74) units, implying a homogeneous distribution of sodium throughout the material. Bhattacharya et al. used 23Na MAS and MQMAS spectra at high field (21.1 T) to distinguish between the glass and ceramic phases of feldspar glass-ceramics.118 The resonance assigned to the crystalline component is much narrower than that from the amorphous component. Based on the chemical shift of the amorphous peak, the authors conclude that the crystallization of the glass-ceramic not only changes the local structure of the sodium environments, but also affects the distribution of sodium and potassium.

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25

Mg

Mg (I ¼ 5/2) has a low gyromagnetic ratio (g ¼  1.64 107 rad s 1 T 1), low abundance (10.0%), and significant quadrupole moment (19.94(20) fm2). However, given the wide range of materials in which Mg is present, significant efforts have been directed towards acquiring NMR spectra of this unreceptive nucleus. High field 25Mg NMR of various Mg salts was first comprehensively studied by Pallister, Moudrakovski, and Ripmeester.119 Laurencin et al. later tested various models in an attempt to relate local structural parameters (e.g., mean MgeO bond length) to the NMR properties of a series of magnesium phosphate materials, using fields of 17.6 T, 20.0 T, and 30 T.120 The 30 T spectra were

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Fig. 16 23Na MAS spectra of a multi-component oxide precipitate from a model nuclear waste glass, collected at 14.1 T and 21.1 T. The experimental spectra are presented at the bottom, while the simulation, and deconvolution, are presented above. Reproduced with permission from Greer, B. J.; Kroeker, S. Phys. Chem. Chem. Phys. 2012, 14 (20), 7375. Published by the PCCP Owner Societies.

collected to specifically enhance any potential effects from CSA, as opposed to mitigating the effects of the quadrupolar interaction. Due to inhomogeneities in the field of the resistive 30 T magnet, precise CSA values could not be determined. Using a field strength of 21.1 T, Xu et al. were able to determine the CQ of the highly-symmetric Mg site in [NH4][Mg(HCOO3)] via observation of the satellite transitions, which are less affected by secondary broadening mechanisms than the CT.92 Romao et al. used 25Mg, 91Zr, and 95Mo EFG tensor parameters, determined using NMR at 21.1 T, to refine the crystal structure of the zero thermal expansion material ZrMgMo3O12.107 A crystal structure candidate determined using powder X-ray diffraction was altered iteratively to minimize the difference between calculated and experimental EFG tensor parameters. The polyhedral distortions in the obtained NMR crystallographic structure agreed well with previously determined relationships between these distortions and the thermal expansion coefficient. Zhou et al. used high field 25Mg MAS and WCPMG to characterize a series of natural and synthetic magnesium borate minerals.121 They relate the 25Mg CQ to a longitudinal strain parameter, calculated as the mean of the difference between each bond length and the mean bond length. By working at high field, the authors were able to collect data from a Mg site with a 18(5) MHz CQ, which improved the range over which their model was predictive. Their model suggests that the Mg site in MgB4O7, conventionally considered to be five-coordinate, is better described by a “5 þ 1” coordination, where a distant O (2.790 Å) contributes additional valence. Shimoda et al. used high field (21.8 T) 25Mg MQMAS to probe the distribution of environments in magnesium silicate glasses.122 Their spectra reveal the presence of distinct Mg2þ environments in MgSiO3 glass, but only a single distribution in K2MgSi2O6 glass. They attribute the difference in behavior in the mixed modifier glass to the difference in the cation field strength (Z/d2) between K (0.12) and Mg (0.46–0.53). In a following work, the authors compare their results at 16.4 T and 21.8 T for similar glasses.123 Sideris et al. used 25Mg MQMAS NMR, acquired at 19.6 T, to probe the structure of magnesium-based layered double hydroxides.124 Their spectra (Fig. 17) revealed the presence of three distinct 25Mg sites, which they assign to relatively symmetric Mg(OMg)6 sites and highly distorted Mg(OMg)3(OAl)3 and Mg(OMg)4(OAl)2 sites.

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Fig. 17 25Mg MQMAS of MgAl-19-NO3, a layered double hydroxide material. Three distinct crystallographic sites can be distinguished in the 2D spectrum acquired at 19.6 T. Reproduced with permission from Sideris, P. J.; Blanc, F.; Gan, Z.; Grey, C. P. Chem. Mater. 2012, 24 (13), 2449–2461.

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27

Al

Al (I ¼ 5/2) possesses a reasonable gyromagnetic ratio (g ¼ 6.98 107 rad s 1 T 1), quadrupole moment (14.66(10) fm2), and has 100% natural abundance. Quadrupolar coupling generally limits the utility of 27Al NMR, often only allowing for the resolution of sites with different coordination numbers. An early demonstration of the value of ultra-high magnetic fields was reported by Gan et al. in 2002.125 They used a resistive 25 T magnet and a (non-series-connected) 40 T hybrid magnet to acquire highly resolved 27Al spectra of 9Al2O3$2B2O3, also known as A9B2. The crystal structure of A9B2 contains two distinct AlO5 sites, along with single AlO6 and AlO4 sites, which are poorly resolved at low magnetic fields. At 25 T, the AlO6 peak is resolved from the others and at 40 T, where the second-order quadrupolar interaction is negligible, all four sites are fully resolved with peak breadths of roughly 5 ppm. In 2017, Gan et al. presented spectra of A9B2 acquired during the commissioning of the 35.2 T SCH magnet.28 While the linewidths of the peaks at 35.2 T were about the same as those acquired at 40 T, the consistent magnetic field homogeneity at the lower field preserved the second-order lineshapes of the four sites, even after 512 scans (Fig. 18). Taoufik et al. later demonstrated that the resolving power of high field 27Al NMR could be further enhanced using 27Al{1H} DHMQC, enabling the resolution of various hydroxyl-linked Al sites at the surface of the g-Al2O3 catalyst, in particular the resolution of well-resolved powder pattern for the 5-coordinate site.126 Rettenwander et al. used the resolving power available at a field of 21.1 T to assign different 27Al sites in cubic garnet solid solutions.127 While the high symmetry sites reduce the effects of the quadrupolar interaction, even slight disorder can result in significant quadrupolar broadening of 27Al peaks at low-fields. At 21.1 T the peaks are nearly isotropic (as demonstrated via MQMAS), as opposed to previous reports of similar compounds at 9.4 T.128 Flemming, Terskikh, and Ye reported 27Al MAS and MQMAS of synthetic clinopyroxene (CaAlAlSiO6) collected at 21.1 T.129 The high field strength was important for resolving the two distinct four-coordinate Al sites and three distinct 6-coordinate Al sites. Notably, a highly distorted tetrahedral site with a 11.8 MHz CQ, which was not visible at 11.75 T, could be detected at 21.1 T. Shubin et al. examined the 27Al MAS spectra of amorphous silica-alumina at 9.4 T and 21.1 T.130 They concluded that at the lower field, 25–30% of the aluminium is “NMR-invisible” due to an inability to adequately excite the contributions from the Al environments with the largest CQ values (Fig. 19). They also note difficulty in reconciling distribution fitting parameters between spectra collected at multiple fields, a point others have noted in the literature.131 Together these points underline the continued importance of collecting measurements at multiple fields. Wisser et al. used high field (18.8 T) DNP to observe 27Al signal from Al(IV), Al(V), and Al(VI) species on amorphous silicaalumina.90 Notably, by using a BDPA-nitroxide asymmetric biradical, and fast MAS, they obtained a DNP enhancement factor 27

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Fig. 18 27Al MAS spectra of 9Al2O3$2B2O3, which features four inequivalent Al sites, collected at various fields. Two spectra collected at 35.2 T are displayed: one where a single scan was acquired, and one where 512 scans were acquired. The lineshapes remain discernable after 512 scans, due to the high stability of the SCH magnet. Data at 14 T and 19.6 T are adapted from Gan, Z.; Gor’kov, P.; Cross, T. A.; Samoson, A.; Massiot, D. J. Am. Chem. Soc. 2002, 124 (20), 5634–5635. Copyright 2002 American Chemical Society. Data at 25 T, 35.2 T, and 40 T are reproduced from Gan, Z.; Hung, I.; Wang, X.; Paulino, J.; Wu, G.; Litvak, I. M.; Brey, P. L. G. W. W.; Lendi, P.; Schiano, J. L.; Bird, M. D.; Dixon, I. R.; Toth, J.; Boebinger, G. S.; Cross, T. A. J. Magn. Reson. 2017, 284, 125–136.

of 86. The sensitivity was roughly 3 times higher than that obtained using the dinitroxide TEKPol (Fig. 11). At 18.8 T the resolution of the three 27Al coordination numbers is considerably higher than comparable data acquired at lower magnetic fields.132–134 In another publication, the same group investigated the use of BDPA as a polarizing agent for the DNP of alumina surfaces, however this only yielded an enhancement factor of 16 at 18.8 T.135 Chen and coworkers used the SCH magnet at 35.2 T to reveal the presence of two distinct framework AlO4 sites in the catalytic HZSM-5 zeolite.136 One-dimensional MAS spectra of dehydrated HZSM-5 have insufficient resolution to distinguish between multiple AlO4 environments, even at 35.2 T. MQMAS spectra at 19.6 T reveal the presence of a second AlO4 environment which is less apparent at 35.2 T due to the minimization of the quadrupole induced shift term, dqis. The two sites are, however, clearly resolved in a 27Al {1H} D-HMQC experiment at 35.2 T (Figs. 19 and 20).

Fig. 19 27Al MAS spectra of amorphous silica-alumina collected at 9.4 T (black) and 21.1 T (red); note the substantial difference in the intensity of the high-CQ Al(V) environment. Modified from Shubin, A. A.; Terskikh, V. V.; Papulovskiy, E.; Lapina, O. B. Appl. Magn. Reson. 2016, 47 (11), 1193– 1205.

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Fig. 20 27Al{1H} D-HMQC NMR of dehydrated HZSM-5 catalysts acquired at (A) 35.2 T, (B) 19.6 T, and (C) 14.1 T. For each spectrum, the 27Al slices are extracted at 1H shifts of 2.8 ppm and 4.2 ppm. Note the difference in axis for the 35.2 T data. Reproduced with permission from Chen, K.; Horstmeier, S.; Nguyen, V. T.; Wang, B.; Crossley, S. P.; Pham, T.; Gan, Z.; Hung, I.; White, J. L. J. Am. Chem. Soc. 2020, 142 (16), 7514–7523. Copyright 2020 American Chemical Society.

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29

Si

Si is not typically studied at high fields due to the fact that it is a spin-1/2 nuclide whose spectra are often dominated by inhomogeneous broadening. High fields are however very useful for measuring the minute CSA of SiO4 tetrahedra and have been used for the refinement of zeolite crystal structures.137,138 There, crystallographic positions were altered to minimize the difference between experimental and calculated chemical shift tensor principal components.

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33

S

S is a challenging NMR target, being a quadrupolar nuclide (I ¼ 3/2; Q ¼  6.94(4) fm2) with a low natural abundance (N.A. ¼ 0.75%) and gyromagnetic ratio (g ¼ 2.06 107 rad s 1 T 1). Sutrisno, Terskikh, and Huang used 33S NMR at 21.1 T to study layered transition metal sulfides.139 They observed a wide range of CQ values, from 0.5(5) MHz in ZrS2 to 9.3(8) MHz in MoS2. O’Dell and Moudrakovski acquired the 33S NMR spectrum of elemental sulfur at 21.1 T.140 By using highly-enriched a-33S8 and a WURST-echo sequence, they acquired the broad spectrum in 6 h with a total of 18 VOCS sub-spectra. WCPMG was not used due to a short T2. Even with the high field, the four crystallographically-distinct 33S sites in a-S8 were not resolved due to them having similar chemical shifts and quadrupolar coupling, as seen using DFT calculations as well as nuclear quadrupole resonance

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161

(NQR). The experimental average CQ was measured to be 43.3(2) MHz, in good agreement with the NQR results,141 and is the largest 33S CQ to have been measured using NMR at the time of writing. Moudrakovski et al. examined various sulfur oxyanions at 21.1 T via both MAS and static 33S NMR.142 The SO42 anion in particular is highly symmetric and yields fairly low CQ values.143 For instance, the sulfur site in K2SO4 has a CQ of 0.959 MHz while other sulfur oxyanions have CQ values ranging from 10.6 MHz to 16.2 MHz. Sasaki et al. used natural abundance 33S MAS and STMAS at multiple fields (9.4 T and 20.0 T) to resolve the disputed structure of the mineral ettringite.144 Previous NMR studies had suggested that the ettringite structure had either one or three

Fig. 21 Experimental MAS Bloch decay (A and F), Hahn echo (B and G) and simulated (C and H) 33S spectra of ettringite collected at 9.4 T (left) and 20.0 T (right). (D) and (I) display experimental STMAS spectra, while (E) and (J) show the simulations. Note that the peaks are clearly resolved at 9.4 T, but not at 20.0 T due to the reduction of the quadrupolar interaction. Reproduced with permission from Sasaki, A.; Ibarra, L. B.; Wimperis, S. Phys. Chem. Chem. Phys. 2017, 19 (35), 24082–24089. Published by the PCCP Owner Societies.

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crystallographically-distinct 33S sites.145,146 The STMAS experiments performed by the authors confirmed unambiguously that there are three distinct 33S sites, but required lengthy acquisitions: the high field spectrum required 92 h of acquisition, while the low field spectrum required 262 h (Fig. 21)! The authors note that at 20.0 T, STMAS is likely feasible for sites with CQ values up to 1 MHz, which would likely include most sulfates but exclude many thio compounds. Halat et al. used 33S DFS-QCPMG NMR at 20.0 T to study the two different sulfur environments in NbS3, which is a potential electrode material for lithium-ion batteries.147 NbS3 contains both S2 and S22 and is expected to have a complex redox mechanism. The authors were able to distinguish S2 and S22 by their dramatically different values of CQ, with the former having values around 4–7 MHz and the latter around 30 MHz. Careful examination of the high-frequency portion of the S22 spectrum revealed the presence of two S22 sites with similar CQ but distinct values of hQ.

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35/37

Cl

Chlorine has two NMR-active isotopes, 35Cl and 37Cl. Both are I ¼ 3/2, with 35Cl having the greater quadrupole moment (Q(35Cl) ¼  8.112 fm2, Q(37Cl) ¼  6.393 fm2), gyromagnetic ratio (g(35Cl) ¼ 2.62 107 rad s 1 T 1, g(37Cl) ¼ 2.18 107 rad s 1 T 1) and abundance (N.A.(35Cl) ¼ 75.8%, N.A.(37Cl) ¼ 24.2%), making it the preferred isotope for NMR investigation. Chlorine NMR can generally be classified into two broad categories: chlorides, and covalent chlorine. Since chlorides possess a full valence shell they have a nearly spherically-symmetric electron distribution and hence small EFG, resulting in small CQ values, typically in the range of a few MHz. Covalent bonds to chlorine produce very significant EFGs which are increased with increases in covalency. Inorganic covalent chlorines have CQ values in the range of 20–40 MHz and carbon-bound chlorines have CQ values of 60–80 MHz.49,148–150 The perfectly covalent Cl sites in Cl2 have a CQ of 108.975 MHz at 0 K.151 Perchlorates, which possess covalent CleO bonds do, however, possess near zero EFGs due to the tetrahedral arrangement of oxygen atoms around the chlorine.152 In an early example of high field 35Cl NMR, Chapman and Bryce demonstrated the utility of high field NMR (21.1 T) in targeting chloride environments interacting strongly with metal centers, thus leading to large quadrupolar interactions (20–40 MHz CQ) in group 13 chlorides.153 Notably their work showed that the 35Cl EFG tensor is highly sensitive to whether the chloride is bridging or in a terminal environment, with the latter having larger CQ values and more axially symmetric tensors. That same year Rossini et al. made a similar observation in studying a variety of transition metal metallocenes where the EFG tensor was shown to be sensitive to whether the complex was monomeric or oligomeric.154 Terskikh, Pawsey, and Ripmeester measured the 35Cl NMR data for some covalently-bonded selenium and tellurium hexachlorides which possess CQ values of 30–40 MHz.150 For comparison, the ionically-bonded triphenyltellurium chloride had a CQ value of 5.1(1) MHz. O’Keefe et al. examined a variety of metal chlorides and metal oxochlorides via high field (21.1 T) 35Cl WCPMG NMR.155 The EFG tensor is clearly dominated by the metal-chlorine bond, with V33 oriented along the bond for all terminal chlorines. In addition, the dimeric NbCl5 and TaCl5 show clear differences between the axial (moderate CQ, low hQ), equatorial (moderate CQ,

Fig. 22 (A) A scale indicating a relationship between the 35Cl CQ and the Sn oxidation state in various tin chlorides. 35Cl WCPMG NMR spectra (bottom, blue) and simulation (top, red) of PhenSnCl2, a Sn(II) compound (B) and PhSnCl2, a Sn(IV) compound (C). Modified from Lucier, B. E. G.; Terskikh, V. V.; Guo, J.; Bourque, J. L.; McOnie, S. L.; Ripmeester, J. A.; Huang, Y.; Baines, K. M. Inorg. Chem. 2020, 59 (18), 13651–13670. Copyright 2020 American Chemical Society.

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163

moderate hQ), and bridging (high CQ, moderate hQ) chlorine environments. The authors also examined WCl6/SiO2 via 35Cl WCPMG NMR, and observed that despite the low loading (5.5 wt% W), a spectrum of the grafted material could be acquired in as little as 16 h; this spectrum resembled most strongly that of bulk WOCl4. Hanson et al. demonstrated that the 35Cl CQ could be used to determine the oxidation state of a metal center.156 Using 35Cl WCPMG at 21.1 T they found that the 35Cl CQ was an effective means of distinguishing between Ge(II) and Ge(IV) chloride complexes, with the chlorine sites bound to the most highly oxidized metal possessing the larger CQ. Lucier et al. demonstrated that the same was true for tin complexes.62 (Fig. 22). This is likely caused by the increased covalency as the metal becomes more electron deficient.

9.07.4.11

39

K

The preferred NMR-active isotope of potassium is 39K (I ¼ 3/2) given that it possesses the greater gyromagnetic ratio (g(39K) ¼ 1.25 107 rad s 1 T 1, g(41K) ¼ 0.69 107 rad s 1 T 1), the greater natural abundance (N.A. 39K ¼ 93.1%, 41K ¼ 6.9%) and the smaller quadrupole moment (Q(39K) ¼ 6.03(6) fm2, Q(41K) ¼ 7.34(7) fm2). 39K, being a low-g quadrupolar nuclide, is difficult to detect by conventional means and greatly benefits from high magnetic fields. Photovoltaic perovskite materials are sometimes doped with potassium iodide in order to improve photovoltaic performance. Perovskites typically have (relatively) high-symmetry sites, mitigating some of the effects of the quadrupolar interaction. Kubicki et al. used 39K NMR at 21.1 T to probe the incorporation of potassium in lead halide perovskites.157 They demonstrated that the potassium is present in a mixture of unreacted KI and non-perovskite phases, which are not detected by techniques such as Xray diffraction (Fig. 23).

9.07.4.12

43

Ca

The NMR-active isotope of calcium, 43Ca, unfortunately possesses a low gyromagnetic ratio (g ¼  1.80 107 rad s 1 T 1), a very low natural abundance (0.135%), and is quadrupolar (I ¼ 7/2; Q ¼  4.44 fm2).158–160 Unlike 17O NMR, isotopic enrichment is also generally cost-prohibitive, rendering high magnetic fields a near necessity when observing this nuclide, although DNP may also be of value.161 Shimoda et al. leveraged the high spin number of 43Ca to collect 7QMAS spectra at high field (21.8 T).162 The substantially reduced sensitivity of the higher-order coherence163 was mitigated by the high field, but nonetheless required several days of acquisition. The experiment revealed three distinct calcium environments in CaSiO3 glass, corresponding to 6-, 7-, and 8-coordinate calcium species.

Fig. 23 39K MAS NMR spectra of a variety of compounds collected at 21.1 T. (A) and (B) (in blue) are of reference compounds KI and KPbI3. (C–E) (in black) present the spectra of hybrid lead iodide perovskites doped with potassium iodide. (F and G) (orange) show spectra simulated from DFT calculations where potassium is incorporated into the perovskite structure at different positions. Modified with permission from Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Zakeeruddin, S. M.; Grätzel, M.; Emsley, L. J. Am. Chem. Soc. 2018, 140 (23), 7232–7238. Copyright 2018 American Chemical Society.

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A fundamental study of the 43Ca NMR parameters in various common calcium salts was published by Bryce, Bultz, and Aebi in 2008.164 As a part of this work they showed that the spectra obtained with the three CaCO3 polymorphs were remarkably different. In a later study, Burgess and Bryce studied the vaterite polymorph in greater detail since its structure remains controversial.165 Using a combination of high field, DOR, MQMAS and isotopic enrichment, the authors could determine the 43Ca chemical shift and EFG tensor parameters which were then compared with DFT calculation to rank the likelihood of the various postulated structures. Bonhomme et al. reported 43Ca spectra of both isotopically-labelled and natural abundance calcium phosphates, including both crystalline and amorphous species, at a magnetic field of 35.2 T.166 The experiments on labelled CaHPO4 provided resolution of the four crystallographically-distinct Ca environments into two groups, with each pair having very similar 43Ca NMR parameters. Notably, at 35.2 T a MQMAS experiment on the labelled sample took only 50 min to acquire (Fig. 24). The authors also were able to acquire one-dimensional spectra of the natural abundance samples in only a few hours per sample. An important finding was that for the amorphous sample, at ultra-high magnetic field the dominant broadening mechanism is likely distributions of chemical shifts and not the quadrupolar coupling. Mayen et al. used multiple high fields to probe the environment of calcium in phosphate-based biomaterials.117 Comparing the 43 Ca MAS spectra collected at 18.8 T and 35.2 T, they concluded that the main broadening influence was chemical shift distributions caused by disorder around the calcium site.

Fig. 24 43Ca MAS (A) and MQMAS (B) of 43Ca-enriched CaHPO4. The MAS spectra were acquired at both 20.0 T and 35.2 T; the peaks at 20.0 T are poorly resolved, while they are almost completely resolved at 35.2 T under MAS, and completely resolved under MQMAS. Reproduced with permission from Bonhomme, C.; Wang, X.; Hung, I.; Gan, Z.; Gervais, C.; Sassoye, C.; Rimsza, J.; Du, J.; Smith, M. E.; Hanna, J. V.; Sarda, S.; Gras, P.; Combes, C.; Laurencin, D. Chem. Commun. 2018, 54 (69), 9591–9594.

High field solid-state nmr of challenging nuclei in inorganic systems 9.07.4.13

47/49

165

Ti

Both of the NMR-active isotopes of titanium have effectively the same gyromagnetic ratio (g(47Ti) ¼  1.5105 107 rad s 1 T 1, g(49Ti) ¼  1.51095 107 rad s 1 T 1) and are thus always observed together. Both are quadrupolar (Q(47Ti) ¼ 30.2(10) fm2, Q(49Ti) ¼ 24.7(11) fm2), although they have different nuclear spin quantum numbers (I(47Ti) ¼ 5/2, I(49Ti) ¼ 7/2), and they have similar abundances (N.A.(47Ti) ¼ 7.44%, N.A.(49Ti) ¼ 5.41%). Rossini, Hung, and Schurko provided an early report of high field 47/49Ti NMR, observing titanocene chlorides at 21.1 T.167 Yamada et al. have reported the 47/49Ti spectrum of various industrial TiO2 samples collected at 21.8 T, observing significant differences in the structural disorder present in the different samples.168 Using 47/49Ti NMR at 21.8 T, Ohashi et al. monitored the change in structure of a TiCl4/MgCl2 catalysts as a function of the preparatory milling time. Increases in milling time led to a change in both the peak position and breadth of the resonances.169 He et al. studied the MIL-125(Ti) MOF using 47/49Ti NMR and found that the quadrupolar coupling was sensitive to the presence of hydroxyls near the Zn as well as guest molecules.170 For additional details on 47/49Ti NMR, the reader is directed to the review by Lucier and Huang.171

9.07.4.14

55

Mn

Mn is a highly-receptive spin-5/2 nuclide (g ¼ 6.64 107 rad s 1 T 1; Q ¼ 33.0(1) fm2), although it is rarely studied as only low-spin Mn(I) and Mn(VII) are diamagnetic, with the exceptions of metal-metal bonded complexes172 and situations of strong antiferromagnetic coupling.173 Nevertheless, many Mn(I) carbonyl complexes have been studied where high magnetic fields enable for the excitation of the entire CT in a single piece.171 High fields lead to the domination of the CSA in some complexes which was found to be particularly sensitive to the HOMO-LUMO gap. Similarly, high fields enable for the clear resolution of 55Mne55Mn J coupling in dimanganese decacarbonyl.174 55

9.07.4.15

59

Co

Co is a spin-7/2 quadrupolar nuclide (Q ¼ 42.0(3) fm2) with a moderate gyromagnetic ratio (g ¼ 6.36 107 rad s 1 T 1). Lowspin Co(I) and Co(III) species are generally accessible to NMR and have been studied at high magnetic fields.175–178 The CSA is a particularly useful metric as it reports directly on the HOMO-LUMO gap and has been shown to be highly sensitive to the identity of the ligands,176 as well as the bond angles between them, varying by as much as 700 ppm in complexes with only minor structural variations.178 59

9.07.4.16

61

Ni

Ni is low-g ( 2.39 107 rad s 1 T 1), has a low natural abundance (1.14%), and is quadrupolar (Q ¼ 16.2(15) fm2; I ¼ 3/2). In its most common oxidation state, þ 2, it is also often paramagnetic. A single 61Ni solid-state NMR study of diamagnetic Ni(0) compounds has been reported by Werhun and Bryce, with both MAS and static WCPMG spectra collected at 21.1 T (Fig. 25).179 61

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63/65

Cu

Cu and Cu (both I ¼ 3/2) have similar gyromagnetic ratios (g(63Cu) ¼ 7.11 107 rad s 1 T 1, g(65Cu) ¼ 7 7.61 10 rad s 1 T 1), but 63Cu is more receptive due to its greater natural abundance (N.A.(63Cu) ¼ 69%, N.A.(65Cu) ¼ 31%). 65Cu has the smaller quadrupole moment (Q(63Cu) ¼  22.0(15) fm2, Q(65Cu) ¼  20.4(14) fm2). Yu et al. reported both 63Cu and 65Cu static NMR spectra, collected at a field of 21.1 T, on a series of Cu(I) phosphines.180 By acquiring spectra from different nuclides of the same element, the authors were able to determine both EFG and CSA parameters at a single field.

63

65

Fig. 25 Static 61Ni solid echo spectrum (and simulation) of Ni(cod)2 acquired at 21.1 T in 66 h. A QCPMG spectrum could be acquired in 17 h. Reproduced with permission from Werhun, P.; Bryce, D. L. Inorg. Chem. 2017, 56 (16), 9996–10006.

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9.07.4.18

67

Zn

Zinc has a low gyromagnetic ratio (g ¼ 1.68 107 rad s 1 T 1), sparse natural abundance (N.A.(67Zn) ¼ 4.1%, I ¼ 5/2), and moderate quadrupole moment (Q ¼ 12.2(10) fm2) and is generally a challenging nuclide to observe. Sutrisno et al. used high field (21.1 T) NMR to study microporous zinc phosphate framework materials via 67Zn WCPMG NMR.181 The compounds are analogous to AlPO4 materials and have a low volume fractions of zinc, typically an order of magnitude less than ZnO. High field 67Zn MAS spectra of crystalline zeolitic imidazolate frameworks (ZIFs) were reported by Sutrisno et al.182 The authors examined both highly-symmetric and less-ordered ZIF structures as a proof-of-concept of applying 67Zn NMR to MOFs. Differences were observed between solvated, partially-desolvated, and fully-desolvated MOF-5, highlighting the sensitivity of 67Zn NMR to local structure. High field static 67Zn NMR spectra of zinc-containing oxide glasses have been reported by Kanwal et al.183 The 67Zn NMR spectra were broad and featureless, characteristic of a distribution of EFG tensor parameters, and were consistent with the coordination number of four determined using neutron diffraction. Xu et al. acquired high field 67Zn spectra of [NH4][Zn(HCOO3)] at 21.1 T.92 The observation of the satellite transitions allowed for the accurate determination of the EFG tensor parameters, while the CT proved to be CSA-dominated. Low field (9.4 T) variabletemperature NMR experiments were used to probe the paraelectric-ferroelectric phase transition which results in large changes in the EFG tensor. Madsen et al. reported 67Zn MAS spectra of ZIF glasses collected at 35.2 T.184 Despite the negligible differences in diso in various ZIF structures (e.g., 295 ppm vs. 296 ppm), the MAS spectra collected at two different fields were able to distinguish between two tetrahedral Zn sites with varying degrees of distortions (Fig. 26). Aside from the gains in sensitivity and resolution, one advantage of working at such high magnetic fields is that the high field approximation describing the quadrupolar interaction is more likely to hold, and hence the position parameter of the Czjzek distribution,185,186 used to describe the distribution of the EFG tensor, is more likely to correspond to the isotropic chemical shift.136 The 67Zn spectra of the ZIF glasses are much broader than those of the crystalline samples due to the inherent structural disorder leading to distribution of chemical shifts that cannot be removed by working at high fields.

9.07.4.19

69/71

Ga

Of the two NMR-active Ga nuclides, 69Ga and 71Ga (both I ¼ 3/2), 71Ga is preferred. Despite having the lower abundance (N.A.(69Ga) ¼ 39.9%, N.A.(71Ga) ¼ 60.1%), it possesses the larger gyromagnetic ratio (g(69Ga) ¼ 6.43 107 rad s 1 T 1, g(71Ga) ¼ 8.18 107 rad s 1 T 1) and the smaller quadrupole moment (Q(69Ga) ¼ 17.1(2) fm2, Q(71Ga) ¼ 10.7(1) fm2). One of the earliest uses of high field 69/71Ga NMR was by Widdifield et al. who used the technique, along with 127I NQR to resolve a structural dispute regarding the structure of GaI.187 It was found to be better represented by the formula [Ga0]2[Ga]þ[GaI4]. High field 71Ga NMR has also been used to elucidate the electronic nature of GaeGa bonds.188 First demonstrated by Perras and Bryce, it was shown that a J-resolved experiment could be performed on an ultra-wideline pattern to reveal J coupling constants in

Fig. 26 67Zn MAS spectra of crystalline (bottom) and glassy (top) ZIF-4 acquired at fields of (A) 19.5 T and (B) 35.2 T. Experimental data are displayed as black solid lines, while simulated spectra are dashed red lines. The spectra of the crystalline sample can be deconvoluted into two distinct sites. Modified from Madsen, R. S. K.; Qiao, A.; Sen, J.; Hung, I.; Chen, K.; Gan, Z.; Sen, S.; Yue, Y. Science 2020, 367 (6485), 1473–1476.

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167

the range of 10 kHz, and effective dipolar couplings of only a few hundred Hz, in the presence of quadrupolar coupling strengths of up to 46 MHz. The same method was later applied by Kobera et al. to determine the nature of multiple GaeGa bonds, in particular the controversial digallyne compound.189 Ma et al. used high field 71Ga NMR of a polynuclear Ga cluster to study the dependence of its EFG tensor parameters on the chemical environment surrounding the Ga center.190 High magnetic fields were critical in resolving the three Ga environments found in Ga13. This is also well demonstrated in a study by Rettenwander et al., where 71Ga MAS NMR is used to observe and assign resonances to different dopant locations in Ga-doped Li-containing garnets.127 Hung and Gan combined high field (19.6 T) NMR with a novel “long-pulse” STMAS sequence to acquire a 2D STMAS spectrum of b-Ga2O3.191 The Ga(IV) site of b-Ga2O3 has a large CQ and is difficult to average via MAS. They found that a “long-pulse” approach, where 68.97 ms excitation and reconversion pulses were applied at an offset corresponding to an integer multiple of the rotor period, was less sensitive to the CQ than conventional hard pulses.

9.07.4.20

73

Ge

The sole NMR-active Ge isotope, 73Ge (I ¼ 9/2), has a low natural abundance (N.A. 7.76%), among the lowest gyromagnetic ratios on the periodic table (g ¼  0.93 107 rad s 1 T 1), and a significant quadrupole moment ( 19.6 fm2). As with all quadrupolar nuclei, acquisition at high field provides significant reductions in breadth and improvements in sensitivity. Hanson et al. conducted a survey of various simple organogermanium compounds collected via both MAS and WCPMG at 21.1 T.192 All of the compounds were tetrahedrally-coordinated, with the occasional substitution of a hydride in place of a mesityl group. In these simple compounds, MAS was effective, with CQ values around 4 MHz. However, one compound, bis(trimethylsilyl) dimesitylgermane, had a CQ of 24.7(3) MHz, necessitating static collection. Michaelis and Kroeker presented a survey of various germanium oxide materials, sampling structures containing four-, five-, and six-coordinate germanium units.193 They found that the 73Ge CQ is sensitive to a number of distortion parameters. They also report the spectra from three amorphous samples, namely vitreous GeO2, a lithium germanate glass, and a sodium germanate glass. The application of 73Ge NMR to germanate glasses was hoped to resolve the origin of the “germanate anomaly,” that is, the non-linear response of various physical properties, such as density, to the alkali concentration in alkali germanate glasses.194,195 Unfortunately, while the use of WCPMG at 21.1 T allowed for the acquisition of 73Ge spectra of various glasses, distinct Ge environments could not be resolved due to the narrow chemical shift range relative to the linewidths. Greer et al. investigated a variety of Ge(II) and Ge(IV) halides by 73Ge NMR, as well as 35Cl and 127I NMR, at 21.1 T.196 Generally, the Ge(IV) halides, and most Ge(II) halides, are highly symmetric, producing narrow resonances due low CQ, while GeBr2 features distorted Ge octahedral and a large CQ (ca. 35 MHz). The low CQ observed in GeCl2 was used as evidence that the GeCl2 structure was most similar to that of GeI2. A different sort of germanium glass has been studied at 19.6 T using 73Ge NMR.197 Sen and Gan, studying germanium selenide glasses, observed two distinct types of Ge environment, which they assigned to GeSe4 and GeSe4-nGen tetrahedra. GeSe4 centers are far more symmetrical and produced the weakest EFGs. Kalmutzki et al. used 73Ge MAS and static NMR at 21.1 T to probe the Ge environment in germanium carbodiimides.198 The germanium environment was found to be very symmetric, with a small CQ and zero hQ.

9.07.4.21

75

As

As is a challenging spin-3/2 nucleus, primarily due to its large quadrupole moment (Q ¼ 31.1(2) fm2). It is 100% abundant and has a moderate gyromagnetic ratio (g ¼ 4.60 107 rad s 1 T 1). Faucher, Terskikh, and Wasylishen undertook a pair of high field (21.1 T) studies of arsenic compounds in 2015, examining arsenic hexafluorometallates and arsenic-containing Lewis acid-base adducts.199,200 Notable within these studies was the observation of 75Ase19F J coupling in KAsF6, as well as 75Ase11B J coupling in BeAs adducts.

75

9.07.4.22

77

Se

Se is a spin-1/2 nucleus with moderate gyromagnetic ratio (g ¼ 5.12 107 rad s 1 T 1) and low abundance (N.A. ¼ 7.63%). Se NMR spectra are typically dominated by CSA, and hence do not experience gains in resolution at increased magnetic fields, requiring faster spinning and hence small sample sizes. Kaseman et al. used magic-angle turning (MAT)/CPMG at 19.6 T to probe the distribution of Se environments in GexSe100  x glasses.201 There high magnetic fields were beneficial as they facilitated the measurement of the CSA. A similar study on was later performed on SxSe100-x glasses.202 77 77

9.07.4.23

79/81

Br

Bromine has two NMR-active isotopes with comparable abundances (N.A.(79Br) ¼ 50.7%, N.A.(81Br) ¼ 49.3%) and gyromagnetic ratios (g(79Br) ¼ 6.72 107 rad s 1 T 1; g(81Br) ¼ 7.24 107 rad s 1 T 1). Both are spin-3/2, with 81Br having the smaller quadrupole moment, making it the preferred isotope (Q(79Br) ¼ 25.79(2) fm2; Q(79Br) ¼ 30.87(2) fm2). These large quadrupole moments lead to CQ values in the range of 600 MHz in covalent systems, which are better studied by NQR. High field 79/81Br

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High field solid-state nmr of challenging nuclei in inorganic systems

NMR has been performed on some alkaline earth bromides and notably was used for the NMR crystallographic refinement of the of MgBr2.203,204 81Br NMR has also been performed to study bromide ions situated in the pores of a MOF where their narrow lineshape, and fast T2, was used as evidence that the anions are highly dynamic.205

9.07.4.24

87

Rb

Rubidium has two NMR-active isotopes, 85Rb and 87Rb. 85Rb has the greater natural abundance (N.A.(85Rb) ¼ 72.2%, N.A.(87Rb) ¼ 28.8%) and spin (I(85Rb) ¼ 5/2, I(87Rb) ¼ 3/2), but is overall less receptive due to its lower gyromagnetic ratio (g(85Rb) ¼ 2.59 107 rad s 1 T 1, g(87Rb) ¼ 8.79 107 rad s 1 T 1) and greater quadrupole moment (Q(85Rb) ¼ 27.6(1) fm2, Q(87Rb) ¼ 13.35(5) fm2). Due to the generally symmetric EFG around a Rbþ cation, 87Rb NMR is typically sensitive even at low magnetic fields. Michaelis, Aguiar, and Kroeker made use of 87Rb at 21.1 T to study the alkali environment in borate glasses.206 Their spectra showed a change in the breadth of the lineshape with increased Rb content, although overall the lineshapes were only indicative of structural disorder. Kalmutzki et al. in their study of germanium carbodiimides (Section 4.18), compared the 87Rb spectra of the germanium carbodiimide with the silicon analogue at 21.1 T.198 Their data suggested that the rubidium environments in both compounds were quite similar.

9.07.4.25

87

Sr

Sr has a low gyromagnetic ratio (g ¼  1.16 107 rad s 1 T 1), low abundance (N.A. ¼ 7.0%), and significant quadrupole moment (Q ¼ 30.87(2) fm2, I ¼ 9/2) and is seldom studied by NMR. In 2012, Bonhomme et al. reported a number of 87Sr NMR spectra from a variety of different strontium-containing compounds, including enriched strontium malonate, enriched strontium phosphates, and as enriched strontium-containing bioactive glass.207 In all cases, WCPMG was used. Acquisition without enrichment was prohibitively time-consuming, with a low S/N spectrum of the bioactive glass requiring approximately 57 h to acquire. The authors used hybrid force field/ab initio molecular dynamics to aid in the analysis of their experimental spectra. In 2015, Faucher et al. reported 87Sr data on a library of strontium-containing compounds.208 The spectra were acquired on both organic and inorganic systems and were uniformly acquired at 21.1 T without isotopic enrichment. Based on their results, and comparison to the other group II compounds, they suggest that 87Sr has a chemical shift range of roughly 600 ppm. 87

9.07.4.26

91

Zr

Zr is a low-g (g ¼  2.50 107 rad s 1 T 1) quadrupolar nuclide (I ¼ 5/2, Q ¼  17.6(3) fm2) with a low natural abundance (11.2%) and is generally challenging to detect. Nevertheless, 91Zr NMR has been performed on various materials and catalysts, see the review by Lucier and Huang for more examples.209 Here we highlight reports where the use of high magnetic fields provided crucial insights. Pauvert et al. investigated the relationship between local structure and 91Zr NMR parameters in Zr halides.210 For most samples, a field of 17.6 T was sufficient, when combined with QCPMG and VOCS acquisitions. However, b-ZrF4 has two crystallographicallyinequivalent Zr sites and required collection at a higher field of 30 T, produced by a resistive magnet. The lack of field homogeneity was not overly concerning when compared to the relative breadth of most resonances.

91

Fig. 27 91Zr WCPMG NMR of the MIL-140A MOF. (A) The experimental spectrum, acquired at 21.1 T. (B) Simulation of the experimental data, with EFG parameters listed at the left. (C) Simulated spectrum using DFT-calculated EFG parameters from a structure with all atomic positions optimized. (D) Simulated spectrum where only the H positions were optimized. Modified from He, P.; Lucier, B. E. G.; Terskikh, V. V.; Shi, Q.; Dong, J.; Chu, Y.; Zheng, A.; Sutrisno, A.; Huang, Y. J. Phys. Chem. C 2014, 118 (41), 23728–23744. Copyright 2014 American Chemical Society.

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169

Rossini et al. showed that 91Zr NMR was accessible in catalytically-important zirconocene complexes even at a lower magnetic field of 9.4 T; however high magnetic fields greatly reduced experiment times and allowed for the distinction of crystallographicallyinequivalent sites.211 The CQ values were generally quite low ( 5 MHz), due to the near tetrahedral symmetry, with the exception of complexes featuring ZreMe bonds and the bulkier indenyl ligand. He et al. report 91Zr spectra of the MIL-140A MOF at 21.1 T.170 The zirconium in this structure is present as a ZrO7 polyhedron, resulting in a large CQ (35.0(4) MHz). The spectrum could be accurately reproduced using plane-wave DFT, albeit only when all crystallographic positions were optimized (Fig. 27).

9.07.4.27

93

Nb

Nb is a 100% naturally abundant, high-g (g ¼ 6.57 107 rad s 1 T 1), spin-9/2 nucleus which possesses the largest magnetic moment of all NMR-active nuclides. Due to its large quadrupole moment (Q ¼ 32.0(20) fm2), however, it does benefit from high field investigation, where the impacts of the CSA are more clearly apparent.212,213

93

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95/97

Mo

Both of the NMR-active isotopes of molybdenum, 95Mo and 97Mo, are spin-5/2 nuclides and possess similar gyromagnetic ratios (g(95Mo) ¼  1.75 107 rad s 1 T 1, g(97Mo) ¼  1.79 107 rad s 1 T 1). The greater abundance (N.A.(95Mo) ¼ 15.9%, N.A.(97Mo) ¼ 9.6%) and substantially lower quadrupole moment (Q(95Mo) ¼  2.2(1) fm2, Q(97Mo) ¼ 25.5(13) fm2) of 95Mo make it the preferred target for NMR. Hu et al. examined molybdenum-containing Mo-ZSM-5 catalysts at 21.1 T.214 Due to the very low volume percentage of molybdenum in these samples, the authors found it necessary to enrich their sample with 95Mo. The molybdenum was found to form phase-segregated MoO3 particles at loadings above 4 wt%. Iijima et al. used 95Mo NMR to characterize polyoxomolybdates.215 They observe two distinct 95Mo resonances in the spectrum of the mixed-valence [Me3NH]6[H2Mo12O28(OH)12(MoO3)4]$2H2O. The Mo(V) species has a negligible CQ when compared to the effects of the CSA, while the opposite is true of the Mo(VI) species. The same authors later revisited 95Mo NMR of polyoxomolybdate 3-Keggin structures and determined that the unpaired Mo(V) d1 electrons are in fact delocalized throughout the cluster.216 Haouas et al. used high field (18.8 T) 95Mo NMR to study the local structure of polyoxometalates containing molybdenum.217 They were able to identify the three distinct sites in the (NH4)42[Mo132O372(CH3CO2)30(H2O)72) polyanion (Fig. 28). Magnin et al. studied model nuclear waste glasses with low MoO3 content (ca. 2.5 mol%) by 18.8 T 95Mo QCPMG NMR spectroscopy and population transfer from the satellite transitions.218 The low loading required the use of signal enhancement methods, along with 95Mo isotopic enrichment in some cases. The 95Mo chemical shift was used to determine that the molybdate anions were most often charge compensated with Ca2þ as opposed to Naþ. Kobera et al. have studied multiple metal-metal-bonded Mo2 complexes using 95Mo NMR.212 The metal-metal quadruple bond in these complexes led to very large CSA (U ¼ 5500 ppm) which, at the high magnetic field of 21.1 T, far surpassed the strength of the quadrupolar interaction.

9.07.4.29

111/113

Cd

Cadmium has two spin-1/2 NMR-active isotopes, 111Cd and 113Cd, with similar gyromagnetic ratios (g(111Cd) ¼  5.70 107 rad s 1 T 1, g(113Cd) ¼  5.96 107 rad s 1 T 1) and natural abundances (N.A.(111Cd) ¼ 12.8%, N.A.(113Cd) ¼ 12.2%). 113Cd is generally preferred for its somewhat greater receptivity.

Fig. 28 Static and MAS 95Mo NMR spectra of dehydrated (NH4)42[Mo132O372(CH3CO2)30(H2O)72] polyoxomolybdate, collected at 18.8 T. Three sites are observed, but could not be specifically assigned to structural features. Reproduced with permission from Haouas, M.; Trébosc, J.; Roch-Marchal, C.; Cadot, E.; Taulelle, F.; Martineau-Corcos, C. Magn. Reson. Chem. 2017, 55 (10), 902–908.

170

High field solid-state nmr of challenging nuclei in inorganic systems

Fig. 29 113Cd MAS echo NMR spectra of hybrid cadmium mixed-halide perovskites, acquired at 21.1 T. The cadmium halide polyhedra responsible for each resonance are displayed at the top. Reprinted with permission from Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Walder, B. J.; Emsley, L. ACS Energy Lett. 2020, 2964–2971. Copyright 2020 American Chemical Society.

Kubicki et al. investigated the role of cadmium in halide perovskites using high field 113Cd NMR.219 Here, high fields were used primarily for increasing sensitivity and increases in CSA were mitigated using moderate MAS rates. Their results showed that cation disorder in formamidinium mixed-halide perovskites can be easily distinguished in the 113Cd spectra (Fig. 29). Cadmium is shown to phase-segregate in organic-inorganic hybrid perovskites at concentrations as low as 1 mol%, but can be successfully incorporated into all-inorganic lead perovskites, with cadmium occupying the lead site.

9.07.4.30

115

In

The two NMR-active isotopes of indium, 113In and 115In, have extremely similar spectroscopic properties, with identical nuclear spins (I ¼ 9/2), similar gyromagnetic ratios (g(113In) ¼ 5.88 107 rad s 1 T 1, g(115In) ¼ 5.90 107 rad s 1 T 1), and quadrupole moments (Q(113In) ¼ 76.1(5) fm2, Q(115In) ¼ 77.2(5) fm2). 115In is generally preferred due to its much higher abundance (N.A.(113In) ¼ 4.3%, N.A.(115In) ¼ 95.7%). Chen et al. studied the 115In NMR spectra of selected indium coordination compounds220 and triarylphosphine indium(III) trihalide adducts at 21.1 T.221 They generally observed CQ values on the order of about 100 MHz, with the notable exception of the highly symmetric Br3In[P(para-methoxybenzene)3]. The presence of an IneP bond also led to the observation of significant 1 115 J( In,31P) coupling in the 31P MAS NMR spectra. He et al. reported 115In spectra of indium-containing MOFs at both 9.4 T and 21.1 T.170 The spectra of the In(BDC)1.5(bipy) and In(BTC)(H2O)(phen) MOFs are compared, which possessed 115In CQs of 79.5(3) MHz and 145.0(4) MHz, respectively. The difference in coupling is attributed to the lower coordination number and narrow IneO bond distribution of the In site in In(BDC)1.5(bipy). Hamaed et al. demonstrated that high field solid-state NMR could be used to study a wide array of low-valent In(I) complexes in a timely manner.222 These sites were shown to be significantly more shielded than the more common In(III) oxidation state (diso   1000 ppm). The largest 115In CQ to have been measured using NMR (247 MHz) was from a terminal In(I) complex.223

9.07.4.31

119

Sn

Tin has three NMR-active isotopes: 115Sn, 117Sn, and 119Sn. All are spin-½. 119Sn has the highest natural abundance (N.A. ¼ 8.6%) and gyromagnetic ratio (g ¼  10.0 107 rad s 1 T 1) and is the preferred isotope. Xia et al. used 119Sn MAT/CPMG spectra at 19.6 T to elucidate the distribution of coordination numbers in SnO-P2O5 glasses.224 The increase in the magnitude of the CSA at high field allowed for the compositional variation in Dd and hCSA to be determined.

High field solid-state nmr of challenging nuclei in inorganic systems 9.07.4.32

171

121/123

Sb

Antimony possesses two NMR-active isotopes, 121Sb and 123Sb, which have similar abundances (N.A.(121Sb) ¼ 57.4%, N.A.(121Sb) ¼ 42.6%). 121Sb has the higher gyromagnetic ratio (g(121Sb) ¼ 6.42 107 rad s 1 T 1, g(123Sb) ¼ 3.48 107 rad s 1 T 1) and the lower quadrupole moment (Q(121Sb) ¼ 54.3(11) fm2, Q(123Sb) ¼  69.2(14) fm2) and hence is preferred. Very few works have been published using 121Sb NMR, although Faucher et al. have shown that it is possible to acquire 121 Sb NMR spectra using WCPMG and VOCS at a high field for some symmetrical complexes, as well as for an asymmetric complex (SbPh4Br; 3 days of acquisition at 21.1 T) where CQ equaled 159 MHz.225 The first observation of J coupling was done using 121Sb NMR in solution using the hexafluoroantimonate(V) ion.226 This J coupling was revisited in the solid state by Faucher et al. who additionally studied its dynamic phase transition using 121/123Sb NMR.199

9.07.4.33

125

Te

Te, the preferred NMR-active isotope of Te, possesses a low abundance (N.A. ¼ 7.07%), a high gyromagnetic ratio (g ¼  8.51 107 rad s 1 T 1), and a nuclear spin of 1/2. High field NMR of 125Te is rarely reported, given that CSA is the predominant broadening mechanism.150 125

9.07.4.34

127

I

I has a 100% natural abundance and a high gyromagnetic ratio (g ¼ 5.39 107 rad s 1 T 1) but is unfortunately a spin-5/2 quadrupolar nuclide with a very large quadrupole moment (Q ¼  68.822 fm2). Like bromine, this prevents the NMR investigation of iodine in systems possessing covalent bonds where 127I CQ values are typically of around 2 GHz.227 In fact, the first observation of fourth-order quadrupole effects was observed using 127I NMR in iodide salts, where the EFGs are negligible.228

127

9.07.4.35

135/137

Ba

Barium has two NMR-active spin-3/2 isotopes with similar gyromagnetic ratios (g(135Ba) ¼ 2.68 107 rad s 1 T 1; g(137Ba) ¼ 2.99 107 rad s 1 T 1). While 137Ba has the larger natural abundance (N.A.(135Ba) ¼ 11.2%, N.A.(137Ba) ¼ 6.6%), it also has the greater quadrupole moment (Q(135Ba) ¼ 16.0(3) fm2; Q(137Ba) ¼ 21.5(5) fm2). To date only a handful of basic barium salts have been studied by 135/137Ba NMR,229,230 with the exception of b-barium borate, a non-linear optical material, where 135/137Ba NMR was used determine its space group.231

9.07.4.36

139

La

La is 99.9% abundant, with a moderate gyromagnetic ratio (g ¼ 3.81 107 rad s 1 T 1) and quadrupole moment (I ¼ 7/2, Q ¼ 20.6(4) fm2). 139La NMR is often used as a spectral proxy for other lanthanides, which are generally paramagnetic. Spencer et al. investigated the structural role of lanthanum in disordered battery materials.232 Their spectra of Li3xLa2/3xTiO3, a potential solid-state electrolyte, show spectral lineshapes characteristic of distributions of EFG tensor parameters. The garnetrelated Li16La32Fe6.4O67, by comparison, reveals the presence of two crystallographically-inequivalent La sites, one relatively ordered, the other comparatively disordered. Dithmer et al. used 139La WCPMG at 21.1 T to probe the structural changes caused by the uptake of phosphorus in Phoslock, a commercial La-containing ion-exchanged bentonite clay.233 They were able to observe a change in the spectrum as the concentration of phosphorus increased, but poor spectral resolution, poor crystallinity, and the possible presence of dynamics complicated the analysis. Kalmutzki et al. used 139La NMR at 21.1 T to compare silicon and germanium carbodiimides.198 Notably, data acquisition at 21.1 T allowed for the use of MAS and the clear characterization of the CSA. The reported 139La CQ of 2.5(2) MHz in RbLa [Si(CN2)4] is one of the smallest reported to date for a site of non-cubic symmetry. He et al. made use of both 139La MAS and WCPMG NMR to study the MOF La2(BDC)3(H2O)4.170 At 14.1 T, the NMR spectrum was dominated by the quadrupolar interaction (Fig. 30) while acquisition at 21.1 T enabled for the clear measurement of the CSA. The La environment in La2(C4H4O4)3(H2O)4 was less symmetric leading to NMR spectra dominated by the quadrupolar interaction at all fields. 139

9.07.4.37

185/187

Re

The two NMR-active isotopes of Re have similar abundances (NA(185Re) ¼ 37.4%; NA(187Re) ¼ 62.6), gyromagnetic ratios (g(185Re) ¼ 6.04 107 rad s 1 T 1, g(187Re) ¼ 6.10 107 rad s 1 T 1), nuclear spins (both I ¼ 5/2) and massive quadrupole moments (Q(185Re) ¼ 218.0(20) fm2; Q(187Re) ¼ 207.0(20) fm2). Due to these large Q, only perrhenates and Re2(CO)10 have been investigated by high field NMR.234 Despite the high magnetic field and symmetric environments, the strong quadrupolar interactions give rise to truly surprising lineshapes that could only be modeled using an exact treatment of the Zeeman-quadrupole Hamiltonian.8

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High field solid-state nmr of challenging nuclei in inorganic systems

Fig. 30 Static 139La NMR spectra of the La2(BDC)3(H2O)4 (A and B) and La2(C4H4O4)3(H2O)4 (C and D) MOFs at the magnetic fields indicated on the Figure. MAS data is also shown in (A). Modified with permission from He, P.; Lucier, B. E. G.; Terskikh, V. V.; Shi, Q.; Dong, J.; Chu, Y.; Zheng, A.; Sutrisno, A.; Huang, Y. J. Phys. Chem. C 2014, 118 (41), 23728–23744. Copyright 2014 American Chemical Society.

9.07.4.38

207

Pb

Pb is spin-1/2, has a natural abundance of 22.1% and a moderate gyromagnetic ratio (5.63 107 rad s 1 T 1). Given that CSA is usually the dominant broadening mechanism, 207Pb NMR does not generally benefit from high magnetic fields. Askar et al. used static 207Pb NMR to determine the distribution of environments in various mixed halide perovskites.235 The use of the higher magnetic field (21.1 T) reduced some of the broadening caused by the dipolar interactions to the halide nuclei and enabled 2D EXSY experiments which were used to follow halide exchange (Fig. 31).

207

Fig. 31 207Pb exchange NMR spectra of formamidinium lead mixed halide perovskites. The evolution of the cross-peaks (dashed lines) indicates fast exchange between various [PbClxBr6  x]4 units, suggesting that the sample is a dynamic solid solution, and is not composed of distinct nanodomains. Modified from Askar, A. M.; Karmakar, A.; Bernard, G. M.; Ha, M.; Terskikh, V. V.; Wiltshire, B. D.; Patel, S.; Fleet, J.; Shankar, K.; Michaelis, V. K. J. Phys. Chem. Lett. 2018, 9 (10), 2671–2677. Copyright 2018 American Chemical Society.

High field solid-state nmr of challenging nuclei in inorganic systems 9.07.4.39

209

173

Bi

Bi (I ¼ 9/2) has high abundance (N.A. ¼ 100%) and a moderate gyromagnetic ratio (g ¼ 4.38 107 rad s 1 T 1) but is plagued by a significant quadrupole moment (51.6(15) fm2), often coupled with non-negligible EFGs. Hamaed et al. reported the first 209 Bi solid-state NMR spectra in 2009, from bismuth oxyhalides, as well as a few organic salts.236 Notably, the chemical shift range spanned several thousand ppm, and CQ values ranged from 78.6(8) MHz to 256(10) MHz. Data acquisition at 21.1 T reduced the number of VOCS sub-spectra by an order of magnitude and led to significantly simpler spectra unaffected by satellite transitions or high-order quadrupole effects. From NQR literature, 209Bi CQ values are known to reach values in excess of 500 MHz.237 209

9.07.5

Conclusions and future outlook

The development of homogeneous high field magnets, in particular the development of hybrid magnets incorporating either hightemperature superconductor or resistive components, has opened a wide array of the periodic table for NMR investigation. Quadrupolar nuclei are the most strongly impacted by these developments, where sensitivity enhancements are as large as B05/2. Inorganic and materials chemistry benefit the most from such developments due to the high proportion of metal nuclei that are quadrupolar. The combination of high field NMR with DNP is expected to open up an even wider array of opportunities as it will enable for the high field investigation of low-population species, such as metal centers in heterogeneous catalysts or dilute sites on the surfaces of nanoparticles.

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L. J. Phys. Chem. Lett. 2010, 1, 3078–3084. 224. Xia, Y.; Marple, M. A. T.; Hung, I.; Gan, Z.; Sen, S. J. Phys. Chem. B 2018, 122, 7416–7425. 225. Faucher, A.; Terskikh, V. V.; Wasylishen, R. E. Solid State Nucl. Magn. Reson. 2014, 61–62, 54–61. 226. Proctor, W. G.; Yu, F. C. Phys. Rev. 1951, 81, 20–30. 227. Szell, P. M. J.; Grébert, L.; Bryce, D. L. Angew. Chem. Int. Ed. 2019, 58, 13479–13485. 228. Widdifield, C. M.; Bryce, D. L. J. Phys. Chem. A 2010, 114, 10810–10823. 229. Hamaed, H.; Ye, E.; Udachin, K.; Schurko, R. W. J. Phys. Chem. B 2010, 114, 6014–6022. 230. O’Dell, L. A.; Moudrakovski, I. L. Chem. Phys. Lett. 2013, 565, 56–60.

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Sutrisno, A.; Lu, C.; Lipson, R. H.; Huang, Y. J. Phys. Chem. C 2009, 113, 21196–21201. Spencer, L.; Coomes, E.; Ye, E.; Terskikh, V.; Ramzy, A.; Thangadurai, V.; Goward, G. R. Can. J. Chem. 2011, 89, 1105–1117. Dithmer, L.; Lipton, A. S.; Reitzel, K.; Warner, T. E.; Lundberg, D.; Nielsen, U. G. Environ. Sci. Technol. 2015, 49, 4559–4566. Widdifield, C. M.; Perras, F. A.; Bryce, D. L. Phys. Chem. Chem. Phys. 2015, 17, 10118–10134. Askar, A. M.; Karmakar, A.; Bernard, G. M.; Ha, M.; Terskikh, V. V.; Wiltshire, B. D.; Patel, S.; Fleet, J.; Shankar, K.; Michaelis, V. K. J. Phys. Chem. Lett. 2018, 9, 2671–2677. 236. Hamaed, H.; Laschuk, M. W.; Terskikh, V. V.; Schurko, R. W. J. Am. Chem. Soc. 2009, 131, 8271–8279. 237. Kravchenko, E. A.; Orlov, V. G.; Fam, S. H.; Kargin, Y. F. Z. Naturforsch. A 1998, 53, 504–513.

231. 232. 233. 234. 235.

9.08 Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry Hellmut Eckert, Instituto de Física de São Carlos, Universidade de São Paulo, São Carlos, Brazil; and Institut für Physikalische Chemie, WWU Münster, Münster, Germany © 2023 Elsevier Ltd. All rights reserved.

9.08.1 9.08.1.1 9.08.1.2 9.08.1.3 9.08.2 9.08.2.1 9.08.2.2 9.08.2.3 9.08.3 9.08.3.1 9.08.3.2 9.08.4 9.08.5 9.08.5.1 9.08.5.2 9.08.6 9.08.7 9.08.8 Acknowledgements References

Introduction and historical background The nuclei and their properties and interactions Scope of this review NMR detection methods Scandium Inorganic complexes and covalent crystalline oxides Inorganic glasses Intermetallic compounds Yttrium Molecular and covalent crystalline oxides and glasses From organometallic complexes to intermetallic compounds Lanthanum Praseodymium to thulium Van Vleck paramagnets Ferromagnets and antiferromagnets Ytterbium Lutetium Conclusions and outlook

178 178 180 180 181 181 182 182 189 189 191 192 198 198 198 200 200 203 203 204

Abstract With the burgeoning interest in rare-earthdbased compounds and materials for the development of modern optical, electronic, and magnetic devices gaining an improved understanding of structure-function relations is an important objective. At the local atomic level, nuclear magnetic resonance (NMR) offers element-selective, inherently quantitative structural information in this regard. While (except for cerium) all the rare-earth elements feature NMR-active nuclei, significant challenges arise from small magnetic moments and strong nuclear electric quadrupole interactions, as well as from the open 4f-shell configurations of many rare earth compounds. This review will highlight the current state of the field, including detection and interaction-selective characterization methods, and the informational content of spectroscopic data obtained in relation to the structural solid-state chemistry of rare-earth compounds and materials.

9.08.1

Introduction and historical background

9.08.1.1

The nuclei and their properties and interactions

With the exception of cerium, all the rare-earth elements feature at least one nuclear isotope that is principally suitable for NMR experiments. Table 1 gives a summary of the isotope-specific properties and characteristics of the rare-earth metal isotopes. In general, the spin Hamiltonian comprises both the Zeeman and the quadrupolar term, H ¼ HZ þ HQ with Hz ¼  g I z B ð1 þ cÞ HQ ¼

 
e2 qQ 1 3I 2Z  IðI þ 1Þ þ hQ I 2þ þ I 2 4Ið2I  1ÞZ 2

(given in angular frequency units) where Iz, Iþ, and I denote the unitless spin angular momentum orientation and ladder operators, I is the nuclear spin quantum number, and B (in units of Tesla) is the magnetic induction specifying the magnetic field strength. The gyromagnetic ratio g, given in units of T 1 s 1 is a nucleus-specific constant proportional to the size of the nuclear magnetic moment. The symbol c denotes the nuclear magnetic susceptibility which enhances the effective magnetic field present at the nuclei; it is responsible for the transferred hyperfine field producing Knight shifts in Pauli paramagnets and enhanced field strengths in van Vleck paramagnets. The second term describes the interaction of the nuclear electric quadrupole moment eQ, which

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Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry Table 1

Available Nuclear Isotopes for NMR Studies of Rare-Earth Nuclei and their Physical Properties.1

Isotope

Spin

Nat. abund

g[107 rad2s 2]

eQ [10 28 m2]

45

7/2 ½ 5 9/2 5/2 7/2 7/2 7/2 7/2 5/2 5/2 3/2 3/2 3/2 5/2 5/2 7/2 7/2 ½ ½ 5/2 7/2 7

100% 100% 0.09% 99.91% 100% 12.2% 8.3% 15.0% 13.8% 47.8% 52.2% 14.8% 15.7% 100% 18.9% 24.8% 100% 22.9% 100% 14.3% 16.4% 97.4% 2.6%

6.509 1.316 3.557 3.808 7.765 1.474 0.913 1.124 0.9175 6.5477 2.9371 0.8273 1.0792 6.4306 0.9206 1.275 7.9884 0.7752 2.1376 4.729 1.303 3.055 2.168

0.22 0 0.45 0.20 0.077 0.61 0.314 0.26 0.078 0.90 2.41 1.27 1.35 1.43 2.51 2.65 3.58 3.57 0 0 2.8 3.49 4.97

Sc Y 138 La 139 La 141 Pr 143 Nd 145 Nd 147 Sm 149 Sm 151 Eu 153 Eu 155 Gd 157 Gd 159 Tb 161 Dy 163 Dy 165 Ho 167 Er 169 Tm 171 Yb 173 Yb 175 Lu 176 Lu 89

179

all nuclei with I > ½ possess, with the static electric field gradient (EFG) present at the nuclear origin. The term CQ ¼ e2Qq/h is known as the nuclear electric quadrupolar coupling constant, which is usually given in units of MHz. The EFG is created by the electronic environment of the nuclei, including the valence electron distribution and the local charges produced by the coordination and lattice environment. It is described by a traceless Cartesian second-rank tensor and conventionally specified in terms of two parameters: its maximum component eq (in the principal axis system where the tensor is diagonal), and the asymmetry parameter hQ, which denotes its deviation from cylindrical symmetry. For spherical electron distributions and cubic site symmetries, eq ¼ 0. The above Hamiltonian may include additional terms, involving magnetic dipole-dipole interactions among the nuclei or between the nuclei and unpaired electrons. Quantization and selection rules for magnetic resonance spectra will depend on the relative strengths of the Zeeman or the quadrupole terms affecting nuclear orientational quantization. If one of them is dominant, energy levels and transition frequencies are calculable by standard perturbation theory, whereas complete diagonalization will be necessary if both terms are of comparable size. From the viewpoint of the practicing NMR spectroscopist using standard pulsed NMR techniques for signal detection at applied external magnetic field strengths of 4.7 Tesla or above, nuclei featuring gyromagnetic ratios below g ¼ 1.5  107 rad2s 2, commonly labeled “low-gamma-nuclei”, and nuclei featuring natural abundances of less than 10% are considered “difficult”, due to their low equilibrium magnetization and resonance frequencies. Furthermore, for nuclei with quadrupole moments exceeding 0.2  10 28 m2 standard pulsed NMR signal detection methods may fail if the nuclei experience strong electric field gradients in highly anisotropic electronic density distributions. Note that many of the rare-earth elements have two isotopes available. Therefore, utilization of both isotopes for NMR studies will give equivalent information to NMR studies at two different applied magnetic field strengths, as the magnitudes of the Zeeman and quadrupolar interactions differ for the two different isotopes. When complicated spectra are observed, consistent analysis of the interactions involving both isotopes can be helpful for separating the different contributions to the NMR spin Hamiltonian in such cases. As the Zeeman frequencies depend on the strength of the applied external magnetic field, experimental values are usually given in terms of chemical shifts defined by dCS ¼

us  uref uref

where the resonance frequency of the sample, us is compared to that (uref) of a well-defined reference standard. Official IUPAC recommendations for reference standards have been given for three of these isotopes.2 They are: 0.06 M Sc(NO3)3 in D2O (45Sc), Y(NO3)3 solution (concentration unspecified) in D2O (89Y), and 0.01 M LaCl3 solution in D2O (139La). In addition, most practitioners of 171Yb NMR have adopted a solution of the [Yb(h-C5Me5)2(thf)2] complex in THF. No recommendations have been made regarding reference standards for the other isotopes. In insulating compounds dCS reflects electronic properties of the valence shell, which are influenced by the covalency of bonding to the coordinating ligand environment, hence the name chemical shift. In

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metallic systems, the dominant effect influencing the resonance frequency is the Fermi-contact interaction of the nuclei with unpaired conduction electron spin density at the Fermi level, denoted as Knight shift in the literature. An important restriction to rare-earth NMR arises from the open f- electronic shell character of the rare-earth element under investigation. If the f-electron spins are delocalized in the conduction band (Pauli-paramagnetic metals) signal detection is not impeded. Also, NMR measurements are possible if the electronic ground state is a singlet. This situation not only applies to the obvious cases of diamagnetic La3þ or Lu3þ, but may also occur in rare earth ions with an even number of electrons (Pr3þ, Eu3þ, Tb3þ, Ho3þ, and Tm3þ) under the influence of the crystal field. Indeed, 141Pr, 159Tb, and 169Tm NMR signals have been observed in such van Vleck paramagnets at sufficiently low (usually cryogenic) temperatures.3 At higher temperatures the signal shifts and eventually disappears as paramagnetic electronic states are increasingly being populated. While in Curie-type paramagnets the rapid electron spin fluctuations limit the life times of the nuclear Zeeman states beyond signal detectability, NMR of rare-earth elements with open-4f-shell electron configurations is possible in ferro- or antiferromagnetically ordered materials. Much of the early literature on NMR of the rare-earth nuclei has been devoted to this subject.4–6

9.08.1.2

Scope of this review

With the advent of modern pulsed high-resolution NMR methods involving magic-angle spinning (MAS), and multiple-pulse, multidimensional techniques for providing correlation and interaction selectivity, new opportunities have arisen for the use of rare-earth metal NMR, making it a useful structural tool in solid state chemistry and materials science. This field started 35 years ago, when Thompson and Oldfield demonstrated the effectiveness of magic angle sample spinning to produce line-narrowing in the NMR spectra of 45Sc, 89Y, and 139La, making these nuclei accessible for detailed structural investigations of inorganic solids.7 Their pioneering study was followed by some early 89Y NMR works seeking empirical correlations of 89Y chemical shifts with local environments and coordination numbers in oxidic yttrium compounds,8 the study of the distributions of paramagnetic dopants in inorganic host lattices and solid solutions9 and explorations of electron density variations in ceramic superconductors.10 Unlike the case of traditional static NMR of metallic and magnetic materials, no comprehensive review of rare-earth NMR exists to this author’s knowledge. This fact may be attributed to the large diversity of rare-earth compounds in contemporary solid state physics, chemistry, and materials science, encompassing materials as diverse as glasses, ceramics, catalysts, magnets, ionic and electronic conductors, and inorganic-organic nanocomposites. This contribution will focus on the methods of obtaining the spectra, the internal interactions affecting them and the local atomic structural information obtained from their analysis. I will only mention in passing the very extensive literature with a distinct solid-state physics focus, seeking an improved fundamental understanding of the electronic and magnetic structure. Unfortunately, an in-depth discussion linking the NMR signal to the fundamental physics involved would be beyond the scope of this contribution.

9.08.1.3

NMR detection methods

As the “NMR personalities” of the nuclei summarized in Table 1 are quite different, the techniques for detecting their magnetic resonance are varied. In the case of 89Y and 45Sc, standard magic-angle spinning at moderate to high magnetic field strengths > 4.7 T is generally possible. The detection sensitivity of the spin-1/2 nuclides 89Y and 171Yb is low because of their low magnetic moments and generally long spin-lattice relaxation times. This situation can be remedied by cross-polarization in samples containing protons11 or by combining multiple-echo acquisition using the Carr-Purcell-Meiboom-Gill sequence,12 see Fig. 1 for the latter.

Fig. 1 Carr-Purcell-Meiboom-Gill (CPMG) sequence with multiple echo acquisition for enhancing the signal to noise ratio of NMR signals in compounds with long spin-lattice relaxation times.12 The detector is closed when the pulses are applied and open in-between the pulses during echo formation. Fourier transformation of the echo train acquired in this fashion leads to a spikelet pattern enveloping the static or MAS-NMR lineshape.

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

181

Fourier transformation of the entire echo train acquired in this fashion leads to a spikelet pattern enveloping the static or MAS-NMR lineshape. The latter can also be obtained directly if all the echoes are co-added prior to Fourier transformation. For quadrupolar nuclei signal measurements usually aim at the detection of the central m ¼ ½ m ¼ -½ Zeeman transition, which is not anisotropically broadened to the first order level of perturbation theory, and thus appears with much higher intensity than the other transitions (see Fig. 2). The moderately strong quadrupolar interactions in scandium compounds usually do produce, however, second-order quadrupolar broadening effects of the central transition lineshape studied at the most common magnetic field strengths of 7.0–17.6 T. Under MAS conditions, this results in highly characteristic lineshapes from which the quadrupolar coupling constants and EFG asymmetry parameters can be extracted by simulation (see Fig. 2, right).13 The simulation also CS yields the Zeeman contribution to the resonance center, i.e. the chemical shifts (or Knight shifts) diso . Complicated spectra with various overlapping components can be simplified by a two-dimensional technique involving multiple-quantum coherence excitation.14 Fig. 3 shows the most commonly used three-pulse sequence. The first pulse P1 creates triple quantum coherence which is allowed to evolve for an incremented time period t1, after which it is converted back to zero-quantum coherence by the second pulse P2. Detection follows after converting the zero-quantum to single-quantum coherence, i.e., transverse magnetization, with a softer pulse P3. For appropriate coherence selection, special phase cycling schemes have to be used. Even more challenging is the NMR of 139 La, which in many cases requires wideband (field-, frequency-, or phase-swept) excitation strategies such as the WURST (wideband uniform rate smooth truncation)15 scheme to be combined with the CPMG acquisition mode. Finally, in the case of 175Lu, which possesses one of the largest quadrupole moments on the planet, only compounds featuring cubic local environments have been measured so far with equipment operating at a fixed magnetic field strength. It is to be anticipated that the NMR of non-cubic lutetium compounds will require either echo-detected field sweep (EDFS) acquisition (as done in pulsed EPR) or the application of WURST-CPMG acquisition with systematic stepping over a wide range of frequencies. Finally, as measuring the low-abundant nuclei 138La and 176Lu and the low-gamma quadrupolar nuclide 173Yb offers no advantages over the use of the higher-gamma isotopes of the same element, the NMR literature on these three nuclei is practically nonexistent.

9.08.2

Scandium

9.08.2.1

Inorganic complexes and covalent crystalline oxides

Of all the nuclear isotopes listed in Table 1, 45Sc is by far the most favorable one in terms of sensitivity and ease of detection. The IUPAC recommendation of using 0.06 M Sc(NO3)3 solution in D2O1 is being widely ignored, and aqueous solutions of ScCl3 and Sc(NO3)3 of various concentrations are in use. It has been pointed out that this may account for some difference on the order of several ppm in the chemical shifts reported in the literature.16 A suitable secondary solid standard is ScPO4 which has a sharp signal as quadrupolar coupling is weak. A large number of inorganic solids have been measured in the recent two decades. Owing to the moderately sized nuclear electric quadrupole moment of 45Sc, the MAS-NMR spectra are generally well-resolved and can be analyzed in terms of magnetic shielding and quadrupolar interactions. As illustrated in Table 2 the chemical shifts in oxidic inorganic compounds span more than 200 ppm. Theoretical calculations using the GIPAW approach predict a clear trend of the isotropic chemical shift to increase with decreasing coordination number over the entire range of coordination numbers (8 > CN > 4) realized in the solid-state chemistry of scandium. As shown in Fig. 4, this trend is also observed experimentally, however, there is significant overlap of the characteristic shift ranges for different coordination numbers, caused by an apparently very strong influence of second-nearest neighbor effects. Because of this overlap 45Sc NMR isotropic chemical shifts cannot be

Fig. 2 Left: Zeeman energy level diagram for a spin-7/2 nucleus affected by first-order quadrupolar perturbations. Middle: resulting lineshape under static conditions, assuming an axial electric field gradient; right: simulated MAS-NMR central transition lineshapes, revealing the effect of the EFG asymmetry parameter hQ.

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Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

Fig. 3 Pulse sequence and coherence path diagram selected via the phase cycling scheme of a triple-quantum MAS-NMR experiment. For spin-3/2 nuclei, coherence orders ranging from þ3 to 3 are possible.

viewed as safe predictors of coordination number in unknown systems such surface phases or glassy materials. An additional problem arises from the fact that only very few model compounds are known that feature a scandium coordination number different from six.

9.08.2.2

Inorganic glasses

45 Sc MAS-NMR spectra of glasses invariably show the broad, asymmetric lineshapes generally observed for quadrupolar nuclei in glasses when second-order quadrupolar perturbation effects are significant.37–43 These lineshapes reflect a wide distribution of quadrupolar interaction strengths affecting the resonances in the regime of second-order perturbation theory. They can be modelled using a Czjzek distribution,44,45 which has already been implemented in standard lineshape simulation software, yielding values of  12 2 CS average chemical shifts/Knight shifts diso and the average quadrupolar coupling parameter SOQE ¼ CQ 1 þ h3 . Alternatively, the

same information can be extracted from 2D- triple quantum ((TQ)MAS)dNMR spectroscopy.14 Table 3 summarizes the 45Sc NMR chemical shifts obtained in this manner. While this table shows significant variations depending on the glass system considered, it is generally assumed that Sc in glasses is six-coordinated. However in view of the above-discussed data scatter in Fig. 4 this conclusion must be considered tentative, and there could be a distribution of coordination numbers as well. More certainty about the local scandium environments may come from dipolar spectroscopy, however. For scandium-containing aluminophosphate glasses, rotational echo double resonance (REDOR) experiments suggest that the second coordination sphere is dominated by phosphorus.40 Scandium environments in fluoride phosphate laser glasses are characterized by a mixed coordination of fluoride and phosphate ligands, which can be controlled by the phosphate/fluoride ratio of the bulk composition. The detailed quantification of these environments, while not possible by chemical shift spectroscopy, could be achieved by 45Sc/19F and 45Sc/31P REDOR. It could also be shown that the ligand distribution around the scandium center can be controlled by the glass composition, in the present case the fluoride to phosphate ratio of the batch. Fig. 5 compares the 45Sc/31P REDOR data on two fluorophosphate glass systems: 25BaF225SrF2-(30-x)Al(PO3)3-xAlF3-(20-z)ScF3:zREF3 (left) and 20BaF2-20SrF2-20ZnF2-10ScF3(30-w)In(PO3)3-wInF3-zREF3 (right). Also shown are the EPR spectra of Yb3þ doped glasses. For the (1-x)Al(PO3)3-xAlF3 based glasses there is a monotonic change in the strength of the dipole-dipole interaction as well as of the position of the EPR line, indicating a gradual increase in the fraction of fluoride ions contributing to scandium’s first coordination sphere as the F/phosphate ratio of the glass composition increases. In contrast for the (1-x)In(PO3)3-xInF3 based system the 45Sc/31P REDOR effect is nearly absent and the position of the EPR signal is almost independent on the F/phosphate ratio. These results indicate that in the indium based system the first coordination sphere of the RE ion is essentially dominated by the fluoride ligand over the entire concentration range of x. Consistent with these observations, the luminescence properties of the two glass systems show very characteristic differences.46

9.08.2.3

Intermetallic compounds

During the past two decades a large database for 45Sc NMR in intermetallic compounds has been built (see47 for a review of the literature up to 2010). CQ values range from zero to about 20 MHz and Knight shifts between zero and 2000 ppm have been observed. By comparing experimental CQ values with those computed theoretically from crystallographic input data, NMR can serve as a convenient method of crystal structure validation. If large deviations between experimental and calculated field gradients are observed, either the proposed structure solution is invalid or there is a discrepancy between the single crystal mounted on the X-ray diffractometer and the bulk polycrystalline material used for the NMR measurement. Such structure validation becomes especially important for compounds based on elements with very similar scattering power, for materials presenting single crystals of low

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry Table 2

183

45

Sc NMR chemical shifts and quadrupolar coupling parameters in crystalline scandium compounds featuring oxygen or halogen coordination. CQ[MHz]

Compound

disoCS[ppm]

Sc(acacCN)3 -I (CN ¼ 7) Sc(acacCN)3 -II(CN ¼ 7) Sc(acac)3 Sc(TMDHD)3 Sc(NO3)3  5H2O Sc(OAc)3 ScCl3  6H2O ScCl3  3THF Sc2O3 Sc2O3 Sc2O3 Sc2O3 X2-Sc2SiO5 C-Sc2SiO5 Y3Sc0.05Al4.95O12 PLZT: 2% Sc Sc2(SO4)3  5 H2O

9.85 6.85 12.49 8.70 82 13.0 89.5 13.1 18.5 6.2 6.2 4.6 125.4 3.9 202 8.4 136/113 15.4/23.4 131.2/110.4 15.4/23.3 128.7/108.0 15.4/23.4 128.2/108.0 15.3/23.4 86.3/95.8 25.7/19.8 77.8 20.7 88 9.1 141 7.8 (SOQE) 15.5 5.60 12.9 4.50 4.7 4.55 10.1 2.1 15.6 2.4 153 7.4 163.2 7.6 153.5 3.4 131.5 9.6 166 32 47 10 148.0 1.6 158.2 14.2 64 11.6 100 11.9 158 9.0 160 13.8 186.9 10.3 180.1 13.4 174.3 14.4 203.9/183.9 12.5/10.2 70–100 8 20–60 9–14 No parameters published 50? 10.3/26.3 6.2/7.8 Spectra shown but not analyzed 43 13 34.7 6.4 23 84 9.2 34.1 7.3(SOQE) 27.4 8.1(SOQE) 6.1 6.4(SOQE) 25.8 7.2 23.0 9.7 13.5/12.0 10.9/6.6 9.4 4.1 22.8 6.3 17.4 5.2 24.5 6.0 48.2 0 42.6 0.63

Sc2(MoO4)3 Sc2(WO4)3 YScO3 YScO3 LaScO3 ScGaO3 Sr2ScGaO5 ZrO2:Sc3þ LiScO2 NaScO2 ScOF Li3Sc(BO3)2 CaSc2O4 CaSc2O4 BaSc2O4 Ba3Sc4O9 Sc3(BTB2) (CN ¼ 5) (CN ¼ 6) MIL-100(Sc) STA-27 Sc(HPO4)2  0.5(N2C2H10) Sc-phosphates (templated) Li1.4Sc0.4Ge1.6(PO4)3 LiScP2O7 Sc(PO3)3 ScBO3 KSc[BP2O8(OH)] RbSc[BP2O8(OH)] CsSc[BP2O8(OH)] Sc(H2O)[BP2O8]  H2O Li2Sc[(PO4)(HPO4)] NaSc(HPO4)2 KSc(HPO4)2 RbSc(HPO4)2 CsSc(HPO4)2 NH4Sc(HPO4)2 ScPO4 (CN ¼ 8) ScPO4 (CN ¼ 8)

hQ

References

0.05 0.05 0.22 0.93 0.75 0.18 0.77 0.30 0.63/0.0 0.63/0.0 0.62/0.0 0.63/0.0 0/0.90 0.45 0

17 17 18 18 18 18 18 18 19 20 21 22 21 21 23 24 25 25 25 26,27 26,27 27 28 27,28 29 30 22 22 22 19 19 19 19 20 20 20 20 31 31 31 32 33 34 35 35 36 36 36 36 36 36 36 36 36 36 36 36 22 19

0.06 1.00 0.50 0.6 0.3 0.74 0.7 0.80 0.7 0.28 0 0.93 0.47 0.52 0.91 . 3

¼ ðea  eb Þ= < e >

(2)

Indeed, in a series of lanthanum compounds CQ was found to correlate well with both parameters, even though a number of exceptions were noted. Overall, these parameters are helpful in reaching a qualitative understanding of nuclear electric quadrupolar

Fig. 16 139La NMR spectra, recorded using the WURST-CPMG technique, of some rare-earth containing fluoride, oxyfluoride and oxide glasses. Reproduced with permission from reference Zhang, X.; Hu, L.; Ren, J. Transparent Aluminosilicate Oxyfluoride Glass Ceramics Containing Upconversion Luminescent CaF2 Nanocrystals: Glass-to-Crystal Structural Evolution Studied by the Advanced Solid-State NMR Spectroscopy. J. Phys. Chem. C 124 (2020), 1594–1608.

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

197

coupling constants measured for 139La and other nuclei belonging to large atoms, such as 87Rb or 137Ba, whenever large coordination numbers are encountered. Most recently the WURST-CPMG method has been used to record the first 139La NMR spectra in glasses.113,121 Fig. 16 shows results on some crystalline model compounds, the standard fluoride glass ZBLAN (53% ZrF4, 20% BaF2, 4% LaF3, 3% AlF3 and 20% NaF), and various spectra on aluminosilicate glasses with composition 55SiO2-10Al2O3-5La2O3-10CaO-20CaF2 (“5La”) and 55SiO2-10Al2O3- 5La2O3-30CaO (“5La-F free”). These results give no indication for LaeF bonding and no evidence for La being involved in the crystallization.121 Based on the 139La WURST-QCPMG spectra as well as the paramagnetic effect of Er3þ on NMR spectra, Ren et al. proved that in the glass ceramics obtained by annealing the rare earth ions are distributed in both the glass phase and the fluoride crystals.121 Their results indicate that the generally held assumption that the rare-earth ions aggregate selectively in the fluoride crystals after ceramization has to be reconsidered. Within the scope of this review, it is impossible to pay tribute to the outstanding role the element lanthanum plays in the design of materials with colossal magnetoresistive, superconducting, and thermoelectric materials. 139La NMR has been widely applied in characterizing magnetic structure, lattice dynamics (“rattling” of guest species), structural and electronic disorder, site distortions, substitutions and phase transitions in these systems, and only a few key papers will be cited here, referring to the thermoelectric skutterudites122–127 and the colossal magnetoresistive material LaMnO3128–130.

Fig. 17 Electronic structure of the non-Kramers ions Pr3þ, Tb3þ, and Tm3þ in the crystal field of elpasolite, denoting the singlet ground state and the quartet first excited state, which is responsible for the compound’s paramagnetic properties.

198

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Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

Praseodymium to thulium

The NMR spectroscopy of these nuclei has focused on low-temperature measurements of van Vleck paramagnets (for 141Pr, 159Tb, and 169Tm), and measurements of transferred magnetic hyperfine fields in ferro- and antiferromagnets (all the nuclear isotopes listed in Table 1).

9.08.5.1

Van Vleck paramagnets

As illustrated in Fig. 17 for the example of elpasolite, the electronic ground states of Pr3þ, Tb3þ, and Tm3þ are predicted to be nonmagnetic singlets in the octahedral crystal field. An applied magnetic field admixes the wave functions of excited states into the single ground state and produces an induced magnetic dipole moment, which in turn produces a hyperfine field at the nucleus. This van Vleck paramagnetism then produces a Zeeman effect, resulting in an enhanced magnetic hyperfine field at the nucleus, that can exceed the applied field by orders of magnitude. As a result, the effective gyromagnetic ratio of the nucleus is increased by an enhancement factor depending on the paramagnetic van-Vleck susceptibility, which in turn depends on the magnitude of the crystal field and can be calculated by second-order perturbation theory. Systematic studies of this effect have been conducted with the above three non-Kramers ions131–136 in zircon-type lattices and other materials, investigating the influence of temperature and pressure, particle size, and substitutional doping. Because of the perturbative nature of the effect, it is usually necessary to measure at very low temperatures. In non-cubic environments the spectra are affected by quadrupolar splittings and the sign of the quadrupolar coupling constant can be determined. As an example, Fig. 18 compares the 141Pr NMR signals of the micro- and nanosized van Vleck paramagnet PrF3, indicating that the NMR lineshape is quite sensitive to particle morphology. The wider line in the nanosized material is attributed to the higher concentration of structural defects.[137]

9.08.5.2

Ferromagnets and antiferromagnets

All of the rare-earth isotopes can be observed using standard NMR methods in ferromagnetic and antiferromagnetic compounds. Much early NMR literature on rare-earth nuclei has been devoted to this subject.[138–146] Radio frequency absorption occurs if the resonance condition is attained in the local static internal magnetic field (hyperfine field) present at the nuclei. Signals are usually extremely wide (on the order of 1–10 MHz), requiring the use of systematic spin echo mapping under frequency variation. The magnetic hyperfine field detected by NMR of the rare-earth isotope consists of (a) the intra-ionic contribution due to the 4f shell, (b) the extra-ionic ones such as the transferred field from neighboring electron spins and (c) the self-polarization field arising from the conduction electron polarization caused by the rare-earth spin at the nuclear site. If the probe nuclei belong to diamagnetic ions such as trivalent Sc, Y, La, and Lu or divalent Yb, the hyperfine field detected by the NMR signal of these isotopes can be safely attributed to the magnetic field of the host lattice that is transferred to the probe nuclei. The NMR spectra of powdered samples reflect the effects of the Zeeman interaction anisotropy anddin the case of non-cubic site symmetries and spin >½ nucleidthat of the nuclear electric quadrupolar interaction. In the strong-field case, HZ [ HQ, first order perturbation theory predicts that the energy levels shift proportional to the square of the Zeeman quantum number, m2, leading to a resonance splitting into 2I components, corresponding to the allowed Dm ¼  1 transitions between adjacent Zeeman states. Fig. 19 shows typical examples for the isotopes

Fig. 18 Effect of particle size on the 141Pr NMR signals of the van Vleck paramagnet PrF3 measured at 19.5 MHz and 1.5 K. (1) particle size 45 mm, (2) particle size 31 nm. Reproduced with permission from Alakshin, E. M.; Gazizulin, R. R.; Klochkov, A. V.; Korableva, S. L.; Safin, T. R.; Safiullin, K. R.; and Tagirov M. S. Annealing of PrF3 Nanoparticles by Microwave Irradiation. Phys. Rev. Optics and Spectrosc. 116 (2014), 721–723.

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

199

Fig. 19 NMR spectra of (a) 147Sm, (b)161/163Dy (I ¼ 5/2) and (c) 175Lu (I ¼ 7/2), in ferromagnetic RFe11Ti (R ¼ Nd, Sm, Tb, Dy, Er and Lu), revealing peak splitting caused by quadrupolar interactions. In part (c) the line near 250 MHz is attributed to an impurity. Reproduced with permission from reference Shimizu, K.; Ogasawara, F.; Ichinose, K. Rare-Earth NMR Measurements on RFe11Ti (R ¼ Nd, Sm, Tb, Dy, Er and Lu). Physica B 237–238 (1997) 584–586.

Fig. 20 Rare earth NMR of ferromagnetic SmMn2Ge2 at 4.2 K. Signals from both isotopes 147Sm and 149Sm are displayed and the peak splitting arises from quadrupolar coupling. Reproduced with permission from reference Lord, J.S.; Riedi, P.C.; Tomka, G. J.; Kapusta, CZ.; Buschow, K. H. J. NMR Study of Ferromagnetic Phases of SnMn2Ge2 as a Function of Temperature and Pressure. Phys. Rev. B 53 (1996), 283–288.

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Sm (I ¼ 7/2), 161/163Dy (I ¼ 5/2 for both isotopes) and 175Lu (I ¼ 7/2) in the ferromagnetic state of rare-earth compounds of the general composition REFe11Ti, revealing the above-mentioned quadrupolar splittings. The peak intensities reflect the theoretically predicted m m-1 Zeeman transition probabilities, which are in the ratio 7:12:15:16:15:12:7 in the order of decreasing orientational quantum number. Early work on this subject has been comprehensively reviewed and extended over the years to structurally and compositionally more complex intermetallic compounds.[145–165] Fig. 20 shows a particularly impressive example of SmMn2Ge2, revealing the responses of both nuclear isotopes and the splitting of the resonance line due to the quadrupolar interactions.[157] Particularly detailed work has also been published on ferro- and antiferromagnetic europium chalcogenides,148–151 the ferromagnet Sm2Co17, elucidating the influence of various types of chemical modifications on its magnetic properties,158–160 and a number of ferromagnetic garnets and related structures[162–165].

147

9.08.6

Ytterbium

Aside from the pioneering ytterbium magnetic moment measurements in Yb metal166 not a single standard 173Yb NMR work has been published to the author’s knowledge. While a few measurements of Knight shifts in metallic and semiconducting systems have been reported,167–175 inorganic ytterbium NMR spectroscopy has been limited to the relatively rare cases of divalent ytterbium compounds having the 4f14 closed-shell configuration. Among the two ytterbium isotopes listed in Table 1 the spin-1/2 isotope 171 Yb is the preferred one owing to its significantly larger magnetic moment compared to 173Yb and the absence of an electric quadrupole moment. Successful detection of signals in YbS, YbCl2, Yb metal,166 and the Laves phase YbAl2170 was later followed by Knight shift measurements of yttrium dihydride (3750 ppm),171 and a characterization of the mixed-valent (Yb2þ/Yb3þ) compound YbPtGe2,175 where only the divalent species was detected. The overall chemical shift range observed in solutions and the solid state spans about 1500 ppm (see Table 9). The commonly accepted chemical shift reference is a thf solution of [Yb(C5Me5)2]. For a series of h-cyclopentadienyl complexes the magnetic shielding tensor components have been measured.176,178,177 Significant differences are found revealing that these parameters are sensitive to both the substituents at the cp* ligand and the nature of additional coordinating base molecules.177 To date, no effort of understanding the large 171Yb chemical shift variations on a first-principles theoretical basis has been reported. Fig. 21 shows an interesting case of the static NMR spectrum of mixed valent YbPtGe2. This compound features the Yb component in a mixed-valent Yb state, the Yb(1) site being trivalent and paramagnetic and the Yb(2) site being diamagnetic. As expected, only the diamagnetic Yb(2) site is observed, featuring a large Zeeman interaction anisotropy, consistent with its orthorhombic site symmetry. The sharp feature observed at the low-field side of the spectrum is attributed to a preferential orientation effect of the powders in the applied magnetic field.

9.08.7

Lutetium

The nuclei 175Lu and 176Lu may well be considered the most “exotic” ones. Their huge nuclear electric quadrupole moments render their NMR spectra particularly sensitive to small local distortions or structural defects even in nominally cubic compounds. As a consequence, few NMR spectroscopic structural studies have been reported, all of which utilize the abundant 175Lu isotope. Earlier works focused on direct nuclear quadrupole resonance of crystalline compounds.179–183 Despite the strong and dominant quadrupolar interaction, NMR spectra can also be observed in applied magnetic fields, if the resonance condition is fulfilled for the Zeeman Table 9

171

Yb chemical shifts measured in solution and the solid state.

Compound

disoCS(liquid) [ppm]

disoCS (solid) [ppm]

References

[Yb(h-C5Me5)2]n [Yb(h-C5Me5)2(thf)2] [Yb(h-C5Me5)2(OEt2)] [Yb(h-C5Me5)2(py)2] [Yb(PPh2)2(thf)4] [Yb(h-C5Me4H)2(THF)2] [Yb(h- C5Me5)2(DME)] [Yb{h- C5Me4 (SiMe3)}2THF] [Yb(h- C5Me5)2(THF),1/2PhMe] [Yb(h- C5Me4 (SiMe2But))2] CsYbI3 RbYbI3 KYbI3

33 (toluene) 0 26 (OEt2) 949 (py) 440.6 131 (THF) 98 (DME/bz) 6 (THF) 28, 28.5 20 (C7H14)

34 24, 29.5 23 782

176,177 178,177 177 177 178 177 177 177 178,177 178 174 173 173

a

Relative to CsYbI3.

123 128 28 30 0 (ref.) 33.5a 58.6a

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry

201

Fig. 21 171Yb NMR spectrum of YbPtGe2. Only the diamagnetic Yb2þ site can be detected. The feature at 8.845 T (green curve) arises from a preferential ordering effect of the powdered sample in the magnetic field. Reproduced with permission from reference Sarkar, R.; Gumeniuk, R.; Leithe-Jasper, A.; Schnelle, W.; Grin, Y.; Geibel, C.; Baenitz, M. Unconventional Magnetism in Multivalent Charge Ordered YbPtGe2 Probed by 195Pt and 171Yb NMR. Phys. Rev. B 88 (2013): 201101.

splitting affecting the pure quadrupolar m ¼  1/2 levels as has been observed for some silicides.183,184 The 175Lu nuclei are also suitable diamagnetic probes for measurements of transferred magnetic hyperfine fields in ferromagnetic compounds, such as pure metals, metallic alloys, intermetallic compounds147,153,154,161,162,185 and garnets.164,186 Again, from the seven-line splitting, the nuclear electric quadrupolar coupling constant can be determined (Fig. 22). To the best knowledge of the author reference164 is the only one reporting a 176Lu signal, occurring at 40 MHz in the internal magnetic field of the lutetium iron garnet, Lu3Fe5O12. Other studies have measured Knight shifts in metals and semiconductors.187,188 We have recently obtained the first 175Lu high-resolution spectra, using magic-angle spinning on some metallic and semiconducting materials.189,190 Owing to the huge size of the quadrupole moment, such studies are limited to compounds with Lu atoms situated on sites with cubic point symmetry, and, even for those, signal detection can be sabotaged by electric field gradients arising from lattice defects. This is the case if there are mixed metal site occupancies, a defect frequently observed in intermetallic compounds, e.g. in Heusler phases. For this reason, 175Lu MAS-NMR spectra are more likely to be observed in lattices where covalent bonding renders such defects thermodynamically unfavorable. Examples include the binary pnictides (LuX, X ¼ P, As, Sb,

Fig. 22 175Lu NMR spectra of the Lu dopants in ferromagnetic Dy and Tb. Reproduced with permission from reference Eagles, D.M.; Lalousis, P. Analysis of 175Lu NMR Data on Dilute Alloys of Lu in Tb and Dy. Hyperfine Interact. 8 (1980), 283–289.

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Fig. 23 14.1 T 175Lu MAS-NMR spectra for some cubic Lu compounds. Central peaks are labeled by asterisks, and minor peaks are spinning sidebands. Reproduced from reference. Benndorf, C.; de Oliveira Junior, M.; Bradtmüller, H.; Stegemann, F.; Pöttgen, R.; Eckert, H. Rare-Earth NMR in Intermetallic Solids: The Case of the 175Lu Isotope. Solid State Nucl. Magn. Reson. 101 (2019), 63–67.

NaCl structure) and various ternary intermetallic compounds crystallizing in the MgAgAs lattice. Fig. 23 summarizes the 175Lu NMR spectra of LuP, LuAs, LuSb, LuPtSb, and LuAuSn measured at 14.1 T. Although the spectra show many common features (as discussed below) there are large variations in the absolute signal intensity, which can be related to the concentration of defects. For example, the cubic compounds LuNiSb, LuCu2In, LuAu2In, and LuPd2Sn yielded no 175Lu NMR signals even when exploring a wide range of measurement conditions. Efforts are underway of applying ultra-wideband detection methods to this problem. By far the strongest signals were observed for the compounds LuP and LuAuSn. In both cases a signal-to-noise ratio sufficient for referencing can already be obtained within a few minutes, and noise-free spectra are available within 2 h. In keeping with the tradition of choosing diamagnetic, non-metallic compounds as reference standards, we propose the compound LuP as the zero ppm standard; its exact resonance frequency at a magnetic flux density corresponding to 100.00 MHz proton frequency is given by 11.324 MHz. The spectra displayed in Fig. 23 reveal various features that can be seen as a common signature of 175Lu NMR spectra in cubic compounds. In all cases, a relatively sharp central peak is seen, which arises from the m ¼ 1/2 m ¼  1/2 transitions of the spin-7/2 isotope. This central signal is flanked by spinning sideband manifolds, arising from the anisotropically shifted noncentral Zeeman (“satellite”) transitions of those 175Lu nuclei experiencing relatively weak electric field gradients produced by defects that are relatively distant. Under MAS conditions, these satellite transitions lead to the featureless spinning sideband envelopes observed in Fig. 23.

Fig. 24 Static 175Lu NMR spectra of LuSb, LuAuSn, and LuPtSb at different magnetic field strengths. Reproduced from reference. Benndorf, C.; de Oliveira Junior, M.; Bradtmu¨ller, H.; Stegemann, F.; Po¨ttgen, R.; Eckert, H. Rare-Earth NMR in Intermetallic Solids: The Case of the 175Lu Isotope. Solid State Nucl. Magn. Reson. 101 (2019), 63–67.

Solid state nmr of the rare earth nuclei: Applications in solid-state inorganic chemistry Table 10

203

175

Lu isotropic chemical shifts, measured at two different magnetic field strengths, and magnetic field dependent linewidths (FWHM) measured under magic-angle spinning and under static conditions. diso[ppm] (2 ppm)

DMAS[kHz] ( 0.2 kHz)

Dstat.[kHz] (0.5 kHz)

Compound

14.1 T

9.4 T

14.1 T

9.4 T

14.1 T

9.4 T

5.6 T

LuP LuAs LuSb LuPtSb LuAuSn

0 20 17 1123 1064

0 n.d. 13 1121 1062

1.9 2.2 2.3 3.2 1.4

2.0 n.d. 2.9 3.0 1.5

n.d. 3.8 3.4 4.5 2.2

n.d. n.d. 3.7 4.6 2.0

n.d. n.d. 2.7 4.5 1.7

The dominant central 175Lu resonances are characterized by isotropic shifts that clearly differentiate between the individual compounds. The peak positions and linewidths are independent of magnetic field strength indicating the absence of secondorder quadrupolar effects for these signals. The resonance frequencies of the two lutetium pnictides are dominated by chemical shifts (diso  20 ppm vs. LuP), while those of LuAuSn and LuSbPt are affected by strong Knight shifts (diso > 1000 ppm vs. LuP). In most of the cases the MAS-NMR linewidths are found independent of spinning frequencies (over the range of 11.0– 30.0 kHz) within experimental error. However, some spectra recorded at higher spinning speeds reveal broader signal components near the base of the peak, suggesting the detection of 175Lu nuclei affected by stronger quadrupolar interactions. Fig. 24 reveals that the width of the static 175Lu spectra of the compounds investigated are approximately field independent. As indicated in Table 10 line narrowing by fast MAS (20 kHz) is only moderate, still producing residual linewidths of several kHz, also independent of magnetic field strength. They turn out to be dominated by the indirect (electronically mediated) heteronuclear interactions between the 175Lu nuclei and the heteronuclei 121Sb, 195Pt, and 115/117/119Sn (historically called pseudo-dipolar interaction) and the indirect homonuclear 175Lue175Lu spin-spin interactions (historically called pseudo-exchange interaction). Similar results have been observed in the MAS-NMR spectra of III–V semiconductors involving heavier elements (such as GaAs or InP). For the present set of compounds the smallest MAS NMR linewidth is observed in LuAuSn, for which the heteronuclear pseudo-dipolar interactions can be considered particularly weak owing to the small magnetic moment of the 197Au isotope and the low natural abundances of the magnetic tin isotopes,115Sn, 117Sn, and 119Sn.

9.08.8

Conclusions and outlook

As illustrated in the preceding sections, the contributions of NMR of the rare-earth isotopes to the structural solid-state chemistry of rare-earth compounds are extensive and diverse, ranging from the characterization of van-Vleck and Pauli paramagnets all the way to magnetically ordered solids and diamagnetic insulating materials. Emphasizing the latter application field, the present review highlights some of the insights NMR can give into the phase distributions and next-nearest neighbor environments of scandium, yttrium, and lanthanum in crystalline solids and solid solutions. Structural factors influencing 45Sc, 89Y and 139La chemical shifts and of 45Sc and 139La quadrupolar coupling parameters have been identified with the help of ab-initio calculations. In addition, interaction-selective experiments, aiming at the quantification of magnetic dipole-dipole interactions have been successfully demonstrated, paving the way of rare-earth NMR, in particular that of the isotopes 45Sc and 89Y, towards applications to more complex materials such as glasses and nanostructured matter. On the other hand, the utility of 139La, 171Yb and 175Lu NMR in this particular application field appear more limited. Ytterbium needs to be divalent in order to be detectable, whereas in the case of 175Lu NMR the electric field gradients created by lattice defects may already produce such wide distributions of local quadrupolar couplings that the signal detection is sabotaged even in cubic lattices. Extended wideband NMR detection methods or pure NQR spectroscopy may be the more promising avenue towards analyzable signals in this case. Finally, the 139La isotope may be seen in an intermediate position between 45Sc and 175Lu, with its future impact likely to increase, as more powerful and more selective wideband NMR detection techniques continue to be developed. In view of the outstanding role of lanthanum compounds in solid state physics and chemistry, it will be of interest to review this field again after the end of the forthcoming decade.

Acknowledgements I wish to thank my academic collaborators over approximately 20 years at the WWU Münster and the University of Sao Paulo, Professor Rainer Pöttgen (WWU Münster), PD Dr. Oliver Janka (Universität des Saarlandes), Professors Andrea de Camargo, Claudio Magon, and Marcos de Oliveira (University of São Paulo), and Professor Long Zhang (Shanghai Institute of Optics and Fine Mechanics). This review contains excerpts from the doctoral theses of Drs. Daniel Mohr, Heinz Deters, and Constanze Fehse (WWU Münster). Financial support by the Deutsche

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Forschungsgemeinschaft through the priority program SPP1166 Lanthanoidspezifische Funktionalitäten in Molekül und Material and to FAPESP (Center of Research, Technology, and Education in Vitreous Materials, 2013/07793-6) is gratefully acknowledged.

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H., Jr. Recent NMR Studies of Thermoelectric Materials. Annu. Rep. NMR Spectrosc. 2017, 92, 137–198. 127. Grippius, A.; Baenitz, M.; Morozova, E.; Leithe-Jasper, A.; Schnelle, W.; Shevelkov, A.; Alkaev, E.; Rabis, A.; Mydosh, J.; Grin, Y.; Steglich, F. Crossover between Itinerant, Ferromagnetism and Antiferromagnetic Fluctuation in Filled Skutterdudites, MFe4Sb12 (M ¼ Na, Ba, La), as Determined by NMR. J. Magn. Magn. Mater. 2006, 300, e403–e406. 128. Trokiner, A.; Verkhovskii, S.; Gerashenko, A.; Volkova, Z.; Anikeenok, O.; Mikhalev, K.; Eremin, M.; Pinsard-Gaudart, L. Melting of the Orbital Order in LaMnO3 Probed by NMR. Phys. Rev. B 2013, 87, 125142. 129. Sakaie, K. E.; Slichter, C. P.; Lin, P.; Jaime, M.; Salamon, M. B. 139La Spectrum and Spin-Lattice Relaxation Measurements of La2/3Ca1/3MnO3. Phys Rev. B 1999, 59, 9382–9391. 130. 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Magn. Magn. Mater. 1987, 70, 178–180. 155. Shimizu, K.; Ichinose, K.; Fukuda, Y.; Shimotomai, M. 143Nd NMR Study of 3d and 4f Magnetism in Nd2(Fe1  xCox)14B and Nd2(Fe1  yNiy)14B. Solid State Commun. 1995, 96, 671–674. 156. Shimizu, K.; Ichinose, K. NMR Study of the Magnetic Properties of Pr2Fe14B. Solid State Commun. 1995, 94, 619–621. 157. Lord, J. S.; Riedi, P. C.; Tomka, G. J.; Kapusta, C. Z.; Buschow, K. H. J. NMR Study of Ferromagnetic Phases of SnMn2Ge2 as a Function of Temperature and Pressure. Phys. Rev. B 1996, 53, 283–288. 158. Figiel, H.; Spiridis, N.; Riedi, P. C.; Graham, R. Samarium NMR in the Sm2Co17 Compound. J. Magn. Magn. Mater. 1991, 101, 401–402. 159. Kapusta, C. Z.; Rosenberg, M.; Graham, R. G.; Riedi, P. C.; Jacobs, T. H.; Buschow, K. H. J. NMR and Magnetocrystalline Anisotropy of Sm2Fe17Nx Compounds. J. Magn. Magn. Mater. 1992, 104-107, 1333–1335. 160. Kapusta, C. Z.; Riedi, P. C.; Buschow, K. H. J. Nuclear Magnetic Resonance of Samarium in SmxY2-xCo17. J. Alloys Compd. 1993, 198, 59–62. 161. Shimizu, K.; Ogasawara, F.; Ichinose, K. Rare-Earth NMR Measurements on RFe11Ti (R ¼ Nd, Sm, Tb, Dy, Er and Lu). Physica B 1997, 237–238, 584–586. 162. Schnelzer, J.; Montbrun, R.; Pilawa, B.; Fischer, G.; Venturini, G.; Dormann, E. Helimagnetism in Gallium Substituted LuMn6Ge6 Studied by Nuclear Magnetic Resonance. Eur. Phys. J. B. 2007, 58, 11–23. 163. Savosta, M. M.; Novak, P.; Marysko, M.; Jirak, Z.; Hejtmanek, J.; Englich, J.; Kohout, J.; Martin, C.; Raveau, B. Coexistence of Antiferromagnetism and Ferromagnetism in Ca1-xPrxMnO3 (x  0.1) Manganites. Phys. Rev. B. 2000, 62, 9532–9537. 164. Gonano, R.; Hunt, E.; Meyer, H. Sublattice Magnetization in Yttrium and Lutetium iron Garnets. Phys. Rev. 1967, 156, 521–533. 165. Shreever, R. L.; Caplan, P. J. NMR Studies of 151Eu and 153Eu in Europium Iron Garnet Single Crystal. Phys. Rev. Lett. 1970, 24, 978–981. 166. Gossard, A. C.; Jaccarino, V.; Wernick, J. H. Ytterbium NMR: 171Yb Nuclear Moment and Yb Metal Knight Shift. Phys. Rev. 1964, 133, A881–A884. 167. Tanida, H.; Ishihara, S.; Takagi, S.; Aoki, H.; Ochiai, A. 171Yb NMR Studies of Charge Ordering in Yb4As3. Physica B 2005, 359-361, 199–201.

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168. Hashi, K.; Oyamada, A.; Maegawa, S.; Goto, T.; Li, D. X.; Suzuki, T. NMR Study of the Magnetic Transition and the Fermi Liquid Behavior in YbAs. J. Magn. Magn. Mater. 1998, 177-181, 335–336. 169. Prandolini, M. J.; Hutchinson, W. D.; Chaplin, D. H.; Bowden, G. J.; Bleaney, B. NMR Thermally Detected by Nuclear Orientation (NMR-TNDO) of 171Yb in Antiferromagnetic YbVO4. J. Magn. Magn. Mater. 1998, 177-181, 1054–1055. 170. Shimizu, T.; Takigawa, M.; Yasuoka, H.; Wernick, J. H. 171Yb Nuclear Magnetic Resonance in YbAl2 and YbAl3. J. Magn. Magn. Mater. 1985, 52, 187–189. 171. Zogal, O. J.; Stalinski, B. 171Yb and 1H NMR in orthorhombic ytterbium dihydride. In Magnetic Resonance and Related Phenomena: Proceedings of the XXth Congress AMPERE; Kundla, E., Lippma, E., Saluvere, T., Eds.; vol. 433; Springer: Berlin, 1979. 172. Ikushima, K.; Kato, Y.; Takigawa, M.; Iga, F.; Hiura, S.; Takabatake, T. 171Yb NMR in the Kondo Semiconductor YbB12. Physica B: Cond. Matter 2000, 281-282, 274–275. 173. Mao, X.; Zhao, S.; Ye, C.; Wang, S. The First Solid State 171Yb Nuclear Magnetic Resonance Spectra. Solid State Nucl. Magn. Reson. 1994, 3, 107–110. 174. Zhao, X.; Mao, X.-A.; Wang, S.; Ye, C. The Properties of 171Yb Nucleus in AYbI3 (A ¼ K, Rb, Cs) in the Solid State. J. Alloys Compd. 1997, 3250, 409–411. 175. Sarkar, R.; Gumeniuk, R.; Leithe-Jasper, A.; Schnelle, W.; Grin, Y.; Geibel, C.; Baenitz, M. Unconventional Magnetrism in Multivalent Charge Ordered YbPtGe2 Probed by 195Pt and 171Yb NMR. Phys. Rev. B 2013, 88, 201101. 176. Keates, J. M.; Lawless, G. A. 171Yb Crosspolarization Magic Angle Spinning NMR Spectroscopic Studies of Organometallic Compounds: Bis(Cyclopentadienyl Derivatives). Organometallics 1997, 16, 2842–2846. 177. Keates, J. M.; Lawless, G. A.; Waugh, M. 171Yb CP MAS NMR Spectroscopy. Chem. Commun. 1996, 1627–1629. 178. Rabe, G. W.; Sebald, A. 171Yb Cross-Polarization/Magic Angle Spinning of Divalent Ytterbium Complexes. Solid State Nucl. Magn. Reson. 1996, 6, 197–200. 179. Dang Khoi, L.; Rotter, M. 175Lu Quadrupole Resonance in Lutetium Iron Garnet. Phys. Lett. 1971, 34, 382–383. 180. Volkov, A. F. Nuclear Quadrupole Resonance of Lutetium-175 in Series of Crystallohydrates. Polymorphism of Lutetium Bromide Octahydrate. Zh. Fiz. Khim. 1980, 54, 3058. 181. Dillon, K. B. Nuclear Quadrupole Resonance Spectroscopy, in Spectroscopic Properties of Inorganic and Organometallic Compounds, Davidson, G., ed;. Roy. Soc. Chem. 2007, 187–196. 182. Beda, A. G.; Bush, A. A.; Volkov, A. F.; Meshcheryakov, V. F. The ESR Spectra of Mn2þIons and the Low-Temperature NQR Spectra of 175Lu in LuNbO4 Crystals. Crystallogr. Rep. 2005, 50, 974. 183. Chu, P.-J.; Gerstein, B. C.; Yang, H. D.; Shelton, R. N. Studies of the Electronic Phase Transition in LuIr4Si10 and LuRh4Si10 by 175Lu-NMR. Phys. Rev. B 1988, 37, 1796–1806. 184. Saeed, M.; Wazumi, T.; Kumagai, K.; Nakajima, Y.; Tamagai, T. NMR Study of Two-Gap Superconductivity in Lu2Fe3Si5. J. Phys. Soc. Jpn. 2013, 82, 064705. 185. Shimizu, K.; Sano, N.; Itoh, J. NMR of 175Lu in Ferromagnetic LuTb and LuDy Alloys. J. Phys. Soc. Jpn. 1975, 39, 539. 186. Chlan, V.; Novak, P.; Stapankova, H.; Englich, J.; Kuriplack, J.; Niznansky, D. Hyperfine Interactions in Lutetium iron Garnet. J. Appl. Phys. 2006, 99, 08M903. _ 187. Zogal, O.; Wawryk, R.; Matusiak, M.; Henkie, Z. Electron Transport and Magnetic Properties of Semimetallic LuAs. J. Alloys Compd. 2014, 587, 190–198. 188. Reddoch, A. H.; Ritter, G. J. Nuclear Magnetic Resonance of 175Lu. Phys. Rev. 1962, 126, 1493–1495. 189. C. Benndorf, PhD thesis, University of Münster 2017. 190. Benndorf, C.; de Oliveira Junior, M.; Bradtmüller, H.; Stegemann, F.; Pöttgen, R.; Eckert, H. Rare-Earth NMR in Intermetallic Solids: The Case of the 175Lu Isotope. Solid State Nucl. Magn. Reson. 2019, 101, 63–67.

9.09

Solution NMR spectroscopy of single-molecule magnets

Markus Enders, Anorganisch-Chemisches Institut, Ruprecht-Karls Universität Heidelberg, Heidelberg, Germany © 2023 Elsevier Ltd. All rights reserved.

9.09.1 9.09.2 9.09.2.1 9.09.2.2 9.09.2.3 9.09.2.3.1 9.09.2.3.2 9.09.2.3.3 9.09.2.3.4 9.09.2.4 9.09.2.4.1 9.09.2.4.2 9.09.2.4.3 9.09.2.5 9.09.3 9.09.3.1 9.09.3.2 9.09.4 9.09.4.1 9.09.4.1.1 9.09.4.1.2 9.09.4.2 9.09.4.2.1 9.09.4.2.2 9.09.4.2.3 9.09.4.2.4 9.09.5 Acknowledgments References

Introduction Theoretical background Magnetic anisotropy and energy barriers in d- and f-block SMMs pNMR of single molecule magnets in solution Simplified treatment of FCS and PCS FCS in the absence of ZFS FCS in the presence of ZFS PCS Temperature dependence of hyperfine NMR shifts Separation of FCS and PCS contributions to the hyperfine shift Methods for the determination of the FCS Methods for the determination of the PCS Purely NMR based methods for the separations of PCS and FCS Effects of partial orientation, RDCs and RQCs Practical aspects for solution NMR measurements of single molecule magnets The choice of the solvent and sample concentration Line widths, magnetic field and acquisition parameters Selected solution pNMR studies of SMMs d-block SMMs SMM cluster compounds Single Ion magnets of transition metals f-block SMMs LnPc2 and related complexes Pc multidecker complexes COT systems Endohedral lanthanide-fullerene SMMs Conclusion and outlook

210 211 211 212 212 213 214 214 215 215 216 216 216 216 217 217 218 219 219 219 219 220 220 222 224 226 226 227 227

Abbreviations CFS Crystal field splitting DFT Density functional theory EXSY Exchange spectroscopy FCS Fermi-contact shift FWHM Full width at half maximum NMR Nuclear magnetic resonance pNMR Nuclear magnetic resonance of paramagnetic compounds PCS Pseudo contact shift RDC Residual dipolar coupling RQC Residual quadrupolar coupling SMM Single molecule magnet SIM Single ion magnet ZFS Zero field splitting

Comprehensive Inorganic Chemistry III, Volume 9

https://doi.org/10.1016/B978-0-12-823144-9.00038-8

209

210

Solution NMR spectroscopy of single-molecule magnets

Nomenclature < Sz > Reduced value of the average spin polarization A Electron-nucleus hyperfine coupling constant ge Free electron g factor gJ Landé g-factor - Planck constant J Total angular momentum quantum number Pc Phthalocyaninato S Total spin quantum number gN Magnetogyric ratio of nucleus N in units of angular frequency per Tesla [rad s
1 T
1] dfc Fermi-contact shift (also FCS) dhf Hyperfine shift dobs Observed chemical NMR shift dorb Orbital shift dpc Pseudo contact shift (also PCS) Dd½ Line width in ppm units Dn½ Line width in frequency units Dc Anisotropy of magnetic susceptibility m0 Permeability of the vacuum mB Bohr magneton c Magnetic susceptibility cax Axial component of magnetic anisotropy crh Rhombic component of magnetic anisotropy

Abstract Solution NMR spectroscopy provides access to important structural, electronic, and magnetic properties of single molecule magnets (SMMs), although such data are recorded well above the temperature at which permanent magnetization is maintained. The magnetic anisotropy, an essential requirement for SMMs, is expressed in the NMR spectra and can therefore be determined experimentally by NMR. Delocalization of unpaired electron density onto the ligand framework is another important aspect, which is obtainable from NMR spectroscopy. From the temperature dependence of the NMR chemical shift, the ligand field energy splitting in lanthanide-based SMMs can be obtained and can thus predict the occurrence and quality of SMMs. In SMMs based on transition metals, the splitting energy of the zero field can sometimes be determined. In this overview, equations are presented which are necessary for the interpretation of NMR spectra of paramagnetic compounds, with particular relevance for SMM research. Current solution NMR studies of soluble lanthanide and transition metal SMMs are then discussed.

9.09.1

Introduction

A traditional magnet is an object that is permanently magnetized, even in the absence of an external magnetic field. Ferromagnetism and magnetic anisotropy are prerequisites for a bulk, permanent magnet which is characterized by magnetic hysteresis. Such a behavior has long been reserved for bulk materials such as iron particles. When the particle size is reduced below a certain level, ferromagnetism and magnetic hysteresis are lost. However, in 1993 magnetic hysteresis was observed at the molecular level for a Mn12 cluster1 and the term Single Molecule Magnet (SMM) was introduced thereafter.2 Later on SMM behavior was also demonstrated for coordination compounds with a single metal center only3 and the term Single Ion Magnet (SIM) was established. The methods of choice for studying the magnetic properties of SMMs are magnetic measurements at low temperatures where magnetic hysteresis or slow magnetic relaxation are found. SMM behavior vanishes at higher temperature and above the socalled blocking temperature (TB) magnetic hysteresis can no longer be observed. To date (2021) the highest TB is 80 K for a dysprosocenium cation.4 Solid-state NMR can be performed at very low temperatures where SMMs can act as permanent magnets. Due to the magnetic field originating from the SMM, NMR transitions were measured in the absence of an external magnetic field.5–12 Solution NMR typically operates in a range of 200–400 K. Consequently, solution NMR studies of SMMs are possible far above TB only. In this temperature regime SMMs behave as simple paramagnets. However, SMMs above TB maintain fundamental magnetic properties like magnetic anisotropy, the total spin quantum number S (for light d-block metal compounds) or the total angular momentum quantum number J (for lanthanide complexes). Solution NMR spectroscopy is able to determine such parameters easily.

Solution NMR spectroscopy of single-molecule magnets

211

The key for the increase of the energy barrier for spin reversal lies in the magnetic anisotropy. The latter is responsible not only for the SMM properties at low temperatures but is also visible at room temperature and in solution, namely in the NMR spectra of dissolved SMMs. In 2003 NMR spectroscopy had already been used for the analysis of the first lanthanoid SMMs but since then NMR for studying SMMs has been applied only by a few researchers. This is surprising since NMR spectroscopy is well suited for a fast investigation of complexes which may show SMM behavior and numerous important structural and magnetic parameters can be obtained from NMR data. Another big advantage of solution NMR spectroscopy is the fact that the magnetic centers are well separated from each other so that the experimental data result primarily from intramolecular effects whereas intermolecular interactions play a minor role. The objective of this article is to promote solution NMR spectroscopy of paramagnetic metal complexes (pNMR) as a fast and generally applicable tool for the analysis of SMMs. As a consequence it should be possible to screen molecular metal complexes as candidates for improved SMMs. Increasing the blocking temperature will not only be accomplished by raising the magnetic anisotropy (which can be measured quickly by NMR) but also through an improvement of the knowledge of the mobility of ligands and their substituents. In addition to that, NMR enables one to study intermolecular interactions between charged SMMs and their counter ions which is also important for the properties of SMMs. Excellent reviews and books have appeared over the years describing comprehensively the theory and application of pNMR.13,14 It has found widespread use in the biomolecular community whereas in synthetic molecular chemistry including molecular magnetism the use of pNMR is rare. This is surprising as NMR spectrometers are available to practically all synthetic chemists. The obstacle for using pNMR by synthetic chemists is high, as exact pNMR theory is voluminous and complex. However, many robust conclusions can be derived from pNMR data if several simplifications and approximations are considered, keeping in mind that a comprehensive and hence more complicated analysis might be necessary in some cases. In this article, we give an overview about some key principles and properties of pNMR spectra useful in the context of SMM research, namely the interpretation of the chemical shift in pNMR, its temperature dependence and effects of partial orientation. Such data give information about magnetic susceptibility, its anisotropy, as well as energy levels due to zero field or crystal field splitting. The effective orientation of the magnetic axis can also be determined easily. These data give valuable information for the understanding and improvement of SMMs.

9.09.2

Theoretical background

9.09.2.1

Magnetic anisotropy and energy barriers in d- and f-block SMMs

Magnetic hysteresis is a result of slow magnetic relaxation which is itself determined by the probabilities of different relaxation pathways. For d-block SMMs the energy barrier for spin reversal Ud is a function of the axial and rhombic zero-field splitting (ZFS) parameter D and E, respectively, and of the total spin S of the ground state: U d ¼ f ðD; E; SÞ

(1a)

U d ¼ rDrS2

(1b)

For axial symmetry and integer spin the relation is:

A negative value of D leads to an easy-axis anisotropy which is a prerequisite for SMM behavior. It has been shown that |D | is inversely proportional to S2, and therefore it is the crucial parameter for the improvement of d-block SMMs.15 For f-block SMMs S has to be replaced by J and axial and rhombic ZFS parameters D and E, respectively, have to be replaced by crystal field splitting (CFS) parameters. The difficulty is, that depending on the symmetry of the compound up to 15 CFS parameters play a role. In the Wybourne notation they are represented by the symbol Bkq16,17:
q U f ¼ f Bk ; JÞ (2) The property which interconnects ZFS- and CFS-parameters is the anisotropy of the magnetic susceptibility, Dc, which is a function of g-anisotropy and ZFS for d-block complexes. In the axial case Eq. (3a) describes the high temperature approximation for dblock complexes:   2 g 2 þ 1g 2 SðS þ 1Þð2S
1Þð2S þ 3Þ m m  m m2 SðS þ 1Þ 0 B  2 t k 2
D$ $ 0 B Dcax ¼ gk2
gt (3a) 3kT 45k2 T 2 In the absence of g-anisotropy Eq. (3a) simplifies to:

Dcax ¼
D$

m0 m2B g 2 SðS þ 1Þð2S
1Þð2S þ 3Þ 30k2 T 2

(3b)

In the simplest case, D may be substituted by the CFS-parameter B20 for f-block complexes leading to:

Dcax ¼
B02 $

m0 m2B gJ2 JðJ þ 1Þð2J
1Þð2J þ 3Þ 30k2 T 2

(3c)

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Solution NMR spectroscopy of single-molecule magnets

The power of NMR spectroscopy in the evaluation of magnetic properties of paramagnetic complexes lies in the ease of determination of Dc through the pseudo-contact shift (PCS, see below) or through effects of magnetic field induced molecular alignments (RDC or RQC, vide infra). Eqs (3a)–(3c) are well suited for compounds where D has to be adapted, leading to Eq. (6c) where < Sz >J is the reduced spin expectation value of the ground state J manifold and gJ is the Landé g-factor. Care must be taken with different sign conventions used for < Sz >J values. They have been calculated for 300 K and at any temperature.34


(6c) hSz iJ ¼
gJ gJ
1 JðJ þ 1Þ If we assume that the principal axes of the c and g-tensor are aligned, the diagonalized matrix elements of both tensors can be converted by Eq. (6d), neglecting the effects of ZFS. 2 ckk ¼ m0 m2B gkk

9.09.2.3.1

SðS þ 1Þ 3kT

(6d)

FCS in the absence of ZFS

FCS originates from delocalization of unpaired electron density onto the nucleus studied by NMR. The electron density must reside in an atomic orbital with probability density at the nucleus. This can be accomplished by different scenarios: 9.09.2.3.1.1 Delocalization of metal centered unpaired electrons In transition metal or lanthanide complexes, unpaired electrons are mainly located at the metal atoms in d- or f-orbitals. However, the molecular orbitals hosting the unpaired electrons (SOMOs) may also be delocalized to some extent onto the ligand atoms, leading to unpaired electron density (so-called spin density) outside the metal centers. This effect is more pronounced in dblock complexes with covalently bound ligands, whereas f-block orbitals interact far less with ligand atomic orbitals. Direct delocalization can go beyond the directly bonded ligand atoms, especially when they are incorporated into a delocalized p-system. 9.09.2.3.1.2 Delocalization from ligand centered radicals Unpaired electrons can also be located within the ligand itself. This leads to considerable spin density at atomic nuclei within the ligand framework. 9.09.2.3.1.3 Spin polarization The spatial distribution of spin-density induces spin-polarization in atomic orbitals nearby leading to non-zero spin density with different sign in these atomic orbitals. By this mechanism spin-density may be transferred from one atom to the next with alternating sign. It is also important for the transfer of spin-density from orbitals without probability at the nucleus (i.e., a p-orbital) to an orbital with probability at the nucleus (e.g., an s-orbital). Spin polarization is responsible for the occurrence of alternating signs of FCS. A correct equation for a singly populated S manifold is14: ! A 1 cxx cyy czz dfc ¼ þ þ (7) Z m0 mB 3gN gxx gyy gzz The temperature dependence of the FCS is covered in the temperature dependence of the c tensor which can be approximated by   substitution of ckk with Eq. (6d). Averaging the principal components of g with g ¼ ð1=3Þ gxx þgyy þgzz leads to Eq. (8a) which is a good choice at high temperature and in the absence of large zero field splitting. A g m SðS þ 1Þ dfc ¼ $ B 3gN kT

(8a)

Equivalent equations use the spin density (r, Eq. 8b and 8c) or the reduced value of the average spin polarization (< Sz >, Eq. 8d). rN has the dimension of an inverse volume and is often expressed in atomic units. With a0 3 ¼ 1:482$10
32 m3 , g ¼ ge , the physical constants and units of ppm, Eq. (8c) is obtained.

214

Solution NMR spectroscopy of single-molecule magnets

dfc ¼

m0 g 2 m2B ðS þ 1Þ rN 9kT

dfc ¼ 23:5$106 $

ðS þ 1Þ a:u: $rN ½ppm T

A m dfc ¼ $ B hSz i Z 3gN kT

(8b)

(8c)

(8d)

Eq. 8b or 8c are often used for calculation of FCS with d-block elements whereas Eq. (8d) is usually applied for lanthanide complexes. Spin densities or hyperfine coupling constants can nowadays be calculated easily by quantum theoretical methods. The program packages often give spin-densities in atomic units and these values have to be converted into SI units. Basis sets with pseudo potentials cannot be used as only all-electron basis sets provide spin-densities or hyperfine coupling constants correctly. For lanthanide ions, calculations can be performed for an isostructural Gd3þ complex since its 8S electronic state bypasses the issue of spin-orbit coupling in open-shell lanthanide complexes. The FCS for other lanthanide ions is then obtained by using Eq. (8d) with the value of A from the Gd3þ calculation and the < Sz > value corresponding to the Ln3 þ ion in the investigated complex. This procedure relies on the isostructurality of Ln complexes with similar ionic radii.

9.09.2.3.2

FCS in the presence of ZFS

In the presence of ZFS with D 1/2 nuclei can be observed at lower magnetic fields and for compounds with smaller magnetic anisotropies. The multiplicity of splittings due to RQCs is 2I and therefore a 2H resonance is split into a doublet. The size of a RQC follows Eq. (17):  2   e qQ


3


 B20 (17) $ cax $ 3cos2 q
1 þ crh $ sin2 qcos24  $ jRQCj ¼ SLS $ h 20m0 kT 2 In Eq. (17) e2qQ/h is the nuclear quadrupole coupling constant which is 186 kHz for a 2H atom in a sp2-C2H group53 or 174 kHz for the sp3-C2H moiety in cyclohexane-d12.54 q is the angle between the axis of the largest principal component of the electric field gradient (EFG) and the main axis of the magnetic susceptibility tensor (czz) and 4 is the angle to the EFG axis and the second magnetic axis (cxx with |czz | > | cyy | > |cxx |). For a CeH group, the CeH bond vector defines the orientation of the EFG tensor of a 2H atom (for the RQC) as well as the axis for a RDC between a 13C atom and a 1H atom. The orientation of the magnetic susceptibility tensor does not necessarily coincide with a symmetry axis of the molecule. However, in the timeframe of a solution NMR experiment, the axis of the effective magnetic anisotropy coincides with the effective molecular symmetry axis. The latter can easily be determined by occurrence of signals from symmetry related nuclei. The ratio of Eqs. (16), (17) gives us the relative size of a RQC versus a RDC of the same atom pair. With a quadrupolar coupling constant for a Ce2H group of 186 kHz and a CH distance of 109 pm, the ratio amounts to:   2  3  rCH  e qQ RQCC
2 H 6p2 $ ¼  $ ¼ 6:05 (18)  RDC13 C
1 H h C
2 H g13 C g1 H Z m0 In a CH2 moiety (e.g., from an alkyl chain), RDCs can be observed between 13Ce1H but also between the two 1H atoms. If we compare the ratio RQC(Ce2H)/RDC(1H1H) of a CH2 moiety, the axis for the RDC is defined by the H$$$H vector whereas the EFG axis lies along the CeH bond. For an equivalent (3cos2q
1)-value the ratio RQC(Ce2H)/RDC(1H1H) also amounts to a factor of more than 6. In addition to that, the line width in pNMR of a 1H signal is larger than that of a 2H signal. Consequently, RQCs give a much better spectral resolution than RDCs. For this reason, RQCs can be observed in pNMR spectra much more easily than RDCs. It is often not possible to observe 13C satellites in 1H pNMR spectra. Therefore, 13C1H RDCs are usually measured in a proton coupled 13C NMR spectrum, whereas the related RQC is obtained from a simple 2H NMR spectrum. The latter has a much higher sensitivity if the sample is deuterated. 2H measurements at natural 2H abundance become possible at high concentrations in combination with cryoprobes and high magnetic fields. The big advantage for the determination of Dc by RDCs or RQCs is their direct mathematical relation. In contrast, Dc can be obtained from the hyperfine shifts only after its deconvolution into PCS and FCS.

9.09.3

Practical aspects for solution NMR measurements of single molecule magnets

9.09.3.1

The choice of the solvent and sample concentration

A prerequisite for the NMR measurement of SMMs is a sufficient solubility of the complex. For 1H or 13C measurements any deuterated solvent is fine. Measurements at variable temperature are important for pNMR and therefore a solvent which stays liquid over a large temperature range is preferred (e.g., CDCl3 better than CD2Cl2, toluene better than benzene). Line widths might be slightly different in different solvents. The necessary dissolved amount in 0.5 ml of solvent depends on the signal line width in the NMR spectrum. As an example, 0.6 mg of the archetypal SIM Pc2Tb (molecular weight ¼ 1183 g mol
1) in 0.5 ml of CDCl3 (corresponds to a concentration of  1 mmol L
1) gives a good 1H NMR spectrum with a normal 400 MHz spectrometer. However, for a 13C NMR spectrum a concentration of at least 10 mmol L
1 is needed. A high field spectrometer with a cryo probe allows the acquisition of good 13C NMR spectra (i.e., sufficient signal to noise ratio) within less than an hour. A useful 13C NMR spectrum of the poorly soluble Pc2Tb is hard to obtain and the signals from carbon atoms closer to the metal center might not be visible. Derivatives of Pc2Tb with higher solubility give good 13C NMR spectra in reasonable time.55 The isotope of choice for pNMR spectra is 2H, if an isotopic enrichment is possible. It has the advantage of better line widths compared to 1H. In addition, the signals might split into doublets due to RQCs which is a big advantage (see above). For 2H NMR a solvent which doesn’t contain any hydrogen at all (e.g., CCl4) is ideal but standard organic solvents with natural isotopic abundance are good as well, if the SMM is enriched in 2H. An isotopic enrichment of 1% is sufficient for a good signal to noise ratio.

218 9.09.3.2

Solution NMR spectroscopy of single-molecule magnets Line widths, magnetic field and acquisition parameters

The quality of pNMR spectra depends primarily on the sensitivity and the signal line width Dn½ (Dn½ ¼ full width at half maximum (FWHM) in frequency units). Dn½ is proportional to the transverse relaxation rate R2N of the nucleus. For pNMR spectra, however, it is better to express signal line width in units of ppm, as this number determines the detectability of pNMR signals and the spectral resolution. Therefore, we use the expression Dd½ which his related to Dn½ by Eq. (19):

Dd½ ¼ Dn½ $

2p 1 $ $106 ½ppm gN B0

(19)

The total transverse relaxation rate in paramagnetic complexes is the sum of three contributions namely the dipolar relaxation, the contact relaxation, and the Curie relaxation: dip

R total ¼ R N þ R contact þ R Curie N N N

(20)

The theory of paramagnetic relaxation is not to be discussed in detail here, only the proportionalities to the signal line widths in the low field (or fast motion) limit (again in units of ppm, vide supra).56 From Table 2 it becomes clear that line width is always proportional to the gyromagnetic ratio of the measured nucleus and consequently a smaller g is better than a larger one (i.e., Dd1/2(1H) ¼ 6.5  Dd1/2(2H)). The spatial distance is very important (dipolar and Curie relaxation) but also the contact shift which is proportional to the square of the hyperfine coupling A. The electron relaxation rate is another important factor which is itself temperature dependent. Consequently, a higher temperature is beneficial for a pNMR spectrum in terms of line width. On the other hand, if line width increases with temperature other effects outweigh this benefit, such as chemical exchange or spin-cross over phenomena. The magnetic field dependence goes in two different directions: At low magnetic field dipolar or contact relaxation are the dominant contributions, whereas Curie relaxation is insignificant. As the magnetic field increases, the lines initially become narrower up to a certain field strength, and then they become wider. The optimum magnetic field in terms of line widths depends on the relative contributions of the different relaxation pathways and therefore there is not “a best spectrometer” for pNMR. The total spin quantum number S or angular momentum quantum number J is important for the magnetic field dependence of the signal line width as contact and dipolar relaxation scale with S(S þ 1) whereas Curie-relaxation scales with the square of the same quantity. In summary, high magnetic fields are preferable for signals further apart from a paramagnetic metal center with small S (J), whereas lower magnetic fields might be better for signals close to a metal with high S (J). A higher magnetic field is of course good in terms of sensitivity but the detection of 1H nuclei close to the paramagnetic center (i.e., one or two bonds apart from the metal ion) might be easier at a smaller magnetic field (i.e., 200 or 400 MHz in comparison to 600 or 800 MHz). On the other hand, the detection of 2H or 13C signals profits a lot from high magnetic fields as the gyromagnetic ratios of these nuclei are smaller which leads to a decrease in line width but also in sensitivity. A probe which offers a maximum of sensitivity combined with strong excitation pulses is advantageous (i.e., inner coil, cryoprobe), especially for low sensitivity nuclei. Another point which has to be kept in mind is the excitation bandwidth of a hard pulse if a large chemical shift range is expected, combined with a large gyromagnetic ratio of the measured nucleus. The excitation frequency range of a hard pulse of duration tp is given in Fig. 1: At lower magnetic field the excitation bandwidth on the ppm scale is larger so that longer pulses can be used. In any case, the pulse power should be as high as possible for the available hardware so that short pulses can be used. Probes where detection is at the inner coil are preferential (i.e., broad band probe for 13C). For high field spectrometers (i.e., 600 MHz and above) sensitivity is not a problem in 1H NMR of SMMs. Therefore very short pulses can be used (for example, 1 ms pulse or even less) in order to excite several hundreds of ppm. A 13C NMR experiment with the same spectrometer should be performed with longer pulses as sensitivity is crucial here. A good compromise between an efficient pulse angle and excitation bandwidth is the use of 60 pulses in 13C NMR.

Table 2

Dd½con Dd½dip Dd½Curie

Proportionalities of signal line width contributions from contact, dipolar and Curie relaxation pathways to a variety of parameters (low field and fast motion limit). gN x

[S(S þ 1)]x

rx

Ax

B0 x

R1e x

1 1 1

1 1 2

0
6
6

2 0 0


1
1 þ1


1
1 0

The numbers in the table correspond to the exponent x of the different contributions to the line widths. A is the electron nucleus hyperfine coupling, r is the distance of the measured nucleus to the paramagnetic center (in the point dipole approximation), and R1e is the longitudinal electron relaxation rate. For lanthanides, S has to be replaced by J.

Solution NMR spectroscopy of single-molecule magnets

219

Fig. 1 Excitation spectrum according to the sinc function of a hard pulse of 5 ms (green) and 2 ms (blue), respectively. A spectral width of 1000 ppm for different nuclei measured at an external magnetic field of 14.1 Tesla (600 MHz 1H frequency) is shown as black bars. The height of the blue curve decreases to an intensity of 50% at a frequency offset of 300 kHz (500 ppm at 14.1 Tesla).

9.09.4

Selected solution pNMR studies of SMMs

9.09.4.1

d-block SMMs

9.09.4.1.1

SMM cluster compounds

9.09.4.1.2

Single Ion magnets of transition metals

Multinuclear clusters like the archetypal SMM [Mn12O12(OAc)16(H2O)4]1 (1) and derivatives thereof as well as clusters with other transition metals have been studied in detail by solid-state NMR spectroscopy.6-12,57–63 Almost all NMR active nuclei in such compounds have been probed, including 1H, 2H, 7Li, 13C, 19F and even the metal nuclei 55Mn and 57Fe.64 At low temperatures, the NMR resonances of the metal nuclei can be observed in the absence of an external magnetic field as the magnetic field created by the SMMs is static on the NMR time scale. In many of these studies the relaxation times of the nuclei were determined as a function of the magnetic field strength and temperature. It changes when the critical temperature for SMM behavior is reached. In a few cases the deconvolution of the experimental hyperfine shift into Fermi-Contact and dipolar terms was done.9 Solution NMR studies of cluster compounds also exist. The 1H NMR chemical shifts of 1 and derivatives where the acetate ligands were replaced by other carboxylic acids lie in the range from
6 to þ 55 ppm. These measurements demonstrate the integrity of the cluster complexes in solution.65–67 The different valence states of the metals remain unchanged. The effective symmetry of the compounds is sometimes increased due to fluxionality of one or more ligands. A tetranuclear SMM with a CoII2CoIII2 core was studied by 1H and 13C NMR and all NMR signals could be assigned.68 Usually no analysis in terms of the different contributions to the paramagnetic shift are reported.

The first decade of SMM research was dominated by multinuclear cluster compounds. The idea was to increase the total spin of the compounds, as the effective barrier for spin inversion scales with S (Eq. 1b). The weaker coupling between paramagnetic metal centers in lanthanides compared to d-block metals meant that lanthanide complexes initially appeared unattractive as SMMs. However, in 2003 a mononuclear lanthanide compound was shown to have unprecedented SMM properties.3 This demonstrated that a single metal ion is sufficient for a good SMM. The reason for that is that the magnetic anisotropy, which is a very important prerequisite for SMMs, is reduced when going from mononuclear to polynuclear complexes.15 In 2010 the first mononuclear SMMs with a single d-block metal center were reported.69 In the following years several other d-block SIMs, most of them based on iron or cobalt centers have been developed but their NMR spectroscopy remained initially unexplored.70–76 In 2015 Novikov and coworkers reported a Co based SIM with a hexadentate ligand creating a trigonal prismatic ligand field. Following earlier NMR studies of lanthanide SIMs (vide infra) it was demonstrated that solution NMR spectroscopy is a valuable tool for the study of Co based SIMs.77–79 The 1H and 13C hyperfine shifts in these compounds originate from PCS and FCS, the latter of which was determined by quantum chemical calculations. Using Eq. (12) (vide supra) a very large axial magnetic anisotropy (i.e., Dcax ¼ 2.25  10
31 m3 mol
1) was determined. In addition, the temperature dependence of the PCS was used to determine the axial ZFS parameter D which is
95 cm
1 in one case and
109 cm
1 in another example. Even higher magnetic anisotropies were determined by pNMR with Dcax ¼ 3.5  10
31 m3 mol
1 for a Co(II) complex80 and Dcax ¼ 3.9  10
31 m3 mol
1 for a Fe(II) complex.81 However, no SMM behavior was reported for the latter two compounds. A Fe(I) SIM stabilized by two cyclic alkyl amino carbenes (cAAC) was studied by 1H and 13C NMR.82 Due to large magnetic anisotropy and efficient delocalization of spin density onto the ligands, FCS and PCS are large. An iterative approach was used starting with an initial signal assignment of a few signals. The DFT calculated structural model and the resulting c tensor were used for calculating PCS of all signals. At the end of this process, most 1H and 13C signals could be assigned and the ZFS parameters D and E were extracted.

220

Solution NMR spectroscopy of single-molecule magnets

Fig. 2 13C NMR spectra of anionic [Tb(obPc)2]
and neutral [Tb(obPc)2]0 and the deconvolution of the signals of the benzene rings (aryl-Cq, arylCH and aryl-CO) into orbital shift, metal centered FCS, metal centered PCS and ligand centered PCS.83

9.09.4.2 9.09.4.2.1

f-block SMMs LnPc2 and related complexes

Bis(phthalocyaninato)lanthanide complexes (LnPc2) are sandwich type compounds with a Ln3 þ ion coordinated by 8 nitrogen atoms. The ligands are redox active so that Pc2Ln exist with a cationic, a neutral, or an anionic charge ([LnPc2]þ, [LnPc2]0 or [LnPc2]
). In the neutral form one unpaired electron is delocalized in p orbitals of the two Pc ligands whereas additional unpaired electrons are located in the f-orbitals of the lanthanide ion. The anionic form, [LnPc2]
, or triple deckers of the type Ln2Pc3 have no p-radical. Magnetic susceptibility and 1H NMR data allowed for the determination of the ligand field energy splitting of sandwich and triple decker complexes [LnPc2]
and Ln2Pc3.20,21 This has led to the discovery of the first lanthanide based SMMs [DyPc2]
and [TbPc2]
respectively.3 Comprehensive NMR studies have been performed with the octabutoxy derivatives [Ln(obPc)2]þ/0/
(Ln ¼ Y, Tb, Dy).83 The good solubility of the compounds and the use of a helium cooled NMR probe allowed the determination of 13C NMR spectra. The axial component of the magnetic susceptibility anisotropy remains practically unaltered upon reduction from neutral to anionic species with ca of 1.04  10
30 m3 for the terbium and 5.64  10
31 m3 for the dysprosium complexes, respectively. The authors separated the different contributions to the chemical shift and could analyze the effect of the p-radical in the neutral form (see Fig. 2). With these data in hand, the ligand-ligand distance of the cationic form [Tb(obPc)2]þ was determined to be 2.65 Å, which is 0.16 Å smaller than in the anionic complex. Recently, the structural data obtained from the pNMR analysis were confirmed by X-ray structure analysis.84 The axial component of magnetic susceptibility anisotropy of the cationic terbium complex was found to be 1.09  10
30 m3, marginally larger than that of the anionic complex.

Fig. 3 Dimerization of a crown-ether TbPc2 derivative by addition of potassium acetate. The formation of the dimeric form was evidenced by pNMR. Reproduced with permission from Horii, Y.; Kishiue, S.; Damjanovic, M.; Katoh, K.; Breedlove, B.K.; Enders, M.; Yamashita, M. Chem. Eur. J. 2018, 24, 4320–4327, Wiley-VCH.

Solution NMR spectroscopy of single-molecule magnets

Fig. 4 Switchable triple decker SMMs. Left: drawing of the molecular constitution. Middle: contour map of the geometric parameter G as a function of the polar coordinate q (see Eq. 12) for the TbeY derivative with and without potassium ions. Right: Magnetic anisotropies determined by pNMR. Reprinted with permission from Martynov, A. G.; Polovkova, M. A.; Berezhnoy, G. S.; Sinelshchikova, A. A.; Khrustalev, V. N.; Birin, K. P.; Kirakosyan, G. A.; Gorbunova, Y. G.; Tsivadze, A.Y., Inorg. Chem. 2021. Copyright American Chemical Society.

221

222

Solution NMR spectroscopy of single-molecule magnets

In another study, the ion pairing in LnPc2 compounds was investigated by analysis of the PCS of the diamagnetic counter ions. In dichloromethane, contact ion pairs are formed and the counter ions are located along the fourfold symmetry axis of the anionic sandwich complexes.85 Depending on the substitution pattern, some LnPc2 compounds are obtained in their protonated form. However, the presence and the precise location of the acidic proton are difficult to determine by X-ray diffraction. NMR can solve this problem: The additional proton in complexes of the type LnPc2H alleviates the D4d symmetry of the anionic double-decker complex and leads to quite complicated NMR spectra with a strongly shifted signal at
152.5 ppm for the acidic proton. Using Eq. (12), the PCS for a proton at the meso N-atom is predicted at
161 ppm whereas a protonation at the indole N-atom would lead to a shift of þ 2070 ppm. Single and double protonation of Tb and Dy double-decker SMMs containing a dibenzotetraaza[14]annulene derivative were studied by a combination of analytical techniques.86 pNMR was handicapped by the close proximity of the H-atoms to the metal centers, leading to broader signals and considerable FCS contributions. However, magnetic anisotropies of all protonation steps could be determined which were close to cax of [Tb(obPc)2]
. The structural changes induced by protonation led to a change in the effective symmetry of the compounds. The position of the proton on the indolenine N-atom was determined by NMR. Protonation and deprotonation in a dichloromethane solution affected the hysteresis opening, the relaxation rate, and the relaxation pathway. A crown ether substituted Pc2Tb derivative shows considerable changes upon addition of either sodium or potassium acetate. pNMR studies showed that four smaller Naþ ions are bound at the four crown ether moieties, whereas the larger Kþ ions lead to a dimerization of two Pc2Tb units (see Fig. 3). The TbeTb distance was estimated from NMR by analyzing the shift differences in the monomeric and dimeric forms using a modified version of Eq. (12). Again, the presence of a p radical in the Pc ligands has to be considered when interpreting the pNMR spectra. Magnetic measurements were performed in solid solutions in a polymethylacrylate polymer in order to preserve the structure as found by NMR. The intramolecular TbeTb interaction in the dimer causes an increase in the blocking temperature from 7 to 15 K.87

9.09.4.2.2

Pc multidecker complexes

Lanthanide ions not only form sandwich type compounds as discussed above but also multidecker complexes. The most common are triple decker compounds which can be homo-bimetallic (Pc3Ln2) or heterobimetallic (Pc3LnLn0 ). With a series of the latter type, pNMR and magnetic data allowed for the experimental determination of crystal field parameters.20 Based on these data, the first single ion magnet was discovered in 2003.3 The low solubility of these compounds and the simple substitution pattern made more elaborate NMR analysis unattractive. Much later, a series of crown ether substituted triple deckers were studied by pNMR.88 The authors were able to identify structural changes induced by coordination of potassium ions (see Fig. 4). The magnetic anisotropies of the different metal ion combinations were also determined by analysis of the PCS using structural models from either X-ray diffraction or DFT calculations. Homo dinuclear triple deckers with alkoxy substituents were synthesized in 2011 and these compounds show SMM behavior as well.89 Due to the good solubility of such compounds, the first comprehensive solution NMR analysis of an SMM was published 2 years later (see Fig. 5 left).55 The authors were able to determine the molecular structure in solution by analysis of the PCS (Eq. 12) and the RDCs (13Ce1H and geminal 1He1H, using a modified form of Eq. 16). The mobility of the butoxy substituents could be determined by the Lipari-Szabo parameter SLS (see Eq. 16) The pNMR analysis was facilitated by the high axial symmetry of the compound. On the other hand, no information about the coordination type (i.e., cubic or square antiprismatic) and the rotational mobility of the Pc rings could be extracted. This could be accomplished by pNMR study of a slipped triple decker SMM (Fig. 5, right and Fig. 6).90

Fig. 5

Axial and slipped homo-dinuclear triple decker SMMs studied by pNMR.55,90

Solution NMR spectroscopy of single-molecule magnets

Fig. 6 Left: 1H NMR spectrum at 350 K of the slipped triple decker complex shown in Fig. 5. Due to the lower symmetry (C2h) as compared to the axial triple decker and a slow rotation of the Pc ligands, 7 different butoxy chains give 49 1H NMR signals (all H atoms in the CH2 groups are diastereotopic). Right: Isoshift lines are given in blue (positive shifts) and red (negative shifts). Reprinted with permission from Morita, T.; Damjanovic, M.; Katoh, K.; Kitagawa, Y.; Yasuda, N.; Lan, Y.; Wernsdorfer, W.; Breedlove, B. K.; Enders, M.; Yamashita, M. J. Am. Chem. Soc. 2018, 140, 2995–3007. Copyright American Chemical Society.

223

224

Solution NMR spectroscopy of single-molecule magnets

The axial component of the magnetic susceptibility tensor at 295 K, cax ¼ 1.39  10
30 m3, is considerably larger than the values for the TbPc2 double deckers or the axial Tb2Pc3 triple decker (0.85  10
30 m3). The rhombic component crh is
0.12  10
30 m3. The pNMR analysis showed, that the two Tb atoms are coordinated in a square antiprismatic manner. EXSY NMR gave cross peaks for slowly rotating Pc rings and allowed for a reliable signal assignment. The energy barrier for the rotation of the Pc ligands was determined for the first time from VT-NMR and found to be 83  10 kJ/mol. Another interesting aspect of the slipped triple decker is a low lying triplet state which contributes
12.4 ppm to the FCS of the linker CH-group at 295 K. In the triplet state, unpaired electron density is distributed in the ligand framework so that the pointdipole approximation for the PCS is no longer valid. The additional spin density adds
4.6 ppm to the PCS of the linker CH atom. Using Cd2þ counter ions, anionic [LnPc]
units can stack giving tetra- penta- and hexadecker complexes. Several of these compounds including oxidized cationic analogues showed SMM behavior.91 The neutral and oxidized forms were studied by pNMR up to the tetracationic pentadecker. Upon oxidation the intermetallic distances decrease. The axial magnetic anisotropy was extracted from PCS data using modified forms of Eq. (12) and DFT optimized geometries (Fig. 7.). In some of the studied poly deckers, one or two unpaired electrons are delocalized in the Pc ligands. This fact can be observed in EPR spectra and in the pNMR shifts of the aromatic CH groups of the Pc core, whereas the signals from the butyloxy substituents are almost unaffected by the ligand centered paramagnetism. Therefore, effects of metal centered PCS and ligand centers PCS could be separated.

9.09.4.2.3

COT systems

Cyclooctatetraene (COT) can act as a planar dianionic ligand for lanthanide and actinide ions. The negative charges are delocalized in a p molecular orbital consisting of p-orbitals from the eight carbon atoms. Due to the large diameter and the orthogonal orientation of the p MO with respect to the ligand plane, an equatorial ligand field is created when two COT ligands bind to a metal center. In contrast, two Pc ligands create an axial ligand field. As a consequence, a lanthanide ion coordinated by two COT ligands should have an opposite sign for the axial magnetic anisotropy when compared to the same ion coordinated by two Pc ligands. A 1H NMR shift of
88 ppm (295 K) was reported for [Er(COT)2]
which was the first SMM with two COT ligands.92 The negative shift is due to the spatial position of the H atoms combined with a positive cax. A series of isostructural complexes with two substituted COT ligands allowed a comprehensive NMR analysis.18 It could be shown that two conformers are in a fast equilibrium and a so-

Fig. 7 Sketch of PcxLnyCdz triple, tetra and pentadecker compounds and changes in the axial magnetic anisotropy as measured by pNMR. Adapted from Horii, Y.; Damjanovic, M.; Ajayakumar, M. R.; Katoh, K.; Kitagawa, Y.; Chibotaru, L.; Ungur, L.; Mas-Torrent, M.; Wernsdorfer, W.; Breedlove, B. K.; Enders, M.; Veciana, J.; Yamashita, M. Chem. Eur. J. 2020, 26, 8621–8630. Creative Commons License, Wiley-VCH.

Solution NMR spectroscopy of single-molecule magnets

Fig. 8 Left: [Ln(tdnCOT)2]
anions (tdn ¼ tetrahydrodinaphtho), middle: three-nuclei plot of selected 13C and 1H NMR signals (Er3þ ion and H3i used as references). right: results from fitting the temperature dependence of the magnetic anisotropies using Eq. (4) (vide supra). lower part: axial magnetic anisotropies at 295 K obtained by fitting the pNMR shifts (Eq. 15) and from the RQC of signal C5e2H5 (Eq. 17). Reprinted with permission from Hiller, M.; Krieg, S.; Ishikawa, N.; Enders, M. Inorg. Chem. 2017, 56, 15285–15294. Copyright American Chemical Society.

225

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Solution NMR spectroscopy of single-molecule magnets

called “three nuclei plot” proved that the compounds are isostructural. PCS and FCS were then separated by using Eq. (15) (vide supra) which also gave the magnetic anisotropies. Introduction of 2H allowed for an independent determination of cax with higher precision (see Fig. 8 lower part). The temperature dependences of the magnetic anisotropies of the whole set of compounds were then fitted with a custom written script using Eq. (4) (vide supra). The results of this fitting procedure gave the energy levels of the J manifold as sketched in Fig. 8 (right). The state with the largest J-level is highest in energy for the prolate ions (Tb3þ, Dy3þ, Ho3þ) whereas it is lowest in energy for the oblate ions (Er3þ, Tm3þ). The latter give easy axis magnetization, a prerequisite for SMM behavior.

9.09.4.2.4

Endohedral lanthanide-fullerene SMMs

Endohedral fullerene lanthanide compounds are an exciting class of SMMs which have also been studied by NMR spectroscopy. [C80-Ih]6
is a stable closed-shell hexaanion, and is a good host for small hexacationic metal clusters such as [Ln2]6 þ or [Ln2ScN]6þ leading to neutral, well soluble compounds. The latter was studied by 13C and by 45Sc NMR.93 The Dy derivative showed the most strongly shifted signals in 13C NMR (i.e., þ 100 compared to þ144 ppm for one of the two 13 C resonances in diamagnetic (Y2ScN)@C80). The hyperfine shift of 
44 ppm is composed of negative FCS and negative PCS. The 45Sc NMR signals are shifted to a larger extend, as the Sc nuclei are much closer to the paramagnetic centers. Again the Dy derivative has the largest shifts which are composed of a smaller negative FCS and a large positive PCS (Fig. 9). By addition of a benzyl group to the C80 core, 1H NMR measurements become possible. In addition, the stable closed shell form is now a pentaanion. In such anions a Ln25 þ ion can be inserted, where a single electron links two Ln3 þ centers. The singly occupied orbital induces strong magnetic coupling between the two Ln3 þ centers. Reduction leads to a Ln24 þ fragment inside the C805
ion. Tb25þ@C80(CH2Ph)5
and Dy25þ@C80(CH2Ph)5
show the strongest PCS and therefore the highest magnetic anisotropies in this series. In accordance with that they are SMMs with high blocking temperatures (28 and 20 K respectively). The single electron leads to strong coupling which results in open hysteresis loops with giant coercive fields (8 T at 10 K for the Tb derivative) (Fig. 10).94

9.09.5

Conclusion and outlook

Solution NMR spectroscopy of single molecule magnets has matured over the past decade and has become a powerful tool for rapid assessment of the structural, electronic, and magnetic properties of SMMs. The magnetic susceptibility anisotropy, Dc, of paramagnetic compounds manifests itself in the pseudocontact shift (PCS) and in the residual dipolar and quadrupolar couplings (RDC and RQC). The sign of Dc, which correlates with the sign of the PCS, allows the distinction between easy axis or easy plane magnetization of paramagnetic molecules and is one of many important parameters available through pNMR. In the lanthanide series, the size of Dc qualitatively correlates with the performance of SMMs. Moreover, a thorough synthetic and NMR spectroscopic study of an isostructural series of lanthanide compounds is able to quantitatively determine the energy splitting of the J manifold of lanthanide based SMMs. For d-block molecules the situation is different: Isostructural complexes cannot be used for the determination of the energy splitting of the S-manifold. However, in favorable cases, pNMR can be used for the determination of the sign and the magnitude of the ZFS. With this knowledge, pNMR is able to determine parameters of d-and f-block molecules in solution that correlate with the properties of SMMs. For example, the influence of systematic changes in a ligand framework on the magnetic property of a molecule can be assessed by pNMR. This enables rapid review of strategies to improve SMMs by ligand design. A further improvement of pNMR for studying SMMs is expected by the future availability of ultra-sensitive and ultra-high magnetic field spectrometers. Another aspect where further improvement is expected, is the accurate measurement and interpretation of temperature effects on chemical shifts, RDCs, RQCs and NMR relaxation behavior.

Fig. 9 Endohedral lanthanide fullerenes Ln25 þ@C80(CH2Ph)5
studied by 45Sc NMR. Reproduced from Zhang, Y.; Krylov, D.; Rosenkranz, M.; Schiemenz, S.; Popov, A. A. Chem. Sci. 2015, 6, 2328–2341. Creative Commons License, Royal Society of Chemistry.

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Fig. 10 1H NMR spectra of endohedral Ln25 þ@C80(CH2Ph)5
(grey lines) and reduction products Ln24 þ@C80(CH2Ph)5
(colored lines). Reproduced from Liu, F.; Velkos, G.; Krylov, D. S.; Spree, L.; Zalibera, M.; Ray, R.; Samoylova, N. A.; Chen, C.-H.; Rosenkranz, M.; Schiemenz, S.; Ziegs, F.; Nenkov, K.; Kostanyan, A.; Greber, T.; Wolter, A. U. B.; Richter, M.; Büchner, B.; Avdoshenko, S. M.; Popov, A. A. Nat. Commun. 2019, 10, 571. Creative Commons License, American Chemical Society.

Acknowledgments My knowledge about NMR of SMMs developed by interaction with two fantastic co-workers, namely Dr. Marko Damjanovic and Dr. Markus Hiller who became experts in the field of paramagnetic NMR and Single Molecule Magnets. I thank Prof. Masahiro Yamashita and Prof. Keichii Katoh for providing us with well soluble Phthalocyanine based SMMs and for their very fruitful cooperation. The scientific exchange with Prof. Naoto Ishikawa is also gratefully acknowledged.

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9.10 Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements Yuji Furukawa, Ames Laboratory, US DOE, Ames, IA, United States; and Department of Physics and Astronomy, Iowa State University, Ames, IA, United States © 2023 Elsevier Ltd. All rights reserved.

9.10.1 9.10.1.1 9.10.1.2 9.10.2 9.10.2.1 9.10.2.1.1 9.10.2.1.2 9.10.2.1.3 9.10.2.2 9.10.2.2.1 9.10.2.2.2 9.10.2.2.3 9.10.2.2.4 9.10.2.2.5 9.10.2.3 9.10.3 9.10.3.1 9.10.3.1.1 9.10.3.1.2 9.10.3.1.3 9.10.3.2 9.10.3.2.1 9.10.3.2.2 9.10.3.3 9.10.4 9.10.4.1 9.10.4.1.1 9.10.4.1.2 9.10.4.1.3 9.10.4.2 9.10.4.2.1 9.10.4.2.2 9.10.4.2.3 9.10.4.3 9.10.5 9.10.5.1 9.10.5.1.1 9.10.5.1.2 9.10.5.1.3 9.10.5.2 9.10.6 Acknowledgments References

Basics of NMR Hyperfine interactions NMR spectrum Antiferromagnets G-type antiferromagnet BaMn2As2 (Ref. ) Background of BaMn2As2 55 Mn NMR in BaMn2As2 Magnetic structure of BaMn2As2 A-type antiferromagnet CaCo2P2 (Ref. ) Background of CaCo2P2 59 Co and 31P NMR in CaCo2P2 Magnetic structure o/CaCo2P2 External magnetic-field dependence of the direction of the ordered moments in CaCo2P2 revealed by NMR line-width Magnetic phase diagram of CaCo2P2 determined by NMR Summary Helical antiferromagnets EuCo2P2 (Ref. ) Background of EuCo2P2 153 Eu NMR in EuCo2P2 AFM propagation vector in EUCo2P2 determined by 59Co NMR EuCo2As2 (Ref. ) 153 Eu NMR in EuCo2As2 59 Co NMR in EuCo2As2: Determination of the AFM propagation vector Summary Molecular nanomagnets Isolated triangular antiferromagnet V15 (Ref. ) Background of V15 51 V NMR inV15 Magnetic ground state of the isolated triangular AFM V15 Ferrimagnetic nanomagnet Mn12 (Refs. ) Background of Mn12 55 Mn NMR in Mn12 Time dependence of 1H NMR in Mn12: Determination of the relaxation time of magnetization Summary Magnetic-field control of domains in magnetic materials Detwinning in EuFe2As2 (Ref. ) Background of EuFe2As2 153 Eu NMR in EuFe2As2 Magnetic field effects on the domain population in EuFe2As2 under in-plane Hext Summary Concluding remarks

231 231 232 232 232 232 234 234 236 236 237 238 239 241 241 241 242 242 242 243 245 245 246 247 247 247 247 248 249 250 250 250 252 253 253 253 253 254 256 256 258 258 258

Abstract In this article, we present a brief overview of nuclear magnetic resonance (NMR) studies on magnetic materials, especially focusing on so-called “on-site” NMR measurements which are measurements of nuclei having finite magnetic moments

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Comprehensive Inorganic Chemistry III, Volume 9

https://doi.org/10.1016/B978-0-12-823144-9.00016-9

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originating from electron spins. NMR is known to be one of the powerful tools to investigate the magnetic properties of magnetic materials from a microscopic point of view. In particular, the “on-site” NMR measurements provide direct information on the direction and the magnitude of electron magnetic moments in the magnetically ordered state in magnetic materials, via hyperfine interactions between nuclear and electron spins. In the following sections, we will show NMR results from various magnetic materials such as antiferromagnets including helical antiferromagnets, and molecular nanomagnets, and also describe some interesting cases where NMR measurements reveal how magnetic states or magnetic domains change with the application of magnetic fields.

9.10.1

Basics of NMR

We start with stating the principle of NMR in terms of the hyperfine interactions between nuclear and electron spins and how one can obtain the magnitude and directions of those interactions from NMR spectra.

9.10.1.1

Hyperfine interactions

An NMR spectrum, which provides important information about magnetic states, is determined by the interactions between nuclei and electrons whose Hamiltonian can be described by1,2 H ¼ HZ þ Hhf þ HQ :

(1)

Here the first term describes the Zeeman interaction between nuclear spin I and external magnetic field Hext written by HZ ¼  gn ZI,Hext ;

(2)

where Z is Planck’s constant divided by 2p, gn is the nuclear gyromagnetic ratio, I is the nuclear spin operator, and Hext is the external magnetic field. The second term describes the hyperfine interaction between nuclear and electron spins, which is one of the most relevant to the investigation of the magnetic properties of magnetic materials. The Hamiltonian for the hyperfine interaction is given by Hhf ¼  gn ZI,Ahf ,S ¼  gn ZI,Hhf ;

(3)

where the major contributions to the hyperfine field Hhf come mainly from the following five sources: the Fermi contact interaction (Hcontact) due to s electrons, the dipolar field from electron spins (Hdip), the orbital motion of electrons (Horb) and the core polarization (Hcore), and the transferred hyperfine field (Htrans). Hhf ¼ Hcontact þ Hdip þ Horb þ Hcore þ Htrans :

(4)

Here Hcontact ¼

X 8p ,gmB dðri ÞSi ; 3 I

Hdip ¼  gmB

(5)

X½Si  3br i ðSi ,br i Þ ri3 i

and Horb ¼ gmB

(6)

  1 ; r3

(7)  

where mB is the Bohr magneton, g (¼ 2) is the spectroscopic splitting g factor, and

1 r3

is an average of r13 over electrons producing

the orbital angular momentum. The origin of Hcore is similar to the Fermi contact interaction. However, it originates from a net spin due to the electrons on unfilled electronic shells other than s shells, which polarizes the filled s electrons and creates non-zero spin densities at the nucleus. Htrans originates from the spin polarization due to a complex overlaps of wave functions between different ions in materials. The last term in Eq. (1) describes the quadrupole interaction, the interaction between the nuclear electric quadrupole moment Q and the electric field gradient (EFG) at the nuclear site:    hvQ 1 2 2 3IZ2  I2 þ h Iþ HQ ¼ þ I : (8) 6 2 2

3e qQ where Q is the electric quadrupole moment of the nucleus Here VQ is the nuclear quadrupole frequency defined by vQ ¼ 2Ið2I1Þh

under investigation, VZZ is the electric field gradient (EFG) at the nuclear site in the coordinates of the principal X, Y, and Z axes of YY with |VZZ |  |VYY |  | VXX |.1 The relationship between the the EFG, and h is the asymmetry parameter of the EFG defined by VXXVV ZZ

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Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

EFG coordinate system (XYZ-system) and the coordinate system defined by the magnetic field (z axis for the quantization axis) is given by Iz ¼

 1  if Iþ e þ I eif sinq þ IZ cosq: 2

(9)

Here q is the polar angle between z axis and VZZ measured from the z axis, and f is the azimuthal angle to VXX direction.

9.10.1.2

NMR spectrum

Utilizing the Hamiltonian Eq. (1), one can calculate the NMR spectrum. Assuming that the magnetic interactions (HZ þ Hhf) are much greater than the quadrupole interaction (HQ) and that HQ can be treated as a perturbation with respect to the magnetic interactions, the resonance frequency f for the transition from Iz ¼ m to m  1 is given within second-order perturbation theory by3–5 f ðm4m  1Þ

  2   

vQ 1 1  2 3cos2 q  1 þ hsin2 qcos2f þ ¼ v0 þ vQ m  1  cos2 q ð102a  2b þ 39Þcos2 q  1  hcos2f  ð6a  2b þ 3Þ 32v0 2 2 3    2  2  h2 vQ 2 51 9 39 a b cos2 f cos2 q  1 ;  1 þ hcos2f þ ½24a  4b þ 9  ð30a  2b þ 12Þcos2 q  3 2 4 4 72v0 (10) where a ¼ m(m  1) and b ¼ I(I þ 1). Thus transition lines, that is the NMR spectrum, depend on the several parameters such as q and f. Fig. 1(A) and (B) show typical q and f dependence of NMR spectra for I ¼ 5/2, respectively, where we used a Zeeman interaction energy of vZ ¼ 100 MHz and a quadrupole interaction energy of vQ ¼ 1 MHz to satisfy the condition of HZ [ HQ. As seen, the NMR spectrum is composed of a central transition line (m ¼ 1/2 4  1/2) and two pairs of satellite lines. Within the first-order   perturbation for the case of h ¼ 0, the positions of the satellite lines are shifted from the central transition line by 12vQ 3cos2 q 1 2 (for the transitions of m ¼ 3/2 4 1/2 and  3/2 4  1/2), and  vQ(3cos q  1) (for m ¼ 5/2 4 3/2 and  5/2 4  3/2). It is interesting to note that the line shape of NMR spectra drastically changes, especially the spacing between the lines, by changing the angle q [see, Fig. 1(A)] where no clear quadrupole splittings of the spectrum can be seen at q ¼ 54.75 . This is called the “magic” angle, satisfying 3cos2q  1 ¼ 0. Thus, by measuring the spacing between the lines, one can obtain the value of q which is the angle between the principal axis of EFG (VZZ) and the quantization axis (z axis) of the magnetic interaction when vQ is known. When h is finite, the NMR spectrum also depends on the angle f as shown in Fig. 1(B). Again, from the spacings between the lines, one can determine the direction of the magnetic field with respect to the EFG coordinates in the system. Thus, from spectrum measurements of single crystal samples, especially from the spacings between the lines, one can estimate the angles q and f which provide important information about the direction of magnetic field with respect to the EFG coordinate system in magnetic materials. In the following sections, we show “on-site” NMR studies of various types of magnetic materials and also describe how one can determine the magnetic structures of the materials from the NMR spectrum measurements.

9.10.2

Antiferromagnets

In this section, we present NMR studies of the two different antiferromagnets with different magnetic structures, namely the socalled “G”- and “A”-types whose schematic views of the spin structures are shown in Fig. 2(A)–(D), in addition to other typical spin structures of antiferromagnets. In the case of A-type, spins are ferromagnetically coupled in plane and the spins between the planes are aligned antiferromagnetically. For the case of G-type, all spins in the planes and also between the planes are coupled antiferromagnetically. In the case of C-type, spins are antiferromagnetically coupled in planes while the moments adjacent along the c axis are aligned ferromagnetically, which is also sometimes called “checkerboard” structure. Fig. 2(D) shows the so-called “stripe”type antiferromagnetic spin structure, often observed in the mother materials of iron-based superconductors.6

9.10.2.1 9.10.2.1.1

G-type antiferromagnet BaMn2As2 (Ref. 7) Background of BaMn2As2

In recent years the large family of AM2X2 (A ¼ Sr, Ba, Ca, Eu, M ¼ Transition metals, X ¼ As, P) compounds has been the subject of intensive research6,8,9 after the discovery of superconductivity in carrier doped BaFe2As2.10 Among them, BaMn2As2 has recently been highlighted, which exhibits an antiferromagnetic (AFM) insulating ground state6,9,11,12 and a metal-insulator transition by carrier doping13,14 or by application of pressure.15 The magnetic properties of the parent compound BaMn2As2 with ThCr2Si2type structure are characterized as a G-type local moment AFM with a high magnetic phase transition temperature (Néel

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

233

(A)

(B)

Fig. 1 (A) Typical q dependence of the NMR spectrum for I ¼ 5/2 (expected for the case of single crystal) when the magnetic interaction is much greater than the quadrupole interaction (here Zeeman interaction energy vz ¼ 100 MHz and quadrupole interaction energy vQ ¼ 1 MHz are used with h ¼ 0). (B) Typical f dependence of NMR spectrum for I ¼ 5/2 with q ¼ 90 and h ¼ 0.25 for the case of vz ¼ 100 MHz and vQ ¼ 1 MHz.

Fig. 2

(A)

(B)

(C)

(D)

Schematic views of the four types of antiferromagnetic structures. (A) A-type, (B) G-type, (C) C-type, (D) stripe-type.

234

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

temperature) of TN ¼ 625(1) K and local ordered moment < m > ¼ 3.88(4)mB/Mn at 10 K.11 The moments arise from Mn2þ ions (3d5) with spin S ¼ 5/2. The crystal structure and the G-type spin structure of BaMn2As2 are shown in the right panel of Fig. 3. Below we show the results of 55Mn zero field NMR measurements (55Mn; I ¼ 52 , g2pN ¼ 10:500 MHz=T, Q ¼ 0.55 Barns) and also show the external magnetic field Hext dependence of the “on-site” NMR spectrum which provides the information of the direction of the Mn ordered moments in the AFM ordered state.

9.10.2.1.2

55

Mn NMR in BaMn2As2

Fig. 3 shows the 55Mn NMR spectrum in the AFM state for a single-crystalline BaMn2As2, measured in zero magnetic field at temperature T ¼ 4.2 K. Five sharp lines were observed, which are characteristic of nuclear spin I ¼ 5/2 with Zeeman and quadrupole interactions, as depicted in Fig. 1(A) and (B). The sharpness of each line indicates the high quality of the single crystal. The peak positions for the observed spectrum are well fitted by a second order perturbation calculation with a large Zeeman interaction (HZ) due to Hext [for the present case, an internal magnetic induction (Bint) at the Mn site] and a small quadrupole interaction (HQ) utilizing Eq. (1). The vertical dotted lines shown in the figure are the calculated positions for 55Mn zero-field NMR (ZFNMR) lines using the parameters | Bint | ¼ 23.05(1) T, vQ ¼ 2.426(1) MHz and q ¼ 0. Here q represents the angle between Bint and the principal axis of the EFG tensor at the Mn sites. Since Bint is parallel to the c axis as will be shown below, the principal axis of the EFG is found to be along the c axis, which is similar to the case of the Co nucleus in Ba(Fe1–xCox)2As2 with the same crystal structure.16 Before going to discuss the magnetic structure from 55Mn NMR measurements, we would like to point out that one can discuss the temperature dependence of the sublattice magnetization of antiferromagnets from the temperature dependence of the spectrum, which normally cannot be obtained from magnetization measurements. Since the resonance frequency (fc) for the 55Mn spectrum  central transition line m ¼ 124 12 is given by fc ¼ g2pN Bint where Bint is proportional to the Mn sublattice magnetization < m>, one can determine the temperature dependence of < m>. The T dependence of fc shows only a slight decrease in frequency from fc ¼ 242.0 MHz at 4 K to 197.8 MHz at 420 K as shown in the inset of Fig. 3. This indicates that < m> decreases by  18% from 4 K to 420 K. The T dependence of fc is similar to the T dependence of < m> calculated with molecular field theory12 for S ¼ 5/ 2 and TN ¼ 625 K, as shown by the solid line.

9.10.2.1.3

Magnetic structure of BaMn2As2

Now let us discuss the spin structure based on the NMR results. First, we need to determine the direction of Bint. In the AFM state, one expects a splitting of the NMR line when Hext is applied along the magnetic easy axis (parallel or antiparallel to ordered moments), while only a shift of the NMR line without splitting is expected when Hext is applied perpendicular to the magnetic easy axis, for Hext smaller than the magnetocrystalline anisotropy field. Thus, we measured 55Mn NMR in a single crystal under an external magnetic field Hext to determine the direction of Bint with respect to the crystal axes. When Hext is applied along the c axis, each line clearly splits into two lines as shown in Fig. 4(A). The Hext dependence of the resonance frequency for the central transition line fc is shown in Fig. 4(C) and the slopes of the field dependence of fc for both lines are  10.5 MHz/T, which is exactly

Fig. 3 55Mn NMR spectrum at T ¼ 4.2 K in the AFM state for BaMn2As2 in zero magnetic field. The vertical dotted lines shown in the figure are the calculated positions. The inset shows the temperature dependence of the resonance frequency (fc) for the central transition line under zero magnetic field. The solid line shows the T dependence of fc calculated by molecular field theory12 with S ¼ 5/2 and TN ¼ 625 K. The right figure shows the crystal and G-type spin structures of BaMn2As2 under zero Hext.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

(A)

235

(B)

(C)

Fig. 4 (A) Hext dependence of 55Mn NMR spectra at T ¼ 4.2 K in the AFM state for Hext parallel to the c axis. (B) Hext dependence of 55Mn NMR spectra at T ¼ 4.2 K in the AFM state for Hext perpendicular to the c axis. (C) External magnetic field Hext dependences of the resonance frequency for the central transition line fc under Hext parallel (solid circles) and perpendicular (open circles) to the c axis at T ¼ 4.2 K.

! ! ! the same as of the Mn nucleus. Since the effective field at the Mn site is given by the vector sum of B int and H , i.e., B eff ¼ ! ! gN ! B int þH , the resonance frequency is expressed as f ¼ B ext 2p eff . Thus the Hext dependence of the spectra clearly indicates that gN 2p

55

the Mn magnetic moments for each of the two sublattices in the AFM state are parallel or antiparallel to the c axis. In the case of Hext applied perpendicular to the c axis, no splitting of the 55Mn NMR lines is observed [see Fig. 4(B)]. In this qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi orientation the applied field is orthogonal to the ordered Mn moments and thus to Bint, so one expects f ¼ g2pN B2int þ H2ext . For our applied field range, Bint > > Hext, any shift in the resonance frequency would be small, which is observed as shown by open circles in Fig. 4(C). These results are consistent with the G-type AFM spin structure reported from neutron diffraction measurements with the ordered moments aligned along the c axis.11 The observed broadening of each line is likely caused by a small misalignment between the Hext and the ab plane, which introduces a small component of the external magnetic field along the c axis. Thus, the 55Mn zero-field NMR and also its Hext dependence clearly evidence the AFM state of BaMn2As2 where the Mn ordered moments point along the c axis. However, unfortunately, it is not possible to determine the G-type AFM only from the 55Mn NMR spectrum measurements under external magnetic field. With the help of NMR spectrum measurements of other nuclei, one can discuss more details of the magnetic structure. Here we show NMR spectrum measurements on 75As (I ¼ 32 , g2pN ¼ 7:2919MHz=T, Q ¼ 0.29 Barns), which provide useful information. As shown in Fig. 3, each As atom is coupled to four Mn atoms. Thus, through 75As NMR, one can probe the magnetism of the Mn sublattice in BaMn2As2 although it is not an “on-site” NMR measurements. Fig. 5 shows the 75As NMR spectrum measured at several temperatures in the AFM state. The observed spectra are typical I ¼ 3/2 spectra with one central peak and a satellite peak on both sides for the case of HZ [ HQ. The central transition peak lies just below the unshifted Larmor field, which is denoted by the vertical dashed line, evidencing that the average internal field at the As sites is approximately zero. Assuming the Gtype AFM state, the internal field at the 75As site can be calculated to be zero due to a perfect cancellation of the hyperfine field produced by four in-plane nearest neighbor Mn ordered moments when the ordered moments are parallel to the c axis.7,12,17 The observed nearly zero internal field at the As site is consistent with the G-type antiferromagnetic state. In the case of other magnetic structures such as stripe-type or A-type AFM structures, one does not expect the perfect cancellation of the hyperfine field at the As site. In fact, one observes finite internal fields at the As sites in mother materials (stripe-type AFMs) of iron-based superconductors such as BaFe2As218 and CaFe2As219 and also at the P site (equivalent to the As site) in CaCo2P2 (A-type AFM). Those differences provide important clues to determine the magnetic structures of materials. In addition, no NMR signal enhancement effect due to “ferromagnetic” exchange couplings is observed in not only 55Mn zero field NMR but also 75As NMR, suggesting that all exchange couplings in BaMn2As2 are antiferromagnetic. Thus, with the combination of “on-site” 55Mn NMR and “offsite” 75As NMR measurements for the case of BaMn2As2, we can successfully determine the G-type AFM state.

236

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

Fig. 5 Temperature dependence of 75As NMR spectra for single crystals of BaMn2As2 in the AFM state below TN ¼ 625 K for the two magnetic field directions Hext parallel and perpendicular to the c axis. The vertical dashed lines are the zero-shift position.

9.10.2.2 9.10.2.2.1

A-type antiferromagnet CaCo2P2 (Ref. 20) Background of CaCo2P2

As described above, a wide variety of the family of AM2X2 (A ¼ Sr, Ba, Ca, M ¼ transition metals, X ¼ As, P) compounds has been studied intensively after the discovery of high Tc superconductivity (SC) in iron pnictides.21 The Co-based compounds also have been found to show a rich variety of magnetic properties and have attracted much attention. Tetragonal SrCo2P2 shows no magnetic ordering and is an exchange enhanced Pauli paramagnet with predominantly ferromagnetic interactions.22–26 A metamagnetic transition from the Pauli paramagnetic to the ferromagnetic state at a high magnetic field of 60T has been reported.24 LaCo2P2 is known to be an itinerant ferromagnet with a Curie temperature of TC ¼ 130 K and a saturated Co moment of 0.4 mB.27–29 In CaCo2P2, on the other hand, an A-type AFM state has been reported below a Néel temperature of TN ¼ 110 K, in which the Co moments are ferromagnetically aligned in the ab plane and the moments adjacent along the c axis are aligned antiferromagnetically,26,30 as shown in Fig. 6. From the neutron diffraction measurements on powder samples of CaCo2P2, the ordered Co moments are estimated to be 0.32 mB.30 The magnetic susceptibility increases by lowering temperature and exhibits a small kink at TN.29,31 Even below TN, the magnetic susceptibility keeps increasing and shows a broad maximum at T*  32–36 K whose origin is not well understood yet.29,31 Teruya et al. suggested that the anomaly at T* is intrinsic and relates to the metamagnetic-like behavior observed in the magnetization data.29 Below we present the results of NMR measurements on 31P (I ¼ 1/2, gn/2p ¼ 17.235 MHz/T) and 59Co (I ¼ 7/2, gn/2p ¼ 10.03 MHz/T, Q ¼ 0.4 Barns) in CaCo2P2 in the AFM ordered state below TN ¼ 110 K.

Fig. 6

The A-type spin structures of CaCo2P2 under zero Hext.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements 9.10.2.2.2

59

Co and

31

P NMR in CaCo2P2

237

Fig. 7 shows “on-site” 59Co and “off-site” 31P NMR spectra of a single crystalline CaCo2P2 sample in the AFM ordered state under zero magnetic field at several temperatures up to 50 K. The spectra consist of two broad peaks around 20 MHz and 24 MHz at 4.2 K. Although the peak around 24 MHz is weak, it is clearly distinguishable and can be observed more clearly at higher temperatures such as 10–30 K as shown in the figure. The broad peak around 20 MHz is assigned to 59Co zero-field NMR (ZF-NMR) which does not show any clear quadrupolar splitting due to the inhomogeneous magnetic broadening.20 The weak signal around 24 MHz is attributed to 31P ZF-NMR.20 The large difference in the signal intensities for the two signals is due to the measurement condition which optimizes the signal intensity for 59Co ZF-NMR.20 Since the ZF-NMR spectrum originates from the Co ordered magnetic moments, the observation of the ZF-NMR signals is direct evidence of the magnetic ordered state below TN. Co From the spectrum, the internal magnetic induction | Bint | for 59Co is estimated to be 2.0 T at 4.2 K. BCo int is proportional to Ahf < m> where Ahf is the hyperfine coupling constant and < m> is the ordered Co magnetic moment. Using BCo int ¼  2.0 T where Co the negative sign is reasonably assumed and Aab ¼ ( 57.6  4.2)kOe/mB/Co obtained from 59Co NMR measurements in the paramagnetic state,20 < m> is estimated to be 0.35 mB which is in good agreement with 0.32 mB reported by the neutron diffraction measurement30 and slightly smaller than 0.4 mB from mSR measurements.32 In the case of 31P zero-field NMR, the internal magnetic induction | BPint | for 31P is estimated to be 1.4 T at 4.2 K. The finite internal field at the P site is consistent with A-type AFM structures. From APab ¼ (5.33  0.30)kOe/mB/Co obtained from 31P NMR measurements in the paramagnetic state,20 < m> is estimated to be 0.65 mB which is much greater than the reported values and also the estimated value from the Co NMR data. The reason for the estimated large value from 31P NMR results is not clear, but the AabP in the AFM state was suggested to be slightly greater than that in the PM state.20 This would be possible if one considers the effects of the next-nearest-neighbor (NNN) Co spins which are assumed to produce a negative hyperfine field at the P site. Since in the AFM state the direction of NNN Co spins is antiparallel to that of the NN Co spins, one expects a positive hyperfine field at the P sites from the NNN Co spins, which increases the positive hyperfine field produced by the NN Co spins. Assuming < m > ¼ 0.32mB (Ref. 30), we thus estimate a  25% additional contribution of the hyperfine field from the NNN Co spins to the total hyperfine field at the P site. P The temperature dependence of | BCo int | and |Bint | is shown in the inset of Fig. 7 where both show smooth decrease with increasing * temperature without any anomalies around T  32–36 K where the magnetic susceptibility shows a maximum. This indicates that the reduction of c below T* is not due to a change in the magnitude of the Co ordered moments at T*. The temperature dependence P of |BCo int | and |Bint | is well reproduced by a Brillouin function which was calculated based on the Weiss molecular field model with

Fig. 7 T dependence of zero-field NMR spectrum. At 4.2 K, the blue and red curves represent the 59Co ZF-NMR and 31P ZF-NMR spectra, respectively. The inset shows the T dependence of the internal magnetic induction |Bint | of the 59Co site (black) and the 31P site (red).

238

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

P S ¼ 3/2 for Co2þ, TN ¼ 110 K, r BCo int r ¼ 2.0 T and Bint ¼ 1.4 T at T ¼ 4.2 K [solid curves in the inset of Fig. 7]. These results indicate that the magnetic state of the Co ions is well explained by the local moment picture although the system is metallic as determined from electrical resistivity measurements29 in the AFM state.

9.10.2.2.3

Magnetic structure o/CaCo2P2

Now we show the external field dependence of 59Co and 31P NMR spectra in the AFM state at 4.2 K. Fig. 8(A) and (B) show the frequency and field-swept 59Co NMR spectra, respectively, measured under several external magnetic fields with the two different directions: Hextkc and Hextkab. As described above, in AFM state, one expects a splitting of NMR line when an external magnetic field is applied along the magnetic easy axis, while only a shifting of the NMR line without splitting is expected when Hext is applied perpendicular to the magnetic easy axis, for Hext smaller than the magnetocrystalline anisotropy field. On the other hand, when Hext is greater than the magnetocrystalline anisotropy field, magnetic moments change the direction to perpendicular to Hext, known as spin flop. As shown in Fig. 8(A), no splitting of the 59Co NMR line is observed at less than  0.1 T for the two magnetic field directions. This indicates that the magnetic anisotropy field of the Co magnetic moments is less 0.1 T and the application of magnetic field makes a spin flop very easily. In fact, as shown in the inset of Fig. 8(C), the magnetization vs. external magnetic field plot exhibits very similar behavior for both the magnetic field directions, suggesting very weak magnetic anisotropy, although metamagnetic-like behaviors are observed around 2.1 T and 5.1 T for Hextkc and around 1.6 T and 5.1 T for Hext t c. Fig. 8(C) shows the external field dependence of resonance frequencies (fres) for 59Co NMR determined by the peak position of each spectrum. We also carried out similar 31P NMR spectrum measurements whose results are also plotted in the figure. The fress are nearly constant below 1 T and increase gradually with increasing Hext. As discussed above, the resonance frequency is proportional (C) (A)

(B)

Fig. 8 (A) Frequency-swept 59Co NMR spectra at T ¼ 4.2 K under several magnetic fields parallel to the c axis (red) and to the ab plane (black). (B) Field-swept 59Co NMR spectra for Hext || c axis (red) and Hext || ab plane (black). (C) Hext dependence of resonance frequency (fres) for both nuclei 59 Co and 31P. fress are mainly determined from the frequency-swept NMR spectra and the Hext-swept NMR spectra below and above 3 T, respectively. The black (red) and the blue (pink) curves are calculated results for 59Co and 31P NMR for H || ab (Hext || c), respectively. The two curves for each nucleus are nearly same. Inset: magnetization curves at 2 K for both magnetic field directions from Ref. 29. Note that metamagneticlike behaviors are observed at Hc1  2.1 T (1.6 T) and Hc2  5.1 T (5.1 T) for Hext || c (Hext || ab).

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

239

(A)

(B)

Fig. 9 (A) Hext dependence of the full-width at half maximum (FWHM) of the field-swept 59Co-NMR spectrum for magnetic fields Hextkc axis (red) and Hextkab plane (black). The curves are calculated results (see text). (B) Hext dependence of angles q0 , Q and q for the case of Hextkc axis. Here we used the magnetization data measured at T ¼ 2 K. Inset: a schematic view of the angles q0 , Q, and q. Note that the direction of Bint for Co is antiparallel to that of the magnetization M while that for P is parallel to the M.

to an effective field (Heff) which is the vector sum of the internal magnetic induction BCo int and the external field Hext, i.e., r Heff r ¼ r BCo int þ Hext r. Therefore, the resonance frequency fres is expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g g fres ¼ n Heff ¼ n H2ext þ B2int þ 2Hext Bint sinq0 : (11) 2p 2p Here q0 is the canting angle of the Co ordered moment from the perpendicular direction with respect to the external magnetic field [see, Fig. 9(B)], which can be expressed as q0 ¼ sin 1(M/Ms) where Ms is the saturation of magnetization. From the magnetization curves from Ref. 29 shown in the inset of Fig. 8(C), we calculated the external field dependence of sinq0 ¼ M/Ms for Hextkc and Hextkab where we used Ms ¼ 0.32 mB.30 Using BCo int ¼  20. T, one can calculate the external field dependence of the resonance frequency. The black and red solid lines representing the calculated Hext dependence of fres for 59Co NMR under the two magnetic field directions reproduce experimental results relatively well. Here we assumed the internal magnetic induction is isotropic for simplicity since the 59Co hyperfine coupling constant is nearly isotropic.20 No clear anomalies due to the metamagnetic-like behavior around 2 T are observed in the external field dependence of the resonance frequencies for not only experimental results but also in the calculated one. Assuming the metamagnetic-like behavior originates from a change in the direction of the magnetization (or the Co ordered moments), the changes are estimated to be only  5 along the magnetic field direction from the magnetization data [see, Fig. 9(C)], which cannot be detected within our experimental uncertainty. Similar to the 59 Co NMR, the external field dependence of resonance frequency for 31P NMR can be reasonably reproduced by Eq. (11) using BPint ¼ 1.4 T obtained from 31P ZF-NMR20 as shown by the blue and pink curves.

9.10.2.2.4

External magnetic-field dependence of the direction of the ordered moments in CaCo2P2 revealed by NMR line-width

Here we present that it is possible to discuss the direction of ordered moments from the line-width of NMR spectrum. Fig. 9(A) shows the Hext dependence of full width at half maximum (FWHM) of 59Co NMR spectra for Hextkc and Hextkab. The filled and open symbols represent the results from the frequency-swept and field-swept 59Co NMR spectra, respectively. In the case of the field-swept NMR spectrum, the plotted values are reduced by a factor of 1.4 to match the results from the frequency-swept NMR

240

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

measurement. This is due to the fact that the field-swept NMR spectrum measurements give rise to greater FWHM than those of the frequency-swept NMR spectra because the slope of fres vs. Hext is less than the value of gn/2p. It is noted that one cannot estimate the FWHM of the 59Co-NMR spectrum at low magnetic fields less than  1 T by sweeping magnetic field. Although the values of FWHM from the field-swept NMR spectra are slightly greater, the intrinsic behavior of the Hext dependence of FWHM is not affected, as may be seen in the Hextkc data in the magnetic field region of Hext ¼ 2–4 T where both data sets exhibit the same magnetic field dependence. As shown in Fig. 9(A), FWHM  0.36 T is nearly independent of Hext for Hextkab. On the other hand, in the case of Hextkc, with increasing Hext the FWHM decreases gradually and show a local minimum around 1.6 T and then starts to increase. No change in the FWHM for Hextkab indicates that the degree of the inhomogeneous magnetic broadening is independent of Hext. Therefore, it is clear that the characteristic behavior of FWHM for Hextkc is not due to the magnetic broadening effect. Here we attribute it to the effects of quadrupole splitting of the spectrum. As described in Sections 9.10.1–9.10.2, the width of the full spectrum including the quadrupole splitting lines (FWHM for the case of 59Co NMR in CaCo2P2) depends on q as FWHM f r 3cos2q  1r where q is the angle between the principal axis of the EFG and the quantization axis of nuclear spin (Heff). When Hext is applied along the c axis (i.e., parallel to the principal axis of the EFG) in the AFM state, the angle q changes by the application of magnetic field [see, Fig. 9(B)]. When Hext is very small compared with Bint, q is close to 90 . With increasing Hext, q decreases and becomes close to 54.74 where FWHM is expected to be a minimum [see Fig. 1(A)]. With further increase of Hext, q will be decreased and eventually becomes close to zero, resulting in a spectrum which is twice as broad compared with that for q ¼ 90 . This scenario, the change in 6 with Hext, qualitatively explains the Hext dependence of FWHM. In order to analyze the experimental results more quantitatively, we have calculated the Hext dependence of FWHM. In the case of Hextkc, utilizing q0 estimated from the magnetization data, one can easily calculate the Hext dependence of Q which is the angle between the direction of Heff and the ab plane, and thus also the angle q between the c axis and Heff corresponding to the quantization axis for nuclear spin. The calculated Hext dependence of Q, q and q0 for Hextkc is shown in Fig. 9(B) for T ¼ 2 K. We simply assumed that the FWHM can be written as FWHM ¼ a r 3cos2q  1r. The solid red curve in Fig. 9(A) shows the calculated result with a ¼ 0.36 T, which reproduces the experimental data well, although one can see the deviation around 1.5 T. The deviation can be due to inhomogeneous magnetic broadening of each line and also a misalignment between the Hext and the c axis since the simple model does not take such effects into consideration. In fact, if we take the magnetic broadening of each line (0.1 T) and the misalignment of 5 , one can reproduce the results a little bit better as shown by the red dashed line. In the case of Hextkab, the nearly constant FWHM  0.36 T can be also well reproduced with a ¼ 0.36 T and q ¼ 90 , as shown by the solid black line (case 1) in the figure. This indicates that Heff is always in the ab plane keeping q ¼ 90 and the spin-flip occurs in the ab plane. If one assumes that the Co ordered moments flip to the c-axis direction when Hext is applied in the ab plane, the FWHM should depend on Hext as shown by the solid blue curve (case 2) which clearly contradicts the experimental results. Thus, these results indicate the ab plane is the magnetic easy plane. As the ab-plane magnetization starts to increase from nearly zero Hext, similar to the case of the c-axis magnetization as shown in the inset of Fig. 8(C), the in-plane magnetic anisotropy is considered to be also very weak. To study the details of the characteristic properties of the magnetic anisotropy in CaCo2P2, it is important and highly required to measure the magnetization for both magnetic field directions in detail at low magnetic fields below 0.1 T. This is a future project. The FWHM ( 0.36 T) of the 59Co ZF-NMR corresponds to the case for q ¼ 90 . This provides evidence that the Co ordered moments are in the ab plane at zero magnetic field, again consistent with the neutron diffraction results.30

Fig. 10

External magnetic field Hext-temperature magnetic phase diagram for Hextkab plane. Hc1, Hc2 and T* are from Ref. 29.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements 9.10.2.2.5

241

Magnetic phase diagram of CaCo2P2 determined by NMR

Finally, in Fig. 10, we present the magnetic phase diagram of CaCo2P2 for Hextkab, based on the 59Co and 31P NMR studies and also the previous magnetization measurements.29 Under zero magnetic field, the system is in the A-type AFM state below TN ¼ 110 K where the Co ordered moments are in the ab plane. When Hext is applied in the ab plane, the Co ordered moments flop immediately to make the perpendicular configuration between it and Hext, and then cant along the Hext direction with increasing Hext, producing the linear increase of the magnetization with increasing Hext as actually observed [see, Fig. 8(C)]. When Hext reaches Hc1, the canting angle q0 jumps by  5 degrees at Hc1 at 2 K, producing the metamagnetic behavior in the magnetization curve. With further increasing Hext, the q0 keeps increasing with a small jump at Hc2 with a change of the canting angle less than  4 degree at 2 K. In the case of Hextkc, with increasing Hext the canting angle q0 increases, similar to the case of Hextkab although no spin flop occurs because of the perpendicular configuration between the Co ordered moments and Hext at the initial condition. With further increase of Hext, the canting angle jumps slightly at Hc1 and Hc2 similar to the case of Hextkab, producing again the metamagnetic behavior in the magnetization curve. The changes in q0 are close to  4 degrees for each jump. The similar slopes in the magnetization curves for Hext parallel and perpendicular to the c axis indicate that the in-plane and out-of-plane magnetic anisotropies are nearly the same. Thus, it is important to note that the NMR measurements provide detailed information on the magnetism of CaCo2P2 and also establish the magnetic phase diagram from a microscopic point of view.

9.10.2.3

Summary

In summarizing this subsection, we have described NMR studies of the two different antiferromagnets with different magnetic structures, namely the so-called “G”- and “A”-types. Utilizing “on-site” NMR (55Mn NMR for BaMn2As2 and 59Co NMR for CaCo2P2), one can directly determine the directions of the ordered moments for the magnetic materials. In addition, with the combination of the results of “off-site” NMR measurements (75As NMR for BaMn2As2 and 31P NMR for CaCo2P2), G-type and A-type antiferromagnetic spin structures are determined for BaMn2As2 and CaCo2P2, respectively. Furthermore, in CaCo2P2, we presented that the behaviors of spin canting of the Co ordered moments produced by the application of external magnetic field can be determined from a microscopic point of view based on the Hext dependence of line width (FWHM) of NMR spectrum.

9.10.3

Helical antiferromagnets

In this section, we present NMR measurements on typical incommensurate helical antiferromagnets of EuCo2P2 and EuCo2As2 and show that the NMR technique is a unique tool for determination of the spin structure in incommensurate helical AFMs. In addition,

Fig. 11 Crystal and magnetic structures of EuCo2P2. The arrows on the Eu atoms indicate the directions of the Eu ordered moments in the incommensurate helical antiferromagnetic state.

242

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

we will describe that, with the combination of “on-site” Eu NMR with NMR measurements of other nuclei, the AFM propagation vector characterizing the helical AFM state can be determined.

9.10.3.1 9.10.3.1.1

EuCo2P2 (Ref. 33) Background of EuCo2P2

EuCo2P2, with the body-centered tetragonal ThCr2Si2-type structure, is reported to exhibit an incommensurate helical AFM ground state below TN ¼ 66.5 K.23,34–37 The neutron diffraction measurements on EuCo2P2 report that the Eu ordered moment at 15 K is 6.9 mB/Eu,37 where mB is the Bohr magneton, consistent with Eu2þ (J ¼ S ¼ 7/2) and spectroscopic splitting factor g ¼ 2. Fig. 11 shows the magnetic structure in EuCo2 As2 where the Eu ordered moments are aligned ferromagnetically in the ab plane with the helix axis along the c axis.37 The AFM propagation vector k ¼ (0, 0, 0.852)2p/c at 15 K was reported by the neutron diffraction measurements,37 where c is the c-axis lattice parameter. The similar value of k ¼ (0, 0, 0.88)2p/c at T ¼ 0 K (Ref. 36) was also obtained by the analysis of the magnetic susceptibility c data on a single crystal below TN using molecular field theory which has been recently formulated to apply to planar noncollinear Heisenberg antiferromagnets.38–40 Below we present the results of NMR measurements of 153Eu (I ¼ 52 , g2pN ¼ 4:632 MHz=T, Q ¼ 2.49 b), 59Co (I ¼ 72 , g2pN ¼ 10:03 MHz=T, Q ¼ 0.4 b), and 31P (I ¼ 12 , g2pN ¼ 17:235 Mhz=T) nuclei using a single crystal (1  1  0.3 mm3) of EuCo2P2.

9.10.3.1.2

153

Eu NMR in EuCo2P2

The bottom panel of Fig. 12 shows the “on-site” 153Eu NMR spectrum in the AFM state for EuCo2P2 (single crystal) measured in zero magnetic field at a temperature T ¼ 1.6 K. The observed spectrum can be well reproduced by the nuclear spin Hamiltonian (Eq. 1) for the case that the Zeeman inter-action is greater than the quadrupole interaction. The red line shown at the bottom panel of Eu r ¼ 25.75 T(¼ 119.3 MHz), Fig. 12 is the calculated spectrum for 153Eu zero-field NMR (ZF-NMR) using the parameters r Bint  vQ ¼ 30.2(2) MHz and q ¼ 90 . Here we used h ¼ 0 because the Eu site in EuCo2P2 has a tetragonal local symmetry (4/mmm). Eu Since the principal axis of the EFG at the Eu site is parallel to the c axis due to the local symmetry,41,42 q ¼ 90 indicates that Bint is perpendicular to the c axis.

Fig. 12 153Eu-NMR spectra at T ¼ 1.6 K in the AFM state for single crystalline EUCo2P2 in Hext ¼ 0 (bottom panel), Hext ¼ 1 T parallel to the ab plane (middle panel) and parallel to the c axis (top panel). The red lines constitute the calculated 153Eu NMR spectrum. The inset shows the external magnetic field dependence of the amount of the splitting of the central transition line (Df). The solid line is the expected Hext dependence of Df described in the text.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

243

BEu int is proportional to Ahf < m> where Ahf is the hyperfine coupling constant and < m> is the ordered Eu magnetic moment. The hyperfine field at the Eu sites mainly originates from core polarization from 4f electrons and is oriented in a direction opposite to that of the Eu moment.43 For rBEu int r ¼ 25.75(2) T and the reported AFM ordered moment < m > ¼ 6.9(1)mB/Eu from neutron diffraction,37 Ahf is estimated to be  3.73 T/mB where the sign is reasonably assumed to be negative due to the corepolarization mechanism. The estimated Ahf is very close to  3.78 T/mB for the case of EuCo2As242 and is not far from the corepolarization hyperfine coupling constant  4.5 T/mB estimated for Eu2þ ions.43 The small difference could be explained by a positive hyperfine coupling contribution due to conduction electrons which cancels part of the negative core polarization field as has been pointed out in the case of EuCo2As2 (Ref. 42). 153 The direction of BEu Eu NMR spectrum measurements on the single crystal in nonzero Hext. When int is also directly confirmed by Hext is applied along the c axis, almost no change of the 153Eu NMR spectrum is observed (see the top panel in Fig. 12 where the simulated spectrum shown by the red line is the same as the case of Hext ¼ 0). Since the resonance frequency is expressed for qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  Eu 2 Hext t < m> as f ¼ g2pN Bint þ H2ext , any shift in the resonance frequency due to Hext would be small for our applied field range Eu where BEu int > > Hext when Hext is perpendicular to Bint. This is actually what we observed. Therefore, we conclude that Hext is perpendicular to the ordered Eu moments. In the case of Hext applied parallel to the ab plane, on the other hand, each line broadens and exhibits a typical two-horn structure expected for an incommensurate planar helical structure as shown in the middle panel of Fig. 12. In fact, the observed spectrum at Hext ¼ 1 T is well reproduced by a calculated spectrum for an incommensurate helical AFM state shown by the red line. The inset of the middle panel of Fig. 12 shows the external field dependence of the amount of the splitting of the central transition line (Df) of the 153Eu ZF-NMR spectra. The Df increases with increasing Hext. Since the peak positions of the two-horn shape of the spectrum are given by Beff ¼ Bint  Hext, the Df is proportional to Hext according to Df ¼ 2HextgN/(2p). As shown by the solid line in the inset, the Hext dependence of Df is well reproduced by this relation. Thus these NMR results reveal an incommensurate helical spin structure with the ordered moments aligned in the ab plane, consistent with recent neutron diffraction measurements37 and magnetization measurements.36 The observed ab-plane alignment of the ordered moments is also consistent with the prediction of the moment alignment from magnetic dipole interactions between the Eu spins.44

9.10.3.1.3

AFM propagation vector in EUCo2P2 determined by

59

Co NMR

We can clearly conclude, from the “on-site” Eu NMR results, an incommensurate helical spin structure with the ordered moments aligned in the ab plane in EuCo2P2. However, unfortunately one cannot determine an AFM propagation vector k which characterizes the helical AFM spin structure, from the 153Eu NMR spectra. Below, we show that the AFM propagation vector can be successfully determined by the excellent way of the combination of 153Eu Eu NMR with NMR measurements on Co nuclei. Fig. 13(A) shows the 153

(A) (B)

(C)

Fig. 13 (A) 59Co zero-field NMR spectra in the AFM state in zero magnetic field at the indicated temperatures. The inset shows the temperature dependence of the turn angle f. (B) Coordinations of nearest-neighbor Eu sites around a Co site. The arrows on the Eu atoms indicate the ordered magnetic moments. (C) Top view of the coordination of nearest-neighbor Eu sites around Co site. The magnetic moment turn angle between adjacent magnetic layers is f.

244

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

temperature dependence of 59Co NMR spectrum under zero magnetic field. From the peak position of the spectrum, the internal magnetic induction at the Co site at 1.6 K is estimated to be rBCo int r ¼ 11.3 kOe which decreases to 10.2 kOe at 30 K. In the following, we describe the internal field Bint at the Co site in the incommensurate AFM state of EuCo2P2, based on the analysis by Yogi et al. for EuGa4 (Ref. 41) and by Kitagawa et al. for BaFe2As2 (Ref. 18). Since the long range dipolar interaction gives only a small contribution to the internal field, we focus on the short range transferred hyperfine interaction between the Co nucleus and the ordered moments on the four nearest neighbor Eu sites [see Fig. 13(B) and (C)]. The internal field at the Co site can be written as the sum of contributions from each Eu sites as BCo int ¼

4 X

Bi ,mi ;

(12)

i¼1

where mi is the ordered moment at the i-th Eu site and Bi is the hyperfine coupling tensor between the Co nucleus and i-th Eu site. We explicitly write components of B1 for the Eu1 site as 1 0 Baa 0 Bac C B C (13) B1 ¼ B @ 0 Baa 0 A; Bca 0 Bcc where we assume that ab-plane components of the hyperfine coupling constant are the same. The coupling tensor for other sites can be determined by symmetry considerations. For example, since the Eu2 site is related to the Eu1 site by mirror reflection with respect to the b axis, B2 is given as 0 1 Baa 0 Bac B C (14) B2 ¼ B Baa 0 C @ 0 A; Bca

Likewise

0

0 Baa B B3 ¼ B @ 0 0

and

0 Baa Bca

0 Baa B B4 ¼ B @ 0 0

0 Baa Bca

Bcc 1 0 C Bba C A Bcc

(15)

1 0 C Bba C A Bcc

(16)

are given for the Eu3 and Eu4 sites, respectively. Consider the helical magnetic structure specified by the wave vector k ¼ (0, 0, f/c) shown in Fig. 13(C),

therefore,

m1 ¼ m2 ¼ m3 eif ¼ m4 eif hm

(17)

  if if BCo ,m int ¼ B1 þ B2 þ B3 e þ B4 e

(18)

Since 0

2B þ 2eif Baa B aa if if B B1 þ B2 þ B3 e þ B4 e ¼ @ 0 0 one gets

BCo int

0   2 1 þ eif Baa B B ¼B 0 @ 0

0

0 2Baa þ 2eif Baa 0

  2 1 þ eif Baa 0

1 0 C C; 0 A if 2Bcc þ 2e Bcc 10

1 CB m C CB C 0 C@ m A   A if 0 2 1 þ e Bcc 0

Taking the real and imaginary components for the a and b directions, respectively, rBint r at the Co site is found to appear in only the ab plane when the Eu ordered moments lie in the ab plane and is finally expressed by

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements BCo int ¼ 2hmiBaa

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 þ 2cosf

245 (19)

where f is the turn angle along the c axis between the Eu ordered moments in adjacent Eu planes, which characterizes the helical structure. Baa is the in-plane hyperfine coupling constant of 59Co (BCo) which can be determined by 59Co NMR measurements in the paramagnetic state. In the case of f ¼ p corresponding to an A-type collinear AFM state, BCo int is zero due to a cancellation of the internal magnetic induction from the four nearest-neighbor Eu ordered moments. On the other hand, if f deviates from p corCo responding to a helical state, one can expect a finite BCo int . Thus the observation of the finite Bint is direct evidence of the planar incommensurate helical AFM state in EuCo2P2. Using hmi ¼ 6.9(1) mB,37 BCo ¼  0.98(9) kOe/mB/Eu estimated from 59Co NMR  measurements in the paramagnetic state33 and BCo int ¼ 11.3(1) kOe, the turn angle f can be estimated to be 131  16 corresponding to a helix wave vector k ¼ (0, 0, 0.73  0.09)2p/c where c is the c-axis lattice parameter of the body-centered tetragonal Eu sublattice. The estimated value of k is slightly smaller than k ¼ (0, 0, 0.852)2p/c obtained from the neutron diffraction data37 and (0,0, 0.88)2p/c estimated from the c data36 on EuCo2P2, and is close to k ¼ (0, 0, 0.73)2p/c determined by the NMR data in EuCo2As2.42 The origin of the small difference in k between the NMR and neutron diffraction (and c) data is not clear, but it could be explained, e.g., if one would take other small contributions to the hyperfine field at the Co site from the NNN Eu spins. The asymmetric shape of the observed 59Co ZF-NMR spectrum originates from a distribution of the internal field at the Co sites. The 153Eu NMR lines are sharp as seen in Fig. 12, indicating homogeneous Eu ordered moments. Therefore, the low-frequency tail of the Co ZF-NMR spectrum suggests a distribution of the turn angle f, i.e., the AFM propagation vector k. Using the values of the internal field distribution of the Co site from 0.6 T (6 MHz) to 1.2 T (12 MHz), the distribution of the turn angle f is estimated to be from 156 to 131 . This corresponds to a change in k from (0, 0, 0.86)2p/c to (0, 0, 0.73)2p/c. It is worth mentioning that the NMR technique determines not only the AFM propagation vector but also its distribution.

9.10.3.2 9.10.3.2.1

EuCo2As2 (Ref. 42) 153

Eu NMR in EuCo2As2

A similar NMR study42 has been performed in the incommensurate AFM EuCo2As2 below TN ¼ 45 K which has a magnetic structure similar to that of EuCo2P2 as shown in Fig. 11.45,46 At the bottom panel of Fig. 14 the “on-site” 153Eu NMR spectrum in the AFM state for a single crystal EuCo2As2 ( 9  8  1 mm3) measured in zero magnetic field at a temperature T ¼ 4.3 K is shown. As in the case of the Eu zero field NMR spectrum in EuCo2P2, the observed spectrum is well explained by the Hamiltonian Eq. (1). The blue lines shown at the bottom panel of Fig. 14 are the calculated positions for 153Eu zero-field NMR lines using the parameters r BEu int r ¼ 27.5(1) T, vQ ¼ 30.6(1) MHz, h ¼ 0, and q ¼ 90 . The observed spectrum in EuCo2As2 is slightly broader than that observed in EuCo2P2, originating from a distribution of Bint probably due to Eu ordered moment distributions. In fact, as shown by the red curve in the figure, the observed 153Eu ZF-NMR spectrum was well reproduced with a broadening of  1.1 T of the calculated lines.

Fig. 14 153Eu-NMR spectra at T ¼ 4.3 K in the AFM state for EuCo2As2 in Hext ¼ 0 (bottom), Hext ¼ 1 T parallel to the ab plane (middle) and parallel to the c axis (top). The red and blue lines are the calculated 153Eu NMR spectra with and without a distribution of BEu int, respectively.

246

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

(A)

(B)

Fig. 15 (A) Coordination of nearest-neighbor Eu sites around Co site. The arrows on the Eu atoms indicate the ordered magnetic moments. The magnetic moment turn angle between adjacent magnetic layers is f. (B) 59Co NMR spectrum at T ¼ 1.6 K in the AFM state in zero magnetic field.

To evidence the incommensurate AFM state in EuCo2As2, we measured 153Eu NMR spectra under magnetic fields as in the case of EuCo2P2. When Hext is applied along the c axis, almost no change of the 153Eu NMR spectrum is observed [see the top panel in Fig. 14 where the simulated spectra shown by blue and red lines are the same as the case of Hext ¼ 0]. This is consistent with that fact that the Eu ordered moments are perpendicular to the c axis. In the case of Hext applied perpendicular to the c axis, on the other hand, each line broadens as shown in the middle panel of Fig. 14. The broadening of each line cannot be explained by the A-type AFM state. In this case, one simply expects a splitting of each line into two lines corresponding to two Eu planes where the Eu ordered moments are parallel or antiparallel to Hext. The blue solid line is a calculated two dimensional powder pattern spectrum for an incommensurate helical AFM state. With the inhomogeneous magnetic broadening due to the same distribution of BEu int as in the Hext ¼ 0 T spectrum, the observed spectrum at Hext ¼ 1 T is reasonably reproduced as shown by the red solid curve. Thus, again, these NMR results reveal an incommensurate helical spin structure with the ordered moments aligned in the ab plane, consistent with recent neutron diffraction measurements.45

9.10.3.2.2

59

Co NMR in EuCo2As2: Determination of the AFM propagation vector

Now let us show the results of 59Co NMR under zero magnetic field, from which one can determine the AFM propagation vector k ¼ (0, 0, k)2p/c, where c is the c-axis lattice parameter of the body-centered tetragonal Eu sublattice in EuCo2As2. As in the case of EuCo2P2, we have succeeded in observing the 59Co zero field NMR spectrum at 1.6 K as shown in Fig. 15(B), where the internal magnetic induction at the Co site is estimated to be r BCo int r ¼ 10.3 kOe. The coordination of nearest-neighbor Eu sites around Co site in EuCo2 As2 shown in Fig. 15(A) is exactly same with that in the case of EuCo2P2. Therefore, one can use the same equation (Eq. 19) to estimate the AFM propagation vector k. Again it is noted that, in the case of f ¼ p corresponding to an A-type collinear AFM state, BCo int is zero due to a cancellation of the internal magnetic induction from the four nearest-neighbor Eu ordered moments, one can easily infer from Eq. (19). On the other hand, if f deviates from p corresponding to a helical state, one can expect a finite Co . Thus the observation of the finite BCo Bint int is direct evidence of the planar incommensurate helical AFM state in EuCo2As2. Using Co hmi ¼ 7.26(8) mB,45 Aab ¼  0.875 kOe/mB/Eu obtained from 59Co NMR measurements in the paramagnetic state42 and Bint ¼ 10.3  kOe, the turn angle f is estimated to be 132 corresponding to a helical wave vector k ¼ (0, 0, 0.73  0.07)2p/c.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements 9.10.3.3

247

Summary

In summarizing this section, we have shown that by analyzing the NMR spectrum in zero field and its external-field dependence, one can determine directly incommensurate helical AFM structures in EuCo2P2 and EuCo2As2. Furthermore we described that the AFM propagation vectors characterizing the incommensurate helical AFM states can be successfully determined to be k ¼ (0, 0, 0.73  0.09)2p/c for EuCo2P2 and (0, 0, 0.73  0.07)2p/c for EuCo2As2 from the internal magnetic fields at the Co sites obtained by 59Co NMR under zero magnetic field. Thus it is important to emphasize that NMR can be a unique tool for a determination of the spin structure in incommensurate helical antiferromagnets.

9.10.4

Molecular nanomagnets

The advances of molecular chemistry in synthesizing molecular magnets provide a unique opportunity to study the properties of materials at the nanoscale level.47–49 Molecular magnets are composed of a relatively small number of magnetic ions with spins, usually surrounded by large organic ligands, resulting in negligible intermolecular magnetic interaction. The small number of magnetic ions leads to discrete energy levels and allows the observation of quantum phenomena. In fact, a quantum tunneling of the magnetization (QTM)50–52 and a quantum coherence53 have been observed in the so-called Mn12 and Fe8 molecules. Another advantage of the discreteness of the energy levels is that one can control the ground state of molecules by applying a magnetic field, and thus they are suitable for the study of the level crossing phenomena.49 These molecules also offer the opportunity to study the effects of spin frustration at nanoscale levels.47,48 The simplest frustrated spin system is three s ¼ 1/2 antiferromagnetically coupled spins with a triangular configuration. In a molecular nanomagnet, this simplest spin frustration system can really exist and one can investigate it experimentally.47 One of the best examples is the so-called “V15” molecule. In this section, we show how “on-site” NMR is powerful to determine the spin structure of such nanoscale molecular magnets.54,55 In the following we present NMR results on the two nanoscale molecular magnets: the isolated triangular antiferromagnet V15 and the ferrimagnet Mn12. In addition, we describe a peculiar example that the relaxation time of the macroscopic magnetization of molecular magnets can be measured by looking at the time dependence of the NMR spectrum following inversion of the applied magnetic field.

9.10.4.1 9.10.4.1.1

Isolated triangular antiferromagnet V15 (Ref. 56) Background of V15

K6[V15As6O42(H2O)]$8H2O (in short, V15) is a model system for an s ¼ 1/2 Heisenberg single triangle antiferromagnet, the simplest frustrated spin system.47 V15 is comprised of 15 V4þ ions with s ¼ 1/2, which are arranged in a quasispherical layered structure with a triangle sandwiched between two hexagons as shown in Fig. 16(A). All exchange interactions between V4þ spins are antiferromagnetic.57,58 Each hexagon of V15 consists of three pairs of strongly coupled spins with J1  800 K. Each V4þ spin in the central triangle is coupled with the spins in both hexagons with J2 ¼ 150 K and J3 ¼ 300 K,59 resulting in a very weak exchange interaction between the spins within the central triangle with J0 ¼ 2.44 K.59 At low temperatures, the magnetic properties of V15 are determined entirely by the three V4þ spins on the triangle (a frustrated s ¼ 1/2 triangular system) because the V4þ spins on the hexagon form a total ST ¼ 0 spin singlet state due to the strong AF interaction of J1  800 K, as confirmed directly by 51V-NMR measurements at very low temperatures.60

(B) (A)

Fig. 16 (A) Schematic view of the relative positions of V4þ (s ¼ 1/2) ions (circles) and the exchange coupling scheme in V15. (B) Magnetic energy level scheme of V15 as a function of the external magnetic field. Solid and broken lines show the nearly degenerate two ST ¼ 1/2 branches and the ST ¼ 3/2 branches, respectively.

248

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

(B)

(A)

(C)

Fig. 17 (A) 51V-NMR spectra for the V4þ ions in the triangle observed in its ST ¼ 3/2 ground state at very low temperature for three different resonance frequencies. The inset shows the external field dependence of the resonance frequency for the peak measured below 100 mK. Typical 51VNMR spectra observed in the ST ¼ 1/2 ground states are shown in (B) and (C).

The magnetic levels of V15 at low temperature can thus be described by a simple model spin Hamiltonian H ¼ ðJ12 S1 ,S2 þ J23 S2 ,S3 þ J31 S3 ,S1 Þ þ gmB H,ðS1 þ S2 þ S3 Þ

(20)

where Si are the individual s ¼ 1/2 for each V site and the exchange parameters between spins can be assumed to be equal in first approximation, i.e., J12 ¼ J23 ¼ J31 ¼ J0. The energy scheme at low temperature is given by two degenerate ground states of total spin ST ¼ 1/2 and an excited state of ST ¼ 3/2 which lies  3.8 K above the ground state,61 as shown in Fig. 16(B). In reality, the two ST ¼ 1/2 states are split with a small energy gap which was estimated to be of the order of 0.08 K from magnetization measurements.62 The possible origins for the gap include a small Dzyaloshiskii-Moriya (DM) interaction,63–66 hyperfine interactions67 and lattice distortion.68 In the following, we present NMR data for 51V nuclei (I ¼ 7/2 and gN/2p ¼ 11.193 MHz/T) in polycrystalline powder samples in the T range 0 0.1 K T 300 K using a 3Hee4He dilution refrigerator (Kelvinox MX100, Oxford instruments) installed at Hokkaido University and also at the Ames Laboratory by the author.

9.10.4.1.2

51

V NMR inV15

Fig. 17(A) shows the Hext dependence of “on-site” 51V NMR signals which can be observed only below 0.1 K.56,60 Above Hext ¼ 2.7 T, where the ground state of the V15 cluster is ST ¼ 3/2, the 51V NMR spectrum consists of a single peak with fullwidth at half maximum of  5 kOe. The peak position of the spectrum shifts to lower magnetic field with increasing resonance frequency as shown in Fig. 17(A). The resonance frequency f is proportional to the vector sum of the internal field Bint and external field Hext:

(A)

(B)

Fig. 18 External magnetic field dependence of the resonance frequency for the three 51V-NMR signals observed in ST ¼ 1/2 ground state at Hext < 2 T. The solid circles represent the stronger signal (P1) shown in Fig. 17. The solid squares and triangles refer to the other two weaker signals P2 and P3, respectively, shown in Fig. 17. The high field data in Fig. 17 have been replotted here for comparison. The solid lines show the fitting results using Eq. (21). The inset shows a schematic view of the expectation values for the spin moment for S1, S2 and S3 sites of the triangle according to the eigenfunctions: (A) ja, (B) jb.

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements f¼

gN ðHext þ Bint Þ 2p

249

(21)

where gN/2p ¼ 11.193 MHz/T is the gyromagnetic ratio of the 51V nucleus. By fitting the data points in the field above 2.7 T, as shown in the inset of Fig. 17(A), Bint is estimated to be  7.6 T. The internal field at the nuclear site in a V4þ ion with s ¼ 1/2 is dominated by the core polarization mechanism which induces a large negative internal field of the order of 100 kOe/mB at the nuclear site.69 The value of  76 kOe is close to the value of  85 kOe reported in VO2.70 Thus this 51V signal can be assigned to V4þ ions with an almost full spin moment of 1 mB. In addition, the good fitting result shown by the solid line in the inset of Fig. 17(A) indicates the direction of the spin moments is parallel to the external field. Thus we conclude that each V4þ ion on the triangle has almost the full spin moment of 1 mB in the direction parallel to the external field, which gives the total spin ST ¼ 3/2 state for the ground state of the V15 cluster above Hext ¼ 2.7 T. This is microscopic evidence of the spin structure of the V15 cluster for the ST ¼ 3/ 2 ground state. On the other hand, three different V sites (P1, P2 and P3) are observed in the case of the ST ¼ 1/2 ground state below Hext ¼ 2.7 T as shown in Fig. 17(B) and (C). The external field dependence of those peak positions are plotted as circles, squares and triangles in Fig. 18. By fitting these data using Eq. (21), the internal fields for three V sites are estimated to be  7.5 T,  4.5 T and 2.5 T for P1, P2 and P3, respectively. Assuming the hyperfine field for the V4þ ions in V15 due to the core polarization is  7.6 T for s ¼ 1/2, spin moments on each V4þ site can be estimated to be  1 mB, 0.6 mB and  0.33 mB for P1, P2 and P3, respectively, where the positive and negative signs of the spin moments correspond to the parallel and antiparallel directions with respect to the external field, respectively. Thus, very interestingly, the 51V NMR measurements evidence that there are at least three different states of the V ions in V15 in its ST ¼ 1/2 state.

9.10.4.1.3

Magnetic ground state of the isolated triangular AFM V15

Now, to discuss the magnetic ground state of the isolated triangular antiferromagnet V15, we compare the above experimental findings with the theoretical predictions. For the simple spin Hamiltonian given in Eq. (20), the two degenerate ST ¼ 1/2 ground states can be expressed by  1  fa ¼ pffiffiffi j[YYi þ ujY[Yi þ u2 jYY[i 3  1  fb ¼ pffiffiffi j[YYi þ u2 jY[Yi þ ujYY[i 3

(22)

where the basis functions of | S1 S2 S3i in which up and down arrows represent up and down spin, respectively, for Sn and u ¼ e2pi/3. These two eigenfunctions correspond to two different chiral spin states in which the V4þ spin rotates 120 degrees with respect to neighboring spins in clockwise and counterclockwise directions, respectively, on the triangle. Other eigenfunctions for the same Hamiltonian can be obtained by making linear combinations of the basis functions. The two functions below are also eigenfunctions for the ST ¼ 1/2 frustrated spin state: 1 ja ¼ pffiffiffi ðjYY[i  jY[YiÞ 2 1 jb ¼ pffiffiffi ð2j[YYi  jY[Yi  jYY[iÞ: 6

(23)

Although the total spin moment for both sets of eigenfunctions (Eqs. 22, 23) is ST ¼ 1/2 (1 mB) as required, the expectation values for local spin moments for S1, S2 and S3 site are estimated to be 1 mB, 0 mB and 0 mB for the ja wavefunction and  1/ 3 mB, 2/3 mB and 2/3 mB for the jb, respectively, as schematically shown in the inset of Fig. 18. On the other hand, the expectation values for the local spin moments for the fa and fb eigenfunctions in Eq. (22) are calculated to be 1/3 mB for each spin. Since experimentally three V4þ ions in the ST ¼ 1/2 ground state with different spin moments (1 mB,  1/3 mB and 2/3 mB) are observed, we conclude that the two eigenfunctions to be associated with the two ST ¼ 1/2 ground states can be expressed by ja and jb. Each of the two eigenfunctions should be assigned to one of the two quasidegenerate ST ¼ 1/2 ground states. Since the measurements were performed at a temperature smaller than the splitting of the two quasi-degenerate states the lower energy state is more populated and thus should yield a greater NMR signal intensity. Since we observe a larger signal intensity for the 51V NMR signal arising from a V4þ moment of 1 mB (see the inset in Fig. 18) we conclude that the lower energy of the two ST ¼ 1/2 states correspond to the eigenfunction ja (see the inset (A) in Fig. 18). The other two weak 51V NMR signals [see Fig. 17(C)] arise from V4þ ions with moments ( 1/3 mB and 2/3 mB) and correspond thus to the eigenfunction jb [see the inset (B) in Fig. 18] pertaining to the higher energy ST ¼ 1/2 state. These conclusions from NMR measurements are in agreement with spin densities calculations.71 Thus, it is important to emphasize that the NMR measurements determine the eigenfunctions for the ST ¼ 1/2 ground state in the V15.

250

Nmr of magnetic materials: Determination of magnetic structures by “on-site” nmr measurements

Fig. 19 55Mn NMR spectra in Mn12 cluster measured at H ¼ 0 and T ¼ 1.5 K. Solid lines in the figure are the results of simulations and the solid curves are the estimated spectrum for each Mn site with appropriate magnetic broadenings. The inset shows the structure of Mn12 cluster and orientation of the Mn moments in the ground state according to the standard picture.

9.10.4.2 9.10.4.2.1

Ferrimagnetic nanomagnet Mn12 (Refs. 72, 73) Background of Mn12

[Mn12O12(CH3COO)16(H2O)4] (henceforth abbreviated as Mn12) is one of the most investigated molecular magnets and the first where quantum tunneling phenomena have been reported.50,51 The inset of Fig. 19 shows the core structure of Mn12, where three symmetry inequivalent Mn sites are present: Mn(1) form a tetrahedron at the center of the cluster while Mn(2) and Mn(3) occupy sites on the outside. It is widely believed that the inner four Mn(1) ions are in the Mn4þ ionic state with S ¼ 3/2 while the Mn(2) and Mn(3) are in the Mn3þ (S ¼ 2) state. Magnetization measurements indicate that the magnetic ground state of the cluster is a total high spin S ¼ 10 state where the four inner Mn4þ spins (S ¼ 3/2) are directed antiparallel to the eight Mn3þ spins (S ¼ 2).74,75 The polarized neutron diffraction measurements76 have confirmed this model for the low temperature ground state magnetic structure. The S ¼ 10 ground state of the cluster can be described by a simple model spin Hamiltonian. H ¼  DS2z  BS4z þ gmB Hext ,S;

(24)

where D  0.6 K and B  1.1 mK are anisotropy parameters. The negative values of the anisotropy terms correspond to a large energy barrier for the reorientation of the S ¼ 10 spin, giving rise to a superparamagnetic behavior at low temperature80 The last term in Eq. (24) describes the Zeeman interaction whereby the direction of the external magnetic field with respect to the easy axis (c axis) is important for observations of QTM phenomena.81 77–79

9.10.4.2.2

55

Mn NMR in Mn12

We have succeeded in observing “on-site” 55Mn NMR signals in zero external field, which are shown in Fig. 19. The narrow low frequency line (P1) originates from the Mn4þ ions, while the two broader lines (P2 and P3) are from the Mn3þ ions whereby the broadening of the latter two lines is of quadrupole origin.72 The solid lines in the figures show the results of spectrum simulations with appropriate quadrupole interactions with the dominant Zeeman interaction due to hyperfine magnetic interaction.72 A detailed discussion of the hyperfine magnetic and quadrupole interactions which account for the observed NMR spectrum in Fig. 19 has been reported in the papers by Goto et al.82 and Kubo et al.83 Now we show the external field dependence of the 55Mn NMR spectrum, which successfully reveals the ferrimagnetic spin arrangement of the Mn ions in the ground state of Mn12. This can be done in an oriented powder sample (prepared using Stycast 1266 under Hext ¼ 9 T at room temperature) by measuring the position of the three lines in the spectrum as a function of an external magnetic field applied parallel and perpendicular to the easy anisotropy axis z of the molecule. The shift of the three lines (P1, P2, P3) versus applied field is shown in Fig. 20(A) and (B) for parallel and perpendicular orientations, respectively. In the case of parallel orientation, P1 (pertaining to Mn4þ ions) shifts to higher frequency with increasing field while the other two peaks P2 and P3 (pertaining to Mn3þ ions) shift to lower frequency. Since the resonance frequency f is proportional to the vector sum of the internal field and the external field, f ¼ (gN/ 2p) (Bint þ Hext), this result indicates that the direction of the internal field at the nucleus in Mn3þ is opposite to that in Mn4þ

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(A)

(B)

Fig. 20 (A) Parallel field dependence of resonance frequency for each 55Mn-NMR peak measured at T ¼ 1.5 K. (B) Transverse field dependence of resonance frequency for each 55Mn-NMR peak measured at T ¼ 1.5 K. The solid lines show the calculated results according to Eq. (25). The inset shows the calculated transverse field dependence of transverse magnetization with a set of parameters of D ¼ 0.6 K, B ¼ 1.1 mK and T ¼ 1.5 K.

ions. Since Bint is dominated by the core polarization,72,73 the Bint is negative and the direction of the internal fields at nuclear sites is opposite to that of the Mn spin moment. From the behavior of the resonance frequency as a function of external field in Fig. 20(A), one can conclude that the spin direction of the Mn4þ ions is antiparallel to the external magnetic field (i.e., easy axis), while that of Mn3þ ions is parallel to the external field. This is a direct confirmation of the ferrimagnetic spin structure for inner magnetic structure of the cluster shown in the inset of Fig. 19. In the case when the external magnetic field is applied perpendicular to the easy axis (which is the common axis of the oriented powder), the field dependence of the resonance frequencies is the one shown in Fig. 20(B). As described above, the resonance frequency is proportional to the effective internal field at the nuclear site, which is the vector sum of Bint due to spin moments ! ! ! ! and Hext due to the external field, i.e., rH eff r ¼ r B int þ H ext r. Thus the opposite field dependence of rH eff r for Mn4þ and 3þ 4þ 3þ Mn ions indicates that the direction of Mn spin moments is antiparallel to that of Mn spin moments. This leads to the conclusion that the individual spin moments of both Mn4þ and Mn3þ ions do not cant independently along the direction of the transverse field but rather rotate rigidly maintaining the same relative spin configuration at least up to 15 T, the highest field investigated. ! To analyze the experimental results more quantitatively, we have calculated the transverse field dependence of rH eff r as has been described in the previous sections. Under the effect of the transverse magnetic field, the direction of Bint does not coincide with the easy-axis because of the canting of the total magnetization (S ¼ 10) due to the field (see Fig. 20). The canting angle, q, between the easy axis and the direction of the magnetization can be expressed as q ¼ sin 1(Mt/Ms) where Ms is the saturation magnetization of the S ¼ 10 ground state. The transverse field dependence of sin q can be obtained by calculating the transverse magnetization Mt using the spin Hamiltonian Eq. (24). The calculated Mt/Ms is shown in the inset of Fig. 20(B). Using the calculated sinq ¼ Mt/Ms, the transverse field dependence of r Heff r at Mn sites can be obtained from qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! ! ! (25) rH eff r ¼ r B int þ H ext r ¼ B2int þ H2ext þ 2Hint Hext sinq;

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(A)

(B)

Fig. 21 (A) Time evolution of 1H NMR spectrum measured at 30.801 MHz and T ¼ 2.4 K in Mn12. The spectrum at the bottom corresponds to the thermal equilibrium state. The 2nd lowest spectrum corresponds to the off-equilibrium situation following the field inversion. The remaining spectra from bottom up are taken at different times after the field inversion. (B) Field dependence of the relaxation time s(H) for magnetization measured at T ¼ 2.4 K by: (C) 1H NMR (>) SQUID.

where the sign of Bint is taken to be negative for Mn3þ ions and positive for Mn4þ ions, respectively. The solid lines in Fig. 20(B), representing the calculated field dependence of resonance frequency for each site, are in excellent agreement with the experimental results. We may thus conclude that the ferrimagnetic spin state of the Mn12 cluster corresponding to S ¼ 10 spin state is not destroyed by the transverse magnetic field and that the model spin Hamiltonian describing the S ¼ 10 ground state works even in high transverse fields.

9.10.4.2.3

Time dependence of 1H NMR in Mn12: Determination of the relaxation time of magnetization

In the following, we show an interesting application of NMR spectrum measurements for the superparamagnetic relaxation-time measurements of the magnetization in Mn12 from the time dependence of the NMR spectrum, although it is proton NMR, not “on-site” Mn NMR.84 We have seen above that, in the 55Mn NMR spectrum at low temperatures in Mn12, the position of the 55Mn-NMR resonance lines depend upon the internal field due to the magnetization of the molecule. This is true even for 1H NMR spectra where several lines with different positions (due to different internal fields) are observed as shown in Fig. 21(A). If an external field is also applied, the position of the line depends on the vector sum of the external field and the internal field, the latter being directed along the magnetization of the molecule. If the direction of the external field is suddenly reversed (or the sample is flipped by 180 ) the position of the NMR line changes in the new off-equilibrium situation. The intensity of that particular line starts from zero and grows back to the full intensity as the magnetization of the molecule relaxes back to equilibrium along the applied field. Thus, one can measure the relaxation time of the magnetization by following the signal intensity after the inversion of the magnetic field. The magnetization of the Mn12 clusters is initially prepared in equilibrium conditions with the magnetic field along the easy axis. By inverting the magnetic field one creates an off-equilibrium conditions whereby the magnetization of each molecule wants to realign along the external field (Sz ¼  10 to Sz ¼ þ 10 transition). At low temperatures and in magnetic fields less than 1 T, this process is prevented by the crystal field anisotropy and proceeds very slowly via spin tunneling and phonon assisted relaxation.85 Fig. 21(A) shows the experimental results. The 1H-NMR spectrum at the bottom of Fig. 21(A) corresponds to the thermal equilibrium state before the inversion, where the easy axis of the clusters is along the magnetic field. Just after the inversion of direction of the sample, the observed spectrum changes drastically as shown in 2nd spectrum from the bottom of Fig. 21(A). In the figure, the time evolution is from the bottom to up. Since the spectra were obtained by sweeping the magnetic field which takes about 30 min, each spectrum does not correspond to a precise off equilibrium state.84 However, since the overall process of relaxation of the magnetization at this temperature takes 200 or 300 minutes, the different spectra give a qualitative idea of the evolution of the NMR spectrum in time. The signals of the shifted peaks (e.g., around Hext ¼ 0.35 T) with positive hyperfine fields disappear, while new signals can be observed at magnetic fields higher than the Larmor field H0, where no signal could be detected before the inversion. After a long time (e.g., 400 min for this case), the spectrum becomes independent of time and it recovers the initial shape before the field inversion. In order to investigate the effect quantitatively one can sit at fixed field on one of the shifted lines [see Fig. 21(A)] and follow its amplitude as a function of time without the need to record the full spectrum. The signal intensity for each shifted peak in the spectrum at thermal equilibrium corresponds to the total number of clusters occupying the magnetic

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Sz ¼  10 ground state. Immediately after the 180 rotation of the oriented sample, the state Sz ¼  10 becomes Sz ¼ þ 10. Then the growth of the signal intensity for each peak after the inversion is proportional to the increase of the number of cluster which return to the Sz ¼  10 new ground state. Therefore, we can measure a relaxation time of magnetization by monitoring the echo intensity as a function of time (for actual measurements, we used the peak around Hext ¼ 0.55 T in the spectrum). In Fig. 21(B), the field dependence of the measured relaxation time s(H) by NMR is plotted, together with the data measured directly by monitoring the magnetization with a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS). Although the two sets of data refer to two different ways of extracting the relaxation time from the recovery curves, one can conclude that the results from both methods are in good agreement. In particular, in both cases one sees minima of s(H) at the level crossing fields i.e., Hext ¼ 0 (only for the magnetization), Hext ¼ 0.45 T, and Hext ¼ 0.9 T. These field values corresponding to the minima in the relaxation time agree with critical fields where the quantum tunneling of the magnetization occurs in Mn12. Thus, by measuring the time dependence of NMR spectrum, one can measure the relaxation time of magnetization. The method has been confirmed by measuring the 55Mn NMR spectrum in Mn12,86,87 with results very similar to the ones obtained with proton NMR.84

9.10.4.3

Summary

In this subsection, we have shown that NMR measurements clearly determine the ferrimagnetic spin structure in Mn12 and also determine the eigenfunction of the ground state of the isolated triangular antiferromagnet V15. To our knowledge, this is the first time to determine directly and experimentally the eigenfunctions for an isolated triangular antiferromagnet, a basic unit of frustrated spin system, showing the powerfulness of NMR technique. In addition, we also presented that the superparamagnetic relaxation-time measurements of the magnetization can be measured from a microscopic point of view by monitoring the time evolution of NMR spectrum.

9.10.5

Magnetic-field control of domains in magnetic materials

In this section, we describe how “on-site” NMR measurements provide direct evidence of how the population of magnetic domains can be controlled by the application of magnetic fields in magnetic materials. The example presented here is EuFe2As2 which is one of the mother materials of iron-based superconductors. In the following, we describe the results of NMR measurements in the compound.

9.10.5.1 9.10.5.1.1

Detwinning in EuFe2As2 (Ref. 88) Background of EuFe2As2

The discovery of iron-based superconductors triggered intense activity in the research field of so-called “electronic nematicity” which can be identified in the orthorhombic structure where the magnitude of the electronic anisotropy cannot be simply explained by the effect of the orthorhombic lattice distortion.6,89,90 Measurements of the intrinsic in-plane physical properties to clarify the characteristics of electronic nematicity are usually hampered by twin formation in nematic state. Up to now, two distinct methods have been mainly employed to detwin the crystals: The application of uniaxial strain91–99 and the application of an in-plane external magnetic field (Hext).100,101 However, both methods may obscure the intrinsic properties of the compounds. For example, uniaxial strain may change the nematic and magnetic transition temperatures.95 In addition, relatively high Hext is required to complete the detwinning (e.g.,  27 T for Ba(Fe1–xCox)2As2 (Ref. 100)), although a change in the relative twin population can be produced by a smaller in-plane Hext (e.g.,  14 T for Ba(Fe1–xCox)2As2 (Ref. 101)). On the other hand, interestingly, it is shown that a small inplane Hext, less than 0.5 T, is enough to complete the detwinning in EuFe2As2. Different from most non-rare-earth bearing so-called 122 iron-based superconductors, EuFe2As2 exhibits two magnetic phase transitions.102,103 The first magnetic ordering state below  189 K is the stripe-type AFM state due to the Fe moments with a concomitant first-order structural phase transition to a low-temperature orthorhombic structure corresponding to the nematic transition. The second one below 19 K is associated with Eu2þ moments, making an A-type AFM structure where the Eu moments are ferromagnetically aligned in the ab plane but the moments in adjacent layers along the c axis are antiferromagnetically aligned,102 as shown in Fig. 22(A). A realignment of the twinning structure by in-plane Hext has been first observed in a singlecrystal neutron diffraction measurement.104 A detailed study of EuFe2As2 using resistivity, thermal-expansion, magnetostriction, magnetoresistance, magneto-optical, and magnetization measurements shows that a very low in-plane Hext of only  0.1 T is sufficient for detwinning below the Eu2þ ordering temperature.105 Thus, this detwinning provides a unique way to study the lowtemperature in-plane physical properties of EuFe2As2. A recent microscopic theory with a biquadratic coupling between the Eu and Fe spins has been proposed to explain the detwinning process in this compound.106 According to the theory, the detwinning can be initiated by the application of a small in-plane Hext less than 0.1 T and then a complete detwinning can be attained at the first detwinning magnetic field H1 around 0.3–0.5 T where only one domain remains. With further application of Hext, a part of the domain spontaneously rotates by 90 where the angle between Hext and the Eu spins is proposed to change from 55 to 25 due to the existence of the biquadratic magnetic interaction106 whereas a simple spin-flip is expected without the interaction.105 Furthermore, the theory proposes that the population of

254

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(A)

(B)

Fig. 22 (A) The crystal and spin structures of EuFe2As2 in the orthorhombic phase under zero Hext. (B) 153Eu-NMR spectrum for Hext ¼ 0 at 4.3 K. The red lines are the calculated 153Eu-NMR spectrum.

the new domain increases with increasing Hext and the new domain dominates at the second detwinning magnetic field H2 around 1 T. Therefore, it is important to investigate the details of how the angles between Eu and Fe spins change during the detwinning processes so as to test the theory where the biquadratic magnetic interaction has been proposed to play an important role. Below, we describe 153Eu NMR data in the magnetically-ordered state of EuFe2As2 from which one can determine the details of the change of the angles between Eu and Fe spins with the application of Hext. Our NMR results provide direct evidence of the magnetic detwinning for in-plane Hext and also of the existence of a biquadratic magnetic interaction as proposed by the theory.106

9.10.5.1.2

153

Eu NMR in EuFe2As2

Fig. 22(B) shows the “on-site” 153Eu NMR spectrum in zero Hext at 4.3 K in the magnetically-ordered state. The observation of the 153 Eu zero-field NMR signals clearly shows that the magnetic moments of Eu 4f electrons order in the magnetic state. Similar to the other Eu-based compounds discussed in previous sections, the peak positions of the spectrum can be explained by the combination of a large Zeeman interaction (HZ) due to Hext [for the present case, an internal magnetic induction (Bint) at the Eu site] and a small quadrupole interaction (HQ). In this case, as described in Section 9.10.1.2, the resonance frequency f for the transition from Iz ¼ m to m  1 is given by Eq. (10). For simplicity, within first-order perturbation theory,3 f(m 4 m  1) can be written as   1 1  3cos2 q  1 þ hsin2 qcos2f : f ðm4m  1Þ ¼ v0 þ vQ m  2 2 Thus, from spectrum measurements, especially from the spacings between the lines, one can estimate the angles q and f which provide important information about the direction of Bint with respect to the EFG coordinate system. The observed line positions Eu were well reproduced by the calculation, as shown by the red lines in Fig. 22(B), with the parameters rBint r ¼ 27.0 T,   vQ ¼ 40.2 MHz, h ¼ 0.25, q ¼ 90 , and f ¼ 90 . The sign of Bint at the Eu site is considered to be negative because Bint mainly originates from core polarization from 4f electrons and is oriented in a direction opposite to that of the Eu ordered moments.43 Comparable values of Bint at Eu sites were described in the previous sections for the helical antiferromagnets EuCo2As2 (Bint ¼  25.75 T)42 and EuCo2P2 (Bint ¼  27.5 T)33 and the A-type antiferromagnet EuGa4 (Bint ¼  27.08 T).41 Since the Eu ordered moments in those compounds are close to 7 as well as in EuFe2As2, the similar value of Bint ¼  27.0 T suggests that the hyperfine field induced

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by Fe moments at the Eu site is negligible and the dominant contribution to Bint at the Eu site is from the Eu ordered moments. To obtain more information about the principal axes of the EFG at the Eu site, we have calculated the EFG using a point-charge model. We found that the X, Y, and Z axes correspond to the b, a, and c axes in the orthorhombic structure, respectively, and h ¼ 0.28 whose value is close to h ¼ 0.25 estimated from fitting the spectrum. Therefore, the results of both q ¼ 90 and f ¼ 90 indicate that Bint is parallel or antiparallel to the a axis, which is consistent with the magnetic structure under zero Hext shown in Fig. 22(A) determined by the neutron diffraction measurements.102 Fig. 23(A) shows the dependence of the 153Eu spectra on Hext applied parallel to the c axis (Hextkc) in the AFM state at 4.3 K. In the AFM state, one expects a splitting of the NMR line when Hext is applied along the magnetic easy axis, while only a shift of the NMR line without splitting is expected when Hext is applied perpendicular to the magnetic easy axis, for Hext smaller than the magnetocrystalline anisotropy field. Since the magnetic easy axis is parallel to the a axis, we do not expect the splitting of the line for Hextkc, as actually observed. The effective field (Heff) at the Eu site is the vector sum of Bint and Hext, i.e., r Heff r ¼ r Bint þ Hext r. Therefore, utilizing the canting angle q0 of the Eu ordered moment from the a axis to the c axis [see Fig. 23(B)], the Heff can be written qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi as Heff ¼ H2ext þ B2int þ 2Hext Bint sinq0 . Here q0 can be calculated from magnetization data since q0 ¼ sin 1(M/Ms) where Ms is the saturation of magnetization. Fig. 23(C) shows the calculated Hext dependence of q0 for Hextkc from the magnetization data reported in Ref. 107 where we used Ms ¼ 7 mB. It is noted that the quantization axis for the Zeeman interaction points in the direction of Heff which is in general not the same as that of Bint as shown in Fig. 23(B). Using Bint ¼  27 T, we calculated the Hext dependence of Q and q and found that the difference between Q and q0 is less than 2 degrees due to the large value of Bint with respect to Hext for our

(A)

(B)

(C)

Fig. 23 (A) Hext dependence of the 153Eu-NMR spectra of EuFe2As2 for Hextkc at T ¼ 4.3 K. The red lines are calculated spectra with different values of q and Heff under different Hext without changing other parameters: BintEu ¼  27.0 T, vQ ¼ 40.2 MHz, h ¼ 0.25, and f ¼ 90 . (B) Schematic view of the configuration for q and the canting angles of q0 and Q between the magnetization and the quantization axis of Eu nucleus, respectively, from the ab plane in Hextkc. (C) Hextkc dependence of the angles q, q0 and Q estimated from the magnetization data at T ¼ 5 K (Ref. 107) and 0 estimated from 153Eu NMR spectrum measurements.

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experimental region, as shown in Fig. 23(C). Therefore, we approximate q0 Q and used this approximation to estimate q shown in Fig. 23(C) which can be compared with the results of NMR measurements. As shown by the vertical red lines in Fig. 23(A), the observed spectra for Hextkc are well reproduced by changing q and Heff with other parameters unchanged. The Hext dependence of q determined from the NMR spectra is in good agreement with q estimated from the magnetization data [see Fig. 23(C)]. Thus we conclude that the Eu ordered moments change the direction from the a axis to the c axis continuously with increasing Hextkc, and eventually will point to the c axis at higher Hext.

9.10.5.1.3

Magnetic field effects on the domain population in EuFe2As2 under in-plane Hext

When Hext is applied in the ab plane, the 153 Eu NMR spectra show quite different behavior as shown in Fig. 24(A) and (B), which evidence control of the domain populations with Hext as will be discussed below in detail. Here we applied Hext parallel to (110) in the tetragonal structure ([110]T). The notation of the tetragonal structure is rotated by 45 along the c axis with respect to the lowtemperature orthorhombic structure. Thus the [110]T direction is parallel to the a (the direction of Fe spins) or b (perpendicular to the direction of Fe spins) axes in the orthorhombic structure [see Fig. 22(A)]. With the application of small Hext, we found that each line splits into three lines as typically shown in Fig. 24(B). This clearly evidences the existence of two domains. For Hextka, one expects the symmetric splitting of the line because Bint is parallel or antiparallel to Hext, i.e., Heff ¼ Bint  Hext. The Hext dependence of the splitted peak frequencies is shown in Fig. 24(C) where the absolute values of the slopes for the Hext dependence are  4 MHz/T, which is close to the g2pN value of the Eu nucleus. On the other hand, when Hext is parallel to the b axis, any shift in the position would be very small. This is actually observed as shown in Fig. 24(C), thus the line can be assigned to be from the domain with Hextkb axis. Hereafter a domain with the a or b axis along Hext is defined as an “a domain” or “b domain”, respectively. With increasing Hext, the signal intensity of the splitted peaks is reduced, indicating that the population of the a domain decreases. Around 0.3–0.6 T, we observed a set of lines only from the b domain, as typically shown at the second panel from the bottom in Fig. 24(A). This magnetic field of 0.3 T corresponds to the first detwinning field H1 whose value is consistent with the results from a recent magnetization measurement106 and is close to  0.4 T estimated from the neutron diffraction measurement,104 although it is slightly higher than  0.1 T reported from the magneto-optical measurements.105 This detwinning process has been explained as follows: since the b domain (i.e., Hext t Eu ordered moments) is lower in energy than the a domain (Hext parallel or antiparallel to the Eu ordered moments), the b domain can push the a domain out once the energy difference between the domains overcomes the domain boundary pinning energy.105 It is noted that from the spacings between NMR-spectrum lines in Fig. 24(A), one can estimate the angle f for the b domain (fb) which corresponds to the angle between Heff and the b axis. Here f can be approximated by 90  f0 since the angle F is close to the Eu spin’s canting angle (f0 ) in the ab plane [see the inset of Fig. 24(B)], similar to the case of Hextkc. The f value in the b domain decreases from 90 at Hext ¼ 0 to 73 at Hext ¼ 0.5 T, corresponding to the Eu spin canting in the ab plane, as illustrated in Fig. 24(A). This phase with dominant b domain is found to have an Hext range of 0.3–0.6 T, which is consistent with the results reported by other techniques.104–106 When Hext is increased to  0.7 T, another set of lines appears as shown in the middle panel of Fig. 24(A). At the similar Hext of 0.7 T, the magnetization was reported to show a sudden increase,105,107 which was either ascribed to a metamagnetic transition107 or a spin-flip transition.105 However, the recent magnetostriction and magnetotransport measurements suggested that the jump in magnetization is associated with the reorientation of domains.106 According to Maiwald et al., if the biquadratic coupling is finite, the system changes domains from b-type to a-type where the angle between the Eu spins and Hext (fH) changes discontinuously from fH > p/4 in the b domain to fH < p/4 in the a domain.106 This is due to the biquadratic magnetic interaction which makes the angle (b) between the Eu and Fe spins small because the energy is proportional to the square of cosine of b (E f  cos2b).106 Since the Fe spins point along the a axis, the retwinning with discontinuous change in fH due to the domain rotation from the b domain to the a domain can be possible, when the energy gain exceeds the pinning energy of the domain boundary.106 The NMR spectrum at Hext ¼ 0.75 T shows the superposition of two spectra originating from the b domain with fb ¼ 55 and the a domain with fa ¼ 80 , clearly evidencing the reappearance of the a domain, as depicted in right-hand sides of the panels in Fig. 24(A). From the values of fb(¼ fH) and fa(¼ 90   fH), it is found that the fH changes discontinuously from  55 in the b domain to  10 in the a domain at 0.75 T [see Fig. 24(E)]. These values of fH are in good agreement with 55 and 25 estimated from the theoretical calculation.106 Thus we conclude that our NMR data provide direct evidence for the existence of the biquadratic coupling in EuFe2As2. The spectral weight moves from the b domain to the a domain when Hext is increased from 0.7 T to around 1 T, as shown in Fig. 24(A) and (B), showing that the population of the b domain decreases while that of the a domain increases. The b domain nearly vanishes around 1 T, leaving only the a domain at this Hext, as shown in Fig. 24(A), which corresponds to the second detwinning field H2  1 T. These NMR results are also consistent with the theory, evidencing the existence of the biquadratic coupling in the system.

9.10.5.2

Summary

In summary, we presented the results of “on-site” 153Eu-NMR measurements on an EuFe2As2 single crystal, which provides evidence for detwinning under a small in-plane Hext from a microscopic point of view. From the detailed NMR spectrum measurements, the

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(A)

(B)

(C)

(D)

(E)

Fig. 24 (A) Hext dependence of the 153Eu-NMR spectrum for Hextk[110]T at T ¼ 4.3 K. The calculated positions of the spectra for the b and a domains are shown by the arrows in magenta and blue, respectively. The insets show a sketch of the spin directions of Eu (green) and Fe (brown) for the a (blue) and b (magenta) domains. (B) Hext dependence of the central peak of the 153Eu-NMR spectrum for Hextk[110]T. The inset shows a schematic view of the configuration for the angles f, f0 and F in the ab plane for the case of Hextkb. (C) Hext dependence of f of the central transition line for an a domain (blue) and a b domain (magenta). The solid lines are linear fits by f ¼ v0  aHeff with a ¼ 4 MHz/T. (D) Hext dependence of domain population. (E) Hext dependence of the angle fH between Hext and the Eu spins for the a and b domains.

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evolution of the angles between Eu and Fe spins during the detwinning process was also determined, which provides the first experimental evidence for the existence of the biquadratic coupling in the system. Finally, although it is not related to the story of the “on-site” NMR measurements which are the focus of this article, it is interesting to comment on the superconductivity that higher superconducting transition temperatures (Tc) for bulk iron-based superconductors have been observed in rare-earth bearing 1111 (Ref. 108) and 122 (Ref. 109) systems. Since our 153Eu-NMR results in EuFe2As2 indicate that the biquadratic coupling between rare-earth and iron moments exists and has a critical role, the enhancement of Tc could be related to the biquadratic coupling in those systems. Further studies in view of the biquadratic coupling are suggested to understand the origin of the high Tc in those systems, which may also provide some clues about the origin of superconductivity in iron-based superconductors where the biquadratic coupling between the Fe spins is considered to play an important role.110,111

9.10.6

Concluding remarks

We presented a brief overview of the nuclear magnetic resonance studies on magnetic materials, especially focusing on so-called “on-site” NMR measurements which are the measurements of nuclei having finite magnetic moments originating from electron spins. We described the NMR results performed on various magnetic materials such as G-type and A-type antiferromagnets, helical antiferromagnets, molecular nanomagnets, and also describe some interesting cases where NMR measurements reveal how magnetic states or magnetic domains change with the application of magnetic fields. In addition, NMR has been proven to be a unique tool for determining the local spin configuration, antiferromagnetic wave vector characterizing helical antiferromagnets, ground state properties and the eigenfunctions for magnetic materials, furthermore, sometimes for measuring the relaxation time of magnetization by looking at the time evolution of NMR spectrum. Here we mainly presented NMR spectrum data which in general provide the static properties of the magnetism of the materials and we did not touch nuclear spin-lattice and spin-spin relaxation times (so-called T1 and T2). However, of course, those quantities of T1 and T2 as a function of parameters such as temperatures and magnetic fields give us very important information of dynamical properties of the magnetism of the materials from a microscopic point of view. We would like to leave the topics for other review papers. At the end of this article, once again, we would like to emphasize the powerfulness of NMR techniques for the investigation of the static and dynamic properties of the magnetism of materials from a microscopic point of view.

Acknowledgments The author would like to acknowledge precious collaborations and fruitful discussions with David C. Johnston, Paul C. Canfield, Sergey L. Bud’ko, Ken-ichi Kumagai, Ferdinando Borsa, Alessandro Lascialfari, Paul Kögerler, Dante Gatteschi, Takao Goto, Satoru Maegawa, Mikhalev Konstantin, Vasily Ogloblichev, Nonoka Higa, Mamoru Yogi, Koji Watanabe, Yusuke Nishisaka, Yuichi Hatanaka, Steven Yaninas, Jin-fang Cui, Paul Wiecki,  Masato Hedo, Takao Nakama, and Yoshichika Onuki. We also would like to thank other collaborators whose name appear in the many papers cited in this article. Special thanks go to Qing-Ping Ding and Khusboo Rana for not only their collaborations but also their critical reading of this manuscript. The NMR work performed at Hokkaido University in Japan was supported by 21st Century COE Programs “Topological Science and Technology” at Hokkaido University and Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology of Japan. The work at Ames Laboratory was supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering. Ames Laboratory is operated for the U.S. DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

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9.11 Solid-state nmr studies of halide perovskite materials with photoconversion potential Guy M. Bernard, Abhoy Karmakar, and Vladimir K. Michaelis, Gunning-Lemieux Chemistry Centre, University of Alberta, Edmonton, AB, Canada © 2023 Elsevier Ltd. All rights reserved.

9.11.1 9.11.1.1 9.11.1.2 9.11.2 9.11.2.1 9.11.2.2 9.11.2.3 9.11.2.4 9.11.2.5 9.11.3 9.11.3.1 9.11.3.2 9.11.3.3 9.11.3.3.1 9.11.3.3.2 9.11.3.3.3 9.11.3.3.4 9.11.4 9.11.4.1 9.11.4.2 9.11.4.2.1 9.11.4.2.2 9.11.4.3 9.11.4.4 9.11.5 Acknowledgments References

Introduction Historical background Emerging interest Solid-state NMR spectroscopy: Background Magnetic shielding Isolated spin pairs: The direct dipolar interaction The quadrupolar interaction: Non-integer spin quadrupolar nuclei Indirect spin-spin interactions: Impact of quadrupolar coupling SSNMR spectroscopy of I ¼ 1 nuclei: Investigations of molecular dynamics SSNMR studies of perovskites Why SSNMR for perovskite studies? Early SSNMR studies of perovskites SSNMR studies of fundamental properties Dynamics Structure/property relationships via SSNMR SSNMR spectroscopy of the halogens Beyond ABX3: SSNMR studies of double perovskites Advanced SSNMR techniques Maximizing the SSNMR response Enhancement techniques Cross polarization Enhancements for quadrupolar nuclei Wide line NMR spectra for solids Dynamic nuclear polarization (DNP) Concluding remarks

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Abstract With the ongoing intense interest in metal halide perovskite materials due to their excellent optical and electrical properties, solid-state NMR (SSNMR) spectroscopy has become an essential local structural tool for perovskite researchers. Key background SSNMR concepts are presented to aid investigators in the interpretation of the NMR data. This is followed by an overview of the important papers discussing SSNMR studies of perovskites, focusing on those published in the past 5 years. Enhancement techniques that permit acquisition of NMR spectra of challenging nuclei, or those that are dilute in the material of interest due to doping or alloying, are discussed. Finally, the potential application of recently developed advanced techniques that may permit SSNMR investigations involving more challenging nuclei are discussed.

9.11.1

Introduction

9.11.1.1

Historical background

In 1839, the German mineralogist Gustav Rose discovered the mineral CaTiO3 in the Ural Mountains of Russia,1 and named the mineral in honor of the Russian mineralogist Lev Perovski. Its crystallographic structure was first described by Victor Goldschmidt in 1926.2 In 1893, H. L. Wells prepared a series of cesium lead halide compounds with structures that were later determined to have the perovskite structure.3 Hence, the term “perovskite” has come to be applied to an entire class of compounds that share the perovskite structure.4 Although initially assumed to be a cubic structure, it was recognized early on that most perovskites, including CaTiO3 itself, have structures that deviate slightly from the cubic structure.5 In 1945, Helen Megaw determined the structure of BaTiO3 using X-ray crystallography.6 In this publication, the author noted that although barium titanate has a tetragonal structure at room

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temperature, this represents a small modification from the ideal cubic structure that perovskites were initially thought to hold; however, a cubic structure was verified by this author at 200  C. The 1960s and 1970s brought what may be considered the “first wave” of excitement about these materials,7 as their potential in applications such as ferroelectricity8 or superconductivity9 was investigated. Interesting in the context of the current excitement about the photoconversion potential of perovskites, discussed in the following section, is the 1958 study by Møller.10 The intense colors of the CsPbX3 (X ¼ Cl, Br, I) perovskites prompted the author to investigate their photoconductivity. The halide perovskites considered here adopt the general formula ABX3, where A is a monovalent cation, B is a divalent cation and X is a halogen anion. The A-site cation is located within the cuboctahedron while the B-site cation is coordinated to six X-site anions in an approximate, or in the case of cubic symmetry, an exact octahedral arrangement11 (Scheme 1). If divalent B(II) sites within the ABX3 perovskite structure are replaced by a combination of monovalent B0 (I) and trivalent B00 (III) cations, then a double perovskite structure (A2B0 B00 X6) is formed,12 as shown in Scheme 1C.

9.11.1.2

Emerging interest

Interest in halide perovskites spiked in 2009 when Kojima et al. reported photoconversion efficiencies (PCEs) of 3.13% and 3.81% for CH3NH3PbBr3 and CH3NH3PbI3, respectively.13 As seen in Fig. 1A, the annual literature citations for perovskite articles have nearly tripled since this discovery. Perhaps not surprisingly, the trend in literature citations since this initial report has mimicked the improvements in PCE over the same period (Fig. 1B). Indeed, the intense interest in perovskites has been described as “Perovskite Fever”!18 With ongoing concerns about the impact of fossil fuels on climate, the “fever” will surely not abate soon. Besides their promising PCE, perovskites also have potential in other applications, such as light-emitting devices,19,20 photodetectors,20 lasers,21 X-ray detection,22,23 g-ray detection,23 or water splitting.24 In 2017, our lab demonstrated that the high sensitivity and linear response of the 207Pb chemical shift to temperature for MAPbCl3 makes it an ideal sample for NMR thermometry in the 178 to 410 K range.25 Perovskites may also find use as part of the solution for off-grid battery devices.26 The adaptability of perovskites to multiple applications as well as its remarkable improvement in PCE from approximately 4% to 25%17 in such a short time may be attributed to the ability to finely tune the material’s optical and electronic properties.27 Initial synthetic work tended to be “hit and miss” as these researchers did not possess the tools to identify and modify structural parameters that impact the physical properties of perovskites. Although many structural characterization techniques have been employed to study perovskites, those based on diffraction have been used most frequently; however, these are limited to providing average long-range structural information. That, of course, is invaluable information, but it is not the complete picture. By providing key information on atomic-level structure and dynamics, solid-state nuclear magnetic resonance (SSNMR) spectroscopy28–37 helps complete the picture; in particular, X-ray diffraction (XRD) does not always inform on the short- and medium-range structural differences in, for example, the case of doped or mixed-ion perovskites that may cause phase inhomogeneity or nanodomains. In this article, an overview of the application of SSNMR spectroscopy to the investigation of perovskite-based metal-halide materials is presented, with an emphasis on papers published in the past 5 years, although some older work is also discussed for a historical background. Table 1 summarizes the NMR properties of nuclei commonly observed in SSNMR studies of halide perovskites.

9.11.2

Solid-state NMR spectroscopy: Background

A major benefit of SSNMR spectroscopy is that it provides information on the local atomic-level structure and dynamics of the material of interest non-destructively. A detailed presentation of NMR theory is beyond the scope of this article, but a discussion of the relevant properties is presented below. Readers are highly encouraged to review the numerous textbooks40–43 or articles,44 as well as online resources45 for further details. The equations below focus on isotropic (i.e., average) interactions, but it is important for readers to understand that NMR parameters such as magnetic shielding and spin-spin interactions are tensor properties46 and thus the observed interaction depends on the orientation of a given tensor relative to the applied magnetic field, B0. In addition,

Scheme 1 (A) Unit cell for a typical ABX3 halide perovskite in the cubic phase and (B) its long-range structure. In (C), the long-range structure of an A2B0 B00 X6 double perovskite is shown.

Solid-state nmr studies of halide perovskite materials with photoconversion potential

263

Fig. 1 Annual published perovskite papers (A), based on a search for the term “perovskite”, for the 2008–20 period.14 (B) illustrates the evolution of reported perovskite photoconversion efficiencies in the 2009–20 period. (B) was prepared from data reported in Refs. 13,15–17.

when more than one tensor is at play, such as may be encountered if a quadrupolar nucleus is subject to both chemical shift anisotropy (CSA) and an electric field gradient (EFG), the relative orientations of these two tensors also impact the line shape.

9.11.2.1

Magnetic shielding

The Larmor frequency, nL, for a given nucleus is given by: nL ¼

gB0 2p

(1)

where g is the magnetogyric ratio for the nucleus of interest. For most SSNMR applications, the sign for nL is ignored. Thus, the observed frequency for a nucleus is dependent on the magnitude of B0. The frequency for the sample, nsample, is perturbed from nL by the local magnetic environment of the observed nucleus, described by the absolute shielding,47 s: nsample ¼ nL ð1  sÞ

(2)

Typically, NMR spectroscopists report a chemical shift, d, based on the difference between the frequency for the sample of interest and that for a standard reference compound, nref.

Table 1

NMR properties for nuclei observed in halide perovskite studies.a

Isotope

I

NA/%

X/% b

Q/fm2

1

1/2 1 1/2 1 1/2 3/2 3/2 3/2 3/2 3/2 3/2 1/2 1/2 5/2 7/2 1/2 1/2

99.9885 0.0115 1.07 99.632 0.368 75.78 24.22 93.2581 50.69 49.31 27.83 12.22 8.59 100 100 70.476 22.1

100.000000 15.350609 25.145020 7.226317 10.136767 9.797909 8.155725 4.666373 25.053980 27.006518 32.720454 22.193175 37.290632 20.007486 13.116142 57.683838 20.920599

– 0.285783c – 2.044 – 8.112c 6.393c 6.03c 30.87c 25.79c 13.35 – – 68.822c 0.343 – –

H H 13 C 14 N 15 N 35 Cl 37 Cl 39 K 79 Br 81 Br 87 Rb 113 Cd 119 Sn 127 I 133 Cs 205 Tl 207 Pb 2

a

Unless otherwise noted, values in Table 1 are those given in Ref. 38. The frequency of the reference compound for the given nucleus, relative to 1H of tetramethylsilane (TMS) at infinite dilution (in practice, < 1% V/V in CDCl3), at 100 MHz.38 c Ref. 39.

b

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Solid-state nmr studies of halide perovskite materials with photoconversion potential nsample  nref d¼ nref


(3)

d is typically given in ppm (i.e., multiply the numerator by 106). Although most NMR spectroscopists report chemical shifts according to Eq. (3), an important consideration, particularly if computational NMR is a part of the study, is the magnetic shielding, s, that one obtains from computations; these values may be converted to chemical shifts according to:

sref  s
z sref  s d¼ (4) 1  sref Note that the approximate definition on the right of Eq. (4) is suitable for nuclei with relatively small chemical shift ranges (and hence 1  sref z 1), but significant errors may occur for nuclei with large chemical shift ranges such as 119Sn and 207Pb if the full equation is not used. When obtaining NMR spectra of solutions or of high-frequency magic-angle spinning (MAS) samples (Fig. 2A), a single peak is observed for an isolated spin-½ nucleus at a crystallographically distinct NMR site, designated by the isotropic chemical shift (diso). However, non-spinning or slow MAS NMR spectra reflect the orientation dependence of magnetic shielding, defined by the principal components of the chemical shift tensor, d11  d22  d33. For NMR spectra of isolated spin-½ nuclei, these generally correspond to the high- and low-frequency shoulders of the spectra (d11 and d33, respectively, while the discontinuity corresponds to d22 (Fig. 2C)). When considering spectra of isolated spins, special cases are if d11 ¼ d22 ¼ d33, yielding an isotropic peak (Fig. 2A), or if either d11 ¼ d22 or d22 ¼ d33, yielding axially symmetric powder patterns as illustrated in Fig. 2D and E, respectively;

Fig. 2 Simulated SSNMR spectra for an I ¼ ½ nucleus with nL ¼ 100 MHz (e.g., 13C at 9.4 T or 1H at 2.35 T). All spectra were simulated with diso ¼ 0 (indicated with a red dotted line) and U ¼ 200 ppm. (A) illustrates the spectrum expected for an isolated spin with an MAS frequency that is much greater than the span; the same spectrum is obtained without sample spinning if d11 ¼ d22 ¼ d33 (i.e., U ¼ 0). Trace (B) illustrates the spectrum expected for a spin-½ nucleus with k ¼ 0 and with a spinning frequency of 2.0 kHz. Traces (C), (D) and (E) illustrate NMR spectra without sample spinning for isolated spin-½ nuclei with k ¼ 0, þ1 and 1, respectively. Trace (F) illustrates an NMR spectrum for a non-spinning sample containing a homonuclear spin-½ pair with RDD ¼ 2.0 kHz and with a ¼ b ¼ 0; (G) used the same parameters as (F) except b ¼ 90 , while for (H), a ¼ b ¼ 90 . Trace (I) illustrates the spectrum for a spin-½ nucleus spin-coupled to an I ¼ 5/2 nucleus (e.g., 17O, 127I, etc.), with RDD ¼ 2.0 kHz and without sample spinning. The principal components of the chemical shift tensor are indicated in (C) as an example. Spectra were simulated with the WSolids program.48

Solid-state nmr studies of halide perovskite materials with photoconversion potential

265

a 13C spectrum of solid acetylene at natural abundance, for example, would yield a powder pattern similar to that illustrated in Fig. 2D. Note that if the MAS frequency is much less than the breadth of the spectrum, than the NMR spectrum breaks into a series of spinning side bands (SSBs), the manifold of which emulates the powder pattern for a non-spinning sample (compare Fig. 2B and C). To describe the chemical shift tensor, it is convenient to use the diso as well as the span, U and the skew, k49: d11 þ d22 þ d33 3

diso ¼

U ¼ d11  d33 k¼

3ðd22  diso Þ U

(5) (6) (7)

Note that this approach, referred to as the Maryland convention, is not universally employed within the SSNMR community and thus, it has been recommended that regardless of which convention used to describe the chemical shift tensor, one should also report the principal components.50

9.11.2.2

Isolated spin pairs: The direct dipolar interaction

There are two spin-spin interactions that NMR spectroscopists concern themselves with: the indirect (i.e., J) coupling, and the direct dipolar interaction.51 The observed splitting pattern arising from the indirect interaction may be impacted by the quadrupolar interaction; this case is considered below. The direct spin-spin interaction, commonly referred to as the dipolar interaction, RDD, yields valuable structural information, since the magnitude of this interaction is inversely related to the cube of the separation between the coupled nuclei51: RDD ¼

 m0 Z g g r 3 4p 2p A B AB

(8)

where m0 is the permeability constant, Z is the Planck constant divided by 2p, gA and gB are the magnetogyric ratios for the coupled spin pair and rAB is the internuclear separation between these nuclei; the angular brackets about the latter term indicate that this is a motionally averaged value. For nuclei subject to significant indirect spin-spin coupling, one measures an effective dipolar coupling, Reff: Reff ¼ RDD 

DJ 3

(9)

where DJ is the anisotropy in the J coupling. Although DJ is difficult to measure, it is important to be aware of this factor if deriving structural information from the dipolar interaction. When nuclei are impacted by two or more interactions (magnetic shielding and the direct dipolar coupling for the case considered in this section), then the observed line shape depends on the relative orientations of these two tensors.52,53 The relationship between tensors is typically described by the Euler angles a, b and g which describe the rotation of one axis system into another.53 As for the notation describing chemical shift tensors, there is not universal agreement on how to describe these rotations, so it is important when using simulation software to ascertain the convention used by the programmers. Figs. 2F–H illustrate the impact of the dipolar interaction on the powder pattern for a non-spinning sample and how different relative orientations of the chemical shift and dipolar tensors impact the line shape. Here, a and b may be treated as polar angles (i.e., a simplified case of Euler angles), with a describing the projection of the dipolar vector with respect to the plane described by d11 and d22, and b describing the orientation of the dipolar vector with respect to d33; note that the case is more complicated if all three Euler angles are required to describe the tensor orientation (e.g., the relative orientations of two magnetic shielding tensors for nuclei of a dipolar-coupled spin pair).

9.11.2.3

The quadrupolar interaction: Non-integer spin quadrupolar nuclei

The nuclear quadrupolar interaction, describing the interaction between the electric field gradient (EFG) and the non-spherical charge distribution of quadrupolar nuclei, is an important consideration for SSNMR studies, since over 70% of magnetically active stable isotopes have a nuclear spin I > ½.54,55 Thus the nuclear quadrupole moment, Q, that describes the nature of the charge distribution, is an important consideration when undertaking NMR studies of quadrupolar nuclei. The interaction between the EFG and the quadrupolar nucleus gives rise to a quadrupolar coupling constant, CQ; this term and the nuclear quadrupolar frequency, nQ, are given by: e2 qZZ Q h

(10)

3CQ 2Ið2I  1Þ

(11)

CQ ¼ nQ ¼

266

Solid-state nmr studies of halide perovskite materials with photoconversion potential

where e is the electron charge, eqZZ ¼ VZZ is the largest magnitude component of the EFG, h is Planck’s constant and I is the nuclear spin number. The EFG tensor is traceless, and thus may be described by two parameters, VZZ and the asymmetry, h, in the EFG tensor: h¼

VXX  VYY VZZ

(12)

Quadrupolar nuclei at a site of high symmetry (i.e., Td or Oh) do not experience an EFG and thus behave essentially as I ¼ ½ nuclei. However, nuclei with large Q values that experience a significant EFG are subject to spectral broadening. In the ensuing discussion, only cases where nL is much greater than the quadrupole frequency (i.e., the high-field approximation, where nL [ nQ) are considered; obtaining spectra that do not meet this criterion (e.g., 127I in perovskites) is extremely challenging. Bryce and coworkers have shown that, in circumstances such as those where the ratio nL/nQ is significantly less than 10, significant errors in the derived NMR parameters may occur.56 However, under the high-field approximation, the impact of CQ may generally be described by the first two terms of the quadrupolar Hamiltonian, and thus SSNMR spectra are often modelled in terms of the firstand second-order quadrupolar interactions. Fig. 3A illustrates the powder pattern one may expect for I ¼ 3/2, 5/2, 7/2 and 9/2 nuclei. The breadth, Dntotal, of a powder pattern including the higher-order transitions (to first-order) is given by:

Dntotal ¼ ð2I  1ÞnQ

(13)

Note that, from Eq. (11), vQ is invariant to magnetic field strength and thus similar spectra may be observed regardless of magnetic field strength (excluding the central transition peak, discussed below and assuming the high-field approximation holds). In principle, one may determine CQ from the breadth of the spinning sideband manifold of an MAS spectrum of a quadrupolar nucleus or, on rare occasions, by obtaining spectra of non-spinning samples, as illustrated in Fig. 3A. Since CQ is very sensitive

Fig. 3 Simulated SSNMR spectra for half-integer quadrupolar nuclei (I > 1/2); all spectra were simulated with diso ¼ 0. In (A), the full breadth of the spectra for I ¼ 3/2, 5/2, 7/2 and 9/2 nuclei, albeit with truncated CT peaks, are shown; the axis is scaled in units of CQ. In (B), simulated 35Cl SSNMR spectra expected at 7.05 T with CQ ¼ 10.0 MHz and with the indicated values for h are shown. The upper trace was simulated with the same parameters as for that immediately below it except that it is the spectrum expected under MAS conditions; the lower three spectra in (B) are those for a non-spinning sample. In (C), simulated 35Cl SSNMR spectra with CQ ¼ 10 MHz, h ¼ 0 and the indicated magnetic field strengths are illustrated; the dashed line indicates diso. The upper three traces in (D) compare the 35Cl SSNMR spectra for stationary samples subject to anisotropic magnetic shielding (U ¼ 5000 ppm) where CQ ¼ 10 MHz, with the indicated orientations of the magnetic shielding tensor relative to the EFG tensor. The lower three traces demonstrate the impact of B0 on the observed line shape. All spectra in this figure were simulated with the WSolids software.48

Solid-state nmr studies of halide perovskite materials with photoconversion potential

267

to structure, such details may provide valuable structural information. The positions of the discontinuities depend on the value for h, so if this is known (e.g., if the nucleus is at a site that requires an axially symmetric tensor), then CQ may also be determined from these discontinuities. In the spectrum of an I ¼ 3/2 nucleus illustrated in Fig. 3A, h ¼ 0, so the separation between the two discontinuities ¼ 0.5CQ. In addition, in some cases, one may identify the spinning sideband manifolds for multiple transitions for nuclei I > 3/2.57 However, because the spectra may span several MHz, obtaining spectra where all transitions are detected is very challenging. Because acquiring NMR spectra that may span many MHz is not always practical (note that the axis in Fig. 3A is scaled in units of CQ which often exceeds 100 MHz), NMR spectroscopists typically concern themselves with the central transition, CT (i.e., m ¼ ½ 4 m ¼ ½), which, if the value for CQ is significant, is also very sensitive to the local chemical environment of the nucleus. These transitions are impacted by the second-order quadrupolar interaction, resulting in sometimes very broad powder patterns. For non-spinning samples, the breadth of this interaction is given by DnCT57:  2  h2 þ 22h þ 25 nQ 3 (14) IðI þ 1Þ  DnCT ¼ nL 144 4 MAS The line width of the central transition peak for an MAS sample, DnCT , is given by:  2 n2  ðh þ 6Þ Q 3 DnMAS IðI þ 1Þ  CT ¼ 4 504 nL

(15)

Eqs. (14), (15) demonstrate that the breadth of the CT peak increases with CQ but decreases with B0 (since nL is directly related to B0) and that, for a given value of CQ, spectra for lower-spin quadrupolar nuclei will be more greatly impacted (consider the impact of I on nQ, Eq. 11). If one can spin the sample at a frequency that exceeds the breadth of the spectrum in the absence of spinning, then that breadth may be reduced by a factor of approximately 3 (Eq. 15), but its line shape is still defined by CQ and the symmetry of the EFG tensor; see Fig. 3B for examples of the impact of h on the observed NMR spectra. Such details inform on the environment about the observed nucleus, thereby yielding further structural information. Another important consequence of quadrupolar coupling is that, unlike the case for I ¼ ½ nuclei, the isotropic chemical shift is not simply defined by the center of mass of the CT peak (Fig. 3C). The shift in the CT peak, commonly referred to as the secondorder quadrupolar shift or Dn½,½ is given by:    n2 3 h2 (16) 1þ Dn½;½ ¼ niso  Q IðI þ 1Þ  30nL 3 4 where niso is the frequency of the CT peak in the absence of CQ.58,59 Because Dn½,½ is inversely dependent on nL, the magnitude of this effect is minimized at higher magnetic fields. niso and hence nQ may be estimated by obtaining spectra at multiple fields if h is known with reasonable certainty (e.g., from the known symmetry at the site of interest). Fig. 3C demonstrates that the breadth of the SSNMR spectra as well as the second-order quadrupolar shift decrease such that, for I ¼ 3/2 and CQ ¼ 10 MHz, the impact of CQ is no longer discerned at a hypothetical magnetic field strength of 240 T. Note that the satellite transitions are also subject to distinct quadrupolar shifts,60 although this usually is only detected in NMR spectra of MAS samples. Fig. 3D illustrates the impact of magnetic shielding anisotropy on the observed line shapes; the upper three traces demonstrate that the relative orientations of the magnetic shielding and EFG tensors are a factor in the observed line shapes, although unrealistically large values for U (5000 ppm) were used here to emphasize the impact. Because magnetic shielding increases linearly with B0 (in frequency units) while the impact of CQ decreases, it is advisable, when practical, to obtain spectra at two or more different applied magnetic field strengths to verify that spectral features have been properly assigned. Fig. 3D illustrates that the effect of doubling the magnetic field strength from 7.05 T to 14.1 T in this hypothetical situation is to reduce the total breadth of the spectrum, but at 35.25 T, the effect of magnetic shielding dominates, such that one would obtain a spectrum that is significantly broadened compared to that obtained at 7.05 T.

9.11.2.4

Indirect spin-spin interactions: Impact of quadrupolar coupling

The indirect coupling is well known from liquids NMR, but in the context of SSNMR studies of perovskites, there are important distinctions. The multiplet pattern is usually much more complex since the observed nucleus is often spin-spin coupled to several halide spin-3/2 or -5/2 nuclei61; for nuclei coupled to 35/37Cl or 79/81Br, the pattern is further complicated by overlapping multiplets from the two magnetically active isotopes for each of these atoms. A further complication in the case of coupling to nuclei with large CQ values, the dipolar coupling may not be averaged to zero by MAS, resulting in what is referred to as residual dipolar coupling.62,63 To describe this effect, it is useful to introduce the term d (Eq. 17 and Fig. 4)46,64: d¼ 


 3CQ Reff  3cos2 b  1 þ hsin2 bcos2a 20nL

(17)

where the angles a and b describe the orientation of the dipolar vector with respect to the EFG tensor. Fig. 4 illustrates the impact of d on I ¼ 3/2 and 5/2 nuclei; similar effects are observed for I ¼ 7/2 and 9/2 nuclei.63 The effect of the residual dipolar coupling (RDC) is to “crowd” the spectrum to high or low frequency, depending on the sign of d, which in turn depends on the signs for Reff

268

Solid-state nmr studies of halide perovskite materials with photoconversion potential

Fig. 4 Simulated 207Pb NMR spectra at nL ¼ 100 MHz, spin-spin coupled to a 35Cl nucleus with CQ ¼ 16 MHz, Reff ¼ 1.0 kHz and J(207Pb,35Cl) ¼ 400 Hz (A), or to a 127I nucleus, CQ ¼ 16 MHz, Reff ¼ 2.0 kHz and J(207Pb,127I) ¼ 400 Hz (B). The signs for d are indicated above the traces; the polar angles a and b were set to 0 . The upper traces were simulated with a line broadening function of 50 Hz, while no line broadening was applied to the lower traces. Spectra were simulated using the WSolids software.48

and CQ; if a and b are known (typically surmised from the molecular symmetry) and if the sign for Reff may be surmised from other measurements, then determining the sign for d offers the only known NMR method of determining the sign of CQ.65 Since the effect depends on the magnitude of CQ and Reff, and is inversely dependent on B0, as for other effects arising from CQ, this effect is more readily observed at lower magnetic fields. In addition, though rarely resolved, the individual peaks within the multiplet contain distinct line shapes (lower traces for Figs. 4A and B). Note that the frequency difference between the inner two peaks corresponds to J regardless of isotope (although the analysis may not be as straightforward as measuring the frequency difference between these two peaks since these may have distinct line shapes), and the observed isotropic chemical shift is not impacted by this interaction.

9.11.2.5

SSNMR spectroscopy of I [ 1 nuclei: Investigations of molecular dynamics

Solid materials, of course, are not static. Important forms of dynamism that greatly impact perovskites and their properties include motions of cations or molecules within the cuboctahedra of these materials, and halide dynamics. Phase transitions also impact their properties; this is discussed in the following section.

Fig. 5 Impact of motion on the observed line shapes for spin I ¼ 1 nuclei, assuming an axially symmetric EFG tensor with no magnetic shielding anisotropy; in (A), the pattern in the absence of motion is shown while (B) and (C) illustrate the pattern observed if the nuclei are subject to rapid C2 or C3 jumps, respectively, and (D) illustrates the pattern observed if the nuclei are subject to rapid isotropic motion. These spectra were simulated with WSolids.48

Solid-state nmr studies of halide perovskite materials with photoconversion potential

269

The distinctive NMR line shapes observed for I ¼ 1 nuclei (i.e., 2H and 14N for the work considered here) in the solid state and their sensitivity to motion (Fig. 5) offers a wealth of information about the nature of that motion.66–69 For example, a deuterated methyl group (i.e., CD3) undergoing rapid C3 jumps about its C–N axis reduces the breadth of the 2H spectrum by a factor of four compared to that expected in the absence of motion, but the pattern is maintained (Fig. 5C). However, if the 2H nuclei are subject to rapid C2 jumps, a very different powder pattern is observed (Fig. 5B), and for rapid isotropic motion, a single symmetric peak is obtained (Fig. 5D). Note that the observed spectra are also sensitive to the nature of the motion (jumps vs diffusion)70 and that the line shapes illustrated in Fig. 5 assume rapid motion (i.e., motional rates comparable to the line widths of the spectra).69 Distinct line shapes are observed for spectra acquired when the nuclei are in the intermediate regime.68,69 Since the line shapes in the absence of motion can generally be predicted with reasonable certaintydfor example, 2H nuclei in CeD bonds experience a nuclear quadrupole interaction of approximately 160 kHz, with an axially symmetric EFG tensor71ddeviations from those line shapes informs on the dynamics for the observed nuclei. Although 14N is a stable isotope with a much higher natural abundance than that for 2H (Table 1), the much greater quadrupole moment for this nucleus (2.044 fm2 for 14N compared to 0.285783 fm2 for 2 H)38,39 yields much broader NMR spectra, and hence the nature of the motion detected may be different. Obtaining such spectra is often challenging, and thus, despite the requirement for isotopic enrichment, many researchers opt for 2H NMR studies when investigating dynamics for compounds even if 14N studies are possible.

9.11.3

SSNMR studies of perovskites

9.11.3.1

Why SSNMR for perovskite studies?

As noted above, a major strength of SSNMR spectroscopy is that it informs on short- (< 5 Å) and medium-range (5–10 Å) structure, information that is invaluable for the elucidation of more complex perovskite structures that cannot be fully characterized based on their repeat structure (e.g., doped or alloyed perovskites, discussed below).35

9.11.3.2

Early SSNMR studies of perovskites

From the earliest days of NMR spectroscopy, researchers realized that the technique could yield information on phase transitions and dynamics of perovskites. For example, in 1972, Bonera et al. determined the 23Na and 93Nb spin-lattice relaxation times for NaNbNO3 and KNbNO3, respectively, as a function of temperature, to investigate the dynamic character of the oxygen atoms in these materials.72 In 1987, Sharma and coworkers investigated a series of lead halide perovskites via 205Tl and 207Pb SSNMR spectroscopy, proposing orientations for the chemical shift tensors that they determined.73 In another early study, Irwin et al. used crosspolarization (CP) and MAS 207Pb NMR spectroscopy to investigate the structures of some lead-based perovskites74; Zhao and coworkers also used 207Pb NMR spectroscopy of MAS and stationary samples to investigate some lead-oxide perovskites.75 For more early examples, see below, as well as early reviews by Putnis76 and Hoch.77

9.11.3.3 9.11.3.3.1

SSNMR studies of fundamental properties Dynamics

In an early NMR study, Wasylishen and coworkers investigated the methylammonium (MA) cation dynamics in MAPbX3, X ¼ Cl, Br, I, via 2H and 14N SSNMR spectroscopy.78 On the basis of the long spin-lattice relaxations times (i.e., T1) and the absence of a quadrupolar splitting pattern at elevated temperatures, the authors surmised that the C–N axis of the MA cation is subject to rapid reorientation. From these preliminary results, the authors concluded that all three perovskites undergo reversible phase transitions and that the high-temperature phases are cubic. X-ray79 and neutron diffraction80,81 studies later verified these conclusions: all three perovskites transition from the high-temperature cubic phase to an intermediate tetragonal phase (two tetragonal phases in the case of X ¼ Br) to a low-temperature orthorhombic phase. In 1990, Knop and coworkers82 undertook a more detailed study of these compounds, utilizing various techniques including SSNMR to determine phase transition temperatures and activation energies. Of course, the heightened interest in the PCEs of perovskites brought with it a renewed interest in the potential of SSNMR to characterize the dynamics in these materials. For example, based on their analyses of 1H and 13C NMR spectra for the MAPbX3 perovskites, Baikie et al.83 confirmed that the MAþ cations in these perovskites undergo dynamic reorientation at ambient temperatures or above, with the cation tumbling in the cuboctahedral cage of the perovskite structure. Based on the narrower 1H peaks for MAPbCl3 compared to the corresponding peaks for MAPbI3, the authors suggest that MAþ tumbles faster in the former. In 2018, Wasylishen and coworkers reinvestigated the dynamics of MAþ in the MAPbX3 perovskites.84 Analyses of the 2H spectra (Fig. 6) and 14N NMR spectra of MAPbI3 in the cubic phase (T > 327 K) yielded symmetric sharp peaks, suggesting essentially isotropic motion of MAþ in this phase. However, even at 326 K (i.e., just below the tetragonal-cubic phase-transition temperature), an approximately axially symmetric powder pattern, albeit with only a minor splitting between the maxima, was observed, indicating a restriction in the motion of MAþ. This pattern broadened with decreasing temperature, until, at 167 K, near the tetragonal-orthorhombic phase-transition temperature, two overlapping deuterium powder patterns were observed (Fig. 6). Below this temperature, a broad powder pattern was observed, indicating that significant motion of MAþ about the C–N axis had ceased, although the observed powder pattern indicated rapid rotation of the ND3 group about the C–N axis; comparable 2H NMR spectra

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Solid-state nmr studies of halide perovskite materials with photoconversion potential

Fig. 6 2H NMR spectra for stationary samples of CH3ND3PbI3 acquired at 11.75 T at the indicated temperatures. Reproduced from Bernard, G. M.; Wasylishen, R. E.; Ratcliffe, C. I.; Terskikh, V.; Wu, Q.; Buriak, J. M.; Hauger, T. J. Phys. Chem. A, 2018, 122, 1560–1573, with permission from the American Chemical Society.

for CD3NH3PbI3 were obtained, yielding similar results. Based on these observations, a six-site model for the MA cation within the cuboctahedron was proposed that is consistent with the observed 2H and 14N NMR spectra. Assuming a rotational diffusion model, Wasylishen and coworkers84 reported a correlation time85 of 1.7  0.6 ps for reorientation of the C–N axis of MAPbI3; in contrast, using a diffusion on a cone model, a value of 108  18 ps was reported by the Emsley Group,86 who used variable-temperature 1H, 2H, 13C and 14N SSNMR spectroscopy to elucidate the dynamics of the MAþ and formamidinium (FAþ) cations in mixed cation (MAþ and FAþ) lead iodide perovskites. They concluded that FAþ rotates faster than does MAþ, and that the photovoltaic properties are related to these dynamics. Kentgens and coworkers also investigated the dynamics of the MAPbI3 perovskite, using multiple techniques, including 14N and 207Pb SSNMR spectroscopy, concluding from 207 Pb T2 measurements that the PbI6 octahedra are subject to slow motion.87 Fabini et al. investigated the dynamics of the FAþ cation in FAPbI3, concluding that its motion is comparable to that for MAþ.88 Recently, Lim et al. also investigated the dynamics of MAPbBr3 by multi-nuclear magnetic resonance.89 Halide migration or exchange, or both, may play an important role in the stability of perovskite materials used for solar cells.90 Yamada et al. investigated the migration of halide ions for APbX3 perovskites (A ¼ Csþ or MAþ, X ¼ Br or I) in the 100 to 500 K temperature range via 207Pb SSNMR spectroscopy.91 The authors attribute line narrowing in the 207Pb NMR spectra for the X ¼ Br perovskite to ion migrations but suggest that the higher-temperature onset of 207Pb line narrowing for the iodide compared to that for the bromide is an indication of lower level of vacancies for the former.

9.11.3.3.2

Structure/property relationships via SSNMR

Understanding the short- and medium-range structures of perovskites and the impact of these structures on the properties of the perovskites is essential for investigators trying to improve their PCEs. Lead-207 NMR spectroscopy has been used extensively to study Pb-halide perovskites. In 2004, Hoatson and coworkers used 1D and 2D 207Pb NMR techniques to investigate the local structure of some disordered perovskite ferroelectrics.92 The 2D-PASS technique93 allowed the authors to determine the chemical shift tensor properties of the materials. Alhabri et al. also used 2D NMR techniques to investigate the impact of introducing ammonium salts at the interface of mixed A- and X-site perovskites,94 demonstrating that the salts form a passivation layer, resulting in improved PCE. Previously, this research group demonstrated via 14N SSNMR spectroscopy that the guanidinium cation may replace MAþ or FAþ in APbI3.95 Lu et al. used 1H and 14N SSNMR spectroscopy to track the conversion of d-FAPbI3, a non-perovskite material with poor PCE, to the a-FAPbI3 perovskite, which has promising PCE.96 Michaelis and coworkers used 207Pb along with 1H and 13C SSNMR spectroscopy to track bulk MAPbI3, along with its decomposition products, MAPbI3 $H2O, (MA)4PbI6 $2H2O and PbI2.97 The authors demonstrated that, although 1H and 13C NMR spectra may inform on the decomposition products of MAPbI3, 207 Pb SSNMR spectroscopy is particularly sensitive to the condition of the sample, which may decompose rapidly under humid conditions. However, under ambient temperatures and modest humid conditions, the monohydrate is obtained from which MAPbI3 can be recovered. More extreme conditions, such as heat or excess water, leads to the irreversible formation of PbI2. In their multinuclear magnetic resonance study of perovskites, Lermer and coworkers suggested that the insertion of cations as spacers to transition to a 2D network, as well as the use of fluorinated linkers, may alleviate the problem of moisture sensitivity98; two

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new hybrid perovskites, (FC2H4NH3)2PbCl4 and (FC2H4NH3)2PbBr3, were identified. The authors suggest that the promising results point investigators in the proper direction for future research. Because of the inherently broad peaks one typically encounters in SSNMR studies, indirect spin-spin (i.e., J) interactions are difficult to detect. In their investigation of MAþ dynamics in MAPbX3 perovskites, Bernard et al.84 estimated 1J(207Pb,35/37Cl) values of 400  40 Hz for MAPbCl3. Note that, assuming one cannot resolve the coupling to the individual chorine isotopes, a 19 peak pattern is expected for six equivalent 35/37Cl isotopes spin-spin coupled to 207Pb. Comparable values were estimated (i.e., assuming no effect from the quadrupolar interaction, see Section 2.4) for this compound and for CsPbCl3 by Aebli et al.,99 who also reported much larger values, 2300 Hz, for 1J(207Pb,79/81Br) of CsPbBr3 and 2350 Hz for MAPbBr3 (Fig. 7). These authors attribute the ability to resolve such spin-spin interactions to structural dynamics and the degree of order in the observed perovskite; higher resolution in their low-temperature 207Pb NMR spectra support this conclusion (Fig. 7). Note that for neither the X ¼ Cl nor Br analogues was the resolution sufficient to resolve the sub-spectra arising from each of the magnetically active isotopes giving rise to J(207Pb,X) (either 35 Cl or 37Cl for the chloride or 79Br or 81Br for the bromide, a consequence of similar g values for the two Cl isotopes as well as for the two Br isotopes, see Table 1). As noted above, another complication is the fact that the quadrupolar halide nuclei may give rise to asymmetric spitting patterns62 and the large nuclear quadrupolar interactions may also lead to fast relaxation of the quadrupolar nuclei100 and hence to self-decoupling. In some cases, cross relaxation may occur if the observed spin-1/2 nuclei have similar Larmor frequencies and are dipolar coupled to quadrupolar nuclei that are subject to rapid relaxation due to large quadrupolar coupling101,102; this may lead to line broadening for the observed nuclei that precludes detection of spin-spin interactions. In another example illustrating the use of 207Pb SSNMR spectroscopy for structure elucidation, Lee and coworkers used twodimensional techniques to characterize Ruddleston-Popper103 lead-halide perovskites; i.e., 2D layers of a perovskite interleaved with cations (butylammonium in this study).104 From HETCOR NMR spectra, the authors were able to distinguish surface from bulk 207Pb sites and to elucidate the structure of the various layers of the structure. Since the discovery of the photovoltaic potential of perovskites, researchers have been striving to resolve two important issues when dealing with lead halide perovskites: their sensitivity to moisture,97 and the ongoing desire to improve their PCE through band gap tailoring. The use of mixed-halide perovskites such as APb(ClxBr(1  x))3 or APb(BrxI(1  x))3 have shown much promise in addressing both issues. Toward that end, synthetic chemists have noted that solvent-free mechanochemical techniques, rather than more common solvent-assisted synthesis methods, often give chemists greater flexibility in tuning the optoelectronic properties of the perovskites.105,106 Although showing promising results, limitations with common characterization methods, such as Xray diffraction, meant that the technique tended to be applied with a “hit-or-miss” approach. This prompted SSNMR spectroscopists to investigate whether the local structural information gained via SSNMR may guide the process.107 Hence, Karmakar et al. used SSNMR to investigate the solid-solution behavior of mixed halide perovskites,108 identifying up to seven distinct PbClnBr6  n octahedra for MAPb(ClxBr1  x)3 materials via 207Pb SSNMR. The authors demonstrated the complementary nature of X-ray diffraction,

Fig. 7 207Pb NMR spectra CsPbBr3 acquired at various field strengths and temperatures (A). In (B) simulated spectra, assuming first-order conditions, along with the deconvolution of individual peaks and the “coupling trees” (top) are shown for CsPbBr3 (left) and MAPbBr3 (right). Reproduced from Aebli, M.; Piveteau, L.; Nazarenko, O.; Benin, B. M.; Krieg, F.; Verel R.; Kovalenko, M. V. Sci. Rep. 2020, 10, 8229, with permission from Nature Publishing.

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Fig. 8 Two-dimensional 207Pb EXSY spectra of MAPbCl3 and MAPbBr3 (upper traces; each spectrum is a superposition of the spectra obtained for both samples) and of MAPb(Cl0.5Br0.5)3 (lower traces) with the indicated mixing time. Reproduced from Karmakar, A.; Askar, A. M.; Bernard, G. M.; Terskikh, V. V.; Ha, M.; Patel, S.; Shankar, K.; Michaelis, V. K. Chem. Mater. 2018, 30, 2309–2321, with permission from the American Chemical Society.

which informs on average long-range structural properties, and SSNMR, which informs on short- and medium-range interactions, and they confirmed the preparation of a solid solution through 2D 207Pb EXSY109 spectra obtained at high field (21.1 T, see Fig. 8), which confirms that halide exchange is occurring, and hence that an atomic-level solid solution has been prepared. In a related study, the same research group also investigated mixed-halide formamidinium-lead perovskites.110 As in their previous study, the authors confirmed that solid solutions were obtained and demonstrated that mechanochemical synthesis allowed more accurate stoichiometric control of the desired products, an important consideration given the sensitivity of the properties to the stoichiometry of the final product. This research group further extended this approach into non-hybrid cesium-lead mixed-halide perovskites,111 demonstrating that mechanochemical synthesis permits accurate bandgap tailorability for bulk 3D and 0D perovskite-based materials. Grüninger et al. investigated mixed FAþ and MAþ lead halide perovskites via 1H, 13C and 207 Pb SSNMR spectroscopy.112 The authors conclude that the material consists of FAþ- and MAþ-rich regions. Anomalous hysteresis behavior in the current-voltage (i.e., J-V) curves for lead-halide perovskites, which may impact their efficiency, has been identified.113 Potassium doping has recently been proposed to overcome this problem114,115; Jacobsson et al. concluded that Kþ was not incorporated on the perovskite structure but nevertheless led to increased fluorescence lifetimes.116 Hence, Kubicki et al. investigated the potassium-containing phases via 39K SSNMR spectroscopy117; the authors relied on a high magnetic field (21.1 T) and MAS to obtain spectra for this challenging nucleus. Based on the 39K NMR spectra, the authors concluded that the potassium is not incorporated in the structure but rather exists in phase-segregated domains such as KPbI3 or unreacted KI. This study was a continuation of a SSNMR investigation of phase segregation by the same research group118 in which 13 C, 14N, 39K, 87Rb and 133Cs SSNMR spectroscopy was used to probe the incorporation of Cs, Rb or K into the FA-based perovskite structure. The authors conclude that Cs readily incorporates into the lattice, to levels of up to 15 mol%, but that Rb separates into Rb-rich phases and K is only detected as unreacted starting material. Recently, Emsley and coworkers also investigated phase segregation in layered two-dimensional perovskites.119 The study included 19F / 13C and 1H / 13C CP NMR spectroscopy to investigate the linkers in these materials, demonstrating the suitability of SSNMR spectroscopy in such studies. Kubicki and coworkers also investigated the impact of Mn2þ and Co2þ doping in lead halide perovskites via 1H and 133Cs SSNMR relaxation measurements.120 From the reduced relaxation times for the Mn2þ doped perovskites, the authors concluded that this cation is incorporated into the CsPbCl3 and CsPbBr3 lattice but that Co2þ is not readily incorporated into the MAPbI3 lattice. Cd2þ doping was also investigated by

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Cd SSNMR spectroscopy.121 The authors concluded that Cd2þ does not incorporate into the lattice for FAþ or MAþ lead halide perovskites, instead forming non-perovskite phases, but does incorporate into the lattice of CsPbBr3. Rosales et al. also investigated phase segregation and alloying for some mixed-halide lead perovskites using 207Pb NMR spectroscopy along with complementary techniques, such as powder X-ray diffraction; the authors also investigated the impact of the preparation method on the final product.122 The research demonstrated the strength of 207Pb SSNMR in characterizing the composition of these materials, clearly an important consideration as researchers strive to improve PCE. In addition to concerns about stability of the most promising lead halide perovskites, concerns about lead toxicity will surely be a roadblock to their routine application in photovoltaic and optoelectronic devices. Hence, researchers have recently been turning to lead-free analogues of these perovskites,123 such as tin-based perovskites.124 In an early SSNMR study of some tin perovskites, Yamada and coworkers obtained 1H NMR spectra of non-spinning MASnX3 samples in the 100–400 K range to investigate the dynamics of the MA cation, concluding that it remains isotropic even at 150 K.125 Later, this group undertook an investigation of ASnBr3 and ASnI3 perovskites, where A ¼ Csþ, MAþ or FAþ, using multiple characterization techniques, including 119Sn SSNMR.126 Depending on the preparation method, broad 119Sn NMR peaks, attributed to the “half-metallic conductivity” of compounds doped with Sn(IV), were obtained. The authors also discuss the effect of motional averaging for the bromide perovskites, noting similar behavior as was observed for the lead halide perovskites.91 In 2020, Kubicki et al. used 119Sn SSNMR spectroscopy to investigate the structure and dynamics of mixed-halide tin perovskites.127 The authors note that the wide range of 119Sn T1 values means that one must carefully choose acquisition parameters to obtain optimum experimental results. From a careful interpretation of variable-field and variable-temperature 119Sn T1 measurements for MASnBr3, the authors conclude that the relaxation is driven by dynamics within the crystal lattice (i.e., diffusion of the Br ions). Karmakar et al. reached similar conclusions for CsSnBr3 in their investigation of CsSn(Cl1  xBrx)3 perovskites.128 Recently, Ha and coworkers also investigated the Sn analogues of the MAPbX3 (X ¼ Cl, Br, I) perovskites as well as the mixed Sn/Pb iodide perovskite, MASn0.5Pb0.5I3 using 119Sn and 207Pb SSNMR spectroscopy.129 The authors discuss the relationship between the bandgap of the materials, an important consideration for photoconduction materials, and the 119Sn chemical shifts; they also demonstrate that the 119Sn CSA is sensitive to the degree of polyhedron distortion about the [SnX6]4  octahedra. Variable temperature SSNMR measurements were also undertaken, and the degradation of MASnI3 over a 36-h period was characterized; a reduction in the degradation rate for MASn0.5Pb0.5I3 was noted. Recently, Karmakar et al. reported a more detailed atomic-level structural investigation of the mixed B-site perovskites CsSnxPb1  xBr3 using multinuclear (119Sn, 133Cs and 207Pb) magnetic resonance spectroscopy.130 The investigators conclude that the Pb and Sn sites are distributed randomly within the perovskite structure. 113

9.11.3.3.3

SSNMR spectroscopy of the halogens

In the preceding, SSNMR studies of nuclei in the A and B sites of perovskites have been discussed. In principle SSNMR studies of the halide nuclei (i.e., X) can also offer information on the local structures of perovskites, as well as on halogen dynamics.131–133 Unfortunately, these nuclei have large nuclear quadrupole moments (Table 1), which, combined with the fact that they are not located at sites of high symmetry for perovskites, result in very broad NMR powder patterns that render acquisition of NMR spectra particularly challenging; the low frequency ratios for 35/37Cl are an added challenge as these appear at or below the tuning range for many NMR probes. Several techniques, discussed in the next section, have been proposed to obtain SSNMR spectra of broad NMR patterns. Some researchers have turned to nuclear quadrupole resonance (NQR) to complement their halide NMR studies134; this entails obtaining NQR data for nuclei, such as 127I, that have very large quadrupole moments, while obtaining NMR data, which yields more local structural information, when practical. Piveteau et al. have recently presented a detailed SSNMR review of perovskites, including a discussion of the complementarity of NMR and NQR applied to lead halide perovskites.36 Such an approach was used by Senocrate et al. in their multinuclear magnetic resonance investigation of ion conduction on MAPbI3100; the authors concluded that such conduction is primarily due to iodine motion. As part of this study, the authors obtained 127I SSNMR spectra of the title compound. Because the central transition peak spans 12 MHz at 21.1 T, only the outer discontinuities in the central transition peak were acquired; each of these required 22 h of acquisition time. For a more detailed investigation of the 127I properties, including some variable temperature studies, the authors turned to NQR spectroscopy. From these data, the investigators concluded that the iodine is subject to in-plane torsional motion. Kovalenko and coworkers recently reported a detailed investigation of bulk and nanocrystalline CsPbX3 perovskites using halide magnetic resonance.135 The large nuclear quadrupole interactions render this spectroscopic technique a sensitive probe of molecular properties, but of course greatly complicate the acquisition of the NMR spectra (vide infra). As is common for SSNMR of halides, the authors turned to NQR for nuclei (e.g., 127I) whose quadrupolar coupling precluded the acquisition of NMR spectra.

9.11.3.3.4

Beyond ABX3: SSNMR studies of double perovskites

An alternative solution to the problem of lead toxicity is the preparation of halide double perovskites of the type A2B0 B00 X6, where B0 and B00 are monovalent and trivalent cations, respectively (Scheme 1C).12 Karmakar et al. used high-field (B0 ¼ 21.1 T) 115In, 133Cs and 209Bi SSNMR spectroscopy to investigate a series of Cs2Bi1  xInxAgCl6 double perovskites, a single material source with potential for white light emission applications.136 They demonstrated that the bandgap of this material can be tailored by adjusting the Bi/In compositional ratio, with the transition from an indirect to a direct bandgap material occurring when the indium content exceeds 50%. The sensitivity of 133Cs NMR spectra to its local environment (Fig. 9) demonstrated that a solid solution had been

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Fig. 9 Experimental (solid lines) and simulated (dashed lines) 133Cs NMR spectra of Cs2Bi1  xInxAgCl6 double perovskites (x ¼ 0, 0.076, 0.915, 1), acquired at 21.14 T at a spinning frequency of 30 kHz. Reproduced from Karmakar, A.; Bernard, G. M.; Meldrum, A.; Oliynyk, A. O.; Michaelis, V. K. J. Am. Chem. Soc. 2020, 142, 10,780–10,793, with permission from the American Chemical Society.

obtained. The authors showed that a maximum photoluminescence quantum yield of 34% is achieved with Bi doping (i.e., x ¼ 0.915). In 2018, Karmakar et al. reported that Cu2þ doping of Cs2SbAgCl6 double perovskites led to dramatic reductions in the bandgaps of the materials to ca 1 eV.137 The authors demonstrated via variable-temperature 133Cs NMR spectroscopy and electron paramagnetic resonance (EPR) that Cu2þ is incorporated within the material. Kubicki and coworkers also used 133Cs SSNMR spectroscopy to investigate Cs2AgBiX6 mixed-halide double perovskites.138 The authors showed that Cl/Br materials form pure phases, but that phase segregation occurs for mixed Cl/I or Br/I materials apart from a narrow range of ratios whereby the iodine mol percentage is less than 3%.

9.11.4

Advanced SSNMR techniques

The intense interest in perovskite materials has pushed researchers to expand their toolkit of characterization techniques. For NMR spectroscopists, this has prompted them to interrogate more challenging nuclei, such as the SSNMR spectroscopy of halides discussed above. A major challenge in obtaining some of these spectra is the extreme breadth imparted to some of the SSNMR spectra due to quadrupolar interactions. Although several techniques have been developed to permit acquisition of wide-line SSNMR spectra,139 to date, the application of these techniques to perovskite studies has been limited, but their potential will surely not be ignored for long by spectroscopists undertaking investigations of perovskites; thus, a brief overview of these techniques is presented here. These can be categorized into two basic techniques: those that minimize the time required to acquire SSNMR spectra by concentrating the signal, and those that enhance to the NMR signal, usually through some form of polarization transfer.

9.11.4.1

Maximizing the SSNMR response

As discussed above, NMR signals from non-spinning solid samples are distributed over a range of frequencies, reflecting, amongst several factors, the anisotropic interactions that the observed nuclei are subject to. One may concentrate the NMR signal into a series of peaks that maintain the structural information provided by these anisotropic interactions while reducing the time required to obtain these spectra. Surely the best-known method of accomplishing this is the MAS technique, used routinely in SSNMR studies. Hanrahan and coworkers demonstrated the benefits of fast (50 kHz) MAS for the acquisition of 1D and 2D 207Pb NMR spectra of hybrid lead halide perovskites (Fig. 10 illustrates NMR spectra obtained for MAPbCl1.5Br1.5).140 The authors demonstrated that a 2D CP HETCOR spectrum could be obtained in a few minutes despite the small sample volume (5 mL), and that fast MAS greatly enhanced the resolution. Another significant benefit of the fast MAS technique is that the short rotor period facilitates the acquisition of 207Pb NMR spectra using echo techniques, which must be synchronized with the rotor frequency. This is an important

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Fig. 10 207Pb NMR spectra for MAPbCl1.5Br1.5; 1D NMR spectra obtained with various techniques (A), 2D 207Pb / 1H CP-HETCOR (B), and a comparison of a spectrum obtained with HETCOR (C, upper trace) with that obtained with a direct spin echo (C, lower trace). Reproduced from Hanrahan, M. P.; Men, L.; Rosales, B. A.; Vela, J.; Rossini, A. J. Chem. Mater. 2018, 30, 7005–7015, with permission from the American Chemical Society.

consideration when acquiring spectra with broad powder patterns and short spin-spin relaxation times (i.e., T2). Alternatively, obtaining spectra of MAS samples spinning at moderate frequencies may be instructive. For example, if the MAS frequency is such that numerous spinning sidebands are obtained, then the chemical shift tensor parameters may be obtained for spectra of isolated spin-½ nuclei using the method of moments of Maricq and Waugh141 or Herzfeld and Berger’s142 graphical routine. Although MAS has been used extensively for SSNMR studies of solids,55 and despite the promising results discussed above, the method does have limitations, particularly when acquiring spectra for which the breadth of the central transition is much greater than the maximum spinning frequency. In addition, the very small NMR coils and sample volumes (a few mL) introduce numerous challenges,143 and probes capable of ultra-high frequency spinning (> 100 kHz) are not readily available. An alternative to MAS has been the Carr-Purcell-Meiboom-Gill (CPMG, or sometimes referred to as QCPMG for the quadrupolar CPMG technique), as applied to SSNMR.144,145 By introducing a series of refocusing pulses in the pulse program, a spectrum is split into a series of peaks (often referred to as spikelets), offering a significant enhancement in the signal. However, the refocusing pulses are only effective if the magnetization from the initial pulse has not fully decayed due to spin-spin relaxation and hence the technique is only applicable to nuclei with significant T2 relaxation times. For example, Fig. 11A–C illustrate a series of 207Pb NMR spectra of PbTiO3 acquired with CPMG, compared to one acquired with a spin echo (Fig. 11D)146; the CPMG NMR spectra were acquired in less than 5% of the time required for the spin echo spectrum. As seen from Fig. 11, the spikelet spacing can be adjusted: a greater spacing improves the sensitivity, but in some cases, fine detail in the spectra may be lost. The resulting spectra appear similar to those obtained with MAS, but there is one important distinction: while spectra of MAS samples yield spectra with peaks appearing at their isotropic frequency (or the center of mass of the peak for spectra of quadrupolar nuclei subject to the second-order quadrupolar shift), spikelets in CPMG spectra are distributed evenly about the transmitter frequency and thus the technique does not directly identify the isotropic frequencies. For example, in a spectrum with multiple NMR sites, only one series of spikelets will be observed. Isotropic chemical shifts may often be determined from simulations of the CPMG NMR spectra, but of course this adds variables to be determined.

9.11.4.2 9.11.4.2.1

Enhancement techniques Cross polarization

For NMR spectroscopy of spin-½ nuclei, the most frequently used enhancement technique is cross-polarization (CP),147 which permits the transfer of magnetization from abundant spins (typically 1H) to the nucleus of interest, yielding a theoretical enhancement equal to the ratio of their magnetogyric ratios; for example, for 13C, the theoretical enhancement is g1H/g13C z 4. But often a greater benefit of the CP technique when observing spectra of spin-½ nuclei is that the recycle delay in these measurements is dictated by the 1H T1 times rather than those of the observed nucleus, which can be orders of magnitude longer. The technique may also be applied to nuclei with spin I > ½, although determining suitable CP conditions for these nuclei can be challenging (vide infra). Application of the CP technique for perovskite studies may be limited since these materials often do not contain 1 H nuclei and in other cases the dynamics of the 1H source (e.g., MAPbX3) leads to challenging CP conditions. Nevertheless, the technique has found applications, for example, as a spectral editing technique. In their study of CsPbBr3 quantum dots, Chen et al. used the 1H / 133Cs CP and CP HETCOR to study the surface chemistry of these materials.148 The authors also obtained surface selective 2D HETCOR NMR spectra through 1H detected CP (i.e., 1H / 207Pb), using the greater 1H sensitivity to detect the small fraction of 207Pb nuclei proximate to the surface.

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Fig. 11 207Pb NMR spectra of PbTiO3 acquired with CPMG (A–C) and with a spin echo (D). Reproduced from Siegel, R.; Nakashima, T. T.; Wasylishen, R. E. J. Phys. Chem. B, 2004, 108, 2218–2226, with permission from the American Chemical Society.

Routine CP techniques are not generally applicable for nuclei yielding broad NMR spectra, since the effective CP bandwidth is limited by the practical spin-lock field strengths used for such measurements149 (spin-lock fields are rarely more than 100 kHz), often resulting in distorted patterns or requiring multiple steps to acquire undistorted spectra. In 2012, Schurko and coworkers149 proposed the use of broadband adiabatic inversion pulses (BRAIN-CP) to allow the acquisition of spectra with excitation profiles up to 10 times greater than that obtained with conventional CP. Of particular interest for research into perovskites, the technique was demonstrated on broad 14N NMR spectra.150 The authors show that the technique permits the acquisition of 14N NMR spectra with improved signal to noise ratios in significantly less time than that required to acquire the spectrum via direct polarization.

9.11.4.2.2

Enhancements for quadrupolar nuclei

Several other enhancement techniques that may find utility in SSNMR studies of perovskites have been reported over the past two decades. With the rotor-assisted population transfer (RAPT) technique, one may improve the sensitivity of the central transition (i.e., ½ 4 ½) by transferring magnetization to this transition from satellite transitions for half-integer quadrupolar nuclei.151 The theoretical enhancement increases with the spin number of the isotope and can be improved with multiple RAPT transfers. Similarly, magnetization transfer from the satellites to the central transition may be accomplished via double-frequency sweeps

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(DFS) of the satellite transitions.152 An advantage of this technique over RAPT is that it may also be used to acquire spectra of stationary samples. However, if MAS is applied, Nakashima et al. showed that the method is more efficient if a single satellite transition spinning sideband is swept rather than the entire spinning sideband manifold.153 In 2004, Siegel et al. suggested that the use of hyperbolic secant inversion pulses were more effective than either RAPT or DFS for signal enhancement of half-integer quadrupolar nuclei.154 Recently, Schurko and coworkers155 presented a preliminary report on the use of optimal control theory (OCT),156 obtaining some improvement over frequency-swept methods such as WURST, discussed below.

9.11.4.3

Wide line NMR spectra for solids

The breadth of some spectra is such that one may not fully excite the entire spectral region using a standard pulse sequence, such as a Bloch decay. An early solution to this problem was the variable offset cumulative spectra (VOCS)157 technique. In this procedure, one simply obtains multiple NMR spectra under identical conditions, apart from the transmitter frequency, which is stepped in increments until the entire spectral region has been acquired; the magnitude of the change in the frequency depends on the excitation profile for the pulse program being used, and the number of steps depends on the breadth of the spectrum. Of course, the technique may be combined with other techniques such as MAS158 (in this case, it is advisable to set the step size to a multiple of the rotor frequency to simplify the addition of the multiple spectra) or with CPMG (Fig. 12).159 The resulting subspectra may be combined by addition, or via the skyline projection technique.160 To address the challenge of acquiring distortion-free (i.e., uniformly excited) NMR spectra that cover a broad spectral range, Kupce and Freeman proposed the wideband, uniform rate and smooth truncation (WURST) technique, which uses adiabatic pulses to achieve broadband excitation.161 In the past decade, the technique has found wide application in NMR studies of a wide range of materials.162,163 Although the excitation profile obtained with the technique is much greater than that obtained with conventional techniques, that is not always sufficient. For example, in the NMR investigation of bulk and nanocrystalline CsPbX3 perovskites by Piveteau et al. discussed above,135 the authors acquired 41 subspectra to obtain the complete 79Br spectrum illustrated in Fig. 13, which spans over 16 MHz.

9.11.4.4

Dynamic nuclear polarization (DNP)

The preceding has demonstrated the great potential of SSNMR in elucidating perovskite structure and dynamics, but its greatest limitation is its inherent insensitivity. Thus, enhancement of the NMR signal has been a persistent goal of NMR spectroscopists. The dramatic enhancements that can be achieved by transferring polarization from electrons to nuclei was recognized by Overhauser in 1953.164 Demonstrated experimentally by Carver and Slichter shortly afterwards,165 the application of DNP has until the past

Fig. 12 27Al NMR spectra of (A) AlMes3 and (B) Al(NTMS2)3 acquired with CPMG and VOCS; the # indicates impurities. Reproduced from Tang, J. A.; Masuda, J. D.; Boyle, T. J.; Schurko, R. W. Phys Chem Phys, 2006, 7, 117–130, with permission from Wiley Interscience.

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Fig. 13 Experimental (black trace) and simulated (blue dashed line) 79Br SSNMR spectra of CsPbBr3, acquired at 16.4 T in multiple steps, using the WURST-CPMG technique. Adapted from Piveteau, L.; Aebli, M.; Yazdani, N.; Millen, M.; Korosec, L.; Krieg, F.; Benin, B. M.; Morad, V.; Piveteau, C.; Shiroka, T.; Comas-Vives, A.; Copéret, C.; Lindenberg, A. M.; Wood, V.; Verel, R.; Kovalenko, M. V. ACS Cent. Sci. 2020, 6, 1138–1149, with permission, from the American Chemical Society.

decade been restricted since the technique could not keep pace with the growing NMR magnetic field strengths: the required highfrequency microwave irradiation was not available.166 With the advent of high-frequency microwave sources, DNP has grown from a niche technique to one that may be applied to high-field NMR spectrometers, allowing access to nuclei that previously were not even considered due to their challenging NMR properties.30,166–174 Development is ongoing; currently a DNP NMR installation is much more complex than that for standard SSNMR lab,175 but in the future the technique will surely be used regularly in NMR studies. To date, there has only been one direct DNP NMR investigation of perovskites, although Nevzorov et al. have also demonstrated the potential for the LiTaO3 perovskite as part of resonators for DNP devices.176 In 2018, Hanrahan and coworkers demonstrated the benefits of fast MAS (vide supra) as well as DNP techniques in studies of halide and mixed halide lead perovskites.140 The authors demonstrated the practicality of obtaining 207Pb NMR spectra of a mixed halide perovskite that yielded a very broad peak, despite a small sample size (Fig. 10). In addition, Stranks and coworkers investigated “perovskite-inspired” zirconiumhalide nanocrystals.177 The authors used DNP167 to obtain the sensitivity needed to obtain 13C and 15N NMR spectra of the nanoparticles and the surface ligands, concluding that the surface is capped with oleate ligands and that the Cs ions are disordered. The paucity of current DNP NMR data in perovskite research may partly be attributed to the novelty of the technique, although there are also practical concerns. Currently, DNP NMR spectroscopy must be performed at low temperatures (typically operating around 100 K); this temperature requirement creates challenges since, as noted above, both dynamics and phase transitions within ABX3 perovskites are important properties that are affected by such low temperatures. Nevertheless, potential applications to studies of perovskites suggest themselves. For example, DNP NMR spectroscopy has been used to obtain 1D 15N, as well as 2D 13C-15N, NMR spectra of samples at natural abundance, saving the time, cost, and challenge of isotopic enrichment.178 Operating perovskite materials are deposited as thin films and thus, obtaining NMR spectra of samples in their operating configuration may be challenging despite favorable NMR properties for the target nuclei; the application of DNP NMR spectroscopy for such studies has been demonstrated for other materials.179 The multiple transmitter offsets required to obtain undistorted NMR spectra of quadrupolar nuclei with broad powder patterns is very time consuming. For example, the 79Br spectrum illustrated in Fig. 13 required 41 steps.135 While DNP by itself would not reduce the number of offset steps, the time required for each step could be greatly reduced with the technique. Another challenge for the application of DNP to the study of perovskites is that most conventional DNP polarizing agents are optimized for 1H enhancements followed by a CP transfer (indirect DNP),170 therefore requiring a proton spin bath. This creates additional challenges when non-hybrid perovskites (i.e., those without 1H) are investigated. If 1H nuclei are present, it may be necessary to transfer 1H polarization to quadrupolar nuclei, which, as noted above can be challenging but may be possible with techniques such as BRAIN-CP.149 In addition, where CP is not possible, direct polarization DNP techniques may be applicable.170

9.11.5

Concluding remarks

The intense interest in perovskites, prompted by the realization of its photoconversion potential, shows no indication of abating. That interest is being pushed by the global demand for green energy sources. As Fig. 1 attests, thousands of articles are published annually on the topic. The sheer magnitude of publications has precluded a complete discussion of published articles, despite restricting ourselves primarily to recent SSNMR research papers. The number and variety of these papers presented herein attest to the flexibility and robustness of SSNMR to address some of the most challenging research questions currently being faced in the field. The puzzles to be addressed in perovskite research will surely continue to grow as researchers push the boundaries of photoconversion potential for these materials while addressing environmental concerns and issues such as material stability or

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photoconversion efficiency. Spectroscopists will continue to use innovative developments in SSNMR spectroscopy as they strive to keep abreast of the demands of the materials community.

Acknowledgments The authors acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada, the Government of Canada Research Chairs program and the University of Alberta for research support. We thank members of the Michaelis Group and Professor Rod Wasylishen at the University of Alberta for many fruitful discussions.

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Khaneja, N.; Reiss, T.; Kehlet, C.; Schulte-Herbrüggen, T.; Glaser, S. J. J. Magn. Reson. 2005, 172, 296–305. 157. Massiot, D.; Farnan, I.; Gautier, N.; Trumeau, D.; Trokiner, A.; Coutures, J. P. Solid State Nucl. Magn. Reson. 1995, 4, 241–248. 158. Altenhof, A. R.; Jaroszewicz, M. J.; Lindquist, A. W.; Foster, L. D. D.; Veinberg, S. L.; Schurko, R. W. J. Phys. Chem. C 2020, 124, 14730–14744. 159. Tang, J. A.; Masuda, J. D.; Boyle, T. J.; Schurko, R. W. PhysChemPhys 2006, 7, 117–130. 160. Hung, I.; Schurko, R. W. J. Phys. Chem. B 2004, 108, 9060–9069. 161. Kupce, E.; Freeman, R. J. Magn. Reson. A 1995, 115, 273–276. 162. O’Dell, L. A.; Schurko, R. W. Chem. Phys. Lett. 2008, 464, 97–102. 163. O’Dell, L. A. Solid State Nucl. Magn. Reson. 2013, 55–56, 28–41. 164. Overhauser, A. W. Phys. Rev. 1953, 92, 411–415. 165. Carver, T. R.; Slichter, C. P. Phys. Rev. 1953, 92, 212–213. 166. Michaelis, V. K.; Griffin, R. G.; Corzilius, B.; Vega, S. Handbook of High Field Dynamic Nuclear Polarization, Wiley: Chichester, 2020. 167. Rossini, A. J.; Zagdoun, A.; Lelli, M.; Lesage, A.; Copéret, C.; Emsley, L. Acc. Chem. Res. 2013, 46, 1942–1951. 168. Ni, Q. Z.; Daviso, E.; Can, T. V.; Markhasin, E.; Jawla, S. K.; Swager, T. M.; Temkin, R. J.; Herzfeld, J.; Griffin, R. G. Acc. Chem. Res. 2013, 46, 1933–1941. 169. Michaelis, V. K.; Ong, T.-C.; Kiesewetter, M. K.; Frantz, D. K.; Walish, J. J.; Ravera, E.; Luchinat, C.; Swager, T. M.; Griffin, R. G. Isr. J. Chem. 2014, 54, 207–221. 170. Ha, M.; Michaelis, V. K. High-Frequency Dynamic Nuclear Polarization NMR for Solids: Part 1 – An Introduction. In Modern Magnetic Resonance; Webb, G., Ed., Springer: Cham, 2017; pp 1–24. 171. Ha, M.; Michaelis, V. K. High-Frequency Dynamic Nuclear Polarization NMR for Solids: Part 2 – Development and Applications. In Modern Magnetic Resonance; Webb, G., Ed., Springer: Cham, 2017; pp 1207–1224. 172. Tan, K. O.; Jawla, S.; Temkin, R. J.; Griffin, R. G. eMagRes 2019, 8, 339–352. 173. Griffin, R. G.; Swager, T. M.; Temkin, R. J. J. Magn. Reson. 2019, 306, 128–133. 174. Hooper, R. W.; Klein, B. A.; Michaelis, V. K. Chem. Mater. 2020, 32, 4425–4430. 175. Bernard, G. M.; Michaelis, V. K. eMagRes 2019, 8, 77–86. 176. Nevzorov, A. A.; Marek, A.; Milikisiyants, S.; Smirnov, A. I. J. Magn. Reson. 2021, 323, 106893. 177. Abfalterer, A.; Shamsi, J.; Kubicki, D. J.; Savory, C. N.; Xiao, J.; Divitini, G.; Li, W.; Macpherson, S.; Gałkowski, K.; MacManus-Driscoll, J. L.; Scanlon, D. O.; Stranks, S. D. ACS Mater. Lett. 2020, 2, 1644–1652. 178. Li, X.; Sergeyev, I. V.; Aussenac, F.; Masters, A. F.; Maschmeyer, T.; Hook, J. M. Angew. Chem. Int. Ed. 2018, 57, 6848–6852. 179. Mollica, G.; Ziarelli, F.; Thureau, P.; Viel, S. Structural Investigations of Polymer Materials by Dynamic Nuclear Polarisation Solid-State NMR. In New Developments in NMR 20. NMR Methods for the Characterization of Synthetic and Natural Polymers; Zhang, R., Miyoshi, T., Sun, P., Eds., Royal Society of Chemistry: London, 2019; pp 533–554. Chapter 22.

9.12

Solid-state NMR of energy storage materials

Kent J. Griffitha, * and John M. Griffinb, a Department of Chemistry, Northwestern University, Evanston, IL, United States; and b Department of Chemistry, Lancaster University, Lancaster, United Kingdom © 2023 Elsevier Ltd. All rights reserved.

9.12.1 9.12.2 9.12.2.1 9.12.2.2 9.12.2.3 9.12.2.3.1 9.12.2.3.2 9.12.2.3.3 9.12.2.3.4 9.12.2.3.5 9.12.2.4 9.12.2.4.1 9.12.2.4.2 9.12.2.4.3 9.12.2.4.4 9.12.3 9.12.3.1 9.12.3.2 9.12.3.2.1 9.12.3.2.2 9.12.3.2.3 9.12.3.2.4 9.12.3.2.5 9.12.3.3 9.12.3.3.1 9.12.3.3.2 9.12.3.3.3 9.12.3.3.4 9.12.3.4 9.12.3.4.1 9.12.3.4.2 9.12.3.4.3 9.12.3.4.4 9.12.3.4.5 9.12.3.5 9.12.4 9.12.4.1 9.12.4.2 9.12.4.3 9.12.4.4 9.12.4.5 9.12.5 Acknowledgment References

Introduction Background to NMR spectroscopy Fundamentals of NMR Acquisition of NMR spectra Spin interactions in solid-state NMR Chemical shielding Dipolar interaction Quadrupolar interaction Paramagnetic interactions Knight shift interaction Experimental techniques in solid-state NMR Magic angle spinning Signal enhancement methods In situ NMR methods Investigating dynamics NMR studies of lithium batteries Fundamentals of batteries Cathodes Stoichiometric (LiMO2) layered oxides Olivine cathodes Manganese-rich spinel cathodes Lithium-rich layered oxides Lithium-rich disordered rocksalt phases Anodes Graphite Silicon and silicon oxides Li metal Early transition metal oxides Electrolytes Garnet NASICON-type Perovskite Sulfide LiPON Interfaces NMR studies of supercapacitors Fundamentals of supercapacitors Observation of adsorbed species NMR studies of pore size and electrode structure Dynamics and diffusion of adsorbed species Insights into supercapacitor charging mechanisms Outlook

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Abstract Electrochemical energy storage in batteries and supercapacitors underlies portable technology and is enabling the shift away from fossil fuels and toward electric vehicles and increased adoption of intermittent renewable power sources.

*

Present address: Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, United States

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Understanding reaction and degradation mechanisms is the key to unlocking the next generation of energy storage materials. This chapter will highlight the diverse applicability and chemical sensitivity of solid-state NMR as a tool for studying bulk and interfacial structures and dynamics. NMR interactions relevant to inorganic battery and supercapacitor materials will be described before moving into sections on lithium battery cathodes, anodes, solid electrolytes, interfaces, and finally supercapacitors. While battery materials vary in maturity, each section focuses on materials that are either in commercial use or development. Multinuclear NMR studies of mechanisms, atomic structure, and ion dynamics are succinctly described and an effort is made to summarize the state of the field for each class of materials.

9.12.1

Introduction

Recent years have seen increasing interest in the development of materials for energy conversion and storage as part of a combined effort to move away from society’s reliance on fossil fuels to mitigate the effects of climate change. While energy storage materials cover a vast range of structure types and categories, the efficiency with which they accept and transfer energy is intrinsically dependent on their structures and mechanisms at the atomic or molecular level. The field of structural chemistry has a wide range of techniques at its disposal to characterize atomic- and molecular-level structure and dynamics, and new techniques are constantly being developed or refined. Among these, solid-state NMR spectroscopy is widely regarded as a powerful probe of local structure and mechanisms. NMR spectroscopy is primarily sensitive to short-range structure, typically on the order of up to 2–3 bond lengths in many materials. This makes it a powerful complement to other solid-state characterization techniques such as diffraction that are more sensitive to the long-range periodic or average structure. Since NMR has no requirement for long- or even short-range order, it can be applied for the study of both crystalline and disordered materials. The fact that nearly all nuclei have non-overlapping NMR resonance frequencies under modern instrument magnetic fields means that NMR is element specific. Thus, for complex materials, a single element of interest can be observed without competing signals or background contributions from other components of the system. NMR is also highly sensitive to dynamics and in principle can be used to observe and quantify motion over a wide range of timescales (> 100 MHz to < 1 Hz) depending on the species and interactions present. These attributes place NMR in a good position to provide detailed information about energy storage materials, which are often complex, disordered, dynamic, or are composed of several different interacting components. In this chapter, we provide an overview of solid-state NMR spectroscopy, with a brief explanation of the basic principles and key experimental techniques of relevance to energy storage materials, specifically batteries and supercapacitors. As it is not possible to cover all battery materials, particularly at the level of detail provided by NMR, this chapter focuses specifically on lithium-based systems and on material families with present commercial activity.

9.12.2

Background to NMR spectroscopy

9.12.2.1

Fundamentals of NMR

The phenomenon of NMR arises from the Zeeman interaction between nuclear spins and a magnetic field. The intrinsic spin angular momentum vector, I, associated with a particular nucleus is characterized by the nuclear spin quantum number, I, which can take any positive integer or half-integer value. When placed in a magnetic field, the projection of I onto the axis defined by the magnetic field is quantized in units of mIZ, where mI is the magnetic spin quantum number and can take values between –I and I in integer steps, resulting in 2Iþ1 possible spin states. The Zeeman energy, E, resulting from a magnetic spin state mI, is given by E ¼ gml ZB0

(1)

where g is the gyromagnetic ratio of the nucleus and B0 is the magnetic field. An NMR experiment detects the frequency corresponding to transitions between Zeeman energy levels, where only transitions between D mI ¼  1 are directly observable. This leads to the definition of the Larmor frequency, u0, which is given by u0 ¼ –gB0 where the units of u0 are rad s

9.12.2.2

–1

(2)

or n0 ¼ u0/2p in Hz.

Acquisition of NMR spectra

At thermal equilibrium, the nuclei within a sample will occupy Zeeman energy levels according to the Boltzmann distribution. The population difference between energy levels leads to a bulk nuclear magnetization which is aligned with the applied magnetic field, and it is this magnetization that is detected as the NMR signal. The magnitude of the magnetization is exponentially dependent on u0. High magnetic field strengths (typically between 4 and 28 T) are generally used in order to maximize the magnetization and therefore the sensitivity and resolution of the NMR experiment. Magnetic field strengths in this range give Larmor frequencies in the radiofrequency (RF) regime (tens–hundreds of MHz).

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In a basic NMR experiment, the sample is placed in the magnetic field within a coil that acts as both a RF transmitter and receiver. In the first part of the experiment, a short RF pulse is applied to the sample. Provided the frequency of the pulse is close to the Larmor frequency of the sample, this causes rotation of the individual nuclear spins (and therefore the magnetization vector) away from the applied magnetic field. The duration of the pulse is chosen such that the magnetization vector rotates through 90 . Following the pulse, the magnetization vector undergoes free precession around the applied magnetic field at the Larmor frequency. This induces an oscillating electrical current in the coil referred to as a free induction decay (FID) which is recorded as the NMR signal. FIDs from multiple repeat scans are coadded to increase the signal-to-noise ratio. The resulting time-domain FID is then subjected to a Fourier transform to convert it to a frequency-domain NMR spectrum. Beyond the basic pulse–acquire sequence, a large number of more complex NMR experiments involving multiple pulses with different durations and phases have been developed to probe specific interactions and phenomena. Indeed, pulse sequence development continues to be an active area of research in NMR spectroscopy. One of the main classes of more complex NMR experiments is two-dimensional (2D) NMR. This approach uses a sequence of pulses separated by a delay during which nuclear spins evolve under an interaction or phenomenon. 2D NMR experiments can be used to draw correlations between different spins in a sample to provide spatial or bonding information, to correlate different transitions associated with the same spin to separate interactions, or to probe dynamic phenomena such as the movement of nuclei between different chemical environments.

9.12.2.3

Spin interactions in solid-state NMR

In addition to the Zeeman interaction, nuclear spins can be subject to a number of other, smaller, interactions with their local environment or with other nearby nuclear spins. It is these interactions that provide information about the local chemical environment and form the basis of NMR spectroscopy as an analytical technique.

9.12.2.3.1

Chemical shielding

The chemical shielding interaction arises from the circulation of electrons within atoms and bonds which induce secondary local magnetic fields that act to “shield” nuclei from the applied magnetic field, thereby altering the apparent Larmor frequency. Importantly, the chemical shielding effect is highly localized and the magnitude depends on the local chemical environment; therefore, nuclei in different environments will resonate at slightly different frequencies and can be distinguished on this basis. In practice, the chemical shielding is difficult to measure directly and so chemical shifts, d, relative to a reference compound in parts per million (ppm) of frequency space are reported instead:
 d ¼ 106  ucs –uref =uref (3) where ucs and uref are the Larmor frequencies of the nucleus of interest and the reference compound, respectively. The precise link between a particular chemical shift and a specific structure is usually difficult to define; however, there are many known empirical trends that can aid assignment of resonances. For example, nuclei in atoms bonded to electronegative elements may tend to exhibit increased chemical shifts (reduced shielding) due to the tendency of electronegative atoms to withdraw electron density thereby lowering the shielding effect in neighboring atoms. Chemical shift ranges vary for different nuclei, with larger ranges observed for heavier elements owing to the presence of larger and more polarizable electronic orbitals. For example, the chemical shift range of 1 H in most materials is approximately 20 ppm whereas 195Pt chemical shifts can occur across several thousand ppm.1 For highly symmetric bonding environments, the electron distribution around a nucleus can be perfectly spherical. However, for non-symmetric bonding environments, the electron distribution around the nucleus is anisotropic and the resulting chemical shielding is described by a second-rank tensor. In this case, the chemical shift varies with the orientation of the shielding tensor according to 

 d ¼ diso þ ðD=2Þ 3cos2 q–1 þ h sin2 q cos2f (4) where diso is the isotropic component of the chemical shift tensor, D and h are the magnitude and asymmetry of the chemical shielding tensor, respectively, and q and f are the angles defining the orientation of the shielding tensor components relative to the magnetic field. This orientation dependence means that the chemical shift of a nucleus will vary with the crystallite orientation. For powdered solids, which have a distribution of all possible crystallite orientations, this chemical shift anisotropy (CSA) results in the observation of a broadened powder lineshape which is made up of a continuum of resonances from individual nuclei with shielding tensors at different orientations to the magnetic field (Fig. 1a). From analysis of the width and intensity profile of the powder lineshape, it is possible to determine diso, D, and h which can be related back to the electronic structure around the nucleus of interest.

9.12.2.3.2

Dipolar interaction

The dipolar interaction is a through-space magnetic interaction between nuclear spins. For an isolated pair of spins I and S, the dipolar interaction results in a splitting of the spectral resonances for each spin. The magnitude of the splitting is proportional to uD ¼ 

 m0 g1 g2 1
2 3 2 3 cos q  1 4p rIS

(5)

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Fig. 1 (a) Illustration of the formation of a CSA powder line shape owing to crystallites at different orientations to the magnetic field having different resonance frequencies, d. (b) Simulated spectra showing the effect of magic-angle spinning (MAS) on a CSA powder line shape.

where g1 and g2 are the gyromagnetic ratios of the two dipolar-coupled nuclear spins, rIS is the internuclear separation, and q is the angle between the internuclear vector and the magnetic field. The orientation dependence of the dipolar interaction means that it also gives rise to characteristic powder lineshapes for polycrystalline powder samples. However, in many systems nuclear spins are not coupled in isolated I–S spin pairs, but instead exist in an extensive network involving simultaneous couplings to many spins around them resulting in distribution of uD values. For this reason, the dipolar interaction is typically manifested as a Gaussian broadening of the NMR lineshape from which very limited information can be obtained. Since the dipolar interaction is proportional to the product of the gyromagnetic ratios for the coupled spins, and inversely proportional to the cube of their separation, the largest interactions are seen for high-abundance, high-g nuclei such as 1H, 19F, 7Li and 31P, where resonances can be broadened by many kHz. In addition to the through-space dipolar coupling interaction, the through-bond J coupling interaction also results in resonance splittings in a similar manner. However, in solid-state NMR, the size of this interaction is often much smaller than the line width and so is rarely observed directly.

9.12.2.3.3

Quadrupolar interaction

Nuclei with spin quantum number I > ½ possess an electric quadrupole moment, Q, which interacts with the electric-field gradient (EFG) at the nucleus. This interaction is referred to as the quadrupolar interaction and its magnitude is parameterized by the nuclear quadrupolar coupling constant, CQ ¼ eQVzz/h, where Vzz is the largest principal component of the second-rank tensor describing the EFG, and Q is the quadrupole moment of the nucleus. The magnitude of the EFG is related to the symmetry of the local bonding environment surrounding the nucleus under study; highly symmetric bonding environments result in small or zero EFGs, whereas low-symmetry environments correspond to large EFGs. In this way, measurement of CQ as well as the asymmetry of the EFG tensor, hQ, can provide information about the local coordination around a spin > ½ nucleus. The quadrupolar interaction is manifested as a perturbation to the 2Iþ1 Zeeman energy levels of the spin I > ½ nucleus. To a first-order approximation, bonding environments with a non-zero EFG lift the degeneracy of the Zeeman energy levels such that a spitting is observed with separation 2uQ, where uQ is the quadrupolar splitting parameter given by:
 
 
(6) uQ ¼ uQ PAS =2 3cos2 q–1 þ hQ sin2 q cos2f –1 where uPAS Q is the quadrupolar splitting parameter in the principal axis system and is given by (in rad s ):

uQ PAS ¼ 3p CQ =ð2Ið2I–1ÞÞ

(7)

For a single crystal at a given orientation (q, f) relative to the magnetic field, the quadrupolar splitting results in 2I resonances separated by 2uQ. For half-integer nuclei, the energy levels defining the central transition are each perturbed by the same amount, meaning that the magnitude of the transition is unaffected. This results in the observation of an unperturbed central transition surrounded by “satellite transitions” defined by the quadrupolar splitting. For powder samples, the orientation dependence of uQ means that characteristic broadened powder lineshapes are observed for the satellite transitions.

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For bonding environments with a non-zero EFG, the quadrupolar interaction is often one of the largest NMR interactions present and the width of the satellite transition powder patterns can extend across many MHz. Although it typically remains smaller than the dominant Zeeman interaction, the large size of the quadrupolar interaction means that second-order (and occasionally thirdorder) effects need to be taken into account to properly describe the appearance of the spectrum. Second-order effects act to further perturb the Zeeman energy levels including the central transition, which is unperturbed to first order. The correction, u(2), to the frequency for a transition q (assuming hQ ¼ 0) is given by:   uPAS   1
1
Q uð2Þ ¼ (8) A0 ðI; qÞ þ A2 ðI; qÞ 3cos2 q  1 þ A4 ðI; qÞ 35cos4 q  30cos2 q þ 3 u0 2 8 where An are spin-dependent coefficients. The orientation dependence of the second-order perturbation means that the central transition is also anisotropically broadened, often by several kHz or tens of kHz, but up to MHz in so called “ultra-wideline” NMR. For a single quadrupolar-broadened resonance, the magnitudes of CQ and the EFG tensor components can be readily obtained from lineshape analysis of the first- and second-order broadened powder patterns. For half-integer spin nuclei, since the first-order satellite transition broadening is much larger than the second-order central transition, spectral acquisition and analysis often focuses solely on the central transition. For integer-spin nuclei, there is no central transition so only the satellite transitions can be measured, which can be difficult to achieve experimentally unless the quadrupolar interaction is relatively small.

9.12.2.3.4

Paramagnetic interactions

In materials with unpaired electrons (e.g., those containing radicals or transition metals in certain electronic configurations), the strong magnetic moment of the electron (spin S ¼ ½) can have a significant influence on shifts and linewidths in the NMR spectrum. Electrons couple with nearby nuclei through two primary mechanisms: the Fermi contact interaction and dipolar or “pseudocontact” interaction. The Fermi contact interaction arises from the transfer of unpaired electron spin density to the nucleus via induced polarization of the surrounding s orbitals. The magnitude of the interaction is defined by the hyperfine coupling constant A/h, given by: A=h ¼ gmB gN rðr¼0Þ m0 =ð3SÞ (9) where g is the electron g-factor, mB is the Bohr magneton, gN is the gyromagnetic ratio of the nucleus, r(r ¼ 0) is the unpaired electron density at the nucleus, and m0 is the permeability of free space. For systems where the longitudinal relaxation time of electron spins in the magnetic field is much shorter than A/h, the NMR shift due to the Fermi contact interaction is directly proportional to the time average of the electron spin, hSz i: dFermi ¼

106 A hSz i u0

(10)

The Fermi contact interaction can occur between an unpaired electron and the nucleus within the same atom, or it can be transmitted across chemical bonds. Fermi contact shifts can be very large for nuclei close to unpaired electrons (several thousands of ppm) and the magnitude typically reduces with increasing number of bonds. For systems where the longitudinal relaxation time of electron spins approaches A/h, considerable line broadening can occur. The pseudocontact interaction takes a similar form to the nuclear dipolar interaction, being scaled by a dipolar coupling constant which is proportional to the inverse cube of the electron–nucleus separation. This has both an isotropic and anisotropic component, with the orientation-dependence of the latter being the same as the nuclear dipolar coupling. However, the magnitude of the pseudocontact interaction is typically very large, resulting in significant line broadening for powder samples. The often large magnitudes of the Fermi contact and pseudocontact interactions can make spectral acquisition very challenging, particularly for nuclei in close proximity to the unpaired electron. In many cases, nuclei within the same atoms as the unpaired electrons are unobservable due to fast nuclear relaxation effects; however, resonances for nuclei further away can often be observed and the large magnitude of the paramagnetic interactions provides high chemical sensitivity.

9.12.2.3.5

Knight shift interaction

Conducting solids exhibit an additional interaction arising from the coupling between nuclei and delocalized conduction electrons which is referred to as the Knight shift. In a conducting solid, conduction electrons occupy a Fermi distribution across the available electronic states. In the absence of a magnetic field, these states are occupied in a pair-wise fashion according to the Pauli exclusion principle; however, when a magnetic field is present, the Zeeman interaction breaks the degeneracy between electronic spin states leading to a net magnetic polarization of the conduction electrons. The nuclei then couple to this average electronic polarization via the same mechanism as for the paramagnetic interactions described above. The Knight shift can be very large if the conduction electrons are composed primarily of s-orbital electrons which have non-zero density at the nucleus. If p- or d-orbital electrons are present, which have nodes at the nucleus, they can induce polarization of the s electrons but the Knight shift can be smaller or negative.

9.12.2.4 9.12.2.4.1

Experimental techniques in solid-state NMR Magic angle spinning

As discussed above, the orientation dependence of most NMR interactions can result in broadening of spectral resonances for powder samples. If multiple chemical environments are present in a sample, or if multiple interactions are present simultaneously,

Solid-state NMR of energy storage materials

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this can significantly reduce resolution to the point where very little information can be obtained. It is therefore often desirable to remove or partially remove anisotropic interactions for the purpose of identifying distinct chemical environments in the sample. The anisotropic components of the chemical shielding, dipolar, and quadrupolar interaction (to first order) all share the same orientation dependence proportional to ½(3cos2q–1). This term has a magnitude of zero at the so-called “magic angle” when q ¼ 54.736 , and in principle anisotropic interactions vanish for any crystallite with the largest component of the interaction tensor oriented at this angle to the magnetic field. However, for a powdered sample it is impractical to align all crystallites at the magic angle. Furthermore, it is often the case that tensors for different interactions are not coincident meaning that no one crystallite orientation would remove all interactions that are present. An elegant solution to this problem is the technique of magic-angle spinning (MAS) in which the sample is rotated around an axis oriented at the magic angle relative to the magnetic field. While this does not change the powder distribution of crystallite orientations present in the sample, the average orientation of each crystallite over a full rotation is that of the rotational axis, i.e., the magic angle. If the MAS rate is comparable to the frequency distribution of the powder lineshape, the spectrum is broken up into isotropic resonances surrounded by “spinning sidebands” separated by the spinning frequency, as shown in Fig. 1b. If the MAS rate is sufficiently rapid, the spinning sidebands are pushed outside of the powder frequency distribution leaving only isotropic resonances. MAS is therefore a very powerful experimental technique to increase resolution and signal intensity and is routinely used in solid-state NMR. In practice, MAS is performed by packing the powdered sample into a rotor consisting of a high-strength zirconia or silicon nitride tube with a fluted end cap which acts as a turbine. The rotor is then spun within the NMR probe using compressed air or nitrogen gas which provides a low-friction gas bearing and drives the rotation via the turbine cap. The maximum rotation rate depends on the rotor diameter used. The largest commercially available rotors have an outer diameter of 7 mm and can achieve MAS rates of approximately 8 kHz, whereas the smallest rotors currently available have an outer diameter of 0.7 mm with a maximum MAS rate of 111 kHz. As discussed above, for quadrupolar nuclei the central transition lineshape is often defined by the second-order component of the interaction which has a more complex orientation dependence. This means that it cannot be fully averaged by sample rotation around a single axis, and instead a partially averaged powder lineshape is observed under MAS which can still be several kHz or tens of kHz in width. Fitting second-order broadening of quadrupolar central transition MAS lineshapes can yield the full quadrupolar interaction parameters which can be related back to the symmetry of the local structure. To achieve fully high-resolution spectra where the second-order broadening is removed, more advanced approaches such as multiple-quantum (MQ) and satellitetransition (ST)MAS or double rotation (DOR) experiments can be performed.2–6

9.12.2.4.2

Signal enhancement methods

Owing to the small Zeeman energy difference between nuclear spin states in magnetic fields used for NMR experiments, NMR is a relatively insensitive form of spectroscopy (in the signal-to-noise definition of sensitivity). While spectra can easily be obtained for high abundance nuclei, sensitivity can become a limiting factor in the experiment when attempting to observe nuclei with low natural abundance. Even for nuclei with high natural abundance, observation can be challenging if they are present as defect, interfacial, or surface species that make up a small atomic fraction of the sample. For these reasons, much of the development of solidstate NMR methodology has been devoted to methods for signal enhancement. One way to increase the sensitivity of low natural abundance nuclei is to artificially increase the abundance through isotopic enrichment. This approach is sometimes used in the study of battery materials to artificially enrich in 6Li (natural abundance 7%) such that 6Li can be observed with greater sensitivity, or residual 7Li can be observed with far weaker homonuclear dipolar interactions for more accurate measurement of quadrupolar parameters.7 This approach can also allow tracking of ion movement between, e.g., an enriched electrolyte and a natural abundance electrode.8 Isotopic enrichment has also been very successful for the study of 17O (natural abundance 0.037%) which is otherwise unobservable under most experimental conditions.9–11 17O-enriched H2O and O2 gas are commercially available at enrichment levels of up to 90% and can be incorporated into oxygen-containing compounds in a variety of ways. H217O can be used as a precursor in synthetic aqueous procedures where it is either used as the solvent or is added in some proportion to the natural abundance H2O used in the procedure. 17O2 gas may also serve as a reagent in oxidation reactions.12 17O can also be introduced post-synthetically through exchange with H217O or by heating in 17O2 gas. Post-synthetic exchange methods have been widely used but require that the sample is stable under the conditions that exchange is carried out and do not necessarily enrich uniformly between all chemical environments or throughout the bulk. The NMR signal can also be enhanced through manipulation of nuclear spin state populations. One of the most widely used approaches is cross polarization (CP) in which polarization is transferred from a high-sensitivity nucleus to a low-sensitivity nucleus by simultaneous RF irradiation on both nuclei. CP transfer occurs via the through-space dipolar interaction and so requires that the low-sensitivity nucleus to be observed is in close proximity (within a few Å) of the high-sensitivity nucleus from which polarization is transferred. In principle, the maximum signal enhancement is equal to gI/gS where gI and gS are the gyromagnetic ratios of the high- and low-sensitivity nuclei, respectively. In practice, even higher sensitivity gains can be achieved owing to the typically faster longitudinal relaxation of highly abundant, high-g spins compared to low-abundance, low-g spins. CP experiments can be performed using standard solid-state NMR hardware making it a very accessible experimental method. It has been widely used for the study of low-abundance nuclei such as 13C and 29Si in systems including electrolytes and electrode interfaces.13–15 One consideration when applying CP is that the distance dependence of the transfer process means that spectra are not strictly quantitative. However, this can be exploited for the purposes of spectral editing to, e.g., selectively enhance species that are in close proximity to a nucleus of interest.

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In recent years there has been increasing interest in the enhancement of NMR sensitivity through hyperpolarization of nuclear spin states. One of the most promising methods is dynamic nuclear polarization (DNP) in which the large polarization inherent to unpaired electrons in a magnetic field is transferred to nuclei prior to the NMR experiment.16–19 The maximum enhancement by this method is related to ge/gn where ge and gn are the gyromagnetic ratios of the electron and the nucleus of interest, respectively. For 1 H, this means that an enhancement factor of up to 658 can theoretically be obtained, and higher enhancements are possible for nuclei with lower gyromagnetic ratios. In practice, the theoretical enhancement factor is rarely obtained, although enhancements of one or two orders of magnitude are often observed. This can dramatically reduce the experimental time required, and also allows observation of low-abundance species such as defects and surface groups that would otherwise not be detectable. The experimental procedure for DNP is significantly more complex and requires additional hardware beyond a standard solid-state NMR spectrometer. In a typical experiment, the unpaired electron source is added to the sample in the form of a solution containing a radical or biradical species such as TOTAPOL20 or TEKPOL21 and experiments are performed under MAS at low temperatures (typically 100 K) in order to freeze the sample and increase the Boltzmann polarization of the unpaired electrons. The electron polarization is transferred to the nuclei by irradiating with microwaves of a specific frequency to drive polarization transfer via one of a number of possible mechanisms.22,23 One of the complications of DNP for the study of energy storage materials is that the addition of a radical solution can be problematic for unstable or reactive samples such as electrode materials which may degrade or undergo surface reactions. To address this problem, a number of studies have explored the possibility of transferring polarization from endogenous unpaired electron sources that are already present in the sample. Leskes and co-workers have shown that it is possible to achieve DNP transfer from Mn(II) and Fe(III) dopants that are incorporated in the electrode materials during synthesis.24,25 The signal enhancement achieved by this approach has enabled observation of natural abundance 17O as well as the inner surface layers of an artificial interphase coating.8

9.12.2.4.3

In situ NMR methods

To fully understand chemical structure and mechanisms in energy storage materials, it is often desirable to change external variables (e.g., temperature) during the NMR experiment, or to study the material within a working device. Standard solid-state NMR hardware allows the sample temperature to be varied relatively straightforwardly during the NMR experiment by either heating or cooling the compressed gas supply used to drive MAS. Since the MAS rotor must undergo free rotation, it is not possible to attach a temperature probe to determine the precise sample temperature. However, the sample temperature can be closely estimated by performing a prior calibration experiment on a sample with a temperature-dependent chemical shift such as 207Pb in Pb(NO3)2.26 For low-temperature measurements, most commercial MAS probes are capable of cooling the sample to approximately 150 K, although frictional heating of the MAS rotor must be taken into account and can increase the sample temperature by several tens of Kelvin depending on the MAS rate. Stable temperatures of 100 K are possible using a cryo-MAS apparatus developed for DNP measurements, although this requires an additional spinning module and large quantities of liquid nitrogen to provide boil-off gas. For high temperature measurements, standard MAS probes can reach upper temperatures of between 420 and 520 K depending on the design. MAS experiments can be performed above 520 K using specialist probes incorporating laser heating (up to 1200 K).27 However, radial and, more severely, longitudinal temperature gradients within the sample can be significant. NMR spectroscopy has received a great deal of recognition for its ability to probe chemical processes in working electrochemical systems. The advantages of in situ NMR on working cells are that the observation of chemical changes in the NMR spectrum can be directly correlated with the electrochemical state of the system, and any short-lived metastable species can be observed without the need for cell disassembly which may otherwise disturb the system. In order to control and monitor the electrochemical properties of the sample at the same time as performing the NMR experiment, a number of practical considerations need to be taken into account with regards to the NMR methodology. Since the cell is connected to an external electrochemical apparatus, free rotation of the sample is not possible and experiments must be performed under static rather than MAS conditions. This significantly reduces spectral resolution, meaning that small or even moderate chemical shift changes may not be detectable if they occur within the broadened linewidth. For this reason, large paramagnetic interactions or Knight shifts can be beneficial as they allow different chemical environments to be distinguished over a frequency range that is larger than the linewidths. High resolution can be obtained in in situ studies of electrolytes owing to the rapid molecular tumbling in solution which averages anisotropic interactions. However, susceptibility effects from cell components and other factors mean that resolution is usually still lower than in conventional liquid-state NMR experiments. NMR shifts can be strongly affected by susceptibility effects and in situ cell geometry, as has been demonstrated in a wide range of electrode and electrolyte/separator systems.28 There are also several practical considerations for the electrochemical cell design. The in situ cell must fit within the NMR detection coil (typically up to 10 mm internal diameter), and solid metal components such as cell casings and foil current collectors must be avoided as these can prevent penetration of the radiofrequency pulse and NMR signals throughout the sample. For the study of working batteries and supercapacitors, one of the most popular in situ cell designs is the so-called “bag cell” whereby the electrodes, current collector, and electrolyte are sealed within a flexible plastic membrane (Fig. 2a).29–31 This cell design is relatively straightforward to assemble and is transferrable to a wide range of different electrode materials and chemistries. In addition, since bag cells are assembled from fresh components for each experiment, the dimensions and shape can be easily matched to the NMR detection coil and any other space considerations within the NMR probehead that is being used. However, bag cells also place some limitations on the electrochemical performance. Due to the flexible nature of the plastic membrane, it is difficult to apply or maintain pressure within the cell, which can impact the electrochemistry. Since foil current collectors stop penetration of the RF pulses and NMR

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signals, cast electrodes cannot be used and instead cells are typically assembled using free-standing electrodes which are pressed against mesh current collectors. Together, these factors mean that most in situ cells have relatively poor rate capabilities compared to coin cells and larger pouch cells. In recent years, the increased interest in in situ NMR has driven a number of advances in cell design, particularly for the study of batteries. In addition to the bag cell design, re-usable plastic cell capsules are now commercially available.32,33 These allow electrodes and other cell components to be arranged in various configurations between the two sides of the cell, and a cylindrical outer capsule allows a degree of pressure to be applied to the cell assembly (Fig. 2b). Modifications to this design also permit cells to be studied under electrolyte flow, which potentially offers interesting possibilities for the study of, e.g., flow batteries or capacitors.34 Goward and co-workers have demonstrated a “jelly roll” battery cell that fits within a conventional MAS rotor, thereby permitting high resolution experiments on a full battery assembly (Fig. 2c and d).35 This does not allow for true in situ measurements (i.e., electrochemical cycling of the cell inside the NMR spectrometer); instead the cell is removed from the NMR spectrometer between measurements and cycled to a different charge state before the measurement is repeated. In this way, it is possible to study a single device to be studied at different states of charge without the need for cell disassembly. Recently, it has been demonstrated that it is possible to obtain NMR spectra for conventional coin cells with metallic casings using a non-standard hairpin NMR coil design to avoid “B1 damming” fields during the RF pulse.36 Although this approach is limited to static NMR experiments, it opens up the possibility to study working commercial batteries without disruption to the cell configuration. Advanced probe designs are also being explored to facilitate battery cell magnetic resonance measurements.37

9.12.2.4.4

Investigating dynamics

The high sensitivity of NMR to the local chemical environment makes it a powerful probe of dynamic effects which may alter the position or orientation of an ion or chemical group over time. Information can be obtained from NMR measurements on either the species undergoing motion, or on nearby spectator species that are also modulated by the motional process. The different sizes of

Fig. 2 (a) Bag cell and (b) capsule cell designs for in situ batteries and supercapacitors. (c) Jelly roll in situ battery cell and (d) comparison of MAS and static 7Li NMR spectra showing the resolution enhancement afforded by the jelly roll cell. Part label a and b: Adapted from Pecher, O.; CarreteroGonzález, J.; Griffith, K. J.; Grey, C. P. Materials’ Methods: NMR in Battery Research. Chem. Mater. 2017, 29 (1), 213–242. doi:10.1021/ acs.chemmater.6b03183 under CC-BY license. Part label c and d: Adapted with permission from Freytag, A. I.; Pauric, A. D.; Krachkovskiy, S. A.; Goward, G. R. In Situ Magic-Angle Spinning 7Li NMR Analysis of a Full Electrochemical Lithium-Ion Battery Using a Jelly Roll Cell Design. J. Am. Chem. Soc. 2019, 141 (35), 13758–13761. doi:10.1021/jacs.9b06885. Copyright 2019 American Chemical Society.

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NMR interactions enable the study of dynamics over a very wide range of timescales, in principle from picoseconds to seconds or even longer. Fast timescale processes can be probed using spin–lattice, or T1, relaxation measurements which are sensitive to motional effects on a similar timescale to the Larmor frequency (i.e., tens or hundreds of MHz). Where motion on this timescale is present, analysis of the variation in T1 as a function of sample temperature can yield rate constants and activation energies. This approach has been extensively applied in the study of ion conductors, where local structural fluctuations that contribute to the diffusion process are sufficient to modulate the T1 relaxation time.38–40 Intermediate timescale motion can be probed using NMR interactions that are comparable in magnitude to the motional rate. Microsecond timescale (or equivalently MHz frequency) dynamics can often be probed via the quadrupolar interaction, for which the first-order component for several commonly studied nuclei is often in the MHz or hundreds of kHz range. This can be done directly through static lineshape analysis, or indirectly through analysis of motional broadening of MAS sideband patterns.7 The spin–spin or T2 relaxation time constant of 7Li nuclei has also been shown to be sensitive to intermediate timescale motion.41 T2 measurements can be performed in situ as a function of state of charge and the dynamic information obtained provides an insight into how the mobility of 7Li within the cathode material changes during charging. Recently, this approach has also been extended to ex situ MAS measurements under MAS to provide increased resolution.42 Slower kHz timescale motions can be probed via a variety of interactions including the second-order component of the quadrupolar interaction, dipolar interactions, and chemical shielding. The magnitudes of these interactions are typically on the order of several kHz for many systems, and therefore motion on this timescale can lead to partial or complete averaging of broadened powder lineshapes, or exchange averaging of isotropic resonances in MAS experiments. A number of simulation packages enable lineshapes and motional broadening and narrowing to be simulated for different motional models. Through comparison of these models with experimental data it is possible to extract rate constants at different temperatures and activation energies through Arrhenius analysis.43–45 In some materials, motional processes occur on even slower timescales from milliseconds to several seconds (e.g., macroscopic diffusion in and out of porous particles). In such cases, if the environments that species are exchanging between have different chemical shifts associated with them, it is possible to track the motion by 2D exchange spectroscopy (EXSY). The EXSY experiment involves a mixing time which, if set to be comparable to the timescale of the motion taking place, results in the appearance of offdiagonal correlation peaks in the 2D spectrum. Through analysis of the correlation peak intensity as a function of mixing time, the exact timescale of the motion can be determined. In this way, sets of EXSY spectra recorded at different temperatures can also provide activation energies via Arrhenius analysis. An alternative NMR method for studying dynamics is pulsed field gradient (PFG) NMR which uses magnetic field gradients to encode spatial information about species of interest within the sample and give direct access to diffusion coefficients.46,47 In PFG experiments, field gradient pulses are applied on either side of an observation delay, during which the diffusion of ions or molecules can be probed. Each measurement comprises a series of NMR experiments performed with different magnetic field gradient strengths, g, and the normalized signal intensity (I/I0) is plotted against a parameter, b, that is proportional to g2. Self-diffusion coefficients, D, are then obtained by exponential fits of the form (I/I0) ¼ exp(–Db). The range of diffusion coefficients that are accessible by PFG NMR depend on a number of factors, particularly T1 and T2 relaxation times which effectively limit the observation time that can be used in the experiment. In general, PFG NMR experiments are performed under static conditions meaning that resolution can be an issue in multisite systems. However, the successful combination of MAS and PFG NMR has been demonstrated for a number of materials.48,49 PFG NMR can give very detailed information on intermediate range (100 nm to few mm) motion in materials, and variable-temperature measurements can give access to activation barriers. However, like many other motional probes, the meaning of the diffusion coefficient obtained needs to be given careful consideration with regards to the material properties and limiting factors such as intracrystallite domains and grain boundary effects which can reduce the effective diffusion coefficient over longer length scales.

9.12.3

NMR studies of lithium batteries

9.12.3.1

Fundamentals of batteries

Lithium batteries, a term that encompasses lithium-ion batteries and lithium metal batteries, are the leading energy storage technology for portable electronics and electric vehicles. Owing particularly to the low mass and high electropositivity of lithium, lithium-based batteries possess the highest energy density among rechargeable electrochemical energy storage devices. The fundamental mechanism of a battery is the storage of charge via redox reactions. On discharge, there is a spontaneous transfer of lithium ions through an electrolyte and electrons through an external circuit from the anode to the cathode. The charge process, driven by an applied potential, reverses the flow of lithium ions and electrons (Fig. 3). The voltage of a battery is determined by the difference in chemical potential of Li, mLi, which is the sum of mLiþ and me–, between the anode with high mLi and the cathode with low mLi. In practice, it is useful to compare individual materials against lithium metal with its reference reduction half-reaction of Liþ/Li. The energy of a battery is capacity  voltage (or !Vi VfQ dq). On this basis, the optimal battery comprises a high-voltage cathode and a low-voltage anode, each possessing high lithium storage capacity per unit weight and volume. Commercially interesting lithium batteries, the focus of this chapter, typically comprise anodes with average voltages ranging from 1.5 to 0 V vs Liþ/Li and cathodes ranging from average voltages of 3.4 to 4.8 V vs Liþ/Li. The alkyl carbonate liquid electrolytes used in standard lithium batteries are only reductively stable down to about 1.0 V vs Liþ/Li and oxidatively stable to about

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Fig. 3 NMR and Batteries. (left) Artistic and (right) schematic representation of a battery. The reversible flow of ions and electrons during discharge and charge is depicted in the schematic.

4.2 V vs Liþ/Li, meaning that most batteries require surficial passivation in the form of a solid–electrolyte interphase (SEI) on the anode and a (less investigated) cathode–electrolyte interphase (CEI). There exist three fundamental structural reaction mechanisms for battery materials: (i) intercalation, (ii) alloying, and (iii) conversion. In general, intercalation involves the insertion of a guest atom into a host with minimal and reversible structural rearrangement. Alloying reactions involve large structural displacements and often lead to amorphization of the host. Conversion reactions are a displacement reaction where, e.g., lithium reacts with a transition metal fluoride to form lithium fluoride and transition metal nanoparticles. Both intercalation and alloying reactions take the form AþB 4 AB while conversion reactions follow ABþC 4 ACþB. Beyond the atomic changes described, large microstructural changes are expected with alloying and conversion reactions while these are often subtle or even absent with intercalation reactions. Note that a given material may go through some combination of intercalation, conversion, and alloying as increasing quantities of lithium are inserted (e.g., SnO2 / LixSnO2 / 2Li2OþSn / 2Li2OþLixSn).50–53

9.12.3.2

Cathodes

Battery cathodes are dominated by late 3D transition metal oxide chemistry, specifically Co, Ni, Mn, and Fe. Commercial lithiumion battery cathodes can be grouped into three families: layered oxides, olivine phosphates, and spinel oxides. The layered oxides include lithium cobalt oxide [LiCoO2, LCO] and lithium nickel manganese cobalt aluminum oxide [Li[NiwMnxCoyAlz]O2 (wþxþyþz ¼ 1), NMC (z ¼ 0), NCA (x ¼ 0), and NMCA]. The olivine phosphates include lithium iron phosphate [LiFePO4, LFP] and lithium manganese iron phosphate [LiMnxFe1–xPO4, LMFP]. The spinel oxides include lithium manganese oxide [LiMn2O4, LMO] and lithium nickel manganese oxide [LiNixMn2–xO4, LNMO]). NMCA, LFP, and LMO offer theoretical capacities of ca. 270 mAh/g, 170 mAh/g, and 148 mAh/g, respectively, making NMCA the present favorite in terms of energy density. Nextgeneration cathodes with higher charge storage capacities may come from an alloying compound such as sulfur, conversion materials such as metal fluorides, or one of two families of lithium-rich oxide materials that may offer anomalously high capacities through anionic (oxygen) redox: the disordered rocksalt structure or the lithium-rich layered structure.

9.12.3.2.1

Stoichiometric (LiMO2) layered oxides

Layered oxides are perhaps the largest and most explored family of lithium-ion battery materials. LiCoO2, discovered by John Goodenough et al., was successfully commercialized as a lithium-ion battery cathode by Sony in 1991 and is still used in most portable electronic devices.54 Archetypal LiCoO2 crystallizes in the a-NaFeO2 structure with alternating layers of Li and Co in octahedral coordination with oxygen. The stacking sequence of the layers follows ABCABC and gives rise to the polytype nomenclature O3 where O designates octahedral lithium and three is the stacking repeat unit. Early 6Li and 7Li NMR studies showed that Co3þ in LiCoO2 is low spin t2g6, giving rise to a diamagnetic lithium resonance.55–59 An insulator-to-metal transition occurs in LiCoO2 as lithium is extracted.56,60,61 7Li NMR revealed that LiCoO2 passes through a paramagnetic regime wherein the signal disappears due to strong hyperfine effects from Co4þ upon being delithiated toward Li0.94CoO2 (Fig. 4).56 It has been noted that the loss of intensity alone is not a sensitive measure of lithium deficiencies that

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Fig. 4 7Li NMR of LixCoO2. (left) Loss in signal intensity as diamagnetic Co3þ is converted to paramagnetic Co4þ during initial lithium extraction. (right) Two-phase region from x ¼ 0.94 to x ¼ 0.75. Reproduced from Ménétrier, M.; Saadoune, I.; Levasseur, S.; Delmas, C. The Insulator–Metal Transition Upon Lithium Deintercalation from LiCoO2: Electronic Properties and 7Li NMR Study. J. Mater. Chem. 1999, 9 (5), 1135–1140. doi:10.1039/a900016j with permission from the Royal Society of Chemistry.

may arise during synthesis unless the signal is quantified relative to other samples.56,57 As more lithium is removed, a two-phase reaction occurs from Li0.94CoO2 to a metallic phase Li0.75CoO2 as indicated by a new Knight-shifted signal arising at 57 ppm (Fig. 4).56 These trends have been monitored in real time, albeit with lower resolution, with in situ 7Li NMR.61a In another study, measurements of 59Co, 6Li, and 7Li at three different magnetic field strengths were used to differentiate the conventional O3 polytype that is obtained from high-temperature synthesis versus the O2 polytype that is formed via ion exchange from P2-Na0.70CoO2 (P ¼ prismatic).59 More recently, 17O NMR was measured as a function of state-of-charge in 17O-enriched LiCoO2.62 A single diminishing resonance was observed at –636 ppm upon delithiation from LiCoO2 until Li0.5CoO2 where a quadrupolar lineshape appeared at 900 ppm. Upon continued lithium extraction, the quadrupolar lineshape disappeared at around Li0.3CoO2 and was replaced by a broad line at 1250 ppm at around Li0.2CoO2 that, too, vanished at Li0.07CoO2. As NMR is sensitive to both atomic and electronic effects and has no requirement for long-range order, it is particularly useful for the indirect and direct characterization of defects. The more strongly quadrupolar nature of 59Co makes it sensitive to minor deviations in the structural symmetry that are not apparent in 6,7Li NMR.59,63,64 On the other hand, lithium NMR has provided detailed insights on samples of lithium cobalt oxide prepared with Li/Co > 1. These “overstoichiometric” compounds show additional resonances that were originally attributed57 to the presence of paramagnetic low-spin Co2þ but later revised65,66 to stem from interactions with paramagnetic intermediate-spin Co3þ. The revised model features exclusively Co3þ and places a small fraction of lithium on the cobalt site, leading to a Co and O deficient stoichiometry of Li[LitCo1–t]O2–t.65,66 The debate remains open, with new authors in a later study proposing that the extra signals are indeed consistent with excess lithium acting as a dopant and partially reducing the compound to form low-spin Co2þ.67 Beyond the intrinsic defects that are present in the former example, additional elements may be incorporated to stabilize the layered structure. 7Li NMR revealed that the Mg2þ extrinsic defect case leads to a combination of oxygen loss and oxidation to Co4þ.68 The incorporation of dopants and substituents with more favorable NMR properties can be monitored directly, for example, 11B and 27Al.64,69–72 The sensitivity of nuclear relaxation to electronic effects such as paramagnetism led Delmas et al. to demonstrate that 7Li T1 measurements of LiCoO2 can be used to track differences in annealing time over 15 days that impact the electrochemical properties but are invisible to diffraction or the 7Li NMR spectra themselves.66 Using the 7Li T1 criterion, it was discovered that the insulator-to-metal transition begins immediately upon delithiation and that the phase transition at Li0.5CoO2 is more distinct in highly pure and ordered LiCoO2.66 LiNiO2 is unstable as a cathode in its pure form and undergoes a series of phase transitions upon delithiation.73–77 However, nickel-rich layered oxides with nickel content of 70–90þ% on the metal site offer high energy density (practical capacities exceeding 200 mAh/g) with minimal need for cobalt and so have become the favored cathodes for electric vehicles. There has been a strong trend to move away from cobalt because it is not only expensive but its supply chain presents geopolitical and ethical challenges. Owing to the very different properties between octahedral Ni2þ (t2g6eg2, paramagnetic), low-spin Ni3þ (t2g6eg1, paramagnetic), low-

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spin Co3þ (t2g6, diamagnetic), and Mn4þ (t2g3, paramagnetic) lithium NMR can differentiate lithium environments based on the identity and oxidation state of their metal nearest neighbors. Paramagnetic NMR shifts in layered oxides and many other cathode materials can be understood qualitatively and quantitatively through bond pathway decompositions of hyperfine shifts.78–84 An early application of this principle was the demonstration of cobalt segregation even in Ni-rich Li[Ni1–xCox]O2.85 When manganese is incorporated into nickel-containing layered oxides, the electrons are distributed such that Ni2þ and Mn4þ are observed, with Ni2þ being redox active and Mn4þ remaining inert above 1.5 V.86–88 6,7Li NMR studies of Li[Ni0.5Mn0.5]O2 showed Li in the transition metal layer (Li2MnO3-like) and strong cation ordering with both Li and Ni preferring Mn neighbors.89,90 The broadening of such spectra is related primarily to Li/Ni antisite defects.91 Lithium NMR within the family of NMC materials containing Ni, Mn, and Co shows that distinct environments can be observed and assigned when close to an end member such as Li[NixMnxCo(1–2x)]O2 with x  0.1 but distinct features are lost at intermediate compositions such as NMC111 (Li[Ni1/3Mn1/3Co1/3]O2) and NMC811 (Li[Ni0.8Mn0.1Co0.1]O2).92–94 As lithium is removed from NMC111 or NMC811, the broad, paramagnetically shifted 7Li resonance at 550–600 ppm moves toward lower frequencies as lowvalent nickel species are oxidized to diamagnetic Ni4þ.94,95 In each case, the lineshape also narrows considerably, which is not consistent with the wide distribution of chemical environments at intermediate charge states, and instead suggests lithium dynamics.94 NCA, a family of Ni-rich materials based loosely around the composition Li[Ni0.80Co0.15Al0.05]O2 was popularized by Panasonic and Tesla. 7Li NMR of a commercial sample of Li[Ni0.80Co0.15Al0.05]O2 revealed that Al3þ ions pin the elongated bond of dynamically Jahn–Teller-distorted Ni3þ (Fig. 5), which reduces strain in the system.72 This model superseded previous 6,7Li resonance assignments that were based on clustering without accounting for the dynamic Jahn–Teller distortion.96,97 Furthermore, as the sample is charged to high voltage, all the paramagnetic Ni2þ/3þ transforms to diamagnetic low-spin Ni4þ and the 7Li NMR resonance shifts to lower frequencies and narrows to eventually leave only a sharp signal at –1 ppm.98 From 27Al NMR, virtually all of the aluminum is paramagnetically shifted and broadened, indicating its atomically homogeneous distribution throughout the sample. DFT bond pathway contributions to the 27Al shift suggest a shift of –220 ppm per Ni3þ neighbor, and the spectrum shows a distribution of Al environments with two to six Ni3þ cations (Fig. 5).72 Notably, the DFT calculations indicate that caution must be exercised when interpreting the intensities because shift dependencies related to the Jahn–Teller distortion can overlap with shifts related to cation ordering. Solid-state NMR of electrode materials, often in conjunction with solution-state NMR of liquid electrolytes, is also a powerful tool for the analysis of degradation processes in battery materials. Taking NCA as an example, the cathode–electrolyte interface (CEI) was probed by 19F NMR and revealed fluorinated degradation products such as OPF3, OPF2OR, OPF(OR)2, (R ¼ methyl, ethyl) and inorganic aluminum-containing species.99 The sources of fluorine are the electrolyte salt LiPF6 and the polymer binder polyvinylidene difluoride (PVDF). Looking into the bulk of the NCA cathode, 7Li NMR suggests changes upon extended cycling as a result of irreversible changes in the nickel oxidation state.98

9.12.3.2.2

Olivine cathodes

LiMPO4 cathodes with the olivine structure and earth-abundant Fe and Mn at the M site are undergoing a renaissance as the enormous demand for batteries for electric vehicles has strained global supply chains for Co and Ni. The surge in interest for LiFePO4 cathodes comes despite their relatively low energy density stemming from a low redox voltage of 3.4 V vs Liþ/Li and a moderate capacity of 170 mAh/g. Replacing Fe with Mn leads to a much more favorable cathode voltage of 4.1 V vs Liþ/Li, but the substitution

Fig. 5 7Li and 27Al NMR of Li[Ni0.80Co0.15Al0.05]O2. (left) experimental 7Li NMR spectrum in good agreement with the simulated spectrum from a model with dynamic Jahn–Teller (JT) distortions. (right) 27Al spectrum showing a distribution in the number of Ni3þ next-nearest neighbors. Adapted with permission from Trease, N. M.; Seymour, I. D.; Radin, M. D.; Liu, H.; Liu, H.; Hy, S.; Chernova, N.; Parikh, P.; Devaraj, A.; Wiaderek, K. M.; Chupas, P. J.; Chapman, K. W.; Whittingham, M. S.; Meng, Y. S.; Van der Van, A.; Grey, C. P. Identifying the Distribution of Al3þ in LiNi0.8Co0.15Al0.05O2. Chem. Mater. 2016, 28 (22), 8170–8180. doi:10.1021/acs.chemmater.6b02797. Copyright 2016 American Chemical Society.

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comes with capacity fade and Mn dissolution challenges.100–102 In the olivine structure, lithium is octahedrally coordinated in onedimensional tunnels with edge- and corning-sharing connectivity to octahedral FeO6 and tetrahedral PO4. Recording NMR spectra of iron-containing materials is particularly challenging owing to strong paramagnetic broadening and rapid relaxation effects. 7Li and 31P NMR of LiFePO4 and related LiMPO4 olivine phases (M ¼ Mn, Co, Ni) each show a single resonance with a large spinning sideband manifold.103–105 The single isotropic resonance for each nucleus is in agreement with the crystal structure, containing a single site for lithium and for phosphorus. Though typically regarded as a two-phase material reacting from LiMPO4 to MPO4, there is some evidence for Li-ordered intermediate compositions, including 7Li and 31P NMR of Li2/3CoPO4.106 In a sample such as LFP, there are shift contributions from the Fermi contact, pseudocontact, and bulk magnetic susceptibility (BMS) interactions as well as dipolar and BMS shift anisotropies.107 Single-crystal NMR and variations in temperature, MAS rate, and magnetic field have been studied to help differentiate the numerous additive contributions.107,108 Hybrid DFT calculations can assist in determining the bond pathway contributions to the observed spectra in LFP and mixed-metal olivines where varying cation next-nearest-neighbor coordinations give rise to distinct 31P resonances (Fig. 6).78,109–114 Incorporating the effects of spin–orbit coupling on calculations of paramagnetic 7Li and 31P NMR shifts in LiMPO4 (M ¼ Fe, Mn, Co, Ni) has advanced our understanding of the NMR spectra.81 Going further and accounting for the effects of particle size and shape has led to a truly refined picture of the hyperfine shifts in these materials, even enabling determination of particle shape from an NMR spectrum.107 Lithium dynamics have been tracked in LiMnxFe1–xPO4 as a function of transition metal ratio and state-of-charge with T2 relaxation measurements.42

9.12.3.2.3

Manganese-rich spinel cathodes

The manganese-based spinel family of cathodes is another earth-abundant alternative to the layered oxides. In the archetypal cubic spinel structure, lithium is tetrahedrally coordinated and diffuses in three-dimensions between a framework of MnO6 octahedra. Spinel cathodes are typically grouped into two families: LiMn2O4 (LMO) and LiNi0.5Mn1.5O4 (LNMO). The distinction is important

Fig. 6 Spin transfer pathways and 31P NMR of LiMn1–xFexPO4. (top left) Interatomic distances and angles in the olivine structure, and (top right) various Mn/Fe cation orderings. (bottom) 31P spectra for three cation ratios of LiMn1–xFexPO4. Adapted with permission from Clément, R. J.; Pell, A. J.; Middlemiss, D. S.; Strobridge, F. C.; Miller, J. K.; Whittingham, M. S.; Emsley, L.; Grey, C. P.; Pintacuda, G. Spin-Transfer Pathways in Paramagnetic Lithium Transition-Metal Phosphates from Combined Broadband Isotropic Solid-State MAS NMR Spectroscopy and DFT Calculations. J. Am. Chem. Soc. 2012, 134 (41), 17178–17185. doi:10.1021/ja306876u. Copyright 2012 American Chemical Society.

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because LMO relies on the Mn3þ/4þ redox couple as lithium is extracted while LNMO relies on the Ni2þ/4þ redox couple without manganese activity. 6,7 Li NMR spectra of pristine LiMn2O4 contain a single paramagnetically shifted resonance at 520 ppm.115–119 Although there is only one crystallographic lithium site, the tetrahedral 8a site, multiple lithium NMR signals might be expected because LiMn2O4 is mixed valent with Mn3þ/4þ. However, electronic hopping is evidently fast enough in comparison to the NMR timescale that lithium see a single dynamically averaged manganese.115,120 Charging of LiMn2O4 proceeds via a combination of solid-solution and twophase regions that can be sensitive to sample and electrode preparation.121 The NMR shows the initial paramagnetic 6Li signal shifting to higher frequency by about 8 ppm with no new peaks until 70–90% delithiation where additional peaks emerge around 650 and 830–950 ppm.121 The higher frequency resonances have been assigned to lithium near Mn4þ sites on the basis of spin transfer pathways and comparisons to other lithium manganese oxide compounds.115,121 Intrinsically defective LMO of the form Li1þ xMn2–xO4 shows improved electrochemical performance by raising the average Mn oxidation state and suppressing the Jahn–Teller distortion that occurs on discharge below 4.0 V vs Liþ/Li.122 6,7Li NMR spectra of Li1þ xMn2–xO4 show additional resonances at ca. 550–650 ppm as well as a weak resonance at 2300 ppm. The signals at 550– 650 ppm have been attributed to lithium in tetrahedral environments located adjacent to localized defect-derived Mn4þ while the high frequency signal has been assigned to octahedral lithium in the 16d site of the spinel structure.115,120,123 The octahedral lithium that replaces manganese introduces electron holes for charge balance; these defects are not randomly distributed but remain clustered as [Li]oct–Mn4þ.123 A similar effect is observed with extrinsic doping of Zn2þ, Ni2þ, or Cr3þ where manganese is oxidized to Mn4þ for charge balance and the lithium NMR is consistent with high-valent Mn4þ clustering around the defect rather than being homogeneously distributed.120 Liþ and Zn2þ dopants lead to the octahedral Li signal because (i) excess lithium cannot occupy the filled tetrahedral sites and (ii) Zn2þ prefers the tetrahedral site and so pushes some Liþ onto the octahedral site.120,124,125 The Mn4þ lithium-rich spinel Li4Mn5O12 (Li[Li1/3Mn5/3]O4) shows a 6Li resonance at 847 ppm corresponding to lithium in the 8a site and a resonance at 1980 ppm corresponding to lithium in the 16d site.115 Anion-deficient lithium-rich Li1þ xMn2–xO4–d shows far weaker defect resonances overall and no evidence for lithium on the octahedral 16d site.123 Subtler details of the lithium local environment have been derived from analysis of the MAS spinning sideband manifolds, which are sensitive to local symmetry and can vary much more than the paramagnetic shifts themselves.124 As lithium is removed from the Li1þ xMn2–xO4 or LiZn0.1Mn1.9O4 structure on charge, the pristine and defect tetrahedral lithium NMR signals quickly convalesce into a single resonance that closely resembles the pristine parent compound LiMn2O4.123,125 Upon further charging, the resonance shifts to higher frequencies, with additional resonances appearing at very high states of charge.123,125 Through variable-temperature measurements, it is clear that the collapse of the tetrahedral fine structure comes not from structural changes but from enhanced ionic and electronic transport upon partial lithium extraction.123 Lithium dynamics between the resonances at 500–700 ppm have been probed directly with 2D 7Li–7Li exchange spectroscopy measurements.126 Lithium can also be inserted into the LiMn2O4-type cubic spinel in a two-phase reaction to produce Jahn–Teller-distorted Li2Mn2O4.127,128 The Jahn–Teller distortion lowers the symmetry and Li2Mn2O4 adopts a tetragonal form of the aristotype rock salt structure that retains the basic LiMn2O4 structure but with lithium in additional octahedral sites.127,129 This tetragonal phase forms upon lithiation even for Li1þ xMn2–xO4 with an initial manganese oxidation state well above þ3.5.130 6Li NMR of the discharged phase Li2Mn2O4 with exclusively Mn3þ shows two overlapping resonances at 101 and 118 ppm from lithium ions on the 8a and 16c sites.115 The two-electron reaction from Mn2O4 (l-MnO2) to Li2Mn2O4 leads to a large capacity of 285 mAh/g, but the Jahn–Teller distortion that occurs upon lithiation from LiMn2O4 to Li2Mn2O4 is associated with a large and sudden change in volume, causing particle fracture and poor cycling stability.131 As nickel is introduced into the spinel structure to form LiNixMn2–xO4, electrons localize on nickel, leading to the end-member compound LiNi2þ0.5Mn4þ1.5O4. Lithium extraction on charging is associated with the Ni2þ/4þ redox couple. Owing to the higher energy required to remove electrons from the eg band of nickel vs manganese, nickel redox in LNMO occurs at 4.7 V compared to the 4.1 V in LMO.132,133 Depending on the synthesis conditions, manganese and nickel may be ordered or disordered in LNMO.134,135 Generally, cation order in LiNi0.5Mn1.5O4 can be achieved by slow-cooling (< 3  C/min) the sample after annealing at approximately 700  C.136,137 Disordered samples synthesized at high temperatures tend to have oxygen vacancy defects and, consequentially, some Mn3þ.137 In one NMR study, a variety of 6Li resonances were observed for samples of LiNi0.5Mn1.5O4 synthesized at temperatures ranging from 500 to 1000  C for 12 h and cooled at 5  C/min.138 This is indicative of disorder because a single resonance would be expected for lithium in ordered LNMO. A deconvolution suggested that lithium occupies sites with a roughly stochastic distribution of Ni and Mn in the 12 nearest-neighbor cation sites, with a possible small preference for Mn.138 Signals toward high frequency were assigned to relatively nickel-rich environments and low frequency signals to relatively manganeserich environments.138 Ordered samples of LiNi0.5Mn1.5O4 do show a single lithium resonance from lithium with three Ni2þ neighbors and nine Mn4þ neighbors in its first cation coordination shell, though there is some discrepancy in the NMR shift position, being reported from 925 to 1040 ppm.139–142 As Mn3þ is introduced, new signals appear at lower frequencies.139 In situ and ex situ 6,7Li NMR of a mostly-ordered LNMO sample showed two essentially two-phase reactions upon delithiation (LiNi0.5Mn1.5O4 / Li0.5Ni0.5Mn1.5O4 / Ni0.5Mn1.5O4) with new signals at 680 and 525 ppm as Ni2þ is oxidized to Ni3þ and Ni4þ, respectively.142 Lithium insertion beyond LiNi0.5Mn1.5O4 leads to three new lithium NMR resonances at 943, 307, and 209 ppm. On the basis of assignments in LMO,115,121 the higher frequency signal in Li2Ni0.5Mn1.5O4 was assigned to lithium near Ni2þ/Mn4þ while the lower frequency signals were assigned to lithium closer to Ni2þ/Mn3þ.142

9.12.3.2.4

Lithium-rich layered oxides

“Lithium-rich” cathode materials refers to compositions with Li/M ratio greater than unity. Such compositions are of interest for lithium-ion batteries owing to their accessible charge storage capacities in excess of 300 mAh/g. Lithium-rich compounds are

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categorized into two primary families: lithium-rich layered oxides and lithium-rich rocksalt oxides, the latter essentially being a disordered variant of the former. The archetypal lithium-rich layered compound is Li2MnO3, which can be rewritten as Li[Li1/ 3Mn2/3O2] in the notation of LiMO2 layered oxides such as LiCoO2. Defect-free Li2MnO3 contains a lithium layer alternating with a “transition metal layer” that actually comprises Li and Mn ions in a 1:2 ratio arranged into a honeycomb ordering. This structure has three octahedral lithium sites in a 1:1:2 ratio in the unit cell. Lithium-rich layered compounds can be combined with stoichiometric LiMO2 phases to form compositions xLi2MnO3$(1  x)LiMO2, which in the case of a blend with NMC would be xLi2MnO3$(1–x)LiNiaCobMn1–a–bO2. In general, the battery performance of these lithium- and manganese-rich layered oxides are plagued by voltage fade,143–146 hysteresis,147–151 and manganese dissolution.152–155 The first paramagnetic 6,7Li NMR study of Li2MnO3 by Morgan et al. demonstrated the advantages (higher resolution, better sideband separation, narrower absolute spectral width) of 6Li as compared to 7Li for resolving the three distinct isotropic resonances corresponding to the crystallographic lithium sites.116 The resonances were correctly assigned on the basis of next-nearest neighbors, bond distances, and signal intensities as later corroborated by analysis of the spinning sideband manifolds124 and DFT calculations.156 Over 400 mAh/g capacity is achieved on the first charge of Li2MnO3, associated with lithium removal from the lithium and “transition metal” layers.157 A small quantity of lithium remains in both layers at a high upper cut-off voltage of 5.0 V vs Liþ/Li.157 Seymour et al. observed two sets of 17O NMR resonances, one at 1600 to 1950 ppm and the other at 2100 to 2450 ppm, which were assigned on the basis of hybrid DFT calculations to 4i and 8j oxygen positions, respectively, in the C2/m space group (Fig. 7).158 Oxygen NMR suffers from the low natural abundance of 17O (0.037%), but good signal-to-noise on Li2MnO3 was obtained in 3.5 h by first isotopically enriching the sample in an atmosphere of 70%-enriched 17O2 gas. Defects in the form of stacking faults, Hþ/Liþ exchange, Li vacancies, O vacancies, and Li2O vacancies have all been suggested in Li2MnO3. Bréger et al. observed additional lithium NMR resonances, manifest as peak splitting, in a sample of Li2MnO3 annealed for one day at 850  C.159 These additional resonances were attributed to stacking faults by bond pathway analysis and could be eliminated by annealing the sample for one month at 1000  C.159 In another study, 17O NMR of Li2MnO3 also displayed additional resonances ascribed to stacking faults (annealed at 650  C for 12 h followed by 850  C for 48 h).158 While XRD can be sensitive to these stacking faults, a recent NMR and DFT study showed that additional resonances arising in defective samples can be attributed not only to stacking faults but also to Li2O vacancies.156 The Bréger et al. study also set the upper bound for Li/Mn disorder in the [Li1/3Mn2/3] layer at 0.2%.159 Multiple NMR studies have investigated the role of proton exchange and determined structural proton insertion does not significantly contribute to the observed voltage fade.156,160 Rather, the voltage fade is associated with bulk structural reordering of cations.160 As Li2MnO3 is reacted with LiMO2 (M s Mn), additional transition metals give rise to more next-nearest neighbor environments for Li and additional resonances appear. Many such systems have been examined with NMR and the bond pathway analysis method.159,161–166 Unlike the aforementioned case of charged Li2MnO3,157 6Li NMR has shown that lithium in the transition metal layer of Li[Li1/9Ni3/9Mn5/9]O2 is fully removed on charge.162,166 The lithium that remains in the Li layer preferentially occupies sites near Ni4þ. The lithium NMR was also suggestive of ordering into Li2MnO3-like regions.162,166 After charging to high voltage (up to 5.3 V), lithium cannot be reinserted into the transition metal layer, suggesting transition-metal migration.166 A 6Li-enriched sample of 0.5Li2MnO3$0.5LiMn0.5Ni0.5O2 was able to identify a small quantity of tetrahedral transition metal atoms (likely Mn) coordinated to LiMn6 units at 1600 ppm.165 This unique environment forms via irreversible transition metal migration during cycling and is strongly correlated to voltage fade and hysteresis.165 Lithium-rich layered oxides are not limited to manganese-rich chemistries. While not practical for commercial batteries, compositions based on Li2RuO3 and Li2IrO3 have been extensively studied as model systems. Tarascon et al. demonstrated a complete

Fig. 7 17O NMR of isotopically-enriched Li2MnO3. (left) Full 17O spectrum showing the large spinning sideband manifold arising from anisotropic paramagnetic interactions. (right) Isotropic 17O shifts of 4i (low frequency Region Y) and 8j (high frequency Region X) oxygen positions. Reproduced with permission from Seymour, I. D.; Middlemiss, D. S.; Halat, D. M.; Trease, N. M.; Pell, A. J.; Grey, C. P. Characterizing Oxygen Local Environments in Paramagnetic Battery Materials via 17O NMR and DFT Calculations. J. Am. Chem. Soc. 2016, 138 (30), 9405–9408. doi:10.1021/ jacs.6b05747. Copyright 2016 American Chemical Society.

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solid solution between Li2RuO3 and Li2MnO3 and found that capacity and reversibility are maximized at intermediate compositions.167 Reeves et al. applied 7Li and 17O NMR and DFT calculations to identify Ru–Ru dimerization and determine the correct space group of Li2RuO3.168

9.12.3.2.5

Lithium-rich disordered rocksalt phases

Another class of lithium-rich materials is the family of disordered rocksalts. Ceder et al. demonstrated that disorder of lithium and transition metal atoms over the cation sublattice sites in the rocksalt structure does not hinder lithium transport in lithium excess Li1þ xMO2 when x is greater than approximately 0.2.169 High-valent d0 metals from Groups 4–6 can stabilize excess lithium in compositions LiMO2–Li2M4þ O3, LiMO2–Li3M5þ O4, and LiMO2–Li4M6þ O5.170,171 Owing to the inherent cation disorder and thus many possible local environments, it is challenging to extract detailed structural information from the relatively broad 6,7Li NMR lineshapes yielded by disordered rocksalts.172 However, lithium NMR can complement information-rich 19F NMR in disordered rocksalt oxyfluorides. Unlike in stoichiometric layered oxides, substitution of fluoride anions into the lithium-excess disordered rocksalt oxides is possible173 and can lead to higher reversible lithium storage capacities.174–177 7Li and 19F NMR have been used to verify the partial incorporation of fluorine into the host structure, though diamagnetic impurities that are likely associated with side products are sometimes also detected.172,174,176,178–180 Paramagnetically broadened 19F signals are observed from the bulk in environments where fluorine is not directly bonded to a paramagnetic cation center.179 Fluorine with paramagnetic nearest neighbors would have NMR signals that are too severely broadened and/or relax too quickly to be observed.172 On the other hand, sharp, diamagnetic fluorine resonancesdmost commonly LiF at –204 ppmdpoint to fluorine that was likely not incorporated into the rocksalt lattice. Though mechanochemical and solid-state methods have been demonstrated as effective fluorine doping routes, direct fluorination with F2 gas leads to a surface LiF layer rather than incorporation into the rocksalt structure.181 In Li1.15Ni0.45Ti0.3Mo0.1O1.85F0.15, a broad and asymmetric 19F signal was observed, which was attributed to fluorine with nickel in the 2nd or 3rd coordination shells by DFT calculations.179 As lithium was extracted from that compound on charge, new fluorine environments appeared that were assigned to breakdown of the LiPF6 electrolyte salt and SEI components (Fig. 8, left).179 The subtle changes in the paramagnetic resonance as a function of the state of charge were supported by the fact that Ni2þ and Ni3þ were calculated to give similar paramagnetic shifts, and low-spin Ni4þ does not contribute a paramagnetic shift.179 Changes in the 19F spectrum after one full cycle point to irreversible cation migration (Fig. 8, right).179 A joint NMR and XAS study of Li1.2Mn0.625Nb0.175O1.95F0.05 revealed surface fluorine loss on the first oxidation and showed that LiF and Li2CO3 are the primary degradation products when the disordered rocksalt is cycled to high voltage in the presence of LiPF6 and LiClO4 electrolyte salts, respectively.182

9.12.3.3

Anodes

Battery anodes should ideally be high capacity and low voltage, as the cell voltage is determined by the difference between that of the cathode and anode. Suitable electrode potentials (< 1 V vs Liþ/Li) for high-energy batteries are realized with graphite, silicon, lithium metal, and a wide variety of alloying elements such as aluminum, tin, germanium, and antimony.183–194 However, issues arise: (i) these highly reducing potentials are outside the stability window of the electrolyte–solvent systems employed in lithiumion batteries and (ii) metallic lithium dendrites can form near 0 V vs Liþ/Li, causing short circuits, rapid heating, cell failure, and even battery fires. The formation of a stable, electronically insulating and ionically conducting solid–electrolyte interphase (SEI) can passivate low-voltage anodes and enable long-term cycling.195–198 Dendrite growth is a more severe challenge and, in practice, limits the rate and temperature conditions under which batteries can charge. High overpotentials or low temperatures exacerbate dendrite formation, so cells with graphite must be carefully managed.199–206 To overcome these limitations, “high-voltage” oxide anodes have been developed that operate between 1 and 2 V vs Liþ/Li. High voltage anodes operate safely above the plating potential of lithium metal but sacrifice energy density at cell level. Materials based on titanium have been the most widely studied for high-voltage anode applications,207–212 leading to the commercialization of lithium-excess spinel Li4Ti5O12,213–216 though niobium-based oxides are emerging commercially.217–221

9.12.3.3.1

Graphite

Graphite is the anode of choice for most lithium-ion batteries owing to its relatively high capacity (372 mAh/g) and low cost. Lithiation of graphite proceeds from C6 to LiC6 via staging processes wherein certain layers are occupied with lithium while others remain empty.222–224 Lithium atoms do not transfer much electron density to carbon in this process, staying effectively metallic.225 The lithium NMR of LixC6 shows discrete resonances at each stage over the series of primarily two-phase reactions (Fig. 9).226–228 Some of the 7Li NMR signals exhibit quadrupolar lineshapes (Fig. 9). LixC6 7Li shifts and quadrupolar frequencies are given in Table 1. Lithium shifts increase with lithium content from the Knight shift as the sample becomes increasingly metallic. Some of the earliest in situ NMR studies of battery materials were performed on graphite and other carbonaceous anode materials.29–31,226,229 A 7Li NMR study of the degradation of lithiated graphite (LiC6) via oxidation by water vapor showed that it proceeds through the intermediate products LiC12 and LiC18 before reaching the products LiOH and graphite.230 The characteristic shifts of 7Li intercalated within graphite differ significantly to those of adsorbed Li within microporous carbon where the dominant contribution to the shift mechanism is the diamagnetic ring-current effect (discussed further in Section 9.12.4).

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Fig. 8 19F NMR of the first cycle of disordered rocksalt oxyfluoride Li1.15Ni0.45Ti0.3Mo0.1O1.85F0.15. (left) Fluorinated degradation products appear on the first charge. (right) The degradation products do not fully disappear on discharge, nor does the original rocksalt lineshape return, signatures of irreversibility. The sharp signal from polytetrafluoroethylene (PTFE) originates from the binder used in the electrode fabrication process. Reproduced with permission from Clément, R. J.; Kitchaev, D.; Lee, J.; Gerbrand Ceder. Short-Range Order and Unusual Modes of Nickel Redox in a FluorineSubstituted Disordered Rocksalt Oxide Lithium-Ion Cathode. Chem. Mater. 2018, 30 (19), 6945–6956. doi:10.1021/acs.chemmater.8b03794. Copyright 2018 American Chemical Society.

9.12.3.3.2

Silicon and silicon oxides

Pure silicon (Si), silicon/carbon composites (Si/C), and silicon oxides (SiOx) are seeing increasing application as advanced anode materials with higher capacity than graphite. The reaction from Si to Li15Si4 stores 3579 mAh/g of charge, though alloying reactions between lithium and silicon (or other elements) are associated with large volume changes and severe mechanochemical degradation. Silicon is now commonly added to graphite in small quantities (5%) to boost the anode capacity. Strategies to stabilize

Fig. 9 In situ 7Li NMR of the first two lithiation/delithiation cycles of graphite. Quadrupolar signals from lithiated graphite are denoted. The Knightshifted resonance from the lithium metal counter electrode appears at 273 ppm. Reprinted from Chevallier, F.; Poli, F.; Montigny, B.; Letellier, M. In Situ 7Li Nuclear Magnetic Resonance Observation of the Electrochemical Intercalation of Lithium in Graphite: Second Cycle Analysis. Carbon 2013, 61, 140–153. doi:10.1016/j.carbon.2013.04.078. Copyright 2013, with permission from Elsevier.

Solid-state NMR of energy storage materials Table 1

7

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Li shifts and quadrupolar frequencies of LixC6.228

Stage

Formula

d (ppm)

nQ (kHz)

1’ 4L 3L 2L 2 dense 1 dense

LidC (dilute) LiC36 LiC27 LiC18 LiC12 LiC6

–2.6 to 1.0 2.0 6.8 12.2 45.0 42.6

8.0–15.0 18.0 18.5 19.0 17.0 22.6

higher silicon content in anodes include forming composites with carbon, synthesizing silicon nanostructures, cycling silicon within a limited capacity range, and/or starting from a silicon oxide (SiOx). Commercial cells that storage charge at the anode primarily or wholly in silicon are beginning to reach the market in specialized applications. Lithiation of crystalline silicon particles proceeds via amorphous intermediates before eventually crystallizing out the metastable phase Li15Si4 at 50–70 mV vs Liþ/Li.231–234 Over time, Li15Si4, which can be non-stoichiometric, reacts with the electrolyte and causes irreversible lithium and capacity loss.231,235,236 The reactive nature of Li15Si4 provides a case where real-time in situ/operando NMR studies are particularly valuable. In order to gain insights on the amorphous intermediates, relations between lithium silicide structural motifs and 6,7Li and 29Si chemical shifts have been studied through model compounds Li7Si3, Li12Si7, Li13Si4, Li15Si4, and Li21Si5 as well as DFT calculations of known and predicted structures.231,232,237–239 Extended silicon clusters and polymeric silicon chains form in the early stages of lithiation (LixSi, x < 2.0) with 7Li chemical shifts from 0 to 10 ppm.231,232,234 In the next stage of lithiation (LixSi, 2.0 < x < 3.5), 7Li resonances at 10–20 ppm are assigned to silicon dimers or small clusters. Finally, near x ¼ 3.5, remaining silicon–silicon bonds break, leaving isolated silicon in a sea of lithium. The exact chemical shifts observed reflect the SieSi cluster size and arrangement.231,232,234 Amorphous, rather than crystalline, silicon is recovered upon delithiation. SiO, a nanocomposite of Si and SiO2 domains with interfacial silicon sub-oxides (SiO2–x),240 is a promising silicon-based anode material that shows good cyclability and is also suitable for forming a composite electrode with graphite. The Si, SiO2, and SiO2–x domains can be differentiated with 29Si MAS NMR.241,242 Crystalline silicon appears at –82 ppm, SiO2 at –107 to –108 ppm, and SiO2–x at –67 ppm.241,242 In situ 7Li and ex situ 7Li and 29Si NMR reveal that the lithiation of the silicon component of SiO proceeds as described for crystalline silicon while the SiO2 and SiO2–x components react with lithium to form Li4SiO4 (d(29Si) ¼ –67 ppm) and amorphous LixSi (Fig. 10). The SiO composite structure and reaction pathway depends on the preparation conditions.242 Upon delithiation, some Li2SiO3 (d(29Si) ¼ –75 ppm) and SiO2–x also form.242 NMR has also been used to study the silicon anode electrode fabrication process. 29Si NMR was used to quantify the degree of oxidation that occurs during aqueous slurry processing of silicon particles.243 The combination of 1H and 1He29Si crosspolarization measurements yielded structural information on the surface silanol chemistry and termination groups.243 Dogan et al. used 29Si NMR to identify the optimal conditions for annealing a CueSi electrode to yield pure silicon with the best electrochemical performance.244 For a discussion of magnetic resonance studies of the silicon–electrolyte interface, see Section 9.12.3.5.

9.12.3.3.3

Li metal

Li metal was adopted as the first lithium battery anode, but it was quickly discontinued due to the proclivity of lithium to deposit as microstructures (dendrites, filaments), leading to electrical short circuits and battery fires.245 Despite the challenges, there is renewed interest in lithium metal anodes owing to their energy-dense nature (3862 mAh/gLi, 0 V vs Liþ/Li). Since the early work on lithium metal batteries, new strategies exist for stabilizing the reactive anode including coating technologies, non-flammable solid-state electrolytes, and new generations of liquid electrolytes.193,246–250 New tools, including a variety of magnetic resonance techniques, also exist for understanding dendrite formation and the SEI on lithium metal.202,251–258 Bulk lithium metal resonates at approximately 240–270 ppm and is dependent on bulk magnetic susceptibility effects.28 The origin of the large shift is a direct Knight shift interaction between the nucleus and the Li s orbitals.259 Differentiation of microstructural lithium such as mossy or dendritic growths from bulk lithium is possible thanks to the BMS effects leading to different observed shifts, with a typical separation of 10–15 ppm. Observation and quantification of microstructural lithium is assisted by the fact that RF electromagnetic radiation penetrates only a skin depth, d, into a metallic sample. Thus, the microstructural qffiffiffiffiffiffiffiffiffiffiffiffiffi lithium signal is amplified relative to bulk lithium. Skin depth follows the expression d ¼ pm rm n0 where r is the resistivity of 0 r

lithium (92.8 nU m), m0 is the vacuum permeability (4p  10–7 m kg A–2 s–2), mr is the relative permeability of lithium (1.00002), and n0 is the NMR Larmor frequency.260–262 The skin depths for 6Li and 7Li are on the order of 10 mm under typical high-field NMR conditions, with 7Li having a smaller skin depth owing to its higher Larmor frequency. Microstructural lithium is typically observed to be on the scale of 1–2 mm, so it is assumed to be quantitatively captured by the microstructural lithium signal with no skin depth limitations, unlike bulk lithium metal where the NMR signal is proportional to the surface area but not the volume.260 The Grey group pioneered the in situ quantification of dendritic lithium metal and initially studied the effect of different electrolytes and current densities.260 A spatial component was added as microstructural lithium was detected in 3D with 7Li MRI.258

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Fig. 10 In situ 7Li NMR of lithium storage in silicon and silicon oxide. (left) The first three lithiation/delithiation cycles of crystalline silicon and amorphous silicon oxide. Phase labels: (i) extended Si clusters; (ii) Li in Super-P/amorphous carbon; (iii) small Si clusters; (iv) metallic LixSi; (v) Li nearby the small Si clusters formed during conversion from crystalline Si to amorphous LixSi; (vi) crystalline Li15Si4-like structures. (right) Reaction pathways for crystalline silicon and amorphous silicon oxide with lithium. Adapted with permission from Kitada, K.; Pecher, O.; Magusin, P. C. M. M.; Groh, M. F.; Weatherup, R. S.; Grey, C. P. Unraveling the Reaction Mechanisms of SiO Anodes for Li-Ion Batteries by Combining In Situ 7Li and Ex Situ 7Li/29Si Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2019, 141 (17), 7014–7027. doi:10.1021/jacs.9b01589. Copyright 2019 American Chemical Society.

MRI techniques have been developed to improve the resolution of lithium metal imaging,263 and these techniques have been applied in situ to solid-state lithium metal batteries with organic ionic plastic crystal and garnet electrolytes.264,265 Another study leveraged the isotope selectivity of NMR to further enhance the microstructural sensitivity.261 By countering an electrode of 6Lienriched metal against a natural abundance (93% 7Li) electrode, it is possible to selectively detect the lithium deposited on a given electrode while ignoring the bulk substrate. Through this method, it is possible to differentiate smooth lithium depositions that appear bulk-like versus microstructural lithium and even different morphologies such as mossy versus dendritic microstructures.261 In situ NMR is a powerful tool to quantify dead lithiumdthat is, lithium particles that have become electrically disconnected from the anode current collector (Fig. 11).266 Chemical shift imaging MRI was used to differentiate microstructure types in a symmetric Li//Li cell and understand the distinct onset of microstructural lithium growth in high and low current regimes and the relationship between salt concentration and lithium deposition.267 Isotopic methods may overcome challenges that are associated with the quantification of lithium metal deposits from 7Li NMR alone.268 For symmetric cells, additional information on coulombic efficiency and dead lithium may be obtained by measuring both electrodes.269 NMR and MRI are unique in both their sensitivity to lithium as well as their non-destructive nature, enabling in situ studies of lithium microstructure growth without disturbing the cell environment. For a discussion of magnetic resonance studies of the lithium metal–electrolyte interface, see Section 9.12.3.5.

9.12.3.3.4

Early transition metal oxides

Titanium and niobium oxides are alternative lithium-ion battery anode materials that operate at an elevated voltagedtypically 1– 2 V vs Liþ/Lidand thus lead to lower full-cell energy density than graphite/silicon/lithium anodes but also have lower propensity to form dendrites. In practice, the high insertion potential, good transport properties, and stability of these phases enable fast charging, high power, and long cycle life. Spinel Li4Ti5O12 (i.e., Li[Li1/3Ti5/3]O4) is used commercially in some electric buses and trains as well as in portable devices such as smartphone stylus pens, among other applications.207,214,216,270 The two-phase reaction from spinel Li4Ti5O12 to rocksalt Li7Ti5O12 has a capacity of 175 mAh/g and reduces 3/5 of the Ti4þ redox centers to Ti3þ. Undergoing development as next-generation oxide anodes are the Wadsley–Roth compounds, particularly those in the families TiO2–Nb2O5 and Nb2O5–WO3 (e.g., TiNb2O7, Nb16W5O55).217–221,271–274 Unlike the many well-studied LixTiyOz phases that typically require nanoscaling, Wadsley–Roth phases have widely exhibited high-rate lithium insertion and extraction in 1–10 mm single crystal particles.273,275,276 While heavier, both Nb5þ and W6þ are capable, in practice, of undergoing two-electron redox to Nb3þ and W4þ, respectively.273 This multielectron redox leads to anodes with accessible capacities in the range of 250–300 mAh/g. Li4Ti5O12 is a lithium-excess spinel with lithium on the tetrahedral 8a site and also mixed with titanium on the octahedral 16d site. The two lithium sites in diamagnetic Li4Ti5O12 are extremely close in chemical shift, separated by less than one ppm. 6Li NMR

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Fig. 11 In situ NMR quantification of “dead” lithium in a lithium metal battery. As lithium is plated onto and stripped from the anode current collector (Cu foil), some lithium particles may become electrically disconnected from the circuit and thus unavailable for reinsertion into the cathode. Reproduced from Gunnarsdóttir, A. B.; Amanchukwu, C. V.; Menkin, S.; Grey, C. P. Noninvasive In Situ NMR Study of “Dead Lithium” Formation and Lithium Corrosion in Full-Cell Lithium Metal Batteries. J. Am. Chem. Soc. 2020, 142 (49), 20814–20827. doi:10.1021/jacs.0c10258 under CC-BY license.

studies are able to differentiate the two lithium sites by the expected ratio (3:1 8a:16d) and peak deconvolution, with 8a appearing at slightly higher frequency than 16d (Fig. 12).214,277,278 Some studies also identify a third site that has been assigned to lithium on the 16c site or an impurity phase such as Li2TiO3.278–280 Pristine Li4Ti5O12 is neither a good electronic nor ionic conductordit is a white, wide bandgap insulator with ultraslow lithium diffusion and a large activation barrier for lithium hopping of 0.6–0.8 eV as determined by 7Li spin-alignment echo and spin–lattice relaxation (averaged across both sites).281,282 The fully lithiated Li7Ti5O12 exhibits only a slightly lower lithium hopping activation barrier of 0.5 eV.282 In Li7Ti5O12, the inserted lithium ions occupy octahedral 16c sites while the lithium ions originally on tetrahedral 8a sites also move across a shared polyhedral face to 16c sites to minimize coulombic repulsions. Lithium on the 16c site in Li7Ti5O12 is also in the presence of a substantial amount of Ti3þ, which leads to a broad signal around –8 ppm.278 At intermediate lithium content Li4þxTi5O12 (x ¼ 0.1–2.0) the ionic and electronic conductivity improves markedly with NMR showing lithium hopping activation barriers of 0.36–0.43 eV.278,280,283 Sample preparation as well as the time and length scale must be considered in the lithium titanate system because domain effects and relaxation between two-phase and solid-solution-like behavior have been observed.280,284–286 As with other electrode materials, substitution and doping can improve the electrochemical properties. Fluorination of lithium titanate improves the capacity and decreases the first cycle capacity loss.287 An NMR study of the fluorination of Li4Ti5O12 with XeF2 and F2 revealed topotactic surface fluorination and Li–F-like 19F and 7Li signals with the milder XeF2 reagent contrasted against structural changes and a TiOF2-like resonance with the stronger F2 reagent.287 Substituting paramagnetic manganese, chromium, or nickel into the spinel lithium titanate structure dramatically increases the 7Li linewidth and spinning sideband manifold.288,289 Manganese dopes into Li4Ti5O12 as Mn2þ on the 8a site while chromium enters as Cr3þ on the octahedral 16d site.288–290 DNP methods have been applied to enhance the weak natural abundance 6Li and 17O NMR spectra of Li4Ti5O12.24,291,292 Enhancement factors on the order of 100–200 are achievable, enabling otherwise challenging natural abundance spectra in a matter of minutes. For the Wadsley–Roth compounds, 6,7Li spectra have been used to track the transition from diamagnetic insulator to localized paramagnet to metallic behavior during the lithiation of TiNb2O7 (Fig. 13).274 In that work, NMR relaxometry and transition-state searching DFT were combined to identify and assign two distinct types of lithium hopping: (i) long-range diffusive motion down the tunnels and (ii) intra-cage non-diffusive motion. The first 7Li PFG NMR measurements on mixed conducting electrode materials were reported for LixNb16W5O55 and LixNb18W8O69, enabled by their favorable superionic lithium conductivity and relatively slow nuclear relaxation (relative to structures with late 3d transition metals).273,293 Room-temperature 7Li PFG diffusion coefficients in

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Fig. 12 6Li NMR spectra of Li4þxTi5O12. (left) The tetrahedral 8a and octahedral 16d lithium sites can be resolved in 6Li spectra but not in 7Li spectra (not shown) owing to the larger homonuclear dipolar coupling of the latter nuclei. (right) A broad lithium-rich phase starts to appear as spinel Li4Ti5O12 is lithiated toward rocksalt Li7Ti5O12. Adapted with permission from Schmidt, W.; Wilkening, M. Discriminating the Mobile Ions From the Immobile Ones in Li4 þ xTi5O12: 6Li NMR Reveals the Main Li þ Diffusion Pathway and Proposes a Refined Lithiation Mechanism. J. Phys. Chem. C 2016, 120 (21), 11372–11381. doi:10.1021/acs.jpcc.6b02828. Copyright 2016 American Chemical Society.

the niobium tungsten oxides on the order of 10–11 m2/s are consistent with DFT and are orders-of-magnitude faster than that of common battery electrode materials.293,294 These diffusion coefficients are more comparable to the fastest superionic solid electrolytes, even approaching liquid electrolytes.273,295 This is believed to account, in part, for their high-rate electrochemical performance even with dense mm-scale particles.

9.12.3.4

Electrolytes

Solid electrolytes in all-solid-state batteries serve the same function as liquid electrolytes in conventional lithium batteriesdto host the conduction of lithium ions while impeding electron transfer. Solid electrolytes have the advantage of having a lithium-ion transference number (the fraction of the charge carried by lithium) of unity, whereas their solution counterparts transfer charge via both anions and cations and have transference numbers well below unity and often below 0.5. An electrolyte should be oxidatively stable against the cathode, reductively stable against the anode, form good interfaces with the electrodes, and be mechanically processable and stable. It is worth noting that a reaction at the electrode/electrolyte interface is acceptable if it is self-passivating and ionically conductivedthis is the basis for the SEI that enables our present generation of lithium-ion batteries. Since no solid electrolyte possesses all the desired properties, a range of material families have emerged as candidates.

9.12.3.4.1

Garnet

Garnet solid electrolytes with the general formula Li7–xLa3M4þ2–xM5þxO12 are promising for their relatively high electrochemical stability.296 The most common garnet solid electrolytes come from the pseudo-binary Li7La3Zr2O12–Li5La3(Nb,Ta)2O12 (LLZO– LLNO), with M3þ aliovalent dopants such as Al3þ and Ga3þ replacing some of the lithium.297–300 Dopants can stabilize the high-temperature cubic polymorph of the garnet structure down to ambient temperature, which is critical as the cubic phase has about two orders-of-magnitude higher lithium-ion conductivity than the tetragonal phase.301 In the cubic structure, lithium occupies tetrahedral 24d sites and split 96h sites. Extensive 6,7Li, 27Al, and 69,71Ga solid-state NMR studies have been carried out to understand the structure and dynamics of garnet lithium-ion conductors.301–315 Spectra of 27Al and 69,71Ga show multiple resonances in the chemical shift region normally attributed to tetrahedral coordination. Through 27Al, 71Ga, and 17O NMR combined with extensive DFT calculations, Karasulu et al. showed that aluminum and gallium exclusively dope onto the four-coordinate 24d lithium site.316 DFT calculations and spectral simulations identified an inverse correlation between the number of corner-sharing LiO4 next-nearest neighbors to the dopant tetrahedron and breadth of the quadrupolar lineshape, accounting for the full breadth of observed resonances.316 Larger ions such as Sc3þ, Y3þ, Nb5þ, and Ta5þ are incorporated on the octahedral transition metal (Zr4þ) 16a site, which can be observed by NMR particularly with favorable nuclei such as 45Sc.308

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Fig. 13 6Li (solid) and 7Li (dashed) MAS NMR spectra of lithiated TiNb2O7. The x value on the right refers to the number of lithium inserted per transition metal, i.e., Li3xTiNb2O7. Reproduced from Griffith, K. J.; Seymour, I. D.; Hope, M. A.; Butala, M. M.; Lamontagne, L. K.; Preefer, M. B.; Koçer, C. P.; Henkelman, G.; Morris, A. J.; Cliffe, M. J.; Dutton, S. E.; Grey, C. P. Ionic and Electronic Conduction in TiNb2O7. J. Am. Chem. Soc. 2019, 141 (42), 1670616725. doi:10.1021/jacs.9b06669 under CC-BY license.

Undoped tetragonal Li7La3Zr2O12 and Li5La3Nb2O12 each exhibit two 6Li resonances corresponding to relatively mobile octahedrally coordinated lithium ions and relatively immobile tetrahedral lithium ions.313,317 As one indication of the differences in mobility in Li7La3Zr2O12dand a warning to keep in mind when measuring lithium spectradthe 6Li T1 relaxation times of the octahedral and tetrahedral sites are 5 s and 1200 s, respectively.313 From NMR relaxometry, tetragonal Li7La3Zr2O12 has an activation barrier for lithium hopping of 0.5 eV301,313,318 comparable to that of Li6La3ZrTaO12319 but substantially higher than the 0.30– 0.35 eV for cubic Al-doped Li7–3xAlxLa3Zr2O12.301,311,313,314,320 Ga-doped Li7–3xGaxLa3Zr2O12 exhibits even faster lithium dynamics, characterized by a lithium hopping barrier of 0.10–0.14 eV.314,321 Micrometer-scale diffusion measurements with PFG NMR are more straightforward in solid electrolytes than in electrode materials owing to the slower nuclear magnetic relaxation and typically faster ionic motion in the former. The apparent diffusion coefficient can depend on measurement parameters such as the diffusion time period (D) and gradient strength (g). For small particles, so-called diffraction effects become relevant.322,323 At longer D and higher g, longer-scale and slower diffusion processes are probed and the apparent diffusion coefficients tend to reach a steady state. Under these conditions the room-temperature lithium diffusion coefficient for garnet Li6.5La3Zr1.5Ta0.5O12 was 1–2  10–12 m2/s, Li6.55Ga0.15La3Zr2O12 was 6.2  10–13 m2/s and that of Li6.55Al0.15La3Zr2O12 was 6.5  10–15 m2/s, highlighting the importance of the aliovalent dopant on the lithium conductivity.314,324

9.12.3.4.2

NASICON-type

NASICON (Na superionic conductor) refers to a family of framework structures.325–327 Focusing here on lithium-based batteries, lithium-conducting NASICONs are generally derived from the parent compound LiTi2(PO4)3. Aliovalent doping is again critical to inducing non-stoichiometric and conductive lithium sublattices. The most common lithium-conducting NASICON phase is Aldoped Li1þ xAlxTi2–x(PO4)3 (LATP) though many other dopants have been investigated.

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Early NMR studies on LATP observed aluminum doping onto the octahedral titanium site via a 27Al signal at –15 ppm.328,329 A second 27Al resonance at 40 ppm corresponding to tetrahedral aluminum was assigned to the impurity phase AlPO4 that can appear during synthesis.329 31P NMR is a useful probe of the metal-site doping in NASICON because it splits from a single resonance in end-member compounds such as LiTi2(PO4)3 to a series of peaks corresponding to phosphorus with different next-nearest neighboring cations (Fig. 14).328,330–338 The NASICON structure features phosphorus tetrahedra that are corner-shared to metal (M) octahedra such that the phosphorus next-nearest neighbor environments can be described as P(OM)4. Scandium-doped Li1þ xScxM2–x(PO4)3 (M ¼ Ti, Ge) NASICON phases have been monitored with 6,7Li, 31P, and 45Sc NMR, showing in this case a solubility limit of x ¼ 0.2–0.3.335,338 Gallium has also been observed in the lithium NASICON structure by 31P and 71Ga NMR though it reaches a similar solubility limit before crystallizing out GaPO4.337,338 Niobium-doped Li1–xNbxTi2–x(PO4)3 again has a similar dopant solubility limit and a 93Nb resonance from the impurity phase NbPO5 can be detected at high niobium concentrations in addition to the 93Nb signal attributed to niobium in the NASICON structure.336 It has been noted that Nb5þ next-nearest neighbors shift the 31P resonance to higher frequencies while M3þ (M ¼ Al, Ga, Sc, In) next-nearest neighbors induce a shift toward lower frequencies.330,336 Note that trivalent dopants lead to lithium-excess stoichiometries while pentavalent dopants induce lithium vacancies. NASICON phases can undergo phase transitions between triclinic, monoclinic, and rhombohedral space group symmetry. Changes in the lithium coordination, number of magnetically distinct environments, and ion dynamics as a function of the polymorphism have been tracked with multinuclear NMR. LiZr2(PO4)3 undergoes a phase transition upon heating just above room

Fig. 14 31P NMR of NASICON LiTi2–xGex(PO4)3. (Top) Calculated 31P chemical shift as a function of the number of Ti and Ge next-nearest neighbors P(OTi)4–n(OGe)n. (Bottom) Experimental 31P spectra of LiTi2–xGex(PO4)3 exhibiting a single resonance at the end members corresponding to the single phosphorus site in the asymmetric unit, and multiple resonances for 0 < x < 2 when the local symmetry is lowered by different next-nearest neighbor compositions and geometries. Adapted with permission from Diez-Gómez, V.; Arbi, K.; Sanz, J. Modeling Ti/Ge Distribution in LiTi2–xGex(PO4)3 NASICON Series by 31P MAS NMR and First-Principles DFT Calculations. J. Am. Chem. Soc. 2016, 138 (30), 9479–9486. doi:10.1021/jacs.6b03583. Copyright 2016 American Chemical Society.

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temperature from a triclinic to a rhombohedral phase with a simultaneous enhancement in lithium conductivity evidenced by NMR relaxometry and the static 7Li linewidth.339–344 The triclinic phase has three distinct 31P environments from –22 to –24 ppm while the rhombohedral phase has just one at –24 ppm.341 The phase transition from low-temperature triclinic to high-temperature rhombohedral occurs just below room temperature for LiHf2(PO4)3 with similar changes in the number of 31P resonances and 7 Li linewidths.345 While they nominally do not alter the lithium stoichiometry and thus the number of charge carriers, isovalent M4þ dopants (M ¼ Ge, Zr, Hf, Sn) on the metal site in NASICON LiTi2(PO4)3 can still influence dynamics.331,345–349 LATP has a lower activation barrier for lithium hopping than most oxide solid electrolytes at ca. 0.16 eV.348 7Li PFG NMR diffusion measurements with long D and high g described in the previous section yield a room-temperature lithium diffusion coefficient of ca. 4  10–13 m2/s for Li1.5Al0.5Ge1.5(PO4)3.323,349,350

9.12.3.4.3

Perovskite

The perovskite crystal structure is one of the most ubiquitous in solid-state chemistry. Perovskite oxides take the composition ABO3 where the A-site cation sits in the middle of a cage of corner-shared BO6 octahedra. In the context of lithium-conducting solid electrolytes, attention has focused around Li3xLa2/3–xTiO3 (LLTO), which varies in symmetry and the degree of cation order based on the composition and the synthetic procedures. In general, lanthanum stabilizes the perovskite structure while the small lithium cations diffuse through channels left by A-site vacancies. 7 Li NMR of Li3xLa2/3–xTiO3 spectra do not resolve multiple resonances but structural considerations and relaxometry data suggest two subsets of lithium, one that is preferentially surrounded by La3þ and another that contains a mix of neighboring La3þ, Liþ, and vacancies.351–353 The center of mass of the 7Li resonance shifts to negative frequencies with increasing lithium (x) content, covering a range of about 3 ppm from x ¼ 0.09 to x ¼ 0.33, in good agreement with calculated values.354 Varying slopes in T1 relaxation vs. temperature curves point to different diffusion dimensionality as a function of the lithium content and cation ordering.351,355 Tetragonal-Li0.33La0.55TiO3 has a room-temperature 7Li diffusion coefficient from PFG NMR of 1  10–13 m2/s that is about an order of magnitude lower than cubic-Li0.33La0.55TiO3.356 LLTO is susceptible to Hþ/Liþ ion exchange leading to LiOH on the surface that can react with CO2 from ambient air to form lithium carbonate that is readily detected with lithium NMR.357,358 Residual protons from solution synthesis methods or from reaction with the air can be removed by thermal annealing as monitored by 1H NMR.353,357,358

9.12.3.4.4

Sulfide

Sulfide solid electrolytes include several families of materials such as LISICON-type (Li superionic conductor), argyrodites, glasses, and glass-ceramics. Despite their inferior electrochemical stability, sulfides have emerged as an alternative to oxides because of their favorable mechanical and ion-conducting properties. It is generally challenging to manufacture and create coherent electrolyte/ cathode interfaces with oxide ceramics, so leading “solid-state” battery developers currently rely on a liquid catholyte. Sulfides, on the other hand, require an additional electrolyte interface passivation step, but can operate in full solid-state batteries without any liquid components. Crystalline, glassy, and glass-ceramic Li2S–P2S5 sulfides comprise similar structural building blocks such as ortho-thiophosphate (PS43–, monomers), pyro-thiophosphate (P2S74–, dimers), meta-thiodiphosphate (P2S62–, dimers), and hypo-thiodiphosphate (P2S64–, PeP dimers).359 From model compounds, the 31P chemical shifts of these motifs have been identified, which is critical for the identification of local structure in the glassy phases: (d31P) PS43– ¼ 87–89 ppm; P2S74– ¼ 91 ppm; P2S62– ¼ 55 ppm; P2S64– ¼ 108–110 ppm.359–364 Compounds within and related to the Li2SeP2S5 family have been investigated as solid electrolytes. In order of increasing phosphorus content within this pseudo-binary, crystalline phases include Li7PS6 (7:1), Li3PS4 (3:1), Li7P3S11 (7:3), Li4P2S6 (2:1 –S)/ Li4P2S7 (2:1), Li2P2S6 (1:1). Of these phases, Li7PS6 adopts the argyrodite structure, Li3PS4 is a LISICON, Li7P3S11 is a glassceramic comprising PS43– tetrahedra and P2S74– dimerized corner-sharing tetrahedra, Li4P2S6 contains P2S64– units featuring PeP bonds, the structure of Li4P2S7 has not been solved, and Li2P2S6 is built up from P2S62– dimerized edge-sharing tetrahedra. Li7PS6, Li3PS4, and Li7P3S11 phases are promising solid electrolytes and will be described in more detail below. While they are not good ion conductors, it is worth noting that solid-state 31P NMR played a role in the structure solution of both Li4P2S6 and Li2P2S6.363,364 Li7PS6 is the archetypal lithium argyrodite structure with an ordered lithium sublattice at low temperature and a disordered lithium sublattice at elevated temperatures.361 The low-temperature polymorph exhibits two sharp 31P resonances versus one broad resonance for the high-temperature polymorph; both in the 80–90 ppm range from the isolated PS4 tetrahedra as in Li3PS4.361 Anion substitution on the phosphorus site induces disorder and generally increases lithium conductivity in the argyrodite phases. Selenium substitution can be fully tuned from Li7PS6eLi7PSe6 with the 31P resonances of the five individual PS4–nSen (n ¼ 0–4) tetrahedra well-resolved over a 160 ppm range (Fig. 15).361 Quantification of the relative PS4–nSen intensities reveals a preference for PeS bonding over PeSe.361 Second-nearest-neighbor anions can even be resolved; for example for a PS4 tetrahedron with S4–nSen in the next anion coordination shell (Fig. 15).361 Furthermore, it is possible to deconvolute the seven crystallographically distinct lithium sites in the absence of motional averaging with low-temperature 6Li NMR despite a shift range of only 2 ppm.361 Aliovalent substitution of a halide for one sulfur in the argyrodite structure induces a lithium vacancy for charge balance and leads to Li6PS5X. The 31P NMR of Li6PS5X (X ¼ Cl, Br, I) exhibits an increasing chemical shift and increased order from Cl to Br to I.365 As the halide content increases, the lithium chemical shift decreases.366,367 Two resonances assigned to

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PS4

PS3Se PS2Se2

PSSe3

PSe4 PS4

Fig. 15 31P NMR of Li7PS6–nSen. (left) Well-resolved PS4–nSen (n ¼ 0–4) environments in 31P spectra of Li7PS6–nSen. (right) Fine structure showing partially resolved second-nearest-neighbor anion environments within the PS4 environment of Li7PS5Se. Adapted with permission from Kong, S. T.; Gün, Ö.; Koch, B.; Deiseroth, H. J.; Eckert, H.; Reiner, C. Structural Characterisation of the Li Argyrodites Li7PS6 and Li7PSe6 and Their Solid Solutions: Quantification of Site Preferences by MAS-NMR Spectroscopy. Chem. Eur. J. 2010, 16 (17), 5138–5147. doi:10.1002/chem.200903023. Copyright Wiley 2010.

two different crystallographic sites for chlorine and bromine can be detected with 35Cl and 79Br NMR in Li6  x–yPS5  x– 366–368 The anion disorder in Li6PS5Cl flattens the potential energy landscape and affords the highest lithium y Cl 1þ xBry . conductivity among the Li6PS5X compounds. Extensive NMR studies of lithium dynamics have been performed on the argyrodite sulfide solid electrolytes. Interestingly, Li6PS5Cl, Li6PS5Br, and Li6PS5I all have similar T1 minima at similar temperatures and similar activation barriers for lithium hopping from 7Li relaxometry despite the fact that the lithium conductivity of Li6PS5I is 2–3 orders-of-magnitude lower than the Cl and Br analogs.365 This is reflected in the extreme 7Li lineshape narrowing that occurs about 100 K lower for Li6PS5Cl and Li6PS5Br than for Li6PS5I.365,369 The substantial differences in bulk conductivity vs the relative similarity in the relaxometry suggests that the local intracage hopping mechanisms are similar but the long-range diffusive intercage hops within the argyrodite structure are limited in the iodine case.365 While lithium is sensitive to the shorter intracage motion, 31P can be an effective probe of the longer-range lithium dynamics.370 Variable-temperature 31P NMR of Li6PS5I shows a low-temperature T1 minimum that is absent in the 7Li data and is assigned to rotational motion of the PS4–nCln tetrahedra.370,371 This T1 minimum shifts to higher temperatures in Li6PS5Br and Li6PS5Cl, suggesting that tetrahedral rotations are suppressed as anion disorder increases.371 Spinlock 31P T1r measurements that probe longer timescales revealed relatively high activation barriers that have been attributed to diffusive intercage lithium exchange in Li6PS5I.370 Nanosizing Li6PS5I improves its lithium conductivity, a phenomenon often observed in poorly conducting materials.372 127I NMR has also been used as a probe of the low-temperature to hightemperature argyrodite phase transition and corresponding increase in lithium dynamics.373 In the related selenide argyrodites, chlorine substitution from Li7PSe6 to Li6PSe5Cl enhances lithium mobility as seen by the –50 K shift in 7Li lineshape narrowing and –115 K shift in the spin-lock 7Li T1r minimum.374,375 Micrometer-scale 7Li diffusion as probed by PFG NMR gave a roomtemperature diffusion coefficient of 4  10–12 m2/s with an activation barrier of 0.28–0.35 eV for Li6PS5Cl.369,376 Calcium or chlorine substitution individually subtly increase the lithium diffusion and decrease the diffusional activation barrier while the co-substitution strategy of calcium and additional chlorine to form the phase Li5.35Ca0.1PS4.5Cl1.55 can reach unprecedented room-temperature 7Li PFG NMR diffusion coefficients as high as 1  10–11 m2/s.376,377 Cation substitutions have also been investigated in the lithium argyrodites, particularly putting germanium on the phosphorus site. 7Li PFG NMR indicates relatively hindered long-range motion in Li7GeS5Br with a room-temperature diffusion coefficient of 5  10–13 m2/s and an activation barrier of 0.46 eV.378 On the other hand, germanium substitution significantly enhances lithium mobility in the ordered Li6PS5I structure by inducing lithium disorder as seen by 7Li and 31P NMR, linewidth measurements, and relaxometry.379 A PFG NMR exploration of high-entropy argyrodites with heavily substituted anionic (Li6PS5Cl0.33Br0.33I0.33) or both anionic and cationic (Li6PS2.5Se2.5Cl0.33Br0.33I0.33 and Li6.5Ge0.5P0.5S2.5Se2.5Cl0.33Br0.33I0.33) sublattices yielded room-temperature diffusion coefficients of 1–2  10–12 m2/s, roughly in line with Li6PS5Cl itself, suggesting that this strategy is not a straightforward route to enhance conductivity.380 The simplest thio-LISICON is Li3PS4, the 3:1 composition along the Li2SeP2S5 pseudo-binary line. High-temperature solid-state methods tend to form the polymorph g-Li3PS4. One method to prepare the favored lithium-conducting polymorph, b-Li3PS4, is from a tetrahydrofuran (THF) complex (Li3PS4 ,3THF).381 31P NMR spectra of b- and g-Li3PS4 each show a single resonance corresponding to the isolated PS4 tetrahedral site in the crystal structures while Li3PS4 ,3THF exhibits three resonances of equal intensity.381,382 All 31P signals are in the range 80–90 ppm. Detailed 1H and 31P NMR highlighted the presence and role of residual THF and amorphous Li3PS4 that can remain after the THF synthetic route under mild annealing conditions.383 Rapid lithium exchange

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precludes the differentiation of the three distinct lithium sites in b-Li3PS4.381 7Li PFG NMR studies have reported or extrapolated room-temperature lithium diffusion coefficients in b-Li3PS4 of 1  10–13 m2/s.381–385 This is in good agreement with the values determined from NMR relaxometry.382,386 Similar values are observed for amorphous Li3PS4.382,384 Compounds in the series Li4SiS4eLi3PS4 (i.e., Li3þxSixP1  xS4) adopting the thio-LISICON structure showed 29Si and 31P resonances corresponding to SiS4 and PS4 tetrahedra but no fine structure could be resolved under low field and/or slow MAS conditions.387 7Li NMR relaxometry of a series of Li4MS4 thio-LISICON phases, namely Li4GeS4 and Li4SnS4 and their selenium analogues, showed a non-monotonic correlation between the lithium tetrahedral volume and the lithium hopping activation energy, suggesting an optimal value around 12.9 Å3.388,389 The discovery of Li10GeP2S12 (LGPS) with record-high solid-state lithium conductivity opened up a new family of LISICON-like compounds.295 7Li PFG NMR and relaxometry studies of Li10GeP2S12, Li7GePS8 (i.e., Li10.5Ge1.5P1.5P2S12), Li10SnP2S12 and Li11Si2PS12 showed room-temperature diffusion coefficients of 2  10–12 m2/s, on par with liquid electrolytes.390–392 All the LGPS phases had PFG and relaxometry-derived activation barriers for lithium motion of 0.19–0.26 eV.390–393 7Li motional narrowing of the LGPS compounds is complete by 190 K, indicative of the extremely high lithium mobility at room temperature. Structurally, 31P NMR can differentiate the 4d and 2b sites in LGPS and the resonance corresponding to the 2b site is sensitive to the next-nearest neighbor cation composition.391 31P relaxometry under MAS conditions where the two phosphorus sites were resolved enabled differentiation of the lithium jump rates around the two channels wherein the larger 4d PS4 exhibits restricted motion.393 Li7SiPS8 (i.e., Li10.5Si1.5P1.5P2S12) exhibited an unexpectedly low 7Li PFG NMR lithium diffusion coefficient of 3  10–13 m2/s and relatively high activation barrier of 0.32 eV.394 29Si and 31P NMR revealed 8 wt% of an amorphous secondary phase with the approximate composition Li3.2Si0.2P0.8S4 that brought down the conductivity of the sample and led the authors to suggest that NMR should be a standard tool for the characterization of superionic solid electrolytes like LGPS compounds.394 Li7P3S11 is a metastable glass-ceramic phase with PS43–and P2S74– building units identified by 31P NMR.362,395,396 6Li spectra of Li7P3S11 show almost complete line narrowing below room temperature while 6,7Li T1 relaxometry shows a maximum in the relaxation rate just above room temperature; both indicators of high lithium conductivity.362,397,398 Extremely low activation barriers (0.04–0.20 eV) for lithium hopping as probed by relaxometry have been attributed to facile local processes that are enabled by the disordered nature of the structure.362,397,398 Longer-range lithium motion has been studied with 7Li PFG NMR, which yields extremely fast room-temperature lithium diffusion coefficients of 1–2  10–12 m2/s.396,399 As in other cases (vide supra), the PFG results are complex but approach a steady state at long D and high g corresponding to longer-range and slower diffusional processes, which appear to be the best conditions for comparison across material families. Fast field-cycling NMR and relaxometry have also been combined to probe lithium dynamics in Li7P3S11 over ten orders of magnitude.400

9.12.3.4.5

LiPON

Lithium phosphorus oxynitride (LiPON), is a glassy lithium-conducting solid electrolyte.401 LiPON films with formula Li2xþ3y–5POxNy have a lower conductivity than most other solid electrolyte candidates at 2–3 mS/cm, but they are also unusually stable when cycled against lithium metal anodes.401–403 As expected, 7Li NMR spectra of LiPON exhibit a rather featureless resonance and do not provide substantial structural information.403,404 7Li linewidth analysis and relaxometry place the lithium hopping activation barrier in LiPON around 0.17–0.25 eV.404 Given its large chemical shift range, 31P NMR provides a high level of detail into this amorphous structure. Aided by DFT calculations403 and studies of model compounds,404 31P resonances from 0 to 25 ppm have been assigned to PO43 at 9.3 ppm, P2O6N5 dimers with bridging nitrogen at 14.6 ppm, PO3N4 at 19.4 ppm, and P2O74 at 5 ppm. In more nitrogen-rich LiPON films, PO2N25 has been suggested to become a prominent species.405,406 2D 31P–31P correlation spectra from different films reach different conclusions regarding whether PO4, PO3N, and PO2N2 tetrahedra are in spatial proximity.405,406 Motional averaging of the 31P resonances does not set in until close to 600  C.405 15N NMR revealed phosphazene P]NeP linkages at 60 ppm and molecular N2 at 290 ppm.404 NMR studies have not found evidence for trigonal nitrogen sites that are sometimes evoked.403,404

9.12.3.5

Interfaces

In addition to the bulk materials making up a battery cell, interfacial structures and processes are also critical factors governing the cell performance. The primary interfaces relevant to battery chemistry are those between the solid electrodes and the liquid or solid electrolyte. To maximize the energy density, anode and cathode pairs are chosen to have an appreciable difference in electrochemical potential. The low voltages of anode materials such as lithium metal, graphite or silicon means that they often operate outside of the stability window of the electrolyte. This leads to electrolyte decomposition at the electrode–electrolyte interface during the first cycle, resulting in the formation of a thin passivating layer known as the solid–electrolyte interphase (SEI).195,197,198 Once formed, the SEI acts to protect the interface from further electrolyte decomposition and also allows ion transport in and out of the electrode during cycling. The structure and chemistry of the SEI is complex and has received increasing interest in recent years owing to recognition of its importance in governing and stabilizing the overall cell chemistry. Solid-state NMR offers a powerful way to gain insight into the SEI structure although the nanoscale thickness can pose challenges from the point of view of signal sensitivity. In an early spatially resolved study of a battery cell, the initial lithiation of a silicon– graphite composite electrode was imaged in situ and revealed concentration gradients associated with SEI formation.407 Michan et al. have used multinuclear NMR to gain insight into the electrolyte decomposition products formed on silicon anodes.14,15,408 19 F MAS NMR confirmed the presence of LiF, POxFy, and SiOxFy that form from the decomposition of the PF6– ions in the electrolyte

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salt. 7Li MAS NMR suggested the presence of lithium carbonate phases but precise identification was hindered by the small chemical shift range of 7Li. The obvious choice of nucleus for studying carbonates is 13C NMR; however, the low natural abundance of 13C makes it challenging to study the very small quantities present in the SEI. Therefore, a 13C isotopically enriched electrolyte was used which not only enhanced the 13C signal, but provided direct insight into the electrolyte decomposition mechanism since carbonate SEI signals could be linked to specific isotopically enriched carbons in the electrolyte molecules (Fig. 16a).15 Following that work, the organic and semicarbonate species of the SEI on silicon in the presence of alkyl carbonates were identified in detail by twodimensional 13Ce13C homonuclear correlation experiments and 1He13C cross-polarization experiments.408 NMR has also been used to gain insights into the SEI on lithium metal. In a multinuclear NMR study, the composition, dead lithium concentration, and density of the SEI on lithium metal were found to vary with the lithium salt type (LiFSI and LiTFSI) and concentration (1–4 M).409 Cycling in 4 M LiFSI in an ether electrolyte solvent led to minimal dead lithium in the SEI and a denser SEI with a substantial LiF component that is thought to enhance stable plating and stripping.409 The study also contains 6 Li standard spectra Li2O, Li2S, LiOH ,H2O, Li2CO3, LiF, LiFSI, and LiTFSI that may serve as a useful reference.409 Another work examined LiFSI salt at different concentrations in an ionic liquid electrolyte solvent and reached similar conclusions regarding the favorable SEI components and properties at higher salt concentration.410 Reaction at the lithium metal interface does not have to be electrochemically driven. Ilott and Jerschow studied SEI formation of alkyl carbonate salts on lithium metal in the absence of any applied current or voltage.411 By using a 6Li isotopically enriched lithium metal anode and natural abundance (93% 7Li) electrolyte, the authors found significant lithium exchange between the electrode and electrolyte even under opencircuit conditions.411 Recently, lithium chemical exchange saturation transfer was demonstrated as a method to detect lithium exchange across the SEI–Li metal interface.412 Additives are often used to tailor the SEI to be more stable and/or ionically conductive. Fluoroethylene carbonate (FEC) is a common electrolyte additive in many lithium battery systems, and its incorporation into alkyl carbonate electrolyte solvents has been studied via in situ and isotope-labeled NMR techniques with lithium metal anodes.413 The presence of FEC accelerates SEI formation (by about a factor of 4) and also forms an SEI that facilitates more rapid lithium transport. The improved transport properties of the SEI formed in the presence of FEC aids uniform lithium plating and thus delays the onset of lithium microstructure formation.413 An NMR and MRI study of FEC and lithium difluorophosphate (LiPO2F2) showed that electrolyte salt polarization is less extreme in the presence of the additives and that a mixture of additives lead to the lowest dead lithium in the SEI and the best cycling, though not necessarily the least SEI formation.414 An in situ NMR study of FEC in an anodeless full celldwhere the cell is assembled with only a copper current collector and lithium is deposited from the cathode on the first chargedrevealed that there is minimal dead Li formation in the presence of FEC but that corrosion is an issue as lithium metal dissolves and interfacial copper oxides are reduced along with SEI formation.266 In situ 7Li NMR showed that a barrier coating suppresses lithium loss and may be necessary to hinder this corrosive reactivity.266 The interface on copper in an anodeless cell changes from its native (as assembled) state once a voltage is applied. The native SEI is primarily inorganic, containing species such as LiF, Cu oxides, and Cu fluorides when copper current collectors are immersed in a LiPF6-based electrolyte.415 As the cell is polarized and lithium is deposited from the cathode, a layer with LixCuO, Li2O, LiOH, and solvent reduction products forms atop the inorganic native SEI.415 Recently, DNP has been used to enhance the sensitivity of species within the SEI for observation by NMR. Hope et al. demonstrated a novel approach using the polarization of conduction electrons in a lithium metal anode to provide a DNP enhancement for the SEI on the surface.253 This enabled 7Li, 1H, and 19F signals from SEI components to be selectively observed without the requirement for a polarizing agent to be added to the sample. Although the enhancement factor achieved was smaller than those typically obtained with exogenous polarizing agents, this approach demonstrates considerable potential for application to in situ NMR cells where it is not practicable to introduce a radical polarizing agent to a working battery. DNP helped Leskes et al. identify and differentiate the inner and outer SEI components on reduced graphene oxide electrodes in different alkyl carbonate electrolyte solvents.416 In addition to the SEI, electrolyte decomposition can also occur at the cathode–electrolyte interface, leading to an analogous layer referred to as the cathode–electrolyte interphase (CEI). The contribution of the CEI to the overall cell chemistry has previously been overlooked, but it is becoming increasingly recognized as one of the key factors governing the electrochemical performance of high-voltage cathode materials. The formation mechanism of the CEI differs from the SEI in that it is driven by transition metal dissolution and oxygen evolution from the cathode. Hestenes et al. have used solid-state NMR and DNP to probe the structure of the CEI on a Li2RuO3 cathode.417 It was found that the CEI composition is similar to the SEI, being largely composed of polyethylene oxide, organic Li salts, carbonates and LiF. However, compositional differences were observed between charged and discharged electrodes suggested that Liþ-coordinating species that make up outer CEI components leave the electrode during delithiation, contributing to capacity loss over multiple cycles. Haber et al. have studied an artificial CEI using DNP with multiple polarization sources to probe different parts of an alkylated LixSiyOz coating on model TiO2 and lithium-rich layered oxide cathode particles (Fig. 16b).8 In exogenous DNP measurements, a radical-containing polarizing agent was used to enhance alkylated groups on the exterior surface of the coating. In endogenous DNP measurements, Fe3þ dopants incorporated within the cathode were used to enhance the interface between the cathode material and the CEI coating. Like the Li metal polarization source mentioned above, endogenous DNP holds particular promise for in situ studies, since no additional polarizing agent is required. However, the effect of any transition metal dopants on the cathode electrochemistry must be minimized and/or taken into account. Another area where interfaces are of high importance is in solid-state batteries. One of the key challenges is the high impedance of the electrode–electrolyte interface formed by the physical contact of two solid materials. Characterizing Li ion exchange across the

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Fig. 16 (a) 13C NMR spectra of silicon anodes extracted from coin cells cycled using 13C-enriched electrolytes to reveal specific functional groups present in the SEI. (b) Endogenous and (c) exogenous 7Li and 29Si DNP-enhanced MAS NMR spectra of an alkylated LixSiyOz interphase layer on a model TiO2 substrate. Panel a: Reproduced from Michan, A. L.; Leskes, M.; Grey, C. P. Voltage Dependent Solid Electrolyte Interphase Formation in Silicon Electrodes: Monitoring the Formation of Organic Decomposition Products. Chem. Mater. 2016, 28 (1), 385–398. doi:10.1021/ acs.chemmater.5b04408 under CC–BY license. Panel b and c: Reproduced from Haber, S.; Rosy, L.; Saha, A.; Brontvein, O.; Carmieli, R.; Zohar, A.; Noked, M.; Leskes, M. Structure and Functionality of an Alkylated LixSiyOz Interphase for High-Energy Cathodes From DNP-ssNMR Spectroscopy. J. Am. Chem. Soc. 2021, 143 (12), 4694–4704. doi:10.1021/jacs.1c00215 under CC–BY license.

electrode–electrolyte interface is necessary in order to understand how the structural chemistry of the two phases is related to battery performance. Yu et al. have used 7Li EXSY NMR experiments to monitor ion exchange across the interface between a Li2S cathode material and Li6PS5Cl or Li6PS5Br solid electrolyte.418,419 The interfacial ion conductivity was found to be several orders of magnitude smaller than the conductivity of the bulk electrolyte determined from 7Li T1 relaxation measurements. In addition, a substantial drop in interfacial conductivity was observed after cycling which was attributed to loss of contact between the two phases from the large volume changes of the cathode and the presence of an interfacial layer with higher activation energy than the bulk arising from redox instabilities at the interface. This work highlights that interfacial chemistry remains a major bottleneck in solid-state batteries and addressing this is a key challenge in the ongoing development of this technology.

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9.12.4

NMR studies of supercapacitors

9.12.4.1

Fundamentals of supercapacitors

In recent years, electrochemical double-layer capacitors, or “supercapacitors” have attracted renewed attention as high-power energy storage devices for a wide range of applications. Supercapacitors store charge electrostatically through the adsorption of liquid electrolyte ions at a charged surface. The classical picture of the charge storage mechanism is shown in Fig. 17. During charging, ions are electrostatically adsorbed, or electrosorbed, at the surface of the oppositely charged electrode forming an electrical double layer with an associated capacitance. During discharge, the ions move away from the electrode, and the stored electronic charge flows through the external circuit. To a first approximation, double-layer capacitance is proportional to the surface area of the electrode–electrolyte interface. For this reason, supercapacitors use porous electrode materials to maximize the surface area. The material of choice is microporous carbon with pore sizes predominantly in the 1–2 nm range and surface areas of up to 2000 m2 g–1. Microporous carbons are non-graphitic carbons into which porosity is introduced by high temperature chemical activation processes. This results in an amorphous structure comprising disordered graphene-like carbon fragments as well as defects giving rise to curvature. Spaces and voids between the carbon fragments form the pore structure through which charge-storing ions move, and the carbon surfaces form the interface for double-layer formation during charging. Microporous carbons also have high electronic conductivity, which is important for electron transport from the current collector to the electrode–electrolyte interface. Supercapacitor electrolytes typically comprise organic salts such as tetraethylammonium tetrafluoroborate (NEt4–BF4) dissolved in organic solvents such as acetonitrile (ACN) or propylene carbonate. These electrolytes give a good compromise between a moderate voltage window of approximately 2.7 V and suitable ionic conductivity. There is also growing interest in aqueous electrolytes based on solutions of Group 1 metal halides, sulfates or other simple salts.420 These also have high ionic conductivities with the advantage of being low cost and more sustainable. Room-temperature ionic liquids (RTILs) have also been studied as supercapacitor electrolytes owing to their wider voltage windows of up to 5 V.421–423 RTILs show good chemical and thermal stability in supercapacitor applications, and they are also non-flammable with low vapor pressures. However, the main disadvantage of RTILs is the higher viscosity which impedes ion transport and reduces the power density. Despite the basic picture of the charge storage mechanism in supercapacitors being relatively straightforward, many fundamental details are still not well understood. Theoretical and experimental studies have shown that additional effects such as ion desolvation,424 rearrangement and confinement,425,426 charge screening,427–429 and pore surface properties427 can have a significant impact on the capacitance and charge storage dynamics. Due to the complex electrode structure and dynamic properties of the electrode– electrolyte interface, it remains very challenging to obtain fundamental experimental insights. In this regard, NMR spectroscopy has emerged as a powerful method for studying supercapacitors as it is one of the few techniques that can selectively observe and quantify adsorbed and electrosorbed species in the presence of the bulk electrolyte.430 The fact that it is element selective also means that charge-storing cations and anions, and solvent species, can be observed separately, allowing their individual contributions to the charge storage process to be investigated and quantified.

9.12.4.2

Observation of adsorbed species

The utility of NMR for the study of supercapacitors largely stems from the so-called “ring current” effect that arises due to the presence of delocalized electrons within the sp2-hybridized carbon electrode surface. In the NMR experiment, the external magnetic field, B0, induces electron circulation within the delocalized p-orbitals in the carbon fragments, resulting in a secondary local magnetic field adjacent to the carbon surface. The induced magnetic field opposes B0 and is inversely proportional to the distance from the carbon surface.431 Therefore, species close to the carbon surface (i.e., those adsorbed within the pore structure) are shielded from B0 with respect to those outside the carbon particles in free solution, enabling adsorbates to be identified by a characteristic shift to low frequency in the NMR spectrum. This is illustrated in Fig. 18 which shows 19F NMR spectra of a model carbon electrode

Fig. 17 Schematic representation of the mechanism of supercapacitance. (a) In the uncharged state, the supercapacitor consists of two conducting electrodes separated by a liquid electrolyte containing mobile ions. (b) During charging, electronic charge accumulates on the electrode surface and is balanced by ionic charge that adsorbs on the electrode surface. Reprinted from Griffin, J. M.; Forse, A. C.; Grey, C. P. Solid-State NMR Studies of Supercapacitors. Solid State Nucl. Magn. Reson. 2016, 74–75, 16–35. doi: 10.1016/j.ssnmr.2016.03.003. Copyright 2016, with permission from Elsevier.

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Fig. 18 19F static NMR spectra of activated carbon electrode films loaded with different amounts of NEt4–BF4/ACN electrolyte. Reproduced from Griffin, J. M.; Forse, A. C.; Wang, H.; Trease, N.M.; Taberna, P.-L.; Simon, P.; Grey, C.P. Ion Counting in Supercapacitor Electrodes Using NMR Spectroscopy. Faraday Discuss. 2014, 176, 49–68. doi:10.1039/C4FD00138A with permission from the Royal Society of Chemistry.

loaded with varying amounts of NEt4BF4/ACN electrolyte. For the lowest loading, a single resonance is observed at –155 ppm corresponding to adsorbed “in-pore” BF4– ions located within the pore structure. As the loading level is increased, the intensity of this resonance grows until the electrode is saturated and a second “ex-pore” resonance is observed at –150 ppm, which is very close to the chemical shift of the neat electrolyte. This resonance corresponds to free electrolyte outside of the carbon particles and continues to grow as more electrolyte is added. Rather than measurement of the absolute chemical shift relative to a reference sample, it is often more informative to quantify the change in chemical shift due to adsorption, Dd, which is given by Dd ¼ din-pore–dneat where din-pore and dneat are the chemical shifts of the in-pore resonance and the neat electrolyte, respectively. The relatively simple observation of a shifted resonance for in-pore species has formed the basis for many NMR investigations of supercapacitors. Because in-pore species are resolved from ex-pore species in the free electrolyte, in principle they can be quantified to give information about electrolyte loading and adsorption. Changes in the in-pore population can be tracked as a function of the state of charge. Furthermore, the magnitude of Dd has been shown to depend upon a number of factors relating to the ion location as well as the pore width and carbon structure.432–434 Careful separation of these effects can therefore provide detailed information about different aspects of the electrode–electrolyte interface including electrode structure and ion behavior and dynamics.

9.12.4.3

NMR studies of pore size and electrode structure

An ongoing question in supercapacitor research is how the structural properties of the electrode influence the electrochemical properties of the device. Owing to the lack of long-range order, microporous carbon structures are very difficult to structurally characterize. 13C solid-state NMR has been applied to study amorphous carbon structures directly, but in general this approach gives limited structural information due to broadening arising from disorder and the local anisotropic susceptibility associated with the carbon fragments within the structure. However, a number of studies have attempted to use NMR experiments on adsorbed species to indirectly probe the carbon structure. The magnitude of the shielding experienced by adsorbed species is dependent upon their distance from the carbon surface. Using a simplified phenomenological model and taking the magnetic susceptibility of graphite as a representative example, Anderson et al. predicted that a nucleus located at a distance z ¼ 3 Å from a graphite surface should be shielded by 10.2 ppm.435 The magnitude of the shielding was proportional to z–3 such that it reduced to < 1 ppm at a distance of 7 Å from the surface. A similar distance dependence was observed by Forse et al., who used DFT calculations to determine nucleus independent chemical shifts (NICS) above coronene-based carbon fragments.433 For a model slit pore comprising a space between two carbon fragments, the NICS was found to be approximately additive such that the shielding at any location between the sheets equaled the sum of the NICS from both surfaces. The distance dependence of the ring-current shielding suggests that the NMR shift of an adsorbed species should be sensitive to the width of the pore in which it is located. Indeed, a number of studies have demonstrated correlations between the average carbon pore size and the observed shift of the adsorbed species.432–434,436 Therefore, in principle, NMR can be used as a method to probe the carbon pore structure and extract parameters such as the average pore width and pore size distribution. Xing et al. used this hypothesis to extract pore size distributions for a range of polymer-derived carbons based on the measured 1H shift of adsorbed H2O.434 The shift was correlated with the pore size via DFT calculations on a model carbon pore approximated as the space between two circumcoronene molecules separated by a defined distance. In this model, the H2O molecules were assumed to undergo fast exchange between all points in the pore such that the observed shift was the fast-exchange average of the ring-current shielding at all locations between the pore walls. Using this approach, it was possible to uniquely map the measured 1H shift to a defined pore size, and the width of the experimental 1H resonance was interpreted in terms of the pore size distribution. From the integrals of the adsorbed H2O resonances total pore volumes were also extracted and found to show good agreement with the pore volume

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measured by gas sorption. This approach is promising in that it offers a method to probe the carbon pore structure and properties that is independent of gas sorption methods, which also rely on assumptions and approximations of the pore structure. However, the validity of the assumption on which the model is based have not yet been extensively tested. In particular, the model is very sensitive to the structural model used in the DFT calculations; the circumcoronene molecule is a significant simplification of the actual carbon structure which is disordered with extensive curvature and defects. Furthermore, the model assumes that adsorbed species reside exclusively between carbon surfaces, whereas chemical effects such as preferential adsorption, the contribution of sheet edge effects, and differences in local ordering of adsorbed molecules compared to the bulk may also need to be taken into account. In addition to the pore width, the carbon domain size has been shown to influence the magnitude of the NICS for nearby species. DFT calculations on model carbon fragments show that larger carbon surfaces give rise to a larger NICS at a given distance from the surface. In this way, the shift of the in-pore resonance can be used to probe the carbon structure, providing other contributions are carefully accounted for. This was demonstrated in a study of the structural evolution of microporous titanium carbidederived carbons during high-temperature heat treatment.437 NICS profiles were determined by DFT for model slit pores formed by spaces between parallel carbon fragments with increasing fragment sizes from coronene to dicircumcoronene. The NICS profiles were then incorporated into lattice simulations to calculate the in-pore shift taking into account the adsorption thermodynamics of the slit pore based on molecular dynamics simulations, as well as a distribution of pore sizes based on experimental gas sorption measurements. Using this approach, it was found that high-temperature heat treatment causes the average carbon domain size to increase from being comparable to the size of a coronene molecule when annealed at 600  C to comparable to a dicircumcoronene molecule when annealed at 1000  C.

9.12.4.4

Dynamics and diffusion of adsorbed species

Electrolyte species adsorbed on supercapacitor electrodes can undergo dynamic behavior on a range of time and length scales. One of the key observations from NMR spectroscopy is that, in general, a single in-pore resonance is observed even for electrodes which contain appreciable pore size distributions or distinct pore sizes. This indicates that in most cases electrolyte species undergo fast exchange between the different pore environments present in the electrode. As an illustrative example, Borchardt et al. studied the adsorption of NEt4BF4/ACN on ordered mesoporous carbide-derived carbon, which has a characteristic bimodal pore size distribution with pores of 1.0 and 4.1 nm.432 Based on the pore-width dependence of the ring-current shift, the bimodal pore structure within ordered mesoporous carbide-derived carbon should result in two separate in-pore resonances; however, only a single resonance was observed with a Dd value of –3.6 ppm (Fig. 19). This is intermediate between that of the same electrolyte adsorbed on titanium carbide-derived carbon (pore size 1.0 nm; Dd ¼ –6.2 ppm) and CMK-3 (pore size 4.5 nm; Dd ¼ –1.7 ppm), suggesting that exchange between the 1.0 and 4.1 nm pores in ordered mesoporous carbide-derived carbon results in averaging of the ring current shifts between the two pore environments. Based on the expected difference in Dd between the two pore environments, the exchange process in this example must happen on the millisecond timescale or faster. The precise inter-pore exchange dynamics for a particular microporous carbon will depend upon the specific structure and pore connectivity in each case, although in general the presence of mesopores acts to increase the rate of diffusion within the structure. However, despite the inter-pore exchange averaging that often takes place, for many systems the in-pore resonance is still broader than the ex-pore resonance and it varies significantly with temperature,438 suggesting that the interpore dynamics are not fully in the fast-exchange regime, and/or that a distribution of locally-averaged shifts remains. In addition to inter-pore exchange, electrolyte species undergo exchange between the in-pore and ex-pore environments on a much longer timescale. At ambient temperature, this process is not fast enough to result in averaging of the in-pore and expore resonances but can be identified through the observation of cross-peaks in 2D EXSY spectra. Wang et al. reported cross peaks at a mixing time of 500 ms in a 11B 2D EXSY spectrum of NEt4BF4/ACN adsorbed on YP17 activated carbon, suggesting that mixing between the in-pore and ex-pore environments takes place on approximately this timescale.439 However, Griffin et al. demonstrated that the build-up of cross-peak intensity as a function of mixing time for the same electrolyte–carbon system does not conform to a simple two-site exchange model.440 Fulik et al. subsequently interpreted the exchange kinetics in terms of a more complex model involving two separate exchange processes with different timescales.441 This gave much better agreement suggesting that the full inpore/ex-pore exchange process comprises a “slow” Hz-timescale component related to the diffusion of electrolyte species from the centers of carbon particles to the surface, and a fast kHz-timescale component relating to in-pore/ex-pore exchange near the particle surface. In reality, the exchange kinetics are likely to be more complex than this, involving a continuum of exchange processes reflecting the continuous variation in exchange kinetics between the ex-pore environment and progressively deeper locations within carbon particles. While the overall in-pore/ex-pore exchange kinetics are not fast enough to average the in-pore and ex-pore resonances, the fast component can lead to partial averaging. This was demonstrated by Fulik et al. who reported small reductions in Dd upon saturation of a microporous carbon sample with NEt4BF4/ACN electrolyte.441 At the point where the sample becomes saturated, the ex-pore electrolyte reservoir is created and in-pore/ex-pore exchange can start to take place. For species close to the surfaces of carbon particles, the millisecond exchange process can be sufficient to produce a measurable effect in the NMR spectrum, shifting the apparent center of gravity of the in-pore resonance to higher frequency. This effect also changes the shift of the ex-pore resonance relative to the free electrolyte, shifting it to lower frequency. The effect was particularly pronounced for smaller BF4 ions and ACN solvent molecules, suggesting that these species are more mobile than the larger NEt4 cations. This work was followed up by Cervini

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Fig. 19 11B MAS NMR spectra of porous carbon materials with different pore-sizes loaded with NEt4–BF4/ACN electrolyte. The observed ring current of the ordered mesoporous carbide-derived carbon (OM-CDC) which has a bi-modal pore size distribution is intermediate between CMK-3 and titanium carbide-derived carbon processed at 1000  C (TiC-CDC-1000) suggesting fast inter-pore exchange. Adapted from Borchardt, L.; Oschatz, M.; Paasch, S.; Kaskel, S.; Brunner, E. Interaction of Electrolyte Molecules With Carbon Materials of Well-Defined Porosity: Characterization by Solid-State NMR Spectroscopy. Phys. Chem. Chem. Phys. 2013, 15 (36), 15177. doi:10.1039/c3cp52283k with permission from the Royal Society of Chemistry.

et al. who compared Dd values for H2O-saturated microporous carbons with different particle sizes.442 For 21-mm-diameter particles, similar effects were reported, whereby the ex-pore resonance was shifted to low frequency and broadened relative to neat H2O due to partial exchange averaging. However, for 80-mm-diameter particles, negligible exchange averaging was observed and the expore shift was very close to that of neat H2O. The differences between the two samples were attributed to the increased in-pore/expore exchange kinetics in the smaller particle system. Overall, these studies highlight that multiple factors can contribute to the measured value of Dd and it should not necessarily be taken as a true representation of the ring-current shift, particularly for carbons with small particle sizes.

9.12.4.5

Insights into supercapacitor charging mechanisms

One of the key research aims in NMR studies of supercapacitors has been to provide information about the charging mechanisms. An important starting point for this is to understand the properties of the electrode before charging, i.e., the spontaneous adsorption of electrolyte species in the absence of an applied potential. In-pore cations and anions can be quantified through straightforward integration of the in-pore resonance for each species. Studies on organic and ionic liquid electrolytes have shown that before charging, approximately equal populations of cations and anions are adsorbed within the microporous carbon electrode, as would be expected in order to maintain local charge neutrality.438,443,444 For high-concentration solvent-based electrolytes, ions fill the pore network and pack densely, even leading to overlap of solvation shells. In contrast, aqueous electrolytes can show different spontaneous adsorption behavior owing to stronger ion–solvent interactions. For a polymer-derived carbon with a relatively small average pore width (0.58 nm) soaked with an aqueous solution of NaF, in-pore H2O molecules were observed in the 1H NMR spectrum, but no in-pore resonance was observed in the 19F NMR spectrum, showing that the solvated F– ions were unable to enter the pores in the absence of an applied potential.445 Similar effects have also been observed in another systematic study where a reduction of the measured Dd for aqueous cations adsorbed on polymer-derived carbon was observed for low electrolyte concentrations.436 It was proposed that at low concentrations, solvated ions preferentially reside in larger pores where there is less distortion or rearrangement of the solvation shell; this indirectly reduces the ring-current shift due to the larger average ion–carbon distance. An important point coming from NMR studies of spontaneous adsorption is that in general cations and anions populate the inpore environment prior to supercapacitor charging. This has significant implications for the traditional picture of the supercapacitor charging mechanism which assumes it to be based purely on the electrosorption of counter ions (i.e., adsorption of ions with opposite charge to the electrode) into the electrode pores (Fig. 20a). While purely adsorptive mechanisms are possible, it is also possible for charging to proceed via swapping of in-pore co-ions (those with the same charge as the electrode) for ex-pore counter-ions (Fig. 20b). A third possible mechanism is for charging to proceed purely via expulsion of co-ions (Fig. 20c). In each case, the excess ionic charge remaining inside the pores balances the electronic charge stored in the electrode surface despite the differences in the resulting in-pore ion populations.440

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Fig. 20 Schematic illustrations of possible charge storage mechanisms within a micropore that contains anions and cations prior to charging. If the electrode surface is positively polarized, an equal negative ionic charge can arise through either (a) adsorption of ex-pore anions into the pores, (b) exchange of ex-pore cations for in-pore anions, or (c) the expulsion of cations from the pores. Reproduced from Griffin, J. M.; Forse, A.C.; Wang, H.; Trease, N.M.; Taberna, P.-L.; Simon, P.; Grey, C.P. Ion Counting in Supercapacitor Electrodes Using NMR Spectroscopy. Faraday Discuss. 2014, 176, 49–68. doi:10.1039/C4FD00138A with permission from the Royal Society of Chemistry.

In principle it is possible to gain insight into the nature of the charging mechanism by NMR through integration of the in-pore resonance at different charge states. This has been done via ex situ measurements on electrodes extracted from cells charged to defined voltages. Deschamps et al. performed MAS NMR experiments on charged supercapacitor electrodes comprising commercial activated carbon and NEt4BF4/ACN electrolyte.443 The high resolution afforded by MAS enabled both the NEt4 cations and BF4 anions to be studied by 13C and 11B NMR, respectively. In positively charged electrodes, the in-pore anion population increased, while the in-pore cation population decreased during charging; in the negative electrode, the opposite behavior was observed. These observations are consistent with an ion-exchange charging mechanism whereby co-ions are expelled from the pores while counterions are simultaneously absorbed. Forse et al. studied the charging mechanism in supercapacitor electrodes containing the RTIL electrolytes 1-methyl-1-propylpyrrolidinium bis(trifluoromethanesulfonyl)imide (Pyr13-TFSI), and 1-ethyl-3-methylimidazolium bis(tri-fluoromethanesulfonyl)imide (EMI-TFSI).438 RTIL electrolytes are more challenging to study by NMR owing to the reduced mobility compared to solvent-based electrolytes, which can lead to broadening in the NMR spectrum. As such, for Pyr13-TFSI and EMI-TFSI, MAS was found to be essential in order to provide sufficient resolution to observe the in-pore resonances. Through a similar process of deconvolution and integration of the in-pore resonances, charging was found to proceed via an ionexchange mechanism in both positively and negatively charged electrodes. However, the relative change in the in-pore anion population was larger than that of the in-pore cation population, indicating a small net adsorption of anions and therefore an increase in the total population of in-pore ions in the positive electrode. The additional anions may be accommodated by ion rearrangement within the pores, or by electrolyte accessing areas of the microporous network that were not wetted before charging. Ex situ MAS NMR studies of supercapacitor electrodes provide increased resolution compared to static measurements, which is advantageous when quantifying in-pore ion populations. However, a key consideration is whether the system can be perturbed during disassembly of the supercapacitor cell. This is potentially more of an issue for supercapacitors than batteries because the charge storage mechanism relies on a precise arrangement of highly mobile ionic species within the pore network. Self-discharge is a more significant issue for supercapacitors than for batteries. For RTIL supercapacitors, Forse et al. showed that there was no appreciable change in the cell voltage during several hours after disassembly, suggesting that RTIL ions are sufficiently viscous that the in-pore ion arrangement is preserved.438 However, this may not be the case for solvent-based electrolytes where partial or complete drying of the electrode (either deliberately or inadvertently during cell disassembly) could potentially perturb the in-pore ion arrangement. In view of this, in situ NMR methods have been pursued in order to ensure that the cell is not disturbed prior to the NMR measurement, and also to ensure that NMR measurements can be precisely coupled with a well-defined electrochemical state.

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The study of supercapacitors by in situ NMR raises some specific practical considerations. One of the main considerations is that, unlike many other electrochemical systems, supercapacitor electrodes are essentially chemically identical and the in-pore resonances associated with the anode and the cathode are therefore unresolved. This is problematic for the study of the charging mechanism because in-pore ion populations cannot be separately quantified for the two electrodes. To address this, Wang et al. introduced a “shifted cell” design whereby the two electrodes are contained within a bag cell and shifted laterally relative to each other, allowing a single electrode to be located within the NMR coil.439 The distance between the electrodes (typically a few mm) is set to provide good selectivity for the electrode within the NMR coil while maintaining satisfactory electrochemical performance.446 This was subsequently refined to an “overlaid” design which gave improved electrochemical performance (Fig. 21). Luo et al. took an alternative approach whereby a traditional parallel electrode geometry was used, but one electrode was shielded by a copper foil to prevent RF penetration.447 This design has the advantage of preserving good electrochemical performance but must be carefully constructed so that none of the observed electrode is shielded. Despite the reduced resolution of in situ NMR, a number of studies have shown that it is possible to quantify in-pore ion populations during charging through deconvolution and integration of the in-pore resonance. Initial studies by Wang et al. on supercapacitors containing NEt4BF4/ACN electrolyte focused on 11B and 19F in situ NMR to observe anions during charging.439 Observation of the NEt4 cations was not possible owing to the low sensitivity of 13C and 15N, and 1H NMR was precluded due to the strong 1H background from the polymer bag cell membrane and separator. In that work, the in-pore anion resonance decreased in intensity for negative electrode polarization and increased in intensity for positive polarization. This shows that coion expulsion and adsorption takes place during charging, although because the cations were not studied, the full mechanism was not characterized. Interestingly, for both positive and negative charging, threshold voltages of 0.50–0.75 V were observed, below which only small changes in the in-pore anion populations were observed. This may be consistent with “ion mixing” that has been observed in electrochemical quartz-crystal microbalance (EQCM) studies for low electrode polarizations,448 although further work would be needed to verify this. Griffin et al. followed up this work with a systematic study of supercapacitors with fluorine-containing electrolytes by 19F in situ NMR.440 Electrolytes were chosen in order to investigate the effect of the relative anion and cation sizes, as well as the chemical properties of the cation. For tetrabutylammonium NBu4BF4/ACN electrolyte, a significant decrease in the in-pore anion population was observed for negative electrode polarization, contrasting previous results for NEt4BF4/ ACN electrolyte where smaller changes were observed. This was taken to suggest that the significantly larger size of the NBu4 cation (with an estimated desolvated diameter of 1.1 nm) prevents it from accessing a larger fraction of the micropores, and so the smaller BF4 anions are forced to make a greater contribution to the charging mechanism. While insights into the charging mechanism can be obtained from NMR studies of a single ionic species, full characterization of the charging mechanism requires quantitative information for both the anions and the cations. This can be challenging to achieve owing to the unfavorable NMR properties of the nuclei within many organic cations; however, phosphonium-based electrolytes allow cations to be quantified by observation of the high-sensitivity 31P nucleus (Fig. 22). Griffin et al. used in situ NMR to study a supercapacitor containing tetraethylphosphonium PEt4BF4/ACN electrolyte at a range of concentrations.444 The in-pore anion and

Fig. 21 Schematic illustrations of conventional, shifted, and overlaid supercapacitor in situ bag cell designs and corresponding cyclic voltammetry profiles demonstrating the superior electrochemical performance of the overlaid design in comparison to the shifted design. Reproduced with permission from Wang, H.; Forse, A. C.; Griffin, J. M.; Trease, N. M.; Trognko, L.; Taberna, P.-L.; Simon, P.; Grey, C. P. In Situ NMR Spectroscopy of Supercapacitors: Insight Into the Charge Storage Mechanism. J. Am. Chem. Soc. 2013, 135 (50), 18968–18980. doi:10.1021/ja410287s. Copyright 2013 American Chemical Society.

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Fig. 22 Quantitative in-pore anion and cation populations in a supercapacitor electrode as a function of the state of charge. (a) In situ 31P (red) and 19 F (green) NMR spectra of the cations and anions, respectively, in a supercapacitor containing PEt4BF4/ACN electrolyte. (b) In-pore ion populations as a function of cell voltage for electrolyte concentrations of 1.5 M, 0.75 M, 0.5 M. Reproduced with permission from Griffin, J. M.; Forse, A. C.; Tsai, W.-Y.; Taberna, P.-L.; Simon, P.; Grey, C. P. In Situ NMR and Electrochemical Quartz Crystal Microbalance Techniques Reveal the Structure of the Electrical Double Layer in Supercapacitors. Nat. Mater. 2015, 14 (8), 812–819. doi:10.1038/nmat4318.

cation populations were separately quantified at voltages between 0 and  1.5 V and correlated with the total electrode charge determined from simultaneous electrochemical monitoring of the cell. Over the voltage range studied, the total ionic charge within the pores showed good agreement with the electronic charge stored in the electrode, confirming that each stored electron is balanced by one unit of ionic charge within the pores. Through analysis of the in-pore ion populations, the full charging mechanism could be determined. For positive electrode polarization, an ion-exchange mechanism was observed, characterized by co-ion expulsion and counter-ion adsorption in approximately equal ratios. Interestingly, for negative electrode polarization, a counter-ion adsorption mechanism was observed, where co-ions remained within the pores while counter-ions were adsorbed. This behavior was independent of the electrolyte concentration, suggesting that the charging mechanism may be influenced by the intrinsic properties of the electrolyte ions such as relative anion/cation sizes or mobilities. Further work needs to be done in this area to fully understand the factors that dictate the charging mechanisms for specific electrode polarizations. In addition to organic electrolytes, in situ NMR studies have also been performed on aqueous electrolytes. For aqueous NaBF4 and NaNO3 electrolytes within positively polarized electrodes, ion-exchange mechanisms have been observed at low potentials, with a transition to a co-ion expulsion mechanism at around 0.6 V.447 Other measurements reveal interesting differences that can be attributed to stronger ion–solvent interactions. For a supercapacitor based on aqueous NaF electrolyte and a polymerderived carbon with sub-nanometer average pore size, Luo et al. demonstrated that F– ions only enter the pores above a “gating voltage” of approximately 0.4 V.445 The gating voltage appears to be necessary in this case to overcome ion–solvent interactions to drive the electrosorption of counter ions. At voltages above 0.8 V, very large negative chemical shift changes were observed; these were attributed to partial desolvation of the F– ions within the electrode pores. Overall, aqueous electrolytes appear to behave differently to organic electrolytes, and further insight into the factors affecting the charging mechanism for both systems will be important in understanding these differences. A further observation in NMR studies of supercapacitor charging is a change in the chemical shift of the in-pore resonance. In general, the magnitude of Dd reduces with increasing electrode charge for both positive and negative polarization.439,446 The fact that this effect is the same for both electrode polarizations suggests that it is not primarily related to changes in ion–carbon distances or other spatial rearrangements inside the pores, which would not be expected to vary in the same way in electrodes of opposite

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polarity. Instead, the shift change during charging is believed to arise from changes in the electronic structure of the carbon electrode as either electrons or holes are added.431 This results in an increasingly paramagnetic contribution to the induced field arising from the ring currents in the carbon surface. DFT NICS calculations have qualitatively reproduced this effect whereby large positive NICS were calculated above the surfaces of positively and negatively charged coronene fragments, although the charge density in these calculations was significantly higher than under experimental conditions.433 The precise relationship between the experimentally observed shift change and the electrode charge remains a subject of interest and requires further investigation. Recent work has shown that ion reorganization during charging also plays an important role and can help to explain differences in the magnitude of the shift change in positively and negatively charged electrodes.449 However, in addition to these contributions, it is still not clear the extent to which other local factors contribute to the shift change, including changes in solvation, dynamics, or local ion concentration during charging.

9.12.5

Outlook

Solid-state NMR will continue to play an important role in the development of batteries and supercapacitors, providing information on local structure, heterogeneity, defects, and dynamics that is often difficult to obtain by other experimental methods. NMR will be vital to understand reaction and degradation mechanisms in state-of-the-art and next-generation energy storage materials that are being developed or yet to be invented. Beyond the capabilities of today, advances in solid-state NMR hardware and pulse sequences will continue to unlock new chemical and structural information with increased spectral, temporal, and spatial resolution. These ongoing efforts are helping to expand our understanding of increasingly complex structures and mechanisms in batteries and supercapacitors, which will lead to new design rules for material discovery and optimization.

Acknowledgment This work was supported by the Joint Center for Energy Storage Research (JCESR), an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences. JMG acknowledges the UK EPSRC (EP/V05001X/1) and Faraday Institution FufureCat consortium (FIRG017) for financial support.

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Unravelling Li-Ion Transport From Picoseconds to Seconds: Bulk Versus Interfaces in an Argyrodite Li6PS5Cl–Li2S All-Solid-State Li-Ion Battery. J. Am. Chem. Soc. 2016, 138 (35), 11192–11201. https://doi.org/10.1021/jacs.6b05066. 420. Fic, K.; Lota, G.; Meller, M.; Frackowiak, E. Novel Insight into Neutral Medium as Electrolyte for High-Voltage Supercapacitors. Energy Environ. Sci. 2012, 5 (2), 5842–5850. https://doi.org/10.1039/C1EE02262H. 421. Lazzari, M.; Mastragostino, M.; Soavi, F. Capacitance Response of Carbons in Solvent-Free Ionic Liquid Electrolytes. Electrochem. Commun. 2007, 9 (7), 1567–1572. https:// doi.org/10.1016/j.elecom.2007.02.021. 422. Arbizzani, C.; Biso, M.; Cericola, D.; Lazzari, M.; Soavi, F.; Mastragostino, M. Safe, High-Energy Supercapacitors Based on Solvent-Free Ionic Liquid Electrolytes. J. Power Sources 2008, 185 (2), 1575–1579. https://doi.org/10.1016/j.jpowsour.2008.09.016. 423. Van Aken, K. L.; Beidaghi, M.; Gogotsi, Y. Formulation of Ionic-Liquid Electrolyte to Expand the Voltage Window of Supercapacitors. Angew. Chem. Int. Ed. 2015, 54 (16), 4806–4809. https://doi.org/10.1002/anie.201412257. 424. Chmiola, J.; Largeot, C.; Taberna, P.-L.; Simon, P.; Gogotsi, Y. Desolvation of Ions in Subnanometer Pores and Its Effect on Capacitance and Double-Layer Theory. Angew. Chem. Int. Ed. 2008, 47 (18), 3392–3395. https://doi.org/10.1002/anie.200704894. 425. Merlet, C.; Rotenberg, B.; Madden, P. A.; Taberna, P.-L.; Simon, P.; Gogotsi, Y.; Salanne, M. On the Molecular Origin of Supercapacitance in Nanoporous Carbon Electrodes. Nat. Mater. 2012, 11 (4), 306–310. https://doi.org/10.1038/nmat3260. 426. Merlet, C.; Péan, C.; Rotenberg, B.; Madden, P. A.; Daffos, B.; Taberna, P.-L.; Simon, P.; Salanne, M. Highly Confined Ions Store Charge More Efficiently in Supercapacitors. Nat. Commun. 2013, 4 (1), 2701. https://doi.org/10.1038/ncomms3701. 427. Feng, G.; Cummings, P. T. Supercapacitor Capacitance Exhibits Oscillatory Behavior as a Function of Nanopore Size. J. Phys. Chem. Lett. 2011, 2 (22), 2859–2864. https:// doi.org/10.1021/jz201312e. 428. Kondrat, S.; Kornyshev, A. Superionic State in Double-Layer Capacitors with Nanoporous Electrodes. J. Phys. Condens. Matter 2011, 23 (2), 022201. https://doi.org/ 10.1088/0953-8984/23/2/022201. 429. Kondrat, S.; Kornyshev, A. Corrigendum: Superionic State in Double-Layer Capacitors With Nanoporous Electrodes. J. Phys. Condens. Matter 2013, 25 (11), 119501. https:// doi.org/10.1088/0953-8984/25/11/119501. 430. Griffin, J. M.; Forse, A. C.; Grey, C. P. Solid-State NMR Studies of Supercapacitors. Solid State Nucl. Magn. Reson. 2016, 74–75, 16–35. https://doi.org/10.1016/ j.ssnmr.2016.03.003. 431. Forse, A. C.; Merlet, C.; Grey, C. P.; Griffin, J. M. NMR Studies of Adsorption and Diffusion in Porous Carbonaceous Materials. Prog. Nucl. Magn. Reson. Spectrosc. 2021, 124–125, 57–84. https://doi.org/10.1016/j.pnmrs.2021.03.003. 432. Borchardt, L.; Oschatz, M.; Paasch, S.; Kaskel, S.; Brunner, E. Interaction of Electrolyte Molecules With Carbon Materials of Well-Defined Porosity: Characterization by SolidState NMR Spectroscopy. Phys. Chem. Chem. Phys. 2013, 15 (36), 15177–15184. https://doi.org/10.1039/c3cp52283k. 433. Forse, A. C.; Griffin, J. M.; Presser, V.; Gogotsi, Y.; Grey, C. P. Ring Current Effects: Factors Affecting the NMR Chemical Shift of Molecules Adsorbed on Porous Carbons. J. Phys. Chem. C 2014, 118 (14), 7508–7514. https://doi.org/10.1021/jp502387x. 434. Xing, Y.-Z.; Luo, Z.-X.; Kleinhammes, A.; Wu, Y. Probing Carbon Micropore Size Distribution by Nucleus Independent Chemical Shift. Carbon 2014, 77, 1132–1139. https:// doi.org/10.1016/j.carbon.2014.06.031. 435. Anderson, R. J.; McNicholas, T. P.; Kleinhammes, A.; Wang, A.; Liu, J.; Wu, Y. NMR Methods for Characterizing the Pore Structures and Hydrogen Storage Properties of Microporous Carbons. J. Am. Chem. Soc. 2010, 132 (25), 8618–8626. https://doi.org/10.1021/ja9109924. 436. Cervini, L.; Lynes, O. D.; Akien, G. R.; Kerridge, A.; Barrow, N. S.; Griffin, J. M. Factors Affecting the Nucleus-Independent Chemical Shift in NMR Studies of Microporous Carbon Electrode Materials. Energy Storage Mater. 2019, 21, 335–346. https://doi.org/10.1016/j.ensm.2019.05.010. 437. Forse, A. C.; Merlet, C.; Allan, P. K.; Humphreys, E. K.; Griffin, J. M.; Aslan, M.; Zeiger, M.; Presser, V.; Gogotsi, Y.; Grey, C. P. New Insights Into the Structure of Nanoporous Carbons From NMR, Raman, and Pair Distribution Function Analysis. Chem. Mater. 2015, 27 (19), 6848–6857. https://doi.org/10.1021/acs.chemmater.5b03216. 438. Forse, A. C.; Griffin, J. M.; Merlet, C.; Bayley, P. M.; Wang, H.; Simon, P.; Grey, C. P. NMR Study of Ion Dynamics and Charge Storage in Ionic Liquid Supercapacitors. J. Am. 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9.13

A review of exotic quadrupolar metal nmr in mofs

Bryan E.G. Luciera, Wanli Zhanga, Andre Sutrisnob, *, and Yining Huanga, a Department of Chemistry, The University of Western Ontario, London, ON, Canada; and b NMR/EPR Laboratory, School of Chemical Sciences, University of Illinois at Urbana-Champaign, Urbana, IL, United States © 2023 Elsevier Ltd. All rights reserved.

9.13.1 9.13.2 9.13.2.1 9.13.2.2 9.13.3 9.13.3.1 9.13.3.2 9.13.3.3 9.13.3.4 9.13.3.5 9.13.3.6 9.13.3.7 9.13.3.8 9.13.3.9 9.13.3.10 9.13.3.11 9.13.4 Acknowledgment References

Introduction NMR background and quadrupolar NMR considerations NMR background Strategies for spectral acquisition Literature review Scope 25 Mg 39 K 43 Ca 45 Sc 47/49 Ti 67 Zn 69/71 Ga 91 Zr 115 In 139 La Outlook

330 331 331 334 336 336 337 341 341 343 350 350 354 356 358 361 362 363 363

Abstract The rapidly expanding field of metal-organic frameworks (MOFs) and their numerous associated applications has captured the interest of researchers worldwide. These materials are often difficult to fully characterize through one specific avenue due to their intricate and occasionally complicated structures, highlighting the need for a multi-pronged characterization strategy. Solid-state NMR is an increasingly popular tool for MOF investigations due to the rich local information it can provide about the target nucleus, which is complementary to long-range structural characterization methods such as X-ray crystallography. The metal centers in MOFs often play an integral role in guest adsorption, catalysis, and other applications; however, their local environment can also be frustratingly difficult to probe through spectroscopic methods. There has been tremendous progress in the characterization of MOFs by directly interrogating the metal center using solid-state NMR experiments, particularly those targeting exotic quadrupolar metals such as 25Mg, 39K, 43Ca, 45Sc, 47/49Ti, 67Zn, 69/71Ga, 91Zr, 115In, and 139 La. In this contribution, we summarize basic principles of exotic quadrupolar metal NMR along with general acquisition strategies, review significant works in the field in the past 8 years, and highlight the types of information researchers can expect to uncover in MOF systems using this approach.

9.13.1

Introduction

Metal-organic frameworks (MOFs) are versatile materials composed of distinct metal centers or clusters joined by organic linkers to form a three-dimensional network on the molecular level. The field of MOFs necessarily involves aspects of materials, inorganic, organic, and supramolecular chemistry, intertwining threads from each discipline, with the ultimate goal to enable rational design of unique materials tailored to address specific applications. Through judicious selection of the metal centers, linkers, and synthetic conditions, MOFs of a specific nature and pore size can be crafted for purposes such as selectively adsorbing and desorbing specific guests, maximizing guest adsorption capacity, exhibiting thermal and chemical stability in specific settings, and acting as a catalyst, among others. Some MOFs have already found commercial applications, and the nearly limitless possibilities of the field continues to spur tremendous amounts of research.

*

Present address: ExxonMobil Research and Engineering Company, 1545 US Route 22 East, Annandale, NJ 08801, USA.

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Understanding the origins of particular MOF properties is crucial, as specific structural features or units are often intimately related to the overall properties of the material, including porosity, adsorption capacity, guest selectivity, and catalytic activity. If a specific aspect can be connected to a certain property, introducing that feature in other MOFs may also impart the desired characteristics, thus unravelling and exploiting structure-property relationships is of the utmost importance. More specifically, the metal center employed in a MOF can strongly influence the overall properties and applications of the material, which is a consequence of the nature of the metal center itself, along with the local environment about the metal center, the bound ligands, and their respective bond angles and distances. In a similar manner, when a metal cluster functions as a MOF node, such as the [Zr6O4(OH)4] unit in UiO-66,1 the choice of cluster metal and its local environment within the cluster can play a significant role in overall MOF topology and properties. Characterizing the metal environment is critical to unravelling links between local structure and MOF applications, as the immediate structure about the metal center has a direct impact on the overall properties of the MOF. In general, comprehensive characterization of MOFs can be challenging due to the nature of these materials; they are crystalline structures that only exist in the solid state and cannot be dissolved for more accessible solution-based characterization. Techniques involving gas adsorption measurements, BET surface area, thermal gravimetric analysis, and various types of spectroscopies can provide significant insight into the properties and structure of MOFs, but often fail to provide targeted analysis of local environments at the molecular level. Given the importance of the local metal environment to structure-property relationships in MOFs, identification of the metal surroundings is also crucial, and poses significant challenges. As the heaviest atoms in MOFs, the metal position in the unit cell is typically straightforward to identify via diffraction-based avenues. Single-crystal X-ray diffraction (SCXRD) is useful for those MOFs in which high quality crystals of a suitable size can be grown. Powder XRD can be used when appropriate crystals are not available; however, this route involves more challenging refinement that can result in a less accurate structure, particularly about the metal center. In both XRD cases, the ligands bound to metals are often much lighter (e.g., H, C, N, O) and thus harder to accurately locate through diffraction, leaving fine structure somewhat ambiguous. When ligand dynamics, framework mobility, or guest species are present, the effective elucidation of local metal environments becomes even more complicated via diffraction pathways. The use of synchrotron X-ray sources and neutron diffraction are plausible solutions, but the accessibility of these resources are typically limited and require careful experimental planning and scheduling. There is a clear need for an alternate spectroscopic route to characterize local structure about the metal centers in MOFs.

9.13.2

NMR background and quadrupolar NMR considerations

9.13.2.1

NMR background

The nuclear isotopes of every element have an intrinsic property known as spin, quantified by a spin number (I), which can be any value from zero upwards and is quantized in units of 1/2. A nucleus must be either spin 1/2 or > 1/2 to be NMR active. Spin 1/2 nuclei are generally straightforward to study via NMR, while nuclei with I > 1/2 have an intrinsic electric quadrupole moment and are known as quadrupolar nuclei, which present more challenging NMR targets (vide infra). The advent of solid-state nuclear magnetic resonance (NMR) began with experiments targeting 1H, the most practically accessible and receptive spin 1/2 nucleus, in the 1940s and 1950s. Since those times, advancements in hardware, software, pulse sequences, and acquisition techniques have unlocked a new age of NMR spectroscopy in which almost any nucleus with I
1/2 is amenable to study both in solution and in the solid state. NMR has been critical to significant advances in diverse fields including medicine, physics, chemistry, biology, biochemistry, and materials science. Solid-state NMR is uniquely positioned to investigate MOFs from the perspective of the metals, linkers, and guests, as all three groups typically involve NMR-active nuclei. The organic linkers and guests bound to metal centers feature the NMR-active isotopes 1 H, 13C, 14N, 15N, 17O, 19F, and 31P, but direct interrogation of the metal itself is often required in order to obtain a fuller understanding of the local metal environment. Many metals feature at least one NMR-active quadrupolar isotope. The asymmetrical distribution of positive charge within a quadrupolar nucleus confers an intrinsic electric nuclear quadrupole moment (Q), which has a unique value for each specific nuclear isotope on the periodic table. The Q interacts with the local electric field gradient (EFG), which arises from nearby nuclear surroundings, in a process known as the quadrupolar interaction (QI). Quadrupolar metal nuclei in MOFs pose specific special challenges to NMR spectral acquisition, but the QI also yields extensive information as it is a delicate probe of the local nuclear environment at the molecular level. Introduction of a sample to the large static magnetic field of the NMR instrument breaks the degeneracy of the þ 1/2 and  1/2 spin states via the Zeeman interaction. In NMR spectroscopy of a spin-1/2 nucleus, the  1/2 4 þ 1/2 transition is the only possible target to irradiate and detect. However, a quadrupolar nucleus has additional spin states according to its spin number, with all spin states separated by an equal energy gap when considering only the Zeeman interaction (i.e.,  5/2 4  3/2,  3/2 4  1/2, etc.). The QI has a significant effect on the spin energy states of a quadrupolar nucleus, and can be treated as a first- and second-order perturbation on the fundamental Zeeman interaction (Fig. 1). To the first order, the QI modifies the energy gap between all spin states except for that of the  1/2 4 þ 1/2 central transition (CT). The second-order QI influences the energies of all spin transitions to a smaller degree, including that of the CT. In a practical sense, the first-order QI spreads the spectra of all spin state transitions except the CT across frequency ranges beyond reasonable NMR detection limits, while second-order QI further broadens the spectra of all spin state transitions to a lesser degree, including the CT. The CT in quadrupolar nuclei remains by far the narrowest frequency range of all spin transitions to irradiate and detect, thus it is targeted in NMR experiments, and the QI can be

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(A)

mI = -3/2 mI = -1/2 I = 3/2 mI = +1/2 mI = +3/2 B0 = 0

Qo

ST

CT Qo

CT

Qo

ST

ST

ST

B0 ≠ 0 (Zeeman effect)

ST

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First-order quadrupolar interac on

(B)

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CT

CT

~

16

ST 4000 3000 2000 1000

12

8

4

0

-4

-8

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-1000 -2000 -3000 -4000 ppm

Fig. 1 In (A), the energy level diagrams of a spin-3/2 nucleus are shown without and with the presence of an applied magnetic field (B0), along with the effects of the first- and second-order quadrupolar interaction. ST denotes a satellite transition and CT the central transition. A simplified illustration of a possible accompanying static quadrupolar NMR spectrum is shown in (B), where  indicates the CT signal has been truncated for clarity. Simulations of the CT static powder pattern were generated using a CQ of 1 MHz, hQ of 0, diso of 0 ppm, a spectral frequency of 130.9 MHz and a magnetic field B0 of 9.4 T.

comprehensively characterized via its impact on the CT spectrum. Herein, all NMR spectra and transitions concern the CT unless stated otherwise. The EFG describes the ground-state electronic environment about the quadrupolar nucleus. Mathematically, the EFG is modeled by a second-rank traceless tensor with three mutually orthogonal components V11, V22, and V33, ordered such that | V33 |
| V22 |
|V11 |. The EFG can be described using two parameters, the quadrupolar coupling constant (CQ) and the asymmetry parameter (hQ). CQ is defined as eQV33/h, where e is the fundamental electric charge. CQ is typically reported in units of MHz for quadrupolar metal nuclei and can be positive or negative; however, only the absolute magnitude of CQ determines most NMR spectral effects. A higher magnitude of CQ indicates a stronger coupling between Q and the EFG, which leads to an NMR resonance that is significantly broadened in the frequency/ppm regime and more difficult to acquire (Fig. 2A). As the QI is anisotropic, the magnitude of CQ is inversely related to the local spherical symmetry of the electronic environment about the metal nucleus in three dimensions; higher spherical symmetry environments give rise to lower CQ values and narrower NMR resonances. The hQ parameter is defined as (V11 – V22)/ V33, and describes the axial symmetry of the EFG tensor. This parameter is dimensionless and ranges from zero, which represents a perfectly axially symmetric EFG tensor, to one, which is a completely axially asymmetric EFG tensor. If a C3 or higher axis of rotational symmetry is present at the target nucleus, hQ must necessarily equal 0. The NMR manifestation of hQ is in the position of the two characteristic quadrupolar spectral “horns,” which can be located anywhere on a continuum from the very outer edges of the broad resonance (“powder pattern”) when hQ is 0, to converging in the center of the powder pattern when hQ is 1 (Fig. 2B). Notably, hQ also has a minor influence on spectral breadth, where the powder pattern becomes slightly broader as hQ moves from 0 to 1. Quadrupolar metal nuclei pose a number of challenges for NMR experiments. The QI spreads quadrupolar metal NMR signal intensity across frequency ranges from tens of kHz to several MHz, reducing the effective NMR signal-to-noise ratio (S/N) at any given location and rendering spectral acquisition considerably more challenging. This is in contrast to spin-1/2 nuclei such as 1 H and 13C, which typically have the same signal intensity spread only across the regime of Hz to tens of kHz. Quadrupolar metal nuclei generally have moderate-to-low gyromagnetic ratios (g), which results in relatively lower resonant frequencies, a smaller population difference between  1/2 and þ 1/2 spins, and poorer S/N in NMR experiments. The resonant frequencies of some quadrupolar metal nuclei can be even lower and classified as “low-g,” which necessitates specialized NMR probes and associated hardware for effective spectral acquisition of the low S/N signals. The resonant frequency of a nucleus is directly proportional to both its g and the applied magnetic field from the NMR magnet. In the last ca. 25 years, ultra-high magnetic fields (i.e., > 19 T) have become broadly available. The use of higher magnetic fields provides a more significant population difference between the þ 1/2 and  1/2 spin states of the CT, which leads to a larger degree of sensitivity in NMR experiments. At high magnetic fields, many quadrupolar metal nuclei resonate at moderate to high NMR frequencies, resulting in higher S/N and less complicated spectra acquisition.

A review of exotic quadrupolar metal nmr in mofs

(A)

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(B)

CQ = 10 MHz

ηQ = 0.0

CQ = 20 MHz

ηQ = 0.5

CQ = 30 MHz

ηQ = 1.0

1000 800

600

400

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-200 -400 -600 -800

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1000 800

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Fig. 2 The effects of QI parameters on the appearance of static quadrupolar NMR spectra are shown using several simulations. In (A), the CQ is varied while hQ is held constant at 0.0, while in (B), hQ is altered while CQ is invariant at 20 MHz. In both (A) and (B), a spectral frequency of 130.9 MHz and a magnetic field B0 of 9.4 T were used.

Moreover, the spectral manifestation of the QI is inversely proportional to the applied magnetic field; use of higher magnetic fields reduces spectral effects of the QI, rendering powder patterns generally narrower and of higher S/N (Fig. 3). The NMR spectra of quadrupolar metal nuclei are also subject to the magnetic chemical shift (CS) interaction, which typically has a smaller influence than the QI. The CS interaction can be modeled by a second-rank tensor with a trace. The CS tensor has three principal components, d11, d22, and d33, arranged such that d11
d22
d33, and one-third the trace is the isotropic chemical shift, diso. Beyond diso, the CS interaction can be characterized by two values, the span (U) and the skew (k). In solid-state NMR, the CS interaction is anisotropic and probes the local magnetic environment in three dimensions about the target nucleus, giving rise to CS anisotropy (CSA) between each orthogonal direction. The U is a measure of the CSA, and can be calculated to an extremely good approximation as U z d11  d33, with higher values indicative of higher CSA. In a practical sense, CT powder patterns influenced by the CS interaction are broadened by an amount commensurate to the value of U. The k is a measure of the axial symmetry of the CS tensor and ranges from þ 1 to  1, with either extreme indicative of an axially symmetric CS tensor, while a k value of 0 indicates a perfectly axially asymmetric CS tensor. The k governs the position of the central spectral horn in a CSA-dominated spectrum, with k of þ 1 placing it at the high frequency limit, 0 at the center of the powder pattern, and  1 at the lowest frequency edge of the powder pattern. The spectral manifestation of the CS interaction scales proportionately with magnetic field; CSA has a stronger influence on the NMR spectrum at higher magnetic fields, while the QI has a weaker influence with increasing field. When considering the competing spectral influences of the QI and CS interaction in experimental design, the most efficient route is normally to acquire quadrupolar metal NMR spectra in MOFs at the highest possible field available, as the QI typically dwarfs the CS interaction.

Static

(A)

M AS

(B)

35.2 T

35.2 T

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40

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Fig. 3 The effect of magnetic field on QI-dominated NMR signals is shown at three different magnetic fields under (A) static and (B) MAS conditions. Note the reduced powder pattern breadth at higher fields. All signal intensities have been scaled; in reality the signals at higher magnetic fields should be more intense than those at lower field, ceteris paribus. The simulations used a CQ of 10 MHz, hQ of 0.0, and spectral frequency of 130.9 MHz.

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A review of exotic quadrupolar metal nmr in mofs Strategies for spectral acquisition

Quadrupolar metal nuclei in MOFs often give rise to broad resonances of a characteristic shape, known as powder patterns. NMR spectra of these powder patterns can be collected under either magic-angle spinning (MAS) or static (i.e., stationary) conditions, with both approaches having distinct advantages and drawbacks. MAS experiments of a sufficient spinning rate can partially average the QI while fully eliminating spectral effects from CSA and the dipolar interaction, yielding a very narrow CT powder pattern at the isotropic chemical shift flanked by a series of spectral artefacts known as “spinning sidebands,” which are spaced at equal intervals of the spinning frequency from the central isotropic shift. Fully or partially eliminating the effect of anisotropic NMR interactions via MAS is advantageous, as it mechanically concentrates the signal intensity of the overall powder pattern into a limited number of narrow spikelets composing the central isotropic resonance(s) and spinning sidebands, maximizing S/N and reducing experimental time. However, anisotropic NMR interactions also convey useful knowledge regarding the local environment, which is partially or fully lost in MAS experiments. Static spectra preserve the full spectral influence and accuracy of all NMR parameters at the cost of experimental time, as the signal is obtained as a continuous, very low S/N manifold rather than concentrated into higher S/N spikelets. Using specific pulse sequences, static NMR spectra of quadrupolar metal nuclei can be obtained within reasonable experimental times. There are several pulse sequences suitable for the effective acquisition of quadrupolar metal NMR spectra under MAS and static conditions. The QI not only broadens NMR spectra, but is also a strong source of transverse (T2) and effective transverse (T2*) magnetization relaxation of the free induction decay (FID) signal after a pulse is applied. The rapid T2* decay of quadrupolar nuclei means that a standard one-pulse Bloch decay experiment (Fig. 4A) is not a feasible strategy for spectral acquisition, as probe ringing tends to dominate the FID immediately after the pulse, and the signal from the quadrupolar metal nucleus has otherwise severely dissipated due to T2* by the time probe ringing subsides, yielding severely distorted lineshapes and inaccurate NMR parameters. A standard Hahn-echo experiment of the form p/2  s1 – p  s2  acq would be the next logical choice in order to exploit the long length of T2 relative to T2*, but the QI effect on the CT is not properly refocused by the p pulse, producing non-representative lineshapes and erroneous NMR parameters. The quadrupolar echo or “solid echo” pulse sequence substitutes a p/2 for the p pulse in order to properly refocus the QI, such that the sequence is p/2  s1  p/2  s2  acq (Fig. 4B). The quadrupolar echo yields accurate undistorted lineshapes that can be simulated to extract reliable EFG and CS tensor parameters, but does result in slightly lower S/N than an equivalent Hahn-echo experiment due to the p/2 refocusing pulse.2 When using the quadrupolar echo under MAS conditions, care should be taken to rotor synchronize the experiment to avoid distortions by making s2  s1 a whole number multiple of the rotor period. The QI not only influences the spin state energy levels and NMR spectral appearance, but also severely reduces the T1 longitudinal magnetization relaxation rate. This is an advantageous effect, as T1 describes how short the delay between NMR scans can be in an experiment; a shorter T1 allows for more scans and thus higher S/N within a given time period. The T2 relaxation rates of quadrupolar metal nuclei are generally in the 1–500 ms regime, which is typically much longer than T2* values and presents an opportunity for S/N enhancement. Acquisition strategies employing an initial excitation pulse followed by a Carr-Purcell Meiboom-Gill (CPMG) train of refocusing or echo pulses can be used to exploit the T2 >> T2* relationship, where CPMG experiments generally follow the form of excitation pulse – s1 – (p – s2 – acq)n (Fig. 4C). This pulse sequence permits refocusing and acquisition of the NMR signal tens to hundreds of times over a single scan after the original excitation pulse before loss of signal coherence occurs, offering tremendous S/N gains at the cost of spectral resolution. A Fourier transform of an echo train obtained using the CPMG pulse sequence in the time domain results in a spectrum consisting of a series of sharp spikelets that trace out the manifold of the overall powder pattern in the frequency domain. The spikelet frequency spacing is determined by the experimental parameters used in the time domain, such that spikelet separation is the inverse of the echo spacing in the time domain; spikelet spacing ¼ 1/ (echo size * dwell). Pulse sequences involving a CPMG train are frequently used for the acquisition of NMR spectra of quadrupolar metal nuclei, as they offer the spectroscopist a finely controllable balance between S/N and resolution, and can enable acquisition of quadrupolar metal NMR spectra in situations where it would otherwise be impossible.3–5 If a CPMG train is used under MAS conditions,4 one should rotor synchronize the pulses with the rotor period. When employing a CPMG-based sequence on a hydrogencontaining system, 1H dipolar coupling to quadrupolar metal nuclei must be considered, as even weak coupling can severely reduce the observed T2 value and have a negative impact on S/N; 1H decoupling should be applied whenever possible while respecting hardware and duty cycle limitations. Within the CPMG pulse sequence, the actual excitation and refocusing pulses can be substituted to acquire NMR spectra of quadrupolar metal nuclei in MOFs more efficiently and accurately. Traditionally, hard p/2 and p square-shaped pulses have been employed as the excitation and refocusing pulses, respectively. The WURST-CPMG pulse sequence uses adiabatic WURST pulses6 that have a broad frequency excitation profile, permitting the acquisition of broader powder patterns in a single experiment in a manner that would not be possible using standard square p/2 pulses. A WURST pulse is frequency swept in the time domain, of fairly constant amplitude, and lasts for a significantly longer duration than traditional “hard” pulses, but is generally of lower power. The same type of WURST pulse can also be used to refocus echoes in a CPMG-type echo train, preserving the broadband excitation characteristics of the WURST pulses while conferring the S/N benefits of CPMG and allowing the spectroscopist to control the spikelet separation and resolution.6–9 The WURST-CPMG pulse sequence (Fig. 4D) has been proven reliable for acquiring accurate, undistorted lineshapes in efficient time periods for quadrupolar and spin-1/2 nuclei.7,9,10 There are some promising emerging avenues for combining WURST experiments with MAS techniques,11,12 however, up to this point the vast majority of WURST and WURST-CPMG experiments have been performed under static conditions. A WURST pulse can also be used in lieu of a rectangular

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(A) One-pulse

π/2

τ

(B) Quadrupolar echo

π/2

π/2

τ1

τ2

(C) CPMG

π/2

π

τ1

π

τ2

τ3

τ4 N

(D) WURST-CPMG

WURST

WURST

τ1

τ2

τ3

N Fig. 4

Various types of pulse sequences that can be used to acquire NMR spectra of quadrupolar nuclei.

p/2 pulse in the quadrupolar echo experiment; the WURST-echo sequence combines the broadband excitation of the WURST pulses with the benefit of a smooth spectral manifold that is not broken up into spikelets. WURST pulses can also be used in crosspolarization schemes such as BRAIN-CP,13 but reports of applications to quadrupolar nuclei have been limited.14,15 Oftentimes, even when using broadband pulses such as WURST, the breadth of quadrupolar metal NMR spectra in MOFs are beyond the excitation limits of a single spectral window and a single experiment. For these broad ultra-wideline powder patterns ranging from hundreds of kHz to MHz across, the variable-offset cumulative spectrum (VOCS) approach is used. The VOCS technique involves obtaining a series of individual spectra using identical experimental parameters, spaced at equal frequency steps of the transmitter, across the entirely of the spectral breadth.16 Each of the “sub-spectra” collected at the individual frequency steps are then processed and co-added in the frequency domain to obtain the overall powder pattern (Fig. 5). Using the VOCS method, ultrawideline powder patterns can be acquired in a reasonable experimental time period. It is crucial to have a firm understanding of the effective excitation bandwidth of the spectrometer, hardware, and pulse profile before determining the appropriate VOCS offset spacing between individual sub-spectra. Without a properly selected VOCS offset, the overall spectrum will be distorted, influencing the accuracy of the associated NMR parameters. The quadrupolar echo, CPMG, and WURST-CPMG pulse sequences can be used in conjunction with the VOCS strategy in order to efficiently capture ultra-wideline NMR powder patterns. MOFs often feature multiple crystallographically unique metal sites, which gives rise to a corresponding number of distinct NMR resonances. The QI can disperse NMR powder patterns that are similar in appearance across breadths larger than the chemical shift range of the isotope, which gives rise to NMR spectra featuring multiple ambiguous overlapping signals that may be simulated using many different possible combinations of EFG and CS parameters. The challenge in obtaining accurate NMR parameters from superimposed quadrupolar metal powder patterns can lie anywhere on the continuum from easy to impossible, yet resolution of individual signals is necessary to conclusively identify both the number of distinct species and their corresponding NMR parameters. The MAS technique cannot fully remove the QI from experimental spectra even when high spinning frequencies are accessible, which is particularly problematic when species of generally similar diso are present. The multiple quantum MAS (MQMAS) pulse

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Fig. 5 A depiction of how the VOCS method is employed for acquisition of broad NMR spectra. Identical experiments are run at evenly spaced transmitter offsets (as indicated in kHz above). The individual sub-spectra at top are then added together to yield the overall powder pattern shown at bottom; this particular example is the 115In static NMR spectrum of the MIL-68(In) MOF obtained at 21.1 T.17 MIL-68(In) features two broad resonances, denoted In1 and In2. This figure has been reproduced with the permission of the copyright holder.

sequence is a two-dimensional NMR experiment that can disentangle overlapping quadrupolar CT NMR resonances, providing individual deconvoluted lineshapes, accurate diso values, and permitting extraction of the EFG and CS parameters for each signal.18,19 This experiment uses rectangular pulses to detect multiple quantum coherences and relies on relatively rapid acquisition of each slice in the direct dimension (F2), as the necessary multitude of slices in the indirect dimension (F1) has an impact on experimental time required. When performed correctly, the MQMAS experiment yields a spectrum of the CT free of any anisotropic QI influence in the F1 dimension, while the F2 dimension features typical MAS spectra of the CT that are influenced by the second-order QI. Access to high-field NMR also greatly enhances the effectiveness of MQMAS experiments, as the spectral impact of the QI is reduced, signals are narrower, population differences are higher, S/N is greatly increased, and thus signals can be more easily separated within reasonable experimental times. The MQMAS experiment is an excellent option for nuclei that resonate at moderate-to-high frequencies and have relatively narrow NMR powder patterns under MAS conditions. The overall strategy can involve two approaches; the spectroscopist may attempt to extract NMR parameters directly from both dimensions of the MQMAS spectrum, or alternately the NMR parameters obtained from F1 can be used to simulate a separate high-quality 1D MAS spectrum and derive refined, final NMR parameters. Advances in pulse sequence design and the availability of higher magnetic fields have steadily pushed NMR forward since its inception. In recent years, the emergence of commercially available dynamic nuclear polarization (DNP)-NMR equipment is a step-change that has suddenly broadened the horizons for investigations of metal nuclei in MOFs. The DNP technique generally involves the transfer of spin polarization via several different mechanisms, moving spin population differences from relatively strongly polarized unpaired electrons residing in MOF surroundings to relatively weakly polarized nuclear spins of interest within the MOF. Polarization transfer can proceed directly from electrons to the target nuclei, or indirectly from electrons to 1H nuclei in the material, and then from 1H to the target nuclei. While no works within the context of this review employed DNP for the investigation of exotic quadrupolar metals in MOFs, there will undoubtedly be future reports in this field given that DNP has shown great promise in studies targeting other nuclei in MOFs.20–24 The reader is directed towards other resources for an introduction to DNPNMR and its applications to materials science.25–29

9.13.3

Literature review

9.13.3.1

Scope

This chapter focuses on reports of solid-state NMR experiments targeting exotic quadrupolar metal nuclei in MOFs since 2014. The term “exotic” is taken to mean quadrupolar metal nuclei which are particularly challenging to acquire,30 which includes nuclei of low resonant frequency, poor natural abundance, and/or large quadrupolar moment, and excludes highly receptive nuclei with

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relatively small QIs such as 23Na and 27Al. Nuclei covered in this review are 25Mg, 39K, 43Ca, 45Sc, 47/49Ti, 67Zn, 69/71Ga, 91Zr, 115In, and 139La. The sections are organized by the nucleus of interest, highlighting important findings and their relevance while informing the reader of how specific experimental methods could be extended to study MOFs in other systems. For those curious about material beyond the scope of this work, there have been several excellent reviews published concerning solid-state NMR in MOFs in recent years,17,31–48 in addition to detailed reviews regarding the state of the art in solid-state NMR spectroscopy.49–56

9.13.3.2

25

Mg

Magnesium has a single, and rather unreceptive, NMR-active isotope in 25Mg. The natural abundance of 25Mg is a low ca. 10%, and this isotope also possesses a large nuclear quadrupole moment, a spin of I ¼ 5/2, and a relatively low resonant frequency, which poses a particular challenge for acquisition in MOF systems because the density of the 25Mg isotope is significantly diluted within the unit cell. Whenever possible, high magnetic fields should be used for S/N enhancement when acquiring 25Mg NMR spectra. Recent NMR reviews of 25Mg NMR spectroscopy are included here for further reading.53,57–59 Our research group reported the first natural abundance 25Mg 1D60 and 2D61 NMR studies of MOFs, which were reviewed in a previous work.17 Since that time, there have been five additional contributions to the field, which are examined below. Mali et al. examined the structure of Mg-based NICS (National Institute of Chemistry, Slovenia) MOFs constructed from benzene tricarboxylate (BTC) linkers and Mg centers in 2015, using techniques including 1H, 13C, and 25Mg NMR spectroscopy alongside ab initio calculations.62 The NICS-3, -4, and -6 MOFs were examined via 25Mg MAS NMR at a magnetic field of 21.1 T, where the authors used a double frequency sweep (DFS) preparation pulse for signal enhancement followed by the QCPMG pulse sequence. The NICS-3, -4, and -6 systems all contained MgO6 octahedral local environments with different specific connectivities to nearby linkers and the extended MOF network. One 25Mg NMR resonance was observed in accordance with the single Mg site in NICS-3, which was well-defined and could be simulated using a single powder pattern. There were two unique 25Mg NMR signals in NICS-4 and -6, which agreed with the two Mg sites determined to exist in each of their structures (Fig. 6). The authors noted that the use of a DFS preparatory pulse unevenly influenced observed spectral intensities, but assignment of specific Mg signals in NICS-4 and -6 to their respective inequivalent Mg sites was still possible. The observed Mg site occupancy ratios should have been 2:1 from NMR experiments; the use of 25Mg DFS-QCPMG NMR techniques only yielded one intense and one weaker signal, which were assigned by designating the stronger 25Mg NMR signal to the Mg site with higher occupancy. The authors also noted that a distribution of diso(25Mg) values were required to fit NICS-6 due to bulk magnetic susceptibility anisotropy. Observed 25Mg NMR parameters did not correlate particularly well with calculated values. Disagreements between the two were attributed to the disparity between room temperature NMR experiments and density functional theory (DFT) approaches that assumed a temperature of 0 K, particularly the accompanying rigid structures and lack of local dynamics. The authors were able to calculate and visualize 25Mg EFG tensors in each system (Fig. 6), with lower CQ(25Mg) sites such as that in NICS-6 connected to rather spherical tensors while the higher CQ(25Mg) sites in more asymmetric coordination environments within NICS-3 and -4 were linked to oblong, elongated EFG tensors and

Fig. 6 25Mg MAS NMR spectra of the NICS-3, -4, and -6 MOFs are shown in the top row, as obtained at a magnetic field of 21.1 T using a DFSQCPMG pulse sequence. In the bottom row, ellipsoid representations of the 25Mg EFG tensors obtained from ab initio calculations are shown. This figure has been reproduced with the permission of the copyright holder.

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broader 25Mg NMR powder patterns. This work showed the utility of combining ab initio calculations and experimental observations to explore the Mg local environment, understand 25Mg EFG tensor orientations, and assign 25Mg NMR signals to specific sites in MOF crystal structures. 25 Mg was used by Xu, Lucier, et al. in 2015 to investigate the ferroelectric-paraelectric phase transition in the two [NH4] [M(HCOO)3] (M ¼ Mg, Zn) MOFs,63 in concert with 13C, 14N, and 67Zn (vide infra) NMR methods. While this MOF is ferroelectric at low temperatures, there was a noted transition to a paraelectric state at higher temperatures, and the transition temperature was dependent on the metal center incorporated in the MOF. This phenomenon originated from a transition from a polar C6 point group with ordered NH4þ cations within the pores at low temperatures to a nonpolar D6 point group with disordered NH4þ cations at higher temperatures (Fig. 7A). In both phases, the Mg center resides in a MgO6 environment of exceptionally high symmetry, giving rise to very narrow 25Mg resonances and permitting rapid acquisition of NMR spectra. At room temperature and 21.1 T it was noted that the static 25Mg NMR spectrum was influenced by both the QI and CSA; the authors acquired the 25Mg ST spectrum to measure the QI, and based on those parameters, were able to accurately simulate the CT using a combination of the QI and CSA. Quantification of the rather small 25Mg CSA may have been impossible without a priori knowledge of the QI parameters. Variable temperature (VT) static 25Mg NMR experiments were performed on the [NH4][M(HCOO)3] MOF from 143 to 293 K at a field of 9.4 T (Fig. 7B), which yielded detailed QI and CS parameters that accurately tracked the phase change. In the high-temperature paraelectric phase, both the QI and CSA influenced the 25Mg NMR spectrum. When experimental temperatures dipped below the phase transition temperature, the CS influence suddenly ceased, leaving a QI-dominated ferromagnetic 25Mg NMR spectrum that looked radically different from that of the paramagnetic phase. The most pronounced change in the 25Mg NMR spectral appearance and accompanying NMR parameters was a diagnostic leap from an hQ value of 0.0 to 1.0 upon the phase transition (Fig. 7B, C).

(A)

(B)

143 K

N3 N1

163 K

Mg2+ O NH4+ C H

N2

173 K

(C) 1

183 K

C (M Hz) or K (dimensionless)

0.9 0.8 0.7

193 K

0.6 0.5 0.4

203 K

0.3 0.2 0.1

213 K

0 0.0033 0.0038 0.0043 0.0048 0.0053 0.0058 0.0063 0.0068 1/Temperature (K )

HT

(D)

V 22 V 33

223 K

LT V 33 O1

O1

O4

O5

V 11

O3

V 22

243 K

O3

293 K

O4

O5

O2

233 K

O2

V 11 O6

O6

50

0

-50

ppm

Fig. 7 The long-range structure of the [NH4][Mg(HCOO)3] MOF is shown in (A), with the smaller blue diamond shape outlining the high temperature (HT) unit cell, while the larger black rhomboid shape delineates the low temperature (LT) unit cell, with the three individual nitrogen sites at low temperature labelled N1, N2, and N3 for clarity. The variable temperature static 25Mg NMR spectra at 9.4 T are shown in (B). A plot of the 25 Mg CQ (blue trace) and hQ (red trace) values are shown in (C) with a vertical dashed lines included to indicate the temperature of the paraelectricferroelectric phase transition. The 25Mg EFG tensor orientations in the HT and LT phases are illustrated in (D), with the reader directed to note the movement of V33 from a D3 to a C1 symmetry axis. This figure has been reproduced with the permission of the copyright holder.

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Complementary DFT calculations revealed the hQ change was due to a significant reorientation of the V33 component of the 25Mg EFG tensor from an orientation at high temperature affording D3 rotational symmetry to one at lower temperatures that had no rotational symmetry (i.e., C1), as shown in Fig. 7D. CQ(25Mg) was also indicative of the phase change and rose gradually with decreasing temperature due to an increasing distortion of MgO6 octahedra, but the authors explained that the jarring hQ movement and stark alteration in spectral appearance was much more readily apparent. The characteristic change in 25Mg NMR spectral appearance, combined with the narrow 25Mg resonance width and ease of acquisition, could allow 25Mg NMR to be used as an indicator in similar MOF systems for in situ phase changes. The observed ferroelectric-paraelectric phase change temperature was in good agreement with previous studies, further reinforcing the potential applications of this approach. Ramakrishna et al. disseminated a work in 2021 that involved the use of 25Mg, 13C and 15N NMR to examine the dielectric transition in the [(CH3)2NH2]Mg(HCOO)3 MOF.64 The authors used a variety of techniques in this study, including variable temperature 25Mg NMR at 18.8 T to examine the local environment about Mg centers in this material and any role the Mg center could play in the dielectric transition mechanism. The authors did not quantify or report any 25Mg EFG parameters, but rather monitored the conveniently narrow 25Mg resonance width in situ as a proxy of the MOF phase. In an interesting contrast to the earlier findings by Xu, Lucier, et al. examining the [NH4]þ cation in a similar Mg-formate system,63 the authors discovered that once the [(CH3)2NH2] Mg(HCOO)3 MOF transitioned to a lower temperature ferroelectric phase, 25Mg resonance width radically decreased and the signal became more well-defined, which was indicative of reduced 25Mg QI interactions. The 25Mg QI findings were ascribed to dynamics of the [(CH3)2NH2]þ cation in this system; at lower temperatures the well-defined position of the cation resulted in a relatively smaller 25Mg QI and narrower well-defined 25Mg resonances, while at temperatures above the phase transition, the 25Mg NMR resonance was rather broad (Fig. 8A). The higher temperature findings were rationalized by explaining the cation was not in sufficiently rapid motion above the phase transition temperature to fully average out its presence and concomitant quadrupolar broadening in the local 25Mg environment on the NMR timescale, leading to a broad 25Mg NMR resonance due to a distribution of chemical environments. At very high temperatures (i.e., 320 K and above), full averaging of the 25Mg QI due to rapid cation motion and reorientation on the NMR timescale began to be realized, which narrowed the 25Mg resonance once again (Fig. 8B). Together with the previous study by Xu, Lucier, et al., this work exemplified how exotic quadrupolar metal NMR can be used to investigate and monitor phase changes in a MOF, particularly those that impact the 25Mg NMR EFG and/or CS tensors. Xu et al. communicated a study in 2017 that primarily described the characterization of an expanded MOF-74 type framework.65 This work included comprehensive 25Mg NMR experiments on several varieties of the Mg2(dobpdc) MOF (dobpdc ¼ 4,40 -dioxido3,30 -biphenyldicarboxylate), which had potential applications in CO2 adsorption but did not have an experimentally determined crystal structure. The authors correctly hypothesized that Mg centers were five-coordinated in MgO5 environments but could interact with MOF guests within the pores to form six-coordinate Mg environments. Using a high magnetic field of 20 T, along with static and MAS 25Mg NMR approaches, the authors were able to obtain a wide variety of spectra that yielded significant insight on the local structure of Mg in this system (Fig. 9). It was shown that natural abundance 25Mg NMR experiments could not provide sufficient S/N to distinguish between individual Mg signals, necessitating 25Mg isotopic labelling. Static 25Mg NMR experiments on 25Mglabelled Mg2(dobpdc) (Fig. 9A) revealed the presence of five-coordinate Mg in the empty activated MOF; the activated 25Mg NMR spectrum of Mg2(dobpdc) was found to be roughly twice as wide as those of guest-loaded variants, clearly showing how the link between local 25Mg spherical symmetry (i.e., CQ(25Mg)) and spectral breadth could be connected to the existence of lower symmetry 5-coordinate Mg sites and broader 25Mg linewidths, while higher symmetry 6-coordinate sites in guest-loaded samples

Fig. 8 The variable-temperature static 25Mg NMR spectra of [(CH3)2NH2]Mg(HCOO)3 obtained at 18.8 T are shown in (A), highlighting the differences that occur at the phase transition temperature. The full width at half maximum (FWHM) of each 25Mg resonance is plotted against temperature in (B). This figure has been reproduced with the permission of the copyright holder.

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corresponded to narrower, better-defined linewidths. The authors used 25Mg NMR data to prove a significant amount fivecoordinate Mg environments had been changed to six-coordinate Mg environments formed after exposure to guest species. Signals could be identified as originating from ordered surroundings due to the characteristic QI-dominated features, while the disordered environments gave rise to generally broad distributions of spectral intensity; the authors were thereby able to quantify the relative proportions of ordered and disordered Mg environments in each sample, with the ordered proportion consistently higher. The authors pointed out how QCPMG experiments, while yielding good S/N, did not provide suitable resolution of the 25Mg spectral manifold to allow for detailed spectral analysis, necessitating echo experiments to achieve higher resolution. MAS experiments (Fig. 9B) were also performed in an attempt to ascertain specific 25Mg chemical shifts to gain additional insight into the Mg2(dobpdc) MOF but there was significant residual linewidth and characteristic QI-dominated spectral features were not present; the lack of clear features and asymmetric tailing of intensity to low frequency confirmed the presence of somewhat disordered sixcoordinate Mg environments in these systems, while the significantly broader 25Mg MAS linewidth of the activated species again confirmed the presence of five-coordinate Mg sites of relatively lower symmetry and thus higher CQ(25Mg). Simulations using well-defined and distributions of Mg sites in these systems yielded detailed 25Mg QI parameters and a more detailed understanding of the MOF structure. Complementary DFT calculations were able to link the local Mg disorder to dynamic framework deformation originating from the linkers, dynamic motion of the guest species, and guest distributions. This study clearly illustrated the use of exotic quadrupolar NMR for identifying metal coordination when no crystal structure is available, and also as a sensitive probe of local disorder in MOF systems. A 2018 study by Chen et al.66 focused on the introduction of guest metals within the MIL-121 MOF, and subsequent comprehensive characterization of the resulting systems and their applications, including analysis of the local guest metal environments. Mg2þ ions were introduced to MIL-121 using the Mg(OAc)2 acetate-based reagent, and 25Mg MAS NMR experiments were performed at a high field of 21.1 T to investigate the local Mg environment in loaded Mg-MIL-121 due to the nature of 25Mg as a challenging, unreceptive NMR-active nucleus. The authors observed a 25Mg NMR signal from Mg-MIL-121 in the same general spectral region as that of Mg(OAc)2 but of increased breadth and reduced detail, which also exhibited a slight asymmetrical distribution of spectral intensity that slightly tailed off towards lower frequencies. For instance, the characteristic quadrupolar “horn” features were possibly indistinguishable from noise due to the low S/N ratio that could be achieved. Given the binding site for guest metals was shown to be uncoordinated -COO groups of the MIL-121 linkers, the 25Mg resonance position is sensible, as Mg would also be bound to the oxygen atoms of carboxyl group in MIL-121 that had a somewhat similar local environment to the acetate environment in the reagent. The broadened 25Mg MAS NMR resonance in Mg-MIL-121 was attributed to a distribution of 25Mg QI parameters, which the authors explained originated from the distribution of similar Mg2þ chemical environments present; in good agreement, some other metals in this study were found to reside in a distribution of local environments.66 The 25Mg MAS NMR signal was simulated using a distribution of sites centered at a CQ value of 3.7 MHz and hQ value of 0.5. The presence of Mg2þ ions within MIL-121 was found to enhance H2 and CO2 adsorption in MIL-121.

Fig. 9 In (A), the static 25Mg echo and QCPMG spectra of various Mg2(dobpdc) MOFs are shown, with experimental spectra in black, overall simulations in red, simulated signal from ordered Mg environments in blue, and simulated signal from disordered Mg environments in purple. In (B), the black experimental and red simulated traces of 25Mg echo MAS spectra are shown, as obtained at a spinning rate of 37.5 kHz. Both sets of spectra were obtained at a magnetic field of 20.0 T. This figure has been reproduced with the permission of the copyright holder.

A review of exotic quadrupolar metal nmr in mofs 9.13.3.3

39

341

K

While potassium has several NMR-active isotopes, 39K is the unanimous choice due to its high natural abundance of ca. 95%. Nevertheless, 39K is a I ¼ 3/2 quadrupolar nucleus of low resonant frequency which presents a very challenging target for NMR experiments in many systems.30,53,59 There has only been one 39K NMR study within the scope of this review, in a report examining guest Kþ metal centers along with many other metal ions loaded within the MIL-121 material in 2018.66 A high magnetic field of 21.1 T, large sample size afforded by a 7 mm rotor, and MAS techniques were all necessary in order to mitigate QI broadening effects on spectral appearance and increase S/N. The authors hypothesized that incorporation of the Kþ ion from the K2CO3 reagent would occur at the unbound COO groups of the BTEC linkers, which were accessible to guests and directed towards the pore interior. The literature had described a well-defined, rather narrow QI-dominated powder pattern for K2CO3 that was centered near ca. 0 ppm. Upon incorporation of Kþ ions, a broad yet featureless 39K MAS NMR signal at a spinning rate of 8 kHz was observed, which appeared to have a slightly asymmetric amount of intensity tailing off towards lower frequencies. The authors were able to simulate this signal using distribution of 39K NMR parameters centered at a CQ value of 2.3 MHz, with a distribution width of 1.4 MHz, and a rather wide distribution of hQ values centered at 0.80 but ranging from 0.2 to 1.0. The presence of a 39K NMR parameter distribution was linked to a distribution of similar local environments about the Kþ guest within the MOF, and taken to mean that Kþ was situated at a rather non-specific location proximate to the eCOO group of the BTEC linker.

9.13.3.4

43

Ca

The biocompatibility, low cost, and relatively high coordination number of calcium makes this a practical choice for the metal center in MOFs. Ca is typically found in the þ 2 oxidation state in MOFs, which is an [Ar]4s2 closed shell electron configuration that can make Ca2þ difficult to interrogate using spectroscopic methods. 43Ca is the only NMR-active isotope of calcium, but unfortunately is accompanied by significant disadvantages, as it is a I ¼ 7/2 quadrupolar nucleus with only a 0.135% natural abundance67 and a low resonant frequency. The very low natural abundance of 43Ca is further diluted by the other constituents of the MOF unit cell, and 43Ca isotopic enrichment is not cost-efficient, making 43Ca a very difficult nucleus to detect in such low densities. Given the many challenges to 43Ca NMR spectral acquisition in MOFs, MAS techniques are typically employed to increase S/N by making resonances as narrow as possible. As the quadrupolar moment of 43Ca is relatively small,68 high MAS rates are not necessarily required to remove a significant amount of quadrupolar broadening and increase S/N, which permits the use of relatively large NMR rotor sizes (i.e., 7 mm outer diameter) that can accommodate significant amounts of sample to partially mitigate the low natural abundance of 43Ca. diso is generally the most diagnostic 43Ca NMR parameter in MOF settings, but QI information can be extracted for analysis in situations where S/N is sufficiently high. The many challenges associated with 43Ca NMR necessitates the use of high magnetic fields to increase S/N whenever possible. Excellent reviews of the 43Ca NMR field were published by Widdifield in 2017,69 Laurencin and Smith in 2013,70 Moudrakovski in 2013,58 and Bryce in 2010.71 Miller et al. published a report of the microporous Ca-based BioMIL-3 MOF in 2013, which has potential applications due to the biocompatible nature of Ca and the coordinatively unsaturated Ca2þ sites in this system that can function as Lewis acids.72 BioMIL3 was found to have two unique Ca sites via single crystal XRD that were 6- and 7-coordinate before the removal of solvent, after which they became 5- and 6-coordinate, respectively. Using a RAPT (rotor assisted population transfer) enhanced experiment at 19.8 T, the authors were able to record a single 43Ca signal of low S/N, which was contrary to the two unique Ca centers expected from crystallographic results. The authors explained the coordination environment of both Ca centers is quite similar, with both populated by oxygen atoms from the carboxylate ligand groups and one disordered solvent. The 7-coordinate Ca site also features a long CaeO bond that could render it a pseudo-6-coordinate environment similar to the other distinct 6-coordinate Ca environment. Both factors would lead to very similar 43Ca chemical shifts and the appearance of a sole Ca signal that encompassed both resonances. Also in 2013, the synthesis and characterization of the calcium-containing coordination polymer BioMIL-4 was reported,73 with a single Ca site identified via XRD. In good agreement, the authors observed a 43Ca NMR signal at a field of 14.1 T that was in close proximity to the DFT-calculated predicted chemical shift, with the featureless nature of the lineshape attributed to local disorder about the Ca center. In 2018, Chen et al. published a comprehensive study documenting the insertion of 14 different metal ions into the MIL-121 MOF via a cost-effective straightforward route targeting unbound carboxyl groups of the MOF linkers.66 MIL-121 is composed of AlO4(OH)2 octahedra forming infinite chains, which are linked by the 1,2,4,5-benzenetetracarboxylate linker to form diamond-shape pores (Fig. 10A). In this system there are uncoordinated eCOOH groups of the linker not joined to the MOF metal centers. These free eCOOH groups remain exposed to the pore interior and present an active site for binding guest metals (Fig. 10B). Characterization of the metal-loaded MIL-121 materials in this study used quadrupolar metal NMR along with a variety of other complementary approaches, including 1H and 13C NMR spectroscopy as well as X-ray methods. The 43Ca NMR spectrum of Ca-loaded MIL-121 at 21.1 T featured two distinct resonances of significantly different chemical shifts (Fig. 10C)), signifying the presence of two unique ordered guest metal local environments. The 43Ca resonance at ca. 50 ppm was close to the reported chemical shift of Ca(OH)2, which led the authors to interpret this signal originated from guest Ca(OH)þ moieties located at the free COO group of the linker. The other 43 Ca resonance at  17 ppm was close to that of calcium acetate monohydrate, and was subsequently attributed to guest Ca2þ ions interacting with both the free carboxylate group of the framework linker along with a guest water molecule present in the MOF pore. The presence of guest Ca2þ in MIL-121 resulted in a significant increase in H2 and CO2 adsorption and decreased uptake of

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Fig. 10 A view of the MIL-121 pore is shown in (A), along with a generalized view of how metal doping occurs at the unbound carboxylate sites in (B). In (C), the 43Ca MAS spectrum of Ca-loaded MIL-121 is shown as obtained at 21.1 T and a spinning rate of 8 kHz, highlighting the two observed 43 Ca resonances corresponding to the two Ca sites in Ca-MIL-121, along with the simulated signal of the Ca(OH)2 reagent for comparison. This figure has been reproduced with the permission of the copyright holder.

N2 over the unmodified MIL-121 MOF. In this case, 43Ca NMR was able to identify the number of Ca guest environments, their locations, and a potential interaction with guest water. An in-depth 43Ca NMR study of calcium-based MOFs was detailed in 2018 by Chen et al., in which various phases of four different Ca-based MOFs were characterized using 43Ca MAS NMR experiments at a field of 21.1 T with support from complementary DFT calculations.74 The authors framed the challenges regarding the dilution of 43Ca spins succinctly by explaining there were 3.67  10 3 Ca atoms nm 3 in the CaSDB MOF, which was over an order of magnitude less density than CaO at 4.86  10 2 43Ca atoms nm 3. CaBDC, CaPDC, CaSDB, and CaBTC were studied, where BDC ¼ benzene dicarboxylate, PDC ¼ 2,5pyridinedicarboxylate, SDB ¼ 4,40 -sulfonyldibenzoate, and BTC ¼ benzene tricarboxylate. The authors used diso as the main diagnostic parameter in this study, with CQ and hQ being employed whenever their influence could be ascertained from the MAS spectra. As-made CaBDC features a CaO8 polyhedral local environment and resonates at  4.2 ppm (Fig. 11A), while desolvation of CaBDC removes an DMF and H2O guest from the Ca coordination environment to yield CaO6 and a corresponding signal at  5.9 ppm (Fig. 11B). Re-hydration of activated CaBDC introduces two H2O molecules to again form a CaO8 environment, but the 43Ca signal was found at  2.5 ppm (Fig. 11C). The discrepancy in diso values between re-hydrated and as-made CaBDC was explained as likely due to the differences in H2O and DMF guests. The changes in diso were also accurately modeled by DFT calculations, illustrating how 43Ca NMR experiments paired with DFT calculations are a sensitive probe of changes in local Ca coordination and bound ligands within a given MOF. For CaBDC in particular, the observed linewidths matched up well with CQ(43Ca) values from DFT calculations, confirming that the primary origin of 43Ca resonance broadening was the QI. The H2O and DMF loaded versions of CaPDC were also examined in this study. CaPDC-H2O contains a seven coordinate Ca local environment and yielded a chemical shift of  4.3 ppm (Fig. 11D), while the DMF-exchanged version termed CaPDC-DMF has an eight-coordinate Ca with a chemical shift of  11.9 ppm (Fig. 11E). The opposing trends in coordination number and chemical shift between the cases of CaBDC and CaPDC illustrated an issue when attempting to solely use 43Ca NMR to determine Ca coordination environments in MOFs. The authors explained there was a lack of clear correlation between Ca coordination number and diso, especially when different ligands were present, necessitating the use of DFT calculations to support experimental observations. The same study also examined CaSDB in its as-made and activated forms, which both feature a single unique octahedral CaO6 local environment, and both exhibited relatively broad signals of low S/N with characteristic QI lineshape features that persisted despite the use of MAS methods (Fig. 12A, B). Both forms of CaSDB corresponded to CQ values of ca. 3.15 MHz and hQ of ca. 0.90, and the small change in chemical shift between as-made and activated CaSDB was within experimental uncertainty bounds. The authors interpreted the striking similarity in 43Ca NMR parameters to mean that there were no major changes in the CaO6 local environment within CaSDB after the activation process was complete. There was good agreement between DFT calculations and experimental CQ(43Ca) values, which suggested that a specific distortion of the CaO6 units was responsible for the signal breadths, as opposed to any significant degree of local disorder. The final MOF examined in the study was the as-made and activated forms of CaBTC, which contains a single Ca site in an eight-coordinate CaO8 local environment in both the as-made and activated forms. 43 Ca MAS NMR experiments confirmed that there was a single unique Ca site present in both forms of CaBTC (Fig. 12C), documenting a diso change of 3.2 ppm from the as-made phase upon activation (Fig. 12D), in good agreement with powder XRD patterns that showed slight differences between the two. This work clearly demonstrated that 43Ca NMR at high magnetic fields is an effective tool for investigation of MOF systems despite the unfavorable NMR properties of the 43Ca isotope. The systems examined illustrated how the 43Ca NMR parameters are extremely sensitive to local structure in MOFs, with experiments yielding the number of unique Ca sites and, in conjunction with DFT calculations, valuable information on changes in Ca local structure in different MOF phases. In 2020, Mukherjee, Chen, et al. described how the Ca(HBTC)$H2O MOF, referred to in the previous study by “as-made CaBTC” and herein referred to as (bnn-1-Ca-H2O)$H2O, could be dehydrated to yield the narrow-pore anhydrate form bnn-1-Ca that has potential as a molecular sieve for H2.75 Among data from several complementary characterization methods, the authors used 43Ca MAS NMR experiments at 21.1 T to understand the Ca local environment and probe any activation-related changes. The 43Ca MAS NMR spectrum of as-made (bnn-1-Ca-H2O)$H2O revealed a single 43Ca resonance at ca. -3 ppm, corresponding to the single Ca site in this material residing in a CaO8 environment (Fig. 13A). Activation of the MOF at 423 K for 2 h removed a coordinated water from the Ca local environment, leaving a CaO7 coordinatively unsaturated site in bnn-1-Ca, reflected by a clear change in 43Ca diso

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Fig. 11 The 43Ca MAS NMR spectra of various forms of the CaBDC and CaPDC MOFs are shown, as obtained at 21.1 T and a spinning frequency of 5 kHz, along with accompanying illustrations of local structure about the green Ca atom. This figure has been reproduced with the permission of the copyright holder.

value but no significant alteration in resonance width (Fig. 13B). When the activation of bnn-1-Ca was allowed to proceed for a substantially longer period of 5 h, the 43Ca resonance was observed at the same chemical shift as after 2 h activation, but was significantly broader and of much lower S/N (Fig. 13C). The authors interpreted these 43Ca MAS NMR spectra to indicate there was no change in local chemical environment between 2 h and 5 h activated samples, but there was an introduction of local disorder at Ca triggered by the extended activation duration. The authors were also able to use 43Ca MAS NMR experiments on an activated sample of bnn-1-Ca that had been left in air for two weeks; the spectrum of rehydrated bnn-1-Ca was nearly identical in linewidth and chemical shift to that of as-made (bnn-1-Ca-H2O)$H2O (Fig. 13D), proving that the activation process on the Ca chemical environment and local crystallinity was reversible upon water adsorption. In this work, 43Ca MAS NMR was able to identify the number of unique Ca sites, indicate when the local Ca coordination environment was altered by activation, and track the introduction and disappearance of local disorder in a MOF system.

9.13.3.5 45

45

Sc

Sc is a 100% naturally abundant67 NMR-active nucleus with a resonant frequency just slightly lower than that of 13C, rendering it an attractive target for solid-state NMR experiments in MOFs across a variety of commonly accessible NMR magnetic fields. The spin of 45Sc is I ¼ 7/2, which gives rise to multiple satellite transitions flanking the CT, but the breadth of 45Sc CT powder patterns in MOFs under MAS conditions is narrow enough in relation to the STs that there is rarely spectral overlap between the CT and STs. Scandium is a somewhat uncommon choice for the metal center in MOFs, but has increased in popularity over the years for a variety of reasons, including the fact that coordinatively unsaturated Sc centers can function as sites for Lewis acid catalysis. Sc often resides in ScO6 octahedral environments within MOFs, but ScO5 local environments have also been documented in activated MOFs after the removal of guests. The diso(45Sc) value is exquisitely sensitive to Sc coordination number and nature of the ligands, while the QI is also very sensitive to the nature of bound ligands in addition to any distortions from spherical symmetry in the Sc local environment about Sc (i.e., ScO6 octahedral distortion). The 45Sc QI magnitude in typical MOF coordination

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Fig. 12 43Ca MAS NMR spectra are illustrated for the as-made and activated forms of the CaSDB and CaBTC MOFs, along with local structure at right. All spectra were obtained at 21.1 T using a spinning frequency of 5 kHz. This figure has been reproduced with the permission of the copyright holder.

environments is often large enough that distinguishing chemical shifts is quite challenging, thus MAS-based techniques to reduce the influence of the QI, in particular 2D MQMAS, may be required in order to determine the number and nature of Sc sites present in a MOF. In recent years, NMR experiments targeting 45Sc in MOFs have involved MAS-based methods, thus extracted 45Sc NMR

Fig. 13 43Ca MAS NMR spectra of various forms of the bnn-1-Ca MOF, as obtained at 21.1 T and a spinning rate of 5 kHz. The 43Ca NMR spectrum of the (bnn-1-Ca-H2O)$H2O MOF is shown in (A), bnn-1-Ca activated at 423 K for 2 h in (B), bnn-1-Ca activated at 423 K for 5 h in (C), and bnn-1-Ca exposed to air for 2 weeks after activation at 423 K for 5 h in (D). This figure has been reproduced with the permission of the copyright holder.

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parameters often include the QI parameters and diso but exclude CSA information. There are several works in the scope of this review featuring the use of 45Sc NMR to ascertain the overall MOF structure as well as the local structure about the metal center. In 2014, Mitchell et al. described the synthesis and comprehensive characterization of the mixed-metal form of MIL-100(Sc), termed MIL-100(Sc,M3 þ), where M ¼ Al3þ or Fe3þ.76 Al and Fe were selected for that study due to their low cost and availability. Given the known Lewis acid catalytic ability and overall stability of MIL-100(Sc), introduction of an additional metal could influence catalytic ability or impart additional catalytic properties. MIL-100(Sc) is composed of Sc3O(O2C)6 trimer units linked by benzene-1,3,5-tricarboxylate (BTC) linkers, where Sc resides in ScO6 units, and this MOF can be activated to convert a portion of ScO6 sites to coordinatively-unsaturated ScO5 metal sites. The expansive dataset and various experiments detailed in this work includes 45Sc and 27Al MAS NMR experiments on a series of MIL-100(Sc,Al) samples of varying Sc:Al ratio, where the proportion of Sc to Al was sequentially varied to gain insight regarding the local metal environments and composition of surrounding trimer units. Experimental 45Sc MAS NMR spectra were found to be rather featureless and asymmetric across all Sc:Al ratios, corresponding to a distribution of 45Sc NMR parameters which were indicative of local disorder about the Sc centers. There was slightly more detail in the lineshapes of low-Sc variants, but no detailed 45Sc NMR parameters could be extracted. The 45Sc NMR signal maxima across all MIL-100(Sc,Al) compositions was located between diso values of ca. 40–60 ppm; the authors used this finding to confirm the presence of octahedrally coordinated ScO6 in the fundamental MIL-100 trimer units. 45Sc MAS lineshapes were interpreted with support from complementary density functional theory (DFT) calculations. The overall asymmetric 45Sc signal was determined to consist of two separate components; a broader signal at lower diso of larger CQ(45Sc) was assigned to Sc with a terminal OH group attached, while the narrower component at slightly higher diso and of smaller CQ(45Sc) was assigned to Sc bound to terminal H2O. The authors were able to posit that when Sc content in MIL-100(Sc,Al) is low, the broader 45Sc signal corresponding to Sc with terminal OH bound is relatively more intense, indicating that the Al metal preferentially substitutes into framework metal sites with a bound H2O species. The 27Al MAS NMR spectra of MIL-100(Sc,Al) also contained a single asymmetric resonance that indicated AlO6 octahedra were present in the MIL-100 trimer units, but both 45Sc and 27Al NMR experiments could not clearly indicate if Al was only present in Sc3O(O2C)6 trimer units or also in mixed AlnSc3-nO(O2C)6 trimers. Cepeda et al. reported the synthesis and characterization of five unique Sc(III)-organic complexes in 2015, one of which was a unique Sc-based MOF with permanent porosity and significant CO2 adsorption capacity.77 45Sc NMR experiments were used to probe three compounds in this study, however the only MOF studied was [Sc2(pmdc)(OH)3Cl]$DMF$2H2O, where pmdc is pyrimidine-4,6-dicarboxylate. The structure of this MOF could not be fully solved via X-ray diffraction, which inspired the authors to employ a variety of complementary structural characterization techniques, including 45Sc MAS and MQMAS NMR experiments (Fig. 14). The 2D 45Sc MQMAS NMR experiments clearly showed that two distinct Sc resonances were present in the Sc2(pmdc)(OH)3Cl]$DMF$2H2O MOF, indicative of two crystallographically unique Sc sites, which could be used to simulate the 45Sc MAS NMR spectrum and yield two sets of 45Sc NMR parameters. The narrow Sc signal corresponded to CQ(45Sc) ¼ 7.3 MHz, hQ ¼ 0.0, and diso ¼ 60.2 ppm, which the authors assigned to a symmetrical hexacoordinate Sc species. The broad resonance was simulated using very different parameters of CQ(45Sc) ¼ 18.0 MHz, hQ ¼ 0.6, and diso ¼ 109.5 ppm, and was assigned to a non-symmetrical Sc local environment with the possible presence of a chloride ion or some other non-oxygen species in the Sc coordination shell. While no further structural comments could be made from this data, the authors were able to use the distinct 45 Sc NMR parameters and their accompanying implications for local structure to determine that two unique metal environments were present. In 2016, Cepeda et al. published a report on the synthesis and characterization of the EHU1(Sc,Li) and EHU1(Sc,Na) scandium/ alkaline mixed metal MOFs.78 45Sc MAS NMR experiments were used to investigate the interesting ScN4O4 local environment in both MOFs, which originated from the pyrimidine-4,6-dicarboxylate (pmdc) linkers and was described as resembling a triangular dodecahedron about Sc. 45Sc MAS NMR experiments indicated the presence of a single Sc site in both instances, in accordance with the crystal structure. Furthermore, hQ(45Sc) was observed to be in good agreement with a local environment of considerable symmetry about Sc, with EHU1(Sc,Li) exhibiting a value of 0.15 and EHU(Sc,Na) a value of 0.06. The CQ(45Sc) values were ca. 11 MHz and diso were ca. 34.5 ppm, but the structural origins of those parameters were not explored further. In 2019, Prasad et al. described the synthesis, characterization, and catalytic properties of the scandium-based STA-27 MOF and its calcined derivative.79 The authors determined that Sc-based MOFs had untapped potential for applications in fields such as adsorption and catalysis, and attempted to make an Sc MOF with a tetracarboxylate linker. STA-27 exhibits Lewis acid catalytic activity and is composed of Sc metal along with the tetrakis(4-carboxyphenyl)pyrazine (TCPP) linker. This MOF is built from infinite rods composed of octahedrally coordinated Sc centers, consisting of pairs of corner-sharing ScO6 octahedra in a Sc2O11 dimer, with the dimers then joined by two carboxylate groups at either end. The TCPP linkers connect the rods to form the MOF, which features diamond-shaped pores along the z axis. In the ScO6 local environment, four O originate from TCPP linkers, one from a bridging m2-OH group, and the last from a terminally bound water molecule. The 45Sc MAS spectrum of STA-27 contains a broad, featureless resonance that yielded relatively little information. 2D 45Sc MQMAS experiments were performed to investigate further, and the authors were able to determine that a single Sc signal was present at an diso value of 39 ppm. A very useful plot of the average quadrupolar product versus diso in Sc MOF ScO6 octahedral environments was created in order to understand the local Sc environment in STA-27, which is of interest to investigators studying related systems containing ScO6 local environments. The 45Sc diso and quadrupolar product of STA-27 was found to lie between those of ScOH chains, Sc3O trimers, and isolated ScO6 octahedra, reflective of the unique Sc environment in this MOF. The authors also documented that heat treatment of the STA-27 MOF at 225  C in N2 followed by air exposure for 4 days resulted in the STA-27-C MOF. STA-27-C shares many structural features with the parent MOF, but XRD indicates the dimeric Sc2O11 double octahedra units in STA-27 were rearranged to isolated ScO6 octahedra in

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Fig. 14 The 1D 45Sc MAS NMR spectrum of [Sc2(pmdc)(OH)3Cl]$DMF$2H2O is shown in (A), with traces of the simulated individual 45Sc signals shown in red and green using an intensity ratio of 1:1.6. The 2D 45Sc MQMAS NMR spectrum is shown in (B), which indicates that two Sc species are present. The asterisk (*) denotes a sample impurity. Spectra were obtained at 14.1 T using a spinning rate of 40 kHz. This figure has been reproduced with the permission of the copyright holder.

STA-27-C, with Sc bound to four carboxylate O atoms and two O atoms from species thought to be carbonate or bicarbonate moieties. The 45Sc MAS NMR spectrum of STA-27-C was quite distinct from that of STA-27, featuring a strong narrow resonance at diso ¼  50 ppm, along with an underlying broad signal of low S/N. The authors used the plot of NMR parameters for Sc local environments to illustrate how the diso value for STA-27-C lies very close to that of isolated ScO6 octahedra. Single crystal XRD data confirmed that isolated ScO6 octahedra were present in STA-27-C, in good agreement with the 45Sc NMR results. This work shows how differences in the local Sc coordination environment within MOFs are clearly reflected in the 45Sc NMR spectra, and illustrates how 45Sc NMR can be an important tool for understanding structural transformations of the overall framework. A comprehensive study on the use of solid-state NMR techniques to verify the formation of coordinatively unsaturated, Lewis catalytically active ScO5 units in activated Sc-MOFs for the first time via NMR was reported by Giovine et al. in 2017.80 This work explored the use of various 45Sc 1D and 2D NMR methods at a high magnetic field of 18.8 T to characterize Sc sites in the Sc3BTB2 (where H3BTB ¼ 1,3,5-tris(4-carboxyphenyl)benzene) and MIL-100(Sc) MOFs (with the BTC linker) before and after activation. The Sc3BTB2 and MIL-100(Sc) MOFs employ different linkers but share similar Sc local environments. Both MOFs have a trimer of corner-sharing ScO6 octahedra, where Sc is bound to four carboxylate oxygens, one m3 bridging oxygen atom, and a terminal water or hydroxyl ligand that can be removed upon activation to form ScO5 units, but the linkers connecting ScO6 trimers differ between the two materials. Activation converts ScO6 sites to ScO5 sites in both MOFs via the loss of a terminally coordinated hydroxyl or water group. The authors highlighted early in the manuscript that using 45Sc NMR techniques to study coordinatively unsaturated ScO5 units in these systems is particularly difficult, as the ratio of ScO5 sites to ScO6 environments is typically rather low, which makes NMR detection and clear signal resolution of ScO5 sites challenging. Furthermore, there are 2 unique Sc environments in Sc3BTB2 but 7 unique Sc sites in MIL-100(Sc), which complicates spectral analysis in both instances due to overlapping signals.

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The 1D 45Sc MAS NMR spectrum of as-made Sc3BTB2 contains a broad signal with subtle detail indicative of two overlapping signals (Fig. 15), in good agreement with the two crystallographically unique Sc sites. 2D 45Sc MQMAS experiments (Fig. 16) offered improved resolution which confirmed the presence of two distinct resonances and two unique Sc sites; both 45Sc signals corresponded to chemical shifts located firmly in the region of an octahedral ScO6 environment. The local structure of Sc in Sc3BTB2 was further explored after heating the sample at various temperatures over 12 h, where more terminal -OH and -H2O groups were removed from ScO6 environments as temperature increased. The authors linked the resulting additional intensity of 45Sc NMR signal at higher diso values to the presence of more ScO5 environments at higher activation temperatures. In 1D 45Sc MAS NMR experiments, relative signal intensity associated with ScO5 grew from 5% at a MOF activation temperature of 170  C to 34% at a temperature of 325  C, while the NMR lineshape also evolved in breadth and features, clearly demonstrating how 45Sc NMR can be used to distinguish both the presence and proportion of Sc active sites in MOFs. 2D 45Sc MQMAS experiments indicated that a distribution of ScO6 and ScO5 sites were formed at lower activation temperatures, and the continued simultaneous presence of 45Sc NMR signals in the ScO6 and ScO5 regions at higher activation temperatures indicated that both local environments were present in activated Sc3BTB2. It was found that ScO5 units in pristine and activated Sc3BTB2 corresponded to diso from 70 to 100 ppm and CQ values of ca. 8 MHz, while ScO6 units displayed distinct diso values of 20–60 ppm and CQ values ranging from 9 to 14 MHz. At higher activation temperatures, the 45Sc MQMAS NMR signals corresponding to ScO5 and ScO6 environments in Sc3BTB2 become more clearly separated (Fig. 16B–D). The MIL-100(Sc) MOF, in its as-made forms and after heating at various activation temperatures, was also explored in the same study.80 The 7 unique Sc environments gave rise to a broad signal in all instances. 1D 45Sc MAS NMR experiments of as-made MIL100(Sc) revealed intensity at ca. 70 ppm that was assigned to ScO6 octahedral units; 2D 45Sc MQMAS experiments on the as-made MIL-100(Sc) MOF could not resolve the seven individual resonances, but indicated the broad signal in 1D 45Sc MAS spectra indeed arose from a distribution of chemical shifts. As the activation temperature of MIL-100(Sc) was increased, the proportion of 45Sc NMR signals corresponding to ScO5 units increased, but only reached ca. 7% of the total 45Sc signal intensity at an activation temperature of 220  C before the collapse of the framework was indicated by an extremely broad signal at 300  C. 2D 45Sc MQMAS

Fig. 15 The 45Sc MAS NMR spectra of MIL-100(Sc) obtained at a field of 18.8 T using a spinning rate of 20 kHz. (A) denotes the as-made MOF, while (B) was obtained after heating the MOF at 100  C for 12 h. The 45Sc MAS NMR spectra of (C) and (D) were obtained after heating the MOF at 150  C and 220  C, respectively. This figure has been reproduced with the permission of the copyright holder.

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Fig. 16 The 45Sc MQMAS NMR spectra of Sc3BTB2 obtained at 18.8 T and a spinning rate of 20 kHz for (A) the as made MOF, and after thermal treatment at (B) 170  C, (C) 275  C, and (D) 324  C, respectively. The black dotted line circles surround resonances assigned to ScO5 units, which are more distinctly separated as the activation temperature increases. Resonances not surrounded by black dotted lines correspond to ScO6 local environments. This figure has been reproduced with the permission of the copyright holder.

experiments on the 220  C activated sample show that both ScO5 and ScO6 environments are present in the MOF, whereas MQMAS experiments after activation at 300  C reveal a distribution of 45Sc chemical shifts corresponding to a variety of ScO5 and ScO6 sites after the collapse of the MOF structure. While 1D and 2D 45Sc NMR experiments were clearly able to monitor and explore the formation of Lewis acid ScO5 sites in both the Sc3BTB2 and MIL-100(Sc) MOFs, the authors were able to further explore the MIL-100(Sc) system using 45Sc-{1H} D-HMQC 2D NMR experiments (Fig. 17). These experiments confirmed the presence of through-space correlations between BTC protons and ScO6 sites, and between SceOH groups and ScO6 sites in as-made MIL-100(Sc), as expected from their close proximity. Activation of MIL-100(Sc) at 220  C served to strengthen the aforementioned correlations due to the removal of physisorbed water and ethanol guests, which otherwise exchange protons with the framework and weaken individual 1He45Sc dipolar couplings. The HMQC experiments confirmed the collapse of the MIL-100(Sc) MOF after activation at 300  C via significant broadening of all spectral cross-peaks, reflective of a broad distribution of somewhat dissimilar Sc local environments after thermal degradation. The authors in this study also detailed the use of a frequency splitter to permit 13C-{45Sc} SFAM-RESPDOR NMR double resonance experiments, which would be otherwise extremely difficult given the very close resonant frequencies of both nuclei. This was the first NMR observation of 13Cd45Sc distances or proximities in MIL-100(Sc), and the authors were furthermore able to use the double resonance techniques to document spatial contraction of MIL-100(Sc) upon MOF activation. They were able to establish the relative distances between Sc and C-containing MOF components, linking the shorter 13Cd45Sc internuclear distances after MOF activation at increasing heat to shrinkage of the overall unit cell of MIL-100(Sc). DFT calculations were also proven to be strong supports for experimental results in this study, highlighting the utility of that complementary approach. Differences in calculated chemical shifts between ScO5 and ScO6 sites were successfully modeled and used to help rationalize the assignment of experimental 45Sc resonances. This work gave a clear blueprint on how 45Sc NMR can be used to comprehensively characterize the local metal environment in MOFs and track the evolution of a MOF across the activation process, yielding rich information on the local metal structure and by extension, the overall MOF structure. In 2019, Xie et al. used 45Sc NMR to shed light on the coordination number and local environment of scandium in the report of a newly synthesized fluorescent Sc2(NH2-BDC)3 MOF,81 accompanied by 1H and 13C NMR, X-ray photoelectron spectroscopy (XPS), Fourier transformed infrared spectroscopy (FTIR), and electron paramagnetic resonance (EPR) characterization. The remarkably thermally and chemically stable Sc2(NH2-BDC)3 MOF has a specialized application as a fluorescence-based sensor; in this case

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Fig. 17 Various 2D 45Sc-{1H} D-HMQC NMR spectra of MIL-100(Sc) in the (A) as-made form, along with the forms obtained after activation at (B) 220  C and (C) 300  C. The broadening of all cross-peaks in (C) is indicative of framework decomposition. This figure has been reproduced with the permission of the copyright holder.

MOF fluorescence was quenched via host-guest interactions upon exposure to Ni2þ and Co2þ cations. 45Sc one-pulse MAS NMR experiments were performed on the pristine Sc2(NH2-BDC)3 MOF, as well as after exposure to Ni(NO3)2 and Co(NO3)2 solutions for 24 h, in order to establish the local environment about Sc nuclei and understand any framework interactions with Ni2þ and Co2þ. The reported 45Sc MAS spectra feature a nearly symmetric narrow signal at ca. 5.1 ppm in all instances, which the authors interpreted to mean that the scandium metal center resided in a hexacoordinate environment within the MOF, but the featureless nature of the signal did not yield further information. The authors attributed the fluorescence quenching in Sc2(NH2-BDC)3 to interactions between Co2þ/Ni2þ and scandium hydroxyl defect species in the MOF crystal structure. In 2020, Zhan et al. were able to synthesize a highly fluorescent Sc-tetracarboxylate MOF, Sc-EBTC (EBTC ¼ diphenylethyne3,30 ,5,50 -tetracarboxylate), which is an exceptional thermally and chemically stable MOF with applications as a sensor for specific analytes via fluorescent quenching of the MOF.82 The quenching effects of several guest nitro-aromatic analytes were explored in this work. 45Sc MAS NMR experiments were employed to investigate the pristine Sc-EBTC MOF, along with the nitro-aromatic 2,4dinitrophenol (2,4-DNP)-treated Sc-EBTC, since this was the most effective fluorescence quenching guest studied. A somewhat broad resonance was observed in pristine Sc-EBTC at 5.34 ppm, which indicated that scandium was in an octahedral coordination environment, in good agreement with the ScO6 units obtained from the crystal structure. After exposure to a 0.1 mM solution of 2,4DNP, the 45Sc resonance was observed at  10.92 ppm, equating to a Ddiso of  16.26 ppm from the pristine MOF. The authors interpreted this change in chemical shift to mean that interactions between Sc-EBTC and 2,4-DNP may directly or indirectly enable MOF ligand-to-metal charge transfer, which would proceed via the electron transfer mechanism to quench ligand-based fluorescence, increase electron density at Sc, reduce diso(45Sc), and thus explain the 45Sc MAS NMR findings. XPS results were also found to be in agreement with this hypothesis. The final conclusions of this work indicated that the both the electron transfer and resonance energy transfer mechanisms were responsible for fluorescence quenching in Sc-EBTC after exposure to nitro-aromatic compounds. In 2022, Guo et al. used a variety of techniques including neutron powder diffraction, inelastic neutron scattering, synchrotron FTIR spectroscopy, and 45Sc NMR experiments to investigate the MFM-300(Sc) MOF.83 This material exhibits very favorable properties for ammonia storage, including reversible adsorption and excellent stability over repeated adsorption/desorption cycles, along with good thermal and chemical stability. MFM-300(Sc) is composed of ScO4(OH)2 secondary building units bridged by m2-OH groups which form repeating chains, along with the linker biphenyl-3,3,5,5,-tetracarboxylate (BPTC). 45Sc MAS NMR experiments were first performed on both pristine and NH3-loaded MFM-300(Sc) (Fig. 18), which yielded chemical shifts of 59.6 and 68.6 ppm, respectively, confirming the Sc environment is six-coordinate in both systems (i.e., octahedral ScO6). While hQ was found to be 1 for the empty and NH3-loaded MOF, CQ(45Sc) increased from 10.8 to 11.5 MHz upon introduction of NH3; the authors explained this relatively small change as evidence the ScO6 octahedra were not significantly distorted by any MOF interactions with NH3 guests. To further probe MFM-300(Sc) host-guest interactions with NH3, 2D 1He45Sc heteronuclear correlation (HETCOR) NMR experiments were performed, which allowed the authors to establish through-space proximity relationships between Sc and various other components of the MOF via the internuclear magnetic dipolar coupling interaction. In empty MFM300(Sc), cross peaks were observed between Sc and both the linker aromatic protons and the bridging hydroxyl protons, which was expected given the short distances from these hydrogen atoms to Sc. 1He45Sc HETCOR NMR experiments on NH3-loaded MFM-300(Sc) featured an additional cross-peak between Sc and the protons of NH3 within the MOF pores, and also revealed that the cross-peak between Sc and m2-OH groups had moved to higher chemical shifts, which was attributed to hydrogen bonding. The authors concluded that NH3 was hydrogen-bonded to the bridging hydroxyl groups in MFM-300(Sc) via the lone pair of electrons on nitrogen, which illustrates how 2D NMR experiments involving quadrupolar metal nuclei can be used to establish guest locations and probe host-guest interactions. Several other important MFM-300(Sc) findings unrelated to 45Sc NMR results were also detailed in this study.

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Fig. 18 The 45Sc MAS NMR spectra of (A) pristine and (B) NH3-loaded samples of MFM-300(Sc) are depicted, along with the accompanying 1 He45Sc HETCOR NMR spectra below in (C) and (D). The connectivity associated with each cross-peak in the HETCOR spectra is indicated with the blue dashed lines and associated text, where the hydrogen atom correlating with Sc is in bold font. These spectra were obtained at a field of 9.4 T while spinning at a rate of 12 kHz. This figure has been reproduced with the permission of the copyright holder.

9.13.3.6

47/49

Ti

Titanium is an attractive choice for MOFs due to its typical adoption of the þ 4 and þ 3 oxidation states, enabling coordination in many local structural motifs. NMR of titanium can be complicated due to its two NMR-active isotopes, which are both quadrupolar with nearly identical resonant frequencies and similar natural abundances. 47/49Ti NMR spectra feature two proximate or overlapping QI-dominated powder patterns for each crystallographically unique Ti in the same spectral window. 47Ti is I ¼ 5/2 with a relatively higher quadrupolar moment than the I ¼ 7/2 49Ti isotope; the broader and less intense of the two NMR resonances in Ti NMR spectra originates from the 47Ti isotope. Titanium NMR was reviewed by Lucier and Huang in 2016,84 with more recent developments covered by Smith in 2020.53 The first and only 47/49Ti NMR study of a MOF system was reported by He et al. in 2014 within a study detailing the investigation of several exotic quadrupolar nuclei in various MOF systems.85 47/49Ti NMR experiments were performed on the MIL-125(Ti) MOF to shed light on the local structure about Ti, the presence of DMF guest molecules, and the local configuration of hydroxyl vs. bridging oxygen groups. Ti resides in a TiO6 environment, where eight TiO6 polyhedra are joined to form rings on the MOF interior, with three of those oxygen atoms attributed to two m2-O2 atoms and one m2-OH group. The specific identity of oxygen sites as a bridging oxygen or hydroxyl group was uncertain because the structure was solved via powder XRD. Static quadrupolar echo experiments at 21.1 T revealed a nearly symmetrical broad, poorly-defined Ti resonance in both instances that suggested a distribution of Ti sites were present, with slightly more broadening around the base that was hypothesized to be the 47Ti signal. Simulations modelling a distribution of sites showed that CQ(49Ti) decreased from ca. 16.4 MHz in as-made MIL-125(Ti) (Fig. 19A) to 13.4 MHz after activation (Fig. 19B), and there was a small movement in diso by ca.  70 ppm, indicating that 47/49Ti NMR was in fact sensitive to the presence of solvent in this MOF despite the featureless NMR lineshape. The authors used complementary DFT calculations on three configurations of m2-O2 and m2-OH arrangements about Ti to show some combination of at least two local structures was present and there was local disorder about the TiO6 centers. In this case, Ti NMR was able to provide information on the presence of guest molecules and disorder in Ti local structure within MIL-125(Ti).

9.13.3.7

67

Zn

Zinc is found in a variety of MOFs and also forms the foundation of the ZIF (zeolitic imidazole framework) family of MOFs, which are a particularly active field of research due to their robust networks and common topologies with several zeolites. Zn can also be found in non-ZIF MOFs, and features the NMR-active quadrupolar 67Zn isotope, which is I ¼ 5/2. Unfortunately, obtaining rich detailed information from 67Zn NMR spectra can be quite challenging due to the decidedly unfavorable NMR properties, which includes a natural abundance of 4.1%, moderate quadrupolar moment, and low resonant frequency, which necessitates the use

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Fig. 19 The 47/49Ti NMR spectrum of (A) as-made and (B) activated MIL-125(Ti) are shown accompanied by simulations for the lineshapes of the respective isotopes. Spectra were acquired under static conditions at 21.1 T. This figure has been reproduced with the permission of the copyright holder.

of high magnetic fields whenever available. Despite the difficulties associated with 67Zn NMR, there is a significant body of published work,46,53 and there have been seven reports detailed in recent years that fall within the scope of this review. The 2014 article from He et al. concerning metal NMR of MOFs used 67Zn NMR to study zinc centers in four different systems, three of which featured multiple Zn sites.85 Using static and MAS approaches, the authors were able to obtain and interpret 67Zn NMR spectra from the Zn-dia, Zn-zni, TIF-1Zn, and TIF-5Zn ZIFs. In general, the use of a high 21.1 T magnetic field was necessary to obtain useful 67Zn NMR spectra given the multiple overlapping signals, and complementary DFT calculations were also typically required in order to verify the number of expected distinct 67Zn signals, guide simulations, and assist in the specific assignment of NMR signals to crystallographic sites. The Zn-dia system (Fig. 20A–C) featured two unique tetrahedral ZnN4 local environments, and in good agreement, gave rise to a 67Zn NMR echo spectrum of irregular lineshape that required the use of two signals to properly simulate (Fig. 20E, F). Interestingly, the 67Zn QI rendered signals too broad for MAS averaging and WURST-CPMG experiments did not provide sufficient resolution to indicate the presence of two 67Zn resonances (Fig. 20D), highlighting the need for researchers to carefully select the NMR experiments performed in order to obtain truly representative data. The Zn-zni system also contained two Zn sites in ZnN4 environments (Fig. 20G–I) which gave rise to a complicated static 67Zn quadrupolar echo NMR spectrum (Fig. 20J, K), but in this instance, the powder pattern was narrow enough to tackle via MAS. The well-resolved 67Zn MAS spectrum (Fig. 20L, M) unambiguously confirmed the presence of two unique Zn centers, which presented distinct 67Zn QI parameters and were assigned to sites with assistance from DFT calculations on a fully geometry optimized structure. The TIF-1Zn ZIF presented a different issue, as the crystal structure indicated there were four unique Zn sites present in a 4:4:4:1 ratio. While WURST-CPMG experiments could not yield sufficient resolution and MAS experiments could not be used due to spectral width, static echo experiments revealed a poorly-defined 67Zn spectrum that appeared to consist of two different 67Zn signals. DFT calculations on TIF1-Zn confirmed that two groups of Zn signals should be present, in which three Zn sites would give rise to similar 67Zn QI parameters, while the fourth would be distinct, creating the illusion of only two signals altogether. The TIF-5Zn ZIF only contained one Zn site, yet rather broad and poorly defined static and MAS 67Zn spectra were obtained. The authors were able to show the 67Zn NMR spectrum arose from local disorder about Zn centers and modeled the spectrum using a distribution of 67Zn parameters originating from a single disordered Zn site. This study underscored the importance of using DFT calculations and multiple types of NMR experiments in order to conclusively assign exotic quadrupolar metal NMR signals to crystallographically unique sites. The dynamic structure in MOF-5 was examined using 67Zn NMR in a 2015 report from Brozek et al.86 MOF-5 features Zn2þ centers in a ZnO4 local environment. The authors observed the presence of DMF solvent in this system via FT-IR and TGA-MS despite thorough activation of the MOF after rigorous thermal treatment and solvent exchange. 67Zn NMR was employed at 21.1 and 11.7 T to probe the local Zn coordination environment and investigate if any local disorder or deviations from predicted coordination were present, given the presence of DMF. The use of exotic quadrupolar NMR was particularly important in this case, as complementary XRD experiments could not yield conclusive high quality data. Natural abundance 67Zn MAS NMR experiments on DMF-exposed MOF-5 at 21.1 T yielded only noise (Fig. 21A), however, an activated sample of MOF-5 produced a very welldefined signal from which accurate 67Zn NMR parameters could be extracted. In order to further explore this system in several other states via NMR, MOF-5 was synthesized using 97% enrichment of the 67Zn isotope. This strategy yielded a much stronger 67Zn NMR signal, which was indicative of two powder patterns originating from two Zn sites in DMF-solvated MOF-5. The relatively narrow 67 Zn MAS resonance was reminiscent of the unsolvated pseudo-tetrahedral ZnO4 signal in evacuated MOF-5, while the other

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Fig. 20 The extended framework and local Zn coordination in Zn-dia is shown in (A–C), along with the static 67Zn NMR spectra acquired using a (D) WURST-CPMG and (E) echo pulse sequence. The simulated spectra using two Zn signals is shown in black within (F). A depiction of the extended framework and local Zn environment in Zn-zni is illustrated in (G–I), along with the static 67Zn NMR echo spectrum in (J) and accompanying two-site simulation in (K). The 67Zn MAS NMR spectrum of Zn-zni at a rate of 5 kHz is shown in (L) with a simulation in (M), where asterisks (*) denote spinning sidebands. All spectra were acquired at 21.1 T. This figure has been reproduced with the permission of the copyright holder.

significantly broader, less defined 67Zn NMR resonance was assigned to a solvated Zn site. In a fascinating strategy, the authors then used static 67Zn NMR experiments at a relatively lower magnetic field of 11.7 T to further investigate this system by exploiting the 67 Zn QI dependency on magnetic field, which involved sacrificing significant spectral resolution and S/N (Fig. 21B). Their approach was successful and yielded a wealth of information; 67Zn NMR parameters could be extracted with a reasonably high degree of accuracy for both the solvated and unsolvated Zn sites in DMF-exposed MOF-5. The relative intensities of the two 67Zn powder patterns indicated that guest DMF molecules were coordinated to one of the four Zn2þ sites in each Zn4O cluster within MOF-4, which was in good agreement with complementary data. In this instance, 67Zn NMR was able to provide intimate information on the Zn coordination within a MOF at the molecular level, yielding the surprising finding that the structure about the metal centers in this MOF constituted a dynamic rather than static system, and providing critical information that was unavailable through other means. The 2015 paper from Xu, Lucier, et al. regarding a ferromagnetic and paramagnetic change in the [NH4][Mg(HCOO)3] MOF (vide supra) also examined a similar phase change in the [NH4][Zn(HCOO)3] MOF.63 The substitution of Mg for Zn resulted in a lower phase change temperature in this system. The largest contrast between the Mg and Zn variants was the primary NMR interaction influencing CT powder patterns in the high temperature paraelectric phase; in 25Mg NMR experiments, the QI was found to largely dominate the CT with a minor influence from CSA, however in 67Zn NMR experiments, CSA was the dominant influence on the CT powder pattern at higher temperatures (Fig. 22A) with only a minor contribution from the 67Zn QI. Using a similar strategy the authors employed for 25Mg, the authors were able to acquire the 67Zn STs at 21.1 T to quantify the 67Zn QI parameters (Fig. 22B), and then use those as a basis for understanding the 67Zn CS influence on the CT powder pattern. At this time, these were the smallest 67Zn CSA spans that had been accurately determined and reported, with a maximum span of 10.0 ppm at 183 K and a skew of  1.0. The variable temperature 67Zn NMR spectra of [NH4][Zn(HCOO)3] underwent a significant change across the paraelectric-ferroelectric phase transition (Fig. 22C), transforming to a QI-dominated NMR spectrum at lower temperatures. The findings from 67Zn NMR experiments were analogous to those of 25Mg experiments; the 67Zn EFG tensor underwent a stark reorientation at the phase transition, moving from coincident to a D3 axis of symmetry in the high temperature paraelectric phase to a C1 axis in the low temperature ferroelectric phase. In good agreement, the observed hQ(67Zn) value jumped from 0.0 to 0.9 across the transition. There was a negligible contribution from 67Zn CSA below 163 K (Fig. 22D). At lower temperatures the CQ(67Zn) value was found to slowly increase due to increasing distortion of the ZnO6 local units, while the hQ value stayed fixed near 0.9, indicating that the 67Zn EFG tensor was not changing orientation. Much like the case of 25Mg NMR experiments in this system, 67Zn NMR experiments on the [NH4][Zn(HCOO)3] MOF were able to be performed expediently at 9.4 T due to the exceptional spherical symmetry about the Zn center in this system. This work laid out the rich information available from NMR across MOF phase transitions, and also reinforced that high magnetic fields are not necessarily required for high resolution in all circumstances when targeting exotic quadrupolar metal nuclei. A different type of Zn center was targeted in the 2018 report of metal-loaded MOFs from Chen et al.66 Using a zinc acetate hydrate reagent, Zn(OAc)2$2H2O, the authors were able to introduce Zn within the MIL-121 MOF forming Zn-MIL-121, where the Zn center was thought to coordinate to the unbound “free” -COO groups of the linkers accessible from the pore interior. Prior accounts of 67Zn NMR of the Zn(OAc)2$2H2O reagent and the related Zn(OAc)2 compound both described well-defined, rather narrow 67Zn NMR powder patterns with characteristic quadrupolar features, however, the 67Zn NMR spectrum of Zn-MIL-121 yielded a quite broad, featureless 67Zn resonance that lacked quadrupolar features and exhibited trailing intensity to the low frequency direction, which indicated a distribution of Zn guest chemical environments were present. The reported resonances for Zn(OAc)2$2H2O and Zn(OAc)2 fell within the region encompassed by the Zn-MIL-121 resonance, hinting Zn may also reside

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Fig. 21 The 67Zn MAS NMR spectra of MOF-5 at 21.1 T is shown in (A), with the top spectrum of natural abundance 67Zn (4.1%) in the empty MOF, the middle spectrum of 97% 67Zn-enriched MOF-5 solvated with DMF, and the bottom spectrum of natural abundance 67Zn MOF-5 solvated with DMF. The blue spectral inset depicts the secondary Zn signal observed within DMF-solvated MOF-5. In (B), the static 67Zn NMR spectrum of 97% 67Zn-enriched MOF-5 solvated with DMF at 11.7 T is shown at bottom, with the overall combined simulation and simulated contribution from both Zn sites traced above. This figure has been reproduced with the permission of the copyright holder.

(A)

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Fig. 22 The experimental and simulated variable temperature static 67Zn CT NMR spectrum of [NH4][Zn(HCOO)3] at 293 K is shown at 21.1 T in (A) along with additional spectra at different temperatures at 9.4 T in (C), while the 67Zn ST NMR spectrum at 293 K and 21.1 T is shown in (B). Enlarged 67Zn CT NMR spectra at 9.4 T are shown in (D); note that high temperature simulations require only CS or both QI and CS contributions, while those at low temperatures only depend on the QI contribution. This figure has been reproduced with the permission of the copyright holder.

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in an acetate-coordinated environment within this MOF, in good agreement with the hypothesized binding to free eCOO groups of the MIL-121 linker. Simulation of the 67Zn signal in Zn-MIL-121 required the use of a distribution of 67Zn NMR parameters, with CQ(67Zn) centered at 11.0 MHz and hQ values centered at 1.00 but ranging from 0.65 to 1.00. The authors interpreted these findings to mean that Zn guests resided in a range of local environments within MIL-121, which was similar to several other metals within this work. In 2019, Wu et al. examined host-guest interactions in the a-Zn3(HCOO)6 MOF, which involved the use of static 67Zn NMR experiments at 21.1 T to investigate the local environment of Zn in four different variations of the MOF, including CO- and CO2-loaded states.87 The 67Zn static NMR spectra of as-made, activated, CO-loaded, and CO2-loaded a-Zn3(HCOO)6 MOFs featured nearly identical powder patterns. This surprising finding was interpreted to mean that the ZnO6 octahedral local environment was extremely similar in all systems, despite the presence of different guests and MOF activation status. The crystal structure of a-Zn3(HCOO)6 indicated that four unique Zn centers are present in each phase residing in very similar local environments, in good agreement, static 67Zn NMR experiments on all forms of a-Zn-formate yielded complicated yet relatively narrow spectra that could not be simulated using any arrangement of multiple Zn signals. DFT calculations were performed using two degrees of geometry optimization, which predicted a 67Zn NMR spectrum somewhat similar to that observed; unfortunately, experimental broadening due to the 67Zn QI interaction prevented any accurate simulation to extract 67Zn NMR parameters from the multiple signals encoded within the challenging lineshape. 67Zn MAS NMR experiments were attempted on the as-made a-Zn-formate MOF spinning at 15 kHz to increase resolution, but yielded a narrow resonance of few features, again indicating that there was a narrow distribution of several similar Zn sites present in agreement with crystallography and DFT calculations. A comprehensive work on crystalline and melt-quenched glass ZIF systems was described by Madsen et al. in 2020.88 The authors used 67Zn MAS NMR experiments employing a spinning rate of 10 kHz on crystalline and glass ZIF materials at 19.5 and 35.2 T, including the ZIF-4, ZIF-62, and Zn-zni frameworks. 67Zn NMR spectra of the crystalline compounds all featured two overlapping 67 Zn NMR powder patterns, originating from the two unique Zn sites present in a 1:1 ratio within the ZIFs. The presence of multiple overlapping powder patterns did not pose a significant problem in light of the use of two high magnetic fields, one of them 35.2 T, which yielded remarkable spectral resolution. The well-defined NMR signals of crystalline compounds in this study illustrated the utility of ultrahigh-fields for 67Zn NMR experiments targeting ZIFs and many other systems. As a result of the very high S/N and resolution, the authors could perform unambiguous extraction of 67Zn QI parameters for all crystalline compounds with only very small uncertainties of 0.2 MHz for CQ and 0.05 for hQ; these spectra also yielded very accurate chemical shift values that were shown to be distinct for each chemically unique Zn species present in a given material. After the vitrification of these MOFs into glasses, 67Zn MAS NMR experiments were used to explore short-range structure about the resulting Zn(ligand)4 tetrahedra and compare these to the crystalline forms. The 67Zn MAS NMR spectra of vitrified ZIFs were quite interesting; the presence of two crystallographically unique Zn sites could no longer be ascertained, as rather broad and featureless 67Zn NMR signals were present that tailed off to low frequency in a manner consistent with a distribution of similar 67Zn NMR parameters, indicating that a distribution of Zn sites in relatively similar chemical environments was present. The residual 67Zn linewidth remaining due to the QI was considerable at 19.5 T, while the spectra at 35.2 T were significantly narrower yet continued to lack clear spectral features indicative of ordered environments. The authors connected these NMR findings to breaking and reformation of ZneN bonds in the vitrification process, which created significant short-range structural disorder in the glasses and a distribution of similar Zn sites. A shift to lower 67Zn diso values was also noted after vitrification, which was hypothesized to signify there was an increase in average ZneN distance in the glasses over their crystalline counterparts. This study clearly showed how the advent of ultrahigh-field NMR has allowed natural abundance 67Zn NMR to evolve from a useful tool in very specific settings and systems to a powerful probe of short-range structure in a wide variety of Zn systems, unrestrained by issues such as structural disorder. Very recently in 2022, Berdichevsky et al. reported the synthesis and characterization of the new potential molecular sieving Zn3(NH2BDC)3DABCO and Zn2Cd(NH2BDC)3DABCO (DABCO ¼ 1,4-diazabicyclo[2.2.2]octane) MOFs, which involved the use of static and MAS 67Zn NMR spectroscopy at 21.1 T in a supporting role to explore the local structure about Zn and complement the long-range structures determined from XRD.89 While both MOFs exhibited unique diso(67Zn) values, they both also gave rise to rather broad, featureless resonances. The authors noted the 67Zn resonance breadth was significantly higher for the MOF incorporating Cd centers, which was interpreted to signify a change in mid-range structure about Zn sites due to the replacement of Zn sites by Cd; this broadening was further ascribed to a resulting distortion of the 67Zn EFG and introduction of local disorder. In good agreement, other methods such as 13C NMR indicated there was local order about Zn in the Zn3(NH2BDC)3DABCO system, while the environment about Zn was disordered in the Zn2Cd(NH2BDC)3DABCO MOF.

9.13.3.8

69/71

Ga

Gallium presents an interesting scenario for NMR analysis, with two accessible NMR-active isotopes available that present distinct advantages and drawbacks. Both 69Ga and 71Ga are I ¼ 3/2 quadrupolar nuclei, with the former 60.4% and the latter 39.6% naturally abundant. These isotopes are challenging nuclei to examine via NMR experiments due to the presence of a rather large quadrupolar moment for 69Ga and a moderate one for 71Ga,68 where CQ(69Ga) ¼ 1.6CQ(71Ga), which renders 69Ga NMR powder patterns significantly broader. Either nucleus is a reasonable target if high magnetic fields are accessible to mitigate QI effects. An attractive aspect of Ga NMR comes to light when both 69Ga and 71Ga NMR spectra are acquired; this strategy typically results in very accurate NMR data because the same Ga QI and CS parameters must fit both spectra, with the exception of CQ. There have been three reports in the literature regarding 69/71Ga NMR of MOFs within the scope of this review.

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A detailed account from Zhang et al. in 2017 described how 69Ga and 71Ga NMR spectroscopy were used at magnetic fields of 9.4 and 21.1 T to investigate the phases and local structure of many different forms of the Ga-MIL-53 MOF,90 including after CO2 adsorption at several different loading levels and exposure to various organic compounds. Ga-MIL-53 features GaO6 local environments that are more accurately described as GaO4(OH)2, where four oxygens originate from separate BDC linkers and the remaining two oxygen atoms are bridging m2-OH groups that connect GaO6 octahedra to form the MOF backbone. The Ga-MIL-53 MOF exhibits a “breathing effect” that alters the MOF phase, with this material manifesting unique pore sizes and dimensions based on the presence of adsorbed guest molecules and external conditions such as temperature and pressure. The authors used 69/ 71 Ga quadrupolar echo and WURST-CPMG pulse sequences to examine different forms of Ga-MIL-53. Due to the significant breadth of the powder patterns, only static techniques could be applied. In all instances, the authors mentioned that although Ga CS tensor parameters could still be obtained, the dominance of the Ga QI prevented any meaningful comparison between Ga CS parameters. 69/71Ga NMR spectra were used to actively monitor and conclusively distinguish between the as-made, high temperature, empty narrow pore, and low temperature phases of Ga-MIL-53 (Fig. 23A), in addition to CO2-loaded and organic molecule loaded variants, with each presenting unique characteristic Ga NMR parameters due to their specific distortions of local GaO6 octahedra. 69/71 Ga NMR spectra of CO2-loaded Ga-MIL-53 samples exhibited an interesting evolution with progressively higher loading levels that suggested the presence of a re-entrant phase transition in this system (Fig. 23B). In an intriguing twist, the spectral impact of CO2 guests was most pronounced in 71Ga NMR spectra obtained at a lower field of 9.4 T. While 21.1 T Ga experiments of CO2loaded Ga-MIL-53 were of high S/N, the two individual Ga powder patterns present upon CO2 introduction were not sufficiently detailed to distinguish the characteristic QI horns of either powder pattern, preventing extraction of accurate QI parameters for either Ga site. The stronger QI effect on spectral appearance at 9.4 T more clearly delineated changes in experimental spectra, producing relatively broader 71Ga spectra that had increased spectral dispersion and more clearly defined features. A gradual change was observed in GaO6 local environments as the CO2 loading level increased, which was connected to the change in local pore shape as CO2 progressively occupied more space in the MOF and triggered pore enlargement. It appeared that the phase change was complete at a loading level of 0.45 CO2/Ga with CO2 evenly occupying all MOF pores. The authors hypothesized that GaMIL-53 underwent a re-entrant phase transition from monoclinic in the empty narrow pore phase, to triclinic in the intermediate-loaded Ga-MIL-53 phase, and back to monoclinic in fully CO2-loaded Ga-MIL-53. This was in agreement with literature on Al- and Fe-MIL-53, and illustrated the utility of Ga NMR as a sensing technique for determining the specific MOF phase and CO2 loading level. Among the many organic guests examined via 69/71Ga NMR within Ga-MIL-53, the polar dimethylformamide and diethylformamide compounds were linked to significant increases in CQ(Ga), which the authors hypothesized was due to solvent-m2OH hydrogen bonding interactions that served to reduce pore size and distort local GaO6 environments away from octahedral symmetry. In 2018, Zhang et al. detailed the synthesis and comprehensive characterization of the Ga- and In-variants of the Al-A520 fumarate-based MOF.91 The authors described local structures with the Ga and In metals residing in a MO6 environment, with four oxygen atoms originating from four fumarate linkers and two m2-OH oxygen atoms from bridging hydroxyl ligands that link the MO6 octahedra together in a corner-sharing fashion. While the Ga local environment in this MOF (Fig. 24A, B) is similar to that of Ga-MIL-53, there is exceptional rigidity to Ga-fumarate, preventing the “breathing effect” noted in the aforementioned

Fig. 23 The static Ga NMR spectra of various Ga-MIL-53 forms at 21.1 T are shown in (A) along with long range depictions of the respective MIL53 structures, while static 71Ga NMR spectra of CO2-loaded Ga-MIL-53 at 9.4 T are shown in (B), with the loading level indicated at left. In all instances, the blue trace indicates experimental results, the red trace is the simulated spectrum, and an asterisk (*) represents signal originating from a small amount of a Ga-containing impurity. This figure has been reproduced with the permission of the copyright holder.

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study and preserving pore dimensions. Refinements of XRD data confirmed porous Ga-fumarate resided in the same space group as Al-fumarate and featured a single Ga center in both the activated Ga-fumarate and rehydrated Ga-fumarate-H2O systems; in good agreement, 69/71Ga NMR spectra of both the activated Ga-fumarate and air-exposed Ga-fumarate-H2O materials at 21.1 T (Fig. 24C, D) could be simulated using one unique Ga powder pattern, validating the single Ga site structure. The authors noted an increase in CQ(Ga) upon introduction of H2O to activated Ga-fumarate due to relatively strong hydrogen bonding interactions between water and the m2-OH groups linking GaO6 octahedra, which triggered a change in GaeO bond length and/or :OeGaeO bond angle distributions. 69/71Ga NMR experiments were also performed on CO2-loaded Ga-fumarate, with no significant changes reported in Ga parameters versus empty Ga-fumarate, which signified that CO2 was not adsorbing at the metal center nor significantly disturbing the GaO6 local environment. The authors also noted that Ga CS parameters had a very slight influence on experimental spectra, as did possible T2 anisotropic relaxation effects in Ga NMR spectra. In this instance, the authors were able to use Ga NMR to prove that there was a single crystallographically unique Ga site in the Ga-fumarate MOF, obtaining accurate NMR parameters by performing 69/71Ga NMR experiments at a high magnetic field of 21.1 T. Ga NMR was also used to monitor the phase change between activated Ga-fumarate and Ga-fumarate-H2O, and exposed the lack of interaction between guest CO2 and the local GaO6 coordination environment. Kobera et al. described the use of 71Ga NMR spectroscopy to investigate the structure and phase composition of a polycrystalline gallium-imidazole (Im) MOF system in 2020.92 The authors synthesized a Ga(Im)6 MOF that was found to have several phases of unknown local structure, which was better described as a polycrystalline system rather than a phase-pure MOF. In conjunction with other complementary techniques, 71Ga NMR experiments at 11.7 and 16.4 T were used as part of an NMR crystallography approach to unravel the actual composition of Ga(Im)6. The authors examined the reaction mixture as it progressed towards formation of the Ga(Im)6 product at 25, 50, and 75 days after initiation using one-dimensional static 71Ga echo and WURST-CPMG experiments, highlighting how Ga NMR identified three signals at each stage in the reaction; one corresponded to residual unreacted “liquidlike” Ga0 signal that decreased in intensity over time, while WURST-CPMG experiments were used to verify the other two signals corresponded to tetra-coordinated GaIV and hexacoordinated GaVI species. After 75 days, 71Ga NMR experiments continued to indicate a distribution of Ga0, GaIV, and GaVI environments were present, providing proof as to how Ga NMR can be used to monitor the progression of slow-moving MOF reactions over time. In order to enhance spectral resolution and further understand the true Ga(Im)6 product composition, a static 2D 71Ga variable pulse width (VPW) experiment was performed (Fig. 25). The 2D VPW spectrum clearly distinguished the presence of three distinct gallium species aside from Ga0 in Ga(Im)6, with one tetra-coordinated GaIV and two unique hexacoordinated GaVI environments present. Additional Ga NMR experiments at multiple fields confirmed the polycrystalline nature of the Ga(Im)6 sample. DFT calculations were correlated with the 71Ga NMR experiments and other results to extract the specific molar fractions of each Ga species present in the polycrystalline Ga(Im)6 product. This report was an excellent example of how exotic quadrupole NMR can be used in conjunction with an NMR crystallography approach to ascertain the number of metal sites and their specific coordination environment across the lifetime of a MOF-forming reaction, including the use of 2D NMR experiments.

9.13.3.9

91

Zr

Zirconium can adopt high coordination numbers and is thus well-suited as a metal center in MOFs, but poses significant challenges for NMR acquisition. The only NMR-active isotope of zirconium is 91Zr (I ¼ 5/2), which is ca. 11% naturally abundant but has a moderate quadrupolar moment and low resonant frequency, making this a challenging NMR target in many systems. With the popularity of Zr in materials such as the UiO-66 and UiO-77 MOF family which feature Zr-oxygen clusters, there is certainly potential for the use of 91Zr NMR to investigate local structure about the metal center. Zirconium NMR was reviewed by Lucier and Huang in 2015,93 with developments since then summarized by Smith in 2020.53

Fig. 24 The local GaO6 structure of the GaO4(OH)2 environment in Ga-fumarate is shown in (A), with the long-range structure of Ga-fumarate-H2O shown in (B). The accompanying static 71Ga and 69Ga NMR spectra at 21.1 are shown in (C) and (D), respectively. The blue traces represent experimental findings while the red traces are simulations. This figure has been reproduced with the permission of the copyright holder.

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Fig. 25 The 2D 71Ga variable pulse width spectrum of the Ga(Im6) MOF is shown in (A), with two slices extracted at 71Ga pulse widths of ca. 0.6 ms and 1.8 ms shown at right. The F2 slice at 1.9 ms is clearly composed of three separate signals, reflective of the three different Ga environments (GaIV, GaVI1, GaVI2) present in this material. This figure has been reproduced with the permission of the copyright holder.

In 2014, He et al. used static 91Zr WURST-CPMG experiments at 21.1 T to investigate the structure of MIL-140A. This was the first documentation of a thorough 91Zr NMR study of a MOF.85 There was uncertainty regarding local coordination about the Zr centers due to the challenges in solving the MIL-140A crystal structure from powder XRD data. The authors clearly outlined the sensitivity challenges for NMR, pointing out that 91Zr atoms constituted only 0.67% of the atoms within the MOF unit cell. In MIL-140A, Zr resides in a ZrO7 local environment, with four O atoms originating from BDC ligands and the remaining three from m3-O2 atoms. The structure about Zr is shown in progressively enhanced images within Fig. 26A–C. The 91Zr WURST-CPMG NMR experimental spectrum of MIL-140A (Fig. 26D) was remarkable in its ca. 800 kHz breadth at 21.1 T and exceptionally high CQ(91Zr) value of 35 MHz, in addition to its dissimilarity to the powder pattern predicted from DFT calculations based on the reported crystal structure. A DFT geometry optimization of the hydrogen atom positions followed by calculation of NMR parameters showed a poor match to experimental observations (Fig. 26G), however, DFT optimization of all atomic positions prior to NMR calculations produced a simulation much closer to experimental results (Fig. 26F). It was found that the reported distribution of ZreO bond lengths and angles within the crystal structure was much wider than those computed from DFT calculations, which resulted in

Fig. 26 The structure of MIL-140A is shown from long-range to local perspectives in (A–C), with the coordination of O units local to Zr shown in (C). In (D, E, F, G), corresponding experimental and simulated static 91Zr NMR spectra based on DFT calculations are shown at 21.1 T; note the agreement between (E) and (F). This figure has been reproduced with the permission of the copyright holder.

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a predicted 91Zr NMR powder pattern much broader than the experimentally observed one. The authors interpreted these findings to mean that fully geometry optimized DFT calculations of NMR parameters did a better job of modelling local structure about the Zr centers and more closely reflected the actual structure at the atomic level, indicating that the reported crystal structure did not accurately describe local Zr structure. In an interesting note, the differences in ZneO local structure between the reported and DFToptimized structures produced nearly identical powder XRD patterns, illustrating the usefulness of exotic quadrupolar metal NMR coupled with DFT calculations as a verification avenue for local structure. There was a report from Koschnick et al. in 2021 regarding the local structure in the PCN-221 porphyrinic Zr MOF, which was notable due to its implications for Zr local structure in the ZneO clusters featured within several other MOF families.94 The authors used a variety of complementary techniques, including 91Zr NMR at 14.1 T and 120 K, to obtain a fuller understanding of Zr local structure in the PCN-224 and PCN-221/dPCN-244 (d ¼ disordered) MOFs. While the original report of the PCN-221/dPCN-244 MOF structure indicated that Zr8O6 clusters composed the metal nodes in the framework, the authors showed that these were in fact Zr6O4(OH)4 clusters with linker vacancies that were oriented in four distinct orientations within the unit cell, which initially presented XRD data which gave the illusion of a Zr8O6 cluster. 91Zr NMR was very useful in corroborating the authors’ position. The name of dPCN-224 was termed a better name for PCN-221, as the MOF was closer in structure to PCN-224 while Zr6O4(OH)4 clusters were shown to be disordered in the system. 91Zr of the dPCN-224 MOF at 14.1 T was performed at a low temperature of 120 K to improve S/N. There was a complicated 91Zr powder pattern observed for both dPCN-224 and PCN-224, which could be fit using four individual powder patterns (Fig. 27). The locally disordered nature of dPCN-224 produced a 91Zr NMR spectra of somewhat low resolution. In agreement with the distribution of binding modes found via multinuclear NMR and other approaches, 91Zr NMR spectra of dPCN-224 indicated a distribution of binding modes were present about Zr, which was attributed to the presence of attached hydroxy-water pairs, leftover modulator molecules, and general strain in the local Zn clusters.94 The findings were also compared to those of the well-defined Zr6O4(OH)4Bz10 reagent used in one of the dPCN-224 synthesis strategies, which featured two 91Zr sites; DFT calculations showed that the broad powder pattern in Zr6O4(OH)4Bz10 was correlated to Zr interacting with bridging carboxylate linkers while the narrower powder pattern corresponded to Zr centers with surroundings involved in mixed binding modes. This study illustrated how NMR of exotic quadrupolar metals can be used to validate or refute overall structural models based on local structure, in addition to confirming the presence of disorder in MOFs. A very recent report from Hangarter et al. included an unsuccessful attempt to study the Zr6O4(OH)4(BPYDC)6 (BPYDC ¼ 2,20 bipyridine-5,5-dicarboxylate) MOF via 91Zr NMR.95 They were unable to obtain a signal from 91Zr QCPMG experiments, and attributed this to local disorder, dynamics, and/or large CQ(91Zr) values.

9.13.3.10

115

In

There are two NMR-active isotopes of In, 113In and 115In, of which 115In (I ¼ 9/2) is the preferred choice for NMR experiments due to its ca. 96% natural abundance. While the resonant frequency of 115In is rather high, its quadrupolar moment is the unfortunately the largest of the main group elements.68 115In NMR powder patterns are often of considerable breadth, low S/N, and challenging to acquire, necessitating the use of high magnetic fields whenever possible to expedite spectral acquisition. Despite the large QI, CSA can make tangible contributions to 115In NMR spectral appearance in some instances. The four works involving 115In NMR in MOFs since 2014 are discussed below.

Fig. 27 91Zr QCPMG NMR spectra of the dPCN-224 and PCN-224 MOFs obtained at 14.1 T, each featuring contributions from four individual 91Zr powder patterns and confirming the presence of Zr6O4(OH)4 clusters with four unique Zn sites. This figure has been reproduced with the permission of the copyright holder.

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He et al. utilized 115In NMR in their 2014 work on a variety of exotic quadrupolar nuclei in MOFs, studying the metal centers within the In(BDC)1.5(bipy) (bipy ¼ 2,20 -bipyridyl) and In(BTC)(H2O)(phen) (phen ¼ 1,10-phenanthroline) MOFs at magnetic fields of 9.4 and 21.1 T.85 This study highlighted the important influences of local geometry and coordination number on 115In NMR parameters. The In(BDC)1.5(bipy) MOF has an 8-coordinate InO6N2 local environment (Fig. 28A, B), while the In(BTC)(H2O)(phen) MOF includes an InO4N2 immediate local coordination sphere with a distant IneO contact that renders it a pseudo 7-coordinate InO5N2 environment (Fig. 28E, F). The use of two different magnetic fields was necessary to exploit the opposing field dependencies of the QI and CS for more accurate determination of 115In NMR parameters. The In(BDC)1.5(bipy) structure yielded a well-defined 115In powder pattern with a CQ value of ca. 80 MHz that was subtly influenced by CSA at 21.1 T (Fig. 28C), which highlights the importance of using high fields when CSA could be present; the CS contribution was nearly undetectable at 9.4 T (Fig. 28D). The In center within In(BTC)(H2O)(phen) compound yielded a relatively broader 115In spectrum at both 9.4 and 21.1 T (Fig. 28G, H) corresponding to a much larger CQ value of 145.0 MHz, with no evidence of CSA influence at either field. The differences in CQ(115In) between the two MOFs were particularly intriguing as both In centers reside in a similar coordination environment, and was attributed to differences in In-ligand bond lengths and local coordination geometry. Analysis of the crystal structure confirmed that the In(BDC)1.5(bipy) MOF had a significantly narrower distribution of In-ligand bond distances versus the In(BTC)(H2O)(phen) MOF, which led the authors to conclude that the CQ(115In) value in these MOFs was correlated primarily to the number of metal-ligand bonds and their respective bond length distribution, while hQ(115In) values tracked well with with the symmetry of local In-ligand bond geometry. The authors noted an aberration for DFT calculations of 115In parameters in this system, where geometry optimization of an increasing number of atoms produced 115In EFG parameters that progressively diverged from experimental results, leading to the conclusion that these MOFs possibly did not crystallize in a truly lowest-energy configuration through the lens of computational chemistry. In a 2014 review focusing on quadrupolar nuclei in MOFs, Huang et al. discussed the novel static 115In NMR spectra of the MIL68(In) MOF at 21.1 T.17 There are two unique In sites in MIL-68(In) (Fig. 29A), both of which reside in InO6 octahedral coordination environments (Fig. 29B) that have varying degrees of distortion from perfect octahedral symmetry (Fig. 29C). The overall 115 In ultra-wideline NMR spectrum was ca. 4 MHz wide, requiring VOCS acquisition, and is an excellent example of a broad spectrum that nevertheless offers well-resolved powder patterns and good spectral resolution. The simulated QI-dominated signals were in good agreement with the crystallographically predicted intensities, featuring two overlapping 115In powder patterns in a 2:1 ratio between the sites (2 of In1 sites per each In2 site) (Fig. 29D). The In2 site corresponded to a CQ value of 300 MHz, while the In1 site was linked to a CQ of 248 MHz. The significant different in observed CQ values despite the similar InO6 octahedral local environments was investigated further, revealing that the In2 environment had a more notable departure from octahedral symmetry, particularly in the HO-In-OH direction. While this case was highlighted by the authors as an example of excellent spectral resolution in an ultra-wideline situation, it also illustrated the sensitivity of 115In QI parameters to subtle distortions in the local coordination environment, and the feasibility of NMR for probing exotic quadrupolar metals in a wide variety of local environments. Zhang et al. used 115In NMR to investigate hydrophobic and hydrophilic indium-based variants of the aluminum fumarate A520 MOF in 2018, in the same report as the 69/71Ga work mentioned earlier.91 There were two different In-based MOFs reported: hydrophilic In-fumarate-E made in ethanol, and hydrophobic In-fumarate-M made in methanol. The topology of both In-fumarate variants was identical to that of Al-fumarate, with InO6 local structure composed of four oxygen atoms of four fumarate linkers plus two oxygen atoms from bridging eOH groups connecting the InO6 octahedra. Multinuclear 1H/13C NMR illustrated how the hydrophobicity of In-fumarate-M originated from bridging eOCH3 groups, while the hydrophilicity of In-fumarate-E was linked to its

Fig. 28 The long-range and local structures in In(BDC)1.5(bipy) and In(BTC)(H2O)(phen) are shown in (A, B) and (E, F), respectively. Their corresponding 115In NMR spectra at two different fields are shown in (C, D, G, H). Additional intensity outside the bounds of the CT powder pattern are attributed to STs, and the # symbol denotes an impurity. This figure has been reproduced with the permission of the copyright holder.

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Fig. 29 The long-range structure of the MIL-68(In) framework is shown in (A–C), highlighting the unique In1 and In2 sites and their associated IneO bond lengths. In (D), the individual subspectra and overall static 115In ultra-wideline NMR spectrum of MIL-68 is shown, along with simulated spectral contributions from both In sites. This figure has been reproduced with the permission of the copyright holder.

bridging eOH groups. In good agreement with the crystal structure solved within this work, 115In NMR yielded evidence of a single unique In site in both forms of In-fumarate. The 115In powder pattern of activated In-fumarate-E corresponded to a lower CQ(115In) of 193 MHz, while water-adsorbed as-made In-fumarate-E-H2O yielded a significantly larger CQ(115In) of 260 MHz (Fig. 30A). The presence of water molecules near the In coordination sphere in In-fumate-E-H2O was hypothesized to distort the already asymmetrical distribution of IneO bond distances and angles present in In-fumarate-E. The hQ value of activated In-fumarate-E was 0.22 while that of In-fumarate-E-H2O was 0.00, indicating that the presence of guest water molecules also produced local
C3 rotational symmetry about the In center, illustrating the opposing trends in 115In QI parameters associated with H2O in this system. The activated hydrophobic In-fumarate-M MOF before and after extended exposure to air presented a 115In In NMR spectrum very similar to that of activated In-fumarate-E (Fig. 30B), proving that there was no significant difference in local In environment beyond the presence of bridging eOCH3 rather than eOH groups; in particular, the 115In NMR results indicated the eOCH3 group in Infumarate-M was not bound directly to the In metal center. The authors also used 115In NMR to examine CO2-loaded versions of activated In-fumarate-E and In-fumarate-M but and did not observe any significant changes in 115In NMR parameters versus the empty MOFs, revealing that the local environment about the In metal center was not impacted by CO2 adsorption. This study was a good example of how 115In NMR experiments could be used to identify the number of unique sites in a novel MOF, probe the effects of guest adsorption, and investigate the origins of hydrophobicity in MOF systems. Chen et al. used 115In NMR at 21.1 T in 2018 to understand the local environment of In3þ guest metals within the MIL-121 MOF.66 The In3þ center was inserted via exposure of MIL-121 to indium acetate salt, with guest In3þ thought to bind to the free carboxylate groups of the BTEC MOF linker. The indium acetate reagent gave rise to a single, well-defined, broad, and QI-

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Fig. 30 The 115In NMR spectra at 21.1 T of (A) as-made In-fumarate-E-H2O, activated In-fumarate-E, (B) activated In-fumarate-M, and activated Infumarate-M followed by exposure to air for 7 days. Activated In-fumarate-E is shown as the lower entry in both columns for comparison. This figure has been reproduced with the permission of the copyright holder.

dominated 115In NMR powder pattern that was ca. 7500 ppm wide, however, the In-MIL-121 species yielded a relatively much narrower, featureless 115In NMR signal perhaps 500 ppm in breadth. The 115In signal was modeled using a distribution of sites and corresponding 115In NMR parameters, with the CQ(115In) distribution centered at 50 MHz. The narrow guest 115In signal was a much narrower and featureless contrast to other 115In signals contained within this review, illustrating how much information 115 In NMR experiments can offer. The narrow 115In NMR signal of In-MIL-121 was interpreted to mean that the guest indium metal dopant was ionic in nature and resided in a relatively narrow distribution of local environments; this was consistent with findings for other guest metals that necessitated the use of NMR parameter distributions for spectral simulations in the same study, and illustrated how NMR of exotic quadrupolar metals can be used to identify the degree of local order about metal centers in MOFs.

9.13.3.11

139

La

Lanthanum is another element that can adopt high coordination numbers and therefore has applications as a metal center within MOFs. There is an attractive 99.9% abundant NMR-active isotope in 139La, but it possesses only a moderate resonant frequency and is spin 7/2 with a significant nuclear quadrupole moment. 139La NMR spectral acquisition can be challenging in many circumstances, particularly when the local La coordination sphere is distorted or otherwise asymmetrical. While La can be readily inserted into MOFs, reports of 139La NMR in MOFs remain somewhat scant, and there have been only two 139La NMR studies of MOFs within the scope of this review. In 2014, He et al. examined the influence of coordination number and linkers in a LaO-type local environment within the La2(BDC)3(H2O)4 and La2(C4H4O4)3(H2O)2$(H2O) MOFs.85 Both MOFs employed BDC linkers and had documented single-crystal XRD structures that allowed the authors to correlate local structural features to 139La NMR parameters with the aid of DFT calculations. The long-range structure of La2(BDC)3(H2O)4 is shown in Fig. 31A, with the short-range local structure in (B), 21.1 T 139 La NMR spectra in (C), and 14.1 T NMR spectra in (D). The single La site in La2(BDC)3(H2O)4 resides in a LaO8 local environment, with six oxygen atoms from BDC linkers and the remaining two from water. Both 139La MAS and static NMR experiments were successful on La2(BDC)3(H2O)4 at 21.1 T, owing to the relatively narrow breadth of the powder pattern; along with static 139 La NMR data at both fields, this dataset allowed for accurate quantification of both the QI and CS parameters. Notably, this system exhibited an unexpectedly significant CS influence, as 139La powder patterns are normally dominated by the QI. La2(BDC)3(H2O)4 yielded a CQ(139La) value of 18.0 MHz and a U of 300 ppm. The La2(C4H4O4)3(H2O)2$(H2O) MOF structure is shown in Fig. 31E, F, with the accompanying 21.1 T spectra in (G) and 14.1 T spectra in (H). In contrast to the LaO8 local structure in La2(BDC)3(H2O)4, La occupies a LaO9 local coordination environment in La2(C4H4O4)3(H2O)2$(H2O), with eight oxygen atoms from BDC linkers and the remaining one from water. This system gave rise to a significantly broader 139La powder pattern with distinct QI features at both magnetic fields, with a CQ(139La) value of 28.0 MHz and span of 100 ppm confirming the dominance of the 139La QI and a much smaller contribution from CSA. The larger breadth of the 139La powder pattern in this case prevented use of MAS methods to more accurately quantify CSA, although the CS contribution was undoubtedly small, and could still be accurately ascertained from the static 139La NMR spectra given the opposing QI and CS magnetic field dependencies. While La2(BDC)3(H2O)4 and La2(C4H4O4)3(H2O)2$(H2O) shared somewhat similar local coordination environments and both exhibited intermediate hQ values, the relatively large 10 MHz difference in CQ(139La) values warranted further examination to determine its local origins. It was discovered that the CQ(139La) values in these systems were not solely determined by the local

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Fig. 31 The long- and short-range structure of La2(BDC)3H2O4 are shown in (A) and (B), respectively, along with 139La NMR spectra obtained at (C) 21.1 T and (D) 14.1 T. In (E) and (F), the structure of La2(C4H4O4)3(H2O)2(H2O) is shown along with the accompanying static 139La NMR spectra at (G) 21.1 T and (H) 14.1 T. Spinning sidebands are marked with asterisks (*) in (C). This figure has been reproduced with the permission of the copyright holder.

LaeO bond length distribution, as the La2(C4H4O4)3(H2O)2$(H2O) MOF had a relatively smaller distribution of LaeO bond lengths yet exhibited a much larger CQ value. The authors determined that in this instance, the CQ values were primarily determined by the spherically symmetric arrangement of ligands in space about La; the La center in La2(BDC)3(H2O)4 was located at the center of a slightly distorted quadratic antiprism, which possesses significant spherical symmetry and thus corresponded to a lower CQ value and a narrower 139La NMR spectrum. Plane-wave DFT calculations in this study supported the structural conclusions drawn from 139La NMR spectra. In 2018, Chen et al. examined the guest loading of La ions within the MIL-121 framework using 139La NMR.66 Using a strategy involving exposure of the MIL-121 parent MOF to La(OAc)3$1.5H2O reagent in solution for 3 days, La ions were introduced and presumably bound to free carboxylate groups on the BTEC linkers. The WURST-CPMG pulse sequence was used at a magnetic field of 9.4 T, illustrating how 139La NMR experiments performed at relatively lower fields still yield useful structural information. The La(OAc)3$1.5H2O reagent and related La(OAc)3 compound both presented relatively narrow and well-defined 139La NMR powder patterns. In contrast, La-loaded La-MIL-121 gave rise to a much broader signal that was approximately 7000 ppm wide at the base. This lineshape exhibited vague details of a QI-dominated NMR spectrum such as two poorly defined quadrupolar “horns” and a tailing of intensity to low frequency, which like other guest metal ions in this study, were determined to arise from a distribution of similar local environments. The NMR spectrum resembled a broader, less detailed version of the La(OAc)3$1.5H2O powder pattern. Simulations of the spectrum required consideration of a QI parameter distribution, with CQ values centered at 34.0 MHz and ranging from 25.0 to 48.0 MHz, along with hQ values centered at 0.7 and ranging from 0.5 to 1.0. Static NMR were employed due to the width of the spectra, as MAS rotational rates would not provide sufficient averaging of the anisotropic QI and CS interactions. The authors used this data to conclude that the guest La metal in La-MIL-121 was coordinated in a disordered fashion to some type of acetate-like units (i.e., the unbound eCOO groups on BTEC linkers) within a distribution of chemically similar local environments.

9.13.4

Outlook

There has been a significant amount of progress in solid-state NMR of exotic quadrupolar metal nuclei in recent years, and we see the future of this research area as exceptionally bright. With the advent of higher magnetic fields, continuing advances in the design of increasingly clever pulse sequences, and rapid expansion of the MOF field, it is envisioned that forward progress will be realized in two directions over the coming decade. First, currently accessible exotic quadrupolar metal nuclei will become feasible targets in many more high-CQ arrangements, which should open the door for detailed 2D NMR experiments that yield even richer structural information. Secondly, exotic quadrupolar nuclei now regarded as inaccessible will eventually be rendered legitimate subjects for NMR experiments, unlocking a plethora of additional MOF families for study. Given that quadrupolar metal nuclei are prevalent in a wide variety of systems and the MOF community continues to expand at a rapid pace, the coming years should realize the adoption of exotic quadrupolar metal NMR as a more common option in the toolbox for MOF characterization, especially given the rich amount of information this avenue affords when combined with complementary methods such as ab initio calculations and X-ray diffraction. Progress using NMR to examine MOF linkers and guests also continues to be realized at a surprising speed, increasingly advancing the frontier of possibilities. Concepts that once seemed distant in the future, such as routine complete comprehensive solid-NMR characterization of MOFs to yield a wealth of local structural information, are now exciting opportunities that draw closer with every passing year.

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Acknowledgment Y.H. thanks the Natural Science and Engineering Research Council (NSERC) of Canada for a Discovery Grant.

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9.14 Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants Daniel Jardo´n-A´lvarez and Michal Leskes, Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, Rehovot, Israel © 2023 Elsevier Ltd. All rights reserved.

9.14.1 9.14.1.1 9.14.1.2 9.14.2 9.14.2.1 9.14.2.2 9.14.2.3 9.14.2.3.1 9.14.2.3.2 9.14.2.4 9.14.3 9.14.3.1 9.14.3.2 9.14.3.3 9.14.3.4 9.14.3.4.1 9.14.3.4.2 9.14.3.4.3 9.14.3.5 9.14.3.6 9.14.3.6.1 9.14.3.6.2 9.14.3.6.3 9.14.4 9.14.4.1 9.14.4.2 9.14.4.3 9.14.4.4 9.14.4.4.1 9.14.4.4.2 9.14.4.4.3 9.14.5 References

Introduction Overview of this chapter Dynamic nuclear polarization NMR in the presence of paramagnetic species Introduction The spin Hamiltonian Relaxation Electron relaxation Paramagnetic relaxation enhancement Signal quenching MAS-DNP at high fields The Overhauser effect The solid effect The cross effect Spreading the hyperpolarization throughout the sample Spin diffusion Direct polarization Experimentally assessing the role of spin diffusion Differences between exogenous organic radicals and endogenous metal ions Applications of DNP from paramagnetic metal ions to inorganic samples OE mechanism SE mechanism CE mechanism Practical considerations Determining homogeneity of metal ions distribution Characterization of the metal ions with EPR Acquisition of MAS NMR spectra with MIDNP Reporting dopant concentrations With known unit cell volume With known density Calculating the mean distance Outlook

367 367 368 370 370 370 372 372 372 375 375 375 377 381 385 385 386 387 387 388 388 388 389 389 389 390 391 393 393 393 394 394 394

Abbreviations BPP Bloembergen-Purcell-Pound CE Cross effect CT Central transition CW Continuous wave DNP Dynamic nuclear polarization DQ Double quantum EPR Electron paramagnetic resonance FC Fermi contact HFI Hyperfine interaction MAS Magic angle spinning MIDNP Metal ions based dynamic nuclear polarization NMR Nuclear magnetic resonance OE Overhauser effect

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PA Polarizing agent PAF Principal axis frame PRE Paramagnetic relaxation enhancement RF Radio frequency SE Solid effect SNR Signal to noise ratio SOC Spin orbit coupling ST Satellite transition TM Thermal mixing ZFS Zero field splitting ZQ Zero quantum mW Microwave

Abstract In this chapter, an introduction to dynamic nuclear polarization (DNP) solid state nuclear magnetic resonance (NMR) is given. The main focus lies in presenting the use of paramagnetic metal ion dopants in inorganic materials as endogenous sources of hyperpolarization. Relevant concepts of NMR in the presence of paramagnetic centers are introduced and the main DNP mechanisms are explained with a quantum mechanical formalism. The presented theoretical basis allows an in-depth discussion of the limits and possibilities of metal ion-based DNP (MIDNP). Conceptual and practical differences of this approach and exogenous DNP are discussed, in particular the advantages offered by MIDNP as a tool for structural elucidation of inorganic solids are highlighted. Finally, practical considerations to help implementing this experimental technique are given.

9.14.1

Introduction

9.14.1.1

Overview of this chapter

Over the last two decades dynamic nuclear polarization (DNP) has had a huge impact on magic angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy. The signal enhancements obtained from DNP translate into enormous time savings, enabling scientists to perform previously unfeasible experiments. Accompanying and fueling this process is the development of new theoretical treatments, novel hardware and experimental procedures for understanding and improving the DNP process itself. Many excellent reviews have come out lately summarizing these achievements. In this contribution we intend to highlight a novel approach to DNP for high sensitivity solid state NMR of inorganic materials. In metal ions DNP (MIDNP) paramagnetic species are introduced as dopants into the lattice where they directly serve as the source of hyperpolarization to the nuclei in the bulk of the solid of interest. While we put the main focus of this chapter on paramagnetic metal ions based DNP for inorganic samples, we also introduce most of the relevant approaches to achieve sensitivity gains through DNP. Our intention is to place the relevance of the MIDNP approach into the proper context, aiming to provide the reader without prior DNP background sufficient knowledge to be able to decide which approach is most suited for tackling the specific question of relevance to their research. Ultimately, we hope this chapter is useful for NMR spectroscopists interested in learning about DNP in general. In the next subsection we introduce the concept of DNP and present the main mechanisms to achieve DNP. We will highlight the historical relevance of some conceptual developments and the role of DNP in assisting NMR as a spectroscopy for structural characterization. In Section 9.14.2 we introduce the basic NMR and EPR interactions and relaxation mechanisms which will be needed for describing the DNP processes, but are also relevant to understand the changes in the NMR properties to expect when introducing paramagnetic species to the sample. In Section 9.14.3 we give an overview of the theoretical concepts which are necessary for laying out the differences between the various possible paths to obtain DNP. While we do not intend to cover all theoretical aspects of DNP, in the presented quantum mechanical framework we try to treat the most important concepts, which should give a solid basis to immerse in more specific problems. In this section we are explicitly general and do not focus uniquely on metal ions based DNP. Instead, we introduce the three main DNP mechanisms: Overhauser-, solid- and cross-effect. This allows us to discuss the possibilities of using paramagnetic metal ions as polarizing agents (PA) for any of the mechanisms and the difficulties to be expected. Further, we discuss how the hyperpolarization is spread through the sample to enhance the NMR signals of interest. Next, we highlight the differences between the MIDNP approach and the more widely used approach using exogenous organic radicals. We finish this section with a discussion on applications of DNP to inorganic materials as well as paramagnetic ions as polarizing agents.

368

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

Finally, in Section 9.14.4, we point out practical aspects to consider when performing metal ions based DNP experiments, mainly concerning sample preparation and characterization. We intend to report some of the expected and unexpected challenges that might occur in MIDNP applied to MAS NMR and highlight strategies which we have found useful for overcoming problems. This section is mostly based on the experience from our group, and as such, it will be incomplete. Nonetheless, we hope that some of these practical considerations can be helpful to other research groups intending to benefit from the MIDNP approach.

9.14.1.2

Dynamic nuclear polarization

Solid state NMR is one of the most important tools to gain structural and dynamical information at the atomic scale on inorganic solids. Especially since the development of magic angle spinning (MAS) for acquisition of high resolution spectra, NMR has become a routine characterization method in solid state chemistry. The full potential of NMR is unraveled by multi-dimensional acquisition schemes as these enable disentangling and correlating NMR interactions which can then be mapped into structural properties. The main limitation of NMR arises from its intrinsically low sensitivity. The signal intensity in an NMR spectrum is directly proportional to the population difference of the Zeeman energy levels of the NMR active nucleus. At thermal equilibrium the ratio of the populations of the two states, raD and rbD, of a spin ½ is given by Boltzmann statistics: 
Na -gI B0 : (1) ¼ exp Nb kB T Where raD is the lower energy state, gI is the gyromagnetic ratio, an isotope specific constant, Z is the reduced Planck’s constant, B0 is the strength of the external magnetic field, kB is the Boltzmann constant and T is the temperature. At ambient temperature, even at high magnetic fields, the number of nuclear spins actually contributing to the NMR signal is only in the order of tens per million for nuclei with large gyromagnetic ratio. Being isotope selective is one of the major advantages of NMR compared to other spectroscopic techniques. In inorganic solids, nuclei of interest can have very low gyromagnetic ratios, be broadened due to anisotropic interactions and/or a distribution of isotropic interactions and can have very long longitudinal relaxation times due to the absence of motion. All these effects contribute to further lowering the sensitivity, limiting the applications of NMR spectroscopy such that in some cases even obtaining one dimensional NMR spectra can be unfeasible. The signal to noise ratio (SNR) can be increased by repeating the measurement multiple times, but since the SNR grows only with the square root of the number of repetitions, experimental times can quickly become prohibitively long. A strategy to increase the sensitivity of an NMR experiment consists of working at non-Boltzmann conditions, where the populations of the nuclear spin energy levels are manipulated to create hyperpolarization. There are various possible approaches to obtain hyperpolarization, among which dynamic nuclear polarization (DNP) stands out mainly due to its large versatility. The basic idea of DNP consists of transferring the degree of polarization of electron spins to nearby nuclear spins. The gyromagnetic ratio, and consequently the polarization, of the electron spins is orders of magnitude larger compared to nuclear spins (for example: ge/g1H z 660 or ge/g17O z 4850). In the following we will briefly introduce the main DNP mechanisms while a more formal theoretical description will be given in Section 9.14.3. In 1953 Overhauser conceived the idea of DNP and postulated that it should be possible to hyperpolarize nuclear spins far beyond their Boltzmann equilibrium by transferring the polarization from electron spins to nearby nuclear spins.1 Soon after, Carver and Slichter2 experimentally confirmed Overhauser’s prediction and achieved a large enhancement of the 7Li NMR signal in metallic lithium upon microwave irradiation. The proposed and observed enhancements occurred via a mechanism now known as the Overhauser effect (OE),3 which, as we will see in the following sections, relies on cross-relaxation processes. The main requirement for efficient enhancements via the OE is that the coupling between electron and nuclear spins undergoes very rapid stochastic fluctuations. This is usually achieved when the unpaired electrons are highly mobile, such as in the conduction band of metals or, alternatively, in liquid samples. In the late 1950s a distinct DNP mechanism enabling nuclear hyperpolarization in solids was discovered.4–7 While electron and nuclear relaxations are still critical parameters determining the DNP efficiency, polarization transfer in this mechanism is no longer mediated by relaxation and consequently, high mobility is not a requisite. For this reason, this DNP mechanism was labeled the solid effect (SE). Instead, in SE DNP the polarization transfer follows saturation of a formally forbidden zero (rabD 4 r baD) or double (r aaD 4 r bbD) quantum transition achieved by microwave irradiation at ue  un, the sum or difference of the electron and nuclear Larmor frequencies. It was soon realized that this method could assist NMR in the chemical characterization of inorganic solids, as the source of unpaired electrons could simply be introduced by doping the diamagnetic host lattice with small amounts of paramagnetic centers. Recently, the same ideas, have led to significant sensitivity gains in the context of high resolution solid state NMR under MAS and at high magnetic fields.8 A third, fundamentally different, mechanism was discovered in the 1960s,9,10 the cross effect (CE). CE DNP can occur in a threespin system consisting of two coupled electrons and one nucleus when the fundamental matching condition | ue1  ue2 | ¼ |un | is satisfied. When this is the case, there will be a degeneracy between two energy levels of the form rabaD 4 r babD, thus involving a triple flip-flop. Saturation of an electron transition of one of the electrons by microwave irradiation will consequently lead to a transfer of polarization to the nuclear transitions. The microwave power requirements for this mechanism are much lower compared to the SE, as irradiation is on an allowed transition. The main challenge consists of finding a pair of electrons matching exactly the condition. In modern MAS DNP, biradicals, specifically tailored for this purpose,11,12 are employed exogenously. If both

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

369

electron spins have distinct relative g-tensor orientations, during a MAS rotor period the electron spins will pass through an orientation at which the frequency matching condition is satisfied and the nuclear hyperpolarization can build up in these, so-called, rotor events. This usually requires that at least one of the electrons of the biradical has a g-anisotropy larger than the nuclear Larmor frequency. In the context of inorganic materials, the use of exogenous biradicals can be exploited mainly for surface selective studies,13 while enhancements of nuclei in the bulk of the sample require efficient spin diffusion for transferring the polarization. In addition, other DNP mechanisms have been observed, including modified versions of the main mechanisms14 as well as pulsed DNP methods, where the electron spins are manipulated by microwave pulses in a process resembling cross polarization experiments.15–17 Most notably, probably deserving of being treated as an independent mechanism, is thermal mixing (TM).9 While in TM the polarization transfer can be described with a three-spin system and in analogy to the CE, the two mechanisms differ in the origin of the frequency difference Due of the two coupled electrons. In contrast to the CE, in TM this difference has homogeneous origin,18 such as complex many-spin interactions which lead to a differential coupling of both electrons with the surrounding bath of electronic spins. As a consequence, the chemical and physical conditions favoring CE and TM can be very different. So far, the role the TM mechanism can play in high resolution solid state NMR of materials is still under debate. In this writing we will not treat this mechanism in detail; instead we refer to Refs. 14,19,20. Based on the simplified concepts introduced so far, it is evident that the performance of the various mechanisms will have a different dependency on the concentration of unpaired electrons. One could imagine how by increasing the concentration of unpaired electrons in a system one should eventually pass through optimal conditions for the SE, CE and TM mechanisms, successively (see Fig. 1). Of course, many aspects need to be considered, making this a very challenging problem; therefore, to the best of our knowledge this has not yet been realized experimentally. Unfortunately, in general, all DNP mechanisms present an adverse dependence on the magnetic field strength. Consequently, as NMR moved to higher fields for higher resolution, the initial enthusiasm of the early days of DNP decreased, and the main research focus of the NMR community switched away from DNP. In addition, at that time high power microwave sources for the required

Fig. 1 Schematic representation of the effect of paramagnetic species on various relevant magnetic resonance properties at standard MAS DNP NMR conditions (100 K and moderate spinning speeds approximately tens of kHz). At very low concentrations couplings among electron spins are likely negligible (width of purple bars indicate expected strength of electron–electron coupling and their effect on the EPR spectrum). At the same time, nuclear spins experiencing strong shifts due to couplings to the paramagnetic centers are scarce and their contribution to the overall NMR spectrum will be small. On the other hand, even at very low concentrations in the absence of efficient diamagnetic relaxation mechanisms paramagnetic relaxation enhancements (PRE) may become the dominant relaxation mechanism, and the effects of signal quenching become relevant (black lines indicate when the presence of paramagnetic center is expected to have an effect on the measurable NMR properties; dashed line highlights that the presence and magnitude of quenching will strongly depend on the relaxation times of the involved electron spins). With increasing concentration electron–electron interactions will strongly alter the EPR properties; paramagnetic shifts and broadenings will modify the shape of the NMR spectra and relaxation times become very short. The efficiency of DNP from the paramagnetic center as polarizing agents depends on all these properties in a non-trivial way. In the last part of the figure a rough estimate is given on when the different DNP mechanisms might be expected to have significant contributions upon changes in the dopant concentration (darker shades of the bars indicate largest expected efficiency of the DNP mechanisms).

370

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

higher frequencies were not available. This changed in the 90s and beginning of the 2000s as Griffin and coworkers introduced the use of gyrotrons capable of producing high power microwaves at hundreds of gigahertz and for long periods of time,21,22 leading to commercially available MAS DNP setups.23 Furthermore, the use of new radicals was introduced, specifically tailored for the purpose of high field DNP. These developments led to a renaissance of the large interest in DNP, seeking its implementation in virtually every area of NMR for improving its capabilities as a spectroscopic technique, but also rewinding and deepening into the underlying theoretical concepts. Today, conceptual and technological advances in DNP are occurring at an impressive pace, and a second detachment from NMR seems inconceivable. Rather we imagine its application alongside NMR becoming routine in an increasing manifold of applications, certainly in solid-state NMR of inorganic materials.

9.14.2

NMR in the presence of paramagnetic species

9.14.2.1

Introduction

The presence of paramagnetic species can have huge effects on the NMR properties of a sample. This area of magnetic resonance is often labeled paramagnetic NMR. Understanding the properties implicated in paramagnetic NMR can be highly complex as a proper description of such systems requires knowledge of the nuclear and electronic spin properties as well as of their interactions. In this chapter we introduce some concepts on magnetic resonance of paramagnetic species and the relevant interactions that will affect the properties of the surrounding nuclear spins. We will restrict this section to phenomena that might be of relevance for MIDNP in inorganic solids. For a broad and much more detailed treatment of NMR in the presence of paramagnetic centers we refer to the excellent publications by Bertini, Luchinat, Parigi and Ravera24 and by Pell, Pintacuda and Grey.25 A significant aspect we would like to emphasize is that the relative importance among all possible effects will strongly depend on the concentration of the paramagnetic agents. For instance, at low dopant concentrations frequency shifts, which reflect local interactions, are likely to have little to negligible effect on the overall spectrum; on the other hand, the relaxation properties might already be completely altered. At low concentrations, the electron spins can be accurately treated as isolated spins, however, as the average distance between electron spins decreases with increasing concentration, electron–electron couplings will manifest in strongly modified properties of the spins. The combination of all these effects will also dictate which DNP mechanism will be possible (if any) at a given dopant concentration. While the complexity of the problem impedes exact predictions, which will anyway also be strongly sample dependent, general trends can be identified and are depicted schematically in Fig. 1.

9.14.2.2

The spin Hamiltonian

The energy states of a spin system consisting of coupled nuclear and electron spins in the presence of an external magnetic field are given by the spin Hamiltonian: b0 ¼ H b EZ þ H b NZ þ H b SO þ H bs þH b ZFS þ H bQ þH b dd þ H b J: H

(2)

b NZ , Zeeman interaction, the spin-orbit coupling (SOC), H b SO , the chemical b EZ , and nuclear, H Which includes the electron, H b b b shielding, H s , the zero field splitting (ZFS), H ZFS , the nuclear quadrupolar interaction, H Q , as well as through space dipolar

b J . Further, each interaction includes the sum over the considered spins and possible b dd , and exchange couplings, H couplings, H spin pairs. The electron and nuclear Zeeman terms describe the interaction of the external magnetic field B0 with the electron, b S, and nuclear, bI, spins. The electron Zeeman and SOC Hamiltonians in the LS coupling regime are given by:   b EZ þ H b SO ¼ mB b L þ ge b H Lb S: S B0 þ lb

(3)

Where b S and b L are the spin and orbital contributions to the Zeeman energy, and only the latter is asymmetric. Further, mB is the electron Bohr magneton and ge is the free electron g value approximately equal to 2.0023. The gyromagnetic ratio is defined as ge ¼  mBge/Z and l is the spin-orbit coupling constant which describes the coupling of the spin and orbital angular momenta. The nuclear Zeeman and the chemical shielding interaction are given by: b NZ þ H b s ¼  -gN bIB0 þ -gN bIsB0 ¼ -gN bIðs  1ÞB0 : H

(4)

Where s is the shielding tensor. This interaction includes only terms present in diamagnetic samples, and is composed of a diamagnetic contribution from the electronic ground state as well as a paramagnetic contribution due to excited electronic states; both contributions have opposite signs. The nuclear quadrupole interaction and the electron zero field splitting are present for spins larger than 1/2 and can lift the degeneracy of the spin energy levels in the absence of an external magnetic field. The nuclear quadrupolar interaction is electrostatic and arises from the coupling of the nuclear electric quadrupole moment with the gradient of the surrounding electric field: h 2 i  e2 qQ bI  I2 þ h bI 2  bI 2 : b PAF ¼ (5) H Q z x y 4Ið2I  1Þ-

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

371

Where e is the charge on a proton, Q is the nuclear quadrupole moment, eq describes the electric field gradient and h is the asymmetry parameter. The electronic ZFS originates from the dipole–dipole coupling between the electron spins and the Hamiltonian is given by:   2  2 2 1 b PAF ¼ DZFS b SðS þ 1Þ þ EZFS b H Sx  b (6)  Sy : S ZFS z 3 Where, DZFS and EZFS give the ZFS interaction tensor in the principal axis frame of the interaction. Both, quadrupolar interaction and ZFS, have the same mathematical form, but following convention the asymmetry of the principal axis components are defined b Q and H b ZFS the spatial and spin parts are defined here by h or the ratio of DZFS and EZFS, respectively. Note that for simplicity in H with respect to the principal axis frame (PAF) of the interaction while all other interactions are defined with respect to the laboratory frame. b J are the direct through space and the exchange interaction Hamiltonians, respectively. Their form is independent of b dd and H H the nature of the coupled spins, which can involve two nuclei, two electrons or one nucleus and one electron. For simplicity we will only consider couplings in the point dipole approximation and disregard effects of the orbital magnetic moment on the couplings. The exchange interaction has the following form:    b J ¼ AIS 1 bI þ b S  þ bI  b S þ þ bI z b Sz : H (7) 2 Where AIS is the exchange interaction coupling constant. When the interaction involves two nuclei it is called indirect spin-spin coupling or J-coupling and is mediated by bonding electrons between the nuclei. When it involves one nucleus and one electron it is called Fermi contact interaction (FC) and it arises when the electron has a finite probability of being at the nucleus. The interaction described by this operator involving two electrons is called the Heisenberg spin exchange coupling, or simply exchange coupling. The through space dipolar coupling Hamiltonian between two spins I and S is given by: 

      b dd ¼ ud AbI z b H (8) S z þ B bI þ b S  þ bI  b S þ þ C bI z b S þ þ bI þ b S z þ D bI z b S  þ bI  b S z þ EbI þ b S þ þ FbI  b S ; with ud ¼  and

m0 gI gS ; 4p r 3

(9)

  A ¼ 3cos2 q  1 ;  1 B ¼  3cos2 q  1 ; 4 3 C ¼ sinqcosq ei4 ; 2 3 D ¼ sinqcosq eþi4 ; 2 3 E ¼ sin2 q e2i4 ; 4 3 2 þ2i4 : F ¼ sin q e 4

(10)

Where m0 is the vacuum permeability, r is the distance between the interacting spins and q and 4 are the polar angles describing the relative orientation of the I–S vector with respect to the external magnetic field. This is known as the dipolar alphabet. Here we have explicitly separated the spin and spatial parts for later convenience. When the two coupled spins are a nucleus and an electron, this is referred to as the through space dipolar coupling part of the hyperfine interaction (HFI). In NMR spectroscopy it is often convenient to work within the secular approximation, which states that the contribution to the energy of the spin system from terms which do not commute with the Zeeman interactions is negligible. This approximation reduces the through space dipolar coupling Hamiltonian to only the first term of the alphabet for unlike spins, or to the first   S  þbI  b S þ of the exchange interaction will be truncated for unlike two terms for like spins. Analogously, the flip-flop terms bI þ b spins. In this chapter however, it is important that we retain the full form of the Hamiltonian for two reasons. First, not only secular but also non-secular terms will contribute to relaxation, and second, the SE and CE DNP mechanisms are mediated by the so-called S z and bI  b S z . These terms refer to contributions which do commute with the electron Zeeman interaction, pseudo-secular terms bI þ b but not with the nuclear Zeeman interaction. It is important to note that in paramagnetic samples, because of the fast electronic relaxation the through space dipolar and Fermi contact interactions manifest in the NMR spectrum as a frequency shift, rather than a splitting of the NMR lines. In this limit of fast electronic relaxation, the nuclear spins are affected by an average of the electronic magnetic moment over the thermally accessible states. The average moment is related to the bulk magnetic susceptibility tensor, and the paramagnetic shifts can therefore be

372

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

described as a tensorial quantity, in analogy to the chemical shielding interaction given in Eq. (4) for a diamagnetic sample. This is usually referred to as paramagnetic shift, which is further classified according to the interaction giving rise to the shift: The contact interaction can be responsible for isotropic and anisotropic (in case of anisotropic g) contact shifts,24 and the through space dipolar interaction for anisotropic dipolar shifts and pseudocontact shifts. For a description of paramagnetic shifts in NMR again we refer to Refs. 24,25. For our purposes it should suffice to point out that increasing concentration of paramagnetic species within the sample can contribute to significant line shifts and broadenings and that these effects have an inherently large temperature dependence. The DNP and relaxation processes we are concerned with in this chapter require the actual form of the electronic spin operator and not its average, therefore, we will describe the interactions between nuclei and electrons in terms of the Hamiltonians given in Eqs. (7) and (8). For completeness we note that fluctuations arising from stochastic motions of the interaction between the nuclear spin and the average electronic magnetic moment can also be a source of nuclear relaxation, the so-called Curie-spin relaxation. However, as it is unlikely to have a significant contribution in rigid solids, we will not consider it further.

9.14.2.3 9.14.2.3.1

Relaxation Electron relaxation

A series of different processes can lead to longitudinal and transverse relaxation (T1e and T2e) of electronic spins in solids. In the direct, Raman and Orbach relaxation processes, modulations of orbital angular momentum by lattice phonons cause electron spin relaxation through the spin-orbit coupling. In the thermally activated processes stochastic motions modulate the relevant spin interactions given in Eq. (2) leading to local magnetic field fluctuations at the site of the electron spins. The latter can be treated in complete analogy to the nuclear relaxation processes presented in the next subsection. For a discussion of the former relaxation processes we refer for instance to Refs. 24,26,27. Describing relaxation in terms of coupling to phonons is most convenient when phonons are scarce, such as in rigid solids at very low temperatures. Stochastic processes, on the other hand, are most relevant in the liquid state. A priori discernment of which relaxation model will be best suited for describing a solid at temperatures of interest in DNP is not trivial. In principle, the distinct temperature dependence of the various relaxation processes could be used to differentiate among them.28 In practice, however, this is an extremely challenging undertaking, as it requires precise measurements of T1e over a wide temperature range. Furthermore, the Raman activated relaxation process changes from a T(n þ 1) dependence at temperatures below the material specific Debye temperature, to T2 above it, where n ¼ 8 for Kramer and 6 for non-Kramer systems.27 The thermally activated process inverts its temperature dependence when the inverse of the correlation time of the motion becomes slower than the electronic Larmor frequency (see later discussion on nuclear relaxation times in terms of spectral densities). Besides the temperature dependence, electron spin relaxation can have a strong concentration dependence when dipolar and exchange couplings among spins become relevant. At high concentration, relaxation mechanisms mediated by these interactions can become dominant.29

9.14.2.3.2

Paramagnetic relaxation enhancement

Nuclear magnetic relaxation is an incoherent effect, and thus non-reversible, caused by random fluctuations of local magnetic fields. The dependency of the relaxation rates on magnitude and fluctuation rate of the local fields was first described by Bloembergen, Purcell and Pound in what today is known as the BPP theory.30 Specifically, longitudinal relaxation, which drives the nuclear magnetization to thermal equilibrium is caused by fluctuations at the Larmor frequency of local fields perpendicular to the external magnetic field. Transverse relaxation, which describes the loss of coherence in the transverse plane, is in addition also influenced by slow fluctuating local fields parallel to the external field. In this section we will give a brief description of the derivation of the relevant relaxation equations. We shall start with the master equation of relaxation, which can be derived from the Liouville von Neumann equation in the presence of a perturbation. A detailed derivation and discussions concerning relevant assumptions can be found for instance in the classic books by Abragam31 or Slichter32; for a more didactic approach the outstanding book by Kowaleski and Mäler33 is recommended. 

r ðt Þ db ¼  dt

Z 0

Nh

ii h e e b ðt Þ; V b ðt þ sÞ; e b b V r ðt Þ  e r 0 ds:

(11)

The master equation of relaxation describes the time evolution of the density matrix, b r , under the presence of a time-dependent b . The overbar indicates an average over the ensemble, the tilde indicates that we moved into the rotating frame repreperturbation, V b b sentation and the thermal correction (e r ðt Þ  e r ) is introduced to ensure a population difference of the different states at 0

equilibrium. b and a time In general, we can write the laboratory frame Hamiltonian of the fluctuating interaction in terms of a spin part, A, dependent spatial part, F(t). Expressed in tensors of arbitrary rank, for generality, we can write: X b q; b ðt Þ ¼ F q ðt Þ A (12) V q

Where q is the order of the tensor. In the Zeeman interaction frame this can be written as:

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants e b ðt Þ ¼ V

X

b q eiup t : F q ðt Þ A p q

373

(13)

q;p

In Table 1 these terms are given for the case of dipolar coupling. Introducing this into Eq. (11) leads to:    ii i uq0 þuq t Z N X h q0 h q q db r ðt Þ 0 p 0 p e e b 0; A b ;;b ¼  A r0 e F q ðt ÞF q ðt þ sÞ eiup s ds: p r ðt Þ  b p dt 0 0 0 q;q ;p;p

(14)

0

We will assume that the contributions from rapidly oscillating terms are negligible, such that exp(i(up0q þ upq)t) ¼ 1 (it can be shown that this is satisfied when p0 ¼ p and q0 ¼  q). The time dependent term is the autocorrelation function, which correlates the stochastic fluctuating function with itself at different points in time and therefore gives a measurement of the timescale of the fluctuations. In the following we will assume that the autocorrelation function follows an exponential decay and define the decay 
constant as the correlation time, sc: F ðt ÞFðt þ sÞ ¼ GðsÞ ¼ Gð0Þexp ssc . The second term in Eq. (14) gives the Fourier transform of the autocorrelation function. The result will consequently be a Lorentzian function, called spectral density, J(u). The spectral density can be understood as a measurement of the density of the presence of a given frequency within the stochastic fluctuation. With these considerations we can rewrite Eq. (14) as: 

ii r ðt Þ db 1 X  q h b ðqÞy h b q  ¼ r ðt Þ  b Jq up A p A p b r : dt 2 q;p 0

(15)

In order to analyze the relaxation behavior of the nuclear magnetization we will follow the effects of the time dependent perturb by looking at its expectation value. Actually, since relaxation processes are stochastic, we are bation on a relevant observable, Q, interested in its average value, given by:  b ðt Þ d Q dt

9 8  1, the J(uI) term dominates the equation and xdd approaches zero. Large coupling factors, thus, require short correlation times, smaller than the inverse of the electron Larmor frequency. At the same time, in order for the leakage factor to be close to unity, this relaxation mechanism, or specifically the double- (for the dipolar case) and zero-quantum (for the FC case) relaxation paths should be most efficient compared to any other relaxation path. This condition in turn is given at uSsc z 1, a value which in general probably represents a good compromise for the largest possibility of efficient OE DNP enhancement. Note that the maximum enhancement obtained from pure dipolar relaxation is only half of the FC case and that both coupling factors actually have opposite signs. Consequently, when relaxation has contributions from both terms, it will lead to a partial cancelation of the enhancement. As the dipolar relaxation introduces the single quantum spectral density J(uI) term, even at low contributions from dipolar couplings, the ultimate fate of the OE is to vanish for increasing fields as soon as uSsc > 1. A curious effect can occur when FC and dipolar relaxation mechanisms have different correlation times; in that case, it is possible that within a small range of magnetic fields the absolute value of the coupling factor increases with field.39

9.14.3.2

The solid effect

In Fig. 4 the basic energy population diagram for describing the solid effect is shown. The basic selection rule is that only single

quantum transitions (O m ¼ 1) between magnetic resonance states are allowed. The pseudosecular terms of the through space hyperfine coupling are responsible for a mixing of states, which is the basis of the solid effect, as it enables the required saturation of the zero (ZQ) or double (DQ) quantum transitions. Pseudosecular refers to terms which can be truncated with respect to the large electron Zeeman interaction leaving only terms which commute with b S z but do not commute with bI z . In this approximation all terms not commuting with b S z are neglected, consequently, the Hamiltonian of the through space dipolar coupling given in Eq. (8) simplifies to: 

   b dd ¼ uen AbI z b S z þ C bI þ b S z þ D bI  b Sz : H (32) d We can write the total spin Hamiltonian in the rotating frame of the electron (indicated by a tilde) under microwave irradiation as

    e e e b b b b b bb b b b ¼ Due b S z þ unbI z þ uen H d A I z S z þ C I þ S z þ D I  S z þ u1 S x ¼ H 0 þ H mW :

(33)

Where the first and second term refer to the electron off resonance and nuclear Zeeman interactions, the third we already mentioned as the dipolar coupling term and the last term refers to the microwave irradiation. Following the treatment and notation introduced by the group of S. Vega14,40 we will go to the eigenstate representation by diagonalizing the Hamiltonian: e e b ¼D b b 0 D: b 1 H L

(34)

The energy levels shown in Fig. 4 refer to the eigenstates in this representation and the corresponding density matrix can be obtained from the original purely Zeeman product state representation in analogy:

The Overhauser Mechanism en n e T1n

Irradiate on electron SQ PW

T1ZQ

If: RDQ > RZQ, R1n

PW

T1DQ

T1n

Fig. 3 Energy level diagram of a two-spin system (electron–nucleus). Populations of the different energy states schematically represented by the size of the blue spheres. At thermal equilibrium the populations are dictated by the Boltzmann distribution (left). Microwave irradiation on the resonance frequency of the electron saturates its single quantum transition. In the Overhauser effect an imbalance in the double (DQ) and zero quantum (ZQ) cross relaxation rates leads to hyperpolarization of the nuclear single quantum transitions (right).

378

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

The Solid Effect Mechanism en n e (A)

T1n

’

’

T1e

’

’

’

’

Irradiate on DQ (or ZQ)

T1ZQ µW

’

T1e

T1DQ

’

T1n

(B)

’

’

’

’ ’ ’ ’ ’

(C)

’

’

’

’ ’ ’ ’ ’

Fig. 4 (A) Energy level diagram of a two-spin system (electron–nucleus). Populations of the different energy states schematically represented by the size of the blue spheres. At thermal equilibrium the populations are dictated by the Boltzmann distribution (left). In the solid effect microwave irradiation at ue  un drives saturation of the zero (ZQ) or double (DQ, shown on the right) quantum transitions. (B) Diagonalization of the Hamiltonian given in Eq. (33) but containing only the relevant Zeeman and pseudosecular terms with C ¼ D, while not showing the secular term from the hyperfine coupling. All Hamiltonians given in the electron Zeeman rotating frame. (C) Frame transformation of the mW irradiation Hamiltonian using the same rotation matrices as in (B), the result shows the appearance of effective zero (blue) and double (green) quantum transition operators, with a nutation strength u1;DQ=ZQ zu1

jC juen d un .

L e b b 1 e b b r ¼D r D:

(35)

The new eigenstates are related to the pure Zeeman eigenstates as: jl1 i ¼ jbai’ ¼ cb jbai þ sb jbbi; jl2 i ¼ jbbi’ ¼ sb jbai þ cb jbbi; jl3 i ¼ jaai’ ¼ ca jaai þ sa jabi;

(36)

jl4 i ¼ jabi’ ¼ sa jaai þ ca jabi With the first term in the ket referring to the electronic and the second to the nuclear spin. For un [ ud the coefficients can be approximated to:

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

379

ca;b z1; jCjuen d : sa;b z 2un

(37)

For simplicity, here and in the following we will only consider the real part of the spatial part of the coupling, thus, C ¼ D. We can now analyze the efficiency of the microwave irradiation on the various transitions by applying the same diagonalization matrices to the microwave term: L e e b 1 H b b b mW D: H mW ¼ D

(38)

To a good approximation the electronic single quantum excitation efficiency is not affected by this transformation; however, it can be shown that the state mixing creates new terms enabling zero or double quantum transitions at ue þ un and ue  un, with an effective nutation frequency of: u1;DQ=ZQ z  u1

jCjuen d : un

(39)

Enhancement of the nuclear polarization can be achieved by microwave irradiation on either the ZQ or DQ transitions. In Fig. 4 these frame transformations are shown in matrix representation for easier visualization. As can readily be seen from Fig. 4, irradiation at the zero and double quantum transitions will lead to nuclear hyperpolarization of opposite signs. This results in the characteristic SE sweep profiles with a minimum and maximum at the double and zero quantum transition, respectively (shown in Fig. 5). These profiles are unique to the solid effect mechanism and therefore, are commonly a good experimental validation of the presence of the SE. When the inhomogeneous broadening of the EPR line

Fig. 5 (A) Idealized EPR spectrum showing the single quantum transition (labeled W1) as well as the double (W3) and zero (W2) quantum transitions of a two spin system (electron–nucleus). (B) Schematic representation of an inhomogeneously broadened EPR spectrum composed of packets of width x. (C) DNP field sweep profile of the system shown in (A), assuming a positive nuclear gyromagnetic ratio. d/2 refers to the polarization at thermal equilibrium, while D/2 to the theoretical polarization enhancement maximum, with D/d ¼ ge/gn. (D) Experimental 1H DNP field sweep profile of a single crystal of La2Mg3(NO3)12$24H2O doped with 1 mol% Ce(III). The difference with the idealized case shown in (C) arises due to the inhomogeneous line broadening. In all figures the horizontal axis corresponds to the magnetic field H ¼ B/m0. Note that the ZQ transition requires a lower magnetic field to be on-resonance with the mW frequency as compared to the DQ transition. In the profile of a frequency sweep with constant field W2 and W3 will appear in reversed order with increasing frequency as compared to the here shown field sweep of constant irradiation frequency. Adapted from Leifson, O. S.; Jeffries, C. D. Dynamic Polarization of Nuclei by Electron-Nuclear Dipolar Coupling in Crystals. Phys. Rev. 1961, 122(6), 1781–1795. https://doi.org/10.1103/PhysRev.122.1781.

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becomes of the order of the nuclear Larmor frequency the positive and negative enhancements will start overlapping, reducing the absolute sensitivity gain. For very large broadenings the strong overlap results in a shift of the maxima increasing their separation, this is shown in Fig. 5(B) and (D). At this point we should emphasize that sweep profiles can be obtained by sweeping the irradiation frequency at a constant external magnetic field or by maintaining the irradiation frequency constant while changing the field. Due to the current available technology the latter is the common option in modern high field DNP instrumentation. In the following, we will analyze the variables that determine the actual enhancement factors. In the common case of short electron relaxation time, we can assume that the electron polarization remains constant at its Boltzmann value, Pe,eq, throughout the DNP experiment. The degree of nuclear hyperpolarization is thus solely determined by the efficiency of saturation of the irradiated transition: Pn =Pe ¼ 

Pe;eq  OpDQ=ZQ Pe;eq

:

(40)

Here O pDQ/ZQ is the population difference between raaD0 and rbbD0 , or between r abD0 and r baD0 . In the absence of saturation,

Eq. (40) simply gives Pn,eq/Pe,eq, while for full saturation (O pDQ/ZQ ¼ 0), unity is reached, equivalent to the maximum theoretical value, where nuclear polarization equals electron polarization. The steady state Bloch equation of saturation gives the deviation from the Boltzmann equilibrium populations reached under continuous irradiation, counteracting the effect of relaxation. For our simple two spin system in the high temperature approximation it can be shown to be42:

OpDQ=ZQ ¼

OpDQ=ZQ;eq 1þR

u1;DQ=ZQ 2

:

(41)

2e ð2R1;DQ=ZQ þ2R1n Þ

Where R1,DQ/ZQ is the longitudinal relaxation rate of the DQ or ZQ transition and R2,DQ/ZQ was assumed to be approximately equal R2e. An interesting approach for estimating R1,DQ/ZQ was proposed by the group of Vega following the same formalism of the eigenstate representation. The underlying assumption is that the electron relaxation rate can be described by a single fluctuation rate responsible for the modulation of the local magnetic field perpendicular to the external static magnetic field. In analogy to the calculation of the effective nutation frequency, applying the previously determined diagonalization matrices on the fluctuating operator should give an estimate of the degree of DQ/ZQ relaxation due to the mechanism (although unknown) responsible for T1e. As relaxation is a second order effect, following this approach one obtains:
en 2 Cud : (42) R1DQ zR1ZQ z4R1e 2un We note that if the PRE is dominating the nuclear longitudinal relaxation, Eq. (41) becomes independent of the dipolar coupling strength between paramagnetic center and the nucleus, as all R1;DQ=ZQ ;R1n ;u1;DQ=ZQ 2 fud 2 . Consequently, the steady state nuclear hyperpolarization is distance independent. Implications of this result on macroscopic DNP enhancements are discussed in Section 9.14.3.4 Spreading the hyperpolarization throughout the sample. The weak effective nutation power, paired with instrumental difficulties in obtaining high power microwave irradiation inside the MAS rotor,43 places a serious challenge in obtaining large saturation efficiencies. The previous equations evidence the importance of long electronic relaxation times T1e and T2e. Fig. 6 shows the dependence of the nuclear hyperpolarization as a function

Fig. 6 Steady-state nuclear polarization, PN ¼ Pn/Pe, relative to equilibrium electron polarization as a function of the electronic relaxation times with T2e ¼ T1e following Eq. (40) assuming a single electron spin S ¼ 1/2, coupled to a single I ¼ 1/2 nucleus with the gyromagnetic ratio of 17O in a 9.4 T magnetic field at 100 K under 0.35 MHz microwave irradiation44 on-resonance with the double quantum transition. From Jardón-Álvarez, D.; Reuveni, G.; Harchol, A.; Leskes, M. Enabling Natural Abundance 17O Solid-State NMR by Direct Polarization from Paramagnetic Metal Ions. J. Phys. Chem. Lett. 2020, 11(14), 5439–5445. https://doi.org/10.1021/acs.jpclett.0c01527.

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of T1e for a fixed microwave irradiation power following Eq. (40). The requirement of long electronic relaxation time is probably the most critical parameter when choosing possible metal ions as polarizing agents. Long relaxation times can be expected for symmetric coordination environments and for half-filled electron shells, vide infra. Generally, electronic relaxation becomes longer at lower temperatures,26 consequently, performing the DNP experiments at cryogenic temperatures can significantly improve obtained signal enhancements. Under MAS any anisotropic interaction will oscillate with the rotor period. As a consequence, under the presence of significant ganisotropy or zero field splitting (ZFS), matching of the SE condition will oscillate for a given crystallite. While in the static case a large inhomogeneous broadening of the EPR line results in not all crystallites being saturated simultaneously under microwave irradiation. When spinning, all crystallites will eventually satisfy the matching condition during one rotor period, but only for a reduced period of time. In this case, the previously introduced theoretical descriptions might no longer be accurate, instead a more rigorous treatment, which takes into account the time dependency of the interactions would have to be considered.45,46 However, based on quantum mechanical simulations and experimental evidence, no significant MAS speed dependence of the SE enhancement was found.46 As MAS plays a critical role in the CE mechanism, a more thorough explanation on how to account for MAS in DNP is given in Section 9.14.3.3 with reference to its effect on the SE. In fact, the distinct dependence on the spinning speed of the SE and CE can be used to differentiate both mechanisms. Although care should be taken, as it can be experimentally challenging to maintain a constant sample temperature at different MAS speeds while spinning with cryogenic gases and under microwave irradiation. All derivations shown so far were done assuming spin ½ for both, nucleus and electron. To our knowledge, possible implications due to the presence of high-spin nuclei have not been treated in a systematic manner. Kaminker et al. showed a difference in the nuclear polarization enhancement factor for a nucleus with spin 1 compared to spin ½ from theoretical considerations, although this treatment referred to the CE mechanism. On the other hand, significant efforts have been given to understand the role of highspin electrons in DNP. The theoretical foundation for high-field DNP from paramagnetic metals with electronic high spin was introduced by Corzilius and an in depth treatment can be found in Refs. 47,48. Of course, for metal ions-based DNP high spin polarizing agents are very relevant. Most importantly, large ZFS and spin orbit couplings severely shorten the electronic relaxation times and broaden the EPR line, this poses a very severe limitation on the possible metal ions to be used as polarizing agents. In paramagnetic metals with half-filled electron subshells placed in highly symmetric environments the (ground-state) orbital momentum is quenched and the ZFS can become much weaker than the Zeeman interaction. Fulfillment of these requirements can lead to a sufficiently sharp central transition (CT) and long relaxation times enabling SE DNP. As the satellite transitions (ST) are affected by the ZFS to first order, in most cases the ST are too broad for a sizeable contribution to the DNP enhancement. Thus, only a fraction of the total number of paramagnetic centers will contribute to the DNP enhancement. More precisely, while at a given time point not all paramagnetic centers are contributing to the DNP enhancement, fast electron relaxation ensures that within the timescale of the DNP process every metal ion will eventually populate every eigenstate for a fraction of time. Consequently, any metal ion will contribute to the DNP enhancement, but only during a reduced fraction of the time. On the other hand, since irradiation is selective on the CT the effective nutation frequency scales with (S(S þ 1)  ms(ms  1))1/2. For instance, this increases the transition probability of the electronic CT of a 7/2 spin (e.g. Gd3þ) by factor 16 compared to a spin ½.47 In addition, as the second order effect of the ZFS is scaled by the inverse of the Larmor frequency, this effect might in some cases alleviate the decrease in enhancement when going to higher magnetic fields.49 A further aspect to consider arises when the paramagnetic metal ion has NMR active isotopes which lead to strong isotropic hyperfine couplings, usually in the range of hundreds of MHz. The resulting splitting of the EPR lines results in a further decrease of total number of polarizing agents contributing to the SE DNP.

9.14.3.3

The cross effect

The basic energy population diagram describing the cross effect mechanism is shown in Fig. 7. The minimum required size of the spin system consists of two electrons and one nucleus e2–e1–n. For simplicity, we will assume the coupling between the second electron and the nucleus is negligible and we will only consider through space dipolar interactions, disregarding effects of the electron–nuclear contact interaction and exchange interaction between the electrons. While the exchange interaction between both electrons can play an important role in the DNP mechanism in biradicals,50,51 it is unlikely to be relevant in metal ions DNP with low concentration of PA. The relevant Hamiltonian in the microwave rotating frame describing this system is given by: 

      e ee b b 1 b b b b b bb b ¼ Due1 b S 1 b S 1z þ Due2 b S 2z þ unbI z þ uen S 2 þ b S 2þ þ u1 b Sx S 1þ b H d Aen I z S 1z þ Cen I þ S 1z þ Den I  S 1z þ ud Aee S z S z  4 e e b0þH b mW : ¼H (43) Where again we have considered the pseudosecular terms of the electron–nucleus dipolar coupling, but only the secular terms of the electron–electron coupling. The CE mechanism can be described by following an analogue procedure to the one shown for the SE in the previous section. First, we apply partial diagonalization of the Hamiltonian, considering only the nuclear Zeeman and electron off-resonance terms as well as the through space hyperfine interaction between the first electron and the nucleus. Next, we analyze the Hamiltonian describing the electron–electron coupling in this new frame. Fig. 7 shows the resulting Hamiltonian

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Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

Fig. 7 (A) Energy level diagram of a three spin system (electron 2–electron 1–nucleus). Populations of the different energy states schematically represented by the size of the blue spheres. At thermal equilibrium the populations are dictated by the Boltzmann distribution (center). Microwave irradiation at ue1 saturates the single quantum transitions of one electron (left). At the cross effect condition (ue1  ue2 ¼ Due12 ¼  un), microwave irradiation at ue1 effectively affects both degenerate states, tending to equalize the populations of the states shown in purple in the right figure. (B) Diagonalization of the Hamiltonian containing only the relevant Zeeman and pseudosecular hyperfine terms with Cen ¼ Den and without the secular term from the hyperfine coupling. Only the relevant central four direct product states are shown. All Hamiltonians are given in the electron Zeeman rotating frame. (C) Frame transformation of the Hamiltonian given in Eq. (43), containing Zeeman, pseudosecular hyperfine and electronelectron dipolar coupling terms, but without the microwave irradiation and secular hyperfine terms, using the same rotation matrices as in (B). The result evidences the state mixing induced by enthe electron-electron dipolar coupling at the CE condition Due ¼  un, green and blue terms, Aee ðt ÞCen ðt Þud . respectively, with the strength uee d 4un

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

383

for the relevant energy levels. By comparing this Hamiltonian with the one obtained for the SE in Fig. 4 the similarities of the role of the electron–electron coupling in the CE and the microwave field in the SE are evident. A closer look at the Zeeman terms shows that the energy levels rabaD and rbabD (with r e1e2nD) will become degenerate when the energy difference between the electronic spins equals the nuclear Larmor frequency, ue1  ue2 ¼ Due12 ¼ un (a second, equivalent, degeneracy is possible with the states rabbD and r baaD). This degeneracy will lead to strong state mixing52,53: jabai’ ¼ cos4CE jabai þ sin4CE jbabi; jbabi’ ¼ cos4CE jbabi  sin4CE jabai;

(44)

With ee 1 jCen juen d Aee ud : tanð24CE Þz 4 un ðDue12  un Þ

Irradiation on any of the electron single quantum transitions will effectively alter the population of both degenerate states, creating hyperpolarization of the nuclear transitions. This is schematically drawn in Fig. 7. Two important advantages of the CE compared to the SE become evident here: first, lower microwave power will be required for achieving saturation, as now the requirement has shifted to saturate allowed single quantum electron transitions. And second, at the ideal CE condition the DNP enhancement will be largely field independent, as the saturation efficiency of an allowed transition is not scaled by the field. However, it is important to note that the probability of encountering a spin pair at the CE matching condition is not field independent. Of course, since the CE matching condition is very specific, one can easily imagine that in the case of a sample with an EPR line dominated by the g-anisotropy, the probability of finding a pair of coupled electrons with effective g values differing exactly by the nuclear Larmor frequency, will be very low. This scenario changes dramatically under sample rotation, as over the course of a rotor period many electron pairs will pass through an orientation at which they match the CE condition. Because the relevant processes, involving changes in the energy level populations, happen on very short timescales, during the so-called rotor events, Thurber and Tycko45 and Mentink-Vigier et al.46,54 realized that the theoretical treatment of the CE mechanism under spinning conditions has some fundamental differences compared to the static case. In the following we will shortly introduce the relevant concepts, more thorough derivations of the effect of MAS on the DNP processes can be found in the original references. Under sample rotation all anisotropic interactions, here, the g-anisotropy and the e–e and e–n through space dipolar couplings, become time dependent. Consequently, the energy of the states change rapidly. For a sufficiently large anisotropy, generally originating from g-anisotropy, during the evolution of a rotor period some energy levels would cross. However, due to the presence of off-diagonal elements of the Hamiltonian, the crossings are avoided, causing instead energy levels anti-crossings. Four different types of level anti-crossings, or rotor events, can be identified. (1) An electron microwave event occurs when one of the electron single quantum transitions is on resonance with the microwave frequency. (2) Analogously, a solid effect microwave event will happen when zero or double quantum transition are in resonance with the MW. (3) In addition, when the frequency of both electrons become equal (Due1 ¼ Due2) the electron dipolar coupling will drive an anti-crossing. (4) And finally, a rotor event occurs at the CE condition between the rabaD and r babD or the r abbD and rbaaD states. During most of the rotor period, the evolution of the populations is simply driven by longitudinal relaxation processes, but when approaching the fast-passage rotor events drastic changes in the populations can occur. The efficiency of the changes in populations caused by these anti-crossing events are most conveniently analyzed in the Landau-Zener formalism,55 first applied for this purpose by Thurber and Tycko.45 The relevant Hamiltonian during a rotor event between two states has the general form: ! Eðt Þ d b H ðt Þ ¼ : (45) d Eðt Þ Where E(t) is given by the respective secular terms of the states in the interaction frame and the off diagonal term d by the perturbing interaction (whose time-dependency during a fast-passage rotor event is negligible d(t) z d). The magnitudes of the interactions for the different events can be evaluated from Fig. 7 and are given by: (1) for the electron mW event dmW ¼ u1; en jC ðt Þju (2) for the SE mW event dmW;SE ¼ u1 en un d ; D (3) for the dipolar event d ¼ Aee(t)udee/4; and (4) for the CE event dCE ¼

Aee ðt Þuee jCen ðt Þjuen d d . 4un

When the changes in the energy levels are slow enough, relative to the interaction, the populations will follow the energy levels, inverting the populations among states, in such case the passage is said to be adiabatic. The probability of population transfer can be quantified by the Landau-Zener expression:  

pd2  1 ðp1  p2 Þbefore ¼ XLZ ðp1  p2 Þbefore: (46) ðp1  p2 Þafter ¼ 2exp  dE=dt

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Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

With (p1  p2) the population difference between both states. The Landau-Zener factor XLZ can take values from 1 (full population transfer), for d2 [ dE/dt, to þ1 (population remains invariant), for d2  dE/dt. Therefore, the different rotor events will have different efficiencies. Successive transitions of rotor events in favorable order can lead to the creation of nuclear hyperpolarization. Even at low individual efficiency of the adiabatic processes, large enhancements can be obtained, as the effects are cumulative over the relevant longitudinal relaxation times. An important difference compared to the static case is that microwave and CE events do not have to occur at the same time, and so this enables most crystallite orientations to contribute constructively to the CE enhancement with a fixed microwave irradiation frequency.56 Looking at the interaction terms d it is interesting to note that this theoretical treatment does predict the same, inverse squared, dependence on the magnetic field strength for the solid- and cross effect. This result is in apparent contradiction with experimental observations, which have shown weaker dependence on field strength for the CE. This evidences that the DNP enhancements and build-up rates for bulk sample are governed by many factors with complex relative contributions and not only the adiabatic crossings efficiency.57 Finally, it should be mentioned that in the absence of microwave irradiation the presented formalism predicts the possibility of depolarization of the nuclear magnetization, an effect which was also proven experimentally.56,58 From the definition of the CE matching condition it can be seen that positive and negative enhancements will be obtained depending on which two states are degenerate and that the corresponding field sweep has to be within the limits of the EPR line itself. This is true for both, the static and spinning case and is in contrast to the SE field sweep, which extends beyond the EPR line by  un. Therefore, in principle, field sweeps can be used to differentiate between both mechanisms (as well as the OE, as it will have a single sign over the entire sweep range). For instance, the sweep in Fig. 8 shows the maximum and minimum separated by a distance less than 2un and the enhancements were therefore attributed to the CE mechanisms. It is possible that the EPR

Fig. 8 Top: EPR spectrum of 3% Cr(III) doped [Co(en)3Cl3]2$NaCl$6H2O at a microwave irradiation frequency of 140 GHz and at 80 K. Bottom: DNP field sweep profile for 13C and 59Co under analogous conditions and at 4 kHz MAS. Dashed red line indicates center of the EPR signal, green and blue dashed lines represent distance from center equivalent to the nuclear Larmor frequencies. Deviation of the enhancement maxima from the green and blue lines towards the center of the EPR line is an indication of the CE mechanisms. The power dependence of the enhancements is shown in the inset. From Corzilius, B.; Michaelis, V. K.; Penzel, S. A.; Ravera, E.; Smith, A. A.; Luchinat, C.; Griffin, R. G. Dynamic Nuclear Polarization of 1H, 13C, and 59Co in a Tris (Ethylenediamine)Cobalt(III) Crystalline Lattice Doped with Cr(III). J. Am. Chem. Soc. 2014, 136(33), 11716– 11727. https://doi.org/10.1021/ja5044374.

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line becomes so broad that the separation of the maxima becomes more than twice the nuclear Larmor frequency even for the CE mechanism; in that case alternative approaches will become necessary for assignment of the DNP mechanism.

9.14.3.4

Spreading the hyperpolarization throughout the sample

So far, we have only looked at a single nucleus. Of course, in order to obtain a sizeable hyperpolarization, every source of polarization (single unpaired electron or pair of electrons) needs to polarize many nuclei. This can happen through two different mechanisms, either direct polarization, where the above described mechanisms apply for every hyperpolarized nucleus in the sample or via spin diffusion. In the latter case only nuclei localized in close proximity to the paramagnetic center are directly polarized but subsequently they spread the polarization to neighboring nuclei via a process mediated by homonuclear dipolar couplings. In the following we will present both mechanisms relevant for the solid state in more detail and discuss under what conditions each mechanism is going to prevail. Finally, we will comment on how to discern between them experimentally.

9.14.3.4.1

Spin diffusion

Under strong homonuclear dipolar couplings, polarization is transferred through a nuclear spin bath mediated by the flip-flop opera b

a b

ator bI þbI  þ bI bI þ . In a dense nuclear spin system with strong couplings the polarization transfer can be highly efficient. The spread of polarization at a macroscopic scale has a strong resemblance with a diffusive process and is therefore called spin diffusion.60,61 Many DNP experiments rely on this mechanism to transfer hyperpolarization to the target of interest. In these cases the polarizing agents only directly hyperpolarize nuclei in their immediate proximity, the so-called core nuclei, while polarization reaches distant nuclei via the spin diffusion process. In the exogenous DNP approach a proper choice of the solvent is crucial to ensure the most efficient transfer of polarization from the polarizing agents to the sample. The two critical parameters for the involved spin bath are the strength of the nuclear dipolar coupling and the longitudinal relaxation times. These two parameters, however, can be correlated if homonuclear dipolar couplings are the main source of relaxation. For instance, in exogenous DNP the proton to deuterium ratio in the solvent is known to be critical for optimum proton enhancements.62,63 Furthermore, the ratio of nuclear spins to polarizing agents in the network also plays a role in the enhancement factor.64 The strong homonuclear dipolar couplings among 1H nuclei make them the ideal medium for spin diffusion (in the absence of fast motions). In DNP SENS (Surface Enhanced NMR Spectroscopy)65 the sample of interest is impregnated with a glass forming solvent containing the polarizing agents and with favorable proton spin diffusion properties, for instance, d8-glycerol/D2O/H2O (60/30/10)66 or 1,1,2,2-tetrachloroethane.67 Under microwave irradiation protons near the polarizing agents are hyperpolarized and the polarization is spread over the volume of the frozen solvent via spin diffusion, finally, polarization can be transferred to heteronuclei on the surface of the sample via cross-polarization. This approach has proven to be very efficient in enhancing the NMR signal of surface sites specifically, thus, highly increasing the relevance of NMR spectroscopy in the study of materials’ surface chemistry.68–70 Under favorable conditions spin diffusion can also transfer the hyperpolarization into the bulk of the sample. More specifically, favorable conditions mean: large dipolar couplings, long T1 relaxation times and the absence of spin diffusion barriers (vide infra). Typically, a characteristic distance L accessible by spin diffusion is estimated by: pffiffiffiffiffiffiffiffiffi (47) L ¼ DT1 : Where D is the spin diffusion constant which depends on the mean dipolar coupling strength and the distance between individual spins.71,72 It was shown that significant polarization enhancements can be obtained through exogenous radicals via proton spin diffusion in the bulk of micrometer sized particles.71,73,74 More remarkably, Emsley and co-workers have demonstrated that large hyperpolarization can also be relayed towards the bulk in non-protonated samples. This was proven not only for nuclei with high natural abundance and high gyromagnetic ratios, but also in weakly coupled spin systems such as 113Cd in CdTe or 29Si in quartz, both at natural isotope abundance.75,76 In these cases, the key for long diffusion distances are very long nuclear relaxation times. Theoretical description of spin diffusion mediated polarization transfer is complex, as it involves a very large number of spins. From a macroscopic point of view, this phenomenon can be understood following thermodynamic arguments based on Fick’s laws.61,74 Many efforts have been devoted to understand the polarization flux on a microscopic scale at the immediate proximity of the polarizing agent and at stepwise increasing distances. A deep understanding of these concepts is critical for relating the observed signal enhancements to the efficiency of the DNP mechanisms. It is known that spin diffusion among nuclei in close proximity to the polarizing agent will be less efficient, first due to reduced T1 times, and second, due to mismatches in energy between spins arising from differential coupling strengths to the electron, which reduces the probability of the flip-flop process according to Fermi’s golden rule.61 The concept of the spin diffusion barrier, introduced by Blumberg, states that nuclear spins within a critical radius from the paramagnetic species will not participate in the spin diffusion process.77 Quantifying not only the size of this radius, but also the strictness of the barrier is extremely challenging; nevertheless, important advances to understand the role of the spin diffusion barrier in DNP mediated spin diffusion have been made for instance with theoretical,78,79 computational64 and experimental80,81 approaches. An additional complication arises when considering MAS. Two competing effects are introduced by MAS, on the one hand, spinning at the magic angle reduces the mean dipolar coupling strength, making spin diffusion less efficient. On the other hand, the introduced oscillation of the anisotropic hyperfine interaction will create a new type of rotor events, nuclear-

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Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

dipolar events which will reduce the strictness of the spin diffusion barrier.54 Recent advances in computational approaches have proven valuable for addressing these phenomena by enabling numerical simulations describing spin systems of increasing size.50,82,83

9.14.3.4.2

Direct polarization

In the theoretical expressions for the SE we have seen that as long as PRE is the dominating nuclear relaxation mechanism the DNP enhancement is independent of the nuclear–electron distance. For nuclear spins with long intrinsic relaxation times, direct polarization from exogenous polarizing sources can yield DNP enhancements beyond the first surface layer of the sample.72,75,84,85 This distance independence has an even more profound consequence for endogenous DNP, as it directly implies that obtaining large and homogeneous DNP enhancements via direct polarization from dopants within the structure is possible. This scenario is particularly appealing for low sensitivity nuclei in the bulk of inorganic samples, where spin diffusion does not play a relevant role in the transfer of polarization. The presence of alternative relaxation mechanisms places a limit to the homogeneity, coverage and magnitude of the enhancements. This behavior has been confirmed experimentally by the observation of an enhancement plateau which is independent of the dopant concentration,42 as shown in Fig. 9. At a certain dopant concentration threshold the PRE becomes the dominating relaxation mechanism. Further increment of dopants concentration merely reduces the build-up times, but does not lead to higher DNP enhancements. The high-concentration limit of this plateau occurs due to a drop in electronic relaxation times, a consequence of the increasing electron–electron couplings.

Fig. 9 DNP enhancements 3 ON/OFF of natural abundance 17O (A) and 6Li (B) MAS NMR spectra of iron-doped Li4Ti5O12 at 100 K and 10 kHz spinning speed. In (C) three possible scenarios of dopant concentration are shown schematically: In I the concentration of paramagnetic agents is not large enough to ensure that PRE is the dominant relaxation mechanism in the entire sample, consequently, not all nuclei have time to reach the maximum enhancement. In II, a critical concentration threshold was reached, which ensures maximum enhancement for all nuclei. In III the concentration is so large that the close dopant distances reduce T1e and therefore, the nuclear enhancements become lower. The grey bar shown in (A) and (B) represents the enhancement plateau, at which the signal enhancement is largely concentration independent and is obtained when the concentration resembles scenario II. The difference in enhancements obtained for 6Li and 17O are not understood yet. Adapted from data given in Jardón-Álvarez, D.; Reuveni, G.; Harchol, A.; Leskes, M. Enabling Natural Abundance 17O Solid-State NMR by Direct Polarization from Paramagnetic Metal Ions. J. Phys. Chem. Lett. 2020, 11(14), 5439–5445. https://doi.org/10.1021/acs.jpclett.0c01527.

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants 9.14.3.4.3

387

Experimentally assessing the role of spin diffusion

In order to anticipate the most appropriate experimental conditions for obtaining largest DNP enhancements it is important to understand which mechanisms will dominate in a given experiment, including how the polarization reaches remote nuclei. Based on the early work by Bloembergen,60 in the 1960s it was understood that the nuclear relaxation behavior in a diamagnetic sample homogeneously doped with paramagnetic agents will strongly differ depending on the efficiency of the spin diffusion mechanism.34,35,77,86 Rapid spin diffusion ensures a homogeneous relaxation behavior among all spins, and the relaxation behavior of the entire sample can be described with a single exponential function: exp( t/T1). Furthermore, the value of T1 will decrease linearly with increasing concentration of paramagnetic species. In the absence of spin diffusion every individual nucleus will relax with a time constant following Eq. (23) derived in Section 9.14.2.3.2. The relaxation of the macroscopic magnetization, composed of the sum of the individual spins, can no longer be accurately described in terms of a single exponential process, instead it was found to approximately follow a stretched exponential behavior, exp((t/T1)b) with the stretch factor b approaching 0.5 in an ideal case. Interestingly, the concentration dependence for this case also changes; based on geometric considerations it can be shown that T1 decreases with the square of the concentration. An in-depth treatment of the intermediate cases is discussed in the literature.34,77 We have used these concepts to distinguish the efficiency of spin diffusion in 6,7Li and 17O in iron-doped Li4Ti5O12 with the aim to understand the subsequent DNP enhancements obtained under microwave irradiation.42 When the paramagnetic species are not homogeneously distributed throughout the sample, these considerations no longer apply. Such is the case in the exogenous DNP approach, where the polarizing agents surround the surface of the sample. Pinon et al. have looked in detail at such cases for DNP purposes by separating the system into two regimes of different relaxation rates and polarization levels, and modeling the time evolution of the system under diffusive processes.74 Their analysis shows the presence of a gradient of buildup times, and thus of enhancements, within the undoped part of the sample. Consequently, the overall magnetization buildup behavior does not follow a single exponential function. An interesting implication of this result is that the enhancement factor will depend on the experimental build-up time, as for short delays contributions from components with shorter relaxation times, and larger enhancement factors, will be accentuated.74 Of course, elucidating the contribution of direct polarization and spin diffusion to the sample hyperpolarization in this case requires a different approach. A first estimate can be obtained in terms of Eq. (47).72 Comparison between DNP measurements obtained from direct excitation with measurements obtained via cross-polarization from protons to the heteronuclei of interest are generally also helpful in determining the role of spin diffusion.72,75,76 As a final remark, we would like to emphasize that spin diffusion and direct polarization are not exclusive and therefore, in many cases it is likely that to some extent both contribute to the hyperpolarization build up.

9.14.3.5

Differences between exogenous organic radicals and endogenous metal ions

In this section we want to list some of the many and important differences between the endogenous MIDNP approach and the more commonly used DNP approach using organic radicals as exogenous polarizing agents. Most of the points have already been mentioned in the preceding theoretical sections, here we want to highlight how they are manifested in the experiments in a qualitative manner and how MIDNP exploits the opportunities arising from these differences to become a unique approach. High spin polarizing agents: The first important difference comprises the electron spin itself. While organic radicals have spin ½, the paramagnetic ions often have higher spin numbers. In fact, half-filled orbital shells are usually desired, as it can lead to an efficient quenching of the spin orbit coupling. Any high spin will have zero field splitting (ZFS) contributions to its energy levels, which, if too large, can impede DNP enhancements due to reduced relaxation times and broadening of the EPR transitions. Since the electron spin central transition is affected by the ZFS only to second order, finding systems with sufficiently small ZFS to enable DNP from the central transition is a reasonable task. However, even for such systems, broadening of the satellite transitions is generally too strong to contribute to the DNP process, thus considerably lowering the DNP efficiency. On the other hand, effective central transition nutation frequencies are larger compared to spin ½ nutation and less power will be needed for saturation under equal relaxation times. Sample preparation: From the previous point it becomes evident that in order to avoid short relaxation times and broad EPR lines, it is crucial that the coordination environment of the paramagnetic dopant is isotropic. This shows an important difference: each sample to be studied with MIDNP needs to be analyzed on its own. While in the exogenous approach, approximately the same DNP routine can be used, eventually with minor modifications in the detection step, independent of the sample, in MIDNP the entire process needs to be reevaluated. This starts with identifying a suitable dopant for a given sample and determining appropriate synthesis routes to introduce the dopant; continues with characterization of the doping efficiency and homogeneity, and the EPR properties of the paramagnetic species in the new environment; and finishes with acquisition of DNP field sweep profiles for determining optimum enhancement conditions. While each of these steps is laborious and includes multiple processes, the reward is the inclusion of a structural spy within the lattice of the material of interest. Part of the structure vs. external source: The most important, and intriguing, difference between endogenous polarizing agents and exogenous polarization sources is that the former are included in the structure of the sample of interest. Doping a material will modify its structure to a certain degree and can affect its macroscopic properties. As MIDNP only requires very small dopant amounts to achieve its full potential, in most materials the introduced modifications will be negligible. Nonetheless, it is important to be aware of this possibility and cautious when drawing conclusions. On the other hand, introducing the polarizing agents into the structure offers an interesting opportunity, as it is well known that the properties of certain functional materials can be altered dramatically by the presence of small amounts of dopants. If tailored for such purpose, MIDNP has the potential to be a unique tool

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Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

for understanding how changes in the local structure surrounding the dopants can lead to improved materials functionality. Ideally, paramagnetic NMR parameters like Fermi contact shifts, pseudo-contact shifts or PRE, which are very rich in structural information,87,88 could be selectively detected in a small portion of an otherwise diamagnetic sample. In principle, the most obvious difference between the exogenous and endogenous DNP approach would be that the former is surface selective, while the latter mainly enhances sensitivity of the bulk. In practice, however, both approaches are to some extent capable of yielding information on both aspects. We have already seen in the previous section that under certain conditions exogenous DNP can give enhancements beyond the surface sites via spin diffusion or direct polarization. But also endogenous DNP can be used to increase the sensitivity from surface sites in an inside-out approach. This is appealing for studying reactive surface sites, whose properties would not remain intact upon impregnation with a solution containing radicals. In a recent publication from our group, the potential of combining both approaches was shown. By comparing the spectra obtained with endogenous and exogenous DNP on the same sample it was possible to study the compositional gradient within the solid electrolyte interphase formed around a cathode material in a lithium ion battery.89 In addition, as the polarizing agents are part of the structure, MIDNP offers the advantage of the possibility of obtaining enhancements via direct polarization, without a cross polarization step from a high sensitivity nucleus. As the theoretical maximum of the enhancement factor depends on the gyromagnetic ratio of the nucleus participating in the DNP mechanism, larger enhancements are possible. Another important difference is that in most cases the paramagnetic ions will occupy well defined sites within the structure, therefore, the tensor orientations will not be random, unlike in the glassy matrix used for exogenous DNP. CE between two magnetically equivalent ions will consequently be highly unlikely even at large dopant concentrations.

9.14.3.6

Applications of DNP from paramagnetic metal ions to inorganic samples

In the following some relevant achievements of DNP applied to inorganic materials as well as of the introduction of metal ions as polarizing agents are highlighted. This is not intended to give a complete review of the applications of DNP in materials science, for that we refer to the very extensive recent report given in Ref. 68. Instead, our goal here is threefold. First, we intend to emphasize the advances which contributed to enabling MIDNP. Next, we summarize the applications of the endogenous MIDNP approach for inorganic materials reported in the literature to date. And finally, based on the previous theoretical discussions, we remark on the limitations and possibilities of MIDNP.

9.14.3.6.1

OE mechanism

Since Carver and Slichter observed OE in metallic lithium, more examples of OE in solid conductors and heavily doped semiconductors have been reported, for instance Refs. 90–92. Recently, an exciting application in the field of materials science was reported, where OE under MAS and at high magnetic fields (9.4 and 14.1 T) was achieved from metallic lithium in the shape of dendrites, a common and undesired byproduct of the charge/discharge process in lithium metal batteries, enhancing the nuclear signal of the metallic lithium as well as of surrounding solid phases.93 To date, most applications of the OE DNP mechanism are found in liquid state NMR using organic radicals.94,95 Unfortunately, typical correlation times found in liquids impose a limit for applications at highest available magnetic fields. An approach to maintain large enhancements at high fields consists in finding systems in which the Fermi contact coupling is the dominant relaxation mechanism,96 this has led to signal enhancements as high as 1000 for 13C in organic compounds at 3.4 T and room temperature.97 In diamagnetic solids with dilute paramagnetic dopants, the probability of encountering efficient OE DNP will be low, as the dipolar relaxation mechanism will dominate over the Fermi contact, and present motions are unlikely to have correlation times on the order of the electronic Larmor period.98 Recently, however, large polarization enhancements in an insulating solid and at high magnetic field via the OE were reported by Can et al.99 This finding was justified by the presence of strong Fermi contact couplings and high frequency vibrations within the molecular structure of the radical BDPA.99,100

9.14.3.6.2

SE mechanism

So far, the most important DNP approach for enhancing the NMR signal of bulk nuclei in inorganic solids via metal ion dopants has been the SE mechanism. The potential of this approach to assist NMR in the characterization of materials with low sensitivity nuclei was recognized early on. For instance, in 1970 the first natural abundance 17O NMR spectrum in a non-symmetric environment could be measured due to the large DNP enhancement obtained from Cr3þ acting as polarizing agent doped into Al2O3.101 During the early days of DNP various metals, such as Ce3þ (see Fig. 5) and Fe3þ, besides Cr3þ, were used to obtain SE DNP enhancements.6,41,101,102 However, until very recently, DNP from metal centers was only performed at very low temperatures, to ensure long electron relaxation times, on single crystals to avoid broad EPR lines due to the anisotropy of the spin orbit coupling and at low field to achieve high SE efficiency. Corzilius et al. demonstrated the use of (high-spin) metal ions as polarizing agents in polycrystalline samples at high magnetic fields and under MAS.103 Initially, Gd3þ and Mn2þ were shown to have a sufficiently narrow central transition in high symmetry complexes, leading to significant enhancements and applications in structural characterization of biomolecules.49 Following, the first high field MAS DNP experiment on a doped crystalline material using metal ions as polarizing agents was reported in 2014 by the same group.59 In that work Cr3þ substituted diamagnetic Co3þ in a molecular crystal. The octahedral symmetry, leads to a d3 ground state with vanishing orbital momentum and relatively small ZFS. The narrow central transition gave DNP enhancements on 1H, 13C and 59Co. Interestingly, only the moderate (factor 2–3) 1H enhancement was uniquely attributed to the SE

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

389

mechanism, while the larger sensitivity gains of 13C and 59Co clearly showed an important contribution from the CE mechanism (further discussion in next subsection). The possibility of obtaining large DNP enhancements in high resolution NMR measurements of inorganic oxides by doping the sample with paramagnetic metal ions was demonstrated by Leskes and co-workers.8,104 This development opens the door to the application of DNP in materials science, providing increased sensitivity for the study of the bulk properties of polycrystalline inorganic samples. The viability of this approach was demonstrated on Mn2þ, Fe3þ and Gd3þ.8,89,104–106 To date, applications have focused on ion conductors with relevance for anode materials in lithium ion batteries or solid electrolytes in solid oxide fuel cells. Signal enhancements of two orders of magnitude (representing four orders of magnitude time savings) enabled, for instance, identification of two distinct oxygen sites in Li4Ti5O12 based on the natural abundance 17O spectra,8 or measuring homonuclear 89Y-89Y correlation spectra despite its very low gyromagnetic ratio.106 Incorporation of Gd3þ and Mn2þ into silicate glasses was also demonstrated to yield SE DNP enhancements of the 29Si signal, although the obtained enhancement factors were more moderate.107 While in principle any paramagnetic metal ion could act as polarizing agent for SE DNP, in practice short electron relaxation times and broad EPR lines in polycrystalline samples due to ZFS and SOC strongly limit the pool of potential candidates. An important requirement is that the metal ion occupies a highly symmetric site when entering the lattice as a dopant, to ensure weak anisotropy. Additionally, this mostly limits us to metals with half-filled shells which ensure quenching of the orbital momentum in the ground state. As a recent exception, V4þ, which has a spin ½, was successfully used as polarizing agent in an organic complex.81 Strong deviations of the isotropic g-value from the free electron value can pose an additional challenge when the magnetic field sweep capability is limited and the microwave frequency fixed, as is the case in commercially available DNP instrumentation.

9.14.3.6.3

CE mechanism

A fundamental ingredient for the large success of DNP with MAS was the development of nitroxide biradicals, specifically designed for giving large DNP enhancements via the CE mechanism.11 The first,65,72 and to date most common,68 applications of MAS DNP to study inorganic materials relied on the CE, in an approach consisting in impregnating the sample with a frozen solution of nitroxide biradicals and hyperpolarizing the nuclei in the surface and subsurface of the sample. Currently, large efforts are being made to develop biradicals with improved properties which are enabling large enhancements at increasing fields, spinning speeds and temperatures.108–110 The possibility of exploiting the advantages of CE using metal ions as polarizing agents was demonstrated by the group of Corzilius when going to high concentrations of the Gd-DOTA complex,49 or specifically by using gadolinium pairs in bis-chelates.111 Matching the CE condition from metal ions doped into the lattice of crystalline inorganic compounds is very unlikely. A prerequisite for the CE is that the EPR line is broader than the nuclear Larmor frequency, otherwise the basic matching condition cannot be met by any pair of electrons in the system. In polycrystalline samples this requirement has to be valid within a single crystallite, as the number of electron spin pairs coupled across crystallites will be negligible. In MIDNP the paramagnetic ions are introduced into the lattice as dopants by substituting specific sites, therefore, unless there is more than one magnetically inequivalent doping site, all dopants will have the same chemical environment and, consequently, the same frequency within a crystallite. To our knowledge, CE originating from metal ions doped into a crystalline lattice was only reported once, in Cr(III) doped [Co(en)3Cl3]2$NaCl$6H2O (en ¼ ethylenediamine),59 where the maxima in the sweep profiles of 13C and 59Co clearly showed a deviation from the SE (shown in Fig. 8). While the exact mechanism has not yet been identified, the authors propose two different scenarios which could account for frequency differences between both paramagnetic centers: either hyperfine coupling with the low abundant NMR active nucleus 53 Cr or, alternatively, coupling between electron spins populating one central and one satellite transition. While the latter has been considered in more detail theoretically,47 neither has been experimentally verified, nonetheless, these mechanisms clearly present some intriguing possibilities. In contrast, the anisotropy within inorganic glasses offers the possibility to encounter the CE mechanism. In fact, DNP mediated by the CE was confirmed in oxide glasses doped with Gd(III) based on the sweep profiles, leading to DNP enhancements of up to factor of 4 at high dopant concentrations.107

9.14.4

Practical considerations

9.14.4.1

Determining homogeneity of metal ions distribution

The success of the MIDNP approach of course depends on a successful introduction of the dopant into the structure. Furthermore, in order to obtain large DNP enhancements, a uniform distribution of the paramagnetic dopant within the sample is critical. Formation of aggregates or dopant rich regions has two important disadvantages: First, the formation of clusters imply the existence of regions with dopant concentrations below the intended value, which are likely to be less efficiently hyperpolarized. And second, the proximity among paramagnetic center can result in an increased electron relaxation rate, which reduces the microwave saturation efficiency. Accurate determination of the homogeneity of a minor dopant within the volume of the sample is a very challenging task; combination of multiple techniques, however, can give a good qualitative assessment of the success of the synthesis route. In the following we discuss some of these techniques (Fig. 10 shows a few examples routinely used in our research):

•

X-ray powder diffraction: According to Vegard’s Law in a solid solution the lattice parameter of a crystalline sample will change linearly with the concentration of the exchanged atom.112 Linear changes in the lattice parameters characterized by XRD are therefore, usually a good indication of a successful and homogeneous inclusion of the dopant in the lattice. A reliable

390

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

Fig. 10 (A) Changes in lattice parameter (in Angstroms) determined from XRD for varying Mn(II) concentration in Li4Ti5O12. (B) High angle annular dark field image and energy dispersive X-ray spectroscopy maps of an Li4Ti5O12 particle doped with Mn(II) with a molar ratio of x ¼ 0.02. (C) Continuous wave EPR spectra of Li4Ti5O12 for various Mn(II) concentrations. From Chakrabarty, T.; Goldin, N.; Feintuch, A.; Houben, L.; Leskes, M. Paramagnetic Metal-Ion Dopants as Polarization Agents for Dynamic Nuclear Polarization NMR Spectroscopy in Inorganic Solids. ChemPhysChem 2018, 19(17), 2139–2142. https://doi.org/10.1002/cphc.201800462.

• •

•

characterization requires a sufficiently large concentration range, significant differences in ionic radii of the exchanged ions and ideally a unique site of exchange. Electron microscopy: Electron microscopy in combination with energy dispersive X-ray spectroscopy allows mapping of the distribution of the paramagnetic species on the surface of the particle. Limitations arise from uncertainties in relating surface to bulk properties and in the sensitivity at low dopant concentrations or when the dopant ion atomic number is not sufficiently different from the sample’s major constituents. NMR: In the previous sections we have seen how the paramagnetic relaxation enhancement changes with dopant concentration, assuming a homogeneous distribution. Therefore, careful analysis of nuclear relaxation times can give an indication of the doping efficiency.113 Difficulties can arise from unknown role of spin diffusion and presence of additional relaxation mechanisms that may mask the measured PRE. Alternatively, quenching due to large paramagnetic shifts have been used to assess the paramagnetic dopant homogeneity.36,37 EPR: In principle, differentiation of homogeneously distributed dopants from clustered agglomerates should be possible even from a simple CW-EPR spectrum at low fields (vide infra). The reason being strong differences in electronic relaxation times and line broadenings. On the other hand, electron relaxation in clusters can become so short that the signal from those sites might not be easily detected, while they still would have a negative impact on the DNP experiment. In this context of quantification of homogeneity of the distribution of paramagnetic dopants in inorganic samples, to our knowledge EPR probably has not yet been exploited to its full potential. Techniques such as double electron–electron resonance (DEER)114 have the potential to accurately map the distance distribution from electron-electron dipolar couplings.

9.14.4.2

Characterization of the metal ions with EPR

The value of a thorough characterization of the paramagnetic transition metal with EPR prior to attempting high field DNP measurements cannot be overstated. EPR spectra, even at considerably lower magnetic fields, enable estimating if a DNP experiment will be possible and under which conditions. Further, these results enable, to some extent, estimating if large enhancement can be expected.

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

391

Some of the parameters which can be extracted from simple CW EPR measurements and will be useful when setting up high field MAS DNP NMR experiments are listed in the following. Of course, further valuable information can be obtained from more advanced pulsed EPR experiments, for the interested reader we refer for instance to Refs. 114,115. (1) Presence of unpaired electrons: EPR is likely the most convenient way of confirming whether doping of the sample with paramagnetic species in the expected spin state was successful. (2) Effective g-values: Knowing geff allows to estimate the EPR transition frequency at high magnetic field. This is required to confirm that the frequency lies within the field sweep capabilities of the DNP instrument and also to estimate the starting point of a field sweep (Fig. 11). (3) Line broadenings: Solid effect requires a narrow EPR line for most efficient polarization transfer. Extrapolation of the linewidth to high fields and comparison with the nuclear Larmor frequency can be used to estimate the overlap between positive and negative enhancements, which ideally should be small for largest DNP enhancements. It is important to keep in mind, that a proper extrapolation requires some knowledge regarding the origin of the line broadenings. Additionally, broad EPR lines can be an indication of strong electron–electron couplings, which could arise either due to high concentrations or localized cluster formations. If possible (and desired) reduction of the dopant concentration and/or modifications in the synthesis route should be considered. (4) Relaxation times: T1e and T2e can be estimated from the power dependence of the signal intensity. Short relaxation times lead to non-efficient saturation of electronic transitions. Therefore, they are usually an indication that DNP will not be efficient. Although, field and temperature dependence of the relaxation can be very complex, low field EPR relaxation measurements are commonly a good indication for the expected saturation efficiency under DNP conditions.

9.14.4.3

Acquisition of MAS NMR spectra with MIDNP

Small differences in spin-orbit coupling contributions can lead to large differences in the effective g-value. This means, that for the same paramagnetic ion, even small changes in the coordination environment can lead to strong shifts of the ideal field position for DNP. Therefore, in contrast to exogenous DNP with organic radicals, where the sample of interest has little to no effect on the EPR properties of the radical, in MIDNP field sweeps should be recorded for every new system. A collection of field sweeps acquired by our group is shown in Fig. 12. Note how in the presence of hyperfine couplings to the metal nucleus the field sweep profiles become very large. This should emphasize again the importance of conducting an EPR characterization of any sample prior to attempting a DNP experiment.

Fig. 11 (A) Simulated pulse EPR spectrum of Li4Ti5O12 doped with 0.5 mol% Mn(II) at a microwave irradiation frequency of 263.5 GHz. Simulation parameters were obtained from a fit to experimental spectrum acquired at W band. (B) and (C) are the DNP sweep profiles of 7Li and 6Li, respectively, of the same sample. From Wolf, T.; Kumar, S.; Singh, H.; Chakrabarty, T.; Aussenac, F.; Frenkel, A. I.; Major, D. T.; Leskes, M. Endogenous Dynamic Nuclear Polarization for Natural Abundance 17O and Lithium NMR in the Bulk of Inorganic Solids. J. Am. Chem. Soc. 2019, 141(1), 451–462. https://doi.org/10.1021/jacs.8b11015.

392

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

Fig. 12 DNP field sweep profiles obtained for 6Li, 7Li, 17O and 89Y with Mn(II), Fe(III) and Gd(III) as polarizing agents. The vertical lines indicate the center of the profiles, related to the effective g-values. The data was taken from Wolf, T.; Kumar, S.; Singh, H.; Chakrabarty, T.; Aussenac, F.; Frenkel, A. I.; Major, D. T.; Leskes, M. Endogenous Dynamic Nuclear Polarization for Natural Abundance 17O and Lithium NMR in the Bulk of Inorganic Solids. J. Am. Chem. Soc. 2019, 141(1), 451–462. Jardón-Álvarez, D.; Reuveni, G.; Harchol, A.; Leskes, M. Enabling Natural Abundance 17O SolidState NMR by Direct Polarization from Paramagnetic Metal Ions. J. Phys. Chem. Lett. 2020, 11(14), 5439–5445. Harchol, A.; Reuveni, G.; Ri, V.; Thomas, B.; Carmieli, R.; Herber, R. H.; Kim, C.; Leskes, M. Endogenous Dynamic Nuclear Polarization for Sensitivity Enhancement in Solid-State NMR of Electrode Materials. J. Phys. Chem. C 2020, 124(13), 7082–7090. Jardón-Álvarez, D.; Kahn, N.; Houben, L.; Leskes, M. Oxygen Vacancy Distribution in Yttrium-Doped Ceria from 89Y–89Y Correlations via Dynamic Nuclear Polarization Solid-State NMR. J. Phys. Chem. Lett. 2021, 12(11), 2964–2969.

All field sweep profiles shown in Fig. 12 where obtained using a fixed microwave frequency of 263.601 GHz. The resonance

frequencies, ue,n, of nuclear and electron spin change with field according to: O ue,n ¼ gn,e O B0. For instance a shift of the electron resonance frequency by 800 MHz, approximately corresponding to the separation of the positive and negative SE enhancement maxima at 9.4 T for proton nuclei, requires a field change of 0.0285 T. Such a field drift would modify the frequency of the proton nuclei by 1.215 MHz. It is useful to note that the frequency shifts expressed in ppm are equal for any spin (in this particular example O ue, n/u0e, n ¼ 3039 ppm). The exact field position can be obtained by measuring the resonance frequency of a nucleus with known chemical shift, uCS, as: B0 ¼ (un  uCS)/gn. A summary of some relevant properties of paramagnetic metal ion dopants which have been used to date as polarizing agents for high field DNP purposes is given in Table 2. Many of the parameters given in this table are sample dependent; the intention of this table, therefore, is to serve as a comparison to estimate how suitable a new system might be for DNP purposes. Prediction of the center value of the DNP field sweeps based on the center peak position from low field EPR measurements is in general a good starting point. However, we have observed some deviation from the expected values, which we have attributed either to frequency shifts due to internal interactions or to small errors in the calibration of the low field experiments. Therefore, effective g-values based on high-field DNP sweep profiles might be the more relevant parameter and, when possible, are given in Table 2. Among the values summarized in Table 2, the zero field splitting (ZFS) parameters have the strongest dependency on the chemical environment. Further it has been shown that the DNP enhancements decrease with the squared of the strength of the ZFS.124 Nonetheless, here we have included some reported ZFS values for the various metal center to show a range of values, at which DNP has proven efficient.

Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants Table 2

393

Properties of paramagnetic metal ions under conditions which have enabled their use as polarizing agents for high field DNP in polycrystalline samples.

Metal ion

Spin

geff a

DZFS (MHz)

Nuclear isotope (spin)/abundance/HF b (MHz)/ref

Cr(III) Fe(III) Gd(III)

3/2 5/2 7/2

1.9871c 2.0057d 1.9985e

740c 2300d 0f-670g

53

Mn(II) V(IV)

5/2 1/2

2.0019h 1.9881i

1100h 0

Cr (3/2)/9.50%/46–53/116–118 Fe (1/2)/2.12%/23–30/27 155 Gd (3/2)/14.80%/10–14 157 Gd (3/2)/15.65%/13–18/119 155 Mn (5/2)/100%/170–280/27 51 V (7/2)/99.75%/t: 150–210; ||:390–540/120 57

The electron spin number, the effective g-value, the zero field splitting (ZFS) interaction values DZFS (see Eq. 6) and the nuclear isotopes of the metal center with NMR active spins, with their natural abundance and their hyperfine (HF) coupling interaction strength with the electron spin. a Values calculated from reported center of DNP field sweep profiles. b Large variations of the hyperfine interaction within a same metal ion are attributed to the coordination symmetry, for instance, in tetrahedral symmetry usually lower HF values are found compared to octahedral symmetry. c In Cr(III) doped [Co(en)3Cl3]2$NaCl$6H2O.59 Here, actual reported g-value instead of effective g-value. Two different centerfield positions for EPR spectrum and DNP sweep profile despite same nominal microwave frequency are reported and attributed to small differences in the frequency of the microwave sources. d In Fe(III) doped Li4Ti5O12.105 e In Gd(III) doped Ce0.9Y0.1O1.95.106 f In Gd(III) doped CeO2.121 In high symmetric environments such as cubic sites in ceria, the second-order ZFS becomes zero, however, in this high symmetric environment higher order terms are known to be important and result in an average ZFS parameter causing significant broadening of the central transition.122,123 g In Gd-DOTA (1,4,7,10-tetraazacyclododecane-1,4,7-tris-acetic acid-10-maleimidoethylacetamide).49 h In Mn(II) doped Li4Ti5O12.8 i In (Ph4P)2[VO(C7H6S6)2].81

9.14.4.4

Reporting dopant concentrations

The dopant concentration plays a critical role in the DNP process. First, the concentration determines the number of NMR active nuclei per paramagnetic site as well as their mean distance from it. This has effects on the number of nuclei that will be hyperpolarized, and/or on the build up times. In addition, the concentration can also have a large effect on the EPR properties of the paramagnetic site due to the distance dependence of the dipolar coupling between electron spins. For this reason, in DNP polarizing agent (PA) concentrations are often given as molar concentrations per volume, [PA]. The mean distance between PA is constant for a given molarity and independent of the sample. In the following discussion we will assume that doping occurs in a homogeneous manner. In solid state chemistry doping is generally quantified by the mole fraction of dopant per unit formula, e.g. Ti1-xMnxO2. Of course, for a given stoichiometry, the mean distance between PA will depend on the number of molecular units within each unit cell and the unit cell’s volume. It is possible to convert back and forth between the stoichiometric mole ratio and the molarity. In the following we will show two possible ways of obtaining this conversion. For simplicity we will assume that the effect of the dopant on density and crystal unit cell parameters is negligible.

9.14.4.4.1

With known unit cell volume

If the volume of the crystallographic unit cell, Vcell, is known, conversion between molarity and stoichiometry is straightforward. Multiplication of the molarity of the polarizing agent, [PA], by the volume of the unit cell of the batch sample, Vcell, gives the mole number of dopants per unit cell. By taking this value times Avogadro’s number, NA, one obtains the number of dopant atoms per unit cell. Finally, dividing by ncell, the number of molecules per cell, gives the dopant per molecule or formula unit, x: x¼

9.14.4.4.2

½PA $ Vcell $NA : ncell

(48)

With known density

The mole fraction, x, of the paramagnetic dopant in xPA$(1 x)batch is given by the moles of the various components: x¼

nPA : nPA þ nbatch

(49)

Using the density we can obtain the mass of the batch sample for a given volume, according to: mbatch ¼ rbatchVbatch. The mass of PA in that same volume is obtained from its molarity: mPA ¼ [PA]MPAVbatch. From this we obtain: x¼

½PAVbatch

Vbatch ½PAVbatch þ rbatch Mbatch

¼

1 : rbatch 1 þ ðMbatch $½PAÞ

(50)

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Dynamic nuclear polarization in inorganic solids from paramagnetic metal ion dopants

9.14.4.4.3

Calculating the mean distance

The mean distance between PA’s can be approximated by the Wigner-Seitz Radius125:
1=3 3 hr i ¼ ; 4prn

(51)

where rn is the number density per unit volume, given by: rn ¼

9.14.5

xNA rbatch : Mbatch

(52)

Outlook

Over the last two decades DNP in solids at high magnetic fields under MAS conditions has been established as a routine method for materials characterization. This was achieved through the use of exogenous polarizing agents, mainly nitroxide biradicals. The use of paramagnetic metal ion dopants as polarizing agents in inorganic materials, on the other hand, has only recently been shown to be a feasible approach to give large sensitivity gains in high field MAS NMR. This delay in development between exogenous and endogenous DNP can be attributed to the difficulties in determining appropriate working conditions. Specifically, in MIDNP every sample presents its own set of challenges. The oxidation states and ionic radii of the paramagnetic ions has to be considered when targeting doping a specific coordination environment. Thus, as more examples of MIDNP with different material classes and paramagnetic ions are being demonstrated, the pool of options grows and a priori identification of promising doping strategies become more evident. Developments of MIDNP are clearly still at early stages, and while this method has largely benefited from insights from exogenous DNP, some intrinsic differences open new questions and exciting opportunities which should be addressed in the future. For instance, among the relevant theoretical and experimental issues that will be beneficial to investigate are deeper understanding of the electron relaxation mechanisms of the polarizing agents. This will allow accurate predictions which would be extremely valuable for assessing optimum dopant concentrations and working temperature regimes. Also, elucidating the interplay between PRE, spin diffusion and polarization enhancement, as well as the implementation of different metal ions will have an important impact on this technique. We do believe that these efforts are worthwhile and that MIDNP has the potential to become a routine complement to NMR of inorganic solids. It represents a complementary approach to conventional DNP because enhancements can be delivered to otherwise inaccessible nuclei, such as low sensitivity isotopes in the bulk of inorganic samples or nuclei in microporous materials, where small pore size inhibits penetration of exogenous polarizing agents. Furthermore, in cases of reactive interfaces that can be encountered in heterogeneous catalysts or battery materials, MIDNP provides a route for high sensitivity NMR without the possibility of chemical interference with exogenous additives. Finally, MIDNP can become a valuable probe of structure by itself, for instance by selectively enhancing the signal from regions near defects or dopant sites, which can be of highest interest for inorganic chemistry and materials science.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.

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95. Griesinger, C.; Bennati, M.; Vieth, H. M.; Luchinat, C.; Parigi, G.; Höfer, P.; Engelke, F.; Glaser, S. J.; Denysenkov, V.; Prisner, T. F. Dynamic Nuclear Polarization at High Magnetic Fields in Liquids. Prog. Nucl. Magn. Reson. Spectrosc. 2012, 64, 4–28. https://doi.org/10.1016/j.pnmrs.2011.10.002. 96. Loening, N. M.; Rosay, M.; Weis, V.; Griffin, R. G. Solution-State Dynamic Nuclear Polarization at High Magnetic Field. J. Am. Chem. Soc. 2002, 124 (30), 8808–8809. https://doi.org/10.1021/ja026660g. 97. Liu, G.; Levien, M.; Karschin, N.; Parigi, G.; Luchinat, C.; Bennati, M. One-Thousand-Fold Enhancement of High Field Liquid Nuclear Magnetic Resonance Signals at Room Temperature. Nat. Chem. 2017, 9 (7), 676–680. https://doi.org/10.1038/nchem.2723. 98. Abragam, A. Overhauser Effect in Nonmetals. Phys. Rev. 1955, 98 (6), 1729–1735. https://doi.org/10.1103/PhysRev.98.1729. 99. Can, T. V.; Caporini, M. A.; Mentink-Vigier, F.; Corzilius, B.; Walish, J. J.; Rosay, M.; Maas, W. E.; Baldus, M.; Vega, S.; Swager, T. M.; Griffin, R. G. Overhauser Effects in Insulating Solids. J. Chem. Phys. 2014, 141 (6), 064202. https://doi.org/10.1063/1.4891866. 100. Pylaeva, S.; Ivanov, K. L.; Baldus, M.; Sebastiani, D.; Elgabarty, H. Molecular Mechanism of Overhauser Dynamic Nuclear Polarization in Insulating Solids. J. Phys. Chem. Lett. 2017, 8 (10), 2137–2142. https://doi.org/10.1021/acs.jpclett.7b00561. 101. Brun, E.; Derighetti, B.; Hundt, E. E.; Niebuhr, H. H. NMR of 17O in Ruby with Dynamic Polarization Techniques. Phys. Lett. A 1970, 31 (8), 416–417. https://doi.org/10.1016/ 0375-9601(70)90371-3. 102. Cowen, J. A.; Schafer, W. R.; Spence, R. D. Polarization of the Al27 Nuclei in Ruby. Phys. Rev. Lett. 1959, 3 (1), 13–14. https://doi.org/10.1103/PhysRevLett.3.13. 103. Corzilius, B.; Smith, A. A.; Barnes, A. B.; Luchinat, C.; Bertini, I.; Griffin, R. G. High-Field Dynamic Nuclear Polarization with High-Spin Transition Metal Ions. J. Am. Chem. Soc. 2011, 133 (15), 5648–5651. https://doi.org/10.1021/ja1109002. 104. Chakrabarty, T.; Goldin, N.; Feintuch, A.; Houben, L.; Leskes, M. Paramagnetic Metal-Ion Dopants as Polarization Agents for Dynamic Nuclear Polarization NMR Spectroscopy in Inorganic Solids. ChemPhysChem 2018, 19 (17), 2139–2142. https://doi.org/10.1002/cphc.201800462. 105. Harchol, A.; Reuveni, G.; Ri, V.; Thomas, B.; Carmieli, R.; Herber, R. H.; Kim, C.; Leskes, M. Endogenous Dynamic Nuclear Polarization for Sensitivity Enhancement in SolidState NMR of Electrode Materials. J. Phys. Chem. C 2020, 124 (13), 7082–7090. https://doi.org/10.1021/acs.jpcc.0c00858. 106. Jardón-Álvarez, D.; Kahn, N.; Houben, L.; Leskes, M. Oxygen Vacancy Distribution in Yttrium-Doped Ceria from 89Y–89Y Correlations via Dynamic Nuclear Polarization SolidState NMR. J. Phys. Chem. Lett. 2021, 12 (11), 2964–2969. https://doi.org/10.1021/acs.jpclett.1c00221. 107. Paterson, A. L.; Perras, F. A.; Besser, M. F.; Pruski, M. Dynamic Nuclear Polarization of Metal-Doped Oxide Glasses: A Test of the Generality of Paramagnetic Metal Polarizing Agents. J. Phys. Chem. C 2020, 124 (42), 23126–23133. https://doi.org/10.1021/acs.jpcc.0c05676. 108. Lelli, M.; Chaudhari, S. R.; Gajan, D.; Casano, G.; Rossini, A. J.; Ouari, O.; Tordo, P.; Lesage, A.; Emsley, L. Solid-State Dynamic Nuclear Polarization at 9.4 and 18.8 T from 100 K to Room Temperature. J. Am. Chem. Soc. 2015, 137 (46), 14558–14561. https://doi.org/10.1021/jacs.5b08423. 109. Lund, A.; Casano, G.; Menzildjian, G.; Kaushik, M.; Stevanato, G.; Yulikov, M.; Jabbour, R.; Wisser, D.; Renom-Carrasco, M.; Thieuleux, C.; Bernada, F.; Karoui, H.; Siri, D.; Rosay, M.; Sergeyev, I. V.; Gajan, D.; Lelli, M.; Emsley, L.; Ouari, O.; Lesage, A. TinyPols: A Family of Water-Soluble Binitroxides Tailored for Dynamic Nuclear Polarization Enhanced NMR Spectroscopy at 18.8 and 21.1 T. Chem. Sci. 2020, 11 (10), 2810–2818. https://doi.org/10.1039/C9SC05384K. 110. Wisser, D.; Karthikeyan, G.; Lund, A.; Casano, G.; Karoui, H.; Yulikov, M.; Menzildjian, G.; Pinon, A. C.; Purea, A.; Engelke, F.; Chaudhari, S. R.; Kubicki, D.; Rossini, A. J.; Moroz, I. B.; Gajan, D.; Copéret, C.; Jeschke, G.; Lelli, M.; Emsley, L.; Lesage, A.; Ouari, O. BDPA-Nitroxide Biradicals Tailored for Efficient Dynamic Nuclear Polarization Enhanced Solid-State NMR at Magnetic Fields up to 21.1 T. J. Am. Chem. Soc. 2018, 140 (41), 13340–13349. https://doi.org/10.1021/jacs.8b08081. 111. Kaushik, M.; Qi, M.; Godt, A.; Corzilius, B. Bis-Gadolinium Complexes for Solid Effect and Cross Effect Dynamic Nuclear Polarization. Angew. Chem. Int. Ed. 2017, 56 (15), 4295–4299. https://doi.org/10.1002/anie.201612388. 112. Vegard, L. Die Konstitution Der Mischkristalle Und Die Raumfüllung Der Atome. Z. Phys. 1921, 5 (1), 17–26. https://doi.org/10.1007/BF01349680. 113. Sen, S.; Stebbins, J. Structural Role of Nd3þ and Al3þ Cations in SiO2 Glass: A 29Si MAS-NMR Spin-Lattice Relaxation, 27Al NMR and EPR Study. J. Non Cryst. Solids 1995, 188 (1–2), 54–62. https://doi.org/10.1016/0022-3093(95)00099-2. 114. Jeschke, G.; Schweiger, A. Principles of Pulse Electron Paramagnetic Resonance, 1st edn.; Oxford University Press: Oxford, 2001. 115. Goldfarb, D.; Stoll, S. EPR Spectroscopy: Fundamentals and Methods, Chichester: John Wiley & Sons Ltd, 2018. 116. Headlam, H. A.; Lay, P. A. EPR Spectroscopic Studies of the Reduction of Chromium(VI) by Methanol in the Presence of Peptides. Formation of Long-Lived Chromium(V) Peptide Complexes. Inorg. Chem. 2001, 40 (1), 78–86. https://doi.org/10.1021/ic000299m. 117. Tarasov, V. F.; Yatsyk, I. V.; Likerov, R. F.; Shestakov, A. V.; Eremina, R. M.; Zavartsev, Y. D.; Kutovoi, S. A. EPR Spectroscopy of 53Cr Monoisotopic Impurity Ions in a Single Crystal of Yttrium Orthosilicate Y2SiO5. Opt. Mater. (Amst) 2020, 105, 109913. https://doi.org/10.1016/j.optmat.2020.109913. 118. Rager, H. Electron-Nuclear Hyperfine Interactions of 53Cr3þ in Mg2SiO4 (Forsterite). Z. Naturforsch. A 1980, 35 (12), 1296–1303. https://doi.org/10.1515/zna-1980-1205. 119. Borel, A.; Kang, H.; Gateau, C.; Mazzanti, M.; Clarkson, R. B.; Belford, R. L. Variable Temperature and EPR Frequency Study of Two Aqueous Gd(III) Complexes with Unprecedented Sharp Lines. J. Phys. Chem. A 2006, 110 (45), 12434–12438. https://doi.org/10.1021/jp065445þ. 120. Cornman, C. R.; Zovinka, E. P.; Boyajian, Y. D.; Geiser-Bush, K. M.; Boyle, P. D.; Singh, P. Structural and EPR Studies of Vanadium Complexes of Deprotonated Amide Ligands: Effects on the 51V Hyperfine Coupling Constant. Inorg. Chem. 1995, 34 (16), 4213–4219. https://doi.org/10.1021/ic00120a029. 121. Hope, M. A.; Björgvinsdóttir, S.; Grey, C. P.; Emsley, L. A Magic Angle Spinning Activated 17O DNP Raser. J. Phys. Chem. Lett. 2020, 345–349. https://doi.org/10.1021/ acs.jpclett.0c03457. 122. Abraham, M. M.; Boatner, L. A.; Finch, C. B.; Lee, E. J.; Weeks, R. A. Paramagnetic Resonance of Gd3þ in CeO2 Single Crystals. J. Phys. Chem. Solid 1967, 28 (1), 81–92. https://doi.org/10.1016/0022-3697(67)90200-4. 123. Rakhmatullin, R. M.; Aminov, L. K.; Kurkin, I. N.; Böttcher, R.; Pöppl, A.; Avila-Paredes, H.; Kim, S.; Sen, S. Electron Paramagnetic Resonance Linewidth Narrowing of Gd3þ Ions in Y-Doped Ceria Nanocrystals with Decreasing Crystallite Size. J. Chem. Phys. 2009, 131 (12), 124515. https://doi.org/10.1063/1.3225487. 124. Stevanato, G.; Kubicki, D. J.; Menzildjian, G.; Chauvin, A.-S.; Keller, K.; Yulikov, M.; Jeschke, G.; Mazzanti, M.; Emsley, L. A Factor Two Improvement in High-Field Dynamic Nuclear Polarization from Gd(III) Complexes by Design. J. Am. Chem. Soc. 2019, 141 (22), 8746–8751. https://doi.org/10.1021/jacs.9b03723. 125. Marder, M. P. Condensed Matter Physics, 2nd edn.; Hoboken: John Wiley & Sons Ltd., 2010.

9.15

NMR of nanoparticles

Cory M. Widdifield and Navjot Kaur, Department of Chemistry & Biochemistry, University of Regina, Regina, SK, Canada © 2023 Elsevier Ltd. All rights reserved.

9.15.1 9.15.2 9.15.2.1 9.15.2.1.1 9.15.2.1.2 9.15.2.1.3 9.15.2.2 9.15.2.2.1 9.15.2.3 9.15.2.3.1 9.15.2.3.2 9.15.2.3.3 9.15.2.3.4 9.15.2.3.5 9.15.2.4 9.15.2.4.1 9.15.2.4.2 9.15.2.4.3 9.15.2.4.4 9.15.2.4.5 9.15.2.4.6 9.15.2.4.7 9.15.2.4.8 9.15.2.4.9 9.15.2.4.10 9.15.2.5 9.15.2.5.1 9.15.2.5.2 9.15.2.6 9.15.2.6.1 9.15.2.6.2 9.15.2.6.3 9.15.2.6.4 9.15.2.6.5 9.15.2.7 9.15.2.7.1 9.15.2.7.2 9.15.2.7.3 9.15.2.7.4 9.15.2.7.5 9.15.2.7.6 9.15.2.8 9.15.2.8.1 9.15.2.8.2 9.15.2.8.3 9.15.2.9 9.15.2.9.1 9.15.2.9.2 9.15.2.9.3 9.15.2.10 9.15.2.10.1 9.15.2.10.2 9.15.2.10.3 9.15.2.10.4 9.15.3

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Introduction and scope NMR of nanoparticles NMR of metal nanoparticles Palladium Gold Platinum Carbon nanoparticles Detonation nanodiamonds Semiconducting nanoparticles Silicon CdSe CdS SnS CsPbBr3 Metal/metalloid oxide nanoparticles Silicon dioxide/silica (SiO2) Titanium dioxide/titania (TiO2) Zinc oxide (ZnO) Zirconium dioxide/zirconia (ZrO2) Cerium(IV) oxide/ceria (CeO2) Aluminum oxide/alumina (Al2O3) Hematite (a-Fe2O3) Maghemite (g-Fe2O3) and magnetite (Fe3O4) Yttrium(III) oxide/yttria (Y2O3) Li4Ti5O12 (LTO) Other oxide-containing nanoparticles Zeolites Bioactive glasses Core@shell nanoparticles Fe@C Co@C Ni@C Pt@mSiO2 and PtSn@mSiO2 CdSe@CdS Molecular organic nanoparticles Compound P Carbamazepine (CBZ) dihydrate & co-crystalline derivative Indomethacin polymorphs Lipid nanoparticles High-density lipoprotein nanoparticles Lignin Polymer nanoparticles Poly(lactic-co-glycolic acid) (PLGA) Polystyrene (PS) Glycopolymers Alloyed nanoparticles CdSeS FexCoyNiz CoxCu1
x Doped/Lithiated nanoparticles Carbon-doped MgB2 Aluminum-doped MnO2 Lithiated Sn (LixSn) Doped a-NaYF4 NMR of nanocomposites, nanocrystalline, and nano-size materials

Comprehensive Inorganic Chemistry III, Volume 9

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https://doi.org/10.1016/B978-0-12-823144-9.00035-2

NMR of nanoparticles 9.15.3.1 9.15.3.1.1 9.15.3.1.2 9.15.3.1.3 9.15.3.1.4 9.15.3.2 9.15.3.2.1 9.15.3.2.2 9.15.3.2.3 9.15.3.2.4 9.15.3.2.5 9.15.3.2.6 9.15.3.2.7 9.15.3.3 9.15.3.4 9.15.3.4.1 9.15.3.4.2 9.15.4 Acknowledgments References

Nanocomposites TiO2-SiO2 Au/Al nanocomposite Cobalt-containing nanoparticles on multi-walled carbon nanotubes Hydroxyapatite/reduced graphene oxide Nanocrystalline inorganic compounds Cobalt Sodium sulfide (Na2S) CaF2 nanocrystals in glass ceramics LaF3 Cs2ZrX6 (X ¼ Cl, Br) Al-doped yttrium-iron garnet (Y3AlxFe5
xO12) Apatites Nanocrystalline cellulose Nano-sized metal-organics Nano-sized metal-organic frameworks (nanoMOFs) Au25(SR)18 clusters Summary remarks

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Abstract Selected accounts of the most recent literature involving nuclear magnetic resonance (NMR) experiments on nanoparticles and nanocrystalline materials are presented. Focus is placed on articles published in the timeframe spanning 2018 up until early 2021 and is on the nanoparticles themselves (rather than related aspects such as stabilizing polymers). This entry is meant to convey the wide array of nanoparticulate systems that may be probed using NMR experiments, but due to space limitations, only a subset is discussed in detail. Examples of systems that will be discussed include: metal and metal/ metalloid oxide nanoparticles, carbon nanoparticles, semiconducting nanoparticles, core@shell nanoparticles, alloyed nanoparticles, doped/lithiated nanoparticles, nanocomposites, molecular organic and polymeric nanoparticles, nanocrystalline inorganic compounds, nanocrystalline cellulose, and nano-sized metal-organics.

9.15.1

Introduction and scope

This contribution is meant to provide the reader with an overview of some areas where nuclear magnetic resonance (NMR) experiments have been applied to study nanoparticles. There will also be some mention of nanocomposite materials and nanocrystalline systems. This account is not comprehensive, and according to recent literature searches (search words: NMR and nanoparticle(s)), the number of publications easily exceeds several thousands. Keyword permutations and more detailed literature searches can uncover several times this amount. Focus is placed on publications from 2018 until early 2021, and the interested reader is referred to other recent reviews, which enumerate further on selected aspects related to the topic at hand.1–14 It is clarified that the focus of this account is on the nanoparticles themselves and not on aspects related to nanoparticle preparation/stabilization (for example, organic polymers used to enhance colloidal stability) nor on chemical species that are anchored onto nanoparticle supports15–19 or in nanopores/mesopores/nanocarriers, or could rather be classified as dendrimers.20 The application of NMR experiments to probe nanoparticles, including their cores and on their surfaces, is sensible as NMR experiments have long been recognized as highly sensitive to local structure and dynamics. A variety of nuclei may serve as sitespecific probes, and each of these nuclei, depending on their intrinsic nature, can be associated with several NMR observables. Typically, the most easily accessed of these observables is the chemical shift (d) relative to a reference material.21 In certain situations, anisotropic chemical shift information22,23 can be obtained, and by performing multidimensional NMR experiments it is possible to correlate many of these observables to clearly establish atom-atom linkages, as well as the proximities of the probe nuclei to one another. The existence and effects of NMR observables on NMR spectra have been summarized in the literature,24 as have the various correlation experiments.

9.15.2

NMR of nanoparticles

9.15.2.1

NMR of metal nanoparticles

9.15.2.1.1

Palladium

There are few accounts of palladium NMR in the literature (in the solid state or otherwise).25 This is due to the very unattractive nuclear properties associated with its only stable NMR-active isotope, 105Pd. In addition to its quadrupolar nature (nuclear spin,

400

NMR of nanoparticles

I ¼ 5/2) and rather substantive nuclear electric quadrupole moment (þ66.0 fm2),26 its meager gyromagnetic ratio leads to a low NMR frequency at even the highest applied magnetic fields (B0) available today. For example, in a magnetic field where the 1H Larmor frequency would be 1.5 GHz, the analogous frequency for 105Pd is 68.6 MHz. Undaunted, Hooper et al. published their work on the direct solid-state NMR observation of 105Pd environments in 2018,27 which included Pd nanoparticle samples. To reduce the effects of NMR signal broadening due to the quadrupolar interaction, the samples considered were known to have Pd in a high symmetry local environment, although the variable offset cumulative spectrum (VOCS) approach28,29 was still required to acquire the 105Pd NMR signal associated with these samples. As could be expected, the 105Pd NMR resonance positions associated with Pd0 environments were very different than those for Pd(IV) compounds, with Knight shifts (K) for the nanoparticles being reported in the range of
31,100 to
32,110 ppm relative to 0.33 M H2PdCl6. It was generally observed that as the particle size distribution shifted to smaller average particle sizes, the 105Pd NMR line shape broadened and shifted its center-of-gravity to less negative shift values (Fig. 1). As the shift values for the Pd sponge and Pd black samples did not depend on the applied field, it was concluded that the 105Pd nuclei associated with the observed signals experience an electric field gradient (EFG) indistinguishable from zero (i.e., are within a cubic environment). The same could not be said for the smaller polymer-stabilized Pd nanoparticles (16 nm average diameter). Transmission electron microscopy (TEM) experiments on the stabilized Pd nanoparticles displayed a high degree of monodispersity; hence, the observed 105Pd NMR line shapes for this sample were attributed to intra-particle interactions. This highlights the sensitivity of the 105Pd nucleus to environments that are slightly distorted from cubic symmetry.

9.15.2.1.2

Gold

Mattoussi and co-workers used diffusion-ordered NMR spectroscopy (DOSY) experiments to measure the diffusion coefficient and hydrodynamic size of 10 nm in diameter gold nanoparticles dispersed in deuterated chloroform (CDCl3).30 Further, the authors compared their findings against these same properties when they were measured using dynamic light scattering (DLS). The authors concluded that DOSY was more effective when characterizing nanoparticles with very small dimensions. On the other hand, relative to DLS, DOSY experiments were noted as needing higher solute concentrations and longer data collection times to produce acceptable signal-to-noise ratios.

9.15.2.1.3

Platinum

In their effort to identify and study quantum size effects (QSE), Okuno et al. used 195Pt NMR experiments on variously-sized platinum nanoparticle samples (average diameters (d) of 2.5, 4.0, 7.4, and 9.8 nm, with each sample being stabilized with polyvinylpyrrolidone, PVP).31 Although QSE were predicted in 1962,32 the identification of QSE remained an experimental challenge. By selecting platinum, the authors hoped to amplify the detectability of QSE. In particular, it was envisioned that separating the NMR signals associated with the surface and core regions would be more likely with 195Pt (I ¼ 1/2), due to its very large shift range.33 The authors calibrated their measurements with samples of bulk platinum, and bulk platinum coated with PVP. Initial

Fig. 1 The 105Pd VOCS static NMR spectra of poly(N-vinyl-2-pyrrolidone) stabilized Pd nanoparticles (16  3 nm), Pd black nanoparticles (20– 150 nm) and Pd metal sponge (44–149 mm) acquired at 14.1 and 7.05 T. All data were referenced to H2PdCl6 (aq) (at diso ¼ 0.0 ppm). Reproduced without modification from Hooper, T. J. N.; Partridge, T. A.; Rees, G. J.; Keeble, D. S.; Powell, N. A.; Smith, M. E.; Mikheenko, I. P.; Macaskie, L. E.; Bishop, P. T.; Hanna, J. V. Direct Solid State NMR Observation of the 105Pd Nucleus in Inorganic Compounds and Palladium Metal Systems. Phys. Chem. Chem. Phys. 2018, 20, 26734–26743. DOI: 10.1039/C8CP02594K, as published by the PCCP Owner Societies, and under the terms of the Creative Commons CC BY 3.0 license (https://creativecommons.org/licenses/by/3.0/).

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measurements were performed at T ¼ 5 K. It was found that the PVP coating did not augment the bulk 195Pt NMR signal, and that this 195Pt NMR signal was consistently found at K 
3%. For each nanoparticle sample, the authors observed very broad 195Pt NMR signals, spanning roughly from K ¼
4% to K ¼ þ0.8%. However, the intensity distribution of the signal varied dramatically between samples. For the largest nanoparticles considered (d ¼ 9.8 nm), the most intense 195Pt NMR signal was found at roughly K ¼
3%, while for the smallest nanoparticles (d ¼ 2.5 nm), the most intense feature was at roughly K ¼
0.4%. From these observations, the authors reasonably concluded that the core region was associated with the highly negative Knight shift, while the surface was associated with the small negative shift. Next, the authors presented results from 195Pt spin-lattice relaxation (i.e., T1) measurements in different temperature regimes for all nanoparticle samples. In the high-temperature regime (> 20 K), all samples were best pffiffiffiffiffiffiffiffiffiffiffiffiffi thought of as metallic since 1=T1 T was a constant value. It was found that this constant value did not depend on the nanoparticle size, and rather depended on the value of the Knight shift experienced at a given 195Pt site. Approaching the low-temperature regime, the authors found that each nanoparticle sample exhibited anomalous 1/T1 behavior. For both the core and surface regions of each nanoparticle, 1/T1 increased as the temperature decreased, and for all samples, a maximum in 1/T1 was observed (although at a different temperature for each sample). After reaching a maximum, further cooling resulted in a very sharp reduction in 1/T1 for all samples. Interestingly, although T1 values changed dramatically as a function of temperature, no spectral changes were observed for any sample, and hence magnetic ordering at low temperatures was ruled out. Because the anomaly was observed for both core and surface environments, it was concluded that this could not arise from a surface effect and that it was independent of the local density of states of the valence d electrons. The authors then considered the possibility that the anomalous behavior was related to sample size. It was found that as the particle size decreased, the anomalous behavior in T1 occurred at progressively higher temperatures (specified as the characteristic temperature (T*), Fig. 2). By plotting T* versus 1/d, a correlation was found that agreed reasonably well with an energy gap between electronic states predicted by Kubo theory (Fig. 2, inset). The anomalous relaxation behavior was therefore due to something akin to a size-tunable metal-insulator transition that was itself induced by a QSE.

Fig. 2 Temperature dependence of 1/T1 of each sample, measured at K 
3% and the same magnetic field of 2.84 T. The yellow +, red A, green n, blue C, and black  symbols show the 1/T1 results obtained with the 2.5-, 4.0-, 7.6-, and 9.8-nm nanoparticles and bulk samples, respectively. The solid and open symbols show the fastest and slowest components, respectively, for the 2.5-, 4.0-, and 7.6-nm samples. In addition, the arrows show the characteristic temperature T* of the anomaly. The solid and dotted lines are guides showing the related data. Inset: Characteristic temperature T*, where 1/T1 deviates from metallic behavior (represented by the arrows in the main figure). The horizontal axis shows the inverse of the mean particle diameters d of the nanoparticles. The calculated value (gray *) was obtained using Kubo theory. Reprinted with permission from Okuno, T.; Manago, M.; Kitagawa, S.; Ishida, K.; Kusada, K.; Kitagawa, H. NMR-Based Gap Behavior Related to the Quantum Size Effect. Phys. Rev. B 2020, 101, 121406(R). DOI: 10.1103/PhysRevB.101.121406. Copyright 2020 by the American Physical Society.

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9.15.2.2 9.15.2.2.1

Carbon nanoparticles Detonation nanodiamonds

Detonation nanodiamonds (DNDs) are typically produced using a mixture of trinitrotoluene (TNT) and hexogen (RDX) explosives. Although their preparation is straightforward, purification steps can be costly. Panich et al. sought to augment the traditional TNT/ RDX precursor mixture to yield DNDs in a more cost-effective manner.34 Specifically, they reported the synthesis and characterization of DNDs produced using some amount of tetryl (2,4,6-trinitrophenylmethylnitramine) precursor. In all, two alternative reactant compositions were considered: the first was composed entirely of tetryl (DNDT1), while the second was a mixture of 70 wt% tetryl, 18 wt% TNT, and 12 wt% RDX (DNDT7). The DNDs produced using these alternatives were compared against DNDs generated using a 40/60 mixture of TNT and RDX (DNDC). Carbon-13 NMR spectra were acquired for all three DND product samples under both static and magic-angle spinning (MAS) conditions. A strong peak at d ¼ 35.6 ppm was observed for all samples and assigned to sp3-hybridized carbons of bulk diamond. An additional broad feature of weak intensity, centered at about 53 ppm, was attributed to carbon atoms near the surface (Fig. 3). Although the 13C NMR spectra for all three product samples were very similar, their T1 values were somewhat different. It was observed that the T1(13C) of DNDs prepared using tetryl was about half when compared against the value for the DNDs prepared using the traditional precursors. It was speculated that this corresponded to increased paramagnetic impurities in the tetrylgenerated DNDs. X-band electron paramagnetic resonance (EPR) measurements were used to quantify the number of paramagnetic centers per gram of material, and it was found that all three samples had similar values, ranging from 7.4  1.1  1019 spins g
1 in sample DNDT1 to 9.3  0.9  1019 spins g
1 in sample DNDC. X-ray diffraction (XRD) measurements were carried out and established that DNDs produced using the tetryl-containing precursors were slightly larger (d ¼ 5.0 nm) than DNDs produced using the TNT/RDX mixture (d ¼ 4.2 nm). Overall, while the product DND particles generated from tetryl-containing mixtures were not identical when compared against the traditional particles, they were similar, and thus the authors concluded that precursor mixtures containing tetryl could potentially be used in DND production.

9.15.2.3 9.15.2.3.1

Semiconducting nanoparticles Silicon

The characterization of silicon nanoparticles/nanocrystals using 29Si NMR spectroscopy has a decently long history,35–45 and a fairly recent and detailed account was provided by Rossini and co-workers involving Si nanocrystals that had been surface-functionalized with either hydrogen atoms or alkyl groups.46 Here, focus is on the as-synthesized material prior to ligand introduction. Hence, for the as-synthesized hydrogen-terminated silicon nanoparticles, the authors used 1H MAS and dipolar-based 1H-1H multiplequantum/single-quantum (MQ/SQ) correlation experiments in the hopes of distinguishing the hypothesized different silicon environments (namely, *SiH, *SiH2, and *SiH3). Unfortunately, resolution of these environments via the above experiments was not possible, and so additional NMR experiments were considered. As such, proton-detected 1H-29Si NMR correlation experiments, either dipolar-based or J-based, were carried out. All experiments used a cross-polarization (CP) block at the start of the pulse sequence to enhance the surface-selective nature of the experiment. The authors did not notice much of a difference between NMR spectra produced using the dipolar-based or J-based experiments, as both featured a broad 29Si signal spanning d(29Si) from
70 to
120 ppm, as well as a relatively narrow and weak signal at
51 ppm. The minor peak was assigned to surface

Fig. 3 Room temperature 13C MAS NMR (6 kHz) spectra of DNDC, DNDT1 and DNDT7 samples. Deconvolution of the DNDT1 spectrum into two components is shown using dashed lines. Sidebands are indicated by asterisks. Reprinted from Panich, A. M.; Shames, A. I.; Mogilyansky, D.; Goren, S. D.; Dolmatov V. Yu. Detonation Nanodiamonds Fabricated From Tetryl: Synthesis, NMR, EPR and XRD Study. Diam. Relat. Mater. 2020, 108, 107918. DOI: 10.1016/j.diamond.2020.107918. Copyright 2020, with permission from Elsevier.

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oxidation, which is well-known to occur in various silicon nanomaterials, while the broad peak was taken as evidence of a distribution of different 29Si chemical environments at the surface. Further J-based 1H-29Si NMR correlation experiments were performed as a function of the 29Si evolution time (s0 ) to identify and estimate the relative proportions of the *SiH, *SiH2, and *SiH3 environments. This approach is sensible as the 1H magnetization should evolve differently depending on whether there are 1, 2, or 3 protons coupled to a given 29Si (Fig. 4). However, the authors noted several effects that may influence the magnetization quantitation process, and as such the values reported should be considered as estimates rather than true measurements. Nevertheless, it was clear that the majority of the surface environments arose from *SiH-type environments, with there being relatively few *SiH3-type environments. The experimental NMR data were supported by density functional theory (DFT) calculations using different hydrogen-terminated silicon facets as surface models (for example, (001), (010), (100), and (110) were considered). It was clear that both the number of hydrogen atoms, as well as the facet selected, influenced the computed 1H and 29Si magnetic shielding values. While it might appear intuitive to use high-field dynamic nuclear polarization (DNP) experiments5,47–49 to enhance the 29Si NMR signal of hydride-terminated silicon nanoparticles in a surface-selective manner, Michaelis and co-workers observed that indirect DNP, which relies on a nitroxide radical solution and transfers polarization to 29Si via nearby 1H spins, could not be usefully employed.50 This was because the hydride-terminated Si nanoparticle surface decomposed the radicals in a matter of hours. Building on an approach developed by Ramanathan and co-workers,51 dangling bonds were used as an endogenous source of radicals. The authors supported their NMR measurements with additional characterization methods (EPR, Fourier-transform infrared (FTIR), powder XRD, X-ray photoelectron spectroscopy (XPS), and TEM). As noted earlier, the surfaces of as-synthesized silicon nanoparticles bear a variety of SiHx groups, with x ranging from 1 to 3. It was noted by the authors that this surface region is disordered, and contrasts with the ordered silicon core. There also exists an intermediate region between the surface and core of the silicon nanoparticle, which was described as semi-ordered. It was therefore hypothesized that the disorder correlates with a higher concentration of radicals at or near the surface, when compared against the core, and that due to this, DNP-enhanced NMR experiments would be selective for the surface and/or near surface regions. To assess the sensitivity of the endogenous dangling bond radical approach, the authors considered a variety of Si nanoparticle diameters (d ¼ 3, 6, 9, 21, and 64 nm). This is because, as the size of the nanoparticle decreases, several competing effects (such as very short T1 values and signal quenching) are expected to dominate the mechanisms by which DNP enhancement operates. Indeed, it was observed that for all hydride-terminated nanoparticles, except the largest, DNP did not offer clear signal enhancements (the largest enhancement value, 3 , was 1.5). For the 64-nm diameter silicon nanoparticles, a modest enhancement (3 ¼ 6) of a 29Si signal located at d(29Si) ¼
85 ppm was quantified, which was attributed to the ordered core and arose from 29Si-29Si spin diffusion from the endogenous surface radicals (Fig. 5). It was estimated that the surface radical concentration was about 0.70 mM, and therefore it was speculated that there may be significant potential for larger DNP enhancements if the radical concentration could be increased. As may be seen in Fig. 5, it was possible to resolve the 29Si NMR signal associated with the subsurface and surface 29Si nuclei, although especially in the later case, the sensitivity was muted.

9.15.2.3.2

CdSe

Sufficiently small nanoparticles of CdSe display very interesting and useful electronic behavior and have been used in consumer electronics for some time now. Piveteau et al. combined multidimensional DNP-enhanced 113Cd NMR experiments and advanced pulse sequences to clearly resolve signals associated with the surface and core 113Cd environments of oleate-terminated CdSe quantum dots and nanoplatelets.52 In particular, the authors demonstrated the use of the two-dimensional phase adjusted spinning sideband phase-incremented echo-train acquisition (PASS-PIETA) pulse sequence53,54 under MAS DNP conditions, which when applied together, allowed for dramatic gains in both experimental sensitivity and resolution. To prevent particle agglomeration during conditions typical for DNP experiments, the authors impregnated a solution containing DNP polarizing agent and the colloidal quantum dots into mesoporous SiO2. For CdSe quantum dots exhibiting a zinc blende (ZB) structure, two 113Cd NMR

Fig. 4 Simulation of s0 evolution curves from the 1H-29Si refocused Insensitive Nuclei Enhanced by Polarization Transfer (INEPT) pulse sequence for the different surface hydride groups. Adapted with permission from Hanrahan, M. P.; Fought, E. L.; Windus, T. L.; Wheeler, L. M.; Anderson, N. C.; Neale, N. R.; Rossini, A. J. Characterization of Silicon Nanocrystal Surfaces by Multidimensional Solid-State NMR Spectroscopy. Chem. Mater. 2017, 29, 10339–10351. DOI: 10.1021/acs.chemmater.7b03306. Copyright 2017, American Chemical Society.

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Fig. 5 Silicon-29 DNP NMR spectrum of H-Si nanoparticles (64 nm) with an endogenous radical acquired at a MAS frequency of 8 kHz (mW on). The corresponding spectrum acquired without microwave irradiation (mW off) is shown below. Inset is the mW on spectrum vertically scaled by 6 to illustrate the surface (blue) of the H-Si nanoparticle. The 29Si resonance at
85 ppm is signal from the crystalline core and the small shoulder to lower frequency (red) is subsurface. Reprinted from Ha, M.; Thiessen, A. N.; Sergeyev, I. V.; Veinot, J. G. C.; Michaelis, V. K. Endogenous Dynamic Nuclear Polarization NMR of Hydride-Terminated Silicon Nanoparticles. Solid State Nucl. Magn. Reson. 2019, 100, 77–84. DOI: 10.1016/ j.ssnmr.2019.04.001. Copyright 2019, with permission from Elsevier.

signals were resolved: one at d(113Cd) ¼
66 ppm, and a second at d(113Cd) ¼
323 ppm. Additional experiments demonstrated that the former signal arose from 113Cd in the CdSe particle cores, while the latter signal was due to surface 113Cd. These findings were in very good agreement with a prior study that also used DNP to enhance the cadmium NMR signals associated with ZB-CdSe quantum dots,55 but the present study had greatly improved resolution due to the PASS element of the pulse sequence. The prior DNP study on ZB-CdSe quantum dots included additional NMR experiments on oleate-stabilized ZB-CdSe (e.g., 77Se, dipolar 13 111 C- Cd heteronuclear multiple quantum coherence (HMQC)) as well as other quantum dot samples (CdTe, InP, PbSe, PbTe, and CsPbBr3), but discussion is not provided here as it is beyond our intended scope. Returning to the present study, the authors also characterized CdSe@CdS nanoparticles (vide infra), ZB-CdSe nanoplatelets, and phosphonate-capped wurtzite (WZ)-CdSe quantum dots. Relative to the DNP-enhanced PASS-PIETA 113Cd MAS NMR spectrum acquired for the ZB-CdSe quantum dot samples, the WZ-CdSe quantum dots yielded rather complex 113Cd NMR spectra, which the authors attributed to the presence of multiple surface facets in WZ-CdSe, as well as potentially due to the swapping of the oleate capping ligands for phosphonate molecules. Using through-bond and through-space 15N-113Cd NMR experiments and samples which had been enriched in 15N and 113Cd isotopes, Noda and co-workers probed the ligand-surface interactions in cysteine-capped CdSe magic-sized clusters (MSCs).56 Examining the interaction between the surface and ligand is important, as ligands can enhance the associated optical properties and serve as linkers for electron transfer from the semiconducting particle core to the substrate. Using CdSe MSCs with a narrow particle size distribution allowed the authors to use the J-coupling interaction as a probe, which is seldom done using nanoparticles as most samples would have an intrinsic inhomogeneity that would make observing J-coupling exceptionally challenging. The 15 N
113Cd J-single quantum filtered (J-1QF) NMR experiment was used to determine the fraction of amines forming a bond on the CdSe surface and provided an estimate for the NeCd bond-length. A 15N-113Cd rotational-echo double-resonance (REDOR) NMR experiment57,58 enabled the 15N-113Cd internuclear distance to be measured and probed the fraction of amines close to the CdSe surface. By comparing the amine fractions from the J-1QF and REDOR NMR experiments, it was concluded that some amines are located near the CdSe surface, yet do not form a chemical bond. Nitrogen-15 CP/MAS NMR spectra gave two peaks: an intense peak at 35 ppm, and a relatively low intensity peak at 95 ppm. The peak at 95 ppm was not observed in the 15N-113Cd J-1QF NMR spectrum, making it clear that only the intense peak at 35 ppm corresponded to directly bonded cysteines. The fashion by which the 15 N peak intensity at 95 ppm varied as a function of echo-time in the 15N-113Cd J-1QF NMR experiment allowed the measurement of JN-Cd ¼ 58.5 Hz. From these data it was also found that ca. 43% of the cysteine ligands experienced a nitrogen-cadmium chemical bond, and it was estimated that the NeCd bond length was in the range of 2.35–2.45 Å. This is a somewhat long bond, suggesting that it is relatively weak. The observed 15N-113Cd REDOR dephasing curve was most consistent with a NeCd bond length of 2.47 Å (Fig. 6), in reasonable agreement with the value reported above. From the REDOR NMR experiments, the authors concluded that  54% of the amines were close to the surface cadmium, which was greater than the value established using the J-1QF experiment and thus suggested that some amines were close to the surface yet did not form a nitrogen-cadmium bond. It was noted that this would skew the apparent bond length measured via 15N-113Cd REDOR NMR experiments to be longer than the true NeCd bond length, and as such the value of 2.47 Å was understood to be an upper limit. As part of their study comparing DOSY NMR experiments with DLS experiments for the measurement of diffusion coefficients and hydrodynamic sizes (vide supra), Mattoussi and co-workers also studied CdSe nanoparticles that were approximately 4 nm in diameter, and CdSe/ZnS core@shell nanoparticles that were either about 5 or 7 nm in diameter.30 In all cases, the nanoparticles were studied while dispersed in CDCl3. The conclusions of their study can be found in Section 9.15.2.1.2.

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Fig. 6 Experimental 15N-113Cd REDOR fractions with their error bars for 15N major (black diamonds) and minor peaks (gray circles) of CdSecysteine, and calculated REDOR curves. The curves were calculated with dipolar coupling constants of 204, 180, and 160 Hz, which correspond to 15 113 N- Cd internuclear distances of 2.37, 2.47, and 2.57 Å, respectively. Reprinted with permission from Kurihara, T.; Noda, Y.; Takegoshi, K. Quantitative Solid-State NMR Study on Ligand-Surface Interaction in Cysteine-Capped CdSe Magic-Sized Clusters. J. Phys. Chem. Lett. 2017, 8, 2555– 2559. DOI: 10.1021/acs.jpclett.7b00909. Copyright 2017, American Chemical Society.

9.15.2.3.3

CdS

9.15.2.3.4

SnS

Cadmium sulfide nanoparticles (d ¼ 3 nm) were one of the materials probed using 113Cd NMR experiments by Pruski et al. during their study on the effects that 1H-detection and fast MAS had on DNP-enhanced NMR experimental sensitivity.59 As these nanoparticles possessed a high surface/core atom ratio, it was possible to clearly observe both the surface cadmium environment, as well as the environment corresponding to cadmium atoms in the nanoparticle core. In all, the authors mentioned resolving three 113 Cd environments, one related to the CdS4 core (
54 ppm), one relating to the CdO2S2 surface (
290 ppm), and a substantial cadmium oxide impurity phase (
630 ppm) that was noted as being a synthetic by-product (Fig. 7). All cadmium shifts were reported relative to dimethylcadmium at room temperature. Though there was a clear decrease in sensitivity for experiments using a 1.3-mm probe relative to those using a 3.2-mm probe, there are fewer peaks in the NMR spectrum associated with the 1.3-mm probe. A benefit of using the smaller rotor size is the ability to perform the 113Cd NMR experiments at a greater rotation frequency (in this case, 31.25 kHz for the 1.3-mm probe versus 10 kHz for the 3.2-mm probe). For surface cadmium atoms, it would be expected that the local environment is asymmetric, which should lead to a large cadmium chemical shift anisotropy and multiple spinning sidebands. Although the intensities of these sidebands can be analyzed to extract potentially useful information about the cadmium local environment, they likewise serve to reduce experimental sensitivity and resolution. For the DNP-enhanced 2D 113Cd{1H} heteronuclear correlation (HETCOR) and 1H{113Cd} inverse-detected HETCOR (idHETCOR) NMR experiments under MAS, it was found that 113Cd detection using a 3.2-mm probe offered superior sensitivity when compared to 1H detection using a 1.3-mm probe. However, there are a few confounding aspects that must be considered. First, the experimental sensitivity of the directly detected 113Cd NMR signal was significantly boosted by a Carr-Purcell Meiboom-Gill (CPMG) echo train,60,61 as it had favorable 113Cd transverse relaxation properties. If the material under study did not have such favorable properties, then clearly this sensitivity boost would not be available. The authors also noted that the additional 113Cd / 1H CP transfer step needed for the idHETCOR NMR experiment reduced its sensitivity. As mentioned earlier, even though there is often a sensitivity penalty when using smaller rotors, there exists a possibility to spin at relatively higher frequencies, which can provide improved spectral resolution due to fewer MAS spinning sidebands.

Panich et al. studied the cubic p-phase of semiconducting SnS nanoparticles using 119Sn NMR and EPR experiments.62 Additional characterization techniques in this study included powder XRD, scanning electron microscopy (SEM), and energy dispersive spectroscopy (EDS). This compound was noted as having potential for incorporation into solar cells and further is less toxic compared to some alternative metal chalcogenides (e.g., PbS, CdS). From the 119Sn NMR experiments (B0 ¼ 8.0 T), two tin environments were resolved at 295 K. Tin-119 chemical shifts were measured relative to Sn(CH3)4 by setting the shift of a secondary reference material, 1 M SnCl2 in dimethyl sulfoxide (DMSO), to d(119Sn) ¼
358 ppm. The authors compared the 119Sn NMR spectrum of the cubic p-SnS nanoparticles to that of the a-SnS microparticles (orthorhombic phase, Fig. 8). Although the two 119Sn NMR spectra might appear qualitatively similar at first glance, when taken in concert with structural data provided by diffraction measurements, several differences were outlined. First, it was mentioned that all tin atoms in the orthorhombic phase are equivalent. Hence, the width of the observed signal results largely from chemical shift anisotropy (CSA, with the following principal components: d11 ¼
23 ppm, d22 ¼
161 ppm, d33 ¼
722 ppm, as indicated in Fig. 8). On the other

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Fig. 7 DNP-enhanced 1H-113Cd spectra of CdS nanoparticles impregnated with a 16 mM solution of TEKPol in 1,1,2,2-tetrachloroethane (TCE), obtained using a 1.3-mm probe (A and C) and a 3.2-mm probe (B and D). In (D) e-DUMBO1–22 1H homonuclear decoupling was used during t1. Reprinted from Wang, Z.; Hanrahan, M. P.; Kobayashi, T.; Perras, F. A.; Chen, Y.; Engelke, F.; Reiter, C.; Purea, A.; Rossini, A. J.; Pruski, M. Combining Fast Magic Angle Spinning Dynamic Nuclear Polarization With Indirect Detection to Further Enhance the Sensitivity of Solid-State NMR Spectroscopy. Solid State Nucl. Magn. Reson. 2020, 109, 101685. DOI: 10.1016/j.ssnmr.2020.101685. Copyright 2020, with permission from Elsevier.

Fig. 8 Room temperature 119Sn NMR spectra of (A) orthorhombic and (B) cubic phases of SnS. Simulations are shown by thin blue lines. Adapted minimally from Panich, A. M.; Shames, A. I.; Abutbul, R. E.; Maman, N.; Goren, S. D.; Golan, Y. NMR and EPR Study of Cubic p-Phase SnS Semiconductor Nanoparticles. Mater. Chem. Phys. 2020, 250, 123206. DOI: 10.1016/j.matchemphys.2020.123206. Copyright 2020, with permission from Elsevier.

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hand, the cubic p-SnS phase is built from SnS3 and SSn3 pyramid-like units and therefore there are two non-equivalent tin environments. The authors therefore deconvoluted the observed 119Sn NMR spectrum for p-SnS into two sites. Each site has an appreciable tin CSA, but both are considerably smaller than in the case of a-SnS. According to the crystal structure, tin atoms associated with the SnS3 groups possesses C1 local symmetry, and thus, as expected, the observed 119Sn CSA pattern did not have axial symmetry (i.e., all principal components are unique: d11 ¼
26 ppm, d22 ¼
123 ppm, d33 ¼
491 ppm). On the other hand, the tin atoms associated with SSn3 groups have C3 local symmetry, which requires the chemical shift tensor to be axially symmetric (i.e., two principal components must be equal in value: d11 ¼ d22 ¼
575 ppm, d33 ¼
811 ppm). The authors further noted that the T1(119Sn) values for each tin site were not equivalent in p-SnS and were an order of magnitude greater than this parameter in aSnS. Consequently, it was opined that the dominant spin-lattice relaxation mechanism in p-SnS nanoparticles was due to spinphonon Raman scattering. This was in contrast with the a form, where the concentration of paramagnetic defects largely determined T1(119Sn). Using EPR experiments and a well-characterized detonation nanodiamond powder sample as a reference, the authors clearly demonstrated the reduced number of paramagnetic sites in cubic SnS relative to orthorhombic SnS (on a constant mass basis).

9.15.2.3.5

CsPbBr3

As the optoelectronic properties of quantum dots depend strongly on their surface environment, Chen et al. used surface-selective solid-state 133Cs MAS NMR experiments, as well as 1H{133Cs} and 1H{207Pb} double resonance experiments, to develop and validate a model for the surface structure of ligand-stabilized cuboidal CsPbBr3 quantum dots.63 Additional NMR experiments probed the interactions between the ligands and the quantum dot surface from the perspective of the ligand, which will not be discussed. From direct excitation 133Cs NMR experiments, a peak at d(133Cs) ¼ 100 ppm was assigned to 133Cs in the bulk, while a low intensity signal at about 235 ppm was attributed to Cs4PbBr6. A very broad and low intensity signal at about 170 ppm was assigned to surface Cs. This assignment was verified by performing surface-selective 2D 1H / 133Cs CP-HETCOR NMR experiments and noting that the signal assigned to surface Cs was now, in relative terms, much more intense. These 2D 1H / 133Cs HETCOR NMR experiments were also used to confirm qualitatively the spatial proximity between the surface Cs and the stabilizing ligands. Direct excitation 207Pb NMR experiments resolved a single broad peak centered at d(207Pb) ¼ 200 ppm, which was assigned to bulk-like Pb environments in CsPbBr3. In contrast with the surface-selective 1H / 133Cs NMR experiments above, analogous experiments that employed 1H / 207Pb CP transfer did not resolve new lead environments when compared against the direct excitation 207Pb NMR spectra. This suggested to the authors that 207Pb was not terminating the surfaces of the quantum dots. Interestingly, 2D 1H / 207Pb CP-HETCOR experiments provided evidence for dipolar interactions between lead environments and the stabilizing ligands. Using various double-resonance experiments, the authors also estimated the internuclear distances between NH3þ protons in the dodecylammonium stabilizing ligands and surface/subsurface Cs/Pb sites, and proposed a model for the CsPbBr3 surface being cesiumterminated with the ligands substituting into cesium A-sites at the surface.

9.15.2.4 9.15.2.4.1

Metal/metalloid oxide nanoparticles Silicon dioxide/silica (SiO2)

Silica nanoparticles are being studied as they can serve as support materials for a variety of applications, including in catalysis and drug delivery. The most obvious probe nucleus associated with this material is 29Si, which has a rather low natural abundance of 4.68%,64 and therefore 29Si NMR experiments can take several hours to perform in some instances. As such, two-dimensional 29 Si-29Si correlation NMR experiments are not routinely pursued at natural abundance. There are a multitude of potential solutions to the sensitivity issue noted above, but recently there have been several examples where DNP is used to acquire 2D 29Si-29Si NMR spectra of SiO2 nanoparticles. For example, using samples of SiO2 nanoparticles whose surfaces had been covered with organosiloxanes, Lee et al. performed DNP NMR experiments under MAS conditions to acquire through-space and through-bond 29Si-29Si NMR spectra.65 Due to the surface-selective nature of the DNP signal enhancements, these experiments allowed the authors to estimate 2JSiOSi values and interatomic distances at/near the particle surface. These experiments also clarified that the surface-supported species formed a lateral self-condensed network structure covering the SiO2 nanoparticle surfaces. Using DNP-enhanced 2D 29Si-29Si NMR experiments, Mobil Composition of Matter (MCM)-41-type mesoporous silica nanoparticles (MSNs) were studied effectively by Kobayashi et al.,66 and the information gained from these experiments allowed the arrangement of organic functional groups at the surface to be determined. The MSN surfaces were functionalized with either propyl (PR) or mercaptopropyl (MP) groups via either a co-condensation method, or a stepwise process involving post-synthetic grafting. The indirect DNP scheme was typically (though not exclusively) selected, which for the current systems involves 1H hyperpolarization from the radical electron source, followed by a 1H / 29Si CP step. In this way, the authors carried out DNP-enhanced 1D 29Si {1H} CP/MAS and 2D 29Si-29Si double-quantum (DQ)/SQ correlation NMR experiments. Prior to performing the DNP-enhanced NMR experiments, the Tn and Qn relative concentrations were established using conventional 1D 29Si MAS NMR experiments. As a result, significant variation in the 29Si site populations was demonstrated across the samples considered. The DNP-enhanced 2D 29 Si-29Si DQ/SQ correlation NMR spectra were acquired using a through-space pulse sequence that is known to not be robust at internuclear distances significantly > 3 Å, and as such, the observed correlations were assumed to be due almost exclusively to nearest 29Si neighbors (i.e., Si-O-Si only). Across the seven different samples, correlations between various silica environments were observed, and the relative peak volumes were quantified. This information allowed the authors to develop a reasonably detailed model explaining how the PR and MP groups attached to the surfaces of the MSNs. For example, 29Si NMR data evidenced that

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grafted samples had considerably higher concentrations of T1 and T2 sites when compared to samples prepared using cocondensation, which was rationalized as being due to a lack of self-condensation when the post-synthetic grafting method was used (Fig. 9). A sample of MSNs functionalized with 3-(N-phenylureido)propyl groups was used as a calibration material by Duong et al. when presenting their Uniform Driven Equilibrium Fourier Transform (UDEFT) NMR experiment.67 By performing careful numerical spin dynamics simulations, supported by experimental 29Si MAS NMR data, the authors demonstrated that a particular composite refocusing pulse, coupled with adiabatic inversion, made the UDEFT NMR experiment robust with respect to rfinhomogeneity, transmitter frequency offset, and chemical shift anisotropy. Compared to a CPMG pulse sequence, the UDEFT experiment appeared to be a particularly sensitive option when attempting to detect T sites. The authors reasonably rationalized that this was due to T sites being subjected to larger 1H-29Si dipolar couplings, which should in turn reduce the spin-spin relaxation (T2) value and therefore limit the sensitivity enhancement offered by CPMG. Fumed silica nanoparticles were subjected to a variety of surface modifications, and the interactions between the silica surface and the supported species were probed using 1H MAS, and 13C or 29Si CP/MAS NMR spectroscopy by Henderson and co-workers.68 Typical silica surface modifications use compounds that are very reactive and moisture-sensitive, and so to combat this, the authors selected several organosiloxanes, which were known to be relatively more stable. Prior to grafting, some organosiloxanes must be modified using thermal degradation followed by somewhat harsh acid treatments. Hence, the authors developed an approach to degrade the organosiloxane precursors using environmentally friendly reagents (either dimethyl carbonate or diethyl carbonate). After grafting poly(methylhydrosiloxane) (PMHS) onto the silica surface, the relatively sharp silanol peak in the 1H MAS NMR spectrum of the pure fumed silica nanoparticles, located at d(1H) ¼ 1.1 ppm, was eliminated. A new peak near 0 ppm was generated after grafting and this was taken as evidence of silica surface functionalization. There was also evidence after grafting of a peak near d(1H) ¼ 4.7 ppm, which was attributed to the Si-H moiety of PMHS. Comparing the 29Si CP/MAS NMR spectrum of fumed silica nanoparticles and the corresponding spectra after grafting with PMHS, key differences were present, as displayed in Fig. 10 below. For example, when using PMHS, a clear decrease in the Q2 and Q3 peaks was consistently observed upon grafting (corresponding to a decrease in surface silanol groups), and methylhydrosiloxane peaks (D1) were present. When reaction conditions used only neat PMHS, there was also evidence of T2 and T3 peaks being created. For this set of reaction products, the authors concluded that the grafted organosiloxane species formed a close-packed amorphous monolayer. Using other organosiloxanes (poly(dimethylsiloxane) and poly(epoxymethylsiloxane)) and 29Si CP/MAS NMR experiments, the authors often observed D- and T-type groups being formed as major products after reacting with fumed silica nanoparticles. The addition of either dimethyl carbonate or diethyl carbonate appeared to offer better surface coverage control when dealing with longer chain organosiloxanes. Although 13C CP/ MAS NMR spectra were acquired, they were not typically as diagnostic in the characterization process when compared to the 1H and 29Si NMR spectra. In addition to 29Si NMR experiments on SiO2 nanoparticles, there are reports of 17O NMR spectroscopy experiments using silica nanoparticles. For example, a large group of researchers were able to acquire DNP-enhanced 17O NMR spectra of SiO2 nanoparticles ( 20% 17O enriched), using either CP or direct excitation, during the testing and validation of the DNP polarizing agent,

Fig. 9 The difference in the formation of Tn sites in MSNs between co-condensation and post-synthesis grafting methods. Si-O-Si linkages shown in blue and red represent Q-T and T-T structures, respectively. Reproduced from Kobayashi, T.; Singappuli-Arachchige, D.; Wang, Z.; Slowing, I. I.; Pruski, M. Spatial Distribution of Organic Functional Groups Supported on Mesoporous Silica Nanoparticles: A Study by Conventional and DNPEnhanced 29Si Solid-State NMR. Phys. Chem. Chem. Phys. 2017, 19, 1781–1789. DOI: 10.1039/C6CP07642D, with permission from the PCCP Owner Societies.

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HyPTEK.69 Based on the type of 17O NMR experiment employed (i.e., CP or direct), the authors were able to distinguish between surface and bulk 17O environments in the SiO2 nanoparticles.

9.15.2.4.2

Titanium dioxide/titania (TiO2)

The facets which define the surface of a nanoparticle have an associated surface energy and therefore strongly dictate the chemical reactivity (and in turn, the potential scope of applications) of the nanoparticle. Different preparation conditions can give rise to different facet distributions, and in some cases, facets can be eliminated altogether (i.e., at temperatures above the roughening temperature). Li et al. developed a surface-selective 17O labeling approach to determine the facet structures of anatase titania nanoparticles using 17O NMR experiments and DFT calculations.70 Samples with mostly (001) exposed facets (NS001), samples with mostly (101) exposed facets (NO101), and non-faceted samples, were prepared. The NMR data were supported with XRD, highresolution TEM (HRTEM), and XPS experiments. Surface-selective enrichment in 17O was achieved using 90% 17O-labeled water. For most samples, this was done by exposing the already prepared and activated nanocrystals to an environment that was saturated with 17O-labeled water vapor. A sample that was enriched non-selectively was also prepared and displayed an entirely different 17O MAS NMR spectrum when compared against samples labeled in a surface-selective fashion. The non-selectively 17O-enriched sample yielded an 17O NMR spectrum similar to bulk anatase TiO2. For both NS001 and NO101, the authors categorized the observed 17O NMR signals into three groups: (i) the highest chemical shifts (d(17O) ranging from 600 to 750 ppm) corresponded to two-coordinate surface oxygens (O2c); (ii) intermediate chemical shifts (d(17O) ranging from 480 to 570 ppm) corresponded to three-coordinate surface oxygens (O3c); and (iii) the lowest chemical shifts (d(17O) ranging from
150 to 300 ppm) were assigned to surface hydroxyl groups and/or water. Even though NS001 and NO101 possessed some broadly similar spectral features, it was immediately obvious that their 17O MAS NMR spectra were distinct from one another and the remainder of the study focused on modeling these two systems computationally. By considering a variety of surface structure models for NS001, the authors concluded that a clean TiO2(001) surface model was inconsistent with the 17O NMR data. Rather, it was noted that the surface underwent reconstruction and partial hydroxylation (the latter aspect due to water dissociation on the surface). For the NO101 surface models, the authors first considered clean anatase TiO2(101), hydrated anatase TiO2(101) with molecular water, and hydrated anatase TiO2(101) with dissociated water. Unfortunately, none of these models were acceptable from the perspective of the 17O NMR data. It was reported that (101) facets often occur with surface defects, such as step edges. Hence, the authors considered a model using anatase TiO2(134) with so-called type-D step-edges, (101) planes, and with water molecules adsorbed at the five-coordinate titanium sites of the type-D step-edges (Fig. 11A). By considering the 17O NMR spectra presented in Fig. 11B, agreement between the computationally generated 17O NMR spectrum, and that observed experimentally, is quite good. The surface structures of anatase TiO2 nanoparticles (A-TiO2), as well as partially reduced anatase TiO2 nanoparticles (Re-ATiO2), were studied by Peng and co-workers via 1H and 17O NMR experiments.71 The partially reduced material was noted as having particularly interesting applications in photocatalytic reactions due to the presence of surface defects, oxygen vacancies, and Ti3þ. As the experiments did not use DNP to enhance experimental sensitivity, to observe the otherwise feeble 17O NMR signal associated with oxygen environments near the particle surfaces, samples were exposed to a saturated H2O environment where the water was 90% 17O-enriched. The 1H and 17O NMR experiments were carried out at B0 ¼ 9.4 T and under MAS frequencies ranging between 14 and 20 kHz. NMR measurements were supported with data from other characterization techniques, including: XRD, TEM, and EPR. Using 1H MAS spin-echo NMR experiments on Re-A-TiO2 nanoparticles, the authors observed that acidic proton species could not be removed entirely even when the sample was heated under vacuum at 400  C. This was in dramatic contrast with the A-TiO2 nanoparticles, which appeared to lose its 1H NMR signal in a nearly quantitative fashion upon heating at temperatures as low as

Fig. 10 29Si CP/MAS NMR spectra of (a) neat fumed silica, (b) modified fumed silica with neat PMHS, modified with (c) mixtures of PMHS and dimethyl carbonate and (d) mixtures of PMHS and diethyl carbonate. Reproduced without modification from Protsak, I. S.; Morozov, Y. M.; Dong, W.; Le, Z.; Zhang, D.; Henderson, I. M. A 29Si, 1H, and 13C Solid-State NMR Study on the Surface Species of Various Depolymerized Organosiloxanes at Silica Surface. Nanoscale Res. Lett. 2019, 14, 160. DOI: 10.1186/s11671-019-2982-2, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

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Fig. 11 The structure model and 17O NMR spectra of NO101-TiO2. (A) The structure model of the TiO2(134) vicinal surface for DFT calculations, which contains type-D steps and (101) planes. (B) The experimental 17O spin-echo NMR spectrum of the fully dried surface-selectively 17O-labeled NO101-TiO2 (black line) and the simulated spectra (colored lines and peaks) created by using parameters obtained from DFT calculations. Water molecules are adsorbed in two orientations (OA and OB). The contributions of both adsorption orientations are also shown in B (dark yellow line for OB and blue line for OA). Other colored peaks denote the individual components of OA, which correspond to the oxygen atoms labeled with the same numbers in the structural model in A. Asterisks denote spinning sidebands, while ampersands denote sidebands that overlap with the signal of the adsorbed water. Reproduced without modification from Li, Y.; Wu, X.-P.; Jiang, N.; Lin, M.; Shen, L.; Sun, H.; Wang, Y.; Wang, M.; Ke, X.; Yu, Z.; Gao, F.; Dong, L.; Guo, X.; Hou, W.; Ding, W.; Gong, X.-Q.; Grey, C. P.; Peng, L. Distinguishing Faceted Oxide Nanocrystals With 17O Solid-State NMR Spectroscopy. Nat. Commun. 2017, 8, 581. DOI: 10.1038/s41467-017-00603-7, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

50  C. It was reasonably speculated that these proton environments associated with the reduced TiO2 nanoparticles may influence its photocatalytic activity when used in high-temperature catalytic processes. In terms of the 17O NMR measurements, both A-TiO2 and Re-A-TiO2 displayed signals that covered four diagnostic regions. The most highly shielded peaks, which occurred at ca. –50 ppm, were assigned to adsorbed water molecules because these peaks could be removed by drying the samples under vacuum. Prior to any heating, the authors also evidenced mobile water species in both systems. This assignment was due to these peaks having near zero values of diso(17O) and very narrow linewidths. In both systems, a moderately broad band centered at about 160 ppm was assigned to surface hydroxyl groups. The 17O NMR signals at considerably higher chemical shift values were assigned to three-coordinate oxygens in OTi3 local environments (d(17O) in 460–600 ppm range) and two-coordinate oxygens in OTi2 local environments (d(17O) in 600–850 ppm range). The three-coordinate oxygen environments originate from the surface or subsurface. As this peak did not change in intensity after heating under vacuum, it indicates that the surface water species do not interact with this oxygen environment. On the other hand, for the two-coordinate oxygen environments, it was reasoned that they occur only at the surface of the A-TiO2 facets. Further, the spectral band assigned to the two-coordinate oxygen atoms broadened and shifted slightly after drying under vacuum, and thus the authors concluded that these oxygen environments interacted with water prior to drying. Further details associated with the TiO2 nanoparticle surface structure were also elucidated: for example, the 17O NMR band corresponding to OTi2 environments in A-TiO2 was composed of at least two distinct signals that arose from steps on (101) surface facets. A similar situation was not found for Re-A-TiO2, where the analogous band in the 17O NMR spectrum appeared to be composed of one type of signal and indicated a higher proportion of exposed (001) surface facets. To correlate the 1H and 17O environments for the Re-A-TiO2 sample, the authors provided brief discussions based on 1H / 17O CP/MAS

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and 1H-17O HETCOR NMR experimental data. Interestingly, in the HETCOR NMR experiment the authors were able to resolve an additional hydrogen environment at d(1H) ¼ 11.2 ppm that was correlated to the surface hydroxyl groups (Fig. 12). Based on a hydrogen bonding model developed to explain 1H NMR chemical shifts in silica glasses,72 the authors concluded that this new peak was due to an intramolecular hydrogen bond and used a DFT model to support their findings.

9.15.2.4.3

Zinc oxide (ZnO)

As part of a study aimed at assessing the long-term stability of nanocrystals, Kahn and co-workers carried out solid-state 17O MAS NMR experiments on dodecylamine-stabilized ZnO nanocrystals.73 ZnO nanocrystals were used as a reference material for metal oxides, in the hopes that any conclusions drawn in the present study could be extended to analogous systems. Two ZnO nanocrystal morphologies were studied: so-called isotropic nanocrystals (which will be the focus here), and nanorods. To enhance the 17O NMR signal of the ZnO nanocrystals, isotopic enrichment was performed with a dry ZnO sample already in the NMR rotor by introducing a small volume (20 mL) of H2O that had been enriched to 20% in 17O. The authors then followed the oxygen exchange process between the H2O and ZnO nanocrystal surfaces by acquiring T1-filtered 17O MAS, as well as 17O MAS and 17O CP/MAS NMR spectra. Three somewhat sharp 17O NMR signals with asymmetric shapes (indicative of a distribution of quadrupolar parameters) were seen. The Czjzek model74 was found to be able to replicate these line shapes with peak maxima at d(17O) values of
17.7,
23.5, and
29.4 ppm. The peak at
17.7 ppm was assigned to the core region of the particles, while the other two were attributed to surface 17O environments. The rates of 17O enrichment were quantified by monitoring the evolution of the signal intensities associated with the three peaks denoted above, and it was found that the kinetic rates associated with the 17O enrichment process were larger for the isotropic ZnO particles when compared against the nanorods. Importantly, it was found that oxygen exchange only occurred at specific surface sites, and that oxygen diffusion from the surface to the core region was present. Additional 17 O NMR data were used to propose that the peak centered at
29.4 ppm was due to surface O atoms and hydroxyl groups, while the peak at
23.5 ppm was due to 17O in the first sublayers (Fig. 13). Supported by XRD measurements, the authors demonstrated that a so-called soft post synthetic process that was composed of successive wetting/drying cycles yielded a more crystalline ZnO structure that was less dynamic and therefore potentially possessed better long-term stability when compared against other approaches. Nagashima et al. presented the first 17O and 67Zn NMR spectra of aluminum-doped ZnO nanoparticles as part of a larger study that sought to observe the local environments of quadrupolar nuclei using surface-enhanced DNP NMR spectroscopy.75 As both nuclei possess unfavorable NMR properties, even under DNP-enhanced conditions, the authors also presented a bespoke dipolar-based refocused INEPT (RINEPT) pulse sequence to efficiently and robustly transfer magnetization from a 1H source to the observe nucleus. The quadrupolar CPMG (QCPMG) pulse sequence76 was appended to the INEPT portion to further enhance sensitivity. For the 67Zn NMR measurements, the authors compared their RINEPT-QCPMG pulse sequence against a more traditional double frequency sweep (DFS)-QCPMG pulse sequence77 and noted important similarities and differences. In terms of similarities, both sequences resolved insulating ZnO4 domains near the nanoparticle surface, as depicted below (Fig. 14). Using a Czjzek model to simulate the asymmetric 67Zn NMR line shape, the authors arrived at diso(67Zn) ¼ 236.9 ppm and quadrupolar coupling constant, CQ(67Zn), of 2.38 MHz. The RINEPT sequence, however, was able to resolve additional zinc

Fig. 12 2D 1H-17O HETCOR NMR spectrum of Re-A-TiO2 (dried under vacuum at 100  C) obtained at 9.4 T. Contact time, 70 ms; spinning frequency, 14 kHz; recycle delay, 0.5 s. A total of 128 and 4096 points were acquired in the F1 and F2 dimensions, respectively, with 9600 scans per time increment. The full 2D spectrum took 1 day and 15 h to acquire. Reproduced with permission from Li, Y.; Wu, X.-P.; Liu, C.; Wang, M.; Song, B.; Yu, G.; Yang, G.; Hou, W.; Gong, X.-Q.; Peng, L. NMR and EPR Studies of Partially Reduced TiO2. Acta Phys.-Chim. Sin. 2020, 36, 1905021. DOI: 10.3866/PKU.WHXB201905021. Copyright 2020, College of Chemistry and Molecular Engineering – Peking University.

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ZnO NC/DDA –17.7

H2O17

–23.5 –29.4

–10 oxygen vacancy/defect filled 17 oxygen vacancy

Isotopically exchange 17O ZnO atoms

–20

–30

–40

(ppm)

17OH

from isotope exchange or water dissociation

Fig. 13 Schematic view of the different oxygen atoms in ZnO nanocrystals. Reprinted with permission from Champouret, Y.; Coppel, Y.; Kahn, M. L. Evidence for Core Oxygen Dynamics and Exchange in Metal Oxide Nanocrystals From In Situ 17O MAS NMR. J. Am. Chem. Soc. 2016, 138, 16322– 16328. DOI: 10.1021/jacs.6b08769. Copyright 2016, American Chemical Society.

Fig. 14 67Zn QCPMG NMR spectra enhanced by (A) indirect DNP using 1H / 67Zn RINEPT-SR412(tt) transfer of the Al-doped ZnO nanoparticles impregnated with 8 mM TEKPol solution in TCE with s ¼ 2.0 ms and (B and C) by DFS of (B) Al-doped ZnO nanoparticles and (C) ZnO microcrystalline powder. All spectra were acquired at B0 ¼ 9.4 T, MAS frequency ¼ 10 kHz, and T ¼ 105 K and are the Fourier-transform of the sum of the QCPMG echoes. Reprinted with permission from Nagashima, H.; Trébosc, J.; Kon, Y.; Sato, K.; Lafon, O.; Amoureux, J.-P. Observation of Lowg Quadrupolar Nuclei by Surface-Enhanced NMR Spectroscopy. J. Am. Chem. Soc. 2020, 142, 10659–10672. DOI: 10.1021/jacs.9b13838. Copyright 2020, American Chemical Society.

environments that were less proximate to a proton source. These included lower intensity peaks at 121 and 46 ppm. Although perhaps somewhat speculative, the authors reasonably assigned these peaks to the tetrahedral and octahedral zinc environments in a partially inverse ZnAl2O4 spinel phase. Further support for the ZnAl2O4 phase was apparently uncovered by acquiring the 17 O NMR signal for this sample using a 1H / 17O RINEPT-QCPMG pulse sequence. At longer recoupling times (s ¼ 1.9 ms), a signal at d(17O) ¼
29 ppm was attributed to ZnO at the surface of the nanoparticle, while a second band centered at 52 ppm was assigned to both Al2O3 and ZnAl2O4 secondary phases. When the authors used a short recoupling time (s ¼ 0.1 ms), the observed signal was predominately due to surface OH groups, thereby confirming the polarization source in the INEPT transfer. Additional confirmatory 27Al RINEPT-QCPMG NMR experiments on the aluminum-doped ZnO nanoparticles were also reported.

NMR of nanoparticles 9.15.2.4.4

Zirconium dioxide/zirconia (ZrO2)

413

Using an approach that involved 17O enrichment, coupled with DFT calculations, Peng and co-workers studied ZrO2 nanoparticles.78 Both monoclinic and tetragonal forms of ZrO2 nanoparticles were prepared according to literature methods and then enriched in a nonselective manner using O2 that had been enriched to 70% in 17O. Surface-selective enrichment was also carried out, and used 90% 17O-enriched water. The authors also considered monoclinic and tetragonal structures that, after their initial syntheses, had been thermally treated at different temperatures. Initial experiments on non-selectively enriched monoclinic ZrO2 nanoparticles were able to cleanly resolve two peaks: a signal at d(17O) ¼ 402 ppm was assigned to three-coordinate oxygen (O3c), while a peak at d(17O) ¼ 325 ppm was assigned to four-coordinate oxygen (O4c). Both signals became sharper as the 17O enrichment temperature increased, due to the enhanced possibility of particle sintering at higher temperatures. Monoclinic ZrO2 nanoparticle samples which had been 17O-labeled in a surface-selective fashion displayed more peaks in comparison to nonselectively labeled samples. In addition to peaks at 402 and 325 ppm, a very wide band at d(17O) ¼ 105 ppm was observed and assigned to surface hydroxyl sites due to its distinct chemical shift and by using 1H / 17O CP/MAS and 17O-1H REDOR NMR experiments. The final well-resolved peak in the 17O MAS NMR spectra for the selectively enriched monoclinic ZrO2 sample was observed at d(17O) ¼ 426 ppm and was speculatively assigned to so-called low-coordinated surface oxygen sites. To enhance confidence in  surface this assignment, spin-polarized DFT calculations using the projector-augmented wave method and a monoclinic ZrO2(111) model were carried out. Importantly, this surface model, which is also the most energetically favorable, naturally possesses a twocoordinate surface oxygen atom. As the quadrupolar interaction was found to be negligible for all environments (except the hydroxyls), the authors did not include quadrupole-induced shifts when making comparisons between computational and experimental data. The computational model yielded chemical shifts for the interior oxygen environments that were in very good agreement with experiment (d(17O4c) ¼ 317 ppm and d(17O3c) ¼ 401 ppm, where d represents the average d value among all subsurface oxygen atoms with the coordination indicated). Three-coordinate oxygen atoms at the surface were computed to have a slightly increased chemical shift of 424 ppm, which led the authors to conclude that the experimental peak at d(17O) ¼ 426 ppm was likely due to 17O nuclei in these environments. The authors did not assign the experimental signal at 426 ppm to two-coordinate surface oxygen environments as DFT calculations associated with these sites led to chemical shifts that were in very poor agreement with  experiment. In addition to this clean DFT model of the monoclinic ZrO2(111) surface, the authors considered a variety of hydrated models, which is sensible as the surface-selective labeling process used water. As expected, these changes in the surface had minimal impact on the core O3c and O4c oxygen environments. Interestingly, there was also not a very significant impact on the predicted chemical shifts for the O3c and O4c surface sites. The authors concluded that the most probable hydration model corresponded to water in a dissociated state. Stick 17O NMR spectra associated with these various surface models, as well as the experimental 17O MAS NMR spectrum of monoclinic ZrO2 nanoparticles, can be seen in Fig. 15. As mentioned, the authors also considered samples of tetragonal ZrO2 nanoparticles, which are not thermodynamically stable under typical laboratory conditions. As such, small amounts of yttrium (either 3 or 8 mol%) were added during the synthesis, as this stabilizes tetragonal ZrO2. The authors used much the same approach to characterize the tetragonal ZrO2 nanoparticles as they did with the monoclinic ZrO2 nanoparticles. It was concluded that monoclinic ZrO2 nanoparticles exhibited stronger acidity than the tetragonal form. Further, for both forms, thermal treatments at temperatures below 200  C appeared to facilitate chemical exchange between surface oxygen atoms having a low coordination number and oxygen environments in the particle cores. Maleki and Pacchioni studied a variety of tetragonal ZrO2 surfaces, as well as zirconia nanoparticles, using DFT calculations.79 In terms of NMR parameters, they reported 17O isotropic chemical shifts and quadrupolar coupling constants for nanoparticles that were either stoichiometric or oxygen deficient. The authors speculated that due to bulk zirconia having several polymorphs, it was thus reasonable to assume that nano-sized ZrO2 samples are a mixture of nanocrystalline and amorphous particles. The stoichiometric zirconia nanoparticles considered were Zr16O32 and Zr40O80, while the oxygen-deficient formulae were Zr19O32 and Zr44O80. For the Zr16O32 model, two types of surface oxygen environments were mentioned (Fig. 16): two-coordinate (O2c) sites had an average calculated diso(17O) value of 545 ppm (with individual sites in the range of 463–639 ppm) and three-coordinate (O3c) sites had an average diso(17O) of 407 ppm (with individual sites in the range of 384–448 ppm). Four-coordinate subsurface oxygens (O4c) were found to have an average diso(17O) of 317 ppm (with individual sites ranging from 267 to 356 ppm). Using the larger Zr40O80 nanoparticle, the average diso(17O) values for the three types of oxygen environment were largely reproduced, with individual chemical shifts being distributed over a narrower range when compared against the Zr16O32 nanoparticle. The authors compared these shift values against the literature values reported by Smith and co-workers,80 and there appeared to be reasonable agreement (on average) for O3c and O4c sites, although there was no comparable experimental peak associated with the O2c sites. The authors noted that perhaps this was because their computational models were of nanoparticles on the order of 1 nm in diameter, while the experimental account involved nanoparticles that were about 15 nm in diameter. The authors further noted that the O2c sites, as they have the lowest coordination number, would be expected to be the most chemically reactive. Thus, these sites might not persist in a significant number after the nucleation phase prior to nanoparticle growth. For the oxygen-deficient nanoparticle models, the authors did not find very large changes in the average diso(17O) values for O3c and O4c sites when compared against the analogous environments in the stoichiometric particles (n.b., O2c were not present in these models as they were eliminated when creating the vacancy). It was reasoned that this finding was sensible, as the resulting excess electron density would be expected to be localized on empty 4d states associated with Zr3þ.

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Fig. 15 17O-1H spin-echo NMR spectrum in comparison to the chemical shifts predicted using various structural models. Reprinted with permission from Shen, L.; Wu, X.-P.; Wang, Y.; Wang, M.; Chen, J.; Li, Y.; Huo, H.; Hou, W.; Ding, W.; Gong, X.-Q.; Peng, L. 17O Solid-State NMR Studies of ZrO2 Nanoparticles. J. Phys. Chem. C 2019, 123, 4158–4167. DOI: 10.1021/acs.jpcc.8b11091. Copyright 2019, American Chemical Society.

9.15.2.4.5

Cerium(IV) oxide/ceria (CeO2)

Due to their potential applications as catalysts and in energy storage, Hope et al. studied CeO2 nanoparticles using solid-state 17O NMR experiments, isotopic enrichment, and direct DNP to selectively enhance the surface NMR signal.81 According to the authors, this was the first time that direct DNP (i.e., not using a 1H source as a polarization relay) was used to perform surface-selective solidstate 17O NMR. The CeO2 nanoparticles were 17O enriched using 17O2 gas. Subsequent manipulation of these samples was done under inert atmosphere to avoid oxygen exchange with the air or water. The solvent selected for DNP experiments was TCE to minimize the chances of oxygen exchange at the surface. Four 17O environments were resolved using DNP-enhanced 17O MAS NMR experiments: a broad peak at d(17O) ¼ 1055 ppm was assigned to oxygen atoms at the surface; broad signals at d(17O) ¼ 893 ppm and d(17O) ¼ 843 ppm were assigned to oxygen atoms in the second and third layers; a sharp signal at d(17O) ¼ 875 ppm was attributed to bulk CeO2. Many of these assignments were based on, and served as confirmation of, findings from an earlier combined NMR/DFT study using 17O-enriched CeO2 nanoparticle samples.82 The authors also measured the DNP build-up times for each of the resolved 17O environments. As expected, the build-up time for the signal assigned to bulk 17O was very large (> 1600 s) when compared against analogous values for the signals assigned to 17O at or near the surface (62– 85 s). This is consistent with a model where surface polarization travels into the particle interior via spin diffusion, which would be particularly slow for the present samples (relative to something involving 1H). Indirect 17O DNP NMR experiments (i.e., using 1 H / 17O CP and pre-saturation pulses) were also attempted, and interestingly painted an entirely different picture (Fig. 17). By suppressing the direct DNP signal, and by requiring a 1H source, two 17O NMR signals were observed, both of which were not seen in the direct 17O DNP NMR experiments. These were assigned to surface hydroxyls and adsorbed H2O. Comparing 17O NMR spectra acquired with different CP contact times demonstrated that the OeH bonding was direct in nature. Gao and co-workers used solid-state 17O NMR experiments to probe crystal facet effects for CO oxidation using CeO2 nanoparticles, where the particle morphology was varied between samples.83 The authors considered CeO2 nanoparticles that were rod-like, cube-like, and octahedron-like. A barrage of characterization methods was used (XRD, Brunauer-Emmett-Teller (BET) surface areas,

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Fig. 16 17O NMR chemical shift (diso, ppm) of oxygen atoms: (A) Zr16O32 nanoparticle; (B) Zr40O80 nanoparticle. Reprinted with permission from Maleki, F.; Pacchioni, G. DFT Study of 17O NMR Spectroscopy Applied to Zirconia Surfaces and Nanoparticles. J. Phys. Chem. C 2019, 123, 21629– 21638. DOI: 10.1021/acs.jpcc.9b06162. Copyright 2019, American Chemical Society.

TEM, XPS, EPR, and in situ diffuse infrared Fourier transform spectroscopy), including solid-state 17O MAS NMR experiments. Both non-selectively enriched (using 17O2) and selectively enriched (using H217O) CeO2 samples were prepared. The 17O MAS NMR experiments were performed either using a conventional approach (but with isotopic enrichment) at B0 ¼ 14.1 T, or were enhanced using DNP (but without isotopic enrichment) at B0 ¼ 9.4 T and 110 K. When preparing selectively enriched samples using H217O, the authors stated that the preparation temperature and particle morphology influenced the resulting 17O MAS NMR signal intensity. This was rationalized in part by noting that different particle morphologies displayed different surface facets (for example, water adsorption on CeO2(111) facets is understood to be relatively more facile when compared to CeO2(100) facets). Irrespective of the morphology, selectively enriched CeO2 nanoparticle samples displayed several 17O NMR signals, which were assigned as

Fig. 17 The indirect DNP 17O NMR (14.1 T) spectra of 17O enriched CeO2 nanoparticles impregnated with TEKPol in TCE, recorded at 12.5 kHz MAS with a recycle delay of 4.3 s, 320 scans and variable contact times for the 1H / 17O cross polarization. The 17O magnetization was presaturated to avoid the direct DNP signal. Reproduced without modification from Hope, M. A.; Halat, D. M.; Magusin, Pieter C. M. M.; Paul, S.; Peng, L.; Grey, C. P. Surface-Selective Direct 17O DNP NMR of CeO2 Nanoparticles. Chem. Commun. 2017, 53, 2142–2145. DOI: 10.1039/C6CC10145C, as published by The Royal Society of Chemistry, and under the terms of the Creative Commons CC BY 3.0 license (https://creativecommons.org/ licenses/by/3.0/).

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follows: a peak at d(17O) ¼ 877 ppm corresponds to 17O in the particle cores; a band ranging from  838–870 ppm is due to 17O near Ce3þ or oxygen vacancies; surface 17O are located at roughly 1050 ppm, and appear to correspond to the particular facet being exposed (either (111) or (100)); 17O that are one layer below the surface occur at  890–896 ppm. Oxygen-17 NMR data from nonenriched samples acquired under DNP conditions interestingly did not yield any signal associated with the surface layer. It was reasoned that this was because of short 17O T1 values for the surface oxygens, caused by hyperfine coupling with radicals near the surface, or because the 17O NMR signal under DNP remained too feeble to be detected. All other 17O NMR signals could be observed under DNP conditions for the non-enriched samples (Fig. 18), and the authors were able to further resolve multiple contributions to the band spanning 838–870 ppm for some morphologies, noting that progressively lower chemical shift bands should correspond to 17O surrounded by more Ce3þ ions. TEM experiments were able to find that the cube-like and octahedron-like CeO2 nanoparticle samples were mainly enclosed with (100) and (111) facets, respectively, while the rod-like samples were not well-faceted. Taking the NMR and TEM data together, it was concluded that only isolated oxygen vacancies occurred in the cube-like samples, while both isolated and vacancy clusters were present in the octahedron-like and rod-like samples.

9.15.2.4.6

Aluminum oxide/alumina (Al2O3)

9.15.2.4.7

Hematite (a-Fe2O3)

In 2017, Mikhalev et al. published their work involving Al2O3 particles, with particle sizes of 3.8, 9, 13, and 2000 nm.84 In contrast with earlier reports on alumina nanoparticles that demonstrated the feasibility of 27Al NMR experiments under typical DNP conditions,85 the present study was done at room temperature and used static and MAS 27Al NMR experiments, powder XRD, and magnetization measurements. As different synthetic approaches may be used to generate these particles, the authors were also interested to see if the Al2O3 crystal structure depended on the synthetic method. Indeed, it was found that different particles possessed different crystal structures: particles with average sizes of 3.8 and 13 nm (laser ablation synthesis) showed the cubic g-phase alumina structure; particles with average size of 9 nm (gas-phase synthesis) formed face-centered cubic (FCC) metallic aluminum and cubic gphase alumina structures; and the 2000 nm particles (synthesized by a chemical method) exhibited the a-phase (hexagonal close packing, HCP) alumina crystal structure. The static 27Al NMR line shapes of samples prepared using laser ablation (denoted as L1 and L2 by the authors) were rather sharp and largely devoid of line broadening due to the quadrupolar interaction. This is expected as these particles correspond to cubic g-Al2O3, but also provided evidence that these samples had a low concentration of structural defects. With that being said, the authors did notice a shoulder in the 27Al NMR line shape at higher frequency. As magnetization experiments on sample L1 indicated the presence of ferromagnetic order, variable temperature 27Al NMR experiments under static conditions were performed. However, even with a decrease in temperature from 300 to 80 K, the position, width, and shape of the 27 Al NMR line shapes did not change noticeably. The authors searched for further NMR signals over a wide frequency range but could not isolate any. Variable-field 27Al NMR experiments also did not yield any support for ferromagnetic ordering in L1. As such, the authors concluded that the ferromagnetic ordering must occur in a separate phase that is likely much less than 1% of the sample by volume (possibly iron oxide). Compared to polycrystalline a-Al2O3, samples L1 and L2 possessed no significant difference in their 27Al NMR spectra, though there was a loss of the first-order satellites (due to the quadrupolar interaction) for the nanoparticulate samples. The static 27Al NMR spectrum of a sample prepared by a gas-phase method (sample G3) showed a clear additional line that was assigned to metallic aluminum in the nanoparticles. To obtain higher resolution for samples L1 and L2, the authors collected additional 27Al NMR data under MAS conditions (Fig. 19). Impressively, the authors decerned three phases of alumina in each sample (and up to three 27Al environments in each phase), although there was a slight difference in the relative amounts of each phase when comparing L1 and L2. In all, the authors observed the aforementioned a and g phases, but also detected a substantial amount of the h phase (25% h phase in L1, 34% in L2). During their study of the deactivation mechanism of Ca3Al2O6-stabilized carbon dioxide sorbents, Kim et al. used solid-state 27 Al NMR experiments (both under MAS conditions and using surface-enhanced DNP spectroscopy).86 Based primarily on data from other characterization techniques (such as SEM), it was discovered that during the deactivation process, Ca3Al2O6 went through a variety of phase changes (including phase segregation), which included the formation of a segregated Al2O3 nanoparticle phase at the surface of the deactivated particles. The surface-enhanced DNP 27Al NMR experiments resolved two 27Al environments, which were assigned to aluminum in tetrahedral and octahedral environments in a form of Al2O3. As the DNP NMR experiment is surface-selective, they confirmed that the Al2O3 nanoparticle phase formed at the particle surface.

The crystal structure of bulk hematite has one iron environment, with the iron being in the 3þ oxidation state. The iron is sixfold coordinated by oxygen atoms, producing a local geometry that is a trigonally distorted octahedron. Some time ago, Bastow and Trinchi collected the 57Fe internal field NMR (IFNMR) spectra of both bulk and nanocrystalline hematite.87 The 57Fe NMR signal associated with the nanocrystalline sample is broader than, and occurs at a lower frequency than, the corresponding signal for bulk a-Fe2O3 (Fig. 20). The nanoparticle sample was noted as having an average particle diameter of 55 nm (established using XRD measurements), and it was mentioned by the authors that if the average crystallite dimensions were to be reduced further, then the ferromagnetic state of the sample would not likely persist. Smaller particle sizes were predicted to be paramagnetic, which would not produce a detectable 57 Fe IFNMR signal. Indeed, the authors attempted to acquire such a signal using other samples of nanocrystalline hematite but were unsuccessful.

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Fig. 18 Natural abundance 17O DNP NMR spectra (black lines) for (A) ceria-rod, (B) ceria-octahedron, and (C) ceria-cube. Best-fitting simulations (gray lines) decomposed into each individual component (blue solid lines for second layer oxygen, green lines for bulk oxygen, and red and purple lines for vacancy-related oxygen atoms). Reprinted with permission from Cao, Y.; Zhao, L.; Gutmann, T.; Xu, Y.; Dong, L.; Buntkowsky, G.; Gao, F. Getting Insights Into the Influence of Crystal Plane Effect of Shaped Ceria on Its Catalytic Performances. J. Phys. Chem. C 2018, 122, 20402–20409. DOI: 10.1021/acs.jpcc.8b06138. Copyright 2018, American Chemical Society.

9.15.2.4.8

Maghemite (g-Fe2O3) and magnetite (Fe3O4)

9.15.2.4.9

Yttrium(III) oxide/yttria (Y2O3)

Payer and co-workers used 57Fe IFNMR spectroscopy to probe the local environments of iron oxide compounds that were stated as being either nanocrystalline or submicron in size.88 Measurements were carried out at a variety of temperatures in the range from 4.2–370 K and used the CPMG pulse sequence. Two nanoparticle samples were considered, one with a relatively smaller average particle size (30–60 nm), and one with a relatively larger particle size (80–110 nm). The 57Fe IFNMR spectra for these two samples were compared against the 57Fe IFNMR spectrum of a single crystal of magnetite. Unsurprisingly, the nanoparticles featured broader line shapes when compared against the bulk single crystal sample. However, even in the nanoparticle samples, the A sites (tetrahedral Fe3þ) were distinguishable from the B sites (octahedral, with the average iron being Fe2.5þ). However, it was not clear if the two B environments, observed in the 57Fe IFNMR spectrum of magnetite, could be resolved in the nanocrystalline samples. The authors also commented that the nanoparticle samples appeared to possess some maghemite-like environments, in addition to magnetitelike environments. It was noted that the 57Fe IFNMR spectra of the 80–110 nm-sized particles varied significantly with temperature, and it was found that some features moved in the frequency-domain in a fashion that was highly similar to magnetite, while others moved in a way that was similar to maghemite.

When attempting to showcase and quantify the experimental sensitivity gains that could be achieved by combining DNP with 1Hdetected heteronuclear correlation experiments, one of the samples considered by Wang and co-workers was nanoparticles of

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Fig. 19 MAS 27Al NMR and static (for comparison) 27Al NMR spectra of Al2O3 nanoparticles (samples L1, L2) measured at T ¼ 300 K in a field of 11.747 T at the rotation frequency of 20 kHz: (A) sample L1 and (B) sample L2. The solid bold lines show the experimental spectra: the static spectrum (wider spectrum, for comparison) and the MAS spectrum. The thin solid lines show the calculated MAS spectra (superposition of lines in the spectrum that belong to different phases). SB symbols denote the rotational satellites. The spectral lines corresponding to different phases are denoted as follows: (the dash-dotted line) g-phase, (dashed line) h-phase, and (dotted line) a-phase. Reprinted by permission from Springer Nature Customer Service Centre GmbH: Pleiades Publishing, Ltd., from Mikhalev, K. N.; Germov, A. Yu.; Ermakov, A. E.; Uimin, M. A.; Buzlukov, A. L.; Samatov, O. M. Crystal Structure and Magnetic Properties of Al2O3 Nanoparticles by 27Al NMR Data. Phys. Solid State 2017, 59, 514–519. DOI: 10.1134/S1063783417030246, copyright 2017.

Fig. 20 57Fe NMR spectrum for a-Fe2O3 (hematite): (a) macrocrystalline and (b) nanocrystalline. Reprinted from Bastow, T. J.; Trinchi, A. NMR Analysis of Ferromagnets: Fe Oxides. Solid State Nucl. Magn. Reson. 2009, 35, 25–31. DOI: 10.1016/j.ssnmr.2008.10.005. Copyright 2009, with permission from Elsevier.

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Y2O3.59 The nanoparticles were noted as being 50 nm (on average) in diameter and the DNP radical solution consisted of 16 mM TEKPol in fully deuterated TCE solvent. DNP-enhanced 89Y{1H} CP/MAS NMR experiments (with the 1H source being hydroxylated yttria sites) used either 1.3 or 3.2 mm probes and were able to resolve two yttrium chemical environments, which differed in the number of –OH groups bound to the yttria surface (Fig. 21). In contrast with other observe nuclei, it was found that the loss in experimental sensitivity upon switching from a 3.2 mm probe to a 1.3 mm probe was modest for 89Y (factor of 2.3), and the authors presented some discussion to rationalize this observation. Supported by numerical simulations of spin dynamics, it was found that CP transfer efficiencies should have been comparable between both probes, even though the rf field strengths that were achievable were very different. It was noted that the 3.2 mm probe that was used suffered from reduced efficiency at the 89Y frequency, which might explain, in part, the observations. In terms of the two-dimensional correlation experiments, it was clear that the 1H-detected NMR experiment (idHETCOR) with a 1.3 mm probe afforded much better sensitivity than an 89Y-detected experiment using a 3.2 mm probe (Fig. 21). Importantly, as this highquality idHETCOR NMR spectrum could be acquired in only 3 h at a standard applied field (albeit under DNP conditions), the authors were able to further optimize their CP transfer parameters to observe a very low intensity yttrium environment at 310 ppm that had escaped prior detection. The authors rationalized that this peak was associated with sub-surface yttrium environments, which underscored the surface-selective nature of these experimental conditions.

9.15.2.4.10 Li4Ti5O12 (LTO) Odziomek et al. prepared nanoparticles of LTO (Li-ion battery anode candidate materials) that were approximately 4–5 nm in size via a variety of glycothermal synthetic routes and probed the product materials using various techniques, including 7Li MAS NMR spectroscopy.91 In all, the authors considered seven different synthetic routes, with precursor identity, solvent identity, and temperature serving as variables. Although the particle sizes were not strongly different across the samples, there was moderate variation in BET surface areas (range: 131–303 m2 g
1) and pore volumes (range: 0.225–0.902 cm3 g
1). In terms of 7Li MAS NMR experiments, one of the above samples, as well as commercial nano-LTO, were considered. For the commercial LTO sample, only a single peak (d(7Li) ¼ 0.13 ppm) was observed. Although the 7Li MAS NMR line shape of the commercial LTO sample was noted as being broad, attempts to deconvolute the peak were unsuccessful. In contrast, for one of the glycothermally prepared samples, the authors were able to deconvolute the 7Li NMR signal into two contributions, which were presumed to be due to lithium ions at 8a and 16d Wyckoff sites, although the relative signal intensities after deconvolution did not agree with the expected ratio according to

Fig. 21 DNP-enhanced 1H-89Y spectra of Y2O3 nanoparticles impregnated with 16 mM solution of TEKPol in TCE-d2, obtained using a 1.3-mm probe (A and C) and a 3.2-mm probe (B and D). In (D), 1H frequency-switched Lee-Goldburg (FSLG)89,90 homonuclear decoupling was used during t1. Reprinted from Wang, Z.; Hanrahan, M. P.; Kobayashi, T.; Perras, F. A.; Chen, Y.; Engelke, F.; Reiter, C.; Purea, A.; Rossini, A. J.; Pruski, M. Combining Fast Magic Angle Spinning Dynamic Nuclear Polarization With Indirect Detection to Further Enhance the Sensitivity of Solid-State NMR Spectroscopy. Solid State Nucl. Magn. Reson. 2020, 109, 101685. DOI: 10.1016/j.ssnmr.2020.101685. Copyright 2020, with permission from Elsevier.

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a [Li]8a[Li1/3Ti5/3]16d[O4]32e structure. The authors suggested that better resolution would be achieved by performing 6Li MAS NMR experiments at a higher applied magnetic field than was used in their study.

9.15.2.5 9.15.2.5.1

Other oxide-containing nanoparticles Zeolites

The formation of Beta zeolites prepared using surfactant was studied by Schmidt and co-workers using an array of complementary techniques, including liquid-state (1H, 1H DOSY, 14N, 27Al, and 29Si) and solid-state (27Al and 29Si) NMR experiments.92 In particular, the nucleation and growth of Beta zeolite nanoparticles were followed for two different synthetic procedures (these samples were referred to as nano-Betagel and nano-Betasol). Liquid-state NMR experiments were performed exclusively on nano-Betasol, while solid-state NMR experiments were carried out on nano-Betagel. The liquid-state 27Al and 29Si NMR spectra of nano-Betasol were analyzed, and it was concluded that the 27Al in the nanoaggregates were connected to silicates to yield a tetrahedral local environment at a very early stage in the synthesis. No evidence of free monomeric or oligomeric silicates was found. The solid-state 29Si {1H} CP/MAS NMR spectra of nano-Betagel rapidly developed a feature at d(29Si) ¼
112 ppm, which was taken as evidence for the formation of ordered zeolite domains. The 1H / 29Si CP transfer efficiency for all 29Si sites, including Q4 sites, was high, which suggested that the surfactant was near the silicate framework. Data from complementary techniques (including small-angle X-ray scattering, powder XRD, and SEM) painted a very detailed picture of other aspects related to particle nucleation, growth, and aggregation.

9.15.2.5.2

Bioactive glasses

Treating certain medical ailments, such as bone fractures, using bioactive glasses is desirable as these glasses are touted as being costeffective and can undergo controlled degradation in the body. However, it is noted that many bioactive glasses require the addition of stabilizing ions, and that the behavior of these stabilizers once in the body is not well known. As such, Marti-Muñoz et al. used solid-state 31P NMR experiments (supported with XRD, DLS, SEM, and other techniques) to study the degradation of stabilizer-free P2O5-CaO nanoglasses.93 These glasses are reasonably well described as a network of phosphate groups that are stabilized by Ca2þ ions, and the relative amount of P to Ca has been found to be related to the bioactive glass degradability. As such, five sample compositions were considered: P100, P65, P55, P30, and P0, with the numeral indicating the percentage of phosphorus atoms in the sample, as determined by EDS. After the formation of the nanoparticles, but prior to heat treatments, the authors noted that all materials were amorphous. In the 31P MAS NMR spectra for all samples except P0, the signals were assigned to Q0-type environments. Calcium hydroxide was denoted as the main phase in P30 and P0, while NH4H2PO4 was the main phase in P100. All samples degraded very rapidly in solution, so to help stabilize the structures, thermal treatments were carried out at either 200 or 350  C. After the heat treatments, the 31P NMR spectra of P30, P55, and P65 all contained Q1- and Q2-type environments (due to phosphate group condensation), in addition to some Q0 environments. The authors assigned the Q2 bands to cyclic or open chained amorphous calcium trimetaphosphate, the Q1 bands to open chained amorphous calcium trimetaphosphate or amorphous calcium pyrophosphate, and the Q0 bands to amorphous calcium orthophosphate. The authors then probed the degradation properties of the various heat-treated samples and concluded that most could be suitable for biomedical applications.

9.15.2.6

Core@shell nanoparticles

9.15.2.6.1

Fe@C

9.15.2.6.2

Co@C

Ramesh and co-workers used 57Fe IFNMR at a temperature of 77 K to probe the magnetic domains of a carbon-coated iron nanopowder sample (i.e., Fe@C).94 A suite of additional characterization tools were also used by the authors (SEM, XRD, Mössbauer, thermal gravimetric analysis (TGA), Raman, etc.). While many of the potentially useful properties of these particles stem from the metallic core, carbon is used as a coating to reduce toxicity. The XRD patterns established that the Fe@C sample contained phases similar to g-Fe, a-Fe, and provided some evidence of amorphous iron carbide. Mössbauer experiments confirmed much of this information regarding the phase composition of Fe@C, but also appeared to demonstrate the presence of paramagnetic Fe-C inclusions. In addition, Mössbauer experiments established the hyperfine fields associated with the various phases, which is very useful when interpreting the 57Fe IFNMR data. The authors were not able to observe any 57Fe IFNMR signals at room temperature but did observe a signal associated with a-Fe at 77 K (Fig. 22). In particular, the authors observed a sharp peak-like feature at about 46.55 MHz, and a shoulder-like feature at around 47.20 MHz. It was argued that the more intense signal corresponded to domain walls, while the shoulder was due to: (i) single domain particles; and (ii) nuclei inside the domains of multidomain particles. The authors attempted to observe the 57Fe IFNMR signals associated with the other phases in Fe@C but were unsuccessful. By measuring the saturation magnetization associated with the sample, the critical size of the single-domain particles was found to be about 16 nm.

Mikhalev et al. used 13C NMR and 59Co IFNMR experiments, as well as XRD, HRTEM, Raman spectroscopy and magnetization measurements to probe the structure of cobalt core nanoparticles that had been encapsulated in carbon.95 The interest in characterizing this type of material stems from potential applications in medicine, capacitive energy storage, and spintronics. It was discovered that although the mean particle size was only  5–7 nm, the particle cores were ferromagnetic. The 59Co IFNMR experiments

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Fig. 22 Plot of echo amplitude versus frequency for Fe@C at 77 K. Reprinted from Manjunatha, M.; Kumar, R.; Sahoo, B.; Damle, R.; Ramesh, K. P. Determination of Magnetic Domain State of Carbon Coated Iron Nanoparticles Via 57Fe Zero-External-Field NMR. J. Magn. Magn. Mater. 2018, 453, 125–131. DOI: 10.1016/j.jmmm.2018.01.017. Copyright 2018, with permission from Elsevier.

were carried out at a variety of temperatures in the range of 77–360 K, used an echo sequence, and were acquired in a point-by-point fashion while stepping across many radiofrequency transmitter values in the region of about 165–230 MHz. A somewhat narrow peak in the high frequency portion of the spectra was assigned to metallic Co (FCC structure). A broad signal spanning much of the lower frequencies was postulated to be due to CoxC carbides, of which Co3C was deemed to be the most sensible based on the magnetic moments of cobalt atoms in various cobalt carbides determined a priori. No evidence of ferromagnetic Co2C or paramagnetic Co3O4 was found in the present sample (attempts at detecting the latter were performed at B0 ¼ 11.747 T). The authors also observed a very broad 13C NMR signal (full width at half-height of  350 kHz, Fig. 23). As such, the 13C environments were highly disordered, and likely similar to amorphous or glass-like carbon.

9.15.2.6.3

Ni@C

Citing their broad areas of application, including in medicine, in spintronics, and as supercapacitors, 13C NMR and 61Ni IFNMR experiments were used to probe nanoparticles composed of a nickel core and carbon coating.96,97 The 13C NMR data were acquired in an applied field of 11.747 T, while no applied field (and T ¼ 4.2 K) was used to acquire the 61Ni IFNMR spectra. A magnetization reversal curve collected at room temperature indicated that the core of the nanoparticles was ferromagnetic in nature, with a saturation value (17.5 emu g
1) substantially lower than bulk metallic nickel (55 emu g
1). The 61Ni IFNMR spectrum of Ni@C displayed several features, as shown below (Fig. 24). The authors assigned the three resolved bands to metallic nickel (nmax ¼ 29 MHz), a Ni:C alloy (nmax  27 MHz), and nickel carbide (nmax  24.5 MHz), and noted that they were in reasonable agreement with information obtained from Mössbauer spectroscopy.98 The 13C NMR spectrum acquired at room temperature was broad and featureless, and was assigned to an amorphous glass-like carbon phase.

Fig. 23 13C NMR spectrum obtained in an external magnetic field of 11.747 T at T ¼ 295 K in nanoparticles of Co@C. Dashed line shows the diamagnetic point. Republished with permission of IOP Publishing, Ltd. from Mikhalev, K. N.; Germov, A. Yu.; Uimin, M. A.; Yermakov, A. E.; Konev, A. S.; Novikov, S. I.; Gaviko, V. S.; Ponosov, Yu. S. Magnetic State and Phase Composition of Carbon-Encapsulated Co@C Nanoparticles According to 59Co, 13C NMR Data and Raman Spectroscopy. Mater. Res. Express 2018, 5, 055033. DOI: 10.1088/2053-1591/aac1f3. Copyright 2018 with permission conveyed through Copyright Clearance Center, Inc.

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Fig. 24 61Ni IFNMR spectrum (n) of carbon encapsulated nickel Ni@C nanoparticles obtained at zero external magnetic field and at T ¼ 4.2 K. Calculated spectrum (bold line) and the components Ni (dash line), Ni:C (dot line), Ni3C (dash dot line) are also shown. Reprinted from Ref., Prokopyev, D. A.; Germov, A. Yu.; Mikhalev, K. N.; Uimin, M. A.; Yermakov, A. E.; Konev, A. S. NMR Study of Phase Composition of Carbon Encapsulated Ni@C Nanoparticles. AIP Conf. Proc. 2019, 2174, 020155. DOI: 10.1063/1.5134306, with permission of AIP Publishing.

9.15.2.6.4

Pt@mSiO2 and PtSn@mSiO2

The encapsulation of transition metal nanoparticles in mesoporous silica (mSiO2) typically improves thermal stability and optical properties. Importantly for catalytic applications, the mSiO2 shell does not prevent small organic molecules from accessing the active metal sites. Bowers and co-workers used both conventional and DNP-enhanced 29Si MAS NMR experiments to probe the various silica surface environments of Pt@mSiO2 and PtSn@mSiO2 nanoparticles.99 Their findings were benchmarked relative to MCM-41, as it is a well-characterized mesoporous silica. Importantly, although other experimental techniques, such as TEM, provided clear evidence of the silica shell around the metal, these approaches could not provide atomic-scale structural details. Room temperature single-pulse 29Si NMR spectra of the core@shell samples provided evidence of the relative amounts of Q2, Q3, and Q4 sites. When compared against one another, the relative amounts of each Q-type site were similar, but when each was compared against MCM-41, it was clear that the Q4 populations were proportionately much greater in the nanoparticle samples. All other NMR measurements were carried out under DNP conditions with the AMUPol or TEKPol radicals being introduced into the samples using the incipient wetness impregnation approach. As the dimensions of these radical-containing molecules are thought to be as large as 2.4 nm, it is unclear to what extent they penetrate into the M@mSiO2 nanoparticles, as the mesoporous channels themselves are about 2.4 nm in diameter. Although the 29Si CP/MAS DNP enhancement factors (using AMUPol) were modest (i.e., 16 for PtSn@mSiO2 and 10 for Pt@mSiO2), the authors noted that a signal-to-noise ratio of 335 could be obtained for PtSn@mSiO2 in 4 min, while under conventional conditions, a signal-to-noise ratio of 66 was realized after signal averaging for 69 h. At the same time, it was demonstrated that the combination of CP/MAS and DNP to acquire the 29Si NMR signal distorted the apparent relative populations of the Q sites in such a fashion that the Q3 peak was vastly greater in intensity relative to the other sites. Further, it was found that direct DNP-enhanced NMR experiments produced an overall 29Si NMR spectrum that was more reflective of the true silica environment distributions (Fig. 25). Thus, although not quantitative, the sensitivity of the 29Si DNP CP/MAS NMR experiment allowed dipolar-based 29Si-29Si 2D correlation NMR experiments to be performed to determine network connectivity of the PtSn@mSiO2 sample. Due to rapid 29Si spin-spin relaxation, and the distance between 29Si nuclei not related as next-nearest neighbors, the authors commented that this 2D NMR experiment probed only 29Si spin pairs that shared a common oxygen atom. From this DNP-enhanced 29Si CP/ MAS NMR experiment, linkages between Q2-Q3, Q3-Q3, and Q3-Q4 environments were observed.

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Fig. 25 29Si MAS NMR spectra of PtSn@mSiO2 nanoparticles obtained by (A) single pulse without radicals at room temperature, (B) direct DNP polarization, and (C) indirect DNP CP. Reprinted with permission from Zhao, E. W.; Maligal-Ganesh, R.; Mentink-Vigier, F.; Zhao, T. Y.; Du, Y.; Pei, Y.; Huang, W.; Bowers, C. R. Atomic-Scale Structure of Mesoporous Silica-Encapsulated Pt and PtSn Nanoparticles Revealed by Dynamic Nuclear Polarization-Enhanced 29Si MAS NMR Spectroscopy. J. Phys. Chem. C 2019, 123, 7299–7307. DOI: 10.1021/acs.jpcc.9b01782. Copyright 2019, American Chemical Society.

9.15.2.6.5

CdSe@CdS

As part of their study involving the PASS-PIETA pulse sequence under MAS DNP conditions (vide supra), Piveteau et al. used twodimensional 113Cd NMR experiments to probe CdSe quantum dots covered with CdS shells of variable thickness (ranging from 0.1 to 0.9 nm thick, Fig. 26).52 As the thickness of the CdS shell was increased, the 113Cd NMR peak associated with the CdSe core was progressively de-shielded (from
66 ppm in the case of no shell to about
37 ppm for a CdS shell with 0.9 nm thickness). This de-shielding trend was also observed for 113Cd probe nuclei at the surface of the CdSe core. In addition, a new peak at d(113Cd)  55 ppm became more prominent with increasing CdS shell thickness and was assigned to 113Cd in the CdS shell.

9.15.2.7 9.15.2.7.1

Molecular organic nanoparticles Compound P

Many new active pharmaceutical ingredients (APIs) have poor solubility in aqueous environments, thus hindering their bioavailability. API nanoparticles offer a potential remedy, as the relatively high surface area and surface energy associated with these particles will often yield improvements in solubility when compared to particles that are larger in size. By performing DNP-enhanced 1 H-13C CP/MAS NMR experiments on the mysterious compound P (while a systematic name was not provided by the authors, a molecular structure was supplied in the main text of their report), Pinon et al. were able to roughly determine the size of the crystalline API core, as well as the thickness of the stabilizing polymer overlayer.100 The polymer-stabilized API nanoparticles were dispersed in D2O, and sufficient 12C enriched glycerol-d8 and H2O were added to generate a composition that was 30% 12Cglycerol-d8/60% nanoparticle-D2O/10% H2O by volume. A small amount of DNP polarizing agent and 13C labeled sodium formate was then dissolved into this solution. DNP-enhanced NMR experiments were performed at a temperature of about 100 K. DNP-enhanced 13C CP/MAS NMR experiments were able to resolve 13C signals from the labeled sodium formate in the radical-containing phase, the surface polymer, and the nanoparticles of compound P. As a function of the polarization delay time (s, Fig. 27), the DNP enhancement for sodium formate was a constant value (within measurement error), which provided evidence that the formate was exclusively in the solution phase outside of the API nanoparticles. Conversely, the DNP enhancement for the compound P nanoparticles increased as a function of the polarization delay and exhibited a larger exponential build-up time (3.3 s) when compared against both the sodium formate and stabilizing polymer (1.2 s). The increased build-up time demonstrates that the polarizing agent is outside of the nanoparticles (as expected), and the variation in the DNP enhancement can potentially be analyzed to establish the dimensions of the nanoparticles. Under the assumption that the DNP buildup curve for the API nanoparticles could be explained by 1H spin diffusion, the authors used a numerical simulation that followed Fick’s second law to arrive at a distribution of API nanoparticle sizes. The distributions themselves were assumed to follow a Weibull distribution with an average particle diameter of 165 nm. Using a similar numerical simulation approach, it was also possible to establish that the stabilizing polymer layer was between 5 and 10 nm thick.

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Fig. 26 (1) DNP enhanced PASS-PIETA NMR spectra of (a) oleate-capped ZB-CdSe quantum dots on which a CdS shell of (b) 0.1 nm, (c) 0.4 nm, and (d) 0.9 nm thickness was grown. (3) Optical absorption spectra illustrate the gradual shift of the excitonic peak to lower energies with increasing shell thickness (reduced quantum confinement). Insets in the absorption spectra are schematics of CdSe and CdSe@CdS core and core@shell quantum dots. The centerband spectra (solid black line in panels 2a–2d, corresponding to the zero frequency cross-sections in panels 1a–1d) show only isotropic chemical shift frequency components, providing qualitative information about the number and distribution of 113Cd species present in the quantum dots. The surface, core and, if present, shell signals are specially labeled in panels 1a, 2a, 1d, and 2d. Spinning sidebands are marked with asterisks. Reprinted with permission from Piveteau, L.; Ong, T.-C.; Walder, B. J.; Dirin, D. N.; Moscheni, D.; Schneider, B.; Bär, J.; Protesescu, L.; Masciocchi, N.; Guagliardi, A.; Emsley, L.; Copéret, C.; Kovalenko, M. V. Resolving the Core and the Surface of CdSe Quantum Dots and Nanoplatelets Using Dynamic Nuclear Polarization Enhanced PASS-PIETA NMR Spectroscopy. ACS Cent. Sci. 2018, 4, 1113–1125. DOI: 10.1021/ acscentsci.8b00196. Further permissions related to the material excerpted should be directed to the American Chemical Society.

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Fig. 27 1H-13C saturation recovery pulse sequence used for the acquisition of spectra. sd is the saturation delay and was set to 20 ms. The number of saturation loops was 20. s is the polarization delay. Reprinted with permission from Pinon, A. C.; Skantze, U.; Viger-Gravel, J.; Schantz, S.; Emsley, L. Core-Shell Structure of Organic Crystalline Nanoparticles Determined by Relayed Dynamic Nuclear Polarization NMR. J. Phys. Chem. A 2018, 122, 8802–8807. DOI: 10.1021/acs.jpca.8b08630. Copyright 2018, American Chemical Society.

9.15.2.7.2

Carbamazepine (CBZ) dihydrate & co-crystalline derivative

9.15.2.7.3

Indomethacin polymorphs

9.15.2.7.4

Lipid nanoparticles

As noted in the above account pertaining to “compound P,” many APIs developed in recent years suffer from poor water solubility, and the preparation of stabilized nano-sized formulations afford one potential route to improve bioavailability. Likewise, the preparation of co-crystalline forms of APIs can improve therapeutic properties.101 Kojima et al. used a variety of NMR experiments to study the structure of CBZ dihydrate nanosuspensions, as well as nanosuspensions of co-crystalline CBZ-saccharin (CBZ-SAC).102 To study these systems from a variety of perspectives, solid-state, liquid-state, and high-resolution MAS (HR-MAS) NMR experiments were conducted. When preparing the nanosuspensions, the API-containing nanoparticles were dispersed at two content levels: 2% (w/v) and 20% (w/v). Solid-state 13C CP/MAS NMR experiments were performed on the 20% (w/v) nanosuspensions only, due to experimental sensitivity issues. The authors noted that MAS (6 kHz) caused sedimentation of the samples onto the inner surface of the NMR rotor, but it was found that the samples could be easily redispersed. As such, it was concluded that MAS did not have a significant impact on the structure of the suspended nanoparticles. The 13C CP/MAS NMR experiments of CBZ dihydrate and CBZ-SAC nanosuspensions demonstrated that crystalline forms of CBZ dihydrate (in the former case) and anhydrous CBZ (in the latter co-crystalline case) were present in the nanosuspensions. The authors provided evidence that hydroxypropyl methylcellulose (HPMC), used as a stabilizer, was also present in the solid phase, and suggested that HPMC solidifies during the wet milling process that was used to nano-size the API-containing particles. From liquid-phase 1H NMR experiments, it was suggested that CBZ and SAC molecules undergo a rapid exchange between the solid and the solution (by rapid, this is meant relative to the NMR timescale). The 1H HR-MAS NMR experiments were used to probe the interfacial structure between the solid and liquid phases, and the data collected were used to conclude that the API-containing nanoparticles possessed a semi-solid phase at and near the particle surfaces that was composed of the API and the stabilizing agents.

Moribe and co-workers used 13C CP/MAS NMR experiments, along with TEM, DLS, and Raman spectroscopy, to investigate the formation and stabilization of three polymer-stabilized forms of indomethacin nanoparticles.103 Additional NMR experiments were conducted to probe the state of the polymer at the surface of the indomethacin particles. Carbon-13 CP/MAS NMR spectra were presented for g-indomethacin, a-indomethacin, amorphous indomethacin, as well as polymer-stabilized nanosuspensions for each of g-indomethacin, a-indomethacin, and amorphous indomethacin. It was found that when either a- or g-indomethacin was used to create the nanosuspension, the polymorphic form was retained. However, when amorphous indomethacin was dispersed and stabilized in the polymer-containing solution, it appeared to convert to the a polymorph.

The targeted delivery of therapeutics to regions where they are needed in the body remains a challenge. One option being researched involves the use of lipid nanoparticles (LNPs) as carrier units, as they appear to offer acceptable penetration into target cells, while also being less toxic than other approaches. Viger-Gravel et al. used DNP-enhanced NMR experiments (including relayed DNP) on frozen LNPs in the presence of cryoprotectant to probe LNP structures.104 The authors studied frozen LNPs without cargo, and LNPs encapsulating small interfering RNA (siRNA) or messenger RNA (mRNA). The DNP-enhanced NMR experiments used 13C and 31P as the observe nuclei. Various DNP-enhanced 1H / 13C CP/MAS NMR experiments of a sample containing LNP with encapsulated siRNA were used to demonstrate stability of the system over a period of about 3 months. The above 1D NMR experiments were found to be useful for fingerprinting certain aspects of the LNP, but features associated with the siRNA could only be resolved using 2D 1H/13C correlation experiments. In contrast, DNP-enhanced 1H / 31P CP/MAS NMR experiments could detect both aspects of the LNP, as well as the cargo, when such cargo was present and had been phosphorothiolated (Fig. 28). The 1H / 31P CP/MAS NMR data were collected under a somewhat low MAS frequency to extract 31P chemical shift anisotropy tensors. For the phosphate groups, a fairly large shift tensor that was not axially symmetric was observed (U(31P)  183 ppm, 31 k(31P)  0.33), while for the S]PO2
3 groups of the siRNA, the shift tensor was slightly larger in magnitude (U( P) 

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Fig. 28 Experimental 31P CP/MAS DNP spectra (solid line) and simulated spectra (dashed lines) acquired with m wave on and a slow spinning frequency (4.5 kHz) for sample (A) LNP containing mRNA, (B) LNP containing 100% phosphorothiolated siRNA strand, (C) 100% phosphorothiolated siRNA strand dispersed in D2O, and (D) native empty LNP. The center bands are highlighted in blue at 10 ppm for the PO43
group of the lipids and S]PO32
group of the cargo in red at 68 ppm. Reprinted with permission from Viger-Gravel, J.; Schantz, A.; Pinon, A. C.; Rossini, A. J.; Schantz, S.; Emsley, L. Structure of Lipid Nanoparticles Containing siRNA or mRNA by Dynamic Nuclear Polarization-Enhanced NMR Spectroscopy. J. Phys. Chem. B 2018, 122, 2073–2081. DOI: 10.1021/acs.jpcb.7b10795. Copyright 2018, American Chemical Society.

198 ppm), and interestingly appeared to present a different shift tensor symmetry depending on if they were in the LNP, or simply dispersed in D2O (k(31P) ¼ 0.39(0.03) for siRNA in LNP; k(31P) ¼ 0.54(0.03) for siRNA dispersed in D2O). As the 31P shift tensor magnitudes of both the siRNA and LNP did not change in detectable manners upon encapsulation, it was suggested that the interaction between the siRNA and the LNP was very weak, in disagreement with prior studies.105 The authors then used relayed DNP NMR experiments to probe the LNP morphology, as no consensus model exists. Based on the marked differences in the DNP enhancement factors of the LNP components among themselves, it was reasonably concluded that the LNPs were heterogeneous (layer model), thereby ruling out an entirely homogeneous core-type model. The authors also provided some discussion on the relative positioning of the cargo with respect to the LNP.

9.15.2.7.5

High-density lipoprotein nanoparticles

Lau et al. have studied reconstituted formulations of high-density lipoprotein (HDL) nanoparticles under several different contexts.106,107 In one account, the orientations of statin-based drug molecules when in these HDL nanoparticles were elucidated using measurements of 19F chemical shift anisotropy and 1H-19F dipolar coupling constants.106 Prior to commenting on details of

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the drug molecules, the authors used 31P and 15N NMR experiments on HDL nanoparticles that had been precipitated from solution. The 31P NMR data yielded an axially symmetric line shape spanning 45 ppm, which indicated that the hydrated lipid bilayer remained after the precipitation process. A 15N CP/MAS NMR spectrum of an HDL sample that was prepared using 15N-enriched apolipoprotein A-I (apoA-I) was consistent with the protein adopting an a-helical structure, as expected. In another account,107 three reconstituted HDL (rHDL) nanoparticle variants were probed: (1) the highly common wild type variety; (2) the Milano (R173C) variant and; (3) the Zaragoza (L144R) variant. The authors commented that the uncommon variants were particularly interesting, as they seemed to be correlated with both low HDL levels and low predispositions to cardiovascular disease. Each of the variants had a mutation in the HDL protein, apoA-I. First, to establish the relationship between the lipid headgroup orientation and the 31P NMR line shape, the authors used atomistic molecular dynamics simulations (10 ms simulation trajectory) and a 200:20:2 palmitoyloleoylphosphatidylcholine (POPC):cholesterol:apoA-I assembly as a model. As a result of the simulation, the authors found that the lipid bilayer distorted to produce concave and convex surfaces. The lipids nearest to the center were oriented such that their long molecular axes were roughly parallel with the principal axis of inertia of the HDL particle (denoted as Iz HDL) while lipids in the outer regions were roughly perpendicular to this axis (Fig. 29). Next, after depositing the rHDL nanoparticles (200:2 POPC:apoA-I by weight, wild-type) on a flat glass surface, the authors determined the lipid headgroup orientations using 31P NMR, but did not observe this curvature effect experimentally. Rather, these experiments found that the lipids in the HDL particle had formed bilayers that were nearly planar. These planar bilayers were present in two populations that were oriented either parallel or perpendicular to the applied field. By preparing two additional rHDL samples that contained uniformly enriched apoA-I protein (one was 13C-enriched, while the other was 15N-enriched), and by performing 13C-13C dipolar correlation and 1H-15N Polarization Inversion with Spin Exchange at the Magic Angle (PISEMA)108,109 NMR experiments, the authors established that the orientation of apoA-I was helical relative to the lipids. By further considering the rHDL variants (with all measurements being performed in triplicate), 31P NMR experiments evidenced that the wild-type rHDL particles were morphologically similar to rHDL R173C particles. In contrast, the 31P NMR spectra of the L144R rHDL particles appeared consistent with the lipid curvature effect seen in the molecular dynamics portion of the study. The authors speculated that this curvature may be linked to its protective properties.

9.15.2.7.6

Lignin

Lignin nanoparticles have received a great deal of attention due to their diverse areas of application, including virus agglomeration, UV-barriers, and radical scavenging. As the lignin surface can be customized, Sevastyanova et al. sought to understand more clearly the surface structure of lignin nanoparticles using liquid-state 1H NMR.110 The authors noted several challenges associated with characterizing lignin nanoparticles using liquid-state 1H NMR, as the liquid phase signal must be suppressed, and the nanoparticles must be dispersed and be sufficiently stable in the dispersing medium to survive while experimental data are collected. The authors looked at both softwood and hardwood kraft lignins, and the dispersing medium was D2O. Residual liquid phase signal was suppressed using presaturation and an excitation-sculped WATERGATE (WATER suppression by GrAdient Tailored Excitation) pulse sequence.111 The authors were able to identify and assign a variety of 1H NMR signals associated with the surface. However, they noted that aromatic protons displayed a relatively lower intensity than would be expected and reasoned that this was due

Fig. 29 The morphology of rHDL nanoparticles and its relationship to the 31P NMR line shape. (A) Final frame after 10 ms molecular dynamics simulation of a 200:20:2 POPC:cholesterol:apoA-I assembly. Orange spheres denote the lipid phosphate groups, the lipid acyl chains are gray, and the apoA-I molecules are red. (B) Simulated line shapes for the HDL principal axis of inertia Iz HDL aligned parallel with or perpendicular to B0, based on the molecular dynamics model (black) or a hemispheroid approximation (red). Adapted minimally from Lau, S.; Middleton, D. A. Sensitive Morphological Characterization of Oriented High-Density Lipoprotein Nanoparticles Using 31P NMR Spectroscopy. Angew. Chem. Int. Ed. 2020, 59, 18126–18130. DOI: 10.1002/anie.202004130, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/ licenses/by/4.0/).

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to them being close to the nanoparticle surface. It was also proposed that the core of the lignin nanoparticles was composed of higher molecular weight components that were packed in a relatively dense fashion, while a shell region was made up of components that were both lower in molecular weight and less dense (primarily methoxy groups). The NMR data were supported in part by TEM and DLS experiments.

9.15.2.8

Polymer nanoparticles

9.15.2.8.1

Poly(lactic-co-glycolic acid) (PLGA)

Polymer nanoparticles having a variety of modalities may be created so that the same particle can have both diagnostic and therapeutic functions. Bombelli and co-workers synthesized and studied several fluorinated PLGA (F-PLGA) co-polymers,112 and analyzed two members of this series in detail by 19F NMR. To generate the two samples, the authors functionalized the PLGA polymer with a fluorinated amine ligand that contained either three (F3-PLGA) or nine (F9-PLGA) equivalent F atoms. Further, the authors were interested in ascertaining the suitability of F9-PLGA nanoparticles to act as 19F NMR probes and drug carriers. When acting as a drug carrier, fluorinated co-polymers are likely to be more compatible with hydrophobic molecules, and so two hydrophobic drugs with a variable number of fluorine atoms were chosen: dexamethasone (DEX) and leflunomide (LEF). The authors measured the 19F T1 and T2 relaxation parameters of both F3-PLGA and F9-PLGA nanoparticles and deemed them to be suitable for 19F magnetic resonance imaging (MRI) applications. When comparing F9-PLGA and PLGA nanoparticles without fluorine modifications, it was found that the F9-PLGA nanoparticles encapsulated a larger amount of both drugs tested. The authors were also able to observe the liquid-state 19F NMR signal of the encapsulated LEF molecules at around
62 ppm, which occurred in addition to the signal from the co-polymer at
70.5 ppm. Interestingly, an additional 19F NMR signal was not observed for encapsulated DEX. For a lyophilized version of the LEF@F9-PLGA system, to explain more clearly the encapsulation interactions, including possible F /F interactions, the authors presented solid-state 1H-13C CP/MAS, 19F-13C CP/MAS, and 19F MAS NMR data. From the 19F MAS NMR data, it was clear that multiple LEF chemical environments existed in the LEF@F9-PLGA sample, but these data could not be used to identify any interactions between LEF and the co-polymer nanoparticles. Additional 19F-19F DQ/SQ NMR experiments also did not demonstrate any through-space interactions between LEF and the encapsulating polymer (Fig. 30), leading the authors to conclude that the encapsulation was non-specific in nature, and also not due to F/ F interactions.

9.15.2.8.2

Polystyrene (PS)

Kim et al. used 1H NMR relaxation measurements, in addition to DLS experiments, to better understand the local relaxation dynamics of nanoparticles composed of a PS core and poly(methyl acrylate) (PMA) as the so-called stabilizing polymer canopy.113 Relaxation dynamics are challenging to study in these types of materials, since both the polymer canopy, as well as the polymer core,

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Fig. 30 F (376.5 MHz) DQ/SQ MAS spectrum of F9-PLGA nanoparticles (A) and LEF@F9-PLGA nanoparticles (B), acquired at a spinning frequency of 32 kHz and using one period of back-to-back (BABA) recoupling. Reprinted with permission from Neri, G.; Mion, G.; Pizzi, A.; Celentano, W.; Chaabane, L.; Chierotti, M. R.; Gobetto, R.; Li, M.; Messa, P.; De Campo, F.; Cellesi, F.; Metrangolo, P.; Bombelli, F. B. Fluorinated PLGA Nanoparticles for Enhanced Drug Encapsulation and 19F NMR Detection. Chem. Eur. J. 2020, 26, 10057–10063. DOI: 10.1002/chem.202002078. Copyright 2020, John Wiley and Sons.

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need to be considered. In addition, interplay between the local dynamics of each region is possible. First, PS cores of variable softness were prepared using different amounts of divinylbenzene (DVB). Increased amounts of DVB are expected to lead to increased cross-linkages and hence a more rigid core. Measurements of 1H T1 values at 298 K and B0 z 20 T established that the PS cores with the largest density of cross-links corresponded to the largest T1 value, which is expected as the local dynamics should be diminished relative to samples with a lower density of cross-links. Additionally, T1(1H) values of the PS cores depended weakly on the surface PMA molecule length, with longer PMA molecules being correlated with decreased T1(1H) values. Similar 1H T1 measurements were performed from the perspective of the PMA molecules, both in free PMA and in PMA anchored on PS cores of variable rigidity. Of these samples, the free PMA had the largest T1 value. The authors thus initially speculated that local subsegmental chain dynamics may have been induced upon grafting, but later revised this statement after calculating associated correlation times (see below) using data acquired at multiple B0. For the longest PMA chains considered, the PMA T1(1H) values appeared to be independent of the PS core rigidity, although for shorter PMA chains, the PMA T1(1H) values were influenced by the relative softness or hardness of the PS core. The authors also measured the PS core and PMA canopy T1 values as a function of B0 and found that a lower applied field correlated with a reduced T1(1H) value for both the core and the canopy protons that were probed. Armed with this information and using a Bloembergen-Purcell-Pound (BPP) model,114 the correlation times of the segmental motions (sc) were extracted (Fig. 31). From these data, the authors detected an interplay between the relaxation dynamics of PMA and the PS core. Specifically, more rigid PS cores were found to slow down the subsegmental relaxation dynamics of the PMA chains in a more pronounced fashion when compared against softer cores. On the other hand, long PMA chains increased the local relaxation dynamics of the PS core more significantly than did short PMA chains.

9.15.2.8.3

Glycopolymers

To gain insight into the structure and efficacy of drug-glycopolymer conjugate nanoparticles as a function of drug loading, Stenzel and co-workers used a variety of characterization methods, including 1H MAS, 1H 2D exchange, 13C CP/TOSS (Total Suppression of Sidebands),115 and 1H-13C HETCOR NMR experiments.116 The glycopolymer was composed of a hydrophilic fructose block, and a poly(methyl methacrylate) (PMMA) block: the former block interacts with the GLUT5 receptor for enhanced uptake, while the latter provided an attachment point for a platinum-containing drug (Phen-Pt). The authors considered two drug loading levels (denoted as HL for high loading and LL for low loading) and used TEM and DLS measurements to elucidate the morphologies of the conjugate nanoparticles. Interestingly, when compared against the HL sample, the LL sample released more of the drug after

Fig. 31 Correlation time of the 1H spin-lattice relaxation in the (A) PS core and the (B) PMA chains in PS-PMA hairy nanoparticles at 298 K. Nanoparticles with cross-linked PS cores prepared with 0.5 mol% of DVB (green circle), 3 mol% of DVB (blue triangle), 10 mol% of DVB (orange square), and untethered PMA chains (violet diamond). Reproduced without modification from Kim, Y.-G.; Wagner, M.; Thérien-Aubin, H. Dynamics of Soft and Hairy Polymer Nanoparticles in a Suspension by NMR Relaxation. Macromolecules 2020, 53, 844–851. DOI: 10.1021/ acs.macromol.9b01813, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

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72 h (72% vs. 55%) and had higher toxicity against two cancer cell lines. When comparing the 13C CP/TOSS NMR spectra for freezedried HL and crystalline Phen-Pt, it was clear that the Phen-Pt was now amorphous, while no evidence of the crystalline phase was observed. Conjugation between Phen-Pt and the polymer was established by 1H-13C HETCOR NMR experiments (Fig. 32). The ultrafast 1H MAS NMR experiments provided evidence of water in the freeze-dried LL sample, but not in the HL sample, demonstrating that the LL sample had a strong propensity to retain water molecules and therefore should correspond to a reduced hydrophobicity for the LL sample. 2D 1H exchange NMR experiments showed that for the LL sample, the Phen-Pt was well dispersed in moderately hydrophobic regions in the glycopolymer matrix, while the HL sample appeared to contain Phen-Pt aggregates within a strongly hydrophobic core region of the particle.

9.15.2.9 9.15.2.9.1

Alloyed nanoparticles CdSeS

The development of quantum dot technologies has attracted significant interest due to their wide-ranging areas of application, including as lasers, in nanoelectronics, and in biosensing. Alloyed colloidal quantum dots in particular have received recent attention due to the sensitivity of the bandgap to chemical composition and structure. Using solid-state 77Se and 113Cd NMR experiments under MAS conditions, Yu et al. studied one type of CdSeS quantum dot whose composition varied as a function of the distance from the nanoparticle core.117 The NMR experiments were supported by other characterization methods, including: powder XRD, TEM, energy-dispersive X-ray spectroscopy (EDX) and XPS. As the core regions of the nanoparticle were expected to be different in composition from the surface, the authors selected different classes of NMR experiments during their characterization. For example, to probe the nanoparticle surfaces, the CP/MAS NMR experiment (with 1H magnetization coming from the stabilizing ligand) was chosen. This led to the observation of a peak at a 113Cd chemical shift of 455 ppm (with respect to Cd(NO3)2 $ 4H2O, Fig. 33A). A further 113Cd MAS NMR experiment using direct 113Cd polarization was able to resolve several additional cadmium environments, although definitive resolution was not achieved. Based on prior 113Cd NMR literature accounts for CdSe and CdS

Fig. 32 1D 13C CP/TOSS NMR spectra. (A) Pure Phen-Pt in the crystalline state, (B) the polymer and (C) HL micelles. (D) 2D 13C-1H HETCOR of HL micelles. Dashed lines are a guide to the eye. Signal marked by a dashed square corresponds to the correlation peak between the aromatic drug and the methyl protons of the polymer backbone, which confirm the conjugation of the Phen-Pt to the polymer. The correlation signals in red, blue, and orange correspond to the MMA, fructose, and Phen-Pt species, respectively. Reprinted with permission from Callari, M.; De Souza, P. L.; Rawal, A.; Stenzel, M. H. The Effect of Drug Loading on Micelle Properties: Solid-State NMR as a Tool to Gain Structural Insight. Angew. Chem. Int. Ed. 2017, 56, 8441–8445. DOI: 10.1002/anie.201701471. Copyright 2017, John Wiley and Sons.

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nanoparticles,118,119 the authors assigned the peak at 701 ppm to a Se-rich inner core region, the peak at 745 ppm to a Se/S equivalent middle region, and the peak at 792 ppm to a S-rich outer region. The core 113Cd NMR signals did not appear to have any spinning sidebands, which was interpreted as evidence of small cadmium chemical shift anisotropy and the presence of a nearly tetrahedral coordination environment about the cadmium. This was in dramatic contrast with the surface cadmium environments seen in the 113Cd CP/MAS NMR spectrum, which displayed many spinning sidebands and therefore would be expected to have an asymmetric coordination environment. Selenium-77 CP/MAS NMR experiments were attempted on this material but produced no observable signal. This was taken as evidence that the amount of selenium atoms on or near the surface was very low and/or not near a 1H source. Using direct polarization 77Se MAS NMR experiments, two different selenium core environments were observed (Fig. 33B), with the least shielded band being assigned to the Se-rich inner region of the alloy nanoparticle. Xing and co-workers focused on several members of the ternary CdSe1
xSx series with two different morphologies (x ¼ 0.85, 0.78, 0.69, and 0.59 for nanoparticles, and x ¼ 0.8, 0.5, 0.4, and 0.2 for nanobelts). They presented discussion on the utility of 113 Cd NMR experiments to not only comment on the sample composition, but to also identify phase-separated species.120 The authors reported that 113Cd NMR chemical shifts did not appear to be highly sensitive to the nucleation time (and hence particle size), which is reasonable as most of the 113Cd NMR signal would arise from the bulk and not the surfaces of the nanoparticles. Although it may be possible to distinguish these differences in theory, it likely requires higher signal-to-noise ratios than could

Fig. 33 Solid-state NMR spectra of alloyed CdSeS quantum dots synthesized at 180  C for 90 min. (A) 113Cd MAS spectrum with 1H high-power decoupling (HPDEC) provides the total Cd signals located at 701 ppm (inner core region), 745 ppm (middle region), and 792 ppm (outer region) labeled by arrows (bottom trace), and 113Cd CP and MAS NMR spectrum emphasizes the surface Cd signal at 455 ppm, with spinning sidebands labeled by asterisks (top trace). (B) 77Se MAS spectrum with 1H HPDEC (where the sharp spike on the shoulder at
503 ppm is an artifact). Reprinted with permission from Zhang, J.; Yang, Q.; Cao, H.; Ratcliffe, C. I.; Kingston, D.; Chen, Q. Y.; Ouyang, J.; Wu, X.; Leek, D. M.; Riehle, F. S.; Yu, K. Bright Gradient-Alloyed CdSexS1
x Quantum Dots Exhibiting Cyan-Blue Emission. Chem. Mater. 2016, 28, 618–625. DOI: 10.1021/ acs.chemmater.5b04380. Copyright 2016, American Chemical Society.

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be achieved by Xing and co-workers. On the other hand, the authors demonstrated a very clear relationship between diso(113Cd) (referenced against 0.1 M Cd(ClO4)2) and the nanoparticle composition (Fig. 34). When combining the above trend for the nanoparticles with data for CdSe1
xSx nanobelts, and data from nanoparticles of CdS and CdSe, the following linear relationship between chemical formula and diso(113Cd) was established: diso(113Cd)/ ppm ¼ 169.71x þ 529.21, where x is the value associated with the sulfur atom in the chemical formula. The authors also commented on the chemical origins for the above relationship, stating that it was due “to metal p and d orbital contributions by the donation of electrons from the ligands to the metal outer p orbitals and by the backdonation of electrons from the metal p orbital to the ligands.”120 The authors also presented data supporting a correlation between elemental electronegativity values and diso(113Cd).

9.15.2.9.2

FexCoyNiz

Ternary Fe-Co-Ni alloys are being developed for their favorable magnetic properties and can be found in high density magnetic recording applications. Unfortunately, these materials typically have high manufacturing costs, thereby hindering development. Ramesh and co-workers developed and presented a low-cost co-precipitation chemical reduction technique to generate Co35Fe35Ni30 nanoparticles.121 The magnetic properties of these nanoparticles were assessed in part using 59Co IFNMR, with the resonance positions in the IFNMR spectrum being determined mainly by local hyperfine fields. The nanocrystalline nature of the alloy particles was supported by XRD and SEM experiments. The broad IFNMR spectrum was acquired at room temperature using an echo experiment, with the echo amplitude being plotted as a function of transmitter frequency in the range spanning 185–260 MHz at 1 MHz intervals. Relative to pure metallic nanoparticles of cobalt, the authors noted that the line width of the NMR spectrum for this ternary alloy was very broad (> 60 MHz, Fig. 35). The resulting broad pattern was deconvoluted into six major contributing local environments about the cobalt atom. The lowest hyperfine field (19.00 T; 192 MHz) was assigned to a cobalt with two nickel atoms in its first coordination sphere (according to XRD data, the system packs in an FCC fashion, and so there are 12 atoms in the first coordination sphere). The largest hyperfine field (24.35 T; 246 MHz) was assigned to a local environment with three iron atoms. Cobalt coordination environments between these two extremes were assigned to the intermediate regions in the spectrum. Using IFNMR, the authors proposed that each Ni atom in the cobalt first coordination sphere serves to reduce the hyperfine field by about 0.75 T, while each Fe atom produces an increase in the hyperfine field by roughly 1 T.

9.15.2.9.3

CoxCu1
x

Building upon their earlier work on granular binary alloys, Dhara et al. used internal field 59Co NMR experiments to elucidate the distribution of ferromagnetic cobalt atoms in CoxCu1
x alloys for x values of 0.10, 0.32, and 0.76.122 All 59Co IFNMR spectra were acquired at 4 K using a solid echo pulse sequence and frequency-stepped data acquisition in the frequency range of 190–230 MHz. For all three samples, the authors obtained rather complex 59Co IFNMR line shapes, but were quick to note that there was no strong domain wall signal, inferring that the samples were composed primarily of single magnetic domains. Assignment of the complex spectra was performed, and it was concluded that both FCC and HCP Co environments were present in all alloy samples. Further, peaks were classified as FCC/HCP Co environments where either one or two of the cobalt atoms in the first coordination sphere

Fig. 34 113Cd NMR spectra for different compositions of alloyed CdSe1
xSx nanoparticles in the solid state. The diameters of these nanoparticles are (A) 8.76  1.27 nm; (B) 7.49  1.09 nm; (C) 9.48  2.06 nm; (D) 9.39  1.71 nm. Reprinted with permission from Xing, B.; Ge, S.; Zhao, J.; Yang, H.; Song, J.; Geng, Y.; Qiao, Y.; Gu, L.; Han, P.; Ma, G. Alloyed Crystalline CdSe1
xSx Semiconductive NanomaterialsdA Solid State 113Cd NMR Study. ChemistryOpen 2020, 9, 1018–1026. DOI: 10.1002/open.202000216. Copyright 2020 The Authors and published by Wiley-VCH GmbH.

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Fig. 35 Deconvoluted NMR peaks obtained from 59Co IFNMR spectra measured at room temperature. Reprinted from Reddy, G. S.; Manjunatha, M.; Ramesh, K. P. 59Co Internal Field NMR Analysis of Co35Fe35Ni30 Alloy Synthesized Via Novel Low Cost Chemical Reduction Technique. J. Phys. Chem. Solids 2021, 148, 109703. DOI: 10.1016/j.jpcs.2020.109703. Copyright 2021, with permission from Elsevier.

were replaced by Cu atoms. Earlier XRD and electron microscopy studies on these samples were not able to detect the HCP phase. It was reasoned that the XRD/microscopy experiments might have probed mainly the FCC outer regions and were relatively insensitive probes of the core. The authors thus revised a prior model associated with these systems, and the new model placed ferromagnetic cobalt clusters in the core of the particles, with a shell region, where for each cobalt atom, one or more cobalt atoms in the first coordination sphere have been replaced by copper.

9.15.2.10 Doped/Lithiated nanoparticles 9.15.2.10.1 Carbon-doped MgB2

The discovery that pristine MgB2 was a type-II superconductor (Tc ¼ 39 K)123 heralded a vast array of studies on the material, as well as numerous MgB2-containing derivatives. One method of improving the properties (i.e., critical fields and critical-current density) of MgB2 involves doping with a carbon source, such as SiC, although there is not a consensus as to why such doping improves these properties. To clarify the mechanism by which carbon improves these properties and to establish the location of 13C in the lattice, Bounds et al. used solid-state 11B and 13C NMR experiments on carbon-doped MgB2 nanoparticles in both the normal and superconducting states.124 Carbon doping was done using chemical vapor deposition with 99% enriched 13C2-ethylene gas, and hence all carbon-doped MgB2 samples were enriched in the NMR-active 13C nuclide. Using powder XRD and magnetic susceptibility 13 C0.05. At room temperature, several measurements, the nanoparticle sample composition was established as approximately MgB1.95 11 NMR experiments were performed (using B0 ¼ 9.4 or 14.1 T), including: (i) B MQMAS; (ii) 11B and 13C MAS; and (iii) 13C-13C double-quantum recoupling. Experiments at cryogenic temperatures were performed under static (i.e., non-spinning) conditions at 13 C0.05 was dominated by a peak at 95 ppm with no B0 ¼ 4.7 or 8.5 T. At room temperature, the 11B MAS NMR spectrum of MgB1.95 evidence of oxidation to B2O3. Compared to MgB2, there appeared to be a second low-intensity peak at a lower chemical shift value, but this was not clearly resolved. The 13C MAS NMR spectrum was composed of a single resolved carbon site at a shift of 200 ppm. 13 C0.05 demonstrated that the 11B environments were less ordered than in pristine Boron-11 MQMAS NMR experiments on MgB1.95 11 MgB2, and a second B peak at 70 ppm was assigned to B4C. The 13C-13C double-quantum NMR experiments did not yield any signal after ca. 60,000 scans, which the authors reasoned meant that the 13C sites were isolated. At cryogenic temperatures (5 K– 80 K), the authors observed signal broadening at both 13C and 11B sites as the temperature decreased (Fig. 36). In addition to the broadening effects, it was clear that the 11B sites experienced a significant shift in their resonance frequency at B0 ¼ 4.7 T, which was attributed to the Meissner effect. On top of these trends, the authors also observed, for a given fixed B0, a decrease in the 11B and 13C shift value as the temperature was reduced, which was ascribed to Knight shift decay. As 11B environments were generally more affected when compared against 13C, this was taken as evidence that 11B were within the vortex field distribution, while 13C occupy the vortex cores. Spin-lattice relaxation measurements were performed for both 11B and 13C at 4.7 T and 8.5 T at various temperatures. Both nuclides deviated from Korringa’s law below the critical temperature with R < 1, which demonstrated that ferromagnetic correlations were present. Spin susceptibility measurements and results from ab initio calculations were presented, and when all the information was taken in concert, it was concluded that carbon substituted for boron 13 when generating MgB1.95 C0.05 and there was no support for models that involved defect formation.

9.15.2.10.2 Aluminum-doped MnO2

Wang and co-workers used in situ 23Na NMR experiments to study the intercalation/deintercalation of sodium ions (and associated degradation process) for aluminum-doped MnO2 nanoparticles that were being developed as battery electrodes.125 Relative to MnO2 nanoparticles that did not involve Al doping, Al-doped nanoparticles had a much greater specific capacitance and possessed excellent cycling stability. By recording the 23Na NMR spectra, the authors were able to resolve a narrow band, attributed to sodium cations in the electrolyte, and a much broader band, which was assigned to intercalated Naþ. It was observed that the broad band changed slightly as each cycle progressed, which the authors assigned to a fast structural change. On top of this was a slower change

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11 Fig. 36 NMR peak shapes of MgB13 B NMR spectra at fields of 8.5 and 4.7 T. (B) 13C NMR spectra at 1.95C0.05 as a function of temperature. (A) fields of 8.5 and 4.7 T. Adapted minimally from Bounds, R. W.; Pavarini, E.; Paolella, M.; Young, E.; Heinmaa, I.; Stern, R.; Carravetta, M. Study of 11 B and 13C NMR on Doped MgB2 in the Normal and in the Superconducting State. Phys. Rev. 2018, 97, 014509. DOI: 10.1103/PhysRevB.97.014509, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

in the average chemical shift of the broad band signal, which moved slightly to lower chemical shifts as the cycle number increased. Supported with data from other experimental techniques (XPS, cycling voltammetry, SEM, and HRTEM) the authors speculated that repeated Naþ intercalation/deintercalation may induce a pulverization process in the MnO2 nanoparticle electrode surface, and that doping with Al3þ somehow slows down this degradation pathway.

9.15.2.10.3 Lithiated Sn (LixSn) High capacity, safe, and portable energy storage solutions are very desirable, with a bewildering array of potential solutions being developed, although nearly all have certain caveats that hinder their widespread application. For example, due to several favorable properties, tin anodes are being developed as they can form stable intermetallic compounds with lithium. The drawback with this material is its severe capacity fade. Unfortunately, the mechanism that accompanies this capacity fade is not well described and therefore deriving potential remedies is problematic. Hence, Lopez et al. used operando 7Li NMR and ex situ 7Li MAS NMR experiments, coupled with pair distribution function (PDF) methods, to study the electrochemical lithiation and delithiation of tin nanoparticles.126 The derivative of the operando 7Li NMR data with respect to time was also taken to generate a derivative Operando (dOp) NMR spectrum.127 Over the course of one lithiation half-cycle, the authors observed the formation (and removal) of many different components, including: Li0 (removal only), Li2Sn5, Li2Sn3, LiSn, Li7Sn3, Li13Sn5, and Li7Sn2. During the initial stages of delithiation, a resonance at d(7Li)  16 ppm (labeled as D0 ) was observed to occur alongside a removal peak associated with the highly lithiated Li7Sn2 phase. As the line shape associated with the D0 phase was highly dissimilar to any phase observed upon lithiation, the authors took a conservative approach when assigning it, but made an initial assignment as a Li13Sn5 phase that possessed many lithium site vacancies. Using operando and ex situ 7Li NMR experiments, the authors observed that the intensity of this signal increased as a function of the cycle number (Fig. 37). As the number of cycles increased, the 7Li NMR peak associated with Li0 dendrites was progressively lower in intensity after complete delithiation. As such, the authors stated that lithium appeared to become trapped in the D0 phase on progressive cycling. Using PDF data, it was found that a model corresponding to a vacancy-rich Li7
zSn3 phase (85.7%) and a LiSn phase (14.3%) yielded the best fit to the data. Addition of phases such as Li13Sn5 and Li5Sn2 did not improve the agreement between the model and the PDF data. At the completion of each cycle, the number of 7Li nuclei in the Li7
zSn3 phase increased, and the cell capacity decreased. Further, although the 7Li NMR signal associated with a solid electrolyte interface grew rapidly during the first few cycles, it soon reached a nearly constant value and thus could not be fully responsible for the capacity fade. Capacity fade was found to only occur during delithiation and not during lithiation. It was concluded that the capacity fade was due to particles losing contact with the carbon-rich binder material. Surprisingly, the disconnected phases appeared to reconnect upon full lithiation.

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Fig. 37 (A) Operando 7Li NMR 2D spectra of 11 cycles of a Sn electrode cell at a sweep rate of 50 mV s
1. (B) Ex situ 7Li MAS NMR spectra of Sn samples cycled to D0 at a sweep rate of 50 mV s
1 after 2 (black), 9 (red), and 13 (blue) complete cycles, lithiated to 0.2 V and then delithiated to 0.58 V to form D0 . The MAS NMR of the cell at 2 cycles shows intense resonances at 42 and 32 ppm corresponding to the two non-exchanging crystallographic sites of LiSn, and a resonance at 15.8 ppm corresponding to the D0 . As more cycles are performed, a decrease in the intensity of the LiSn resonance and an increase in the intensity of the D0 resonance is observed. Republished with permission of the Royal Society of Chemistry from Lopez, J. L. L.; Grandinetti, P. J.; Co, A. C. Phase Transformations and Capacity Fade Mechanism in LixSn Nanoparticle Electrodes Revealed by Operando 7Li NMR. J. Mater. Chem. A 2019, 7, 10781–10794. DOI: 10.1039/C9TA03345A. Copyright 2019 with permission conveyed through Copyright Clearance Center, Inc.

9.15.2.10.4 Doped a-NaYF4

Developing on pioneering studies involving nanophase NaYF4,128–130 Augustine and co-workers used wide line 19F and 23Na NMR experiments to probe various local environments in NaYF4 nanoparticles doped with Yb3þ and Er3þ.131 These materials have potential applications in areas that require long-lasting light emission at specific wavelengths. Although bulk characterization of these materials can be easily performed using alternative methods, the authors selected 19F NMR experiments to elucidate the local structure and/or distributions of the trivalent lanthanide atoms. Due to the paramagnetic nature of the samples, the 19F NMR data were acquired under static conditions over a very broad frequency range, spanning 350–375 MHz, and using an applied magnetic field of 9.4 T. In addition to collecting 19F NMR spectra, 19F T1 values were measured. While broad 19F NMR spectra were expected, the authors found that the 19F NMR line width of their a-NaY0.8Er0.2F4 sample was at least 66,450 ppm (Fig. 38). To isolate the various contributions to the 19F spin-lattice relaxation rates, the following equation was used: 1 1 ¼ þ RYb x þ REr y þ RYbYb x2 þ RErEr y2 þ RYbEr xy T1 T1dia where the first term on the right-hand side of the equation is meant to capture the spin-lattice relaxation in the absence of any paramagnetic dopant atoms and spin diffusion. The x and y parameters correspond to the mol % of added Yb3þ and Er3þ, respectively. All R-containing parameters in the above equation were determined by fitting different sets of experimental data using a least-squares approach. As such, wide line 19F NMR experiments served as a sensitive probe of both dopant ion identity and concentration. Discussion was provided to support a Yb3þ-Er3þ interaction at high doping levels, and absence of 19F-19F spin diffusion due to paramagnetic quenching. Sodium-23 solid-state NMR spectra were found to be generally insensitive to both dopant identity and concentrations, but there was a correlation between dopant concentrations and the 23Na T1 values.

9.15.3

NMR of nanocomposites, nanocrystalline, and nano-size materials

9.15.3.1

Nanocomposites

9.15.3.1.1

TiO2-SiO2

To motivate their study on TiO2-SiO2 core-shell nanocomposites, Masion and co-workers noted that it is quite common for sunscreen formulations to include TiO2 as the UV filter material.132 Relative to organic UV filters, the inorganic material is viewed as superior when it comes to potential human and environmental health concerns. However, this does not infer that TiO2 is benign, and the titania particles in the formulations need to be coated with aluminum- or silicon-based materials to enhance product safety. The authors thus studied the stability and aging properties of commercial TiO2-SiO2 nanocomposite samples under simulated

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Fig. 38 Wide line 19F NMR spectra for a-NaY0.7Yb0.3F4 (A), a-NaY0.97Er0.03F4 (B), and a-NaY0.8Er0.2F4 (C). Reprinted with permission from Martin, M. N.; Newman, T.; Zhang, M.; Sun, L. D.; Yan, C. H.; Liu, G. Y.; Augustine, M. P. Using NMR Relaxometry to Probe Yb3þ-Er3þ Interactions in Highly Doped Nanocrystalline NaYF4 Nanostructures. J. Phys. Chem. C 2019, 123, 10–16. DOI: 10.1021/acs.jpcc.8b07553. Copyright 2019, American Chemical Society.

freshwater and seawater conditions. In particular, the authors used single-pulse MAS, CP/MAS, and DNP-enhanced CP/MAS 29Si NMR experiments to probe the silicon environments in the protective SiO2 shell before and after aging. EDX experiments were also used during the study and elucidated a SiO2 layer thickness of 3.6  0.3 nm in pristine samples. Likewise on a pristine sample, a single-pulse 29Si MAS NMR experiment found that about 80% of the 29Si NMR signal could be attributed to core region Q4 environments, with about 20% being assigned to surface environments (i.e., Q2, Q3, etc.). The authors lamented that this single-pulse NMR experiment required 2.5 days of spectrometer time (B0 ¼ 9.4 T) and was not of sufficient signal-to-noise to permit additional analysis. To remedy this, and to selectively probe the silica surface, DNP-enhanced 1H / 29Si CP/MAS NMR experiments were used. In the resulting DNP-enhanced 29Si NMR spectrum, Q2 and Q3 environments were easily resolved, as was an additional peak at d(29Si) ¼
82.6 ppm. Interestingly, this additional peak was assigned entirely to Si-O-Ti environments, which would denote that the shell was strongly attached to the core. While certainly plausible, this assignment is also possibly surprising when noting the highly surface-selective nature of the experiment and considering that EDX measurements on pristine samples demonstrated a 3.6 nm shell thickness. Upon aging in simulated freshwater and saltwater environments for 96 h, inductively coupled plasma atomic emission spectroscopy (ICP-AES) experiments found that nearly all of the SiO2 protective layer was lost in both environments. These findings were largely confirmed using DNP-enhanced 29Si CP/MAS NMR experiments, as a very large fraction of the silicon surface environments were absent after aging (Fig. 39). In addition, 29Si NMR experiments were able to discern differences between samples aged in simulated freshwater versus those aged in simulated seawater. For the freshwater-aged sample, the peak assigned earlier to Si-O-Ti linkages was maintained to a significant extent, while all environments were strongly reduced for the seawater-aged sample. As the Si-O-Ti linkages were retained in the freshwater-aged sample, the authors argued that the degradation mechanism must have been (so-called) outside-in and did not involve delamination. For the seawater-aged sample, it was clear that silica dissolution was near complete and did not spare these more stable linkages, although a mechanism was not put forward. The authors concluded that as sunscreens are typically on the body for only a few hours, direct harm to the body would be limited. However, as the silica layers were largely absent after a mere 4 days, there is a potential for negative environmental effects against several types of biota.

9.15.3.1.2

Au/Al nanocomposite

Kislyuk et al. used a variety of NMR experiments (1H, 13C, 27Al, and 35Cl), along with EPR measurements, to track the synthesis of Au/Al nanosystems.133 The 35Cl NMR experiments, including variable temperature measurements, were used to establish the

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Fig. 39 Normalized DNP-enhanced 29Si CP/MAS solid-state NMR spectra of the pristine and aged TiO2-SiO2 nanocomposites (green: pristine material; red: freshwater aged; blue: seawater aged). Inset: comparison between the DNP-enhanced 29Si CP/MAS spectra (black traces) and the standard 29Si CP/MAS spectra (brown/red traces, magnified four times) for the TiO2-SiO2 nanocomposites aged in freshwater and seawater. Reproduced from Slomberg, D. L.; Catalano, R.; Ziarelli, F.; Viel, S.; Bartolomei, V.; Labille, J.; Masion, A. Aqueous Aging of a Silica Coated TiO2 UV Filter Used in Sunscreens: Investigations at the Molecular Scale With Dynamic Nuclear Polarization NMR. RSC Adv. 2020, 10, 8266–8274. DOI: 10.1039/D0RA00595A, with permission from the Royal Society of Chemistry. Copyright 2020.

importance of the chloride anion in directing aspects of the nanocomposite synthesis. From this, it was also found that a temperature range spanning 310–325 K was likely most appropriate for the synthesis of the Au/Al nanocomposite. Aluminum-27 NMR measurements provided evidence that the initial chemical environments of the Al3þ prior to adding the reducing agents (tannin and citrate) were eliminated over the course of the synthesis, and a new environment, attributed to an aluminum polymer oxide, was created. EPR data provided evidence that the reduction of the Au3þ precursor ions to create the gold core was incomplete, as Au2þ and Auþ environments were observed in addition to Au0.

9.15.3.1.3

Cobalt-containing nanoparticles on multi-walled carbon nanotubes

By decorating the surfaces of multi-walled carbon nanotubes (MWCNTs) with cobalt nanoparticles, materials with new properties can be generated and applied in areas as diverse as energy storage, catalysis, and drug delivery. Various Co/MWCNT nanocomposites were studied by Kazakova et al. using powder XRD, HRTEM, and 59Co IFNMR spectroscopy.134 The HRTEM experiments were able to demonstrate that when the MWCNTs were pretreated with nitric acid, the Co nanoparticles were generally located inside the MWCNT pores, and when this pretreatment was not carried out, the Co nanoparticles were exclusively on the outsides of the MWCNTs. For three of the pretreated samples, 59Co IFNMR experiments were used to determine the Co phase (for example, FCC or HCP) and whether the 59Co was in a single-domain or multi-domain particle. Although the line shapes were not wellresolved, it was reported that for each sample, its 59Co IFNMR spectrum could be explained as being generated from five different 59 Co environments. Irrespective of the sample, a maximum in the signal intensity was observed at approximately 216.5 MHz, which was assigned to FCC Co in single-domain particles. Three of the higher-frequency bands ( 219,  221.5, and  224 MHz) were attributed to HCP cobalt with a large magnetic anisotropy. The relatively weak band centered at  213.5 MHz was explained as being from FCC 59Co in multi-domain particles. For Co nanoparticles on MWCNTs with average diameters of 7.2 and 9.4 nm, the associated 59Co IFNMR spectra were rather similar when compared against the analogous 59Co NMR spectrum for cobalt nanoparticles on MWCNTs with an average diameter of 18.6 nm. In the latter case, there was a larger presence of FCC Co within multidomain particles.

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In addition to the study above, many of the same authors studied CaO-supported Co and CoFe2 nanoparticle catalysts that were used in the synthesis of MWCNTs.135 As before, a variety of characterization techniques were used (such as TEM and XRD), including 59Co IFNMR experiments. The 59Co IFNMR spectra of the activated CoFe2 nanoparticle catalysts spanned a very large region of the frequency domain (200–320 MHz), and although there was only modest resolution, the spectrum could be understood to arise from 59Co in FCC cobalt domains, in FCC cobalt domain walls, in disordered Co/Fe alloys that were Co-rich, in an ordered Co-Fe phase, and in Co/Fe alloys that were Fe-rich. By considering the signal intensities within certain spectral ranges, the most commonly observed 59Co environment was that of the ordered Co-Fe phase. Using 59Co IFNMR experiments, the authors also characterized how this phase structure evolved as a function of the catalyst activation time and proposed a multistage activation mechanism for the reaction.

9.15.3.1.4

Hydroxyapatite/reduced graphene oxide

As it has numerous application areas (energy storage, sensing, etc.) and is biocompatible, Rajesh et al. were motivated to study the interactions between nanoscale hydroxyapatite (nanoHAP) and reduced graphene oxide (rGO).136 The authors characterized nanoHAP and rGO samples both individually, and when each component was present in the nanocomposite. Proton and 31P MAS NMR experiments were performed and the results discussed alongside a variety of probe/force microscopy observations. From the 1H NMR data, both precursor materials appeared to have adsorbed H2O molecules (d(1H)  4.6–4.9 ppm), although these broad signals were drastically reduced upon nanocomposite formation. To probe specifically 31P nuclei close to a proton source, 1H / 31P CP/MAS NMR experiments were carried out on nanoHAP and the nanocomposite. A signal at d(31P)  2.6 ppm was attributed to interior PO43
groups and was seen to increase upon formation of the composite, while the signal at d(31P)  2.3 ppm, denoted as arising from surface PO43
groups, was seen to decrease. This could be qualitatively explained by the loss of a surface proton source upon nanocomposite formation. Consistent with this notion, a 31P peak at 0.8 ppm, assigned to protonated POxH
groups, was observed in nanoHAP, but was not observed in the composite. Based on prior work by many of the same authors,137 it was concluded that the POxH
groups from the nanoHAP interact with epoxy carbon atoms of the rGO.

9.15.3.2 9.15.3.2.1

Nanocrystalline inorganic compounds Cobalt

The particle morphology and phase content (i.e., FCC or HCP) of cobalt nanoaggregates as a function of the solvent used during synthesis was studied by Sahoo and co-workers using several methods, including 59Co IFNMR.138 Samples were prepared using either glycerol, ethylene glycol, or ethanol as the solvent, leading to samples CoGL1, CoEG2, and CoET3, respectively. Powder XRD data were analyzed using Scherrer’s equation, which allowed the average size of the crystalline domains to be determined. Cobalt-59 IFNMR experiments were conducted on all samples at both 77 K and room temperature, and several overlapping signals were detected. By carefully deconvoluting these peaks, the authors were able to assign different regions of the 59Co IFNMR spectrum to aspects of structure. This included 59Co at grain boundaries, 59Co in an FCC phase (either within the domain or at the domain wall), and 59Co in an HCP phase (either in the domain or at the domain wall). These five different environments were observed across all samples at both experimental measurement temperatures, but there was significant variation in the relative intensities. As such, it was concluded that the use of different solvents during synthesis can tailor the morphology and (FCC/HCP) phase content of these cobalt nanoaggregates, which also allows for variation in the resulting magnetic properties.

9.15.3.2.2

Sodium sulfide (Na2S)

In an effort to develop alternatives to lithium battery materials, Bensch et al. synthesized the layered compound Ni2P2S6.139 Various properties, such as the reversible capacity, were established, and it was demonstrated that sodium uptake upon discharge led to a reduction of the Ni2þ species to Ni0 and the formation of a new Na4P2S6 phase. Further increases in sodium content were found to produce nanocrystalline Na2S. Evidence for the nanocrystalline phase was provided in part by the observation of a strong 23Na NMR signal centered at 36 ppm, which was noted as being in accordance with prior reports. This finding was supported by XRD data and pair distribution function analyses. The authors concluded that the following chemical reaction could be responsible for the process: Ni2 P2 S6 þ 12 Naþ þ 12 e
/2 Ni þ 2 P þ 6 Na2 S

9.15.3.2.3

CaF2 nanocrystals in glass ceramics

Glasses doped with rare-earth ions, such as Er3þ, have an array of potential applications, including in bioimaging and temperature sensing. Some of the materials chosen to host these rare-earth ions, such as PbF2, are not environmentally friendly. Calcium fluoride is a relatively benign optical material that is highly compatible with rare-earth ions, and there is some evidence that the formation of CaF2 nanocrystals in the product materials leads to better optical properties for certain applications. Ren and co-workers used a variety of solid-state NMR methods to characterize the local environment in glass ceramics that contained CaF2 nanocrystals.140 Starting with a glass precursor of composition 55SiO2–15Al2O3–10CaO–20CaF2, the authors found that heating it to temperatures of 700  C and above generated a cubic CaF2 phase (verified using XRD). By analyzing the diffraction peak widths using the Scherrer equation, the authors estimated the sizes of the nanocrystalline phases produced and found them to range from 9.3 to 19.1 nm. This

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estimate was broadly consistent with TEM spectra. Using 19F MAS NMR experiments, the authors were able to comment on how the fluoride anions in the precursor glass re-organized at high temperature to form the nanocrystals. Unsurprisingly, a significant fraction of the F
came from ions bound to calcium in the precursor glass, but by using additional 27Al MAS and 19F{27Al} Rotational Echo Adiabatic Passage DOuble Resonance (REAPDOR)141,142 NMR data, it was also reasonably clear that a significant amount of fluoride came from Ca-F-Al environments in the precursor. This latter finding was only true when relatively low amounts of Al2O3 were in the precursor glass (< 20 mol%), as higher amounts suppressed the formation of nanocrystalline CaF2. The authors then probed how doping with a rare-earth ion (La3þ, which served as a diamagnetic proxy for paramagnetic Er3þ) modified the structures of the precursor glass and the product glass ceramic. Using 19F MAS NMR data collected from a precursor sample, an additional peak at roughly
40 ppm was attributed to F-La linkages. Aluminum-27 MAS NMR spectra displayed a drop in the amount of Al(V) and Al(VI) environments, suggesting that the new F-La bonds were coming at the expense of F-Al linkages. Upon heating glass precursor samples to 750  C, the authors found that a sample doped with 2 mol% La2O3 greatly reduced the formation of nanocrystalline CaF2, and when doped with 5 mol% La2O3 (sample 5La) this critical phase was essentially eliminated. Thankfully, heating at higher temperatures (850  C) for longer periods of time recovered the nanocrystalline CaF2 phase. Importantly, the authors found that the newly formed F-La linkages in the precursor was not a F
source for the resulting nanocrystalline CaF2 phase (Fig. 40), although upconversion luminescence measurements established that rare-earth ions entered the CaF2 phase to some extent. The authors also made several important findings regarding the structural evolution of the other glass components (including the acquisition of 139La NMR spectra), but these will not be detailed here as they are out of scope.

9.15.3.2.4

LaF3

Vogel and co-workers prepared samples of nanocrystalline LaF3 sheets of different thicknesses (6 and 18 nm) and characterized them using several methods (SEM, powder XRD, and low-temperature argon adsorption), including 19F MAS NMR experiments.143 Both nanocrystalline samples were found to have the tysonite crystal structure, but differed in terms of their morphology. Unsurprisingly, relative to bulk LaF3, both nanocrystalline samples possessed broadened 19F NMR line shapes. Interestingly, both samples also possessed a new broad spectral feature, which was integrated and found to contain about 4% of the 19F spins. It was speculated that the new signal corresponded to LaF2OH, LaF(OH)2 or (HF)n(H2O)m, and that whatever the identity of the compound, it was located at the LaF3 nanocrystal surface. As each nanocrystalline sample had a unique morphology and surface area, it was reasonably speculated that the fluoride ion dynamics would be different. To probe this, the authors selected 19F static field gradient (SFG) NMR experiments at an applied magnetic field of 3 T and temperatures as high as 800 K. For all temperatures considered, the diffusion coefficient for the 6 nm sample exceeded that of the 18 nm sample by 1–2 orders of magnitude. Relative to bulk LaF3, the activation barriers associated with the process were greatly reduced for each nanocrystalline sample (Ea(bulk LaF3) ¼ 1.2 eV, Ea(6 nm) ¼ 0.23 eV, Ea(18 nm) ¼ 0.76 eV).

Fig. 40 (A) 19F MAS NMR spectra of 5La glass heated at 850  C for different times (2, 5, and 12 h). The asterisks denote spinning sidebands. (B) Evolution of F species in 5La glass during the CaF2 crystallization. Reprinted with permission from Zhang, X.; Hu, L.; Ren, J. Transparent Aluminosilicate Oxyfluoride Glass Ceramics Containing Upconversion Luminescent CaF2 Nanocrystals: Glass-to-Crystal Structural Evolution Studied by the Advanced Solid-State NMR Spectroscopy. J. Phys. Chem. C 2020, 124, 1594–1608. DOI: 10.1021/acs.jpcc.9b10433. Copyright 2020, American Chemical Society.

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9.15.3.2.5

Cs2ZrX6 (X ¼ Cl, Br)

At the time of writing, metal halide perovskites are being intensively studied due to their very good performance in various optoelectronic devices and their ease of fabrication. The general form of this class of material is ABX3 (A ¼ cation; B ¼ metal cation, in many cases Pb2þ; X ¼ halide), but when B ¼ Pb2þ, there arise many issues related to toxicity, and as such there is interest in generating lead-free perovskites. Abfalterer et al. presented the colloidal synthesis and optical properties for two lead-free vacancy-ordered double perovskites with the form Cs2ZrX6 (X ¼ Cl, Br).144 A variety of solid-state MAS NMR experiments were performed on either Cs2ZrCl6 bulk powders, or dried Cs2ZrCl6 nanocrystal samples, including 1H / 13C and 1H / 15N CP/MAS NMR experiments (both under DNP surface-enhanced NMR spectroscopy (SENS) conditions), and 133Cs MAS NMR experiments (both with and without DNP SENS enhancement) (Fig. 41), which probed the local environments of both the nanocrystals, as well as the stabilizing ligand. The 133Cs NMR experiments on nanocrystal samples provided evidence that the cesium cations at the surface of the crystals were disordered. This finding was supported by surface-enhanced DNP 1H / 133Cs NMR data, which are known to selectively enhance the signals associated with the surface. The NMR experiments using other probe nuclei demonstrated that the nanocrystals were likely capped with oleate ligands, although there was some ambiguity as to whether the signal was associated with surface-

Fig. 41 Solid-state MAS NMR characterization of Cs2ZrCl6 samples. (A) 133Cs echo-detected spectrum of Cs2ZrCl6 bulk powders (at 10 kHz MAS) and a Bloch decay (single pulse) spectrum of Cs2ZrCl6 nanocrystals (at 12 kHz MAS) at 16.4 T and room temperature. The spectra are vertically offset for clarity. The arrow indicates a broad signal corresponding to surface Csþ sites of the Cs2ZrCl6 nanocrystals. (B) 1H-13C CP spectrum of the carbon-containing species in a Cs2ZrCl6 nanocrystal sample recorded under DNP SENS conditions. The asterisks (*) indicate spinning sidebands. (C) 1 15 H- N CP spectrum recorded under DNP SENS conditions evidencing the presence of highly disordered –NH3þ environments in a Cs2ZrCl6 nanocrystal sample. (D) Schematic of an oleate-capped Cs2ZrCl6 nanocrystal. Reproduced without modification from Abfalterer, A.; Shamsi, J.; Kubicki, D. J.; Savory, C. N.; Xiao, J.; Divitini, G.; Li, W.; Macpherson, S.; Gałkowski, K.; MacManus-Driscoll, J. L.; Scanlon, D. O.; Stranks, S. D. Colloidal Synthesis and Optical Properties of Perovskite-Inspired Cesium Zirconium Halide Nanocrystals. ACS Mater. Lett. 2020, 2, 1644–1652. DOI: 10.1021/acsmaterialslett.0c00393, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

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bound ligands or was simply due to free ligands that were dispersed in the frozen sample matrix. Several additional characterization methods, such as powder XRD and TEM, rounded out the very thorough characterization of these samples, while additional tools were used to probe the optical properties (e.g., UV-Vis, photoluminescence).

9.15.3.2.6

Al-doped yttrium-iron garnet (Y3AlxFe5
xO12)

9.15.3.2.7

Apatites

Due to its ferrimagnetic nature, yttrium iron garnet (YIG) materials are considered for applications as microwave filters and acoustic transmitters. Sahoo and co-workers used powder XRD, 57Fe IFNMR experiments, and Mössbauer spectroscopy to study a wide variety of aluminum-doped YIG samples in terms of their structural and magnetic properties.145 In addition to probing the variation in properties as a function of Al doping, the authors were also interested in ascertaining if these properties (as well as the phase purity) would be influenced by the solution combustion approach chosen to synthesize these materials. Data from powder XRD experiments established that, so long as a sufficiently high calcination temperature was used (1200  C), the aluminum-doped YIG samples were phase pure. Further, it was seen that the Al atoms substituted for iron at both the tetrahedral and octahedral sites, but with a strong preference for the former. The 57Fe Mössbauer experiments clearly showed a reduction in the hyperfine field at the iron with increasing Al content, followed by a collapse in the ferrimagnetic nature at Al doping equal to approximately x ¼ 1.6 (i.e., YAl1.6Fe3.4O12). Room temperature 57Fe IFNMR experiments were noted as being very insensitive, with only 3 (out of 12) samples producing a detectible signal. These also corresponded to the samples with the lowest relative amounts of Al doping. For undoped YIG, two 57Fe NMR peaks were detected at room temperature: one at  54.4 MHz, which was assigned to 57Fe nuclei at tetrahedral sites; and a second at  67.1 MHz, which was attributed to 57Fe nuclei at octahedral sites. With increased Al doping, a small decrease in the resonance frequencies was noted (corresponding to reductions in the hyperfine fields), as well as a more drastic decrease in the signal intensities. At T ¼ 77 K; however, the authors were able to collect 57Fe IFNMR spectra for all samples, except the one with the greatest Al content (Fig. 42). However, even at this lower temperature, the authors observed a clear degradation in the magnetic properties of Al-doped YIG samples with increasing Al content. At x ¼ 1.8, the samples were now in a paramagnetic phase, and no IFNMR signal could be detected.

Lee et al. characterized samples of nanocrystalline carbonated hydroxyapatite (Ca10(PO4)6(OH)2, C-HAp), which is an important calcium-based biomaterial present in bones and teeth, by way of solid-state 1H and 43Ca MAS NMR experiments.146 Experimental sensitivity was typically enhanced with DNP. The use of DNP is nearly essential for 43Ca, as this nuclide possesses a very low natural abundance (0.14%), small gyromagnetic ratio, and is spin-7/2. Importantly, the authors recorded 2D correlation experiments at natural isotopic abundance in 43Ca and could differentiate between core and surface 43Ca sites in a C-HAp nanoparticle sample. To estimate the sensitivity gains afforded by DNP, the authors performed 1H MAS NMR experiments at  100 K and 9.4 T on a pure powder of C-HAp, and using a C-HAp sample that had been modified using incipient wetness impregnation and the biradical polarizing agent AMUPol. The absolute sensitivity ratio was measured to be 35, which translates into a substantial experimental time savings of 352. Additional 1H MAS NMR experiments using the pure powder and AMUPol-impregnated sample highlighted that almost all protons of the C-HAp nanoparticles participated in the DNP process, although interestingly, the 1H spin baths of the solvent and OH
groups were not strongly coupled. The authors also demonstrated the superior sensitivity of the DNP-enhanced 43 Ca NMR experiment (even when using an inefficient CP step to transfer the DNP-enhanced 1H polarization to the 43Ca nuclei),

Fig. 42 The IFNMR spectra of the Y3AlxFe5
xO12 powder samples measured at 77 K. Adapted minimally from Mahour, L. N.; Manjunatha, M.; Choudhary, H. K.; Kumar, R.; Anupama, A. V.; Damle, R.; Ramesh, K. P.; Sahoo, B. Structural and Magnetic Properties of Al-Doped Yttrium Iron Garnet Ceramics: 57Fe Internal Field NMR and Mossbauer Spectroscopy Study. J. Alloys Compd. 2019, 773, 612–622. DOI: 10.1016/ j.jallcom.2018.09.213. Copyright 2019, with permission from Elsevier.

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relative to an experiment that used only DFS to enhance the 43Ca NMR signal. Encouraged by the sensitivity associated with the DNP-enhanced 1D 1H / 43Ca CP/MAS NMR experiment, the authors attempted 2D 1H-13C and 1H-43Ca HETCOR NMR experiments, which for the latter experiment, was believed to be the first ever that did not employ 43Ca labeling (Fig. 43). Intriguingly, the authors observed two correlation peaks in the 1H-43Ca HETCOR NMR spectrum. The correlation peak associated with d(1H)  0 ppm was assigned to 43Ca sites nearby hydroxyl groups within the columnar channels of the nanoparticles. However, the strongest correlation peak in the 1H-43Ca HETCOR NMR spectrum was due to 1H environments with d(1H)  3 ppm and was assigned to hydroxyl groups at the particle surface (i.e., OH
groups interacting with surface water via H-bonds, or surface-adsorbed solvent molecules), or chelating glycerol molecules. The authors were similarly able to distinguish core and surface environments using 1H-13C HETCOR NMR data.

9.15.3.3

Nanocrystalline cellulose

As part of their excellent review of the solid-state NMR of nanocrystals, Buntkowsky and co-workers reviewed nanocrystalline cellulose and cellulose-based materials,10 and so the interested reader is referred there for further details. There is also literature on nanocrystalline cellulose films,148 which is not covered in detail here. Although nanocrystalline cellulose possesses a range of favorable properties (e.g., highly abundant, biodegradable, high surface area, etc.) that make the material well-suited in several applications, there are associated stability concerns. To improve thermal stability under melt processing conditions, Spinella et al. modified the surfaces of cellulose nanocrystals with PMMA.149 Both unmodified and PMMA-modified nanocrystalline cellulose were characterized using several techniques, including solid-state 13C CP/MAS NMR. The authors produced different samples of PMMA-modified nanocrystalline cellulose by varying the initiator and the weight percent of grafted PMMA. Carbon-13 NMR resonances typical of the Ib polymorph of cellulose, PMMA, and amorphous regions associated with cellulose nanocrystals, were observed. Relative to 13C CP/MAS NMR spectra of the precursor materials, in the PMMA-modified material, a new low intensity peak at d(13C) ¼ 95 ppm was observed. This peak was speculated as being from a structural modification in an amorphous cellulose domain, presumably due to PMMA grafting, however the authors noted that further confirmatory experiments would be required. In addition to thermal stability issues, nanocrystalline cellulose also has somewhat poor compatibility with organic solvents and polymer matrices. To combat this, Yoo and Youngblood used a green one-pot synthetic approach to generate surface-

Fig. 43 MAS-DNP HETCOR spectra of C-Hap. Both were recorded at 100 K, 9.4 T, and using a MAS frequency of 8.5 kHz. (A) 1H-13C HETCOR spectrum with associated 13C skyline projection (top), recorded using a CP contact time of 7 ms. (B) 1H-43Ca HETCOR spectrum with associated 43Ca (top) and 1H (right) skyline projections, recorded using a CP contact time of 3 ms. Both spectra were recorded using FSLG homonuclear decoupling during the indirect acquisition and SPINAL-64 heteronuclear decoupling147 during the direct acquisition. Also shown (far right, purple) is the DNPenhanced 1H Hahn-echo MAS NMR spectrum, for comparison. Reproduced without modification from Lee, D.; Leroy, C.; Crevant, C.; BonhommeCoury, L.; Babonneau, F.; Laurencin, D.; Bonhomme, C.; De Paëpe, G. Interfacial Ca2þ Environments in Nanocrystalline Apatites Revealed by Dynamic Nuclear Polarization Enhanced 43Ca NMR Spectroscopy. Nat. Commun. 2017, 8, 14104. DOI: 10.1038/ncomms14104, and under the terms of the Creative Commons CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

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hydrophobized cellulose nanocrystals.150 To mitigate some of the environmental impacts associated with the synthesis of these modified cellulose nanocrystals, the authors selected an aqueous syrup of DL-lactic acid to undergo oligomerization, thus producing polylactic acid (PLA) oligomers. The PLA oligomers in turn served as solvent and precursor to generate PLA-grafted cellulose nanocrystals (CNC-g-PLA). Once grafted to PLA, the resulting material could be reacted easily with a variety of fatty acids (hexanoic acid, oleic acid, linseed oil, etc.), thereby completing the hydrophobization process. To characterize their materials, the authors selected 13 C CP/MAS NMR spectroscopy, along with a variety of other methods (FTIR, elemental analysis, powder XRD). The authors observed components of cellulose that were either crystalline or amorphous in nature. The authors also used the 13C NMR data to estimate the average degree of polymerization for the grafted PLA, which ranged from 2.1 to 8.2 across the different fatty acid-containing CNC-g-PLA samples, as well as the degree of surface substitution.

9.15.3.4

Nano-sized metal-organics

Due to the exceedingly large variety of compounds in this class, it is noted that the following is not at all comprehensive. Rather, a couple of recent literature examples are highlighted.

9.15.3.4.1

Nano-sized metal-organic frameworks (nanoMOFs)

The knowledge that certain metal-organic frameworks (MOFs) can host drug molecules is hardly new, but a somewhat more recent discovery is that nano-sized MOFs (nanoMOFs) are also potentially suitable for the task. While the iron-based nanoMOF MIL100(Fe) might be optimal for drug carrying applications, the metal linkers are paramagnetic, which presents a challenge for analysis using most traditional solid-state NMR approaches. As such, Martineau-Corcos and co-workers set their aims on the structurally similar, yet diamagnetic, nanoMIL-100(Al).151 A series of room temperature NMR experiments (1H, 27Al, 31P, 1H-27Al, 27Al-31P, and 31P-31P) under MAS conditions were selected to probe the loading of adenosine triphosphate (ATP) in a nanoMOF that had been subsequently capped with cyclodextrin-phosphate (CD-P) (Fig. 44). Aluminum-27 MAS NMR experiments were not terribly sensitive to drug loading or cyclodextrin coating, but two-dimensional 27 Al MQMAS NMR experiments provided evidence of modest structural changes at the surface and in the nanoMOF pores. Attempts to resolve interactions between CD-P and the nanoMOF surface via 1H-27Al MAS NMR experiments were unsuccessful due to the large signal associated with the MOF linker protons, but fortunately a dipolar-based 27Al{31P} HMQC experiment was fruitful. In particular, the 27Al{31P} NMR data featured an aluminum peak at
5 ppm, which is consistent with hexacoordinated aluminum near a phosphate and suggests the presence of an Al-O-P fragment. A moiety of this sort would likely confer additional in vivo stability. Phosphorus-31 MAS NMR data partially resolved the ATP and CD-P signals when they were interacting with the nanoMOF, and 31P DQ/SQ NMR experiments showed that the triphosphates of ATP are largely preserved after loading and interact strongly with the framework aluminum sites.

9.15.3.4.2

Au25(SR)18 clusters

In the hopes of better understanding the ferromagnetism observed in gold nanoparticles, Tong and co-workers studied several members of the Au25(SR)18 cluster family (R ¼ C5H11, C6H13, C8H17).152 Both electrically neutral, as well as monoanionic Au25(SR)18 clusters were generated and probed while in deuterated benzene or toluene using 13C NMR experiments. The anionic systems were necessary to study as they provided a diamagnetic reference, while the neutral systems served as models of ferromagnetic Au nanoparticles. Focus was placed on the carbon atoms directly bound to the sulfur atoms at the so-called in and out locations. The interested reader is referred to the article for further details concerning this notation, but in brief, carbon atoms that were referred to as 1in and 1out would be the most proximate carbon atoms relative to the gold core. As such, these carbon atoms would be expected to be the most sensitive 13C probes of the magnetic structure associated with the core of the electrically neutral compounds. Due to the symmetry of the cluster, 12 equivalent ligands are associated with the in position, while 6 equivalent ligands are in the out positions. This naturally produces a 2:1 ratio and immediately informs if a given carbon was in or out. To enhance the contrast between the 1in/1out and 2in/2out carbon atoms on each ligand, additional 13C NMR experiments were performed on samples where the C1 carbon was enriched to 10% (the natural abundance of 13C is approximately 1.1%). By comparing the 13C NMR spectra of the anionic and neutral forms, the authors stated they had observed a large Knight shift for the 1in carbon ( 65 ppm). Substantially smaller Knight shifts (order of a few ppm) were observed for the 1out carbon and all other carbon atoms, and did not depend strongly on the identity of R. The authors found correlations between the measured 13C Knight shifts and: (i) the distance from the anchoring sulfur atom and, (ii) the unpaired spin density calculated using a restricted open shell hybrid DFT approach (Fig. 45). Additional 13C NMR experiments at variable temperatures provided evidence that the 13C Knight shifts associated with the 1in/ 1out sites displayed Curie-Weiss-type behavior and that the magnetism was ferrimagnetic in nature for these clusters.

9.15.4

Summary remarks

The utility of NMR experiments to resolve atomic-level details regarding the structures and dynamics of nanoparticles, nanocomposites, and nanocrystalline materials (perhaps collectively also thought of as being within “nanomaterials”) was hopefully made clear by the preceding discussions. This is due to the large array of nuclei that may be used as probes (e.g., 1H, 7Li, 13C, 15N, 17O, 19F,

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NH2 O

O

HO P O P O OH

OH

N

O P O OH

O

N

N

Cyclodextrin-phosphate

N

ATP

Cross the large window

OH OH

Too bulky to cross the windows

~9Å

OH2 L

L

O O Al

OO

O O O

O

Al HO

Al

OO

O

O

L L O

L 2 phosphate molecules 2 H 2O

O O

O

Al

L

O Al

OO

O

L L O

O phosphate

L

HO O

O O Al

OO

HO OH2

L

OH O

HO O

OH O

Fig. 44 Upper panel: Schematic representation of the highly porous MIL-100(Al) nanoparticles loaded with ATP and then coated with CD-P. Bottom panel: close up of Al trimers coordinated to trimesate ligands (L). Two molecules of bound water can be replaced either by phosphates from the drug or by phosphate grafted on the cyclodextrin molecules. Phosphates bound to CD can only access sites located close to the external MOF surface. CD dimensions: cage 6–6.5 Å, external diameter 15.4 Å, height 8 Å. ATP molecule has about a 7 Å radius. Reproduced without modification from Porcino, M.; Christodoulou, I.; Le Vuong, M. D.; Gref, R.; Martineau-Corcos, C. New Insights on the Supramolecular Structure of Highly Porous CoreShell Drug Nanocarriers Using Solid-State NMR Spectroscopy. RSC Adv. 2019, 9, 32472–32475. DOI: 10.1039/C9RA07383C, and under the terms of the Creative Commons CC BY 3.0 license (https://creativecommons.org/licenses/by/3.0/).

Fig. 45 Exponential fits of Knight shifts of carbon atoms in (A) “in” ligands and (B) “out” ligands for Au25(SC8H17)18, Au25(SC6H13)18 and Au25(SC5H11)18 as a function of distance from the sulfur atom. (Decay constants: b ¼ 1.70 and 0.41 Å
1 for “in” and “out”, respectively). Insets: experimental Knight shifts vs. spin density from DFT calculations. The straight lines are linear fits with R2 ¼ 0.99 and 0.94. Reprinted with permission from Zheng, R.; Bevacqua, G. M.; Young, N. R.; Allison, T. C.; Tong, Y. J. Site-Dependent Spin Delocalization and Evidence of Ferrimagnetism in Atomically Precise Au25(SR)180 Clusters as Seen by Solution 13C NMR Spectroscopy. J. Phys. Chem. A 2020, 124, 7464–7469. DOI: 10.1021/acs.jpca.0c02915. Copyright 2020, American Chemical Society.

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Al, 29Si, 57Fe, 59Co, 61Ni, 77Se, 105Pd, 111/113Cd, 133Cs, 207Pb, etc.), advances in experimental techniques (including surfacesensitive dynamic nuclear polarization, multidimensional pulse sequences, and the miniaturization of the samples needed for magic-angle spinning NMR experiments), and substantial development in the computational tools available to the average researcher. Perhaps most importantly, much of this research is motivated by the very attractive properties that many of these nanoparticles/nanomaterials have. It is also emphasized that NMR methods are generally seen to complement the various other characterization techniques. It might be envisioned that this complementary nature will become increasingly appreciated in the near future, which could lead to substantial advances in understanding the structures of nanoparticles, their dynamic interactions with the environment, and how these aforementioned aspects evolve across the lifespan of the nanoparticle/nanomaterial in whatever the particular application happens to be.

Acknowledgments The authors would like to thank Ms. Honey Patel and Ms. Azalea Upson for helpful comments during the preparation of this account. C.M.W. acknowledges the Faculty of Science at the University of Regina for student support and a startup grant. N.K. would like to thank the Department of Chemistry and Biochemistry for a Teaching Assistantship and Graduate Scholarship.

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17O Distances. J. Am. Chem. Soc. 1998, 120, 4406–4409. https://doi.org/10.1021/ja9732183. 143. Gulina, L. B.; Schikora, M.; Privalov, A. F.; Weigler, M.; Tolstoy, V. P.; Murin, I. V.; Vogel, M. Influence of Morphology of LaF3 Nano-Crystals on Fluorine Dynamics Studied by NMR Diffusometry. Appl. Magn. Reson. 2019, 50, 579–588. https://doi.org/10.1007/s00723-018-1077-z. 144. Abfalterer, A.; Shamsi, J.; Kubicki, D. J.; Savory, C. N.; Xiao, J.; Divitini, G.; Li, W.; Macpherson, S.; Gałkowski, K.; MacManus-Driscoll, J. L.; Scanlon, D. O.; Stranks, S. D. Colloidal Synthesis and Optical Properties of Perovskite-Inspired Cesium Zirconium Halide Nanocrystals. ACS Mater. Lett. 2020, 2, 1644–1652. https://doi.org/10.1021/ acsmaterialslett.0c00393. 145. Mahour, L. N.; Manjunatha, M.; Choudhary, H. K.; Kumar, R.; Anupama, A. V.; Damle, R.; Ramesh, K. P.; Sahoo, B. Structural and Magnetic Properties of Al-Doped Yttrium Iron Garnet Ceramics: 57Fe Internal Field NMR and Mossbauer Spectroscopy Study. J. Alloys Compd. 2019, 773, 612–622. https://doi.org/10.1016/j.jallcom.2018.09.213. 146. Lee, D.; Leroy, C.; Crevant, C.; Bonhomme-Coury, L.; Babonneau, F.; Laurencin, D.; Bonhomme, C.; De Paëpe, G. Interfacial Ca2þ Environments in Nanocrystalline Apatites Revealed by Dynamic Nuclear Polarization Enhanced 43Ca NMR Spectroscopy. Nat. Commun. 2017, 8, 14104. https://doi.org/10.1038/ncomms14104. 147. Fung, B. M.; Khitrin, A. K.; Ermolaev, K. An Improved Broadband Decoupling Sequence for Liquid Crystals and Solids. J. Magn. Reson. 2000, 142, 97–101. https://doi.org/ 10.1006/jmre.1999.1896. 148. Ohashi, R.; Michal, C. A.; Hamad, W. Y.; Nguyen, T.-D.; Mizuno, M.; MacLachlan, M. J. Solid-State 23Na NMR Spectroscopy Studies of Ordered and Disordered Cellulose Nanocrystal Films. Solid State Nucl. Magn. Reson. 2019, 97, 31–39. https://doi.org/10.1016/j.ssnmr.2018.12.001. 149. Spinella, S.; Samuel, C.; Raquez, J.-M.; McCallum, S. A.; Gross, R.; Dubois, P. Green and Efficient Synthesis of Dispersible Cellulose Nanocrystals in Biobased Polyesters for Engineering Applications. ACS Sustain. Chem. Eng. 2016, 4, 2517–2527. https://doi.org/10.1021/acssuschemeng.5b01611. 150. Yoo, Y.; Youngblood, J. P. Green One-Pot Synthesis of Surface Hydrophobized Cellulose Nanocrystals in Aqueous Medium. ACS Sustain. Chem. Eng. 2016, 4, 3927–3938. https://doi.org/10.1021/acssuschemeng.6b00781. 151. Porcino, M.; Christodoulou, I.; Le Vuong, M. D.; Gref, R.; Martineau-Corcos, C. New Insights on the Supramolecular Structure of Highly Porous Core-Shell Drug Nanocarriers Using Solid-State NMR Spectroscopy. RSC Adv. 2019, 9, 32472–32475. https://doi.org/10.1039/C9RA07383C. 152. Zheng, R.; Bevacqua, G. M.; Young, N. R.; Allison, T. C.; Tong, Y. J. Site-Dependent Spin Delocalization and Evidence of Ferrimagnetism in Atomically Precise Au25(SR)180 Clusters as Seen by Solution 13C NMR Spectroscopy. J. Phys. Chem. A 2020, 124, 7464–7469. https://doi.org/10.1021/acs.jpca.0c02915.

9.16

NMR studies of 2D and pseudo-2D systems

Kristopher J. Harris, Department of Chemistry, Louisiana Tech University, Ruston, LA, United States © 2023 Elsevier Ltd. All rights reserved.

9.16.1 9.16.1.1 9.16.1.2 9.16.1.3 9.16.1.4 9.16.1.5 9.16.1.6 9.16.2 References

Introduction Carbon nanotubes Graphene 2D phosphorus sheets Hexagonal boron nitride sheets Silicate sheets MXenes Conclusions

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Abstract 2D materials analogous to graphene, as well as pseudo-2D materials which are just a few atomic layers thick, offer materials scientists fascinating new properties. Perhaps even more interesting, most materials in this class include the ability to tune behavior via chemical modification. These materials are always produced as a range of sheet sizes and edge termination types (and sometimes also a range of surface termination groups). A range of site types within the sheet itself (i.e., distant from edges) is also often observed, due to differing termination groups, sheet sizes, number and type of dopants/vacancies, perforations, etc. These material qualities pose an extremely difficult challenge for any characterization method, and quite often, solids NMR spectroscopy has been the only means of determining many of the chemical features of these 2D and pseudo-2D materials. This review summarizes NMR spectroscopic studies on graphene and carbon nanotubes and some of their modified or doped analogs, phosphorenes, hexagonal boron nitride sheets, silicate sheets, and MXenes. The text focusses on the chemical information obtained from the NMR spectroscopy measurements in an effort to inform the reader about what type of results may be available on future materials. A particular effort is made to relay the types of NMR techniques that are connected to each type of chemical measurement, to assist readers in planning future studies.

9.16.1

Introduction

The development of nanoparticles provided a paradigm shift in chemistry when it was discovered that properties can change drastically when particle sizes enter the nanoscopic scale. Understandably, there has been a similar interest in developing materials that are nanoscopically thin and investigating their properties. In fact, a material such as monolayer graphene can theoretically be well under a nanometer in thickness. Many interesting properties have been discovered in 2D materials and in pseudo-2D materials (those just a few layers thick), though this review will focus mostly on the characterization of the materials rather than their chemical behavior and discusses only those properties that are directly related to the NMR measurements. There are many difficult questions that arise when synthesizing and characterizing 2D and pseudo-2D materials. These materials are most often produced as powders containing disordered arrays of many different sheet sizes with tortuously connected voids that may contain many side products, impurities, and solvents. Such disordered materials are quite difficult to characterize using traditional methods, leaving researchers to piece together knowledge of the chemical structures using a variety of methods that provide incomplete information. As shown below, NMR spectroscopy often provides the most important pieces of the puzzle because of its unrivaled resolution in differentiating chemical sites, its unique ability to correlate signals from different sites and/or different nuclei, and the unparalleled detail it provides into atomic-level motion. In addition to assigning the chemical structures of the sheets and characterizing trapped impurities, it is perhaps less well recognized that one must also determine the termination moieties at the edges of the sheets. As shown below, NMR spectroscopy is unmatched in its ability to address this difficult question. This review is organized by the class of material presented first, and then by spectroscopic method within each class. Graphene and its rolled-up cousindthe carbon nanotubedare covered first, followed by phosphorene, boron nitride sheets, then thin silicate sheets and finally the new class of material known as MXenes. There are a few themes that are common to the study of many of these materials: (i) conductive samples often require pulverizing to small particle sizes and/or dilution with an electrically insulating material (ii) dynamic nuclear polarization is useful in this arena to boost the signals of rare sites or difficult to work with nuclides (iii) anisotropic bulk magnetic susceptibilities may cause troublesome line broadening and frequency shifts1 (iv) whenever possible, correlation experiments should be performed to correctly determine whether multiple peaks are from the same local region (v) separation of the broad signals from the many different sites and impurities may be aided by filtering or modifying the signals with correlation experiments, T1 or T2 filters, different isotopic labeling or temperature variation. Some other themes

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are applicable only within one class of material or across only a few, so these are discussed below. This article is not intended as an exhaustive review on the chemistry of each class or material or every measurement done, but rather attempts to cover the range of techniques that have been used and are helpful for addressing the questions unique to 2D and pseudo-2D materials.

9.16.1.1

Carbon nanotubes

Perhaps the most well-known, and also perhaps the most conceptually simple, nanoscale material is graphene sheets and the closely related nanotubes. These materials have many applications2 and have also caught the public eyedparticularly after carbon nanotubes were mentioned in the 1996 Nobel prize for fullerenes, and the 2010 Nobel prize was awarded for the shockingly unusual electronic properties of graphene. The wide range of chemical diversity in carbon nanotubes and in the derivatives of graphene has driven researchers to look for answers using SSNMR. Carbon nanotubes, CNTs, can be obtained with a wide range of different lengths as well as different widths/diameters. For any given diameter of CNT, there are often multiple distinct forms because there are different ways to arrange the C6 hexagons with respect to the long axis of the tube.2 This gives rise to the so-called (n,m) notation for CNTs, and the impact on the properties can be profound, such as chiral vs. achiral or semi-conducting vs. metallic.2 CNTs may be synthesized both as single-walled versions, SWCNTs, or nested together as multi-walled versions, MWCNTs. In general, a synthetic method produces a range of CNT lengths, diameters, (n,m) structures, and layer numbers; complicating characterization efforts.2 13 C SSNMR spectroscopy of carbon nanotubes has been successfully applied in a number of cases.3 The spectra are somewhat difficult to acquire given that large linewidths are caused by one or more of: (i) the extreme diversity of site types in what are typically intractable mixtures of CNT types and sizes, (ii) T2 effects from metallic electrons, (iii) nearest-neighbor effects from bundles of tubes or solvents used for dispersal, (iv) anisotropic bulk magnetic susceptibility1 effects from the “all interface” nature of these materials, and (v) insufficiently fast rotation of the CNTs or CNT bundles for solution NMR experiments. Because of these large linewidths, the lack of 1H for cross polarization (CP), and the fact that T1 values can be in the tens of seconds, many studies employ isotopic 13C labeling to obtain reasonable signal to noise ratios. Soon after the 1991 discovery of CNTs, 13C NMR was employed for their investigation.4,5 It is very important to realize that only incredibly broad spectra are produced unless care is taken to remove any strongly magnetic catalysts used to grow the tubes.6 Once this is done, much narrower peaks are obtainable, though these are often still much wider than those seen in molecular systems, e.g., the linewidth at half height (LWHH) in the first study7 of a SWNT mixture cleaned of metal impurities was circa 50 ppm. With careful control of sample preparation LWHHs as low as 10–15 ppm have been obtained in some cases, likely due to smaller distributions of sizes/types of CNTs, fewer defects, and perhaps more regular stacking of the CNTs. Isotropic chemical shifts are in line with what is expected for sp2 carbons, at circa 120 ppm.7–15 Among the most notable conclusions is that it has proven possible to distinguish metallic from semi-conducting SWNTs in mixtures by assigning enhanced relaxation rates in portions of the sample to the conduction electrons in metallic SWNTs.16 It was later shown that 13C chemical shifts could be used to distinguish the two classes of SWNTs using solution NMR spectroscopy first,8 and then, surprisingly, with higher resolution using solids NMR spectroscopy, see Fig. 1.8,9 The increase in resolution in the latter report is most likely due to improvements in chemical rather than spectroscopic methods (i.e., from a smaller range of chemical environments). The two 13C chemical shift studies found a ca. 20 ppm differences between the two types of tube in solution, but only 1–5 ppm when in the solid state. These shift changes are not in exact agreement, but they are of the same order and one would not expect them to match perfectly given interactions with the polymer used9 or to differences in the exact size and (n,m) type of CNTs present. The chemical shift change from an insulator to a metal, i.e., the Knight shift, is more typically on the order of thousands of ppm, but this small change agrees with theoretical estimates which show a relatively small amount of conduction electron density at the carbon nucleus in the metallic form of CNTs.11,17,18 Because the effect of conduction electrons on the 13C nuclear-spin relaxation has a different temperature dependence than other relaxation mechanisms, such studies can provide further useful insight into the electronic character of CNTs.6,7,14,16,19 It has also been demonstrated that the chemical shifts depend quite heavily on the diameter of the nanotubes, as isotropic shifts were found to systematically track the tube diameter, covering a range of approximately 30 ppm see Fig. 2.10 Extremely careful separation work has also proven both metallic and semi-conducting SWCNTs display a similar dependence of chemical shift on the tube’s diameter.21 For a theoretical discussion of the relationship between chemical shifts and CNT structures, see the review by Autschbach and Zurek.18 While CNTs are relatively unreactive materials, methods for decorating the surfaces in a variety of ways have been devised, with one common intermediate being formed from the reaction with elemental fluorine. The inorganic carbon/fluorine nanotubes display some complicated chemistry that has been investigated using NMR spectroscopy. Due to the same reasons as in pure CNTs, the peaks are also generally quite broad. For example, the first 19F NMR study of fluorinated nanotubes used a solution sample and yielded a peak at
175 ppm that was deemed too broad to include in the manuscript.22 On the other hand, 13C NMR spectroscopy of solid fluorinated-SWNTs proved feasible, and a typical CNT sp2 carbon signal at 128 ppm could be observed in addition to one at 83.5 ppm from sp3 carbon atoms at the attachment points.23 Theoretical calculations suggest that the 19F chemical shift tensor may provide a more sensitive measure of the tube diameter and electronic structure than 13C NMR, but experimental verification is lacking at this point in time.24,25 One of the most interesting aspects of nanomaterials such as CNTs is that they can accept guest intercalants. Guests may be inside the bore of the tubes if they are uncapped, in addition to the likely occupancy of the interstitial channels between the tubes. Doping tubes with alkali metals has received considerable interest due to the applications in electronics and in rechargeable lithium

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Fig. 1 Carbon-13 MAS NMR spectra of single-walled nanotubes. Sample A is 94% metallic, 6% semi-conducting. Samples B–E are prepared with decreasing amounts of metallic nanotubes (76%, 60%, 34%, 8%). Sample A and E are indicative of nearly pure metallic CNTs and nearly pure nonmetallic CNTs, with chemical shifts of 123 and 122 ppm, respectively. Reprinted with permission from Engtrakul, C.; Davis, M. F.; Mistry, K.; Larsen, B. A.; Dillon, A. C.; Heben, M. J.; Blackburn, J. L. Solid-State 13C NMR Assignment of Carbon Resonances on Metallic and Semiconducting Single-Walled Carbon Nanotubes. J. Am. Chem. Soc. 2010, 132 (29), 9956–9957. Copyright 2010 American Chemical Society.

Fig. 2 Experimental and calculated carbon-13 NMR chemical shifts versus inverse tube diameter for CNTs. Experimental results (with error ranges) shown as circles, and results of two different ab initio calculation methods plotted as square10 and triangle20 markers. Reprinted with permission from Abou-Hamad, E.; Babaa, M. R.; Bouhrara, M.; Kim, Y.; Saih, Y.; Dennler, S.; Mauri, F.; Basset, J. M.; Goze-Bac, C.; Wågberg, T. Structural Properties of Carbon Nanotubes Derived from 13C NMR. Phys. Rev. B - Condens. Matter Mater. Phys. 2011, 84, 165,417. Copyright 2011 American Physical Society.

batteries. In this case, the alkali-metal’s valence electrons are donated, though perhaps not completely, to the bands of the CNT. 13C NMR spectra are a measure of this new electronic state of the CNT, and NMR spectra of the guest alkali metal are also possible. Saturation with Li intercalants yielded a 10 ppm increase in the isotropic 13C chemical shift.13 In cesium- and rubidium-doped SWNTs, an essentially identical result was obtained at low loadings.26 However, at high cesium loadings, it was found that the

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13

C isotropic shifts are sensitive enough to reflect the type of interstitial site, as two different peaks can be observed: a similar peak at 5–10 ppm higher frequency than the pristine tubes, but another at 19 ppm lower frequency.26 Following up on the 13C spectra with 133 Cs MAS NMR spectra of the various doping levels provides even more insight into the two types of guest sites: the 133Cs shift corresponding to the high-frequency 13C peak is indicative of a Cs atom that has essentially donated its entire valence electron to the nanotube and is therefore (somewhat) distant from the tube. The 133Cs shift corresponding to the low-frequency SWNT 13 C shift, however, displays a significant Knight-shifted value of 2700 ppm;27 which clearly indicates Cs atoms sitting very close to the nanotube surface and sharing the density from the valence electron it has partially donated into a metallic band, see Fig. 3.26,27 Another interesting feature in the 13C spectra of alkali-doped CNTs is the very large reduction of the span of the 13C CS tensor: by ca. 200 ppm in lithiated SWCNTs13 and similar numbers in Cs-doped SWNTs.27 A wide variety of organic moieties attached to CNTs have been investigated using NMR spectroscopy,13,15,28–34 while they are not the subject of this inorganic review, it should be noted that the peaks of these pendant groups are subject to broadening and therefore weakening as “residues approach the aromatic walls” and not all signals were observable.35 However, recording the peaks of more distant sites can at times enable the use of more traditional liquids-NMR experiments that are very information rich.35–38 The metallic or semiconductor band structure of CNTs provides them with the potential to act as catalytic surfaces similar to pure metals, and recent research trends have included attempting to modify the band structure to improve catalytic behavior. And, since NMR chemical shifts are intrinsically linked to electronic structure, they are a natural way to track such changes. Recently, CNTs codoped with both phosphorus (1.1%) and nitrogen (6.2%) atoms were investigated via 31P SSNMR spectroscopy.39 The 31P signal under MAS that is hundreds of ppm broad is centered at 250 ppm is indicative of P atoms directly incorporated into the tube walls (see also Section 9.16.1.2). Filtration experiments with 1H demonstrate the absence of any nearby protons, further demonstrating the reaction of the triphenylphosphine starting material, and transformation into a pure carbon/phosphorus (and nitrogen) tube.

9.16.1.2

Graphene

The monolayer sheets of sp2-hybridized carbon that are now commonly known as graphene were theorized about but not experimentally available for study until Novoselov and Geim demonstrated a facile method for obtaining small quantities of it in a very pure form.40 The physics community was extremely excited about the unusual electronic structure because it leads to quasiparticles that behave like completely massless electrons, and thereby allows the study of relativistic properties on a bench top rather than in exotic high-energy experiments.40 Chemists were likewise enthused about this new nanostructural platform with a wide range of novel electronic properties. Applications from catalysts to sensors have quickly filled the literature with studies of graphene and modified graphenes.

Fig. 3 Cesium-133 MAS NMR spectra of CNTs reduced with cesium metal vapor. The ratio of Cs to C atoms, X, is shown at the left of each spectrum. For an s-shell atom like Csþ, a large shift such as the 2700 ppm shown here can only be explained by the presence of a Knight shift produced by the conduction electrons created by the reduction of the nanotubes. Reprinted from Abou-Hamad, E.; Goze-Bac, C.; Nitze, F.; Schmid, M.; Aznar, R.; Mehring, M.; Wågberg, T. Electronic Properties of Cs-Intercalated Single-Walled Carbon Nanotubes Derived from Nuclear Magnetic Resonance. New J. Phys. 2011, 13, 053045. © Deutsche Physikalische Gesellschaft. Reproduced by permission of IOP Publishing. CC BY-NC-SA.

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Since graphene is not so different from a CNT that has been unwound, many of the same structural questions apply. In addition to there being a large range of possible sizes, there is also an analog of the multiwalled nanotubes: few-layer graphene. It is important to consider whether truly monolayer graphene is present, few-layer graphene, or flakes of material that contain so many sheets of graphene that they differ little from bulk graphite. Switching from CNTs to graphenes creates some entirely different considerations though, because if we imagine “unzipping” a CNT along its long axis, there must be some type of chemistry involved in terminating the sheet that a capped CNT does not require for stability. Mapping these terminations out and understanding them is certain to be important for controlling the exact electronic structure and capabilities of any finite-sized sheet of graphene. Furthermore, recalling that distinct CNT types are created when the tube’s long axis is at a different angle with respect to the fundamental hexagonal building block of sp2 carbon sheets demonstrates that the graphene sheets may also have distinct shapes of the termination edges. NMR spectroscopy appears to be an excellent method for characterizing these issues, though work is just beginning. The first 13C SSNMR attempt at observing graphene yielded a chemical shift of 117 ppm with an extremely broad LWHH of 30– 40 ppm, see Fig. 4.41 While the isotropic chemical shift is as expected for an sp2 carbon, and very similar to the CNT results above, the linewidth suggests that this is an unusual material. Elemental analysis showed significant amounts of oxygen remained from the graphene oxide starting material, as well as some nitrogen from the hydrazine reducing agent that was used to remove most of the oxygen. Evidently, some part of the complicated topology of epoxides and alcohols of graphene oxidedthese have been extensively mapped out with carbon-13 NMR42 spectroscopydmust have remained or converted to different oxides (peroxides are likely43 also present). Further, Raman spectroscopy showed a material that has many small domains of sp2 carbons. Since the topology of the material is not the extended flat sheet of idealized graphene, it appears to be important to distinguish between model graphene and the more complicated and disordered structure of reduced graphene oxide (RGO). Gao et al. studied RGO under successive reduction steps that lowered the oxygen content first to 19.4%, then to 12.7%, and finally to under 0.5% by weight. As the graphitic portion of the sheets grows, the isotropic 13C chemical shift of the peaks moves to low frequency: from 122 ppm, to 119 ppm, and finally to 105 ppm in the nearly fully reduced material.44 Perhaps counterintuitively, the 13C linewidths increased as the conversion to higher sp2 content proceeded, suggesting that it is not a varied speciation from residual oxygen content that dominates the line widths in the various RGO formulations. Interestingly, these 13C MAS NMR linewidths of ca. 30–40 ppm are very similar to the linewidth found in an earlier measurement of 350 nm thick layers of amorphous carbon formed via highly energetic deposition on silica wafers.45 There, both DFT calculations and thermal annealing experiments suggest that the largest factor responsible for the broad lines was a distribution of local bonding environments. The linewidth of the 13 C spectra of reduced graphene oxide may therefore be sensing that this RGO is a composite of small domains, there is a distribution of bonding types from the energetic formation reaction, or there is a non-flat sheet topology, in addition to the linewidth factors (i)–(iv) noted above in Section 9.16.1.1 for CNTs. While some of the interest in the fundamental electronic properties of graphene may require large graphene domains, other technological applications actually benefit from the disordered array of small graphitic domains in RGO,46 so it is important to develop an understanding of this material. Park et al. studied RGO using 99% isotopic 13C labeling of the starting material as well as 98% 15 N labeling of the hydrazine reducing agent.47 The tremendous signal boost that this provides made it possible to very accurately measure that the conversions of ketones at the edges of the sp2 sheets (either at external sheet edges or at perforation sites) that occur at ca. 190 ppm in graphene oxide44 are essentially completely removed.47 The double isotopic labeling made it possible to not only acquire extremely high-quality 13C and 15N MAS NMR spectra, but also to correlate 13C chemical shifts with proximal 15N nuclei via dipolar dephasing experiments. It was therefore possible to selectively observe 13C peaks at 140 and 157 ppm that are adjacent to a 15N site that resonates at 190 ppm; this 190 ppm 15N site itself being bonded directly to a 1H atom. In data sets of this type, i.e., connectivity information between sites with specific “fingerprint” chemical shifts in a disordered material, NMR spectroscopy certainly has no equal, and probably not even a rival. In RGO, the data points work together to describe the hydrazine reducing

Fig. 4 Carbon-13 MAS NMR spectra of graphene oxide (GO) as well as the deoxygenated (reduced) version of the material generated when attempting to chemically produce graphene from GO. Reprinted from Stankovich, S.; Dikin, D. A.; Piner, R. D.; Kohlhaas, K. A.; Kleinhammes, A.; Jia, Y.; Wu, Y.; Nguyen, S. B. T.; Ruoff, R. S. Synthesis of Graphene-Based Nanosheets via Chemical Reduction of Exfoliated Graphite Oxide. Carbon 2007, 45 (7), 1558–1565, with permission from Elsevier.

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agent as successfully removing much of the oxygen functionality while also converting some of the edge-terminating ketones into 5membered aromatic rings that incorporate both nitrogen atoms of the hydrazine reagent (i.e., pyrazole rings are created).47 Instead of hydrazine-reduction leading to partial N incorporation at sheet edges, it is also possible to include nitrogen as a base element in the formation of the graphene sheet. Such heteroatom dopants can shift the electronic band structure of graphene, and may impute beneficial catalytic properties. As above, correlation experiments that are unique to NMR spectroscopy were key to solving the chemical identity of the three types of nitrogen site.39 Without the ability to perform correlation experiments, highresolution XPS spectroscopy is not able to assign the three observed sites with the same specificity.39 Together, the NMR correlation experiments, empirical chemical shifts, and DFT calculations48 show: (i) pyridinic nitrogen atoms at sheet edges or perforations that place them beside protonated sheet terminating C-H or C-OH groups at 145.7 ppm, (ii) pyridinic nitrogen again at edges (or perforations) of the sheets, but this time at zigzag or armchair edges so that there are no adjacent protons needed for sheet termination, and (iii) three-coordinate planar nitrogen sites directly composing part of the graphene sheet at 220–375 ppm, see Fig. 5.39 The protons adjacent to pyridinic sites (i) can also be observed at 7.2 ppm, as can adsorbed water molecules at 0 and
2.7 ppm provided careful 1H background suppression or correlation techniques are used. It is also possible to introduce phosphorus into graphitic sheets. Matthews et al. demonstrated that many-layer graphene (5 mm thick) can successfully be doped with phosphorus.49 In this case, the heterogeneous material contains a significant amount of elemental phosphorus, some of which may be present between the graphitic sheets. The chemical shift of
521 ppm easily labels this as the white phosphorus polymer; though interestingly, a similar peak at
445 ppm tracks with the water content, suggesting that this peak represents a hydrate that is close in structure to white phosphorus’ tetrahedral building blocks. There are also significant phosphate impurities, though spectroscopically, their peaks can be removed from the 31P NMR spectrum through clever use of a Hahn echo employed as a T2 filter. Another polymorph of phosphorous was also observed: red phosphorus at 20 ppm. Two different types of phosphorus incorporated directly into the graphitic sheet were also observed as extremely broad peaks at 210 and 370 ppm, though it is difficult to estimate the percentage of the phosphorus atoms that are sheet dopants vs. those present in elemental or phosphate forms. Interestingly, Li atoms can be observed moving into this material when employing it as a battery cathode by using NMR spectroscopy, because LiP3 peaks begin appearing at
250 ppm for 31P and 7.6 ppm for 7Li. An alternative form of phosphorus-doped thin layer graphite has been studied by MacIntosh et al.39 The material observed there was closer to isolated graphene sheets than the thicker stacks interleaved with intercalants that was investigated by Matthews et al. Due to the much lower amount of intercalants, the total phosphorus content was much lower, at closer to 1%, though the exact amount incorporated as part of the sheets is difficult to quantitatively measure. Two batches were studied using 31P MAS NMR

Fig. 5 Top: 15N NMR spectra of nitrogen doped graphene nanosheets, demonstrating how 1H-15 N distance correlation spectroscopy, either via 1D CP experiments or 2D dipolar-excited HMQC experiments, can be used to better deconvolute the overlapping lineshape and provide peak assignments. Bottom: Assignment of measured 15N chemical shifts in doped graphene using NMR-derived distance constraints and quantumchemical calculations. Reprinted with permission from MacIntosh, A. R.; Jiang, G.; Zamani, P.; Song, Z.; Riese, A.; Harris, K. J.; Fu, X.; Chen, Z.; Sun, X.; Goward, G. R. Phosphorus and Nitrogen Centers in Doped Graphene and Carbon Nanotubes Analyzed through Solid-State NMR. J. Phys. Chem. C 2018, 122 (12), 6593–6601. Copyright 2018 American Chemical Society.

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spectroscopy, one with the oxygen more completely removed (0.03 atomic % residual oxygen) while the other was stopped just before full reduction (at 3.36%). At both oxygen contents, the broad 31P lineshape covers an extremely wide chemical shift range (see Fig. 6), that is similar to the line width observed in the study of Matthews et al.49 The chemical shifts, however, are distinct: the thinner sheet version appears at lower chemical shifts of 75 ppm for the lower oxygen content and 150 ppm for the higher;39 these are both somewhat different from the 210 and 370 ppm peaks seen for the thicker sheets.49 Given that: (i) differing chemical shifts are observed for these doped graphene nanosheets (and for doped nanotubes) and (ii) chemical shifts are by nature sensitive to a material’s band structure; NMR spectroscopy appears to be an excellent method to study attempts at modifying this property for catalytic or other purposes. Others have also found 13C NMR a useful tool to track the chemistry of different graphene formulations.50–53 It has been particularly useful in studying the attachment of modified pendant groups to the 2D surface. For example, organic linker groups attaching sulfonic-acid groups to graphene can be observed;51,52 and interestingly, high surface coverage leads to a “zippering up” action as the sheets are pulled together by the attractions between the pendant groups.51 One must always remember that it is not only the NMR peak positions, but also the lifetimes of those spin states that encodes chemical information. For example, Panich et al. were able to show that the manganese used for the formation of the graphene precursor remains present at low concentrations on the surface of the large graphene sheet by studying the effects of these paramagnetic ions on the 13C relaxation time constants.54 The large 13C linewidths in this class of materials is a significant hindrance to these studies, and has precluded the investigation of some samples. Historically, NMR studies of stationary samples often use echo trains to increase the signal-to-noise ratio through a chain of repeated observations in every scandthe so-called Carr-Purcell/Meiboom-Gill (CPMG) experiment.55,56 In the particular case of quadrupolar nuclei, NMR spectra include a lineshape contribution from the portion of the anisotropic quadrupolar interaction that cannot be averaged away by MAS, and may be extremely broad. In that case, the incorporation of CPMG echo trains to increase signal strengths greatly increased the scope of samples amenable to NMR spectroscopy through this hybrid QCPMG-MAS method.57,58 Along similar lines, spin-1/2 nuclei subject to large amounts of line broadening can be aided via the use CPMGMAS.56,59 While one wouldn’t generally think of carbon NMR spectroscopy as an arena in which line widths are the critical factor in determining the viability of an experiment, CPMG-MAS is a technique that should be considered. For example, a sample of just a few mg of graphene nanosheets produces a useful spectrum when observed using CPMG-MAS, whereas signal observation without it produces only a signal that is too weak to reliably separate from the noise,60 see Fig. 7.

9.16.1.3

2D phosphorus sheets

Phosphorus is in some ways analogous to carbon, as it can be prepared as several allotropes, one of which, black phosphorus or BP, is composed of infinite sheets of covalently linked atoms that are held together only by weak van der Waals forces. This similarity of BP and graphite extends onward to graphene, as similar exfoliation methods can be employed to produce thin flakes of phosphorene. Crucially though, a phosphorene sheet is a sort of corrugated wave such that its height is 2 atoms thick rather than the single-atom plane of graphene. The electronic structure of phosphorene does not provide massless electrons and their associated relativistic effects the way graphene’s does, but many of the other reasons for interest in graphene and its derivatives are mirrored in its phosphorus analog. In particular, the tunability of the band gap for electronic or catalytic purposes is an active area of research. The small 0.3 eV bandgap of bulk BP grows to 1.88 eV for a single phosphorene sheet,61 so pursuing different flake thicknesses or widths, or adding dopants or pendant groups are all interesting areas of research. Crucially, all these areas of synthetic research produce complicated structural, chemical, and electronic questions that NMR spectroscopy is likely to be helpful in answering.

Fig. 6 31P MAS NMR spectra of phosphorus atoms doped directly into graphene nanosheets and nanotubes. A significant change is observed in the 31P chemical shift for phosphorus sites within a graphene sheet (blue) vs. in a phosphorus/nitrogen co-doped carbon nanotube (red), demonstrating the sensitivity of NMR spectra of the dopants to the electronic structure of the atomically thin materials. Reprinted with permission from MacIntosh, A. R.; Jiang, G.; Zamani, P.; Song, Z.; Riese, A.; Harris, K. J.; Fu, X.; Chen, Z.; Sun, X.; Goward, G. R. Phosphorus and Nitrogen Centers in Doped Graphene and Carbon Nanotubes Analyzed through Solid-State NMR. J. Phys. Chem. C 2018, 122 (12), 6593–6601. Copyright 2018 American Chemical Society.

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Fig. 7 13C NMR spectra of graphene nanosheets collected using CPMG-MAS (top) versus that collected as a simple Bloch-decay spectrum. Note that it is only the tops of the “spikelets” of the CPMG-MAS spectrum that contain information on the linewidth given that their tops trace out what would be the lineshape of a spectrum collected (or processed) as single FIDs. Reprinted with permission from Harris, K. J.; Reeve, Z. E. M.; Wang, D.; Li, X.; Sun, X.; Goward, G. R. Electrochemical Changes in Lithium-Battery Electrodes Studied Using Li-7 NMR and Enhanced C-13 NMR of Graphene and Graphitic Carbons. Chem. Mater. 2015, 27 (9), 3299–3305. Copyright 2015 American Chemical Society.

The isotropic 31P chemical shift of bulk BP has been reported as 22.2 ppm (Fig. 8)62 and 17.5 ppm;63 anddperhaps surprisingly given the expected change in band gapdthe shift has not been observed to change significantly upon exfoliation. Chemical shifts of between 17.1 and 22.2 ppm have been reported for various preparations of BP flakes or exfoliated BP, including measurements of free-standing powders, suspensions in polymers or in solvents, admixtures with other nanomaterials, or with guest molecules on the surfaces.63–70 The thicknesses of the studied flakes likely varied even within each sample, but values down to 5 nm (ca. 8 sheets

Fig. 8 Phosphorus-31 MAS NMR spectrum of bulk black phosphorus. Inset shows the layered structure of black phosphorus and the absence of covalent bonding between the layers. This is analogous to graphite/graphene, apart from the layers of P being corrugated in the phosphorus system. Reprinted with permission from Lange, S.; Schmidt, P.; Nilges, T. Au3SnP7@Black Phosphorus: An Easy Access to Black Phosphorus. Inorg. Chem. 2007, 46 (10), 4028–4035. Copyright 2007 American Chemical Society.

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thick) have been reported in these NMR studies, so it is possible that 31P chemical shifts may begin to change once thickness of 2, 3, or 4 sheets are able to be studied, given that this is where theoretical calculations suggest the band gap begins to increase.70 The lineshape comparison of phosphorene versus other simple organophosphorus molecules is strikingly different from the analogous comparison of graphene versus other carbons. Graphene’s 13C signal is so broad that it difficult to observe, while phosphorene’s 31P signal is narrow and its lineshape well-resolved. As discussed in the preceding section, some of this difference may be due to the harsher chemical changes in the synthetic route, i.e., graphite /graphene oxide / graphene, but there is also another important consideration. The phosphorus site in BP appears to be in a higher symmetry environment, as the 31P chemical shift tensor has an anisotropy of only 13 ppm.64 Indeed, much of the linewidth is from 31P-31P dipolar interactions rather than the chemical shift.64 It is therefore also quite possible that the anisotropy in the bulk magnetic susceptibility is small, and therefore ABMS broadening effects are minimal in phosphorenes. One of the issues with attempts at utilizing phosphorenes for chemistry or devices is the moderately poor stability of thin BP flakes. The exact chemical composition of the breakdown products has been elucidated using solids NMR.64–69 Interestingly, surfactant coatings may improve the stability of BP flakes, and NMR spectra of the surfactant coatings collected from suspensions of BP flakes proves the strong interaction between the two.71 For example, 1H DOSY spectra of cetrimonium bromide (CTAB) molecules in a CTAB/BP suspension resolves the slowed diffusion rates of surfactant molecules adhering to the sheets, and demonstrates that the interaction strength keeps the same molecules attached to the surface throughout the duration of the experiment.71 Changes in the sign of the 1H NOE of suspensions in CTAB proves the surface binding via the greatly slowed molecular tumbling rate of bound vs. free surfactant molecules see Fig. 9.71 Suspension in a tetrabutylammonium hydroxide (TBAOH) surfactant demonstrated similar binding effects via the NOE, Fig. 9, but the residence lifetime was short enough that DOSY spectra do not distinguish separate diffusion constants for free vs. bound surfactant molecules.71

Fig. 9 1H NOESY NMR spectra of phosphorene in D2O with two surfactants present. The surfactant CTAB shown in e also depicts the peak assignments shown in the corresponding NOESY spectrum for this surfactant shown in c. Similarly, assignments for TBAOH surfactant shown on the structure in f label the peaks shown in spectrum d. The signs of the cross peaks with respect to the diagonal peaks provide the sign of the NOE and thereby verify the surfactant molecules have slowed tumbling from adhering to the surface of the phosphorene. Furthermore, NOE cross peaks between the head and tail groups of the large surfactant implies intermolecular NOEs and therefore multiple surfactant groups lying flat on the phosphorene surface. Reprinted with permission from Jain, R.; Singh, Y.; Cho, S. Y.; Sasikala, S. P.; Koo, S. H.; Narayan, R.; Jung, H. T.; Jung, Y.; Kim, S. O. Ambient Stabilization of Few Layer Phosphorene via Noncovalent Functionalization with Surfactants: Systematic 2D NMR Characterization in Aqueous Dispersion. Chem. Mater. 2019, 31 (8), 2786–2794. Copyright 2019 American Chemical Society.

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Hexagonal boron nitride sheets

The hexagonal form of boron nitride, h-BN, exists as stacks of infinite sheets in a structure that closely mimics graphene except that each hexagonal ring unit is composed of three N and three B atoms (Fig. 10). And, similar to graphene research, extensive efforts have gone into developing exfoliation and chemical modification methods. NMR spectroscopy has recently played an important role in elucidating the sheet-edge terminations in the exfoliated material. The first experimental insight into the chemistry of the edge groups came from solid-state 1H MAS NMR spectroscopy.72 Analyzing the 1H NMR spectra in conjunction with moleculardynamics simulations demonstrated the presence of -B-OH and -B-H and/or N-H moieties on the sheet edges. Evidently, these groups form from reactions with water to terminate the sheets as they are broken up into a suspension in the liquid. Further insight into the h-BN nanosheet edge termination sites came via Gervais et al. who were able to transfer polarization from protons at the edges of the stack of sheets in bulk h-BN crystals to 15N atoms at the edges73 (large crystals still must have some sort of edge terminations, though they may not be the same as those in the nano-flake versions). Since the desired signal was such a small fraction of the total sample, these authors had to employ isotopic 15N labeling. The proposed edge groups were later confirmed to be present on h-BN nanosheets themselves when Dorn et al. polarized the protons at the sheet’s edges using dynamic nuclear polarization (DNP),74 allowing signal collection at natural 15N abundance.75 In the nanosheets, four different 15N

Fig. 10 Solid-state DNP-MAS NMR spectroscopic study of h-BN nanosheets (h-BNNS). (A) Model structures used for calculations predicting the NMR parameters. Color coded rectangles/hexagons on the atomic sites label the site assignments in the spectral simulations in the other parts of the figure. (B) 11B spectrum of h-BNNS with site assignments used in spectral simulations shown in (C–E). (G) 2D 1H-14N dipolar-HMQC correlation spectrum, with total 14N projection and color-coded atomic site assignment shown in (H). (F) 1H-15N CP-MAS spectrum and color-coded atomic site assignments. Note that when comparing the 15N vs. 14N 1D traces (in F and H), there is a difference in the apparent resolution because the quadrupolar 14N nuclei are subject to not only the chemical shift but also the quadrupole-induced shift. Reprinted with permission from Dorn, R. W.; Ryan, M. J.; Kim, T.-H.; Goh, T. W.; Venkatesh, A.; Heintz, P. M.; Zhou, L.; Huang, W.; Rossini, A. J. Identifying the Molecular Edge Termination of Exfoliated Hexagonal Boron Nitride Nanosheets with Solid-State NMR Spectroscopy and Plane-Wave DFT Calculations. Chem. Mater. 2020, 32 (7), 3109–3121. Copyright 2020 American Chemical Society.

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sites were observed: the two lowest chemical-shift peaks could be tentatively assigned to proton-terminated edge sites (B2NH) using both empirical chemical shift data and plane-wave DFT calculations.75 Further confirmation that the two lowest-frequency 15N peaks are from edge B2NH sites came from proton-detected 14N spectroscopy.75 The 14N isotope is present at a much higher natural abundance (249  higher!), but 14N spectra are often extremely broad and difficult to acquire because this is a spin-1 isotope and therefore has no central ½ / H½ transition which would be unaffected by the quadrupole interaction to first order. However, using proton detection (and in this case, DNP for signal enhancement), it can be possible to acquire relatively high-resolution 14N spectra under MAS using the dipolar version of the heteronuclear multiple quantum coherence experiment, D-HMQC.76,77 There are two important advantages to this technique: (i) in addition to the chemical shift, the spectrum reflects the EFG through the lineshape and/or a quadrupole-induced shift, and (ii) the 2D correlation spectra can offer increased information content and/or resolution via the 1H chemical shifts. In this case, the EFG observed in the D-HMQC spectrum contributes to the site assignment through comparison with empirical data and planewave DFT calculations. Even further, direct evidence for the assignment type was found via quantitative analysis of the 1H-15N coherence-transfer dynamics in the D-HMQC experiment, as a transfer rate was consistent only with the internuclear distance of a direct, covalent NeH bond. Both of the low-frequency peaks in the 14N/15N spectra are therefore B2NH edge sites, and planewave DFT calculations assign one as an armchair site and the other as a zigzag sheet edge, via excellent agreement with the experimental measurements for both chemical shift and EFGs. The two higher chemical shift peaks can also be assigned from plane-wave DFT calculations as “internal,” i.e., NB3 type sites, that are near edges terminated with either zigzag or armchair edges. MAS NMR spectra of the (also quadrupolar) 11B nuclei are less resolved than are the 15N or 2D heteronuclear 14N-1H spectra.72,75 Here again, polarization transfer from protons at the sheet edges separates out the signals from the edge moieties from what would otherwise be the dominating signals of the center of the sheets.75 There are clearly spectral regions in spectra of both bulk and nanoflake versions of h-BN: a relatively sharp resonance near zero and a broad grouping of peaks at a slightly higher frequency (5– 30 ppm, depending on the applied field strength). The narrower peak (or overlapping peaks) must correspond to sites with a small CQ, and empirical data makes it clear that these must be four-coordinate sites. DFT calculations agree with this assignment, suggesting that one possible assignment is if the general trigonal planar BN3 site of the bulk reacts to form a sheet-termination site similar to BNO(OH2), where the O is a bridging oxygen to a second boron edge site. The broader grouping of peaks was not possible to separate, but variable-field data shows that the CQ’s must be in the 2.5–3 MHz range, and empirical data shows that these coupling constants and the chemical shifts are likely to reflect trigonal planar boron sites with oxygen or hydroxide overlapped with the BN3 sites of the sheets. DFT calculations bear out this type of assignment for the edge groups as well. Furthermore, 2D 11B-1H correlation spectra (collected using dipolar reverse insensitive nuclei enhancement by polarization transfer) show that these boron sites are connected to protons resonating at 7 ppm, consistent with R2BOH sheet-terminating sites.72,75 Finally, boron-boron transfer experiments using spin diffusion were enabled via DNP signal enhancement, and these strongly suggest that the signals assigned to edge groups are indeed edges of the sheets and not separate phases, as coherence transfer from the sheet edges to the bulk via this mechanism shows their close proximity.75 One of the most fascinating aspects about this class of material is, of course, how the electronic and chemical properties of a layer change when it is inside the 3D stack of the bulk material versus when a truly isolated layer is obtained. New insight into this behavior has recently been obtained using an incredibly inventive new class of NMR experiments in which an optically active nitrogen vacancy just below the surface of a small diamond is used to detect the magnetic field of nuclei in molecules place on the diamond’s surface. Lovchinsky et al. were able to use this technique to compare the local environment around nuclei in both monolayers and bilayers of h-BN vs. those observed in thicker flakes.78 In particular, the quadrupole coupling constant of 11 B nuclei was found to be 2.9221  0.0006 MHz in the bulk material, and are about 7.5 kHz smaller in the bilayer, and about 17 kHz smaller in the monolayer versus the bulk. Incredibly, the results on the monolayer are obtained from only around 900 nuclei, which is fantastically higher sensitivity than an NMR or DNP-NMR measurement. Perhaps the most interesting aspect of the experimental study is that DFT calculationsdwhich reproduce the experimental results reasonably welldshow that the change in quadrupole coupling is due to a reorganization of electron density near the boron atoms that occurs upon separation from neighboring sheets. This type of property change when moving to the 2D form demonstrates why researchers are so compelled to investigate such materials.

9.16.1.5

Silicate sheets

Silicates are an incredibly varied structural classdfrom minerals to glassesdwhose structure and chemical behavior have often been determined using NMR spectroscopy. Perhaps more commonly known are the 3D network silicates formed from [-O-Si-] linkages and their many technologically important relatives such as zeolites. However, the layered class of silicates known as phyllosilicates, in which the O-Si network is terminated in some fashion to form distinct slices of material, are widely seen in nature. Natural cleavage of layered silicates into sheets less than 100 nm thick are known and have been studied via NMR spectroscopy,79–83 and it is even possible to form sheets thinner than 1 nm when individual sheets are separated and supported by surfactants.83 Without 3D ordering, single-crystal diffraction methods cannot be used for structure solution of the sheets, suggesting a need for NMR spectroscopy. Interestingly, the layered silicates reported on thus far are extremely well-ordered planes, despite lacking 3D registry between the sheets. This translates to narrow 29Si NMR lineshapes that provide high sensitivity and excellent resolution. Accordingly, the already well-developed 29Si NMR toolkit for silicates is in many ways applicable, after some adjustment to the two-dimensional nature.

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These materials serve as in important example that while many nanoscale materials are highly disordered and yield weak, broad, and challenging NMR spectra, some nanoscale materials can produce nearly ideal spectradthough the analysis and interpretation may still require a fair amount of ingenuity. For these materials, the 29Si chemical shifts readily quantify the amount of each type of silicon site present in terms of whether the oxygen atoms they are connected to are bridging to other Si atoms or to terminal oxygen (OH) groups, i.e., their Q(n) identity. More challengingly, 29Si-29Si correlation spectroscopy can be used to map out the nearest Si neighbors when mediated through the bonds, and can even be used to measure the distance to nearest Si neighbors when mediated through the direct dipolar coupling. Combining this information with partial knowledge of the symmetry of the sheet from powder X-ray diffraction and exhaustive lists of known structural forms of silicates can produce excellent information on the structures of the 2D sheets. Christiansen et al. studied lamellar silicate mesophases synthesized from tetramethyl orthosilicate in the presence of a wide range of ionic surfactants.81 The extremely narrow 29Si and 1H SSNMR spectra clearly show that the silica sheets separated by cationic surfactants are extremely well ordered, without significant disorder in the bond lengths and angles that would induce line broadening from distributions of chemical shifts. Because the surfactants sit on the surface of the silicate sheets, it is possible to probe the interface by transferring magnetization across it. 2D CP HETCOR experiments transferring 1H magnetization in the surfactant tails into the silicate sheets can conclusively determine which 29Si sites sit within 1 nm of that interface. For example, Fig. 11 shows that all five Si sites in the C16NMe2Etþ/silicate mesophase occur close to the surface of the silicate sheet (as a lamellar phase of indeterminate thickness, these sites may also be present in layers lying further from the interface). Probing this same material for 29Si-29Si connectivity through correlations using the Si-O-Si J couplings (i.e., an INADEQUATE spectrum) measures which sites are adjacent and provides a direct map of the interconnectivities, Fig. 11. Without even examining all of the details, it is immediately apparent this type of measurementdshowing that all sites are interconnecteddcan be incredibly instructive as it demonstrates that only a single phase is present in a complicated heterogeneous material. Such information is not available from any other characterization technique when single-crystal diffraction is impossible. Later on, this same material was studied using double-quantum correlation spectra that were generated using the dipolar coupling instead of the J coupling.79 This alternative method allows self-correlations to be measured (INADEQUATE spectra measure only the inter-site correlations) and also allows more distant correlations (next-to-nearest Si neighbors) to be studied given the larger magnitude of dipolar couplings as compared to J couplings. Setting two dimensions of the unit cell from the powder XRD data, the authors were able to propose a full structure of the material. It should be noted that it is not generally possible to make the leap from distance constraints to a proposed structure, only chemical intuition from exhaustive knowledge of zeolite structures would make this possible. To deal with that difficulty and develop a general means for solving this class of structure, a computer algorithm has been developed to propose and refine structures against the NMR-derived connectivity data.82 This method is expected to be most accurate when full double-quantum buildup and decay curves (which accurately correspond to internuclear distances) are measured for every spin pair in the system. The C16NMe2Etþ/silicate mesophase system discussed at length here has been studied in that fashion and a trustworthy structure has been proposed (to be more accurate, a family of very similar structures has been produced via multiple runs of the same algorithm with different seedings). The authors have explored the use of DFT energy minimizations, and incorporating comparisons to DFT-calculated isotropic chemical shifts and J-couplings in the selection of candidate structures, showing that all can be useful means of using NMR data to determine structures of these challenging materials. Interestingly, it has also been shown that such silicate nanosheets can be converted in-place into zeolitic nanosheets. 29Si-29Si correlation NMR spectra mediated by the dipolar coupling demonstrate intimate contact between the original layered silicate and final structured zeolitic nanosheet phase.80 Such close contacts demonstrate that the reaction takes place homogeneously as opposed to dissolution/recrystallization or a moving reaction front with distinct phase barriers. Because solids NMR spectroscopy is such a uniquely powerful means of studying disordered phases such as this reaction intermediate, it provides access to this type of detailed information that is unlikely to be available via other means. Finally, it should be noted that the supportive surfactant coating is quite mobile at the temperatures utilized in the spectroscopic studies, and the cationic surfactant head groups likely interact quite strongly with the oxygen atoms on the Q3 silicon sites, and so the spectra are quite sensitive to cooling. Here again, NMR spectroscopy provides an excellent means of investigating the freezing out the surfactant motion.83

9.16.1.6

MXenes

Another new class of atomically thin and technologically important materials are the MXene sheets. This entire class of materials was not discovered until 2011, but has already found a cornucopia of applications. One of the strengths of this family of materials is that there is an incredibly diverse range of chemical compositions that can be used to tune the various properties of interest. These materials are generated by taking one of the ca. 100 members of the 3D-layered MAX phases (alternating atomic layers of a metal, “M”, an element from the IIIA-VIA groups of the periodic table, “A”, and either carbon or nitrogen, “X”), and etching out the “A” layers to leave just MX sheets. The resulting pseudo-2D sheets are then named after graphene sheets: MAX / MXene. Depending on the original MAX phase, the MXene sheets are a minimum of 5 atomic layers thick: T-M-X-M-T layers where the T specifies a termination layer that is either O, OH, F, or a mixture of these formed during etching. MXenes with up to 9 M/X layers are also well known. As a non-crystalline nanosheet with an often-indeterminate surface chemistry and an incredibly diverse range of chemical

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Fig. 11 MAS NMR spectra of C16NMe2Etþ/silicate mesophase collected at 4.2 or 11.75 T. At top is the 1D 1H-29Si spectrum demonstrating the extremely high resolution, at middle is the 1H-29Si CP HETCOR spectra that measures the spatial proximity between each silicate site and the

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compositions, there are a correspondingly large number of chemical and structural questions to be answered. NMR spectroscopy is playing a growing role in addressing these. The etching process is performed with the application of a reactive fluoride-containing reagent (e.g., HF or HCl/LiF), and the fluoride ions involved generally form at least part of the termination layer atop the sheets. Understanding the properties of this mixed fluoride layer is a key goal of NMR spectroscopic studies, as is distinguishing the termination layer from intercalated impurities such as AlF3, HF, etc. in order to assign the stoichiometric formula of the sheets more accurately than can be done using bulk elemental-analysis methods. The first 19F NMR measurements of an MXene were from V2CTx, and these showed an extremely broad peak (ca. 300 ppm at half height) at
265 ppm.84 This
265 ppm site is found to have a ca. 20 ms T1 relaxation-time constant, confirming that these fluorine sites are close to the conduction-band electrons in this electronically conductive material. In fact, probing relaxation times or using them for filtering spectra to show either rapidly or slowly relaxing sites is a very useful technique for MXenes (see Fig. 12).84 Similarly broad peaks at
227 and
255 ppm have been reported for Ti3C2Tx prepared using two different etching methods, values which are in the range of that for V2CTx but demonstrate that the different sites are still easily distinguishable.85 19 F spectra of Nb2CTx and its thicker analog Nb4C3Tx are yet more challenging and push right up to the limits of viability: partly because of even larger spectral broadeningdthough the MATPASS experiment was found to assist heredbut also because of worsened spectral overlap from the increased numbers of MXene sites and impurities.86 It should be noted that the 19F nuclide is sensitive enough for NMR experiments that it can be an open question whether it is better to use ultrafast MAS and/or MATPASS or whether one should opt for a lower applied magnetic field. In this case however, the higher applied field was likely the key to successful filtration of the spectra through the also-NMR-active 93Nb nuclei using the TRAPDOR sequence. Selection of neighboring 19 93 F- Nb spin pairs allowed the assignment of
20 and
132 ppm chemical shifts to termination sites in Nb2CTx and
80 and
190 ppm for the terminations in Nb4C3Tx (see Fig. 13).86 1H/19F correlation spectroscopy is another useful source of information, though this technique requires specialized hardware that is not widely available. In particular, such 2D correlation spectra are inherently distance dependent, so correlation of termination F and OH sites proves that these MXenes have intermixed termination groups as opposed to containing either separate particles or distinct regions with either F or OH terminations.85,86 The information from 1H spectroscopy on the termination layer of MXenes complements and extends that available from 19F spectra. Assignment, quantification, and tracking of the pervasive byproducts is certainly a key benefit when studying this type of

τ = 100 ms τ = 10 ms τ = 5 ms τ = 2 ms τ = 1 ms τ = 500 μs τ = 250 μs τ = 0 μs

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Fig. 12 Overlay of F (at left) and H (at right) NMR inversion-recovery spectra of V2CTx collected at 7 T under 60 kHz MAS, color-coded with the noted inversion recovery periods. This can be an effective means of unwinding and assigning spectra, e.g., in the yellow 19F trace: the
158 ppm peak is positive while the
265 ppm remains negative, demonstrating that these two sites are from distinct regions with distinct T1 values. Similarly, the orange 1H trace shows that where 85 ppm peak (OH sites) is fully recovered, while none of the others are. Reprinted with permission from Harris, K. J.; Bugnet, M.; Naguib, M.; Barsoum, M. W.; Goward, G. R. Direct Measurement of Surface Termination Groups and Their Connectivity in the 2D MXene V2CTx Using NMR Spectroscopy. J. Phys. Chem. C 2015, 119 (24), 13713–13720. Copyright 2015 American Chemical Society.

=

surfactant groups on the surface, at bottom is the 29Si double-quantum correlation (INADEQUATE) spectrum encoding all of the Si-O-Si connectivities. Reprinted with permission from Christiansen, S. C.; Zhao, D.; Janicke, M. T.; Landry, C. C.; Stucky, G. D.; Chmelka, B. F. Molecularly Ordered Inorganic Frameworks in Layered Silicate Surfactant Mesophases. J. Am. Chem. Soc. 2001, 123 (19), 4519–4529. Copyright 2001 American Chemical Society.

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Fig. 13 19F NMR spectra of Nb2CTx at 11.7 T under 50 kHz MAS, with pulse sequence names shown. The bottom 19F,93Nb TRAPDOR difference spectrum selects only these spin pairs and allows assignment of the
20 and
132 ppm sites to the surface fluoride termination layer (the weak
330 ppm is assigned as ionic Nb/F byproducts). Reprinted with permission from Griffith, K. J.; Hope, M. A.; Reeves, P. J.; Anayee, M.; Gogotsi, Y.; Grey, C. P. Bulk and Surface Chemistry of the Niobium MAX and MXene Phases from Multinuclear Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2020, 142 (44), 18924–18935. Copyright 2020 American Chemical Society.

solid material where conventional purification methods are not possible. Determination of the content of water that is too well trapped in the tortuous voids to be removed through the application of a vacuum may be particularly important. The separation between peaks is generally much less for 1H than for 19F because the chemical shift range of the simple 1s shell of 1H is so much smaller, but the chemistry is such that most sites can still be distinguished. In particular, the surface hydroxides that are key to the surface chemistry of MXenes are susceptible to Knight shifts in the conductive materials, thus generating very unusual chemical shifts. For example, an extremely broad peak (ca. 200 ppm wide) centered at 85 ppm was observed for V2CTx.84 This peak furthermore displayed very rapid longitudinal relaxation, with a relaxation time constant of ca. 1 ms, further confirming its identity as a hydroxide on the surface of this conductive material. Given the unusually broad linewidth for the surface hydroxide peak in V2CTx, it is likely good practice to test new MXenes using ultrafast spinning together with an echo to prevent dephasing. A second signal in the 1H spectrum, at a few percent of the total intensity, occurs at 27 ppm, very similar to the 26 ppm observed86 in Nb2CTx, which is also assigned to surface hydroxides. The chemical shifts of the hydroxide peaks in various MXenes are found to vary by synthesis method and by dehydration, in fact, the Nb2CTx mentioned above yields hydroxide peaks at 19.5 and 12.2 ppm. Similarly, Ti3C2Tx has been reported to yield surface-hydroxide peaks at 20 and 15 ppm,87 18.6 and 12.5 ppm,85 and in yet another study at 0.5–2 and 3.6 ppm.88 Bare Ti2CTx or Ti2CTx with alkali metal intercalants has been reported to display shifts of 0 to 7 ppm.89 It appears likely that the range of chemical shifts is at least in part due to changes in hydrogen bonding between the hydroxide layer and a water layer above it, but more experimental work seems called for to understand the effects of other changes in chemistry (such as Cl terminations71 or other chemical changes) as well as other experimental considerations such as bulk magnetic susceptibilities and poor rf penetration of conducting materials. Given such complications, correlation experiments demonstrating direct ties between surface hydroxides and other sites such as the carbide layer,85 metal layer,86 or the fluoride surface layer85,86 are an excellent means of corroborating the assignments. For example, the 1H-13C CP-HETCOR NMR spectrum of Ti3C2Tx clearly demonstrates that the connectivity between the surface-hydroxide peak at 26 ppm and the MXene carbon layer at 382 ppm (see Fig. 14). 1 H-1H correlation spectroscopy provides insight into both the hydroxide layer and the water layer strongly bound to it. A DQ/SQ correlation spectrum of the remarkably broad 1H peak of V2CTx shows strong dipolar-mediated self-correlation between these surface hydroxide peaks (see Fig. 15). Therefore, not only are the OH and F sites intermixed, as visible in the 19F/1H NMR data, the 1H DQ/SQ spectrum demonstrates that OH sites are also intermixed. The ability of NMR spectroscopy to identify the chemistry of sites as well as intersite proximities makes it a uniquely capable technique for investigating complicated surface chemistries like those of the MXenes. MXenes also generally have a layer of water strongly bound to their hydrophilic surface. SQ/SQ proton correlation spectroscopy can demonstrate connectivity between relatively stationary water molecules and the surface hydroxides84 with RFDR, or physical exchange between types of adsorbed water molecules with EXSY experiments.84,88 When trying to develop and control chemistry in new MXene applications, the fact that the surface termination layer is so difficult to determine can be frustrating as one may not even know if it is the same in the batches used for different tests. Fluorine,

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Fig. 14 1H-13C CP-HETCOR spectrum of Ti3C2Tx recorded under 40 kHz MAS at 7.05 T proving close proximity between the internal carbide layer of the MXene and the surface termination hydroxide groups. Reprinted with permission from Hope, M. A.; Forse, A. C.; Griffith, K. J.; Lukatskaya, M. R.; Ghidiu, M.; Gogotsi, Y.; Grey, C. P. NMR Reveals the Surface Functionalisation of Ti3C2 MXene. Phys. Chem. Chem. Phys. 2016, 18 (7), 5099–5102.

Fig. 15 1H DQ-SQ correlation spectrum of V2CTx collected at 7 T under 60 kHz MAS. The peak lying along the diagonal here reflects DQ states between neighboring OH termination sites in the MXene, proving their proximity within a few Angstroms. Reprinted with permission from Harris, K. J.; Bugnet, M.; Naguib, M.; Barsoum, M. W.; Goward, G. R. Direct Measurement of Surface Termination Groups and Their Connectivity in the 2D MXene V2CTx Using NMR Spectroscopy. J. Phys. Chem. C 2015, 119 (24), 13713–13720. Copyright 2015 American Chemical Society.

oxygen, or chlorine atoms are the possible termination groups, but significant intercalated impurities preclude the application of simple elemental analysis for ascertaining the stoichiometries. Furthermore, one would ideally like to have at least some idea of the distribution (relative arrangement) of these surface groups. 19F NMR spectra are useful for speciating the inseparable byproducts of the highly energetic formation reaction,84-86,90 but furthermore, their resolution is enough to use calibrated spin-counting experiments to identify the moles of F per formula unit. Therefore, NMR is often the only means to convert the vague empirical formulas such as M2XTx to specific ones such as M2X(F)a(OH)b(O)c. 1H experiments can be employed similarlydthough are likely of lower resolutiondfor confirming these stoichiometries, or to complete the assignments if other termination groups such as Cl are also present. Furthermore, and as mentioned above, 1H-19F correlation experiments conclusively prove the intermixture of these two termination groups, greatly increasing the detail in our picture of these materials. It is only with NMR spectroscopy’s high resolution

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for chemical speciation, quantitative peak heights, and local distance-measurement abilities that much of the current information on these fascinating new materials is available. While characterization of the intermixed and varying surface layer is the most obvious question, characterization of the interior of the thin MXene sheets also provide important insight into these materials. By studying the internal atoms, the electronic structure of the materials and how they change with preparation route, substitutions, and/or surface terminations may be studied. Furthermore, disordered impurities trapped in the tortuous voids of the material that are otherwise difficult to characterize may be tracked. From a distance, the planar carbon layer of the MXenes looks like that of its namesake graphene, but is very different chemically as it is a carbide layer whose atoms are spaced much farther apart than the covalent bonds in graphene. The 13C chemical shifts are therefore quite different, and should be very sensitive to the structure of the wavefunction near the Fermi level. The disorder and conductivity of these samples causes broad peaks, making such spectroscopy difficult. At times, the CPMG technique mentioned above can be a useful means of increasing the signal strength enough for it to be observable (see Fig. 16). Perhaps most tellingly, the 13C shifts observed in two preparations of Ti2CTx (Fig. 16) are quite different.85 The material produced using an etchant of LiF/ HCl produces a broad 13C peak at 412 ppm, while etching with HF produces a similarly broad peak at 382 ppm (with perhaps a shoulder at 412 ppm). Since MXenes show promise as catalystsdwhose behavior might be improved by tuning the material’s band gap or electronic structure near the Fermi surfacedNMR spectra of the internal atoms may be an excellent means of progressing such studies. The chemical shift of the 1H atoms in terminal hydroxides and 19F in the terminal fluorides also detects such changes,85 so multinuclear studies appear poised to provide multipronged insight into the electronic structure. Carbon chemical shifts have also been reported for V2CTx, Ti3C2Tx, Nb2CTx, Nb4C3Tx, and Mo2CTx;84-86,91 the Nb and Ti systems all resonate near 400 ppm, but V2CTx resonates at 260 ppm and Mo2CTx appears at 125 ppm. The V2CTx, Nb2CTx, and Nb4C3Tx MXenes show increases in 13C chemical shift upon exfoliation while Ti3C2Tx and Mo2CTx show decreases.

Fig. 16 13C CPMG-MAS spectra of vanadium and titanium MXenes that also show significant amounts of the MAX phase starting materials. Note that CPMG data can equivalently be presented as spikelets whose tops trace the MAS spectrum, as in (A), or they can be processed by adding together the echoes to generate more conventional looking spectra, as in (B). Different authors prefer different formats as the latter format can be easier to read but the former more directly displays the resolution inherent to the observation. (A) Reprinted with permission from Harris, K. J.; Bugnet, M.; Naguib, M.; Barsoum, M. W.; Goward, G. R. Direct Measurement of Surface Termination Groups and Their Connectivity in the 2D MXene V2CTx Using NMR Spectroscopy. J. Phys. Chem. C 2015, 119 (24), 13,713–13,720. Copyright 2015 American Chemical Society. (B) Reprinted with permission from Hope, M. A.; Forse, A. C.; Griffith, K. J.; Lukatskaya, M. R.; Ghidiu, M.; Gogotsi, Y.; Grey, C. P. NMR Reveals the Surface Functionalisation of Ti3C2 MXene. Phys. Chem. Chem. Phys. 2016, 18 (7), 5099–5102.

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In some cases, it is possible to also observe the metal layer in the MAX and MXene phases. NMR spectra of 93Nb, a spin-9/2 nucleus with a moderate quadrupole moment, can be collected from the Nb2AlC MAX phase, and the chemical shift and quadrupole parameters match very well with plane-wave DFT calculations.86 Investigation of the MXene created from this parent MAX phase shows a (perhaps surprisingly) simple static 93Nb NMR spectrum. At the resolution level available in a static spectrum, it appears to be a simple overlap of starting MAX phase and a single type of Nb site, see Fig. 17. The significant change in chemical shift (
475 to
790 ppm) suggests that 93Nb spectroscopy is an excellent candidate for tracking changes in band structure when seeking specific electronic properties via inclusion of dopants or alteration of termination layers. The chemical information contained in the 93Nb quadrupolar coupling observed in Nb2CTx, CQ and hQ, is also very informative. Calculations show that CQ is much larger than in the parent MAX phase, but is certainly too small for Nb to be the terminating layer of the stacked structure: yet more confirmation of the Tx layer of MXenes. Comparison to calculations of a few model structures suggest the best agreement is with oxide and/or fluoride terminating groups, and perhaps there is some room for even finer chemical detail if higher resolution spectra using MAS and higher applied magnetic fields is investigated and compared with exhaustive computational models containing a large array of local site types. Analogous investigations of the thicker MAX/MXene pair Nb4AlC3 demonstrates that the 93Nb spectroscopy is more difficult in this system, but the two types of Nb site in the MAX phasedadjacent vs. distant from the Al layerdcan be resolved via a combination of rapid spinning, higher applied field, and the MATPASS experiment. The quadrupole couplings at these two sites are quite distinct, with the Nb site between two C layers having a much smaller CQ value versus the Nb site sandwiched between C and Al layers, at 2 and 32 MHz, respectively. The MXene produced from this MAX phase yields an easily observable static 93Nb spectrum, but one where overlap precludes evaluation of specific parameters and site types. Still, an upper limit may be placed on CQ, and calculated CQ values for model structures demonstrate again that there must be a termination layer on the Nb sheet.

9.16.2

Conclusions

The fascinating 2D class of materials has already displayed enough promising behavior that they will certainly be a fixture in future research, and will most likely appear in future technologies. Whenever new 2D materials are developed or properties of existing sheets are tuned via chemical modification, significant characterization challenges will be created. Tracking any catalytic behavior of such materials also engenders difficult characterization problems. By their nature, 2D materials are not ordered and crystalline substances, they generally have multiple edge and/or surface termination modalities, and they are generally synthesized using “hot” methods that produce a range of local environments which may be even more varied if dopants are employed. Such attributes

Fig. 17 Central-transition 93Nb NMR spectra of stationary samples of Nb2CTx and Nb4C3Tx MXenes. The thinner MXene appears to be associated with sites having very similar quadrupolar coupling and chemical shift parameters and can be simulated to extract these values. The thicker MXene on the other hand evinces excellent signal quality, but is not separable into specific site types from just this data set. Reprinted with permission from Griffith, K. J.; Hope, M. A.; Reeves, P. J.; Anayee, M.; Gogotsi, Y.; Grey, C. P. Bulk and Surface Chemistry of the Niobium MAX and MXene Phases from Multinuclear Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2020, 142 (44), 18,924–18,935. Copyright 2020 American Chemical Society.

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render many characterization methods ineffective, and much of the NMR-derived chemical information summarized above was not able to be determined using any other methods. In particular, the extremely high sensitivity of NMR observables to changes in chemical bonding, and the ability of NMR spectroscopy to measure correlations between local sites is unmatched by other techniques. As new versions of the materials presented above are developed, and as entirely new 2D materials are discovered, there can be no doubt that NMR spectroscopy will play a key role in measuring the exact chemical sites that are generated, and in guiding synthetic efforts to make new materials and technologies.

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9.17

NMR of catalytic sites

Kuizhi Chen, Yuting Sun, and Guangjin Hou, State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China © 2023 Elsevier Ltd. All rights reserved.

9.17.1 9.17.2 9.17.2.1 9.17.2.2 9.17.2.3 9.17.2.4 9.17.2.5 9.17.2.6 9.17.3 9.17.3.1 9.17.3.2 9.17.3.3 9.17.4 9.17.4.1 9.17.4.1.1 9.17.4.1.2 9.17.4.1.3 9.17.4.2 9.17.4.2.1 9.17.4.2.2 9.17.4.3 9.17.4.3.1 9.17.4.3.2 9.17.5 9.17.5.1 9.17.5.2 9.17.5.3 9.17.5.3.1 9.17.5.3.2 9.17.6 Acknowledgments References

Introduction NMR principles and basic interactions NMR spectroscopy without interactions NMR spectrum with internal spin interactions The importance of powder patternsdBeyond isotropic chemical shift Removal of CSA and dipolar coupling interactions Quadrupolar interaction NMR sensitivity Chemical shift and quadrupolar patterns for investigating catalytic sites Isotropic chemical shift for revealing catalytic sites CSA for revealing catalytic sites Quadrupolar interaction for revealing catalytic sites Investigation of catalytic sites via internuclear correlations Dipolar coupling and J-coupling Dipolar coupling J-coupling Applications Constructing 2D NMR correlations Homonuclear correlation spectroscopy Heteronuclear correlation spectroscopy Probing internuclear distances Dephasing curves for distance measurement Build-up curves for distance measurements Use of in-situ NMR Batch in-situ NMR In-situ NMR under flow reaction condition Use of probe molecules Zeolites Metal oxides and modified metal oxides Summary and outlook

473 474 475 475 476 477 478 480 480 481 482 483 484 484 485 486 487 489 490 491 496 497 498 499 500 503 504 505 507 508 509 509

Abbreviations AlPOs Aluminophosphates BA Brønsted acid BAS Bridging acid site CAVERN Cryogenic adsorption vessel enabling rotor nestling CF Continuous flow CORD Combined R2nv-driven spin diffusion CP Cross polarization CQ Quadrupolar coupling constant CSA Chemical shift anisotropy CST Chemical shift tensor CT Central transition DARR Dipolar-assisted rotational resonance DAS NMR Dynamic angle spinning NMR DCC Dipolar coupling constant DIPSHIFT Dipolar-coupling chemical-shift correlation

Comprehensive Inorganic Chemistry III, Volume 9

https://doi.org/10.1016/B978-0-12-823144-9.00151-5

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NMR of catalytic sites

DNP Dynamic nuclear polarization DOR NMR Double rotation NMR DQ Double quantum DREAM Dipolar recoupling enhanced by amplitude modulation EFG Electric-field gradient FID Free induction decay fpRFDR Finite pulse RF driven recoupling HETCOR Heteronuclear chemical shift correlation HORROR Homonuclear double-quantum rotary resonance INADEQUATE Incredible natural abundance double quantum transfer experiment INEPT Insensitive nuclei enhanced by polarization transfer IR Infrared spectroscopy LA Lewis acid LA-REDOR Low alpha rotational echo double resonance MAS Magic-angle spinning MAT Magic angle turning MIRROR Mixed rotational and rotary resonance MOFs Metal-organic frameworks MQMAS Multiple-quantum magic-angle spinning NMR Nuclear magnetic resonance NOESY Nuclear Overhauser enhancement spectroscopy PDSD Proton driven spin diffusion PMLG Phase modulate Lee-Goldburg PMRR Phase modulated rotary resonance POST-C7 Permutationally offset stabilized C7 PSD Proton spin diffusion R3 Rotary resonance recoupling REAPDOR Rotational echo adiabatic passage double resonance REDOR Rotational echo double resonance RESPDOR Resonance-echo saturation-pulse double-resonance RF Radio frequency RFDR Radio frequency driven recoupling RINEPT Refocused insensitive nuclei enhanced by polarization transfer RNCSA RN-symmetry CSA recoupling RN-DIPSHIFT RN-symmetry based DIPSHIFT ROCSA Recoupling of CSA SD Spin diffusion SQ Single quantum ssNMR Solid-state nuclear magnetic resonance ST Satellite transition STMAS Satellite-transition magic-angle spinning SUPER Separation of undistorted powder patterns by effortless recoupling T1 Longitudinal relaxation time T2 Transverse relaxation time TMP Trimethylphosphine TMPO Trimethylphosphine oxide TQ Triple quantum TRAPDOR Transfer of population in double resonance VT Variable temperature

NMR of catalytic sites

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Abstract Heterogeneous catalysis, one of the most important technologies in modern industry, primarily relies on inorganic solid catalysts and is typically complex in both the catalyst itself and the catalytic mechanism, unlike its homogeneous analog. The catalytic sites on solid catalysts often reside on surfaces and interfaces and lack long-range orders, posing challenges to detailed structure-reactivity elucidations. Solid-state NMR (ssNMR) is a well-known technique for characterizing catalytic sites in heterogeneous catalysis, as it provides a variety of approaches to probe the nature of catalytic sites including their atomic-level local structures, intrinsic reactivity, and site-site proximities, owing to its sensitivity to local electronic environments and internuclear interactions. Specifically, such features have been widely exploited to characterize bonding types, lengths, strengths, and geometry of catalytic site structures, etc., which are of general interest for the catalysis community. Further, NMR is also capable of providing valuable in-situ information with appropriate modifications to the instrument. In this chapter, we will discuss NMR fundamentals focusing on practical aspects (to avoid spin physics) and demonstrate how modern ssNMR techniques help in solving real catalytic problems with selected but intuitive examples, hoping to inspire more applications to unleash the power of NMR.

9.17.1

Introduction

Catalysis is one of the most important technologies in the world, playing pivotal roles in industrial productions and remedies for environmental pollution, and has been recognized as one key technology for the much-needed sustainable development, such as the highly demanded energy shift from fossil fuels to sustainable sources nowadays. Heterogeneous, homogeneous and biocatalysis are the key disciplines for modern catalysis, each of which has advantages and disadvantages depending on specific desires of the product molecule or chemical process. Among the three disciplines, heterogeneous catalysis, capable of catalyst regeneration, recyclability and product separation, allows for continuous processes and thus enables faster, large-scale production and selective product formation. However, unlike the homogeneous analog, heterogeneous catalysis is typically complex in both the catalyst itself and the catalytic mechanism. Direct structure-reactivity assessment is often challenging due to the complex structures of the catalyst as well as the complicated thermal-dynamic and kinetic behaviors of catalytic reactions. To date, many designs and optimizations of heterogeneous catalysts are still strongly based on chemical intuition and empirical methods. To solve the puzzle and enable tailored heterogeneous catalysis, one clear approach is to gain full understanding to the nature of active sites, given that they are at the origins of all the catalytic performances, which would involve, in particular, the molecular level understanding of the structures, locations, and evolutions of the active sites. Among many characterization methods, solid-state NMR (ssNMR) has been playing indispensable roles in revealing the nature of catalytic sites in solid catalysts, and its capability and crucial roles in characterizing catalytic sites in solid catalysts will be the main topic in this chapter. The catalytic sites on solid catalysts often reside on surfaces and interfaces, and in many cases lack long-range order, consequently making diffraction-based techniques inadequate. Techniques such as X-ray Absorption Spectroscopy (XAS) and X-ray Photoelectron Spectroscopy (XPS) can provide elemental and chemical-state specific information of the catalyst materials, but only in the form of average structure. The same drawback applies to neutron diffraction techniques. Spectroscopic techniques such as Infra-Red (IR) and Raman spectroscopy provide site-specific information but suffer from limited resolution or severe base line distortion. In contrast, NMR characterizes the local interactions between nuclear-nuclear and/or nuclear-electron spins, thereby not relying on long-range ordered structures, and can provide site-specific information. Appropriate manipulations of the spins, i.e., using appropriate NMR methods, offer to probe an enormous number of characteristics of the catalytic sites, both structurally and dynamically. In practice, catalytic sites in solid catalysts vary widely and are fundamentally different, from Brønsted/Lewis acid sites to exposed crystalline facets, surface morphologies, atom vacancies, single metal atoms and to metal hydrides, etc. To reveal the nature of these catalytic sites, NMR is powerful in various aspects which allow for probing the most concerned characteristics including their site-specific chemical structure, structural evolution, local environment, activity, quantity as well as site-reagent interaction in some cases, via direct detection of the catalytic site itself or indirect means through a wide selection of probe molecules or probe reactions. The information provided by NMR can be complementary or even irreplaceable, compared to other characterization methods. NMR active isotopes commonly encountered in studying catalytic materials are tabulated in Table 1 with basic spin parameters.1 In this chapter, we will first discuss in Section 9.17.2 the general NMR fundamentals including universal NMR interactions, chemical shielding, dipolar coupling and quadrupolar interaction, etc. Then, Section 9.17.3 shows examples of practical applications using such basic interactions. In Section 9.17.4, the focus will be shifted to internuclear interactions, including onedimensional (1D) and two-dimensional (2D) NMR experiments for homonuclear and heteronuclear interactions, with and without quadrupolar nuclei involved. Particularly, dipolar coupling, J-coupling and quadrupolar coupling interactions as well as internuclear correlation spectroscopy and internuclear distance determination will be reviewed and demonstrated with application examples. In Section 9.17.5, in-situ NMR and probe molecule/reaction approaches for probing catalytic sites will be demonstrated and discussed with application examples. However, it should be noted that many advanced NMR techniques are not popularized in the most needed catalysis community due to the specialties required for experimental designs, setups, analyses, and the inconvenience of accessing NMR instruments. One purpose of this chapter is to demonstrate up-to-date NMR techniques developed and employed in resolving problems for studying catalytic sites in solid materials, and hopefully to inspire more applications to unleash the power of NMR.

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NMR of catalytic sites Table 1

NMR isotopes relevant to the characterization of catalyst materials.

Isotope

I

Abundance a

Receptivity b

1

1/2 1 1 3/2 3/2 1/2 1/2 5/2 1/2 3/2 5/2 5/2 1/2 1/2 3/2 5/2 7/2 7/2 7/2 5/2 3/2 1/2 5/2 5/2 1/2 1/2 1/2 9/2 9/2 1/2 1/2 7/2 1/2 1/2

99.985 0.015 7.4 92.6 80.4 1.1 0.368 0.037 100 100 10.0 100 4.7 100 93.2 7.4 5.4 99.8 100 4.1 39.6 100 11.22 15.9 100 38.2 12.3 4.3 95.7 8.6 26.4 99.9 33.8 22.6

5.87  103 6.52  10
3 3.79 1.59  103 7.77  102 1.00 2.25  10
2 6.5  10
2 4.9  103 5.45  102 1.58 1.22  103 2.16 3.91  102 2.79 0.918 1.20 2.25  103 1.64  103 0.692 3.35  102 0.70 6.26 3.06 0.186 0.290 7.94 88.5 1.98  103 26.6 33.6 3.56  102 20.7 11.8

H H 6 Li 7 Li 11 B 13 C 15 N 17 O 19 F 23 Na 25 Mg 27 Al 29 Si 31 P 39 K 47 Ti 49 Ti 51 V 59 Co 67 Zn 71 Ga 89 Y 91 Zr 95 Mo 103 Rh 109 Ag 113 Cd 113 In 115 In 119 Sn 129 Xe 139 La 195 Pt 207 Pb 2

Q (10
28 m2) c 2.7  10
3
8  10
4
4.5  10
2 3.6  10
2
2.6  10
2 0.12 0.20 0.15 5.8  10
2 0.3 0.25 0.3 0.4 0.15 0.11
0.18
2.2  10
2

0.80 0.81 0.2

X (MHz) d 100.0 15.4 14.7 38.9 32.1 25.1 10.1 13.6 94.1 26.5 6.1 26.1 19.9 40.5 4.7 5.6 5.6 26.3 23.6 6.2 30.5 4.9 9.3 6.5 3.2 4.7 22.2 21.8 21.9 37.3 27.8 14.1 21.4 20.9

a

Natural abundance of the isotope. Receptivity relative to 13C. c Approximate value for the quadrupole moment. d Larmor frequency of the observed nucleus normalized to the 1H Larmor frequency at 100 MHz. Values adapted from Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Goodfellow, R.; Granger, P. NMR Nomenclature: Nuclear Spin Properties and Conventions for Chemical Shifts: IUPAC Recommendations 2001. Solid State Nucl. Magn. Reson. 2002, 22, 458–483. b

9.17.2

NMR principles and basic interactions

NMR spectroscopy offers a variety of means to probe chemical structure, nuclear distance, and dynamic behavior, etc., via the welldefined NMR interactions inclusive of the chemical shift which originates from the local magnetic field induced by electron shielding, as well as the relatively more complicated dipolar coupling interaction originated from two or multiple spin systems, and quadrupolar coupling specifically associated to I > 1/2 spins, namely, the quadrupolar nuclei. These interactions are doubleedged, knowing that they can lead to unwanted broadenings to the linewidth of NMR spectra, thereby reducing the spectral resolution and sensitivity, but are also important descriptors of the local environment at the atomic scales. Besides the very basic but most used one-dimensional NMR spectroscopy, such as single-pulsed Bloch decay or Hahn-echo (or spin-echo) experiments that provide chemical shift values as for componential or structural identifications, a tremendous amount of advanced NMR techniques have been developed, e.g., by manipulating spin dynamics or relaxometries, to decipher structural and dynamic information encoded in these NMR interactions. This section will focus on introducing the fundamental NMR concepts, showing how the NMR signal is created and how the signal lineshape changes from sharp peaks (as in solution NMR) to complicated and broadened patterns, and essentially, how those broadening patterns can be manipulated by NMR techniques such as magic-angle spinning (MAS) and radio frequency (RF) field irradiation to obtain useful information. In particular, the interactions for uncoupled spins, i.e., chemical shielding and quadrupolar interactions, will be the main focus in this section and their applications will be discussed

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separately in Section 9.17.3. Dipolar coupling interaction is only briefly introduced here as a source of inhomogeneous broadening, but will be discussed more intensively in Section 9.17.4 along with other internuclear interactions. For investigating catalytic sites in inorganic materials, solid-state NMR has played pivotal, even irreplaceable roles in elucidating site structures, interactions as well as activities. Different from solution NMR where typically “sharp” signals with high resolution are observed, ssNMR spectra are usually much broader. The broadenings can be largely attributed to the so-called internal nuclear spin interactions that are usually described by spin Hamiltonians, of which the rough relative magnitudes2 are illustrated in Fig. 1. On the contrary, there are also external interactions originated from the static magnetic field B0 and RF fields, but do not reflect the intrinsic spin natures, which are not included here. B0 and RF fields, however, play key roles in manipulating the internal spin interactions. One would immediately realize from Fig. 1 that the prevailing internal interactions are chemical shift, dipole-dipole (DD) and quadrupolar couplings; in solution, such anisotropic interactions are averaged out by rapid molecular motion, which is the reason that high resolution spectra are typically obtained. Here, we will not present very detailed NMR spin physics which has been well documented in a variety of books and publications,2–4 but only focus on practical aspects such as the origins of lineshapes in ssNMR and the way to interpret them.

9.17.2.1

NMR spectroscopy without interactions

Pulsed-NMR is most common in modern NMR. When applying an appropriate-length RF pulse at the Larmor frequency of an NMRactive nucleus, one can transfer the net magnetization of the spin from the z-axis (along the external field B0) to the xy-plane. Then a few things will happen: (1) the magnetization precesses around the z-axis which is known as evolution, (2) the magnetization dephases in the xy-plane which is known as the transverse (T2) relaxation, or spin-spin relaxation and (3) the magnetization relaxes back to the z-axis which is known as the longitudinal (T1) relaxation, or spin-lattice relaxation. The precession/evolution of the magnetization creates a current in the NMR detection coil, which leads to the free-induction decay (FID) signal, and Fourier transform of the FID signal will yield a typical NMR signal in frequency domain, as shown in Fig. 2a. The transverse relaxation causes the signal to decay quickly, leading to a broadening of the FT NMR spectrum. In the absence of the three prevalent interactions, e.g., in solution, NMR excitation and acquisition will generate a relatively simple Lorentzian-shaped peak in frequency-domain, mathematically defined as in Eq. (1), where u0 is the Larmor frequency determined by the B0 strength. S0 is the signal intensity, R ¼ T2
1 is the transverse relaxation rate, and U is the resonant frequency of the observed spin, as an offset to the Larmor frequency. The frequency domain spectrum illustrated in Fig. 2a is a simulated Lorentzian peak of such type. SðuÞ ¼

9.17.2.2

S0 R ðu0
UÞ2 þ R2

(1)

NMR spectrum with internal spin interactions

However, cases become complicated for solid materials in the presence of CSA (chemical shift anisotropy), dipolar and quadrupolar interactions, each of which could introduce significant anisotropic broadenings to the spectrum, as visualized in Fig. 2b–e. Specifically, CSA arises from chemical shielding which describes the local magnetic field induced by the external electron surrounding the nucleus; dipolar coupling arises from the interaction of two or multiple dipoles in spatial proximity, given that each nuclear spin is essentially a magnetic dipole; and quadrupolar coupling arises from the interaction between the electric quadrupole moment of the nucleus and the electric-field-gradient (EFG) at the nuclear site.2,5 The uniquely defined patterns of CSA, dipolar coupling as well as quadrupolar coupling illustrated in Fig. 2b–e are all functions of the randomly distributed orientations of crystallites, and thus referred to as powder patterns.6 Important information concerning the local structural symmetry is encoded in the powder pattern lineshapes, which will be presented vide infra. In addition to the three major interactions of magnitude from hundreds to several kHz, one should also keep in mind the importance of the relatively weak J-coupling (normally within a few hundred Hz) between different nuclei, as shown in Fig. 1, which is exclusively generated through electronic overlap in chemical bonds. Although Jcoupling is often very weak in solids, it can sometimes provide crucial information for structural elucidations as an identifier of

Fig. 1

Rough relative magnitudes of internal NMR interactions.

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Fig. 2 Scheme showing (a) NMR time domain FID (free induction decay) and Fourier transformed frequency domain signal for a single Lorentzian peak, and (b)–(d) the lineshapes of a single peak affected by CSA, dipolar coupling and both of them as indicated in the figure.

bond formation. Furthermore, it survives under MAS and thus can be used to filter out strong interactions to simplify the spectrum. Spin-rotation interactions are normally not considered in solid materials. The internal interactions are double-edged, as on one hand, they broaden the spectrum and reduce resolution, while on the other hand, they contain structural information and create the basis for the development of advanced and powerful NMR methodologies, such as the important “internuclear correlation” methods demonstrated in Section 9.17.4.

9.17.2.3

The importance of powder patternsdBeyond isotropic chemical shift

The powder patterns of CSA, quadrupolar coupling and dipolar coupling can usually be described by second-rank tensors. Here, the former two, both intramolecular dominated interactions, will be introduced regarding their relative tensors, i.e., chemical shift tensor (CST) or electric-field gradient (EFG) tensor, which determines the static powder lineshapes and reflects the electron structures surrounding the observed nucleus. We will briefly show the concept of connecting powder pattern lineshapes to tensor components for CSA and quadrupolar interactions at static condition. The quadrupolar interaction still gives rise to a powder pattern under MAS and will be discussed in more detail in Section 9.17.2.5. Dipolar coupling lineshapes will be discussed separately in Section 9.17.4 as these arise from internuclear interactions. Chemical shifts arise from B0 induced fields where the orientation dependence can be described by CST, particularly by three principal components (dXX, dYY, dZZ) and an asymmetry parameter h. In solution where all internal interactions are mostly averaged out by fast molecular tumbling, the isotropic chemical shift diso is observed corresponding to the mean value of three principal components, i.e., diso ¼ 1/3 (dXX þ dYY þ dZZ). The averaged value diso is usually referred to when the “chemical shift” term is used. In contrast, CST reflects detailed orientation dependence of the shielding (s) regarding the surrounding electrons to the bare nucleus, and hence provides more intuitive information to the local electronic structure. CST can be typically denoted in the “Haeberlen” convention,2,7 where the principal components are defined by following the ordering |dZZ
diso |  | dXX
diso |  |dYY
diso |, and CSA is defined as the largest deviation in chemical shift from the isotropic value, i.e., daniso ¼ dZZ
diso. The difference between the other two components is measured as the asymmetry parameter (sometimes termed biaxiality), defined as h ¼ (dYY
dXX)/daniso. With such notation, the powder pattern of CSA can be well described as illustrated in Fig. 3a. There are also other conventions of the CST notations, which are all interchangeable. Another common one is called the “Mehring notation,”3 where the key parameters are the isotropic chemical shift (diso), three principal components (d11  d22  d33), the span (U), and the skew (k). The span U is defined as the difference between the largest and smallest principal components, U ¼ d11
d33, while the skew k is a measure for the asymmetry of the tensor, k ¼ 3(d22
diso)/U. The quadrupolar coupling arises from the interaction between the nuclear quadrupole moment, generated by the non-spherical distribution of its electric charge, and the electric field gradient (EFG) generated by the surrounding environment.5 It is often that only the central transition (CT) is observed in the spectrum, and its lineshape is defined by the quadrupolar powder pattern determined by the second-rank EFG tensor. Similar to CST, the EFG tensor can be specified by three principal values (VXX, VYY, VZZ) and an asymmetry parameter hQ (0 < hQ < 1), where VZZ is defined as the largest component, VXX þ VYY þ VZZ ¼ 0 and hQ ¼ (VXX
VYY)/VZZ. The magnitude of EFG that determines the linewidth of the pattern is closely related to a term called the quadrupolar coupling constant, denoted CQ ¼ e2qQ/h, which is the product of a nuclear property (eQ) and a crystal property (eq). The static powder pattern as a function of hQ is simulated in Fig. 3b, which contains the important information on the local

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Fig. 3 Simulated spectra demonstrating powder patterns of CSA (a) and quadrupolar coupling (b) corresponding to asymmetry parameters and related tensor components, under static conditions.

chemical structure such as coordination number/environment at the nucleus. Considering the increased complexity of quadrupolar interaction, a more detailed discussion will be also given in Section 9.17.2.5. Powder patterns contain valuable structural information, but can also cause severe line broadenings and overlap, which deteriorate the spectral resolution and lead to challenges in both experimental and analytical processes. Indeed, it should be noted that most solid materials do not contain the well-defined powder patterns as shown in Fig. 3 that often yielded from crystalline samples containing long-range orders, e.g., single molecular site in crystalline materials. Instead, the majority of solid-state samples encountered in material sciences such as solid catalysts, solid battery materials and polymers are either non-crystalline/with low crystallinity or crystalline but contain too many sites, and therefore yield broad signals without distinguishable patterns. Characterizing such materials is usually challenging for NMR, but also for other modern techniques; however, advanced NMR techniques, such as double rotation (DOR), fast MAS and many 2D pulse methodologies provide promising opportunities to extract useful structural information.8,9 The spectral broadenings generated by CSA, dipolar and quadrupolar coupling are all anisotropic, also known as inhomogeneous broadenings. In contrast, there are also homogeneous broadenings caused by, for example, homonuclear coupling or T2 decay. Both homogeneous and inhomogeneous broadenings could be of very large magnitudes and make NMR spectroscopy too complex for analysis. Hence, it is of crucial importance to remove these anisotropic interactions to enhance the spectral resolution, and to break through NMR applications on limited crystalline materials. A brief introduction of the removal of the internal interactions is discussed in the following section.

9.17.2.4

Removal of CSA and dipolar coupling interactions

Magic-angle spinning (MAS). Scientists have worked for decades to suppress unwanted broadenings to enhance the spectral resolution of ssNMR, hoping to be comparable to that of solution NMR. In general, by employing the so-called magic-angle spinning pffiffiffi (MAS) technique, i.e., mechanically rotating the samples at qm ¼ arctan 2z54:7+ relative to the B0 field, as depicted in Fig. 4a, the dipolar coupling and CSA interactions can be significantly reduced, or almost fully suppressed when approaching sufficiently high spinning speeds. The MAS suppression of inhomogeneous interactions originated from CSA and heteronuclear dipolar couplings are notably different compared to homogeneous broadenings caused by homonuclear coupling (the case of quadrupolar broadening is discussed separately in Section 9.17.2.5). Quantum theories show the former can be sufficiently removed and yield a solution-like high-resolution isotropic peak, along with spinning sidebands separated by the spinning frequency.3 A visualization of MAS suppression of CSA (heteronuclear dipolar coupling will be similar) is demonstrated in Fig. 4b. In contrast, homonuclear broadenings induced from homonuclear couplings, such as the often encountered 1H-1H coupling arising from proton networks in polymers or metal-oxide surfaces, is not completely removed by MAS but the resulting isotropic peak resolution can be improved as a function of the MAS rate and/or with homonuclear decoupling sequences applied, as shown in Fig. 4c.10 An explanation of the differences is provided in Section 9.17.4. Radio-Frequency (RF) decoupling. An alternative technique for suppressing both hetero- and homo-nuclear dipolar coupling interactions is to employ specially defined RF radiations to “decouple” the coupled spins. Decoupling hetero- and homo-nuclear interactions are fundamentally different. Continuous wave (CW) decoupling is the simplest technique to remove the effects of heteronuclear dipolar coupling, where the RF irradiation is applied on the non-observed nucleus. However, high power CW

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NMR of catalytic sites

Fig. 4 Scheme magic-angle spinning (MAS) (a) and its removal of CSA in demonstration (b). The MAS averaging of heteronuclear dipolar coupling is similar to that of CSA in (b). The MAS averaging of homonuclear dipolar coupling is more difficult, i.e., spinning rate dependent and may require homonuclear RF recoupling, as demonstrated in (c). (b) Adapted with permission from Leskes, M.; Steuernagel, S.; Schneider, D.; Madhu, P. K.; Vega, S. Homonuclear Dipolar Decoupling at Magic-Angle Spinning Frequencies up to 65khz in Solid-State Nuclear Magnetic Resonance. Chem. Phys. Lett. 2008, 466, 95–99, Copyright 2008 Elsevier Ltd. (c) Adapted from Moran, R. F.; Dawson, D. M.; Ashbrook, S. E. Exploiting NMR Spectroscopy for the Study of Disorder in Solids. Int. Rev. Phys. Chem. 2017, 36, 39–115.9.

irradiation is usually required for the effective decoupling. Alternatively, the phase modulated RF irradiations can achieve the desired decoupling efficiency with acceptable RF powers, such as TPPM (two pulse phase modulation),11 XiX,12 SPINAL (small phase incremental alteration),13 etc. In the case of homonuclear dipolar decoupling, multiple-pulse sequences are used. When applying the appropriate multiple pulse sequences on the nucleus, the effect of the homonuclear dipolar coupling can be zero at certain points where the data point acquisition is usually performed. Representative homonuclear decoupling sequences include WAHUHA,14 FSLG,15 PMLG,16 DUMBO,17 etc. MAS and RF decoupling are often employed complementarily to provide the best removal of internal nuclear interactions. A demonstration of homonuclear decoupling under MAS can be found above in Fig. 4c. Particularly, in the case of homonuclear dipolar decoupling, the averaging effect of MAS can potentially interfere with the applied pulse sequences, and thus the multiple pulse sequences must be exactly synchronized with the MAS rotation, known as CRAMPS17 (combined rotation and multiple pulse sequences). It is also worth noticing that associated to the resolution enhancement is a gain of sensitivity, as narrowing signals automatically leads to increased signal intensity. For spin-1/2 nuclei, the averaging of CSA and dipolar interactions can essentially provide much improved resolution of the spectrum, leaving only the isotropic chemical shift diso for analysis. The numeric value of diso provides a simple way to differentiate the nucleus in different chemical structure and could directly reveal the intrinsic nature of catalytic sites in some cases, such as the acidity of acid site; such feature makes it possibly the most used NMR parameter to track changes on catalytic sites. Indeed, a tremendous amount of work has been done by merely analyzing the diso of active sites, or tracking the changes of the active sites or adsorbed reagents by in-situ NMR techniques, which will be discussed in Sections 9.17.3.1 and 9.17.5. However, for I > 1/2 quadrupolar nuclei, the NMR spectrum becomes complicated and will be discussed separately as follows in the next section.

9.17.2.5

Quadrupolar interaction

In addition to CSA, dipolar- and J-coupling interactions of importance for spin-1/2 nuclei, the quadrupolar interaction could dominate for quadrupolar (I > 1/2) nuclei. In fact, more than 75% NMR active nuclei are quadrupolar, many of which can be commonly found in solid catalysts, such as 27Al, 11B, 71Ga, 17O, 23Na and 67Zn (also see Table 1). This type of nuclei could possess a large quadrupole moment that interacts with the surrounding electric-field-gradient (EFG), hence leading to quadrupolar interactions

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from a few kHz to tens of MHz. Such significant line-broadenings can severely reduce the spectral resolution, and thus may be required to be removed or separated. In theory, the quadrupolar interaction of spin S placed in the external field consists of 2S þ 1 energy states due to the Zeeman interaction, resulting in a central transition (CT) and several satellite transitions (STs) in the NMR spectrum, as illustrated in Fig. 5a and b. Each transition can be expressed using the Average Hamiltonian theory18 as: full HQ ¼ HQ(1) þ HQ(2) þ ., where HQ(1) and HQ(2) are referred to as the first- and second-order quadrupolar interactions, respectively. The higher order terms are usually negligible in many practical situations. For half-integer quadrupolar nuclei, it is very often that only the relatively narrow CT can be observed, for which, fortunately, the relatively large first-order terms vanish. However, the CT is still affected by the second-order quadrupolar interaction, containing high-rank anisotropic terms that cannot be completely averaged by MAS, hence resulting in a remaining quadrupolar broadening to the spectrum, as shown in the simulated spectrum in Fig. 5c. The detailed derivation and discussion of the quadrupolar NMR theory can be found in multiple publications and books,5,19,20 and thus is not presented here. For integer-spin quadrupolar nuclei, there is no CT. In short, MAS NMR spectra of quadrupolar nuclei are more complex than those of spin-1/2 nuclei because of the remaining quadrupolar broadening. The quadrupolar spin dynamics are uniquely different from spin-1/2 nuclei, and the second-order quadrupolar broadening of the CT signal is inversely proportional to the magnetic field, as demonstrated in a real example using magnetic fields of up to 40 T in Fig. 6a.21 Therefore, high magnetic fields and specially designed quadrupolar pulse sequences are normally employed to suppress and separate the quadrupolar broadening, thus providing NMR spectra suitable for extracting meaningful structural information. To date, a few powerful methods have been developed, namely, dynamic angle spinning (DAS),22,23 double rotation (DOR) NMR,22,23 multiple-quantum magic-angle spinning (MQMAS),24,25 and satellite transition magic-angle spinning (STMAS).26,27 Among them, two-dimensional (2D) MQMAS and STMAS methods are more frequently used as they can be performed on conventional MAS probes; the others would usually require specially designed probes. MQMAS and STMAS provide a means where the isotropic and quadrupolar terms are recorded in the indirect and direct dimensions, respectively. An example of an MQMAS spectrum is shown in Fig. 6b,8 demonstrating that the four quadrupolar Al sites in the A9B2 material yielded overlapped signals in the 1D MAS spectrum that can only be resolved at a very high field at 40 T (Fig. 6a), which, in contrast, can be completely separated by MQMAS at a relatively moderate field of 19.6 T. To date, 2D MQMAS has probably become the most useful and robust method to untangle quadrupolar and isotropic interactions and played a pivotal role in extracting structural information on catalytic sites involving quadrupolar nuclei.

Fig. 5 Cartoon showing the Zeeman states and Boltzmann distribution of a spin-5/2 nucleus (a), and the corresponding resonances for satellitetransition (ST) and central-transition (CT) signals in a static NMR spectrum (b), with the asymmetry parameter hQ ¼ 0. The expanded spectrum in the CT region is shown in (c), with MAS averaging of second-order quadrupolar broadenings illustrated at finite and infinite spinning rates. (d) demonstrates the CT lineshape at MAS as a function of the asymmetry parameter hQ.

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NMR of catalytic sites

Fig. 6 Field-dependence of quadrupolar broadening (a) and MQMAS spectroscopy for separating quadrupolar and isotropic interactions (b). (a) Adapted with permission from Gan, Z.; Gor’kov, P.; Cross, T. A.; Samoson, A.; Massiot, D. Seeking Higher Resolution and Sensitivity for NMR of Quadrupolar Nuclei at Ultrahigh Magnetic Fields. J. Am. Chem. Soc. 2002, 124, 5634–5635, Copyright 2002 American Chemical Society. (b) Adapted with permission from Chen, K. A Practical Review of NMR Lineshapes for Spin-1/2 and Quadrupolar Nuclei in Disordered Materials. Int. J. Mol. Sci. 2020, 21, 5666.

9.17.2.6

NMR sensitivity

Sensitivity is a practical problem for NMR characterization, especially for catalytic materials. Fundamentally, it is a function of the gyromagnetic ratio g, natural abundance and experienced quadrupolar interaction (if spin > 1/2) of the observed nucleus. If one considers a universal situation for all nuclei, regardless of spin-1/2 or quadrupolar types, the NMR signal-to-noise (S/N) ratio is related to g and B0 as, S/N f |g|5/2(B0)3/2, and therefore the sensitivity largely depends on the type of observed isotope and the field strength, which applies for both spin-1/2 and quadrupolar nuclei.2 For example, for the same sampling numbers of 1H and 15N nuclei, the former provides 300 larger S/N than the latter, corresponding to 90,000 times of time saving, and that has not included the sensitivity difference of the natural abundances, i.e., 100% for 1H and < 0.5% for 15 N. Because the gyromagnetic ratio is a fixed intrinsic property of the spin, enriching the materials with NMR active isotopes and increasing the field strength are most straightforward methods to enhance the sensitivity. A quick estimation from the above equation shows that doubling B0 provides 23/2 ( 3) folds of S/N enhancement. Further, line narrowing can add further contributions to the sensitivity enhancement. Increasing the field strength will result in additional enhancement for quadrupolar nuclei (specifically for half-integer spins), given the field-dependent second-order quadrupolar broadening as discussed above. For instance, doubling the field strength will narrow the CT linewidth by a factor of 4 and may lead to a S/N enhancement of 20-fold,28 compared to that of 3-fold for spin-1/2 nuclei. In short, this discussion provides a rough but practical guideline for evaluating NMR sensitivities when carrying out NMR experiments for new materials. With the major NMR interactions introduced above, it would be convenient and logical to separate them into two categories, one concerning uncoupled spins and the other concerning coupled spins. For uncoupled spins, CSA and quadrupolar coupling are considered as they offer important information on local structure and electronic geometry encoded in the powder patterns. For coupled spins, dipolar coupling and J-coupling play pivotal roles as they offer information on spatial proximities, chemical bonding, as well as internuclear distances within a few bonds. The determination of coupling parameters such as the dipolar coupling constant (DCC), asymmetry factor, and the angular terms between the nuclear dipoles would reveal valuable information on molecular structure and dynamical motions. In Section 9.17.3, we will show with detailed applications how CSA and quadrupolar coupling can help resolve the structures of catalytic sites. The coupled spin systems are much more complex but provide richer structural information, which will be discussed in Section 9.17.4.

9.17.3

Chemical shift and quadrupolar patterns for investigating catalytic sites

As shown in the above section, the isotropic chemical shift, CSA and quadrupolar coupling interactions are well-understood NMR terms that contain very important structural information and therefore can serve as useful tools to characterize the structures of catalytic sites. In fact, such terms have been widely employed for investigating various types of catalytic materials, e.g., zeolites, oxides and metal supported oxides. Here, we will illustrate practical applications of these fundamental NMR features for understanding catalytic problems.

NMR of catalytic sites 9.17.3.1

481

Isotropic chemical shift for revealing catalytic sites

Among the many NMR parameters, the isotropic chemical shift is probably the most straightforward for studying catalytic sites, as only a numerical value of the averaged chemical shift needs to be considered. Despite this simplicity, the isotropic chemical shift has proven to be robust and powerful in the history of characterizing the structures of catalytic sites, especially for spin-1/2 nuclei in the absence of quadrupolar coupling interaction. Among all NMR active nuclei, proton is notably special owing to its spin-1/2 nature and high sensitivity, and its prevalence on surface hydroxyl groups, solid acid sites and many other catalytically-active structures, making 1H MAS NMR a remarkable tool since the early days of the development of MAS NMR. Zeolites are one type of catalyst that have benefited greatly from 1H MAS NMR, thanks to the lack of strong homonuclear 1H-1H dipolar couplings. Under MAS condition, important proton species such as bridging acid sites (BAS), silanol (SiOH) and aluminol (AlOH) groups can all be well resolved in a 1H MAS NMR spectrum, as shown in Fig. 7.29 BAS are the key catalytic sites of most reactions catalyzed by zeolites and such well resolved spectra lead to convenient investigations into its intrinsic chemical nature as well as interactions with reactive molecules or physisorbed probe molecules, rendering the basis for implementing advanced NMR techniques such as twodimensional correlation NMR and in-situ NMR discussed in Sections 9.17.4 and 9.17.5. NMR is also well-known for its ability to provide reliable quantitative information as an intrinsic property of the technique itself. As a comparison, IR spectroscopy can also be used to quantify species but suffers severely from distorted baseline and optical artifacts.30 With a known amount of polydimethylsiloxane (PDMS) introduced as internal reference, the quantity of each species in the zeolite spectrum in Fig. 7 can be precisely measured upon peak deconvolution, with results shown on the righthand side of the spectrum. Such quantitative evaluation of species can sometimes be indispensable for understanding the nature of catalysts. Apart from zeolites, 1H MAS NMR has also been recognized as a crucial tool for unraveling many other catalytic structures containing surface hydroxyl groups and even hydrides such as in metal oxide-based catalysts, owing to the spin-1/2 nature and high NMR sensitivity. However, proton-rich hydroxyl group networks commonly exist on metal oxide surfaces which lead to prospective broadenings to the spectrum, mostly due to homonuclear 1H-1H dipolar couplings. As discussed in Section 9.17.2.4, for spin-1/2 nuclei the major inhomogeneous broadenings such as CSA and heteronuclear dipolar coupling are sufficiently removed by MAS, and spinning rates allowed by typical commercial NMR instruments nowadays, i.e., > 20 kHz, render efficient suppression of the broadenings. However, such MAS rates are not yet sufficient to produce resolved 1H spectra for samples with strong homonuclear 1 H-1H couplings. Fig. 8 shows a series of 1H MAS NMR spectra obtained for surface hydroxyl species of In2O3, an important n-type semiconductor functional material, but made recent rapid development in heterogeneous catalysis for CO oxidation, perfluorooctanoic acid decomposition, and CO2 hydrogenation.31 The In2O3 surface possesses complicated proton networks that lead to spectra dominated by broadenings induced by 1H-1H dipolar couplings, prohibiting further analyses of the data. As shown in Fig. 8a–c, at MAS < 20 kHz, although the field strength increases from 9.4 to 18.8 T, still fails to resolve the species. In contrast, the resolution is greatly improved as increasing the MAS rate stepwise to 40 and 60 kHz, making possible the identification of three domains of proton species indicated by m1, m2, m3 in the figure and even finer structures of each domain. Although only examples of proton spectroscopy are shown, this is by no means the only nucleus probed successfully in NMR characterizations. Other nuclei commonly found in catalytic materials such as 27Al, 29Si, and 31P are investigated, strongly relying on their diso values, benefitting from the simplicity of interpretations. For example, diso (27Al) at ca.
10–10, 20–30 and 50– 70 ppm regions unambiguously reveal the 6-, 5, and 4-coordinated Al atoms, i.e., Al(VI), Al(V) and Al(IV), which is greatly useful for studying Al included catalysts such as zeolites, alumina and amorphous aluminosilicates. However, diso has some limitations. In

Fig. 7 1H MAS NMR spectrum showing resolved proton species in zeolite catalyst HZSM-5 at Si/Al ¼ 15 (a) and quantitative information of species obtained from deconvoluted peaks (b). Adapted with permission from Abdolrahmani, M.; Chen, K.; White, J. L. Assessment, Control, and Impact of Brønsted Acid Site Heterogeneity in Zeolite HZSM-5. J. Phys. Chem. C 2018, 122, 15520–15528, Copyright 2018 American Chemical Society.

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NMR of catalytic sites

Fig. 8 Resolving nested proton species on In2O3 surfaces via high-speed MAS 1H NMR. By increasing the MAS rate to 60 kHz, at 18.8 T, 1H-1H homonuclear coupling is significantly suppressed and multiple species are resolved as indicated in the spectrum. Adapted with permission from Han, Q.; Gao, P.; Liang, L.; Chen, K.; Dong, A.; Liu, Z.; Han, X.; Fu, Q.; Hou, G. Unraveling the Surface Hydroxyl Network on In2O3 Nanoparticles with High-Field Ultrafast Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy. Anal. Chem. 2021, 93, 16769–16778, Copyright 2021 American Chemical Society.

many cases, especially in structurally disordered materials, multiple sites with very little variations in diso values may overlay with one another, broadening the spectrum inhomogeneously, which is known as chemical shift distribution. Such broadening holds a constant width in ppm, which scales in Hz with the B0 strength and therefore cannot be removed by increasing B0, nor by designed pulse sequences. However, 2D NMR experiments may be helpful in providing useful information under certain circumstances.31–33 In cases of catalysts containing spectroscopically overlayed but chemically distinct crystalline sites, such as aluminophosphates (AlPOs) and zeolites, computational tools could be of great importance to assist in revealing structure-spectrum relationships. For example, trivial 27Al diso differences in the tetrahedral region for zeolite catalysts provide the information of structural deviations caused by the changes of AleOeSi bond-angles and bond-lengths of framework acid sites, but such small changes can only be meaningfully investigated in the combination with DFT calculations.34 In other studies, Ashbrook and coworkers used a combination of 31P NMR spectroscopy and DFT calculations to help understand the local structure of AlPOs crystalline sites, including the number of crystallographic P sites, their relative populations, and the positions of any dopant atoms in the framework35; they also showed that for zeolitic SiO2, framework SieO bond length, as well as the relationship between SieOeSi bond angle and 29Si NMR diso values, can be well predicted by computational simulations.36

9.17.3.2

CSA for revealing catalytic sites

Although diso is convenient for tracking species, one should recall that chemical shielding is anisotropic, and the detailed CSA parameters, i.e., principal components and asymmetry parameter, are orientation dependent and thus very sensitive to the local hybridization and electron structure at the observed nucleus.37 Such information can be unique and essential for understanding certain catalytic sites, especially for single-site catalysts.38 Therefore, sometimes it is desirable to measure CSA, which usually requires static or slow MAS conditions to intentionally avoid averaging it out, or employ specially designed pulse sequence to reintroduce CSA interaction under MAS conditions.39 Static NMR spectra provide the powder patterns and are most convenient for measuring CSA, but this approach usually suffers from sensitivity issues. Alternatively, spinning the sample at slow MAS rates yields a series of spinning sidebands as shown in Fig. 4b, resembling the CSA powder pattern which allows for the extraction of CSA parameters. However, as CSA patterns are usually broad, it is more often that overlapped CSA patterns are observed for samples containing multiple sites, which makes the direct evaluation from the 1D NMR spectroscopy extremely challenging. In that case, sideband separation experiments, such as magic-angle turning (MAT)40 or phase-adjusted spinning sidebands (PASS)41,42 can be employed, which allows to separate the CSA spinning sidebands with their diso in a 2D spectrum so that the CSA of individual sites

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can be evaluated. Alternatively, CSA parameters can be measured by performing proper rotor-synchronized recoupling sequences at moderate, or even fast MAS rates, such as Separation of Undistorted Powder patterns by Effortless Recoupling (SUPER),43 Recoupling Of CSA (ROCSA),44 RNCSA,45 etc. An example using CSA to study local structures is shown in Fig. 9 with characteristic spectroscopic signatures from metal-ligand bonds, in Mehring notation.46 As metal-carbon single, double, or triple bonds are formed, the 13C chemical shift tensors (CST) are notably different, because chemical shift is a sensitive probe of the relative energy of s (M-C) and p (M-C) symmetric frontier orbitals. For metal alkyls (Fig. 9a), a weak yet important p (M-C) interaction takes place, evidenced by a relatively large deshielding of the d11 component. For metal alkylidenes and metal alkylidynes (Fig. 9b and c), the deshielding gets markedly larger (more positive value of d11) as the partial p-interaction turns into a full p-bond. Besides this general trend, the CST is an interesting descriptor of interaction between d-orbital electron and p-accepting ligand, and hence allows to reveal reactivities such as olefin insertion, sbond-metathesis reaction as well as decomposition pathways of such molecules.47,48 The alkyl chemical shift on transition metals also showed that, interestingly, strongly p-accepting ligands such as CO can introduce weak p orbitals with contribution on the metal, even for compounds with d6 electron configuration, such as Fischer carbenes.48,49 Such evidence intuitively shows that CO, although often seen as a poison, can bring about reactivity, which is of great help to understand the complicated FischerTropsch process. It shall be noted that while the CSA interaction can be essential for structural elucidation, practical challenges often arise in obtaining the numerical values, as well as their interpretations in terms of structure. Thanks to the rapid development of computational power as well as the theoretical strategies in DFT and first principle calculation, etc., it is convenient to use computational approaches to assist in understanding the relationship between NMR parameters and the molecular structures.50–52

9.17.3.3

Quadrupolar interaction for revealing catalytic sites

For I > 1/2 nuclei, the quadrupolar broadening can usually be overwhelming and thus impede direct evaluation of chemical shielding parameters, while it is important to know that the quadrupolar interaction is also a reliable tool to trace local chemical environment of the observed nucleus via measuring the EFG tensor and the quadrupolar coupling constant CQ, as introduced in Section 9.17.2.5. A good example of applications of quadrupolar NMR to catalysis can be found in Fig. 10, demonstrating how the fine structure of aluminum species is characterized exclusively by 27Al NMR.53 The high NMR sensitivity of 27Al isotope has made NMR an excellent and convenient tool for studying Al species in zeolites compared to other characterization methods. Nonetheless, challenges remain because (a) the quadrupolar interaction is extremely strong, e.g., CQ up to 17 MHz and (b) aluminum species of interest, i.e., Al(IV), Al(V) and Al(VI), are susceptible to trace water intrusion. For example, only two tetrahedral Al species Al(IV)-1 and Al(IV)-2 present in the dehydrated zeolite as shown in Fig. 10a, as indicated by the simulated quadrupolar lineshapes, with very broad quadrupolar peak widths. However, once hydrated, those two tetrahedral Al species become much narrower and converge to the ca. 50–60 ppm region due to reduced CQ; meanwhile, Al(V) and Al(VI) emerge at ca. 30 and 0 ppm, respectively. The main reason can be attributed to the change of EFG and/or coordination numbers of Al by water molecules. Each Al species can be

Fig. 9 Simulated chemical shift tensors on the a-carbon and main orbital interactions of the single (a) double (b) and triple (c) metal
carbon bonds, in Mehring notation. The p-character orbitals originate from a low-lying vacant orbital on the metal that can interact with the p orbital on the a-carbon atom in a p-symmetric interaction. Notably larger deshielding is observed in (b) and (c) indicative of the presence of multiple bonds. Adapted with permission from Gordon, C. P.; Lätsch, L.; Copéret, C. Nuclear Magnetic Resonance: A Spectroscopic Probe to Understand the Electronic Structure and Reactivity of Molecules and Materials. J. Phys. Chem. Lett. 2021, 12, 2072–2085, Copyright 2021 American Chemical Society.

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Fig. 10 Zeolite aluminum species revealed by quadrupolar 27Al NMR for (a) 1D NMR at dehydrated conditions, (b) 1D NMR at hydrated conditions at different field strengths as indicated, (c) 2D MQMAS NMR at dehydrated conditions and (d) 2D MQMAS NMR at hydrated conditions. Adapted with permission from Chen, K.; Gan, Z.; Horstmeier, S.; White, J. L. Distribution of Aluminum Species in Zeolite Catalysts: 27Al NMR of Framework, Partially-Coordinated Framework, and Non-Framework Moieties. J. Am. Chem. Soc. 2021, 143, 6669–6680, Copyright 2021 American Chemical Society.

well resolved by 2D MQMAS experiments as shown in Fig. 10c and d, for dehydrated and hydrated zeolites, respectively. Such detailed but complex information can hardly be obtained from other characterization methods.

9.17.4

Investigation of catalytic sites via internuclear correlations

Characterization of the fine site structure, the site-site proximity, as well as site/reagent interactions is critical to understanding the nature of catalytic sites. In that sense, NMR, as a well-known powerful tool providing rich information about internuclear interactions, has played pivotal roles in solving catalytic problems by revealing spatial and/or bond connectivities among atom or active sites, as well as quantitative spatial distances. As a matter of fact, coupled spins are more common than uncoupled spins in solid catalytic materials, which makes these internuclear correlations extremely efficient and valuable. From the NMR perspective, the internuclear correlations can be established via dipolar coupling and J-coupling interactions. Hence, it is very important that the physical and spectroscopic characteristics of dipolar- and J-coupling interactions are addressed, as they are the basis of NMR characterizations of internuclear interactions. It shall be noted that chemical exchange can sometimes be revealed by internuclear correlation as well, as a spectroscopic analog to spin-spin interaction. In the following discussion, necessary concepts of dipolar- and J-coupling interactions are first introduced, followed by discussions of how they are exploited in NMR to reveal internuclear correlations and finally, selected practical applications are demonstrated.

9.17.4.1

Dipolar coupling and J-coupling

Dipolar coupling plays a leading role in investigating internuclear correlations compared to J-coupling, because of its much larger magnitude. Usually, to establish internuclear correlations under MAS, techniques termed “recoupling” are necessarily employed. As shown in the preceding section, dipolar coupling interactions on one hand broaden the spectra and are often suppressed by MAS

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and/or RF decoupling for resolution enhancement; on the other hand, associated with this suppression is the loss of structure- and dynamics-related information encoded in the interaction. Therefore, the anisotropic spin interactions need to be reintroduced under the MAS condition, in order to allow investigations into the structural information, which opens up an important field called “recoupling.” Recoupling techniques are capable of restoring either CSA or dipolar coupling as required,39 but the latter is more important for probing internuclear interactions and thereby CSA recoupling is not involved in the discussion here. Detailed and systematic recoupling techniques have been developed by numerous NMR researchers54–56 and reviewed recently by Hou et al.,39 which are great sources for further readings. Indeed, recoupling techniques are the basis of modern NMR spectroscopy for characterizing coupled spin systems and can be implemented in both 1D and multi-dimensional (MD) NMR experiments. For example, the well-known cross polarization (CP)57,58 can transfer polarization from sensitive nuclei, e.g., 1H, to insensitive nuclei such 13C, 15N, 29Si, to enhance their sensitivities in 1D NMR; such polarization transfer technique can also be used to construct 2D correlation NMR spectroscopy, which untangles overlapped signals in 1D NMR spectrum and provides invaluable information for revealing local chemical structures. To date, a variety of pulse sequences and recoupling methods have been developed for constructing 2D correlations in ssNMR, including CP,57 Heteronuclear Multiple-Quantum Correlation (HMQC),59,60 Heteronuclear Single Quantum Correlation (HSQC),60 Refocused Insensitive Nuclei Enhanced by Polarization Transfer (RINEPT)60,61 for heteronuclear correlations, and Nuclear Overhauser Effect Spectroscopy (NOESY),62 Radio Frequency Driven Recoupling (RFDR),63 COmbined R2vn-driven spin Diffusion (CORD),64 Double-Quantum Single-Quantum (DQ-SQ)65 for homonuclear correlation, which have been widely used in solid state materials in recent years. Another important application of recoupling techniques is their role in probing internuclear distances, where the dipolar coupling constant (DCC) is often measured by employing NMR recoupling methods such as the classic Rotational-Echo DOuble-Resonance (REDOR)66 and its derivations including Resonance-Echo Saturation-Pulse DOuble-Resonance (RESPDOR),67 Rotational Echo Adiabatic Passage DOuble Resonance (REAPDOR),68 etc., as well as other approaches including CP with Variable Contact-time (CP-VC),69 RN-symmetry-based DIPSHIFT (RNDIPSHIFT)70 and Phase-Modulated Rotary Resonance PMRR,71 for heteronuclear distances, as well as RFDR,63 Dipolar Recoupling At the Magic Angle (DRAMA),72 Permutationally Offset STabilized companion (POST-C7)73 and Back to Back (BABA)74, on the other hand, for homonuclear distances. It is also important to distinguish between spin-1/2 and quadrupolar nuclei, although both work with essentially all the recoupling-involved double-resonance methods. CP and REDOR, for example, are very common recoupling schemes in solidstate NMR, but were initially designed for spin-1/2 nuclei but not for quadrupolar nuclei. For the latter, recoupling becomes complicated due to the involvement of multiple transition states and the second-order quadrupolar coupling, as illustrated in Fig. 5, which can lead to significantly reduced recoupling efficiency as well as lineshape distortions. Fortunately, suitable modifications on these recoupling methods have been proposed specifically for quadrupolar nuclei, such as BRoadband Adiabatic INversion CP (BRAINCP),75 REAPDOR,68 RESPDOR.67 In contrast to dipolar coupling, J-coupling interaction has an important feature, i.e., the isotropic component does not vanish under MAS. In addition, it arises from nuclei sharing electron orbitals, and thus can exclusively probe the bonding connectivity among atoms, which is exceedingly critical for elucidating molecular structure in certain situations. Such connectivities are typically restrained to a few (e.g., 1–3) chemical bond distances. However, J-coupling applications in ssNMR can be challenging, as its size (typically within a few hundred Hz) is much weaker than other anisotropic interactions. Hence, it is often difficult to directly observe J-coupling in a 1D ssNMR spectrum given the large homogeneous and/or inhomogeneous broadenings in solids, unless all the line broadenings can be sufficiently removed and efficient spectral resolution is achieved. Considering the above discussion, it would always be beneficial to exploit both dipolar and J-coupling interactions as complementary tools for investigating molecular structures in search of through-space and through-bond information. Before moving forward to NMR techniques and specific experiments, it would be necessary to first introduce some detailed concepts of the dipolar coupling interaction in order to understand how it helps to reveal internuclear correlations; J-interaction is relatively simple and will be introduced briefly after dipolar-interaction.

9.17.4.1.1

Dipolar coupling

Dipolar coupling arises from two magnetic dipoles and represents the direct nucleus-nucleus magnetic interaction. The full Hamiltonian of the dipolar coupling consists of secular and non-secular terms,2,4 of which the former is time independent and the latter is time dependent. At most NMR field strengths (which is typically high), only the secular term is considered because the non-secular part is averaged to zero. Also note that the time-dependent frequencies of non-secular term are u0 and 2u0, much higher than the secular frequency. Such treatment is also known as secular approximation.4 However, the mathematical form of the secular term still depends on whether the spins being coupled are the same isotopic species or not. For isotopes being the same, i.e., homonuclear coupling, there exists a flip-flop term causing transition between different states of the two coupled spins, leading to homogeneous broadening of the spectrum which can only be stepwise suppressed by increasing the external field strength or MAS rate. Note that this is the reason for the “stepwise” homonuclear decoupling by MAS observed previously in Fig. 4c. As stated in that section, specially designed homonuclear decoupling sequences such as WAHUHA,14 FSLG,15 PMLG16 and DUMBO17 are RFdecoupling options for suppressing such broadenings. The Hamiltonian describing the secular part of the dipolar coupling interaction is expressed in Eq. (2), where D is the DCC, - is Planck’s constant, Î1 and Î2 are the angular momentum operators of spin I1 and I2, with Î1z and Î2z being their z components, and q is the angle between the internuclear vector and the external magnetic field B0, as illustrated in the scheme shown in Fig. 11.

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(A)

(B)

NMR spectrum

Dipolar coupling: Through space

Dipolar-split: Pake powder pattern

(C) (D)

(E)

NMR spectrum

J-split

J-coupling: Through bond

Fig. 11 Schemes showing dipolar (a) and J-coupling (c) interactions and their characteristic effects (b), (d) and (e) on NMR spectroscopy, respectively.

   ^ D;sec ¼
D Z 3^I1z^I2z
^I1^I2 3cos2 q
1 H 2 D¼

m0 g1 g2 Z 4p r 3

(2)

(3)

The expression of the dipolar coupling constant D is shown in Eq. (3), where g is the gyromagnetic ratio, m0 is the vacuum permeability and r is the internuclear distance. The equations show that both heteronuclear and homonuclear dipolar couplings depend on the orientation of the inter-nuclear vector and the inverse cube of the distance. Without MAS rotation, such interactions in crystalline powders often give rise to the Pake powder pattern,76 as shown in Fig. 11, where the separation between the two strong singularities (also known as dipolar coupling frequency) provides the DCC. The pattern is similar for homonuclear and heteronuclear cases except that there is a scaling factor of 1.5 for the split frequencies as indicated in the expression for DII and DIS in the figure. Measuring the magnitude of the dipolar coupling constant D is very important because it allows one to determine internuclear distances. Pulse sequences such as TMREV,77 LG-CP78 and RN-DIPSHIFT70 have been developed to directly measure the dipolar split frequency at MAS conditions, by employing appropriate RF irradiations during the indirect dimension. Alternatively, the DCC can also be measured by fitting the evolution of dipolar dephasing with recoupling sequences such as REDOR and RESPDOR. However, it should be mentioned that in practical solid materials the dipolar interaction often presents between many abundant spins, thus cautions must be paid in choosing a proper recoupling technique for measuring internuclear DCCs. For instance, REDOR or RESPDOR is only an optional method when there are isolated spin pairs such as the Al-H pair in zeolites, while RN-DIPSHIFT is well-suited for samples containing multiple abundant spins.

9.17.4.1.2

J-coupling

J-coupling (also known as indirect or scalar-coupling) arises from indirect nucleus-nucleus magnetic interaction mediated by the surrounding electrons, as shown in Fig. 11. In contrast to the through-space dipolar coupling, J-coupling is exclusively established through bonds. Using a two-spin system as an example, a small magnetic field arises from the electron perturbation to one nucleus, and such small field would lead to a split of the frequency of the other spin. Spin-orbital, spin-dipolar and Fermi contact interactions are the most considered sources for the J-coupling interaction.4 The Hamiltonian of J-coupling can be expressed as, HJ ¼ h J12 I1 $I2

(4)

where J is the J-coupling constant. It should be pointed out that there is no B0 dependence in the Hamiltonian, which makes Jcoupling simpler than the dipolar coupling interaction presented above. Fig. 11d and e show that the major spectroscopical effect of J-coupling is the isotropic splitting of the resonant peak observed in the NMR spectrum. The splitting pattern of the resonance

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depends on the number and type of coupled spins. Generally, if the observed spin I is coupled to a single spin-1/2 nucleus, the resonant peak will be split into two peaks separated by the J-coupling value. If it is coupled to two identical spin-1/2 nuclei, the split will result in three peaks separated by the J-coupling value, with an intensity ratio of 1:2:1. The magnitude of the J-coupling depends on bond numbers (e.g., single, double or triple bond), the gyromagnetic ratio, and the degree of orbital overlap. Also, heavy nuclei usually generate larger J-couplings as they have more extensive orbitals. The amplitude of J-coupling can sometimes be obtained by performing J-resolved experiments.79 Last but not least, for the basic concept of internuclear couplings, it is important to mention the cases of dipolar- and/or Jcoupling with the involvement of quadrupolar nuclei.80,81 The quadrupolar effect from a quadrupolar nuclear spin S can affect the NMR spectrum of a spin-1/2 nucleus that is coupled to it. If J-coupling exists, the spectrum of the spin-1/2 nucleus will be split into a 2S þ 1 multiplet, as shown in Fig. 12, due to the fact that there are 2S þ 1 energy states in first-order Zeeman perturbation. In contrast, if the quadrupolar nucleus is observed, the J-coupling can cause a split to the second-order quadrupolar powder pattern, also shown and indicated in Fig. 12. Usually, the first type, i.e., the quadrupolar effect on the spin-1/2 spectrum is most interesting to catalytic materials, as the small J-couplings are often obscured by the quadrupolar broadening in the second type. With that considered, we will take a further look into how the quadrupolar effect changes the splitting patterns in three cases. (1) If the quadrupolar coupling constant (CQ) of spin S is zero, the 2S þ 1 multiplet will be equally spaced. (2) If CQ > 0, the dipolar coupling starts to play a role, causing residual quadrupolar couplings (“R” as indicated in Fig. 12) to further shift each peak in the multiplet. Briefly, this effect arises because the nonsecular parts of the dipolar and quadrupolar Hamiltonians interfere positively and create cross-terms that are not averaged out by MAS. As a result, the spin-1/2 nucleus is further shifted by the second-order quadrupolar terms of the quadrupolar spin, depending upon the quadrupolar spin state m, the crystallite orientation, and the relative orientation between the EFG and the dipolar interaction. This situation can occur in various types of catalytic materials or catalytic sites, such as zeolites (directly bonded 1H-17O, 31P-27Al), metal hydrides (1H-27Al, 1H-69/71Ga), etc. The exact splitting pattern has been comprehensively described in quantum theory in the literature,81 which is not discussed here. (3) If only the dipolar interaction exists (J ¼ 0), i.e., in cases where the spin-1/2 and quadrupolar nuclei are not directly bonded, the multiplet will merge, and the total effect is described by vm;iso ¼

  vIS vq  SðS þ 1Þ
3m2 3cos2 b
1 þ h sin2 bcos2a 10vS

(5)

where nm, iso is the isotropic frequency displacement for resonance peak of the observed spin-1/2 nucleus, S is the spin number of the quadrupolar nucleus, nIS is the dipolar coupling constant, nq is the quadrupolar frequency, nS is the Zeeman (or Larmor) frequency of spin S, and a and b are the polar angles describing the relative orientation between dipolar and quadrupolar coupling tensors. Clearly, the  m states will contribute equally to the shift. This type of effect has been used to study the bridging acid site (BAS) of zeolite catalysts, where the chemical shifts of protons are perturbed by the nearby 27Al atoms possessing large quadrupolar coupling constants.82

9.17.4.1.3

Applications

In this section, a few recent applications using these J- and quadrupolar-coupling induced spectral split on revealing the structures of catalytic sites are demonstrated as follows. As an example using J-splitting to solve real catalytic problems, Fig. 13 demonstrates a single-atom Pt/13CO interaction probed by 195Pt/13C MAS NMR.83 Noble metal atoms are often capable of activating thermally stable small molecules such as CO and H2,

Fig. 12 Schematic representation of the effect of the J-coupling between a spin-5/2 quadrupolar nucleus Q and a spin-1/2 nucleus I. The secondorder broadening lineshape of central transition of the quadrupolar nucleus Q (top, in blue) is split into two by the J-coupling to I (in green). The signal of the nucleus I is split into a 2S þ 1 (e.g., 6 for S ¼ 5/2) multiplet. Additional second-order broadenings and shifts arise when R (the dipolar quadrupolar cross term) becomes significant. Adapted from Massiot, D.; Fayon, F.; Deschamps, M.; Cadars, S.; Florian, P.; Montouillout, V.; Pellerin, N.; Hiet, J.; Rakhmatullin, A.; Bessada, C. Detection and Use of Small J Couplings in Solid State NMR Experiments. C. R. Chim. 2010, 13, 117–129.

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Fig. 13 J-coupling interaction (split) as exclusive evidence of formation of single-atom sites for (a)–(g) Pt/13CO and (h) Ag3H, with details described in the related context. (a)–(g) Adapted with permission from Liu, K.; Hou, G.; Mao, J.; Xu, Z.; Yan, P.; Li, H.; Guo, X.; Bai, S.; Zhang, Z. C. Genesis of Electron Deficient Pt1(0) in PDMS-PEG Aggregates. Nat. Commun. 2019, 10, 996, Copyright 2019 Springer Nature. (h) Adapted with permission from Baba, T.; Komatsu, N.; Sawada, H.; Yamaguchi, Y.; Takahashi, T.; Sugisawa, H.; Ono, Y. 1H Magic Angle Spinning NMR Evidence for Dissociative Adsorption of Hydrogen on Ag þ-Exchanged A- and Y-Zeolites. Langmuir 1999, 15, 7894–7896, Copyright 1999 American Chemical Society.

and their single-atom dispersions on the catalyst surface are highly desired for achieving best catalytic performances. However, single atoms tend to aggregate into clusters or nanoparticles, and efficient and robust detection of single atom characteristics has remained challenging. The material shown in Fig. 13a–c demonstrates mononuclear electron-deficient Pt prepared on PDMS (polydimethylsiloxane) and further dispersed on SiO2 surface (Fig. 13a), which were subsequentially treated with CO (Fig. 13c) and 13 CO (Fig. 13b) for adsorption. Solid-state 195Pt MAS NMR spectra of the catalyst with CO treatment showed a peak at
3226 ppm (Fig. 13e), but split to a doublet separated by J(195Pt-13C) ¼ 1750 Hz when treated instead by 13CO (Fig. 13d), because of the formation of a PteC bond on single Pt atom sites which yields electronic overlap between Pt and CO. The same J(195Pt-13C) values were simultaneously observed in 13C MAS NMR spectra (Fig. 13f and g). Via such a robust characterization method, it was remarkably found that the catalyst carrying single atom Pt/CO remained stable for over 6 months stored at ambient temperature, as evidenced by almost identical 195Pt NMR spectra periodically measured. Another example is illustrated in Fig. 13h, where a quadruplet induced by J-coupling observed in 1H MAS NMR spectrum, on Ag3 species dispersed at bridging acid sites of zeolite catalysts. The quadruplet splitting unambiguously identified the Ag3 cluster, which could be difficult to observe by many other characterization methods.84 As shown in Fig. 12, quadrupolar interaction from a spin I > 1/2 spin can induce splitting in the spectrum of observed spin-1/2 nucleus via J-coupling. This effect can be applied as a unique approach to probe metal hydrides (M-H), given the direct metal/ hydrogen bonding and high sensitivity of 1H NMR. Metal hydrides are of special interest due to their high reactivity in both inorganic and organometallic chemistry and are considered important catalytic intermediates; however, their small quantity and high reactivity make most characterizations challenging. In fact, the actual chemical pathways leading to their formation were usually the subject of assumptions. With that considered, characterizing metal hydrides with the highest possible accuracy is urgently demanded. Infrared spectroscopy (IR) used to be one, if not the only method to probe metal hydrides, but given the low

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Fig. 14 (a) Preparation of surface Al-H hydrides. (b) and (c) 1H MAS NMR spectra of the hydride recorded at 9.4 T and 18.8 T. (d) J-HMQC-filtered 1 H MAS spectrum with 27Al decoupling (18.8 T). (e) J-resolved slice (B0 ¼ 18.8 T). Adapted from Mazoyer, E.; Trébosc, J.; Baudouin, A.; Boyron, O.; Pelletier, J.; Basset, J.-M.; Vitorino, M. J.; Nicholas, C. P.; Gauvin, R. M.; Taoufik, M.; et al. Heteronuclear NMR Correlations to Probe the Local Structure of Catalytically Active Surface Aluminum Hydride Species on g-Alumina. Angew. Chem. Int. Ed. 2010, 49, 9854–9858.

concentration of M-H and baseline distortions of IR, the extractable information is limited. Interestingly, a recent report shows that NMR can uniquely probe Al-H hydride species, as shown in Fig. 14.85 Al-H species on an alumina surface were synthesized via organometallic methods as described in Fig. 14a. The prepared Al-H hydride, i.e., structure 2, was characterized by a simple acquisition of a 1D 1H MAS NMR spectrum, as shown in Fig. 14b and c. The spacing of 376 Hz between the innermost lines in Fig. 14b is a direct measure of the 1H-27Al J-coupling, and the large value indicates the presence of metal hydride species. The interval between the outer lines of the multiplet can be explained by the J þ R patterns shown in Fig. 12, which is a function the aluminum Larmor frequency (Eq. 5); it therefore explains the larger spreading of the multiplet observed at 9.4 T compared to 18.8 T. Moreover, a 2D Jresolved experiment provides a direct measurement of the splitting, as 381 Hz, in accordance with that observed in the 1H MAS spectrum. In short, this work shows that the quadrupolar-induced internuclear interaction is not only capable, but powerful to render exclusive and accurate structural specifics of catalytic sites, and can be used as an alternative method for IR spectroscopy and others. In short, although dipolar- and J-coupling are different, they are all essentially magnetic interactions between different nuclei with similar common characteristics. First, they both lead to perturbed energies for the observed nuclei, which consequently leads to splitting patterns containing the coupling frequencies in the NMR spectrum. The difference is that dipolar-coupling is averaged out by MAS but J-coupling survives. Second, they both can serve as intermediates for constructing internuclear correlations, which will be included in the following two sections. It should be noted that solid materials allowing for the direct assessment of the dipolar- or J-coupling split frequencies are rare, because in most cases, their spectra consist of overlapped patterns or the spectrum is simply too broad. Therefore, it would always be a good idea to try employing double-resonance experiments to construct 2D correlation spectra or to indirectly measure the DCCs (thus the internuclear distance).

9.17.4.2

Constructing 2D NMR correlations

Although 1D NMR, whether static or MAS, is of great importance and extensively used in solid state catalysis, 2D NMR provides a very advanced platform for exploiting NMR capabilities.86 In general, 2D NMR normally requires much longer instrument time and complex pulse sequence designs, especially for those involving quadrupolar nuclei, but has many advantages over 1D spectroscopy and remains irreplaceable in investigating catalytic sites. On one hand, 2D NMR can offer straightforward interatom correlations which cannot be obtained in 1D NMR. On the other hand, 2D NMR can serve as a filter, as only coupled spins or desired spin Hamiltonians are selected to show in the spectrum, and thus simplifies the spectrum. As coupled spins are common in solid catalytic materials, and crucial atomic/molecular-level structural information is encoded in the coupled internuclear interactions, we will present relatively expanded discussions of the 2D NMR techniques in this section. However, it still needs to be mentioned that in addition to the scan accumulations for second dimension that significantly increase the experimental time, the polarization transfer efficiency (necessarily needed for building up correlations) is typically low, < 20% in general and could be far-under 10% for quadrupolar nuclei, which leads to further demands for scan accumulations. Therefore, one should always

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evaluate the sensitivity of the nuclei being observed as well as their concentrations in the material prior to conducting 2D NMR experiments. For instance, catalytic sites on surface species are typically in small quantity to the bulk phase and loaded catalytic sites on supports are typically in small quantity as well. In addition, the internuclear couplings (e.g., DCCs) are also frequently used for probing spatial distances, which is a different topic and will be discussed separately in the next section. ssNMR correlation spectroscopy can be classified into two categories, namely, homonuclear correlation experiments and heteronuclear correlation experiments. In a 2D NMR experiment, one acquires a common FID signal in the direct dimension F2, while recording the time-domain evolution of desired spin interaction/Hamiltonian terms in the indirect dimension F1. Fourier transform of both dimensions will yield a 2D NMR spectrum in frequency domain, where the correlated signals in F2 and F1 appear as crosspeaks. For example, for homonuclear couplings, if a single-quantum term is selected and evolves in F1 dimension, a SQ-SQ correlation spectrum is obtained, such as the spin-diffusion driven NOESY experiment for homonuclear correlations (1H-1H, 13C-13C, 31 31 P- P, etc.); while if a double-quantum term evolves in F1 dimension, a DQ-SQ correlation spectrum is obtained, such as the extensively used dipolar coupling based 1H-1H DQ-SQ for investigating correlations of hydroxyl species on catalysts and J-coupling based 13C-13C Incredible Natural Abundance DoublE QUAntum Transfer Experiment (INADEQUATE)87 experiments. Similarly, for heteronuclear correlation (HETCOR), the evolution of a spin term involving a different isotope is recorded in the indirect F1 dimension, such as the 2D experiments via CP- or HMQC-based experiments (1H-13C, 1H-27Al, etc.). These common 2D NMR correlation schemes are illustrated in Fig. 15, where each scheme will be further discussed as follows.

9.17.4.2.1

Homonuclear correlation spectroscopy

Normally homonuclear correlation experiments are achieved via SQ-SQ and DQ-SQ methods, i.e., by recording the evolution of single-quantum (SQ) or double-quantum (DQ) spin terms in the indirect dimension. In Fig. 15a, a typical 2D SQ–SQ correlation is illustrated, of which the correlation is normally established between spins which undergo magnetization exchanges or chemical exchanges, known as spin-diffusion or chemical exchange experiments. Although the detailed pulse sequences are not shown, it should be noted that both experiments share the same concept of pulse sequence design, allowing the correlation buildup in the z-direction during the mixing time and consequently, the signal decay is dominated by much longer spin-lattice T1 relaxation rather than T2 relaxation, rendering a great advantage to avoid signal loss. The difference between spin-diffusion and chemical exchange is that the first relies on dipolar coupling-based magnetization exchange while the latter relies on actual atom exchange. In that sense, spin-diffusion usually probes relatively long distances up to 10 Å; chemical exchange does not probe the internuclear distance, but the properties of physical exchanges between the observed atoms, as has been shown for revealing proton exchanges in solid acid catalysts.88,89 A simple way to differentiate spin-diffusion and chemical exchange is to conduct variable-temperature (VT) experiments, where it is expected that chemical exchange rates are significantly affected by temperature variations, while this is not the case for spin-diffusion. Common applications of the SQ-SQ correlations are, for example, 1H-1H correlation to investigate hydroxyl-rich materials such as zeolites or metal oxides, and 13C-13C correlation to investigate the adsorbed hydrocarbon species

Fig. 15 Schematics showing 2D NMR spectroscopy for homonuclear and heteronuclear correlations: (a) SQ-SQ homonuclear, (b) DQ-SQ homonuclear and (c) heteronuclear. Adapted from Qi, G.; Wang, Q.; Xu, J.; Deng, F. Solid-State NMR Studies of Internuclear Correlations for Characterizing Catalytic Materials. Chem. Soc. Rev. 2021, 50, 8382–8399. doi: 10.1039/D0CS01130D.

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on catalysts. However, due to the small size of residual 13C-13C dipolar coupling under MAS, the SD-based 13C-13C correlations are mostly built with proton assistance, for example, proton-driven spin diffusion (PDSD) without RF irradiation on protons, and the pulse sequences with employing constant-amplitude, or amplitude- and/or phase-modulated RF irradiations on protons, such as DARR,90 MIRROR,91 RDSD92 and CORD,64 etc. In addition, it needs to be mentioned that SQ-SQ homonuclear correlations can also be achieved by performing the recoupling pulse irradiation directly on the observed nuclei, such as RFDR,63 DREAM93 and R-symmetry-based zero-quantum recoupling sequences,94 although they are always accompanied with relatively fast signal decays. It must be noted that in this type of experiments, diagonal peaks are inevitably generated according to the way that the pulse sequence is designed, which is a main limitation as it conceals diagonal peaks of the coupled like-species and obscures cross peaks close to the diagonal. Alternatively, DQ-SQ spectroscopy is a complementary method for probing homonuclear correlations, as the DQ coherences are excited only for two or more coupled spins that yield 2D spectra free from the diagonal background. With homonuclear dipolar recoupling methods employed, the correlation can be established even at fast MAS conditions. In the DQ–SQ spectrum, the correlation of different sites is observed as a cross peak where its chemical shift (ppm or Hz) in the double-quantum dimension (F1) is the summed chemical shifts (ppm or Hz) of the coupled pairs in the single-quantum dimension, as illustrated in Fig. 15b. For instance, for the coupled pair with isotropic chemical shifts of uA and uB, their correlation is observed as two cross peaks horizontally aligned at uDQ ¼ uA þ uB in the double-quantum dimension (F1). The crosspeaks at 2uA or 2uB in F1 dimension, if present, correspond to the species coupled to their own type, termed autocorrelation peaks. A diagonal line with slope of F1/F2 ¼ 2 is usually drawn to assist in the interpretation of the spectrum. 1H-1H and 31P-31P DQ-SQ homogeneous correlations have proven to be very useful in characterizing the spatial proximity between zeolite active sites and the adsorbed probe molecules (e.g., trimethylphosphine). The homonuclear DQ correlation can also be achieved via J-coupling to provide through-bond correlations, such as INADEQUATE which is often used for probing 13C-13C bond-connectivities. It is worth noting that multiple quantum (MQ) MAS spectroscopy of dipolar coupled spins, similar to the DQ-SQ experiment but instead recording higher order coherences arising from clustered atoms, is useful for characterizing the cluster sizes and their topologies. For example, TQ-SQ correlation will only provide correlations of three-spin systems and exclude spin pairs.31 For homonuclear correlations of I > ½ quadrupolar nuclei, the NMR experiment becomes complicated and faces a few challenges. Due to the large quadrupolar interaction, the response of spin terms to RF pulses is different from that of the spin-1/2 nuclei, and therefore, most methods developed for spin-1/2 systems cannot be directly applied on quadrupolar nuclei. First, compared to spin-1/2 nuclei, additional complexity of recoupling is introduced due to the fact that satellite transition frequencies are modulated and cross the RF window periodically while spinning the sample at MAS condition. Specifically, it creates an obstacle in the way that when manipulating the internuclear spin interactions via CT transitions, there will be magnetization leakage generated between satellite transitions on the quadrupolar spin itself and thus cause undesired signals to be observed in the spectroscopy. Such complex and unwanted transitions are clearly illustrated in Fig. 16a for two coupled S ¼ 3/2 spins.65 Those unwanted transitions will also significantly reduce the polarization transfer efficiency, making the experiments exceedingly challenging. Second, the second-order broadening of the central line under MAS can be large enough to cause non-uniform excitations from the RF pulses, being another source to reduce the recoupling efficiency and can create distorted lineshapes in the spectrum. Hence, special pulse sequences are normally designed for recoupling quadrupolar nuclei. As a rule of thumb, application of weak (selective) RF pulses are desired to ensure that only the CT coherences are excited, and to reduce the ST interferences. The DQ-SQ experiment is still the most desirable method for establishing homonuclear correlations for quadrupolar nuclei, as it will naturally quench the strong diagonal signals occurring in SQ–SQ correlation spectrum, which is highly needed considering the general poor spectral resolution for quadrupolar nuclei. The main difficulty lies in suppressing the intra-atomic double-quantum coherences, i.e., signals caused by the central transition and the adjacent levels of satellite transitions as shown in Fig. 16a, while keeping the internuclear double-quantum coherences between CTs. Mali et al. solved the problem by simply introducing a central transition selective 180 pulse, which selectively inverts the inter-atomic DQ coherences without affecting the satellite transitions.95 Yet, it should be noted that this method is not suitable for nuclei with small quadrupolar couplings. In general, HORROR (homonuclear double-quantum rotary resonance) condition (RF at 1/2 MAS frequency), initially introduced for spin-1/2 nuclei, is the most commonly implemented to create quadrupolar nuclear DQ coherences; its weak RF field strength will benefit the recoupling efficiency for quadrupolar nuclei, but leads to high sensitivity to offsets and to RF field mismatch and inhomogeneity.65,95 Symmetry-based recoupling sequences were later implemented to simultaneously compensate the RF mismatch and resonance offset, where the RF strength of recoupling pulse sequences is 1/2n of the MAS frequency.96,97 It is also noteworthy that the implementation of J-coupling for homonuclear correlation of quadrupolar nuclei is has not been successful, largely due to its small values along with the short transverse relaxation times. As an example, a quadrupolar DQ-SQ homonuclear correlation experiment helped to resolve surface oxygen species in one of the most commonly used industrial catalysts, Al2O3, where 17O-17O (spin-5/2) homonuclear correlation is established by using the pulse sequence proposed by Mali et al. to selectively generate internuclear DQ coherences, as shown in Fig. 16b and c.98 Clearly, autocorrelations A-A, B-B, C-C, D-D and off-diagonal correlations B-D, B-E, C-D provide invaluable evidence for understanding the structure and distribution of surface oxygen species illustrated in Fig. 16c.

9.17.4.2.2

Heteronuclear correlation spectroscopy

In addition to homonuclear correlation, 2D heteronuclear correlation (HETCOR) NMR spectroscopy is another valuable tool for investigating catalytic active sites or related chemical interactions under MAS conditions. HETCOR renders a couple of benefits as it (a) untangles the overlapped signals in 1D spectroscopy due to the separation of species by crosspeaks as a nature of 2D

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Fig. 16 (a) Schemes showing the complex spin-states of coupled S ¼ 1/2 and S ¼ 3/2 spins, leading to challenges in selecting the internuclear interaction. (b) 17O-17O DQ-SQ homonuclear correlation revealing fine surface structures on Al2O3 catalyst, which is illustrated the schemes in (c). (a) Adapted with permission from Edén, M. Homonuclear Dipolar Recoupling of Half-Integer Spin Quadrupolar Nuclei: Techniques and Applications. Solid State Nucl. Magn. Reson. 2009, 36, 1–10, Copyright 2009 Elsevier Ltd. (b) and (c) Adapted with permission from Wang, Q.; Li, W.; Hung, I.; MentinkVigier, F.; Wang, X.; Qi, G.; Wang, X.; Gan, Z.; Xu, J.; Deng, F. Mapping the Oxygen Structure of g-Al2O3 by High-Field Solid-State NMR Spectroscopy. Nat. Commun. 2020, 11, 3620, Copyright 2020 Springer Nature.

NMR, (b) allows for manipulating the signal of an isotope via a spy nucleus and (c) allows for differentiating through-space and through bond connectivities, via D- and J-type of experiments, respectively. Compared to homonuclear correlation experiments that only require a single-channel for RF irradiation (except for proton-assisted ones), HETCOR usually requires at least two RF channels, and are thus referred to as double-resonance NMR experiments. To date, a variety of HETCOR pulse sequences have been proposed as illustrated in Fig. 17.99 Cross polarization (CP) is the most routine double-resonance experiment, where RF irradiations are simultaneously applied on two coupled spins, with their magnetizations spin-locked in the x-y plane. For heteronuclear spin pairs I-S (e.g., 1H-13C, 1H-17O, and 31P-27Al), the magnetic polarization can be transferred from one to another when the applied RF irradiations meet the Hartmann–Hahn (HH) matching condition. There are special requirements for the HH matching condition, i.e., y1,I ¼ y1,S for static and y1,I  y1,S ¼  nyr for MAS conditions, where y1,I and y1,S are the RF frequencies of spin I and S, respectively, yr is the MAS frequency and n is an integer number.39,100 CP transfer is routinely used to transfer polarizations from abundant spins like 1H, to “dilute” or insensitive spins S like 13C and 29Si, in order to enhance the sensitivity of the latter. Importantly, such transfer

NMR of catalytic sites

Fig. 17 Schematic classification of 2D heteronuclear correlation NMR experiments, which can be employed to characterize solid state compounds under MAS condition. The paths corresponding to D-HMQC and DHSQC sequences are highlighted (top). Pulse sequence schemes for CP-HETCOR and D-HMQC are illustrated (bottom). Top figure adapted with permission from Lafon, O.; Wang, Q.; Hu, B.; Vasconcelos, F.; Trébosc, J.; Cristol, S.; Deng, F.; Amoureux, J. -P. Indirect Detection via Spin-1/2 Nuclei in Solid State NMR Spectroscopy: Application to the Observation of Proximities Between Protons and Quadrupolar Nuclei. J. Phys. Chem. A 2009, 113, 12864–12878, Copyright 2009 American Chemical Society.

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Fig. 18 First-formed phosphorous species in H3PO4 treated zeolite HZSM-5 by 31P-27Al dipolar and J-coupling based HECTOR NMR (a), (c), (d) and 27Al MQMAS (b). Adapted with permission from Chen, K.; Zornes, A.; Bababrik, R.; Crouch, J.; Alvarez, W.; Wulfers, M.; Resasco, D.; Wang, B.; Crossley, S.; White, J. L. First-Formed Framework Species and Phosphate Structure Distributions in Phosphorus-Modified MFI Zeolites. J. Phys. Chem. C 2022, 126, 227–238, Copyright 2021 American Chemical Society.

can be readily extended to a 2D experiment (CP-HETCOR sequence in Fig. 17) which will result in a HETCOR spectrum (such as Fig. 15a), where 1H appears in the direct dimension and the dilute spins 13C and 29Si appear in the indirect dimension. In addition to CP, 2D HETCOR spectra are frequently acquired using different regimes of pulse sequences such as Refocused Insensitive Nuclei Enhanced by Polarization Transfer (RINEPT)50 and Heteronuclear Multiple-Quantum Correlation (HMQC)59,60 MAS NMR experiments, which can be achieved by either D- or J-coupling based sequences, i.e., to probe connectivities through space or through bond, as shown in the top diagram Fig. 17, where the sequences are also classified according to the mode of detection, direct or indirect, and the order of coherences evolved in the F1 dimension. Generally, the D-INEPT, D-HMQC and DHSQC methods derive from J-INEPT, J-HMQC and J-HSQC schemes that were initially developed to characterize chemical bonds in liquids; the difference is that the D-type of experiments normally require MAS and heteronuclear dipolar recoupling sequences are applied during the mixing times. For instance, the developed recoupling sequences such as REDOR, R3, SR4 and PMRR,61,71,101,102 etc., can be replaced as recoupling building blocks in the INEPT, HMQC or HSQC schemes, as shown representatively in the HMQC pulse sequence in Fig. 17. The specificity of dipolar recoupling sequences and detailed discussions can be further accessed in the literatures.39,102 As shown in Fig. 17, CP and D-RINEPT belong to the D-HETCOR methods using direct detection, while HMQC as well as HSQC and double CP103,104 belong to the indirect detection method. The sensitivity of D-HETCOR experiments depends on the gyromagnetic ratios g, longitudinal relaxation times T1, and spectral line widths of the detected nucleus; hence, it is always worth evaluating such properties of the correlated nuclei to choose between the direct and indirect method, e.g., between D-INEPT and D-HMQC experiments. More details of the HETCOR methods can be accessed from the review article by Lafon et al.99 As for HETCOR spectroscopy of the coupled spins containing quadrupolar nuclei, similar to the situation of homonuclear correlation discussed above, the NMR experiment faces the typical problems arising from quadrupolar interactions, i.e., the interaction of ST transitions and broad lines. Hence, special considerations for the CP condition, including spin-locking of quadrupolar nuclei as a function of the quadrupolar interaction, the MAS rate, and the RF spin-locking are usually of central importance, which will not be discussed here but can be accessed from the literatures.105–107 In general, CP polarization transfer becomes very inefficient for quadrupolar nuclei, and is not preferably used. In contrast, HMQC and RINEPT methods have emerged notably in the past two decades

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Fig. 19 NMR for distance measurement using the REDOR method. (a) REDOR difference spectrum. (b) simulated REDOR dephasing curve (c) internuclear distance of 30 Hz dipolar coupling as a function of commonly encountered nuclei. (a) Adapted from Qi, G.; Wang, Q.; Xu, J.; Deng, F. Solid-State NMR Studies of Internuclear Correlations for Characterizing Catalytic Materials. Chem. Soc. Rev. 2021, 50, 8382–8399. doi: 10.1039/ D0CS01130D. (c) Adapted with permission from Shcherbakov, A. A.; Medeiros-Silva, J.; Tran, N.; Gelenter, M. D.; Hong, M. From Angstroms to Nanometers: Measuring Interatomic Distances by Solid-State NMR. Chem. Rev. 2022, 122, 9848–9879, Copyright 2021 American Chemical Society.

for constructing 2D NMR correlations for quadrupolar nuclei, where the recoupling pulse irradiations are usually applied on the spin-1/2 nucleus but simple CT-selective weak pulse(s) on the quadrupolar nucleus. Here, we show an example with White et al.’s recent work on how HETCOR NMR helps to improve the understanding of the structure of complex phosphorus-modified zeolite catalysts.108 It was found in the 1970s that zeolite acidity and shapeselectivity can be modified by post-synthetic treatments with phosphorus precursors such as H3PO4.109,110 Usually, phosphorus species can act in zeolites either as a promoter, e.g., it is well known to improve the hydrothermal stability of zeolite HZSM5,111 or as a poison, as it is deleterious for NH3-SCR (selective catalytic reduction) nitrogen oxide-removing applications.112 However, despite the large amount of work on the effects of phosphorus on zeolites reported, the exact nature of phosphoruszeolite interaction has always been in controversy, which makes the structural elucidation from fundamental perspective strongly demanded. Among the many possible models proposed over the years, one main division of opinions regards the question of whether a permanent phosphorus-framework interaction exists. Fortunately, such a system is suited well for NMR characterization, due to the high sensitivity of 1H, 27Al and 31P isotopes, which are all important elements constructing phosphorus-zeolite species. As shown in Fig. 18a and b, a few aluminum species can be well resolved in both 1D and 2D MQMAS spectra, setting the basis for further correlation experiments with other nuclei. Indeed, a 27Al-31P HETCOR spectrum was successfully obtained via HMQC experiments, utilizing both D- and J-interaction, of which 1D spectra generated from 27Al to 31P polarization transfer resembles the spectrum pattern of a normal spin-echo spectrum (Fig. 18a), and the 2D spectrum shows strong correlations to 31P species in the range of
10 to
40 ppm (Fig. 18c and d). A comparison of the D- and J-HMQC results unambiguously shows that not only permanent, but actually chemically bonded phosphorus-framework interactions exist. Those robust NMR experiments allow to track to Pzeolite samples with very small P loadings, and further determine that the chemically bonded species are the first species formed during P-treatment. As a short conclusion, both dipolar coupling and J-coupling interactions can serve as intermediates to establish 2D correlation spectroscopies, for either homonuclear or heteronuclear purposes via the few methods discussed above. In general, the D-based experiments are more efficient than the J-based experiments, due to the large size of dipolar coupling that allows for the efficient polarization transfer using short recoupling times, which minimizes the T2 decay. J-based methods, however, if applicable (with strong J-coupling constants), can serve a special purpose to exclusively probe the presence of chemical bonding. 2D correlations for quadrupolar nuclei are often challenging, mostly due to the low sensitivity affected by the satellite transitions and/or second-order broadening issues on the observed central transition (CT) signal; however, a tremendous number of applications of quadrupolar-2D NMR have been successfully seen in solving real catalytic problems. Besides 2D correlation spectroscopy, NMR also allows to extract quantitative spatial proximities between coupled spins, which will be introduced in the next section.

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Fig. 20 (a) REDOR curve of coupled spin-1/2 and spin-3/2 nuclei as a function of the quadrupolar coupling constant (c in the figure), showing that the dephasing curve is severely deviated from the ideal curve with large quadrupolar interaction. (b) 1H MAS and REAPDOR dephased spectra of dehydrated MFI-14 zeolite. (c) REAPDOR measurement of 27Al-1H distance for 4 and 6 ppm species in (b); black and blue dotted lines are real data points for 4 and 6 ppm signals and smooth/dashed lines are simulated curves of “I” and “I þ III.” (a) Adapted with permission from Gullion, T.; Vega, A. J. Measuring Heteronuclear Dipolar Couplings for I ¼1/2, S>1/2 Spin Pairs by REDOR and REAPDOR NMR. Prog. Nucl. Magn. Reson. Spectrosc. 2005, 47, 123–136, Copyright 2005 Elsevier Ltd. (b) and (c) Adapted with permission from Schroeder, C.; Siozios, V.; Mück-Lichtenfeld, C.; Hunger, M.; Hansen, M. R.; Koller, H. Hydrogen Bond Formation of Brønsted Acid Sites in Zeolites. Chem. Mater. 2020, 32, 1564–1574, Copyright 2020 American Chemical Society.

9.17.4.3

Probing internuclear distances

Given the dipolar coupling constant (DCC) is a function of the gyromagnetic ratios of the coupled spins and the cube of their internuclear distance, i.e., r3, as shown in Eq. (3), it has been long used to measure internuclear distances. In ssNMR, recoupling methods are typically required for measuring DCC. For heteronuclear cases, CP-based methods, Rotational-Echo DOuble-Resonance (REDOR) and its derivations, as well as symmetry-based recoupling sequences are mostly used. Among them, REDOR is possibly the most popular one, but only suited for isolated spin pairs in the absence of homonuclear dipolar couplings; otherwise, symmetry-based recoupling sequences (e.g., SR4, RN-DIPSHIFT and PMRR) are preferred. For homonuclear cases, recoupling sequences are relatively limited, RFDR, HORROR, BABA and symmetry-based sequences. Although DCC can be readily obtained via the direct measurement of the powder pattern shown in Section 9.17.4.1, it is in fact more common to determine the DCC value by employing the above-mentioned recoupling pulse sequences, where a dephasing or build-up curve is recorded and then fitted by numerical simulations, as solid samples usually yield complex spectroscopies.

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Fig. 21 Distance measurements using build-up curves extracted from crosspeak intensities via DQ-SQ (a) and (b) and D-HMQC (c)–(h) 2D NMR spectroscopy. Adapted with permission from Brouwer, D. H.; Darton, R. J.; Morris, R. E.; Levitt, M. H. A Solid-State NMR Method for Solution of Zeolite Crystal Structures. J. Am. Chem. Soc. 2005, 127, 10365–10370, Copyright 2005 American Chemical Society. Adapted with permission from Chen, K.; Gan, Z.; Horstmeier, S.; White, J. L. Distribution of Aluminum Species in Zeolite Catalysts: 27Al NMR of Framework, Partially-Coordinated Framework, and Non-Framework Moieties. J. Am. Chem. Soc. 2021, 143, 6669–6680, Copyright 2021 American Chemical Society.

9.17.4.3.1

Dephasing curves for distance measurement

REDOR is one of the most used method for measuring internuclear distances between coupled heteronuclear spins, i.e., I-S. Specifically, by applying 180 pulses on spin S every half rotor period, one reintroduces I-S dipolar coupling and consequently, the signal

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intensity of the observed spin I is attenuated. As an example, a comparison of the signals S0 and S0 is shown in Fig. 19a, and usually, a difference spectrum (DS ¼ S0
S0 ) is shown for better illustrating the coupled nuclear sites. This dipolar recoupling is often affected by the transverse relaxation T2, as the spin echo formation is required for refocusing the chemical shifts. Therefore, the T2-normalized intensity can be written as DS/S0, which can be further plotted as a function of recoupling time (sometimes called mixing time), or the dimensionless parameter l as demonstrated in Fig. 19b.113 A numerical fitting of such a curve yields the dipolar coupling constant value.114 Although a large number of heteronuclear dipolar recoupling sequences have been developed for MAS NMR since the invention of REDOR, it is still arguably the most widely used technique due to its simplicity, large recoupling scaling factor and robustness to RF inhomogeneity, etc. For probing internuclear distances in multi-spin systems, REDOR suffers from the influence of inefficient homonuclear dipolar decoupling, while the symmetry recoupling sequences provide accurate measurement of heteronuclear DCCs with efficient homonuclear dipolar decoupling. Once the DCC is obtained, it is simple to obtain the internuclear distance, by using Eq. (3). For a straightforward demonstration of the dipolar-distance correlation, Fig. 19c illustrates the dipolar coupling constant as a function of distance for common heteronuclear spin-1/2 pairs, using 30 Hz as the lower bound of readily measurable dipolar couplings.115 Notably, the gyromagnetic ratio of the nucleus plays a dominant role for determining the measurable internuclear distance. Note that although only REDOR is shown, the same analytical procedure can be extended to many other recoupling schemes, including applications to quadrupolar nuclei. In the latter case, REDOR becomes problematic mostly due to satellite transition interaction, as discussed in the above section. Fig. 20a clearly shows how the REDOR curve deviates from ideal dephasing curves as the quadrupolar coupling constant increases stepwise to 1 MHz for a I ¼ 3/2 spin.68 To overcome the quadrupolar issue, methods like TRAPDOR116 and REAPDOR68 were designed and more recently, techniques such as RESPDOR67 or LA-REDOR117 were developed. A detailed comparison among the recoupling techniques for quadrupolar involved distance measurement has been reviewed by Goldbourt118 and thereby is not discussed here. Fig. 20b and c illustrate 1H-27Al distance measurements on zeolite catalyst MFI14,119 where the 1H spin-echo, the 1H{27Al} REAPDOR dephased and the difference spectra are illustrated in Fig. 20b and the dephasing curve as a function of recoupling time is displayed in Fig. 20c. This method overcomes the quadrupolar effect of 27Al and helps to determine very detailed local environments, i.e., fine internuclear spatial relationships in this case. As shown in Fig. 20c, the black and blue dotted lines are real data points for 4 and 6 ppm signals and smooth/dashed lines are simulated curves as indicated in the figure. The dephasing curve for the 4 ppm is the BAS site and can serve as a model system. At recoupling time < 2 ms, the simulated curve (blue smooth line) fits well with the simulated three-spin system, 1H-27Al-27Al, where the first H-Al distance is at 2.52 Å and the second at 5.0 Å, corresponding to the distance of a BAS proton to the directly associated Al atom and the Al on the neighboring BAS site, respectively. Whereas a deviation is observed at recoupling time > 2 m, by incorporating the fourth spin at 8 Å (Al atom from the third BAS site), the simulated curve (dashed line) shows strong agreement with the experimental data. The 6 ppm signal, in contrast, yields more complicated dephasing curve at long recoupling times, indicating more complex spin systems of such species.

9.17.4.3.2

Build-up curves for distance measurements

In contrast to using dephasing curves, an alternative way is to analyze build-up curves, which measure the signal growth originated from polarization transfers between coupled nuclei as a function of recoupling time. The polarization transfer method can be CP or HMQC, HSQC, etc., with various recoupling methods incorporated. Typically, REDOR- or DIPSHIFT-like pseudo 2D pulse sequences require resolved signals in the direct dimension for accurate determination of heteronuclear DCC; otherwise, an additional chemical shift dimension should be incorporated for resolving the spectrally overlapped sites. If species must be resolved in 2D correlation spectroscopy, the dipolar coupling constant can be measured by fitting the intensity of relevant crosspeak as a function of build-up mixing time. Note that a series of 2D correlation spectra with different recoupling times need to be recorded, where the scan numbers usually remain constant. For instance, Si-Si distances were successfully obtained by conducting 29Si-29Si DQ-SQ experiments on a specific zeolite sample, as shown in Fig. 21a and b.120 Specifically, the 2D spectrum clearly reveals correlations between four distinct Si sites, indicated as A, B, C and D. The integrated intensity of each paired sites can be plotted against recoupling time, as of the build-up curves shown in Fig. 21b. Subsequently, numerical fittings of the build-up curves provide quantitative 29 Si-29Si distances, which were of great importance for understanding the crystallographic structure. Similar methods can be applied to heteronuclear correlation experiments, with an example demonstrated in Fig. 21c–h, where 27Al-1H distances of dehydrated proton-formed zeolite HZSM-5 were measured by 2D D-HMQC experiments.53 Fig. 21c shows the 2D 27Al-1H correlation spectrum and Fig. 21d shows the build-up curves plotted using the integrated intensity of boxed region as indicated in Fig. 21c against recoupling time. The Al-H distance of species in each boxed region can be obtained by fitting the build-up curves as shown in Fig. 21e–h. Apparently, such information cannot be obtained by REDOR-type experiments given the poor resolution of the 27Al spectrum. However, some drawbacks of these type of experiments are worth mentioning. First, the acquisition of a series of 2D correlation spectra would consume a significant amount of instrument time. Second, uncertainties remain in the obtained distances, as additional parameters such as T2 relaxation need to be considered in the fittings of the build-up curves. As a short summary of this section, ssNMR provides a variety of methods to take advantage of internuclear dipolar- and Jcoupling interactions, including constructing heteronuclear/homonuclear correlations to show the connectivities between atoms, and performing recoupling pulse sequences to measure internuclear distances between coupled nuclei. There are fundamental differences between dipolar coupling and J-coupling, with one exclusively probing through-space and the other exclusively probing through-bond interactions. To date, a tremendous number of D- and J-coupling based NMR methods have been developed, which

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Fig. 22 Schematic illustration of the experimental setups for in situ MAS NMR apparatus under batch reaction conditions. (a) Glass ampoules as inserts for NMR rotors. (b) Device developed by X. Bao and coworkers. (c)–(e) Three generations of CAVERN apparatus for in-situ NMR developed by Haw and coworkers. Adapted from Ivanova, I. I.; Kolyagin, Y. G. Impact of In Situ MAS NMR Techniques to the Understanding of the Mechanisms of Zeolite Catalyzed Reactions. Chem. Soc. Rev. 2010, 39, 5018–5050. doi: 10.1039/C0CS00011F.

can and should be used complementarily for best probing the nature of the catalytic sites at micro-scale, i.e., atomic or molecular levels. Also importantly, quadrupolar interaction of I > 1/2 nuclei complicates the internuclear interactions as a result of their complex spin dynamics, but can still serve as a valuable tool with the utilization of specially designed pulse sequences.

9.17.5

Use of in-situ NMR

Studying a catalyst or catalytic reaction at “working” conditions differs significantly from investigating the catalyst before or after the reaction, as the whole picture of the events occurring on the catalyst during the reaction could possibly be missing for the latter. In the spirit of monitoring the active site, reaction mechanism and kinetics at real “working” conditions, scientists were strongly motivated to develop in-situ techniques. Upon the development of other in-situ techniques including vibrational, optical, X-ray absorption, emission and photoelectron spectroscopies, etc., in-situ MAS NMR techniques is of great value allowing for non-invasive investigations of the active species and catalytic reactions at reaction conditions. Because of the specialty of rapid sample spinning in MAS ssNMR, real-time monitoring of catalysts or reactions requires the development of specific techniques. The basic idea is to use the MAS NMR rotor filled with catalyst particles as a microreactor to simulate the reaction processes. In general, there are two approaches developed for the in-situ NMR experiments, i.e., under batch-like or continuous-flow (CF) conditions. The batch system was first developed by Haw and coworkers in the early 1990s.121–124 Such a system turned out to be greatly useful for adsorbing gas or liquid phased reagents to a catalyst at active or working condition, and allow for subsequent NMR characterizations without exposure to ambient environment. The

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Fig. 23 Water interaction with zeolite catalysts investigated by in-situ NMR experiments using (a) CAVERN and (b) capillary inserts for controlled water adsorption. (a) Adapted with permission from Chen, K.; Gumidyala, A.; Abdolrhamani, M.; Villines, C.; Crossley, S.; White, J. L. Trace Water Amounts can Increase Benzene H/D Exchange Rates in an Acidic Zeolite. J. Catal. 2017, 351, 130–135, Copyright 2017 Elsevier Ltd. Spectrum in (b) adapted with permission from Xu, M.; Harris, K. D. M.; Thomas, J. M. Mapping the Evolution of Adsorption of Water in Nanoporous Silica by in situ Solid-State 1H NMR Spectroscopy. J. Am. Chem. Soc. 2008, 130, 5880–5882, Copyright 2008 American Chemical Society. Top scheme in (b) adapted with permission from Xu, M.; Harris, K. D. M.; Thomas, J. M. In Situ Solid-State 1H NMR Studies of Hydration of the Solid Acid Catalyst ZSM-5 in its Ammonium Form. Solid State Nucl. Magn. Reson. 2009, 35, 93–99, Copyright 2009 Elsevier Ltd.

continuous-flow system was also of great interest as it resembles a real fix-bed reactor, and among a few proposed designs, the most successful one was developed by Hunger and coworkers.125–127 However, it should be mentioned that the reported CF systems do not reproduce completely the conditions in real flow catalytic reactors, but were a significant step forward compared to the batch systems. Yet, the batch systems have their own advantages that cannot be accomplished by the flow system such as low costs, robustness of experimental setups, as well as its suitability for quantitative adsorptions, variable-temperature (VT) experiments and investigation of kinetics, etc. Hence, the batch type of in-situ NMR has been seen of more extensive applications than the other. Nonetheless, the two methods should be implemented complementarily for catalytic investigations if available. In addition to the batch and flow in-situ techniques, several other in-situ techniques have been developed to meet the special requirements for fast reactions or capture reaction intermediates, such the laser-heating technique,126 radio-frequency heating technique128 and the pulse-quench technique,129 because (1) the NMR sensitivity can sometime be low and long acquisition time is required for signal accumulation, and (2) heating the samples to target temperature could take rather long time (from 5 to 10 min). The special pulse-quench reactor system proposed by Haw et al. consists of a standard flow reactor, continuous and pulse feeding device, and fast gas switching device, and the system can rapidly start reaction by switching on flow through the catalyst bed and quench the reaction immediately with liquid nitrogen, allowing to freeze the reaction intermediates that can be further charactered by NMR offline.130,131 Such a system has played crucial roles in elucidating reaction mechanism including the detailed studies on hydrocarbon pool species in zeolite-based catalysis. In-situ NMR techniques have been reviewed comprehensively in the literature.132,133 Here, we will briefly introduce the development of in-situ NMR with a focus on batch and flow techniques, but not the pulse-quench system as it is more used for investigating reaction mechanisms.

9.17.5.1

Batch in-situ NMR

Batch-like in-situ NMR is the first kind of attempt to investigate catalysts or catalytic reactions at working conditions. Usually, the sample preparation including catalyst activation and reactant adsorption had to be handled ex-situ before loading to the MAS rotor and the NMR probe. Key challenges are to keep the catalyst/reaction out of ambient exposure and ensure NMR acquisition as quickly as possible. However, no matter how well the system is designed, there is always inevitably a period of sample preparation. For catalysts not sensitive to air or moisture, the preparation time can be as quick as several minutes, whereas for catalyst-adsorbate samples that are air or moisture sensitive, the preparation requires vacuum-line or glove box procedures that can take up to tens of minutes. Considering these practical issues, the batch in-situ system is suitable for slow reaction, low temperature experiments and probe molecule adsorption that do not require immediate NMR acquisition after catalyst-reagent contact. This system is also

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Fig. 24 (a) and (b) Schemes showing the two different designs for the NMR stator allowing for CF NMR experiments. (b) Demonstration of reaction results: On-line gas chromatography (top) and 13C MAS NMR spectra (bottom) of zeolite H-Beta recorded during the synthesis of methyltert-butylether (mtbe) under a continuous flow of isobutene (ib) and methanol (me) with a molar ratio of 2:1, at reaction temperatures of 333 K (left) and 353 K (right). (a) Adapted with permission from Isbester, P. K.; Zalusky, A.; Lewis, D. H.; Douskey, M. C.; Pomije, M. J.; Mann, K. R.; Munson, E. J. NMR Probe for Heterogeneous Catalysis With Isolated Reagent Flow and Magic-Angle Spinning. Catal. Today 1999, 49, 363–375, Copyright 1999 Elsevier Ltd. (b) and (c) Adapted with permission from Hunger, M. In Situ Flow MAS NMR Spectroscopy: State Of The Art and Applications in Heterogeneous Catalysis. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 53, 105–127, Copyright 2008 Elsevier Ltd.

suitable for quantitative adsorption or probe molecules with appropriate adaptions to the device, which is indeed a unique and useful feature in probing catalytic sites in controlled manner. An important advantage of the batch systems is that they can be house-built based on materials and equipment commercially available. In general, two approaches have been widely employed to achieve the batch in-situ NMR characterizations, with the unique purpose of maintaining the catalyst’s integrity to avoid unnecessary contaminations while loading it into a MAS rotor. The first approach is based on using glass ampoules as inserts for NMR rotors, which can be loaded with catalysts and flame sealed on the vacuum line.134,135 Among a few attempts, a simple design shown in Fig. 22a has become popular due to its robustness and

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is now commercially available (Wilmad-LabGlassÔ) for most MAS rotor types. In such a setup, the ampules are designed to perfectly fit the NMR rotor diameters and allow for in-situ thermal activation/reagent treatment and flame sealing. With the catalyst loaded in the bottom ampoule meanwhile the top opening attached to a vacuum line, the narrow waist allows for convenient flame sealing of the bottom insert, making it possible to achieve highly symmetrical sealing required for mechanical magic-angle spinning. However, it should be noted that the re-addition of reagents is impossible once the sample is sealed. Alternatively, a second approach fundamentally different from the above one is proposed by Haw and co-workers, which further simplifies the process by using the NMR rotor itself as the sealing body. In this approach, a special design, abbreviated as CAVERN (Cryogenic Adsorption Vessel Enabling Rotor Nestling) is developed, as shown in Fig. 22c–e. Using such devices, a grooved spacer usually made of polymer materials such as TeflonÔ or KEL-FÒ can be inserted to the MAS rotor to create an air-tight seal. The most significant advantage of this approach is that it greatly speeds up the sample preparation by avoiding using the glovebox, and further reduces any possible contaminations from the glove box and sample transfer procedures. There were three generations of CAVERN apparatus reported by Haw and co-workers, as shown in the schemes individually in Fig. 22c–e. The first generation was nearly a prototype design, with the mechanical parts made of stainless-steel owing to the convenience of machining metal components and is rarely used nowadays. The concept having been proven successful, the second and third versions were later developed, where the mechanical parts were replaced by glass/quartz components, and have become the most popular devices for in-situ NMR. Following the second and third versions of the CAVERN systems, Zhang and Ma et al.133 designed a new system for on-line treatment of powder samples as shown in Fig. 22b. Limited by the working temperatures of glass or quartz, the batch in-situ apparatus shown in Fig. 22 allowed catalyst samples to be heated up to 700–1000 K in vacuum for dehydration and subsequent exposure of probe molecule adsorbates. The CAVERN apparatus has been widely used for catalytic studies. For example, water molecules interact extremely actively with zeolite acid sites, forming hydronium cations and other protonic species, and thus generate a complex system with multi-site chemical exchanges. Revealing how water interacts with zeolites, e.g., the proton-hopping mechanism, deprotonation energy of acid site by water molecules, intra- and inter-acid site water dynamics, formation of water clusters, is of essential importance for understanding the intrinsic acidity/reactivity of acid sites. To investigate such a complex system, quantitative water adsorption at controlled sub-equivalent levels (i.e., water/acid site < 1) is of crucial necessity. White et al. had managed to introduce water into zeolite at small but controlled loadings, and revealed fundamental behaviors of water molecules by monitoring the 1H MAS spectroscopy,136 as displayed in Fig. 23a. With the help of a modified CAVERN device, the formation of water species and its spectroscopical evolutions associated to quantitative water loadings were demonstrated. However, even though being extensively implemented, all the batch in-situ methods introduced above suffer from a problem that they could not provide information about adsorption or reaction at early stages, due to the long sample preparation time. For that purpose, Xu et al. proposed a method by placing a sealed glass capillary containing adsorbates into the rotor loaded with catalyst sample,137 and the mechanical spinning of MAS breaks the capillary and thus “triggers” the contact of catalyst and adsorbate, to start up the adsorption process. With this method, the evolution of the adsorption process for acetone or water on

Fig. 25 Probing Bronsted acid sites located in 8-MR and 12-MR in zeolite MOR catalyst via adsorptions of deuterated pyridine and deuterated acetonitrile. Detailed analysis is described in the corresponding context. Adapted with permission from Yi, X.; Xiao, Y.; Li, G.; Liu, Z.; Chen, W.; Liu, S.-B.; Zheng, A. From One to Two: Acidic Proton Spatial Networks in Porous Zeolite Materials. Chem. Mater. 2020, 32, 1332–1342, Copyright 2020 American Chemical Society.

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Fig. 26 Probing Bronsted and Lewis acid strengths in zeolite catalysts via 31P MAS NMR using TMP and TMPO as probe molecules. (a) 31P MAS NMR spectrum of TMP adsorbed on zeolite catalyst. (b) Calculated 31P chemical shift correlation to the binding energy of TMP of adsorbed active sites. (c) and (d) Schemes of TMPO adsorbed on model MFI zeolite with different O-H distances and calculated result showing the corresponding 31P chemical shift as a function of the O-H distance. (a) and (b) Adapted with permission from Chu, Y.; Yu, Z.; Zheng, A.; Fang, H.; Zhang, H.; Huang, S. -J.; Liu, S. -B.; Deng, F. Acidic Strengths of Brønsted and Lewis Acid Sites in Solid Acids Scaled by 31P NMR Chemical Shifts of Adsorbed Trimethylphosphine. J. Phys. Chem. C 2011, 115, 7660–7667, Copyright 2011 American Chemical Society. (c) and (d) Adapted with permission from Zheng, A.; Liu, S. -B.; Deng, F. 31P NMR Chemical Shifts of Phosphorus Probes as Reliable and Practical Acidity Scales for Solid and Liquid Catalysts. Chem. Rev. 2017, 117, 12475–12531, Copyright 2017 American Chemical Society.

MCM-41, were recorded by 1H MAS NMR spectra,138,139 as shown in Fig. 23b. Hydrocarbon based catalysis can be investigated by such method by filling the capillary with relevant hydrocarbon reagents. While the above in-situ MAS NMR designs at batch conditions opened a venue and have prompted numerous important research, clearly it is still a step away from the real working condition. The next breakthrough was the development of NMR rotors and associated devices which allow in-situ MAS NMR investigations to be carried out under continuous-flow conditions, as discussed below.

9.17.5.2

In-situ NMR under flow reaction condition

Given that most industrial processes using heterogeneous catalysts function under flow conditions, it has long been desirable to develop an in-situ flow reactor. However, implementing MAS of at least a few kHz while introducing continually flowing gases through the rotor has been extremely difficult. Upon maintaining a continuous flow of carrier gas/reactant in the rotor under MAS, additional challenges arise from (a) total separation of the reactant flows and the gas used for driving the rotor spinning, and (b) incorporating a heating system in the NMR probe head in order to provide suitable temperatures for the reaction taking place. Despite the difficulties, a few flow MAS probes have been developed and two representative designs are discussed here.

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Fig. 27 The acid site acidity in zeolite HZSM-5 investigated by a room-temperature probe reaction: H-D exchange between isobutane-d10 and the acid site. Adapted with permission from Truitt, M. J.; Toporek, S. S.; Rovira-Truitt, R.; White, J. L. Alkane C
H Bond Activation in Zeolites: Evidence for Direct Protium Exchange. J. Am. Chem. Soc. 2006, 128, 1847–1852, Copyright 2006 American Chemical Society.

As for the first approach introduced, Munson et al. designed a probe consisting of a stator equipped with bearing cartridges at the bottom and top, a reactant gas endcap, a product gas endcap, a rotor, and a driving turbine,140 as shown in Fig. 24a. The rotor is made of one piece of boron nitride with two distinct parts, a hollow straight tubing at the bottom and a sample chamber at the top. The reactant gas enters from the bottom tubing flows into the sample chamber. The turbine outside the straight tubing is rotated by driving gas for achieving MAS rotation. In this way, reactant gas and driving gas are completed separated and a separated heating gas pathway can be incorporated as shown in the figure. Such probe is suitable for reaction temperatures up to about 600 K and spinning rates of 1–2 kHz. As for the second approach, which is possibly the most widely used design, Hunger et al. developed a probe that can be attached to GC and/or UV–vis systems for simultaneous on-line analyses. In this idea, the key part is a modified Bruker 7 mm MAS NMR rotor, with straight tubing as shown in Fig. 24b playing the key role to guide the reactant gas into the rotating sample. In an early version,125 heating is available via heating gas system, as in Munson’s version. Later, in an upgraded version,126 a quartz glass window was equipped at the bottom of the 7 mm MAS NMR rotor with associated glass fiber, allowing for on-line UV– Vis analyses in addition to GC, and further enabling Laser-heating instead of air-heating. 7 mm Bruker and 7 mm Doty MAS NMR probes were both modified according to the design in Fig. 24b, the integration of laser heating eventually allowing the sample to be heated to 723 K under ambient flow pressures and MAS rates of 3 kHz using the Doty probe.127 A demonstration showing the CF NMR/GC monitoring a reaction is shown in Fig. 24c, where the conversion of methyl-tert-butylether from a continuous flow of isobutene and methanol were simultaneously monitored by 13C NMR and online GC spectroscopies.125 Clearly, this method is suitable for capturing/identifying hydrocarbon species/intermediates owing to the well-resolved 13C NMR spectrum as well as for investigating kinetic behaviors of the reaction, as it is convenient to track peak changes in real time. Noteworthy, this technique has made great contributions to capture and characterize the initial steps and/ or species formed on the bridging acid sites in zeolites in MTO reactions.141,142 It is important to mention that Hunger et al. suggested four different protocols for conducting in-situ flow MAS NMR experiments, namely, continuous-flow, switched-flow, stopped-flow and pulsed-flow mode. Further details can be found in the review article.127

9.17.5.3

Use of probe molecules

The performance of catalysts is closely related to their intrinsic structures/properties, as well as their concentration, location, and spatial interactions. For example, for zeolite catalysts, Brønsted acid sites originating from the bridging hydroxyl group AlO(H)Si and Lewis acid sites from the coordination-unsaturated Al centers such as Al(III) in extra-framework aluminums are the most important catalytic sites. As for metal oxides, the morphology and thus the terminal facet of metal oxide nanocrystallites is of great significance to tailor their performances, as a result of controlling the surface active sites inclusive of oxygen vacancies and hydroxyl groups that can play as Lewis and Brønsted sites. For catalysts possessing NMR sensitive nuclei (e.g., 1H, 27Al, 29Si) in the active sites such as zeolites, alumina and silica-alumina, although direct NMR characterization is available, extractable structural information can possibly be limited, as (a) NMR parameters are not sensitive to the topological structure (e.g., 8 vs 12 member rings in zeolites)

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Fig. 28 31P MAS NMR spectra of TMP adsorbed on (a) TiO2, (b) SO42
/TiO2, (c) Al2O3, and (d) SO42
/Al2O3. Asterisks denote spinning sidebands. The weak signal at 34 ppm in (c) is arising from trimethylphosphine oxide (TMPO) due to partial oxidation of TMP. Adapted with permission from Zheng, A.; Liu, S.-B.; Deng, F. 31P NMR Chemical Shifts of Phosphorus Probes as Reliable and Practical Acidity Scales for Solid and Liquid Catalysts. Chem. Rev. 2017, 117, 12475–12531, Copyright 2017 American Chemical Society.

and (b) small changes of local environment can become diverse and significantly increase the complexity of the system, thus posing challenges to NMR characterization. Also, another group of catalysts such as metal oxides ZnOx, CeO2 and TiO2 do not contain NMR-friendly nuclei, making direct NMR detection of the catalytic sites even more challenging. With those situations considered, it has been shown that adsorptions of probe molecules offer alternative and/or powerful ways to provide rich and irreplaceable information to the catalyst property, inclusive and not limited to the acidity, quantity, siting as well as local confinement and proximity of the catalytic sites. Here, we will demonstrate the utilization of probe molecules for characterizing catalytic sites in zeolites and some metal oxides; however, it must be noted that similar methods and choices of probe molecules can be extended to other catalytic systems.

9.17.5.3.1

Zeolites

Taking the extensively encountered Brønsted and Lewis acid sites in zeolites as an example, their strengths and quantities can be measured through the adsorption of probe molecules, which act as bases, i.e., proton acceptor or electron donor that can titrate the relevant acid sites. As of Brønsted sites, for instance, with a probe molecule adsorbed, the acid proton moves toward the probe molecule, leading to chemical shift changes of the acid site in the 1H NMR spectrum, such as in the case of the pyridine/pyridinium and acetonitrile systems. The change of BAS (bridging acid site) chemical shift after adsorptions of probe molecules is illustrated in Fig. 25, where zeolite MOR containing two sizes of pores (8- and 12-MR) is adsorbed with fully deuterated pyridine and acetonitrile.143 Prior to the adsorption, the BAS yields a single proton resonance at 4.0 ppm (Fig. 25a), which, however, shifts to 13.5 and 15.6 ppm upon adsorption of deuterated pyridine (Fig. 25c and e); comparably, new peaks at 10.5 and 12.2 ppm were observed upon the adsorption with deuterated acetonitrile (Fig. 25b). BAS located in 8- and 12-MR rings accounts for the two peaks observed in each case. In other words, the adsorption of pyridine and acetonitrile molecules distinguishes acid sites in 8- and 12-MR rings which were not distinguishable in typical 1H NMR. This method even reveals quantitative co-adsorption behaviors of pyridine and acetonitrile (Fig. 25d and f). The intensities of the new peaks are in accordance with increasing the partial pressures of each probe molecule, which further supports the assignments. An alternative way is to observe the chemical shift of nuclei on the probe molecules other than the intrinsic nuclei on the catalyst. Fortunately, NMR chemical shift provides high accuracy and specificity to examine the consequences of the proton transfer and Lewis binding strength, as shown in Fig. 26, where the schemes of utilizing 31P-TMP as probe molecules adsorbed on Brønsted, Lewis sites as well as physiosorbed states are shown in Fig. 26a.144 In particular, the acidity of the Brønsted acid site can be evaluated by the protonation degree of the probe molecule145 (Fig. 26c and d) and similarly, the Lewis acidity can be evaluated by the binding energy of the base probe molecule144 (Fig. 26b), both of which will be reflected by the chemical shift values of specified nuclei on the probe molecule, e.g., 13C in acetone and 31P in trimethylphosphine (TMP) and trimethylphosphine oxide (TMPO).133,145–147 In general, 31P (I ¼ 1/2) is a preferable NMR-sensitive nucleus compared to 1H and 13C, given its 100% natural abundance and high gyromagnetic ratio. Moreover, its chemical shift spreads in a considerably wider range (Dd31P > 650 ppm) that significantly enhances the resolution of the spectrum. Therefore, since the early development by Haw et al., the P-containing molecules TMP and TMPO have been widely utilized as NMR probes for characterizing acid properties of solid catalysts over the past few decades.145,146 Clearly, such method provides a robust way to distinguish the type (BA or LA) of acid sites, and also a way to characterize their distribution and concentration, as long as the NMR resonances are resolved after probe molecule titration. The strength of acid sites, on the other hand, can be characterized reliably with assistance from computational calculations as demonstrated in Fig. 26b and d, where clear trends can be found for the calculated d (31P) of 31P-TMP adsorbed on Lewis acid sites (Al, B and Ti metal centers) as a function of the binding energy (Fig. 26b), or d (31P) of 31P-TMPO adsorbed on the Brønsted acid site in zeolites as

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Fig. 29 (a) 31P MAS NMR spectra (TMP adsorbed) of ZnO plate, rod and powder with deconvoluted resonances shown as indicated in I, II, III and IV. (b) DFT calculated molecular interaction and adsorption energy between TMP and various surface features. (c) Summarized distribution, concentration and percentage of surface features yielded from analyses in (a) and (b). Adapted with permission from Peng, Y. -K.; Ye, L.; Qu, J.; Zhang, L.; Fu, Y.; Teixeira, I. F.; McPherson, I. J.; He, H.; Tsang, S. C. E. Trimethylphosphine-Assisted Surface Fingerprinting of Metal Oxide Nanoparticle by 31P Solid-State NMR: A Zinc Oxide Case Study. J. Am. Chem. Soc. 2016, 138, 2225–2234, Copyright 2016 American Chemical Society.

a function of the O(P)eH bond distance (Fig. 26d), which probes the extent of proton transfer from the BA site to the TMPO molecule, as an indicator of the intrinsic acid strength.

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In addition to titration-type probe molecules, small hydrocarbon molecules are also used to directly probe the reactivity of acid sites, such as deuterated methane, ethane, and isobutane. Fig. 27 displays the result of adsorbing isobutane-d10 on to zeolite HZSM-5, with the CAVERN apparatus shown in Fig. 22d.148 The adsorption, surprisingly, triggered an H-D exchange reaction between the BAS site and the CeD bond on the methyl groups of the isobutane molecules at room temperature, evidenced by a stepwise decrease of the BAS signal at ca. 5 ppm and increase of the methyl peak at ca. 1 ppm. The schemes of favored H-D exchange transition states are displayed in Fig. 27b. This type of probe reaction provides fundamental knowledge of how the strong CeH bond can be activated by special active sites such as BAS in zeolites, which may bring insight into developing catalyst for activating hydrocarbons at lower temperatures.

9.17.5.3.2

Metal oxides and modified metal oxides

Besides zeolites, metal oxides are another important category of solid catalysts or catalyst supports used in refinery and chemical industries, including sulfated-zirconia, titanium oxides, zin oxides and other assorted metal oxides. Yet, similar to zeolites, Brønsted and Lewis sites are of central importance during the catalytic process, where the former arise from bridging and/or terminal hydroxyl groups and the latter from coordinatively saturated and unsaturated metal atoms. Moreover, for metal oxides, the exposed crystalline facets and defects such oxygen vacancies are other crucial factors for altering the catalytic properties. Fundamental understanding such properties is indispensable for designing new and promoting existing catalysts, but challenges exist. A comprehensive review of 31P NMR studies on P-associated probe molecules can be found in the literature.145 Here, we selectively show two examples of how probe molecules are incorporated to understand the acid sites and exposed facets on metal oxide catalysts. Probing acid sites. The trend of chemical shift characteristics of TMP adsorption on Brønsted acid (BA) and Lewis acid (LA) sites in zeolite catalysts shown in Fig. 26 can be readily applied to metal oxides. What is more, the acidity characterization by TMP 31P NMR is actually a more sensitive to Lewis acidity rather than Brønsted acidity, mainly because when bound to LA sites, TMP molecules yield 31P resonances over a considerable chemical shift range of ca.
20 
60 ppm, while TMPs bound to BA sites yield protonated TMPHþ ions which normally lead to a 31P resonance range of only ca.
2 
5 ppm.145 Sulfation pretreatment is commonly used to promote their catalytic performances by enhancing the acidity of metal oxides. Such enhancement can be probed by the 31PTMP NMR. Fig. 28a and b display the 31P MAS NMR spectra of TMP adsorbed on anatase titania TiO2 and its sulfated version SO42
/ TiO2, respectively. TMP adsorbed on TiO2 yields a single 31P NMR resonance peak centering at
35 ppm (Fig. 28a), which can be assigned to adsorption on LA sites. Such signal, however, shifts notably to
27 ppm in the case using SO42
/TiO2 catalyst (Fig. 28b), indicating an enhancement in acid strength of LA sites; meanwhile, a new 31P signal at
4 ppm was observed, indicating the formation of BA sites. In comparison, Fig. 28c and d display the spectra for bulk alumina (Al2O3) and its sulfated counterpart (SO42
/Al2O3), and similar results were observed. The sulfation treatment caused the 31P signal of the adsorbed TMP at LA sites shift from
51 ppm (Fig. 28c) to
49 ppm (Fig. 28d), while with a new signal produced at
3 ppm due to protonated TMPHþ. Overall, the TMP-NMR probe molecule approach not only proved that sulfation treatment of metal oxide catalysts provokes enhancement of Lewis acidic strength, but also revealed the formation of additional BA sites, which should be created at the expense of the original weaker LA sites in the pristine metal oxide. Probing morphology and defects. The acidic property and catalytic activities of metal oxide nanoparticles can also be affected by their morphologies, or specifically, surface features such as exposed facets/planes, defects and chemical functionalities. Probe molecule/ NMR has proven to be a simple and robust technique for their characterization. Single-crystalline nanoparticles (NPs) with tailored facets have attracted increased interest in heterogeneous catalysis compared to their polycrystalline counterparts. It is found that the catalytic performance can be greatly improved with the exposure of a specific facet, and the chemical bond breakage and formation between reactant and product is closely associated with the coordination environment of the surface active atoms.149,150 As an example, zinc oxide (ZnO) NPs have drawn considerable R&D interest recently due to their superior performances in solar cells and photocatalysis, showing facet-dependent acid properties. Both BA and LA sites present on the surfaces of ZnO nanocrystals, but with preferences on specific surface facets as well as structural defects such as oxygen vacancies (VO). Fig. 29 displays the 31P ssNMR spectra of TMP adsorbed on ZnO NPs with plate-like, rod-like, and powder morphologies, showing that such method can provide indispensable information on the surface fingerprinting and facet-specific properties of the metal oxide NP.151 Impressively, both qualitative and quantitative information of VO on specific facets were attained by the TMP-assisted NMR technique. For all three morphologies of ZnO NPs, the overlapped 31P MAS NMR signal can be deconvoluted into four resonances (yet still broad) accounting for four different TMP adsorption sites, namely site I (
43 ppm), site II (
48 ppm), site III (
55 ppm), and site IV (
61 ppm), as shown in Fig. 29a. Intriguingly, the NMR spectra show that the distribution of adsorption sites differ from each morphology, i.e., (II, III), (I, III), and (III, IV) are predominant sites for the plate, rod, and powder ZnO samples, respectively. Moreover, the adsorption energy and theoretical d(31P) were assessed by DFT calculations, as summarized in Fig. 29b. Such theoretical results helped to gain further insights into the four possible adsorption structures of TMP and facilitated the assignment of the four regions of signals, i.e., exposed (100) facets to site I at
43 ppm observed for the rod-like sample, exposed (002) facets to site II at ca.
48 ppm, whereas Zn-(002)Zn-OH and/or O-(002)Zn-OH to site III and weakly adsorbed TMP on nonpolar (100)Zn-OH. Further, the amount of TMP adsorbed at each site were quantified as shown in Fig. 29c. The concept of using probe molecules largely expands the means of characterizing active sites in catalysts. As a summary of this section, we show that the probe-molecule-assisted 1H NMR and 31P NMR approaches are robust and reliable techniques for providing qualitative and quantitative information on types, distributions, strengths and concentrations of active sites in zeolites and metal oxides, as well as characteristic surface features such as exposed facets and defects for the latter. Undoubtedly, probe-

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molecule coupled with NMR can sometimes provide richer or even complementary information compared to conventional methods such as IR, photoluminescence (PL) and electron paramagnetic resonance (EPR). Further, although single-resonance spectra of 1H, 31P NMR characterizations are usually carried out, it is usually important to probe the proximity between the BA (or LA) and P-molecule, or the distance between distinct BA (or LA) sites; as such, heteronuclear and homonuclear correlation NMR methods such as 1H-1H double-quantum (DQ-SQ), 31P/27A1 (TRAPDOR, REAPDOR, RESPDOR, HMQC, etc.), 1H-31P heteronuclear correlation (REDOR, CP-HETCOR, HMQC, etc.) and 31P-31P double-quantum (DQ-SQ, CORD, etc.) correlation can be employed according to the desired circumstance. Sometimes, isotopically enrichment can help to provide additional useful information, such as using 15N-enriched pyridine and 13C-enriched acetone. Last but not least, diverse information of the active site can also be obtained depending on size and chemical property of the probe molecule, such as ammonia vs pyridine, pyridine vs acetonitrile. For instance, the bulky amine (perfluorotributyl amine) can be used as titrants to distinguish internal and external Brønsted sites in zeolites. Overall, the approach of probe-molecule-assisted NMR method has proven to be essential and will keep playing important roles in characterizing catalytic sites.

9.17.6

Summary and outlook

In this chapter, we described how various ssNMR techniques can be applied to investigate molecular level structures, which is crucial for understanding a catalytic system. Particularly, the basic NMR fundamentals of how NMR signals are originated and how they are influenced by local structures near the observed nucleus, and in turn, how to retrieve structural information from the NMR spectroscopy, were introduced based on well described NMR interactions, i.e., chemical shielding, quadrupolar coupling and dipolar coupling. Then, we discussed dipolar and J-coupling interactions, which are particularly powerful in probing internuclear interactions, including constructing 2D correlation NMR spectra and measuring internuclear distances. Important NMR pulse sequences were overviewed accordingly in the related context. Last and importantly, in-situ NMR techniques that have made great contributions to revealing catalytic sites and reactions were described, including the basic concepts and their capabilities, advantages, and limitations in solving catalytic problems. It is also shown with selected application examples that the implementation of these ssNMR techniques can and have largely enlarged one’s understanding of the nature of catalytic sites. In fact, some molecular level insights were gained largely, if not only, relying on NMR characterizations. Typical heterogeneous catalysts can be found as metals, oxides, zeolites, sulfides, carbons/carbides, nitrides, phosphides, chlorides and essentially, any other type of materials with a surface catalytic activity. Characterization of these materials is normally motivated by a desire to understand the nature of the catalytic sites, including elucidating their fine structures at atomic/molecular level, their intrinsic reactivities, i.e., capability to activate or break chemical bonds of reactant molecules, and their quantity and spatial distributions which can all impact the much-concerned overall catalytic performance of the catalysts. ssNMR provides a variety of options to meet such demands. As shown in this chapter, it can unravel atomic level structures of solid acid sites by 1D and 2D correlation experiments, probe single-atom catalytic sites and even metal-hydrides, reveal intrinsic reactivities and active site quantity/distribution by in-situ and/or probe-molecule-assisted NMR techniques, etc. However, despite the successful applications of ssNMR for characterizing catalytic materials, it is not hard to notice that among such a broad range of catalysts listed above, NMR is only suitable for a small part of them, and the key reason centers in sensitivity. Indeed, the inherent low sensitivity of the many observed nuclei is what limits further applications of NMR for characterizing catalytic materials; inspecting the periodic table, although many isotopes are NMR active, only a few of them with high natural abundance and/or high g (gyromagnetic ratio) are frequently investigated. In fact, studying low sensitivity isotopes, either caused by low g or broadline issues from CSA or large quadrupolar couplings, remains mostly as research topic in NMR rather than application community. The problem is especially pertinent in catalysis given that often only a small fraction of the sample is interested, as catalysts (or catalytic sites) are often prepared at low loadings. Remedies for the sensitivity issues include developments in magnet and probe technologies (e.g., high-field NMR, cryoprobes, probes capable of ultrafast MAS, low-temperature (LT) MAS probes), isotope enrichment, paramagnetic relaxation enhancement (PRE), the use of large amount of sample, pulse sequence methods such as Carr–Purcell–Meiboom–Gill (CPMG), double frequency sweep (DFS) and multiple cross polarization (MCP), etc., as well as special hyperpolarization techniques such as Dynamic Nuclear Polarization (DNP), laser-induced hyperpolarized 129Xe NMR,152 and Parahydrogen Induced Polarization (PHIP),153 which would require special devices or setups and might only be suitable for limited classes of materials. High-field and/or ultrafast MAS NMR, in comparison, are universal solutions regardless of material type and have started to emerge in recent years, thanks to the fast development of hardware technologies. Given the crucial importance of the NMR sensitivity in characterizing catalytic sites, at the end, we would like to review some recent development of those methods with high future potentials to our perspective as follows. High-Field NMR. As discussed in Section 9.17.2.6, NMR sensitivity is highly dependent on the external magnetic field B0, doubling the field strength for a spin-1/2 and a half integer quadrupolar nucleus provides ca. 3-fold and 20-fold S/N enhancement, corresponding to 9- and 400-fold of time saving, respectively. Hence, persuing higher fields has been a constant goal for the NMR researchers. Up to now, the highest operational field allowing for long-time NMR experiments is achieved at 35.2 T (1H 1.5 GHz) by a recent lab-built Series-Connected Hybrid (SCH) instrument.154 And promisingly, more stable commercial GHz-class NMR spectrometers have been successfully delivered as well.155 Ultrafast MAS NMR. Benefitting from high sensitivity and high natural-abundance ( 100%), proton NMR has played a crucial role in the characterizations of a wide of organic or proton-containing materials, especially in solution NMR. The major obstacle to

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successful applications of 1H based NMR experiments in solids is the inability to sufficiently suppress the 1H-1H dipolar couplings, which can be overcome by implementing recently rapidly evolving fast/ultrafast MAS techniques. Although ultrafast MAS NMR is a more demanded technique for characterizing biological systems due to the strong 1H-1H dipolar network, its application in catalysis is emerging, especially for metal-oxide systems containing rich proton networks such as the example shown in Fig. 8. Remarkable advances have been made on fast MAS technology over the past decade, and to date, the commercially available ultrafast MAS NMR probes can achieve the spinning rates up to 110 kHz. Dynamic Nuclear Polarization (DNP). DNP is an important and fundamentally different approach compared to the former two, and is capable to boost NMR S/N by factors up to 102. Despite being an early concept, DNP was not widely adopted until the introduction of gyrotron microwave-driven DNP by Griffin and coworkers, and its practical application to materials has not been recognized until the recent decade, upon important hardware developments. Fundamentally, DNP increases NMR sensitivity by transferring paramagnetic electron polarization to the detected NMR nuclei, taking advantage of the much larger gyromagnetic ratio of the electron (around 660 times higher than that of 1H). Detailed discussion of DNP is beyond the scope of this chapter but can be further accessed at a few excellent review articles.156–161 It is worth noting that DNP is specifically suited for investigating catalytic problems, owing to its selective signal enhancement of the surface species and that heterogeneous catalysis often takes place on surfaces. However, as of the current technique, radical reagents are usually added to the system to provide paramagnetic electrons, which may potentially change the original surface environment of the catalyst or cannot enter the micropores of the catalyst such as zeolite. Besides, due to the general fast electron spin relaxations, current DNP experiments are operated at very low temperatures, which is a major limitation for many potential MAS DNP applications. Nonetheless, since around 2010, DNP has been successfully applied to a tremendous amount of works in understanding the structure and surface functionalization of solid catalysts, nanoparticles, oxides as well as polymers, cellulose systems and MOFs, and has made possible the direct detection of weakly-sensitive nuclei such as 15N and 17O in natural abundance,162 which was not imaginable in the past.

Acknowledgments We are grateful for the financial supports from the National Natural Science Foundation of China (Nos. 21773230 and 91945302), National Key R&D Program of China (2021YFA1502803), Liao Ning Revitalization Talents Program (XLYC1807207), DICP&QIBEBT UN201808 and DICP I202104.

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115. Shcherbakov, A. A.; Medeiros-Silva, J.; Tran, N.; Gelenter, M. D.; Hong, M. From Angstroms to Nanometers: Measuring Interatomic Distances by Solid-State NMR. Chem. Rev. 2022, 122, 9848–9879. 116. Grey, C. P.; Vega, A. J. Determination of the Quadrupole Coupling Constant of the Invisible Aluminum Spins in Zeolite HY with 1H/27Al TRAPDOR NMR. J. Am. Chem. Soc. 1995, 117, 8232–8242. 117. Nimerovsky, E.; Gupta, R.; Yehl, J.; Li, M.; Polenova, T.; Goldbourt, A. Phase-Modulated LA-REDOR: A Robust, Accurate and Efficient Solid-State NMR Technique for Distance Measurements Between a Spin-1/2 and a Quadrupole Spin. J. Magn. Reson. 2014, 244, 107–113. 118. Goldbourt, A. Distance Measurements to Quadrupolar Nuclei: Evolution of the Rotational Echo Double Resonance Technique. Magn. Reson. Chem. 2021. https://doi.org/ 10.1002/mrc.5150. n/a. 119. Schroeder, C.; Siozios, V.; Mück-Lichtenfeld, C.; Hunger, M.; Hansen, M. R.; Koller, H. Hydrogen Bond Formation of Brønsted Acid Sites in Zeolites. Chem. Mater. 2020, 32, 1564–1574. 120. Brouwer, D. H.; Darton, R. J.; Morris, R. E.; Levitt, M. H. A Solid-State NMR Method for Solution of Zeolite Crystal Structures. J. Am. Chem. Soc. 2005, 127, 10365–10370. 121. Munson, E. J.; Ferguson, D. B.; Kheir, A. A.; Haw, J. F. Applications of a New CAVERN Design to the Study of Reactions on Catalysts Using In Situ Solid-State NMR. J. Catal. 1992, 136, 504–509. 122. Beck, L. W.; White, J. L.; Haw, J. F. Reliable Method for Sealing Glass Ampules for MAS-NMR Experiments on Air-Sensitive Samples. J. Magn. Reson. (1969) 1992, 99, 182–183. 123. Munson, E. J.; Murray, D. K.; Haw, J. F. Shallow-Bed CAVERN Design for in Situ Solid-State NMR Studies of Catalytic Reactions. J. Catal. 1993, 141, 733–736. 124. Hunger, M. In Situ NMR Spectroscopy in Heterogeneous Catalysis. Catal. Today 2004, 97, 3–12. 125. Hunger, M.; Seiler, M.; Horvath, T. A Technique for Simultaneous In Situ MAS NMR and On-Line Gas Chromatographic Studies of Hydrocarbon Conversions on Solid Catalysts under Flow Conditions. Catal. Lett. 1999, 57, 199–204. 126. Hunger, M.; Wang, W. Formation of Cyclic Compounds and Carbenium Ions by Conversion of Methanol on Weakly Dealuminated Zeolite H-ZSM-5 Investigated via a Novel In Situ CF MAS NMR/UV-Vis Technique. Chem. Commun. 2004, 584–585. https://doi.org/10.1039/B315779B. 127. Hunger, M. In Situ Flow MAS NMR Spectroscopy: State Of The Art and Applications in Heterogeneous Catalysis. Prog. Nucl. Magn. Reson. Spectrosc. 2008, 53, 105–127. 128. Ferguson, D. B.; Haw, J. F. Transient Methods for in Situ NMR of Reactions on Solid Catalysts Using Temperature Jumps. Anal. Chem. 1995, 67, 3342–3348. 129. Haw, J. F.; Goguen, P. W.; Xu, T.; Skloss, T. W.; Song, W.; Wang, Z. In Situ NMR Investigations of Heterogeneous Catalysis with Samples Prepared under Standard Reaction Conditions. Angew. Chem. Int. Ed. 1998, 37, 948–949. 130. Nicholas, J. B.; Xu, T.; Haw, J. F. NMR and Theoretical Studies of Solid Acids: Super and Otherwise. Top. Catal. 1998, 6, 141–149. 131. Haw, J. F. In Situ NMR of Heterogeneous Catalysis: New Methods and Opportunities. Top. Catal. 1999, 8, 81–86. 132. Ivanova, I. I.; Kolyagin, Y. G. Impact of In Situ MAS NMR Techniques to the Understanding of the Mechanisms of Zeolite Catalyzed Reactions. Chem. Soc. Rev. 2010, 39, 5018–5050. https://doi.org/10.1039/C0CS00011F. 133. Zhang, W.; Xu, S.; Han, X.; Bao, X. In Situ Solid-State NMR for Heterogeneous Catalysis: A Joint Experimental and Theoretical Approach. Chem. Soc. Rev. 2012, 41, 192– 210. https://doi.org/10.1039/C1CS15009J. 134. Gay, I. D. A Magic-Angle Spinner for Vacuum-Sealed Samples. J. Magn. Reson. (1969) 1984, 58, 413–420. 135. Adrian Carpenter, T.; Klinowski, J.; Tilak, D.; Tennakoon, B.; Smith, C. J.; Edwards, D. C. Sealed Capsules for Convenient Acquisition of Variable-Temperature ControlledAtmosphere Magic-Angle-Spinning NMR Spectra of Solids. J. Magn. Reson. (1969) 1986, 68, 561–563. 136. Chen, K.; Gumidyala, A.; Abdolrhamani, M.; Villines, C.; Crossley, S.; White, J. L. Trace Water Amounts can Increase Benzene H/D Exchange Rates in an Acidic Zeolite. J. Catal. 2017, 351, 130–135. 137. Xu, M.; Harris, K. D. M.; Thomas, J. M.; Vaughan, D. E. W. Probing the Evolution of Adsorption on Nanoporous Solids by In Situ Solid-State NMR Spectroscopy. ChemPhysChem 2007, 8, 1311–1313. 138. Xu, M.; Harris, K. D. M.; Thomas, J. M. Mapping the Evolution of Adsorption of Water in Nanoporous Silica by in situ Solid-State 1H NMR Spectroscopy. J. Am. Chem. Soc. 2008, 130, 5880–5882. 139. Xu, M.; Harris, K. D. M.; Thomas, J. M. In Situ Solid-State 1H NMR Studies of Hydration of the Solid Acid Catalyst ZSM-5 in its Ammonium Form. Solid State Nucl. Magn. Reson. 2009, 35, 93–99. 140. Isbester, P. K.; Zalusky, A.; Lewis, D. H.; Douskey, M. C.; Pomije, M. J.; Mann, K. R.; Munson, E. J. NMR Probe for Heterogeneous Catalysis with Isolated Reagent Flow and Magic-Angle Spinning. Catal. Today 1999, 49, 363–375. 141. Wang, W.; Buchholz, A.; Seiler, M.; Hunger, M. Evidence for an Initiation of the Methanol-to-Olefin Process by Reactive Surface Methoxy Groups on Acidic Zeolite Catalysts. J. Am. Chem. Soc. 2003, 125, 15260–15267. 142. Sun, T.; Chen, W.; Xu, S.; Zheng, A.; Wu, X.; Zeng, S.; Wang, N.; Meng, X.; Wei, Y.; Liu, Z. The First Carbon-Carbon Bond Formation Mechanism in Methanol-toHydrocarbons Process over Chabazite Zeolite. Chem 2021, 7, 2415–2428. 143. Yi, X.; Xiao, Y.; Li, G.; Liu, Z.; Chen, W.; Liu, S.-B.; Zheng, A. From One to Two: Acidic Proton Spatial Networks in Porous Zeolite Materials. Chem. Mater. 2020, 32, 1332–1342. 144. Chu, Y.; Yu, Z.; Zheng, A.; Fang, H.; Zhang, H.; Huang, S.-J.; Liu, S.-B.; Deng, F. Acidic Strengths of Brønsted and Lewis Acid Sites in Solid Acids Scaled by 31P NMR Chemical Shifts of Adsorbed Trimethylphosphine. J. Phys. Chem. C 2011, 115, 7660–7667. 145. Zheng, A.; Liu, S.-B.; Deng, F. 31P NMR Chemical Shifts of Phosphorus Probes as Reliable and Practical Acidity Scales for Solid and Liquid Catalysts. Chem. Rev. 2017, 117, 12475–12531. 146. Haw, J. F.; Hall, M. B.; Alvarado-Swaisgood, A. E.; Munson, E. J.; Lin, Z.; Beck, L. W.; Howard, T. Integrated NMR and Ab Initio Study of Acetonitrile in Zeolites: A Reactive Complex Model of Zeolite Acidity. J. Am. Chem. Soc. 1994, 116, 7308–7318. 147. Jiang, Y.; Huang, J.; Dai, W.; Hunger, M. Solid-State Nuclear Magnetic Resonance Investigations of the Nature, Property, and Activity of Acid Sites on Solid Catalysts. Solid State Nucl. Magn. Reson. 2011, 39, 116–141. 148. Truitt, M. J.; Toporek, S. S.; Rovira-Truitt, R.; White, J. L. Alkane C
H Bond Activation in Zeolites: Evidence for Direct Protium Exchange. J. Am. Chem. Soc. 2006, 128, 1847–1852. 149. Tian, N.; Zhou, Z.-Y.; Sun, S.-G.; Ding, Y.; Wang, Z. L. Synthesis of Tetrahexahedral Platinum Nanocrystals With High-Index Facets and High Electro-Oxidation Activity. Science 2007, 316, 732–735. 150. Chrzanowski, W.; Wieckowski, A. Surface Structure Effects in Platinum/Ruthenium Methanol Oxidation Electrocatalysis. Langmuir 1998, 14, 1967–1970. 151. Peng, Y.-K.; Ye, L.; Qu, J.; Zhang, L.; Fu, Y.; Teixeira, I. F.; McPherson, I. J.; He, H.; Tsang, S. C. E. Trimethylphosphine-Assisted Surface Fingerprinting of Metal Oxide Nanoparticle by 31P Solid-State NMR: A Zinc Oxide Case Study. J. Am. Chem. Soc. 2016, 138, 2225–2234. 152. Xu, S.; Zhang, W.; Liu, X.; Han, X.; Bao, X. Enhanced In situ Continuous-Flow MAS NMR for Reaction Kinetics in the Nanocages. J. Am. Chem. Soc. 2009, 131, 13722– 13727. 153. Green, R. A.; Adams, R. W.; Duckett, S. B.; Mewis, R. E.; Williamson, D. C.; Green, G. G. R. The Theory and Practice of Hyperpolarization in Magnetic Resonance Using Parahydrogen. Prog. Nucl. Magn. Reson. Spectrosc. 2012, 67, 1–48. 154. Gan, Z.; Hung, I.; Wang, X.; Paulino, J.; Wu, G.; Litvak, I. M.; Gor’kov, P. L.; Brey, W. W.; Lendi, P.; Schiano, J. L.; et al. NMR Spectroscopy up to 35.2T Using a SeriesConnected Hybrid Magnet. J. Magn. Reson. 2017, 284, 125–136. 155. Luchinat, E.; Barbieri, L.; Cremonini, M.; Banci, L. Protein In-Cell NMR Spectroscopy at 1.2 Ghz. J. Biomol. NMR 2021, 75, 97–107.

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156. Rankin, A. G. M.; Trébosc, J.; Pourpoint, F.; Amoureux, J.-P.; Lafon, O. Recent Developments in MAS DNP-NMR Of Materials. Solid State Nucl. Magn. Reson. 2019, 101, 116–143. 157. Liao, W.-C.; Ghaffari, B.; Gordon, C. P.; Xu, J.; Copéret, C. Dynamic Nuclear Polarization Surface Enhanced NMR Spectroscopy (DNP SENS): Principles, Protocols, and Practice. Curr. Opin. Colloid Interface Sci. 2018, 33, 63–71. 158. Lilly Thankamony, A. S.; Wittmann, J. J.; Kaushik, M.; Corzilius, B. Dynamic Nuclear Polarization for Sensitivity Enhancement in Modern Solid-State NMR. Prog. Nucl. Magn. Reson. Spectrosc. 2017, 102–103, 120–195. 159. Kobayashi, T.; Perras, F. A.; Slowing, I. I.; Sadow, A. D.; Pruski, M. Dynamic Nuclear Polarization Solid-State NMR in Heterogeneous Catalysis Research. ACS Catal. 2015, 5, 7055–7062. 160. Michaelis, V. K.; Ong, T.-C.; Kiesewetter, M. K.; Frantz, D. K.; Walish, J. J.; Ravera, E.; Luchinat, C.; Swager, T. M.; Griffin, R. G. Topical Developments in High-Field Dynamic Nuclear Polarization. Isr. J. Chem. 2014, 54, 207–221. 161. Rossini, A. J.; Zagdoun, A.; Lelli, M.; Lesage, A.; Copéret, C.; Emsley, L. Dynamic Nuclear Polarization Surface Enhanced NMR Spectroscopy. Acc. Chem. Res. 2013, 46, 1942–1951. 162. Perras, F. A.; Wang, Z.; Naik, P.; Slowing, I. I.; Pruski, M. Natural Abundance 17O DNP NMR Provides Precise O-H Distances and Insights into the Brønsted Acidity of Heterogeneous Catalysts. Angew. Chem. Int. Ed. 2017, 56, 9165–9169.

9.18 The expanding frontier between mechanochemistry & solid state NMR: Special focus on inorganic components of materials Ce´sar Leroya, Thomas-Xavier Me´trob, and Danielle Laurencina, a ICGM, University of Montpellier, CNRS, ENSCM, Montpellier, France; and b IBMM, University of Montpellier, CNRS, ENSCM, Montpellier, France © 2023 Elsevier Ltd. All rights reserved.

9.18.1 9.18.2 9.18.2.1 9.18.2.2 9.18.2.3 9.18.3 9.18.3.1 9.18.3.2 9.18.4 9.18.4.1 9.18.4.2 9.18.5 References

Introduction Solid state NMR as an analytical tool for studying the structure, texture and properties of materials prepared under mechanochemical conditions ssNMR for the structural analysis and phase identification of materials prepared using a mechanochemical step ssNMR for the study of crystallinity and microstructure of (nano)materials prepared by mechanochemistry ssNMR for understanding properties of materials prepared by mechanochemistry Mechanochemistry as a synthetic method for enabling new developments in solid state NMR Mechanochemical enrichment of molecules and materials in NMR-active isotopes Change in nuclear relaxation rates through mechanochemical treatment Synthetic and instrumental developments performed at the interface of mechanochemistry and NMR Understanding mechanosynthesis through NMR In situ NMR analysis of reaction media during ball-milling Conclusion

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Abstract While the research fields of mechanochemistry and solid state NMR (ssNMR) have been developing in independent ways for many years, there are an increasing number of studies in which both topics meet. On one hand, ssNMR can be used to perform advanced characterizations of the structure, morphology and also properties of materials prepared by mechanochemistry. On the other, syntheses performed using mechanochemistry can help push forward the current frontiers of solid state NMR, for example through the development of new phases enriched in NMR-active isotopes. Lastly, studies at the interface between mechanochemistry and ssNMR are increasingly being carried out, notably to help elucidate reaction mechanisms in ball-milling (BM). In this chapter, illustrations of investigations along these lines will be provided, focusing on the synthesis and characterization of materials with an inorganic component, such as oxides, metal-organic frameworks, and zeolites, just to name a few.

9.18.1

Introduction

In view of designing molecules and materials exhibiting novel properties, chemists have been actively exploring different synthetic pathways, one of which is mechanochemistry.1–3 In mechanochemistry, reactions are induced by the direct and/or indirect absorption of mechanical energy by reagents.4,5 The mechanical input can be provided in different ways, by simply mixing the reagents with a mortar and pestle, or by using dedicated equipment such as ball-mills. Such mechanical treatments imply that reacting particles will undergo different types of mechanical forces (impact, shear, etc.), which most often lead to the reduction of their size, their efficient mixing, and to chemical reactions at their interfaces. While mechanochemical reactions had initially been used for the preparation of inorganic materials (e.g., alloys and oxides), they are now increasingly employed for the preparation of a variety of organic and organometallic compounds, coordination complexes (including coordination polymers and metal-organic frameworksdMOFs), as well as hybrid (nano)materials. This new impetus has been driven by various factors, among which are the search for more ecological and atom-efficient chemical processes, and the possibility to form original products compared to those traditionally isolated under classical conditions (e.g., by syntheses in solution, or under hydrothermal conditions, etc.).6 Indeed, as most mechanochemical reactions proceed in the absence of bulk solvent, and with a very good atom efficiency (implying minimal waste), they have been qualified as “green” synthetic approaches.7 Moreover, in a number of cases, they have been shown to lead to “unique” products (not observed yet in solution), due to the very different concentrations, solvation states, and kinetics involved.8,9 Because mechanochemical reactions generally proceed in the solid state, analyses of the progress of reactions have been made possible thanks to analytical techniques like IR/Raman spectroscopies, powder X-ray diffraction (pXRD), and also solid state NMR (ssNMR). Each of these analytical tools provides different information on the composition of the reaction medium (e.g., vibration

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modes of specific bonds/functional groups, crystallinity, or local environment of the different nuclei in the reagents/products), meaning that they are highly complementary, and therefore important to use together to help understand the formation of a given product. Regarding NMR spectroscopy, several ssNMR analyses of mechanochemical reactions have been reported, focusing on the study of organic or inorganic components, depending on the nature of the molecule/material prepared. The purpose of this chapter is to focus on the ssNMR analyses which have been reported for mechanochemically-prepared compounds which contain an “inorganic” component, by looking more specifically at the local environment of the nuclei within this inorganic component (many of these nuclei being suitable for ssNMR studies).10,11 Examples of such materials include functional oxides, fluorides and borides, metals and alloys, zeolites and MOFs. In a first part, we will illustrate how ssNMR has been used as an analytical tool to understand the structure, texture and properties of materials prepared using a mechanochemical step. Then, we will show how mechanochemistry can actually be a valuable synthetic process for the development of advanced ssNMR analyses. Lastly, examples of research studies which have been carried out at the interface of ssNMR and mechanochemistry will be discussed, showing the strong complementarity of these two methods.

9.18.2 Solid state NMR as an analytical tool for studying the structure, texture and properties of materials prepared under mechanochemical conditions 9.18.2.1

ssNMR for the structural analysis and phase identification of materials prepared using a mechanochemical step

Mechanochemistry is one of the common synthetic methodologies used for the preparation of functional materials. It can either serve as a means to intimately mix the solid reagents prior to a heat-treatment/sintering/aging step, or as a way to directly prepare the targeted phase. While X-ray diffraction techniques are still the most frequently used to study the structure of these materials, ssNMR analyses have been found to provide complementary information, including for the identification of different phases synthesized, for the analysis of possible phase-segregation events occurring in the solid state, or for the detection of amorphous phases or impurities. When looking at the work published over the past 20 years, several examples of the application of ssNMR to investigate the structure of inorganic and hybrid materials prepared using a protocol involving mechanochemistry can be found. These include ssNMR studies of materials containing an “inorganic” component, such as oxides (generally in a ceramic or glassy/amorphous form),12–18 oxycarbides,19 fluorides,20 hydrides,21 borides,22,23 apatites,24–26 and alloys/intermetallics.27–29 Moreover, important classes of functional materials such as zeolites,30–35 AlPOs,36 MOFs,37,38 as well as perovskites,39–47 have also been the object of such investigations. A few recent illustrations of the purpose and advantages of these analyses are provided in the following paragraphs. Regarding oxides, one remarkable example concerns the study of ZrMgMo3O12,16 a material of interest due to its “zero thermalexpansion” properties. This compound was synthesized by mixing and mechanically activating ZrO2, Mg5(CO3)4(OH)2$5H2O and MoO3 precursors by high-energy ball-milling (BM), pelletizing the reaction mixture under high pressure, and lastly performing a reactive sintering at 700
C. A 17O-enriched version of this material was also prepared in a similar way, by using a 17O-enriched MoO3 precursor. In addition to powder X-ray diffraction (pXRD), Raman, dilatometry, differential scanning calorimetry and thermogravimetry analyses, one of the original features of this study was to perform high-resolution ssNMR studies on the material, by looking at all the NMR-active isotopes, namely 25Mg, 91Zr, 95Mo and 17O. The purpose of the latter analyses was to help gain very detailed knowledge of the structure of the material through an “NMR crystallography” approach,48 because the ZrMgMo3O12 material could not be grown as a single crystal. To be more specific, ssNMR analyses enabled confirmation of the Pna21 space group which had been established from the pXRD data, with notably three distinct 95Mo NMR signals resolved at 21.1 T. Moreover, electric field gradient (EFG) parameters were extracted from the NMR spectra, and then used to assist in the DFT-refinement of the structure, as they are very sensitive to the local geometry of the coordination polyhedra of the Mg, Zr and Mo. With this approach, a quality of refinement similar to what could have been obtained using single-crystal X-ray diffraction (SCXRD) analyses was achieved. Importantly, 17O ssNMR analyses were subsequently used as a means to cross-validate the structure: a very good agreement between DFTcalculated and experimental 17O NMR parameters (diso and PQ) was found, further confirming the quality of the structure obtained by NMR-crystallography (Fig. 1). In the field of MOFs, because ball-milling is increasingly being used as a synthetic approach,38,49 and because it yields phases in a powdered form (thus unsuitable for SCXRD), much effort is being made in developing advanced characterization methodologies to assist in structure determination. Notably, like for oxides, NMR-crystallography approaches are also increasingly being applied.50 One recent study which illustrates this is the work by Schurko, Fri
s
cic, and co-workers, on cadmium-(methyl)imidazolate frameworks (which are a sub-class of zeolitic imidazolate frameworks - ZIFs).37 These were synthesized starting from CdO, imidazole (or 2-methylimidazole), as well as additional reactants in some cases (i.e., ammonium nitrate, ammonium sulfate, and caffeinium hydrogensulfate). Ball-milling was used as a first step to mix the reagents, and then an “accelerated aging” treatment was performed on the mixture (by heating at 45
C in a chamber maintained at 100% relative humidity). As part of the same work, one phase was also prepared by performing the ball-milling of Cd(OH)2 and 2-methylimidazole at 60
C (by thermally controlling the temperatures of the jars). pXRD as well as multinuclear ssNMR analyses were performed on the materials, looking not only at the organic ligand (through 1H, 13C and 14N NMR), but also the metal ion, Cd2þ, through 1H / 111Cd cross-polarization (CP) studies (Fig. 2), performed both under static and magic angle spinning (MAS) conditions. From these analyses, the isotropic chemical shifts (diso) and other chemical shift tensor parameters were extracted, to reach information on the coordination geometry of the metal ion. Notably, for one of the structures (dia-Cd(Im)2), the large chemical shift span measured (U ¼ 225 ppm) was found to be indicative

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Fig. 1 NMR-refined structure of ZrMgMo3O12 (O atoms in red, MgO6 polyhedra in orange, ZrO6 polyhedra in green, and MoO4 tetrahedra in purple), together with the multiple-magnetic field 25Mg, 95Mo and 91Zr ssNMR analyses (experimental spectra in black, overall fits in red, and contributions from different crystallographic sites in blue). Adapted with permission from reference Romao, C. P.; Perras, F. A.; Werner-Zwanziger, U.; Lussier, J. A.; Miller, K. J.; Calahoo, C. M.; Zwanziger, J. W.; Bieringer, M.; Marinkovic, B. A.; Bryce, D. L.; White, M. A. Zero Thermal Expansion in ZrMgMo3O12: NMR Crystallography Reveals Origins of Thermoelastic Properties. Chem. Mater. 2015, 27 (7), 2633–2646.

of a non-tetrahedral coordination environment of the Cd2þ. Moreover, 111Cd-14N J-couplings could also be observed in some cases, allowing the number of coordinated ligands to be counted. Lastly, using all the information extracted from the multinuclear NMR studies (notably regarding the Cd2þ local structure), it was possible to determine the structure of the “dia-Cd(MeIm)2$HMeIm” phase, using an NMR-crystallography approach. Because mechanochemical reactions essentially occur in the solid state, the question of phase segregation between the reacting solids can arise. This was notably highlighted recently by Kalisvaart and co-workers, in a study aiming at synthesizing and characterizing ternary Li-Sb-Bi alloys, which are of interest for replacing graphite in Li-ion battery anodes.29 Ternary phases of general formula Li3SbxBi1-x (x ¼ 0.25, 0.50, 0.75) were synthesized by ball-milling, by mixing Li metal with pre-synthesized SbeBi binary phases for 5 h. pXRD analyses showed that crystalline and single phase materials were isolated for x ¼ 0.25 and 0.75, but that an Li3Bi impurity was present for x ¼ 0.50. To gain further knowledge on the structure of these materials at the atomic scale, 7Li and 121 Sb NMR analyses were performed. The 7Li chemical shift was found to globally increase as a function of the “x” fraction of Sb in the material, with yet a notable deviation from a linear trend for x ¼ 0.25 (Fig. 3). More careful analysis of the MAS NMR data showed that the 7Li resonance at this composition is asymmetric, and can be deconvoluted in two components, one of which corresponds to a Sb-rich phase. For other compositions, asymmetric 7Li lineshapes were also noticed, indicating that there are local variations in the Sb/Bi ratios, and thus suggesting the beginning of a form of phase segregation occurring locally. Static 121Sb NMR experiments further confirmed the presence of several Sb environments within the ternary alloys. Overall, this study clearly highlights how ssNMR can provide complementary information to XRD analyses, by pointing to the formation of Sb-rich domains/ clusters.

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Fig. 2 (A/) 1H / 111Cd CP NMR analyses of Cd-(methyl)imidazolate MOFs prepared by mechanochemistry (followed by accelerated aging), showing the sensitivity of NMR parameters to the local Cd environment. (B/) Illustration of the variation of diso (111Cd) as a function of the Cd2þ local environment (number of ligands and nature of the coordinated atom). Adapted with permission from reference O’Keefe, C. A.; Mottillo, C.; Vainauskas, J.; Fábián, L.; Fri
s
cic, T.; Schurko, R. W. NMR-Enhanced Crystallography Aids Open Metal–Organic Framework Discovery Using SolventFree Accelerated Aging. Chem. Mater. 2020, 32 (10), 4273–4281.

Lastly, in addition to helping identify the nature of materials prepared by ball-milling, ssNMR analyses are also useful for verifying their purity. One illustration of this was recently provided by Zaikina and co-workers in a study on ternary alkali metal borides.23 In their case, a novel synthetic route was developed, starting from LiH, Ni and B precursors. Due to the high sensitivity of these reagents to ambient atmosphere and humidity, they were introduced in grinding jars in an Ar-filled glove box, and subsequently milled for 12 min. The mixture of powders was then placed in a metal container, which was sealed, and heated up to 1173 K for 12 h, after which different heating or cooling steps were applied. The LiNi3B1.8 and Li2.8Ni16B8 phases were thus isolated, and extensively characterized, including using 7Li and 11B ssNMR. Analyses under MAS revealed that the main resonances observed were consistent with the structural models of these materials. For example, for LiNi3B1.8, the chemical shifts of the 7Li and 11B signals (positioned at d(7Li)  28 ppm and d(11B)  170 ppm, respectively, under the measurement conditions used) were found to confirm the metallic nature of the material, while the broadness of the resonances could be explained by the splitting of the Ni sites over different positions and partial B occupancy in the crystal structure (as deduced from careful analysis of the diffraction data), leading to a distribution in local environments around both of these nuclei. Importantly, the detection of additional 7Li and 11B resonances on the spectra revealed the presence of small amounts of impurities in the isolated phases (some of which had not been detected by X-ray diffraction), which were assigned in the case of the LiNi3B1.8 material to lithium-containing phases like

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Fig. 3 7Li and 121Sb NMR analyses of Li-Sb-Bi ternary alloys, prepared using mechanochemistry. The asymmetry of the 7Li and 121Sb resonances accounts for the presence of locally Sb-rich domains within the material. Adapted with permission from reference Kalisvaart, W. P.; Chaudhary, M.; Bhattacharya, A.; Michaelis, V. K.; Buriak, J. M. Mixing, Domains, and Fast Li-Ion Dynamics in Ternary Li–Sb–Bi Battery Anode Alloys. J. Phys. Chem. C 2022, 126 (5), 2394–2402.

Li2O, LiOH$H2O, LiOH and Li2CO3, and to boron containing phases like amorphous boron oxide and Ni2B. It was further shown using 7Li NMR analyses that the Li-salts could be largely removed by washing the final material with water. Overall, here, we have illustrated how ssNMR can provide useful information on the general structure of solids which are prepared using mechanochemistry as one of the synthetic steps. Yet, the potential of ssNMR goes beyond the identification or elucidation of the structure of the end-products, as highlighted in the following sub-sections.

9.18.2.2

ssNMR for the study of crystallinity and microstructure of (nano)materials prepared by mechanochemistry

During mechanochemical processes, the size and surfaces/interfaces of the milled compounds are greatly affected. Size reduction, polymorphic or allotropic transformations or even amorphization caused by ball-milling have been investigated by various ssNMR studies, due to the ability of the method to probe local environments.13,17,51–54 For example, Speight et al. have studied the effect of BM on elemental cobalt and its allotropic transformations (from hexagonal-close-packed (hcp) to the face-centered-cubic (fcc)) through the use of internal field 59Co NMR spectroscopy.55 In their study, they showed the advantage of ssNMR techniques for more easily probing deformation and stacking faults compared to XRD. Fig. 4 shows the changes in the size of particles and 59 Co internal field NMR spectra of three different commercial elemental cobalt sources with significantly different particle sizes (referred to as Aldrich, Alfa and 325 Alfa), before and after 24 h of ball-milling. Specific signals for the metastable fcc phase (in blue), the majority hcp one (in green) as well as hcp (in orange) and fcc (in grey) deformation faults can easily be distinguished using 59Co NMR. The decreasing amount of fcc phases is explained by the highenergy brought during BM, which allows these phases to be transformed into the more stable hcp ones. Such observations could also explain the reduction of the few fcc/hcp deformation faults signals observed on the BM 59Co NMR spectra (in the grey and orange zones). Overall, unfaulted hcp phases increased after BM by up to 17% (in green). Furthermore, as witnessed by particle size plots, the particle size distribution was homogenized to around 6–9 mm diameter after 24 h of milling for the three different starting materials (see red dotted lines).

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Fig. 4 59Co internal field NMR spectra of all three cobalt powders (Aldrich, 325 Alfa and Alfa) before (A/) and after (B/) BM during 24 h. The shaded colored rectangles show the positions of the different cobalt environments (depending on the crystal structure). The magnetic field below the frequency scale is the corresponding internal field. Plots showing the particle size distribution (PSD) relative to each spectrum, as measured by laser diffraction, are shown on the left (in logarithmic scale). Adapted with permissions from Speight, R.; Wong, A.; Ellis, P.; Hyde, T.; Bishop, P. T.; Smith, M. E. A 59Co NMR Study to Observe the Effects of Ball Milling on Small Ferromagnetic Cobalt Particles. Solid State Nucl. Magn. Reson. 2009, 35 (2), 67–73.

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As mentioned in Section 9.18.2.1, for a few years now, mechanochemical syntheses have also been used to form porous materials such as MOFs and zeolites, notably because these protocols are considered as user-friendly and green. Yet, amorphization of such compounds can lead, in many cases, to a loss of interesting properties (loading capacity, catalytic or sensing properties, among others). In the course of a study comparing the structural collapsing of porous materials such as ZIFs and zeolites, Baxter et al. studied the amorphization of a cadmium based ZIF (CdIF-1, Cd(mIm)2 with mIm standing for 2-methylimidazole) through BM.56 They used multinuclear ssNMR (13C, 15N and 113Cd) in order to clearly reveal the increasing disorder caused by the milling. Firstly, it was found that all signals were broadened for the amorphous compounds formed upon milling for 20 or 40 min (noted am-CdIF-1-20 and am-CdIF-1-40, respectively) compared to the crystalline counterpart (noted CdIF-1). For example, the 113 Cd signals of am-CdIF-1-20 and am-CdIF-1-40 showed a broad resonance (at 375 ppm) of  4500 Hz full-width at halfmaximum (FWHM). Similarly, 13C NCC signals ( 125 ppm) exhibited a broadening by nearly a factor of 8.5 between the crystalline and amorphous counterparts (FWHM of 40 Hz vs. 340 Hz). Secondly, changes in local environments of nuclei in the amorphous phases compared to the crystalline equivalent were also observed by the shifting of specific frequencies. In the case of 13C, shifts were about 0.6 to 1.4 ppm for diso(13C)NCN and diso(13C)NCC, respectively, while for 113Cd, the amorphous resonances were shifted by about 35 ppm compared to crystalline phase. Finally, authors noted the appearance of new signals on the 13C NMR spectra, which were attributed to de-coordinated mIm from the Cd center, and with 113Cd ssNMR signatures which could correspond to Cd centers in octahedral coordination environments: their intensities increased according to the milling time of the porous material. It worth mentioning here that similar amorphization processes for a variety of compounds have also been followed by ex situ characterization strategies using ssNMR, as developed in other sections (vide infra, 2.3 and 4.1). Here, we have briefly developed a few examples of materials’ structural evolutions under milling conditions. These changes in crystallinity, particle size or surface states are well-described through the use of ssNMR, quite often in combination with other analytical techniques such as XRD, TEM (transmission electron microscopy) or Raman spectroscopy to name a few. These structural modifications are known to alter partially or even completely the properties of the designed materials, which means that in such cases ssNMR can also be used in order to understand the variation of properties, as we will see in the next sub-section.

9.18.2.3

ssNMR for understanding properties of materials prepared by mechanochemistry

As mentioned previously, the relatively recent success of mechanochemical syntheses has brought a new scope for designing original and innovative materials that were not conceivable via alternative synthetic pathways. Some of these new materials have been shown to outperform the properties of their counterparts synthesized with more standard routes. Once again, ssNMR is often considered as an important analytical tool to study in depth local environments: such ability makes it a method of choice for justifying some of the interesting properties of the materials produced by mechanochemistry. A good illustration of this is found in a contribution from Kuhn et al., in which they have compared the lithium conductivity and diffusion of crystalline b-spodumene (LiAlSi2O6) to the ones of the corresponding glass.57 Both types of compounds were submitted to BM, and 7Li NMR analyses were then performed. Fig. 5A shows the evolution of 7Li T1 spin-lattice relaxation times as a function of the milling time for crystalline and glassy LiAlSi2O6. Milling both materials induces a reduction of the particle sizes down to the nano-scale. In doing so, the conductivity and the Li diffusion within the materials are significantly affected. These properties can be observed through the 7Li T1 spin-lattice relaxation rates (plot on Fig. 5A). The crystalline LiAlSi2O6 rate (0.8 s 1) increases to 2.15 s 1 after 8 h of milling, while the glassy one decreases from 6.0 s 1 to the same converged value of 2.15 s 1. Thanks to this spin-lattice relaxation NMR study, along with impedance spectroscopy analyses, the authors were able to propose a model of the milled structures of both starting materials (see Fig. 5B). For the crystalline b-spodumene, a heterogeneous material is obtained after mechanical treatment of several hours, which consists of crystalline grains with disordered interfacial regions, providing fast diffusion pathways for the Li ions. After long milling times, both milled materials exhibit similar Liþ transport behavior, which could be explained by a mechanically induced structural relaxation in the glass, and by the fact that the nano-structured glass properties resemble those of the amorphous-like grain boundaries of nanocrystalline LiAlSi2O6. Stacking faults, disorder and microstructural modifications can also be generated by mechanochemical treatments, using BM or simple pestle and mortar grinding for example, consequently modifying the materials’ properties. Such structural alterations can easily be perceived, and sometimes deciphered through the use of various ssNMR experiments as shown in the previous paragraph and in Section 9.18.2.2. In this context, among other examples in which ssNMR has been used to rationalize the properties of mechanochemically synthesized materials, one can mention the studies of the atomic and magnetic properties of ferromagnetic YFe2 or cobalt and gadolinium intermetallics,58–60 the investigation of the capturing properties of a clay mineral for cadmium decontamination and the reactivity of kaolin,61,62 the studies on the improvement of catalytic activities of cesium ion-exchanged zeolites,63 or more recently on various lithium-based energy materials.29,64 To conclude on this part of the chapter, we have shown a few selected examples of how mechanochemical syntheses can be used to shape new materials either by forming new compounds, changing their structures at different scales (introduction of stacking faults, increased disorder, reduction of particle sizes), and thus modify their relative properties. ssNMR spectroscopy has been used in this context to observe, investigate and understand the various alterations brought through the high energy mechanical treatments. In the following part, we would like to show how mechanochemistry can also be used in order to improve, facilitate and sometimes affect the ssNMR experiments.

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Fig. 5 (A/) Plot of the diffusion induced 7Li NMR spin-lattice relaxation rate T11diff of crystalline and glassy LiAlSi2O6 versus the milling time (tmill). (B/) Sketch of the structural evolution of the two LiAlSi2O6 materials by BM. The interfacial regions of the nanocrystallites is similar to the structure of the nanoglass. Adapted with permissions from Kuhn, A.; Wilkening, M.; Heitjans, P. Mechanically Induced Decrease of the Li Conductivity in an Alumosilicate Glass. Solid State Ion. 2009, 180 (4–5), 302–307.

9.18.3

Mechanochemistry as a synthetic method for enabling new developments in solid state NMR

The interplay between mechanochemistry and ssNMR goes well beyond the simple use of ssNMR to study the structure and functionalities of materials prepared by ball-milling. Notably, in recent years, it has been shown that the way in which mechanochemical reactions are conducted could be highly beneficial for ssNMR spectroscopists. Key illustrations of this are provided below.

9.18.3.1

Mechanochemical enrichment of molecules and materials in NMR-active isotopes

Many mechanical reactions occur using “liquid assisted grinding” (LAG), which consists of adding minute quantities of solvent to the solid reagents (typically less than 1 mL per mg). This has been shown to be highly beneficial to mechanochemical reactions, by favoring mass transfer between reacting particles, facilitating diffusion processes at interfaces, and enabling reactions to occur faster than under “dry milling” conditions.65 Moreover, it was found that depending on the nature of the “liquid-assisted grinding agent”, it is possible to alter the selectivity of some reactions, and favor for example the formation of specific polymorphs.66 The possibility of using isotopically-labeled solvents in LAG appeared early on, as a means to enable advanced spectroscopic characterizations on the phases which had been synthesized by mechanochemistry. One of the first illustrations of this dates back to 2010,67 in a study in which Bowmaker and co-workers showed that the N-H bond in 1-methylimidazole-2-thione could be deuterated mechanochemically when grinding with a mortar and pestle  20 mg of powder with 2 drops of D2O, which was useful for the identification of IR vibration bands. In a more recent work by Lukin et al., benzoic acid was deuterated under mechanochemical conditions using D2O.68 The rate of the isotopic exchange between 1 equivalent of D2O and 1 equivalent of benzoic acid was followed by Raman spectroscopy, showing that the H/D isotopic exchange equilibrium was reached after just 30 min (under the milling conditions they had used, i.e., by working on the 2 mmol scale). It was then further demonstrated how more quantitative deuteration of benzoic acid by mechanochemistry could be achieved by performing 3 successive H/D exchange steps with 2 equivalents of D2O each, corresponding to a total amount of D2O consumed which was estimated to be  60-fold lower than if the deuteration had been carried out in solution. Although such deuteration reactions shed light on the reaction mechanisms occurring through ball-milling (thanks to the monitoring of the changes in Raman spectra during operando analyses),68,69 they can also be valuable for ssNMR applications. For example, in a methodological study on the 1H / 2H BRAIN-CP NMR sequence, Schurko and co-workers reported the 2H NMR spectra of various deuterated compounds, one of which was a benzoic acid phase which had been deuterated on the OH group by ball-milling.>[70] More recently, the possibility to use LAG to deuterate the crystallographic water molecules within a hydrated mineral (calcium oxalate monohydrate, CaC2O4$H2O) was thoroughly investigated by Goldberga and co-workers, thereby opening the way to a more complete understanding of the labeling mechanism, and to 2H NMR analyses of the dynamics of the water molecules within crystal structure.71 Performing deuteration of molecules using LAG rather than more standard solution-based synthetic protocols is advantageous from an economical perspective, as it enables one to significantly reduce the amount of D2O needed to perform the isotopic enrichment (from a few mL down to a few tens of mL). Yet, such a reduction in volume and thus in cost is even more advantageous when it comes to enriching the phases of interest in 17O, which is the only NMR-active stable isotope of oxygen. Indeed, while 99%-labeled D2O costs less than 2 euros per mL, the price of 90% 17O-enriched water is > 1000 times higher, making it highly expensive to perform isotopic labeling using standard solution-based synthetic methods. In 2017, the possibility of using LAG to perform 17 O-isotopic labeling of a variety of organic and inorganic compounds in view of 17O ssNMR analyses was demonstrated for the first time by Métro, Laurencin and co-workers.72 Notably, it was shown that metal hydroxides like Mg(OH)2, Ca(OH)2 and Al(OH)3 could be enriched very efficiently in the presence of small amounts of 17O-enriched water (less than 2 equivalents), by

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performing the milling for just 30 min. The 17O MAS NMR spectra of the corresponding compounds were recorded in just a few hours (Fig. 6). Such synthetic conditions, in themselves, were seen as a real step forward compared to other synthetic protocols which had been described before in the literature for these phases, because they were extremely fast, user-friendly, and costefficient. The enriched hydroxides were then very easily converted into the corresponding oxides (which are key precursors for the preparation of ceramics and glasses), by heat-treatment under inert atmosphere (Fig. 6). Following this initial work, it was shown that it is also possible to directly label in 17O oxides like SiO2, Al2O3, ZrO2 and TiO2.73,74 Here, starting materials were chosen to be all initially under the form of porous phases with surface areas exceeding 80 m2/g. By performing the ball-milling of these oxides in the presence of stoichiometric amounts of 17O-enriched water, it was possible to isolate the labeled materials in milling times varying between 1 min and 1 h, using labeling conditions much milder and more cost-efficient than what had been proposed previously for such materials. The high-resolution 17O MAS NMR analyses, as well as DNP-enhanced 17O NMR studies, showed that both the core and surface-sites of the materials had been labeled in 17O. In the case of Al2O3, a systematic investigation of the influence of the milling time on the extent of isotopic labeling was carried out, revealing that more core-like 17O environments became enriched when increasing the milling time, as illustrated in Fig. 7.74 Regarding silica, following the initial studies, in which the milling conditions used were too harsh (leading to the presence Fe and Cr impurities coming from the stainless steel milling jar and beads after 1 h of grinding, which can be detrimental to high resolution NMR analyses due to increased relaxation rates),74 an optimized protocol involving shorter milling times on increased amounts of silica precursor was subsequently implemented (Fig. 7).73 In these conditions, metal impurities were no longer detected by energy-dispersive X-ray spectroscopy (EDXS). Moreover, the 17O isotopic level was found to reach  5% after only 15 min of LAG, which is 2 orders of magnitude higher than the natural abundance of 17O (0.04%), and sufficient for performing highresolution 17O NMR experiments at high magnetic field. This can be seen in the 17O{1H} D-HMQC experiments shown in Fig. 7, which were recorded in only  6 h at 18.8 T. It is worth noting that the enriched SiO2 and TiO2 phases were also subsequently used to study the reactivity of oxide particles during ball-milling, as further described in Section 9.18.4.1. In addition to the enrichment of simple metal oxide and hydroxide phases, it was also demonstrated that it is possible to label in 17 O functional materials or minerals, using a LAG approach. For example, Hu and co-workers enriched in 17O mixed metal oxides like LiCoO2, which is of interest as a cathode material in lithium-ion batteries, using a LAG approach, and were thus able to monitor the evolution of oxygen local environments during LiCoO2 charging through ex situ 17O NMR analyses.75 Moreover, Ashbrook, Morris and co-workers showed that the hydrolysis of zeolites prepared according to an “ADOR” method (Assembly, Disassembly, Organization, and Reassembly) could be performed mechanochemically, and that this was actually very valuable to help introduce 17 O in the zeolite framework in an economical way.76 Regarding coordination polymers and MOFs, Métro, Leroy, Laurencin et al. showed that it is possible to selectively label hydroxyl and aqua ligands by introducing 17O-enriched water during the mechanosynthesis of the materials, without enriching the carboxylate moieties.69,72 Lastly, regarding biomineral-related phases, Goldberga and co-workers recently demonstrated that it is also possible to selectively enrich in 17O the water molecules in calcium oxalate monohydrate and dihydrate (CaC2O4$nH2O, with n ¼ 1 and 2 respectively), by milling the starting phases for just 5 min in presence of microliter quantities of 17O-enriched water. In the former case, extensive 17O ssNMR analyses were subsequently performed, including at variable temperatures, to help understand water dynamics.71

Fig. 6 Illustration of the synthetic strategy for the 17O-isotopic labeling of metal hydroxides using liquid assisted grinding (in presence of mL quantities of 17O-labeled water), and 17O MAS NMR spectra recorded in just a few hours at 14.1 T. Adapted with permission from reference Métro, T.-X.; Gervais, C.; Martinez, A.; Bonhomme, C.; Laurencin, D. Unleashing the Potential of 17O NMR Spectroscopy Using Mechanochemistry. Angew. Chem. Int. Ed. 2017, 56 (24), 6803–6807.

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Fig. 7 (A/) Illustration of the synthetic strategy for the direct 17O-isotopic labeling of oxides using LAG (in presence of mL quantities of 17O-labeled water). (B/) 17O-labeling of alumina using LAG: (1/) 17O MAS NMR spectra recorded at 14.1 T after different milling times; (2/) evolution of the relative amount of OAlx environments as a function of the milling time (as determined by integration of the 17O MAS data), and (3/) Change in the 17O MAS NMR spectrum recorded at 14.1 T, after heat-treatment under Ar, showing the disappearance in AlxOH sites. (C/) 17O-labeling of silica using LAG: (1/) Optimized labeling conditions (with a TEM image of the fumed silica precursor, and a photo of the powder after BM), and (2/) 17O{1H} D-HMQC NMR spectra recorded at 18.8 T, using two different mixing times. Adapted with permission from references Chen, C.-H.; Mentink-Vigier, F.; Trébosc, J.; Goldberga, I.; Gaveau, P.; Thomassot, E.; Iuga, D.; Smith, M. E.; Chen, K.; Gan, Z.; Fabregue, N.; Métro, T.-X.; Alonso, B.; Laurencin, D. Labeling and Probing the Silica Surface Using Mechanochemistry and 17O NMR Spectroscopy. Chem. – A Eur. J. 2021, 27 (49), 12574–12588 and Chen, C.-H.; Gaillard, E.; Mentink-Vigier, F.; Chen, K.; Gan, Z.; Gaveau, P.; Rebière, B.; Berthelot, R.; Florian, P.; Bonhomme, C.; Smith, M. E.; Métro, T.-X.; Alonso, B.; Laurencin, D. Direct 17O Isotopic Labeling of Oxides Using Mechanochemistry. Inorg. Chem. 2020, 59 (18), 13050–13066.

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Overall, the cost-efficiency, rapidity and user-friendliness of such 17O-isotopic labeling procedures based on LAG have already found many applications for the enrichment of a variety of inorganic and organic precursors,72-74,77–79 as demonstrated in several recent works, but also of functional materials.69,71,75,76 These labeling strategies are expected to open the way to advanced 17O ssNMR characterizations on complex molecules and materials, oxygen-17 being a highly attractive target for NMR spectroscopy.80–82

9.18.3.2

Change in nuclear relaxation rates through mechanochemical treatment

As mentioned in previous Sections 9.18.2.2 and 9.18.3.1, the milling process can affect solids in many ways, including through the reduction of particle sizes, the creation of defects, but also the introduction of impurities coming from the milling jars and beads, such as iron and chromium. It turns out that these features can all affect the relaxation properties of the NMR-active nuclei present in the materials, as shown, among others, for “organic solids” (including some of pharmaceutical interest),83–85 as well as metal fluorides,54 and mixed halide perovskites.46,86 This has been pointed out as potentially advantageous for decreasing NMR analysis times,84 but also, in some cases, to help further study the structure of milled materials, as exemplified below. Regarding inorganic materials, Abdellatief and co-workers performed an extensive study on the effect of ball-milling on fluorite (CaF2), which is of interest for applications as an ionic conductor.54 Mechanochemical treatments of different durations were applied to a crystalline fluorite phase, with milling times ranging between 4 h and 64 h, after which pXRD (with line-profile analysis) and 19F ssNMR studies (including T1 relaxation measurements) were performed. In the latter case, it was found that in comparison to pristine CaF2, which exhibited a single T1 rate of 54.3 s, two distinct T1 relaxation times were observed for milling times from 4 h to 16 h (one ranging between 2.6 s and 20.5 s, while the other between  0.04 s and 1.7 s). Moreover, after 32 h, a single short T1 value of  0.04 s was observed. Interestingly, although the progressive increase in Fe-contamination from the jar was shown as a function of the milling time (Fig. 8, left), the relaxation times and the one- or two-fraction T1 behaviors observed did not appear to follow this trend (Fig. 8, right). Moreover, similar changes in T1 were found when performing the milling with tungsten carbide (WC) jars and balls (which cannot shed such metal impurities). The presence of two T1 components in the samples milled for 4–16 h was interpreted by the presence of two populations of CaF2 particles, corresponding to little-ground crystals (fraction A, with larger crystal size and smaller dislocation density) and well-ground crystals (fraction B, with smaller crystal sizes and larger dislocation density). The proportion between both populations, as extracted from T1 measurements, was then used as a “constraint” for the modelling of pXRD data. It was thus shown that “B- type” particles quickly reached a domain size of  10 nm, with

Fig. 8 Influence of the duration of high-energy ball-milling on CaF2 particles: increase in iron contamination as a function of time (bottom left), and variation in T1 relaxation times of the 2 populations of ground particles (noted A and B). Adapted with permission from reference Abdellatief, M.; Abele, M.; Leoni, M.; Scardi, P. Solid State Nuclear Magnetic Resonance and X-Ray Diffraction Line Profile Analysis of Heavily Deformed Fluorite. Thin Solid Films 2013, 530, 44–48.

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Fig. 9 (A/) Illustration of a possible mechanism of formation of AlPO4–5 by solvent-free synthesis. (B/) 27Al and (C/) 31P MAS NMR spectra of the samples isolated after different crystallization times. (D/) Corresponding 2D 31P-{27Al} J-HMQC spectra of samples isolated after various crystallization times. Adapted with permissions from Sheng, N.; Chu, Y.; Xin, S.; Wang, Q.; Yi, X.; Feng, Z.; Meng, X.; Liu, X.; Deng, F.; Xiao, F.-S. Insights of the Crystallization Process of Molecular Sieve AlPO4-5 Prepared by Solvent-Free Synthesis. J. Am. Chem. Soc. 2016, 138 (19), 6171–6176.

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a dislocation density growing as a function of the milling time. Hence, this work clearly underscored the true interest of T1 analyses for understanding the changes in particle size and homogeneity caused by high-energy ball-milling. In summary, in this part of the chapter, it has been shown how mechanochemical treatments can be favorable for ssNMR analyses, through new isotopic labeling strategies or reduced relaxation times, both of which can reduce the overall time of NMR analyses. Notably, while changes in relaxation times caused by mechanochemical treatments can be seen as an advantageous feature for better understanding the structural changes induced by ball-millling,46,54,86 as discussed above for fluorite, from a more practical perspective, increased T1 relaxation rates can also allow faster NMR analyses, making them attractive for more routine analyses by ssNMR of organic crystals and pharmaceutical formulations.84

9.18.4

Synthetic and instrumental developments performed at the interface of mechanochemistry and NMR

The complementarity between mechanochemical syntheses and ssNMR spectroscopy also lies in the possibility to use the latter analytical tool for following and better understanding the processes in action, in the solid state, at a molecular level. Indeed, ssNMR can be used to follow the evolution of specific nuclear resonances over time during the mechanochemical methods applied (e.g., milling, grinding, etc.). The interest and complementarity of this technique for the study of reactions in real-time (operando) or through in situ and ex situ analyses has been highlighted as valuable in comparison to other analytical techniques like Raman and pXRD, by shedding light on the presence of intermediates, or on the chemical reactions taking place. In the following parts, a few selected contributions adopting the combination of ssNMR and mechanochemical syntheses by ball-milling are enlightened, in which the goal is to decipher the numerous mechanisms into play during these syntheses.

9.18.4.1

Understanding mechanosynthesis through NMR

During mechanochemical syntheses and more specifically BM ones, the reactions take place in closed milling jars, quite often made of stainless-steel, which does not allow easy analysis of what is going on inside the jars. Indeed, to elucidate the different phenomena unfolding during the milling by ssNMR, the synthesis needs to be stopped at different times and part of the mixture needs to be extracted for analysis, requiring the jar to be opened. However, while the milling is paused, the reaction medium might continue to evolve in the jar. Furthermore, exposing the mixture to ambient atmosphere (for analytical purposes) might also alter the chemical processes at play and the compounds produced. To circumvent this issue, one of the methods consists of repeating the solid-state syntheses with different milling times, so that a more accurate description of the time-evolution of a reactive system during the milling can be reached. This approach has notably been used by Chen and co-workers in the study of the kinetics of 17 O-isotopic labeling of alumina (see Section 9.18.3.1, Fig. 7B/2).74 One set of studies in which ssNMR has been extensively used for understanding mechanochemical syntheses and solvent-free processes concerns the work by the group of F.-S. Xiao and co-workers on zeolites and related microporous phases.87 Indeed, in order to form various zeolites and aluminophosphates (AlPOs), one of their methods has involved grinding the reagents together (using a pestle and a mortar) for 5–20 min, before transferring the ground mixture in an autoclave, and then heating/crystallizing it between 120
C and 200
C for several hours, and performing the ssNMR analyses on the isolated materials. For example, the solvent-free synthesis of AlPOs was performed by grinding boehmite along with di-n-propylamine phosphate (DPA$H3PO4) and tetraethylammonium bromide (TEABr) at room temperature, and then heating/crystallizing the mixture for 24 h at 200
C, leading to the formation of the AlPO4–5 structure based on UV, Raman and ssNMR spectroscopies.36 ssNMR analyses right after the grinding step (Fig. 9, t ¼ 0 h spectra) display only one aluminum and one phosphorus environment. No Al-O-P bridges could be detected by 31P-{27Al} J-HMQC (Fig. 9D). Nevertheless, the mixing of these precursors by mechanical grinding is efficient, as Al-O-P bonds can be detected after only 1 h of heating of this mixture, and that progressive crystallization of the AlPO4–5 phase subsequently occurs. Importantly, thanks to 27Al and 31P ssNMR experiments, an important evolution of the mixture is clearly perceived in the first 2 h of heating (see Fig. 9B and C). The remaining heating time ensures the formation of a better defined and well-crystallized AlPO4–5 phase, as notified by 1D 27Al and 31P ssNMR. Moreover, 2D 31 P-{27Al} J-HQMC experiments at different times show an evolution in the P-O-Al units, and thus the formation of different four- and six-membered rings. In brief, a first intermediate is observed on the 31P-{27Al} J-HQMC spectrum after 1 h of heating, as shown by the correlation signal between diso(31P) ¼  12.2 to  15.4 ppm with d(27Al) at  4.8 and  1.0 ppm (see Fig. 9D), which can tentatively be attributed to a linear chain of tetrahedral Al and P units [(P-O-Al)n]. After 2 h of heating, 27Al as well as 31P resonances show noticeable evolutions. The 31P signal at  18.9 ppm becomes more intense, and was assigned to P(OAl)3(]O) and/or P(OAl)3(eOH) species, while the simultaneous appearance of the resonance at diso(31P) ¼  27.9 ppm was assigned to P(OAl)4 environments, alongside with the signal at d(27Al)  39 ppm. The final 31P signal (29 ppm) was then attributed to the tetrahedral P environment of the crystalline AlPO4–5. All these conclusions are in agreement with complementary Raman studies, and permit the proposal of a detailed formation pathway of AlPO4–5, as shown in Fig. 9A. Similar methodologies have been used to study the formation and crystallization of various zeolites by solvent-free synthesis through ssNMR, such as silica-based zeolites (MFI, BEA and EUO), aluminophosphate zeolites and other silicoaluminophosphate-based zeolites.3033,35 In this context, the work by Xiao, Feng and co-workers also displayed the usefulness of 27Al MQMAS experiments for following the crystallization of Na-zeolites after 10 min of milling and subsequent heating.34 They concluded on the spontaneous reaction of

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Fig. 10 (A/) Top: Schematic representation of the dry-milling of TiO2 and SiO2, starting from non-labeled (white) or pre-labeled (pink/red) oxides, and 17O MAS NMR analyses at 20.0 T, as well as 1H / 17O DNP CPMAS NMR studies at 14.1 T. (B/) Schematic comparison of dry-milling vs. LAG synthetic approaches for enriching SiO2 and TiO2 mixtures in 17O using mechanochemistry, together with the 17O MAS ssNMR spectra of the resulting mixtures after 3 min of milling. * indicates spinning sidebands and A indicates zirconia rotor. Adapted with permissions from Chen, C.-H.; Mentink-Vigier, F.; Trébosc, J.; Goldberga, I.; Gaveau, P.; Thomassot, E.; Iuga, D.; Smith, M. E.; Chen, K.; Gan, Z.; Fabregue, N.; Métro, T.-X.; Alonso, B.; Laurencin, D. Labeling and Probing the Silica Surface Using Mechanochemistry and 17O NMR Spectroscopy. Chem. – A Eur. J. 2021, 27 (49), 12574–12588 and Chen, C.-H.; Gaillard, E.; Mentink-Vigier, F.; Chen, K.; Gan, Z.; Gaveau, P.; Rebière, B.; Berthelot, R.; Florian, P.; Bonhomme, C.; Smith, M. E.; Métro, T.-X.; Alonso, B.; Laurencin, D. Direct 17O Isotopic Labeling of Oxides Using Mechanochemistry. Inorg. Chem. 2020, 59 (18), 13050–13066.

Fig. 11 Left: Pictures of the in situ BM ssNMR probe without the aluminum shield, the insert shows in more detail the miniature BM and the coil. Right: Schematics of the working principle of the BM inside the coil. The rotational motion (eccentric wheel on the right) is translated into transversal shaking of the milling jar inside the NMR coil. Adapted with permissions from Schiffmann, J. G.; Emmerling, F.; Martins, I. C. B.; Van Wüllen, L. InSitu Reaction Monitoring of a Mechanochemical Ball Mill Reaction with Solid State NMR. Solid State Nucl. Magn. Reson. 2020, 109, 101687.

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the different reagents (sodium aluminate and hydrated silica), with the nucleation of the final product occurring on the surface of the amorphous solid particles, before further crystallization resulting from the assembly of zeolite specific building units. The milling of another aluminosilicate phase which was followed by ssNMR experiments, is worth highlighting: it concerns mullite (Al6Si2O13), which is used in ceramics for increasing mechanical strength and thermal conductivity properties.88 Actually, in two separate contributions, K. J. D. MacKenzie and collaborators investigated the effects of milling on the mullite structure, and also on some of its possible precursors (bayerite, a-Al(OH)3, and silicic acid, SiO2$nH2O or silica gel, SiO2).89,90 By using 27Al 1D MAS and MQMAS experiments after different times of milling, they were able to follow the amorphization of the various compounds. For mullite, the two tetrahedral aluminum sites (positioned at dcs(27Al) ¼  45 and 60 ppm) as well as the octahedral one (dcs(27Al) ¼ 1–2.6 ppm) were found to decrease in intensity and slightly shift upon milling, while a pentahedral coordination type of environment appeared (dcs(27Al) ¼ 30 ppm). These effects were completely reversed by annealing up to 1200
C the ground samples. Regarding the precursors, the grinding of bayerite with silicic acid (or silica gel) revealed the progressive evolution of the octahedral Al-site of bayerite (dcs(27Al) ¼ 8 ppm) to a similar 27Al NMR spectrum, as observed for amorphous mullite in the first article (dcs(27Al) ¼ 56, 32 and 8 ppm for AlIV, AlV and AlVI respectively).90 Interestingly, they were also able to decipher different kinetics of formation of mullite for the two different silica precursors: in the case of silicic acid, the kinetics were slower due to the hydrous nature of the sample, that favors the formation of more Al/Si-O-H terminal groups, inhibiting the formation of AlO-Si bonds. Furthermore, the presence of this extra water seemed to favor the evolution of AlV environments into more stable coordination environments (AlIV and/or AlVI).

Table 1 Isotope

Examples of NMR-active nuclei present in reaction mixture or materials prepared using mechanochemistry, and which have been studied by ssNMR. Spin

Spin-1/2 nuclei 1 H 1/2 13 C 1/2 15 N 1/2 19 F 1/2 29 Si 1/2 31 P 1/2 57 Fe 1/2 77 Se 1/2 89 Y 1/2 111 Cd 1/2 113 Cd 1/2 119 Sn 1/2 207 Pb 1/2 Quadrupolar nuclei 2 H 1 6 Li 1 7 Li 3/2 11 B 3/2 14 N 1 17 O 5/2 23 Na 3/2 25 Mg 5/2 27 Al 5/2 35 Cl 3/2 39 K 3/2 43 Ca 7/2 59 Co 7/2 71 Ga 3/2 87 Rb 3/2 91 Zr 5/2 95 Mo 5/2 121 Sb 5/2 133 Cs 7/2 155 Gd 3/2 157 Gd 3/2 209 Bi 9/2

N.A./%

Gyromagnetic ratio g/107 rad s 1 T 1

99.99 1.07 0.36 100.0 4.68 100.0 2.12 7.63 100.0 12.80 12.22 8.59 22.1

26.75 6.73 2.71 25.18 5.32 10.84 0.87 5.13 1.32 5.70 5.96 10.03 5.58

0.01 7.59 92.41 80.10 99.64 0.038 100.0 10.00 100.0 75.76 93.26 0.135 100.0 39.89 27.83 11.22 15.90 57.21 100.0 14.8 15.7 100.0

4.11 3.94 10.40 8.58 1.93 3.63 7.08 1.64 6.98 2.62 1.25 1.80 6.33 8.18 8.79 2.50 1.75 6.44 3.53 0.82 1.08 4.37

Q/mb

Examples of studies on mechanochemistry and ssNMR 21,25,84,93–97 33,36,37,56,84,96–106 56,100,102 20,33,52,54,95,107 18,19,24,25,30-35,61,63,108 17,18,25,31,35,36,53,61,92,109,110 60 111 58,64 37 45,56,62 15,44,46,86 40,42,43

2.86 0.81 40.10 40.59 20.44 25.58 104.0 199.4 146.6 81.12 60.3 44.4117 420.0 107.0 133.5 176.0 22.0 543.0 3.43 1270.0 1350.0 516.0

96,105,70 21,22 17,23,27,29,57,64,112,113 17,23,33,114 37,45,96,105,106 16,69,71-79,115 21 16,28 14,17,21,24,30-32,34-36,51,61,63,90,108 46,98,116 39 18 55,60 13 39 16 16 29 41,43,46,86 60 60 29

The properties of nuclear spins are mainly taken from references >118 and >119. For each nucleus, one or several references are provided (but the list of references is not meant here to be exhaustive).

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529

The last example highlighted here, concerning the understanding BM mechanisms for inorganic systems through ssNMR, relies on the use of 17O-enrichment and subsequently, high-resolution 17O NMR experiments, and DNP (dynamic nuclear polarization) analyses. More specifically, in two recent contributions by Chen and co-workers, the formation of bonds between reacting oxide particles, namely SiO2 and TiO2, was extensively studied using both dry milling and LAG approaches.73,74 As shown in Fig. 10A (top), it was found that when milling together SiO2 with Ti*O2 (the latter phase having been pre-labeled in 17 O), it is possible to observe after just 3 min of milling the signature of 17O-isotopically labeled siloxanes (diso(17O)Si-O-Si  42 ppm).73,74 This demonstrates that a very fast change in oxygen bonding environments occurs during the mechanochemical process, which could not have been accounted for using more standard analytical tools like IR spectroscopy or pXRD. More complete investigations of the reaction between these two oxides were then carried out (with either one or both of the oxides enriched in 17O), which were then studied by high-resolution 17O NMR and DNP, revealing that Ti-O-Si bridges are also formed during the first minutes of milling (their resonance being centered at  203 ppm at 14.1 T).73 Moreover, it was shown that different 17 O-isotopic distributions could be achieved within mixtures of oxides, depending on whether SiO2 and TiO2 are mixed in presence of 17O-enriched water (using a LAG-type process, Fig. 10B),74 or whether 17O-pre-labeled TiO2 and/or SiO2 phases are mixed under dry-milling conditions (Figs. 10A and B), due to the difference in relative strength of the oxygen-containing bonds in SiO2 and TiO2. Such detailed information on bond rearrangements around oxygen occurring during ball-milling are highly valuable, as they should help reaching a much more complete understanding of the mechanisms taking place in the solid state. Overall, the different examples provided above highlight how high-resolution NMR analyses can be used for helping understand the reaction mechanisms which occur between solid reagents, by enabling to show whether Al-O-P or Ti-O-Si bridges form between reacting particles. Yet, all these analyses have been carried out ex situ. An alternative to such ex situ approaches was proposed by Bryce and co-workers in their study on the formation of triphenylphosphine oxide/para-diiodotetrafluorobenzene cocrystals.91 By mixing together pre-ground samples (potentially in presence of a small amount of additional liquid, as in LAG protocols), and then packing a rotor, they were able to follow over time the consumption of reagents and formation of products by MAS solid state NMR. In such work, which enabled to investigate the influence of many parameters on reaction kinetics, such as the nature and volume of liquid added, it is more the “aging” of the pre-ground mixture of reagents which was analyzed by NMR. First attempts towards actual in situ characterizations of ball-milling media are provided in the next subsection.

9.18.4.2

In situ NMR analysis of reaction media during ball-milling

To the best of our knowledge, the first and only system developed for undertaking ssNMR in situ analyses of BM syntheses has been proposed recently by Schiffman et al.92 The set-up allows BM syntheses to be achieved directly inside the NMR probe and more specifically in the coil, so that ssNMR experiments can be realized on the mixture directly in the NMR sample holder (which here plays the role of a milling jar). In this miniature BM set-up (see Fig. 11), the authors were able to monitor the reaction between zinc acetate (Zn(OAc)2$2H2O, ZA) and phenylphosphonic acid (PhPO3H2, PA) thanks to static 31P ssNMR experiments. With this original set-up, the authors managed to mill up to a frequency of 35 Hz (for comparison a Retsch MM400 horizontal mixer-mill maximum milling frequency is 30 Hz). However, they optimized the milling frequency for their synthesis at 25 Hz in order to be able to slow down the kinetics and thereby observe a two-step reactions profile. Similarly, with this home-built probe, they were able to use up to 100 zirconia beads (1 mm diameter) inside the  0.5 mL volume “reactor”, but noted the best results with 50 beads. In these conditions, they analyzed a total mass of 152 mg of reagents (88 mg (0.4 mmol) of ZA and 64 mg (0.4 mmol) of PA), and assessed a transformation of about 89% of the PA into the final zinc phenylphosphonate in 1 h of milling. Despite being a very interesting first proof-of concept that should pave the way for further technical developments into in situ/ operando ssNMR probes, this set-up exhibits several drawbacks at this stage, which will deserve to be addressed: (i) it is still limited to static ssNMR analyses, thus limiting the scope of applicability due to the lack of resolution, (ii) because of RF inhomogeneity of the coil, it has been used as an in situ technique rather than an operando one, since the milling had to be stopped for allowing the acquisition of the NMR signals, and (iii) the home-built probe is a single channel probe that does not allow simultaneous tuning to 1H and X, and thus 1H decoupling or 1H / X CP experiments could not be applied.

9.18.5

Conclusion

In this chapter, we have provided several illustrations of research investigations involving mechanochemistry as a synthetic procedure, and ssNMR as an analytical tool. While examples were essentially centered on the study of inorganic materials (or of the inorganic component of hybrid materials), many other works have been reported, focusing on organic systems, polymers or ligands. Indeed, one of the main assets of ssNMR is that it enables looking at the local environment of many different nuclei, making it potentially adapted to the analysis of a variety of synthetic mixtures. This is clearly visible in Table 1, which summarizes list of some of the NMR-active isotopes present in reaction mixtures or products which have been prepared by mechanochemistry, and which have been studied by ssNMR. Among recent developments, an increasing number of works are being performed at the interface of mechanochemistry and ssNMR, with the aim of using one of the techniques to help better understand or improve the other. Notably, it is worth highlighting the possibility to use ssNMR to help elucidate reaction mechanisms in mechanochemistry, and to use LAG as a means to label in

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a cost-effective and user-friendly way molecules and materials in NMR active isotopes like 17O. Such developments are expected to find more and more applications in the years to come.

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74. Chen, C.-H.; Gaillard, E.; Mentink-Vigier, F.; Chen, K.; Gan, Z.; Gaveau, P.; Rebière, B.; Berthelot, R.; Florian, P.; Bonhomme, C.; Smith, M. E.; Métro, T.-X.; Alonso, B.; Laurencin, D. Direct 17O Isotopic Labeling of Oxides Using Mechanochemistry. Inorg. Chem. 2020, 59 (18), 13050–13066. 75. Geng, F.; Shen, M.; Hu, B.; Liu, Y.; Zeng, L.; Hu, B. Monitoring the Evolution of Local Oxygen Environments during LiCoO2 Charging Via Ex Situ 17O NMR. Chem. Commun. 2019, 55 (52), 7550–7553. 76. Rainer, D. N.; Rice, C. M.; Warrender, S. J.; Ashbrook, S. E.; Morris, R. E. Mechanochemically Assisted Hydrolysis in the ADOR Process. Chem. Sci. 2020, 11 (27), 7060–7069. 77.
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Sci. 2007, 96 (4), 777–787. 84. Lou, X.; Shen, M.; Li, C.; Chen, Q.; Hu, B. Reduction of the 13C Cross-Polarization Experimental Time for Pharmaceutical Samples with Long T1 by Ball Milling in Solid-State NMR. Solid State Nucl. Magn. Reson. 2018, 94, 20–25. 85. Dempah, K. E.; Lubach, J. W.; Munson, E. J. Characterization of the Particle Size and Polydispersity of Dicumarol Using Solid-State NMR Spectroscopy. Mol. Pharm. 2017, 14 (3), 856–865. 86. Karmakar, A.; Bhattacharya, A.; Sarkar, D.; Bernard, G. M.; Mar, A.; Michaelis, V. K. Influence of Hidden Halogen Mobility on Local Structure of CsSn(Cl1  xBrx)3 Mixed-Halide Perovskites by Solid-State NMR. Chem. Sci. 2021, 12 (9), 3253–3263. 87. Wu, Q.; Meng, X.; Gao, X.; Xiao, F.-S. Solvent-Free Synthesis of Zeolites: Mechanism and Utility. Acc. Chem. Res. 2018, 51 (6), 1396–1403. 88. Li, C.; Bian, C.; Han, Y.; Wang, C.-A.; An, L. Mullite Whisker Reinforced Porous Anorthite Ceramics with Low Thermal Conductivity and High Strength. J. Eur. Ceram. Soc. 2016, 36 (3), 761–765. 89. Schmücker, M.; Schneider, H.; MacKenzie, K. J. Mechanical Amorphization of Mullite and Thermal Recrystallization. J. Non Cryst. Solids 1998, 226 (1–2), 99–104. 90. Ashbrook, S. E.; MacKenzie, K. J. D.; Wimperis, S. 27Al Multiple-Quantum MAS NMR of Mechanically Treated Bayerite (a-Al(OH)3) and Silica Mixtures. Solid State Nucl. Magn. Reson. 2001, 20 (3–4), 87–99. 91. Xu, Y.; Champion, L.; Gabidullin, B.; Bryce, D. L. A Kinetic Study of Mechanochemical Halogen Bond Formation by In Situ 31P Solid-State NMR Spectroscopy. Chem. Commun. 2017, 53 (71), 9930–9933. 92. Schiffmann, J. G.; Emmerling, F.; Martins, I. C. B.; Van Wüllen, L. In-Situ Reaction Monitoring of a Mechanochemical Ball Mill Reaction with Solid State NMR. Solid State Nucl. Magn. Reson. 2020, 109, 101687. 93. Filibian, M.; Elisei, E.; Colombo Serra, S.; Rosso, A.; Tedoldi, F.; Cesàro, A.; Carretta, P. Nuclear Magnetic Resonance Studies of DNP-Ready Trehalose Obtained by Solid State Mechanochemical Amorphization. Phys. Chem. Chem. Phys. 2016, 18 (25), 16912–16920. 94. Chartrel, T.; Ndour, M.; Bonnet, V.; Cavalaglio, S.; Aymard, L.; Dolhem, F.; Monconduit, L.; Bonnet, J.-P. Revisiting and Improving the Preparation of Silicon-Based Electrodes for Lithium-Ion Batteries: Ball Milling Impact on Poly(Acrylic Acid) Polymer Binders. Mater. Chem. Front. 2019, 3 (5), 881–891. 95. Trzeciak, K.; Kazmierski, S.; Druz_ bicki, K.; Potrzebowski, M. J. Mapping of Guest Localization in Mesoporous Silica Particles by Solid-State NMR and Ab Initio Modeling: New Insights into Benzoic Acid and p-Fluorobenzoic Acid Embedded in MCM-41 Via Ball Milling. J. Phys. Chem. C 2021, 125 (18), 10096–10109. 96. Alanazi, A. Q.; Kubicki, D. J.; Prochowicz, D.; Alharbi, E. A.; Bouduban, M. E. F.; Jahanbakhshi, F.; Mladenovic, M.; Milic, J. V.; Giordano, F.; Ren, D.; Alyamani, A. Y.; Albrithen, H.; Albadri, A.; Alotaibi, M. H.; Moser, J.-E.; Zakeeruddin, S. M.; Rothlisberger, U.; Emsley, L.; Grätzel, M. Atomic-Level Microstructure of Efficient FormamidiniumBased Perovskite Solar Cells Stabilized by 5-Ammonium Valeric Acid Iodide Revealed by Multinuclear and Two-Dimensional Solid-State NMR. J. Am. Chem. Soc. 2019, 141 (44), 17659–17669. 97. Lin, R.; Li, X.; Krajnc, A.; Li, Z.; Li, M.; Wang, W.; Zhuang, L.; Smart, S.; Zhu, Z.; Appadoo, D.; Harmer, J. R.; Wang, Z.; Buzanich, A. G.; Beyer, S.; Wang, L.; Mali, G.; Bennett, T. D.; Chen, V.; Hou, J. Mechanochemically Synthesised Flexible Electrodes Based on Bimetallic Metal–Organic Framework Glasses for the Oxygen Evolution Reaction. Angew. Chem. Int. Ed. 2022, 61 (4), e202112880. 98. Vojvodin, C. S.; Holmes, S. T.; Watanabe, L. K.; Rawson, J. M.; Schurko, R. W. Multi-Component Crystals Containing Urea: Mechanochemical Synthesis and Characterization by 35Cl Solid-State NMR Spectroscopy and DFT Calculations. CrystEngComm 2022, 24 (14), 2626–2641. 99. Lan, L.; Chen, H.; Lee, D.; Xu, S.; Skillen, N.; Tedstone, A.; Robertson, P.; Garforth, A.; Daly, H.; Hardacre, C.; Fan, X. Effect of Ball-Milling Pretreatment of Cellulose on its Photoreforming for H2 Production. ACS Sustain. Chem. Eng. 2022, 10 (15), 4862–4871. 100. Al-Terkawi, A.-A.; Lamaty, F.; Métro, T.-X. Efficient CO2 Sequestration by a Solid–Gas Reaction Enabled by Mechanochemistry: The Case of l-Lysine. ACS Sustain. Chem. Eng. 2020, 8 (35), 13159–13166. 101. Beillard, A.; Quintin, F.; Gatignol, J.; Retailleau, P.; Renaud, J.-L.; Gaillard, S.; Métro, T.-X.; Lamaty, F.; Bantreil, X. Solving the Challenging Synthesis of Highly Cytotoxic Silver Complexes Bearing Sterically Hindered NHC Ligands with Mechanochemistry. Dalton Trans. 2020, 49 (36), 12592–12598. 102. André, V.; Hardeman, A.; Halasz, I.; Stein, R. S.; Jackson, G. J.; Reid, D. G.; Duer, M. J.; Curfs, C.; Duarte, M. T.; Fri
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cic, T. Mechanosynthesis of the Metallodrug Bismuth Subsalicylate from Bi2O3 and Structure of Bismuth Salicylate without Auxiliary Organic Ligands. Angew. Chem. Int. Ed. 2011, 50 (34), 7858–7861. 103. Szell, P. M. J.; Dragon, J.; Zablotny, S.; Harrigan, S. R.; Gabidullin, B.; Bryce, D. L. Mechanochemistry and Cocrystallization of 3-Iodoethynylbenzoic Acid With NitrogenContaining Heterocycles: Concurrent Halogen and Hydrogen Bonding. New J. Chem. 2018, 42 (13), 10493–10501. 104. Schmidt, M. W. I.; Knicker, H.; Hatcher, P. G.; Kögel-Knabner, I. Does Ultrasonic Dispersion and Homogenization by Ball Milling Change the Chemical Structure of Organic Matter in Geochemical Samples?dA CPMAS 13C NMR Study with Lignin. Org. Geochem. 1997, 26 (7–8), 491–496. 105. Kubicki, D. J.; Prochowicz, D.; Hofstetter, A.; Saski, M.; Yadav, P.; Bi, D.; Pellet, N.; Lewinski, J.; Zakeeruddin, S. M.; Grätzel, M.; Emsley, L. Formation of Stable Mixed Guanidinium–Methylammonium Phases with Exceptionally Long Carrier Lifetimes for High-Efficiency Lead Iodide-Based Perovskite Photovoltaics. J. Am. Chem. Soc. 2018, 140 (9), 3345–3351. 106. Tavakoli, M. M.; Tress, W.; Milic, J. V.; Kubicki, D.; Emsley, L.; Grätzel, M. Addition of Adamantylammonium Iodide to Hole Transport Layers Enables Highly Efficient and Electroluminescent Perovskite Solar Cells. Energ. Environ. Sci. 2018, 11 (11), 3310–3320. 107. Ruiz-Preciado, M. A.; Kubicki, D. J.; Hofstetter, A.; McGovern, L.; Futscher, M. H.; Ummadisingu, A.; Gershoni-Poranne, R.; Zakeeruddin, S. M.; Ehrler, B.; Emsley, L.; Milic, J. V.; Grätzel, M. Supramolecular Modulation of Hybrid Perovskite Solar Cells Via Bifunctional Halogen Bonding Revealed by Two-Dimensional 19F Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2020, 142 (3), 1645–1654. 108. Yuan, Y.; Chen, H.; Lin, J.; Ji, Y. Surface Modification of Calcined Kaolin with Toluene Diisocyanate Based on High Energy Ball Milling. Appl. Surf. Sci. 2013, 284, 214–221. 109. Morin, V. M.; Szell, P. M. J.; Caron-Poulin, E.; Gabidullin, B.; Bryce, D. L. Mechanochemical Preparations of Anion Coordinated Architectures Based on 3-Iodoethynylpyridine and 3-Iodoethynylbenzoic Acid. ChemistryOpen 2019, 8 (11), 1328–1336.

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110. Dong, J.; Wang, J.; Wang, J.; Yang, M.; Li, W.; Shen, M. Thermally Stable g-Alumina Developed from the Fumigation Byproduct of Phosphide Aluminum. J. Alloys Compd. 2018, 741, 256–264. 111. Dolotko, O.; Hlova, I. Z.; Pathak, A. K.; Mudryk, Y.; Pecharsky, V. K.; Singh, P.; Johnson, D. D.; Boote, B. W.; Li, J.; Smith, E. A.; Carnahan, S. L.; Rossini, A. J.; Zhou, L.; Eastman, E. M.; Balema, V. P. Unprecedented Generation of 3D Heterostructures by Mechanochemical Disassembly and Re-Ordering of Incommensurate Metal Chalcogenides. Nat. Commun. 2020, 11 (1), 3005. 112. Kosova, N. V.; Devyatkina, E. T.; Stepanov, A. P.; Buzlukov, A. L. Lithium Conductivity and Lithium Diffusion in NASICON-Type Li1þxTi2–xAlx(PO4)3 (x¼ 0; 0.3) Prepared by Mechanical Activation. Ionics 2008, 14 (4), 303–311. 113. Yu, C.; Li, Y.; Adair, K. R.; Li, W.; Goubitz, K.; Zhao, Y.; Willans, M. J.; Thijs, M. A.; Wang, C.; Zhao, F.; Sun, Q.; Deng, S.; Liang, J.; Li, X.; Li, R.; Sham, T.-K.; Huang, H.; Lu, S.; Zhao, S.; Zhang, L.; van Eijck, L.; Huang, Y.; Sun, X. Tuning Ionic Conductivity and Electrode Compatibility of Li3YBr6 for High-Performance All Solid-State Li Batteries. Nano Energy 2020, 77, 105097. 114. Le Ruyet, R.; Berthelot, R.; Salager, E.; Florian, P.; Fleutot, B.; Janot, R. Investigation of Mg(BH4)(NH2)-Based Composite Materials with Enhanced Mg2þ Ionic Conductivity. J. Phys. Chem. C 2019, 123 (17), 10756–10763. 115. Xu, Y.; Viger-Gravel, J.; Korobkov, I.; Bryce, D. L. Mechanochemical Production of Halogen-Bonded Solids Featuring P¼ O$$$I-C Motifs and Characterization Via X-Ray Diffraction, Solid-State Multinuclear Magnetic Resonance, and Density Functional Theory. J. Phys. Chem. C 2015, 119 (48), 27104–27117. 116. Peach, A. A.; Hirsh, D. A.; Holmes, S. T.; Schurko, R. W. Mechanochemical Syntheses and 35Cl Solid-State NMR Characterization of Fluoxetine HCl Cocrystals. CrystEngComm 2018, 20 (20), 2780–2792. 117. Sahoo, B. K. Nuclear Quadrupole Moment of 43Ca and Hyperfine-Structure Studies of Its Singly Charged Ion. Phys. Rev. A 2009, 80 (2), 012515. 118. Harris, R. K.; Becker, E. D.; Cabral de Menezes, S. M.; Goodfellow, R.; Granger, P. NMR Nomenclature. Nuclear Spin Properties and Conventions for Chemical Shifts (IUPAC Recommendations 2001). Pure Appl. Chem. 2001, 73 (11), 1795–1818. 119. Pyykkö, P. Year-2017 Nuclear Quadrupole Moments. Mol. Phys. 2018, 116 (10), 1328–1338.

9.19 Advances in the characterization of inorganic solids using NMR correlation experiments Andrew G.M. Rankina, Fre´de´rique Pourpointb, Nghia Tuan Duongc, Laurent Delevoyea, Jean-Paul Amoureuxb,d, and Olivier Lafonb, a Univ. Lille, CNRS, INRAE, Centrale Lille, Univ Artois – IMEC, Lille, France; b Univ Lille, CNRS, Centrale Lille, Univ. Artois, UMR 8181 – UCCS – Unité de Catalyse et Chimie du Solide, Lille, France; c Aix Marseille Univ. CNRS, ICR, Marseille, France; and d Bruker Biospin, Wissembourg, France © 2023 Elsevier Ltd. All rights reserved.

9.19.2 9.19.3 9.19.3.1 9.19.3.2 9.19.3.2.1 9.19.3.2.2 9.19.4 9.19.4.1 9.19.4.1.1 9.19.4.1.2 9.19.4.1.3 9.19.4.2 9.19.4.2.1 9.19.4.2.2 9.19.4.2.3 9.19.5 9.19.5.1 9.19.5.1.1 9.19.5.1.2 9.19.5.1.3 9.19.5.2 9.19.5.3 9.19.5.4 9.19.6 Acknowledgments References Further reading

Introduction Correlations between identical nuclei Through-bond homonuclear correlations Through-space homonuclear correlations Between spin-1/2 nuclei Between half-integer quadrupolar nuclei Correlations between distinct nuclei Through-bond heteronuclear correlations Between spin-1/2 isotopes Between spin-1/2 and half-integer quadrupolar isotopes Between two half-integer quadrupolar isotopes Through-space heteronuclear correlations Between spin-1/2 isotopes Between spin-1/2 and quadrupolar isotopes Between two half-integer quadrupolar isotopes Applications Microporous materials AlPOs Zeolites MOFs Metal oxide catalysts Minerals and biomaterials Glasses Conclusion

535 536 537 539 539 543 544 544 544 545 546 547 547 555 561 561 562 562 562 563 564 566 567 568 569 569 581

Glossary Chemical shift anisotropy (CSA) For a solid, the shielding of the static magnetic field B0 depends on its orientation because of the anisotropy of the electron density around the nuclei. Central transition (CT) Transition between energy levels, mI ¼ þ1/2 and 1/2, with mI the magnetic quantum number, of a half-integer spin quadrupolar nucleus. Connectivity Path of covalent bonds between two nuclei. Correlation NMR experiments 2D NMR experiment based on coherence transfer and allowing the observation of connectivities or proximities between identical or distinct isotopes. Cross-polarization (CP) Transfer of magnetization between distinct isotopes by irradiating simultaneously the transitions of these isotopes with rf fields satisfying the Hartmann-Hahn condition. Dipolar interaction Magnetic interaction between the magnetic dipole moments of two nuclei. Dipolar recoupling NMR technique, usually a sequence of radiofrequency (rf) pulses, which reintroduces the dipolar interaction under MAS conditions. Dipolar truncation Attenuation of the coherence transfer between distant nuclei by the large interaction between nearby nuclei. Dynamic nuclear polarization (DNP) Transfer of magnetization from unpaired electrons to nuclei used to enhance the sensitivity of NMR experiments.

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Magic-angle spinning (MAS) Rotation of the sample at 54.736 with respect to the static magnetic field B0, which averages out the anisotropic NMR interactions, such as CSA and dipolar interaction, and hence, improves the resolution and the sensitivity of NMR spectra. Multiple-quantum magic-angle spinning (MQMAS) 2D NMR experiments, which refocuse the second-order quadrupolar broadening of half-integer spin quadrupolar nuclei by correlating their triple-quantum coherences with the single-quantum coherences of their CT. Quadrupolar interaction Interaction between the electric quadrupole moment of a quadrupolar nucleus and the surrounding electric field gradient. Quadrupolar nucleus Nucleus with a spin I  1. Rotary resonance recoupling (R3) Reintroduction of anisotropic NMR interactions when the nutation of the coherences is equal to an integer multiple of the MAS frequency. Rotational resonance (R2) Reintroduction under MAS of the homonuclear dipolar interaction occurring when the difference in resonance frequencies between two nuclei is equal to an integer multiple of the MAS frequency. Satellite transitions (ST) Transition between energy levels, mI and mI þ 1, with mI s -1/2, of a half-integer spin quadrupolar nucleus.

Nomenclature t1 Indirect evolution period of a 2D NMR experiment t2 Acquisition period of a 2D NMR experiment. The free-induction decay (FID) is detected during this period T2’ Time constant for the decay of transverse magnetization, which is not refocused by a 180 pulse g Gyromagnetic ratio n1 Rf field amplitude in Hz nR MAS frequency sR Rotor period

Abstract As a local characterization technique endowed with atomic resolution, solid-state NMR spectroscopy provides unique insights on the atomic-level structure and dynamics of inorganic and hybrid materials. In particular, two-dimensional through-bond and through-space correlation experiments allow the observation of covalent bonds and proximities between identical or distinct isotopes, thus providing detailed information on the arrangement of atoms in the materials. Compared to biological and organic samples, inorganic and hybrid materials contain additional NMR-active nuclei, and notably quadrupolar isotopes with nuclear spin I  1, such as 11B, 27Al and 71Ga, which are often subject to large quadrupolar interaction. Therefore, specific NMR correlation experiments have been developed to probe the local environment of these quadrupolar isotopes. We provide here an in-depth overview of correlation experiments, which have been employed for the characterization of inorganic and hybrid materials. We present first the through-space and through-bond correlation experiments to probe connectivities and proximities between identical nuclei, and then their counterparts for distinct isotopes. In both cases, we describe the experiments employed for spin-1/2 and quadrupolar isotopes. We indicate the stateof-the-art technique and the isotopes, for which they have been applied. Finally, we present how these correlation NMR experiments have provided essential information on the atomic-level structure of different classes of inorganic hybrid materials, including (i) microporous materials (aluminophosphates, zeolites, metal-organic frameworks (MOFs)), (ii) metal oxide catalysts, such as amorphous silica alumina as well as supported metal complexes on alumina or silica, (iii) minerals and biomaterials and (iv) glasses.

9.19.2

Introduction

Correlation NMR techniques are a given class of two-dimensional (2D) NMR experiments. They provide information on the through-bond connectivities and through-space proximities between nuclei in solids by coherence transfers during the mixing period through J- and dipolar couplings, respectively. The 2D correlation NMR spectra indicate between which spins the coherences are transferred. For improving resolution and sensitivity, these experiments are performed under magic-angle spinning (MAS) conditions. These experiments are classified into two types: the homo- and hetero-nuclear correlation NMR experiments, which probe the connectivities or proximities between identical and distinct nuclei, respectively, which can be either spin-1/2 or quadrupolar isotopes (see Fig. 1).

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Fig. 1 Schematic classification of 2D correlation NMR experiments, which can be employed to probe connectivities and proximities in solids under MAS conditions. S  1 denotes the integer and half-integer spin quadrupolar isotopes, whereas I or S ¼ n/2 with n  1 denotes solely the halfinteger quadrupolar nuclei. In the case of quadrupolar nuclei, the coherence transfer in 2D heteronuclear correlation experiment can be mediated by the sum of J-coupling and the second-order quadrupolar-dipolar cross terms, which are not average out by MAS.1,2

Correlation NMR experiments, including correlation spectroscopy (COSY)3 between identical nuclei and heteronuclear singlequantum coherence (HSQC)4 scheme between distinct isotopes, have been initially introduced at the end of the 1970s to probe connectivities between spin-1/2 nuclei in isotropic solutions. In 1980s and 1990s, these correlation experiments were adapted for the study of spin-1/2 isotopes in solids under MAS conditions. Solid-state correlation experiments were first introduced to probe heteronuclear proximities in organic and inorganic solids.5,6 Then they were applied to observe homonuclear connectivities in plastic crystals7,8 and later in inorganic solids.9,10 As regards covalent bonds between distinct isotopes, they have been detected using correlation experiments first in inorganic solids,11 before their observation in organic solids.12 Correlation experiments to probe homonuclear proximities have been reported first for solid-state amino-acids,13 before their use for phosphate compounds.14 The correlation solid-state NMR experiments, which are listed above, were first demonstrated for spin-1/2 isotopes. A further advance was their use for quadrupolar nuclei with spin I  1, which was demonstrated in the 1990s and 2000s. Heteronuclear correlation experiments have been developed to probe proximities15,16 and later connectivities17 between spin-1/2 and half-integer quadrupolar nuclei, such as 31P and 27Al with I ¼ 5/2. Then these experiments were also applied to observe proximities18 and later connectivities19 between distinct half-integer quadrupolar nuclei, such as 27Al and 17O with I ¼ 5/2. These heteronuclear correlation experiments were also combined with the multiple-quantum MAS (MQMAS) scheme to refocus the second-order quadrupolar broadening and hence, allow the acquisition of high-resolution NMR spectra.20,21 Homonuclear correlation experiments have also been introduced to detect proximities between identical half-integer quadrupolar nuclei, such as 23Na or 11B with I ¼ 3/2.22,23 Conversely, to the best of our knowledge, these experiments have not yet been applied to detect connectivities between quadrupolar nuclei. Another major advance was the development of heteronuclear correlations for the indirect detection of 14N nuclei, which do not exhibit a central transition (CT) contrary to half-integer quadrupolar nuclei, via spin-1/2 isotopes, such as 1H.1,2 This approach has more recently been applied for the indirect detection of spin-1/2 nuclei subject to large chemical shift anisotropy (CSA), such as 195Pt.24 The robustness of through-space correlation NMR experiments has also been improved by the development of more robust dipolar recoupling schemes designed using symmetry25 and built from composite26 or adiabatic pulses.27 These experiments have also been modified so that they enable (i) the observation of longer-range proximities,28 (ii) are compatible with high MAS frequencies29 and (iii) are less affected by the random fluctuations of MAS frequencies, which cause t1-noise.30,31 The sensitivity of these heteronuclear correlation experiments has notably been improved using indirect detection via protons at high MAS frequencies.32 Several reviews about homo- and hetero-nuclear recoupling sequences, mainly for spin-1/2 nuclei, have been published.33–41 Through-bond correlation experiments, primarily for spin-1/2 isotopes in organic solids,42,43 as well as correlation experiments for quadrupolar nuclei44–48 have also been surveyed. Furthermore, through-bond and through-space correlation experiments for both spin-1/2 and quadrupolar nuclei were presented in reviews about solid-state NMR of a specific class of inorganic materials, including oxide glasses,49–51 crystalline and amorphous aluminophosphates,52 heterogeneous catalysts,53–56 zeolites57–59 and metal-organic frameworks.58,60 We provide here an overview of correlation NMR experiments for inorganic solids. We notably highlight the state-of-the-art techniques to probe homo- and hetero-nuclear connectivities and proximities of spin-1/2 and quadrupolar nuclei. We also show how these techniques have provided new insights into the atomic-level structure of inorganic materials, including microporous materials, heterogeneous catalysts, minerals, biomaterials and glasses.

9.19.3

Correlations between identical nuclei

Connectivities and proximities between identical nuclei can be probed by homonuclear correlation experiments employing coherence transfers based on J- and dipolar-couplings, respectively. These experiments can be classified based on the coherences, which are selected during the indirect evolution period, t1, and which can be either single-, double- or triple-quantum (1Q, 2Q or 3Q) coherences, whereas the 1Q coherences are always detected during the acquisition period, t2.35,61 The sensitivity of these

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experiments decreases with increasing coherence order during the t1 period. Nevertheless, 2Q-1Q correlations allow probing the connectivities or proximities between sites with close resonance frequencies, whereas 3Q-1Q correlations permit the observation of triplets of nuclei.61 We present first the through-bond homonuclear correlations, before the discussion of through-space variants.

9.19.3.1

Through-bond homonuclear correlations

Connectivities between spin-1/2 nuclei in inorganic solids have been first probed using the COSY experiment, which is a 1Q-1Q correlation and is identical to the experiments used for liquids.8–10,62 Nevertheless, the conventional COSY experiment suffers from disadvantages that (i) the diagonal and cross-peaks cannot be displayed simultaneously in double absorption mode, (ii) the intense diagonal peaks can obscure cross-peaks in 2D COSY spectra and (iii) the anti-phase components of the cross peaks reduce their overall intensity. The first and second of the above difficulties can be circumvented by the use of the doublequantum filtered COSY (DQF-COSY) experiment, for which the diagonal and cross peaks can be phased in double-adsorption mode.62 Nevertheless, the DQF-COSY experiment is not optimal for the characterization of solids since it yields anti-phase line shapes, which reduce the intensity of the cross peaks for unresolved couplings. This limitation can be circumvented by using total through-bond correlation spectroscopy (TOBSY), in which radiofrequency (rf) irradiation synchronized with MAS removes the anisotropic interactions, such as dipolar couplings and CSA, as well as the isotropic chemical shifts and only allows the homonuclear J-couplings.63 In particular, this selection of homonuclear J-coupling can be achieved using the symmetry-based R30614 scheme, which is highly robust to offset and rf field inhomogeneity.64 The TOBSY sequence has been used to record 2D 31P 1Q1Q through-bond homonuclear correlations and hence, to probe 31PeOe31P connectivities in phosphate crystalline phases.64,65 Nevertheless, the 1Q-1Q correlations, such as DQF-COSY and TOBSY, do not allow the observation of connectivities between nuclei with close resonance frequencies, which is an important limitation for the use in inorganic solids, since these samples often contain nearby sites with similar resonance frequencies. This limitation can be side-stepped by the use of 2Q-1Q correlations using the incredible natural abundance double quantum transfer experiment (INADEQUATE). The technique was originally introduced in 1980 by Freeman and co-workers in order to probe natural abundance 13Ce13C J-couplings in the solution state.66–68 Fyfe et al. were amongst the first to recognize the potential for the sequence to be used to study solid materials, reporting in the early 1990s the use of 29Si INADEQUATE for the elucidation of the three-dimensional (3D) lattice structures of zeolites.69,70 However, one difficulty in applying the INADEQUATE sequence used for liquids to the solid-state is that it yields anti-phase correlations, leading to reduced intensity for unresolved couplings. Hence, this sequence is only suited to solid samples that generate narrow spectral lineshapes, such as the well-defined framework structures studied in the aforementioned works. In 1999, Lesage et al. proposed a modified version of the pulse sequence designed to overcome the limitations of the original technique.71 This variant, termed “refocused INADEQUATE”, is displayed in Fig. 2. The evolution under homonuclear dipolar interactions and CSA is suppressed by the synchronization with MAS, i.e., the delays between the centers of the rf pulses are equal to an integer multiple of rotor period, sR ¼ 1/nR, where nR is the MAS frequency, whereas the 180 pulses in the middle of the first and second s delays, termed defocusing and refocusing delays, respectively, refocus the evolution under isotropic chemical shifts. During the defocusing delay, the transverse magnetization evolves under homonuclear J-couplings into anti-phase 1Q coherences, which are converted into 2Q coherences by the second 90 pulse. In the absence of losses, the creation of 2Q coherences for an isolated S2 spin pair is maximum for s ¼ 1/(2JSS), where JSS denotes the J-coupling constant between the observed S spins. These coherences evolve at the sum of the isotropic chemical shifts of the correlated nuclei during the t1 period and are converted back into anti-phase 1Q coherence by the third 90 pulse. In contrast with the original INADEQUATE sequence, the refocused INADEQUATE scheme includes a refocusing delay between the third 90 pulse and the acquisition to transform the anti-phase 1Q coherences into in-

Fig. 2 Pulse sequence of 2D 31P refocused INADEQUATE experiment along with desired coherence transfer pathways. The initial 90 pulse can be replaced by 1H / 31P cross-polarization (CP) transfer to enhance the sensitivity and/or to select the 31P nuclei near protons. Figure adapted from Ref. Fayon, F.; Massiot, D.; Levitt, M. H.; Titman, J. J.; Gregory, D. H.; Duma, L.; Emsley, L.; Brown, S. P. Through-Space Contributions to TwoDimensional Double-Quantum J Correlation NMR Spectra of Magic-Angle-Spinning Solids. J. Chem. Phys. 2005, 122 (19), 194313. doi: 10.1063/ 1.1898219.

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phase signal before the acquisition. This sequence is especially useful for the study of disordered solids exhibiting NMR signals broader than the strength of the homonuclear J-couplings.71,72 If the refocused INADEQUATE sequence was first applied for the observation of connectivities between 13C nuclei in organic solids, its utility to detect J-coupling between 31P nuclei, which has a 100% natural isotopic abundance, has been later demonstrated in phosphorus-containing crystalline and amorphous solids, notably by the solid-state NMR group at CNRS Orléans, France. Several publications have demonstrated the use of 2D 31P refocused INADEQUATE for the structural characterization of PeOeP connectivities in Zn2P2O773 and SnP2O7 crystalline powders (see Fig. 3)74 as well as lead phosphate glasses.73,75 The J-coupling constants between 31P nuclei through PeOeP linkage typically range from 16 to 34 Hz.74,76 It has also been shown that the 2D INADEQUATE spectrum can exhibit diagonal peaks in the absence of J-coupling between 31P nuclei with the same isotropic chemical shift but distinct magnitudes or orientations of their CSA tensors since the n ¼ 0 rotational resonance (R2) reintroduces the dipolar interaction between them.77 The intensity of these anomalous diagonal peaks decreases at higher MAS frequency and lower static magnetic field. 2D 31P 3Q-1Q homonuclear correlation spectra have also been recorded for Pb3P4O13 crystalline compound and phosphate glasses using the same sequence as refocused INADEQUATE but distinct phase cycling.61 These spectra allow for the observation of PeOePeOeP trimers. As mentioned above, INADEQUATE experiments have also been used to probe connectivities between 29Si nuclei in solids. The two-bond J-coupling constant, 2JSiOSi, between 29Si nuclei of SieOeSi linkages is typically lower than 15 Hz in silicate materials.78 Furthermore, the natural abundance of the 29Si isotope is only 4.68% and hence, the probability of having two sites containing 29Si isotope is as low as 0.22%. Therefore, the first reported 2D 29Si INADEQUATE experiments on isotopically unmodified zeolites lasted several days.69 The sensitivity of this experiment has been improved by 29Si isotopic enrichment79 and/or dynamic nuclear polarization (DNP) under MAS (see Fig. 4).80–82 This latter technique enhances the NMR signal by transferring the polarization of unpaired electrons to the nuclear spins through microwave irradiation.83 The unpaired electrons can be exogenous biradicals, which are incorporated into the sample by impregnation with a solution of biradicals. In these conditions, DNP primarily enhances the NMR signals of nuclei located near surfaces.84,85 Therefore, DNP-enhanced 2D 29Si INADEQUATE experiments have been mainly applied to probe the 29Sie29Si connectivities near the surface of particles.80,81 Nevertheless, unpaired electrons in the bulk region of the materials, such as oxygen vacancies in g-irradiated fused quartz, can also be used as a source of polarization for DNP to enhance the sensitivity of 29Si INADEQUATE experiment.86 Furthermore, the use of the 2D 29Si refocused INADEQUATE sequence allows the observation of 29Sie29Si connectivities in disordered and amorphous materials, for which the linewidths exceed the 29Sie29Si Jcoupling constants.87,88 In addition, a variant of the 2D 29Si refocused INADEQUATE sequence incorporating a z-filter between the refocusing delay and the acquisition period has been employed to eliminate undesired antiphase contributions due to multiple

Fig. 3 2D 31P refocused INADEQUATE spectrum of SnP2O7 crystalline powder acquired at a static magnetic field B0 ¼ 7 T with nR ¼ 10 kHz. This spectrum shows 46 pairs of cross-correlation peaks resulting from PeOeP connections. Reprinted with permission from reference Fayon, F.; King, I. J.; Harris, R. K.; Gover, R. K. B.; Evans, J. S. O.; Massiot, D. Characterization of the Room-Temperature Structure of SnP2O7 by 31P Through-Space and Through-Bond NMR Correlation Spectroscopy. Chem. Mater. 2003, 15 (11), 2234–2239. doi: 10.1021/cm031009d. Copyright 2003, American Chemical Society.

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Fig. 4 (a) Schematic structure of the interlayer region of the calcined form of the zeolite SSZ-70. The terminal and interlayer-bridging O atoms are shown in red, whereas the others have been omitted. (b) DNP-enhanced 29Si refocused INADEQUATE 2D spectrum of isotopically unmodified SSZ-70 zeolite at 9.4 T and 100 K with nR ¼ 8 kHz. The DNP-enhanced 1H / 29Si CPMAS 1D spectrum acquired under the same conditions is shown along the 1Q dimension. The blue and red lines indicate the connectivity paths to isolated silanol (on the left of subfigure a) and nested silanol groups (on the right of subfigure b), respectively. Figure adapted from Ref. Smeets, S.; Berkson, Z. J.; Xie, D.; Zones, S. I.; Wan, W.; Zou, X.; Hsieh, M.-F.; Chmelka, B. F.; McCusker, L. B.; Baerlocher, C. Well-Defined Silanols in the Structure of the Calcined High-Silica Zeolite SSZ-70: New Understanding of a Successful Catalytic Material. J. Am. Chem. Soc. 2017, 139 (46), 16803–16812. doi: 10.1021/jacs.7b08810. Copyright 2017, American Chemical Society.

couplings.88,89 Finally the sensitivity of 2D 29Si INADEQUATE experiments can be improved by the Carr-Purcell Meiboom-Gill (CPMG) scheme, i.e., the acquisition of a train of echoes during the acquisition period by applying a train of 180 pulse.90 More recently, a DNP-enhanced refocused INADEQUATE scheme has been applied to probe the connectivities between surface and core 113Cd nuclei of CdS quantum dots.91 This experiment relies on 113CdeSe113Cd J-coupling constants, which are approximately equal to 100 Hz. To the best of our knowledge, 2D homonuclear correlation between quadrupolar nuclei via homonuclear J-couplings has not been reported. Conversely, connectivities between 27Al nuclei connected via O bridges to the same 31P nucleus in microporous crystalline AlPO4-14 compounds have been probed using relay via two-bond 31P-27Al J-couplings and 2D through-bond homonuclear correlation experiment derived from heteronuclear single-quantum correlation (HSQC) sequence.92

9.19.3.2

Through-space homonuclear correlations

Through-space homonuclear correlations, which rely on coherence transfer via homonuclear dipolar couplings, allow the observation of proximities between identical nuclei and hence, complement through-bond homonuclear correlations. For isotopes in the first periods of the periodic table, the homonuclear dipolar couplings are usually larger than the J-couplings and yield faster coherence transfers. As a result, through-space homonuclear correlation experiments are usually more efficient than their through-bond counterparts. These experiments can be classified based on the order of the Hamiltonian governing the through-space coherence transfer as well as the coherence order during t1 period. Through-space homonuclear correlation experiments have been applied to both spin-1/2 and half-integer quadrupolar nuclei.

9.19.3.2.1

Between spin-1/2 nuclei

Through-space homonuclear correlations can be achieved through either the first- or second-order Hamiltonian involving the homonuclear dipolar interaction.

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First-order recoupling. The contribution of dipolar interactions to the first-order Hamiltonian is averaged out by MAS. Nevertheless, this interaction is reintroduced between sites having isotropic chemical shifts differing by a multiple of the MAS frequency, i.e., the R2 condition.93–95 This approach has been recently applied to record 2D 89Y 1Q-1Q through-space homonuclear correlation spectra of yttrium-doped ceria.96 To compensate the long longitudinal relaxation time of the 89Y isotope, which typically reaches hundreds of seconds, and its low gyromagnetic ratio (|g(89Y)/ g(1H)| ¼ 4.92%), the sensitivity of this 2D 89Y homonuclear correlation was enhanced using DNP transfer from paramagnetic Gd(III) dopants. Nevertheless, the R2 approach is a frequency-selective recoupling, which reintroduces the dipolar couplings only between specific sites at a given MAS frequency. A more broadband and versatile approach to reintroduce the homonuclear dipolar couplings under MAS in the first-order Hamiltonian relies on the application of rf pulses, which prevent its refocusing by MAS. In particular, some first-order homonuclear dipolar recoupling schemes have been developed, which selectively restore the homonuclear dipolar coupling, while removing the unwanted interactions, such as isotropic and anisotropic chemical shifts as well as heteronuclear J- and dipolar couplings. The firstorder recoupling schemes allow the detection of proximities between the nearest neighbors. Weak cross-peaks are observed for nuclei further apart owing to the dipolar truncation, i.e., the large homonuclear recoupled dipolar interactions between nearby nuclei attenuate the coherence transfers between distant nuclei.97 A widely used first-order homonuclear dipolar recoupling to acquire 2D 1Q-1Q correlations is the radio-frequency drivenrecoupling (RFDR), where one 180 pulse is applied every rotor period.13 This recoupling is robust, easy to set-up and works at all MAS frequencies. Nevertheless, when the pulse length represents a significant fraction of the rotor period, the amplitude of the recoupled dipolar interaction depends on the rf field strength. This variant has been called finite-pulse RFDR (fp-RFDR).98 The RFDR scheme has notably been employed to acquire 2D 1Q-1Q through-space correlation spectra of 31P, 29Si and 1H nuclei of inorganic and hybrid materials.99–101 Nevertheless, the 1Q-1Q through-space correlations do not allow the observation of proximities between nuclei with close resonance frequencies. This limitation can be circumvented by the acquisition of 2Q-1Q through-space correlation spectra (see Fig. 5). Various first-order homonuclear dipolar recoupling schemes have been designed to excite and reconvert the 2Q coherences between identical nuclei, including back-to-back (BaBa) scheme,14,102 RFDR bracketed by 90 pulses (denoted [fp-RFDR]),103,104 and symmetry-based sequences, such as POST-C7,26 SPC5,105 SR2611106,107 and R2029.108 The choice of the recoupling sequence 4 depends on the MAS frequency and the strength of the spin interactions. The 2D 31P and 29Si 2Q-1Q through-space correlation spectra are usually acquired at moderate MAS frequencies, nR z 10 kHz, which are compatible with the use of POST-C7 and 107,109 SR2611 In particular, the SR2611 4 sequences, which require nutation frequencies, n1 ¼ 7nR and 6.5nR, respectively. 4 recoupling 29 29 benefits from high robustness and hence, is especially beneficial to observe the small Sie Si dipolar couplings. Conversely, 2D 1 H 2Q-1Q through-space correlation experiments are carried out at high MAS frequencies, nR  50 kHz, to improve the spectral resolution by averaging out the 1He1H dipolar interactions (Fig. 6). For that purpose, symmetry-based first-order homonuclear dipolar recoupling schemes, such as R1252, with short cycle time and low rf field requirement (n1 ¼ 3nR) have been introduced.110 Besides organic solids, these recoupling sequences have been used to probe 1He1H proximities in hybrid solids, including metalorganic frameworks, as seen in Fig. 6.111 The pulse sequence and the coherence transfer pathway of 2D 2Q-1Q through-space homonuclear correlation are displayed in Fig. 5. The first recoupling scheme transforms the longitudinal magnetization into 2Q coherences, which evolve during the t1 period. The second recoupling scheme reconverts these coherences into longitudinal magnetization, which is transformed into observable transverse magnetization by the 90 pulse. Signals passing through 2Q coherences during the t1 period are selected by a four-step phase cycle of the recoupling scheme used either for excitation or reconversion. Like for through-bond correlation, the sensitivity of 29Si through-space correlation can be enhanced by CPMG112 as well as DNP to detect 29Sie29Si proximities near surfaces.80,113 Similarly, the sensitivity gain provided by DNP has been leveraged to observe proximities between 31P sites near the

Fig. 5 Pulse sequence of 2D 2Q-1Q through-space homonuclear correlation for isotope I along with desired coherence transfer pathways. During the excitation (exc.) and reconversion (rec.) blocks, the IeI dipolar interactions are reintroduced in the first-order Hamiltonian by recoupling schemes, 5 1 such as BaBa, [fp-RFDR], POST-C7, SPC5, SR2611 4 or R122. The initial longitudinal magnetization can be created by H / I CP transfer followed by a flip-back 90 pulse on the I channel.

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Fig. 6 2D 1H 2Q-1Q through-space homonuclear correlation of Zr-based metal-organic framework (MOF) functionalized with OH groups acquired using R1252 recoupling at B0 ¼ 18.8 T with nR ¼ 62.5 kHz. Figure adapted from Ref. Devautour-Vinot, S.; Maurin, G.; Serre, C.; Horcajada, P.; Paula da Cunha, D.; Guillerm, V.; de Souza Costa, E.; Taulelle, F.; Martineau, C. Structure and Dynamics of the Functionalized MOF Type UiO-66(Zr): NMR and Dielectric Relaxation Spectroscopies Coupled with DFT Calculations. Chem. Mater. 2012, 24 (11), 2168–2177. doi: 10.1021/cm300863c. Copyright 2012, American Chemical Society.

surface of nanoparticles.114 2D 2Q-1Q through-space homonuclear correlation experiments have also been employed to probe 19 Fe19F proximities in inorganic fluorides.115–118 These experiments require robust first-order homonuclear dipolar recoupling since 19F nuclei often exhibit large isotropic and anisotropic chemical shifts. Note also that the proximities between three protons have also been probed using 2D 3Q-1Q through-space homonuclear correlation experiments.119–121 Second-order recoupling. These schemes rely on cross-terms between distinct homonuclear dipolar interactions or homo- and hetero-nuclear dipolar interactions in the second-order Hamiltonian. Hence, these cross-terms contain products of operators of three distinct spins. These recoupling schemes are less susceptible to dipolar truncation than first-order recoupling and they allow probing longer-range distance. Nevertheless, the magnitude of the second-order Hamiltonian is inversely proportional to the MAS frequency and hence, these second-order recoupling are less efficient at high MAS frequency. In the case of nuclei subject to several large homonuclear dipolar interactions, such as protons and 19F nuclei, proximities can also be probed using spin diffusion experiments, which have been first introduced for polymer blends122 and then have been applied for organic molecules adsorbed in zeolites123,124 and later inorganic fluorides.125,126 The pulse scheme used for these spin diffusion experiments is identical to the NOESY sequence and is shown in Fig. 7a. The 1Q coherences excited by the first 90 pulse evolve during the t1 period. The second 90 pulse stores the magnetization along the direction of the B0 field during a mixing time, s. During this delay, spin diffusion can exchange magnetization between distinct sites. The last 90 pulse converts the longitudinal magnetization into transverse magnetization, which is detected during the acquisition period, t2. After 2D Fourier transform, we obtain a 2D 1Q-1Q through-space correlation spectrum, as seen in Fig. 7b. Nevertheless, these 2D 1Q-1Q correlation experiments do not allow the observation of proximities between nuclei with close resonance frequencies. This limitation can be circumvented by the use of 2D 2Q-1Q through-space correlations relying on crossterms between homonuclear dipolar couplings, such as the dipolar homonuclear homogeneous Hamiltonian (DH3) scheme,127 which has notably been employed to probe proximities between 19F nuclei in inorganic fluorides and fluorinated aluminophosphates.128 Nuclei other than 1H and 19F, such as 13C or 31P, are subject to smaller homonuclear dipolar couplings and spin diffusion due to cross-terms between homonuclear dipolar couplings is quenched under MAS. A first possibility to circumvent this issue is to use the 2D 1Q-1Q SHHS sequence, in which the S-edited 1H longitudinal magnetization is exchanged by 1He1H spin diffusion during a mixing period placed between two CP transfers (see Fig. 7c). This experiment has been applied to probe the proximities between organic functional groups bound to silica surface (see Fig. 7d).113 Nevertheless, cross-terms between homonuclear dipolar interactions and heteronuclear dipolar interaction with protons can transfer magnetization between nuclei with different frequencies. This process is referred to as proton-driven spin diffusion (PDSD).129 The corresponding pulse sequence is shown in Fig. 7e and is identical to that of spin diffusion experiment for the detected nucleus, I, except that the initial 90 pulse is replaced by a 1H / I CP transfer and heteronuclear dipolar decoupling schemes are applied on 1H channel during the t1 and t2 periods to suppress 1HeI dipolar couplings. Conversely, during the mixing time, s, no irradiation is applied in the case of PDSD sequence so that the cross-terms between 1HeI and IeI dipolar couplings transfer magnetization between I spins. Nevertheless, the efficiency of this transfer decreases for MAS frequency and B0 field strength above 20 kHz and 14.1 T (1H Larmor frequency of 600 MHz). Irradiation on the 1H channel can be applied during the mixing time, s, to restore these cross-terms under fast MAS and at high magnetic field. For instance, the sequences called dipolar-assisted rotational resonance (DARR)130 or radio frequency assisted diffusion (RAD)131

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Fig. 7 (a) Pulse sequence of 2D 1H or 19F spin diffusion experiment along with desired coherence transfer pathways. (b) 2D 1H spin diffusion spectrum of methyl ammonium lead iodide containing 4% tetrapropylammonium at B0 ¼ 18.8 T with nR ¼ 35 kHz. (c) Pulse sequence of 2D 1Q-1Q SHHS experiment. (d) DNP-enhanced 2D 13C CHHC spectrum of bifunctionalized mesoporous silica nanoparticles. (e) Pulse sequence of 2D 1Q-1Q homonuclear correlation experiments, such as PDSD, DARR and PARIS, between S ¼ 13C or 31P nuclei. These experiments differ by the rf irradiation applied on 1H channel during the mixing time s. (f) DNP-enhanced 2D 13C DARR spectrum of 13C-enriched methionine adsorbed on Pd nanoparticles supported on g-alumina and impregnated with a TEKPol solution in 1,1,2,2-tetrachloroethane (TCE) at B0 ¼ 9.4 T and 105 K with nR ¼ 12 kHz. Figures (b, d and f) adapted from Refs.Krishna, A.; Akhavan Kazemi, M. A.; Sliwa, M.; Reddy, G. N. M.; Delevoye, L.; Lafon, O.; Felten, A.; Do, M. T.; Gottis, S.; Sauvage, F. Defect Passivation via the Incorporation of Tetrapropylammonium Cation Leading to Stability Enhancement in Lead Halide Perovskite. Adv. Funct. Mater. 2020, 30 (13), 1909737. doi: 10.1002/adfm.201909737. Kobayashi, T.; Slowing, I. I.; Pruski, M. Measuring LongRange 13C–13C Correlations on a Surface under Natural Abundance Using Dynamic Nuclear Polarization-Enhanced Solid-State Nuclear Magnetic Resonance. J. Phys. Chem. C 2017, 121 (44), 24687–24691. doi: 10.1021/acs.jpcc.7b08841. Johnson, R. L.; Perras, F. A.; Kobayashi, T.; Schwartz, T. J.; Dumesic, J. A.; Shanks, B. H.; Pruski, M. Identifying Low-Coverage Surface Species on Supported Noble Metal Nanoparticle Catalysts by DNPNMR. Chem. Commun. 2016, 52 (9), 1859–1862. doi: 10.1039/C5CC06788J, respectively. Copyright 2020, Wiley, 2017, American Chemical Society, 2016, Royal Society of Chemistry.

employ continuous wave rf irradiation with nutation frequency equal to 1 or 2 times the MAS frequency during the mixing time, whereas phase-alternated irradiation, such as phase-alternated recoupling irradiation scheme (PARIS),132,133 improves the magnetization transfer at high MAS frequencies. The 1Q-1Q correlation techniques have been widely employed for the observation of 13 Ce13C proximities in biomolecules.41 Nevertheless, they have also been recently applied to probe proximities between C sites

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of 13C-enriched organic molecules adsorbed at the surface of nanoparticles or in zeolites (see Fig. 7f).134,135 Homonuclear correlation experiments for 31P nuclei have also been applied to probe the proximities between Lewis and Brønsted acid sites in zeolites using P-containing probe molecules.136

9.19.3.2.2

Between half-integer quadrupolar nuclei

Like for spin-1/2 nuclei, through-space homonuclear correlation experiments have been developed to probe proximities between identical half-integer quadrupolar nuclei, including 11B, 17O, 23Na and 27Al.44,47,137 Nevertheless, these experiments are more challenging for these isotopes than for spin-1/2 nuclei owing to the larger size of the density matrix, equal to (2I þ 1)2 for a spin-I nucleus, and the presence of large anisotropic quadrupolar interaction. This interaction has a magnitude much larger than the rf irradiation and the MAS frequency, resulting in complicated spin dynamics during rf irradiation under MAS conditions. Therefore, 2D through-space homonuclear correlation experiments were initially achieved using recoupling techniques, which do not involve rf irradiation, such as (i) cross-terms between homonuclear dipolar couplings and either first-order quadrupolar interaction138,139 or heteronuclear dipolar couplings to protons140,141 in the second-order Hamiltonian, (ii) R2 condition142 or (iii) off-magic-angle spinning.23,143,144 Nevertheless, this latter approach reintroduces other unwanted interactions and hence, decreases the spectral resolution, whereas the R2 method requires the MAS frequency matching the difference in isotropic chemical shifts between the recoupled spins and the transfer efficiency of second-order recoupling decreases at higher MAS frequencies. Dipolar couplings between identical half-integer quadrupolar nuclei have also been restored by the rf irradiation of the CT between energy levels mI ¼ 1/2 and þ1/2 with mI the magnetic quantum number.145,146 This approach has the advantage to be more versatile than those without rf irradiation. Nevertheless, the applied rf field should be weak to avoid the excitation of satellite transitions (STs) and the related signal losses. In particular, efficient recoupling has been achieved using homonuclear rotary CT recoupling (HORROR) condition, nCT nut ¼ (I þ 1/2)n1 ¼ nR/2, where nnut is the nutation frequency of the CT and n1 is the rf field 147 The robustness to offset and rf field inhomogeneity has been improved by the use of RNnn symmetry-based recoupling strength. and supercycling.148–153 Zero-quantum (0Q) dipolar recoupling, such as SR212, can be employed to acquire 2D 1Q-1Q correlation spectra,148,151,152 whereas 2Q recoupling, such as BR212, can be applied to record 2D 2Q-1Q correlation experiments.149,150,153 The 1Q-1Q correlation pulse sequence is identical to that shown in Fig. 7a, except that the 90 pulse are selective of the CT and 0Q recoupling scheme is applied during the s delay. The 2Q-1Q correlation spectra between half-integer quadrupolar nuclei are acquired using the pulse sequence of Fig. 5. Nevertheless, a CT-selective 180 pulse must be applied during the t1 period to eliminate 2Q coherences between energy levels mI and mI þ 2 of a single I-spin nucleus.147 The 2Q-1Q variant has the advantage to allow the observation of proximities between nuclei with close resonance frequencies (Fig. 8). Furthermore, the BR221 recoupling benefits from high robustness to offset, which contributes to the reintroduction of the homonuclear dipolar couplings.153 Nevertheless, the

Fig. 8 2D 27Al 2Q-1Q through-space correlation spectrum of HY zeolite calcined at 700  C. The isotropic shifts are indicated near the peaks. The peak resonating at 59 ppm is assigned to framework AlO4 species of Brønsted acid sites SiOHAl, whereas those at 32 and 3 ppm stem from extraframework AlO5 and AlO6 sites, respectively, acting as Lewis acid sites. The auto-correlation peaks on the diagonal indicate proximities between identical sites, whereas the cross peaks outside the diagonal reveal proximities between distinct Al sites. Figure adapted from Ref. Yu, Z.; Zheng, A.; Wang, Q.; Chen, L.; Xu, J.; Amoureux, J.-P.; Deng, F. Insights into the Dealumination of Zeolite HY Revealed by Sensitivity-Enhanced 27Al DQ-MAS NMR Spectroscopy at High Field. Angew. Chem. Int. Ed. 2010, 49 (46), 8657–8661. doi: 10.1002/anie.201004007. Copyright, 2010, Wiley.

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efficiency of this recoupling drops on resonance and hence, the carrier frequency must be carefully chosen. The intensity of these homonuclear correlation experiments between CTs of half-integer quadrupolar nuclei can be enhanced by the irradiation of the STs at the beginning of the pulse sequence, in such way that the population difference across the CT is enhanced.148–150 Note that 3D 14N/14N/1H through-space correlation has been developed to probe proximities between 14N nuclei since their lack of CT prevents the application of the above correlation experiments based on the selective irradiation of the CT.154 Nevertheless, they have only been applied so far to solid-state peptides.

9.19.4

Correlations between distinct nuclei

Connectivities and proximities between distinct isotopes, I and S, can be observed using heteronuclear correlation experiments based on coherence transfers through J- and dipolar couplings, respectively. These experiments rely on either a single coherence transfer I / S, when the excited and detected isotopes differ, or two successive coherence transfers S / I / S, when the excited isotope is identical to that detected. The relative sensitivity of these two approaches depends on the gyromagnetic ratios, longitudinal relaxation times, T1, coherence lifetimes and line widths of the correlated nuclei.32 The heteronuclear correlation experiment, in which the S spin is detected and the I spin is indirectly observed, is denoted S{I} hereafter.

9.19.4.1

Through-bond heteronuclear correlations

The connectivities between distinct isotopes in inorganic solids have been probed using through-bond heteronuclear correlation experiments11 similar to those used in isotropic solution, including the refocused insensitive nuclei enhanced by polarization transfer (J-RINEPT) based on a single transfer I / S17,155,156 as well as the heteronuclear multiple-quantum coherence (J-HMQC) scheme relying on a double transfer I / S / I.12,157,158 These experiments are carried out under MAS to average out anisotropic interactions and hence, to improve the resolution. Furthermore, the J-coupling constants between nuclei separated by two or more covalent bonds usually do not exceed a few tens of hertz. Hence, these coherence transfers are only efficient when at least one of the correlated isotope exhibits a sufficiently long time constant, T20 , for the decay of transverse magnetization, which is not refocused by a 180 pulse.

9.19.4.1.1

Between spin-1/2 isotopes

The J-RINEPT pulse sequence is displayed in Fig. 9. The first 90 pulse on the I channel excites the I-spin transverse magnetization, which is encoded by the isotropic chemical shift during the t1 period since the 180 pulse applied to the S channel in the middle of the t1 period refocuses the evolution under I-S J-couplings. During the defocusing delay, s, the simultaneous 180 pulses on I and S channels refocus the evolution under the isotropic chemical shifts but not that under I-S J-couplings. This evolution converts the inphase transverse magnetization of the I nuclei into antiphase magnetization with respect to the I-S J-couplings. The simultaneous 90 pulses on I and S channels convert this antiphase magnetization of the I spin into antiphase magnetization of the S spin, which

Fig. 9 Pulse sequence along with desired coherence transfer pathways of 2D S{I} through-bond heteronuclear correlation using I / S J-RINEPT transfer. The evolution under I-S J-couplings is refocused during t1 and t2 periods.

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is subsequently converted into in-phase magnetization of the S spin during the refocusing delay, s0 . This in-phase magnetization is detected during the t2 period. For an isolated IeS pair and in the absence of losses, the optimal s and s0 delays are equal to 1/(2JIS). The J-coupling constants between covalently bonded 1He13C nuclei, 1JCH, are typically equal to 140 Hz and the 13C{1H} JRINEPT sequence based on these coupling has been employed to observe HeC bonds of organic molecules, such as surfactants, in mesoporous silica.159 It has been shown that the transfer efficiency of 1He13C J-RINEPT scheme can be improved by reducing the coherence losses due to 1He1H dipolar couplings during s and s0 delays using 1H homonuclear dipolar decoupling160 or fast MAS.161 In particular, the T20 time constants of 1H and 13C nuclei are proportional to the MAS frequency.161 Furthermore, a threefold enhancement in sensitivity of 2D 1He13C J-RINEPT experiment, which corresponds to a time saving by almost an order of magnitude, has been achieved using indirect detection of 13C nuclei via protons (1H{13C}) under fast MAS (see Fig. 10).161 Similarly, the HeSi bonds in poly(cyclosilane) have been observed using 29Si{1H} J-RINEPT scheme incorporating 1H homonuclear dipolar decoupling and based on coherence transfer via 1JSiH coupling constants, which are typically equal to 170 Hz.108 The sensitivity of this experiment has been improved using DNP to detect silicon hydride sites (SiH) at the surface of silicon nanoparticles.91 The strength of the J-coupling constant decreases for increasing number of bonds between the coupled spins. Nevertheless, geminal couplings through two covalent bonds can be large enough to achieve J-RINEPT transfer. For instance, the geminal 29 SieOe31P J-coupling constants typically range from 4 to 15 Hz and have been leveraged to correlate the 29Si and 31P signals of a mixture of silicophosphate crystalline phases.156 Fig. 11 shows the pulse sequence of J-HMQC experiment. The first 90 pulse on S channel creates transverse magnetization of S nuclei, which evolves under JIS coupling into antiphase magnetization during the first s delay and then is converted into heteronuclear multiple-quantum coherences by the 90 pulse on I channel. These coherences are encoded during t1 period by the isotropic chemical shift of I nuclei before being converted back into antiphase magnetization of S nuclei by the second 90 pulse on I channel. For an isolated IeS pair and in the absence of losses, the optimal s delays are equal to 1/(2JIS). The J-HMQC experiment has notably been employed to correlate the 29Si and 31P signals of a mixture of silicophosphate crystalline phases (see Fig. 12)158 as well as to probe 19Fe207Pb and 19Fe31P covalent bonds in b-Pb2ZnF6162 and oxyfluoride glass-ceramics,163 respectively. More recently, as shown in Fig. 13, the sensitivity of 77Se{113Cd} J-HMQC experiment has been enhanced by DNP to probe the 77See113Cd covalent bonds near the surface of CdSe nanocrystals.164

9.19.4.1.2

Between spin-1/2 and half-integer quadrupolar isotopes

9.19.4.1.2.1 Without high-resolution J-RINEPT and J-HMQC experiments have also been used to probe connectivities between spin-1/2 and half-integer quadrupolar isotopes in inorganic solids. The employed pulse sequences are identical to those used to correlate the signals of spin-1/2 isotopes, except that CT-selective pulses are applied to the quadrupolar nuclei. Furthermore, when the excited nucleus is a half-integer quadrupolar nucleus, the signal intensity can be enhanced by irradiating the STs at the beginning of the sequence, in such way that the population difference across the CT is increased.165 When the T20 time constant is much longer than that of the apparent decay of the transverse magnetization, T2  ; the signal intensity can be enhanced by the acquisition of a train of echoes using CPMG scheme for

Fig. 10 (a) 2D 1H{13C} J-RINEPT spectrum of cetyltrimethyl ammonium bromide (CTAB) surfactant in mesoporous silica recorded in 50 min at B0 ¼ 14.1 T with nR ¼ 40 kHz. The initial 90 pulse on I ¼ 13C channel is replaced by 1H / 13C CP transfer. Furthermore, the residual initial 1H magnetization, which is not transferred to 13C nuclei, is eliminated by the application of purge pulses. (b and c) Selected cross sections along the (b) 1 H and (c) 13C dimensions of the 2D 13C{1H} (top traces) and 1H{13C} (bottom traces) J-RINEPT spectra acquired under the same experimental conditions. The noise level is shown as an inset with a vertical expansion by a factor of 10. Figure adapted from Ref. Mao, K.; Wiench, J. W.; Lin, V. S.-Y.; Pruski, M. Indirectly Detected Through-Bond Chemical Shift Correlation NMR Spectroscopy in Solids under Fast MAS: Studies of Organic– Inorganic Hybrid Materials. J. Magn. Reson. 2009, 196 (1), 92–95. doi: 10.1016/j.jmr.2008.10.010. Copyright, 2009, Elsevier.

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Fig. 11

Pulse sequence along with desired coherence transfer pathways of 2D S{I} J-HMQC experiment.

spin-1/2 nuclei or the quadrupolar CPMG (QCPMG) variant for half-integer quadrupolar nuclei, in which 180 pulses are CTselective.166,167 When half-integer quadrupolar nuclei are indirectly detected using J-HMQC sequence, the losses can be reduced by accelerating the coherence transfer through the irradiation of STs during the s delays.168,169 DNP has been recently employed to enhance the sensitivity of J-RINEPT experiments in order to probe connectivities of surface sites.81 As seen in Tables 1 and 2, the J-RINEPT and J-HMQC experiments have been applied for several spin-1/2 isotopes, including 1H, 13 C, 19F, 29Si, 31P and 77Se, as well as a few half-integer quadrupolar nuclei, such as 11B, 17O, 27Al, 51V and 71Ga. An example of 2D 19 F{27Al} J-HMQC spectrum allowing the observation of 19Fe27Al covalent bonds is shown in Fig. 14. These experiments have been demonstrated for isotopes with high or moderate gyromagnetic ratios, since the strength of the J-coupling increases with increasing gyromagnetic ratios. Furthermore, the J-coupling constants usually decrease when the number of bonds between the coupled nuclei increases. Isotopic enrichment and/or DNP are often required to detect connectivities of isotopes with low natural abundance, such as 17O (0.0373%) and 29Si (4.67%). Heteronuclear correlation experiments between isotopes exhibiting close Larmor frequencies, such as 13C and 27Al, for which these frequencies are only 3.6% apart, are not possible with conventional MAS NMR probes and require the use of a frequency splitter.171,179 9.19.4.1.2.2 With high-resolution In 2D J-RINEPT and J-HMQC spectra, the signals of quadrupolar nuclei are broadened by the second-order quadrupolar interaction.180,181 This broadening, which can mask differences in isotropic chemical shifts, can be removed using a 2D MQMAS scheme, which combines the evolution of multiple-quantum and 1Q coherences.182,183 These 1Q coherences of the quadrupolar isotope at the end of the MQMAS block can be transferred to spin-1/2 nucleus via J-coupling using the J-RINEPT sequence, as shown in Fig. 15, which displays the sequence of 3Q-J-RINEPT experiment.21,184 The sensitivity of this experiment can be enhanced by the use of soft pulse added mixing (SPAM), i.e., the insertion of a 90 CT-selective pulse after the reconversion pulse of the MQMAS block.184 The 3Q-J-RINEPT sequence has been applied to acquire 2D 31P{27Al} and 29Si{27Al} through-bond correlation spectra of aluminophosphate and aluminosilicate materials, respectively, with high-resolution along the 27Al dimension (see Fig. 16). Highresolution J-HMQC spectra can also be acquired by substituting the initial CT-selective 90 pulse on the S channel (see Fig. 11) by a MQMAS block exciting 3Q coherences of the detected quadrupolar isotope.185 Nevertheless, this experiment requires a 3D acquisition, instead of a 2D one for 3Q-J-RINEPT technique.

9.19.4.1.3

Between two half-integer quadrupolar isotopes

The 27Ale17O covalent bonds in 17O-enriched aluminate glass and alumina have been observed using 2D 27Al{17O} J-HMQC experiments based on one-bond 17Oe27Al J-couplings, as seen in Fig. 17.19,169 The sensitivity of this experiment has been improved by the irradiation of 27Al STs at the beginning of the sequence to enhance the population difference across the CT, but also the irradiation of 17O STs during the defocusing and refocusing delays to accelerate the coherence transfers, and hence, to reduce the losses during this delay.169 These losses can also be limited by spinning slightly off the magic angle, which lengthens the T20 time constant of the 27Al and 17O nuclei.186

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Fig. 12 2D 31P{29Si} J-HMQC spectrum of a mixture of Si5O(PO4)6 and SiP2O7 polymorphs acquired at B0 ¼ 7 T with nR ¼ 14 kHz. The 1D 29Si and 31 P MAS NMR spectra are displayed along the 29Si and 31P dimensions of the 2D spectra, beside the projections. The bottom spectrum displays an expansion of the circled region in the top spectrum. Figure adapted from Ref. Coelho, C.; Azais, T.; Bonhomme-Coury, L.; Maquet, J.; Massiot, D.; Bonhomme, C. Application of the MAS-J-HMQC Experiment to a New Pair of Nuclei {29Si,31P}: Si5O(PO4)6 and SiP2O7 Polymorphs. J. Magn. Reson. 2006, 179 (1), 114–119. doi: 10.1016/j.jmr.2005.11.015. Copyright, 2009, Elsevier.

9.19.4.2

Through-space heteronuclear correlations

Coherence transfers based on heteronuclear dipolar couplings can be used to acquire 2D heteronuclear correlation spectra. These through-space heteronuclear correlations complement their through-bond counterparts. Furthermore, for isotopes in the first periods of the periodic table, the heteronuclear dipolar couplings are usually larger than the J-couplings, which results in faster coherence transfers and hence, higher sensitivity. Like the through-bond heteronuclear correlations, the through-space variants have been applied for pairs of spin-1/2 isotopes, pairs of spin-1/2 and quadrupolar isotopes as well as pairs of half-integer quadrupolar nuclei (Fig. 18).

9.19.4.2.1

Between spin-1/2 isotopes

The NMR signals of distinct spin-1/2 nuclei distant by a few angstroms have been mainly correlated using 2D heteronuclear correlation (HETCOR) sequence based on CP transfer.5 This CP-HETCOR sequence shown in Fig. 19 is a direct detection method employing a single I / S polarization transfer. The 90 pulse on the I channel creates transverse magnetization of the I nuclei,

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Fig. 13 DNP-enhanced 2D 77Se{113Cd} J-HMQC spectrum of CdSe nanoplatelets mixed with hexagonal boron nitride and impregnated with 16 mM TEKPol solution in TCE. The 77Se transverse magnetization is excited using 1H / 77Se CPMAS transfer. A structural model of the surface of CdSe nanoplatelets along with the observed connectivities is shown on the left of the figure. Figure adapted from Ref. Chen, Y.; Dorn, R. W.; Hanrahan, M. P.; Wei, L.; Blome-Fernández, R.; Medina-Gonzalez, A. M.; Adamson, M. A. S.; Flintgruber, A. H.; Vela, J.; Rossini, A. J. Revealing the Surface Structure of CdSe Nanocrystals by Dynamic Nuclear Polarization-Enhanced 77Se and 113Cd Solid-State NMR Spectroscopy. J. Am. Chem. Soc. 2021, 143 (23), 8747–8760. doi: 10.1021/jacs.1c03162. Copyright, 2021, American Chemical Society. Table 1

List of the pairs of spin-1/2 and quadrupolar isotopes, between which covalent bonds have been probed by 2D J-RINEPT or J-HMQC experiments in hybrid or inorganic solids.

I ¼ 1/2 a

S  1/2 a

1

2D experiments

Sample

References

1

27

13

27

376 71 –b –b 23–34 120–130 500–800

J-HMQC J-HMQC J-HMQC J-HMQC J-HMQC J-HMQC J-RINEPT J-HMQC

Al hydride on g-Al2O3 Alkylaluminium Fluoroborosilicate glass Fluorinated aluminophosphate Silica Na5P3O10 crystals Gallium selenide crystal and glass

170 171 172 128 165 173 167

H C 19 F 19 F 29 Si 31 P 77 Se

Al Al 11 B 27 Al 17 O 17 O 71 Ga

JIS/Hz

a

In this table, the I and S symbols do not denote the indirectly detected and spy isotopes, contrary to Figs. 9 and 11. Not measured.

b

Table 2

List of the pairs of spin-1/2 and quadrupolar isotopes, between which two-bond connectivities have been probed by 2D J-RINEPT or JHMQC experiments in hybrid or inorganic solids.

I ¼ 1/2 a

S  1/2 a

2

29

11

29

27

– 1–6

31

11

31

27

31

51

31

71

Si Si P P P P

a

B Al B Al V Ga

JIS/Hz b

–b 15–25 40 12

2D experiments

Sample

References

J-HMQC DNPþJ-RINEPT J-HMQC J-HMQC J-RINEPT J-HMQC J-HMQC J-HMQC

Layered borosilicates Silicated alumina Aluminosilicate glasses Borophosphate glass Aluminophosphate crystals Aluminophosphate crystals Pb4(VO2)(PO4)3 Gallophosphate crystal

174 81 175 176 17 157 177 178

In this table, the I and S symbols do not denote the indirectly detected and spy isotopes, contrary to Figs. 9 and 11. Not measured.

b

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Fig. 14 2D 19F{27Al} J-HMQC spectrum of crystalline fluorinated aluminophosphate AlPO4-CJ2 at B0 ¼ 9.4 T with nR ¼ 10 kHz. This spectrum allows probing 19Fe27Al covalent bonds and hence, the local OH/F distribution in this material. Figure adapted from Ref. Martineau, C.; MellotDraznieks, C.; Taulelle, F. NMR Crystallography of AlPO4-CJ2: From the Topological Network to the Local (OH)/F Distribution. Phys. Chem. Chem. Phys. 2011, 13 (40), 18078–18087. doi: 10.1039/c1cp22424g. Copyright, 2011, Royal Society of Chemistry.

Fig. 15 Pulse sequence along with desired coherence transfer pathways of 2D S{I} 3Q-J-RINEPT experiment for I  5/2. The first pulse on I channel employs high rf power to excite the 3Q coherences. The second and third pulses on this channel corresponds to the SPAM block, whereas the other pulses are selective of the CT.

which is encoded by the isotropic chemical shift during the t1 period. This magnetization is then transferred to the S spin by CP during the contact time, sCP. This CP transfer relies on the simultaneous rf irradiation of I and S isotopes. These rf fields lock the transverse magnetization of the two isotopes along a particular direction in the rotating frame. The CP transfer is effective provided the nutation frequencies of the I and S isotopes, denoted n1I and n1S hereafter, fulfill the Hartmann-Hahn conditions under MAS:

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Fig. 16 Comparison of 2D 29Si{27Al} (a) J-RINEPT and (b) 3Q-J-RINEPT spectra of a mixture of microcline and albite aluminosilicate minerals acquired at B0 ¼ 9.4 T with nR ¼ 10 kHz. Figure reprinted from Ref. Wiench, J. W.; Tricot, G.; Delevoye, L.; Trebosc, J.; Frye, J.; Montagne, L.; Amoureux, J.-P.; Pruski, M. SPAM-MQ-HETCOR: An Improved Method for Heteronuclear Correlation Spectroscopy between Quadrupolar and Spin-1/ 2 Nuclei in Solid-State NMR. Phys. Chem. Chem. Phys. 2006, 8 (1), 144–150. doi: 10.1039/B512246E. Copyright, 2006, Royal Society of Chemistry.

Fig. 17 (a) Build-up of the signal of 1D 27Al{17O} population transfer (PT)-J-HMQC and J-HMQC experiment of 17O-enriched g-Al2O3 sample. In PTJ-HMQC variant, the 17O STs are irradiated during the defocusing and refocusing delays, s, which accelerates the coherence transfer by approximately a factor of 2 and hence, reduces the losses. (b) 2D 27Al{17O} PT-J-HMQC of the same sample. The spectra are acquired at B0 ¼ 18.8 T with nR ¼ 20 kHz. Figure reprinted from Ref. Wang, Q.; Li, Y.; Trébosc, J.; Lafon, O.; Xu, J.; Hu, B.; Feng, N.; Chen, Q.; Amoureux, J.-P.; Deng, F. Population Transfer HMQC for Half-Integer Quadrupolar Nuclei. J. Chem. Phys. 2015, 142 (9), 094201. doi: 10.1063/1.4913683. Copyright, 2015, American Institute of Physics.

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Fig. 18 2D 29Si{1H} CP-HETCOR-CPMG spectrum of mesoporous silica nanoparticles functionalized with allyl groups acquired at B0 ¼ 14.1 T with nR ¼ 40 kHz. Because of the CPMG detection, this direct detection experiment is more sensitive than indirect detection via protons. Figure adapted from Ref. Wiench, J. W.; Lin, V. S.-Y.; Pruski, M. 29Si NMR in Solid State with CPMG Acquisition Under MAS. J. Magn. Reson. 2008, 193 (2), 233– 242. doi: 10.1016/j.jmr.2008.05.007. Copyright, 2008, Elsevier.

Fig. 19 Pulse sequence along with desired coherence transfer pathways of S{I} CP-HETCOR experiment. During the CP transfer, the rf field applied to the I isotope is linearly ramped.

n1I þ 3 n1S ¼ nnR

(1)

where the coefficient 3 is equal to 1 for the 0Q-CP and þ1 for 2Q-CP and n ¼ 1 or 2. The terms 0Q-CP and 2Q-CP are related to the rank of the spin operator in the Hamiltonian of the recoupled dipolar interaction.188,189 At slow MAS, the 0Q-CP condition is preferred, whereas at fast MAS, both 0Q-CP and 2Q-CP can be employed. The most efficient CP transfer is usually achieved for n ¼ 1. As most NMR coils produce inhomogeneous rf field, the Hartmann-Hahn condition is only fulfilled in a limited region of the sample volume. Hence, the rf field applied to I or S isotope is usually linearly swept so that the different regions of the sample contribute to the detected signal and hence, the signal intensity is enhanced. The optimal sCP time depends on 187,188

552 Table 3

Advances in the characterization of inorganic solids using NMR correlation experiments List of the pairs of distinct spin-1/2 isotopes, for which their signals have been correlated using direct detection methods.

I

S

DNP

Sample

References

1

13

1

15

No No No No No Yes Yesa Yes Noa No Yesb Yes No

Mesoporous aluminosilicates Silica-supported Ta complexes Fluorohectorite Amorphous hydrogenated silicon Phosphate crystals and glasses Y-doped BaZrO3 CdS nanoparticles Sn/SnOx nanoparticles Functionalized mesoporous silica Fluorinated aluminophosphate Organically functionalized silicon nanoparticles Zirconium phosphate nanoparticles Silicophosphate

191 192 193 6 194,195 196 197 198 199 200 91 201 202

H H 1 H 1 H 1 H 1 H 1 H 1 H 19 F 19 F 29 Si 31 P 31 P

C N 19 F 29 Si 31 P 89 Y 113 Cd 119 Sn 29 Si 31 P 13 C 13 C 29 Si

Except 2D 13C{29Si} HETCOR spectrum, for which TEDOR transfer was employed, other HETCOR experiments were recorded using CP transfer. a Using CPMG detection. b Using TEDOR-HETCOR.

the IeS dipolar coupling and the relaxation during the spin locks. After the CP transfer, the free-induction decay (FID) of the S nuclei is detected during the t2 period. If necessary, notably when I ¼ 1H, the broadening of NMR signals of S nuclei due to residual dipolar couplings with I spin can be removed by applying heteronuclear dipolar decoupling sequence during the t2 period. The sensitivity of CP-HETCOR experiments can be enhanced by using CPMG detection, when T20 ðSÞ >> T2  ðSÞ; notably for S ¼ 29Si,190 and DNP.84 Table 3 lists pairs of spin-1/2 isotopes, for which 2D HETCOR spectra have been recorded using direct detection. Nevertheless, CP transfer has some limitations. In the case of CP-HETCOR experiments with protons, a first drawback is that 1H spin diffusion during sCP can exchange the transverse magnetization between protons, which results in relayed correlation and may prevent the observation of proximities between a given nucleus and its nearest protons. This issue is particularly acute for long sCP delay and hence, notably for small heteronuclear dipolar couplings. It can be circumvented using Lee-Goldburg CP (LG-CP), which averages out 1He1H dipolar interaction during the CP transfer and hence, the 1H spin diffusion.203,204 This technique has been first introduced to record 13C{1H} CP-HETCOR spectra of organic solids, and then has been applied to acquire 31P{1H} CP-HETCOR spectra of phosphate materials.205,206 Another drawback of CP transfer is the requirement to fulfill the Hartmann-Hahn conditions, which are narrower for small hetero- and homo-nuclear dipolar interactions as well as at high MAS frequencies. In particular, CP transfer involving isotopes other than 1H and 19F exhibits narrow Hartmann-Hahn conditions. Furthermore, the optimization of the rf field strength to fulfill the Hartmann-Hahn condition is only feasible in the case of sensitive CPMAS experiments. Therefore, for HETCOR experiments, that do not involve protons or 19F, an alternative to CPMAS is the use of the transferred-echo, double-resonance (TEDOR) scheme, which derives from RINEPT transfer.207 In TEDOR scheme, a rotational-echo, double-resonance (REDOR) recoupling208 is applied to one of the two isotopes during the defocusing and refocusing delays to reintroduce the I-S dipolar couplings. The REDOR recoupling consists of a train of 180 pulses and hence, is easier to optimize than CPMAS transfer. Furthermore, contrary to CP, TEDOR recoupling is not affected by dipolar truncation and hence, is more efficient for long-range polarization transfer.36,209 For instance, DNP-enhanced TEDOR experiment has been employed to acquire 2D 13C{29Si} through-space HETCOR spectrum of functionalized silicon nanoparticles.91 For HETCOR experiments between protons and another isotope, the resolution along the 1H dimension is improved by fast MAS, with nR  40 kHz.190 Under lower MAS frequencies, the resolution of 1H signals can also be increased by the application of homonuclear dipolar decoupling sequences, such as frequency-switched Lee-Goldburg (FSLG), on the 1H channel during the t1 period.210 Nevertheless, fast MAS is more robust and is easier to set up. In addition, under fast MAS, indirect detection via nuclei with high gyromagnetic ratio, such as 1H or 19F, usually improves the sensitivity, in spite of the lower sample volume of rotors with small diameter.32,211 Pairs of distinct spin-1/2 isotopes, for which their NMR signals have been correlated using indirect detection methods, are listed in Table 4. For instance, it has been shown that the sensitivity for the detection of 13C nuclei at the surface of organically functionalized mesoporous silica can be enhanced by a factor of three through the indirect detection of nuclei via protons using the double CP (DCP) scheme displayed in Fig. 20a.161,212 In this scheme, the transverse magnetization of the excited nuclei, S, is transferred to the I isotope using a first CP transfer. Then a 90 pulse stores the generated transverse magnetization of the I nuclei along the B0 field direction, while the remaining S magnetization is destroyed by saturation blocks. For S ¼ 1H or 19F, an efficient saturation can be achieved by rf irradiation with n1 ¼ nR/2 corresponding to the HORROR condition, which reintroduces the SeS dipolar interaction.211 The second 90 pulse on the I channel converts the longitudinal magnetization of I nuclei into transverse magnetization, which is encoded by the isotropic chemical shift during the t1 period. Finally a second I / S CP transfer reconverts the transverse magnetization of the I nuclei into transverse magnetization of S nuclei, which is detected during the t2 period. The DCP scheme has been applied

Advances in the characterization of inorganic solids using NMR correlation experiments Table 4

553

List of the pairs of distinct spin-1/2 isotopes, for which their signals have been correlated using indirect detection methods employing two consecutive coherence transfers S / I / S.

S

I

Sequence

Sample

References

1

H H 1 H 1 H 1 H 1 H 1 H 1 H 1 H 1 H 1 H 1 H

13

1

15

19

13

31

113

DCP DCP DCP DCP DNP þ DCP DCP Double D-RINEPT DNP þ DCP D-HMQC DCP Double D-RINEPT D-HMQC TONE-D-HMQC T-HMQC DCP D-HMQC

Organically functionalized mesoporous silica Organically functionalized mesoporous silica Phosphane/borane Yttrium complex Y2O3 nanoparticles Rh complex Rh complex CdS nanoparticles Sn-b zeolite (NH4)2WS4 (NH4)2WS4 Cisplatin and transplatin Silica-supported Pt complexes Cisplatin and transplatin Functionalized mesoporous silica Cd3P2 nanoparticles

212 213 214 215 197 215 215 197 216 215 215 24,217 218,219 220 199 91

F P

C N 31 P 89 Y 89 Y 103 Rh 103 Rh 113 Cd 119 Sn 183 W 183 W 195 Pt C Cd

for the indirect detection of 13C and 15N nuclei via protons at the surface of organically functionalized mesoporous silica (see Fig. 21).161,212,213 The 19F nuclei have also been used as spy spins for the indirect detection of 13C nuclei using DCP scheme in the case of mesoporous silica functionalized with fluorinated organic moieties.199 More recently, the DCP sequence has been employed for the indirect detection via protons of low-g spin-1/2 isotopes, including 89Y, 103Rh and 183W, in inorganic and hybrid materials215 as well as 31P nuclei in phosphane/borane.214 The sensitivity of DCP experiments with 1H detection has also been enhanced using DNP.197 Like the 2D CP-HETCOR spectra, 2D DCP ones with S ¼ 1H can exhibit relayed correlations owing to 1H spin diffusion during the second CP transfer. This problem is more pronounced for long contact times, like in the case of low-g I isotopes subject to small dipolar couplings with protons. Therefore, a DCP variant using LG-CP scheme during the I / 1H transfer has been introduced to suppress 1H spin diffusion and relayed correlations.221 As mentioned above, a limitation of CP transfer is the need to optimize the rf field amplitudes in order to fulfill one of the Hartmann-Hahn conditions. This issue can be circumvented by substituting in the DCP sequence the CP transfers by 1H / I and I / 1H dipolar-mediated RINEPT (D-RINEPT) schemes, which derive from the J-RINEPT sequence shown in Fig. 9, but where heteronuclear dipolar recoupling blocks are applied on 1H channel during the s delays to reintroduce the 1HeS dipolar couplings.215 Nevertheless, the efficiency of this double D-RINEPT sequence was still lower than that of DCP for the employed SR412 heteronuclear dipolar recoupling.222 Another drawback of DCP the technique is the limited excitation bandwidth of the CP transfer owing to the use of long spin-lock irradiations. As a result, the DCP sequence is not applicable for isotopes subject to large CSA, such as 113Cd or 195Pt. For instance, the CSA of 195Pt nuclei can exceed 7000 ppm, leading to spectral breadth of 500 kHz at B0 ¼ 9.4 T.223 An alternative for the indirect detection of 195Pt nuclei via protons relies on the use of the dipolar-mediated HMQC (D-HMQC) sequence, which derives from the J-HMQC scheme shown in Fig. 11, but where 1He195Pt dipolar couplings are reintroduced during the s delays by the application of heteronuclear dipolar recoupling schemes, such as SR412, on the I channel.24,217 The D-HMQC sequence has been combined with the magic-angle turning (MAT) scheme to refocus the 195Pt CSA during the t1 period and correlate the 1H signal with the 195Pt centerband.224 The D-HMQC experiment has also been used for the indirect detection of 111Cd and 113Cd nuclei via 13C and 31P isotopes near the surface of CdSe and Cd3P2 nanoparticles.91,225 Nevertheless, a limitation of the basic D-HMQC scheme is the t1-noise, which produces spurious streaks along the indirect spectral dimension and hence, reduces the sensitivity. These artefacts stem from the random fluctuations of the MAS frequencies, which prevent a correct refocusing of the 1H CSA reintroduced by the SR412 blocks at the end of the defocusing delay, and result in signal amplitude variation from scan to scan.226 As a result, the uncorrelated signal is not perfectly canceled by the phase cycling, which leads to t1-noise. It has been shown that the t1-noise can be decreased by refocusing the 1H CSA during the s delays by inserting two simultaneous 180 pulses on the 1H and I channels in the middle of these delays. For I ¼ 195Pt, short high-powered adiabatic (SHAP) pulses can be employed as 180 pulses.218,227 Hence, these t1-noise-eliminated (TONE) D-HMQC experiments must be preferred for the indirect detection via protons of spin-1/2 isotopes subject to large CSA. Furthermore, in the TONE-2-D-HMQC variant shown in Fig. 20b, a 90 pulse at the end of the defocusing delay flips back the uncorrelated 1H magnetization along the B0 field direction, thus reducing the intensity of the uncorrelated signal and hence, that of the t1-noise. The TONE-D-HMQC experiments have been applied for the indirect detection via protons of 195Pt nuclei of platinum complexes grafted on silica surfaces.218,219 This sequence has also been combined with MAT to suppress the spinning sidebands of 195Pt nuclei and to correlate the 1H NMR signal only with its centerband.219 Furthermore, we recently showed that 195Pt nuclei can be indirectly detected via protons in solids using the T-HMQC sequence shown in Fig. 20c, in which the 1He195Pt dipolar interactions are reintroduced

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Fig. 20 Pulse sequences along with desired coherence transfer pathways for the indirect detection of I nuclei via S spins: S{I} (a) DCP, (b) TONE-2D-HMQC and (c) T-HMQC schemes.

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Fig. 21 2D 1H{15N} DCP spectrum of isotopically unmodified mesoporous silica nanoparticles functionalized with 3-(3-phenyl ureido)propyl groups (see the structure displayed as an inset) acquired at B0 ¼ 14.1 T with nR ¼ 40 kHz in 46 h. Figure adapted from Ref. Althaus, S. M.; Mao, K.; Stringer, J. A.; Kobayashi, T.; Pruski, M. Indirectly Detected Heteronuclear Correlation Solid-State NMR Spectroscopy of Naturally Abundant 15N Nuclei. Solid State Nucl. Magn. Reson. 2014, 57–58, 17–21. doi: 10.1016/j.ssnmr.2013.11.001. Copyright, 2014, Elsevier.

Fig. 22 2D 1H{195Pt} T-HMQC spectrum of an aged mixture of trans- and cis-platin acquired at B0 ¼ 18.8 T with nR ¼ 64 kHz. Figure adapted from Ref. Bayzou, R.; Trébosc, J.; Hung, I.; Gan, Z.; Lafon, O.; Amoureux, J.-P. Indirect NMR Detection via Proton of Nuclei Subject to Large Anisotropic Interactions, Such as 14N, 195Pt, and 35Cl, Using the T-HMQC Sequence. J. Chem. Phys. 2022, 156 (6), 064202. doi: 10.1063/5.0082700. Copyright, 2022, American Institute of Physics.

during the s delay by the application of long rf pulses on 195Pt channel.220 These long pulses also excite and reconvert 195Pt 1Q coherences, which are encoded by the isotropic chemical shifts during the t1 period. Since the long pulses are applied to the 195 Pt channel, they do not reintroduce the 1H CSA and hence, the 2D 1H{195Pt} T-HMQC spectra exhibit low t1-noise (see Fig. 22).

9.19.4.2.2

Between spin-1/2 and quadrupolar isotopes

9.19.4.2.2.1 Without high-resolution Through-space heteronuclear correlation experiments relying on one (I / S) or two (S / I / S) coherence transfers have also been applied to probe proximities between spin-1/2 and quadrupolar isotopes in solids.44–46,48 In the case of half-integer

556 Table 5 I 1

Advances in the characterization of inorganic solids using NMR correlation experiments List of the pairs of spin-1/2 and half-integer quadrupolar isotopes, which have been correlated using single coherence transfer I / S. S

H

17

1

H B 11 B 11 B 17 O 19 F 27 Al

43

11

1

27

23

27

29

Al Al 27 Al

O

Ca H 29 Si 31 P 29 Si 27 Al 1 H Na Si 31 P

Sequence

Sample

References

CP-HETCOR DNP þ PRESTO-II DNP þ CPMAS CP-HETCOR CP-HETCOR CP-HETCOR CP-HETCOR CP-HETCOR CP-HETCOR D-RINEPT-R3 D-RINEPT- SR421 D-RINEPT-R3 TEDOR CP-HETCOR CP-HETCOR D-RINEPT-R3

Zeolites Mg(OH)2 and Ca(OH)2 Hydroxyapatite nanoparticles Borosilicate zeolite Borosilicate glass Borophosphate glass 17 O-enriched silicate glass Fluorinated aluminophosphate Mesoporous aluminosilicate Crystalline aluminophosphate AlPO4-14 g-Alumina Crystalline aluminophosphate Zeolites Crystalline aluminophosphate VPI-5 Aluminophosphate glass Crystalline aluminophosphate AlPO4-14

228 229 230 231 232 233 234 200 191 235 236 235 237 16 238 235

quadrupolar isotopes, this correlation has been achieved first using CP-HETCOR experiments15 and later the TEDOR sequence,16 which derives from the RINEPT method. Table 5 lists pairs of spin-1/2 and half-integer spin quadrupolar isotopes, which have been correlated using a single coherence transfer. The CP-HETCOR sequence is identical to that employed for spin-1/2 isotopes (see Fig. 19). Nevertheless, it requires the spin locking of the magnetization of the quadrupolar isotope, which is difficult to achieve under MAS.239,240 During the spin lock, the modulation of the quadrupolar interaction by MAS results in crossing of energy levels. Adiabatic crossings are usually difficult to achieve since they require large rf fields, which are not compatible with the rf power specifications of most NMR probes. An alternative is to spin lock the magnetization of the CT using low rf field, which results in sudden-passage energy level crossings. Nevertheless, even under these conditions, some losses often occur during the energy level crossings, which decreases the efficiency of CPMAS transfer, and the magnetization of quadrupolar nuclei cannot be spin locked for some crystallite orientations, which results in line-shape distortions.241,242 Furthermore, the low rf field used to spin lock the magnetization of the CT leads to a high sensitivity to offset and CSA.240,243,244 In addition, the CPMAS experiment requires a careful adjustment of the rf field applied to the quadrupolar isotope to fulfill the Hartmann-Hahn conditions under MAS:   1 n1I þ 3 S þ n1S ¼ nnR (2) 2 assuming the S spin is the quadrupolar isotope, while avoiding the rotary resonance recoupling (R3) condition n1S ¼ 

knR

 S þ 12

(3)

with k ¼ 0, 1, 2 or 3.240,243 These issues are circumvented by the use of magnetization transfer that do not employ spin lock of the quadrupolar isotope but instead two or three CT-selective pulses. These sequences include the dipolar-mediated RINEPT (D-RINEPT) techniques,16,235,236,245 such as TEDOR, and phase-shifted recoupling effects a smooth transfer of order (PRESTO).229,246–248 In these sequences, the heteronuclear dipolar interactions are reintroduced by applying the heteronuclear recoupling to the spin-1/2 isotope. In the case of spin-1/2 nuclei other than 1H and 19F, which are subject to small homonuclear dipolar couplings, heteronuclear recoupling schemes, such as REDOR or R3 with n1I ¼ nR, reintroducing the |m| ¼ 1 space component of the heteronuclear dipolar interaction must be employed since they result in larger recoupled dipolar interactions and hence, faster magnetization transfers.235,245 The R3 scheme has the advantage to be g-encoded, which limits the t1-noise.245 Conversely, when the spin-1/2 nuclei are subject to large homonuclear dipolar interactions, like in the case of protons, recoupling schemes reintroducing the |m| ¼ 2 space component of the heteronuclear dipolar interaction, such as those based on the SR421 symmetry,222 are required since they suppress the contribution of homonuclear dipolar interactions to the first-order average Hamiltonian.236,249,250 Furthermore, we have recently demonstrated that the efficiency of the D-RINEPT transfer from protons to half-integer quadrupolar nuclei can be improved by employing the SR421 recoupling built from composite or adiabatic tanh/ tan inversion pulses, continuous wave irradiation during the windows and composite 90 and 180 pulses on the 1H channel.250–252 These modifications limit the losses due to 1He1H dipolar interactions and improve the robustness to rf field inhomogeneity. The corresponding sequence, termed D-RINEPT-CWc, is shown in Fig. 23a. The use of adiabatic pulses as basic inversion element of SR421 recoupling provides the highest transfer efficiency and robustness at low MAS frequencies, nR  15 kHz, whereas at higher MAS frequencies, 270x90y composite pulse must be employed since the rf requirement of adiabatic pulses is not compatible

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Fig. 23 Pulse sequences along with desired coherence transfer pathways for (a) D-RINEPT-CWc using SR421 recoupling and (b) PRESTO-III using RNnn recoupling.

with the specifications of MAS probes. The D-RINEPT sequence using SR421 recoupling is not affected by dipolar truncation and hence, allows the observation of both short- and long-range proximities. The SR421 recoupling also reintroduces the 1H CSA but this term commutes with the recoupled 1HeI dipolar interactions, and hence, does not affect the magnetization transfer. The PRESTO sequence is an alternative to the D-RINEPT sequence for the transfer of magnetization from protons to half-integer quadrupolar nuclei. This sequence, displayed in Fig. 23b, employs a symmetry-based recoupling, RNnn that reintroduces the |m| ¼ 2 space component and the 1Q terms of the heteronuclear dipolar interaction. The R2272 recoupling built from single 180 pulses results in good transfer efficiency and robustness at low MAS frequencies, nR  20 kHz, whereas at high MAS frequencies (nR z 60 kHz), R1676 recoupling using 270x90y composite pulse as a basic inversion element must be employed.249,250 These recoupling schemes are affected by dipolar truncation and hence, PRESTO experiment complements D-RINEPT by allowing the selective observation of short-range proximities. These recoupling sequences also reintroduce the 1H CSA, which does not commute with the recoupled 1HeI dipolar interactions and hence, can interfere with the magnetization transfer. In the case of large 1HeI dipolar interactions, e.g., for covalently bonded 1H and I nuclei, and moderate 1H CSA, notably at low B0 fields, the PRESTO-II sequence with only two pulses applied to the quadrupolar isotope is generally the most efficient variant of PRESTO. Conversely, the PRESTO-III

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Advances in the characterization of inorganic solids using NMR correlation experiments

scheme shown in Fig. 23b results in higher efficiency in the case of small 1HeI dipolar interactions and large 1H CSA because the interference of 1H CSA is limited by the application of CT-selective 180 pulse to the quadrupolar isotope and the simultaneous overall phase shift of the recoupling applied to 1H channel, which refocus partly the 1H CSA while preserving the recoupled 1 HeI dipolar interactions.247 In the PRESTO sequence, the first 90 pulse excites the 1H transverse magnetization, which is encoded by the isotropic chemical shift during the t1 period. The second 90 pulse flips back this transverse magnetization along the B0 field direction. The RNnn 1Q heteronuclear recoupling converts the 1H longitudinal magnetization into 1H 1Q coherences antiphase with respect to the quadrupolar isotope, which is transformed into 1Q coherences of the quadrupolar isotope antiphase with respect to the protons by the 90 pulse on the S channel. These antiphase 1Q coherences of S spins evolve during the refocusing delay into inphase transverse magnetization, which is detected during the t2 period. The sensitivity of 2D PRESTO experiments has been improved using DNP and QCPMG detection to correlate the signals of 1H and 17O isotopes in natural abundance (see Fig. 24).229,253 The 1H resolution of heteronuclear correlation spectra between protons and quadrupolar isotopes is improved at high MAS frequencies (nR  40 kHz).250 At lower MAS frequencies, the resolution can be enhanced by the application of homonuclear dipolar decoupling, such as FSLG, on 1H channel during the t1 period.229 However, fast MAS is easier to set up and more robust than the homonuclear decoupling. As mentioned above, the choice of the excited and detected isotopes in heteronuclear correlation depends on the gyromagnetic ratios, longitudinal relaxation times, T1, coherence lifetimes and line widths of the correlated nuclei.32,236 In the case of heteronuclear correlation experiments between spin-1/2 and half-integer quadrupolar isotopes relying on a single coherence transfer, the highest sensitivity is often achieved by exciting the quadrupolar isotope, which exhibits faster longitudinal relaxation than spin1/2 nuclei. Furthermore, the sensitivity can be further improved by irradiating the STs at the beginning of the sequence to enhance the population difference across the CT.254 Nevertheless, in the case of DNP experiments, higher sensitivity is usually achieved by exciting the protons since the 1He1H spin diffusion efficiently transports the DNP-enhanced 1H polarization into the sample.255,256 Nevertheless, the above heteronuclear correlation experiments relying on a single coherence transfer cannot correlate the signals of protons and the 1Q coherences of 14N nuclei, which are broadened over several megahertz by first-order quadrupolar interaction for this spin-1 isotope and hence, are difficult to spin lock or to invert by 180 pulse. CP-HETCOR and PRESTO-II sequences have been applied to correlate the signals of protons and 14N 2Q coherences between energy levels mI ¼ 1 since these coherences are only broadened by second-order quadrupolar interactions.257,258 However, the overtone excitation and detection at twice the Larmor frequency are less efficient than those of 14N 1Q coherences at the 14N Larmor frequency. Therefore, through-space HMQC (DHMQC) experiments have been proposed for the indirect detection of 14N coherences via 13C nuclei1,2, and later protons.259 These experiments, which derive from the J-HMQC scheme shown in Fig. 11, are advantageous since they do not employ any spin lock or inversion pulse on 14N channel. They have been applied for the indirect detection of 14N 1Q and 2Q coherences. The indirect detection of 14N 1Q coherences requires an accurate adjustment of the magic angle with an accuracy better than 0.002 and fluctuations of the MAS frequency smaller than a few hertz to refocus the first-order quadrupolar interaction. The indirect detection of 14N 2Q coherences is less demanding in terms of accuracy and stability of the MAS but is often less efficient.260–263 Coherence transfers have

Fig. 24 2D 17O{1H} DNP-enhanced PRESTO-II-QCPMG spectrum of isotopically unmodified mesoporous silica nanoparticles with pore diameter of 3.4 nm dried in vacuo at 25  C and impregnated with 16 mM TEKPol solution in TCE. This spectrum was acquired at B0 ¼ 9.4 T with nR ¼ 12.5 kHz. FSLG homonuclear decoupling was applied to the protons during the t1 period to improve the spectral resolution of the 1H dimension. Figure adapted from Ref. Perras, F. A.; Chaudhary, U.; Slowing, I. I.; Pruski, M. Probing Surface Hydrogen Bonding and Dynamics by Natural Abundance, Multidimensional, 17O DNP-NMR Spectroscopy. J. Phys. Chem. C 2016, 120 (21), 11535–11544. doi: 10.1021/acs.jpcc.6b02579. Copyright, 2016, American Chemical Society.

Advances in the characterization of inorganic solids using NMR correlation experiments

559

been mediated by first residual dipolar splitting,1,2,259 which is the sum of the J-coupling and the second-order quadrupole-dipole cross term. Nevertheless, it has been shown that more efficient coherence transfers can be achieved by reintroducing Se14N dipolar couplings through the application of heteronuclear recoupling on S channel during the defocusing and refocusing delays.260,264,265 When S ¼ 1H, the SR412 recoupling built from single 180 pulse is generally used.266 Furthermore, the through-space HSQC sequence has also been employed for the indirect detection of 14N coherences via protons but is less efficient than D-HMQC.267 An additional challenge for these experiments is the excitation of 14N coherences using rf fields with amplitude of few tens of kilohertz, which is two orders of magnitude lower than the first-order quadrupolar interaction. Various schemes have been proposed, but sideband selective long pulses combine good efficiency, high robustness and easy set up.263 The indirect detection via protons of 14 N 1Q coherence using the D-HMQC sequence has notably been employed to investigate host-guest interactions in MOFs268 as well as the structure of layered aluminophosphate containing amine structure directing agents269 (see Fig. 25a). It has also been shown that the resolution along the 14N dimension can be improved by applying homonuclear decoupling schemes on 1H channel during t1 period.270 As mentioned in the Section 9.19.3.2.1, a limitation of the D-HMQC sequence is the t1-noise produced by the random fluctuation of MAS frequency, which prevents the correct refocusing of 1H CSA and results in random signal amplitude modulation. In the case of the indirect detection of 14N nuclei, this issue cannot be circumvented by the use of TONE D-HMQC sequence, since this scheme includes 180 pulses, which are difficult to achieve for spin-1 nuclei. An alternative consists in reintroducing the 1He14N dipolar interactions by applying two identical long pulses, similar to those used in transfer of population in double resonance (TRAPDOR),271,272 during the defocusing and refocusing delays on 14N channel instead of 1H channel.273–276 These pulses do not reintroduce the 1H CSA, which limits the t1-noise. We have recently shown that this combination of TRAPDOR and HMQC schemes, called T-HMQC, can allow the indirect detection of either 14N 1Q or 2Q coherences with similar efficiency.220 Furthermore, the 2Q variant benefits from slightly higher resolution. Nevertheless, to the best of our knowledge, T-HMQC experiments have so far only been applied for the indirect detection of 14N nuclei in organic solids, but not yet for inorganic or hybrid solids. The D-HMQC experiment has also been applied to correlate the signals of spin-1/2 and half-integer quadrupolar nuclei in solids46,235,244,277 since depending on the correlated isotopes and the sample, the S / I / S consecutive transfers can be more sensitive than the S / I single transfer. Table 6 lists pairs of spin-1/2 and half-integer quadrupolar nuclei, which have been correlated using the D-HMQC sequence. In that case, the recoupling scheme is applied to the spin-1/2 isotope to minimize the number of pulses applied to quadrupolar nuclei and the associated losses. The pulses applied to the quadrupolar isotope are selective of the CT. It is often preferable to detect indirectly the spin-1/2 nuclei via the quadrupolar isotope since the longitudinal relaxation of quadrupolar nuclei is often faster and the application of the recoupling on the indirect channel limits the t1-noise. The recoupling employed in the D-HMQC sequence reintroduces the longitudinal two-spin order term (SzIz) of the heteronuclear dipolar interaction. Hence, the D-HMQC sequence is not affected by dipolar truncation and CSA interference.277 Furthermore, it has been shown that the D-HMQC sequence is more efficient than the D-HSQC variant.278 When the spin-1/2 isotope is not subject to large homonuclear dipolar interactions, the heteronuclear dipolar couplings can be reintroduced by the recoupling scheme with simultaneous amplitude and frequency modulations equal to the MAS frequency (SFAM-1)289 (see Fig. 25b). This recoupling reintroduces the |m| ¼ 1 space component of the heteronuclear dipolar interaction and hence, results in fast coherence transfer.277,290 Furthermore, because of the amplitude and frequency modulations, it is more robust to offset, CSA and rf field inhomogeneity than the REDOR and R3 schemes. At low MAS frequencies, nR  15 kHz, the symmetry-based recoupling built from adiabatic tanh/tan (tt) pulses, such as R21 1 (tt), benefits from higher robustness than SFAM-1 and has been applied to correlate quadrupolar nuclei with spin-1/2 nuclei subject to large CSA, such as 207Pb.281 When the spy isotope is subject to large homonuclear dipolar interactions, like 1H, a recoupling reintroducing the |m| ¼ 2 space component of the heteronuclear dipolar interaction, such as SR421, must be employed since it eliminates the contribution of homonuclear dipolar interactions to the first-order average Hamiltonian.222,277 Furthermore, the resolution along the indirect dimension of proton-detected D-HMQC experiment can be improved by applying homonuclear decoupling schemes on 1H channel during t1 period.278 The D-HMQC sequence allows the indirect detection of half-integer quadrupolar nuclei via protons, which can enhance the sensitivity, notably at high MAS frequencies, nR  40 kHz.236 Nevertheless, this experiment exhibits t1-noise, as already mentioned in Section 9.19.3.2.1. When the indirectly detected isotope is a half-integer quadrupolar nucleus, the TONE DHMQC sequence, shown in Fig. 20b, can be employed by applying CT-selective 180 pulses during the defocusing and refocusing delays.226 This technique has been used for indirect detection via protons of 27Al and 25Mg quadrupolar nuclei (see Fig. 25c). For I ¼ 3/2, an alternative consists in the use of the T-HMQC scheme, which has been recently applied for the indirect detection via protons of 35Cl 1Q, 2Q and 3Q coherences.220,291 Nevertheless, to the best of your knowledge, it has not yet been employed for inorganic or hybrid materials. 9.19.4.2.2.2 With high-resolution As for through-bond HETCOR experiments, high-resolution versions of through-space HETCOR sequence between spin-1/2 and half-integer quadrupolar isotopes have been developed. These high-resolution spectra have been first acquired using sequences deriving from 3Q-J-RINEPT scheme, in which the J-RINEPT block is substituted by CPMAS,20,292 D-RINEPT245 or PRESTO293 transfer. As explained above, the D-RINEPT and PRESTO transfers are more robust than CPMAS. Furthermore, the sensitivity of these experiments is enhanced using soft pulse added mixing (SPAM), which increases the efficiency of the reconversion of 3Q coherences into 1Q ones of the quadrupolar isotope.184,293 The sensitivity of these high-resolution HETCOR experiments can be further improved by a factor of at least 2 by substituting the 3QMAS block by a satellite transition MAS (STMAS) scheme, which correlates

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Advances in the characterization of inorganic solids using NMR correlation experiments

Fig. 25 (a) 2D 1H{14N} D-HMQC-SR412 spectrum of layered aluminophosphate containing amine structure directing agents acquired at B0 ¼ 18.8 T with nR ¼ 62.5 kHz. (b) 2D 11B{29Si} D-HMQC-SFAM-1 spectrum of boron nitride supported on dendritic fibrous silica nanoparticles acquired at B0 ¼ 18.8 T with nR ¼ 14.286 kHz. (c) 2D 1H{25Mg} TONE D-HMQC-SR412 spectrum of MgeAl double layered hydroxides acquired at B0 ¼ 9.4 T with nR ¼ 60 kHz. (a) Figure adapted from Ref. Bouchevreau, B.; Martineau, C.; Mellot-Draznieks, C.; Tuel, A.; Suchomel, M. R.; Trébosc, J.; Lafon, O.;

Advances in the characterization of inorganic solids using NMR correlation experiments Table 6

561

List of the pairs of spin-1/2 and half-integer quadrupolar isotopes, for which their signals have been correlated using the D-HMQC sequence in inorganic or hybrid materials.

S

I

Sequence

Sample

References

1

H H 1 H 1 H

14

1

23

1

43

1

71

D-HMQC- SR421 D-HMQC- SR421 TONE D-HMQC D-HMQC-R3 TONE D-HMQC D-HMQC-R3 D-HMQC- SR421 D-HMQC- SR421 D-HMQC- SR421 D-HMQC-SFAM-1 D-HMQC- R21 1 (tt) D-HMQC-SFAM-1 D-HMQC-SFAM-1 D-HMQC- SR421 D-HMQC- SR421 D-HMQC- SR421 D-HMQC-R3 DNPþ D-HMQC- SR421 D-HMQC- SR421 D-HMQC-SFAM-1 D-HMQC- SR421 D-HMQC-SFAM-1 D-HMQC-SFAM-1 D-HMQC-R3

Layered aluminophosphate NaH2PO4 Layered double hydroxide Crystalline aluminophosphate AlPO4-14 Layered double hydroxide Hydroxyapatite Gallium complex B2O3/BN supported on silica Borosilicate glass Borophosphate glass Crystalline lead borate Alkylaluminium Alkylaluminium Silica-supported catalysts Zeolites Crystalline sodium phosphate Crystalline aluminophosphate Silica and silica alumina g-Alumina Alkylaluminium Montmorillonite clay Aluminophosphate glass Vanadophosphate glass Gallium-doped calcium phosphate ceramics

269 278 226 235 226 279 236 280 46 244 281 171 171 282 283 284 235 285 286 171 287 235 244 288

H H 11 B 11 B 11 B 11 B 13 C 13 C 17 O 17 O 23 Na 23 Na 29 Si 27 Al 27 Al 27 Al 27 Al 51 V 71 Ga

N Na 25 Mg 27 Al Ca Ga 1 H 29 Si 31 P 207 Pb 7 Li 27 Al 1 H 29 Si 29 Si 31 P 17 O 1 H 13 C 29 Si 31 P 31 P 31 P

the satellite transition and the CT to remove the second-order quadrupolar broadening.294,295 Nevertheless, this STMAS version requires the adjustment of the magic angle with an accuracy of 0.002 and a very stable MAS frequency. Therefore, its implementation is usually more difficult than that of 3QMAS version. These sequences have been employed to correlate the high-resolution spectra of half-integer quadrupolar nuclei, such as 23Na and 27Al, with the spectra of spin-1/2 isotopes, such as 1H and 31P (see Fig. 26). Note also that in the case of spin I ¼ 3/2, STMAS technique can also be combined with D-HMQC scheme.296

9.19.4.2.3

Between two half-integer quadrupolar isotopes

Proximities between distinct half-integer quadrupolar isotopes, such as 11B and 27Al, have been probed using CP-HETCOR using either continuous wave (CW) irradiation18,297 or train of rotor-synchronized pulses.298 However, the spin-lock and the CPMAS transfer lack robustness in the case of quadrupolar nuclei. This issue has been circumvented by the use of D-HMQC and D-RINEPT sequences.299,300 For these sequences, the highest robustness has been achieved using synchronous phase inversion R3 (SPI-R3) scheme, which corresponds to the C221 symmetry.299 Furthermore, we have shown that this recoupling scheme must be applied to the dephaser isotope with magnetization parallel to B0 field to minimize the losses during the transfer.300

9.19.5

Applications

In this section, we review how correlation experiments have been employed for the characterization of different classes of materials: microporous materials, heterogeneous catalysts, minerals, biomaterials and glasses.

=

Amoureux, J.-P.; Taulelle, F. High-Resolution Structural Characterization of Two Layered Aluminophosphates by Synchrotron Powder Diffraction and NMR Crystallographies. Chem. Mater. 2013, 25, 2227–2242. Copyright, 2013, American Chemical Society. (B) Figure adapted from Ref. Belgamwar, R.; Rankin, A. G. M.; Maity, A.; Mishra, A. K.; Gómez, J. S.; Trébosc, J.; Vinod, C. P.; Lafon, O.; Polshettiwar, V. Boron Nitride and Oxide Supported on Dendritic Fibrous Nanosilica for Catalytic Oxidative Dehydrogenation of Propane. ACS Sustainable Chem. Eng. 2020, 8 (43): 16124–16135. doi: 10.1021/ acssuschemeng.0c04148. Copyright, 2020, American Chemical Society. (c) Figure adapted from Ref. Venkatesh, A.; Luan, X.; Perras, F. A.; Hung, I.; Huang, W.; Rossini, A. J. T1-Noise Eliminated Dipolar Heteronuclear Multiple-Quantum Coherence Solid-State NMR Spectroscopy. Phys. Chem. Chem. Phys. 2020, 22 (36), 20815–20828. doi: 10.1039/D0CP03511D. Copyright, 2020, Royal Society of Chemistry.

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Fig. 26 Comparison of 2D 31P{27Al} (a) D-RINEPT and (b) 3Q-D-RINEPT spectra of layered aluminophosphate acquired at B0 ¼ 18.8 T with nR ¼ 22.222 kHz. Figure reprinted from Ref. Martineau, C.; Bouchevreau, B.; Taulelle, F.; Trébosc, J.; Lafon, O.; Amoureux, J.-P. High-Resolution through-Space Correlations between Spin-1/2 and Half-Integer Quadrupolar Nuclei Using the MQ-D-R-INEPT NMR Experiment. Phys. Chem. Chem. Phys. 2012, 14, 7112–7119. doi: 10.1039/c2cp40344g. Copyright, 2012, Royal Society of Chemistry.

9.19.5.1

Microporous materials

Correlation experiments have provided unique insights into the structure of microporous materials (with pore diameters 1000  C), leading to an amorphous structure that exhibits a similar short-range (< 0.3 nm) structure as that encountered in a crystalline phase of comparable chemical composition. Yet, the rapid melt cooling effectively yields a “frozen melt” and prevents the structure from reaching equilibrium and developing a long-range order/periodicity. The glass structure is disordered at all length scales, although the short-range disorder is mainly limited to larger spreads in bond lengths/angles than its crystalline counterpart. Current structural theories/models for network glasses constitute extensions of the archetypal continuous random network (CRN) model of Zachariasen and Warren,1–3 where the glass is viewed as a polymeric network of FO4 tetrahedra that are interlinked randomly by corner-sharing of their O atoms. Although tetrahedral coordination is most common for the F atoms in oxidebased glasses, some network formers exist in larger FOp polyhedra (such as Al and Ge), where the F atom is symmetrically surrounded by p O atoms located at the corners of the polyhedron. However, it has been known for several decades that for multi-component glasses, the FOp interlinking is not fully random, but merely subject to preferences in, for instance, the types of F–O–F0 linkages encountered among the various coexisting network formers; such bonding preferences introduce some structural order over a sub-nanometer scale (roughly across 0.3–0.7 nm), which is henceforth referred to as the medium-range structure. The amorphous nature and absence of long-range order of glasses complicate their structural characterization by standard diffraction or scattering techniques, while the structure of most inorganic network glasses normally alters by high-dosage electron irradiation, thereby precluding application of high-resolution transmission electron microscopy to gain atomic-scale structural insight. Consequently, most of our understanding concerns the short-range glass structure, as deduced from information gathered by spectroscopic methods, notably infrared (IR), Raman, X-ray absorption (XAS), and solid-state NMR.4–6 NMR probes the structure from the local viewpoint of the nuclei in the glass, which along with the low energy of the radio-waves utilized in NMR spectroscopy renders the technique both noninvasive and nuclide-specific, while offering an exceptionally high degree of experimental control (relative to any other spectroscopy) for selectively studying various targeted structural features of a glass. Moreover, solid-state NMR has not only proved immensely useful for probing the short-range glass structure but also offers a plethora of options for gaining quantitative insight into its medium-range organization. More than 30 elements of The Periodic Table are well suited for NMR studies. Solid-state NMR investigations of both glasses and structurally ordered network materials often involve the 17O, 27Al, 11B, 31P, and 29Si nuclei as structural probes of the network organization (discussed in Sections 9.20.9–9.20.13), while information about the local environments of several “network modifiers” (see Section 9.20.2) is readily available for most alkali metals, such as the cations of 6Li/7Li,7–20 23Na,21–32 87Rb,9 and 133Cs.9,33,34 However, for reasons explained in Sections 9.20.4, 9.20.5, and 9.20.7, most of the other metal cations are (much) more difficult to exploit as structural probes, although a few NMR studies have been reported for most of the alkaline-earth metals (25Mg35–40; 43 Ca41,42; 87Sr43) along with some transition metals, such as 67Zn44 and rare-earth metals (45Sc45–50 and 89Y48,51–53). This paper assumes no prior knowledge from the reader of either topic of “glass structure” or “magic-angle spinning (MAS) NMR”, which are introduced in Sections 9.20.2, 9.20.3 and 9.20.4, respectively. As will become evident from the remaining text, NMR studies of glasses may benefit enormously by also considering the somewhat more “problematic” group of halfinteger spin quadrupolar nuclei (introduced in Section 9.20.5), to which the important 17O, 27Al, and 11B nuclear species belong, along with the nuclides of nearly all metal cations. Since our aim is to combine breadth and depth, we provide an ample referencing to both the early and the most recent literature, along with some details that may be useful also to more experienced solid-state NMR practitioners in the scope of glass structure characterizations. For instance, we provide a detailed review on chemical-shift/ structure relationships in Section 9.20.6. Section 9.20.7 gives a brief overview of the complications for MAS NMR applications to amorphous materials (whose NMR observables are subject to distributions), as well as the accompanying opportunities for gaining structural insight. Then after an introduction to high-resolution NMR techniques for quadrupolar nuclei (Section 9.20.8), the remaining of the text is devoted to discussing various NMR applications for characterizing glass structures over both the short-range (Sections 9.20.9–9.20.14) and medium-range (Sections 9.20.15–9.20.17) scales.

9.20.2

Introduction to glass structure

9.20.2.1

Basic building blocks

The most common glass-network formers are B3 þ, Al3 þ, Si4 þ, and P5þ. The polymeric network of interlinked FOp units in an oxidebased glass structure involves dominantly covalent bonds, whose degree of “ionic character” depends on the electronegativity of F. Phosphorus is exclusively present in tetrahedral coordination (PO4) in glasses, as may be verified from Fig. 1A that depicts a network fragment from a borophosphosilicate glass. Although SiO4 groups also prevail in (amorphous) silicates (Fig. 1A) and higher Si coordinations are negligible in glasses prepared at ambient pressure,54,55 significant fractions of SiO5 and SiO6 polyhedra may occur in glasses that are formed at very high pressure (T8 GPa)56–59 or in P-rich phosphosilicate glass compositions, where the higher propensity for P to remain as PO4 introduces Si[5] and/or Si[6] species.60–64 Here and onwards, the coordination number ZE of a species E with respect to O is denoted by a superscript (E[p]), whereas nE denotes the stoichiometric amount of E. Whenever not required, we omit specifying the coordination numbers of P and Si due to the vast dominance of P[4] and Si[4]. Moreover, while AlO4 groups are most common in Al-bearing glasses, higher-coordination Al[5] and Al[6] species (i.e., AlO5 and AlO6 groups) occur frequently in (for instance) aluminophosphate65–71 and rare-earth (RE) bearing aluminosilicate47,72–78 glasses, as discussed further in Section 9.20.11. Also B tends to assume tetrahedral coordination (B[4]; BO4), but the small B3þ cation is

586

Solid-state nmr of glasses

(B)

(A)

BO NBO Si B [3] B [4] P(QP0 ) P(QP1 )

Fig. 1 (A) Network fragment from a borophosphosilicate glass of composition 24Na2O–23CaO–15B2O3–34SiO2–4P2O5, only displaying the BO/NBO and the network-forming (Si, B, P) atoms. (B) Structural motif around a NaO5 polyhedron, indicating its coordination to four BO and two NBO species and their respective bonds to Si and P. The structure fragment in (A) is reproduced from Yu, Y.; Stevensson, B.; Edén, M. Medium-Range Structural Organization of Phosphorus-Bearing Borosilicate Glasses Revealed by Advanced Solid-State NMR Experiments and MD Simulations: Consequences of B/Si Substitutions. J. Phys. Chem. B 2017, 121, 9737–9752, with permission from The American Chemical Society. Copyright the American Chemical Society (2017). The structure fragment in (B) is reproduced from Edén, M., In: Molecular Dynamics Simulations of Glass Structure, in Encyclopedia of Materials: Technical Ceramics and Glasses, Pomeroy.M.; Eds. Elsevier, 2021, with permission from Elsevier.

frequently found as planar BO3 groups (B[3]) in glasses (Fig. 1A), whereas the vitreous B2O3 structure is built entirely from interconnected BO3 groups, as discussed further in Section 9.20.12. An O atom connecting either two identical (F–O–F) or distinct (F–O–F0 ) network formers is referred to as a “bridging oxygen” (BO) atom (O[2] coordination); see Fig. 1A. Glasses prepared solely from oxides of one (e.g., SiO2 or B2O3), two (e.g., Al2O3–SiO2 or B2O3–P2O5) or multiple network formers are formally devoid of ionic charges. Both SiO2 and B2O3 readily enter a vitreous (“glassy”) state by rapid melt cooling, whereas Al2O3 does not, nor do several combinations of the {B, Al, Si, P} glass formers over large composition ranges. However, the glass-forming capacity normally improves by including oxides or carbonates of at least one glass-network modifier cation Mz þ which constitutes the least electronegative species of the glass, and is typically an alkali (Mþ) or alkaline-earth (M2 þ) metal ion. The introduction of an Mz þ cation converts z BO atoms into z non-bridging oxygen (NBO) anions (O[1]), according to F – O½2 – F 0 þ MO/F – O½1 /M2þ /O½1 – F 0 zþ

(1) 

Here “/” indicates an electrostatic (“ionic”) interaction between the M cation and the NBO (O ) species. Note, however, that while the network modifiers prefer coordinating the negatively charged NBO anions, their coordination shells also involve bonds to BO atoms, as may be verified from Fig. 1B. The trivalent charge of the B3þ and Al3þ ions implies that one negative unit charge is delocalized over all BO atoms of the [AlO4/2] and [BO4/2] tetrahedra (in contrast to the formally charge-neutral SiO4/2 group), where the 4/2 subscript emphasizes that each O atom at the tetrahedron is bridging. Hence, while we for simplicity refer to the Mz þ cations as “glass-network modifiers,” they also act as charge compensators of the AlO4 and BO4 groups in Al and B bearing glasses, where for instance an [AlO4/  þ 2] /M moiety is formally uncharged. Since the Mz þ cations are larger than their network former counterparts, they exhibit higher coordination numbers with respect to O, where ZM  5–7 are most common, such as for the similar-sized Naþ and Ca2þ cations; see Fig. 1B. However, the cations of heavier elements (notably those of periods 6 and 7 of The Periodic Table) generally prefer higher coordination numbers of six to nine, whereas the small Mg2 þ ion may even participate in the glass network as MgO4 groups (see Section 9.20.14.2). The cation field-strength (CFS) of the glass network modifier has profound bearings on both the short- and medium-range glassstructure orderingdand thereby also the NMR spectral resolution from several nuclei. For a cation Mz þ with charge z and radius r, the CFS is given by CFS ¼ z=r 2

(2)

Hence, large CFS values are encountered for small and highly charged cations. Sometimes the closely related cation potential (z/ r) is encountered in the literature. The radius r depends on the coordination number, where comprehensive lists of ionic radii are provided by Shannon.79 Notably, the Mz þ ions normally feature a distribution of {M[p]} coordination numbers (whose details are normally unknown and very difficult to estimate experimentally), and it is customary to compare CFS values for M[6] coordinations.

9.20.2.2

F–O–F0 bonding “rules”

To minimize the accumulation of local negative charges in the glass network, the following structural groups are considered “forbidden” in conventional models/theories of glasses incorporating Al5,10,80–82 or/and B83–87: (A) Al[4]–O–Al[4], B[4]–O–B[4],

Solid-state nmr of glasses

587

and AI[4]–O–B[4] linkages, i.e., directly interlinked pairs of AlO4 and/or BO4 tetrahedra. (B) Al[4]–NBO and B[4]–NBO bonds. The postulated absence of Al[4]–O–Al[4] linkages is known as the “Loewenstein Al avoidance rule” (which was initially proposed by Loewenstein on the basis of steric rather than electrostatic reasons88), which holds strictly for crystalline aluminosilicate phases, such as zeolites and minerals.5,89–91 The “B[4] avoidance” analog was proposed even earlier by Abe,83 who argued for the absence of [BO4]–[BO4]– motifs in borosilicate glasses by indeed invoking charge-repulsion arguments. In practice, neither “rule” (A) nor (B) holds strictly in glasses, and both relax significantly in the presence of high-CFS modifiers in the structure, as discussed further in Section 9.20.15.4. By analogous charge-based principles, both B3þ and Al3þ exhibit strong preferences for forming Al–O–P and B–O–P bonds with the highly charged P5þ cation; such P–O–Al/B motifs dominate the F–O–F0 bridges in borophosphate92–104 and aluminophosphate65– 69,71,105–108 glasses, and are strongly favored whenever P along with Al and/or B are present together with Si as network formers.62,109–111 Most F–O–F0 bonding preferences may be explained from Pauling bond strengths (bond valence sums),112–114 as for instance discussed in the contexts of aluminoborate and aluminophosphate glasses by Brow, Kirkpatrick and co-workers65,66,115 and more recently applied to Pb/Ga bearing glasses by Hannon.116

9.20.2.3

NBO distribution among network formers and the Qn notation

The affinity for coordinating NBO ions among the {Al, B, P, Si} network formers roughly decreases concurrently with the electronegativity117 of the element: P[B½3 TSi[Al½4 > Al½5 TAl½6

(3)

This trend is compiled from literature data (as reviewed in Ref. 6,82,118) and may partially be rationalized by the optical basicity concept.119 The following is noteworthy: (i) besides the well-known strong P–NBO affinity and the reluctance of Al[4]/B[4] to form bonds with NBO, the relative propensities for F–NBO bond formation of Eq. (3) only serves as rough rules of thumb and are in general difficult to quantify experimentally. (ii) The structural role of the higher-coordination Al[p] species is a source of much confusion in the glass community; the Al[5] and Al[6] species are often referred to as “excess Al” and even classified as “network modifiers,”120,121 whereas we (and others) merely consider them as integral parts of the glass network, i.e., as network formers.82,122– 124 (iii) The literature is extremely sparse on discussions on the relative propensities for NBO accommodation at the AlO5 and AlO6 polyhedra relative to AlO4 and SiO4, where the decreasing degree of Al[p]–NBO contacts for increasing coordination number p (Eq. 3) is predicted from molecular dynamics (MD) simulations of aluminosilicate glasses.77,125–127 (iv) The propensity for B[4]– NBO bond formation is expected to be similar as for Al[4], while moreover MD simulations predict B[4]–NBO bond formation in borosilicate glasses,128–133 but a direct experimental proof of their existence remains to be seen. For the tetrahedrally coordinated Si and P network formers, we will employ the frequently adopted “Qn” nomenclature,5 where “Q” stands for “quaternary” to stress the fourfold coordination. Consequently, the symbols QSin and QPn denote an SiO4 and PO4 tetrahedron with n BO atoms (and thereby 4–n NBO ions), respectively.5,6,134 Note that while Al[4] and B[4] species would in direct analogy be denoted QAln and QBn, respectively, the overall very minor Al[4]–NBO and B[4]–NBO bond formation (vide supra) along with the current limitations of resolving the various QnAl (or QnB) resonances renders that notation less useful. As discussed in Sections 9.20.9 and 9.20.10, the fractional populations {x0Si, x1Si, x2Si, x3Si, x4Si} and {x0P, x1P, x2P, x3P} of the corresponding {Q0Si, Q1Si, Q2Si, Q3Si, Q4Si} and {Q0P, Q1P, Q2P, Q3P} groups that may potentially co-exist in Si and P bearing glasses, respectively, may (sometimes) be determined by 29Si and 31P NMR. Note that the Qn#3 restriction stems from the presence of a formally nonP bridging P]O bond at the PO4 moiety. Yet, it is relieved in glasses with additional network formers (such as Al and B), in which Q4P groups are abundant, then typically forming four bonds to Al and/or B65,67,68,97,98,100 (see Section 9.20.2.4). The {xnSi} and {xnP} sets in a glass directly reflect its NBO content. As an aggregate indicator of the average polymerization degree of the silicate and phosphate tetrahedra, we employ the corresponding silicate network connectivity and the phosphate network connectivity concepts,134 each representing the average number of BO atoms per SiO4 and PO4 group, respectively, and given by the following weighted averages: Si

N BO h

4 X

nxnSi

(4)

nxnP

(5)

n¼0

P

N BO h

3 X n¼0

P with the fractional populations obeying the normalization nxEn ¼ 1. An alternative nomenclature for specifying the topology and network connectivity of silicates and phosphates employs the prefixes “ortho”, “pyro” and “meta”, which refer to stoichiometries giving a structure solely built from Q0Si/Q0P, Q1Si/Q1P, and Q2Si/Q2P   Si species, respectively. For example, a pyrosilicate crystal structure consists of Q1SiQ1Si pairs N BO ¼ n ¼ 1 , whereas a metaphos  P phate network involves rings or chains of interconnected Q2P groups N BO ¼ n ¼ 2 . Moreover, silicate structures comprising solely Q3Si and Q4Si groups are referred to as “phyllosilicates” and “tectosilicates,” respectively. Note, however, that a disordered glass

588

Solid-state nmr of glasses

network normally comprises several coexisting Qn groups (Section 9.20.7), meaning that the ortho/pyro/meta notation is not to be taken literally. Hence, while the phosphate speciation of a pyrophosphate glass is normally dominated by QP1 tetrahedra, variable amounts of QP0 and QP2 moieties are also present. This is why the silicate/phosphate network connectivity concept becomes useful,
P < since it conveys the average n value over the {QnSi} or {QnPi} speciation. Phosphate glasses whose compositions conform to N
P  3 are also termed “polyphosphate” and “ultraphosphate” glasses, respectively. 2:5 and 2:5  N BO

9.20.2.4

BO

Extended Qn notation for second coordination sphere

As discussed further in Section 9.20.6, the NMR observables are sensitive not only to the BO/NBO constellation in the first coordination sphere of F, but also depend on the nature of the neighboring network forming atoms/ions F0 in the second coordination shell across an F–O–F0 linkage. To incorporate such effects, the notation QnF(mF0 ) will be employed for a F(OF0 )m(OF)n  m(O)4  n moiety, where m # n. We and others have employed such a QSin(mAl) notation for SiO4 groups with m Si–O–Al bonds and hence n– m Si–O–Si bonds in aluminosilicate glasses.5,6,10,80,82,134,135 In contrast, a distinctly different notation for the PO4 tetrahedra prevails in the literature on aluminophosphate67,68,71,106–108,136 p and borophosphate97–101,104 glasses. Here, the notation Qp(mF) [or QmF ] is employed, which does not convey the condensation degree of the tetrahedron (i.e., the number n of BO atoms), but merely specifies a P(OF)m(OP)p moiety with F ¼ {Al, B}. This notation is in our opinion unfortunate, because it obscures the (even more important) information about the net number of BO atoms at the PO4 group, which is given by n ¼ m þ p. To exacerbate the confusion, the literature often employs the Qp(mF) notation along with the “traditional Qn” counterpart, thereby intermixing two nomenclatures with very different meanings of their superscripts. In the following, we consistently adopt the QPn(mB) and QPn(mAl) notation defined above, which we recommend using for improved claritydor alternatively, the even more explicit QPn(mAl, pP) option (with n ¼ m þ p) that directly conveys the net condensation degree, as well as both numbers m and p of P–O–Al and P–O–P bonds, respectively.

9.20.3

Principles of NMR

9.20.3.1

Nuclear spin–The prerequisite for NMR

NMR exploits that many nuclides of the Periodic Table exhibit “spin,” which is an intrinsic property of the nucleus (as well as of all electrons) that renders it magnetic and thereby interacting with any magnetic fields in its surroundings. Up to Section 9.20.5, we assume NMR on “spin-1/2” nuclei, where 1H, 13C, and 15N are heavily exploited in biomolecular NMR, whereas 29Si and 31P have proven very useful for structural characterizations of the wide groups of crystalline and amorphous silicate- and phosphate-based phases, respectively. An NMR-active nuclide “S” with a spin quantum number S > 1/2 is called a quadrupolar nucleus: while integer spins (S ¼ 1, 2, 3, .) are rare (e.g., 2H, 14N), quadrupolar nuclei with half-integer spin, S ¼ {3/2, 5/2, 7/2, 9/2}, account for z 70% of NMR-active nuclides and represent a majority of those relevant for NMR studies of glasses, encompassing 11B, 27Al, and 23Na along with the isotopes of nearly all other metals, as well as the only NMR-active isotope of O (17O).

9.20.3.2

Zeeman interaction

The sample to be examined by NMR, which for solid phases is normally a powder, is placed inside a super-conducting magnet, whose magnetic-field magnitude (B0) is specified in Tesla. Typical field strengths employed for solid-state NMR nowadays span 9.4–18.8 T. The Zeeman interaction is the coupling between the magnetic moment of the nuclear spin and the external magnetic field. It is associated with the Larmor (“resonance”) frequency (n0),137,138 which is given by n0 ¼ 

gB0 ½in Hz 2p

(6)

where the magnetogyric ratio (g) is a nuclide-specific constant in units of rad s 1 T 1. The magnitude of g tells “how magnetic the nucleus is” and strongly affects the NMR-signal strength (see Section 9.20.4.3). From Eq. (6) follows that the Larmor frequency scales directly with the magnetic field strength. Values of g and n0 at 14.1 T are listed in Tables 1 and 2 for the most commonly exploited spin-1/2 and quadrupolar nuclides for NMR characterizations of glasses. Most Larmor frequencies are in the  100 MHz range. Since the value of g is constant for a give nuclear type, the Zeeman interaction and its Larmor frequency are the same for all nuclear spin sites of a given nuclide type in a sample, regardless of their spatial positions. Hence, while the Zeeman interaction is a prerequisite for NMR itself, it does not reveal any structural information. What renders NMR useful are all other “spin interactions,” each of which conveys a given type of information, such as the “chemical shift” that is sensitive to the electronic (“chemical”) environment of the nucleus, and the dipolar interactions that informs about interatomic distances, as reviewed below.

Solid-state nmr of glasses Table 1

589

Nuclear spin properties of spin-1/2 nuclides relevant for NMR on glassesa.

Nuclide

n.a. (%)

g (107 rad s 1 T 1)

n0 (14.1 T) (MHz)

Standard reference

RS/RH

1

99.99 1.07 0.37 100.00 4.68 100.00 100.00 51.84 48.16 22.10

26.7522 6.7283 2.7126 25.1815 5.3190 10.8394 1.3163 1.0889 1.2519 5.5805

600.3 151.0 60.9 565.1 119.4 243.2 29.5 24.4 28.1 125.2

TMS TMS NH4Cl(s)b CCl3F TMS H3PO4(aq)c Y(NO3)3 AgNO3 AgNO3 Pb(CH3)4

1.00 1.7  10 4 3.8  10 6 0.83 3.7  10 4 6.7  10 2 1.2  10 4 3.5  10 5 4.9  10 5 2.0  10 3

H C 15 N 19 F 29 Si 31 P 89 Y 107 Ag 109 Ag 207 Pb 13

Values of the natural abundance (n.a.) of each listed nucleus, along with its magnetogyric ratio and receptivity (RS) relative to that for 1H (RH). The “standard reference” defines d ¼ 0 of the chemical shift scale: note that some of the standards for solid-state NMR differ from the those recommended by the International Union of Pure and Applied Chemistry (IUPAC) for solution NMR.139 Unless stated otherwise, liquid standards are in their neat forms (such as TMS; tetramethylsilane) and all as-specified salts are dissolved in water at a 1.00 mol/L concentration. However, solid-state NMR often lacks well-defined and/or widely accepted chemical-shift standards and the footnotes below only constitutes a selection of suggestions/remarks from the literature. b Defines dN ¼ 0. Conversion to a shift scale relative to the primary standard (CH3NO2) is performed by subtracting the measured shift by 341.0 ppm; if 15NH(NO3)(s) is used as secondary standard, the conversion is made by subtracting 358.4 ppm.140 c 85 wt% H3PO4. a

Table 2

Nuclear spin properties of quadrupolar nuclides relevant for NMR on glassesa.

Nuclide

Spin

n.a. (%)

g (107 rad s 1 T 1)

n0 (14.1 T) (MHz)

Quadrupole moment (fm2)

Standard reference

RS/RH

2

1 1 3/2 3 3/2 1 5/2 3/2 5/2 5/2 3/2 3/2 7/2 7/2 7/2 3/2 9/2 3/2 9/2 7/2 7/2

0.01 7.59 92.41 19.90 80.10 99.63 0.04 100.00 10.00 100.00 0.76 93.26 0.14 100.00 99.75 39.89 7.73 27.83 7.00 100.00 99.91

4.1066 3.9372 10.3977 2.8747 8.5847 1.9338 3.6281 7.0808 1.6389 6.9763 2.0557 1.2501 1.8031 6.5088 7.0455 8.1812 0.9360 8.7864 1.1639 3.5333 3.8083

92.2 88.4 233.3 64.5 192.6 43.4 81.4 158.9 36.8 156.6 46.1 28.1 40.5 146.1 158.1 183.6 21.0 197.2 26.1 79.3 85.5

0.3 0.1 4.0 8.5 4.1 2.0 2.6 10.4 19.9 14.7 6.8 5.9 4.1 22.0 5.2 10.7 19.6 13.4 33.5 0.3 20.0

(CD3)4Si LiCl LiCl BF3$Et2Ob BF3$Et2Ob NH4Cl(s)c D2O 0.1 M NaCld MgCl2 Al(NO3)3 (NH4)2SO4 KCl CaCl2e Sc(NO3)3 VOCl3 Ga(NO3)3 (CH3)4Ge RbCl SrCl2 CsNO3 LaCl3

1.11  10 6 6.45  10 4 0.27 3.95  10 3 0.13 1.00  10 3 1.11  10 5 9.27  10 2 2.68  10 4 0.21 1.72  10 5 4.76  10 4 8.68  10 6 0.30 0.38 5.71  10 2 1.09  10 4 4.93  10 2 1.90  10 4 4.84  10 2 6.05  10 2

H Li 7 Li 10 B 11 B 14 N 17 O 23 Na 25 Mg 27 Al 33 S 29 K 43 Ca 45 Sc 51 V 71 Ga 73 Ge 87 Rb 87 Sr 133 Cs 139 La 6

a

Values of the spin quantum number (S) and natural abundance (n.a.) of each listed nucleus, along with its magnetogyric ratio and receptivity (RS) relative to that for 1H (RH). The “standard reference” defines d ¼ 0 of the (chemical) shift scale: note that some of the standards for solid-state NMR differ from the those recommended by the International Union of Pure and Applied Chemistry (IUPAC) for solution NMR.139 Unless stated otherwise, liquid standards are in their neat forms and all as-specified salts are dissolved in water at a 1.00 mol/L concentration. However, solid-state NMR lacks often lacks well-defined and/or widely accepted chemical-shift standards and the footnotes below only constitutes a selection of suggestions/remarks from the literature. b Defines dB ¼ 0. Some NMR spectra in the literature are referenced against H3BO3(aq); those shifts may be converted relative to the recommended primary standard by adding 19.6 ppm. c Defines dN ¼ 0. Conversion to a shift scale relative to the primary standard of neat CH3NO2(l) is performed by subtracting the measured shift by 342.4 ppm.141 d Defines dNa ¼ 0. 23Na shifts in the literature are often reported relative to NaCl(s) at 0 ppm; those shifts may be converted relative to the primary standard by adding 7.2 ppm.142 e The measured 43Ca shift depends strongly on the CaCl2 concentration, and the most reasonable compromise between a decent NMR-signal sensitivity and an accurate (chemical) shift is to use 1.00 M CaCl2(aq) to define dCa ¼ 0.143,144

590 9.20.3.3

Solid-state nmr of glasses Single-pulse NMR experiment

The so-called thermal equilibrium condition is the starting point of any NMR experiment. Then, the magnetic moments from all nuclear spins in the sample sum constructively to a microscopic “longitudinal magnetization vector” (Mz) that points along the external magnetic field direction (B0 ¼ B0ez), as depicted in Fig. 2A. However, the longitudinal magnetization is not directly detectable by conventional NMR. Consequently, any NMR experiment also involves a radio-frequency (rf) field, which constitutes a time-dependent magnetic field of (maximum) amplitude B1 (typically, B1  10 4 B0) that oscillates at a frequency (nrf) close to n0. Application of a short ( ms) but intense rf pulse rotates each magnetic moment of the spin ensemble, and thereby also their resulting magnetization vector. In the simplest NMR experiment, referred to as a “single-pulse” NMR experiment, the rf pulse is applied such that the magnetization vector is rotated by 90 around an axis perpendicular to B0 (Fig. 2A), which results in “transverse magnetization”, i.e., a magnetization vector along any direction in the xy plane, as shown in Fig. 2B. The Zeeman interaction now makes the transverse magnetization rotate around the B0 direction (i.e., the z-axis of the coordinate system) at a rate close to the Larmor frequency (Fig. 2C). The rotating magnetization vector induces a weak electric current in a coil placed around the sample inside the NMR “probehead” (which holds is the sample); this electric current constitutes the NMR signal; see Fig. 2D. In the NMR literature, the “rotating transverse magnetization” is more formally referred to as single-quantum coherence (1QC) associated with the two Zeeman states with magnetic quantum numbers m ¼ 1/2 and m ¼  1/2 of the spin-1/2 nucleus137,138; also see Section 9.20.5.1.

z

(A)

Mz

y x

rf pulse z

(B)

y x

Zeeman interaction z

(C)

y x (D)

90x

s(t)

Fig. 2 Illustration of the longitudinal magnetization vector (Mz), resulting from the sum of magnetic moments from a nuclear spin ensemble at thermal equilibrium, and aligned with the external magnetic field direction, B0 ¼ B0ez. During an applied rf pulse, the magnetization vector rotates around the x axis, schematically indicated by the red arrow in (A). (B) Result after a “90 pulse”: the magnetization vector now points along the ( y) direction, and thereby constituting “transverse magnetization.” Due to the Zeeman interaction, the transverse magnetization rotates around the z-axis at a rate given by the Larmor frequency, with a snapshot shown in (C). (D) A compact schematic illustration of a “single-pulse” NMR experiment, where the rectangle depicts the rf pulse, after which the oscillating (time-dependent) NMR signal is detected due to the rotational motion of the transverse magnetization vector.

Solid-state nmr of glasses

591

Fourier transformation (FT) of the NMR signal produces an NMR spectrum comprising one “peak” for each inequivalent nuclear site in the structure.137,138 The integrated NMR signal intensity of each detected peak/resonance, I0 (i.e., the “peak area”), is directly proportional to the number of nuclei in that chemical/crystallographic environment; hence, for a given well-crystalline sample, I0 relates directly to its crystallographic multiplicity. The single-pulse NMR experiment described above is the by far most utilized one for NMR investigations of the local structure of glasses. However, more advanced experimental NMR techniques may involve application of tens or hundreds of rf pulses before the NMR signal is detected. A nice feature of NMR is that even relatively complex rfpulse sequences may be visualized as a series of consecutive rotations of the magnetization vector, as illustrated for one rf pulse in Fig. 2. By knowing the rotation rate of the magnetization vector during the pulse, i.e., the spin nutation frequency (c.f. Eq. 6), n1 ¼ rgrB1 =ð2pÞ ½in Hz

(7)

and a careful selection of the rf-pulse duration (sp), the net rotation angle of the spin-ensemble magnetization vector due to the rf pulsedreferred to as the “flip angle” and given by bp ¼ 2pn1spd is under accurate control by the NMR experimentalist.137,138 bp may be specified in either degrees or radians, and relates to the integrated NMR-signal intensity, I(sp), according to     I sp ¼ I0 sin 2pn1 sp ¼ I0 sin bp (8) Note that the maximum intensity I0 results for bp ¼ np/2, where n is any odd integer. Moreover, the rotation axis around which the magnetization vector from the spin ensemble rotates is controlled by the rf phase parameter, fp, which may be selected arbitrarily within the range 0  # fp < 360 (0 # fp < 2p radians) to arrange a rotation around any direction/axis of the transverse plane; see Fig. 3. Because the outcome of a given rf pulse only depends on the {bp, fp} parameter-pair (within some caveats for MAS NMR), a compact description of a series a rf pulses (i.e., a “pulse sequence”) results by expressing each pulse according to (bp)f, or by specifying the rotation axis itself by the subscript, e.g., (bp)0 h (bp)x, as in Fig. 2D. We refer to Levitt138 for further details about rf pulses.

9.20.3.4

Chemical shifts and the NMR shift scale

As its name implies, the chemical shift reflects the “chemical” environment of a nuclear spin site in a structure thanks to its dependence on the electron configuration around the nucleus that reflects the bonds to nearby atoms and their identities, thereby serving as a “fingerprint” of a nuclear site in a given molecular/crystallographic site. Hence, the dependence on the local electronic environment alters the resonance frequency (nj) of a given nuclear spin site (j) in a structure:     nj ¼  gB0 1 þ dj ¼ n0 1 þ dj ½in Hz (9) where the chemical shift dj of site j is a dimensionless number in the order of 10 6–10 4, and is specified in “ppm” (e.g., a shift of 1.2$10 5 corresponds to 12 ppm). Notably, despite that the chemical shift is typically 104–105 times smaller than the Zeeman interaction, the tiny difference between nj and n0 is readily detected by NMR. The as-recorded NMR spectrum obtained by FT of the NMR time-domain signal is a set of amplitudes as function of frequency (in Hz). It follows from Eq. (9) that the chemical shift frequency scales directly with the external magnetic fielddin direct analogy with the Zeeman interaction, Eq. (6). To eliminate the frequency dependence on B0 in Eq. (9), a “shift scale” in ppm is arranged by feeding all frequency values (n) through the equation d¼

n  nref nref

(10)

y

-x

x

-y Fig. 3 Relationship between the value of the rf phase (fp) and the transverse plane axes (looking down the z axis). While the figure only maps rf phases with their corresponding x/y axes, the magnetization vector from the spin ensemble may be made to rotate around any arbitrary direction in the transverse plane by selecting the rf phase to the a value in the range 0  fp < 2p (for instance fp ¼ p/4 corresponds to the rotation axis right in-between the x and y directions).

592

Solid-state nmr of glasses

where nref is the resonance frequency of a selected “standard” (or “reference”) compound that defines d ¼ 0. By convention, the (chemical) shift scale is plotted with d increasing from right to left, implying that that a “shielded” nucleus exhibits a low(er) shift and its NMR peak appears to the right, whereas a “deshielded” nucleus features a high(er) chemical shift and the resonance appears to the left in the NMR spectrum. Note that the precise reference standard is selected for each nuclide type: for instance, 31P involves 85% H3PO4(aq), whereas tetramethylsilane (TMS) serves as standard reference for all of 1H, 13C, and 29Si. Tables 1 and 2 lists the precise standards used for the most commonly exploited nuclide types for solid-state NMR experiments on glasses. In such experiments, the value of nref is obtained by a separate single-pulse NMR experiment, while in NMR on solutions, the reference compound is normally dissolved together with the compound to be analyzed.

9.20.4

NMR on powders

NMR studies on glasses are performed exclusively with powders, where a typical sample volume comprises 106–108 of randomly oriented mm-sized particles. All NMR interactions have anisotropic components, meaning that their spectral responses depends on the precise orientation of the particle relative to the external magnetic field direction B0, where the orientational dependence is described by a second-rank tensor. For further details and gentle introductions to the anisotropy concept and its formal tensor description in NMR, see Refs. 138,145. We initially focus on the effects from the anisotropic chemical shift component. In an “isotropic solution,” i.e., a solution/liquid where all molecules undergo rapid and unrestricted rotational motions over a ns-to-ms timescale, only the orientational average over of the chemical-shift tensor/interaction is observed. This is called the isotropic chemical shift, djiso, and represents the average over the principal values {djxx, djyy, djzz} of the (second rank) chemical shift tensor138,145,146:  1 j j diso ¼ dxx þ djyy þ djzz (11) 3 The anisotropic features of the chemical shiftdas well as from all other NMR/spin interactionsdare very evident in solid-state NMR spectra of powders, as outlined below.

9.20.4.1

NMR on static powders

We now assume NMR on a mm-sized single crystal comprising one crystallographically unique spin-1/2 site. While there is a huge number of nuclear spins in that crystallite, they all produce an NMR peak at a given chemical shift. Hence, each such crystallite contributes with one narrow NMR peak to the NMR spectrumdas in solution NMRdbut with the crucial distinction that the precise resonance frequency from the crystallite is not simply given by the isotropic chemical shift, but also depends on the anisotropic partdreferred to as the chemical shift anisotropy (CSA), whose precise frequency value, naniso(U), depends on the orientation U of the crystallite relative to B0.138,145,146 Now because the various crystallites within a powder are randomly distributed, the NMR spectrum observed from the powder yields a broad peak, referred to as a “powder pattern,” because it constitutes the superposition of NMR responses from the huge number of crystallites in the powder; see Fig. 4. The “width” of the powder pattern reflects the CSA of the nuclear spin site j, which is given by138,145 j

j

daniso ¼ djzz  diso

(12)

while its “shape” (Fig. 4) is dictated by the asymmetry parameter (hCS), according to j

j

j

hCS ¼

j

dyy  dxx djzz

j  diso

j

; with 0  hCS  1

The principal values are identified by the convention138 140        j j   j   j  dzz  diso Pdjxx  diso Pdjyy  diso 

(13)

(14)

j and are experimentally accessible from the NMR powder pattern, as illustrated by Fig. 4. Note that the sign of daniso is for many j practical purposes irrelevant and that a low/high value of | daniso | implies a small/large anisotropy. j j As illustrated further in Section 9.20.9, the parameter-pair {daniso , hCS } reflects the deviation of the electronic cloud (around the nuclear site j) from a perfect tetrahedral, octahedral, cubic, or higher symmetry. In such (practically very rare) cases, the CSA vanishes j is observed (Eq. 11) in the NMR spectrum, just as from an isotropic solution. The identically, whereupon only the average value diso same scenario applies for all other “anisotropic” NMR interactions reviewed below, although we stress that such cases of truly symmetric electronic environments of the nuclear spins in network-based inorganic materials are in practice extremely rare. Note j j ¼ daniso n0) and is typically in the that, as for the isotropic chemical shift, the CSA in frequency units scales directly with B0 (naniso 103–104 Hz range. For a sample comprising several crystallographically inequivalent sites, the observed NMR spectrum from the powder typically reveals a complex lineshape of overlapping “powder patterns”, as illustrated for the 13C NMR spectrum recorded from a sample of

Solid-state nmr of glasses

593

solution

(A)

powder (B)

0

(C)

0.25

(D)

0.5

(E)

0.75

(F)

1.00

Fig. 4 Schematic NMR spectra from a sample comprising one unique nuclear site with an isotropic chemical shift diso, as observed either from (A) an isotropic solution or (B–F) a polycrystalline powder. The NMR responses from the powder are reflected by a broad “powder pattern,” whose singularities relate to the principal values [dxx, dyy, dzz} and obeying Eq. (14) indicated in (B–F). The NMR spectra of (B–E) only differ in their asindicated asymmetry parameter hCS, whose value reflects the lineshape.

glycine in Fig. 5A. While the spectral broadening from the CSA is normally a nuisance and significantly lowers the resolutiondthereby leading to assignment ambiguitiesdthe broad lineshape of the “powder spectrum” also reveals useful information about the symmetry of the local electronic environment of the spin sites, as discussed further in the contexts of 29Si (Section 9.20.9) and 31P (Section 9.20.10) NMR on glasses.

9.20.4.2

Magic-angle spinning

Although the CSA, and all other spin-interaction anisotropies reviewed below, may offer valuable structural information, for NMRpeak assignment purposes it is highly desirable to improve the NMR spectral resolution and sensitivity from powders to better discriminate between the responses from structurally distinct spin sites, thereby avoiding that each net NMR intensity is spread over several kHz (see Fig. 5A). Hence, to approach the scenario of NMR on solutions for which the anisotropic broadening is absent altogether, the MAS technique147–150 was introduced to emulate the (unrestricted) molecular rotations in an isotropic liquid and thereby averaging out the anisotropic interactions, such that only the orientation-independent isotropic chemical shift is observed. MAS involves a mechanical rotation around solely one axis, where the cylindrical sample holder (“rotor”) comprising the powder is rapidly rotated around its pffiffiffi long axis that subtends the magic angle, bm ¼ arctan 2 z54:74 , relative to the B0 direction/vector. The rotation rate is given by the MAS frequency, nr, whereas the rotor period (sr), sr ¼ n1 r ½in s

(15)

is the time taken for the sample/rotor to make one complete rotation. If the MAS rate exceeds the magnitude of the CSA in frequency units, r djanison0 r, only a narrow NMR centerband is observed at the j j , or niso in units of Hz, as shown in Fig. 5D. Besides the obvious resolution improvement in the MAS isotropic chemical shift, diso NMR spectrum relative to its counterpart from the static powder (Fig. 5), a very significant signal-sensitivity boost is observed from

594

Solid-state nmr of glasses

(A)

static

(B)

MAS 2.50 kHz

(C)

5.30 kHz

(D)

10.00 kHz

-20

-15

-10 13

-5

0

5

10

15

20

C frequency (kHz)

Fig. 5 13C MAS NMR spectra recorded from a powder of 13C enriched glycine, where the resonances from the 13COO and 12CH2 sites are assigned in (A). The NMR spectra were obtained either from (A) a static powder, or (B–D) under MAS conditions at the as-indicated spinning rates.

the concentration of all intensity into the narrow NMR centerband for each (crystallographically) unique spin site. For spinning j r, however, the MAS NMR spectrum reveals a spinning sideband (ssb) manifold (Fig. 5B–D), where the centerband rates nr < r naniso j (k ¼ 0) at the isotropic chemical shift frequency (nj (0) ¼ niso ) is flanked by sidebands appearing at frequencies nj (k) ¼ nj (0) þ knr 145,150 (k ¼  1,  2,  3, .), where the index k is called the sideband order. Note that under such “slow MAS” conditions, the ssb j j , hCS } envelope resembles the NMR powder pattern from the static powder, which may also be exploited to derive the {daniso parameters. Unless stated otherwise, we onwards solely consider NMR spectra acquired under MAS conditions. In most of the following, we will for simplicity omit to specify the “site” index j.

9.20.4.3

NMR relaxation and sensitivity concerns of solid-state NMR

While the structural information content available from solid-state NMR experimentation far exceeds that attainable from other spectroscopic techniques, particularly if advanced MAS NMR experimentation is employed (Sections 9.20.15–9.20.17), the Achilles heel of NMR is its much lower signal sensitivity relative to essentially all other structural characterization techniques; whereas vibrational spectroscopy measurements take minutes, the recording of solid-state NMR spectra often takes hours or days. While all NMR experiments but those of 1H are relatively time-consuming, NMR acquisitions from liquids (“solution NMR”) are typically completed 10–100 times faster than those of MAS NMR on powders. The reasons why all NMR experiments are more time-consuming than other spectroscopiesdand why solid-state NMR experimentation is much slower than its solution NMR counterpartdmay be understood from the features of the signal-averaging process

Solid-state nmr of glasses

595

required to achieve NMR spectra with decent signal-to-noise (S/N). The detected NMR signal is usually too weak from one sole single-pulse experiment, referred to as one “signal transient” or “scan”. Hence, several transients/scans (M) needs to be recorded pffiffiffiffiffi and co-added, i.e., “signal averaged”; the S/N grows as M because the NMR signal intensity scales linearly with the number of pffiffiffiffiffi transients, while the spectral noise increases as M. Yet, the repetition rate of the signal averaging procedure is limited by the requirement that the nuclear spin ensemble must return to thermal equilibrium (Fig. 2A) before application of the next rf pulsedthis time period is referred to as the “relaxation delay.” The equilibration is controlled by the spin-lattice (T1) relaxation process,137,138 which is driven by rapid rotational molecular motions. Such free reorientational motions are present in an isotropic liquid, but in general not in the solid state. Hence, while thermal equilibrium is typically established within a few (or tens of) seconds in a liquid, this process usually takes minutes to hours in a solid sample. Hence, a completed signal averaging procedure is in general (at least) one order of magnitude slower in solid-state NMR. Moreover, the S/N per transient is much higher in NMR spectra obtained from solutions than from powders, because the responses from solid samples are 1–2 orders of magnitude broader, assuming that MAS is employed. A lower limit of the NMR peakwidth relates to the 1QC lifetime, which is dictated by the spin–spin (T2) relaxation, which affects the transverse magnetization component of the spin ensemble.137,138 Here, a large (low) value of the T2 time constant implies a slowly (rapidly) decaying NMR signal, which by the properties of the Fourier transform implies a narrow (broad) peak in the frequency-domain NMR spectrum. However, while in general the T2 relaxation process limits the NMR peakwidths in solution NMR, normally the broadenings from anisotropic interactions in static powdersdas well as the chemical-shift distribution in glasses (see Section 9.20.7)ddictate the peakwidths from solid powders. The NMR-signal “sensitivity” of a given spin-S nuclide “S” is approximated by its receptivity (Rs),151 RS  aS g3S SðS þ 1Þ

(16)

where aS is the natural abundance (in %) of S. Tables 1 and 2 list the values of aS, gS, and the relative receptivity (RS/RH) with respect to 1H, whose 100% natural abundance and overall largest magnetogyric ratio among all nuclides (except for the practically irrelevant 3H nuclide) render protons the most receptive species in NMR. From Tables 1 and 2 follow that the combination of a large gS and a high natural abundance of 7Li, 19F, 31P, 11B, 23Na, and 27Al make them very favorable for NMR, and rationalizes why these spin probes have become ubiquitous for MAS NMR studies on glasses. For nuclides with very low natural abundance, such as 17 O and 43Ca, it is necessary to work with isotopically enriched glasses, whereas the NMR-signal strength of several low-abundance nuclides with modest magnetogyric ratios, notably 29Si and 6Li, may be boosted by utilizing larger sample volumes (however, at the price of lower attainable MAS rates). Moreover, NMR of all nuclides are facilitated by working at high magnetic fields, because the NMR-signal sensitivity grows roughly as (B0)3/2 (Ref. 151), which is of particular utility for nuclear species with low/moderate magnetogyric ratios. A caveat, however, is that the receptivity concept is formulated from solution NMR standpoints and neither accounts for important NMR properties such as T1-relaxation times in the solid state, nor for broadening from quadrupolar interactions (Section 9.20.5) and/or structural disorder in the NMR on glasses (Section 9.20.7). Consequently, predictions from receptivity-values may sometimes be very misleading.

9.20.4.4

Through-space dipolar interactions

The through-space dipolar interaction reflects the mutual coupling between the magnetic moments of two nuclei in close spatial proximity, where the local magnetic field generated by one nuclear site (j) is experienced by a neighboring site k in the structure. Here j and k may constitute the same (homonuclear) or distinct (heteronuclear) nuclides. For the latter, we employ the notation “S” and ”I” for the two nuclides, which possess spin quantum numbers S and I, respectively. The heteronuclear dipolar coupling constant (bjkS  I) 138,145 exhibits an inverse cubic dependence on the Sj–Ik internuclear distance (rSI jk ), according to 3  m0 bSI g g Z rjkSI ½in Hz (17) jk ¼  8p2 1 S while the homonuclear counterpart is given by the analogous expression  3 m bjk ¼  02 g2 Z rjk ½in Hz 8p

(18)

Owing to the gIgS and g2 dependence for the hetero- and homo-nuclear dipolar interactions, respectively, bjkS  I and bjk may span a wide range of magnitudesdfrom tens of Hz for two spins with low magnetogyric ratio(s) that are separated by several Å, up to z35 kHz for the 1H-1H interaction in a structure-bound H2O molecule. For the most relevant homonuclear spin-pairs in oxide glasses, dipolar interactions among two network former sites separated by an O bridge are typically a few hundred Hz for 27 Al–O–27Al and 160–200 Hz for 29Si–O–29Si, but about 700–900 Hz across 11B–O–11B, 31P–O–31P, and 11B–O–31P linkages. The through-space dipolar interaction is purely anisotropic, with an asymmetry parameter of zero. The dipolar frequency may be expressed schematically as njk(U) bjk and njkS  I(U) bjkS  I for the homonuclear and heteronuclear interaction, respectively (in direct analogy to the CSA), where the magnitude of the dipolar coupling constant is a measure of the “anisotropy size”. Hence, if being sufficiently large (several kHz), the dipolar interaction may broaden NMR peaks observed from static powders significantly,

596

Solid-state nmr of glasses

although the broadening is typically minor relative to that from the CSA (that applies, for instance, for the 13C NMR powder pattern of Fig. 5A). Moreover, by its absence of an isotropic component, the through-space dipolar interaction is not observed in NMR spectra from isotropic solutions, while its effects are removed by MAS, provided that nr well exceeds the dipolar frequency: the latter scenario holds for all of the comparatively weak dipolar interactions of relevance for structural studies of glasses (vide supra). Although we will herein only consider qualitative information from the through-space dipolar interaction for establishing proximities and connectivities among spin sites in glasses, the orientation-dependence and sensitivity to molecular motions of the dipolar interaction render it a versatile source for quantitative interatomic-distances and a probe of molecular geometries and dynamics,152–156 which has proven particularly powerful in structural biology.154,155,157 The arrangement of MAS NMR experimental conditions for which the peak broadening from the CSA is eliminated, but the internuclear-distance information of the smaller dipolar interactions are restored, is referred to as “dipolar recoupling” and has been utilized heavily in MAS NMR for z 40 years.152–156 Recoupling of both homonuclear and heteronuclear dipolar interactions are normally achieved by a carefully designed rf-pulse train, which leads to a partial restoration of the dipolar interaction.152–156 All such pulse schemes were initially developed for spin-1/2 recoupling for structural investigations of bio-molecules. Homonuclear dipolar recoupling techniques for half-integer quadrupolar nuclei, on the other hand, were not explored until the new millennium.158–162 This area remains much less developed than for recoupling spins-1/2 nuclei, which mainly stems from the significant challenges to accurately control their spin dynamics by rf pulses, as explained in Sections 9.20.5.4 and 9.20.15.1, and discussed further in Refs. 163,164. However, over the past decade, such recoupling applications have become much more common for glasses. Homo- and hetero-nuclear dipolar experimentation are discussed further in Sections 9.20.15–9.20.17.

9.20.4.5

Through-bond J interactions

While the through-space dipolar interaction is the by far most utilized tool for probing interatomic connectivities in the solid state (or more precisely, interatomic proximities; see Section 9.20.15.1), for NMR applications to solutions it only becomes relevant for anisotropic liquids, such as liquid crystals or (too) slowly tumbling proteins in solution. In the NMR on isotropic liquids, on the other hand, the through-bond (J) interaction is the primary vehicle for establishing internuclear connectivities. As for its through-space counterpart, the through-bond interaction scales as the product of the magnetogyric ratios of its contributing nuclear species (Eqs. 17 and 18), but is mediated through chemical bonds and is normally absent for nuclei of non-bonded atoms, no matter how spatially proximate the two spin sites j and k may be.138,145 The through-bond interaction shares the properties of the chemical shift in that its response to rotations is described by a tensor that exhibits both isotropic and anisotropic components.138,145 However, solely the isotropic part is observed in solution NMR, where it is usually referred to as the “J coupling”, whose value (in Hz) specifies the interaction strength. The J coupling constant is typically much smaller than its through-space counterpart, where “large” J values may range up to  200 Hz (depending on the nuclide species). As it is mediated by the overlap between the electron clouds between the two interacting nuclear spin sites, the J-coupling magnitude diminishes rapidly as the number of bonds are increased between the nuclei. Hence, in oxide-based network materials such as glasses, interacting nuclei of two network formers are separated by two chemical bonds, i.e., a –O– linkage, which results in very small J coupling constants, which are denoted “2J.” For instance, 2J(31P–O–31P) and 2J(29Si–O–29Si) values are typically 15–25 Hz165–167 and < 10 Hz,168–170 respectively. In solid-state NMR, both (an)isotropic components of the through-bond interaction are present. The anisotropic part, referred to as the “J anisotropy,” has identical bearings on the NMR spectrum as the through-space dipolar interaction, and their respective contributions are very difficult to distinguish. Hence, the typically one order of magnitude smaller J anisotropy is normally ignored and only the orientationally independent J coupling constant is considered. Yet, despite its instrumental importance of offering connectivity information, the small J-couplings often make the through-bond interaction difficult to exploit in solid state NMR on glasses, as discussed further in Section 9.20.15.1.

9.20.4.6

Two-dimensional NMR

Two-dimensional (2D) and higher-dimensional 3D and 4D NMR experiments are central ingredients in structural characterizations of (particularly) biomolecules in solution as well in the solid state. Such 2D NMR experiments not only adds another dimension to the NMR spectrum, but to NMR spectroscopy itself as a structural characterization technique, where the pivotal importance of twoand multi-dimensional NMR is mirrored in two Nobel Prize awards: to Richard Ernst in 1991 and to Kurt Wütrich in 2002. The enormously expanded structural information content from multi-dimensional NMR experiments stems from the unlimited possibilities of correlating various types of structural information, each unveiled by a corresponding NMR parameter. For instance, in Section 9.20.16 we discuss 2D NMR schemes relying on through-space and through-bond interactions that inform about which of the 11B[3] and 11B[4] coordinations that preferentially bond to PO4 tetrahedra in borophosphate glasses, while Section 9.20.15 reviews another 2D 11B NMR protocol that unveils the various B[3]–O–B[4] linkages of borosilicate glasses, which recently provided unambiguous proof for the existence of directly bonded BO4 groups in such glasses,133 thereby settling one long-term controversy about their (non)existence. A 2D NMR experiment comprises two time coordinates, t1 and t2, each conveying its own type of information, where t2 is formally identical to the “real-time” time-coordinate of the corresponding 1D NMR experiment, i.e., the directly detected NMR signal from a given nuclide.137,138 A 2D NMR experiment involves the recording of an array of time-signals, s(t1, t2), for increasing

Solid-state nmr of glasses

597

{t1, t2}, whereupon a 2D FT results in a 2D NMR spectrum that exhibits two frequency coordinates, {n1, n2}. Such a 2D NMR spectrum is normally depicted graphically in two dimensionsdwhereby convention the n1 and n2 coordinates appear along the vertical (“indirect”) and horizontal (“direct”) dimension of the 2D spectrum, respectively,137,138 whereas the 2D NMR signal intensities are represented as contour levels, as for a topographic map for which the number of contours reflects the altitude of a hill. An inherent drawback of multidimensional NMR stems from its “arrayed NMR acquisition” nature, where 101–102 separate “1D NMR experiments” must be acquired for each dimension introduceddeach of which prolongs the experimental time by 101–102 orders of magnitude. Consequently, the time-consuming signal averaging normally limits experiments to two dimensions for MAS NMR applications to inorganic network materialsdand notably glasses, whose inherent structural disorder further reduces the NMR-signal sensitivity (Section 9.20.7). Consequently, 3D NMR demonstrations on crystalline inorganic materials are rare and hitherto restricted to relatively simple “model systems.”171–173 Hence, we will herein only consider 2D NMR experiments.

9.20.5

NMR on quadrupolar nuclei

9.20.5.1

Central and satellite transitions

An half-integer spin-S nucleus exhibits 2S þ 1 Zeeman energy levels/states with corresponding magnetic quantum numbers m in the range { 1/2,  3/2, .,  S},82,138,174,175 which implies that there are S detectable single-quantum coherences (1QC) involving the {m, m  1} states, and often referred to as “transitions.” (We herein only consider the detectable  1Q coherences; see Refs. 82,138,176 for details). The 1/2 /  1/2 transition is called the “central transition” (CT),82,174,175 which constitutes the sole 1Q transition for S ¼ 1/2 nuclei; see Section 9.20.3.3. All other single-quantum transitions are referred to as satellite transitions (STs). Hence, a single-pulse NMR experiment on an ensemble of spin-S nuclei leads to S detected NMR signals, one for each CT and ST, which may be visualized as the presence of S distinct transverse magnetization vectors, the rotational motion of each around B0 induces an NMR signal in the coil.

9.20.5.2

First-order quadrupolar interaction

All S s 1/2 nuclei interact with magnetic fields in their surroundings, just as their spin-1/2 counterparts. However, in contrast with spins-1/2, which features a spherical/uniform nuclear charge distribution, a quadrupolar nucleus (S s 1/2) manifests a non-spherical charge distribution reflected by its nuclear (electric) quadrupolar moment, eQ, where e is the elementary charge. As for the magnetogyric ratio, eQ is a nuclide-specific property; see Table 2. A nuclear quadrupolar spin site interacts with variations of electric fields (electric field gradients; EFG) in its vicinity, where the EFG is a second-rank tensor with principal values {Vxx, Vyy, Vzz}. Such electric field gradients exist naturally in any molecular structure due to the presence of other nucleidand particularly electronsdnearby the nucleus. In contrast with all other hitherto reviewed NMR interactions, the quadrupolar interaction is merely of electrical origin. We henceforth only consider the dominant group of half-integer spins. There are two types of quadrupolar interactions, referred to as “first order” and “second order”, and stemming from perturbation theory analyzes of the combined effects from the Zeeman and quadrupolar interactions. Here, we do not provide any details, but refer to Refs. 82,174,175 for more complete theoretical accounts. The first-order quadrupolar interaction-strength is proportional to the quadrupolar frequency (nQ), nQ ¼

CQ 2Sð2S  1Þ

½in Hz

(19)

which involves the quadrupolar coupling constant (CQ), CQ ¼ ðeqÞ$ðeQÞ=h ¼ e2 qQ=h

½in Hz

(20)

that constitutes the product of the nuclear quadrupolar moment and the largest component Vzz ¼ eq of the EFG tensor. As for the principal values of the chemical shift tensor (Eq. 14), the EFG counterparts are ordered according to Vzz Vxx Vyy (Refs. 138,145,146) and relates to the asymmetry parameter 0  hQ  1 of the EFG according to   hQ ¼ Vyy  Vxx =Vzz (21) 82,174,175

In contrast with the chemical shift and through-bond interactions, but in direct analogy with the through-space dipolar interaction, the first-order quadrupolar interaction has no isotropic (orientation-independent) part because Vxx þ Vyy þ Vzz ¼ 0. Therefore, all its effects vanish in an isotropic liquid and for a fully symmetric charge-distribution around the nucleus in the solid state. Hence, depending on the value of the nuclear quadrupole moment and the (lack of) symmetry of the charge-distribution around the nucleus, CQ may range from zero to very large values in the 1–100 MHz range, which may even exceed the Larmor frequency (see Table 2). In practice, even in the most ordered inorganic structures, minor differences in bond lengths and bond angles introduce sizable quadrupolar coupling constants for tetrahedrally or octahedrally coordinated sites (e.g., 27AlO4, 27AlO6), notably in glasses, as discussed further in Section 9.20.7. The first-order quadrupolar interaction shares many qualitative features with the CSA (Section 9.20.4), although nQ is typically j 3–4 orders of magnitude larger than naniso . Hence, in a static (nonrotating) powder, the orientation dependence of the first-order

598

Solid-state nmr of glasses

Al-1 94 ppm

(A)

Al-1 89 ppm

(B)

CT signal is broadened & shifted by the second-order quadrupolar interaction

Al-2

B0=9.4 T * 500

*

ST spinning sidebands from first-order quadrupolar interaction

*

*

250

*

*

0 27

-250

*

* -500

*

Al-2

*

*

1000

500

0 27

Al shift (ppm)

*

B0=4.7 T *

-500

*

*

-1000

Al shift (ppm)

Fig. 6 27Al MAS NMR spectra recorded at magnetic fields of (A) 9.4 T and 4.7 T from the oxynitride “S phase” Ba2Al2Si10N14O4.177,178 The spectra are zoomed around the CT-signal region, but also reveal narrow spinning sidebands from the STs and the first-order quadrupolar interaction (marked by asterisks). The structure comprises two non-equivalent Al sites, Al-1 and Al-2, the latter exhibiting CQ ¼ 4.2 MHz. Although the former site is associated with a small coupling constant of CQ ¼ 2.0 MHz, it is sufficiently large to produce noticeably different NMR peak-maximum positions in spectra obtained at distinct external magnetic fields, where both peaks appear at shifts lower than the isotropic chemical shift of diso ¼ 97 ppm. Note that the NMR spectra are presented over the same frequency-span.

quadrupolar interaction leads to a “powder pattern” from each ST, whose spectral width is proportional to nQ, and thereby extending over a 105–106 Hz range, whereas in powders undergoing MAS, a ssb manifold is observed, as exemplified by the 27Al MAS NMR spectra of Fig. 6.177,178 Fortunately, however, the first-order quadrupolar interaction solely affects the STs and not the CT. This property holds for all half-integer spins S, and significantly facilitates their MAS NMR applications.

9.20.5.3

Second-order quadrupolar interaction

The independence of the CT on the first-order quadrupolar interaction, however, is not the end of the story: all transitions, including the CT, are subjected to second-order quadrupolar interactions that scales as n(2)Q(U) nQ2/n0, thereby typically amounting to (20 kHz. (Carefully distinguish n(2)Q from the square of nQ, i.e., nQ2). The second-order quadrupolar interaction involves (i) an anisotropic part, nQ aniso(U), where U is the orientation of the EFG tensor relative to the external magnetic field; (ii) an orientation-independent Q isotropic part, niso , which assumes an identical role as the isotropic chemical shift and produces an overall NMR-peak displacement (Fig. 6): ð2Þ

Q nQ ðUÞ ¼ nQ iso þ naniso ðUÞ 

C2Q f ðSÞ gB0 ½Sð2S  1Þ2

(22)

Here, f (S) depends on the spin quantum number S; see Refs. 82,174,175 for details. Before examining each isotropic/anisotropic portion of the second-order quadrupolar interaction further, we underscore the following general features following from Eq. (22): Q Q both niso and naniso (U) scale as the square of the quadrupolar coupling constant, while for a fixed CQ-value, they decrease for an increase in either S or B0. Consequently, NMR experimentation targeting quadrupolar nuclei is markedly facilitated by utilizing high magnetic fields B0 T 14 T, particularly for nuclides with low spin numbers (S ¼ 1 and S ¼ 3/2), and/or small magnetogyric ratios g, for which the second-order interaction become substantial (> 10 kHz) even for modest quadrupolar coupling constants of a few MHz. Concerning the anisotropic second-order quadrupolar interaction, it broadens the NMR responses of all CT/ST transitions observed from static powders (but to different extents82,174,175), and produces ssb manifolds under MAS conditions, in direct analogy with the CSA, dipolar, and first-order quadrupolar interactions. A fundamental difference to all hitherto discussed NMR interactions, however, is that owing to the complex orientation-dependence of n(2)Q(U), its NMR-peak broadening cannot be Q removed completely by MAS, regardless of the MAS rate employed. Provided that nr > r naniso (U)r, all spinning sidebands are concentrated into the CT NMR centerband peak (as in Fig. 6), while the CT NMR peak is narrowed by a factor of z3.6.82,174,175 Yet, a second-order quadrupolar broadening remains, which for quadrupolar sites in ordered environments lead to a “powder Q pattern”, whose width and shape is reflected by the values of naniso and hQ, respectively. This is evident from the 27Al MAS NMR spectrum shown in Fig. 7A, which was recorded from a well-crystalline sample of SrSiAlD that exhibits one crystallographically unique 27Al site with CQ ¼ 7.5 MHz and a nearly axially symmetric EFG tensor (hQ z 0; see Section 9.20.9.4).179 Typically, the second-order quadrupolar-broadened NMR powder pattern spans a few kHz to tens of kHz, meaning that the CT NMR spectral resolution observed from quadrupolar nuclei under MAS conditions is often comparable to those observed from spin 1/2 nuclei in static powders. We next consider the isotropic second-order quadrupolar frequency, which for the CT is given by82,175

Solid-state nmr of glasses

(A)

(B)

599

(C)

T-O-T layer

H

brucite layer

Sr Al

Si SrSiAlD

** 300

** 150 27

* 0

* -150

chlorite

*

* * * * * 300

-300

150 27

Al shift (ppm)

Lu Al Si O glass

0

-150

-300

* **

* * *

* * * * * * *

300

150 27

Al shift (ppm)

0

-150

** -300

Al shift (ppm)

Fig. 7 27Al MAS NMR spectra recorded from phases with increasing structural disorder: (A) a well-ordered SrSiAlD with one crystallographic 27Al site (CQ ¼ 7.5 MHz; hQ z 0)179; (B) chlorite, a synthetic phyllosilicate mineral of composition (Mg9.0Al3.48)(Si5.0Al2.53)O20(OH)16 that comprises Al[4] and Al[6] coordinations180; (C) a 24La2O3–25Al2O3–51SiO2 glass involving three {Al[4], Al[5], Al[6]} coordinations.75,77 The structural disorder is increased. Reproduced from Edén, M. Update on 27Al NMR Studies of Aluminosilicate Glasses. Annu. Rep. NMR Spectrosc. 2020, 101, 285–410, with permission from Elsevier.

nQ iso

¼

  3C2Q 1 þ h2Q =3 ½3  4SðS þ 1Þ 160n0 S2 ð2S  1Þ2

½in Hz

(23)

and may be converted into its corresponding “shift” by Q dQ iso ¼ niso =n0 ½in ppm

(24)

diso is often referred to as the quadrupolar induced shift (QIS). The resulting center-of-gravity (CG) shift of the CT MAS NMR peak is the sum of the isotropic chemical and second-order quadrupolar shifts: Q

dCG ¼ diso þ dQ iso

(25)

Q The following is noteworthy: (i) it follows from Eqs. (23) and (24) that diso depends on n0 2 (i.e., on B0 2), meaning that the observed (CT) NMR peak position is directly dependent on the precise magnetic field used for recording the NMR spectrum, notwithstanding that the isotropic chemical shift (diso) is independent on B0 (Eq. 10). Consequently, we recommend labeling the axes of NMR spectra recorded from quadrupolar nuclei simply by “shift” (e.g., see Figs. 6 and 7)das opposed to “chemical Q is always negative for the CT, implying that the isotropic quadrupolar shift shift.” (ii) Regardless of the spin quantum number S, diso displaces the center-of-gravity shift (dCG) to a ppm-value that is lower than diso; this effect may be verified from the 27Al MAS NMR spectra recorded at two different magnetic fields and shown in Fig. 6. The isotropic chemical shifts of quadrupolar nuclei will for simplicity be denoted as for spins-1/2 nuclei, i.e., either as “dE” or E “diso ” for a nuclide of element E, depending on whether it is obvious from the context that the isotropic chemical shift is considered. Whenever needed, the coordination number of the structural site will be specified as a superscript, e.g., dE[4] and dE[6] label the isotropic chemical shift of the E[4] and E[6] coordinations, respectively.

9.20.5.4

Quadrupolar nuclei and Rf fields

For NMR on spins-1/2, it is in general possible to arrange sufficiently high n1 values (typically spanning 50–150 kHz) that far exceed the magnitudes of the anisotropic spin interactions, encompassing the CSA and the through space interactions. However, the size of the first-order quadrupolar frequency (which is normally > 100 kHz) complicates an accurate control of the magnetization vectors from quadrupolar nuclei by rf pulses. In the most typical case of n1  nQ, the nutation frequency of the quadrupolar spin during an rf pulse

600

Solid-state nmr of glasses

ν1/νQ 8

1.0

1.39

signal intensity

0.8

0.56

0.6 0.4

0.28

0.2 0

τp /μs

-0.2

0.14

-0.4

0.07 0

Fig. 8 Calculated CT NMR-signal intensity observed from an S ¼ 5/2 site in a single crystallite for variable pulse-lengths sp and ratios n1/nQ (Eq. 8), for a nutation frequency n1 ¼ 41.67 kHz. The cases n1/nQ  N and v1/vQ  0 correspond to non-selective and selective excitation, respectively. In the “linear” excitation regime of very short pulses, the NMR signal buildup is independent of vQ. Adapted from Fenzke, D.; Freude, D.; Frölich, T.; Haase, J. NMR Intensity Measurements of Half-Integer Quadrupolar Nuclei. Chem. Phys. Lett. 1984, 111, 171–175, with permission from Elsevier.

depends on both n1 and nQ in a complicated manner, meaning that the nutation frequency cannot in general be predicted, unless nQ is a priori known181–184; see Fig. 8. Hence, in the case of several quadrupolar sites with widely differing quadrupolar frequencies, each NMR-signal intensity no longer convey the quantitative site population in the structure. The nutation frequency only becomes independent on the first-order quadrupolar frequency if the magnitudes of n1 and nQ differ by an order of magnitude (or more). Hence, the sole two following scenarios result in a readily predicted value of the spin nutation frequency during the rf pulse: (i) n1 [ nQ, referred to as non-selective excitation. Then, the quadrupolar nucleus exhibits an identical response as S ¼ 1/2 nuclei, meaning that all 1Q coherences of the central and satellite transitions are excited uniformly and their magnetization vectors rotate at the nutation frequency given by Eq. (7). However, such cases are very rare, except for rf pulses applied to quadrupolar nuclei in isotropic solutions (where the rapid molecular tumbling averages the quadrupolar interaction to zero) and for nuclei with low electric quadrupolar moments, such as 2H (S ¼ 1), 6Li (S ¼ 1), and 133Cs (S ¼ 7/2); see Table 2. (ii) n1 nQ: This so-called selective excitation regime implies that the rf-field only excites one transition, where we only consider the most important case of “CT-selective excitation,”181,185–187 for which the CT nutation frequency during the rf pulse is a factor of (S þ 1/2) higher than n1,181,186,188,189 implying that the CT magnetization vector rotates at the rate

 if n1 nQ (26) nCT nut ¼ ðS þ 1=2Þn1

Then, provided that n1 nQ is obeyed for all quadrupolar-spin sites in the structure (such as the various 27Al[p] coordinations), their CT magnetization vectors rotate in synchrony, and the observed integrated NMR intensities quantitatively reflect the various site (e.g., Al[p]) abundances. Although CT-selective rf pulses are frequently employed in more advanced MAS NMR experimentation (see Sections 9.20.15 and 9.20.16), the use of very low rf powersdtypically such that n1 < 10 kHzdbecomes problematic for ensuring a uniform excitation across all second-order broadened MAS NMR powder lineshapes in a multi-site structure, particularly for nuclides such as 27 Al and 17O, whose wide chemical-shift spans produce large frequency spreads at (moderately) high fields of B0 P 9.4 T. Then, the control of the CT magnetization vector diminishes due to off-resonance effects. The resonance offset (Dj) of a nuclear spin site j is the difference between the oscillation frequency of the rf field (nrf) and the spin resonance frequency nj. Unless n1 [ {Dj, Dk, .} for all chemically distinct quadrupolar sites in the structure, an offset-dependent spin nutation frequency results. Hence, in practice, the window of CT-selective rf-pulse control is narrow, where the upper and lower limits of n1 are dictated by nQ and the largest Dj value, respectively. To summarize, non-selective rf excitation is usually irrelevant for achieving quantitative NMR spectra from quadrupolar nuclei, while CT-selective excitation may be problematic for samples exhibiting quadrupolar sites with widely different quadrupolar products and/or spread of resonance frequencies. Fortunately, there is one more option, which in practice is the most useful one because it simultaneously excites all CT and ST resonances uniformly by employing strong (i.e., n1 z 100 kHz) but very short (0.3–0.5 ms) rf pulses to obey the condition5,190,191

Solid-state nmr of glasses

sp #

1 12ðS þ 1=2Þn1

601

(27)

In this linear excitation regime where bp is small, the NMR signal excitation becomes to a good approximation independent on nQ (Fig. 8), thereby conforming to Eq. (8). The price paid, however, is a markedly lower NMR-signal intensity from all quadrupolar sites, owing to the small flip angles employed.

9.20.6

Chemical-shift/structure relationships

The most detailed chemical-shift/structure correlations established to date derive from density functional theory (DFT) computations, particularly those based on plane-wave calculations with the Gauge Including Projector Augmented Wave (GIPAW) approach,192,193 as reviewed in Refs. 194,195 in the context of glasses. Such state-of-the-art calculations typically reproduce experimental 11B, 17O, 27Al, 29Si, and 31P chemical shifts within a few ppm. Although the precision of DFT/GIPAW calculations is much lower for atoms with d and f electrons, the significant hurdles in obtaining high-resolution NMR spectra with decent S/N from most of those nuclides anyway render such calculations the currently best approach for improving the insight into chemical-shift/structure relationships. In the following sub-sections, we review the current consensus of which structural factors primarily dictate the isotropic chemical shifts of the network formers and modifiers along with 17O and 1H in oxide-based glasses. While we solely consider isotropic chemical shifts, that aspect is for reasons of brevity not stressed throughout, where we also remind that the isotropic chemical shift of a given 11B, 27Al and 17O quadrupolar site neither coincides with its shift at the peak maximum nor with its CG shift observed in the MAS NMR spectrum (Section 9.20.5.3).

9.20.6.1

A simplified model for chemical-shift predictions

In the following, we discuss the primary structural factors that control the isotropic chemical shifts of the network formers in oxidebased glasses, which are illustrated for the F ¼ {11B, 27Al, 29Si, 31P} species. Yet, the general shift trends outlined below also apply to other network formers. Since the chemical shift directly reflects the local electronic environment at the nuclear site, the degree of alterations thereof stemming from a structural modification diminish rapidly when progressing from the first to second and third coordination spheres of the nucleus. Hence, the bearings from other atoms present in the third coordination shell are in practice negligible and cannot normally be detected by MAS NMR experimentation from powders, and let alone from glasses (that manifest distributions in all NMR parameters, as reviewed in Section 9.20.7). To rationalize the shift-structure relationships, we will employ a very simple approach/model, which despite of its simplicity usually offers a sufficient predictive power for qualitative assessments of the chemical-shift trends in oxide-based glasses. It was illustrated for the relationships between isotropic 27Al chemical-shift and structural features in Refs. 82,196. Yet, as pointed out in those reviews, the model also applies for other network formers in an oxide-based glass, which may additionally incorporate other electronegative elements, such as nitrogen or fluorine. Note the increase in electronegativity along the series Mz þ < F {N, O, F}. The net isotropic chemical shift of a nucleus is given by the sum of its diamagnetic and paramagnetic shift (or more precisely; “shielding”) contributions, which decrease and increase the chemical shift, respectively.138,192,194,195 While the diamagnetic shift/shielding dominates because it originates from the core electrons, their configuration remains the same for all nuclear sites regardless of their “chemical environment”; the latter depends on the valence electrons, which are responsible for the paramagnetic shift that effectively determines the (isotropic) chemical shift range of any network former site in an oxide-based (glass) structure. The paramagnetic shift correlates with the electron density at the F nucleus and augment (diminish) for increasing (decreasing) electron density: when the electron density is increased, the nucleus is deshielded, i.e., its chemical shift is increased (and vice versa). Hence, if comparing two distinct local structural fragments, the one exhibiting the highest electron density at the nucleus is predicted to exhibit the largest dF value. Notably, the picture portrayed above is (over)simplified and cannot predict any absolute chemical-shift values. Yet, it readily offers a qualitative prediction of the experimentally determined shift-trends for 11B, 27Al, 29Si, and 31P summarized in Fig. 9 and discussed in the following Subsections (9.20.6.2–9.20.6.6), which are organized to proceed from the most to the least important structural factors that influence the chemical shift of the network formers. For more formal and rigorous shift/structure correlations, we refer to the early literature on 31P,65,197–199 29Si,200–202 and 27Al191,203 shifts in glasses and other oxide-based materials. We refer to Refs. 5, 204, 205 for extensive sets of tabulated chemical shifts.

9.20.6.2

Coordination number

A change in coordination number, F[p] / F[p þ 1], and the accompanying elevated number of O atoms around the F nucleus results in the by far most drastic reduction in its electron density as compared with any other structural alteration. Hence, the chemical shift decreases significantly, which for 29Si translates into a z 50 ppm shift-displacement from dSi4 z 110 ppm of the QSi4 groups in vitreous SiO210,81,206–210 to around 150  10 ppm for 29SiO5 groups54,55,57 and  200  20 ppm for SiO6 octahedra56,57,60,61,63,64,211 (Fig. 9). Notably, the smaller chemical-shift spans of the higher-coordination Si[6] and (notably) Si[5] species

602

Solid-state nmr of glasses

27

Al [4]

Al 80

Al [5]

70

60

50

40

Al [6]

30

20

10

0

pm) 11

B[4]

B[3]

B 24

20

16

12

8

4

0

-4

0 NBO B[3]

1 2 3

23 22 21 20 19 18 17 16 15 14 13

pm) Q3 31

Q2

P 1

Q 0

Q 10

0

-10

-20

-30

-40

-50

pm) 29

Si [5]

Si [4]

Si

Si [6]

-60 -80 -100 -120 -140 -160 -180 -200 -220

Q4 3

Si [4]

Q 2

Q 1

Q Q0 -60

-70

-80

-90

-100 -110 -120

pm) Fig. 9 Ranges of isotropic chemical shifts for 27Al, 11B, 31P, and 29Si in oxide-based glasses, also showing the typical spans of 29Si and 31P shifts for each respective QSin and QPn species, as well as the shift-ranges of 11BO3 groups with 0, 1, 2, or 3 NBO ions (white number in each respective bar). These 27Al[p], 11B[p], 31P, and 29Si chemical shift ranges are representative for multi-component glasses for which O is the sole anion but comprising arbitrary Mz þ cations and combinations of the various F ¼ {Al, B, P, Si} network formers. The only exception concerns the 27Al[p] chemical shifts, which are typical for aluminate and aluminosilicate glasses, but significantly lower for aluminophosphate and aluminoborate glasses (not shown).

mainly stem from their very rare occurrence and consequently modest shift data-bank. Nonetheless, this underscores that the primary task for NMR and other structural characterization techniques are merely to discriminate among the various local Si[4] environments. Likewise, Fig. 9 reveals that the 27Al and 11B chemical shift of an {Al[4], Al[5], Al[6]} and {B[3], B[4]} species decrease by z30 ppm5,65,66,191,203,212,213 and 15–20 ppm24,84,214–217 for each unit increase in its number of coordinated O atoms, respectively. For instance, in aluminosilicate glasses, dAl[p] values of 60–70 ppm, 35–40 ppm and 0–10 ppm are typically observed for the respective 27AlO4, 27AIO5, and 27AlO6 polyhedra.5,80,205,218 The precise shift observed from 27AlO4 in an aluminosilicate glass depends on the glass network polymerization and the molar nA1/nSi ratio,80,81,218–221 which relate to the relative numbers of BO/NBO and Si/Al neighbors in the first- and second-coordination spheres of 27Al, respectively (vide infra).

9.20.6.3

BO4NBO substitutions in the first coordination sphere

The higher negative charge of NBO anions makes them less prone to withdraw electrons from their bonded atoms. Hence, an BO/ NBO substitution at the FOp polyhedron and the accompanying increase of the electron density within the first-

Solid-state nmr of glasses

603

coordination sphere of the F nucleus results in a significantly higher chemical shift (i.e., the nucleus becomes deshielded). For 29Si, this amounts to a 7–12 ppm deshielding for each QSin / QSin 1 conversion (Fig. 9) from the typical shift dSi z 110 ppm of QSi4, and with the larger (smaller) change across the 7–12 ppm range observed for QSi4 / QSi3 (QSi1 / QSi0). With the 31P chemical shift the QP3 group of vitreous P2O5 (dP z 47 ppm)222 as the reference, each consecutive 3 QP / QP2 / QP1 transformation reveals a 31P chemical-shift increase of about 15–20 ppm (Fig. 9),197,199,223–229 which underpins the much higher resolution of 31P relative to 29Si MAS NMR, as elaborated on further in Section 9.20.10. Yet, as for 29Si, the QP1 and QP0 groups typically manifest a markedly smaller chemical-shift difference of 8–10 ppm.197,199,223–229 Hence, while the identification of each resonance from QP1 and QP0 groups is non-problematic within a given Mz/2O–P2O5 glass system, shiftdegeneracies may occur for QP1/QP0 species in M(2)O – M0 O  P2O5 glasses, where for instance the 31P chemical shift of a given QPn group in an amorphous CaO–P2O5 phase is typically z 8 ppm lower than its Na2O–P2O5 counterpart of similar composition; consequently, both QP0 and QP1 moieties surrounded by Ca2þ and Naþ cations, respectively, resonate in the 0–3 ppm range.197,199,223–229 In general, the chemical shift of a network forming species F of an NBO-bearing FOp polyhedron is increased concurrently for decreasing electronegativity117 of the Mz þ cation (or with the closely correlated CFS/cation potential parameters) of the F– O[1]/ Mz þ motifdsuch as along the series Mg2þ < Ca2þ < Naþdas is well documented for 29Si and 31P in binary silicate8,10,12,81,230 and phosphate197–199,223,231–233 phases. This trend is readily rationalized from the simple picture of electrondensity evaluations described above, because the higher the electronegativity of the Mz þ cation, the lower the electron density at F, and thereby the lower its chemical shift. Next considering 11B and 27Al chemical shifts, Fig. 9 reveals a minor increase in the 11B[3] shift for each BO /NBO replacement,234–243 whereas there is no literature on the chemical-shift responses of the 11B[4] and the higher-coordination 27 [5] 27 [6] Al / Al species upon a BO/ NBO replacement. Al[4]–NBO bonds are known to form in CaO–Al2O3–SiO2 glasses that are rich in both Si and Ca,244–246 and are present in minor amounts in rare-earth (RE) based aluminosilicate glasses over wide composition ranges126,247,248 (Section 9.20.16.2). Yet, the chemical-shift alteration upon a BO/ NBO conversion at an AlO4 tetrahedron is not known precisely, but is expected to match that of 29Si, as suggested by the 27Al chemical-shift span of 65–75 ppm observed for QAl3 groups in crystalline phyllosilicate phases relative to those of QAl4 in tectosilicates (55–65 ppm).5,205,249 Moreover, weak but consistent deshielding effects of a few ppm are also observed in aluminosilicate glasses for increasing NBO content,218,221,244,245,250 whose subtle effects naturally stem from the reluctance of Al[4]–NBO bond formation.126,244,247

9.20.6.4

Anion substitutions in the first coordination sphere

As anticipated from the correlation between the electron density and the chemical shift, the electronegativity of the ligand atom around the network former affects its chemical shift markedly. Although fluorine may be incorporated in significant amounts in (alumino)silicate glasses, it usually associates with the network modifiers rather than forming bonds to Si and Al. Nonetheless, F-for-O replacements lead to a substantially reduced electron density at the nucleus of a network former. For instance, O / F substitutions at AlO6 octahedra reduce the 27Al chemical shift of a few ppm per F atom, altogether amounting to around 20 ppm lower 27 Al chemical shifts of 27AlF6 octahedra relative to 27AlO6.251 We henceforth consider N-for-O substitutions at FO4 groups, where each 27Al, 29Si, and 31P chemical shift is typically increased by 8–12 ppm for every O / N replacement. Hence, the very similar deshielding effects at the F nucleus from O / N and BO/ NBO substitutions render 27Al/29Si/31P MAS NMR-peak assignments from oxynitride glasses a nightmare: the Qn notation is typically abandoned (with one notable exception252) and inferences merely become restricted to (tentative) resonance assignments of the various 27AlO4  mNm, 29SiO4  mNm, and 31PO4  mNm moieties. Considering the altogether limited number of NMR studies of oxynitride glasses, we make the following remarks/caveats based on the existing data-bank of crystalline and amorphous oxynitride phases; these comments also illustrate the dangers of drawing generalized conclusions about chemical shift/structure trends in solid phases: (i) Considering the difficulties of resolving the resonances of all potentially coexisting 27AlO4  mNm motifs in crystallinedand let alonedamorphous (alumino)silicate-based oxynitride phases,253–259 the 8–12 ppm increase in the 27Al chemical shift for one N-for-O bond replacement should be taken as a rough value. Yet, it is consistent with the (isotropic) chemical-shift span of z55 ppm between the 27AlN4 tetrahedra (dAl z 114 ppm253,254,260) of crystalline AlN, and 27AlO4 groups in aluminosilicate glasses (dAl z 60 ppm; Fig. 9). (ii) The literature is very sparse on 31P chemical shifts from amorphous oxynitride phases, which predominantly stem from M–P–O–N glasses with M ¼ {Li, Na} (or together with Pb2þ) across a relatively small stoichiometry range, where N was incorporated into a metaphosphate (i.e., QP2-dominated) based glass.211,252,261–264 (iii) The decent 29Si chemical-shift data bank from oxynitride phases (e.g., see Refs. 178,205,256,257,259,265–270) suggests a larger shift difference between the pair of SiO4/SiO3N groups (z20 ppm) than that of SiON3/SiN4 (8–10 ppm; c.f. Section 9.20.6.3); this observation is commensurate with the (on the average) z 15 ppm deshielding predicted per N-for-O bond replacement across the 29Si shift span of z60 ppm between the two extremes of QSi4 groups in SiO2 phases (dSi z 110 ppm)10,81,206–210 and the SiN4 tetrahedra of crystalline Si3N4 that resonate around 50 ppm.271–275

604 9.20.6.5

Solid-state nmr of glasses Second coordination sphere

The chemical-shift alterations of the F nucleus from structural changes in its second coordination sphere typically amount to a few ppm. Here, the most influential factor is the electronegativity of the neighboring F0 species across the F–O–F0 linkage, where the chemical shift of F is decreased upon an F–O–F / F–O–F0 substitution along the F0 series of Al < Si < P. For 29Si, this results in a 3–6 ppm deshielding for each 29Si–O–Si /29Si–O–Al bond replacement, where QSin groups in (alumino)silicate glasses only involving 29Si–O–Si and 29Si–O–Al linkages account for the lower and upper chemical-shift ranges in Fig. 9, respectively.5,135,200,230,249 An exception concerns the QSi4 groups in phosphosilicates, which manifest the globally lowest 29Si[4] shifts ( 1/2 nuclei even at low/moderately high magnetic fields of 4.7–11.7 T as that accomplished by MAS alone for spins-1/2 in powders. Indeed, while Fig. 11A and B reveals significantly narrowed and better resolved 27Al[p] resonances in the 27Al MAS NMR spectrum recorded from a La2O3–Al2O3– SiO2 glass at B0 ¼ 14.1 T relative to that at B0 ¼ 9.4 T (reflecting the scaled second-order quadrupolar broadening discussed in Section 9.20.5.3), an even better discrimination among the 27Al[4], 27Al[5], and 27Al[6] NMR signals is offered by the triple quantum MAS (3QMAS) NMR spectrum displayed in Fig. 11C. Since the first MAS NMR demonstrations on half-integer spin quadrupolar nuclei in the early 1980s, significant research efforts have been devoted to enjoy high spectral resolution. There are currently four general options: dynamic angle spinning (DAS),320,321 double rotation (DOR),320–323 satellite-transition MAS (STMAS)324,325 and 3QMAS.326,327 Whereas DAS and DOR NMR experimentation require specialized NMR probeheads, STMAS and MQMAS experiments may be implemented with standard MAS NMR equipment. Here we only discuss 3QMAS NMR because it is the only method hitherto applied extensively to glasses. We guide the reader to Refs. 174,175,328–330 for further information about the alternative high-resolution techniques for quadrupolar nuclei, as well as for the more general multiple-quantum MAS (MQMAS) incarnations, such as “5QMAS”. 3QMAS belongs to the class of 2D NMR experiments introduced in Section 9.20.4.6. Fig. 12A and B shows two 3QMAS NMR rf-pulse schemes, referred to as the (A) Z-filter331,333 and (B) shifted-echo332,334,335 protocols. For applications to glasses, the shifted-echo 3QMAS option offers decisive advantages over its Z-filter counterpart. “3QMAS” NMR is more precisely termed 3Q–1Q correlation NMR, because it correlates triple-quantum coherence (3QC) that evolves during the “t1” time coordinate with 1QC evolution during the “t2” time segment; see Fig. 12. Note that only 1Q coherences correspond to a rotating transverse magnetization vector which induces an NMR signal in the coil (Section 9.20.3.3). For the multi-Zeeman level structure of a quadrupolar nuclide with S P 3/2 (Section 9.20.5.1), 3Q coherences involve transitions such as m 4 m  3, i.e., they correspond to a difference of 3 in the magnetic quantum numbers (or more precisely:  3). Although such high-order (“multiple-quantum”) coherences are not directly detectable by NMR, they may be observed indirectly along the “indirect” dimension of the 3Q–1Q correlation 2D NMR spectrum; see Fig. 11C. After a processing procedure of the as-recorded 3QMAS NMR spectrum referred to as “shearing”,137,336 the vertical/indirect dimension of the 3QMAS NMR spectrum becomes free from second-order quadrupolar broadenings326,327,332 and is therefore referred to as the “isotropic dimension”, while the horizontal dimension of the 3QMAS NMR spectrum reveals a very similar NMR response as that obtained by a direct single-pulse 1D MAS NMR acquisition (ideally, they should be identical). The latter is herein referred to as the “MAS dimension”, as in Fig. 11. However, while quadrupolar broadenings are absent along the isotropic dimension of the 3QMAS spectrum recorded from a glass, the isotropic chemical-shift and second-order quadrupolar dispersions remain intact. The diso/CQh-distributions manifest in 3QMAS spectra by broad ridges extending along both 2D NMR spectral dimensions, as is evident from Fig. 11C.

610

Solid-state nmr of glasses

(A)

t1 Z 3Q

3Q Z

t2 =kt1 +3 0 -3

(B)

t1 Z 3Q

FAM

t2 =

echo

+kt1

+3 +1 0 -1 -3 Fig. 12 Schematic rf pulse diagrams of the (A) Z-filter331 and (B) shifted-echo332 3QMAS NMR experiments, shown together with their coherencetransfer pathways137 beneath. Note that the precise implementation of the shifted-echo protocol depends on the spin quantum number, where the incarnation shown in (B) applies for S ¼ 5/2 nuclei (e.g., 27Al and 17O). The time-signals at t1 ¼ 0 and t1 > 0 are depicted by dotted gray and solid black traces, respectively, with the top of the echo shifting in time by kt1, where k ¼ 19/12 for S ¼ 5/2.

Although the recommended convention for representing 2D NMR spectra137,336 plots the “indirect” and “direct” dimensions along the vertical and horizontal axes, respectively, these axes are unfortunately often swapped in many published 3QMAS spectra.

9.20.9

29

9.20.9.1

Silicate speciations

Si MAS NMR

Notwithstanding the relatively poor 29Si NMR-signal sensitivity stemming from the low natural abundance (4.7%) and modest magnetogyric ratio of 29Si (Table 1) coupled with slow T1 relaxation in glasses, 29Si MAS NMR has been employed extensively over decades to probe the network organization of silicate glasses involving one or several glass-network modifiers. Its primary value is that deconvolution of the single-pulse 29Si MAS NMR spectrum may offer quantitative fractional populations {xSin} of the {QSin} species, thereby informing about the NBO distribution among the silicate groups. However, its success depends crucially on whether the various 29Si resonances are sufficiently resolved. Unfortunately, that usually only holds for binary M2O–SiO2 glasses and silica-rich M2O–M’O–SiO2 glasses, as illustrated in the following. Fig. 13 displays 29Si MAS NMR spectra recorded from binary Na2O–SiO2 and K2O–SiO2 glasses, for which the 29Si resonances from the various {QSin} species remain well resolved to admit NMR spectra deconvolutions over a wide glass composition range. Such excellent NMR-signal discrimination is only observed across the entire glass-forming regions of the binary Li, Na and K silicate glass systems. Yet, 29Si MAS NMR has revealed valuable insight into the relationship between the {QSin} speciations and the NBO content for all alkali-based M2O–SiO2 glass systems: Li,7–12,318 Na,8–12,319,337–339 K,9–12,337,340,341 Rb,9,11,341 and Cs.9,341 However, a noticeable loss of 29Si NMR spectra resolution is observed for binary silicate glasses that either incorporate high-CFS species, e.g., divalent alkaline-earth and trivalent rare-earth metal cations,10,337,342–345 or additional network formers, such as B or Al (vide infra). Yet, a sufficient 29Si NMR-signal separation is sometimes observed among the QSi3 and QSi4 moieties in SiO2-rich multi-component silicate-based glasses,118,346 as is illustrated by Fig. 14. While a minor 29Si resonance-broadening is observed by the introduction of small amounts of B and Al in the glass (Fig. 14B and D) relative to the spectrum observed from the 16.7Na2O–11.7CaO–71.6SiO2 counterpart in Fig. 14A, all NMR spectra admit deconvolutions to derive the {xSin} values.118

Solid-state nmr of glasses

(A)

611

(B) K2O mol %

Na2O mol %

29

29

Si chemical shift (ppm)

Si chemical shift (ppm)

29

Fig. 13 Si MAS NMR spectra recorded from (A) Na2O–SiO2 and (B) K2O–SiO2 glasses, revealing increasing populations of higher-n QSin groups and more polymerized glass networks for decreasing M2O content from top to bottom. Panels (A) and (B) are reproduced from Maekawa, H.; Maekawa, T.; Kawamura, K.; Yokokawa, T. The Structural Groups of Alkali Silicate Glasses Determined by 29Si MAS-NMR. J. Non Cryst. Solids 1991, 127, 53–64, and Malfait, W. J.; Halter, W. E.; Morizet, Y.; Meier, B. H.; Verel, R. Structural Control on Bulk and Melt Properties: Single and Double Quantum 29Si NMR Spectroscopy on Alkali-Silicate Glasses. Geochim. Cosmochim. Acta 2007, 71, 6002–6018, respectively, with permission from Elsevier.

9.20.9.2

The NBO distribution among silicate groups

Si MAS NMR studies of Na2O–SiO2 glasses8,9,319,337 concluded a silicate speciation solely represented by a binary model
Si ¼ 0; 1; 2; where only two species, QSin and QSin þ 1, build the glass network, except for glass stoichiometries associated with N BO Si n 118,347
3 and 4, for which one sole QSi group with n ¼ N exists. However, subsequent results from other binary silicate glass

Early

29

BO

systems merely suggested an NBO partitioning among the SiO4 tetrahedra that is intermediate of the binary model and a statistical NBO distribution, the latter corresponding to a set {xSin} given by a binomial distribution.118,347 The deviations from the binary distribution model accentuates for (i) increasing modifier content of the glass, (ii) growing CFS (or cation potential) of the network modifier (Mz þ) cation(s),10,12,232,348 and (iii) higher fictive temperature of the glass (i.e., more rapid melt cooling).12,319,348–350 The element of “randomness” may be rationalized from “disproportionation equilibria,” according to9,10,12,337,341,345,350 nþ1 2QnSi %Qn1 Si þ QSi ; with n ¼ 1; 2; 3

(32)

Hence, most binary silicate glass systems normally reveal (at least) three coexisting species, {QSin  1, QSin, QSin þ 1}, as observed for glasses of the Li,7,11,12 Na,11,12,338 K,11,12,341 Rb,9,11 and Cs9,341 systems. Yet, to a first approximation, all remain closer to the binary n-distribution than a random/binomial scenario, whereas alkaline-earth MO–SiO210,342,343,351–354 and PbO–SiO2 glasses manifest {xSin} values closer to a statistical NBO distribution.232,348 However, the NMR spectra analysis of PbO–SiO2 glasses is compromised by an overall very poor spectral resolution among QSin groups and that Pb may partially act as a network former in lead-rich glasses.232,348,355 A {QSin} speciation represented by three coexisting {QSin  1, QSin, QSin þ 1} groups was also inferred for more complex phosphosilicate glasses incorporating both Na and Ca as network modifiers227,229 (also see Section 9.20.10.3), where the results of Fig. 15 confirm an NBO-partitioning among the SiO4 groups that is intermediate between the binary and random n distributions.229

9.20.9.3

Multicomponent silicate glasses: Limitations of 29

29

Si MAS NMR

A further accentuated Si resonance broadening occurs in silicate-based glasses that either incorporate significant amounts of anions of other electronegative elements (e.g., N or C) and/or additional network formers (e.g., Al or/and B). Here, the deshielding effects from Al[p]/B[4] sites in the second coordination sphere of 29Si lead to a continuum of SiO4 environments with similar but

612

Solid-state nmr of glasses

3

Q -92 ppm

(A)

4

2

Q

Q

(NC)S

(B)

(NC)AS (C)

(NC)BS (D)

(NC)ABS

-70 29

-80

-90 -100 -110 -120

Si chemical shift (ppm)

Fig. 14 Deconvolutions of experimental 29Si NMR spectra (black traces) recorded at B0 ¼ 9.4 T from various Na–Ca–(Al)–(B)–Si–O glasses of increasing complexity in their network former constituents: (A) 16.7Na2O–11.7CaO–71.6SiO2; (B) 16.3Na2O–11.4CaO–6.1Al2O3–66.2SiO2; (C) 16.2Na2O–11.2CaO–5.5B2O3–67.1SiO2; (D) 16.9Na2O–11.7CaO–4.0B2O3–1.5Al2O3–65.9SiO2. The gray traces peaking at around 101 ppm, 92 ppm and 82 ppm represent the peak components from the QSi4, QSi3 and QSi2 groups, respectively. The curve beneath each spectrum represents the deviation between the experimental and best-fit spectra. Reproduced from Edén, M.; Sundberg, P.; Stalhandske, C. The Split Network Analysis for Exploring Composition-Structure Correlations in Multi-Component Glasses: II. Multinuclear NMR Studies of AluminoBorosilicates and Glass-Wool Fibers. J. Non Cryst. Solids 2011, 357, 1587–1594, with permission from Elsevier.

distinct chemical shifts, which explains why 29Si MAS NMR spectra are almost always poorly resolved from oxynitride,256,257,259,268,269 aluminosilicate,10,80,81,218,219,337,356–359 borosilicate,87,215,217,242,276,277,279,360–362 and aluminoborosilicate278,363–369 glasses, unless the N, Al and/or B contents are low (Fig. 14). The 29Si peakwidth widens for increasing CFS of the network modifier, which leads to particularly broad resonances from RE-based aluminosilicate glasses, where moreover La-based glasses reveal narrower resonances than those from similar RE2O3–Al2O3–SiO2 glass compositions with the higher-CFS Lu3þ, Y3þ, and Sc3þ cations.47,72,73,75,77,259,370,371 In contrast with the glass compositions considered in Fig. 14, we now turn to the more common case of significant incorporation of B or Al into silicate glasses. Fig. 16 illustrates the degradation of the MAS NMR spectral resolution for a series of borophosphosilicate glasses formed by substituting B2O3 for SiO2 in a 24.1Na2O–23.3CaO–48.6SiO2–4.0P2O5 base glass.372 From the latter
Si ¼ 2:54 was predicted, from which it is anticipated that QSi2 and QSi3 tetraglass composition, a silicate network connectivity of N BO

hedra dominate the silicate network. That is indeed confirmed by its 29Si MAS NMR response shown in Fig. 16A, which is mainly a superposition of two Gaussian peaks centered around  80 ppm (QSi2) and  88 ppm (QSi3), which account for 40% and 57% of the total integrated NMR intensity, respectively.372

Solid-state nmr of glasses

n

fractional population of QSi

0.8

_ Si NBO 2.11

613

random MD NMR binary

0.6 0.4 0.2 0.0

2.50 0.8 0.6 0.4 0.2 0.0

2.74

n

fractional population of QSi

0.8 0.6 0.4 0.2 0.0

2.93 0.8 0.6 0.4 0.2 0.0 0

1

2

n

3

4

Fig. 15 QSin fractional populations {xSin} from different Na2O–CaO–SiO2–P2O5 glasses determined either by 29Si NMR or by molecular dynamics (MD) simulations,229 and plotted against the number of BO atoms (n) at each SiO4 group. Results are shown for increasing silicate network connectivity Si (N
BO ; Eq. 4). Note that while the glasses comprise minor P2O5 contents (6 mol%), nearly all P is present as orthophosphate groups that do not contribute to the glass network.229 The experimental and modeled data are compared with the predictions from binary and random NBO/BO distribution calculated from the expressions of Ref. 118. Reproduced from Mathew, R.; Stevensson, B.; Tilocca, A.; Edén, M. Toward a Rational Design of Bioactive Glasses with Optimal Structural Features: Composition-Structure Correlations Unveiled by Solid-State NMR and MD Simulations. J. Phys. Chem. B 2014, 118, 833–844, with permission from The American Chemical Society. Copyright the American Chemical Society (2014).

Although the somewhat fortunate dominance of only two QSin groups in this phosphosilicate glass network allowed for spectral deconvolutions, they are not warranted for the counterparts recorded from the borophosphosilicate glasses, 24.1Na2O–23.3CaO– xB2O3–(48.6  x)SiO2–4.0P2O5, that were derived from the phosphosilicate base glass and shown in Fig. 16B: despite that up to 50% of the silica reservoir was gradually replaced by B2O3, the 29Si NMR peak maximum remains at around  83 ppm throughout, while the CG shifts change only marginally.372 The main difference between the NMR spectra concerns the intensity in the spectral

614

Solid-state nmr of glasses

2

QSi

(A)

3

QSi 4

40

QSi

57

1

Q Si 1.1 1.5

-70

-80 29

-90

-100

Si shift (ppm)

(B)

mol% B2O3 0 2 7 24

-65

-70 -75 29

-80

-85 -90

84.9 84.4 84.2 84.0

-95 -100 -105

Si shift (ppm)

Fig. 16 (A) 29Si MAS NMR spectrum obtained at 9.4 T and 7.00 kHz MAS from a phosphosilicate glass of composition 24.1Na2O–23.3CaO– 48.6SiO2–4.0P2O5 (black trace), shown together with the set of {QSin} component peaks (gray traces) obtained by spectra deconvolution. Each gray number either within or on top of an NMR peak specifies its corresponding QSin population in %. The curve beneath each NMR spectrum represents the difference between the experiment and the corresponding best-fit. (B) NMR spectra obtained from a borophosphosilicate glass series, 24.1Na2O– 23.3CaO–xB2O3–(48.6  x)SiO2–4.0P2O5, where SiO2 is progressively replaced by B2O3 (x  24.3 mol%) in the base glass of (A).372

region around  90 ppm. These spectral alterations originate from a complex interplay between two counteracting 29Si chemicalshift effects discussed in Section 9.20.6: (i) 29Si deshielding from Si–O–B[4] bond formation (whereas 29Si–O–B[3] and 29Si–O–Si motifs manifest essentially equal chemical shifts), and (ii) 29Si shielding from Si–NBO / Si–BO bond replacements that accompany the B2O3-for-SiO2 substitutions at constant modifier content131; hence, the QSi3 population increases concurrently with the B2O3 content, although the 29Si NMR spectral intensity diminishes in the shift region normally associated with such groups in silicate glasses that are devoid of B. Consequently, if the influences from B[4] species on the 29Si chemical shift are ignored, a “facevalue” assessment of the NMR spectra of Fig. 16B would lead to the incorrect inference that the silicate network depolymerizes by the B2O3-for-SiO2 replacements, whendin factdthe polymerization degree is increased.131,372 We comment that P does not contribute significantly to the networks of the borophosphosilicate glasses, as discussed further in Section 9.20.10.3. The discussion of the previous paragraph has the following important message: we strongly discourage from attempting deconvolutions of poorly resolved 29Si MAS NMR spectra recorded from glasses comprising significant amounts of other glass-network formers into an over-simplified (too small) set of {QSin} species, by using guesses of “typical” chemical shifts obtained from the silicate glass analog. The influences on the 29Si chemical shift from the additional glass formers must be accounted for, the difficulty of which alone should be sufficient to discourage quantitative analyzes altogether. 29Si MAS NMR deconvolutions are only warranted in the light of additional information, such as from heteronuclear NMR experiments (Section 9.20.16) or trends observed across a large series of glasses with variable compositions, from where the (absence of) constant 29Si chemical shifts may be verified. We also guide the reader to Refs. 373,374 for advanced J/dipolar-coupling based techniques capable of discriminating among the various {QSin(mAl)} groups in aluminosilicates with distinct n and m parameters.

9.20.9.4

Structural information from CSA

The compromised 29Si MAS NMR spectral resolution from most silicate glasses precludes accurate estimates of the {QSin} populations by spectra deconvolutions. Yet, these problems may often be mitigated by exploiting the distinctly different anisotropic 29Si chemical shift parameters of the various QSin groups.11,12,340,349,350,375 Fig. 17 depicts schematic 29Si NMR spectra from static glass powders, illustrating the relationship between the {daniso, hCS} parameters and the local symmetry of the electron cloud around the 29 Si nucleus. Given that daniso vanishes for a perfect tetrahedral symmetry, very modest values of | daniso | ( 20 ppm result for the two most symmetrical tetrahedral groups, i.e., those involving solely BO (QSi4) and NBO (QSi0) species.200,376,377 Larger anisotropies

Solid-state nmr of glasses

615

4

QSi

3

QSi

2

QSi

1

QSi

0

QSi

Fig. 17 Prototypical 29Si NMR spectra observed from the various QSin groups in static glass powders. The distinctly different local symmetries of the 29Si electron environments lead to different values of the {daniso, h} parameters. Note the opposite signs of daniso for the QSi1 and QSi3 units. Reproduced from Eckert, H. Structural Characterization of Noncrystalline Solids and Glasses Using Solid State NMR. Prog. Nucl. Magn. Reson. Spectrosc. 1992, 24, 159–293, with permission from Elsevier.

are observed for the less symmetric 29Si environments of the tetrahedra with 1, 2, and 3 NBO ions, whose ranges are given within brackets: QSi1 [33, 72] ppm, QSi2 [ 35,  89] ppm, and QSi3 [ 45,  75] ppm.200,353,354,376 The presence of one sole BO (NBO) atom at the QSi1 (QSi3) group leads (ideally) to an axially symmetric 29Si chemical shift tensor,11,337,340,350–352,378,379 implying hCS ¼ 0 and a cylindrical-shaped electron cloud. In practice, however, due to variations in bond and lengths and bond angles (Section 9.20.7), significant deviations from a strict axial symmetry are sometimes observed, even for well-ordered silicate phases.289,376 Also note that the QSi3 (daniso < 0) and QSi1 (daniso > 0) tetrahedra may be discriminated from their opposite signs of their CSA11,340,350– 352,378 ; see Fig. 17. The widely differing anisotropies between the QSi3 and QSi4 groups (as well as between QSi0 and QSi1) may be exploited for their discrimination and quantification, as exemplified by Fig. 18. This represents one scenario where NMR on static powders may resolve ambiguities present in the 29Si MAS NMR spectrum due to overlap between the “typical” chemical shift ranges of the QSi3 and QSi4 groups (Fig. 9): for instance, unique 29Si MAS NMR peak assignments are sometimes not possible from multi-site crystalline samples, while the broad and overlapping resonances from QSi3 and QSi4 groups in glasses compromise accurate spectral deconvolutions to deduce the xSi3 and xSi4 values. 2D MAS NMR experimentation offers powerful means to simultaneously extract both the isotropic and anisotropic 29Si chemical shift parameters of the various coexisting QSin groups in silicate glasses, along with their fractional populations,351–354,377,379–383 thereby yielding a more complete picture of the local 29Si electronic environment and its relationship with the glass composition and nature of the glass-network modifier.379,382,383 The gist is to arrange a correlation between the isotropic and anisotropic 29Si

616

Solid-state nmr of glasses

Fig. 18 Experimental and simulated 29Si NMR spectra from a static powder of a silica-rich K2O–SiO2 glass, revealing narrow and broad resonances from QSi4 and QSi3 groups, respectively. Reproduced from Sen, S.; Youngman, R. E. NMR Study of Q-Speciation and Connectivity in K2O–SiO2 Glasses with High Silica Content. J. Non Cryst. Solids 2003, 331, 100–107, with permission from Elsevier.

NMR parameters along each respective “t1” and “t2” dimension. The currently most exploited option is the magic-angle flipping (MAF) 2D NMR protocol,351,384 which has been utilized for probing the relationships between the 29Si chemical-shift parameters and the glass composition in numerous alkali- and alkaline-earth-metal based binary silicate glasses.351–354,379,382,383

9.20.10

31

9.20.10.1

31

P MAS NMR

P versus

29

Si NMR: Similarities and differences

With a 100% natural abundance of 31P (S ¼ 1/2) and the highest magnetogyric ratio of all commonly encountered nuclei for studying bulk glass structures (then excluding the more rare 1H and 19F nuclides), 31P offers the most rapid experimentation for reaching high-quality MAS NMR spectra among all (slowly relaxing) spin-1/2 nuclides in glasses. While 29Si sites in amorphous silicates often require relaxation delays of > 1 h to reach thermal equilibrium, such long delays are normally only encountered for 31P sites of a few well-ordered phosphate phases (such as a-Ca3(PO4)2; Ref. 385), whereas delays of 10–20 min are normally sufficient for P-bearing glasses. Moreover, the receptivity of 31P is 181 times that of 29Si (Table 1), whereas the ratio (gP/gSi)3 z 8.5 alone (Eq. 16) implies almost an order of magnitude stronger 31P NMR signal/transient acquired from a phosphate glass relative to that from a 100% 29Si enriched silicate glass of equal stoichiometry. The highly charged P5þ cation promotes P–NBO bonds (Section 9.20.2.3), which along with the inherent P]O bond renders 2 QP , QP1, and QP0 groups the most frequently encountered ones in phosphate glasses, whereas QP3 groups are only found in vitreous P2O5 and modifier-poor phosphate glasses. This is in stark contrast with most silicate glass networks, which are built from higherconnectivity {QSi4, QSi3, QSi2} groups. Moreover, although orthosilicate glasses are in general difficult to prepare, orthophosphate groups in amorphous environments are abundant in mineralizing bone tissue, where amorphous calcium phosphate (ACP), i.e., an HPO4- and CO32-bearing Ca3(PO4)2 , nH2O phase,386 is believed to constitute a transient precursor phase of bone mineral.387,388 Except for these (practical) distinctions to 29Si MAS NMR in silicates, 31P experimentation on binary M(2)O–P2O5 glasses revels analogous disproportionation equilibria (Eq. 32) that control the n-distribution of {QPn} groups.389 Indeed, CaO–P2O5 glasses around the metaphosphate composition manifest noticeable deviations from a binary {QPn, QPn þ 1} distribution,197 which accentuate for increasing modifier content and become substantial for pyrophosphate glasses, particularly for high-CFS ions, such as Mg2þ, Pb2þ and Zn2 þ.232,233,390–393 Notably, however, the stronger P–NBO affinity renders the equilibrium constants smaller for M(2)O–P2O5 glasses than their silicate counterparts. For the extensive literature on early studies on binary phosphate glasses by 31P MAS NMR during the 1980s and 1990s, we guide the reader to previous reviews by Eckert, Kirkpatrick, and Brow.378,394,395

Solid-state nmr of glasses

617

3

QP

2

QP

1

QP

0

QP

Fig. 19 Schematic 31P NMR spectra observed from the various QPn tetrahedra in static glass powders. Note the very similar trends as those observed for 29Si in Fig. 17, with the main exception that the formally non-bridging P]O bond at the PO4 tetrahedron precludes formation of QP4 groups. Reproduced from Eckert, H. Structural Characterization of Noncrystalline Solids and Glasses Using Solid State NMR. Prog. Nucl. Magn. Reson. Spectrosc. 1992, 24, 159–293, with permission from Elsevier.

As witnessed by Fig. 19, the relationships between the 31P {daniso, hCS} parameters parallel those for 29Si in Fig. 17. However, the PO4 groups in crystalline as well as amorphous phosphate phases exhibit much larger 31P chemical-shift anisotropies that those of 29 Si: only the 31P sites of the most symmetric QP0 moieties reveal modest | daniso | values of 10–40 ppm, whereas daniso spans [53,102] ppm, [ 107,  167] ppm, and [ 195,  202] ppm for the QP1, QP2, and QP3 groups, respectively.223,232,310,396,397 Hence, for the typical MAS rates of 10–20 kHz employed for 31P MAS experimentation of phosphate glasses at B0 P 7.1 T, significant spinning sideband intensities are observed throughout (e.g., see Refs. 30,44,232,398,399). 31

9.20.10.2 Multicomponent phosphate-based glasses Owing to the larger chemical-shift separations among the QPn tetrahedra relative to their QSin counterparts (Fig. 9) but similar FWHM values of z 8–14 ppm, the 31P MAS NMR-signal discrimination among the QPn species is in general markedly better than offered by 29Si MAS NMR. Indeed, the NMR peaks from the distinct QPn groups of a given glass system remain wellresolved also for glasses incorporating network modifiers with moderate/high CFS197,232,233,390–393 (c.f. Section 9.20.9), or even multiple Mþ/M2 þ species.30,44,229,399,400 The improved resolution is particularly evident in 31P MAS NMR spectra from glasses involving additional anion species (e.g., oxynitride glasses211,252,261,262,264) or other network formers, such as Al,65–71 which sometimes yield sufficient resolution to enable spectral deconvolutions. Yet, one fundamental problem plagues 31P MAS NMR on aluminophosphate, borophosphate, and aluminoborosilicate glasses, namely that while the distinct-n QPn moieties are usually well-resolved, the markedly higher structural complexity still precludes detailed analysis by deconvolutions into the plethora of different QPn(mAl), QPn(mB), and QPn(mSi) groups with variable number of bonds to Al, B, and Si. Here, advanced heteronuclear NMR experimentation has proved extremely valuable for constraining the 31 P chemical-shift ranges for the various coexisting phosphate groups in aluminophosphate71,106 and borophosphate97,98,100,101 glasses, which may subsequently be used for more reliable deconvolutions of the 31P MAS NMR spectra to quantify the respective sets of {QPn(mAl)} and {QPn(mB)} populations.

618

Solid-state nmr of glasses

9.20.10.3 Bioactive (boro)phosphosilicate glasses Thanks to their bone-bonding properties and readily degraded glass networks on their contact with body fluids,401–403 phosphosilicate glasses rich in network modifiers but with low P contents ( 6 mol% P2O5) are utilized as biomedical implants. Most of such bioactive glasses (BGs) are members of the Na2O–CaO–SiO2–P2O5 system, or variations formed by partially substituting Naþ and/or Ca2þ by other cations, such as Kþ, Mg2þ or Sr2 þ.404,405 Routine 31P and 29Si MAS NMR experimentation has been exploited extensively over the past 25 years to better understand the BG glass structure organization.224–229,406–411 The structural role of P in such glasses is a central but debated topic, in particular the (non)existence of QP1 groups in the networks and whether they imply a P–O–P or P–O–Si bonding, as well as how the PO4 tetrahedra are distributed across the glass structure. While 31Pbased NMR experimentation has already provided unequivocal answers to each of these questions,228,229,408,409 they remain as a source of confusion in the BG community, partly stemming from misconceptions of what routine 31P and 29Si MAS NMR spectra candand cannotdinform about, as elaborated on in Ref. 411. Although the phosphate speciation in Na2O–CaO–SiO2–P2O5 glasses is dominated by orthophosphate (QP0) anions, QP1 groups exist in minor amounts,224,225,229 whose precise populations depend on the particular modifier cation in the glass61,225 and increase concurrently with the silicate network connectivity229: they remain modest (xP1 ( 0.1) in bioactive glass compositions and may reach up to xP1 z 0.2 in more polymerized (and therefore non-bioactive) phosphosilicate networks.132,229 Moreover, all such QP1 groups involve Si–O–P bonds (as opposed to P–O–P), as proved unambiguously by heteronuclear 31P–29Si MAS NMR experimentation408 (see Section 9.20.16). The main orthophosphate species are randomly distributed across the Na2O–CaO– SiO2–P2O5 glass structure, where they assume interstitial positions around the silicate networks,228,409 whereas a minor QP0 clustering effect is reported for a CaO–SiO2–P2O5 glass composition,408 which presumably stems from the sole presence of the higherCFS Ca2þ ion. Recent 31P MAS NMR structural studies have also examined borophosphosilicate glasses131,372,412,413; see Fig. 1 and Section 9.20.9.3. The introduction of B into a Na2O–CaO–SiO2–P2O5 glass enhances its degradability in body fluids.402,414 When SiO2 is replaced by B2O3 on an equimolar basis at constant network modifier content, the silicate network connectivity is increased, which leads to a concurrently increased QP1 population for growing B2O3 content of the borophosphate glass.131,132,372 Yet, as concluded from both heteronuclear 11B–31P NMR experimentation (Section 9.20.16) and MD simulations, a majority of the QP1 units remain bonded to Si throughout the range of B contents in the glass, notwithstanding a slight preference for P–O–B[4] bond formation relative to P–O–Si, while P–O–B[3] linkages are absent.131,132

9.20.11

27

Al (S ¼ 5/2) NMR

As for 31P, the 100% natural abundance of 27Al combined with its moderately high magnetogyric ratio render 27Al MAS NMR experimentation straightforward and rapid, largely thanks to the fact that the sizable quadrupolar moment (Table 2) does not manifest too severely in the (relatively) symmetric 27Al environments of the AlO4, AlO5 and AlO6 polyhedra present in oxide-based glasses. Hence, the central task of 27Al (3Q)MAS NMR is the characterization of the Al speciation, which is what this section revolves around.

9.20.11.1 The Al speciations of common glass systems In P-rich aluminophosphate glasses, Al assumes octahedral coordination, which prevails for increasing Al2O3 content up to z10 mol%, where AlO4 groups become most abundant, after a transition regime where all three {Al[4], Al[5], Al[6]} coordinations co-exist in significant amounts.65–71 Owing to the strong propensity for Al–O–P linkages (Section 9.20.2.2), the AlOp polyhedra act as cross-linking sites in phosphate-based glass networks, whereas Al–O–Al bonds are essentially absent, as confirmed by more recent dipolar-based NMR experimentation.107,108 Likewise, alkaline-earth based aluminoborate glasses comprise significant higher-coordination Al[5] and Al[6] species.415–417 As concluded from the first 27Al MAS NMR studies during the 1980s, AlO4 dominates the Al speciation in most aluminosilicate glasses based on network modifiers with low or moderately high CFS, i.e., all cations of the alkali and alkaline-earth metals (except for Mg2þ).10,80,81,218,219,418 According to the “conventional” aluminosilicate glass model,5,10,80–82,121 this scenario applies for all Mz þ-based glass stoichiometries nMMOz/2–nAlAlO3/2–nSiSiO2 with (A) nAl/nSi # 1 that moreover enable charge-balance of all Al species as Al[4] by also obeying (B) nAl/nM # z. Prerequisite (A) stems from the Loewenstein Al avoidance rule (Section 9.20.2.2), which cannot be fulfilled if all Al species are in tetrahedral coordination for nAl/nSi > 1, whereupon highercoordination Al[p] species form.356,419 (Conditions (A) and (B) are only approximate; see Stevensson and Edén247 for rigorous criteria). At the nAl/nSi ¼ 1 boundary, the conventional/mainstream glass model predicts a “tectosilicate” structure similar to that holding strictly for crystalline aluminosilicates,5,89 i.e., a 3D aluminosilicate network involving only O[2] species and built from strictly alternating Si–O–Al[4] bonds between QSi4QAl4 pairs. The perpetual hardware improvements of higher magnetic fields and, in particular, faster MAS capabilities have significantly improved the detection limits of the minor AlO5 and AlO6 populations that in the pioneering 27Al MAS NMR spectra remained buried in the tail of the dominant second-order quadrupolar-broadened 27Al[4] response.10,80,81,218,219,418 Accumulating experimental evidence over the past 25 yearsdwhere 27Al and 17O (3Q)MAS NMR have played major rolesdreveals significant deviations from the “conventional” aluminosilicate glass structural mode, as first highlighted by the presence of a few percent of NBO species

Solid-state nmr of glasses

619

in tectosilicate glasses.420 Subsequently, minor AlO5 contributions to the Al speciation ((7%) were reported for tectosilicate CaO– Al2O3–SiO2 glass compositions220,221,421,422 and they increase dramatically for increasing Mz þ CFS.75,423,424 Hence, AlO5 and AlO6 moieties are abundant structural motifs in Mg2þ (Ref. 46,419,422,424–430) and RE3 þ (Ref. 47,72–78) bearing aluminosilicate glasses, as may be verified from the 27Al MAS NMR spectra of Figs. 7 and 11. Moreover, the higher-coordination Al species enhance the physical and mechanical glass properties, where the microhardness of RE2O3–Al2O3–SiO2 glasses with RE ¼ {La, Y, Lu, Sc} increases linearly with the average Al coordination number (ZAl).77,431 Moreover, very recent research suggests that AlO5/AlO6 groups are also beneficial for reducing the crack resistance,432–434 where glasses that combine a high microhardness with a high crack resistance are difficult to achieve due to the brittleness typically observed for hard glasses; see Edén82 for further discussion.

9.20.11.2 Extracting

27

Al[p] NMR parameters

Onwards focussing on glasses where Al is not exclusively in tetrahedral coordination, the identification and quantification of the various AlOp polyhedra is readily addressed by standard single-pulse and 3QMAS 27Al NMR experimentation, as well as the estimation of the NMR parameters of the 27Al[p] species. Below we review some strategies for achieving these tasks: although here illustrated in the context of the Al[p] coordinations in Al-bearing glasses, they are in general applicable also other half-integer spin quadrupolar nuclei in glasses for which the resonance of the various coordination species are resolved, notably 11B and 17O. For detailed procedures and further discussion, see Edén.82 We recall that the center of gravity shift (dCG) of the 27Al[p] MAS NMR peak from an AlOp group is always lower than the average Q ) in Eq. (25). Nowaisotropic chemical shift, which must be disentangled from the isotropic second-order quadrupolar shift (diso n o ½p
½p
½p days, the two most common approaches to simultaneously determine the x ; d ; C parameter triplet for each AlOp populaAl

iso

Qh

tion involves (i) deconvolution of the experimental CT MAS NMR spectra region by iterative fitting of numerically simulated spectra, typically by assuming a Gaussian distribution of isotropic chemical shifts (see Section 9.20.7) along with the Czjzek distribution of the quadrupolar product435–437; (ii) the CG shifts of 3QMAS 27Al NMR spectra readily offer an extraction of the n o
d½p ; C
½p parameter pair, whereas the integrated 2D 27Al NMR peak gives a (rough) assessment of the fractional population xAl[p]. Qh iso o n ½p
½p Depending on the method used for deriving the
dAl ; C Qh parameters, the magnitudes of the average quadrupolar products differ significantly among literature reports for comparable glass compositions: for accurate results, we discourage the use of 3QMAS NMR spectra, because the 3QC excitation/reconversion processes depend on the precise values of the set n o
½p ,281,327,438,439 even if using 3QMAS protocols mitigating this dependence (such as the fast amplitude modulation scheme440 C Qh


½p values obtained implemented in the shifted-echo scheme of Fig. 12B), and/or applying approximate correction procedures.423 C Qh from 3QMAS NMR are usually underestimated, accompanied by a slight overestimation of the average isotropic chemical shift.76,441 Although such underestimations are normally less than < 20%, they are strikingly evident when (for instance) contrasting the
½4 values of 4–5.5 MHz from La and Y aluminosilicate glasses in Ref. 74 that are only half of those around 3QMAS-derived C Qh

9.5–11 MHz reported in Refs. 76–78 that employed numerical fitting of the 1D 27Al MAS NMR spectra with the Czjzek distribution. ½p
½p by exploiting Besides options (i) and (ii), two prevailing alternatives in earlier literature involve the estimation of
d and C iso

Qh

½p

the different dependencies of the chemical and second-order quadrupolar shifts on the external magnetic field, where
diso is indeQ pendent of B0 whereas diso scales as B0 2 (Section 9.20.5.3). Hence, by recording MAS NMR spectra at multiple magnetic fields, the Q is proportional to the slope of the line.151,442 The average quadB0 ¼ 0 intercept in a plot of dCG against B0 2 yields
diso , whereas diso rupolar product is then calculated via Eqs. (23) and (24). For spin-5/2 nuclei, such as 17O and 27Al, another approach that neither requires elaborate fitting procedures nor 3QMAS NMR nor multiple-field NMR experimentation, is to utilize the information from the much narrower ST MAS NMR signals associated with the  1/2 4  3/2 m-transitions.5,190,191 Determining the CG shifts of the o n ½p
½p parameters,5,190,191 as described in detail in CT MAS NMR peak along with those of the ST spinning sidebands yields the
d ; C iso

Qh

Ref. 82. Although in general much less useful for S ¼ 3/2 nuclei and other half-integer spins with S s 5/2 due to their similar ST and o n ½p
½p parameters for 11B and 23Na in CT MAS NMR peak widths, this approach has also found use for deriving the
d ; C iso

Qh

glasses.24,32,216,372

9.20.11.3 Quadrupolar-product trends among the

27

Al[p] sites

Two trends emerge when contrasting literature data on the sets of {27Al[4], 27Al[5], 27Al[6]} quadrupolar products from various (MOz/ 2)–Al2O3–SiO2 aluminosilicate glasses from the CaO–Al2O3–SiO2 (Ref. 221), MgO–Al2O3–SiO2 (Refs. 422, 426, 430), RE2O3– Al2O3–SiO2 (Refs. 47, 74–78), and Al2O3–SiO2 (Refs. 443–445) systems, along with thin films of amorphous Al2O3 o n
½p values increase concurrently with the CFS of the Mzþ cation according to Ca2þ < Mg2þ < La3þ < (Refs. 446,447): (i) all C Qh

Y3þ < Lu3þ < Sc3þ. (ii) For a given glass composition, the average quadrupolar product decreases for increasing coordination

620

Solid-state nmr of glasses


½4 > C
½5 > C
½6 . number: C Qh Qh Qh Remarkably, the overall largest quadrupolar products are observed for the seemingly most different glasses, namely RE2O3– Al2O3–SiO2 glasses and those devoid of modifiers, i.e., Al2O3–SiO2 and amorphous Al2O3. For the high-CFS RE3 þ bearing glasses, the trend is attributable to more significant AlOp distortions caused by the firmer control of the REOp environments by the high-CFS cations (relative to those with low field strengths). For the amorphous aluminosilicate phases devoid of glass network modifiers, on the other hand, a formally similar scenario is at play: the aluminosilicate glass structure must adapt towards a “self-compensation” for the negatively charged AlO4 tetrahedra, which also leads to significant deviations from perfect tetrahedral, pentahedral, and octahedral Al[p] environments. See Ref. 82 for further discussions on the shared structural features (such as O[3] coordinations) between RE2O3–Al2O3–SiO2 and Al2O3–SiO2 glasses, i.e., those that formally offer the “most” and “least” charge-compensation of their AlO4 groups, respectively.
½p values from glasses of the Note that trend (ii) above is not restricted to aluminosilicates, but is also evident from reported C Qh

M(2)O–Al2O3–B2O3 (M ¼ {Na, Ca, Mg}),417 Na2O–Al2O3–P2O5,69,71,105 La2O3–Al2O3–P2O5,136 and Al2O3–B2O3–P2O5448 systems. However, for Al-bearing glasses with low-CFS modifier speciesdsuch as Naþ, Kþ, and to a lesser extent also Ca2þdthe
½p values lead to several exceptions, where particularly C
½5 (C
½4 is frequently observed.69,71,105,221 overall lower C Qh

Qh

Qh

11

9.20.12

B (S ¼ 3/2) NMR

9.20.12.1 NMR signatures of the

11

BO3 and

11

BO4 groups

11

The high receptivity of B (stemming from its large magnetogyric ratio and high natural abundance (80%)) along with a low quadrupolar moment (Table 2), have rendered solid-state NMR an ubiquitous probe of the borate speciations in numerous crystalline and amorphous B-bearing phases, including structural studies of the commercial Pyrex glass.449–451 In crystalline compounds, the highly symmetric 11BO4 tetrahedra are associated with very modest quadrupolar coupling constants, CQ[4] ( 0.8 MHz throughout (and more typically 300–500 kHz), producing a near-Gaussian MAS NMR peak. The less symmetric planar 11BO3 groups, on the B[3]

B[4]

14.8 11.3

B[4]

B[3]

0 ppm

B[4]

–0.1 ppm

–0.3 ppm

14.8 11.3

B[3] 14.8 11.3

R

(A)

2Q dimension (ppm)

-8

N2.0–0.26

N4.0–1.2 B[4]–B [4]

N2.0–0.5

0

–0.5

8 13.0 ppm

B[3]–B [4]

16 24

22.7

B[3]–B [3]

29.2

32

(D)

(E)

-8

2Q dimension (ppm)

(C)

(B)

NR

NC4.0–3.3

(F)

NC2.0–0.5

NC4.0–1.2 –0.3

0 8

13.0 ppm

16

22.8

24

29.4

32 20

15

10

5

0

-5

1Q dimension (ppm)

20

15

10

5

0

-5

1Q dimension (ppm)

20

15

10

5

0

-5

1Q dimension (ppm)

Fig. 20 2Q-1Q correlation 11B NMR spectra obtained at B0 ¼ 14.1 T and 24.0 kHz MAS from Na2O–(CaO)–B2O3–SiO2 glasses with variable compositions specified as NK–R and NCK–R for Na and mixed-Na/Ca glasses, respectively, where K ¼ n(SiO2)/n(B2O3) and R ¼ n(Na2O)/n(B2O3). The 2D NMR spectra reveal the presence of B[3]–O–B[3], B[3]–O–B[4], and B[4]–O–B[4] linkages in the borosilicate glass networks, as identified in (C). Projections along the 2Q and 1Q dimensions are displayed to the right and at the top of each 2D NMR spectrum, respectively, together with the MAS NMR spectrum recorded directly by single pulses (red trace); the shaded areas in (A) show deconvolution results of the MAS NMR peakshape from 11 BO3 groups in “ring” (R) and “non-ring” (NR) moieties; see Section 9.20.12.3. Reproduced from Yu, Y.; Stevensson, B.; Edén, M. Direct Experimental Evidence for Abundant BO4–BO4 Motifs in Borosilicate Glasses From Double-Quantum 11B NMR Spectroscopy. J. Phys. Chem. Lett. 2018, 9, 6372–6376, with permission from The American Chemical Society. Copyright the American Chemical Society (2018).

Solid-state nmr of glasses

B

621

[4]

(A)

B

[3]

(NC)BS

*

*

(B)

(NC)ABS *

*

*

*

(C)

80

40

0

11

-40

GF -80

B shift (ppm)

Fig. 21 11B NMR spectra recorded at B0 ¼ 9.4 T and 8.80 kHz MAS from (A) 16.2Na2O–11.2CaO–5.5B2O3–67.1SiO2 and (B) 16.9Na2O–11.7CaO– 4.0B2O3–1.5Al2O3–65.9SiO2 glasses, along with (C) a commercial glass fiber sample (“GF”), which constitutes a complex aluminoborosilicate glass of composition 16.4Na2O–0.6K2O–9.0CaO–2.3MgO–3.7B2O3–1.4Al2O3–66.6SiO2. Note the significant degradation of the spectral resolution among the 11B[3] and 11B[4] resonances in (C) relative to (B), which stems from broadenings from paramagnetic Fe2 þ/Fe3 þ and Mn2 þ species in the glass fiber. Asterisks mark spinning sidebands. Reproduced from Edén, M.; Sundberg, P.; Stalhandske, C. The Split Network Analysis for Exploring Composition-Structure Correlations in Multi-Component Glasses: II. Multinuclear NMR Studies of Alumino-Borosilicates and Glass-Wool Fibers. J. Non Cryst. Solids 2011, 357, 1587–1594, with permission from Elsevier.

other hand, exhibit larger quadrupolar coupling constants within a narrow range of 2.4–2.8 MHz (regardless of the composition and structural ordering of the phase),214,237,239,243,452,453 as revealed by a characteristic second-order quadrupolar MAS NMR peakshape. 11B chemical shift anisotropies are low ((10 ppm454) and readily averaged out by moderately fast MAS. The asymmetry parameter of the 11B[3] EFG tensor correlates with the number of BO/NBO species at the triangular BO3 moiety, where each case of three BO or NBO atoms at the 11BO3 triangle reveals the typical powder lineshape of a nearly axially symmetric tensor (hQ z 0),237,239,453 as that observed for the 27Al site of SrSiAlD (Fig. 7), as well as the 29Si and 31P sites of Q1/Q3 tetrahedra of static powders shown in Figs. 17 and 19, respectively. The 11B nuclei of trigonal borate groups that accommodate one or two BO/NBO atoms, on the other hand, exhibit larger asymmetry parameters within the range 0.4 ( hQ ( 0.8.237,239,243,453 Because the EFG tensor and the associated quadrupolar interaction predominantly reflects the local symmetry of the 11B sites, the
½3 and C
½4 ) in glasses remain close to those of crystalline phases.84,215– typical values of corresponding quadrupolar products (C Qh

217,239,242,285,369,452,455–458

Qh

Hence, the distinctly different peak widths and chemical shift separation of 15–20 ppm (Section 9.20.6.2) among the two 11B[3] and 11B[4] coordinations make them readily discriminated in the MAS NMR spectrum without application of 3QMAS or other high-resolution techniques. At (moderately) high magnetic fields of B0 14.1 T, the narrow 11BO4 MAS NMR peak is well-resolved in the low-shift spectral region, as witnessed by the MAS NMR spectra shown by red traces in Fig. 20 and recorded at 14.1 T from various borosilicate glasses.133 11B MAS NMR spectra obtained at low fields (B0 # 7.1 T) also offer excellent signal discrimination among the two B coordinations, with the 11B[4] NMR peak appearing as a narrow peak within the much broader second-ordered quadrupolar powder pattern of the 11B[3] species. The least transparent discrimination among the two 11 [p] B resonances occurs at B0 ¼ 9.4 T, where the 11B[4] peak superimpose with the lower-ppm region of the 11B[3] resonance, as illustrated by the 11B MAS NMR spectra recorded from various multi-component B-bearing glasses shown in Fig. 21A and B.118 Yet, although the accuracy of the estimated quadrupolar product of the 11BO3 groups is most affected by the overlapping NMR signals, accurate fractional populations of 11B[3] (xB[3]) and B[4] (xB[4]) are accessible by deconvolutions of both spectra of Fig. 21A and B (see Section 9.20.11.2). Note that xB[3] þ xB[4] ¼ 1 (Eq. 31). We comment that xB[4] is in most of the literature denoted “N4”, although it does not refer to an (absolute) number/quantity of BO4 groups in the glass structure but merely to the fraction thereof out of all B[p] species. This is one example where a misleading notation in the glass community has been perpetuated for almost a century; see Ref. 6 for other, much more problematic, examples of jargon notation persisting in the glass science nomenclature.

622

Solid-state nmr of glasses

(A)

(B)

(C)

(D)

(E)

(F)

Fig. 22 Illustration of superstructural units well-known to build the structures of crystalline borates and/or borosilicates, and proposed to exist in borate and/or borosilicate glasses.456,463–465,468,469 Note that all O atoms are bridging, where Ointra refers to O within each superstructural unit, whereas Ointer denotes atoms shared with neighboring units (not shown).

9.20.12.2 Paramagnetic broadening The 11B MAS NMR spectrum of Fig. 21C was recorded from a glass fiber specimen of similar chemical composition as the aluminoborosilicate glass of Fig. 21B. Here, the striking loss of spectral resolution and markedly broader NMR responses from both B[3]/ B[4] coordination species stem neither from the complex multi-component character of the glass fiber nor from the normally dominating second-order quadrupolar broadening, but merely originates from minor amounts of paramagnetic Fe3þ and Mn2þ species present in the glass fiber (0.14 mol% Fe2O3 and 0.13 mol% MnO).118 The very large magnetic moment of the unpaired electrons of paramagnetic ions couple strongly with the nuclear spins via a similar mechanism as the through-space dipolar interaction (Section 9.20.4.4), but are orders of magnitude larger than any spin–spin dipolar interaction. Notwithstanding the inherently broad resonances from distributions of NMR parameters in (for example) 29Si, 31P, and 11B MAS NMR spectra from glasses, the NMR signals of all nuclei within a radius of a few Å from a paramagnetic center may be broadened beyond detection. See Refs. 180,249,459 for further illustrations of paramagnetic effects in the context of minerals, which often comprise non-negligible amounts of Fe2þ/Fe3þ and other paramagnetic cations. The paramagnetic NMR signal-broadening also stems from a significant acceleration of the T2 relaxation process that controls the NMR-signal lifetime (see Section 9.20.4.3). Yet, while that broadening is highly undesirable, the paramagnetic species also accelerate the T1 relaxation, which results in a much faster return to thermal equilibrium. Consequently, a deliberate doping of the glass with paramagnetic species in amounts (0.2 wt% is a common trick to significantly speed up the NMR signal averaging by shortening the required relaxation delays, where a compromise must be made between achieving sufficiently rapid spin-lattice relaxation, while the undesirable paramagnetic broadening is minimized to avoid too detrimental spectral resolution losses.

9.20.12.3 Structural models of borate-based glasses The detailed structures of borate and borosilicate glasses are long-standing controversies, which in the early literature was often referred to as an “enigma.” Two main branches of structural models/theories of borate-based glasses have been debated over

Solid-state nmr of glasses

623

decades without a firm consensus: (i) models that represent extensions of the CRN theory of Zachariasen and Warren,1–3 where the borate/borosilicate glass forms networks of randomly interconnected {BO3, BO4, SiO4} groups, subject to additional bonding preferences, such as a postulated absence of B[4]–O–B[4] bonding83–87,460–462 (yet, see Section 9.20.15.5). (ii) As proposed by KroghMoe463–466 and building on earlier ideas by Hägg,467 an alternative description of borate-based glasses involves a random mixing of “superstructural units”, each representing a larger aggregate of interconnected {BO3, BO4, SiO4} moieties and effectively constituting the smallest network building blocks. Fig. 22 depicts some common superstructural units proposed to exist in M(2)O–B2O3–(SiO2) glasses. They are indeed encountered in numerous crystalline borate/borosilicate phases, where we refer to the excellent review by Wright468 for details. While no widely spread consensus is hitherto reached concerning the presence/absence of superstructural units in borate-based glasses, qualitative support thereof is given by the 11BO3 NMR responses, whose second-order quadrupolar powder patterns (e.g., see Fig. 20) remain close to those observed from well-ordered structures, hence giving evidence for a much lower distribution in the quadrupolar products, and thereby geometrical parameters, than (for instance) their 27Al[p] counterparts in Al-bearing glasses (Figs. 6, 7, and 11). Yet, notwithstanding ample circumstantial evidence from both Raman and 11B NMR spectroscopies of all superstructural units displayed in Fig. 22 in borate-based glasses, an unambiguous evidence thereof remains to be presented; irrefutable proof only exist for the boroxol rings (B3O6; Fig. 22A) in vitreous B2O3, whose presence is confirmed by multiple structural characterization techniques,466 encompassing neutron diffraction,470–472 Raman spectroscopy,469,473,474 as well as 17O and 11B MAS NMR.475–477 Much more dubious is the common 11B NMR analysis approach of deconvoluting the MAS powder lineshape from the 11BO3 groups into “ring” and “non-ring” contributions (see Fig. 20), whose precise meaning are ill-defined and differ among various reports, but are often taken to imply B[3] sites of boroxol rings along with “non-ring” B[3] counterparts present in linear B[3]–O–{B[3]/B[4]/Si} constellations.131,217,235,242,284,372,478,479 Notably, the well-accepted structure of amorphous B2O3 involves a hybrid of the CRN and superstructural-unit descriptions, involving z 73% of all B[3] sites incorporated into B3O6 rings that are interconnected with “non-ring” BO3 groups.466,468,470–472 Hence, it is likely that the more complex M(2)O–B2O3–(SiO2) glasses also manifest features of both models, with structures involving of a random intermixing of superstructural units interleaved by one or several interlinked {BO3, BO4, SiO4} groups. The so-called “boron anomaly”84,460,464 of borate and borosilicate glasses manifests as nonlinear trends in their physical properties, such as the density,83,480–483 glass transition temperature,83,462,483 and microhardness,482 all of which are enhanced when low/moderate amounts of network modifiers are added to a B2O3 melt. These effects are nowadays fully understood and no longer considered a “mystery.” In contrast with the SiO2 and P2O5 glass formers, melt-quenching of a mixture of B2O3 and a minor amount of M(2)O does not produce a glass with NBO anions. Rather, for each positive unit charge, one planar BO3 group converts into a [BO4/2] tetrahedron,84,460,464,468 leading to an increased density, glass transition temperature, and microhardness. For M(2)O–B2O3–(SiO2) glasses, such BO3 / [BO4] conversions prevail for increasing M(2)O content until the fractional B[4] population (xB[4]) is maximizeddand hence also the physical properties. The precise maximum value of xB[4] depends on the CFS of the network modifier, where higher field-strength cations promote NBO formation.133,242,364,365,484–486 For a borosilicate glass, xB[4] also depends on the relative amounts of Si and B.455,456,487 For a further increase in the modifier content (nM), the physical properties diminish because the reverse [BO4] / BO3 process occurs, while NBO species formdnow with an equimolar relationship with nM; see Section 9.20.12.4. In M(2)O–Al2O3–B2O3–SiO2 glasses, there is a competition of the charge compensation between the [BO4/2] and [AlO4/2] tetrahedra, which is “won” by Al,27,363–367,369,488,489 and implying that an effectively smaller Mz þ reservoir is available for driving the BO3 / [BO4] transformation. Hence, up to moderately large modifier contents, the BO4 (BO3) population in the aluminoborosilicate glass is lower (higher) than its M(2)O–B2O3–SiO2 counterpart of otherwise equal stoichiometric nM:nB:nSi proportions.

BO4 fraction

MD NMR YDBX

– =x(Na2O)/x(B 2O3) Fig. 23 BO4 fractional populations plotted against the molar ratio R ¼ x (Na2O)/x (B2O3) for Na2O–B2O3–SiO2 glasses with x (SiO2)/x (B2O3) ¼ 2. The solid lines represent predictions from the Yun-Dell-Bray-Xiao (YDBX) model,455,456 whereas all open symbols stem from experimental 11B NMR results from the literature,24,235,279,283,455,456,478,492–494 and the solid squares are results from MD simulations.132 Adapted from Stevensson, B.; Yu, Y., Edén, M. Structure–Composition Trends in Multicomponent Borosilicate-Based Glasses Deduced from Molecular Dynamics Simulations With Improved B–O and P–O Force Fields. Phys. Chem. Chem. Phys. 2018, 20, 8192–8209, with permission from the PCCP Owner Societies.

624

Solid-state nmr of glasses 11

9.20.12.4 A

B NMR-derived structural model of borosilicate glasses

Large parts of the current understanding of borate and borosilicate glass structures stem from the 11B (MAS) NMR work pursued over decades by Bray and co-workers,84,452,455,456,484,490,491 which culminated in the Yun–Dell–Bray–Xiao (YDBX) structural model for RNa2O–B2O3 and RNa2O–B2O3–KSiO2 glasses parameterized by the stoichiometric ratios R ¼ n(Na2O)/n(B2O3) and K ¼ n(SiO2)/n(B2O3).455,456 The YDBX model successfully predicts the xB[4] alterations for borosilicate glasses with increasing R455,456 as illustrated by Fig. 23 that contrasts the predicted fractional BO4 population with those observed by 11B NMR experiments24,235,279,283,455,456,478,492–494 and atomistic MD simulations.132 Evidently, the YDBX model accounts very well for the borate speciation in RNa2O–B2O3–KSiO2 glasses, where four composition regimes were identified456: for low Na2O contents (regions I–II), BO3 / BO4 conversions occur up to R # Rmax ¼ K/16 þ 1/2, meaning that Naþ assumes a sole charge-compensating role of the [BO4] tetrahedra. The borosilicate structure was proposed to consist of a borate network built from diborate groups (Fig. 22D), interconnected with a silicate network via “reedmergnerite” motifs,455,456 B[4](OSi)4, illustrated in Fig. 22E. Hence, glass compositions with R < Rmax exhibit networks comprising only B[3]–O–B[3], Si–O–Si, and B[4]–O–Si linkages, whereas NBO anions emerge only for R > Rmax (region III of Fig. 23), all of which locate at the SiO4 tetrahedra, whereas B[3]–NBO bonds occur for Na-richer glass compositions with R > (K þ 1)/4 (region IV of Fig. 23).456 Despite its success in fully rationalizing the “boron anomaly” for Na2O–B2O3–(SiO2) glasses, as well as for qualitatively predicting the {BO3, BO4} populations of other Mþ/M2 þ based borate/borosilicate glasses,361,485 the obvious shortcoming of the YDBX model is its formulation in terms of complex superstructural units based on results from routine 11B NMR data alone.455,456,491 Indeed, subsequent 11B, 29Si and 17O (3Q)MAS NMR studies suggest an overall less ordered glass structure than that of the YDBX model, where the {BO3, BO4, SiO4} network building blocks are markedly more intermixed with all types of B[3]/B[4]– O–B[3]/Si linkages encountered,22,24,87,215,235,276,284,478,479,495 along with a more uniform NBO partitioning among the SiO4 and BO3 moieties.24,87,235,276,277,284,360,361,478,495,496 Given that the sole presence of diborate and reedmergnerite units is likely an oversimplification, other 11B NMR and Raman spectroscopy results suggest that “danburite” rings (Fig. 22F) may also coexist with the reedmergnerite motifs.215,242,487

9.20.13

17

O (S ¼ 5/2) NMR

When it comes to structural studies of oxide-based glasses and if one would be restricted to NMR experimentation on one sole nuclide, the choice would inarguably be 17O, as it may provide a wealth of information. The sharp-eyed reader will notice that several glass-structure aspects highlighted in this section on routine 17O (3Q)MAS NMR experimentation connect to several other sections of this review, which underscores that 17O alone can independently address numerous types of structural problems. An important caveat, however, is that the minute natural abundance of 17O (0.04%) requires preparation of glasses with expensive 17 O enrichment, typically introduced from precursors such as Si17O2 and Al217O3, which are normally synthesized from commercially available 17O-enriched water. The typical 17O fractions of 20–30% of all O nuclei in glasses employed for NMR provide a decent 17O MAS NMR-signal sensitivity, mainly thanks to the small quadrupolar moment of 17O and the high O contents of oxide glasses, where the modest magnetogyric ratio of 17O primarily limits the NMR sensitivity. For instance, at equal contents of the two spin-5/2 nuclides 27Al and 17O, the ratio gAl/gO renders the 27Al NMR signal (1.92)3 z 7.1 times stronger than that for 17O (Eq. 16). Notably, 17O NMR experimentation without isotopic enrichment was precluded up to the recent option of exploiting dynamic nuclear polarization (DNP) coupled with NMR, which may offer substantial NMR-signal sensitivity enhancements. However, despite a few 17O DNP NMR studies on various ordered inorganic materials,497,498 this technique has to our knowledge not yet been attempted on glasses, presumably due to the practical limitations of finding efficient paramagnetic sources for the probing of the bulk glass structure.

9.20.13.1 Dependence of

17

O NMR parameters on local structure

Experiments and DFT calculations reveal that both the isotropic 17O[2] chemical shift and the quadrupolar coupling constant in silicates depend on dO–Si, dO–M as well as qSi  O  Si.28,293,294,296–298 The quadrupolar coupling constant of the BO sites increases concomitantly with the O[2]–Si (Ref. 499) and O[2]–M (Ref. 500, 501) distances, while wider qSi  O  Si bond angles lead to larger CQ[2] values28,291,297–299,301,318,499,500,502 but lower 17O[2] chemical shifts295,298–300 (Section 9.20.6.8). The NMR parameter correlations with geometrical parameters also imply that CQ[p] correlates linearly with a negative slope against either the EFG asymmetry parameter (hQ) or the isotropic 17O[p] chemical shift.28,299–301,502 Yet, we comment that (i) while similar trends are expected for aluminosilicate glasses,295,300 the thus far few reports on correlations between 17O NMR parameters and geometrical factors generally indicated a significant data scatter295,300; (ii) Refs. 299,318 only observed a correlation between the quadrupolar coupling constant and dO–Si for the NBO sites. From the dependence of the 17O chemical shift and quadrupolar parameters on the local geometrical factors, it follows that 17O NMR offers an independent route to determining the Si–O–Si bond-angle distribution in vitreous SiO2 and silicate glasses,28,209,291,503–505 besides 29Si NMR (Section 9.20.7). An overall very good agreement was obtained between 29Si and 17O

Solid-state nmr of glasses

625

(A)

(B)

Fig. 24 17O 3QMAS NMR spectra recorded at B0 ¼ 14.1 T from aluminoborosilicate glasses incorporating (A) K and (B) Ca. Resonances stemming from various F–O–F0 and Si/B–NBO structural motifs are indicated. Reproduced from Du, L.-S.; Stebbins, J. F. Network Connectivity in Aluminoborosilicate Glasses: A High-Resolution 11B, 27Al and 17O NMR Study. J. Non Cryst. Solids 2005, 351, 3508–3520, with permission from Elsevier.

NMR-derived
qSi–O–Si values that yielded the respective estimates of 147 and 148 in amorphous silica,291 whereas average Si–O–Si angles of z133 (29Si) and z130 (17O) were observed from a binary silicate glass of composition 0.43Na2O–0.57SiO2.28 Moreover, 17O DAS NMR experiments on vitreous silica at high pressure revealed a decrease in
qSi–O–Si accompanied by an increase in
dO–Si with increasing pressure.506 Besides the decent chemical-shift separation between the 17O[1] and 17O[2] sites in oxide glasses that assists their resonanceassignments in (3Q)MAS NMR spectra (see Section 9.20.6.8 and Figs. 10 and 24), the NBO and BO environments also exhibit distinctly different magnitudes of their quadrupolar products. It is known for crystalline structures that CQ of a given 17O site correlates with the fractional ionicity (I) of the bonds to its neighboring cations, where CQ is decreased for increasing ionicity,296,507,508 where the latter follows the trend of decreasing electronegativity117 of F/M, i.e., I(O–P) < I(O–B) < I(O–Si) < I(O–Al) I(O–M).
½1 and/or C
½2 values in silicate phases reviewed Indeed, several of the established correlations between geometrical parameters and C Q

Q

½p


from the CFS and the number of Mz þ cations in the proximity of O.298,499,500 Yet, as for above suggested significant bearings on C Q 17 the isotropic O chemical shifts (Section 9.20.6.8), the quadrupolar parameters of the various BO/NBO species were examined separately. Hence, no universal correlation was reported between the quadrupolar product and structural parameters in glasses until recently, when Jaworski et al.126 demonstrated an excellent linear correlation between the DFT/GIPAW-derived average quadrupolar
½p of each 17O[p]–Sip–mAlm environment and its associated average fractional ionicity,
I ¼ ðcO  c
Þ=cO , in Y/Sc alumiproduct C Qh


is the group electronegativity obtained nosilicate glasses. Here, cE is the Pauling electronegativity of element E (Ref. 117) and c as the average over the contributions from the triplet of {p – m, m,
q} bonds to {Si, Al, Mz þ} (and the values of
q were obtained by MD simulations)126:
¼ c

ðp  mÞcSi þ mcAl þ
qcRE p þ
q

(33)

Because the bond ionicity is largest for the O–M bonds, the quadrupolar product depends primarily on the number of such contacts.126 However, the latter also correlates with the number of O[p]–Si/Al bonds (Eq. 28): this feature underlies the well-

626

Solid-state nmr of glasses

30 ppm

75 ppm

9.4 T 14.1 T

140

155

80

MAS projection NBO

NBO

BO

(A)

BO

(B)

-A -O Al

-250

l

-200

Si i -S -O

-O Si

-150

i

-S

isotropic dimension (ppm)

-300

-100 -50

Y AS

Sc AS

250 200 150 100

50

0

-50

MAS dimension (ppm)

250 200 150 100

50

0

-50

MAS dimension (ppm)

Fig. 25 3QMAS 17O NMR spectra recorded at B0 ¼ 9.4 T (black traces) and B0 ¼ 14.1 T (red traces) from aluminosilicate glasses with compositions (A) 22Y2O3–39Al2O3–39SiO2 and (B) 17Sc2O3–28Al2O3–55SiO2 glasses.126 Projections along the horizontal MAS dimension are shown at the top of the 2D NMR spectra, along with CT-selective single-pulse-acquired NMR spectra (topmost). Reproduced from Jaworski, A.; Stevensson, B.; Edén, M. The Bearings From Rare-Earth (RE¼La, Lu, Sc, Y) Cations on the Oxygen Environments in Aluminosilicate Glasses: A Study by SolidState 17O NMR, Molecular Dynamics Simulations, and DFT Calculations. J. Phys. Chem. C 2016, 120, 13181–13198, with permission from The American Chemical Society. Copyright the American Chemical Society (2016).


Q =C
Qh value of an 17O[p]–Sip–mAlm motif in a crystalline/amorphous structure increases for decreasing coorknown trend that the C dination number p, and for an increasing number m of O–Al bonds.245,502,509–511
Qh (specified within parentheses): Al–NBO (1.5–2.3 MHz); Si– These properties are reflected in the following typical ranges of C NBO (1.7–2.8 MHz); Al–O–Al (2.0–2.8 MHz); Si–O–Al (3.3–4.3 MHz); Si–O–Si (4.5–5.8 MHz); P–NBO (3.8–5.5 MHz); P–O–P
½2 values of the B–O–B and B–O–Si linkages in borosilicates are similar to those of Si– (7.0–8.0 MHz).126,205,296,507,508,512,513 The C Qh

O–Si.235,478,495

9.20.13.2 (3Q)MAS spectral resolution and NMR peak assignments Fig. 24 displays 3QMAS 17O NMR spectra recorded from K and Ca based aluminoborosilicate glasses,514 which serve as nice examples of the capability of 3QMAS experiments to resolve (most of) the coexisting 17O[1] and 17O[2] resonances. Onwards focussing on aluminosilicate glasses, single-pulse-derived 17O MAS NMR spectra may often discriminate between signals from 17O[1] and 17O[2] environments, which applies, for instance, to MOz/2–Al2O3–SiO2 glasses based on Kþ (Ref. 515), Ca2þ (Refs. 244,245,420,427), and RE3 þ (Refs. 74,126) cations, as opposed to those of Liþ (Refs. 46,423), Naþ (Refs. 423,516–518), and Mg2þ (Refs. 427,430). In scenarios where the BO/NBO sites are not already separated in the 17O MAS NMR spectrum, 3QMAS does in general not offer improved spectral resolution, with some exceptions, such as for Na2O–Al2O3–SiO2 glasses.423,516–518 The main utility of 3QMAS 17 O NMR merely lies in the often much better signal-separation among the various F–17O[p]–F0 linkages, as witnessed by the 2D
Qh NMR spectra from aluminoborosilicate glasses in Fig. 24.519 Because the improved resolution often stems from the distinct C values among different 17O[2] environments, they are often better resolved by experiments conducted at low magnetic fields B0 < 9.4 T. This applies, for instance, to the discrimination between Si–O–Al and Si–O–Si linkages, where the markedly higher quadrupolar products of the latter manifest as a broad NMR-signal ridge extending away from the direction of the chemicalshift dispersion (see Fig. 24); e.g., see Ref. 425. As for all other nuclei (Sections 9.20.9 and 9.20.11), the 17O MAS NMR spectral resolution degrades markedly for increasing zþ M CFS, as for instance reflected in increasing 17O[2] peakwidths of z25 ppm, z 35 ppm, and 60–75 ppm in MAS NMR spectra recorded from aluminosilicate glasses based on Naþ (Ref. 518), Ca2þ (Ref. 520), and RE3 þ (Ref. 126) cations, respectively. However, the most striking impact from increasing CFS concerns the progressively reduced resolution improvements offered by 3QMAS relative to single-pulse MAS NMR, as is evident when comparing the single-pulse 17O MAS NMR spectra from Y and Sc

Solid-state nmr of glasses

627

based glasses with their 3QMAS counterparts shown in Fig. 25.126 Whereas a slight resolution improvement is observed in the MAS NMR spectra obtained at the higher field of 14.1 T, the two 3QMAS counterparts reveal comparable signal separation at 9.4 T and 14.1 T. Indeed, the reduction in quadrupolar broadening at the higher field is offset by the larger broadening from the chemical-shift distribution, such that the peakwidths across the MAS dimension of the 3QMAS spectra in Fig. 25 are almost equal (in Hz, not ppm). As commented on above, the signal ridge from the Si–17O–Si linkages is even better discerned in the 3QMAS spectra obtained at the lower field of 9.4 T. The dominance of the isotropic 17O chemical shift dispersion at B0 ¼ 14.1 T suggest that no resolution improvements are expected by performing 3QMAS 17O NMR experiments at higher magnetic fields for RE2O3–Al2O3–SiO2 glasses.126 The arguably largest limitation with (3Q)MAS 17O NMR experimentation is that it has hitherto not offered unambiguous discriminations between O[1] or O[2] sites that bind to distinct B[p] or Al[p] coordinations, e.g., to differentiate between Si–17O– Al[4] and Si–17O–Al[5] linkages, or between Si–O–B[3] and Si–O–B[4]. This is for instance evident from the lack of explicit B[3]/ B[4] and Al[4]/Al[5]/Al[6] assignments made in Figs. 24 and 25, respectively. Some reports have attempted at achieving such discrimination and quantification among (for instance) linkages involving B[3] and B[4] sites by deconvoluting the 3QMAS 17O NMR spectra projection along the “isotropic dimension”.235,284,478 While it may sometimes be warranted, a warning flag is raised, not the least for several assignments in the literature concerning Al[5] coordinations from 3QMAS 17O NMR spectra on aluminosilicate glasses.

9.20.13.3 Al/Si intermixing By mainly exploiting 3QMAS 17O NMR, Lee, Stebbins, and co-workers have provided quantitative assessments of the deviations from the Loewenstein Al avoidance rule in several M(2)O–Al2O3–SiO2 glass systems with different network modifiers.425,430,509,521,522 Here, the focus is on the 17O NMR intensities from the two Si–O–Si and Al–O–Al linkages, whose mere presence in aluminosilicate glass networks with nAl ¼ nSi is a direct qualitative proof that the strict –Si–O–Al–O–Si– alteration predicted from the Loewenstein Al avoidance cannot apply. The Al[4]–O–Al[4] population is demonstrated to grow concurrently with the CFS of the Mz þ cation, as reflected in M(2)O– Al2O3–SiO2 glasses with nAl z nSi and incorporating Naþ, Liþ, Ca2þ, and Mg2þ cations, which reveal the respective deviations of about 6%, 7%, 15%, and 35% from a perfect Loewenstein Al avoidance.430,509,521 Note that a statistical Al/Si intermixing corresponds to a 100% deviation from the Loewenstein avoidance. As expected, the Al[4]–O–Al[4] population elevates strongly for glass networks with nAl/nSi > 1,520,523 as well as for glasses prepared by faster melt-cooling and thereby associated with higher fictive temperatures.516 Moreover, Al[4]–O–Al[4] bonding is promoted in NBO-rich aluminosilicate glasses, because the strong preference for Si–NBO over Al–NBO bonding (see Sections 9.20.2 and 9.20.16.2) limits the number of available Si–BO bonds at the SiO4 groups that may form Si–O–Al linkages.78,245,247,359,425,524 This aspect is discussed further in Section 9.20.15.5 for the B[4]–O–B[4] analog in borosilicate glasses. Stevensson and Edén247 recently derived strict criteria on the aluminosilicate glass stoichiometry for which Al[4]–O–Al[4] may be absent if the Loewenstein Al avoidance rule would operate.

9.20.13.4 Modifier cation intermixing around the BO and NBO sites 17

O (3Q)MAS NMR experimentation has also proved valuable for probing the constellations of network modifiers around the various BO/NBO sites. As commented in Section 9.20.2.3, it is well-known that the network modifiers coordinate both BO and NBO species (see Fig. 1B), as for instance corroborated by 17O 3QMAS NMR experiments.245,429,518,525,526 Most 17O (3Q)MAS reports on the intermixing of distinct modifiers concern ternary M(2)O–M0 (2)O–SiO2 glasses. Here, such glasses that incorporate one cation species each of Mþ and M2 þ overall confirm the as-expected preference for M2 þ–NBO contacts, whereas the M þ cations associate to a higher extent with BO sites, as observed for Na2O–CaO–SiO2 (see Ref. 525 and comments in Ref. 31), Na2O–MgO– SiO2 (Ref. 526), Na2O–BaO–SiO2 (Ref. 527), Li2O–BaO–SiO2 (Ref. 20), and K2O–MgO–SiO2 (Ref. 528) glasses. Turning to the perhaps more interesting cases of ternary silicate glasses that either involve two alkali metal or two alkaline-earth metal cations, for which the charge no longer dictates the preference for Mþ–BO and M2 þ–NBO contacts, such that the cation sizes may control the Mz þ–BO/NBO partitioning, 17O 3QMAS (or DAS) NMR studies suggest a random cation intermixing in Na2O– K2O–SiO2 (Ref. 529) and CaO–MgO–SiO2 (Ref. 528) glasses, whereas the MgO–BaO–SiO2 counterparts revealed a strong preference for Ba–NBO contacts.527 Likewise, as already reiterated several times, in glass networks involving Si along with Al and/or B, the Mz þ cations not only assume a traditional “modifier” role, but also act as charge compensators of the [AlO4/2] and/or [BO4/2] groups. The (formal) unit negative charge of the latter makes them naturally balanced by alkali metal cations (Mþ). Hence, it was early on suggested that in NBO-bearing aluminosilicate glasses incorporating both Naþ and Ca2þ species, the former mainly associates with the AlO4 groups, while the latter balance NBO anions of QSin # 2 moieties.121 These preferences were subsequently confirmed by 3QMAS NMR experiments,517 and recently quantified by Sukenaga et al.,530 who employed a combination of J-based 17O{23Na} and 17O{27Al} NMR experiments (see Section 9.20.16) that enabled the discrimination between Na–BO and Na–NBO bonds in the Na2O–CaO–Al2O3–SiO2 glass, from which BO:NBO ratios of 1.4:1.0 and 1.0:2.7 were inferred for Naþ and Ca2þ, respectively.

628

Solid-state nmr of glasses

(A)

25

Mg shift (ppm)

(B)

25

Mg shift (ppm)

25

Fig. 26 Mg NMR spectra recorded at 18 kHz MAS and two magnetic fields (16.4 T/21.8 T) for silicate glasses with compositions (A) MgSiO3 and (B) K2MgSi2O6.38 Asterisks mark CT spinning sidebands stemming from the second-order quadrupolar interaction. Reproduced from Shimoda, K.; Nemoto, T.; Saito, K. Local Structure of Magnesium in Silicate Glasses: A 25Mg 3QMAS NMR Study. J. Phys. Chem. B 2008, 112, 6747–6752, with permission from The American Chemical Society. Copyright the American Chemical Society (2008).

9.20.14 NMR on selected network modifiers 9.20.14.1

23

Na (S [ 3/2)

Thanks to the high receptivity of 23Na, MAS NMR applications thereof are reported from several glass systems. However, while Na assumes coordination numbers of 5–7, the various 23Na[p] resonances strongly overlap (as for many other modifier cations; see Section 9.20.14.3) and are not possible to resolve by (3Q)MAS NMR,22,23,25–31 thereby limiting precise inferences about the local Na[p] environments in glasses. Here 23Na MAS NMR experimentation alone may only address the average isotropic 23Na chemical   shift
dNa taken over the entire {23Na[p]} ensemble.21,32,33,142,531 Yet, it is known both from NMR experiments and DFT calculations of (alumino)silicate21,26,28,29,299,531–533 and B-based33,34,130,532,533 glasses that
dNa decreases for an increase in either the  
Na Þ or the mean Na–O distance
average coordination number of Na ðZ dNa–O . dNa–O from phases within each individual siliMacKenzie and Smith205 summarized correlations established between
dNa and
cate, borate, and germanate system. However, discussions on structure–shift correlations among distinct systems are very sparse,532,533 where the most comprehensive 23Na chemical-shift/structure correlations is that of Yu et al.,32 who demonstrated    
Na ;
dNa–O parameter-pairs obtained from atomistic molecular the following relationship between NMR-derived
dNa data and Z dynamics (MD) simulations for a set of 34 silicate-based glasses incorporating B and/or P along with Naþ or Naþ/Ca2þ as network modifiers32: 


dNa ¼ 550:04 þ 6:08Z
Na  2:30
dNa–O =pm ; with R2 ¼ 0:95 (34) where R2 is the correlation coefficient. Moreover, the isotropic 23Na chemical shift also correlates well with the total atomic fraction of network modifiers, x(Mtot) ¼ xNa þ xCa,31,32 with the following relationship deduced32:
dNa ¼  14:30 þ 80:18xðMtot Þ; with R2 ¼ 0:97 (35)

Solid-state nmr of glasses

9.20.14.2

25

629

Mg (S [ 5/2)

2þ

Whereas Mg normally acts as a network modifier, the large CFS of the small ion opens up for a (partial) network-forming role where MgO4 tetrahedra may contribute to the glass network, as has been proposed and/or deduced from circumstantial evidence for Mg-bearing silicate,407 borate,490 and aluminoborosilicate369 glasses. Here the direct observation of the Mg[p] coordinations by 25 Mg NMR is a promising route to settling such issues. Yet, despite relatively small 25Mg quadrupolar products of around 3– 4 MHz,38 25Mg (3Q)MAS NMR reports on glasses are relatively sparse, mainly due to the low magnetogyric ratio of 25Mg (Table 2) and the need for isotopically enriched specimens (yet, see Ref. 39). As illustrated by Fig. 26,38 high magnetic fields and fast MAS helps reducing the substantial second-order quadrupolar broadening and for concentrating the CT NMR intensity into the centerband, which otherwise tend to overlap with CT spinning sidebands from the large nQ(2)(U) values stemming from the low magnetogyric ratio (Eq. 22), whereas experimentation at B0 < 14.1 T appears to be precluded.36 Nearly all of the hitherto reported 25Mg MAS NMR studies targeted silicate glasses,35–39 encompassing the following compositions: MgSiO3,37,38 Li2MgSi2O6,38 Na2MgSi2O6,37 Na2MgSi3O8,35 K2MgSi2O6,35–38 K2MgSi5Oi2,35–38 CaMgSi2O6,35–38 Ca2MgSi2O7,37,38 along with several members along the MgSiO3–Mg2SiO4 join,39 the latter recorded from glasses with 25Mg at natural abundance. As for other cations, the isotropic 25Mg[p] chemical shift decreases for increasing coordination number, where
diso of Mg[4] and [6] Mg coordinations span about 30–50 ppm and 5–15 ppm, respectively,38,534 whereas the shift ranges of other Mg[p] coordinations remain poorly confined. From the examined Mg-bearing silicate glasses listed above, MgO4 tetrahedra prevail in glasses incorporating the low-CFS Naþ and Kþ species,35–38 whereas Mg prefers octahedral coordination in MgO–SiO2 glasses,38,39 or when present together with other cations with moderate (or high) field strengths, such as Liþ and Ca2 þ.35,38 We are unaware of 25Mg NMR reports on B-based glasses, but in the large set of silicate glasses reported by Shimoda et al.,37,38 one aluminosilicate glass (Mg3Al2Si3O12) was included. Moreover, in a multinuclear MAS NMR study on the complex amorphous matrix of an Mg-bearing aluminosilicate slag, Shimoda and co-workers attributed two NMR signals resolved in the 3QMAS 25Mg NMR spectrum as stemming from MgO6 octahedra, although contributions from MgO4 and MgO5 groups could not be excluded.40

(A)

W

89

Y chemical shift (ppm)

(B)

8 89 89

Y chemical shift (ppm)

Fig. 27 Experimental Y MAS NMR spectrum from an aluminosilicate glass of composition 17Y2O3–28Al2O3–55SiO2, displayed together with the DFT/GIPAW-derived chemical shift ranges from a glass model generated by MD simulations.48 The gray rectangle depicts the entire calculated 89Y DFT shift-span (Wiso), while the blue counterpart displays the range of DFT derived shifts around the average value
diso . (B) Ranges of DFT-derived ½p  isotropic chemical shifts for each 89Y[p] coordination, with the average shift
diso marked by a white line. Reproduced from Jaworski, A.; Charpentier, T.; Stevensson, B.; Edén, M. Scandium and Yttrium Environments in Aluminosilicate Glasses Unveiled by 45Sc/89Y NMR Spectroscopy and DFT Calculations: What Structural Factors Dictate the Chemical Shifts?. J. Phys. Chem. C 2017, 121, 18815–18829, with permission from The American Chemical Society. Copyright the American Chemical Society (2017).

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Solid-state nmr of glasses

9.20.14.3

45

Sc (S [ 7/2) and

89

Y (S [ 1/2)

Reports on Sc (S ¼ 7/2) and Y (S ¼ 1/2) NMR on glasses are very sparse, which may be traced to the very slow spin-lattice relaxation and low receptivity of 89Y (owing to its low g value, and in spite of a 100% natural abundance; see Table 1), whereas for the very receptive 45Sc nucleus it stems entirely from its large quadrupolar moment (Table 2) that yields very broad MAS NMR resonances. Current 45Sc MAS NMR studies have targeted Sc2O3–Al2O3–SiO2 glasses47,48 or aluminosilicate glasses with minor Sc doping,46 as well as Sc-doped Na2O–Al2O3–P2O545 and fluoro-(alumino)phosphate glasses.49,50 89Y MAS NMR demonstrations on glasses are restricted to the Y2O3–Al2O3 (Ref. 53), Y2O3–Al2O3–SiO2 (Ref. 48), and Y2O3–Al2O3–B2O3 (Refs. 51,52) systems. Jaworski et al.48 examined 89Y and 45Sc chemical-shift/structure correlations of glasses of the ternary Y2O3–Al2O3–SiO2 and Sc2O3–Al2O3–SiO2 systems by utilizing MAS NMR experiments in conjunction with DFT/GIPAW chemical shift calculations of the 89Y[p] and 45Sc[p] environments in glass models generated by MD simulations. The latter predicted a distribution of coordination numbers for both Y and Sc: the Y speciation was dominated by YO6 (z 50%) and YO7 (z20–30%) polyhedra, whereas the smaller Sc3þ cation revealed mainly ScO5 (z50%) and ScO6 (z30–35%) groups. Moreover, both the 89Y[p] and 45Sc[p] isotropic chemical shifts were found to depend primarily on the coordination number pda unit increase of which (i.e., Y[p] / Y[p þ 1] and Sc[p] / Sc[p þ 1]) decreased the chemical-shift by z50 ppm and z40 ppm for 89Y and 45Sc, respectively.48 Yet, the strongly overlapping chemical shift ranges among the various {Y[p]} and {Sc[p]} coordinations preclude unambiguous NMR-peak assignments of the 89Y/45Sc MAS NMR spectra alone,48 as is evident from the 89Y MAS NMR spectrum and DFT-derived chemical-shift span for each 89 [p] Y species displayed in Fig. 27. The large spread of isotropic 89Y[p] and 45Sc[p] chemical shifts for a given coordination number p was identified to dominantly originate from a significant impact from the {RE3 þ, Al3þ, Si4þ} cations in the second coordination sphere of the RE3 þ ¼ {Y3þ, Sc3þ} cation48: the RE[p] chemical shift is decreased for an increase in the number of RE–O–Si bonds, but increases concurrently with the number of RE–O–Al, and particularly, RE–O–RE linkages. Further modeling studies revealed a preference for RE–O–RE bond formation at the expense of the RE–O–Al and (particularly) RE–O–Si counterparts.535 45

89

9.20.15 Homonuclear connectivities among network formers The short-range chemical-shift interaction alone may in general not inform about the spatial arrangements and the preferential connectivities among atoms in an oxide-based glass. Here we review 2D NMR correlation techniques that enable such information, where the key players are the through-space dipolar and through-bond J interactions (Sections 9.20.4.4 and 9.20.4.5). Application of such advanced NMR experimentation has offered unique possibilities to probe “exotic” and energetically unfavorable structural motifs in glasses, such as the presence of Al[4]–O–Al[4] linkages in RE-based aluminosilicate glasses78,248 (Section 9.20.15.4), along with very recent irrefutable proof for B[4]–O–B[4] bonds in borosilicate glass networks (Section 9.20.15.5).131,133

9.20.15.1 2Q–1Q correlation NMR experiments Fig. 28A shows a schematic rf pulse protocol for a dipolar-based double-quantum–single-quantum (2Q–1Q) correlation experiment under MAS conditions,152–154,156 where we initially assume spin-1/2 applications. The protocol involves two pulse blocks of dipolar recoupling, normally of equal duration (sexc ¼ srec), and referred to as the “excitation” (sexc) and “reconversion” (srec)

t1

(A)

t2 2Q→Z

Z→2Q

π

(B)

t1

t2 2QCT→Z

Z→2QCT 2M

Fig. 28 Schematic rf-pulse diagrams for homonuclear 2Q–1Q correlation NMR experiments that utilize the through-space dipolar interactions to establish spatial proximities/connectivities. (A) Prototype rf-pulse protocol suitable for spin-1/2 nuclei,152,153,156 which involves an rf pulse block for homonuclear dipolar recoupling of duration sexc that “excites” (creates) two-spin 2QC in pairs of spatially proximate spins. The 2Q coherences then evolve during t1 and are subsequently converted into transverse magnetization by application of another dipolar recoupling block (srec ¼ sexc) and a p/2 (90 ) pulse. The NMR signal is detected during t2. (B) Rf pulse protocol suitable for 2Q–1Q correlations among the CTs of dipolar-coupled half-integer spins.536 Note that all rf pulses in (B) are CT selective (Section 9.20.5.4). All black rectangles in (A and B) represent p/2 pulses.

Solid-state nmr of glasses

(B)

2Q dimension

(A)

631

(D)

(E)

(F)

2Q dimension

2Q dimension

(C)

1Q dimension

1Q dimension

31

Fig. 29 Schematic 2Q–1Q correlation P NMR spectra expected from progressively longer chains of 2 to n connected phosphate groups, as specified by the number at the bottom corner of the respective 2D spectrum. Each 2D peak is assigned to its corresponding Q1,j or Q2,jk site in the phosphate network, as discussed further in Section 9.20.15.2. Reproduced from Witter, R.; Hartmann, P.; Vogel, J.; Jäger, C. Measurements of Chain Length Distributions in Calcium Phosphate Glasses Using 2D 31P Double Quantum NMR. Solid State Nucl. Magn. Reson. 1998, 13, 189–200, with permission from Elsevier.

stages. The excitation block creates so-called double-quantum coherences (2QC)138 within each homonuclear spin-pair (e.g., 31 P–31P or 29Si–29Si), which requires a non-negligible through-space dipolar coupling constant bjk. Next follows a t1-evolution interval during which each 2QC evolves with its characteristic “shift”, which constitutes the sum of the (isotropic) chemical shifts jk dj and dk of the two spin sites j and k, respectively: d2Q ¼ dj þ dk. However, as 2QC and other higher-order multiple-quantum coherences (MQC) are not directly detectable (Section 9.20.8), the second dipolar recoupling pulse block converts the 2QC into 1QC (i.e., transverse magnetization) that is subsequently detected during t2, yet, only for the spin sites (j, k, .) that participated into a 2QC during t1. Then, a 2D FT performed on the recorded {s(t1, t2)} data array produces a 2D NMR spectrum that correlates jk each 2QC shift (d2Q ) along the vertical “2Q dimension” with its respective “1Q shifts,” d1Q ¼ dj and d1Q ¼ dk, which appear along the horizontal “1Q dimension”. Consequently, each jk spin-pair produces two 2Q–1Q correlation peaks at coordinates jk jk , dj}, {d2Q , dk}}. {d2Q, d1Q} ¼ {{d2Q Fig. 29 depicts schematic 2Q–1Q 31P MAS NMR spectra that convey how the various QPn–QPm pairs building a phosphate (glass) network may be identified.537 The details are discussed in Section 9.20.15.2, here we merely stress the basic 2Q–1Q correlation NMR signatures for 31P sites residing in two equivalent (e.g., QP1–QP1) or inequivalent (e.g., QP1–QP2) phosphate groups: the former jk case illustrates the concept of an “auto-correlation,” which features dj ¼ dk and a 2Q shift of d2Q ¼ 2dj, thereby producing one sole

632

Solid-state nmr of glasses

2D NMR peak at {d2Q, d1Q} ¼ {2dj, dj}; see Fig. 29A. In the more general scenario of two interconnected PO4 tetrahedra with distinct 31 P chemical shifts (dj s dk), two 2Q–1Q NMR peaks appear (vide supra), as shown in Fig. 29B. The generation/excitation rate of a given 2QC scales as | bjksexc |2, meaning that each 2D NMR peak intensity of the 2Q–1Q correlation NMR spectrum conveys qualitative interatomic-distance information.152–154,156 Yet, there is an important caveat of the 2Q– 1Q correlation NMR scheme of Fig. 28A for establishing connectivities: because 2QC are generated by the through-space-mediated dipolar interactions, the equivalence between a “close internuclear proximity” and a “connectivity via chemical bonds” (e.g., 31P– O–31P) is only strict when sexc is kept sufficiently short so as to confine 2QC excitation among nuclei separated by a few Å. Formally, this requires selecting the 2QC excitation period such that   sexc bjk  1 (36) An obvious option for mitigating (although not eliminating166) these ambiguities of the dipolar-based NMR experimentation is to employ analogous 2Q–1Q correlation schemes utilizing the through-bond J interaction for the 2QC excitation. The archetypical protocol is 2D INADEQUATE, originally introduced for solution NMR538,539 and refined for MAS NMR applications by the “refocused INADEQUATE”540 version and extensions,167 which have been exploited to probe QPn–QPm and QSin–QSim connectivities in both phosphate and silicate based glasses.136,165,167,264,283,341,399,541,542 A significant obstacle with such J-based NMR experiments, however, is the very modest 2J(31P–O–31P) and 2J(29Si–O–29Si) values, which require comparatively long 2QC excitation periods to yield significant NMR-signal intensities, while magnetization damping by T2 relaxation usually lead to substantial NMR-signal losses. Unfortunately, these practical deficiencies of J-based 2D NMR preclude their implementation for many glass samples, notably for the probing of connectivities among half-integer spins, where J-based 2Q–1Q NMR applications remain to be reported. We next turn to dipolar-based 2Q–1Q correlation NMR implementations for probing pairs of quadrupolar spin sites in glasses, as displayed in Fig. 28B.161,536 Among other homonuclear correlation 2D162,543–545 and 3D171–173 NMR options, the 2Q–1Q NMR experiment has remained the most versatile and the by far most utilized to glasses. To yield spatial proximity/connectivity information, the experiment exploits 2QC among the central transitions (2QCT) of two half-integer spin sites.161,163,164,536,546–548 For spins-1/2, excitation of 2QC is a direct proof of two sites in close spatial proximity, because such nuclei cannot produce 2QC unless they experience a non-negligible dipolar interaction. This is in stark contrast to the case of a “single” quadrupolar nucleus, whose multiple Zeeman states readily admits excitation of single-spin 2QC and 3QC; see Sections 9.20.5.1 and 9.20.8). Note that the two-spin 2Q–1Q correlation NMR experiment of Fig. 28A yields connectivity information, whereas the 3Q–1Q correlation scheme (3QMAS) does in general not (yet, see Section 9.20.13). Hence, it is necessary to discriminate the targeted 2QCT from undesirable “single-spin 2QC” associated with non-interacting quadrupolar sites, which may be accomplished by the clever approach of Mali et al.161 Except for the 11B applications discussed in Section 9.20.15.5, 2Q–1Q correlation applications are still relatively sparsely applied to glasses, and particular care must be exercised to obey Eq. (36) to ensure the probing of direct F–O–F0 linkages (as is, unfortunately, not often made in recent literature), while the necessity of using strictly CT-selective rf pulses introduces nonnegligible resonance-offset effects (Section 9.20.5.4). For further reading on dipolar recoupling among half-integer spins and homonuclear 2D correlation NMR, we refer to our previous reviews.163,164,247

9.20.15.2

31

P-31P connectivities

Excluding 1H and 19F, 31P offers the most favorable NMR properties of all nuclides for 2Q–1Q correlation NMR studies. Not surprisingly, this is mirrored by numerous 31P applications for probing the medium-range order of phosphate glass networks, which appeared soon after the introduction of homonuclear dipolar recoupling techniques for 2QC excitation in the mid-1990s.152–156 A glimpse of the key to the substantially enhanced information content from 2Q–1Q correlation 31P NMR experimentation is given by the schematic 2D NMR spectra of Fig. 29,537 which not only reveal each QPn–QPm connectivity in the glass, but may in favorable cases also discriminate between (for example) a QP2 group that binds either to two other QP2 moieties along a phosphate chain/ring, or to a terminal QP1 group. Here, the additional superscripts QPn,jk.. in Fig. 29 inform about the n values of the {QPj, QPk, .} neighbors that share a BO atom with the central QPn group, where the number of such {j, k, .}indices are equal to n.537 For instance, a phosphate glass network built solely from QP1 groups (i.e., an idealized pyrophosphate glass in the absence of an QP1 % QP0 þ QP2 disproportionation; see Eq. (21) and Section 9.20.10), comprise QP1,1–QP1,1 pairs/dimers (Fig. 29A), whereas QP1–QP2–QP1 triplets feature two terminal QP1,2 tetrahedra, interconnected by a QP2,11 group (Fig. 29B). As the phosphate chain is lengthened (Fig. 29C–F), the distinct types of QP2,jk units along the chain exhibit slightly different 31P chemical shifts, depending on whether they connect to two other QP2 tetrahedra (i.e., constitute QP2,22 moieties), or locate next to a terminal QP1 group (i.e., QP1,2). While the resonances from these distinct QP2,jk groups remain unresolved in the 31P MAS NMR spectrum, they are in favorable nm ¼ dm þ dn, as illustrated in Fig. 29E and F. Witter cases resolved in the 2Q–1Q 2D NMR spectrum by their distinct 2Q shifts, d2Q 537 et al. presented an analysis strategy that combined the phosphate-group connectivity information from the 2Q–1Q 31P NMR spectrum with the quantitative nature of the single-pulse 31P MAS NMR counterpart; the latter may be deconvoluted by iterative fitting into the larger set of chemical shifts from the {QPn,jk..} groups, thereby enabling the determination of the average phosphate chain-length of the polymeric networks of binary phosphate glasses. We refer to the original article537 and our previous review6 for details of the protocol. It has been utilized to monitor the successive shift of the {xPn} populations towards lower n and the accompanying chain-length shortening (c.f. see Eq. 5) for increasing modifier content in various binary M(2)O–P2O5 glass systems,

Solid-state nmr of glasses

633

Fig. 30 J-mediated 2Q–1Q correlation 31P NMR spectrum recorded at B0 ¼ 11.7 T by the refocused INADEQUATE technique540 from a glass of composition 5La2O3–95NaPO3.136 Each 2D NMR peak is assigned to the as-indicated QP2–QP2, QP1–QP2, and QP1–QP1 pairs, where the minor La3þ doping creates a non-negligible population of QP1 groups that terminate the phosphate chains, whereas QP1–QP1 dimers are essentially absent, as is also evident from the slices along the horizontal 1Q spectral dimension shown to the right. Reproduced from Shi, F.; Hu, L.; Cui, Y.; Ren, J. Revealing the Structures in Short- and Middle-Order of Lanthanum-Doped Al2O3–NaPO3 Glasses by Solid State NMR Spectroscopy. J. Phys. Chem. C 2021, 125, 2097–2110, with permission from The American Chemical Society. Copyright the American Chemical Society (2021).

encompassing those involving Naþ,549 Liþ,252 Mg2þ,390 Ca2þ,537,542 Zn2þ,233,391 and Pb2 þ.165,232 For example, across a wide range of xZnO–(1  x)P2O5 glass compositions, Wiench et al.233 deduced average numbers of {19.2, 7.8, 4.0, 2.7} phosphate groups per chain for the corresponding ZnO mole fractions of x ¼ {0.50, 0.55, 0.60, 0.65}. Recent 2Q–1Q correlation NMR applications also encompassed Na/Zn-based phosphate glasses, with44 or without400 Ca2þ as a third network modifier. Although the spectral resolution of 2Q–1Q 31P NMR experiments from multicomponent P-bearing glasses is usually insufficient for discriminating among the various QPn,jk.. moieties, valuable QPn–QPm inter-connectivity information have nevertheless been gained from a multitude of more complex phosphate glasses, such as Na-based phosphate glasses incorporating Ti,550 Bi551 and combinations thereof,552 as well as from systems incorporating additional anions, e.g., Ag2O–AgI–P2O5 (Ref. 553), and M–P–O–N (M ¼ Li, Na).252,262,264 A notable progression over time in the area of 31P–31P connectivity information in P-bearing glasses is also reflected by a more frequent application of J-interaction-based 2Q–1Q 31P NMR experimentation to phosphate-based glasses,136,165,264,399,541,542 as well as further developments of the refocused INADEQUATE protocol.167 As one example, we single out the very recent study by Shi et al.136 of La-bearing (alumino)phosphate glasses: Fig. 30 shows a J-based 2Q–1Q 31P NMR spectrum obtained from a Na metaphosphate glass with a minor La2O3 doping, revealing an expected dominance of QP2–QP2 connectivities along the phosphate chains, yet with significant amounts of terminal QP1 groups, whereas isolated QP1–QP1 pairs are essentially absent.136

9.20.15.3 Silicate-glass network models and

29

Si-29Si connectivities

The NBO distribution among the SiO4 groups in a silicate glass is encoded by its set of {xSin} values, which is sometimes accessible by routine 29Si MAS NMR (Section 9.20.9), then conveying the average topology of the silicate network via the silicate network connectivity (Eq. 4). Yet, an equally important aspect concerns the nature of the QSim–QSin inter-connectivities of the network. 2Q–1Q correlation 29Si NMR experiments offer the arguably most direct experimental insight into this medium-range structural problem, which relates to the spatial distribution of the network modifier cations that balance the negative charges of each QSin moiety (see Section 9.20.16). The Zachariasen–Warren CRN glass model1–3 postulates a fully randomized glass network without preference for any particular F–O–F0 or F–O[1]/ Mz þ contact. Such a glass lacks medium-range order, which is since long known to be a grossly over-simplified model, not the least for borate glasses; see Section 9.20.12.3. The absence/presence of preferences for certain QSim–QSin connectivities in alkali-metal-ion modified silicate networks remains debated over decades. For an Mz þ cation with a (moderately) high field strength, the mere difficulty to prepare homogeneous MOz/2–SiO2 glassesdparticularly for glass compositions with low modifier contentsdis a strong indication of a non-uniform NBO/Mz þ distribution. Indeed, a glass-in-glass separation occurs for some Li2O– SiO2 compositions,7,8,15,507 and strongly restricts the glass formation region of binary silicate glasses based on M2 þ and M3 þ

634

Solid-state nmr of glasses

[4]

Al 58

Al 30

[5]

[6]

Al 0 ppm

(B)

(A)

58

30

45

45

24La2O3 19Al 2O3 57SiO 2

2Q dimension (ppm)

30

0 ppm

60 90

86 ppm

120

118 ppm

44

150 90

60

30

0

-30

90

1Q dimension (ppm) [4]

Al 58

Al 29

[5]

60

30

0

-30

1Q dimension (ppm)

[6]

Al 0 ppm

(C)

(D)

58

29

0 ppm

19La2O3 30Al 2O3 51SiO 2 55

2Q dimension (ppm)

30 45

60

60 ppm

90

86 ppm

120

116 ppm

45

44

150 90

60

30

0

1Q dimension (ppm)

-30

90

60

30

0

-30

1Q dimension (ppm)

Fig. 31 (A and C) 2Q–1Q 27Al correlation NMR spectra recorded at B0 ¼ 14.1 T and 24.0 kHz MAS from two La-based aluminosilicate glasses with compositions (A) 24La2O3–19Al2O3–57SiO2 and (C) 19La2O3–30Al2O3–51SiO2. The scheme of Fig. 28B was employed. The 2D spectra are shown together with their projections along both spectral dimensions. The respective single-pulse MAS NMR spectra are displayed topmost in (A and C), along with deconvolution results into the 27AlO4, 27AlO5 and 27AlO6 NMR signal components (gray traces). (B and D) Slices along the 1Q dimension taken through the as-indicated 2Q shifts in (A and C), revealing the main 27Al[p]–O–27Al[q] connectivities (labeled by pq) contributing to the given 2Q shift. Reproduced from Jaworski, A.; Stevensson, B.; Pahari, B.; Okhotnikov, K.; Edén, M. Local Structures and Al/Si Ordering in Lanthanum Aluminosilicate Glasses Explored by Advanced 27Al NMR Experiments and Molecular Dynamics Simulations. Phys. Chem. Chem. Phys. 2012, 14, 15866–15878, with permission from the PCCP Owner Societies.

cations, unless other glass former cations (notably Al3þ) are also incorporated, which becomes crucial for the preparation of homogeneous glasses based on trivalent rare-earth (RE3 þ) cations, such as La3þ, Y3þ, Lu3þ, and Sc3 þ.47,75,344,554–559 Given the tendencies of binary silicate glasses that incorporate high-CFS cations to phase separate over length-scales readily detectable by electron microscopy, one anticipates that the structural inhomogeneities may start forming already at the mediumrange scale up to z1 nm for lower-CFS cations (e.g., Naþ and other alkali metal ions) before they become detectable across longer length scales, as indeed recently revealed by 2Q–1Q correlation 29Si NMR experiments on Si-rich Na2O–SiO2 glasses.169 Along these lines, Bockris et al.560 suggested already in the mid-1950s a binary silicate glass picture of “islands” of interconnected QSi4 groups embedded in modifier-rich domains of QSin < 4 moieties. Three decades later, Greaves and co-workers proposed the very similar

Solid-state nmr of glasses

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modified random network (MRN) description of binary silicate glasses, on the basis of extended X-ray fine structure (EXAFS) experimental data.561,562 The MRN model involves fully polymerized domains of QSi4 groups that are interleaved with “channels” of network-modifier cations that associate with another silicate domain of interconnected QSi 1/ 2) throughout srec573,574,606; see Fig. 32D. Both the REAPDOR and TRAPDOR protocols were introduced for handling S ¼ 1/2 and I > 1/2 scenarios. We recommend using REAPDOR, because its output data set may be analyzed quantitatively, as opposed to that of TRAPDOR.573,574,606 An alternative S{I} REDOR version has also been introduced,608,609 which only differs from REAPDOR in that the adiabatic-passage pulse of Fig. 32C is replaced by a p pulse. For crystalline structures with one sole or a few Sj–Ik pairs, their precise internuclear distances may be determined from an S{I} REDOR or REAPDOR dephasing experiment.571,607 However, the huge number of spin-pairs/dipolar interactions in the amorphous network structure of a glass precludes estimates of individual rjkS – I distances. Yet, quantitative information about the relative I–S contacts is available from the Van Vleck dipolar second moment,610 M2 ðS–IÞ ¼

NS X NI h i6 m20 Z2 g2I g2S X rjkSI 4 64p NS j¼1 k¼1

¼ NS1

NS X NI h X

bSI jk



unit: s2 ¼ Hz2



i2

(39a)

(39b)

j¼1 k¼1

which is proportional to the sum over the inverse sixth power of the interatomic distance of each Sj–Ik pair in the structure. Here, m0 is the permeability of vacuum, whereas NI and NS denote the total numbers of I and S nuclei in the glass, respectively (which are obtained from the glass stoichiometry). The value of M2(S–I) may be extracted by fitting the experimentally obtained data set to the expression,417,609,611,612

DS=S0 h½S0 ðsrec Þ  Sðsrec Þ=S0 ðsrec Þ ¼

A M2 ðS–IÞs2rec IðI þ 1Þ

(40)

where A ¼ 1 for REDOR NMR applications with I ¼ 1/2,417,608,611,612 while A must be determined empirically by separate experiments on model compounds for implementations involving I > 1/2 nuclei,417,608,609,611,613 as well as for REAPDOR.612 Moreover, the numerical fitting must be confined to short recoupling periods and small DS/S0 values, where we recommend to only include data with DS/S0 ( 0.131,612,613 (if possible). This limit is lower than previous recommendations of DS/S0 ( 0.2417,608,609 or DS/ S0 ( 0.3.611,614,615

Solid-state nmr of glasses

(A)

(B)

BO 0.71

NBO–Al

639

S 0( S(

NBO–Si 0.02

BO

) ) NBO–Si

Y AS

0.62

NBO–Al

(C)

(D)

0.59 0.07

Lu AS 0.81

250 200 150 100 17

50

0

-50

250 200 150 100

O shift (ppm)

17

50

0

-50

O shift (ppm)

Fig. 33 17O{27Al} TRAPDOR NMR spectra recorded at B0 ¼ 9.4 T and 14.0 kHz MAS from glasses with compositions (A and B) 21Y2O3–37Al2O3– 42SiO2 and (C and D) 24Lu2O3–25Al2O3–51SiO2. The spectra labeled by S(srec) and S0(srec) were obtained in the presence and absence of dipolar recoupling for srec ¼ 2.5 ms, respectively. Note that their difference reflects the strength of the 17O–27Al dipolar interactions for the BO, NBO–Al and NBO–Si moieties, where the number on top of each 17O NMR peak indicates the degree of dephasing, DS/S0; see Section 9.20.16.1. (B and D) Experimental S0(srec) NMR spectra (black traces) shown together with the component peaks (gray traces) obtained by spectra deconvolution. The curves beneath each NMR spectrum represents the difference between the experimental and best-fit results. Reproduced from Jaworski, A.; Stevensson, B.; Edén, M. Direct 17O NMR Experimental Evidence for Al–NBO Bonds in Si-Rich and Highly Polymerized Aluminosilicate Glasses. Phys. Chem. Chem. Phys. 2015, 17, 18269–18272, with permission from the PCCP Owner Society.

9.20.16.2 Heteronuclear connectivities involving

17

O

17

Dipolar dephasing NMR experimentation with O detection has recently proven to be a powerful information source about the various BO and NBO environments in multicomponent (alumino)silicate based glasses, where a selection of such opportunities are reviewed below.

9.20.16.2.1

Al-NBO bonding in aluminosilicate glasses

9.20.16.2.2

17

Conventional models of Al-bearing glasses assume the absence of Al[4]–NBO bonds (Section 9.20.2), owing to the dominant preference for Si–NBO bond formation over Al[4]–NBO.77,126,244–248,524 Yet, by employing 17O{27Al} TRAPDOR and 27Al / 17O CPMAS NMR experimentation, Jaworski et al.126,248 recently offered conclusive evidence for significant amounts of Al–NBO motifs in several RE2O3–Al2O3–SiO2 systems and glass compositions, where O[1]–Al accounts for z10% of all O[1]–Si/Al bonds. Unambiguous assignments of the 17O MAS NMR peaks appearing in the high-ppm range > 200 ppm (Fig. 10) were offered by the 17O {27Al} TRAPDOR NMR results of Fig. 33,248 where the application of a “short” dipolar recoupling interval only leads to significant NMR-signal attenuations from 17O[p] sites that form direct bonds with Al, which besides O[1]–Al also encompass the Si–O–Al and Al–O–Al linkages. The Al–NBO population grows roughly linearly with the product nAlnNBO77,126,247,248 (and is also increased by an accelerated melt-quench in the glass preparation246). This also rationalizes the (near) absence of Al–NBO bonds in all aluminosilicate glasses incorporating Mþ/M2 þ modifiers with low/moderately high CFS, although they occur in Al-rich CaO–Al2O3–SiO2 glasses (nAl/ nSi T 3) that simultaneously comprise large NBO contents244–246 to overcome the around 8–14 times stronger propensity for the NBO sites to coordinate Si.247

O NMR peak-assignments in aluminoborosilicate glasses

The 17O{Al} TRAPDOR NMR experimentation utilized for unambiguously proving Al–NBO bonding in RE2O3–Al2O3–SiO2 glasses248 was extended and applied further to aluminoborosilicate glasses by LaComb et al.616 By exploiting a clever combination of 17O{Al} and 17O{11B} TRAPDOR experimentation, they accomplished a complete assignment of the large number of coexisting 17 [1] O and 17O[2] resonances involving Al, B, and Si, despite their extensive overlap in the 17O MAS NMR spectrum. This strategy of combining heteronuclear various NMR experiments also enabled rough estimations of the corresponding 17O[1] populations of the three Al–NBO, B–NBO, and Si–NBO moieties, as well as for assessing those of the altogether six distinct F–17O[2]–F0 linkages with {F, F0 } ¼ {Al, B, Si}. Notably, considering that each 17O{27Al} and 17O{11B} TRAPDOR NMR result informs directly that a given 17 O environment involves (at least) one bond to 27Al and 11B, respectively, the NMR signals devoid of significant dephasing in both TRAPDOR implementations may be attributed to Si–NBO and Si–O–Si motifs.616 We expect further developments and applications of such 17O-based dipolar dephasing experimentation to glasses, notably their coupling with high-resolution NMR techniques, such as 3QMAS.327

640

Solid-state nmr of glasses

9.20.16.2.3

Heteronuclear experiments targeting network modifiers

9.20.16.2.4

Detection of oxygen triclusters and free oxygen ions

Dipolar-dephasing NMR experiments are of course not limited to the probing of direct bonds between 17O and the glass network formers, but may also inform about the network-modifier constellations around the various BO/NBO sites. This was for example utilized by a 17O{45Sc} TRAPDOR NMR implementation in Ref. 126, which revealed the strongest NMR signal dephasing from the most negatively charged O sites in a Sc2O3–Al2O3–SiO2 glass, i.e., the 17O[1]–Si/Al and Al–17O–Al sites, as expected from their larger number of O/ Sc3þ contacts in Eq. (28). Consequently, the 17O{45Sc} TRAPDOR results also gave further (yet circumstantial) support for the assignment of the 17O[2] resonance at z 80 ppm in Fig. 10 to Al–17O–Al linkages, thereby confirming the violation of the Loewenstein Al avoidance in RE-bearing aluminosilicate glasses, besides that offered by the NMR peak assignments made by DFT/GIPAW calculations126 (Fig. 10) and 2Q–1Q 27Al NMR experimentation (Section 9.20.15.4). Similar dipolar dephasing and/or heteronuclear correlation NMR experimentation involving (for example) 17O{7Li} and 17O 23 { Na} would be of great value for exploring the various BO/NBO environments in Li2O–Al2O3–SiO2 and Na2O–Al2O3–SiO2 glasses, respectively, where we already highlighted the determination of the BO/NBO partitioning around the Naþ and Ca2þ cation sites in a Na2O–CaO–Al2O3–SiO2 glass (Section 9.20.13.4) by the utilization of J-based 17O{23Na} NMR.530

O[3] species are referred to as oxygen triclusters because they interlink three SiO4/AlOp polyhedra,617 and are known to exist in several ordered aluminate, aluminosilicate, and borate phases. Yet, while MD simulations often predict significant O[3] populations in aluminate and aluminosilicate glasses77,125–127,535,618–620 (e.g., see Fig. 10), a direct and irrefutable experimental proof is still lacking. The hitherto most convincing evidence for the occurrence of minor O[3] contents in glasses concerns their detection in a CaAl2O4 glass composition by J-based 27Al{17O} HMQC NMR experiments.621 Moreover, amorphous Al2O3 is expected to comprise significant amounts of oxygen triclusters, which were probed by 17O 3QMAS NMR,622 whereas similar experimentation on a borate glass of composition SrB4O7 (whose crystalline analog is known to comprise O[3] sites) suggested that oxygen triclusters would only account for a few percent of the O speciation.623 “Free O2 ions” (O[0] coordinations) represent another “exotic” O species, which only coordinate the network modifier cations, and thereby reflect Mz þ clustering tendencies. Although their existence in “conventional” (alumino)silicate glasses has been debated for decades,75,344,352,624–628 they are frequently observed in MD-derived RE2O3–Al2O3–SiO2 glass models, and their abundance is expected to increase concomitantly with both the CFS of the modifier cation and its content in the glass.77,125,126,535 Yet, free O2 species are indeed anticipated in modifier-rich “orthosilicate” glasses (also referred to as “invert glasses”), which are built from QSi0 groups together with some QSi1 and free O2 ions that balance each other via 2QSi0 % 2QSi1 þ O2.39,629 By exploiting 17O / 29Si CPMAS-based 2D NMR experimentation on a 33CaO–33MgO–34SiO2 glass, Hung et al. found that free O2 ions constituted z8% of all O sites.630 They furthermore concluded that a strong overlap is expected among MAS NMR signals from 17O[1] and 17O[0] sites, thereby hampering the identification of the latter species by routine experiments.630

9.20.16.3 Heteronuclear connectivities among network formers This section reviews heteronuclear 2D correlation and dipolar dephasing NMR experiments for probing interconnectivities among distinct network formers in various glass systems. In contrast with the comparatively sparse homonuclear dipolar-based NMR experimentation targeting quadrupolar nuclei in glasses (Section 9.20.15), a vast number of reports utilizing various heteronuclear dipolar recoupling protocols are accumulated over the past 25 years, encompassing any combination of F–O–F0 connectivities among the network formers {F, F0 } ¼ {11B, 27Al, 29Si, 31P}. Given the plethora of heteronuclear MAS NMR reports on glasses, in the following we only make brief accounts on a few (rather arbitrarily) selected examples of (very) recent work in the field.

9.20.16.3.1

Aluminophosphates

Amorphous aluminophosphates are the likely most well-studied systems by heteronuclear NMR. Since the pioneering studies of Na2O–Al2O3–P2O5 glasses by routine 27Al and 31P MAS NMR experimentation by Brow, Kirkpatrick and co-workers in the early 1990s,65,66 detailed pictures of the medium range structure have emerged for several M(2)O–Al2O3–P2O5 glasses, mainly thanks to the insight gained from numerous 27Al–31P based heteronuclear 2D correlation and dipolar dephasing NMR experiments conducted by several groups.67–71,105–109 Here we highlight the advanced protocol by van Wüllen and co-workers,71,106 which merged several complementary heteronuclear dipolar recoupling experiments to reach an unprecedented detailed insight into the network organization of K2O–Al2O3–P2O5 glasses; we refer to the original literature71,106 and our previous detailed review on the protocol.6 Recent research in the scope of heteronuclear NMR on aluminophosphate glasses have targeted more complex systems. For instance, Eckert and co-workers examined the proximities between phosphate groups and Sc3þ species in Sc-bearing aluminophosphate glasses by 31P{45Sc} REAPDOR NMR experiments,45 as well as the Sc3þ/P and Sc3þ/F  contacts in fluoro-(alumino)phosphate glasses by 45Sc{31P} and 45Sc{19F} REDOR NMR, respectively.49,50

9.20.16.3.2

Alumino(boro)silicates

Despite a vast number of 27Al and 29Si MAS NMR applications on aluminosilicate glasses, results from heteronuclear doubleresonance experimentation involving both nuclei are very sparse, presumably mainly due to the comparably low sensitivity of 29 Si combined with a slow spin-lattice relaxation to reach thermal equilibrium, thereby making dephasing experimentation very

Solid-state nmr of glasses

641

time-consuming, and notably 2D NMR acquisitions. Current reports in the literature are limited to 27Al / 29Si CPMAS experiments on La–Al–Si–O–(N) glasses,259 and 29Si{27Al} REAPDOR NMR applied to Al2O3–SiO2 glasses445 and Na/Mg-based alumino(boro) silicate glasses.631 In the latter study by Bradtmüller et al., a decelerated 29Si NMR-signal dephasing was observed when the higherCFS Mg2þ ion replaced Naþ, which was attributed to the emergence of Al[4]–O–Al[4] and/or Al[4]–NBO moieties at the expense of the overall dominating Si–O–Al linkages.631 Moreover, 11B{27Al} REDOR NMR revealed B[3]–O–Al[4] bonds in their structures, with the dipolar contacts increasing concurrently with the Al content, but being independent on the presence of Naþ or Mg2þ in the glass.631 The dephasing results overall suggested a statistical intermixing of the various {Si, B[3], B[4], Al[4]} network formers, except for the near absence of B[4]–O–Al[4] linkages.631

9.20.16.3.3

Phosphosilicates

As opposed to the bioactive glasses discussed in Section 9.20.10.3 that feature low P but high modifier contents and essentially exclusively silicate networks, P-rich phosphosilicate glasses with low amounts of modifiers manifest distinctly different structures. For increasing P2O5 content of M(2)O–SiO2–P2O5 glasses, the modifier cations are consumed to minimize the polymerization degree n of the QPn tetrahedra, but the modifier content eventually becomes insufficient for charge-balancing all PO4 groups as orthophosphates, leading to P-dominated phosphosilicate networks that exhibit an extensive Si and P intermixing by Si–O–P bond formation.61–63 As the P content is increased further, the phosphosilicate network repolymerizes until only QSi4 and QP2/ QP3 groups are present, whereupon SiO6 octahedra forms61–64 (Section 9.20.9.3). Early work on Na2O–SiO2–P2O5 glasses concluded the absence of Si[4]–O–Si[6] bonds632 (as deduced from homonuclear 29Si–29Si correlation 2D NMR experiments), whereas P share BO atoms with both Si[4] and Si[6] species.63,632 These inferences were corroborated by the recent study by Ren and Eckert,64 who reached a detailed structural picture of 29Si enriched Na2O–SiO2–P2O5 glasses by utilizing a combination of several advanced homonuclear and heteronuclear MAS NMR techniques. Here, J-interaction-based 2Q–1Q 29Si MAS NMR experiments gave evidence for Si[4]–O–Si[4] linkages in the glass networks (i.e., QSi4–QSi4 pairs) but that neither Si[4]–O–Si[6] nor Si[6]–O–Si[6] bridges are present, whereas J-based 29Si{31P} HMQC NMR experimentation revealed pairwise QSi4–QP2 and QSi4–QP3 contacts.64 The various NMR results altogether amounted in a glass network description where QSi4 groups bond to each of the QSi4, QP2, and QP3 species, along with Si[6]–(QP3)6 superstructural units, where each BO atom of the SiO6 octahedron connects with an QP3 tetrahedron, thereby suggesting an extensive medium range structural order.64

(B)

P–B[3] P–B[4]

(A)

B[4]

B[3]

(D)

P–B[3] P–B[4]

(C)

Fig. 34 (A) Dipolar and (C) J interaction-based 11B{31P} HMQC NMR spectra recorded from a borophosphate glass of composition 45Li2O–35B2O3– 20P2O5.99 The 1D spectra shown to the left of each 2D spectrum are slices along the vertical 31P dimension taken at the shift of each 11B[3] and 11 [4] B resonance. (B) 11B{31P} REDOR NMR data and (D) 1D 11B{31P} HMQC NMR spectra recorded from 45M2O–35B2O3–20P2O5 glasses with different cations M þ ¼ {Liþ, Naþ, Kþ, Agþ}.99 Reproduced from Tricot, G.; Raguenet, B.; Silly, G.; Ribes, M.; Pradel, A.; Eckert, H. P–O–B3 Linkages in Borophosphate Glasses Evidenced by High Field 11B/31P Correlation NMR. Chem. Commun. 2015, 51, 9284–9286, with permission from the Royal Chemical Society.

642

Solid-state nmr of glasses

9.20.16.3.4

Borophosphates

The network organization of borophosphate glasses has received considerable attention during the past 15 years,92–104 where the intermixing among the phosphate groups and the two coexisting B[3] and B[4] coordinations is a key problem to address by the exceedingly favorable 11B–31P spin-pair for heteronuclear NMR experimentation (i.e., in sharp contrast to the 29Si-based counterparts reviewed above). It is well known that B enters primarily as B(OP)4 groups in P-rich M(2)O–B2O3–P2O5 glasses,94,95,102 where the strong preference for B–O–P linkages imply a significant B/P intermixing. For increasing B2O3-for-P2O5 substitution, however, BO3 groups starts forming, and although there would be no reason not to expect that also those interlink with P, doubts thereof were raised by the work of Jäger et al.,92 who presented the first heteronuclear 2D NMR experiment on a borophosphate glass. Here, the 31P{11B} HETCOR NMR spectrum obtained from a Na2O–B2O3–P2O5 glass only revealed 11B[4]–31P correlations.92 While the authors themselves commented that the (seeming) absence of 11B[3]–31P signals in the 2D NMR spectrum could well stem from artifacts of the particular experimental implementation, and their complementary 11B{31P} REDOR experiments revealed a significant 11B[3] NMR signal dephasing, it remained somewhat unclear whether those effects could stem from longerrange 11B–31P dipolar interactions of spin-pairs not forming 11B[3]–O–31P linkages. Conclusive evidence for the presence of B[3]–O–P bridges was provided a decade later, when Tricot et al.99 presented both dipolar- and J-based 11B{31P} HMQC NMR experiments on a Li2O–B2O3–P2O5 glass. The results are shown in Fig. 34A and C, where clear correlation signals are observed between 31P and both 11B[3] and 11B[4] coordinations, and the J-mediated experimentation moreover proves that both HMQC results indeed reveal 11B[3]–O–31P and 11B[4]–O–31P structural fragments. That directly interlinked BO3–PO4 moieties are general features of borophosphate glasses were shown by the additional 11B{31P} REDOR NMR results shown in Fig. 34B, which were recorded from various 45M2O–35B2O3–20P2O5 glasses with M ¼ {Li, Na, K, Ag}.99 To remove any ambiguity about the conclusions from the dipolar-based REDOR NMR experiments, the latter were complemented by the J-mediated 11B{31P} HMQC NMR spectra presented in Fig. 34D (each 1D NMR spectrum corresponds to the projection along the horizontal 11B dimension of the corresponding 2D HMQC spectrum). As only 11B[p] resonances from B[p]–O–P bridges are observed, this offered irrefutable proof that both B[3] and B[4] coordinations interlink with phosphate groups.99

9.20.17 Distribution of modifier cations Along with the F–O–F0 bonding preferences and NBO partitioning among the glass network formers, the distribution of the network modifier cations (Mz þ) and their propensities to charge-balance the NBO anions of the FOp polyhedra and/or the [BO4] and [AlO4] tetrahedra have pivotal bearings on the structure and properties of the glass. For instance, the nature of the spatial distribution of Mz þ cations around the silicate network directly reflects its NBO distribution. Hence, knowledge of whether the cation distribution is “uniform” (here taken to be identical to “homogeneous”), “random”, or “clustered” may be used for discriminating among the CRN and MRN structural models (see Section 9.20.15.3). Moreover, glasses that involve (at least) two MAz þ and MBz þ cations often exhibit different tendencies of the network modifiers to associate with distinct network groups, such as between the QSi3/QSi2 pair or between QSi3/[AlO4]; this is henceforth referred to as the “cation intermixing”, which reflects the MAz þ and MBz þ cation constellation in the second coordination sphere of F[p]. It is well known that a silicate glass that incorporates two distinct alkali cations exhibits an impaired MAþ/MBþ mobility, which manifests as a reduced electrical conductivity of the (MA)2O– (MB)2O–SiO2 glass relative to each individual (MA)2O–SiO2 and (MB)2O–SiO2 counterpart with the same net modifier content.633–635 Significant efforts have been spent over decades to better understand the mechanisms behind this so-called “mixed-alkali effect,” where insight into the nature of the cation intermixing is central. However, while the modifier distribution across the glass structure has been probed indirectly via its tightly related NBO distribution both by 2Q–1Q 29Si NMR (Section 9.20.15.3) and 17O 3QMAS NMR (Section 9.20.13.4), an attractive alternative is to directly observe the network modifiers, where static “spin echo” NMR experiments187,636,637 may reveal valuable information. In direct analogy with the heteronuclear dephasing experiments, the spin echo NMR-signal decay may be analyzed to extract a homonuclear dipolar second moment, M2(S–S), as frequently exploited for 23Na,16,33,637–642 and to a lesser extent, 7Li (Ref. 17). Moreover, assessments of the modifier cation intermixing is offered by the heteronuclear NMR techniques introduced in Section 9.20.16.1, along with related methods performed on static (non-spinning glass) samples, such as spin-echo double resonance (SEDOR),15,16 which enables M2(S–I) quantifications. Moreover, besides homonuclear 7Li spin-echo experimentation, assessments of the spatial distribution of Liþ species are available from heteronuclear 7Li{6Li} SEDOR experiments19 that involves both NMR-active isotopes of Li (Table 2).

9.20.17.1 Silicate and aluminosilicate glasses An early study on Li2O–Na2O–SiO2 glasses inferred randomly distributed Li and Na species across the structure and a nonpreferential Li/Na intermixing.16 Subsequent reports on M2(Li–Na) and M2(Na–Li) heteronuclear dipolar second moments along with the M2(Li–Li) and M2(Na–Na) counterparts, however, concluded a pronounced Liþ clustering in binary Li2O–SiO2 and ternary Li2O–Na2O–SiO2 glasses, as well as preferences for Li–Li and Na–Na associations at the expense of Li–Na.15,17–19 Hence, for Libearing silicate glasses in the Si-rich regime, the MRN network model561,562 is overall supported (Section 9.20.15.3).

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643

Modifier clustering effects were more recently also concluded for aluminosilicate glasses,359,643 even for the low-CFS Naþ and Kþ ions.643 To unveil the role of Na in aluminosilicate glasses with variable Na and K contents, Le Losq et al.643 performed 27Al{23Na} and 23Na{27Al} REDOR NMR experiments on glasses with increasing K-for-Na substitution. Their results suggested a preference for Naþ (relative to Kþ) to charge compensate the [AlO4] groups,643 altogether pointing to an aluminosilicate glass organization where clustered modifier cations form “ion channels” along the lines of the MRN model. A similar ion-channel constitution was proposed for CaO–MgO–Al2O3–SiO2 glasses from MD simulations and circumstantial experimental evidence from 29Si MAS NMR spectra deconvolutions.359 We stress that the inhomogeneities of the modifier intermixing and the overall cation dispersion are most relevant/evident for highly polymerized silicate glasses, i.e., at low total modifier contents. In the fragmented silicate networks of modifier-rich Na2O– CaO–SiO2–P2O5 glasses (Section 9.20.9.3), on the other hand, 31P{23Na} REAPDOR NMR experiments and MD simulations revealed an almost statistical Na/Ca partitioning among the various silicate {QSin} and {QP0, QP1} groups, yet with minor preferences for Naþ and Ca2þ to accommodate at the least and most negatively charged silicate/phosphate groups, respectively,31 i.e., there is a slightly higher association of Ca2þ and Naþ cations around the {QP0, QSi2, QSi1} and {QSi4, QSi3, QP1} moieties, respectively, as compared with a statistical Na/Ca partitioning. These minor preferences among the various network groups, however, diminish for increasing total modifier content.31

9.20.17.2 Phosphate and borate glasses Whereas several inferences from different NMR experiments suggest a non-negligible network-modifier cation clustering in the modifier-poor regime of several alkali-based silicate glass systems,15,17–19,169,339 the cation distribution/intermixing is markedly more homogeneous in borate and phosphate glasses. Here, spin-echo-derived M2(23Na–23Na) data along with heteronuclear REDOR NMR results suggest a random spatial distribution of Naþ cations in binary Na2O–P2O5 glasses,642 as well as in binary xNa2O–(1  x)B2O3 (Refs. 33,639) glasses with x ( 0.2, whereas the Na dispersion becomes more uniform for higher Na concentrations.33,639 The same holds for the Csþ distribution in Cs2O–B2O3 glasses.33 Concerning the intermixing of distinct alkali metal cations, an overall random cation intermixing is reported for borate glasses incorporating Na together with either Li or K,18,33,638 whereas Na/K metaphosphate398 and Na/Rb borate640 glasses manifest a nearstatistical Na/K and Na/Cs intermixing, respectively, yet with a slight preference for homonuclear Na–Na and K–K (Rb–Rb) contacts relative to heteronuclear Na–K (Na–Rb) pairs. These observations were attributed primarily to stem from differences in the cation sizes.398,638,640 For mixed alkali/alkaline-earth phosphate glasses, on the other hand, a similar scenario applies as for silicate networks (vide supra), i.e., a preference for divalent cations (e.g., Ca2þ, Sr2þ) over Naþ for balancing the more negatively charged QP1 tetrahedra relative to their QP2 counterparts.30,397,399

9.20.17.3 Glasses with multiple network formers Assessing the spatial distribution of each modifier species and their intermixing become more complicated for glasses that involve more than one network former, where the modifier species may prefer to associate with a specific network former species (see Section 9.20.17.1). Reports on spatial distributions and the intermixing among distinct modifier cation species by direct NMR observation of the cation nuclei are sparse for glasses with multiple glass network formers. From homonuclear M(23Na–23Na) data and 23Na{31P} REDOR NMR dephasing results from mixed Na/Li aluminophosphate glasses of low Al contents, Behrends et al.644 concluded a random Na spatial distribution as well as a statistical intermixing with Li, thereby mirroring the consensus reached earlier for (Al-free) phosphate glasses.642 For a large set of 32 members of the borosilicate and borophosphosilicate glass systems with Naþ as sole modifier or present together with Ca2þ, Yu et al.613 examined the spatial distribution of Naþ in the glasses using spin-echo 23Na NMR. The M2(23Na–23Na) data were analyzed together with M2(B[p]–Na) and M2(Na–B[p]) results for each B[3] and B[4] species in the boro(phospho)silicate glasses, where the two {M2(B[p]–Na)} and {M2(Na–B[p])} sets were extracted from one sole set of 11B{23Na} REDOR experiments using the procedure of Ref. 612. Both the Naþ distribution across the glass structure and the partitioning of the Na ensemble among the BO3 and BO4 groups were found to depend primarily on the NBO content of the glass (and thereby its total modifier content), which applied regardless of the precise {B, Si, P} glass constituents, where two regimes were identified613: (A) for low modifier contents, the Naþ cations are relatively uniformly dispersed across the structure, while there is a strong preference for B[4]–Na associations. (B) For moderate and high modifier contents for which B[3]–NBO bonds are present, Naþ distributes randomly and with non-preferential associations among the BO3 or BO4 species. The presence of Ca2þ only influences the nature of the Naþ distribution indirectly by an enhanced tendency of NBO formation for increasing Ca content, which promotes the transition from regime (A) to (B).613 The alterations from a strong [BO4]–Naþ association to a more uniform partitioning of Naþ between the BO3 and BO4 groups for increasing modifier content in borosilicate glasses613 parallels that inferred from various Na2O–(M2O)–B2O3 glasses by 11B {23Na} REDOR NMR experimentation.638–640,645 However, whereas the nature of the Naþ and Ca2þ distributions across the boro(phospho)silicate glass structures appears to be closer to those encountered for phosphate and borate glasses than their silicate counterparts, the consensus of a more uniform Naþ dispersion in the modifier-poor regime relative to modifier-richer glasses613 is unusual, and at odds with the findings from Na2O–B2O3 glasses, where the Naþ distribution was merely found to alter from

644

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a random to a more uniform dispersion as the Na content was increased.33,639 The more uniform Naþ dispersion in the modifierpoor regime was rationalized as stemming from the strong [BO4]–Naþ associations coupled with a more uniform dispersion of the [BO4] moieties across the borosilicate glass network613 due to the disfavoring of B[4]–O–B[4] motifs and preferences for B[3]–O– B[4] and Si–O–B[4] linkages131,133 (Section 9.20.15.5). We comment that the (sometimes differing) conclusions among reports on the spatial distribution of cations in nominally very similar glasses partially stem from how different authors interpret their data and define the meaning of a “homogeneous” distribution and “clustering.” This is discussed further in Refs. 33,409,646, which share their definitions of “clustering.”

9.20.18 Outlook We have reviewed the possibilities and limitations of MAS NMR spectroscopy for probing the structure of glasses across a subnanometer scale. Regarding the future trends/developments in the field of NMR on glasses, we comment on a remark made in our previous review on the subject from 2012: “...the past 15–20 years have witnessed a shift in focus to (i) characterizing also medium-range order of these fundamental model systems [silicate and phosphate glasses], such as extended network fragments and the distribution of glass modifier cations over the structure; (ii) exploring more complex glass systems involving three (or more) network formers and several modifier cations”.6 As is evident from the present account, such investigations have been pursued over the past decade, along with the following notable progress: (I) First and perhaps foremost, the coupling of DFT/GIPAW computations of NMR parameters of glass models generated by MD simulations with MAS NMR-derived experimental chemical shifts has almost become routine.194,195 These results have proved extremely valuable for establishing/consolidating many of the herein reviewed chemical-shift/structure relationships. With the perpetual increase in computational speed, such work is bound to develop furtherdand perhaps more importantdalso enabling the exploration of larger MD-generated glass-structure models used as input to the DFT calculations, thereby improving the statistics and the validity of the inferred shift/structure correlations. (II) A synergetic evaluation of results from large glass models generated by MD simulations with those from advanced homo/hetero-nuclear MAS NMR experiments (Sections 9.20.15–9.20.17) have offered new opportunities for probing the medium-range glass structure. This fruitful route to enhancing the insight into the glass organization across a sub-nanometer scale was essentially unexplored until the past z 10 years; see Refs. 31,78,131,413,613,643 for examples. Moreover, we foresee a significant expansion of heteronuclear NMR experimentation targeting 17O, which is a remarkably underexploited area, as reflected in the fact that essentially all of the relatively few reports thereof have appeared over the past decade. Indeed, despite a vast number of 17O NMR studies on numerous groups of oxide-based glasses since the early 1980s, nearly all of them were based on routine single-pulse MAS and 3QMAS NMR experiments, which feature some limitations (see Section 9.20.13). Yet, most of them may be addressed by further NMR technique developments. We also anticipate the advent of DNP/ NMR investigations targeting 17O for MAS NMR studies of glasses, as well as studies of other nuclides that as of today are considered “hopeless”. Such advances would significantly expand the possibilities to examine minor/minute O species in glasses, such as the “exotic” O[0] coordinations, as well as for enhancing the feasibility to identify and quantify (for instance) Al–O–Al and Al–NBO moieties in glasses for which such motifs are minor and hitherto assumed to be absent.

Acknowledgments I gratefully acknowledge Baltzar Stevensson for help with the manuscript preparation, in particular for preparing the tables and several figures.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

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A Molecular Dynamics Simulation Interpretation of Neutron and X-Ray Difraction Measurements on Single Phase Y2O3–Al2O3. J. Phys. Condens. Matter 2009, 21, 205102–205111. 619. Jakse, N.; Bouhadja, M.; Kozaily, J.; Drewitt, J. W. E.; Hennet, L.; Neuville, D. R.; Fischer, H. E.; Cristiglio, V.; Pasturel, A. Interplay between Non-Bridging Oxygen, Triclusters, and Fivefold Al Coordination in Low Silica Content Calcium Aluminosilicate Melts. Appl. Phys. Lett. 2012, 101, 201903. 620. Bouhadja, M.; Jakse, N.; Pasturel, A. Striking Role of Non-Bridging Oxygen on Glass Transition Temperature of Calcium Aluminosilicate Glass-Formers. J. Chem. Phys. 2014, 140, 234507. 621. Iuga, D.; Morais, C.; Gan, Z.; Neuville, D. R.; Cormier, L.; Massiot, D. NMR Heteronuclear Correlation Experiments Between Quadrupolar Nuclei in Solids. J. Am. Chem. Soc. 2005, 127, 11540–11541. 622. Lee, S. K.; Ryu, S. Probing of Triply Coordinated Oxygen in Amorphous Al2O3. J. Phys. Chem. Lett. 2018, 9, 150–156. 623. LaComb, M.; Stebbins, J. F. Tricluster Oxygen Atoms in Crystalline and Glassy SrB4O7: High Resolution 11B and 17O Nuclear Magnetic Resonance Analysis. J. Non Cryst. Solids 2015, 428, 105–111. 624. Nesbitt, H. W.; Bancroft, G. M.; Henderson, G. S.; Ho, R.; Dalby, K. N.; Huang, Y.; Yan, Z. Bridging, Non-Bridging and Free (O2) Oxygen in Na2O–SiO2 Glasses: An X-Ray Photoelectron Spectroscopic XPS and Nuclear Magnetic Resonance NMR Study. J. Non Cryst. Solids 2011, 357, 170–180. 625. Sawyer, R.; Nesbitt, H. W.; Bancroft, G. M.; Thibault, Y.; Secco, R. A. Spectroscopic Studies of Oxygen Speciation in Potassium Silicate Glasses and Melts. Can. J. Chem. 2015, 93, 60–73. 626. Thompson, L. M.; McCarty, R. J.; Stebbins, J. F. Estimating Accuracy of 17O NMR Measurements in Oxide Glasses: Constraints and Evidence From Crystalline and Glassy Calcium and Barium Silicates. J. Non Cryst. Solids 2012, 358, 2999–3006. 627. Stebbins, J. F.; Sen, S. Oxide Ion Speciation in Potassium Silicate Glasses: New Limits From 17O NMR. J. Non Cryst. Solids 2013, 368, 17–22. 628. Stebbins, J. F. Anionic Speciation in Sodium and Potassium Silicate Glasses Near the Metasilicate ([Na,K]2SiO3) Composition: 29Si, 17O, and 23Na MAS NMR. J. Non-Cryst. Solids: X 2020, 6, 100049.

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629. Nasikas, N. K.; Edwards, T. G.; Sen, S.; Papatheodorou, G. N. Structural Characteristics of Novel Ca–Mg Orthosilicate and Suborthosilicate Glasses: Results From 29Si and 17O NMR Spectroscopy. J. Phys. Chem. B 2012, 116, 2696–2702. 630. Hung, I.; Gan, Z.; Gor’kov, P. L.; Kaseman, D. C.; Sen, S.; LaComb, M.; Stebbins, J. F. Detection of “Free” Oxide Ions in Low-Silica Ca/Mg Silicate Glasses: Results From 17 O /29Si HETCOR NMR. J. Non Cryst. Solids 2016, 445–446, 1–6. 631. Bradtmüller, H.; Uesbeck, T.; Eckert, H.; Murata, T.; Nakane, S.; Yamazaki, H. Structural Origins of Crack Resistance on Magnesium Aluminoborosilicate Glasses Studied by Solid-State NMR. J. Phys. Chem. C 2019, 123, 14941–14954. 632. Knight, C. T. G.; Kirkpatrick, R. J.; Oldfield, E. The Connectivity of Silicon Sites in Silicate Glasses, as Determined by Two-Dimensional 29Si Nuclear Magnetic Resonance Spectroscopy. J. Non Cryst. Solids 1990, 116, 140–144. 633. Day, D. E. Mixed Alkali GlassesdTheir Properties and Uses. J. Non Cryst. Solids 1976, 21, 343–372. 634. Vessal, B.; Greaves, G. N.; Marten, P. T.; Chadwick, A. V.; Mole, R.; Houde-Walter, S. Cation Microsegregation and Ionic Mobility in Mixed Alkali Glasses. Nature 1992, 356, 504–506. 635. Swenson, J.; Matic, A.; Karlsson, C.; Börjesson, L.; Meneghini, C.; Howells, W. S. Random Ion Distribution Model: A Structural Approach to the Mixed-Alkali Effect in Glasses. Phys. Rev. B 2001, 63, 1322021–1322024. 636. Haase, J.; Oldfield, E. Spin-Echo Behavior of Nonintegral Spin Quadrupolar Nuclei in Inorganic Solids. J. Magn. Reson. Ser. A 1993, 101, 30–40. 637. Gee, B.; Eckert, H. 23Na Nuclear Magnetic Resonance Spin Echo Decay Spectroscopy of Sodium Silicate Glasses and Crystalline Model Compounds. Solid State Nucl. Magn. Reson. 1995, 5, 113–122. 638. Ratai, E.; Chan, J. C. C.; Eckert, H. Local Coordination and Spatial Distribution of Cations in Mixed-Alkali Borate Glasses. Phys. Chem. Chem. Phys. 2002, 4, 3198–3208. 639. Epping, J. D.; Strojek, W.; Eckert, H. Cation Environments and Spatial Distribution in Na2O–B2O3 Glasses: New Results From Solid State NMR. Phys. Chem. Chem. Phys. 2005, 7, 2384–2389. 640. Epping, J. D.; Eckert, H.; Imre, Á. W.; Mehrer, H. Structural Manifestations of the Mixed-Alkali Effect: NMR Studies of Sodium Rubidium Borate Glasses. J. Non Cryst. Solids 2005, 351, 3521–3529. 641. Zwanziger, J. W.; McLaughlin, J. C.; Tagg, S. L. Sodium Distribution in Sodium Tellurite Glasses Probed With Spin-Echo NMR. Phys. Rev. B 1997, 56, 5243–5249. 642. Alam, T. M.; McLaughlin, J.; Click, C. C.; Zonzone, S.; Brow, R. K.; Boyle, T. J.; Zwanziger, J. W. Investigation of Sodium Distribution in Phosphate Glasses Using Spin-Echo 23 Na NMR. J. Phys. Chem. B 2000, 104, 1464–1472. 643. Le Losq, C.; Neuville, D. R.; Chen, W.; Florian, P.; Massiot, D.; Zhou, Z.; Greaves, G. N. Percolation Channels: A Universal Idea to Describe the Atomic Structure and Dynamics of Glasses and Melts. Sci. Rep. 2017, 7, 16490. 644. Behrends, F.; Eckert, H. Mixed-Alkali Effects in Aluminophosphate Glasses: A Re-Examination of the System [xNa2O(1–x)Li2O]0.46[yAl2O3(1–y)P2O5]0.54. J. Phys. Chem. C 2011, 115, 17175–17183. 645. Janssen, M.; Eckert, H. 11B{23Na} Rotational Echo Double Resonance NMR: A New Approach for Studying the Spatial Cation Distribution in Sodium Borate Glasses. Solid State Ion. 2000, 136–137, 1007–1014. 646. Johnson, J. A.; Benmore, C. J.; Holland, D.; Du, J.; Beuneu, B.; Mekki, A. Influence of Rare-Earth Ions on SiO2–Na2O–RE2O3 Glass Structure. J. Phys. Condens. Matter 2011, 23, 065404.

9.21

Solution NMR of transition metal complexes

Zi-Ling Xuea and Tabitha M. Cookb, a Department of Chemistry, University of Tennessee, Knoxville, TN, United States; and b Department of Chemistry and Biochemistry, Berry College, Mount Berry, GA, United States © 2023 Elsevier Ltd. All rights reserved.

9.21.1 9.21.2 9.21.2.1 9.21.2.2 9.21.2.3 9.21.2.4 9.21.2.5 9.21.3 9.21.3.1 9.21.3.2 9.21.3.3 9.21.4 9.21.4.1 9.21.4.2 9.21.4.3 9.21.5 9.21.5.1 9.21.5.2 9.21.5.3 9.21.6 9.21.6.1 9.21.6.2 9.21.6.3 9.21.7 9.21.7.1 9.21.7.2 9.21.7.3 9.21.8 9.21.8.1 9.21.8.2 9.21.8.3 9.21.9 9.21.9.1 9.21.9.2 9.21.9.3 9.21.10 9.21.10.1 9.21.10.2 9.21.10.3 9.21.11 9.21.11.1 9.21.11.2 9.21.11.3 9.21.12 9.21.12.1 9.21.12.2 9.21.12.3 9.21.13 9.21.13.1 9.21.13.2 9.21.13.3 9.21.13.4 9.21.13.5

660

Introduction Group 3 (Sc, Y, La, Lu and Ac) Scandium complexes Yttrium complexes Lanthanum complexes Lutetium complexes Actinium complex Group 4 (Ti, Zr and Hf) Titanium complexes Zirconium complexes Hafnium complexes Group 5 (V, Nb and Ta) Vanadium complexes Niobium complexes Tantalum complexes Group 6 (Cr, Mo and W) Chromium complexes Molybdenum complexes Tungsten complexes Group 7 (Mn, Tc and Re) Manganese complexes Technetium complexes Rhenium complexes Group 8 (Fe, Ru and Os) Iron complexes Ruthenium complexes Osmium complexes Group 9 (Co, Rh and Ir) Cobalt complexes Rhodium complexes Iridium complexes Group 10 (Ni, Pd and Pt) Nickel complexes Palladium complexes Platinum complexes Group 11 (Cu, Ag and Au) Copper complexes Silver complexes Gold complexes Group 12 (Zn, Cd and Hg) Zinc complexes Cadmium complexes Mercury complexes NMR properties shared by complexes of more than two transition metals. Experimental and theoretical/computational studies NMR of metals in the complexes NMR of ligand nuclides in the complexes Theoretical and computational studies of NMR Advanced NMR techniques and methods 2-D NMR PGSE and DOSY EDNMR, HYSCORE, and ENDOR Measurement of the relaxation time Dynamic and variable-temperature (VT) NMR from chemical exchanges and reactions

Comprehensive Inorganic Chemistry III, Volume 9

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https://doi.org/10.1016/B978-0-12-823144-9.00051-0

Solution NMR of transition metal complexes 9.21.13.6 9.21.13.7 9.21.13.8 9.21.13.9 9.21.14 Acknowledgment References

NMR studies using parahydrogen (p-H2) High-pressure NMR Rapid-injection NMR Other advanced NMR techniques and methods Conclusion

661 719 719 720 720 720 721 721

Abstract This review covers the literature between 1990 and 2019. NMR of transition metal nuclides, such as 45Sc and 199Hg, and a-atoms of ligands is discussed, with the exception of 1H, 13C, 19F and 31P. Complexes of the 32 transition metals, including La, Lu and Ac, are arranged into 10 sections based on the groups in the periodic table. Later, properties (and features) shared by complexes of three or more transition metals are summarized. At the end, an overview is given about advanced NMR techniques and methods.

9.21.1

Introduction

Solution NMR, especially 1H, 13C, 19F and 31P NMR of ligands, is now among the most widely used spectroscopies to characterize transition metal complexesdtheir structures and reaction mechanisms. Many methods, including those to obtain NMR of metal nuclides, became fairly mature before 1990, leading to their extensive uses over the past 30 years. NMR of transition metal nuclides can provide direct information about physical and chemical environments of the metal centers, and it was the subject of a 1991 book edited by Pregosin and completed in 1990.1 Earlier, Harris and Mann edited the 1978 book “NMR and the Periodic Table”,2 and Mason edited the 1987 book “Multinuclear NMR”,3 summarizing the achievements on NMR of transition metal compounds to the times. Since 1991, there have been books4–8 and reviews9–11 on fundamentals of NMR as well as selected subjects, including a 2016 book on NMR of paramagnetic molecules5 and a 1993 review on paramagnetic metalloproteins9 by Bertini and coworkers, a 2013 book on NMR in organometallic chemistry by Pregosin,6 a 2011 review on NMR applications in inorganic chemistry,11 a 2004 book about how to conduct >200 NMR experiments by Berger and Braun,8 a 1997 book on NMR of non-metallic elements,12 a 1996 book on applications of NMR to organometallic chemistry,13 a 1996 article on NMR of metallic nuclei in clusters,14 and a 1991 review on transition metal NMR of organometallic compounds.10 A special 2008 issue of Coordination Chemistry Review edited by Pregosin was published on the applications of NMR to inorganic and organometallic chemistry, covering some 15 topics.15 Solution NMR of transition metal complexes was not covered in Comprehensive Inorganic Chemistry II published in 2013.16 The first edition, Comprehensive Inorganic Chemistry, was published in 1973.17 Given that the 1991 book on the NMR of transition metal nuclides reviewed the literature till early 1990,1 we decided to cover the literature on the solution NMR of transition metal complexes between 1990 and 2019. Publications on the subject in SciFinder over the 30-year period were selected for consideration here. For each transition metal, nuclear properties of NMR-active nuclide(s) are briefly reviewed, followed by discussion of main papers on the NMR of the metal nuclide(s). Given the large number of papers on the solution NMR of complexes of 32 transition metals (including La, Lu18,19 and Ac) over the 30 years, we were able to review only part of the literature on the subject. In other words, this is not a comprehensive review. Our goal is to give an overview of the solution NMR of transition metal compounds reported in 1990–2019, providing the reader a general understanding of the developments during the period. For the 4th-row transition metals including Lr (lawrencium), other than one paper on the 31P NMR spectrum of a ligand in an Ac complex,20 we did not find papers on NMR of these elements. For the ligands in metal complexes, the focus of the current review is on NMR of a-atoms on the ligands bound to the metal atom. Since 1H, 13C, 19F and 31P NMR is extensively used, these nuclides are generally not discussed in this review, except when they are part of special techniques or rarely used for the transition metals. The reader may find more detailed discussion of NMR of the non-metallic elements in the 1997 book by Berger, Braun, and Kalinowski,12 and a 1996 article on the 29Si NMR in organometallic compounds.21 Unless noted, the chemical shifts cited in this review are at room temperature. Quadrupolar nuclides [nuclear spin >1/2;22,23 quadrupole moment Q (or more precisely the geometrical part of the quadrupole moment eQ) s 0] in non-cubic (i.e., non-Td or non-Oh) complexes usually give relatively broad NMR peaks of the nuclides, as a result of short T1 and T2 (relaxation times) from efficient quadrupolar relaxation processes.22 Among 43 NMR-active, transition metal nuclides, 32 have a quadrupole moment.24 NMR properties of complexes with these quadrupolar nuclides were a subject of a 2007 review.24 Peak widths and errors in the chemical shifts and other properties, including natural abundances of nuclides25 and kinetic and thermodynamic parameters of chemical reactions, are not listed in the current review. Certain details, such as solvents used to make

662

Solution NMR of transition metal complexes

the NMR solutions and coupling constants are generally not provided. The author may find the information in the references. For coupling constants JA-B listed in the current review, the mass numbers of the element A or B are not listed (as in 1JNb-F), unless there is more than one NMR-active nuclide for A or B (as in 1J51V-eC or 1J51V-e15N). After NMR of each transition metal is discussed, a section is devoted to the properties (and features) shared by complexes of three or more transition metals. Afterwards, advanced NMR techniques and methods are summarized. IUPAC (International Union of Pure and Applied Chemistry) made recommendations in 2001 (IUPAC Recommendations 2001) about a unified scale to report the NMR chemical shifts of all nuclides relative to the 1H resonance of SiMe4 (tetramethylsilane or TMS).26 Additional recommendations for NMR shielding and chemical shifts (IUPAC Recommendations 2008) were published in 2008.27 The unified scale is based on a precise ratio (in %), X, of the resonance frequency of a given nuclide to that of the 1 H resonance of TMS in dilute solution (volume fraction 60,000-fold enhancement of 89Y NMR signals.100 Such hyperpolarized Y complexes were pH-sensitive NMR probes99 and used to probe kinetics of Y-ligand complexation101 with potential for direct imaging of metal ions in biological systems by magnetic resonance.100

( 12 )

( 13 )

For NMR of ligands, the dissociation of dimer (Cp*2YH)2 to the monomer was studied via VT 1H NMR.102 Below 40  C, the hydride ligand was coupled to two 89Y nuclei making a sharp triplet. As the temperature was raised, the hydride resonance shifted and broadened. This was attributed to the increasing rate of dissociation and the loss of the hydride coupling to the 89Y nuclei.102

9.21.2.3 139

Lanthanum complexes

La is one of two NMR-active nuclides and the only one used in studies of La complexes that we found in 1990–2019, as indicated in Table 1. The other nuclide, 138La (spin 5)32 with low (0.08881%) natural abundance and a fairly large quadrupole moment, is not practical for NMR studies.1 139La shifts of diamagnetic complexes are typically between d 1090 for (Bun4N)3(LaBr6) and d 772 as one of two peaks for Cp4La anion.1 Line widths of 139La peaks were often reported mostly because of quadrupole-dominated relaxation.1 139 La NMR was used to probe coordination of La(III) ions to N- and O-containing ligands, including macrocyclic ligands,82 103 D-ribose with LaCl3 in aqueous solution, acetohydroxamic acid [MeC(]O)NHOH] with La(ClO4)3,104 and p-sulfonatocalix 105 139 La NMR was also used to study MeOH-substituted lanthanum halides, including [La(H2O)7([4]arene with LaCl3. MeOH)2]Br3 (d 32.7), LaBr3(MeOH)5 (d 34.7), [(MeOH)4Cl2La(m-Cl)]2 (d 31.2), and [La(MeOH)9]I3$MeOH (d 35.1).106 Interactions of ZnCl2 with La(dtpa) and other La(III) complexes containing dtpa derivative ligands have been probed by 139La NMR.107 Multinuclear NMR study, including the use of 139La NMR, was performed to study the La(III)catalyzed alkylation of ethylene glycol with maleate.108 Addition of H5IO6 to aqueous solution of La(NO3)3 gave a 139La resonance at d 11.36 Organometallic complexes studied by 139La NMR include those with allyl ligands. La(h3-C3H5)2X$2THF (X ¼ Cl, d 520; Br, d 550; I, 585),109 La(h3-C3H5)3$L [L ¼ MeOCH2CH2OMe (dme), d 440;110 Me2NCH2CH2NMe2 (tmed), d 475;110 2O]P(NMe2)3, d 285;110 1,5-dioxan, d 440109], and Cp and Cp* allyl complexes, CpLa(h3-C3H5)2(1,5-dioxan)0.2 (d 13), Cp*La(h3-C3H5)2 (d 95), Cp2La(h3-C3H5) (d 214), and Cp*2La(h3-C3H5) (d 167).111 139La shift of Cp3La$L are d 560 for L ¼ thf111 and d 558 for triindenyl complex (C7H9)3La$thf.112 139La NMR was used to study Schlenk-type equilibria for cyclopentadienyl complexes Cp3La, CpLaI2, and [(h5-1,3-R2C5H3)2La(m-Cl)]2 (R ¼ SiMe3) as well as with bimetallic complexes X2La-Ru(CO)2Cp (X ¼ Cp, h5-1,3-R2C5H3).113 139 La NMR of endofullerenes was reported, including La2@C72 (d 575.6),114 La2@Cs(17490)-C76 (d 617.8),115 La2@C80 (d 402.6)114 and silylated116 and pyrrolidine117 derivatives as well as the anion of La@C82 (d 470) and derivatives.118 Binding of La(III) ions in La(NO3)3 to aqualysin I, a heat-stable protease with two Ca2þ-binding sites, was probed by 139La NMR.119 For NMR of ligands, La(III) was added to a solution containing dcf [dcf ¼ methyl dicarboxy-a-D-fructofuranoside (14)] and the product was studied via 17O NMR in order to seek evidence of a fourth donor cite in this ligand in the complex La(dcf)2.120 The

666

Solution NMR of transition metal complexes

dihedral angles of the protons were estimated from the coupling constants J. From the J values, it was determined that the arrangement of the ligand around the metal ion effectively allowed for a fourth coordination site for the La(dcf) moiety in La(dcf) 2 as shown in 15.120

( 14 )

9.21.2.4

( 15 )

Lutetium complexes

We did not find reports of 175Lu NMR which was also not discussed in the 1991 book edited by Pregosin1 or the 1987 book on multinuclear NMR edited by Mason.3 For NMR of ligands, 15N and 13C NMR was used to characterize Lu isocyanate complexes [(H2O)5Lu(NCS)]2þ through [(H2O) Lu(NCS)5]2.121 The 13C and 15N signals showed a noticeable concentration dependence, which was used to identify the signals of the five complexes. The 13C and 15N shifts of the mono- to penta-isothiocyanato complexes were all more shielded than that of free NCS (d 165 referenced to 15NO3).121

9.21.2.5

Actinium complex

We did not find reports of 227Ac NMR which was also not discussed in the 1987 and 1991 books edited by Mason3 and Pregosin,1 respectively. Among Ac isotopes which are all radioactive, 227Ac has the longest half-life of t1/2 ¼ 21.772 years20 and is found in traces in uranium and thorium ores along with traces of 228Ac (t1/2 ¼ 6.15 h122). Reaction of Ac(III) in nitric acid with 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetra(methylene)phosphonic acid [H8dotp (16)] gave Ac(dotp)5 which showed a sharp 31P NMR resonance at d 20.2. This peak was 3 ppm deshielded from that of its La(III) analog La(dotp)5.20 The NMR spectrum was collected with microscopic reagent quantities (27.8 mg of Ac3þ and 67 mg dotp8 in 25 mL), giving reasonable S/N within 12 h.20

( 16 )

9.21.3

Group 4 (Ti, Zr and Hf)

For Ti and Zr, NMR of both the metals (twinned 47Ti and 49Ti, 91Zr) and ligands have been reported. For Hf, we have found only papers on NMR of ligands. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 2.

Solution NMR of transition metal complexes Table 2

Nuclide 47

Ti Ti 91 Zr 177 b Hf 179 b Hf 49

Nuclear and NMR properties of 47Ti, 49Ti, 91Zr, Natural abundance (%) a

Spin

DH (1H ¼ 1.00)

7.44 5.41 11.22 18.60 13.62

5/2 7/2 5/2 7/2 9/2

1.56  104 2.05  104 1.07  103 2.61  104 7.45  105

667

177

Hf and 179Hf.26 Quadrupole moment Q (fm2)

X (frequency, MHz;

DC (13C ¼ 1.00)

Gyromagnetic ratio (107) (rad s1 T1)

0.918 1.20 6.26 1.54 0.438

1.5105 1.51095 2.49743 1.086 0.6821

30.2 24.7 17.6 336.5 379.3

5.637534 5.639037 9.296298 (4.007)c (2.517)c

Relative receptivity

H ¼ 100 MHz, 2.3488 T)

1

Reference sample TiCl4 (neat) Cp2ZrCl2 (CH2Cl2) –

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 Although we did not find reports of 177Hf and 179Hf NMR, they are listed here for comparison. c Value in parenthesis was calculated from literature data on nuclear magnetic moments.26 b

9.21.3.1

Titanium complexes

Ti NMR spectra show both 47Ti and 49Ti peaks with the 49Ti peak more deshielded by 266 ppm from the 47Ti peak.1 The twinning is a result of very similar gyromagnetic ratios and thus NMR frequencies. The 49Ti peak has a better S/N ratio even though the 49Ti natural abundance is smaller. The sharper 49Ti signal is a consequence of the larger 49Ti nuclear spin and its slightly smaller quadrupole moment. Because of the quadrupole moments, sharp 47Ti and 49Ti signals with well-resolved multiplets were only observed for complexes with cubic Oh or Td symmetry such as TiF62.1 Line widths of 47,49Ti peaks were often reported mostly because of quadrupole-dominated relaxation.1 The range of 47,49Ti shifts for diamagnetic complexes spans d 1375 for Ti(CH2CMe2Ph)4123 to d 1389 for Ti(-II) Ti(13CO)62 [with K(2.2.2-cryptand)þ cation].1 Selected complexes with reported 47,49Ti shifts are listed in Table 3. 47,49Ti and 13C NMR spectra of Ti-containing catalysts were reported, many of which were in Table 3.123 It should be noted that shifts of same Ti complexes in different papers may be slightly different.125–129 49 Ti shifts of half-sandwich complexes, including those listed above, were reported in several papers.125–129 47,49Ti shifts of (h5C5H4X)TiCl3 with a silyl-substituted cyclopentadienyl ligand (X ¼ SiR3; R3 ¼ Me3, Me2Cl, MeCl2, Cl3, Me2F, MeF2, F3) showed a nearly linear relationship with lmax (wavelength of the first charge-transfer band in the UV–visible spectra) of the complexes, revealing that both 49Ti NMR shifts and lmax demonstrated the electron-releasing and -withdrawing nature of the X substituents.129 These (h5-C5H4X)TiCl3129 and Cp*TiMeX0 2 [X0 2 ¼ (Me)C6F5, (Me)OC6F5, (OC6F5)2]127 were initiators for olefin polymerization. Half-sandwich complexes with allyl and enantiomeric alkoxide ligands were used in the enantioselective allyltitanation of aldehydes.126

Table 3

47,49

Ti chemical shifts of selected Ti complexes.

Complexes

47,49

TiCl4123 TiBr4123 (NH4)2TiF6123 Ti(NMe2)4123 Ti(NEt2)4123 Ti(OEt)4124 Ti(OPri)4123 Ti(OPri)3Cl123 Ti(OPri)2Cl2123 Ti(OPri)Cl3123 Ti(OBut)4123 Ti(OCH2But)4123 Ti(CH2CMe2Ph)4123 CpTiCl3125 (h5-C5H4Me)TiCl3126 (h5-C5H4SiMe3)TiCl3126 Cp*TiCl3126 Cp*TiMe3127 Tp*TiCl3 [Tp* ¼ tris(3,5-dimethyl-1-pyrazolyl)borate]124 Cp2TiCl2123 Cp*2TiCl2123 Cp2TiII(CO)2124 [K(2.2.2-cryptand)]2[Ti(13CO)6]1

0.0 471.3 1160.9 230 216 825 (CH2Cl2) 856 749 598 358 896 851 1375 396.5 332 361 85 551 406 769 439 1156 1389

Ti shifts (d)

668

Solution NMR of transition metal complexes

49

Ti shift of TiCl4 in ambient-temperature ionic liquid (also known as molten salt), AlCl3-1-ethyl-3-methylimidazolium chloride (ImCl), was d 4, while in basic (chloride-rich) liquids, 49Ti shift of TiCl62 was d 237.130 47,49 Ti shifts of electron donor-acceptor complexes between 9-methylanthracene and TiCl4 were reported.131 Spin-lattice relaxation times T1 for several complexes were reported: TiCl4 (47Ti: 86.1 ms; 49Ti: 265 ms), TiBr4 (47Ti: 90.4 ms; 49Ti: 303 ms), Ti(OBut)4 (47Ti: 9.74 ms) and Ti(OPri)4 (47Ti: 3.67 ms).123 Spin-spin relaxation times T2 have also been reported for TiCl4 (47Ti: 72 ms; 49Ti: 191 ms).123 49 Ti shifts of TiX4 (X ¼ Cl, Br, F), TiClnMe4n (n ¼ 0–3), Cp2TiX2 (X ¼ F, Cl, Br) and Ti(CO)62 were calculated by a DFT method.132 For NMR of ligands, dmf exchange on [Ti(dmf)6]3þ was studied as a function of temperature and pressure by 1H and 17O NMR in order to expand upon the trend in exchange in hexa-solvated, trivalent, first-row transition metal cations.133 Along this row of metal ions and Ga(III), the mechanism changed from an associative activation mode for the earlier elements, such as Ti(III), to a dissociative activation mode for the later elements and Ga(III).133 17O NMR was used to analyze Ti(IV) tartrates and alkoxides, such as [Ti(dipt)(OPri)2]2 [d 293, 268, 180 and 177; dipt ¼ (þ)-diisopropyl tartrate (17) enriched with 17O at the hydroxyl positions] and Ti(OPri)4 (d 295).134 In order to gain an understanding about the reactivity of metal peroxo complexes, such as those containing Ti(IV), V(V), Mo(VI), and W(VI), several complexes were studied via the 17O NMR, electronic charge transfer band, OeO vibrational frequency, and the length of the oxygen-oxygen bond in the peroxo ligand.135 The peroxo ligands of Ti(O2)(C2O4)22 and Ti(O2)(dipic)(H2O)2 (dipic ¼ pyridine-2,6-dicarboxylate) had 17O shifts of d 591135 and 585,136 respectively. The other metalloperoxide complexes will be discussed in sections of other transition metals in the current review.

( 17 )

( 18 )

17 O shifts of Ti(IV) oxo porphyrin complexes, such as Ti(TMP)(]O) (d 1010 referenced to H2O; H2TMP ¼ 5,10,15,20tetramesitylporphyrin, also known as tetramesitylporphyrin), were probed.137 Diphenylchalcogenoate complexes (m,h5:h5Pn)2[Ti(EPh)]2 [18, Pn ¼ 1,4-(SiPri3)2-C8H4, E ¼ S, Se, Te] were analyzed via 29Si NMR (d in the 2.74–5.20 range).138 The Se and Te complexes were also studied via 77Se and 125Te NMR, respectively. The resonances at dSe 511 and dTe 418 were both more shielded compared to those of most other Ti(IV) selenolate and tellurolate complexes such as Cp2Ti(SePh)2 (dSe 847) and Cp2Ti(TeSiPh3)2 (dTe 709).138 The NMR studies of several Ti s-borane complexes were discussed in a 2008 review.139

9.21.3.2 91

Zirconium complexes

Zr NMR is more favorable than 49Ti, as the 91Zr nuclide (Table 2) has higher natural abundance, larger relative sensitivity and receptivity, and smaller quadrupole moment with a larger resonance frequency (closer to that of 1H NMR).1 Line widths of 91Zr peaks were often reported mostly because of quadrupole-dominated relaxation.1 91Zr shifts of diamagnetic complexes are typically in the range of d 893 for Zr(NMe2)4140 to d 348 for Cp2Zr(h4-butadiene).1 Hydrolysis of Cs2ZrF6 (d 191) in aqueous solution and in 30% H2O2 solution was probed using 91Zr and 19F NMR.141 In aqueous solutions, only ZrF62 and F ions were observed. However, in the water-peroxide medium, a peroxo intermediate (dimer F5Zr-OO-ZrF54) was detected.141 91 Zr shifts and line widths were used as indicators of coordination geometry distortions in 32 zirconocene complexes,140 including Cp2ZrCl2 (d 112), Cp2Zr(Cl)Me (d 126), Cp2ZrMe2 (d 386), (h5-C5H4Me)2ZrCl2 (d 69), (h5-C5H4Me)2ZrMe2 (d 401), Cp*2ZrCl2 (d 85), Cp*2ZrMe2 (d 443) and a number of other ring-substituted and -bridged zirconocene complexes. They were compared with those of Zr(NMe2)4 listed above and ZrCl4$2THF (d 628).140 For Cp0 2ZrX2 (Cp0 ¼ substituted and -bridged cyclopentadienyl; X ¼ Br, Cl, Me), ab initio computations suggested that the magnitude of the electric field gradient (EFG) at the Zr atom dominated line widths when the ligands X were varied, while substituents at Cp0 rings affected much less the computed EFGs.140 91Zr shifts of additional non-ansa alkyl-substituted cyclopentadienyl and phospholyl complexes, which were used in the ethylene polymerization, were reported.142,143 Reactions of Cp2ZrMe2 with fluorocarbon acids such as H2C(SO2CF3)2 were studied, giving, e.g., Cp2ZrMe[HC(SO2CF3)2] (d 20) and Cp2Zr[HC(SO2CF3)2]2 (d 331).144 91Zr shifts of a series of zirconocene products were given.144 The new compounds from the reactions with fluorocarbon acids were compared with those of Cp2ZrCl2, Cp2Zr(Cl)Me, and Cp2ZrMe2.144

Solution NMR of transition metal complexes

669

Zr shifts of CpTpZrCl2 [Tp ¼ hydrotris(pyrazolyl)borate, HB(C3H3N2)3; d 22] and Cp[H2B(C3H3N2)2]ZrCl2 (d 53) were studied.145 The complexes, when activated by methylalumoxane (MAO), became catalysts for olefin polymerization.145 91 Zr shifts of acetylacetonate (acac) complexes, (acac)3ZrCl (d 77) and Zr(acac)4 (d 46), were also reported in the study of their potentials, when activated by MAO, as catalysts for olefin polymerization.145 After reacting with MAO, 91Zr shifts are as follows: (acac)2ZrCl2/MAO (d 9.2), (acac)3ZrCl/MAO (d 156.6), and (acac)4Zr/MAO (d 147.5) in toluene solution at the Al:Zr ratio of 1000:1.145 In comparison, (dbm)3ZrCl/MAO [d 35.7; dbm ¼ dibenzoylmethanate ¼ 1,3-diphenylpropanedionate (19)].145 DFT calculations predicted d 1500 for the Zr@C28 endohedral compound, after it was detected by mass spectrometry.146 91

( 19 ) For NMR of ligands, the tetrameric Zr(IV) cation [Zr4(OH)8(H2O)8(H2O)8]8þ was studied via several spectral methods including O NMR (d 180).147 In this cation, there are two labile and two inert water molecules per Zr atom.147 11B and 31P NMR were used to analyze Zr and Hf polyhydride complexes M3H6(BH4)6(PMe3)4 and M2H4(BH4)(dmpe)2 (M ¼ Zr, Hf).148 B-containing diamide complexes (ButN-BPh-NBut)2M(THF) and Li2[M(ButN-BPh-NBut)3] (M ¼ Zr, Hf) were synthesized from the reactions of PhB(ButNLi)2 with the metal halides.149 These complexes were analyzed via 1H and 11B NMR and X-ray crystallography.149 A large series of zirconocene and hafnocene silyl complexes were synthesized and analyzed via 1H, 13C, and 29Si NMR.150 The in-situ polymerization of hyperpolarized 1-hexene with either [(EBI)ZrMe]B(C6F5)4 [EBI ¼ rac-C2H4(1-indenyl)2] or (Cp2ZrMe)B(C6F5)4 was analyzed via dissolution DNP NMR.151 With this technique, several aspects of the reaction such as stereochemistry, measurement of kinetic rate constants, and identification of deactivation processes could be studied simultaneously.151 Stop-flow NMR was also used to directly observe the kinetics of 1-hexene polymerization with either [(EBI)ZrMe]-B(C6F5)4.151 Diffusion NMR was used to study the individual components and combinations of a ternary system containing Cp2ZrMe2/MAO (DMAO) in 2,6-But2-phenol (MAO ¼ methylaluminoxane, DMAO ¼ AlMe3-depleted MAO).152 Variable-pressure 2-D (2dimensional) 1H Exchange Spectroscopy (EXSY) was used in the assignment for the cis/trans-isomerization of ZrCl4[O] P(OMe)3]2.153 For an overview of EXSY, see Section 9.21.13.1. Heptacoordinated Zr and Hf complexes M[MeC(NPri)2]3Cl (M ¼ Zr, Hf) and M[MeC(NPri)2]3R (M ¼ Zr, Hf; R ¼ Me, Et) were analyzed via several methods including 1He15N gHMBC NMR.154 The average bond lengths of MeN in M[MeC(NPri)2]3Cl were shorter than those in M[MeC(NPri)2]3Et as observed in their crystal structures. Since fast exchange was needed to detect the HMBC cross peaks, the 2-D NMR experiments for M[MeC(NPri)2]3Cl were performed at an elevated temperature (60  C).154 The 1He15N gHMBC NMR of M[MeC(NPri)2]3Me was also obtained at elevated temperatures (45  C).154 The 11B NMR spectrum was obtained for [(Zr6BI12)(H2O)6]þ (d 215.2) which was formed from the dissolution of KZr6BI14 in deoxygenated water.155 17

9.21.3.3

Hafnium complexes

We did not find reports of 177Hf or 179Hf NMR which were also not discussed in the 1991 book edited by Pregosin1 or a 1987 book on multinuclear NMR edited by Mason.3 For NMR of ligands, the silyene complex (h-C5H4-Et)2(PMe3)Hf]Si(SiMeBut2)2 was analyzed via 1H, 13C, 31P, and 29Si NMR.156 This was the first example of a stable Schrock-type silyene complex and the first complex with a Hf]Si double bond.156 For polyhydride complexes Hf3H6(BH4)6(PMe3)4,148 Hf2H4(BH4)(dmpe)2,148 B-containing diamide complexes (ButN-BPhNBut)2Hf(thf) and Li2[Hf(ButN-BPh-NBut)3],149 and heptacoordinated Hf[MeC(NPri)2]3Cl,154 see previous Section 9.21.3.2 on their Zr analogs.

9.21.4

Group 5 (V, Nb and Ta)

For V and Nb, NMR of both the metals (51V, 93Nb) and ligands have been reported. For Ta, we found only papers on NMR of ligands in 1990–2019. It should be pointed out that solution 181Ta NMR of the TaF6 anion prepared by dissolving Ta metal in HF/HNO3 was reported in 1973 in order to determine the 181Ta nuclear gyromagnetic ratio and its magnetic moment.157 Later, 181Ta NMR spectra of (Et4N)(TaCl6), (Et4N)[Ta(CO)6], and K2(TaF7) in solution were published in 1986.158 Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 4.

9.21.4.1

Vanadium complexes

We did not find papers published in 1990–2019 on 50V NMR. The reader may find a summary of 50V NMR work published by 1990 in Ref. 1.

670 Table 4

Solution NMR of transition metal complexes Nuclear and NMR properties of 51V, 93Nb, and 181Ta.26 Gyromagnetic ratio (107) (rad s1 T1)

Quadrupole moment Q (fm2)

X (frequency, MHz;

Spin

DC (13C ¼ 1.00)

0.250 99.750 100

6 7/2 9/2

1.39  104 0.383 0.488

0.818 2.25  103 2.87  103

2.6706490 7.0455117 6.5674

21.0 5.2 32.0

9.970309 26.302948 24.476170

99.98799

7/2

3.74  102

220

3.2438

317.0

11.989600

Nuclide (50V)b,c 51 V 93 Nb 181

Ta

Relative receptivity DH (1H ¼ 1.00)

Natural abundance (%) a

1 H ¼ 100 MHz, 2.3488 T)

Reference sample VOCl3 (neat/C6D6) KNbCl6 (MeCN) or NEt4(NbCl6)159,160 (MeCN or CD3CN) KTaCl6 (MeCN) or NEt4(TaCl6) (1:1 MeCN: Me2CO158)

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 V is radioactive with t1/2 > 3.9  1017 years.32 c50 V in parenthesis is considered to be the less favorable of the element for NMR.26

b50

51

V NMR is one of mostly used metal NMR spectroscopies with many papers. In fact, 51V nuclear properties in Table 4 make its NMR among the easiest in transition metals even for compounds with nearly no symmetry.1 Solution 51V shifts of diamagnetic complexes are typically in the range of d 2375 for Cp*2V2(m,h2-Se2)(m-Te)21 to 2054 for (NEt4)[CpV(CO)3(SnPh3)].161 51V NMR studies of VV, VIII, VI and VI complexes up to 1990 were reviewed in detail in Refs. 1,162. Biological applications of 51V NMR were discussed in another 1990 review.163 In addition, 51V NMR of organometallic complexes at VV, VIV (in VeV bonded dimers), VIII, VI, and VI oxidation states was surveyed in depth in a 2008 review.164 51V NMR developments during 1997–2008 were reviewed in 2008.165 Complexes with VO bonds, including vanadate (VO43) derivatives, polyoxometalates, and peroxo derivatives, continue to be a focus of 51V NMR studies driven in large part to find insulin-mimetic V compounds in diabetic treatments. Vanadate derivatives typically contain N,O,166,167 O,O,168–170 O,N,O171–173 and O,N,N174 ligands. Reported complexes with N,O ligands included those with NH2OH,166 MeNHOH,166 and 8-hydroxyquinoline-5-sulfonic acid [H(8-HQS) (20)],167 suggesting, e.g., that 5- (d 527) and 6-coordinated (d 537 and 540 from isomers) V centers were present in the 8-HQS complexes.167 The equilibria of vanadate with b-alaninehydroxamic acid (H2NCH2CH2CONHOH),168 aldaric acids (D-saccharic acid and mucic acid),169 1,2-dimethyl-3-hydroxy-4-pyridinone175 in aqueous solution, giving O,O complexes, were studied by 51V NMR, showing, e.g., d 520 and 450 for 1:1 and 1:2 V:ligand (ligand ¼ b-alaninehydroxamate) complexes, respectively.168 Interactions of vanadate with adenosine, and imidazoles in aqueous solution were probed by potentiometry and 51V NMR.176 O,N,O complexes included those from vanadate reactions with iminodiacetic acid [HN(CH2CO2H)2], N-(2-hydroxyethyl)iminodiacetic acid [HOCH2CH2N(CH2CO2H)2],171 N,N-bis(2-hydroxyethyl)glycine [(HOCH2CH2)2NCH2CO2H],171 2,6pyridinedicarboxylate,173 and 4-hydroxypyridine-2,6-dicarboxylic acid (H2-dipic-OH),172 forming products with tridentate ligands such as Na[VO2(dipic-OH)] (d 529.0).172 Tridentate O,N,O complexes 21 with (E)-N0 -[1-(5-acetyl-2,4-dihydroxyphenyl)ethylidene] hydrazide-type ligands were synthesized and characterized, including by single-crystal diffraction for a few complexes.177 Their 51V NMR showed resonances in the d 534.0 to 547.8 range.177 O,N,N complexes include those from the reactions of vanadate(V) with dipeptides (Val-Gln, Ala-Gln, Gly-Gln, Gly-Glu, and Ala-Gly), which were characterized by multinuclear (51V, 14N, 13 C) NMR.174

( 20 )

( 21 )

Solution NMR of transition metal complexes

671

51

V NMR was used as a pH-dependent probe for acidification of reverse micellar nanodroplets by CO2 in the confined space.178 Multinuclear NMR approaches, in particular 51V, were employed to elucidate the nature of vanadates and peroxovanadates in hydrophilic ionic liquids, (bmim)BF4 and (bmim)(OTf) [bmimþ ¼ 1-n-butyl-3-methylimidazolium (22)], indicating that ionic liquids had a strong influence on the vanadate chemistry both for the formation of the aggregates (with and without H2O2) and the rate of peroxide consumption catalyzed by vanadium.179 V2O5 was dissolved at >70  C in, e.g., (bmim)AlCl4 ionic liquid, giving different species as a function of melt acidity.180 51V, 1H, and 13C NMR and IR indicated that, in basic and neutral melts, VO2Cl2 and a metavanadate species, [(VO3)n]n, were the products. While VO2Cl 2 was prominent in basic melts, but as the melt became neutral or as the concentration of V2O5 was increased, the concentration of [(VO3)n]n increased.180

( 22 ) Vanadate (VO43), stable in the highly alkaline region (pH > 13), oligomerized as basicity was reduced. At pH 2–6, the main 181 species was polyoxovanadate V10O6 Structural studies of polyoxometalates 28 , which could exist in several protonated forms. by 51V and 17O NMR were reviewed in 2006.182 Time-resolved 51V NMR EXSY was used to probe kinetics of the oligomerization of vanadate into dimer, tetramer, and pentamer in aqueous solutions, giving rate constants.183 The existence of linear tri- and tetravanadate anions, V3O105 [51V d 554.3 (Vterminal), 586.6 (Vcentral); 273 K] and V4O136 [51V d 554.3 (Vterminal), 585.4 (Vcentral)], in aqueous solution were confirmed by 51V and 17O NMR and potentiometry, yielding constants of their formation from Hþ and 4 3 17 HVO2 O-riched solution.184 17O 4 (d 537.2) through dimer intermediates V2O7 (d 558.8) and HV2O7 (d 559.9) in 5% 17 NMR resonances were in the d 920–360 range. O magnetization-transfer experiments indicated that the O atoms in V3O5 10 184 and V4O6 When a neutral, 3% 17O-riched aqueous vanadate 13 underwent exchanges likely through intramolecular processes. solution in NaCl was rapidly acidified at room temperature to pH 1.5, transient tridecavanadate H12V13O3 40 , containing 12 V atoms (d 538.0) around a central, tetrahedrally coordinated V atom (d 523.3) in a Keggin structure, was identified by 51V and 17O NMR.185 17O NMR peaks at d 981, 853, and 575 from solvent O atoms were observed. The tridecavanadate had a half-life of 80 min at 298 K.185 Dodecavanadate, V12O4 32 , is a bowl-type host with a 4.4-Å-diameter cavity entrance that reacted with guest    5 51 V NMR and anion X (X ¼ CN, OCN, NO 2 , NO3 , HCO2 , and CH3CO2 ) to form host–guest complexes, V12O32(X) , as X-ray crystallographic analyses showed.186 187 Vanadate could also form mixed-metal polyoxometalates such as a-H2W11VO7 and heteropolymetalates with 40 (d 543) 5 þ 51 29 main group oxyanions such as the Keggin-type a-SiVW11O40 (Na salt; V d 551.3; Si d 81.87).188 Two tungstovanadates, 5 2  51 51 51 WV9O5 29 and mer-W3V3O19 , were identified in equilibrated aqueous solution of WO4 and VO3 using V NMR and Ve V COSY (Correlation Spectroscopy) which supported structures analogous to known molybdovanadates.189 51V and 17O NMR showed that 3 2 silicate anions reacted with HVO2 4 in aqueous alkaline solution, forming H2VSiO7 , H3VSiO7 and related monovanadooligosi190 3 3 licates. Molybdovanadates with high Mo:V ratios in aqueous solution, such as cis-Mo4V2O4 19 , cis-HMo4V2O19 , Mo5VO19 , 4 5 51 17 95 191 , HMo V O , and b-Mo VO , were characterized by V and O NMR as well as Mo NMR for some species. ReacMo4V5O5 27 4 5 27 7 26 51 tion of NaVO3 with Na2WO4 in NaCl-containing aqueous solution yielded several tungstovanadates, such as cis-W4V2O4 19 ( V 5 51 7 51 d 511.3), WV9O28 ( V d in the range of 428.2 to 525.7), and a-H2W11VO40 ( V d 544.3) in equilibrium with 3 192 51 H2V10O4 V, 183W and 17O NMR and potentiometry were used to characterize the mixtures.192 Mixing of Na2HVO4 28 and VO4 . with varying proportions of Na2WO4 and Na2MoO4 in NaCl-containing water, followed by acidification with HCl, yielded the 193 51 complete series of hexametalate anions V2MonW4nO4 V shifts 19 (n ¼ 0–4) in the Lindqvist structure with two cis V atoms. of the species in the d 497.9 to 513.7 range and their monoprotonated tetraanions in the d 511 to 541 range were assigned.193 Reaction of hydrous niobium oxide with V2O5, H3PO4 and NMe4OH in water at 130  C gave a Keggin-type polyoxoniobate (NMe4)9[PV2Nb12O42] (51V d 540; 31P d 2.4; pH 7.3) containing a central P site and two capping V sites.194 51V NMR (for VV component), EPR (for VIV component) and voltammetry were used to study the initial reduction of 1- and 4[S2VW17O62]5 forming VIV products.195 When a mixture of Na7H(Nb6O19), NaVO3, and NaHCO3 in water was heated at 220  C in an autoclave, the reaction gave a bicapped a-Keggin vanadododecaniobate, Na9H4[VNb12O40[NbO(CO3)]2].196 51V NMR and ESI-MS data indicated that this anion in solution was in equilibrium with VNb12O15 40 and oligomeric species from disso196 ciation of the NbO(CO3)þ fragments.196 In the presence of Kþ, the same reaction gave VxNb24On 76 (x ¼ 4, n ¼ 12; x ¼ 3, n ¼ 17). A V-Co cluster, [Co4(tacn)4V4O12(OH)4](OTf)4 [tacn ¼ 1,4,7-triazacyclononane (2, R3 ¼ H3)], was prepared from the reaction of Na3VO4 with [Co(tacn)(H2O)3](OTf)3 (whose 59Co NMR was given below) in aqueous triflic acid solution.197 The triflate product could be converted to Cl, Br or ClO4 derivatives. 51V and 59Co NMR of the cation solution show d 380 and 9650, respectively.197 For the use of electron-electron double resonance (ELDOR)-detected NMR (EDNMR), hyperfine sub-level correlation (HYSCORE), and electron-nuclear double resonance (ENDOR) to study hyperfine interactions in polyoxometalate PV2Mo10O406 with one reduced V(IV) ion,198 see Section 9.21.13.3. Vanadium peroxo compounds were of interest mainly due to their role in biological systems and their application in oxidation reactions.199 Vanadium peroxo compounds were identified as a new class of powerful insulin mimetic agents.200 Vanadium peroxo

672

Solution NMR of transition metal complexes

materials were also found to be in haloperoxidases that likely play a key role in the production of biogenic organohalogens in the environment.201 Addition of H2O2 to NH4VO3 in acid aqueous solutions gave monoperoxo VO(O2)þ (dV 540.5) or diperoxo VO(O2)2 (dV 693.1) complexes.202 In the presence of bidentate ligands L, e.g., picolinic or pyrazinic acid (HL), complexed peroxo vanadium species such as VO(O2)L, VO(O2)L2, and VO(O2)2L2 were identified by 51V NMR,202 and their shifts in 12 solvents were also studied.203 In MeCN, the picolinate complex, VO(O2)(picolinate)(H2O)2, was found to oxidize hydrocarbons and the spin trap 3,3,5,5-tetramethyl-pyrroline-N-oxide (TMPO), forming V(IV) species, as 51V NMR and EPR studies showed.204 51 V NMR revealed that reactions of aqueous monoperoxo VO(O2)þ with amino acids such as glycine or proline gave two types of bis(amino acid) products, in which the two amino acid ligands were either bidentate or one bidentate and one monodentate through the amino group.201 No reaction of VO(O2)þ with imidazole or the imidazole ring of histidine was observed. In contrast, reactions of aqueous diperoxo VO(O2)2 with amino acids give monodentate products. Imidazole, as the free ligand or as the side chain in histidine, complexed strongly to diperoxovanadate, as did N-methylimidazole and also pyridine.201 Quantitative 51V NMR and potentiometric studies of the speciation in the vanadate-peroxide-imidazole systems also showed that imidazole binds strongly to diperoxovanadate.205 When L-lactic acid [CH3CH(OH)COOH] and H2O2 at pH 1–7 was added ammonium vanadate(V), the reaction gave three dimersdTwo are 2:2:1 (metal:ligand:peroxo) isomers and the third is a 2:2:2 species.199 At pH < 2, an additional 1:1:1 complex was formed.199 Similar reactions with glycolic acid206 and L-malic acid207 were studied. The speciation of H2VO4 and H2O2 with L-a-alanyl-L-histidine (23) in acidic aqueous solution was studied by quantitative 51V NMR and potentiometry, showing the formation of four 1:1:1 (metal:ligand:peroxo) and four 1:1:2 products.208 Reaction of K3[VO(O2)2(oxalate)] or VO(O2)2(D2O)/VO(O2)2(HOD) with glycyl-histidine (24) in aqueous (H2O or D2O) solution gave two VO(O2)2(glycylhistidine) isomers with VeN bonds to either the 3-N or d-N atom in the imidazole ring, as VT NMR, Diffusion-Ordered Spectroscopy (DOSY), HMQC and DFT calculations showed.209 Additional discussion of HMQC4 and DOSY4 is given in Section 9.21.13.1 below. NMR studies (including 1H, 13C, 14N, 51V and DOSY) of the reaction between K3[VO(O2)2(oxalate)] with ethylenediamine (H2NCH2CH2NH2 ¼ en) in aqueous solution indicated the formation of 6-coordinated [OV(O2)2(en)] with one VeN bond.210 In contrast, a similar mixture with HNEt2 instead did not lead to the formation of a new complex.210 Reaction of siloxy VO2(OSiPh3)2 with H2O2 gave oxoperoxo complex VO(O2)(OSiPh3)2 (d 596.8).211 51V NMR, ESI-MS, and ab initio calculation techniques were used to study vanadium triperoxo complexes such as V(O2)3 in protic solvents, showing a step-by-step decomposition process.212 When Na[V(O2)3]$3H2O was dissolved in strongly basic water (pH 14), its decomposition from the blueviolet (triperoxo vanadate; d 847) to yellow (diperoxo vanadate) was slowed down, allowing the characterization by 51V NMR.212

( 23 )

( 24 )

Cysteine oxidation to cystine by oxo diperoxo complexes [VO(O2)2(L)]n (L ¼ oxalate, n ¼ 3; L ¼ picolinate, n ¼ 2; L ¼ bipyridil, phenanthroline, n ¼ 1) with insulin-mimetic activity was studied by 51V NMR, UV, and stopped-flow techniques.200 The oxalate ligand underwent a total ligand dissociation during the reaction, while the other three complexes held their ligands in solution.200 DNA-photocleavage by peroxo V(V) complexes irradiated at 365 nm in aqueous solution was studied by 51V NMR, showing VO3 as the vanadium product.213 Photolysis-EPR spin-trapping experiments supported the notion that singlet oxygen was the reactive species.213 Nuclease activity of VO(acac)2 and its derivatives was studied by several techniques including 51V NMR, showing that the mechanism was oxidative and associated with the formation of reactive oxygen species (ROS).214 Interactions of vanadate with bovine Cu,Zn-superoxide dismutase was probed by 51V NMR, suggesting that the vanadate tetramer bound to the two lysine residues in the solvent channel of Cu,Zn-SOD.215 51 V NMR of organometallic complexes was discussed in a 2008 review, as indicated earlier.164 51V shifts of selected complexes are listed in Table 5.164 51V NMR was used to characterize [VO(m-OCH2CF3)(OCH2CF3)(C6F5)]2 (d 481), [VO(m-OCH2CF3)(OCH2CF3)2]2 (d 570), O]V(NEt2)3 (d 205), and (F5C6)3B)O]V(NEt2)3 (d 57).216 Catalytic activities of vanadium complexes were studied by 51V NMR.217–219 Cyclohexene oxidation by cumyl or t-butyl hydroperoxides to cyclohexene oxide, catalyzed by VO(acac)2(OR) (R ¼ But, d 477; CMe2Ph, d 475), was probed by 51V NMR.217 The alkoxides were converted to peroxide complexes VO(acac)2(OOR) (R ¼ But, d 351; CMe2Ph, d 365) which then transferred an O atom to cyclohexene. In acid isopropanol/water solution under aerobic conditions, Bun4NVO3 catalyzed autoxidation of PriOH to acetone and O2 reduction to H2O2.218 The V-substituted, Lindqvist-type polyoxotungstate VW5O193 in MeCN promoted cyclooctene epoxidation by H2O2 into cyclooctene oxide.219 Oxidative carbonylation of toluene to p-toluic acid by CO and O2 using Rh(CO)2(CF3COO)3 as catalyst and [V(m-O)O(CF3COO)]2 (d 634 in toluene; 545 in D2O) as co-catalyst were studied by

Solution NMR of transition metal complexes Table 5

51

673

V chemical shifts of selected V organometallic complexes from Ref. 164.

Complexes

51

ButeN]V(CH2But)3 ButeN]V(CH2SiMe3)3 ButeN]V(OBut)3 O]V(CH2SiMe3)3 O]V(OSiPh3)3164 (ButCH2)3V]NeN]V(CH2But)3 CpV(CO)4

879 877, 1JV-N ¼ 86 Hz 751 1205 723 1237, 1J51V-14N ¼ 48 Hz, 1J51V-15N ¼ 76 Hz 1534, 1J51V-C ¼ 107 Hz

V shifts (d)

103

Rh, 51V and 13C NMR.220 In the catalytic cycle, [VV(m-O)O(CF3COO)]2 reoxidized Rh(I) to Rh(III), forming VIVO(CF3COO)2, and the dimer structure of the former was based on DFT calculations. DFT calculations were performed to obtain the geometry and electronic structures and solution 51V and 17O NMR shifts of a series of 7 oxo-peroxo V(V) complexes with tetradentate tripodal amine ligands, which mimicked the active site of vanadium bromoperoxidase.221 The more reactive complexes for bromide oxidation contained weakly electron donating amine ligands and more deshielded 51V and 17O resonances. For ligands, 17O NMR of oxo complexes was discussed earlier. In addition, 17O NMR of peroxide ligands in monomer V(V) complexes135,136 and diperoxyo vanadium complexes were obtained to probe the complexes.135,136 17O and 35/37Cl NMR spectroscopies were used to study the hexa-aqua V(III) cation structure in various mixed acid-based electrolyte solutions used in vanadium redox flow batteries.222

9.21.4.2

Niobium complexes

Nb NMR was used to characterize [NbF4(diphosphine)2](NbF6) [diphosphine ¼ o-(PMe2)2-C6H4, Me2P(CH2)2PMe2 (dimethylphosphinoethane or dmpe)] produced from the reactions of NbF5 with diphosphine in MeCN, showing the binomial septet at d 1553 for the anion NbF6 and a broad peak at d 1110 and 1062 for the cations, respectively (Table 6).160 93Nb shifts of NbF5(SMe2) and NbF5(SeMe2) (77Se) were also reported (Table 6).223 In [NbF4(dithioether)2](NbF6) [dithioether ¼ RS(CH2)2SR (R ¼ Me, Et or Pri)], the anion NbF6 was observed as a binomial septet at d 1551 to 1554 (JNb-F ¼ 335 Hz) at 220 or 243 K (Table 6).223 The 93Nb shifts of the cations [NbF4(SMe2)4]þ and [NbF4(dithioether)2]þ at 295 K are listed in Table 6.223 Chalcogenoether complexes NbCl5(SBun2) and NbCl5(SeBun2) and dinuclear (NbCl5)2[m-o-(CH2SEt)2-C6H4] were prepared from the reactions of NbCl5 with respective chalcogenoethers, and they were characterized by 93Nb and 77Se NMR (Table 6).225 These complexes were tested as potential single-source precursors for chemical vapor deposition of NbS2 or NbSe2 films. NbCl3(S2CNEt2)2 and [Nb(S2CNEt2)4](NbCl6) were prepared from the reaction of NbCl5 with dithiocarbamate Me3SiSC(]S)NEt2.224 93Nb shifts of NbCl3(S2CNEt2)2,224 NbCl2(S2CNEt2)3,226 NbBr2(S2CNEt2)3,226 and [Nb(S2CNEt2)4](NbCl6)224 are given in Table 6. [NbCl3(thf)2]2(m-N2) was prepared from NbCl5 and (Me3Si)2NN(SiMe3)2, and its 93Nb resonance is listed in Table 6.226

93

Table 6

93

Nb chemical shifts of selected Nb compounds. 93

Nb shifts (d)

Complexes

Cation

Anion a

77

[NbF4[o-(PMe2)2-C6H4]2](NbF6)160 [NbF4(dmpe)2](NbF6)160 [NbF4(dithioether)2](NbF6) [dithioether ¼ RS(CH2)2SR (R ¼ Me, Et or Pri)]223 [Nb(S2CNEt2)4](NbCl6)224 NbF5(SMe2)223 NbF5(SeMe2)223 NbCl5(SBun2)225 NbCl5(SeBun2)225 (NbCl5)2[m-o-(CH2SEt)2-C6H4]225 NbCl3(S2CNEt2)2224 NbCl2(S2CNEt2)3226 NbBr2(S2CNEt2)3226 [NbCl3(thf)2]2(m-N2)226

1110 1062 1540 to 1550

1553 1553 1551 to 1554

– – –

325 1440 1509 97 123 94 418 315 545 532

0

The anion NbF6  appeared as a binomial septet with 1JNb-F ¼ 335 Hz.

a

Se shifts (d)

– 247.2 – 273.6

674

Solution NMR of transition metal complexes

Alcoholysis of NbCl5 (d 2.6) by MeOH was probed by 93Nb NMR in benzene, showing formation of NbCl5x(OMe)x (x ¼ 1, d 497; 3, d 810; 4, d 1010; 5, d 1160) with increasing shielding of the Nb atom with replacement of Cl by OMe ligands.227 Similar NMR properties were also observed in MeOD solution.228 In a mixture of NbCl5(CD3CN), MeOH and H2O, 93Nb resonances of NbCl4(OMe)(MeCN) and NbCl4(OH)(MeCN) were found to be at d 560 and 495, respectively.229 Quinolinol derivatives Nb4(m-O)4(m-OEt)2(ONC10H8)2(OEt)8 and Nb4(m-O)4(m-OEt)2(ONC9H5Cl)2(OEt)8, prepared from the reaction of Nb(OEt)5 with 8-hydroxy-2-methylquinoline (HONC10H8) and 5-chloro-8-hydroxyquinoline (HONC9H5Cl), showed 93Nb resonances at d 206, 131 for the former and 197, 122 for the latter.230 Both peroxo complexes K[Nb(OH)(O2)2(8-quinolinolate)] and K [Nb(O2)2(8-quinolinolate)2] in D2O give 93Nb resonances at d 739.159 Polyoxoanion complex (Bun4N)4(NbW5O18)2O with a NbeOeNb oxo bridge gave a broad 93Nb resonance at d 975.231 17O-enriched sample (Bun4N)3[Nb(17O)W5O18] showed the 17O resonance at d 795.231 A 1991 review summarized 93Nb NMR of organometallic compounds by then,10 showing its chemical shift range of ca. 3000 ppm. The subject was discussed in a 1996 article.232 93 Nb NMR showed increasing shielding on the Nb atom in d4 NbX(CO)2(EtChCEt)(PEt3)2 when the halide ligand X changed from Cl (d 799.4) to Br (d 834.3) and I (d 931.4), the least electronegative of the three halogen elements.233 d2 (h5MeC5H4)2Nb(h3-allyl) gave a 93Nb resonance at d 1738.234 93Nb shifts were reported for a series of d0 (silox)3NbX2 and d2 (silox)3NbL complexes (silox ¼ But3SiO).235 A few (referenced to saturated NbCl5 in acetonitrile) are selected here: X2 ¼ NN¼CHSiMe3 (d 965), ¼O (d 947), Cl2 (d 755), ½(m:h1,h1-N2) (as a dimer with N2 bridging ligand, d 570), ¼CH2 (d 11.1), ¼PMe (d 660). For d2 (silox)3Nb(CH2¼CH2) with both olefin and metalacyclopropane character, d 296.235 DFTcalculated 93Nb shifts correlated with the experimental values, and indicated that, in the (silox)3NbX2 complexes, d was generally proportional to 1/c (c ¼ Pauling electronegativity of the atoms bonded to Nb), with most electronegative more shielded from the shifts of other complexes. This trend was derived from the paramagnetic contribution.235 93 Nb shifts in 19 Nb complexes, NbX6nYn (n ¼ 0–6; X, Y ¼ F, Cl, and Br) were calculated by the ab initio Hartree-Fock method, giving calculated values in very good agreement with the experimental data.236 93Nb shifts were found to be dominated by the paramagnetic contributions and were due to the d-d* transition and excitation energy DE. The computations also showed that the 93Nb shift was related to the electronegativity of the ligand atom, net charge, and the d-electron population of the Nb   atom.236 DFT computations of 93Nb shifts of a series of complexes, such as NbF 6 , NbCl6 , Nb(CO)6 , Nb2(OMe)10, CpNb(CO)4, and Cp2NbH3, were performed and the calculated shifts were compared with experimental shifts.237 Trends in the 93Nb peak line 2  widths for anionic Nb(CO)3 5 , Nb(CO)5H , and Nb(CO)5(NH3) were rationalized in terms of computed electric field gradients at the Nb atom. Nb oxoclusters stabilized by ionic liquid (Bu4nN)(lactate) were probed by 93Nb NMR, showing three resonances at d 849, 1108, and 1036 in D2O.238 The stabilized oxoclusters catalyzed epoxidation of olefins and allylic alcohols by H2O2, and catalytic cycle was followed by 93Nb NMR, including the identification of a peroxo intermediate. For NMR of ligands, reactions of (Me4N)6Nb10O28 with bases such as KOH, NaOH and Me4NOH formed several polyniobates, including hexaniobate anion Nb6O198, that were monitored via 17O NMR over the course of weeks.239 For Nb6O198 formed by different bases, such as KOH or Me4OH, ranges of the 17O shifts of the ONb, ONb2, and ONb6 were found to be at d 612–648, 378–393, and 29–41, respectively.239 NMR studies of several Nb s-borane were discussed in a 2008 review.139. 1 He15N HMBC (Heteronuclear Multiple Bond Correlation) was also used to obtain 15N (spin 1/2) NMR shifts of Nb complexes with NbeN bonds at the 15N natural abundance of 0.364%.240–243 The discussion of the inverse detection method is given in Sections 9.21.7 and 9.21.13.1.

9.21.4.3

Tantalum complexes

As noted earlier, for tantalum complexes, we have found only papers on NMR of ligands in 1990–2019. However, solution 181Ta NMR of complexes were reported before 1990, including TaF6.157 (Et4N)(TaCl6), (Et4N)[Ta(CO)6], and K2(TaF7).158,232 Parahydrogen-induced polarization (PHIP) was used to observe the kinetic, unsymmetric isomer of Cp*2TaH2Cl, where the hydride ligands were next to each other in the complex.244 Since PHIP requires that H2 adds pairwise in nonequivalent proton sites, this unsymmetric isomer would be the only isomer exhibiting polarization in PHIP.244 For NMR techniques that are based on parahydrogen (p-H2), see Section 9.21.13.6. 1 He15N HMBC was also used to obtain 15N (spin 1/2) NMR shifts of Ta complexes with TaeN bonds at the 15N natural abundance of 0.364%.240–243 DOSY studies of cis- and trans-[Ta(m-OMe)Me(]NSiMe3)[N(SiMe3)2]]2 in equilibrium demonstrated that they exist as dimers in solution.245 For an overview of DOSY, see Section 9.21.13.2.

9.21.5

Group 6 (Cr, Mo and W)

For Cr, Mo and W, NMR of both the metals (53Cr, 95Mo, 183W) and ligands have been reported. In addition to Ref. 1, NMR of the three metals was reviewed in 1996.246 Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 7.

Solution NMR of transition metal complexes Table 7

Nuclear and NMR properties of 53Cr, 95Mo, 97Mo and 183W.26

DC (13C ¼ 1.00)

Quadrupole moment Q (fm2)

1 H ¼ 100 MHz, 2.3488 T)

3/2 8.63  105

0.507

1.5152

15.0

5.652496

95 Mo 15.84 (97Mo)b,c 9.60

5/2 5.21  104 5/2 3.33  104

3.06 1.95

1.751 1.788

2.2 25.5

6.516926 6.653695

183

1/2 1.07  105

0.0631

1.1282403

–

4.166387

53

Cr

W

Natural abundance (%) a

Spin DH (1H ¼ 1.00)

9.501

14.31

Relative receptivity

X (frequency, MHz;

Gyromagnetic ratio (107) (rad s1 T1)

Nuclide

675

Reference sample K2CrO4 (aq) or Cr(CO)6 (d 1795 in THF1) Na2MoO4 (aq) or Mo(CO)6 (d 1856 in THF1) Na2WO4 (aq) or W(CO)6 (d 3483 in THF1)

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 We only found publications in 1990–2019 on solution 95Mo NMR of inorganic compounds and did not find a paper on 97Mo NMR in 1990–2019. However, 97Mo properties are listed here for comparison. Additional discussions about this issue are given below. c97 Mo in parenthesis is considered to be the less favorable of the element for NMR.26 b

MO42 (aqueous solution, Kþ or Naþ salt) in alkaline D2O solution (pD 11) is reference.1 M(CO)6 in THF solution are used as secondary standards, particularly in organometallic chemistry (Table 7).1 The ratio of the chemical shift ranges for 183W and 95Mo is ca. 1.6, which relates empirically the d values of both nuclides in isostructural compounds.1 Although the ratio has no theoretical support, it was used to predict, e.g., 183W resonance regions of W compounds when 95Mo shifts of their Mo analogs were known.1 Isotropic NMR shielding constants were obtained using DFT with gauge-including-atomic-orbitals (GIAO) in a spin-free formalism for the metal nuclides in MO42 and M(CO)6 (M ¼ Cr, Mo, W).247 Relativistic effects for NMR shielding constants were calculated using the zero-order-regular-approximation (ZORA) for relativistic effects.

9.21.5.1

Chromium complexes

The number of 53Cr NMR data are small due to several factors.1,246 53Cr is a quadrupolar nuclide (Table 7), leading to NMR peak broadening in complexes of low symmetry. Its natural abundance and the overall receptivity are insufficient to offset a rather small magnetic moment resulting in a low Larmor frequency (5.653 MHz at 2.3488 T) which, in turn, leads to a low sensitivity. Carbonate-containing capsule (NBun4)2L2(CO3) [L ¼ tris(2-aminoethyl)amine-based 3-cyanophenyl-substituted tripodal urea (25), a urea-based anion receptor] dissolved in CH2Cl2 was found to extract chromate CrO42 from water, forming (NBun4)2L2(CrO4) with 53Cr shift at d 99.98 (vs. d 0 for CrO42 in water as reference).248 The chromate-containing capsule was structurally characterized by single-crystal X-ray diffraction and 1H and 13C NMR.248

( 25 ) For 53Cr and 14N NMR of Cr(CO)5(CNBut) and Cr(CO)4(CNBut)2 in ambient acetone-d6, pressurized liquid CO2 or supercritical CO2, see Section 9.21.12.1.249 53 Cr shifts of CrO42, Cr2O72, CrO3X, CrO2X2 (X ¼ F, Cl), and Cr(CO)5L (L ¼ CO, PF3, ]CHNH2, ]CMeNMe2) were computed by the DFT methods, and the computed shifts were compared with experimental values.250 Also, 53Cr shifts were predicted for CrO3, (h6-C6H6)2Cr, (h6-C6H6)Cr(CO)3, and, with reduced reliability, for Cr2(m-O2CH)4. In NMR studies of a atoms of ligands, 17O NMR shifts of Cr diperoxo complexes were found to be between d 726 and 818, which were more deshielded than those of other metal diperoxo complexes at d 350–460.135 Along with the anomalous 17O shifts, the diperoxo Cr complexes show other features, including lower energy lmax values for ligand-to-metal charge transfer (LMCT) transitions in UV–visible spectra, higher OeO bond vibrational frequencies, and shorter OeO bond lengths than the other diperoxo complexes studied.135 The 17O shift of Cr(IV) oxo porphyrin complexes, such as Cr(TMP)(]O) (d 1247 referenced to H2O; H2TMP ¼ tetramesitylporphyrin) were studied.137

676

Solution NMR of transition metal complexes

Nitride complexes, including [NhCr(NPri2)2(PMe2Ph)]þ and [NhCr(NPri2)2(PMe3)]þ with several counter anions such as PF6 and B(C6F5)4, were studied via 14N NMR.251 The linewidths in the 14N NMR spectra in several paramagnetic Cr(III) amine and diamine complexes such as [Cr(NH3)6]3þ, [Cr(en)3]3þ, cis-[CrF2(en)2]þ, trans-[CrF2(en)2]þ were investigated and compared with those of similar diamagnetic Co(III) complexes.252 The peaks of the Cr complexes range from d 322.7 to 345.9.252 The 11 B NMR signal for the borylene complex (OC)5Cr]BSi(SiMe3)3 was found to be at d 204.3 which was more deshielded than d 92.3 in (OC)5Cr]B]N(SiMe3)2.253

9.21.5.2

Molybdenum complexes

95

Mo NMR is preferred to 97Mo NMR, even though the two nuclides have the same spin quantum number and resonate at very similar frequencies. This is because 95Mo has a significantly higher natural abundance, a smaller quadrupole moment, and a greater sensitivity, as listed in Table 7. 95 Mo NMR of inorganic compounds was extensively used in inorganic chemistry.1,246 In addition to a 1990 book chapter1 and a comprehensive review covering the literature in 1985–1995, structural studies of polyoxometalates by 95Mo and 17O NMR were reviewed in 2006.182 Thus, for polyoxometalates, the current review covers the literature since 2006 and, for other inorganic complexes, the literature since 1996 is surveyed. 95 Mo shifts cover the range of d 4199 for quadruple-bonded MoII2(m-O2CCF3)4(py)2 to d 2953 for (Cp2MoVIH3)Cl based on the publications that we found.254 Analysis of 95Mo shifts of 11 MoVI oxo and peroxo complexes with mono- (N) and poly-dentate (N,N, N,O, or N,N,N) ligands showed a correlation of electronic densities on the metal atoms with the 95Mo shifts. The correlation was used to indicate whether a complex was hexa- or hepta-coordinated.255 95Mo NMR was employed, along with other spectroscopies and DFT calculations, to study reactions of Na2MoO4 with 8-hydroxyquinoline-5-sulfonic acid [H(8-HQS) (20)] in water, forming one dimeric [Mo2O4(8HQS)2(m-O)]2 (d 36) and two monomeric MoO2(8-HQS)22 (d 88 and 109) complexes.256 Reactions of Na2MoO4 with 2-phospho-D-glyceric acid and 3-phospho-D-glyceric acid, gave one and four products containing 2-phospho-D-glycerate and 3phospho-D-glycerate ligands, respectively.257 Multinuclear NMR and DFT studies were used to identify the complexes. 95Mo shifts were in the ranges of d 99 and 55. 17O shifts were in the ranges of d 867–760 for terminal oxo ligands and d 399–300 for bridging oxo ligands.257 1H, 13C, 14N, 17O and 95Mo NMR showed that the complex of MoO42 with triethanolamine in dmso or dmso-d6 contained one free and two bound hydroxyethyl arms, and three arms of the ligand readily exchange.258 The 95Mo shift was found at d 129.7, and the 14N signal was at d 323, while two 17O resonances at d 876.4, 841.4 were assigned for the two terminal Mo]O ligands.258 95Mo shifts of several Mo(V) dithiocarbamate complexes such as [MoO(S2CNMe2)]2(m-O)`(m2-OC2H4S) (d 329), in which both the S and O atoms of 2-mercaptoethanolate ligand bridged the Mo atoms, were obtained.259 When the Me groups on the dithiocarbamate S2CNMe2 ligands were replaced by bulkier groups such as Ph (d 345), the line width of the 95Mo peak increased (270 Hz for Me; 470 Hz for Ph).259 (Et4N)2[MoS(edt)](m-S)2(d 1465, edt ¼ ethane-1,2-dithiolate) was used to react with 1 equiv. of M(PPh3)3þ (M ¼ Cuþ, Agþ) to give incomplete cubane-like clusters (Et4N)[Mo2(edt)2M(PPh3)(m-S)3(m3-S)] (26, M ¼ Cu, d 1800; Ag, d 1656).260 When 2 equiv. of Cu(PPh3)3þ was used, the reaction yielded cubane-like Mo2(edt)2Cu2(PPh3)2(m3-S)4 (27, d 2002).260

( 26 )

( 27 )

( 28 )

95 Mo shifts of octahedral Mo(II) halide clusters (Bun4N)2(Mo6X14) (X ¼ Cl, d 2937; X ¼ Br, d 3203; X ¼ I, d 3256) were used to compare with those from quantum chemical calculations to study the influences of different factors on the quality of the calculated shifts.261 95Mo shifts of their mixed halide analogs (Bun4N)2[(Mo6X8)Y6] (X, Y ¼ Cl, Br, I) were found to correlate with first- and second-order spinorbit coupling constants (in the ranges of 620–870 and 50–99 cm1, respectively) of the clusters.262 95 Mo and 17O NMR studies of polyoxomolybdate Mo7O246 at pH 7–1 in 0.3–6 M HClO4 showed that shifts of Mo atoms with terminal oxo ligands are in the d 20–34 range, while those of central Mo atoms with no terminal oxo ligands were d 200–210.263 17 O shifts of terminal and bridging oxo ligands were d 745–837 (terminal ¼ O), 354–784 (m-O), 293–339 (m3-O), and 121–122 (m4-O).263

Solution NMR of transition metal complexes

677

For the use of electron-electron double resonance (ELDOR)-detected NMR (EDNMR), hyperfine sub-level correlation (HYSCORE), and electron-nuclear double resonance (ENDOR) to study hyperfine interactions in polyoxometalate PV2Mo10O406 with one reduced V(IV) ion,198 see Section 9.21.13.3. Organometallic Mo(IV) complex [[(h5-C5H4Me)2Mo(m-H)2]2Ag]PF6 gave a very broad 95Mo peak at d 3953.264 cis-Mo(CO)4(bdmsa) [bdmsa ¼ bis(2-dimethylstibanylbenzyl)methylamine, MeN(CH2-o-SbMe2-C6H4)2] containing a chelating bis-stibine ligand was synthesized, giving a 95Mo resonance at d 1729.265 95Mo and 77Se NMR were used to characterize cisMo(CO)4[o-(CH2SeMe)2-C6H4] with a chelating bis-seleno-ether ligand, giving resonances at 95Mo d 1393 and 77Se d 157.6.266 Analogous complexes were also prepared and characterized. NMR studies of Mo(CO)5L with a tellurophene ligand [L ¼ 1,3-dihydro-benzo[c]tellurophene (28)] gave 95Mo d 1731 and 125Te d 418.267 95Mo and 77Se NMR were used to characterize di- and tri-substituted complexes cis-Mo(CO)4L2 (95Mo d 1550; 77Se d 468) and fac-Mo(CO)3L3 (95Mo d 1320; 77Se d 532).267 Studies of 95Mo spin-lattice relaxation times T1 for Mo(CO)6 encapsulated in dried 13-Å NaeY zeolite at 223–323 K showed that Mo(CO)6 experienced significant rotational freedom in the zeolite supercages.268 The activation energy for rotation was about 40(4) kJ/mol and rotational correlation time, sc, at ambient temperature was approximately 3 orders of magnitude longer than that in solution. Molecular topology was used to show that there was a positive correlation between experimental 95Mo shifts in potassium oxothiomolybdenates [MoO42 (d 0), MoO3S2 (d 497), MoO2S22 (d 1066), MoOS32 (d 1654), MoS42 (d 2258)] and bondparameterized topological indexes.269 Randic earlier developed the Randic connectivity indices to characterize molecular branching of, e.g., hydrocarbons.270 Extended Randic index developed later by Zhang and Xin was used for inorganic compounds, and expanded further here by Li and You to correlate with the 95Mo shifts.271 Semi-empirical, CNDO and ab initio MO methods were used to calculate 95Mo shifts of the oxothiomolybdenates.272 The work showed that shift was mainly determined by the increasing d,p-orbital electron populations on the Mo atom from the softer S atom and better overlap between the 3s,3p orbitals of the S atoms with the Mo valence orbitals. Large electron populations increased the paramagnetic contribution to the 95Mo shift.272 In NMR studies of a atoms of ligands, the peroxide 17O shifts of monoperoxy Mo complexes were found to be at d 487– 536.135,136 17O shifts of the diperoxyo Mo(VI) complexes were more shielded at d 412–468 than those of the monoperoxo complexes.135,136 Other 17O studies were performed on Mo complexes derived from desferrioxamine B,273 acetohydroxamic acid,273 and hydroxypyridinonate systems.274 (ButO)3Moh15N was synthesized via the heated reaction of MeCh15N with (ButO)3MohN, which was monitored via 15N NMR. The 15N signal for (ButO)3Moh15N was found at d 828.8.275 When (ButO)3MohN reacted with its W(VI) analog (ButO)3Wh15N, both (ButO)3Moh15N and (ButO)3Wh15N were found via 15N NMR,275,276 indicating a rapid metathesis process. VT 1H, 15N, and 2-D 1Hh1H ROESY (ROESY ¼ Rotating Frame Overhauser Effect Spectroscopy) spectra indicated a rapid 0 exchange of the proton on one N atom and the hydride ligand on [CpMo(H)(CO)(PR2NR 2H)](BArF4) complexes (29, R R0 P 2N 2 ¼ 1,5-diaza-3,7-diphosphacyclooctane diphosphine with R groups on N and P atoms; R ¼ Ph, But, R0 ¼ Ph, But, CH2Ph).277 For additional discussion of ROESY, see Section 9.21.13.1.

( 29 )

9.21.5.3 183

Tungsten complexes

W is a spin 1/2 nuclide with 14.31% natural abundance. However, both its gyromagnetic ratio and sensitivity (relative to 13C) are low. In addition, there are technical difficulties in 183W NMR spectroscopy, including relatively slow relaxation requiring long delays between NMR pulses for data collection and low NMR frequency near the lower limit of many commercial instruments. Thus, 183W NMR studies had been limited for several years even though its chemical shift range is >11,000 ppm.69,246 183 W NMR of inorganic compounds reported before 1996 was reviewed.246 Thus, the current review focuses on the publications since then. Polyoxometalates were a focus in the studies using 183W NMR. As discussed in the section on vanadium complexes, 51V, 183W and 17O NMR was used to characterize the mixtures of tungstovanadates from the reaction of NaVO3 with Na2WO4, such as cisW4V2O194 (183W d 69.0) and WV9O285 (183W d 74.5).192 17O NMR shifts in the range of d 1191 to 68.2 were assigned to different O ligands in the complexes. For a-H2W11VO407, six 183W resonances, centered around d 123, were observed.192 For Preyssler hetn15 eropolyoxoanions MnþP5W30O110 (Mnþ ¼ Naþ, Ca2þ, Sr2þ, Y3þ, La3þ and Th4þ), their 183W NMR spectra (shifts in the range of

678

Solution NMR of transition metal complexes

d 196 to 291) were used to identify the atomic origin of the LUMO states, which were composed primarily of orbitals from the ring of five W atoms near the Mnþ ion.278 Reaction of H3PW12O40 with K2CrO4 led to the formation of K13(KP2W20O72) which was characterized by 183W NMR and other spectroscopies.279 The reaction of Na10(a-SiW9O34) with Ce4þ and Hf4þ in CH3COONa buffer solution leads to the formation of sandwich polyoxometalates Ce4(m3-O)2(SiW9O34)2(CH3COO)210 and Hf3(mOH)3(SiW9O34)211, respectively.280 The compounds with a polynuclear cluster fragment stabilized by two a-SiW9O3410 polyanions were characterized by 183W NMR, giving several resonances (d 147.9 to 180.2) for the former and two resonances (d 145 and 175) for the latter. 29Si NMR of the two compounds showed one sharp resonance at d 84 and 85, respectively, consistent with two equivalent SiW9O3410 units in the molecules.280 (Et2NH2)8[a-PW11O39M(m-OH)(H2O)]2 (M ¼ Zr, Hf), containing dinuclear Zr and Hf fragments sandwiched between 2 mono-lacunary a-Keggin polyoxometalates, were prepared and characterized by 183 W and 31P NMR.281 The 183W spectra showed six resonances for each compound in the range of d 107.6 to 155.5 in aqueous solution.281 Equilibrium of the proton cryptate polyoxometalate, a-H2W12O406 þ Hþ # H3W12O405 (as Bun4Nþ salt) in CD3CN was characterized by 1H and 183W NMR and other techniques.282 The studies show that, in nonaqueous media, the internal cryptand cavity of a-H2W12O406 (1H d 6.01; 183W d 99) reversibly accommodated only one Hþ ion to yield H3W12O405 (1H d 6.81; 183 W d 88). Speciation and equilibria during base decomposition of a-PW12O403 (183W d 96.7) were probed using 31P and 183W NMR at pH 0.7–13.5.283 183W resonances of chiral polyoxotungstats a-P2W17O6110 (17 peaks each in the range of d 108.5 to 226.1) was assigned to the W atoms in the clusters using selective 31Pe183W decoupling and 183We183W COSY NMR.284 183 W NMR was used, along with other spectroscopies and DFT calculations, to study reactions of Na2WO4 with 8hydroxyquinoline-5-sulfonic acid [H(8-HQS) (20)] in water, forming one dimeric [W2O4(8-HQS)2(m-O)]2 (d 74.5) and two monomeric WO2(8-HQS)22 (d 20.7 and 63.3) complexes.256 Reactions of Na2WO4 with 3-phospho-D-glyceric acid, giving five products,257 which were identified by multinuclear NMR and DFT studies.257 183W shifts were in the ranges of d 48.0 and 241.8. 17O shifts were in the ranges of d 647–526 for terminal oxo ligands and d 342 for bridging oxo ligands.257 The 17O shifts of the tungsten 3-phospho-D-glycerate complexes (d 554, 526 for terminal W ¼ 17O; 342 for bridging We17OeW)257 were more shielded than the Mo analogs (d 867, 842, 833 for terminal Mo ¼ 17O; 381 for bridging Moe17OeMo),257 which followed a trend for multiple-bonded ligands.285 Reaction of peroxotungstates, prepared from H2WO4 and H2O2, with H2SeO4 gave Secontaining dinuclear complex, (Bun4N)2[(m-SeO4)W2O2(O2)4], which was characterized by 77Se (d 1046) and 183W (d 569.2) NMR and other techniques.286 This complex was a catalyst for the epoxidation of homoallylic and allylic alcohols with H2O2. (Bun4N)2WO4 catalyzed fixation of CO2 with o-phenylenediamine into 2-benzimidazolone.287 Reaction of (Bun4N)2WO4 with o-phenylenediamine gave an adduct through hydrogen bonds between the NeH groups and the oxo ligands, shifting 183W resonance in WO42 to d 16.4 which is more shielded by 14.7 ppm.287 Reaction of (Bun4N)2WO4 with CO2 gave (Bun4N)2[WO4(CO2)] (183W d 57.8) and (Bun4N)2[WO4(CO2)2] (183W d 22.6), in which the oxo ligands were believed to bind to the C atom in CO2.287 183 W NMR was also used to characterize organometallic complexes. 183We31P HMQC spectra were employed to obtain indirectly 183W shifts of cis and trans isomers of diphosphines W(CO)4(PPh3)(PR3) [R3 ¼ Bun3, Me3, Me2Ph, MePh2, Ph3, (4-OMeC6H4)3, (4-Me-C6H4)3, (4-F-C6H4)3] and phosphine phosphites W(CO)4(PPh3)[P(OR)3] [R3 ¼ (OMe)3, (OEt)3, (OPh)3].288 183 W shifts of trans-W(CO)4(PPh3)(PCy3) (d 797) and trans-W(CO)4(PPh3)[P(NMe2)3] (d 824) were similarly measured. The 183 W shift range of the complexes was d 964 for cis-W(CO)4(PPh3)[P(4-F-C6H4)3] to 722 for trans-W(CO)4(PPh3)[P(OMe)3] with, e.g., d 842 and 849 for trans-W(CO)4(PPh3)(PMe3) and cis-W(CO)4(PPh3)(PMe3), respectively.288 How the shifts were correlated with Tolman electronic factors and cone angles of the PR3 and P(OR)3 ligands was discussed.288 Spectroscopic, structural and computational studies of the starting complex (30) in Fig. 2 indicated that it was a heterocyclic ylide complex (dW 3303).289 The product of the reaction (31) (dW 3221) may be formally considered to be a phosphanylcarbene complex. Calculations of 183W shifts were reported in several publications, including the use of DFT methods for polyoxometalates290 and to optimize structures of the four isomers of SiW11O398, calculating their 183W NMR spectra, which were compared with experimental shifts.291 Relativistic DFT methods were used calculate 183W shifts of polyoxometalates,292 polyoxotungstates,293 counterion effects on the 183W NMR spectra of the lacunary Keggin polyoxotungstate PW11O397,294 and 183W and 17O NMR shifts for large polyoxotungstates such as W6O192.295 Extended Hückel MO calculations were employed to analyze 183W and 17O NMR shifts in polyoxometalates.296 In NMR studies of a atoms of ligands, the 17O shifts of the peroxide ligand in diperoxyo W complexes were found at d 346– 400.135,136 Several peroxotungstate species, such as [WO(OH)(O2)2] and [W4O12(O2)2]4, prepared from the reaction of

( 30 ) Fig. 2

Reaction of 30 with (Me3O)BF4 to give 31.

( 31 )

Solution NMR of transition metal complexes

679

Na2(WO4) with H2O2, were identified by 17O NMR using the ratio of the shift of the O atom in the W anion to the shift of the O atom in the known Mo anion.297 This ratio was consistently around 79%. Many of these signals in the NMR were pH dependent.297 (ButO)3Wh15N was synthesized via the reaction of MeCh15N with (ButO)3WhN, which was monitored 15N NMR. The 15N signal for (ButO)3Wh15N was at d 791.8.275 Several metathesis reactions of organic and inorganic complexes containing the nitride hN group were carried out with (ButO)3Wh15N in order to study the degree of 15N scrambling.275,276 Several techniques such as 15N, 13C INEPT, and 19F NMR were used to analyze WOF4(aph) (aph ¼ acetone phenylhydrazonate, Me2C]N-(Ph)N).298 It was found that the aph acted as an N,N donor ligand, and stereoisomeric interconversion occurred in WOF4(aph) at elevated temperatures with activation parameters of DHs ¼ 78.5 kJ/mol, DSs ¼ 56.78 J/mol K, DGs313 K ¼ 60.71 kJ/mol.298 119Sn NMR was used to monitor the conversion of (m-Cl)3W2(SnCl3)(CO) to (m-Cl)3[W(SnCl3)(CO)3]2 over time in CDCl3 or CD2Cl2 solution.299

9.21.6

Group 7 (Mn, Tc and Re)

For the three elements, NMR of both the metals (55Mn, 99Tc, 187Re) and ligands have been reported. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 8. The receptivities (relative to 13C) of the nuclides are fairly large, and their resonance frequencies (with 1H ¼ 100 MHz) are relatively high. However, all are quadrupole nuclides with modest to large quadrupole moments. Thus, line widths sometimes lead to sensitivity losses.

9.21.6.1

Manganese complexes

Publications using 55Mn NMR that we found were mostly on manganese carbonyl derivatives,265–267,300–313 many of which were published in the 1990s and early 2000s.267,300–313 Selected complexes are discussed here, and their 55Mn shifts may be compared with d 2353 in Mn2(CO)10.1,303 C-Glycosyl compounds function as nucleoside surrogates and they served as biochemical probes.311 RMn(CO)5 (e.g., R ¼ glycosyl) were studied as starting materials to make carbonyl derivatives through migratory insertion. 55Mn NMR shifts of methylether derivatives of, e.g., b-glucosyl-Mn(CO)5 (32, d 2059) were found to be in a narrow range (10 ppm), typical for alkyl-Mn(CO)5 complexes.311

( 32 ) (4-X-C6H4)3Sn-Mn(CO)5 (X ¼ H, Me, OMe, SMe, F, Cl) were characterized by 55Mn, 119Sn and 13C NMR, giving, e.g., 55Mn d 2502 and 119Sn d 11.93 for Ph3Sn-Mn(CO)5 (X ¼ H).313 The 55Mn and 119Sn shift ranges are d 2479 to 2526 and d 1.13 to 11.93, respectively, for the complexes.313 [(OC)5Mn]3(m3-E) (E ¼ As, Sb, Bi), containing one E atom bonded to three Mn(CO)5 groups in trigonal pyramid structures, were characterized by 55Mn NMR.302 The shifts (d) of the three pnictogen compounds, E ¼ As (2020), Sb (2230), Bi (2320), show an increase of shielding on the Mn atom in the order E ¼ As, Sb, Bi.302 Stibine complexes Mn2(CO)9(SbPh3) and (Ph3Sb)(OC)4MneMn(CO)4(SbPh3) [with the SbPh3 ligand(s) in the axial position(s)] show two 55Mn resonances for the former (d 2389 and 2394) and one resonance (d 2070) for the latter.304 Distibine Table 8

Nuclear and NMR properties of 55Mn, 99Tc and 187Re.26 Relative receptivity

Nuclide 55

Mn Tc

99

Natural DH DC Gyromagnetic ratio (107) abundance (%) a Spin (1H ¼ 1.00) (13C ¼ 1.00) (rad s1 T1) 100 (b decay)

(185Re)b,c 37.40 187 Reb 62.60 a

5/2 0.179 9/2 –

1.05  103 6.6452546 21341 6.046

5/2 5.19  102 305 5/2 8.95  102 526

6.1057 6.1682

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 We did not find a publication in 1990–2019 on the 185Re or 187Re NMR of a metal complex. c185 Re in parenthesis is considered to be the less favorable of the element for NMR.26 b

Quadrupole moment X (frequency, MHz; 1 Q (fm2) H ¼ 100 MHz, 2.3488 T)

Reference sample

33.0 12.9

24.789218 22.508326

218.0 207.0

22.524600 22.751600

KMnO4 (aq) NH4TcO4 (aq) KReO4 (aq)

680

Solution NMR of transition metal complexes

complexes Mn2(CO)8(m-R2SbCH2SbR2) (R ¼ Me, Ph) give 55Mn shifts at d 2317 and 2195, respectively.303 55Mn resonance for Mn(CO)3[MeN(CH2-o-SbMe2-C6H4)2](OTf) containing a chelating bis-stibine ligand is d 850.265 Multinuclear NMR, including 55 Mn, was used to study a series of Mn(I) phosphine, arsine, and stibine carbonyl halide complexes, such as facMnX(CO)3(Ph2PCH2CH2CH2PPh2) (d X ¼ Cl, 916; Br, 1005), showing that the less electronegative Br ligand led to more shielding on the Mn(I) ion.309 55Mn shifts of the stibine analogs, such as MnX(CO)3(Ph2SbCH2CH2CH2SbPh2) (d X ¼ Cl, 880; Br, 1006) and As compounds, such as MnX(CO)3(Ph2AsCH2CH2AsPh2) (d X ¼ Cl, 932; Br, 1046), were also reported.309 55 Mn and 77Se NMR were used to characterize Mn(CO)3Cl[o-(CH2SeMe)2-C6H4] with a chelating bis-selenoether ligand, giving 55 Mn and 77Se resonances (Table 9) for different invertomers of the complex.266 Invertomers are isomers interconverted by inversion of an atom with a lone pair of electrons. NMR studies of the di-tellurophene complex fac-MnCl(CO)3L2 [L ¼ 1,3dihydro-benzo[c]tellurophene (28)] showed 55Mn and 125Te resonances (Table 9).267 The NMR shifts of telluroether complexes fac-MnCl(CO)3(TeMe2)2 and its mer,trans isomer were studied (Table 9),307 and compared with thioether and selenoether analogs MnCl(CO)3(EMe2)2 (E ¼ S, Se, Table 9),307 showing increasing shielding of the Mn(I) ion in the order S, Se and Te. This order is consistent with the electronegativity decrease from S, Se to Te, thus placing most electron density on the Mn(I) ion in the Te compound. For Mn organometallic complexes without CO ligand, 55Mn NMR of CpMn(h6-C6H6) and derivatives with substituents on either the Cp or benzene ligand as well as on both ligands was studied, showing, e.g., d 180 for CpMn(h6-C6H6).314 Calculations and electronic analyses of NMR chemical shifts for Mn(CO)5X (X ¼ F, Cl, Br, I, and Me) showed that the origin of the chemical shifts was the paramagnetic effects from d-d transitions on the Mn ions.315 In NMR studies of a atoms of ligands, reaction dynamics of water exchange on Mn(II) polyoxometalate [Mn4(H2O)2(P2W15O56)2]16 has been determined as a function of pH using VT 17O NMR.316 The NMR signals were compared with monomeric [Mn(H2O)6]2þ. While the water exchange rate of [Mn(H2O)6]2þ was affected by pH in the 3.2–6.0 range, the rate of exchange of the polyoxometalate ion varied greatly.316 Water exchange dynamics in Mn porphyrin317 and salen318 complexes was also studied via 17O NMR. 15 N-enriched guanine (G) was incorporated into self-complementary oligodeoxynucleotides containing the GG doublet and GGG triplet in order to study the reactivity differences in the G runs.319 The line broadening in the 15N NMR showed that siteselective binding of Mn(II) and Co(II) ions to G runs was correlated with HOMO distribution obtained by MO calculations.319 In other words, the binding of electron-deficient metal ions to the N atom of electron-rich G is likely a HOMO-controlled process.319 Several silane complexes and s-borane Mn complexes, which were studied by 29Si and 11B NMR, respectively, were discussed in a 2008 review.139

9.21.6.2

Technetium complexes

Technetium is the only transition metal in the 3d, 4d and 5d series (and the lightest element in the periodic table) whose isotopes are all radioactive. 99Tc (used in NMR) decays to stable 99Ru as a weak beta emitter with a half-life of 2.111  105 years.320 It is the most significant long-lived fission product of U fission. Tc chemistry was inspired to a large degree by applications of the short-lived metastable nuclear isomer 99mTc in molecular imaging and radiopharmacy.320 99mTc decays by isomeric transition to 99Tc with a half-life of only 6 h, making it difficult to characterize 99mTc complexes directly. Thus, the long-lived 99Tc analogs are often used. Binding of TcO4 to uranyl ion was also studied, as TcO4 was co-extracted with UO22þ, PuIV and ZrIV from irradiated nuclear fuel dissolved in HNO3.321,322 Solution 99Tc NMR of inorganic compounds reported up to 2004 was reviewed.323 A figure showing the correlation between 99Tc chemical shifts and Tc oxidation states in reported complexes was given in a 2017 paper.324 We focus on the publications since 2004 in the current review. Speciation of Tc(VII) pertechnetate in concentrated HClO4 and HNO3 was studied by several techniques, including 99Tc NMR, showing that pertechnetic acid, HTcO4, formed in >8 M HClO4 while in concentrated HNO3, TcO4 was still the predominant species.325 In 12 M H2SO4, experiments and DFT calculations showed the formation of yellow TcO3(OH)(H2O)2 (d 300).326

Table 9

NMR chemical shifts of selected Mn carbonyl complexes with thio-, seleno- or telluroether ligands. 55

Complexes 307

MnCl(CO)3(SMe2)2 MnCl(CO)3(SeMe2)2307 fac-MnCl(CO)3(TeMe2)2307 mer,trans-MnCl(CO)3(TeMe2)2307 Mn(CO)3Cl[o-(CH2SeMe)2-C6H4]266 (different invertomers) fac-MnCl(CO)3L2 [L ¼ (28)]267

77

125

57 205 637 920 42, 77, 113

– 66 – – 147.8, 124.1, 122.5, 120.5

– – 161 271 –

600

–

472

Mn shifts (d)

Se shifts (d)

Te shifts (d)

Solution NMR of transition metal complexes

681

When HTcO4 solution was concentrated, likely products with different colors, such as H5TcO6, HTcO4$H2O, and Tc2O5, were probed by 99Tc NMR among others.327 Reaction of HTcO4 with MeOH and 12 M H2SO4 studied by spectroscopies (e.g., 99Tc NMR) and ab initio calculations showed the formation of reduced Tc(V) oxo sulfate species that lack 99Tc NMR signals in the d 0–800 region.328 The 99Tc NMR spectrum of the aqueous pertechnetate ion with natural abundance of 17O (0.038%, spin 5/2) and 18O (0.205%, spin 0) isotopes25 was sensitive to the O isotopes and temperature of the solution.329 Since 17O and 18O atoms have one and two more neutrons, respectively, than an 16O atom (99.757% natural abundance, spin 0), the 99Tc ion in Tc(16O)3(17O) and Tc(16O)3(18O) was more shielded than that in Tc(16O)4. This is a result of the isotope effects on nuclear shielding.330 Since the Ta]17O and Ta]18O bonds with the heavier O isotopes are the shorter than the Ta]16O bond, the shorter bonds in the heavier isotopomers lead to larger shielding of the 99Tc nuclei and thus isotope shifts of the 99Tc resonance to become more shielded. The shift of the Tc(16O)3(18O) resonance [dTc(16O)3(18O)  dTc(16O)4 ¼ 0.428 ppm] is well resolved from the peak of Tc(16O)4 at 10  C.329 Coupling by the 17O atom in Tc(16O)3(17O) gave a sextet with the 99Tc resonance (extracted by averaging the six lines) showing an isotope shift of Tc(16O)3(17O) [dTc(16O)3(17O)  dTc(16O)4 ¼ 0.241 ppm] at 10  C.329 Isotopomers with more 18O atoms, such as Tc(16O)2(18O)2, Tc(16O)(18O)3 and Tc(18O)4, showed additional isotope shifts to be more shielded.331 TcO4 ions coordinated directly to actinides in the presence of O]PR3 ligands, yielding [O3Tc(m-O)]2UO2(O]PPh3)3 and [O3Tc(m-O)]4Th(O]PBun3)4, both giving broad 99Tc resonances.322 When chelating bis(diphenylphosphino)methane dioxide ligand [Ph2(O])PCH2P(]O)Ph2] was used, a similar reaction yielded [O3Tc(m-O)UO2[Ph2(O])PCH2P(]O)Ph2]2](TcO4) with two 99Tc resonances (d 2.0 and 16.9) for coordinated and uncoordinated TcO4, respectively.321 99 Tc shifts of Ph3EOTcO3 (E ¼ C, d 67.3; Si, d 68.3; Ge, d 25.2; Pb, d 7.0) and (THF)Ph3SnOTcO3 (d 5.1) and related Tc(VII) complexes were reported.332 99Tc NMR was used to characterize Ta(VII) complexes with the TcO3þ core and multi-dentate ligands such as TcO3(bpza) [d 220; Hbpza ¼ di-1H-pyrazol-1-ylacetic acid (33)] with the N,O,N ligand.333

( 33 ) Organometallic Tc complexes characterized by 99Tc NMR are mainly Tc(I) carbonyl compounds, especially those with facTc(CO)3þ fragment for its high stability.334 Kinetics of water exchange processes in fac-Tc(CO)3(H2O)3þ was investigated by 17O (d 52) and 99Tc (d 868, 1JTc-O ¼ 80 Hz) NMR.334 Conversion of fac-Tc(CO)3(H2O)3þ in 10 M NaOH and 5 M NaOH caustic solution was studied by 99Tc NMR, showing that fac-Tc(CO)3(H2O)3þ (d 869) was deprotonated stepwise to form fac-Tc(CO)3(H2O)2(OH) (d 1069), fac-Tc(CO)3(H2O)(OH)2 (d 1146), and fac-Tc(CO)3(OH)32 (d 1204) based on DFT calculations, as the Tc(I) ions were increasingly shielded with deprotonation.335 Theoretical modeling of 99Tc NMR shifts was developed based on DFT calculations and the calculated shifts were compared with the experimental values of fac-Tc(CO)3(H2O)3þ and facTc(CO)3(H2O)3-n(OH)n(n1).335 When fac-Tc(CO)3(H2O)3þ was exposed to 13CO (49 atm) in water in a sapphire NMR tube (99Tc d 866.7), stepwise replacement of CO ligands to form fac-Tc(13CO)3(H2O)3þ at 4  C in several days was probed by 99Tc NMR.336,337 The 99Tc NMR spectrum of fac-Tc(13CO)3(H2O)3þ (Fig. 3)337 showed an isotope shift as well as the coupling by three 13 CO ligands, giving a 1:3:3:1 quartet at d 869.7 (1JTc-C ¼ 354 Hz).336 In 3 weeks at room temperature, substitution of water ligands by 13CO, yielding fac-Tc(13CO)6þ (d 1961 as a septet, 1JTc-C ¼ 261 Hz), was used to follow the reaction.336,337 Since 99m Tc was a precursor to radiopharmaceutical agents,334 the kinetic properties, which were important to the preparation, uptake and clearance of the 99mTc agents, were reviewed in 2008.337 Properties of fac-Tc(CO)3(OH2)3n(OH)n1n (n ¼ 0–3) in aqueous solutions with high ionic strength, including 99Tc NMR, were studied to help identify and treat Tc speciation in nuclear waste.338 Tc(CO)5X (X ¼ Cl, Br, I) gave 99Tc resonances at d 1745, 1802 and 2034, respectively, showing the most shielded Tc(I) ion in Tc(CO)5I with the least electronegative iodine in the halide series.339 The perchlorate analog Tc(CO)5(ClO4) containing a TceO bond showed the 99Tc resonance at d 1353.340 Nitrosyl complex (NEt4)2[Tc(CO)2(NO)Cl3] (d 460) and a dimer [TcCl(m-Cl)(CO)2(NO)]2 (d 389) were prepared and characterized by 99Tc NMR among others.341 99Tc resonances of several cyclopentadienyl nitrosyl complexes CpTc(NO)(PPh3)X (X ¼ OTf, d 242; O2CCF3, d 19; SCN, 820; I, 668; I3, 679) were measured.342 99Tc shifts of other Tc(I) complexes, such as Cs[Tc(NO)(PPh3)2(OOCCF3)2F] (d 952) and [Tc(NO)(dppe)2(OOCCF3)](PF6) (d 627; dppe ¼ Ph2PCH2CH2PPh2), as well as those at Tc(III), Ta(V) and Tc(VII) oxidation states were summarized in a figure in Ref. 324. 99 Tc shifts of several Tc(VII), Tc(I) and Tc(0) species were computed by DFT methods.343 Complexation to aqueous uranyl, UO22þ, was predicted to only slightly affect the 99Tc shift of TcO4.343 DFT calculations were also performed to obtain 99Tc NMR parameters for Tc(CO)3(N,N,O) (34) containing a tridentate N,N,O ligand, as its 99mTc isomer is a potential breast cancer radiopharmaceutical.344

682

Solution NMR of transition metal complexes

CO CO

CO Tc

OH2

H2O H2O

13

CO

13

13

CO

CO

Tc OH2

H2O H2O

–860

–870 δ / ppm

–880

Fig. 3 99Tc NMR spectra of fac-Tc(CO)3(H2O)3þ and fac-Tc(13CO)3(H2O)3þ under 13CO (49 atm), demonstrating 13C-isotope shifts and the 1JTc-C coupling. Helm, L. Ligand exchange and complex formation kinetics studied by NMR exemplified on fac-[(CO)3M(H2O)]þ (M ¼ Mn, Tc, Re). Coord. Chem. Rev. 2008, 252, 2346–2361. doi: 10.1016/j.ccr.2008.01.009.

( 34 ) For the NMR studies of a atoms of ligands, see the previous discussion in this section on the use of complexes.

9.21.6.3

17

O and

13

C NMR of Tc

Rhenium complexes

We did not find a publication in 1990–2019 on either 185Re or 187Re NMR of metal complexes, as indicated in Table 8. Very few solution 185Re or 187Re NMR spectra have been reported. Thus, the following reports before 1990 are briefly discussed. Solution NMR spectrum of NaReO4, showing both 185Re and 187Re resonances, was reported in 1970,345 1986,346 and 1987.347 In 1981, 185,187Re resonance of the Re(I) complex [Re(CO)6]Cl$HCl in THF at 295 K was found to be d 3400 relative to aqueous NaReO4.348 185,187Re resonances of (Ph4P)(ReO4) in HCONMe2/toluene (d 0) and (Et4N)(ReS4) in MeCN/CH2CI2/Me2S]O at 305 K [d(185Re/187Re) 3200/3435] were reported in 1986.346 In NMR studies of a atoms of ligands, the diperoxo complex ReO(O2)2Me(H2O) was synthesized and characterized by 17O NMR and X-ray crystallography.135,349 The 17O shifts of the peroxide ligands were found to be at d 363 and 422.135 Several silane complexes and s-borane Mn complexes, which were studied by 29Si and 11B NMR, were discussed in a 2008 review.139 The sborane Mn complexes were compared with a s-borane Re analog.139 In the studies of Re(h5-C5H4Pri)(CO)(PF3)Xe by several NMR spectroscopies including 19Fe129Xe HMQC and 19Fe31P HMQC,350 the Xe chemical shift was determined to be about d 6179 with 2JXe-P ¼ 41.8 Hz, and 3JXe-F ¼ 5.1 at 163 K.350 15N NMR was conducted after the addition of Lewis acids and H-bond donor molecules, such as B(C6F5)3 or C6H5OH, to 15Nlabeled trans-Re(N2)Br(depe)2 [depe ¼ 1,2-bis-(diethylphosphino)ethane].351 The additions of these acids and donors caused a shift in the 15N NMR resonances to be more shielded. For example, upon addition of B(C6F5)3, one peak shifted from d 61.3 to  173.3 and the other from d 91.1 to 93.8.351 Organorhenium (VII) oxides complexes with general formulas ReO3R or ReO3R$Ln (e.g., R ¼ Me, SiMe3, Cp; L ¼ quinuclidine, pyridine; n ¼ 1, 2) were studied by 17O NMR,352 showing that shifts of the oxo ligands were affected by the donor ability of the R ligands.352 The 17O shifts of the oxo ligands were also affected by the solvent, especially if the R ligand was not a strong donor or did not cause steric hinderance in the complex.352 17O NMR was used to follow the reactions of EtReO3 and (2,6-Me2-C6H3)ReO3 as epoxidation catalysts in the presence of ButOOH.353,354 17O-enriched MeReO3 was used to transfer the labeled 17O to water and

Solution NMR of transition metal complexes

683

subsequently transfer the 17O atoms to the water-sensitive EtReO3 or (2,6-Me2-C6H3)ReO3.353,354 17O NMR showed that the oxygen insertion into the ReeC bond, giving the respective alkoxide trioxorhenium compounds, led to decomposition of the catalyst.353,354 Other catalytic systems such as aldehyde-olefination using the catalyst MeReO2(PhC^CPh) and PPh3 were also investigated using 17 O NMR.355 Water exchange on fac-(CO)3Re(H2O)3þ using 17O-enriched water was followed by 17O NMR.356 With mono- and bidentate ligands of various nucleophilicities [e.g., CH3CN, Br, Me2S, CF3COOH, thiourea, bipy, and phenanthrene (phen)] were followed by 17O NMR as well.356 The pKa values for the successive dissociation of ReO(H2O)(CN)4þ were determined to be 1.31 and 3.72 via 17O and 13C NMR.357 Line broadening of the 17O signals occurred at lower pH values. Other complexes such as Re2O3(CN)84 and ReO(NCS)(CN)42 were also analyzed via 17O NMR.357

9.21.7

Group 8 (Fe, Ru and Os)

For the three elements, NMR of both the metals and ligands have been reported. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 10. 57Fe, 99Ru and 187Os NMR spectroscopies are, however, challenging mainly from the unfavorable magnetic properties of the nuclides.1 The spin 1/2 nuclides 57Fe and 187Os have low sensitivity to detection and their receptivities are lower than that of 13C nuclide by about three orders of magnitude.69 For quadrupolar 99Ru, 101Ru and 189Os, they are much more sensitive than 57Fe and 187Os, but quadrupolar broadening may be substantial, making their detection challenging. The chapter on the NMR of these three metals by Benn in the 1991 book edited by Pregosin gave a detailed review of the literature up to 1990.1 Inverse detection methods were developed to increase the sensitivity of the nuclides to indirectly determine chemical shifts by 2D correlation experiments using coupling (J) to another magnetically active nuclide such as 1H or 31P. These methods for spin 1/2 nuclides 57Fe359–361 and 187Os362,363 using HMQC (Heteronuclear Multiple Quantum Coherence),4 HSQC (Heteronuclear Single Quantum Coherence)4 or HMBC (Heteronuclear Multiple Bond Correlation)4 spectroscopy make the detection and acquisition of their chemical shifts much easier. Both HMQC and HSQC were based on 1-bond coupling such as 1JPeFe, while HMBC is based on 2–4 bond coupling such as 24JPeFe. The difference between the HMQC and HSQC methods is that during the HMQC evolution, both 31P and 57Fe magnetization evolve. In the HSQC evolution, only 57Fe magnetization is allowed to evolve. Thus, HMQC is affected by the 1JPeFe coupling during the evolution, while HSQC is not affected, as there is no 31P magnetization during the evolution. An alternative to obtain 57Fe NMR for compounds with natural abundance is based on polarization transfer (PT) techniques such as 1He57Fe INEPT, enhancing the signal/noise ratio with respect to single pulse detection.364,365

9.21.7.1

Iron complexes

The reported 57Fe NMR shift range is about 12,000 ppm,359 including complexes with unpaired electrons. The shift is very sensitive to both steric and electronic factors. Thus, it provides an excellent probe of changes within the coordination sphere of the metal atom. 57 Fe shifts of Fe(CN)64 (Kþ salt, d 2455) and [C(NH2)3]2[Fe(CN)5(NO)] [C(NH2)3þ ¼ guanidiniumþ, d 2004] in D2O, two prominent textbook examples in coordination chemistry, were obtained using 25% 57Fe-enriched samples.366 14N shifts of d 5.1 (NOþ), 100 (broad for unresolved cis and trans CN ligands), and 310 for the C(NH2)3þ cation in [C(NH2)3]2[Fe(CN)5(NO)] vs. 105 for Fe(CN)64.366 The fact that the Fe(II) ion in Fe(CN)5(NO)2 was more shielded than that in Fe(CN)64 was the subject of theoretical studies discussed below. Table 10

Nuclear and NMR properties of 57Fe, 99Ru and 187Os.26

Natural abundance Nuclide (%) a

Relative receptivity DH DC Gyromagnetic ratio Spin (1H ¼ 1.00) (13C ¼ 1.00) (107) (rad s1 T1)

57

2.119

1/2 7.24  10

99

12.76 17.06 1.96 16.15

5/2 5/2 1/2 3/2

Fe

Ru Rub 187 Os 189 Osc 101

7

1.44  104 2.71  104 2.43  107 3.95  104

X (frequency, MHz; Quadrupole moment Q (fm2) 1H ¼ 100 MHz, 2.3488 T)

3

4.25  10

0.8680624

–

3.237778

0.848 1.59 1.43  103 2.32

1.229 1.377 0.6192895 2.10713

7.9 45.7 – 85.6

4.605151 5.161369 2.282331 7.765400

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 We did not find a publication in 1990–2019 on 101Ru NMR. It is not used due to the larger quadrupole moment of 101Ru nuclide than 99Ru. comparison. c We did not find a publication in 1990–2019 on 189Os NMR. It is not used as 189Os is a quadrupolar nuclide and 187Os is not.

Reference sample Fe(CO)5 (C6D6) or Cp2Fe (d 1540 in toluene358) K4Ru(CN)6 (aq) OsO4 (CCl4)

a

b

101

Ru properties are listed here for

684

Solution NMR of transition metal complexes

57

Fe NMR of iron porphyrin complexes was one major focus of research. 57Fe shifts of several diamagnetic Fe(II) porphyrin carbonyl complexes, including Fe(protoporphyrinate IX)(py-d5)(CO) (35, d 8205), were reported.367 Using an inverse detection method based on the 31Pe57Fe correlation and 94.5% 57Fe-enriched samples, 57Fe NMR shifts of over 25 diamagnetic Fe(II) porphyrin complexes with PMe3 ligands were obtained in 5 mm NMR tubes in as little as 20 min.359 The complexes include Fe(TPP)(PMe3)2 (36, H2TPP ¼ tetraphenylporphyrin, d 7652), Fe(TPP)(PMe3)(CO) (d 7627), and Fe(TPP)(PMe3)(py) (d 8973), and Fe(OEP)(PMe3)2 (H2OEP ¼ octaethylporphyrin, d 7873).359 A correlation was found between Mössbauer quadrupole splittings (mm/s) and 57Fe NMR shifts of diamagnetic Fe(II) porphyrin complexes such as Fe(TPP)(PMe3)2 and Fe(OEP)(PMe3)2.368 57 Fe shifts of stereo-hindered heme model compounds (with the so-called superstructures) and atropisomers (stereoisomers from hindered rotation about a single bond) showed that the shifts were very sensitive to deformation (ruffling) of the porphyrin geometry.369,370 57Fe shifts in metalloporphyrins may be predicted from 13C NMR shifts of the meso-C atoms of the TPP2 ligands in the complexes.370

( 35 )

( 36 )

( 37 )

Fe and 15N shifts in Fe(II) phthalocyanine (Pc) complexes Fe(Pc)[P(OEt)3]L [37, L ¼ H2N(n-decanyl)], 57Fe d 6764;15N d 1.34; [L ¼ H2NCH2Ph, 57Fe d 6794, 15N d 3.45] were obtained from 31Pe57Fe HMQC and 1He15N gradient-selected HMQC (gHMQC) NMR, respectively.361 15N shifts of other diamine complexes Fe(Pc)L2, such as L ¼ H2N(n-decanyl), H2NCH2Ph, were also reported.361 For organometallic complexes, 57Fe NMR for ferrocene Cp2Fe with natural abundance was acquired with the 1He57Fe INEPT polarization transfer (PT) technique.364 Substituted ferrocenes were a focus of 57Fe NMR studies with a report of 57Fe shifts of CpFe(h5-C5H4R) (R ¼ SiMe3, d 1626; SnMe3, d 1611) and Fe(h5-C5H4R)2 (R ¼ CMe3, d 1621; R ¼ SiMe3, d 1728; R ¼ GeMe3, d 1690; R ¼ SnMe3, d 1692).371 For eight ferrocenes with monoamine substituents, 15N and shifts of other nuclides were reported, including CpFe(h5-C5H4NH2) (57Fe d 1639; 15N d 345.7) and CpFe(h5-C5H4[N(SiMe3)(BEt2)]) (57Fe d 1702; 15N d 285; 11B d 55.7; 29Si d 8.4).372 57Fe shifts of additional aminoferrocene and 1,10 -diaminoferrocene were reported, such as CpFe(h5C5H4NPh2) (d 1664) and Fe(h5-C5H4NH2)2 (d 1709).358 57Fe shifts of ferrocenes with sulfinylamino365 or p-acceptor373 substituents as well as bridged [1]ferrocenophanes Fe[(h5-C5H4)2SiMe2]374 were also studied. For substituted neutral ferrocenes, there was a linear relationship between Mössbauer quadrupole splittings (mm/s) and 57Fe shifts.375 The more shielded 57Fe ions (with more upper field 57Fe shifts), the larger the quadrupole splittings.375 57 Fe, 119Sn, 13C and 31P NMR were used to characterize a series of CpFe(SnPh3)(CO)(PR3) complexes (R ¼ Me, 57Fe d 447; 119Sn d 46.71; R ¼ OMe, 57Fe d 316; 119Sn d 47.76).376 57Fe NMR was used to characterize 35 cyclopentadienyl Fe(II) complexes with the general formulas CpFe(CO)2R, CpFe(CO)(PPh3)X, CpFe(CO)L(COMe) (L ¼ PR3, and CO) and (h5-C5H4Y)Fe(CO)(PPh3)Me (Y ¼ Me, SiMe3, NEt2, Ph, I, COOMe, COPri),360 including CpFe(CO)2Me (d 684), CpFe(CO)(PPh3)H (d 536), CpFe(CO)(PMe3)(COMe) (d 1374), and (h5-C5H4Me)Fe(CO)(PPh3)Me (d 1367).360 NMR of dimer Fe2(CO)6(m-SNH) was studied, giving 57Fe d 1315 and 15N d 374.7.377 Iron tricarbonyl complexes containing a substituted silole or analogous ligand were also studied by 57Fe NMR.378 Inverse-detection techniques were used to indirectly measure 57Fe spin-lattice relaxation times for CpFe(CO)(PPh3)(COMe) [T1 ¼ 4.4 s at 9.4 T (or 400 MHz 1H NMR) and 2.1 s at 14.1 T (600 MHz 1H NMR)].379 As indicated in the 57Fe shifts summarized above, the Fe(II) ion in Fe(CN)5(NO)2 is more shielded than that in Fe(CN)64.366 Since both complexes were prominent textbook examples in coordination chemistry, the shifts were studied theoretically to provide an understanding. Large geometry dependence of the shifts was found from a combined QM/MM (quantum mechanics/molecular mechanics) approach.380 Thermal and solvent effects on these shifts were simulated with two molecular-dynamics (MD)-based approaches.381 The computed trends for the chemical shifts could be rationalized by a large sensitivity of the magnetic shielding on the Fe-ligand distances.381 57Fe NMR shifts were calculated by a DFT method for Fe(CO)5, Fe(CO)3(H2C]CHCH]CH2), Fe(CO)3(cyclo-C4H4) and CpFe(CO)2R (R ¼ Me, Bun, Pri).382 In NMR studies of a atoms of ligands, the reaction mixture of excess 15NH2OH and Fe(CN)5(NH3)3 at pH 9 was monitored by 15 N NMR,383 leading to the identification of the intermediate species Fe(CN)5(N2H2)3 (d 76).383 Several Fe P,N,N pincer complexes, including (P,N,N)Fe(CO)2 [38, P,N,N ¼ 2-[(di-tert-butylphosphino)methyl]-6-[1-(2,4,6-mesitylimino)ethyl]pyridine], 57

Solution NMR of transition metal complexes were characterized by several NMR techniques including 1He15N HMQC and 1He31P HMQC, giving 259.2 for the pyridine and imido N atoms in the P,N,N ligand of the complex 38, respectively.384

685

N shifts of d 258.1 and

15

( 38 ) Reaction of electrophile Me3SiOTf with Fe(0) Fe(15N2)(dmpe)2 was conducted, followed by addition of triflic acid to the residual product solid in a study of nitrogen fixation. In a test analyzed by 1He15N HMQC before the addition of triflic acid, Fe(h2-15N2H4)(dmpe)22þ (d 387.0) and Fe(15NH3)2(dmpe)22þ (d 422.6) were identified.385 In another reaction analyzed after the addition of triflic acid, 15NH4þ as well as FeH(15N2)(dmpe)2þ were detected.385 Fe(NH3)2(dmpe)22þ was independently prepared via the treatment of FeCl2(dmpe)2 with NH3 in methanol.385 The nitroxyl ligand in Fe(CN)5(HNO)3 was analyzed by 1H (d 20.2), 15N (d 640), and 17O (d 1099) NMR.386 The complex Fe4(m3-S)2(m2-NO)2(NO)62 with bridging and terminal NO ligands was synthesized and characterized via several methods including 15N NMR.387 An enriched version of Fe4(m3-S)2(m2-NO)2(NO)62 was prepared as the sample for 15N NMR.387 At 320 K, there was a single broad singlet at d 58.3. However, at 220 K, there were signals at d 200.8 and 200.1 (referenced to MeNO2) for the bridging 15NO ligands and d 79.7, 73.5, 43.9, 30.3, 27.1, and 21.9 for terminal 15NO ligands.387 15N NMR of oxidized 15N-labeled histidine Rieske iron-sulfur protein from the bacterium Thermus thermophilus was followed as a function of pH from 11.7 to 5.75 in order to determine the pKa values of the Fe-bound histidine.388 Several reactions of Cp*Fe2(CO)4(m-CO)(m-PPh2) with various hydrosilanes, such as Ph2SiH2 or (p-tol)2SiH2, were analyzed by 29 Si and 31P NMR.389 Fe(II) dicarbollide 1-(h6-MenC6H6n)-closo-1,2,3-FeC2B9H11 (39, n ¼ 1–6)390 and Fe(III) bis(dicarbollide) [3-Fe-(1,2-C2B9H11)2] (40),391 were analyzed via 1H and 11B NMR. For complex [3-Fe-(1,2-C2B9H11)2], DFT calculations were used in order to aid the 11B NMR assignments.391

( 39 ) Water exchange dynamics of several iron complexes, including porphyrins NMR.394–396

9.21.7.2

( 40 ) 392

and polyaminecarboxylates,393 was studied by 17O

Ruthenium complexes

The range of reported 99Ru NMR shifts we found is 18000 ppm set by Ru(OH2)62þ (d 16050397) and Cp2Ru (d 1270 at 346 K398). This range was determined in the 1980s. NMR of 99Ru and ligand donor atoms in metal complexes in aqueous solutions was reviewed in 2016.399 99 Ru, 14N and 17O NMR were probed to study hydrolysis of (NH4)2[Ru(NO)Cl5] (d 99Ru 4190; 14N -36; 17O 379), which initially formed cis-Ru(NO)(H2O)Cl4 (d 99Ru 4450; 17O 380 for NOþ and 79 for H2O ligand).400 Subsequently, both isomerization and additional Cl replacement in the Ru(II) compound gave trans-Ru(NO)(H2O)Cl4 (d 99Ru 3920; 14N -18; 17O 411 for NOþ and 0 for H2O ligand) and fac- and mer-Ru(NO)(H2O)2Cl3, respectively.400 99 Ru shifts of Ru(II) complexes with N,N chelating ligands, [Ru(bpy)3]Cl2 (d 4534, bpy ¼ 2,20 -bipyiridine) and its analogs such as [Ru(phen)3]Cl2 (d 4642, phen ¼ phenanthrene), were reported.401 These were in comparison to d 7821 of Ru(NH3)6Cl2 reported

686

Solution NMR of transition metal complexes

earlier.398 [Ru(bpy)2(2,3-dpp)](PF6)2 [41, 2,3-dpp ¼ 2,3-bis(2-pyridyl)pyrazine] containing an N,N pyridyl-substituted pyrazine ligand was characterized by 99Ru NMR (d 4535).402

( 41 ) For organometallic Ru(II) complexes, 99Ru shifts of Ru(CO)2(dab)XY [X, Y ¼ halide, alkyl, SnR3, GePh3, PbPh3, Mn(CO)5, CpRu(CO)2; dab ¼ Pri-N]CH]CH]NPri (1,4-diisopropyl-1,4-diaza-1,3-butadiene)] were studied, giving, e.g., d 1993 (X ¼ Y ¼ Cl), 1036 (X ¼ Y ¼ I), 794 (X, Y ¼ Me, Cl), 712 (X, Y ¼ Me, Br), 551 (X, Y ¼ Me, I), 316 (X ¼ Y ¼ SnMe3), 116 (X ¼ Y ¼ SnPh3), and 200 (X ¼ Y ¼ PbPh3).403 For Ru cluster complexes, the 99Ru shift of Ru3(CO)12(d 1208) was reported earlier.398 Shifts of HRuCo3(CO)12 (d 202), (NEt4)[RuCo3(CO)12] (d 68), RuCo3(CO)11(NO) (d 241 in addition to 59Co NMR shifts discussed below), and RuCo2(CO)11 (d 597) were obtained,404 along with their 59Co NMR shifts discussed below. For RuCo3(CO)12(NO), 99Ru shift at 241 was observed.404 Computations of 99Ru shifts were the subject of a few studies using DFT methods.405–409 99Ru shifts of several species, including K4Ru(CN)6, Cp2Ru, Ru3(CO)12, Ru(CO)3Cl3, Ru(CO)2Cl42, Ru(bpy)32þ, and Ru(CO)2(dab)XY (X ¼ Y ¼ Cl, I or SnMe3; X, Y ¼ Me, Cl or Me, I) discussed above, were computed and compared with those from experiments.408 Relativistic effects, influence of the density functional and solvent effects on fac-Ru(CO)3I3 were investigated.405 Influence of molecular geometry on the nuclear shielding in RuCl2(dmso)4 and a-PW11RuO39(dmso)5 containing RueS bonds was examined, helping the assignment of 99Ru NMR resonances in the compounds.406 In the NMR studies of a atoms of ligands, the 17O shift of Ru(VI) dioxo porphyrin complexes such as Ru(TMP)(]O)2 (d 775 referenced to H2O; H2TMP ¼ tetramesitylporphyrin) were studied.137 Ru(H2O)62þ reacted with H2 under pressure to give the h2-H2 complex [Ru(H2)(H2O)5]2þ and was characterized via 1H (d 7.65), 2H (d 80.4, JH-D ¼ 31.2 Hz) and 17O [dax 177.4 (for water ligand cis to H2), deq 80.4] NMR.410 When a solution of [RuCl(OEt2)(PNNP)]þ (PNNP ¼ (1S,2S)-N,N-bis[o-(diphenylphosphino)-benzylidene]cyclohexane-1,2diamine) and N-benzylidene-1,1-diphenylmethanamine is treated with excess 15N-eda (eda ¼ ethyl diazoacetate, N2]CHCOOEt) at 78  C, the complex trans-RuCl(eda)(PNNP)þ was the major species below 20  C.411 Reactions of a series of azolylpyridines with RuCl2(PMe3)4 yielded [(N,N)RuCl(PMe3)3] (42) with pyridinylazolate N,N ligands.412 1He15N HMBC was used to clarify the electronic influence of the substituents on the azolyl ring.412 15N-NMR studies were performed at pH 5 of the reaction Ru(edta)(H2O) with excess 15NO.413 The 15N NMR of this reaction showed three signals at d 17.6, 52.4 and 228.5.413 The first two resonances pertained to coordinated 15NOþ and 15NO2 ligands in Ru(edta)(NO)(NO2), respectively.413 The shift at d 228.5 signified the occurrence of free 15NO2 in solution.413 Reactions of [(h6-biphenyl)RuCl(en)]PF6 with amino acids L-cystine,414 L-methionine,414 L-histidine415 as well as cytochrome c or the oligonucleotide d(TATGTACCATGTAT) were investigated using 1He15N HSQC and 1H TOCSY.415

( 42 ) 1

31

Several NMR studies, such as He P HMQC NMR or 11B NMR, and analysis JSi-H of Ru silane, disilane, and borane complexes were discussed in a 2008 review.139

Solution NMR of transition metal complexes 9.21.7.3

687

Osmium complexes

187

Os is the least sensitive nuclide in the Periodic Table, as shown by its receptivity with respect to 13C in Table 10.69,416 Inverse detection methods to indirectly determine 187Os chemical shifts by 2-D correlation experiments, which were reported in 1985,363 significantly expanded the use of 187Os NMR to inorganic compounds.362 Prior to the development of the techniques, only 187Os NMR shift of OsO4 was reported.1 NMR of 187Os and ligand donor atoms in metal complexes in aqueous solutions was reviewed in 2016.399 A 19Fe187Os correlation spectrum was used to obtain 187Os shift of cis-OsO2F4 (d 1431).416 The cis structure for the Os(VIII) complex is based on DFT calculations. Several Os(II) complexes were characterized. 187Os NMR of 37 (h6-arene)Os(PR3)X2 complexes (h6-arene ¼ 1,4-Me,Pri-C6H4 or p-cymene) were probed by either 1He187Os or 31Pe187Os HMBC techniques, yielding, e.g., (h6-p-cymene)Os(PMe3)X2 (d X ¼ Cl, 2226; Br, 2495; I, 3260; H, 5265) vs. d 2431 for (h6-C6H6)Os(PMe3)Cl2 and d 1829 for (h6-C6Me6) Os(PMe3)Cl2.417 The shifts of the 31 (p-cymene)Os(PR3)X2 complexes span the range of d 1697 for (p-cymene)Os(PCy3)Cl2 to 5265 for (h6-p-cymene)Os(PMe3)H2.417 187Os NMR shifts of several [(h6-p-cymene)Os(CO)(PR3)I](PF6) complexes were similarly measured by the HMQC techniques, giving, e.g., d 4430 for [(h6-p-cymene)Os(CO)(PMe3)I](PF6).418 187Os shifts and 1JOs-C coupling constants of CpOs(CO)2Me (187Os d 5340, JOs-C ¼ 48.9 Hz) and Cp*Os(CO)2Me (187Os d 4985, 1JOs-C ¼ 51.5 Hz) were also determined.418 Inverse-detection techniques, based on the 1He187Os or 31Pe187Os dipole-dipole interactions, were used to indirectly measure 187Os spin-lattice relaxation times (T1) for (h6-p-cymene)Os(PMe3)(H)Cl at 300 K [T1 ¼ 4.7 s at 9.4 T and 2.2 s at 14.1 T (600 MHz 1H NMR)].379 The 187Os shift of di-arene [Os(h6-C6H5-Ph)2](OTf)2 (d 4715) was determined by 1He187Os HMBC.419 The d value in the Os(II) complex was shifted significantly from the average (3000) ppm of mono-arene complexes [(h6-arene)Os(PR3)X2](OTf)2 as a result of the increased shielding provided by the second arene ligand in [Os(h6-C6H5-Ph)2](OTf)2.419 187 Os shifts of CpOsL2R (L ¼ phosphine, phosphite) were determined from 1He187Os and 31Pe187Os spectra by the inverse detection techniques.420 For CpOs(PPh3)2X, e.g., the shifts are d 2595 for X ¼ Cl, 3008 for X ¼ Br, and 3530 for X ¼ I.420 Coupling constants 2JOs-H and 1JOs-P were determined as well. 187Os spin-lattice relaxation times [T1, X ¼ Cl, 0.5 s; Br, 0.6 s at 9.4 T and 300 K (or 400 MHz 1H NMR)] were determined indirectly by the 31Pe187Os dipole-dipole interaction.420 187 Os NMR of triosmium clusters containing bridging hydrides, including Os3(m-H)2(CO)10 (43) and several chelating diphosphine derivatives such as Os3(m-H)2(CO)8(m-P,P) [e.g., P,P ¼ Ph2PCH2PPh2 (dppm) (44); (R)-2,20-bis(di-4-tolylphosphino)-1,10binaphthyl (tol-BINAP) (45)], was studied by HMQC, HSQC and HMBC using 1JHeOs or 2JHeOs couplings.362 HMQC and HSQC based on one-bond 1JHeOs gave identical d for the Os atoms (Os1) directly bound to the bridging H ligands, while HMBC based on two-bond 2JHeOs yielded d for the Os atom (Os2) not bound to the H ligands.362 For Os3(m-H)2(CO)10 (43), dOs1 –11302, dOs2 –14021. For Os3(m-H)2(CO)8(m-dppm) (44), dOs1 –11525, dOs2 –14001. For Os3(m-H)2(CO)8(m-tol-BINAP) (45) containing a chelating chiral phosphine ligand, dOs1 11,345, dOs2 14,023.362 For Os3(m-H)2(CO)10 (43) with two types of Os atoms (two bound to the H ligand and one not bound), the satellite from the long-range 2JHeOs coupling is buried under the central peak.421 A method based on varying evolution delays in HMQC spectra led to the extraction of the 1JHeOs (44 Hz), 2JHeOs (2 Hz) and 2JHeC (12 Hz) values for Os3(m-H)2(CO)10 (43).421

( 43 )

( 44 )

( 45 )

A unique NMR method was used to follow s,p-vinyl interchange in a series of 5,6-dihydro-m3-h3-quinolyl complexes Os3(mH)(CO)9[m3-h3-C9H6(5-R)(6-R0 )N] such as 46 (R ¼ CMe2CN, R0 ¼ Me) in Fig. 4.422 For a typical s,p-vinyl interchange involving metal carbonyl complexes in Fig. 4A, VT 13C NMR of the CO ligands on the M atoms bound to the s,p-vinyl moiety was usually used to follow the interchange. At the low temperature limit, environments at the two M atoms were different. The onset of the interchange averaged the environments and the barrier to the interchange could be obtained from the pairwise exchange rates of these CO ligands.422 However, the chiral centers in, e.g., Os3(m-H)(CO)9[m3-h3-C9H6(5-R)(6-Me)N] (R ¼ CMe2CN, 46, Fig. 4B)423 made Os1 and Os2 (as well as Os3 and Os4) atoms to be magnetically non-equivalent, even when the s,p-vinyl interchange process was rapid on the NMR time scale. The unique NMR method was to examine the 1He187Os satellites in 1H NMR of the hydride ligand of a sample with 187Os at 1.96% natural abundance. The molecules of 46 had essentially one or no 187Os isotope in the cluster because of its low abundance. When the s,p-vinyl interchange was slow on the NMR time scale at 295 K, there were two isotopomers: One group of molecules with 187Os isotopes at Os1 and Os3 atoms; Another group of molecules with 187Os

688

Solution NMR of transition metal complexes

(A)

(B)

Fig. 4 (A) s,p-interchange in m-h2-vinyl complexes. (B) s,p-vinyl interchange in cis-Os3(m-H)(CO)9[m3-h3-C9H4(5-R)(6-Me)N] (46). Os1 and Os2 in the left isomer are magnetically inequivalent from Os3 and Os4, respectively, in the right isomer.

isotopes at Os2 and Os4 atoms. Two sets of 1He187Os satellites (1JH-Os ¼ 30.7 and 35.4 Hz) were present in the hydride resonance at d 17.00 in the 1H NMR spectrum. At 373 K, the interchange became rapid on the NMR time scale. The two sets of the satellites merged to a single set with 1JH-Os ¼ average of the two values observed at 295 K.422 In essence, the interchange was monitored at one Os atom per isotopomer. Thus, two Os atoms did not need to become magnetically equivalent for the process to be averaged on the NMR time scale. Only a single Os atom was required to see an average environment. This method circumvented inherent asymmetry in these quinolyl complexes.422 A hybrid DFT method was implemented to calculate the NMR shielding tensors and 187Os NMR shifts for CpOs(PMe3)2X (H ¼ H, Me, Br).424 For NMR of ligands, complexes TpOs(N)X2 (X ¼ CH3COO, Cl, CF3COO, CCl3COO, CBr3COO, Br, NO3, 0.5 oxalate) were studied via several techniques including 15N NMR using enriched complexes.425 The 15N singlet for the complexes was between d 821 and 922.425 Solvent exchange of H2O and CH3CN on trans-Os(en)2(h2-H2)(solvent)2þ (solvent ¼ H2O, CH3CN) was studied as a function of temperature and pressure by 17O NMR line-broadening and isotopic labeling experiments for H2O and 1H NMR isotopic labeling experiments for CH3CN.426 The rate constants and activation parameters were found to be kex ¼ 1.59 s1 at 298 K, DH⧧ ¼ 72.4 kJ/mol; DS⧧ ¼ þ1.7 J/(mol K), and DV⧧ (activation volume) ¼ 1.5 cm3/mol for water exchange and kex ¼ 2.74  104 s1 at 298 K, DH⧧ ¼ 98.0 kJ/mol; DS⧧ ¼ þ15.6 J/(mol K), DV⧧ ¼ 0.5 cm3/mol for acetonitrile exchange.426

9.21.8

Group 9 (Co, Rh and Ir)

For Co and Rh, NMR of both the metals (59Co, 103Rh) and ligands have been reported. For Ir, we could only find the NMR of the ligands. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 11. 59 Co (spin 7/2, natural abundance of 100%) has a relatively large gyromagnetic ratio, thus giving a convenient resonance frequency and a relatively high sensitivity.1 However, its quadrupole moment is fairly large, and the line width leads to the sensitivity loss. 103 Rh, with spin 1/2 and natural abundance of 100%, has a small gyromagnetic ratio, leading to low sensitivity and resonance frequency. In addition, its spin-lattice relaxation, T1, is relatively long.1 Inverse detection methods, similar to those discussed in the section on Group 8 (Fe, Ru and Os), were used for 103Rh NMR to increase the sensitivity of the nuclides.427,428 2-D HMQC, based on, e.g., 1-bond coupling 1JPeRh, makes the acquisition of chemical shifts of spin 1/2 103Rh much easier.

Solution NMR of transition metal complexes

689

Nuclear and NMR properties of 59Co, 103Rh, 191Ir and 193Ir.26

Table 11

Relative receptivity Natural DH DC Gyromagnetic ratio (107) Nuclide abundance (%) a Spin (1H ¼ 1.00) (13C ¼ 1.00) (rad s1 T1) 59

Co

103

Rh

1.64  103 6.332

100

7/2 0.278

100

1/2 3.17  105 0.186

(191Ir)b,c 37.3 193 b Ir 62.7

0.8468

3/2 1.09  105 6.38  102 0.4812 3/2 2.34  105 0.137 0.5227

Quadrupole moment Q (fm2)

X (frequency, MHz;

Reference sample

42.0

23.727074

–

3.186447

81.6 75.1

(1.718)d (1.871)d

K3Co(CN)6 (aq) Rh(acac)3 (CDCl3) –

1

H ¼ 100.0000 MHz, 2.3488 T)

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 We did not find a publication in 1990–2019 on the 191Ir or 193Ir NMR of a metal complex. None was included in the 1991 book edited by Pregosin.1 c191 Ir in parenthesis is considered to be the less favorable of the element for NMR.26 d Value calculated from literature data on nuclear magnetic moments. b

9.21.8.1

Cobalt complexes

59

Co NMR is one of the most used metal NMR spectroscopies with many publications. Its application in coordination chemistry was reviewed in detail in 1991,429 in addition to that in Ref. 1. 59Co shifts of about 800 complexes were tabulated, with spin-spin coupling constants J for 20 nuclear pairs.429 59 Co NMR shifts cover the largest known shielding range, including d 15100 for Co(H2O)63þ to 4220 for KCo(PF3)4, as earlier studies show.429 Low-spin, octahedral d6 Co(III) complexes, which are diamagnetic, comprise a large class of compounds probed by 59 Co NMR. Their shifts are typically in the range of d 15100 for Co(H2O)63þ to 2600 for Co[1,2-C6H4(PMe2)2]33þ.429 For complexes with Co atoms at lower oxidation states, 59Co shifts include those in HCo(CO)4 (d 3721), NaCo(CO)4 (d 3100), Co2(CO)8 (d 2101), Cp2Coþ (d 2410), and CpCo(C2H4)2, in addition to Co(-I) KCo(PF3)4.429 In coordination chemistry, K3[Co(CN)6], dissolved in organic solvents by cryptand 222, showed the solvent influence on the dd transition energies and 59Co shift of the complex.430 Similarly, studies of [Co(en)3]Cl3,431 cis- and trans-[Co(en)2(N3)2]NO3,431 K [Co(edta)],432 and K3[Co(ox)3] (ox ¼ oxalate)432 showed that their 59Co shifts were solvent-dependent. 59Co, 13C and 15N shifts of Co(CN)5X3 (X ¼ CN, Cl, Br, I), Co(CN)5(NH3)2 (L ¼ py, NH3, H2O), Co(NH3)5(CN)2þ, and Co(NH3)5(NC)2þ revealed a common tendency that the shifts varied with the identity of the sixth coordinated ligand and correlated with ligand-field parameters including the nephelauxetic ratio.433 The ligand exchange reactions between Co(NO2)63 and N3, NCS or NH2OH was probed to develop an improved empirical method to estimate the variation of the ligand field strength of the NO2 ligand and 59 Co shifts.434 59 Co NMR was shown to be a facile tool to probe configurational isomerism in fac-Co(L-S,O)3 complexes containing S,O ligands [e.g., H(L-S,O) ¼ PhC(O)NHC(S)NMeEt].435 Different configurations of the three ligands led to EEE, EEZ, EZZ, ZZZ fac-Co(LS,O)3 configurational isomers, each of which gave a resonance.435 Co(dmgBF2)2(H2O)2 [dmgBF2 ¼ difluoroboryldimethylglyoximate (47)] and its pyridine derivative Co(dmgBF2)2(H2O)(py), both containing a planar N,N,N,N ligand were characterized by 59 Co NMR (d 2996 and 2443, respectively).436 59Co NMR of fac- and mer-Co(NH2CH2CH2O)3 (d 10175 and 10016, respectively) was reported.437

( 47 )

( 48 )

( 49 )

Stereoisomerization of Co(III) complexes with polydentate amine ligands, diethylenetriamine, triethylenetetramine, tetraethylenepentamine, and 1,4,8,11-tetraazacyclotetradecane in aqueous solutions was probed by 59Co NMR.438 mer-[Co(diethylenetriamine)(NO2)2(NH3)]Cl was the dominant of four observed isomers.438 59Co NMR was used to characterize Co(terpy)F3 [d 8179, terpy ¼ 2,20 :60 ,200 -terpyridine (48)] and Co(Me3-tacn)X3 [d 9093 for X ¼ F; 10190 for X ¼ Cl; Me3-tacn ¼ 2 (R3 ¼ Me3)].439 [Co(tacn)(H2O)3](OTf)3 [tacn ¼ 2 (R3 ¼ H3)] which was used as a starting material in the preparation of a V complex as described

690

Solution NMR of transition metal complexes

in the section on vanadium NMR,197 showed a 59Co peak at d 9535.440 Reaction of [Co(tacn)(H2O)3](OTf)3 with Na2MoO4 yielded the polyoxomolybdenate complex, [Co(tacn)]2Mo3O12, with the 59Co peak moved to d 9776.440 59Co NMR of [Co(tpa)(CO3)] ClO4, [Co(Me-tpa)(CO3)]ClO4, [Co(Me2-tpa)(ClO4)]ClO4, and [Co(Me3-tpa)(CO3)]ClO4 [tpa ¼ tris(2-pyridylmethyl)amine (d 7965); Me-tpa (d 8606), Me2-tpa (d 9162), and Me3-tpa (49, d 10251) as tpa derivatives containing one, two, and three 6methylpyridyl rings, respectively] are consistent with the decreasing ligand field strength of the N,N,N,N-tripodal tetraamine ligands in the order tpa > Me-tpa > Me2-tpa > Me3-tpa.441 Studies of similar tripodal tetraamine complexes also showed the correlation.442 Co complexes with a R-alaninate (50) and different tetraamine ligands, including [Co(R-alaninate)(N,N,N,N)](ClO4)2 [N,N,N,N ¼ 1,9-diamino-3,7-diazanonane (51), d 7935] and its tetramethyl analog [N,N,N,N ¼ (6R,8R)-6,8-dimethyl-2,5,9,12tetraazatridecane (52), d 8615] showed that methyl substitutions on the tetraamine ligand significantly affected the ligand field strength, as indicated by characteristic 59Co shifts.443 59Co was used to characterize clathrochelate dioximate complexes, such as (H2NEt2)[Co(dioximate)3(SnCl3)2] (d 4603) surrounded by a distorted trigonal antiprismatic coordination sphere from a ligand (53) with six N atoms cross-linked with SnCl3.444 Co(III) complex K[Co(oct-dhpta)] [54, oct-dhpta ¼ n-heptyl-CO2-CH [CH2N(CH2CO2)2]24], containing an N,N,O,O,O,O ligand with a long alkyl chain, showed that the 59Co NMR shift (d 10378) could be used to probe the aggregation of a surfactant with a Co(III) complex as a polar group.445

( 50 )

( 51 )

( 53 )

( 52 )

( 54 )

59 Co shifts of distibine complexes [Co[1,2-(CH2SbMe2)2-C6H4]2X2]Y (X ¼ Br, Y ¼ BPh4, d 4550; X ¼ Y ¼ I, d 6680) were reported,446 as the shifts of two Co chloride complexes containing the tripodal triphosphine ligand MeC(CH2PMe2)3.447 Several Co(III) crown thioether complexes were characterized by 59Co NMR, including, e.g., [Co(18S6)](ClO4)3 [18S6 ¼ 18thiacrown-6 or 1,4,7,10,13,16-hexathiacyclooctadecane (55), d 1646].448 59Co NMR properties of dithio-, thioseleno- and diseleno-carbamate complexes show, e.g., 59Co NMR of d 6790, 6850, and 6890 for Co(S2CNEt2)3, Co(SSeCNEt2)3, and Co(Se2CNEt2)3, respectively, demonstrating a deshielded shift with increasing substitution of the more electronegative S atoms by Se atoms in the complexes.449 77Se shifts of the Se-containing complexes Co(SSeCNEt2)3 (d 392, 373) and Co(Se2CNEt2)3 (d 461) were also measured.449 Both 59Co and 77Se shifts were obtained for diseleno-ether [Co(MeSeCH2CH2SeMe)2X2]BPh4 (X ¼ Cl, 59Co: trans-isomer, d 8694; iso-isomer d 8310; 77Se: d 259. X ¼ Br, 59Co: trans-isomer, d 8310; iso-isomer d 8228; 77Se: d 257. X ¼ I, 59Co: trans- and iso-isomer, d 7689; 77Se: d 256).450 59Co shifts were reported for ditelluro-ether [Co[1,2C6H4(TeMe)2]X2]BPh4 (X ¼ Br, trans-isomer, d 8329; iso-isomer d 8248; X ¼ I, trans- and iso-isomer d 8773).450 59Co shifts of trans-[Co(C12H24Se4)X2]PF6 [C12H24Se4 ¼ 1,5,9,13-tetraselenacyclohexadecane (56); X ¼ Cl, d 9590; Br, d 9125; I, d 8436] containing a macrocyclic tetradentate selenoether ligand also showed a similar trend with different halide.451 For the Cl and Br analogs, 77Se shifts are X ¼ Cl, d 197; Br, d 169.451 Co(III) complexes with substituted macrobicyclic ligands revealed a correlation of their 59Co shifts with inductive (or polar) substituent constants from a Hammett-type treatment.452

Solution NMR of transition metal complexes

( 55 )

( 56 )

( 57 )

691

( 58 )

The spin-lattice (or longitudinal) relaxation time T1 of Co(acac)3 in MeCN was measured at concentrations of 0.020–0.110 M and several temperatures, showing that the relaxation rate was linearly dependent on the concentration of the complex up to approximately 0.080 M.453 Macroscopic viscosity of the solution was the predominant factor in this dependence.453 VT 59Co NMR of 12 octahedral Co(III) complexes were studied to measure spin–lattice relaxation times T1 and line widths, showing that the quadrupolar mechanism of relaxation was dominant in aqueous solution.454 The study indicated a need for the use of dilute solutions to measure T1. Quadrupolar coupling constants in the complexes were determined.454 Optical isomers D- and L-[Co(en)3] in aqueous solutions of chiral salts, such as L- or D-tartrates, show that their 59Co NMR properties (chemical shifts, relaxation rates) were different, which could be used for chiral discrimination.455 59Co NMR quadrupole splitting of D-[Co(en)3] in liquid crystals comprising chiral N-dodecanoyl-L-alanine (57) was different than that in liquid crystals comprising its enantiomer N-dodecanoyl-D-alanine, leading to chiral discrimination.456 59Co NMR relaxation studies of D[Co(chxn)3]3þ ion [chxn ¼ trans-(1R,2R)-1,2-diaminocyclohexane (58)] revealed that the decrease in the 59Co NMR relaxation rates, when SO42 or PO43 anion ( Cl > H2O resulted in slightly longer PtCl bonds trans to the OH ligands in PtCln(OH)62  n (n ¼ 1–5), resulting in the absence of isotopomer effects in contrast to     PtClm(H2O)64mm (m ¼ 2–5).585 195Pt shifts of PtXmY62  m (1  m  6; X, Y ¼ F , Cl , Br , I ) showed an inverse linear relation2 ship with the overall sum of ionic radii of halide ligands,565,566 as Pt(II) complexes PtXmY4m (1  m  4; X, Y ¼ Cl, Br, I)565 and Pt(h2-CH2]CH2)(2,9-dimethyl-phen)XY565–567 discussed earlier in the paragraph on Pt(II) chemistry. 195Pt NMR study of the speciation of aqueous PtCl62, PtBr62, and the mixed PtCl6mBrm2 (m ¼ 0–6) anions by OH substitution was probed.586 Of the 56 possible PtCl6mnBrm(OH)n2  (m, n ¼ 0–6) complex anions in solution under dynamic conditions, 195Pt shifts of 52 observable species [spanning over the range of d 3275 for Pt(OH)62 to 1882 for PtBr62] were assigned, 33 of which had not been reported previously.586 195Pt NMR was used to characterize cis bis-stibine complex PtMe3I[MeN(CH2-2-C6H4SbMe2)2] (d 4400) prepared from PtMe3I and the bis-stibine compound.265 Many theoretical and computational studies were conducted in 2007–2019, often involving different DFT methods, to investigate 195Pt NMR shifts/shieldings in a variety of complexes.587–601 The complexes included anticancer agents,593,594,598,599,601 Pt]O 2 (1  m  6; X, Y ¼ F, Cl, Br, I),588,590 products from speciation and hydration/solvation of PtX62 compounds,587,589 PtXmY6m 592,600 (X ¼ Cl, Br), and azides (PteN3).596 Correlation between 195Pt shifts and electronic transitions among d orbitals in pincer NCN Pt(II) complexes was studied.591 195Pt NMR of Pt(NHC-Dip2)(SiMe3)2 [104, NHC-Dip2 ¼ 2,6-diisopropylphenyl-containing N-heterocyclic carbine] with an unusual Y-shaped structure was significantly different from those of Pt(II) complexes but close to

Solution NMR of transition metal complexes

703

those of typical Pt(0) complexes. Theoretical study showed that Pt(NHC-Dip2)(SiMe3)2 was more likely a Pt(0) s-disilane (105) rather than a Pt(II) disilyl complex (104).597

( 104 )

( 105 )

( 106 )

Reactions of Pt(0) Pt(C2H4)(PEt3)2 with diselenides RSeSeR [R ¼ Ph, Fc (ferrocenyl)] gave oxidative addition products transPt(SeR)2(PEt3)2, showing 77Se NMR shifts of the products [R ¼ Ph, d 78; R ¼ Fc (Fc ¼ ferrocenyl), d 47 referenced to SeMe2].602 Pt[TeC4H(4,6-Me)2N2]2(dppm) (106) with two pyrimidyltelluride ligands gave the 125Te resonance at d 472 (referenced to TeMe2).574 1 He195Pt HMBC of a Pt(IV) mono azido mono triazolato complex (107) revealed two 195Pt environments (d 689 and 785) that showed the complex was in a dynamic exchange (Fig. 10).603 This complex was also characterized by other NMR techniques including COSY and ROESY.603 Pt(II) complexes with selenium adducts of germa- and stanna-closo-dodecaborate Pt(dppp)(Se-GeB11H11)22 and Pt(dppp)(SeSnB11H11)22 (108) were characterized by NMR including 31P [d 3.3 (Ge complex) and 1.8 (Sn complex)], 77Se [d 227.9 (Ge complex), 108.3 (Sn complex)], 195Pt [d 4777 (Ge complex), 4726 (Sn complex)], and 119Sn [d 338 (Sn complex)].604

Fig. 10

Dynamic exchange between two isomers of complex 107.

704

Solution NMR of transition metal complexes

A series of organotin platinum complexes, such as cis- and trans-PtPh(Sn2Ph5)(PEt3)2 and Pt complexes with bidentate bisstannylene ligands, were synthesized and characterized via 31P and 119Sn NMR.605,606 In order to generate a silylene complex, (dippe)PtMeCl [dippe ¼ Pri2P(CH2)2PPri2] reacted with (thf)2LiSiHMes2 (Mes ¼ 2,4,6Me3-C6H2). The product was found to be a silyl complex, (dippe)PtMe(SiHMes2), and was analyzed by NMR (29Si, d 28.70; 31P, d 66.54).607 Reaction of the silyl complex (dippe)PtMe(SiHMes2) with B(C6F5)3 yielded the silylene hydride [(dippe)(H)Pt(] SiMes2)][MeB(C6F5)3] (31P, d 77.2; 19F, d 132.2, 165.1, 167.2; 29Si, 338.1).607 Both 1- and 2-D 15N NMR were used to study Pt complexes, including anticancer compounds, Pt-DNA complexes, cis-platin, and other Pt complexes with PteN interactions.608–622 For example, hydrolysis of the 15N-labeled anticancer complexes cisPtCl2(NH3)(2-picoline) and cis-PtCl2(NH3)(3-picoline) were monitored via 1He15N HSQC.614 After 1 h, the cross-peaks (dH/ dN) in cis-PtCl2(NH3)(2-picoline) went from dH (4.15)/dN (66.52) to dH (4.40)/dN (64.41) and dH (4.32)/dN (87.25).614 These peaks pertained to the hydrolysis of the Cl trans to the 2-picoline and NH3 ligands, respectively.614 After 2.5 h, both Cl ligands were replaced by a new cross-peak at dH (4.41)/dN (82.91).614 A similar experiment was conducted on the cis-PtCl2(NH3)(3picoline), and the results were compared.614 Both of the Cl ligands in the 2-picoline Pt complex hydrolyzed more slowly than those in the 3-picoline Pt complex.614 In the 3-picoline Pt complex, the Cl ligand trans to NH3 hydrolysed faster than that trans to 3-picoline.614 A family of platinum bis-boryl complexes, such as Pt(PPh3)2(Bpin)(Bcat) (109, pin ¼ 1,2-O2C2Me4, cat ¼ 1,2-O2C6H4), were prepared via oxidative addition of unsymmetrical diborane derivatives and analyzed via 11B NMR.623 Water exchange on (NCN) Pt(H2O)þ [110, N,C,N ¼ 2,6-(CH2NMe2)2-C6H3] was monitored as a function of pressure and temperature via 17O NMR.624

( 109 ) 15

( 110 ) 15

( 111 )

( 112 )

15

N-labeled complexes Pt(Se2 N2)(PMe2Ph)2 (111) and Pt(TeS N2)(PMe2Ph)2 (112) have were also analyzed via 77Se, 125Te, and P NMR.625 The following shifts were observed: For 111, dPt 4050, dSeA 1819, dSeB 1383, d15NA 486, d15NB 402; For 112, dTe 1196, d15NA 360, d15NB 256.625 Characterization of PtLi4[Si(3,5-Me2pz)3]4556 (86) was discussed in Section 9.21.9.2. For 77Se NMR of (NBun4)2[Pt(C3Se5)2] with a diselenolate ligand,626 see Section 9.21.12.2. 31

9.21.10 Group 11 (Cu, Ag and Au) For Cu and Ag, NMR of both the metals (63Cu, 109Ag) and ligands were reported in 1990–2019. For Au, we found only papers on NMR of ligands. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 14.

9.21.10.1 Copper complexes Of the two nuclides, both with spin 3/2, 63Cu is more than twice as abundant as 65Cu and has larger relative receptivities. Thus, 63Cu was typically selected for Cu NMR, although both 63Cu and 65Cu were used.627 Of the two principal oxidation states for copper, Cu(II) complexes with d9 configuration are often paramagnetic, while Cu(I) complexes are diamagnetic. We found publications in 1999–2019 on 63Cu NMR of Cu(I) complexes. 63 Cu NMR of inorganic compounds was reviewed in 1999.627 Thus, we focus on publications on Cu NMR in 1999–2019 in the current review. Temperature effect on 63Cu NMR on the nitrile complex [Cu(PhCN)4]BF4 was studied.628 63Cu NMR line widths of CuOTf and CuClO4 in acetonitrile solutions containing salts, water or Cl were also investigated.629 Studies of solvation of Cu(I) salts, such as CuClO4 in mixed solvents of MeCN or PhCN containing other nitriles (EtCN, PriCN), dmso, or D2O, probed by 63Cu/65Cu NMR were reviewed.630 Cu phosphine complex [Cu(dppmb)2]BF4 [dppmb ¼ 1,2-bis(diphenylphosphinomethyl)benzene, o-(CH2PPh2)2-C6H4] gave a 63Cu resonance at d 193, which is typical for Cu(I)-P4 complexes.631 Similarly, phosphine perfluorinated carboxylates, such as

Solution NMR of transition metal complexes Table 14

705

Nuclear and NMR properties of 63Cu, 65Cu, 107Ag, 109Ag and 197Au.26 Relative receptivity

Natural DH Nuclide abundance (%) a Spin (1H ¼ 1.00)

DC Gyromagnetic ratio (13C ¼ 1.00) (107)(rad s1 T1)

Quadrupole moment Q (fm2)

X (frequency, MHz;

Reference sample

63

382 208 0.205 0.290 0.162

22.0 20.4 – – 54.7

26.515473 28.403693 4.047819 4.653533 (1.729)d

[Cu(MeCN)4] ClO4(MeCN) AgNO3 (aq)

Cu Cu (107Ag)b 109 Ag 197 Auc 65

69.15 30.85 51.839 48.161 100

3/2 3/2 1/2 1/2 3/2

6.50  102 3.54  102 3.50  105 4.94  105 2.77  105

7.1117890 7.60435 1.0889181 1.2518634 0.473060

H ¼ 100.0000 MHz, 2.3488 T)

1

–

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 Ag in parenthesis is considered to be the less favorable of the element for NMR. c Although we did not find reports of 197Au NMR, it is listed here for comparison. d Value in parenthesis was calculated from literature data on nuclear magnetic moments. b107

[Cu(dppp)2](OOCC2F5), showed broad 63Cu bands at ca. d 230.632 63Cu NMR was used to characterize several Cu(I) phosphite perfluorinated carboxylates, such as Cu2[P(OPh)3]4(m-OOCC2F5)2 (d 105), showing that 63Cu shifts of the phosphites were more shielded than those of phosphine analogs.633 63Cu NMR studies of Cu(I) complexes with P-donor ligands, such as phosphines and phosphites, were reviewed in 2006.634 In addition to complexes with N- and P-containing ligands, Cu(I) compounds with Sb-containing stibine ligands were characterized by 63Cu NMR. [Cu(R2SbCH2SbR2)2]PF6 (R ¼ Me, Ph) showed 63Cu resonances at d 170 (R ¼ Me) and 197 (R ¼ Ph).635 Their analogs, [Cu(dmsmb)2]BF4 [dmsmb ¼ 1,2-bis(dimethylstibanylmethyl)benzene, o-(CH2SbMe2)2-C6H4] and [Cu(bdmsa)2] BF4 [bdmsa ¼ bis(2-dimethylstibanylbenzyl)methylamine, MeN(CH2-o-SbMe2-C6H4)2] showed 63Cu resonance at d 171446 and 203,265 respectively. Cu(I) complexes containing chalcogen (S, Se, Te) elements were also studied by 63Cu NMR, including [Cu[o-(CH2EMe)2C6H4]2]BF4 (E ¼ S, 63Cu d 132; E ¼ Se, 63Cu d 2, 77Se d 87; E ¼ Te, 63Cu d 16, 125Te d 98).636 Di-tellurium substituted 18crown-6, 1,4,10,13-tetraoxa-7,16-ditelluracyclooctadecane ([18]aneO4Te2, an analog of 1 shown earlier), used its two Te atoms to bind to the Cu(I) ion as a ligand to give [Cu([18]aneO4Te2)2]BF4, showing resonances of 63Cu d 59 and 125Te d 166.637 A series of organometallic Cu(I) carbonyl complexes with tridentate N,N,N ligands were investigated by 63Cu NMR, including Tp*CueCO (d 716), [(TpC)CueCO]ClO4 [d 504, TpC ¼ tris(2-pyridyl)carbinol (113)], and [(Me-tacd)CueCO]ClO4 [d 585, Metacd ¼ 1,5,9-trimethyl-1,5,9-triazacyclododecane (114)].638 Intermetalloid cluster Cu@Sn93 in [K([2.2.2]-cryptand)]3[Cu@Sn9] [[2.2.2]-cryptand ¼ 115] showed 63Cu and 119Sn resonances at d 330 and 1440 (1J119Sn–Cu ¼ 280 Hz), respectively.639 The crystal structure of the cluster revealed that the Cu(I) is in the center of the cluster with an almost spherical environment.

( 113 )

( 114 )

( 115 )

Cu NMR of the Cuþ site in blue copper protein azurin in frozen solution was investigated at 10 K using an 800 MHz (18.8 T) spectrometer, giving a 65Cu quadrupole coupling constant of 71.2 MHz which corresponds to an electric field gradient of 1.49 a.u. at the Cu site and an asymmetry parameter of 0.2.640 Azurin is a small, periplasmic, bacterial blue copper protein. The sample used here was 97% 65Cu-enriched. The studies here provided the nuclear quadrupole interaction as an exquisitely sensitive measure of the electron density around the Cu(I) ion and the electronic structure and environment. Earlier experiments to obtain nuclear quadrupole interactions in Cu(I) complexes and the reduced form of the enzyme superoxide dismutase were conducted at zero field by nuclear quadrupole resonance (NQR).640 For NMR of ligands, reactions of O-phospho-L-serine [Ser-P ¼ (HO)2P(]O)OCH2CH(NH2)CO2H] with Cu(II) ions were conducted in order to investigate the coordination of the Cu ion with the amine, carboxyl, or phosphate groups in Ser-P.641 1He15N NMR by the HETCOR method was used to determine if the Cu ion was coordinating to the amine group.641 The amine and carboxyl groups were involved in coordination in Cu(Ser-P)2.641 17 O NMR was used to study the effects of the pressure, temperature, and magnetic field on the water or solvent exchange reactions of [Cu(tmpa)(H2O)]2þ [116, tmpa ¼ tris(2-pyridylmethyl)amine],642 [Cu(fz)2(H2O)]2 [117, fz ¼ ferrozine or 5,6-bis(4-sulfonatophenyl)-3-(2-pyridyl)-1,2,4-triazine],642 [Cu(tren)(H2O)]2þ (118, tren ¼ 63),643 and [Cu(dmf)6]2 þ (119).644 65

706

Solution NMR of transition metal complexes

( 116 )

( 117 )

( 118 )

(119)

9.21.10.2 Silver complexes NMR of 109Ag (spin 1/2) was considered challenging mostly due to its low X value and relative receptivities/sensitivity (Table 15).69 Complexes characterized by 109Ag NMR that we found were those at the Ag(I) oxidation state. In Ag complexes coordinated by N-containing ligands, [Ag(NH3)2]NO3 in aqueous NH3(aq) solution and [Ag(NH3)3]NO3 in liquid NH3(l) showed 109Ag shifts of d 450 and 570, respectively.645 These shifts were compared with those of Agþ salts (AgNO3 or AgClO4) in other liquids such as CD3CN (d 240), PBun3 (d 1125) and P(OMe)3 (d 1260). The effect of anions was negligible.645 Dinitramide compounds AgN(NO2)2, [Ag(MeCN)][N(NO2)2], and [Ag(py)2][N(NO2)2] were studied by 109Ag and 14N NMR with the chemical shifts listed in Table 15.646 109Ag shift of [Ag(py)2][Au(CF3)2] was found to be at d 404.647 When [Ag(9-EtGH)2]NO3 [9-EtGH ¼ 9-ethylguanine (91)] was dissolved, 109Ag NMR showed the equilibria involving the 1:1 complex of Ag:ligand.648 The 109Ag shift became gradually more deshielded from d 200 (at the Ag:ligand ratio ¼ 1:2) to d 245 (at 1:4 ratio).648 For the disilver cryptate complex (120) with a thiophene-spaced azacryptand hexa-Schiff base, 1H NMR spectrum revealed three-bond (HeC]NeAg) coupling of imino CH proton atoms to 107,109Ag, which was confirmed by the 109Ag INEPT (Insensitive

Table 15

109

Ag and 14N NMR shifts of Ag(I) dinitramide compounds646.

Complexes

109

14

AgN(NO2)2 [Ag(MeCN)2][N(NO2)2] [Ag(py)2][N(NO2)2]

137 212 306

17 (NO2), 73 [N(NO2)2] 16 (NO2), 68 [N(NO2)2], 157 (MeCN) 13 (NO2), 91 [N(NO2)2], py in the same region as N(NO2)2, making the two indistinguishable; py may be displaced by solvent THF.

Ag shifts (d)

N shifts

Solution NMR of transition metal complexes

707

Nuclei Enhanced by Polarization Transfer) spectrum with a peak at d 610.649 Structure of an Ag(I)-mediated cytosine-Ag(I)-cytosine base pair within DNA duplex (121) was determined with solution NMR, showing 1J15N-Ag ¼ 83 and 84 Hz and the N3eAgeN3 linkage.650 The 109Ag and 15N (of the N atom bound to the Ag ion) shifts were d 442 and 172, respectively.650 Reaction of AgPF6 with the chiral 5,6-Chiragen ligand (122), containing two condensed a-pinene/bipyridine units, gave an enantiomerically pure, helicate [Ag6(5,6-Chiragen)6](PF6)6 in the hexagonal shape.651 109Ag NMR spectrum of the hexamer (d 224) at 221 K showed its equilibrium with the tetramer [Ag4(5,6-Chiragen)4](PF6)4 (d 249).652 IreAg mixed metal complexes Cp*(pz)Ir(m-pz)3Ag(PPh3) and [(Ph3P)AgA(m-pz)Cp*Ir(m-pz)2AgB(PPh3)]BF4 (123, py ¼ pyrazole) were characterized by 107,109Ag NMR.653 For Cp*(pz)Ir(mpz)3Ag(PPh3), 109Ag shift was observed at d 902.8; 15N shifts were obtained at N(-Ir) d 165.5 and N(-Ag) at d 93.1 with 1 J15N–15N ¼ 14.2 Hz, 1J15N-Ag ¼ 38 Hz and 2J15N-Ag-P ¼ 13.6 Hz.653 For 123, 109Ag shifts are at d 884.3 (for AgB) and 562.9 (AgA). Its N(-Ir) shifts at d 168.5 to 170.8 and N(-Ag) shifts at d 90.7 to 105.2 with 1J15N–15N ¼ 13.5–13.7 Hz, 1J15NAg ¼ 36.5–73.8 Hz and 2J15N-Ag-P ¼ 13.2–18.5 Hz.653 Trisilver complex 124 with a chiral ferrocene ligand was studied as a model homogeneous catalyst.654 The number of coordinated P atoms and the coordination of the chiral side chain were determined using 109 Age31P, 109Age1H, and 31Pe1H HSQC and HMQC, showing 109Ag shifts at d 690 (AgA) and 540 (AgB) in 124.654

(120 )

(121 )

(122 )

(123 )

(124 )

(125 )

In Ag complexes coordinated only by P-containing ligands, reactions of AgNO3 with 1,2-bis(di-2-pyridylphosphino)ethane (d2pype ¼ 125) give monomer [Ag(d2pype)2]NO3 with the Ag(P,P)2þ structure, dimer [(d2pype)Ag(m-d2pype)2Ag(d2pype)](NO3)2 with the [(P,P)Ag(m-P,P)2Ag(P,P)]2þ-type cation and a trimer.655 109Ag shifts of the monomer and dimer at 243 K were observed at d 1411 and 1417, respectively. The trimer and analogs with bis(di-n-pyridylphosphino)ethane (n ¼ 3, 4) were also characterized by 109Ag.655 For Ag(I) complex 126 with a B-templated catechol phosphine, 109Ag shift was observed at d 702 with 1JP-107/109Ag ¼ 571/494 Hz.656 Complex with a tetradentate P,S,S,P ligand, [Ag[Ph2P(CH2)2S(CH2)2S(CH2)2PPh2]]BF4, was characterized by 109Ag NMR with the resonance at d 1117.657 For Ag(I) complexes with As- (arsine) and Sb (stibine)-containing ligands, several tetra-coordinated compounds were characterized by 109Ag NMR, including [Ag(AsPh3)4]BF4 (d 1056),658 [Ag(SbMe3)4]BF4 (d 1085),658 [Ag(SbPh3)4]BF4 (d 1166),658 and [Ag(dmap)2]BF4 [d 1120, dmap ¼ Me2Sb(CH2)3SbMe2].658 109Ag shift of [Ag(dpsm)2]BF4 (dpsm ¼ Ph2SbCH2SbPh2) was observed at d 521, suggesting that the complex is probably di-coordinated (SbeAgeSb).635

( 126 )

( 127 )

( 128 )

708

Solution NMR of transition metal complexes

Ag(I) complexes containing chalcogen (S, Se, Te) elements were also studied by 109Ag NMR, including [Ag[MeE(CH2)3EMe]2] BF4 (E ¼ S, 109Ag d 840; E ¼ Se, 109Ag d 829, 77Se d 41; E ¼ Te, 109Ag d 1053, 125Te d 24) and their analogs with the PhE(CH2)3EPh ligands.659 [Ag[o-(EMe)2-C6H4]2]BF4 (E ¼ S, 109Ag d 788; E ¼ Se, 109Ag d 912, 77Se d 180; E ¼ Te, 109Ag d 1128, 125Te d 433), showing the more deshielded 109Ag shift from the S, Se to the Te analog.660 For other AgeS complexes, reaction of Ag(I) ions with 1-methyl-2(3H)-imidazolinethione (Hmimt ¼ 127) led to the formation of [Ag(Hmimt)3](NO3), which showed by X-ray crystal diffraction to contain three AgeS bonds, and gave 109Ag d 791.5.661 109Ag NMR of Ag(I) di-thiourea complex [Ag[S] C(NH2)2]2]NO3 revealed the resonance at d 671.8,662 while mono-thiourea complex Ag[S]C(NH2)2]CN gave the resonance at d 651.8.663 A series of other Ag(I) substituted-thiourea and -thione complexes were characterized by 109Ag NMR,663,664 showing, e.g., 109Ag d 654.9 for mono-N,N-dimethylthiourea complex Ag[S]C(NHMe)2]CN663 and d 656.1 for di-N,N-dimethylthiourea complex [Ag[S]C(NHMe)2]2]NO3.664 Hydride complex (Bun4N)5[Ag8(H)[S2CC(CN)2]6] containing AgeS bonds with 1,1dicyanoethylene-2,2-dithiolate (128) ligands showed 109Ag d 1136 and 1H resonance of the hydride ligand at d 9.65.665 For Ag(I) complexes containing S ligands with biological applications, oligomeric Ag(I) thiomalate complex Na[Ag [O2CCH(SH)CH2CO2]] with AgeS bonds showed 109Ag d 868.7.666 Antimicrobial activities of such complexes were studied.666 Ag(I)ecysteine solution showed a mean AgeS bond distance of 2.47(2) Å by EXAFS (extended X-ray absorption fine structure) and 109Ag NMR resonance at d 1103, which were consistent with the product being a partially oligomeric AgS3 species.667 For Ag(I)-penicillamine solution, the mean AgeS bond distance was 2.40(2) Å by EXAFS and 109Ag NMR resonance was observed at d 922, indicating that mononuclear AgS2 coordinated complexes dominated in the solution.667 Here, the studies of the Ag(I)cysteine and -penicillamine interactions stemmed from the historical use of Ag(I) in antimicrobial agents, as the increasing bacterial resistance against antibiotics renewed the interest in newer and more efficient Ag-based antimicrobial biomaterials.667 109 Ag shift of (H2NPri2)Ag[PhCH]C(S)COO] containing the di-anionic O,S ligand PhCH]C(S)COO was at d 840.8.668 Ag(PPh3)[PhCH]C(SH)COO] containing the mono-anionic O,SH ligand showed the 109Ag shift at d 936.3.669 For AgeSe and AgeTe complexes, see previous discussion on [Ag[MeE(CH2)3EMe]2]BF4 (E ¼ S, Se, Te),659 their analogs with the PhE(CH2)3EPh ligands,659 and [Ag[o-(EMe)2-C6H4]2]BF4 (E ¼ S, Se, Te).660 For other AgeSe complexes, 107Ag NMR was used to study selenourea complexes Ag(selenourea)NO3 (d 810.5) and [Ag(selenourea)2]NO3 (d 784.3), which are >600 ppm more deshielded than that of AgNO3 (d 166.0).670 These resonances are also deshielded from those of AgeS analogs, Ag(thiourea) NO3 (d 685.9) and [Ag(thiourea)2]NO3 (d 671.8).670 Various Ag(I)-selenone complexes were probed by 109Ag NMR, including Ag(N,N-dimethylselenourea)NO3 (d 748.6) and [Ag(N,N-dimethylselenourea)2]NO3 (d 839.8).671 For Ag(I) organometallic complexes (including CN compounds), 109Ag NMR was used to study (Ph3Te)[Ag(CN)2] (d 593).672 Ag(I) trinitromethanide Ag[C(NO2)3] in various solvents was studied, showing, e.g., its 109Ag resonance at d 27.5 in D2O and at d 429.7 in CD3CN.673 109Ag NMR was used to characterize hydride-centered heptanuclear silver clusters, Ag7(H)[S2P(OEt)2]6 (d 1117) with dithiophosphate ligands and its Se analog Ag7(H)[Se2P(OPri)2]6 (d 1126) with diselenophosphate ligands.674 Ag(I) cluster Ag8(m4-H)[Se2P(OPri)2]6þ containing H bridges (Ag-m-H-Ag) in tetracapped T symmetry inside an Ag8 core was prepared with PF6 anion.675 Both 109Ag, 1He109Ag HMQC and 77Se spectroscopies were used to characterize the complex (109Ag d 1155 ppm, 1JH-109Ag ¼ 35.0 Hz; 77Se d 0.2).675 Re(I)eAg(I) hydride-carbonyl clusters Ag(m-H)4[Re2(m-H)(CO)8]2, Ag(mH)4[Re4(m-H)3(CO)16]2, and Ag(m-H)4[Re2(m-H)(CO)8][Re4(m-H)3(CO)16], with OTf anions, were studied by 1He109Ag HMQC to give 109Ag resonances at d 1844, 1243, and 1520, respectively.676 Ag(I) trifluoromethyl complex [Ag(dmf)2] [Ag(CF3)2] showed the 109Ag shift of d 569.8 for the anion [Ag(CF3)2].677 Other perfluoroalkyl Ag(I) complexes [Ag(C2F5)2] and [Ag(n-C4F9)2] were also characterized by 109Ag NMR.677 Oligomer Ag(I) [Ag(C^CBun)]m showed the 109Ag resonance at d 1060.678 Ag(III) trifluoromethyl complexes [Ag(CF3)4] and [Ag(CF3)nX4n] [X ¼ CN (n ¼ 1–3), CH3, C^CC6H11, Cl, Br (n ¼ 2, 3) and I (n ¼ 3); cation ¼ PPh4þ or PNPþ (Ph3P]N]PPh3þ)] showed significantly deshielded 109Ag resonances from Ag(I) complexes, such as d 2233 for [Ag(CF3)4], d 2404 for Ag(CF3)3(dmf), and d 2046 for [Ag(CF3)3Me].679 109Ag shifts of the Ag(III) complexes were tabulated in Ref. 679. Several Ag(I) complexes with N-heterocyclic carbene (NHC) ligands were studied by 109Ag NMR.680–684 [Ag(IMes)2]OTf [IMes ¼ 1,3-mesitylimidazol-2-ylidene (129)] showed its 109Ag resonance at d 642.4.680 N,N-diferrocenyl-NHC (130) complex [Ag(1,3-diferrocenylimidazol-2-ylidene)2]BPh4 gave the 109Ag resonance at d 727.681 Hydride dimer [(SIDipp)Ag(m-H)Ag(SIDipp)]OTf (SIDipp ¼ 131) and its deuteride isotopologue [(SIDipp)Ag(m-D)Ag(SIDipp)]BF4, with direct Ag/Ag interactions, showed interesting H/De109Ag and 107Age109Ag couplings in their 109Ag NMR spectra (Fig. 11).682 Since naturally occurring silver consists of ca. 52% 107Ag and 48% 109Ag (Table 14), both with spin 1/2, the H-bridged Ag2þ ion therefore comprised a mixture of roughly 1:2:1 (27:50:23) of [107AgeHe107Ag]þ, [107AgeHe109Ag]þ and [109AgeHe109Ag]þ. Among the three isotopologues, the first with only 107Ag isotopes did not show up in the 109Ag NMR spectrum. The last one, [109AgeHe109Ag]þ, was observed as a doublet split by the H ligand with 1JH-109Ag ¼ 134 Hz. In the middle isotopologue with one 107Ag and one 109Ag ion, [107AgeHe109Ag]þ, the 109Ag signal was split into a doublet of doublets by the 1H and 107Ag nuclides (1J107Ag-109Ag ¼ 113 Hz), as shown in Fig. 11A.682 In the spectrum of the D compound in Fig. 11B, coupling between 109Ag and 2H (spin 1) gives rise to a 1:1:1 triplet, which 107Ag splits further into a 1:1 doublet of 1:1:1 triplets. This pattern indicates the large 109Age107Ag coupling and the smaller 109Age2H coupling (1JD-109Ag ¼ 18.7 Hz).682 109Ag NMR was used to characterize the Ag(I)-NHC complex (dbdpi) Ag(acetate) [d 476, dbdpi ¼ 1,3-dibenzyl-4,5-diphenylimidazol-2-ylidene (132)] and its analogs.684 The antibiotic activities of the Ag(I)-NHC complex and its analogs was evaluated.684 1H(13C)109Ag triple resonance NMR technique was developed to obtain 109 Ag NMR resonances in a labile Ag(I)-carbene complex.683 In Ag complexes, indirect detection of 109Ag resonances via

Solution NMR of transition metal complexes

(A) SIDipp

Ag + Ag H

109

Ag

109

Ag

107

Ag

SIDipp

109

Ag

107

Ag

+ H

+ H

709

107 Ag + H not observed

530

525

(B) SIDipp

Ag + Ag D

520 G (ppm)

515

SIDipp

510 109

Ag

109

Ag

107

Ag

109

Ag

107

Ag

+ D

+ D

107 Ag + D not observed

530

525

520 G (ppm)

515

510

Fig. 11 (A) 109Ag NMR spectrum of [(SIDipp)Ag(m-H)Ag(SIDipp)]OTf in CD2Cl2. (B) 109Ag NMR spectrum of [(SIDipp)Ag(m-D)Ag(SIDipp)]BF4 in CD2Cl2. Insets: interpretation of signals from each isotopologue. Adapted with permission from Tate, B. K.; Wyss, C. M.; Bacsa, J.; Kluge, K.; Gelbaum, L.; Sadighi, J. P. A Dinuclear Silver Hydride and an Umpolung Reaction of CO2. Chem. Sci. 2013, 4, 3068–3074. doi: 10.1039/C3SC50896J. Copyright: Royal Chemical Society.

1 He109Ag HMQC frequently encountered small or absent 1JH-109Ag couplings or rapid ligand dissociation. H(X)Ag triple resonance spectroscopy used the large one-bond 1JX-109Ag coupling (where X is the relay nuclide). 1H(13C)109Ag HMQC NMR experiment was performed for a Ag(I)-NHC complex at natural 13C (1.1%) abundance and variable temperatures, showing that was superior to the 1 He109Ag HMQC detection above 20  C.683

( 129 )

( 130 )

( 131 )

( 132 )

710

Solution NMR of transition metal complexes

[HB[3,5-(CF3)2-Pz]3]AgSn(N3)[(Prn)2ATI] (133) [HB(3,5-(CF3)2-Pz)3 ¼ hydrotris[3,5-bis(trifluoromethyl)pyrazolyl]borate, (Pr )2ATI ¼ N-(n-propyl)-2-(n-propylamino)troponiminate] was characterized by 119Sn NMR, showing a doublet at d 90 with 1 J119Sn-107/109Ag ¼ 4866 Hz.685 119Sn and 29Si shifts were also reported for products of the reactions between Sn[CH(SiMe3)2]2 or Sn[CH(SiMe3)2]2X2 (X ¼ NCO, I) and AgX (X ¼ NCS, CN, NCO, I).686 n

( 133 ) NMR of a atoms of ligands was also used to study Ag complexes. In a DNA oligonucleotide with three consecutive imidazole nucleotides in its center, Ag(I) ions were found to mediate the pairings in three imidazole-Ag-imidazole interactions.687 The confirmation of the Ag-mediated base pairs was obtained from 1J15N-107/109Ag (86 Hz) couplings upon using 15N-labeled imidazole.687 VT 31P NMR was used to study the coordination chemistry of equimolar amounts of Ag(I) with the diphosphine ligands Ph2P(CH2)nPPh2 (n ¼ 6, 8, 10, 12).688 The 1JP-107Ag for all reaction mixtures was 500 Hz, indicating that the Ag(I) ion was coordinated to two P atoms in a linear fashion.688

9.21.10.3 Gold complexes As indicated in the footnote of Table 14, we did not find a publication in 1990–2019 on the 197Au NMR of a metal complex. Reactions of [Au(cis-dach)Cl2]Cl and [Au(cis-dach)2]Cl3 (cis-dach ¼ cis-1,2-diaminocyclohexane) with K13C15N were conducted and followed by 15N NMR.689 For example, after the reaction of [Au(cis-dach)Cl2]Cl with K13C15N in a 1:2 ratio, a signal in the 15N NMR spectrum at d 281 pertaining to Au(13C15N)4 appeared.689 When the amount of the [Au(cis-dach)Cl2]Cl was increased, the resonance of Au(13C15N)4 (d 262) was observed, showing that it was produced as a second product.689 Synthesis of bis-silyl Au(III) complexes were investigated using DFT calculations and NMR spectroscopy such as 31P and 29Si.690 For example, the reaction of (Ph3P)AuCl with, e.g., (PhMe2Si)2 in the presence of GaCl3 at 80  C produced [Au(PPh3)(SiMe2Ph)2](GaCl4) (dSi 40.7, dP 60.9).690 For 77Se NMR of (NBun4)[Au(C3Se5)2] containing diselenolate ligands,626 see Section 9.21.12.2.

9.21.11 Group 12 (Zn, Cd and Hg) For the three elements, NMR of both the metals (67Zn, 113Cd, and 199Hg) and ligands were reported in 1990–2019. Nuclear and NMR properties of the nuclides, including recommended and commonly used references, are given in Table 16.

9.21.11.1 Zinc complexes The small natural abundance of 67Zn and its low resonance frequency (X) lead to slight relative receptivities. In addition, as a spin 5/2 nuclide, it has a quadrupole moment. These properties limited the use of 67Zn NMR in inorganic compounds.1 Earlier 67Zn NMR studies by 1990 were reviewed in Ref. 1, including following compounds: zincate Zn(OH)42 (d 220 in 16 M KOH), ZnCl42 (d 257), ZnBr42 (d 169), ZnI42 (d 35), Zn(NH3)42þ (d 288), Zn(SMe)42 (d 362), Zn(SPh)42 (d 267), and Zn(SePh)42 (d 224). These complexes are in highly symmetric ligand environment, minimizing the contributions of 67Zn quadrupole moment to the peak width. In the 1990–2019 period, interactions of silicates with Zn(II) and Al(III) ions in highly alkaline, aqueous solution were studied by 67Zn, 29Si and 27Al NMR.691 When 0.84 M ZnO and 0.86 M SiO2 were dissolved in 10.0 M KOH, (HO)3ZnOSiO2(OH)4, formed from the reaction of zincate Zn(OH)42 with monomeric silicate, was observed at 67Zn d 286 (line width 2500 Hz) and 29 Si d 71.4. The shift and width of the 67Zn peak in comparison with those of zincate Zn(OH)42 (d 220, width 554 Hz) were consistent with the formation of the Zn(II)eSi(IV) anion with lower symmetry than zincate.691 29Si NMR was used to probe

Solution NMR of transition metal complexes Table 16

711

Nuclear and NMR properties of 67Zn, 111Cd, 113Cd, 199Hg, and 201Hg.26 Relative receptivity

Natural abundance Nuclide (%) a

DH DC Gyromagnetic ratio (107) Quadrupole Spin (1H ¼ 1.00) (13C ¼ 1.00) (rad s1 T1) moment Q (fm2)

67 Zn (111Cd)b 113 Cd 199 Hg 201 Hgf

5/2 1/2 1/2 1/2 3/2

4.04 12.80 12.22 16.87 13.18

1.18  104 1.24  103 1.35  103 1.00  103 1.97  104

0.692 7.27 7.94 5.89 1.16

1.676688 5.6983131 5.9609155 4.8457916 1.788769

15.0 – – – 38.6

X (frequency, MHz;

H ¼ 100.0000 MHz, 2.3488 T)

1

Reference sample

6.256803 21.215480 22.193175 17.910822 6.611583

Zn(NO3)2 (aq) Cd(ClO4)2 (aq)c HgCl2 (d 1550 in D2O)d,e

a

Unless noted, the isotopes are stable. The natural abundances are based on the NIST data.25 Cd26 in parenthesis is considered to be the less favorable of the element for NMR. c CdMe2 (neat) is the reference by IUPAC.26 Most publications have used Cd(ClO4)2 at d 0.00 as a reference.1,2 d The highly toxic HgMe2 (neat) is the reference for 199Hg and 201Hg NMR by IUPAC.26 The high toxicity of HgMe2 means its direct use should be strongly discouraged.26,27 e In addition to HgCl2 in D2O, Hg(ClO4)2 in H2O at d 2253 was also used as a secondary reference.1 f199 Hg is a useful spin 1/2 nuclide for NMR.26 b111

reactions of zincate with dimeric silicate and cyclic silicate trimer, forming (HO)(SiO2)O(SiO2)OZn(OH)36 and (HO)3Zn(SiO3)37, respectively. Aluminate and zincate, when present together, competed roughly equally for a deficiency of silicate to form (HO)3ZnOSiO2(OH)4 and (HO)3AlOSiO2(OH)3 which exchanged the 29Si moiety at a fast but measurable rate.691 High-energy density aqueous redox flow battery was reported, which was based on the use of Zn/Zn2þ and I/I3 redox couples (Overall reaction: I3 þ Zn # 3I þ Zn2þ, E ¼ 1.2986 V).692 Unlike traditional batteries, such flow-based energy storage systems separated the energy storage and power generation by storing the electro-active species in externally flowing electrolytes (i.e., anolyte and catholyte), while maintaining the redox reactions at the electrode surface.692 Such a design allowed the redox flow batteries to scale the power and/or energy independently, which was a characteristic advantage. In the aqueous redox flow battery here, Zn(H2O)5(I3)þ, a Zn(II)-polyiodide electrolyte was identified and found to initiate precipitation in the catholyte.692 67Zn NMR studies were performed on aqueous ZnNO3 and ZnI2 solutions at different Zn(II) concentrations as well as the pristine and fully charged ZnI2 catholytes with and without EtOH. The work showed that, when EtOH was present in the aqueous electrolyte solution, Zn(II) ions form Zn(H2O)5(EtOH)2þ which might partially hinder the formation of Zn(H2O)5(I3)þ. In other words, the I3 dissociation and subsequent precipitation reaction might be mitigated due to the Zn(II)eEtOH complexation.692 DFT quantum chemical investigation was performed on 67Zn NMR shifts and electric field gradients in Zn(II) complexes.693 The calculated shifts were compared with those from experiments. NMR studies of a atoms of ligands in Zn(II) complexes were also conducted. The crystal structure of [MeSi(SiMe2N(ptol))3Sn]2Zn (134) is different from its group 12 analogs [MeSi(SiMe2N(p-tol))3Sn]2M (M ¼ Cd, Hg) in that the Zn ion formed an asymmetrical complex where there was a ZneN bond and the SneZneSn interaction.694 The irregularity of the structure was also shown in 119Sn NMR with peaks at d 153.5 and 91.2.694 The binding of the Zn(II) ion to the dodecamer [d(GGTACCGGTACC)]2 was investigated via 1He15N HMBC.695

( 134 ) For 77Se NMR of (PPh4)2[Zn(C3Se5)2] with a diselenolate ligand,626 see Section 9.21.12.2.

9.21.11.2 Cadmium complexes Cd NMR is relatively easy to obtain, given that both 111Cd and 113Cd are spin 1/2 nuclides with rather high X (and thus frequencies) and receptivities (Table 16). Both 111Cd and 113Cd NMR of inorganic compounds have been reported, although the latter is preferred. Unless noted (in Ref. 696), the discussion below is based on Cd(ClO4)2 in D2O as a reference for Cd NMR (Table 16). Effects of solvents such as py, MeCN, MeOH, EtOH on the 113Cd shift of Cd(ClO4)2 (in comparison to that in D2O) were probed by 113 Cd NMR.697

712

Solution NMR of transition metal complexes

113

Cd chemical shifts are very sensitive to the environments that the metal ions are in, including donor atoms, coordination number, geometry and solvent. In CdeN coordination chemistry, 113Cd NMR spectra were used to study the reactions of 15Nenriched KNCS with Cd(OTf)2 in aqueous solution of acetone and HCF2Cl (Freon-22) at 110  C, showing Cd(H2O)3(NCS)þ, Cd(H2O)2(NCS)2, Cd(H2O)(NCS)3, and Cd(NCS)42.698 Each NCS substitution led to a deshielded shift of the 113Cd resonance in the d 19–190 range. 15N shifts of the species were in the d 39 to 60 range. 1J113Cd-15N decreased continuously from 251 Hz for Cd(H2O)3(NCS)þ to 219 Hz for Cd(NCS)42.698 [Cd(5,50 -diamino-2,20 -bipyridine)3]Cl2 with a bipy-analog ligand (135) was characterized by 113Cd NMR, showing the resonance at d 254.699 Exchanges of CdNO3 with benzimidazole (136) were studied by 113Cd NMR.700

( 135 )

( 136 )

( 137 )

( 138 )

For Cd(II) complexes with mixed N,X ligands, TpPhCdeO2CMe with a hydrotris(3-phenylpyrazol-1-yl)borate (TpPh ¼ 137) ligand, was a catalyst for the formation of polycarbonates from epoxides and CO2.701 Binding of the epoxides to the complex was probed by 113Cd NMR, as the activation of an epoxide by interaction with the N3,O Cd(II) center was a key step in the copolymerization.701 [Cd(m-F)(m-dpz)2Cd](BF4)3 [dpz ¼ m-([CH(3,5-dimethyl-1-pz)2]2C6H4) (138)] with two bridging tetra-dentate N4 ligands and a bridging F ion showed 113Cd shift at d 25.1 with 1J113CdF ¼ 28 Hz.702 For chemistry of Cd(II) complexes with O-, S- or Se-containing ligands, complexes with mono- and di-carboxylic acids in aqueous solution were investigated using 113Cd NMR.703 For mono-carboxylic acids such as HCO2H, CH3CO2H, and PhCO2H, a single averaged chemical shift was observed even at reduced temperature from rapid exchange in solution. In case of dicarboxylic acids HO2C(CH2)nCO2H (n ¼ 0–3), the 113Cd nuclei showed increasing shielding with larger n.703 For (RS)Cd(mSR)2Cd(SR) [R ¼ Si(OBut)3] with mixed S,O-ligands, in which one of O atoms in each Si(OBut)3 group formed a dative bond with the Cd(II) ion, 113Cd shift was observed at d 402.704 In Cd(II) organometallic chemistry, several Tp*CdeR complexes with different alkyl or aryl ligands were studied by 113Cd NMR, including R ¼ Me (d 437.6), Et (d 382.9), Prn (d 386.2), Pri (d 338.6), and Ph (d 359.8).705 The rather large shift differences between Tp*CdeMe and Tp*CdeEt as well as between Tp*CdePrn and Tp*CdePri were attributed to the b effect, i.e., adding a b-C to the alkyl ligands.705 Perfluoro-alkyl and aryl complexes Cd(CF3)2, Cd(C2F5)2, Cd(n-C3F7)2, Cd(i-C3F7)2, and Cd(C6F5)2 as diglyme adducts, were probed by 113Cd NMR, giving 113Cd shifts (referenced to CdMe2) for Cd(CF3)2 (d 489.7), Cd(C2F5)2 (d 432.4), Cd(n-C3F7)2 (d 439.1), Cd(i-C3F7)2 (d 288.3), and Cd(C6F5)2 (d 290.0).696 The shift differences between Cd(CF3)2 and Cd(C2F5)2 as well as between Cd(n-C3F7)2 and Cd(i-C3F7)2 were probably also the result of the b effect,696 as in Tp*CdeR.705 113 Cd NMR was used to study Cd(II) bio-inorganic chemistry,706–718 including proteins706–712,718 and enzymes.713,714 A large range of 113Cd shifts was observed for 113Cd-substituted metalloproteins from d 100 for Cd(II) with octahedral O ligands to d 760 ppm for Cd(II) with tetrahedral S ligands.706 For the tetrahedral S sites in proteins such as rubredoxin and desulforedoxin, 113 Cd shifts were ca. d 720–745. New 113Cd shifts for 113Cd-substituted, overexpressed and mutated homologous desulforedoxinlike Fe(S-Cys)4 proteins, were obtained to show a correlation between the 113Cd shifts and structures at the metal sites.706 1He113Cd correlation and 1He1H COSY NMR studies established two distinct protein domains in blue crab Callinectes sapidus metallothionein-I.708 Metallothioneins are small, cysteine-rich proteins found throughout Nature.709 They are able to bind different metals at several stoichiometric ratios, making the family of the proteins important for essential metal (e.g., Zn2þ and Cuþ) homeostasis, metal storage, metal donation to nascent metalloenzymes and heavy metal detoxification.709 In addition, metallothioneins are considered to protect cells against oxidative stress with its 20 cysteines. Investigations of the mechanistic details of metal binding to mammalian metallothioneins, including the use of 113Cd NMR, were reviewed in 2018.709 For Zn(II)-containing Bud31p, a 157residue yeast protein containing an unusual Zn3Cys9 cluster, 113Cd NMR experiments with 113Cd-substituted samples were performed to reveal the unusual metal cluster in the solution structure of the yeast splicing protein Bud31p.712 Cd(II) derivatives of ovotransferrin and human serum transferrin were investigated by 113Cd and 13C NMR.718 113Cd NMR was also used to observe directly the exchange dynamics of water at a Cd(II) binding site within two de novo designed metalloprotein constructs, showing the residence time of the Cd(II)-bound water molecule was tens of nanoseconds at 20  C in both proteins.711 In addition to the proteins and enzymes, Cd(II) bindings to dinucleosides and DNA containing modified nucleosides 4-thio-20 -deoxyuridine (s4dU) and 4-thio-20 -deoxythymidine (s4dT) as metal ion binding sites was probed by 113Cd NMR.716 In computational studies of 113Cd NMR, ab initio and DFT methods were reproduced to within 50 ppm of the shifts for Cd(II)substituted metal ion containing proteins.719 113Cd shifts were also calculated using Hartree-Fock and DFT methods for Cd(II) complexes, such as CdMe2, CdEt2, CdMeEt, Cd(NO3)2$4H2O, and Cd(O2CCH3)2$2H2O.720

Solution NMR of transition metal complexes

713

For NMR of ligands, 113Cd NMR of [MeSi[SiMe2N(p-tol)]3Sn]2Cd (139) showed two signals (d 310 and 201), and the 119Sn NMR showed signals at d 142.7 and 22.2.694 The crystal structure showed it to be a symmetric molecule. 1H ROESY and VT 1 H experiments were conducted to study the dynamic exchange between two isomers of 139 (Fig. 12).694 The asymmetric isomer is an analog of the Zn(II) complex 134. Tetrahedrally coordinated (Et3NH)6[Cd(SnB11H11)4] (140) was synthesized via the reaction of stanna-closo-dodecaborate with CdBr2 and analyzed via 113Cd (d 42), 119Sn (d 377) and 11B (d 13.8) NMR.721

( 140 ) In order to elucidate weaker binding sites for Mg(II) in an RNA sample (D1kz), Cd(II) was used in order to more easily study these sites in D1kz by NMR, as discussed earlier in the section on cobalt complexes.500 15N-labeled and/or 13C-labeled D1kz samples were titrated with Cd(ClO4)2 or 113Cd(NO3)2.500 1H, 1He15N HSQC, 31P, 113Cd, and 1He13C HSQC NMR spectra were studied after each addition of the metal complex.500

9.21.11.3 Mercury complexes Hg [spin 1/2, a natural abundance of 16.87%, relative receptivity DC ¼ 5.89 with respect to 13C, and X ¼ 17.910822%] is a good nuclide for NMR. There are three major features of 199Hg NMR of inorganic complexes: (a) Chemical exchange often faster than Cd(II) complexes; (b) Large chemical shift anisotropies; (c) Large coupling constants.1 199 Hg NMR was the subject of a review in 1992.722 Using multinuclear NMR to probe speciation of Hg complexes was reviewed in 2006.723 In Hg(II) coordination chemistry, solvation of Hg(ClO4)2 in H2O, dmso, HC(]S)NMe2, and liquid NH3 was studied by 199Hg NMR.724 The work showing a pronounced dependence on the coordination number of the Hg(II) ion with 199Hg shifts of >1200 ppm between tetrahedral and octahedral complexes as well as electron donor properties of the solvents. The 199Hg spinlattice relaxation times in the solvates were measured in several applied magnetic fields, concentrations, temperatures, and isotope substitutions.724 Additional studies of solvation of Hg(ClO4)2 in liquid NH3 and aqueous ammonia solution (when the molar ratio NH3:Hg(II) > 4) showed the formation of [Hg(NH3)4](ClO4)2, which was characterized by single-crystal diffraction.725,726 When HgCl2 or HgBr2 was dissolved in liquid NH3, Hg(NH3)42þ [d 1065 to 1163 relative to HgMe2 (at d ¼ 0) or d 1188 to 1090 relative to Hg(ClO4)2 (at d ¼ 0)], although 199Hg NMR indicated weak Hg(II) to Br association.726 In liquid NH3, HgI2 formed Hg(NH3)2I2 at d 1902 relative to HgMe2 [d 351 relative to Hg(ClO4)2] with the Raman m(IeHgeI) symmetric stretching frequency at 132 cm1.726 199Hg NMR shifts of the stable HgCln2n (n ¼ 0–4) were determined in 50 mM aqueous Hg(II) solution as a function of the Cl concentration.727 HgCl2[N,N0 -ButNSe(m-NBut)2SeNBut] was obtained from the [2 þ 2] cyclodimerization of tbutylselenium diimide SeIV(]NBut)2 with HgCl2, which was characterized by 199Hg (d 1190) and 77Se (d 1093) NMR.728 Linear 199

Fig. 12

Dynamic exchange between two isomers of 139.

714

Solution NMR of transition metal complexes

complex Hg[N(SiMe3)2]2 was studied by 199Hg and 15N NMR, including their spin-lattice relaxation times T1 at 243–403 K, 14N quadrupolar cross-correlation coefficient, and J199Hg-15N ¼ 316.2 Hz.729 Demethylation of (MeO)3P]O by (NMe4)2[Hg(SPh)4] and (NBun4)[Hg(SPh)3] gave MeSPh, (MeO)2P(]O)2, and Hg(SPh)3 from (NMe4)2[Hg(SPh)4] and MeSPh and Hg(SPh)2[(MeO)2P(]O)2], respectively.730 199Hg was used to characterize the reaction mixtures by comparing with 199Hg shifts of (NMe4)2[Hg(SPh)4] (d 421) and (NBun4)[Hg(SPh)3] (d 354) in the identification of the products.730 A series Hg(II) complexes containing thiacrown and related aza and mixed thia/aza macrocycles were characterized by 199Hg NMR.731 The 199 Hg shifts of these complexes are listed in Table 17. In Hg(II) organometallic chemistry, dependence of 199Hg NMR spectra of a variety of polyfluoroaryl complexes, such as Hg(C6F5)2 (d 851), Hg(4-CF3-C6F4)2 (d 915), Hg(4-MeO-C6F4)2 (d 811), Hg(4-F-C6H4)2 (d 734), C6F5HgEt (d 604), (4-F-C6H4)HgEt (d 536), on solvents (shifts listed above in CH2Cl2), concentrations, temperatures, and ligands was studied.732 199 Hg NMR spectra of substituted vinyl Hg(II) halides, such as ClHC]CHHgCl (Z, d 1141; E, d 1160), PhHC]CHHgBr (Z, d 1018; E, d 1200), and MeHC]CHHgBr (Z, d 1056; E, d 1131), showed that shifts of the Z isomers were deshielded from those of the E isomers.733 Experimental (199Hg and 13C NMR) and theoretical studies of Hg(C^CPh)2 were conducted to obtain shielding and indirect spin-spin coupling tensors in the presence of a heavy atom.734 199Hg and 13C spin-lattice relaxation times were studied to probe solution dynamics of Hg(C^CPh)2 and shielding anisotropy of its acetylenic C and Hg nuclides.735 For thiosulfatemercuriomethanates Nan[CH4n(HgS2O3)n] (1  n  4), their 199Hg shifts became gradually more deshielded with increasing n: n ¼ 1, d 677; n ¼ 2, d 577; n ¼ 3, d 496; n ¼ 4, d 453.736 A series of HgeMo complexes XeHgeMoCp(CO)2(PAr3) (X ¼ F, Cl, Me, OMe),737 Hg[MoCp(CO)2(PAr3)]2,737,738 derivatives with substituted cyclopentadienyl ligands XeHgeMoCp#(CO)3739 and Hg[MoCp#(CO)3]2739 (Cp# ¼ C5HMe2Ph2) were studied by 199Hg NMR. 199Hg shits of selected complexes include the following: (a) Hg(I) compounds CleHgeMoCp(CO)2[P(4CleC6H4)3] (d 523),737 IeHgeMoCp(CO)2(PPh3) (d 921),737 XeHgeMoCp#(CO)3 (X ¼ Cl, d 644; X ¼ Br, d 827; X ¼ I, 1169);739 (b) Hg(0) compounds Hg[MoCp(CO)3]2 (d 235.3)738 and Hg[MoCp#(CO)3]2 (d 98) with MoeHgeMo bonds.739 In Hg bioinorganic chemistry, 199Hg NMR was used probe Hg(II) binding with L-cysteine,740 glutathione,741 2-(a-hydroxybenzyl) thiamin pyrophosphate (Hhbtp) as a model for metal binding in thiamin enzymes,715 and the metal sites in Hg(II)mediated thymine (T)–thymine base pair,742 blue copper proteins,743 and the metal receptor site in MerR and its protein-DNA complex.744 Hg(II) complexes with L-cysteine (H2Cys) in aqueous alkaline solutions were structurally characterized by extended X-ray absorption fine structure (EXAFS) spectroscopy,740 aided by 199Hg NMR and Raman results. In the reaction of Kþ salt of 2-(a-hydroxy-benzyl) thiamin pyrophosphate, Kþ(hbtp), with HgCl2, the product was K2[Hg(hbtp)2Cl2] showing 199Hg shift at d 804.715 In the reaction of Hg(II) ions with 15N-labeled thymidine (T), one of the four nucleobases in the nucleic acid of DNA, 199Hg and 15N NMR studies indicated that the product was linear TeHgeT, giving 199Hg d 1784, 15N d 184, and 1 J199Hg-15N ¼ 1050 Hz.742 199 Hg NMR spectra of the 199Hg-substituted blue copper proteins exhibited shifts of d 749 for 199Hg-plastocyanin and d 884 199 for Hg-azurin.743 For the metal receptor site in MerR and its protein-DNA complex,744 structural insights were provided by 199Hg NMR. The 1- and 2-D NMR data showed a trigonal planar Hg-thiolate coordination environment consisting only of Cys side chains.744 In theoretical studies, microsolvation of (HgMe)þ in water, including structures, energies, bonding and 199Hg, 13C and 17O NMR constants (chemical shifts and coupling constants), was investigated by Hartree–Fock (HF) and second-order perturbation theory (MP2) calculations within the scalar and full relativistic frames.745

Table 17

199

Hg NMR shifts of Hg(II) thiacrown and related aza and mixed thia/aza complexes.731

Complexes

199

[Hg(9S3)2](ClO4)2 (9S3 ¼ 1,4,7-trithiacyclonane) [Hg(10S3)2](ClO4)2 (10S3 ¼ 1,4,7-trithiacyclodecane) [Hg(12S3)2](ClO4)2 (12S3 ¼ 1,5,9-trithiacyclododecane) [Hg(14S4)](ClO4)2 (14S4 ¼ 1,4,8,11tetrathiacyclotetradecane) [Hg(16S4)](ClO4)2 (16S4 ¼ 1,5,9,13tetrathiacyclohexadecane) [Hg(15S5)](ClO4)2 (15S5 ¼ 1,4,7,10,13pentathiacyclopentadecane) [Hg(18S6)](ClO4)2 (18S6 ¼ 1,4,7,10,13,16hexathiacyclooctadecane) [Hg(18S4N2)](PF6)2 (18S4N2 ¼ 1,4,10,13-tetrathia-7,16diazacyclooctadecane) [Hg(9N3)2](ClO4)2 (9N3 ¼ 1,4,7-triazacyclononane)

275 598 795 827

Hg shifts (d)

1120 484 Not observed 737 and 816; Two different diastereoisomers from the relative orientations of the two H (in NeH) atoms 948 and 1313; The solution is believed to be a mixture of [Hg(9N3)]2þ and [Hg(9N3)2]2þ.

Solution NMR of transition metal complexes

715

NMR studies of a atoms of ligands in Hg complexes were also conducted. There was only one signal in both the 199Hg (d 267.8) and 119Sn (d 266.2) NMR spectra of {MeSi[SiMe2N(p-tol)]3Sn}2Hg, an analog of the Cd(II) complex 139 (Fig. 12 in Section 9.21.11.2), showing that this complex was a symmetric with respect to the Hg(II) ion and it did not isomerize as its Cd(II) analog.694 The interaction between the oligonucleotide [d(CGCGAATTCGCG)]2 and Hg(II) was studied via several NMR methods including 1He15N HMQC.746 The HMQC studies confirmed that the Hg(II) ions interfered with the AT tract of the oligonucleotide.746 Hg(II)-mediated TeT (thymine-thymine) pairings were studied via 1-D 15N NMR and 2-D 1He15N HSQC with J-coupling (2J15N–15N) of 2.4 Hz for the NeHgeN moiety.747 The tetrahedrally coordinated (Me3NH)6[Hg(SnB11H11)4] was synthesized via the reaction of stanna-closo-dodecaborate with Hg2Cl2 and analyzed via 199Hg (d 630), 119Sn (d 320) and 11B (d 14.4) NMR.721 This complex and its Cd analog (Et3NH)6[Cd(SnB11H11)4] (140), discussed in Section 9.21.11.2, were the first examples of coordination complexes with this stanna-closo-dodecaborate ligand and group 12 metals.721

9.21.12 NMR properties shared by complexes of more than two transition metals. Experimental and theoretical/computational studies NMR properties shared by complexes of two transition metals are discussed in their respective sections.

9.21.12.1 NMR of metals in the complexes We found that NMR chemical shifts of d0 transition metal compounds showed the following trends:285 (1) For single-bonded ligands such as MeH, MeCR3, M)NR3, MeSiR3 and M)PR3, 1H, 13C, 15N, 29Si and 31P shifts of these a atoms in the complexes of both first- and third-row transition metals are typically more deshielded than those of second-row analogs with a “V-shape” (Trend 1). (2) For multiple-bonded ligands including those with d-p p bonds, such as M¼CHR, M^CR, M¼NR, M¼O and M ) F, 13C, 15N, 17O and 19F shifts of the a atoms in the complexes of first-, second- and third-row transition metals become 

consecutively more shielded (Trend 2).285 NMR shifts of lanthanum(III) complexes help interpret Trend 1 in Group 3 congeners. Scandide (d-block) and lanthanide (f-block) contractions and relativistic effects were believed to contribute to the NMR shifts, leading to the observed trends. Comparisons were made with NMR chemical shifts of dn complexes and organic compounds. Since many chemical properties of the second- and third-row congeners such as Zr and Hf are similar, as a result of lanthanide contraction, the NMR chemical shifts were a rare property to distinguish compounds of the otherwise nearly identical congeners. Our narrative interpretations of the trends were provided.285 Substituent influence on reported 51V, 55Mn, 57Fe, 59Co, 61Ni, 95Mo, 103Rh, 183W, 187Os and 195Pt NMR shifts (d) and coupling constants JM-P (M ¼ Mn, Fe, Mo, Rh, W, Os) in organometallic complexes were analyzed, showing shifts depended on the inductive, resonance, and polarizability effects of substituents.1,748 The role of polarization effect on the NMR of heavy nuclides (51V, 55Mn, 57 Fe, 95Mo, 103Rh, 187Os and 195Pt) was reviewed.749 Another study was conducted on the polarizability effect in transition metal CO complexes.750 NMR peak line widths of quadrupolar nuclides 14N, 53Cr, 59Co, 91Zr and 95Mo in supercritical solvents and low-viscosity liquefied gases were smaller than in ambient solvents.249 For example, both 53Cr and 14N (spin 1, natural abundance ¼ 99.636%, Q ¼ 2.044 fm2, relative sensitivity ¼ 1.00  103, receptivity ¼ 5.90, gyromagnetic ratio ¼ 1.9337792  107 rad T1 s1, X ¼ 7.226317%)25,26 are quadrupolar nuclides with broad NMR peaks. 53Cr and 14N NMR of Cr(CO)5(CNBut) and Cr(CO)4(CNBut)2 in ambient acetone-d6, pressurized liquid CO2 or supercritical CO2 were compared.249 For Cr(CO)5(CNBut), 53Cr shifts were d 17.9, 15.7 and 36.1, respectively, in the three media with peak width reduced from 90 Hz in acetone-d6 to 35 Hz in the two CO2 media. Its 14N shifts were d 171.4, 176.1 and 175.6, respectively, in the three media.249 For Cr(CO)4(CNBut)2, 53Cr shifts were d 60.4 and 52.4 in acetone-d6 and liquid CO2, respectively, with peak width reduced from 44 Hz in the former to 34 Hz in the latter. Its 14N shifts were d 174.5 and 178.6 in acetone-d6 and liquid CO2, respectively.249 The studies here tested the reduction of quadrupolar relaxation rates in solvents with low viscosity such as supercritical fluids. In another example, 91Zr peak width of Cp2ZrCl2 in thf-containing supercritical CO2 (CO2:thf ¼ 93:7; v/v) at 323 K was found to be 210 Hz, a significant decrease from 375 Hz in ambient thf at 296 K.249 The addition of a small amount of acetone, thf, and CH2Cl2 increased the solubilities.

9.21.12.2 NMR of ligand nuclides in the complexes Multinuclear NMR was demonstrated to be a good tool to characterize complexes with s-silane and s-borane ligands, distinguishing them from the corresponding hydride silyl or hydride boryl oxidative addition products.139 The studies in the area were reviewed in 2008.139 Several heterometallic cluster complexes with Mo and Te, including (Cp*Mo)2B4TeH5Cl and (Cp*Mo)2B4(m3-OEt)TeH3Cl, were characterized via 11B NMR.751 119 Sn NMR was used to characterize transition metal complexes LnMeSnR2 with terminal stannylene ligands, including (OC)5WSn(OSiPh3)2 (d 303, 1J119Sn-W ¼ 1660 Hz), MeSi[SiMe2N(p-tolyl)]3SneRh(PEt3)(cod) (d 140.5, 1J119SnRh ¼ 846 Hz), and (Ph3P)3PteSn(acac)2 (d 601, J119Sn-Pt ¼ 1.289  104 Hz).752 The research in the area was reviewed in

716

Solution NMR of transition metal complexes

2009.752 119Sn NMR was also used to characterize CpM(CO)3[Sn(C6H3-2,6-Mes2)] (Mes ¼ 2,4,6-Me3-C6H2; M ¼ Cr, Mo, W), CpM(CO)3[Sn(C6H3-2,6-Trip2)] (Trip ¼ 2,4,6-Pri3-C6H2; M ¼ Cr, Mo, W), and (h5-1,3-ButC6H3)Mo[Sn(C6H2-2,6-Trip2)] (d 2543).753 15 N coordination shifts in transition metal complexes with N-containing heterocycle ligands (azines, azoles, and azoloazines) were reviewed and discussed with respect to the metal ions and the donor atoms in trans position with respect to the 15N atom.754 Here, the coordination shifts are the differences between 15N shifts of the N atoms in the complex and the free ligand [D(15N) ¼ dcomplex  dligand].754 14 N and 15N NMR studies of imide ligands were conducted for 37 Ta, Mo, W, Re and Os complexes, including Ru3(mH)2(m3-15NH)(CO)9 (d 297.7), trans-TaCl(15NPh)(PMe3)4 (d 76.6), W(NBut)2(OBut)2 (d 11), [Mo(15NH)-(S2CNEt2)3]Cl (d 40.0), trans-[ReCl(15NH)(dppe)2]Cl2 (d 67.1), and Os(NBut)4 (d 155.6).755 The studies showed that 14N and 15N NMR spectroscopy was a probe of bonding, bending and fluxionality of the imido ligands.755 Reviews in 2008756 and 2013757 together covered the 15N NMR and the 31P NMR of over 300 complexes. These complexes contain metal ions such as Ni(0), Pd(II), and Au(III) with N- or P-containing heterocyclic ligands such as pyridine, 1,10-phenanthroline, or phosphorin.757 Line broadening in variabletemperature and -pressure 14N, 13C, and 1H NMR spectra was used to study the exchange of bidentate ethylenediamine (en) ligands in Co(II), Fe(II), and Mn(II) complexes.758 Further studies of solvent exchange of N-containing ligands 1,3-propanediamine (pa) and n-propylamine (tn) were conducted with variable-temperature 14N NMR, and the results were compared with the data from the en exchange studies.759 The rate constants for these exchanges increase in the order of en < tn < pa for each metal ion. For example, the rate constants (k298) for Mn(II) are 1.7  106 s1 for en, 2.5  106 s1 for tn, and 3.7  107 s1 for pa.758,759 1 He15N HSQC and super-WEFT 1H NMR (WEFT ¼ water elimination Fourier transform), a method to suppress water signals, were used to probe the coordination of Co(II), Ni(II), and Zn(II) ions to a section of DNase domain of colicin E9.760 The interactions of Ag(I)- and Cd(II)-substituted amicyanin with the periplasmic enzyme MADH (methylamine dehydrogenase) were investigated via several NMR techniques including 1He15N HSQC and 15N-decoupled TOCSY.761 15N and 19F NMR spectroscopies as well as DFT calculations were used to investigate the linearity of the MeNO section of the [RuF5NO]2 anion by comparing the splitting patters and line widths of the signals of the 15N-enriched and nonenriched samples of [RuF5NO]2.762 The data for the Ru compound was compared also to the 13C and 15N NMR of the structurally similar [Fe(CN)5NO]2 (15N- and 13C-enriched) anion.762 17O NMR was also used to probe the kinetics of the proton exchange on dioxytetracyanometalate complexes [MO2(CN)4](nþ2) (M ¼ Mo, W, Tc, Re; n ¼ 0, 1, 2)763 as well as of oxygen exchange on di- and monoprotonated complexes [MO(OH2)(CN)4]n (M ¼ Mo, W, Tc, Re; n ¼ 1, 2) and [MO(OH)(CN)4](nþ1) (M ¼ Mo, W, Tc, Re; n ¼ 1,2).764 17O NMR has also been used to study water and other oxygen-containing solvent exchanges on metal compounds such as aquapentakis(amine)metal(III) complexes,765 e.g., [Co(CH2NH2)(H2O)]3þ, and paramagnetic aminopolycarbonate complexes, e.g., [Fe(TMDTA)]2 (TMDTA ¼ trimethylenediaminetetraacetate).396 Water and Hþ exchange processes on metal ions, studied by 17O NMR, were the subject of a 2005 review.766 17O NMR spectrum of an 17O-enriched sample of PW11O397 and results from other techniques “indicate that previously assigned terminal Pt-oxo and Au-oxo complexes are in fact cocrystals of the all-tungsten structural analogues with noble metal cations, while the Pd-oxo complex is a disordered Pd(II)-substituted polyoxometalate.”767 In other words, the oxo wall768 stands. 17 O NMR shifts of oxo metalloporphyrin complexes of Ti, Cr, and Ru, such as M(TMP)(]O) (H2TMP ¼ tetramesitylporphyrin) were found to correlate with the strength of the M¼O bonds.137 The fluxional behaviors of [(Rh(cod))2(V4O12)]2 and [(Rh(cod))(V4O12)]3 (cod ¼ h4-1,5-cyclooctadiene) were studied via 51V and 103Rh NMR along with variable-temperature 17O NMR.769 Carbonyl complexes (1,3,5-Me3C6H3)Cr(CO)3, (1,3,5-Me3C6H3)W(CO)3, [(1,3,5-Me3C6H3)Mn(CO)3]BF4, (1,3,5-Me3C6H3)Co4(CO)9, (1,3,5-Me3C6H3)Ru6C(CO)14, and Ru6C(CO)17 show 17O shifts in the range of about d 340–400.770 Since the 17O signals could not be observed for all the complexes in a single solvent, various solvents such as CH3CN, CDCl3, and (CD3)2CO were utilized.770 33 S NMR was used to characterize several bidentate thiometallate complexes (NEt4)2[MS4] (M ¼ Mo, d 373; M ¼ W, d 183) and (NH4)2[MS4] (M ¼ Mo, d 344; M ¼ W, d 149).771 33S NMR was also used to study heterometallic complexes (NPrn4)2[(CN)CuS2MS2] (M ¼ Mo, d 445; M ¼ W, d 248), (NPrn4)2[(CN)AgS2MoS2] (M ¼ Mo, d 257; M ¼ W, d 106), (Prn4N)2[(CN)-CuS2MoS2Cu(CN)] (M ¼ Mo, d 139; M ¼ W, d 16), and (NPrn4)2[(PhS)CuS2MoS2] (d 436).771 77 Se NMR was used to characterize several complexes with the 1,3-diselenole-2-selone-4,5-diselenolate ligand [C3Se52 (141)], including (PPh4)2[Zn(C3Se5)2] (d Se1, 105; Se2, 1067; Se3, 1134), (NBun4)2[Pt(C3Se5)2] (d Se1, 420; Se2, 1116; Se3, 1227), and (NBun4)[Au(C3Se5)2] (d Se1, 729; Se2, 1121; Se3, 1330).626

( 141 )

Solution NMR of transition metal complexes

717

9.21.12.3 Theoretical and computational studies of NMR Several reviews were published on calculations of transition metal NMR parameters,772–775 including the DFT methods to calculate NMR shifts,772,773 methodology and computations of nuclear shielding and spin–spin coupling constants,774 and developments of theoretical methods between 1999 and 2004.775 1 H NMR shifts of agostic H atoms in planar d8 transition metal complexes were in a rather large range of 5 to 10 ppm.776 When the agostic H atom points to a local Lewis acidic center at the metal, the 1H NMR peak is shifted to be more shielded than that of the complex where the H atom is opposing a local charge concentration at the metal. The origin of the relationship was studied by a topological method.776 11 B NMR of (Cp*M)2B5H9 (M ¼ Cr, Mo, W) showed shifts of the two types of B atoms directly bound to the metal atoms experienced a large, more shielded shift going from Cr to Mo to W, whereas the shifts for the B atoms connected to the metal atoms via MeHeB bridge bonds were invariant.777 Molecular orbital analysis of the trend traced the origin to two high-lying filled MOs and two low-lying unfilled MOs, both with M and B character. The energy differences of these sets of MOs correlated well with the observed chemical shifts.777 DFT computational studies of structures and properties of transition metal dicarbollide complexes were conducted and reproduced the 11B NMR shifts reasonably well.778 Thermal effects and vibrational corrections were studied in the calculations of NMR shifts of 49Ti, 51V, 55Mn, and 57Fe shifts.779

9.21.13 Advanced NMR techniques and methods This section provides an overview of advanced solution NMR techniques and methods used to characterize transition metal compounds.

9.21.13.1 2-D NMR The 2-D NMR methods were discussed in a recent book by Lambert.4 The use of 2-D NMR to study supramolecular complexes was reviewed in 2007.780 2-D NMR methods, in particular, inverse detection such as HMQC, HSQC, or HMBC to increase the sensitivity of the nuclides, indirectly determine chemical shifts of, e.g., 57Fe359–361 and 187Os362,363 (Section 9.21.7), 183W (Section 9.21.5.3), and 103Rh (Section 9.21.8.2). 1He15N HMBC was also used to obtain 15N (spin 1/2) NMR shifts of complexes at the natural abundance of 0.364%.240–243,361,521,781 Often, different versions of the techniques such as gradient-selected gHMQC, gHSQC,781 and gHMBC240–243,361,521 were used. In addition to obtaining NMR of the less sensitive nuclides, HMQC,4 HSQC,4 and HMBC4 such as 1He13C spectra were used to assign 1-D 1H and 13C spectra and structures of the complexes.6,154,781–784 Homonuclear 1He1H COSY (Correlated Spectroscopy)4,6,781,785 and 1He1H TOCSY (Total Correlated Spectroscopy)781,785 were also used to assign spectra and structures of the complexes, giving through-bond correlations via spin-spin coupling in the molecules. When studying H atoms that are close to each other in space but are not bound, 1He1H NOESY (Nuclear Overhauser Effect Spectroscopy)4,786 was used to study the signals from the through-space correlations via spin-lattice relaxation,781,787 including solution structures of ion pairs such as the through-space 1H/1H interactions between the cation and anion in trans[Ru(CO)(en)(PMe3)2(COMe)]BPh4.788 NOESY could be used to detect chemical and conformational exchanges,780,789–792 which is also called EXSY when it is used for this purpose.780,789,790 13 Ce13C NOESY was demonstrated to be an attractive alternative for studying large macromolecules.793 Direct 13C detection provides a valuable alternative to 1H detection to overcome fast relaxation because of its smaller magnetic moment.793 Applications of the 13Ce13C NOESY for studying metalloproteins were recently reviewed,794 including advantages and drawbacks of the method as a function of the molecular size of the metalloproteins. It provided information on the presence/absence of multiple conformations in slow or semi-slow exchange on the NMR chemical shift time scale for amino acid side chains. 13Ce13C NOESY was the gold standard for the observation of NMR signals in the 480 kDa ferritin nanocage and for monitoring its interaction with Fe ions in the protein. When the protein size was decreased, the technique gradually lost its importance as a tool for the detection of the complete spin pattern of the amino acid side chains, as exemplified by Ni-dependent regulatory protein, NikR (molecular mass of the homotetramer 80 kDa). In very small proteins, such as mitochondrial cytochrome c (12.3 kDa), only cross peaks between adjacent 13C nuclei were detected, which was used to assign the 13C core resonances of the porphyrin in a uniformly enriched heme.794 ROESY4,795 is a 2-D NMR spectroscopy similar to NOESY. In NOESY, cross relaxation from an initial state of z-magnetization is observed. In ROESY, equilibrium magnetization is rotated onto the x axis and then locked so it cannot process. ROESY is particularly suitable for medium size molecules (molecular weight around 700–1200) whose nuclear Overhauser effect is too weak to be detectable. HOESY (Heteronuclear Overhauser Effect Spectroscopy), such as 1He19F HOESY,788,796–798 was used to characterize solution structures of ion pairs such as the through-space 1H/19F interactions between peripheral H atoms on the cation and Fcontaining anion in [Au(PPh3)2]BF4.796

718

Solution NMR of transition metal complexes

9.21.13.2 PGSE and DOSY Pulsed-Field Gradient Spin-Echo (PGSE) and Diffusion-Ordered Spectroscopy (DOSY) are diffusion NMR techniques to determine the size and shape of many molecular systems in solution.780,799 When PGSE spectra are presented in a 2-D format, in which the chemical shifts are displayed in one dimension and the diffusion coefficient in the second one, the technique is called DOSY.4782 These two techniques were reviewed, especially their applications in inorganic and organometallic chemistry.780,799 The applications included assessing aggregation state of molecules or supramolecules, character of intermolecular interactions, stability or association constants between different hosts and guests. DOSY has been called “NMR chromatography” for its ability to “separate” the components of a complex mixture according to their diffusion coefficients.780 PGSE measurements using 1H, 19F, 31P or 35Cl NMR were performed on phosphine ligands and transition-metal complexes such as Pt(PMe2Ph)2Cl2, [Pt(PMe2Ph)Cl(m-Cl)]2, [Pd[o-(Ph3P]N)-C6H4](PPh3)(Me2NCH2CH2NMe2)]OTf, demonstrating that the four nuclides were complementary for PGSE.800 Solvent dependence of the diffusion values of several Pd(II) salts suggested that ion pairing was a major contributor in HCCl3, important in CH2Cl2, but small in acetone and MeOH.800 PGSE NMR studies were performed to determine sizes of dendritic phosphine-gold(I) thiolate complexes.801 DOSY studies of cis- and trans-[Ta(m-OMe)Me(]NSiMe3)[N(SiMe3)2]]2 in equilibrium demonstrated that they existed as dimers in solution.245 DOSY was used to characterize paramagnetic transition metal complexes, demonstrating that the technique was capable of assessing the purity and speciation of paramagnetic complexes, and also provided a convenient method to provide qualitative and sometimes quantitative molecular weight data.802

9.21.13.3 EDNMR, HYSCORE, and ENDOR For paramagnetic compounds with unpaired electrons, electron-electron double resonance (ELDOR)-detected NMR (EDNMR),803 hyperfine sub-level correlation (HYSCORE),804,805 and electron-nuclear double resonance (ENDOR)805–807 were used to detect hyperfine couplings between magnetic nuclides and unpaired electrons, thus helping to elucidate molecular and electronic structures. These techniques were employed to study hyperfine interactions in polyoxometalate PV2Mo10O406 with one reduced V(IV) ion.198 In the 17O-enriched anion, 95Mo, 17O, 51V and 31P nuclides had hyperfine interactions on the EPR resonance. The stronger interactions with 95Mo and 17O were probed by EDNMR and the weaker ones with 51V and 31P were studied by ENDOR.198 The EDNMR technique803 led to the observations of EPR, (95Mo and 17O) NMR, and ELDOR transitions and determination of 17O and 95Mo Larmor frequencies.198 2-D HYSCORE spectra correlate nuclear frequencies from different electron-spin manifolds and resolve the hyperfine couplings. The studies here showed that there were two isomers of PV2Mo10O406 in solution.198 ENDOR has also been used to study metalloenzymes and other metalloproteins.805,807

9.21.13.4 Measurement of the relaxation time Deuterium 2H NMR spin-lattice relaxation times (T1) were measured in solution for the D ligands of transition metal hydride complexes and used for the calculation of deuterium quadrupole coupling constants and of the ionic contribution to the MeD bonds.808 13 C and 17O T1 times were measured for M(CO)6 (M ¼ Cr, Mo, and W) at two temperatures in CDCl3.809 13C T1 values at two magnetic field strengths were utilized to calculate reorientational correlation times which, together with 17O T1 values, yielded values for the quadrupole coupling constants for 17O nuclides in the molecules, which were used to investigate p bonding in the compounds.809 This method was also used to study p bonding in W(CO)5L (L ¼ pyrazine, pyridine, quinuclidine, NMe3) and M(CO)5(quinuclidine) (M ¼ Cr, Mo).810 Inverse-detection methods were reported to determine spin-lattice relaxation times (T1) of transition metal nuclides.379 For insensitive spin 1/2 transition-metal nuclides, direct T1 measurements were challenging, as very long measurement times were required even for large volumes of highly concentrated or labeled samples. The inverse-detection methods were demonstrated for 57Fe, 103Rh, and 187Os in organometallic complexes.379 Indirect measurements of nuclear spin relaxation rates of nuclides with low gyromagnetic ratio (g) was recently demonstrated using the satellite exchange.811 The method did not require the observation of the low-g nuclide, but required that it be scalarcoupled to an NMR observable nuclide, such as 31P or 1H. Thus, this method was especially attractive for the study of diamagnetic transition metals in complexes. When spin relaxation was dominated by chemical shift anisotropy (CSA), it is possible to determine T1 of the metal by the method, as illustrated for 195Pt and 107/109Ag.811

9.21.13.5 Dynamic and variable-temperature (VT) NMR from chemical exchanges and reactions The use of EXSY to study chemical exchanges was overviewed in Section 9.21.13.1. Other methods to study chemical exchanges were discussed in two monographs published in 1975812 and 1982.813 They were also covered in later books on NMR.6,814 Exchanges between two isomers or ligands at the NMR time scale may be studied by VT NMR. This method has been widely used to obtain exchange rate constants at different temperatures,815–818 leading to the calculations of activation energies, enthalpies and entropies.816–818 For example, alkyl alkylidyne (Me3SiCH2)3W(^CSiMe3)(PMe3) and its bis-alkylidene isomer (Me3SiCH2)2W(]

Solution NMR of transition metal complexes

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CHSiMe3)2(PMe3) were found to undergo tautomerization, reaching an equilibrium.816,819 The exchange was studied by VT NMR at 273–301 K, giving forward and reverse rate constants k ¼ 1.42  105 s1 and k0 ¼ 1.16  106 s1, respectively, at 278 K. The activation parameters are DHs ¼ 67.8 kJ/mol and DSs ¼ 92 J/mol K for the forward reaction and DHs ¼ 75.3 kJ/mol and DSs ¼ 88 J/mol K for the reverse reaction.816,819 Chemical reaction converting reactants to products were also studied by VT NMR to obtain rate constants.820,821 Pentaneopentyltantalum Ta(CH2But)5 was directly observed as a precursor to the archetypical Schrock-type alkylidene complex (ButCH2)3Ta] CHBut.820,822 Ta(CH2But)5 was, however, short lived, and its 1H NMR resonances were mixed with those of other species in a fairly narrow region.822 D-labeled Ta(CD2But)5 was prepared and kinetic and mechanistic studies of its conversion to (ButCD2)3Ta] CDBut were performed by VT NMR at 273–298 K, giving DHs ¼ 82.3 kJ/mol and DSs ¼ 17 J/mol$K for the a-D abstraction reaction.820 This work resolved a long-standing issue in inorganic and organometallic chemistry regarding the pathway in the formation of the archetypical alkylidene complex.820 The equilibrium mixture of W(CH2SiMe3)3(^CSiMe3)(PMe3) and its bis(alkylidene) tautomer W(CH2SiMe3)2(]CHSiMe3)2(PMe3) discussed in a previous paragraph underwent an a-H abstraction reaction in the presence of PMe3 to form alkyl alkylidene alkylidyne W(CH2SiMe3)(]CHSiMe3)(^CSiMe3)(PMe3)2 at 333.2–363.2 K with the elimination of SiMe4. In the presence of PMe3, the conversion to W(CH2SiMe3)(]CHSiMe3)(^CSiMe3)(PMe3)2 followed first-order kinetics, and the observed rate constant was found to be independent of the concentration of PMe3, giving activation parameters for the reaction, DHs ¼ 118 kJ/mol and DSs ¼ 13 J/mol$K.821

9.21.13.6 NMR studies using parahydrogen (p-H2) For reactions involving H2, p-H2 may be used to improve NMR sensitivity and probe the mechanism of reactions such as catalytic hydrogenation of organic substrates. The studies in the areas were reviewed.823–828 H2 with two spin 1/2 nuclides occurs in two isomeric forms, one with its two spins aligned parallel (orthohydrogen, o-H2; spin I ¼ 1, 2I þ 1 ¼ 3) and the other with the spins aligned antiparallel (parahydrogen, p-H2). p-H2 (I ¼ 0, 2I þ 1 ¼ 1) is in a lower energy state than o-H2 in approximately p-H2: o-H2 ¼ 1: 3 at room temperature and thermal equilibrium, reflecting the 3-fold degeneracy of o-H2 and nearly equal population of the four energy levels. When H2 is cooled, o-H2 slowly converts to p-H2, reaching 1:1 ratio at 77 K. The use of such p-H2-enriched hydrogen in chemical reactions may lead to p-H2-induced polarization (PHIP), as the NMR signal intensity depended on the population difference, giving enhanced signals in the spectra of molecules derived from pH2.828 Also, the associated resonances had antiphase character. Before the system re-established the Boltzmann population distribution via relaxation, NMR may be used to probe the newly formed spin state and larger than normal coherences could be generated for detection.828 Applications of p-H2 NMR included detection of intermediates, rapid product characterization, detection of hereronuclei, deduction of reaction stereochemistry, elucidation of pairwise reaction mechanisms, and measurements of reaction kinetics.828 In the reactions of Pt[(h-CH2]CHSiMe2)2O](PCy3) with HSiEt3, p-H2 and PR3, yielding cis-Pt(PCy3)(PR3)(H)2 (PR3 ¼ PCy2H, PPh3 or PCy3), p-H2-enhanced NMR methods enabled the detection of the Pt(II) dihydride complexes which then underwent hydride site interchange and H2-reductive elimination on the NMR timescale.829 p-H2-induced polarization was used to investigate alkyne hydrogenation and oligomerization using, e.g., Pd(dcpe)(OTf)2 (dcpe ¼ Cy2PCH2CH2PCy2) as a catalyst precursor.830 The enhanced NMR resonances led to the identification of an alkyl palladium intermediate [Pd(dcpe)(CHPhCH2Ph)]OTf.830 Other NMR techniques were developed based on the use of p-H2, including SABRE (Signal Amplification by Reversible Exchange) as a recently emerged hyperpolarization method.825,831–833 In this method, hyperpolarization of substrate molecules may be obtained even when they weakly associated to a suitable metal complex together with p-H2. The reversible association provided a transient scalar coupling network through which the spin order of p-H2 could be transferred to the nuclear spins of the substrate.831 When a suitable co-substrate was used, substrates may be hyperpolarized at concentrations below that of the metal complex.832 SABRE approach was used to hyperpolarize the substrates indazole and imidazole in the presence of the co-ligand MeCN in, e.g., [Ir(IMes)(H)2L3]Cl [IMes ¼ (129), L ¼ indazole or imidazole as substrate] prepared using p-H2.833 Quantitative trace analysis of mixtures using SABRE hyperpolarization was reported with [Ir(IMes)(H)2L3]Cl (L ¼ substrate).831 DFT computations and EXAFS work were performed to study the interaction of [Ir(IMes)(H)2L3]Cl (L ¼ py, 1-methyl-1,2,3-triazole) generated by p-H2 with substrate (py) and co-substrate (1-methyl-1,2,3-triazole) that were relevant for SABRE in dilute systems.832 It was also demonstrated that the hyperpolarized labile ligand/substrate L in [Ir(IMes)(H)2L3]Cl (L ¼ nicotinamide, nicotinate, niacin, pyrimidine, and pyrazine), which was obtained from the reaction of IrCl(IMes)(cod) with p-H2 and L, dissociated from the Ir(III) center.834 The L molecules may then replace an OTf ligand in Pt(OTf)2(bdppp) (bdppp ¼ bis-diphenylphosphinopropane), thus transferring the hyperpolarization to the second metal complex. 31P NMR resonance of the Pt(II) complex was found to be enhanced.834 In other words, the hyperpolarization at the initial Ir(III) complex was passed onto the Pt(II) complexes in the SABRE-relay process.834

9.21.13.7 High-pressure NMR High-pressure NMR were reviewed in 1996, giving details of the technique and its applications in organometallic chemistry.835

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1

H and 17O NMR studies of dmf exchange with [Ti(dmf)6]3þ as a function of pressure were discussed in Section 9.21.3.1.133 The Tc NMR spectrum of fac-Tc(13CO)3(H2O)3þ under 13CO (49 atm, Fig. 3) was discussed in Section 9.21.6.2.336,337 In Section 9.21.8.1 on Co NMR, the use of 59Co NMR line-shape analysis to study Co carbonyl complexes249,480,484 and the hydroformylation reaction in supercritical CO2 was discussed.484 High-pressure NMR was often used to study homogeneous catalytic reactions involving, e.g., H2 or CO.336,337,836–838 Solution NMR studies under the high pressure of a gas were often conducted in a sapphire NMR tube.336,337 A new, convenient flow cell for high-pressure NMR for in-situ study of homogeneous catalysis was reported, which could operate over the pressure range of 1 to 197 atm and temperature range of 40 to 175  C.836 High-pressure NMR was used to study the reaction of Pt(bdpp)Me(SnCl3) [bdpp ¼ (2S,4S)-2,4-bis(diphenylphosphino)pentane (142)] with CO and CO/H2 mixture.837 Under 49 atm, CO/H2 ¼ 1/1 pressure at 273 K, Pt(bdpp)MeH was detected, which then converted to [PtMe(CO)(bdpp)]SnCl3 and [Pt(COMe)(CO)(bdpp)] SnCl3.837 High-pressure NMR studies were conducted on the migratory CO insertion on PtMe(P,P)Cl and [PdMe(P,P)(MeCN)] OTf containing a variety of bidentate, Cs-symmetrical 1,4-diphosphines such as 1,2-(Ph2PCH2)2-C6H4.839 The studies yielded rate constants.839 99

( 142 ) High-pressure 17O NMR studies of polyoxoions in water, focusing on the metal ions of interest in environmental chemistry and geochemistry, were reviewed in 2008.840 These polyoxoions included monomeric Al(H2O)63þ, M3(m3-E)(m-E)3(H2O)94þ (M ¼ Nb, Mo, W; E ¼ S, O), HxM6O19(8x) (M ¼ Nb, Ta), HxM10O28(6x) (M ¼ V, Nb, Ta), and MO4Al12(OH)24(H2O)127/8þ (M ¼ Al, Ga, Ge).840 The 2008 review focused on the clusters for which high-pressure 17O NMR yielded reaction kinetics and activation parameters.840

9.21.13.8 Rapid-injection NMR A rapid-injection NMR method was reported in 2010 to allow the observation of fast chemical reactions in real time by NMR.841 Design, validation, and implementation of the system were reported.841 The method was used to study pre-transmetalation intermediates in the Suzuki-Miyaura reaction, which had been elusive. Species with Pd(II)eOeB linkages, such as (4FeC6H4)(Pri3P)2Pd-O-B(OH)(4-F-C6H4), were identified,546 with more details of the studies published later.547

9.21.13.9 Other advanced NMR techniques and methods Several other advanced NMR techniques and methods were used in the studies of transition metal compounds. LED-illuminated NMR spectroscopy was reported for mechanistic studies of photochemical reactions.842 This approach involves placing in-situ light illumination [using a light-emitting diode (LED)] inside an NMR spectrometer. This method, e.g., was used to study photodecomposition of ferrioxalate ion Fe(C2O4)33 in solution to Fe(C2O4) and CO2 (detected directly by 13C NMR).842 1 H NMRD (Nuclear Magnetic Relaxation Dispersion) was used to study phthalate dioxygenase,843 which was involved in the degradation of phthalate by the soil bacterium, Pseudomonas cepacia DB01. T11 measurements at magnetic fields between 0.01 and 50 MHz, showing evidence for displacement of water on binding substrate. NMRD is a tool to estimate parameters influencing nuclear relaxation.843 Combination of 2-D EXSY and 1-D saturation transfer method was used to study the binding of imidazole, 1-methylimidazole, 1-ethylimidazole to the heme iron in metmyoglobin.844 Some heme peripheral H resonances were assigned. The rates and equilibrium constants for the binding of the compounds to metmyoglobi were calculated from the EXSY peak amplitudes.844

9.21.14 Conclusion Over the 30 year span (1990–2019) covered in the current review, there was much progress in NMR techniques and applications. The vast number of NMR shift data led to the finding of trends of the NMR shifts in transition metal complexes, as we recently found for d0 complexes.285 Among the challenges that remain are solution 175Lu, 227Ac, 177Hf/179Hf, 193Ir and 197Au NMR of their complexes, as we did not find papers on the solution NMR of these nuclides and they were not reported in earlier books.1,3 We hope to see breakthroughs in the solution NMR of these nuclides. Solution 181Ta and 185Re/187Re NMR spectra of their complexes were reported prior to 1990 and we did not find papers on their NMR in our search of the literature since 1990. Similarly, 105Pd NMR of H2PdX6 (X ¼ Cl, Br) was first reported in 1984 with additional details provided in 1996.399 Given the importance of these

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transition metals in, e.g., catalysis and materials sciences, we hope to see more use of the NMR of these nuclides in the studies of their complexes. NMR of both metals and ligands will continue to play a critical role in the studies of transition metal complexes.

Acknowledgment The authors thank the US National Science Foundation (NSF CHE-1900296 and CHE-2055499 to Z.-L.X.), University of Tennessee, and Berry College for support to write this review.

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Reson. 2020, 51, 1177–1200. https://doi.org/10.1007/s00723-020-01246-6. 805. Cutsail, G. E.; Telser, J.; Hoffman, B. M. Advanced Paramagnetic Resonance Spectroscopies of Iron–Sulfur Proteins: Electron Nuclear Double Resonance (ENDOR) and Electron Spin Echo Envelope Modulation (ESEEM). Biochim. Biophys. Acta Mol. Cell Res. 1853, 2015, 1370–1394. https://doi.org/10.1016/j.bbamcr.2015.01.025. 806. Murphy, D. M.; Farley, R. D. Principles and Applications of ENDOR Spectroscopy for Structure Determination in Solution and Disordered Matrices. Chem. Soc. Rev. 2006, 35, 249–268. https://doi.org/10.1039/B500509B. 807. Hoffman, B. M. ENDOR of Metalloenzymes. Acc. Chem. Res. 2003, 36, 522–529. https://doi.org/10.1021/ar0202565. 808. Nietlispach, D.; Bakhmutov, V. I.; Berke, H. Deuterium Quadrupole Coupling Constants and Ionic Bond Character in Transition Metal Hydride Complexes From 2H NMR T1 Relaxation Data in Solution. J. Am. Chem. 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Fernández, I.; Pregosin, P. S.; Albinati, A.; Rizzato, S. X-ray Diffraction, PGSE Diffusion, and Related NMR Studies on a Series of Cp*-Based Ru(IV)(Cp*)(h3-CH2CHCHPh) Allyl Complexes. Organometallics 2006, 25, 4520–4529. https://doi.org/10.1021/om060448u. 816. Morton, L. A.; Wang, R.; Yu, X.; Campana, C. F.; Guzei, I. A.; Yap, G. P. A.; Xue, Z.-L. Tungsten Alkyl Alkylidyne and Bis-alkylidene Complexes. Preparation and Kinetic and Thermodynamic Studies of Their Unusual Exchanges. Organometallics 2006, 25, 427–434. https://doi.org/10.1021/om050745j. 817. Sharma, B.; Callaway, T. M.; Lamb, A. C.; Steren, C. A.; Chen, S.-J.; Xue, Z.-L. Reactions of Group 4 Amide Guanidinates with Dioxygen or Water. Studies of the Formation of Oxo Products. Inorg. Chem. 2013, 52, 11409–11421. https://doi.org/10.1021/ic4016965. 818. Lamb, A. C.; Wang, Z.; Cook, T. M.; Sharma, B.; Chen, S.-J.; Lu, Z.; Steren, C. A.; Lin, Z.; Xue, Z.-L. 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819. Morton, L. A.; Zhang, X.-H.; Wang, R.; Lin, Z.; Wu, Y.-D.; Xue, Z.-L. An Unusual Exchange between Alkylidyne Alkyl and Bis(alkylidene) Tungsten Complexes Promoted by Phosphine Coordination: Kinetic, Thermodynamic, and Theoretical Studies. J. Am. Chem. Soc. 2004, 126, 10208–10209. https://doi.org/10.1021/ja0467263. 820. Abbott, J. K. C.; Li, L.; Xue, Z.-L. Preparation and Use of Ta(CD2But)5 To Probe the Formation of (ButCD2)3Ta]CDBut. Kinetic and Mechanistic Studies of the Conversion of Pentaneopentyltantalum to the Archetypical Alkylidene Complex. J. Am. Chem. Soc. 2009, 131, 8246–8251. https://doi.org/10.1021/ja901251c. 821. Morton, L. A.; Chen, S.; Qiu, H.; Xue, Z.-L. Preparation of Tungsten Alkyl Alkylidene Alkylidyne Complexes and Kinetic Studies of Their Formation. J. Am. Chem. Soc. 2007, 129, 7277–7283. https://doi.org/10.1021/ja067914r. 822. Li, L.; Hung, M.; Xue, Z. Direct Observation of (Me3ECH2)5Ta (E ¼ C, Si) as the Precursors to (Me3ECH2)3Ta]CHEMe3 and (Me3SiCH2)2Ta(m-CSiMe3)2Ta(CH2SiMe3)2. Kinetic and Mechanistic Studies of the Formation of Alkylidene and Alkylidyne Ligands. J. Am. Chem. Soc. 1995, 117, 12746–12750. https://doi.org/10.1021/ja00156a011. 823. Bowers, C. R.; Jones, D. H.; Kurur, N. D.; Labinger, J. A.; Pravica, M. G.; Weitekamp, D. P. Symmetrization Postulate and Nuclear Magnetic Resonance of Reacting Systems. Adv. Magn. Opt. Reson. 1990, 14, 269–291. https://doi.org/10.1016/B978-0-12-025514-6.50018-6. 824. Eisenberg, R. Parahydrogen-Induced Polarization: A New Spin on Reactions With Molecular Hydrogen. Acc. Chem. Res. 1991, 24, 110–116. https://doi.org/10.1021/ ar00004a004. 825. Duckett, S. B.; Mewis, R. E. Improving NMR and MRI Sensitivity with Parahydrogen (in Hyperpolarization Methods in NMR Spectroscopy Edited by Lars T. Kuhn). Top. Curr. Chem. 2013, 338, 75–104. https://doi.org/10.1007/128_2012_388. 826. Köckenberger, W.; Matysik, J. Hyperpolarization Methods and Applications in NMR. In Encyclopedia of Spectroscopy and Spectrometry; Lindon, J. C., Ed., 2nd Ed.; Academic Press: Oxford, 2010; pp 963–970 https://doi.org/10.1016/B978-0-12-374413-5.00054-3. 827. Duckett, S. B.; Wood, N. J. Parahydrogen-Based NMR Methods as a Mechanistic Probe in Inorganic Chemistry. Coord. Chem. Rev. 2008, 252, 2278–2291. https://doi.org/ 10.1016/j.ccr.2008.01.028. 828. Duckett, S. B.; Blazina, D. The Study of Inorganic Systems by NMR Spectroscopy in Conjunction with Parahydrogen-Induced Polarisation. Eur. J. Inorg. Chem. 2003, 2901– 2912. https://doi.org/10.1002/ejic.200300119. 829. Godard, C.; López-Serrano, J.; Gálvez-López, M.-D.; Roselló-Merino, M.; Duckett, S. B.; Khazal, I.; Lledós, A.; Whitwood, A. C. Detection of Platinum Dihydride Bisphosphine Complexes and Studies of Their Reactivity Through Para-Hydrogen-Enhanced NMR Methods. Magn. Reson. 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O¨kten U¨ngo¨r, Tyler M. Ozvat, Josef V. Grundy, and Joseph M. Zadrozny, Department of Chemistry, Colorado State University, Fort Collins, CO, United States © 2023 Elsevier Ltd. All rights reserved.

9.22.1 9.22.2 9.22.2.1 9.22.2.2 9.22.3 9.22.3.1 9.22.3.2 9.22.3.2.1 9.22.3.2.2 9.22.3.2.3 9.22.3.2.4 9.22.4 9.22.4.1 9.22.4.2 9.22.5 9.22.5.1 9.22.5.2 9.22.5.2.1 9.22.5.2.2 9.22.5.2.3 9.22.5.2.4 9.22.5.2.5 9.22.5.2.6 9.22.5.2.7 9.22.5.2.8 9.22.5.2.9 9.22.5.2.10 9.22.6 Acknowledgements References

Introduction NMR spectroscopy of transition metal nuclei Nuclear spin and quadrupolar interactions The relevant NMR transition Metal ion chemical shifts and temperature dependence Chemical shift ranges and Ramsey’s equation Temperature sensitivity of the chemical shift Electronic structure influence on temperature sensitivity Molecular structure influence on temperature sensitivity Vibrational structure Persisting need for understanding temperature sensitivity Temperature-dependent relaxation dynamics Spin-lattice relaxation T1 Spin-spin relaxation T2 Literature survey Light-element nuclei Transition metal nuclei 45 Sc 47/49 Ti 51 V 53 Cr 55 Mn 57 Fe 59 Co 61 Ni 63/65 Cu 67 Zn Conclusion and future directions

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Abstract Variable-temperature nuclear magnetic resonance spectroscopy is a promising route toward high-resolution noninvasive thermometry. Capabilities of this sort would provide valuable new efforts toward disease monitoring and treatment. A persistent challenge is in identifying specific classes of magnetic nuclei that yield strong temperature-dependent signals. In contrast to light elements (e.g., 1H), which are by far the most common nuclei investigated by NMR, metal nuclei exhibit highly temperature dependent properties, in many cases with much stronger dependence than light elements. In this book chapter, we cover the fundamentals of the temperature dependence of static (i.e., chemical shift, or resonant frequency) NMR properties and dynamic NMR properties (i.e., spin-lattice and spin-spin relaxation) in metal nuclei. Toward the end of the chapter, we highlight some specific future areas of inquiry that appear promising toward higher temperature dependent properties.

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Introduction

The focus of this book chapter is on the fundamental science behind applying nuclear magnetic resonance (NMR) for measuring temperature via the properties of the nuclear spins of metal atoms/ions (Fig. 1). The ability to design thermometers at a molecular scale would enable new possibilities for biomedical diagnostics.1–3 For example, in vivo thermometry through magnetic resonance imaging (MRI) may yield temperature gradients of physiological tissues, enabling precisely guided thermal ablation therapies and early-stage detection of critical illnesses.4,5 Beyond simple diagnostic capabilities, noninvasive thermometry may reveal new aspects

Comprehensive Inorganic Chemistry III, Volume 9

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Fig. 1 Graphical overview of the foci of this book chapter, which are electronic, structural, and vibrational ways of tuning the temperaturedependent nuclear magnetic resonance characteristics of metal nuclei.

of physiology that would be challenging to detect otherwise.6 Toward all these applications, designing highly temperaturedependent magnetic resonance signals in molecules is desirable.8 The temperature-dependent shift in the proton (1H) resonance frequency (PRF) thermometry is the most intuitive initial system for thermometry. The main advantages of this nucleus include abundance in the body and a linear dependence on T over a relatively large temperature range (such as 10–60
C).9–12 However, there are also some key challenges to using 1H as endogenous thermometers, including resolution constraints from a relatively weak temperature sensitivity, a strong sensitivity to local tissue and diffusion, and others.12–14 Respiratory motion and cardiac activity also constitute physiological constraints that govern the accuracy of PRF MR (magnetic resonance) thermometry and dictate the viable window of data acquisition.15 Several MR parameters have been reviewed for monitoring reliable temperature measurements, together with the real-time image processing and accelerated MRI acquisition techniques.1,4 Addressing all of the current obstacles to implementing MR thermometry requires stronger temperature responses from magnetic resonance signals.4,11 One possibility for engendering stronger temperature response signals is to exploit the temperature dependence of the nuclear magnetic resonance signals from nuclei other than 1H. Indeed, many elements have at least one isotope that can theoretically produce a temperature-dependent signal. Furthermore, these other isotopes are of other elements which have different chemical and electronic properties. Hence, the possibility of designing new levels of temperature sensitivity should immediately leap out to the reader, and indeed we will cover those instances below. Of particular interest are metal nuclei for this purpose, as molecules containing these species have highly tunable electronic and physical structures that are advantageous for thermometry relative to light-element species. This book chapter covers what is known about measuring temperature through metal-ion nuclear magnetic resonance spectroscopy. It first covers some of the physical principles of NMR relevant to understanding temperature dependence, followed by specifics of temperature measurements using the resonant frequency and spin dynamics of the given metal-ion nucleus. We then discuss the state of the art for variable-temperature NMR phenomena in transition metal complexes, focusing on the NMR properties of the metal-ion nuclei themselves.

9.22.2

NMR spectroscopy of transition metal nuclei

The application of nuclear magnetic resonance spectroscopy to metal complexes is limited only by the number of NMR-active isotopes for the metal in question.16 Every transition metal possesses at least one stable isotope with a nuclear magnetic moment (m), thus, almost all molecules with metal ions are potentially detectable by NMR. Chemists use NMR every day to study the 1H isotope, but many other elementsare often studied as well for organic compounds, e.g., carbon (13C), nitrogen (15N), oxygen (17O), fluorine (19F), silicon (29Si), phosphorus (31P), chlorine (35Cl), and bromine (79Br). Each of these nuclei possesses

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characteristic magnetic properties, and the same is true for metal nuclei. A key feature of this nuclear magnetism is its ability to report on its local molecular structure, such as the identity, number, and relative positions of the neighboring atoms, as well as the nature of the bonds holding them together. Thus, NMR spectroscopy is a premier structural investigation technique providing critical insight to the local environment of atoms that form complex molecules, and the same is true for metal nuclei. To a synthetic inorganic chemist, NMR finds its use by probing the structure of ligands for metal-centered coordination complexes, yet less attention is generally given to the metal-center itself. Generally, this oversight is due to a range of complicating factors introduced by the metal-center and makes metal-targeted NMR challenging. The extent of these challenges is divided according to (1) the nuclear magnetic properties of the metal nucleus, and (2) the molecular properties (i.e., physical, and chemical) of the coordination complex. First and foremost, a nucleus must be sufficiently NMR-active, and this is governed by compounding factors such as nuclear spin magnetic moment and natural abundance. Even if a particular metal nucleus possesses favorable NMR activity, the molecular properties of the complex may render NMR unsuitable. For example, metal-ion oxidation state and coordination geometry may produce a paramagnetic species by the presence of one or more unpaired electrons. The presence of an open-shell species complicates the NMR measurements as the unpaired electron possesses its own magnetic moment and interferes with the observation of nearby nuclear magnetic moments. Despite these challenges, there are several cases in which the nuclear magnetic properties are sufficient, and the molecular properties of the coordination complex provide few to no barriers to addressing the transition-metal nucleus. The purpose of this section is to define the common NMR properties relevant to metal nuclei and contextualize those properties in terms of which are important for temperature readout.

9.22.2.1

Nuclear spin and quadrupolar interactions

We provide here some basic concepts of NMR relevant to transition metal nuclei and hen contextualize them with respect to variable-temperature properties. A nucleus is fundamentally NMR-active if it possesses nuclear spin, I and a nuclear magnetic moment, m. In a given isotope, the spin quantum number depends on the number of protons and neutrons in that isotope according to the nuclear shell model. If there is equal pairing of proton and neutron spins, then no nuclear spin is present and I ¼ 0. In many isotopes, however, there are odd numbers of protons and neutrons, leading to nuclear spin and I > 0. The magnitudes of I span 1/2 to 7 in the periodic table, but only reaches 7/2 among the first-row transition metals (Fig. 2). As is relevant to NMR, simply changing the temperature of the sample is unlikely to trigger any change in nuclear spin (indeed, nuclear reactions to switch between isotopes are extraordinarily high energy processes). Instead, the properties of the nuclear spin are the primary mechanisms through which a change in temperature is connected to its magnetic resonance readout. If a nucleus is I ¼ 1/2, the nucleus is said to be dipolar and have spherical charge distribution, but most transition-metal nuclei bear greater magnitudes of nuclear spin (Fig. 3). If the nuclear spin is greater than 1/2 the nucleus is quadrupolar and has a nonspherical charge distribution in the nucleus (Fig. 3) which is the case for nearly all transition metal nuclei. A quadrupolar nuclear spin possesses an electronic quadrupole moment, eQ. The value of eQ represents the degree of asymmetric charge distribution, where a uniformed sphere has eQ ¼ 0. A positive eQ indicates concentration of positive along the axis of spin and a negative eQ indicates distribution perpendicular to that axis. The interaction between this asymmetric moment and the electrostatic potential imposed by the atoms bound to the nucleus is the quadrupolar coupling. For many metal ions, the quadrupolar coupling has a significant impact on relaxation dynamics of the nuclear spin, which then is temperature dependent and an important mechanism of thermometry. In practice, this impact is most noticeable in the spectral linewidths. Nuclei with large quadrupolar couplings (e.g., 55Mn or 59Co) tend to have much larger linewidths than those with smaller couplings (e.g., 51V).

9.22.2.2

The relevant NMR transition

NMR transitions of interest for thermometry are those producing strong intensity and sharp linewidth. A transition of this type follows the NMR selection rule, DmI ¼  1. For an I ¼ 1/2 nucleus, following the selection rule is always the case, because the only mI levels are 1/2 (Fig. 4). For nuclei with I > 1/2, however, there are a larger number of mI levels, ranging from values of þ I to  I in steps of  1. For example, for a quadrupolar 14N nucleus (I ¼ 1) there are three mI levels: þ 1, 0, and  1, and for a 59Co nucleus (I ¼ 7/2) there are eight mI levels: þ7/2, þ5/2, þ3/2, þ1/2, 1/2, 3/2, 5/2, and  7/2 (Fig. 4). A simplified depiction of the observed transition between different mI levels for either I ¼ 1/2 nucleus or I > 1/2 nucleus (here, I ¼ 7/2) is shown in Fig. 4. The energy E, of a given mI level is given by the expression E ¼ –g-mIB0, where g is the gyromagnetic ratio of the nucleus, - is Planck’s constant, mI the spin quantum number, and B0 the applied magnetic field strength. The negative sign in this expression stabilizes positive mI levels and destabilizes negative mI levels, in agreement with the energetics of spins aligned and opposed to B0, respectively. In following the NMR selection rule of DmI ¼  1, the DE of an NMR transition between two levels separated by DmI ¼  1 is therefore DE ¼ g-DmIB0. For an I ¼ 1/2 system there will be resonance response to radiofrequency waves matching that DE under a given B0. For an I > 1/2 system, there are many possible mI levels, and one could theoretically draw many different transitions between them, however, the DmI ¼  1 selection rule ensures only some transitions are possible. Indeed, only one transition is typically observed in solution. For I > 1/2 nuclei, a change in the electric field gradient, stemming from a distortion of a molecule’s geometry around a quadrupolar nucleus, for example, will shift the energies of the mI levels through the quadrupolar coupling interaction.17 The practical outcome of this effect is inhomogeneously broadened DmI ¼  1 transitions or facilitated spin relaxation if the values of mI are greater than 1/2. Importantly, the coupling does not affect the mI ¼ 1/2 levels. So, for a half-integer nuclear spin (I ¼ 3/2,

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Transition metal nmr thermometry

Fig. 2 Nuclear spin values (I) of the various elements on the periodic table and tabulated NMR-relevant parameters for the observable nuclei in the first row. This book chapter will focus primarily on these nuclei in molecules and their potential for thermometric applications.

/2, 7/2, etc.), the observed NMR transition is the one between the mI ¼ 1/2 levels. This “central quadrupolar transition” is the important one for the solution measurements of many metal nuclei.18,19 For nuclei with integer I values, there is no transition between mI ¼ 1/2 levels, and therefore all transitions are typically broad.

5

Fig. 3 Graphical depiction of nuclei with and without nuclear spin. For large-spin nuclei (I > 1/2), we also depict the asymmetry in their charge distribution with varying types of quadrupolar moments.

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Fig. 4 Splitting of the mI levels of I ¼ 1/2 (a) and I ¼ 7/2 (b) nuclear spin systems in a magnetic field B0. Spins orientations (arrows) are shown for clarity; a “down” facing depiction is one that is aligned against the applied magnetic field. The central quadrupolar transition is depicted for the I ¼ 7/2 example.

The field-dependent transitions pictured in Fig. 4 vary slightly with changes in temperature and molecular geometry, thus positively or negatively altering B0, and provides the mechanism for thermometry via nuclear magnetic resonance. In the equation depicting the resonance condition for NMR, recall that DE ¼ -gDmIB0 where - and g are constants, and DmI is the differences in mI spin levels. In large part, the external magnetic field physically represents the applied field of the NMR magnet or magnetic resonance imaging scanner, yet local chemical changes are known to slightly enhance or diminish the effect of B0 at the nucleus, thus affecting the DE transition energy accordingly. For an I ¼ 1/2 nucleus, effective changes in the local magnetic field are what drive temperature dependence of the magnetic resonance signal. For an I > 1/2, changes can stem from quadrupolar coupling (discussed further down). The changes in local magnetic field are caused by changes in local electron density that shift the signal in NMR frequency of the nucleus. This shift, which then varies as a function of the chemical properties of local chemical environment (e.g., solvent, but also the number and type of atoms directly bonded to the nucleus of interest), is known as the chemical shift. The chemical shift and the mechanisms by which it is useful for thermometry is described in detail in Section 9.22.3. Outside of chemical shift, any dynamic structural process that impacts the local field or quadrupolar coupling will also affect the dynamics of the NMR transition, and hence dynamic magnetic resonance processes can also be useful readouts for thermometry, as covered in Section 9.22.4.

9.22.3

Metal ion chemical shifts and temperature dependence

The study of the temperature dependence of NMR chemical shifts and 59Co NMR are intimately tied together. Our modern understanding of chemical shift, d in nuclear magnetic resonance spectroscopy, can be tied back to some of the first 59Co NMR studies from the 1950s.20,21 The term chemical shift generally describes the shift in resonance frequency of a given nucleus away from a chemical standard due to differing chemical environments. However, this understanding would not take shape until large differences in expected resonance frequencies were observed by W. D. Knight for many nuclei.22 For instance, one of the first reports of chemical shift was by 14N NMR and showed an approximate 300 ppm difference in resonance frequency between NH4þ and NO3 salts.23 Here it was first addressed that the large shift in resonance frequency of the 14N nucleus may depend upon its molecular structure. Soon after, large differences in the resonance frequencies of first-row transition metal nuclei were also reported including the 59Co nucleus by Proctor and Yu.21 It was this landmark study that reported the largest chemical shift difference for a nucleus between two different chemical species at 13,000 ppm between Co(acac)3 and K3[Co(CN)6]. It was also discovered that the 59Co chemical shift was remarkably sensitive to temperature (on the order of 1 or more ppm
C 1) unlike the temperature-driven chemical shifts of lighter nuclei. Furthermore, the temperature sensitivity of the chemical shift changed between different molecules, implying that aspects of the metal complex identity controlled not only the chemical shift, but also the temperature dependence thereof. In the following parts of Section 9.22.3, we describe in detail the origin of the relative wide windows of reported chemical shifts of metal nuclei and how that leads to temperature sensitivity. We focus primarily on metals, and much of the basics will be described in the context of 59Co. Our focus here on 59Co is for its historical significance and pedagogical utilitydit has the highest sensitivity of the metal chemical shift to electronic structure and thus is the best demonstrator of the concepts relevant to understanding temperature sensitivity. The general points we cover can be extended to other metal ions, and we will bring in additional metal nuclei where necessary. We also focus primarily on the solution phase, as this phase is the one of relevance to long-sought bioimaging applications. In nearly all discussions, we will present the temperature dependence in terms of the units of ppm
C 1, facilitating easier comparison with relevant body temperatures (ca. 37
C).

9.22.3.1

Chemical shift ranges and Ramsey’s equation

The chemical shift range of a nucleus is, in some respects, predictive of the extent of temperature sensitivity. For molecules with no unpaired electrons, the total magnetic field felt at the nucleus of interest is a sum of the applied field, B0, and local magnetic fields,

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the nuclear shielding (s). Two types of shielding are most important (again, in the absence of any unpaired electrons). First is the diamagnetic (sd) shielding, which originates from the diamagnetism of the local pairs of electrons and effectively lowers the local field. Second is the paramagnetic (sp) shielding, not relating to open-shell ground states, which enhances the local field. These effects usually oppose one another and follow the relationship: Blocal ¼ B0(1(sd þ sp)) where sp is often a negative term and sd a positive term.24 Most of the changes in chemical shift magnitude for a metal nucleus from complex to complex is from the paramagnetic component. For example, roughly 84% of the diamagnetic shielding of the 59Co nucleus stems from the first and second shell of core electrons, which will not change substantially with ligand/counterion/etc.25 Thus, large observed variation in d(59Co) over all the complexes that have been studied must be driven by factors related to the valence electrons in the frontier orbitals.25,26 The reason behind this dependence is responsible for the high variation in d and its temperature sensitivity. The origin of the paramagnetic shift is from spin-orbit coupling that couples the closed-shell ground state of a given metal ion with excited states. This relationship is described by Ramsey’s equation (Eq. 1): 8             9 b b > j b * +  >  L j0 > jn 2r 3L j0 j0 2r 3L jn jn  b 2 < 0  L jn = X> e2 x2 þ y2 e2 j jj þ s¼ j  (1) 0 0 > > E E 2mc2 r3 2mc2  E  E n 0 n 0 > n > : ; Ramsey’s equation on chemical shielding may be distilled down to s ¼ sd  sp where the left and right terms are the diamagnetic and paramagnetic shielding terms, respectively. In a practical sense, the presence of the minus sign indicates that increasing sd shifts the NMR signal upfield, while increasing sp pushes the NMR signal downfield. The equation contains constants e, the charge of a proton, m, the mass of a proton, and c, the speed of light. Looking at the sd term, Cj0 | represents the ground-state wavefunction, where r is the distance of an electron to its nucleus. The only wavefunction considered in this term is the ground state Cj0 | , thus no field-induced excited state mixing occurs. On the contrary, the paramagnetic shift term sp does involve field-induced mixing of the ground state Cj0 | and excited state Cjn | wavefunctions. This term includes the orbital angular momentum operator b L, and En  E0

(i.e., DE) is the difference between the ground and excited-state energies. The summation of this term is over all excited state wavefunctions and energies. However, the inverse relationship between sp and DE means that it is commonplace to simply consider the DE of only the lowest energy excited state.27 The paramagnetic shift is what sets the metal-ion NMR of transition metal complexes apart from other systems in terms of chemical shift ranges. As stated earlier, the key terms of interest in sp includes j0 and jn, the ground-state and excited-state configuration identities, which are coupled by the orbital angular momentum operator L, and then the energy differences between those two configurations. The dependence of the terms on the excited-state configuration identities means that some analyses of spin-orbit directed magnetic phenomena for electron spins28 can be analogously applied to magnetic nuclei. Moreover, for metal-ions, the energies are defined either by d-d transitions or metal-to-ligand or ligand-to-metal transitions depending on the metal. Hence, for metal complexes, where these transitions occur in the visible spectrum, the denominators of sp are generally much smaller than organic complexes (where the lowest energy transitions are frequently in the UV). The low-lying energies for metals are dictated by ligand-field considerations, which are also intimately related to the structure of the complex. Experimental relationships between the sp and ligand field considerations were established for the 59Co nucleus. In a publication by Freeman et al.,20 a series of lowspin Co3þ octahedrally coordinated complexes were studied to investigate the dependence of 59Co NMR chemical shift on their electronic absorption energies. Later, Griffith and Orgel27 explained the relationship between electronic transition energies and paramagnetic shielding through application of Ramsey’s theory of chemical shifts. The effect of paramagnetic shielding is immediately evident when comparing the range of metal-ion NMR chemical shifts with those of common nuclei. The typical range of 1H chemical shifts of small organic molecules occur over a 12-ppm window. The chemical shifts of 13C occur over several hundred ppm. However, NMR-active transition metal nuclei exhibit chemical shift ranges

Fig. 5 Reported chemical shift ranges (current as of 2022) of the first-row transition metals, which range from less than 1000 ppm (Sc) to ca. 20,000 ppm (Co).

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orders of magnitudes beyond the 1H nucleus (Fig. 5).29 These relative changes stem directly from the energy difference terms in the denominator of sp. Trends in the chemical shift ranges of metal ions can be drawn back to ligand field considerations. Within 59Co, where the most commonly studied compounds are S ¼ 0, d6 Co(III) complexes, the lowest-energy transitions are from the t2g (dxz, dyz, dxy) orbitals to the eg* (dx2–y2, dz2) orbitals. As such, a stronger ligand field decreases sp, pushing transitions upfield, and is why K3[Co(CN)6] exhibits an upfield shift relative to Co(acac)3.20,26 The wide 20,000 ppm window that is reported for 59Co demonstrates that the chemical shift is highly tunable as a function of ligand choice (or any choice that affects the ligand-field splitting Do). A similarly wide chemical shift window, 11,500 ppm, is reported for low-spin d6 Fe(II) for similar reasons.29,30 In contrast a smaller, ca. 10,000 ppm window is reported for 103Rh in d6 Rh(III) complexes, because Do is generally larger for second-row transition metals relative to first row31 Co(III). Hence, a lower range of d is observed from smaller sp variations. These ligand-field arguments can be extended to other nuclei where the lowest energy excited states are higher in energy, and thus reported ranges are smaller. The reported range in chemical shift reflects the sensitivity of sp to changes in the local electronic/physical structure of the metal ion. It is important to note that the reported range is not a physical limit to these values (or sd or sp) in any waydit is likely that there may be other metal species that have not been discovered with d values outside the currently reported chemical shift windows. Furthermore, magnetic interactions such as hyperfine couplings (which will be mostly ignored in this chapter, outside of a few select examples) could push d values outside the reported windows as well.32 However, the chemical shift range is evidence of how much d will change to relatively tiny changes in the ligand field of a closed-shell complex. Small changes in temperature may produce small changes in a metal ion’s ligand field via small changes in bond distances and angles, providing the source of temperature sensitivity of the chemical shift. It is important to note that the nuclei with the highest temperature sensitivities (i.e., 59Co) are also those with the greatest reported chemical shift windows!

9.22.3.2

Temperature sensitivity of the chemical shift

The mechanism of the temperature dependence of the metal-ion NMR shift is a physical or chemical means that changes d. In the context of Ramsey’s equation, this sensitivity derives from structural changes or electronic changes that modify sd or sp. In metals, the magnitude of sd is predominantly affected by the core electrons (e.g., 84% in 59Co).25 Variations in temperature are unlikely to drive such electronic changes, which typically require strong, ionizing radiation. Hence, the observed changes in d are attributed to changes in sp, which is tied to the ligand field for a metal complex, or, more generally, the energy gaps between the ground electronic state and excited ones. In the following subsections, we will cover the main ideas that are known about the temperature sensitivity and how they relate to electronic/physical structure. The big-picture takeaway lesson is that the temperature dependence of the metal-ion chemical shift is an incredibly tunable phenomenon, since sp is dictated by the ligand field, and because different ligands may impose different temperature-dependent structures. The specific examples described in Section 9.22.5 highlight key examples of this fact.

9.22.3.2.1

Electronic structure influence on temperature sensitivity

Electronic structure plays a central role in determining the sp of a metal ion. For octahedral metal complexes, the temperature dependence can be readily visualized from changes in Do driven by changes in structure. A proposed, albeit simplistic, representation of the mechanism for a 59Co nucleus in a complex is illustrated in (Fig. 6). Here, small changes in bond distances with thermal expansion and compression would be expected to drive changes in Do (Fig. 6), ultimately influencing d. The presented picture is consistent with observations of temperature dependence of the metal-ion chemical shift. Here, contraction of the Co–L6 primary coordination sphere (though could be generalizable to other metal ions) with decreasing temperature leads to stronger Do, increasing DE, and reducing sp. As a result, the NMR peak would be expected to move upfield with decreasing temperature, an observation that is consistent with many variable-temperature studies of metal complexes. Similarly, a down-field shift is often observed with increasing temperature, as expansion of the coordination shell would weaken DE and increase the magnitude of sp.

Fig. 6 Representation of how variations in physical structure affect electronic structure in octahedral Co(III) complexes. The depicted temperaturedriven structure drives change in electronic structure, impacts sp, and finally leads to a change in d(59Co).

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Transition metal nmr thermometry

A related important point about electronic structure is that temperature-dependent changes in d are predicted to be linear in changes in 1/DE, not DE, by Ramsey’s equation. Consider two complexes, one with a strong ligand field and one with a weak ligand field, undergoing the same magnitude of DE fluctuation from a change in temperature (Fig. 7). The change in DE is going to produce a larger percentage variation of the total magnitude of the ligand field if the system is a weak-field complex with small Do. Hence, one may expect a relatively larger change in 1/DE and therefore a larger change in sp. In contrast, a strong-field complex with that same change in DE will represent a smaller percentage variation of the total energy, producing a smaller change in sp and thus weaker temperature dependence of the chemical shift. One would surmise, then, that greater temperature dependence of sp will arise in complexes with weaker ligand fields than stronger ligand fields. Experimental evidence of correlation between the overall ligand field strength and high temperature sensitivity in metal ion NMR is weak, yet the largest temperature sensitivity for a Co(III) complex’s 59Co chemical shift is that for Co(acac)3 (Do ¼ 16,750 cm 1), a relatively weaker-field complex than K3[Co(CN)6] (Do ¼ 32,150 cm 1).20 This specific example underlines the possibility of high temperature dependence in weak-field complexes (Fig. 7). The correlation between DE and temperature sensitivity can be extended to other nuclei to enable basic rationalization of temperature sensitivities. For example, Mn(I) complexes exhibit sensitivities of the 55Mn chemical shift of 0.7 ppm
C 1 and below, with decreasing temperature sensitivities for increasing ligand field strength, which decreases sp.33 The temperature dependences of 51 V NMR shifts are often smaller than other metal ions, because the DE is large and assigned to ligand-to-metal charge transfer transitions.34 A similar argument can be made for highly oxidized Mn complexes.35 Finally, temperature dependences of 103Rh chemical shifts in Rh(III) complexes31 are smaller than 59Co in Co(III) complexes,36 because the Do values are larger in the former. More examples for this trend are presented in Section 9.22.5.

9.22.3.2.2

Molecular structure influence on temperature sensitivity

The electronic structure of a metal ion is dictated by the physical structure, namely, the coordination sphere and the ligands bound to the metal. Hence, the temperature dependence of the chemical shift for a metal ion is intrinsically related to the ligands themselves and how they affect the variable-temperature structure of a molecule. Yet, surprisingly little is known in this area, and so the effects of common ligand-based features such as denticity37 are just now being mapped. The simple expansion/contraction model above was developed by Jameson and coworkers and provided the first estimates of the needed changes in bond lengths to account for observed metal-atom NMR signals.34 Estimates were given at ca. 0.0001 Å
C 1 in magnitude to produce the ca. 1 ppm
C 1 values observed in many metal-ion NMR experiments. The model of Jameson and coworkers closely reproduced experimental values in 51V complexes, and thus is worth further work to define it for other nuclei as well. Furthermore, the model was developed solely for monodentate ligands. A recent test of Jameson’s theory via extended X-ray absorption fine structure allowed for solution-phase assessment of variable temperature bond changes and attempted correlation with temperature sensitivities of the 59Co chemical shifts in Co(III) complexes.38 The five studied Co(III) complexes varied connectivity between the N donor atoms of the first coordination shell, varying from a molecule where the donor atoms were

Fig. 7 (a) Graphical illustration of the inverse relation between d(59Co) and DE where the same change in DE for different complexes (which could be driven by changes in temperature) results in vast differences in d(59Co). (b) Figure of inverse relationship between DE and d(59Co) highlighting change in d(59Co) vs DE as a function of O < N < C donor atoms.

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independent of one another, [Co(NH3)6]3þ, to one where there was a high degree of connectivity between each donor atom, [Co(diNOsar)]3 þ (diNOsar ¼ dinitrosarcophagine). These studies revealed changes in CoeN bond distances ranging from 0.0256 (6) to 0.0020 (5) Å over a temperature window of  10–60
C. Importantly, the largest changes in metal-ligand bond lengths did not match with the largest changes in 59Co chemical shift, as was expected. The current hypothesis for structural level design is that changes in bond distances and angles must both be considered. Indeed, one may expect that for highly interconnected coordination shells, a small perturbation in M–L distances for one donor atom would affect another. In this way, there may even be a cooperative effect, amplifying the temperature sensitivity over metal nuclei with ligand shells saturated in monodentate ligands. A simple example where changes in bond angles could be impactful is a temperature-driven transition between octahedral Oh and trigonal prismatic D3h-symmetric complexes (Fig. 8). Here, a twisting motion would cause the gap separating the orbitals to decrease, which should manifest in a lower DE and hence, larger sp. Extensive experimental and theoretical investigations have shown a unique interplay between physical and electronic driving forces in [Co(diNOsar)]3 þ attributable to molecular strain, which could guide the temperature sensitivity.39–42

9.22.3.2.3

Vibrational structure

In this section we describe how a physical change in a molecule would actually manifest and what we know about how that influences chemical shift. In Section 9.22.3.2.1 we described how variation in electronic structure would drive changes in chemical shift, and Section 9.22.3.2.2 described some of what we know about how changes in physical structures affect the chemical shift. However, it is important to note that in solution, the structure of a complex is highly dynamic. Bond distances and angles are changing as a given molecule is colliding with solvents and counterions while tumbling through solution. The timescales of these variations are fast, picosecond timescales, much faster than the NMR experiment. Hence, we only ever observe a single peak that effectively results from the average structure in solution, and that structure is likely not the same as extracted from single-crystal X-ray diffraction experiment. Thus, we must think of the general variation in structure in solution for a molecule as realistically being the average of its possible conformations. The mechanism by which a molecule obtains the energy is to change its average structure is through collisions with the environment, transferring energy into the vibrational modes of the molecule. Indeed, even initial attempts at understanding the high temperature dependence of metal-ion NMR signals invoked the populations of vibrational states.26 Later, many researchers would apply the theoretical evaluation of rovibrational effects in various nuclei including 19F, 51V, 59Co, 93Nb, 195Pt, etc.34,43–46 In these examples, it is rationalized that lowered temperatures decrease the populations of excited state vibrations, which effectively contracts bond distances, leading to an increase in DE and lower sp.47 The likely relevant vibrations are the normal modes for a metal complex, more specifically those that directly affect the coordination shell of the metal. In this picture, understanding and controlling the temperature dependence of the metal-ion NMR signal is considerably more complex than the seeming surface-level coordination chemistry considerations of ligand and metal ion selection. Indeed, it appears one must think more deeply about how to control the vibrational spectra of a complex. One way of exerting control over vibrational modes is by changing the mass of ligands or donor atoms, in the latter case by isotopic selection, which can affect vibration energies and alter temperature dependent physical structure. For example, a mass-increased ligand can be obtained via 1H/2D exchange in [Co(NH3)6]3þ, [Co(en)3]3 þ, and others with exchangeable protons, which affect the d(59Co) chemical shift (Fig. 9).48–51 Observations of this kind can also be shown via other isotopic changes, e.g., using 16O vs 18O donor atoms.52 In these complexes, changes in chemical shift are induced because the ligand field strength of a ligand will change slightly with mass. In

Fig. 8 Example of how a structural distortion with temperature from one geometry to another could change DE and influence sp. Such a distortion is not accounted for by the model of Jameson and coworkers.

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Fig. 9 Isotopic 1H/2D exchange of [Co(en)3]Cl3 and [Co(diNOsar)]Cl3 complexes via treatment with D2O. Corresponding 59Co NMR spectra of each complex after equilibration show an ensemble of 59Co peaks representative of the individual isotopomers. Greater amounts of deuteration increase Do, pushing the chemical shift toward lower ppm values. Constructed with data from Ozvat, T. M.; Rappé, A. K.; Zadrozny, J. M. Isotopomeric Elucidation of the Mechanism of Temperature Sensitivity in 59Co-NMR Molecular Thermometers. Inorg. Chem. 2022, 61, 778–785.

a dynamic fluid environment, a higher-mass donor atom will persist closer to a metal ion over time. Hence, the average ligand field strength will be greater (and hence higher DE, lower sp). Changes in ligand mass impact changes in the temperature sensitivity of the metal ion nuclear magnetic resonance. An increase in mass for an atom participating in a vibrating bond moves that vibration to lower energy. This decrease in the energy can bring more vibrations to lower energies, affecting their relative populations, the molecule’s average structure, and finally, the metal-ion chemical shift. However, it is important to note that not all types of vibrations are relevant here. Between IR-active vs Raman-active modes, the largest-amplitude changes in computed metal ion chemical shift ranges (for 59Co) are attributed to Raman modes, not IR modes.49 Here, Raman-active modes involving symmetric, breathing-type vibrations produce the largest changes in metal-ligand overlap, Do, and hence the chemical shift. IR vibrations, in contrast, contain molecular motions that can cancel out changes overlap,

Fig. 10 Correlation between the 59Co temperature sensitivity Dd/DT v. the population of Raman-active normal modes for various low-spin d6 octahedral Co3þ complexes (logarithmic scale). Shaded areas highlight the impact of mass-induced Dd/DT for different isotopomers of the same complex. Compound 1 in this figure is [Co(en)3]Cl3 and compound 2 is [Co(diNOsar)]Cl3. The structure of Co(acac)3 is also shown to the right. Constructed with data from Ozvat, T. M.; Rappé, A. K.; Zadrozny, J. M. Isotopomeric Elucidation of the Mechanism of Temperature Sensitivity in 59Co-NMR Molecular Thermometers. Inorg. Chem. 2022, 61, 778–785.

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thus in orbital energies, and produce remarkably smaller variations in d ranges. What is interesting is that simply comparing the populations of low-lying Raman modes with temperature sensitivity of the metal-ion chemical shift (for 59Co) produces a correlation (Fig. 10). Importantly, individual connections between specific vibrations and changes in temperature sensitivity have not yet been found. If the data in Fig. 10 imply a design strategy for increasing temperature sensitivities in metal ions, they suggest a design strategy that is holistic and that tuning of the entire low-energy vibrational spectrum is key. This nuance is likely in contrast to the instinct of a coordination chemist, who may wish to find connections between individual vibrations which could be manipulated in a straightforward manner.

9.22.3.2.4

Persisting need for understanding temperature sensitivity

The foregoing factors list several ways in which electronic structure, physical structure, and vibrational spectra are important for dictating temperature sensitivity. However, beyond preliminary correlations, ways of systematically increasing temperature sensitivity by design are lacking. For example, it is not known whether the ideal ligand is a chelating ligand vs monodentate, strongfield vs weak-field ligand, etc. Even though there are general trends presented above, there are problematic exceptions. For example, Co(acac)3 has the highest temperature sensitivity of the 59Co resonance, while Co(tBu2acac)3, with nearly the same ligand shell, has substantially lower temperature sensitivity.53 Furthermore, the complex [Co(tn)3]3 þ (tn ¼ 1,3, diaminopropane), which has a weaker ligand field strength than [Co(CN)6]3, displays a lower temperature sensitivity.37 Hence, while there are conceptual bases for temperature sensitivity in metal ions, the above exceptions underline the fact that we simply do not know what features will produce a molecular probe capable of high-resolution thermometric imaging via NMR chemical shift. Above, we detailed the basics of the phenomena mostly in the context of 59Co owing to the authors’ expertise, yet there is no precise theoretical established reason why this nuclei is to be the end of the story.

9.22.4

Temperature-dependent relaxation dynamics

Changes in resonant frequency (chemical shift) are only one mechanism by which a nuclear spin can provide a temperature readout via magnetic resonance. The dynamics, or relaxation times, of a spin, are a separate and potentially useful way of doing so. Nuclear spin relaxation is the process by which a given nuclear spin returns to alignment with a magnetic field after being reoriented by a pulse of radiofrequency waves. There are two main timescales for this process. The first is the longitudinal or “spin-lattice” relaxation rate, T1 1, which describes how fast a spin returns to alignment from direct opposition to an applied magnetic field. The second is the transverse or “spin-spin” relaxation rate, T2 1, which represents how fast a spin loses alignment after being aligned perpendicular to the applied magnetic field direction. For any relaxation process to occur, a local magnetic field must be present fluctuating at rates comparable to the Larmor frequency of the relaxing nucleus. The origins of these rates are therefore manifold, as there are many processes that are sufficient to trigger relaxation, namely motions of environmental spins (e.g., nearby protons on solvent or within the molecule itself). These processes vary with temperature and solvent viscosity, and since the Larmor frequency is magnetic-field dependent, relaxation processes exhibit a field dependence. The study of relaxation dynamics is an incredibly deep area, and there are many mechanisms that trigger it.54–58 We seek here to describe relaxation in the simplest way so that the variabletemperature nature of it can be appreciated by the reader, and to facilitate the discussion of literature examples in Section 9.22.5.

Fig. 11 Top Left: Inversion-recovery NMR pulse sequence experiment. Left: Basics of nuclear spin behavior in an applied magnetic field (B0) where inversion (alignment against the field) via radiofrequencies is achieved at the 180
pulse of the sequence. Relaxation describes the time for the nuclear spin magnetization to recover by realigning with B0. Right: Example T1 data that show the inversion recovery curves of a nucleus.

756 9.22.4.1

Transition metal nmr thermometry Spin-lattice relaxation T1

In a practical sense, the spin-lattice relaxation time, T1, enables a readout of temperature. One straightforward way of evaluating temperature is simply knowing the temperature dependence of T1, and that could be used analogous to as the chemical shift measurements in Section 9.22.3. Direct measurement of T1 proceeds through an inversion recovery experiment (Fig. 11). Here, a nuclear spin is flipped into opposing alignment with B0 using radiofrequency-based pulses. The signal intensity of the free induction decay is then measured as a function of time after the initial inverting pulse, and the timescale of the recovery of the signal enables one to extract T1. Measurement of T1 can be a long process requiring extensive signal averaging. Hence, using this measurement to give a T1 and correlating that value to a temperature for an image in a clinical setting would likely take far too much time to do! An alternative method of using T1, more advantageous for imaging, produces a readout of temperature through magnetic resonance signal intensity. Note that a magnetic resonance signal exhibits the greatest signal to noise when the system is at equilibrium and as many spins as possible are aligned with the magnetic field. However, the signal to noise from a single scan is often insufficient quality, and thus, an instrument will often perform a large number of scans to signal average. Each one of these scans is separated by a period of time known as the recycle delay; a version of this delay is depicted at the beginning of the inversion recovery pulse sequence in Fig. 11. If the recycle delay is too short relative to T1, then the initial scan will deliver the highest signal to noise and all further scans will yield diminishing signal intensities, as the system does not have time to return to equilibrium after measurement. In contrast, if the delay is appropriately long, all scans will yield high signal to noise and averaging will yield useful signal. When T1 is temperature dependent and scans are collected at the same recycle delay across a species with heterogeneous temperature regions, variations in signal intensity can yield temperature information. In an imaging situation, this variation would manifest in for example, one section of an image having a bright signal because the T1 is much shorter in that region than the recycle delay, while a separate section of the image has a suppressed signal because the T1 is long in that region relative to the recycle delay. In principle, this use would require extensive calibration for the probe and patient and conditions.59 Nevertheless, using a probe for imaging in this or related ways requires a fundamental understanding of what governs T1 and how these factors vary with metal ion. For nuclei with I ¼ 1/2, which tend to be lighter nuclei (and 57Fe), varying temperatures change the molecular tumbling rate of a molecule (the correlation time, sc), which controls relaxation. In this case, changes in dipole-dipole interactions between the nucleus of interest and surrounding spins are what direct the spin-lattice relaxation. With varying temperatures, internuclear distances and dynamics of molecular motions, and the reorientation of structures change, this results in a change in T1. Most transition metal nuclei, however, possess spins higher than I ¼ 1/2 (indeed, up to I ¼ 7/2), and thus the nuclei are quadrupolar. Quadrupolar nuclei possess their own electric quadrupole moment (Q) that interacts with the local electric field gradient (EFG). This quadrupolar nucleus drives the spin lattice relaxation rate through the below equation:  2 2   1 3ð2I þ 3Þ e Qq h2   Z2 sc ¼ (2) 1 þ 3 T1Q 400 I2 ð2I  1Þ In Eq. (2) T1Q is the quadrupolar relaxation time, I the nuclear spin, e, Q, q, and Z are defined as in described in Section 9.22.2, h is the asymmetry parameter that describes deviation from axial symmetry of the coordination environment, Z2 is a term that accounts for the Larmor frequency and motion in solution, and sc is the correlation time.60 In the case of metal complexes, the EFG is produced by the donor atoms in the ligand shell, and therefore the implications of Eq. (2) are the following: (1) Highly symmetric environments produce small field gradients while asymmetric environments produce large ones, leading to slower and faster spin-lattice relaxation, respectively. (2) The larger the quadrupolar moment of a nuclear spin, the faster the spin-lattice relaxation rate. Examples of this trend can be seen within sets of molecules of the same nucleus, e.g., for 59 Co, where long T1 times can be found in octahedral, highly symmetric complexes (like K3[Co(CN)6], T1 ¼ 103.0 ms) vs lesssymmetric multidentate analogs (i.e., T1 ¼ 91 ms for [Co(en)3]Cl3).18,25 But even more pronounced trends can be observed when comparing across nuclei. For example, 51V, which has a very small quadrupolar moment and tends to show longer T1 times in solution.61 Finally, (3), the quadrupolar relaxation rate will have a temperature dependence that is guided by changes in sc, though the dependence will again follow the magnitude of the quadrupolar interactions. In practice, this means that quadrupolar relaxation will produce a T1 with an exponential temperature dependence and activation energy defined by any structural changes that affect Q.62,63

9.22.4.2

Spin-spin relaxation T2

Spin-spin (or transverse) relaxation time T2 quantifies the rate of the decay of the magnetization within the xy plane. The spin-spin relaxation is related to spin-lattice relaxation since an increase in z-magnetization without a decrease in the magnetization in the xy plane is not possible: T2  T1 (in solutions T2 z T1 and in solids T2  T1). The most important implication of spin-spin relaxation with respect to thermometry is that it is inversely related to the linewidth of the NMR peak for a given nucleus. Therefore, if the mechanisms that govern T2 are temperature dependent, then the NMR signal should exhibit a linewidth that is likewise temperature dependent. The most important mechanisms that govern T2 for metal ion nuclei are threefold. The first is highlighted in the foregoing section: quadrupolar relaxation. When quadrupolar relaxation is dominant and T1 equals T2, then the temperature-dependent mechanisms that guide T1 will likewise guide T2 and the linewidth. However, the two other mechanisms are different and relate

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to how a metal ion nuclear spin interacts with the species around it. These mechanisms are referred to as “scalar relaxation” mechanisms. The first kind of this mechanism originates when a metal spin is J coupled to a nearby nucleus and that coupling fluctuates (e.g., by bond movement or vibration). The second kind is caused by the impacts of the dynamics (e.g., the T1 and T2) of the coupled spin on the metal ion nucleus. Scalar relaxation is effectively controlled in metal complexes based on the donor atoms of the ligand shell, and we will use 59Co as a brief example of this fact. More details on a nucleus-by-nucleus basis are provided in the next section. Bryant and coworkers showed that scalar relaxation of the second kind from 59Co coupled to 14N in high-symmetry N-bonded cobalt complexes contributes to T2,64,65 and the linewidths for C- or O-donor complexes are typically quite sharp (e.g., [Co(CN)6]3, < 6 Hz linewidth).66 As one additional piece of evidence of the role of donor atom spins on linewidth through scalar relaxation, there is one 14N-decoupling experiment (from 1979!) that demonstrates notable sharpening of the 59Co linewidth (by a factor of 3) in [Co(NH3)6]Cl3.67 The importance of the scalar mechanisms on the temperature dependence of the linewidth is only possible if there is a temperature dependent component to the scalar mechanism, e.g., the bonding, or the T1 and T2 of the coupled spin. Finally, there is one potential additional contribution to the linewidth of the metal-nucleus NMR signal, which is sample temperature heterogeneity. A heterogeneous temperature range within the NMR tube could effectively spread out the NMR signal. The effect of this would be that T2 values extracted from linewidths are actually the lower limits for a given ion. In terms of sensing of temperature, the linewidth of a peak should be compared with the temperature sensitivity to give an estimate of the resolution of the thermometry. In principle, a higher ratio of temperature sensitivity of the chemical shift (Dd/DT) to intrinsic linewidth of the peak would be desired for higher resolution.

9.22.5

Literature survey

Each metal is unique in its chemical shift range, preferences for certain coordination numbers, electronic structures, and molecular structures/geometries. Hence, each metal provides an intrinsically unique platform for thermometry. This fact suggests that the potential for thermometry, either from chemical shift sensitivity or relaxation time changes, would be a huge area of focus for the coordination chemist to explore, a “scientific playground” in the colloquial sense. Yet studies of metal-nucleus chemical shifts are not common, owing to challenges in the NMR experiment (e.g., high linewidths, preference for only open-shell oxidation states, etc.). In the following section, we cover the known studies of temperature dependent metal-ion NMR. We briefly highlight the temperature sensitivities of the chemical shifts (Dd/DT) and relaxation times for light element nuclei first because this information is important context for the heavier-element material that follows. Then we focus primarily on the first row of the transition metal block, the temperature dependence of the NMR chemical shifts, and any notable additional magnetic mechanisms that affect that property. We note that the preference for sensitivities that we discuss will be in terms of those that drive changes in sp. This preference implies that we will generally avoid discussions where temperature dependence stems from chemical changes to a given molecule (e.g., ligand substitutions) and instead focus on small bond distance/angle changes that affect sp. We will briefly mention reaction-driven changes occasionally where necessary for clarification.

9.22.5.1

Light-element nuclei

The focus of this chapter is on metal nuclear spins not light-element nuclei. We note that light nuclei should not be completely disregarded for thermometry in bioimaging situations because of the high quantity of endogenous light-element nuclei, e.g., 1H. Furthermore, these nuclei tend to have sharp linewidths owing to their I ¼ 1/2 nuclei and absence of quadrupolar coupling. We briefly mention some details of these nuclei because they provide useful context for observations made on metal nuclei. Thermometry in 1H NMR experiments typically demonstrates small temperature sensitivities. For example, Reeves showed that the between 298 and 423 K, decanoic acid exhibits a Dd/DT of 1.2  10 2 ppm
C 1 for the carboxyl proton. In this case, the temperature sensitivity is attributed to the formation of dimers at low temperatures that dissociate as the sample warms.68 Similar arguments have been made for other species.68 These small sensitivities are dependent on chemical transformations because sp values are extremely small, as are their temperature dependence. Indeed, standard predictive scales for 1H ppm trace almost entirely to changes sd, not sp, unlike metal nuclei.69 Carbon has one NMR active isotope, 13C, and has a larger chemical shift range than 1H, from 0 to 200 ppm. 13C NMR thermometry likewise demonstrates sensitivities that are slightly higher than 1H. For example, Quast et al. investigated potential 13C NMR thermometers and found a Dd/DT of 0.051 ppm
C 1 near 300 K. Nitrogen has two NMR-active isotopes, 15N with I ¼ 1/2 and 14N with I ¼ 1 and natural abundances of 0.37% and 99.63% respectively. Although 14N has a much higher natural abundance than 15N, 14N spectra are often unobservable due to signals that are extensively broadened by quadrupolar interactions. 15N NMR is more commonly used and exhibit a large reported chemical shift range of 1200 ppm. Alei et al. investigated the temperature sensitivity of methylated analogs of ammonia, finding Dd/DT values in the window of ca. 2  10 2 ppm
C 1. Like with 1H and 13C, the temperature sensitivity of the 15N nucleus was postulated to arise from chemical effects, namely thermal perturbation of intermolecular interactions.70 Fluorine has one NMR active isotope in 19F with 100% natural abundance and is the second most NMR sensitive nucleus on the periodic table at 0.833 compared to 1H.71–74 It is not endogenous, leading to the imaging advantage of a very weak background. 19F has a spin of I ¼ 1/2 and tends to yield sharp signals with a relatively wide chemical shift range for a light element, 700 ppm

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from  300 ppm. Investigations by Berkowitz and coworkers reported that the T1 had a dependence on the temperature.75,76 These same studies also report a linear dependence on temperature for the 19F chemical shift of perfluorocarbons of Dd/ DT ¼ 5  10 2 ppm
C 1. More studies are needed to elucidate the mechanisms behind the temperature dependence of the 19F chemical shift, but the low background signal is still alluring. The final light element nucleus worth briefly mentioning is 31P. The 31P nucleus has a relatively high gyromagnetic ratio (17.235 MHz T 1), a 100% natural abundance, and a nuclear spin of 1/2 which makes spectra relatively easy to interpret. Gordon and Quin recorded the temperature dependence of 31P chemical shifts of some trivalent phosphorus compounds.77 Among many derivatives they studied, only small shifts (Dd/DT < 0.05 ppm
C 1) were observed with changes in temperature. A recent study of 31 P nuclei coordinated to Fe(III) exhibited a relatively enormous change in thermal sensitivity of the 31P chemical shift (Dd/ DT ¼ 34 ppm
C 1).78 Interactions between the 31P nucleus and the paramagnetic Fe(III) ion, primarily through pseudo-contact and Fermi contact mechanisms are responsible for the large Dd/DT not a change in sp.

9.22.5.2 9.22.5.2.1

Transition metal nuclei 45

Sc

The Sc nucleus (I ¼ 7/2) has a relative sensitivity more than 1700 times that of 13C and a 100% natural abundance which makes 45 Sc the sixth most favorable NMR nucleus in terms of signal to noise. 45Sc is a quadrupolar nucleus (I ¼ 7/2) and both spin-lattice and spin-spin relaxation times are expected to be governed by the quadrupole relaxation mechanism. With regard to sp, Sc is most often isolated as the Sc3þ oxidation state, meaning that the lowest energy transitions relevant for Ramsey’s equation are commonly higher-energy ligand-to-metal charge transfer transitions. As a result, sp is not very strong, and the reported window of chemical shifts reflects that fact, occurring over only a few 100 ppm. Studies of the temperature dependence of the 45Sc chemical shift are not very common. There is a slight temperature sensitivity of Sc(NO3)3 in acidic conditions: a single and sharp resonance with a temperature sensitivity of 0.076 ppm
C 1 (Fig. 12).79 Other systems demonstrate larger sensitivities, but these tend to be from chemical changes, e.g., ligand substitution, not related to changes in sp. For example, hexacoordinated Sc complexes in the form ScCl6Lnn–3 where L ¼ triethyl phosphate (TEP) in various solvents and concentrations demonstrate sensitivities of ca. Dd/DT ¼  2 ppm
C 180 and 45Sc atoms within C84 also produce larger changes (ca. Dd/DT ¼  2 ppm
C 1) as a result of structural changes within the C84 capsule.81 These latter species underscore an intriguing design strategy for merging chemical stability and strong temperature dependence. 45 Sc NMR spectra often yield broad lines in all complexes except those with cubic symmetry because the nucleus is quadrupolar. As a result, there is a temperature dependence of the linewidths. Indeed, the temperature dependence of the linewidth of an acidified Sc(NO3)3 solution in the temperature range 293 to 363 K illustrates quadrupole-dominated relaxation, meaning that the relaxation 45

Fig. 12 (a) 45Sc NMR peak position vs temperature of Sc(NO3)3 as an HNO3 acidified aqueous solution at 25 mM. Spectra were recorded at 87.5 MHz (via 1H 360 MHz system). The large light gray sphere is scandium and red, blue, and white spheres are oxygen, nitrogen, and hydrogen, respectively. (b) Solid state 47/49Ti NMR data of cubic BaTiO3 perovskite structure. Data were collected at 22.56 MHz with a 400 MHz (1H) spectrometer. The light blue sphere is titanium, and red and green spheres are oxygen and barium, respectively. We note the depiction of solid-state data here, which is attributed to the paucity of solution-phase analyses for this nucleus. The temperature dependence, which we note is opposite to that of the 45Sc example, is due to an interaction with the conduction electrons in the material. Constructed with data from Rehder, D.; Speh, M. An Exploratory Scandium-45 NMR Study Into the Complexation of Alanine and Oligopeptides. Inorg. Chim. Acta 1987, 135, 73–79; Brown, M. D.; Levason, W.; Murray, D. C.; Popham, M. C.; Reid, G.; Webster, M. Primary and Secondary Coordination of Crown Ethers to Scandium(iii). Synthesis, Properties and Structures of the Reaction Products of ScCl3(thf)3, ScCl3$6H2O and Sc(NO3)3$5H2O With Crown Ethers. Dalton Trans. 2003, 857– 865; Bastow, T. An NMR study of 137Ba and 47,49Ti in ferroelectric BaTiO3. J. Phys.: Condens. Matter 1989, 1, 4985; Forrester, W. F.; Hinde, R. M. Crystal structure of barium titanate. Nature 1945, 156, 177.

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times increase with increasing temperature. In general, T1 values are in the range of 100 ms to ms at room temperature and T2 in that same range.81

9.22.5.2.2

47/49

9.22.5.2.3

51

9.22.5.2.4

53

Ti

Titanium has two low-sensitivity NMR active nuclei, 47Ti (7.28% abundance) and 49Ti (5.51% abundance), which are I ¼ 7/2 and I ¼ 5/2, respectively. For Ti compounds, typical NMR analyses are applied to high-oxidation state systems, e.g., Ti(IV), which, like for Sc(III), feature lowest-lying energies related to high-energy ligand to metal charge transfers that suppress the tunability of sp. Alternatively, lower oxidation states can be accessed but only with strong-field ligands that encourage spin pairing and again suppress the tunability of sp. Hence, the chemical shift window is relatively small, ca. 2000 ppm wide. This suggests a relatively small temperature sensitivity for this nucleus, and variable-temperature studies thus far have only shown negligible temperature dependence, to the best of our knowledge (Fig. 12).82 The high spin nuclei for 47/49Ti are quadrupolar, suggesting a high sensitivity of the nuclear spin relaxation times temperature. Indeed, McGlinchey et al. utilized 47/49Ti NMR to investigate the chemical shift data for a range of Ti(IV) compounds82 and a detailed study of spin-lattice relaxation rates of the Ti nuclei in various TiCl4 solutions. Inversion recovery experiments for both Ti nuclei are recorded to reveal T1 values for TiCl4. T1 ¼ 160 ms for 49Ti and 59 ms for 47Ti were found for TiCl4 at room temperature.83 T2 values for both nuclei were calculated by using the linewidth values. T2 ¼ 131 ms for 49Ti and 41 ms for 47Ti at room temperature. Lastly, TiF62: T1 ¼ 160 ms for 49Ti and 59 ms for 47Ti at room temperature. The temperature dependence of 49Ti is generally higher than 47Ti (assuming the same molecule) because of the larger quadrupolar moment for the former.83 Overall, however, the difficulties are encountered in Ti NMR measurements owing to the large quadrupolar moment of both 47 Ti and 49Ti and the low sensitivity. Most of the interesting compounds do not give observable signals or, if they do, the lines are broad and weak, which makes 47/49Ti difficult nuclei to study for thermometry applications.

V

The V isotope is a quadrupolar nucleus (I ¼ 7/2) with 99.76% abundance and is one of the most studied transition metal nuclei by NMR. Despite its high spin, it is worth noting that 51V NMR investigations often yield relatively sharp signals because the quadrupolar moment for the 51V nucleus is so small relative to other large-spin nuclei, and its chemical shift range varies from 0 to  2000 ppm.61 51V NMR signals are observed for a number of coordination complexes and oxidation states. The narrowest peaks occur for the Oh-symmetric [V(CO)6] complex bearing peak broadness near 1.4 Hz at full-width half-max.61 The ease with which NMR may be used to study relationships between electronic and molecular structure is shown in many publications and literature reviews.84–86 The only oxidation state of vanadium ions active in 51V NMR is V(V), owing to its diamagnetism. Indeed, the other oxidation states (V2þ, V3þ, and VO2þ) are paramagnetic, likely giving rise to extreme broadenings in solution. The relatively small values of Dd/DT observed in these complexes are attributable to the chemical features of the complexes. The most common 51V NMR applications are made to V(V) complexes, which bear no d electrons. Instead, the lowest energy transitions contributing to sp are from ligand to metal charge transfer transitions, which are high energy. Hence, slight changes to structure with temperature because of bond expansion/compression are not as effective at mediating Dd/DT. Additionally, 51V NMR studies on the tetrahedral V(V) VO(O-iPr)3 show a large temperature-dependent linewidth, increasing from 10 to 610 Hz with decreasing temperatures. This relationship follows the Arrhenius law (T1 1 ¼ exp.(Ea/RT)) suggesting that molecular correlation times are a contributing factor to increased linewidths as they are driven by decreased temperatures. The takeaway is the fact that with lowered temperature, the 51V nucleus is deshielded and suggests a loss of molecular symmetry.87 The relatively low quadrupolar moment for 51V also is advantageous regarding thermometry because it provides a generally sharper linewidth for analyses. Owing to its practical measurability, thermometry with the 51V nucleus via its chemical shift and relaxation dynamics is reasonably noted. Rehder et al. originally established temperature sensitivities of the d(51V) and Dn½ in solution for the octahedral (Et4N) [V(CO)6] complex where the 51V NMR signal shifts linearly by 0.3 ppm
C 1 within a temperature range of 200–340
C (Fig. 13).61 Beforehand, Paulsen et al. similarly showed the temperature sensitivities of the VO(O-iPr)3 tetrahedral complex in THF with a familiar increase in d(51V) with increased temperatures, yet, relative to octahedral complexes, sensitivities varied drastically and non-linearly.87 The magnitude of Dd/DT of the 51V nucleus was shown to exponentially increase at lower temperatures. Later, Jameson et al. would apply a physical lens to the mechanisms of Dd/DT in these complexes by associating changes in shielding to temperature-driven bond lengths, rM–L (Å), thus chemical shift.34 Considering all these findings and their importance in metabolism and biological studies, 51V nuclei could be a potential candidate utilizing in NMR thermometers as long as substantial temperature sensitivities are achieved. 51

Cr

The one stable NMR-active isotope of chromium is the quadrupolar 53Cr nucleus (I ¼ 3/2). Compared to most other transitionmetal isotopes, 53Cr is less explored due its unfavorable nuclear magnetic properties. For one, it possesses a meager 9.55% natural abundance and a low gyromagnetic ratio g ( 1.512  107 rad T 1 s 1), both of which are responsible for its low receptivity (0.5 times lower than 13C). Data collection of 53Cr nuclei commonly requires high-field spectrometers (the Larmor frequency is just 22.62 MHz at 9.4 T, for example) to offset the low gyromagnetic ratio.88,89 Despite these challenges, 53Cr NMR has been successfully applied to various octahedral Cr(0) and Cr(VI) complexes in solution to determine 53Cr chemical shift, d(53Cr), and the linewidth of Dn½.88 In fewer cases, tetrahedral Cr(VI) complexes have also been

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Transition metal nmr thermometry

Fig. 13 Variable-temperature 51V NMR peak positions of octahedral [V(CO)6]. For the depicted structure of V(CO) 6 the pink, gray, and red spheres are vanadium, carbon, and oxygen. The variable temperature peak positions of the tetrahedral VO(OiPr)3 complex is also shown (in MeCN). Both spectra are collected at ca. 23.6 MHz. Constructed with data from Jameson, C. J.; Rehder, D.; Hoch, M. Isotope and Temperature Dependence of Transition-Metal Shielding in Complexes of the Type M(XY)6. J. Am. Chem. Soc. 1987, 109, 2589–2594; Rehder, D. A Survey of 51V NMR Spectroscopy. Bull. Magn. Reson. 1982, 4, 33–83; Calderazzo, F.; Pampaloni, G.; Vitali, D.; Zanazzi, P. F. The Reaction of Hexacarbonylvanadium With Aromatic Compounds. Part 4. Properties of Tetracarbonylvanadium Arene Cations and the Crystal and Molecular Structure of Tetracarbonyl(1,2,4,5Tetramethylbenzene)Vanadium(I) Hexacarbonylvanadate(1d). J. Chem. Soc., Dalton Trans. 1982, 1993–1997.

studied.90 Early reports by Hafner give d(53Cr) and Dn½ in 50 different octahedral Cr(0) complexes of type Cr(CO)5L, where L is a varied carbene ligand. Trends in the identity of L vary in p-donor/acceptor properties, affecting the ligand field strength, Do, and thus sp (Fig. 14). This tunability is reflected in d(53Cr), and within the octahedral set of complexes, a chemical shift range of  300 ppm downfield is observed from the established 0 ppm standard Cr(CO)6. Since then, few 53Cr NMR studies have been published to investigate the full extent of the chemical shift range of the 53Cr nucleus. The only temperature-dependent chemical shift data reported for 53Cr is in the work of Hafner et al.88 and indicate a minor temperature dependence.88 The molecule (CO5)Cr]C(NMe2)Ph over a 80
C temperature range, and in that range yielded less than a 0.1 ppm shift range. Thus, the Dd/DT chemical shift sensitivity of this compound is approximately 0.00125 ppm
C 1, which is extremely small, even smaller than 1H. However, the temperature dependence of the linewidth showed a moderate range over the 80
C window, broadened to 49.2 ppm (1000 Hz) at  40
C and 12.3 ppm (250 Hz) at 40
C. Owing to its quadrupolar nucleus, the impacts of temperature on Dn½ suggests the nuclear relaxation is sensitive to minute structural fluctuations. Furthermore, the narrowing of linewidths with

Fig. 14 Example peak positions of the 53Cr NMR spectra of class I chromium carbene complexes to demonstrate sensitivity of d to ligand identity. 53 Cr NMR spectra collected at 20.33 MHz on a Nicolet NT-360 MHz (1H) wide-bore spectrometer with a single frequency home-built probe. Samples collected at 0.4 M in acetone sealed under nitrogen. Constructed with data from Hafner, A.; Hegedus, L. S.; DeWeck, G.; Hawkins, B.; Doetz, K. H. Chromium-53 Nuclear Magnetic Resonance Studies of Pentacarbonylchromium Carbene Complexes. J. Am. Chem. Soc. 1968, 110, 8413–8421.

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increased temperature is resemblant of reduced correlation times and is a common feature in the solution-phase NMR of quadrupolar nuclei such as 51V, 59Co, 103Rh, etc.91–94 In a different study, the relaxation times have been measured in aqueous solutions of K2[CrO4] (0.5– 3.0 m).89 A slight increase in T1 (determined by the inversion-recovery method) occurred as the concentration decreased and extrapolation to zero concentration gave T1 ¼ 55  5 ms. The T1 values at the lower concentrations were similar in magnitude to the T2 values determined from the linewidths which suggest that the quadrupole relaxation mechanism determines the observed linewidths. It is worth noting that the many common oxidation states available to the synthetic chemist working with Cr (I, II, III) frequently introduce an open-shell electronic structure that is unfavorable for measuring NMR spectra. In the examples above, one is either exploring high-valent Cr(VI), which has no unpaired d electrons, or d6 Cr(0), a low-valent oxidation state stabilized by extremely strong-field ligands. In the former case, sp. is small because the lowest-energy state is a high-energy ligand to metal charge transfer. In the latter case, the lowest-energy state is from a d-d transition, but that d-d transition is extremely high energy because of the strong-field CO ligands. Furthermore, even in the latter case, strong CeCr bonding may only permit extremely minor changes in bond distances and angles with temperature. Hence, for both cases, the anticipated small flexibility of sp (indicated by the relatively small range of 53Cr chemical shifts), portends relatively minor temperature sensitivities.

9.22.5.2.5

55

Mn

The 55Mn isotope is I ¼ 5/2 and has a 100% natural abundance, making it potentially useful for NMR thermometry studies. Indeed, the nucleus is nearly 100 times more receptive than 13C. Yet the 55Mn nucleus bears a quadrupole moment, which does complicate the collection of 55Mn NMR spectra in low-symmetry complexes via rapid nuclear relaxation. Relevant oxidation states for Mn ions that can be studied are somewhat limited. The most common oxidation states for synthetic chemists interested in designing metal complexes are Mn(II, III, and IV) but these are open-shell electronic structures. Hence, systems with higher oxidation states, e.g., d0 Mn(VII), or lower oxidation states but with strong-field ligands, e.g., d6 Mn(I) are the systems of choice. Indeed, [MnO4] is commonly used as the standard for 55Mn NMR.35,95–97 Thermometry of the 55Mn nucleus appears in limited cases but is well demonstrated by Nielson et al. for octahedral complexes of the d6 Mn(I) ion.33 A system of [MnL6](BF4) salts, where a series of isocyanide ligands (L ¼ CNR and R ¼ Me, Et, iPr, tBu, cyclohexyl) produce subtle electronic structure consequences, shows ligand-specific temperature-dependent chemical shifts. Temperature sensitivities of the 55Mn nucleus range from values of Dd/DT ¼ 0.443 to 0.707 ppm
C 1 over a temperature range of  35 to 45
C in acetonitrile. Similar to chemical shift thermometry of other transition metals, d(55Mn) shifts downfield with increasing temperature, induced by greater sp through lowered DE. But the magnitudes of the changes are still relatively small compared to other species because of the necessity of a strong field ligand to stabilize the Mn(I) oxidation state. An interesting observation here is

Fig. 15 Variable-temperature 55Mn NMR peak positions for [Mn(CNC6H11)6]– collected at 49.52 MHz on a Nicolet NT200WB (200 MHz 1H) Spectrometer. Sample measured at 0.02 M solution in acetonitrile. Structure drawn for clarity. Constructed with data from Nielson, R. M.; Wherland, S. Multinuclear NMR Studies of Mn(CNR)6þ,2þ: R ¼ Methyl, Ethyl, Isopropyl, Tert-Butyl, Cyclohexyl, Benzyl, Phenyl, p-Tolyl, and p-Anisyl. Inorg. Chem. 1985, 24, 3458–3464.

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Transition metal nmr thermometry

that Dd/DT exhibits a decrease with greater ligand bulk in that prior series. Vibrational analyses of these experiments may enable a better understanding the impact of the ligand on Dd/DT. Nielson and Wherland reported the temperature-dependent 55Mn (I ¼ 5/2) NMR spectra in Mn(L)6 complexes Mn(I) where L ¼ CNR isocyanides varying the R groups (Fig. 15).33 Over the range  35 to þ 45
C in acetonitrile, the 55Mn chemical shift increased linearly with temperature. For all the complexes, except methyl and ethyl, the line width decreased monotonically with temperature. The magnitude of the line width change was 290 Hz for cyclohexyl and only 9 Hz for isopropyl over a similar temperature range. The line width increased slightly with temperature for the complexes with methyl and ethyl groups. The 55 Mn NMR spectra were also obtained for the cyclohexyl complex in (CH3)2SO, C2H5OH, (CH3)2CO, C6H5Br, and CHCl3 at various temperatures. The chemical shift again increased linearly with temperature, and the slopes were quite similar. The line widths decreased with temperature in the same manner as observed in acetonitrile, with the greatest effect, 360 Hz, being observed in C6H5Br. The spin-rotational mechanism is more important for molecules of small size, and this is observed since only the methyl and ethyl complexes’ line widths increase with temperature. For these same [MnL6](BF4) complexes, peak broadness of the 55Mn NMR signal was found to be exceptionally temperature dependent and determined by the R functional group of the CNR isocyanide ligand. Thus, both T1 and T2 relaxation dynamics are potentially controllable via synthetic means. Variation in the linewidths for the R ¼ Me and Et groups were found to change in opposite fashion from larger R ¼ i-Pr, t-Bu, and cyclohexyl groups. These data exemplify the implications of molecular symmetry to the quadrupolar coupling relaxation mechanism in 59Co systems, where decreased symmetry of the primary coordination sphere induces larger electric field gradients.35,98

9.22.5.2.6

57

Fe

The lone NMR active isotope of iron, 57Fe, has a natural abundance of only 2.12% and the receptivity relative to 1H is only 7.4  10 7 which makes direct detection methods difficult unless the species is isotopically enriched. 57Fe has a nuclear spin of I ¼ 1/2 and has a chemical shift range of approximately 12,000 ppm.99 NMR spectra for 57Fe are referenced to Fe(CO)5 at 0 ppm. The majority of studies on the temperature dependence of 57Fe chemical shifts has been performed on iron(II) porphyrinate compounds and its derivatives. Polam et al., Mink et al., and Balzter all showed that different iron(II) porphyrinate derivatives showed chemical shift dependencies of approximately 2.0–3.0 ppm
C 1.99 These chemical shifts have been loosely attributed to rotations of bonds in the porphyrinate rings at different temperatures.99 The relatively high Dd/DT values here are on the order of what is typically observed for 59Co. Low-spin Fe(II) is isoelectronic with low-spin Co(III), and hence both ions exhibit relatively low-lying excited states that contribute to sp and engender its strong temperature dependence. The astute coordination chemist would argue that Fe(II) ligand fields are typically weaker than the higher charge Co(III), and thus 57Fe should have an even wider reported chemical shift range and correspondingly higher temperature sensitivities than 59Co. It could be argued that this disagreement is simply the fact that Fe(II) is much more likely to be isolated as a high-spin species. Hence, an extraordinarily large window of 57Fe d values are inaccessible because the complexes possessing those chemical shifts are high spin. Time will tell whether this rationale is correct for chemical shift, but there is still enormous promise for the temperature sensitivities in those molecules that can be observed. The relaxation dynamics of 57Fe are relatively unique among the first row of the period table because the nucleus is I ¼ 1/2. As a result, 57Fe relaxation dynamics are not driven by quadrupolar relaxation, as is common in the rest of the series. Instead, relaxation dynamics are proposed as stemming from spin rotation or chemical shift anisotropy.57 Scalar coupling with ligand nuclei is possible

Fig. 16 Variable-temperature 57Fe NMR peak positions for [TMPFe(PMe3)(2-MeImH)], collected at 16.2 MHz (500 MHz 1H). Sample was enriched to 94.5% in 57Fe to facilitate analyses. Structure of related species [TMPFe(PMe3)2] depicted for clarity of structure type. Constructed with data from Mink, L. M.; Polam, J. R.; Christensen, K. A.; Bruck, M. A.; Walker, F. A. Electronic Effects in Transition Metal Porphyrins. 8. The Effect of Porphyrin Substituents, Axial Ligands, “Steric Crowding", Solvent, and Temperature on the 57Fe Chemical Shifts of a Series of Model Heme Complexes. 1995, 117, 9329–9339.

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and that can influence relaxation, but the systems where that exists show coupling between 57Fe and 14N and quadrupolar relaxation of 14N within a narrow “intermediate” time range.100 Some experimental evidence of a chemical shift anisotropy stems from work by Polam, Mink, Baltzer, and others, which showed that different iron(II) porphyrinate derivatives generally exhibit a wider linewidth with increasing chemical shift, which would suggest the activity of chemical shift anisotropy (Fig. 16).99 The larger the chemical shift, the larger the expected linewidth due to the larger expected chemical shift anisotropy. Baltzer and Oldfield later suggested that the chemical shift anisotropy determines the T1 and T2 relaxation times and hence the line widths of 57Fe signals by providing an effective mechanism of nuclear spin relaxation that includes the rotational correlation time of the molecule.101,102 A genuine challenge in the understanding of the spin relaxation mechanisms of 57Fe is simply the paucity of data! In order to make analysis easiest, one has to isotopically enrich their samples, which is expensive. Yet, the sharp linewidths are an intriguing possibility for high temperature sensitivity via relaxation.

9.22.5.2.7

59

Co

Cobalt is 100% abundant in the 59Co isotope, which bears an I ¼ 7/2 nuclear spin and a relatively large quadrupolar moment. The receptivity is also relatively large (0.3 vs 1H). This nucleus has the highest reported chemical shift window of the first row of the transition metal block, with molecules demonstrating peaks over a nearly 20,000 range of ppm. The oxidation states most commonly probed for 59Co are Co(III) and Co(I), as these oxidation states enable closed-shell configurations, with Co(I) appearing upfield of Co(III) and the general 59Co standard, [Co(CN)6]3–. Studies of the temperature sensitivity of the 59Co chemical shift are far more abundant than other metal nuclei. The initial investigation of Co(acac)3 (acac ¼ acetylacetonate) revealed 3.15 ppm
C 1 Dd/DT values in CDCl3 and spurred the first suggestion that 59 Co NMR spectroscopy could provide useful NMR thermometers.36 There is even one study of trying to capitalize on this discovery for use in vivo.103 Beyond the cursory assignment of a high sensitivity stemming from a strong temperature dependence of sp, the exact molecular strategies for controlling Dd/DT are unknown. Indeed, Co(acac)3 still displays the record temperature sensitivity for low-spin Co(III) complexes despite decades of work. Some examples of attempts to increase Dd/DT beyond the Co(acac)3 limit include studies to manipulate the acac ligand backbone,53 examine the role of ligand encapsulation,37 and ligand deuteration.49,51 All of these studies still produce sensitivities below 3.15 ppm
C 1 (Fig. 17). There are several promising routes for developing even higher Dd/DT values based on 59Co. For one, oxidation state dependence of Dd/DT is an alluring prospect– Co(I) would be anticipated to have more diffuse 3d orbitals, potentially imparting a higher Tsensitivity of the Co(I) electronic structure (and thus, greater change in d with T). However, investigations of Dd/DT for Co(I) are to the best of our knowledge unreported. A second possibility, revealed only extremely recently, would be the use of Co(II). For many of the foregoing metal nuclei, it was explicitly mentioned that open-shell oxidation states are best avoided owing to the unpaired electron. Yet, a relatively recent report of a putative Co(II) species exhibited a Dd/DT of 8.5 ppm
C 1, much higher than what is typically possible with Co(III) complexes.104 Even more recently, spin crossover in Co(III) was harnessed to reveal record Dd/DT values of 150 ppm
C 1, which is the largest for any known magnetic nucleus.7 This latter effort appears to exploit

Fig. 17 (a) Examples of six-coordinate Co(III) complexes studied for variable-temperature 59Co chemical shifts and their associated temperature dependencies. (b) variable-temperature 59Co NMR peak positions, normalized to the low temperature data points. Data were collected at ca. 118 MHz (500 MHz 1H) for all complexes except Co(acac)3, which was analyzed at 36 MHz (ca. 150 MHz 1H). Constructed with data from Levy, G. C.; Bailey, J. T.; Wright, D. A. A Sensitive NMR Thermometer for Multinuclei FT NMR. J. Magn. Reson. 1980, 37, 353–356; Ozvat, T. M.; Peña, M. E.; Zadrozny, J. M. Influence of Ligand Encapsulation on Cobalt-59 Chemical-Shift Thermometry. Chem. Sci. 2019, 10, 6727–6734; Krüger, G. J.; Reynhardt, E. C. New Investigation of the Structure of Trisacetylacetonatocobalt(III). Acta Cryst. Sect. B 1974, 30, 822–824; Górska, N.; Inaba, A.; Hirao, Y.; Mikuli, E.; Holderna, N. Structure, Molecular Motion, and Phase Transition of a Highly Disordered Crystal [Co(NH3)6](ClO4)3. RSC Adv. 2012, 2, 4283–4291; Iwata, M.; Nakatzu, K.; Saito, Y. The Crystal Structure of (þ)D-Tris(Ethylenediamine)Cobalt(III) Chloride Monohydrate, (þ)D-[Co(en)3]Cl3.H2O. Acta. Cryst. Sect. B 1969, 25, 2562–2571; Nagao, R.; Marumo, F.; Saito, Y. The Crystal Structure of (–)589-TRIS(1,3-Diaminopropane)Cobalt(III) Chloride Monohydrate, (–)589-[Co(tn)3]Cl3.H2O. Acta. Cryst. Sect. B 1973, 29, 2438–2443; Geue, R. J.; Snow, M. R. Structure, Conformational Analysis and Optical Activity of a Bis(Tridentate)Cobalt(III) Complex. (þ)589-Dll-Bis[1,1,1-Tris(Aminomethyl)Ethane]Cobalt(III) Chloride (þ)589-(R,R)-Tartrate Hydrate. Inorg. Chem. 1977, 16, 231–241; Geue, R. J.; Hambley, T. W.; Harrowfield, J. M.; Sargeson, A. M.; Snow, M. R. Metal Ion Encapsulation: Cobalt Cages Derived From Polyamines, Formaldehyde, and Nitromethane. J. Am. Chem. Soc. 1984, 106, 5478–5488.

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a change in the local hyperfine field engendered by a S ¼ 0 to S ¼ 2 conversion of the Co(III) ion hosting the 59Co nuclear spin not changes in sp for the abnormally high Dd/DT. The relaxation dynamics of 59Co and their temperature dependence are largely driven by quadrupolar relaxation mechanisms. As a result, changes in the coordination geometry massively affect spin-lattice relaxation, and in many cases, the impact on T1 is manifest in the apparent linewidths. For example, T1 at 25
C for K3[Co(CN)6] (T1 ¼ 120 ms) and Co(acac)3 (T1 ¼ 1.78 ms) show that this spin property varies drastically with structure even for both putative Oh geometries. The linewidths are likewise impacted, which is common in many N-donor metal complexes. Indeed, Doddrell et al., demonstrated this fact in several symmetric bidentate cobalt(III) complexes, where solvent-assisted molecular vibrations account for the fluctuations of the field gradient at the central cobalt nucleus.105,106 In some cases the linewidths are also driven by scalar relaxation, particularly for N-donor ligands. [Co(CN)6]3 is possibly an outlier owing to the strong ligand field and relatively nuclear-spin-free CN ligands. Being driven by an extremely strong ligand field stabilization energy to Oh geometry. As a result, this species exhibits an anomalously sharp NMR linewidth, and the predominant mechanism is actually a spin-rotational mechanism.67 Here, the noted difference in relaxation mechanism arises from assuming the linewidth is directly tied to T1 (i.e., T2 is limited by T1) and the linewidth exhibits a temperature dependence at odds with the expected linewidths for a quadrupolar relaxation process. Linewidths are highly influenced by extrinsic features of the cobalt complexes, e.g., their local environment. Au-Yeung et al. previously reported that the linewidths of the 59Co resonances of complexes of low symmetry show large increases when measured at high magnetic fields.107 The linewidths in different solvents are expected to vary due to the difference in viscosities of the solvents. Au-Yeung et al. also reported that the larger linewidths are found in the solvents with higher viscosity but that in some cases the linewidths vary by more than a factor of 20 in different solvents.108 The broader lines and more pronounced field dependences were associated with the stronger hydrogen bonding solvents.109 In the context of temperature sensing via relaxation, the foregoing discussion seems to underline the promise for 59Co. Temperature-dependent structures could be one mechanism of governing T1 (and thus linewidth), as these would cause T-dependent changes in the quadrupolar moment. But moreover, sensitivity to the solvent nature (and viscosity) would be exciting new ways of detecting that chemistry on a local level. It remains to be seen how far the 59Co nucleus can be pushed in this regard. One of the key challenges is that, at least on current instrumentation, for many geometries the quadrupolar relaxation process can be so fast that T1 relaxation is on the timescale of the pulse lengths that are possible with instrumentation. That then makes understanding the relaxation phenomena challenging because measurements are difficult.

9.22.5.2.8

61

Ni

The collection of 61Ni NMR spectra is challenging, let alone variable temperature measurements. The receptivity is approximately 20% of 13C and the natural abundance of the 61Ni isotope (the only magnetically active isotope of nickel) is only 1.19%. Short T2 relaxation times of the 61Ni nucleus are largely attributed to a quadrupolar relaxation mechanism that stems from the I ¼ 3/2 spin of the nucleus. The linewidth of 61Ni NMR spectra tends to be quite broad, especially in asymmetric complexes, due to large a quadrupolar moment of 0.128  10 28 m2.110 Ni(CO)4 is often used as a standard reference for 61Ni NMR with a chemical shift of 0 ppm in C6D6. The most common oxidation state of nickel is Ni(II) and said complexes are typically S ¼ 1, discouraging analysis. Hence 61Ni is far more successful when applied to less common (and closed-shell) Ni(0) oxidation states, and the reported window of 61Ni chemical shifts is about 1400 ppm. Still, the low resonance frequency of 26.8 MHz (with 1H is 300 MHz) often leads to severe ringing effects and rolling baselines; rendering the detection of broad signals with a chemical shift about 2000 ppm very difficult.111 The relevant energy gap for Ni(0) complexes (and the Cu and Zn sections that follow) stand in contrast to the metals studied so far. For the early transition metals, ligand-to-metal transitions guided sp because of the absence of 3d electrons. For the middle transition metals, d-d transitions were important. However, for Ni(0), the 3d orbitals are all filled. Hence, the relevant transitions of importance are the metal-to-ligand charge transfer transitions. Temperature sensitivities for the chemical shifts of 61Ni nuclei are not substantial, as expected from the relatively small chemical shift window (Fig. 18). However, the one instance of a variable-temperature 61Ni chemical shift study highlights nicely the control of Dd/DT via ligand field. In this series, tricarbonyl Ni(0) monophosphine complexes exhibited a smaller Dd/DT of 0.5 ppm
C 1 vs dicarbonyl diphosphine complexes, which were closer to Dd/DT of 0.8 ppm
C 1. In these systems, there is an apparent attempt to minimize the correlation time and thus they attempted to minimize the correlation time and thus the linewidth. However, the linewidth showed only minimal changes when the solvent and temperature varied. For example, measurement of the triphenylphosphine nickel complex in toluene at 298 K gave a linewidth value of 0.75 kHz and 0.74 kHz at 360 K. Additionally, these species have different metal-to-ligand charge transfer transitions, and tuning Dd/DT via this parameter is a promising strategy to be explored in the future. Alternatively, Ni(0) complexes with chelating isocyanide ligands offer long-lived 3MLCT states, an unexplored area in terms of 61Ni NMR, which could provide insights into maximizing Dd/DT.112 In the same study reported by Behringer, “easy” NMR methods to overcome the inherent properties of the 61Ni nucleus, including shimming, adjusting the signal-to-noise ratio due to broad lines, and pulse lengths for the relaxation studies were investigated. They measured the T1 values by using custom-made solenoid probe heads. They displayed short ring-down delays with a maximum of 10 ms, which is crucial for 61Ni NMR since the T1 values for the most nickel compounds are very short (< 10 ms). They reported the T1 values for complexes (CO)2Ni(PPh3)2 and Ni(CO)3(PPh3) as 0.4 ms and 19.9 ms, respectively. Lastly, Hao, Schrobilgen et al. reported a 61Ni NMR study on various Ni(0) complexes including Ni(PF3)4, Ni[P(OMe)3]4, Ni [P(OEt)3]4, Ni(CO)4, Ni(PCl3)4.110 In all compounds studied, the 61Ni linewidths are sufficiently narrow ( varies from 3.9 Hz

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Fig. 18 (a) Example 61Ni NMR peak positions for various 4-coordinate Ni complexes. (b) Structure of Ni(cod)2 and variable-temperature 61Ni NMR peak positions for this molecule collected on saturated C6D6 solutions, displaying 0.4 ppm
C 1 temperature dependence. Spectra were collected at ca. 36 MHz (400 MHz 1H). Green, gray, and white spheres represent Ni, C, and H atoms in the structure. Constructed with data from Werhun, P.; Bryce, D. L. Structural and Crystallographic Information from 61Ni Solid-State NMR Spectroscopy: Diamagnetic Nickel Compounds. Inorg. Chem. 2017, 56, 9996–10006; Macchi, P.; Proserpio, D. M.; Sironi, A. Experimental Electron Density Studies for Investigating the Metal p-Ligand Bond: the Case of Bis(1,5-Cyclooctadiene)Nickel. J. Am. Chem. Soc. 1998, 120, 1447–1455.

for Ni(CO)4 to 90 Hz Ni[P(OMe)3]4,) which allowed the observation of nuclear spin-spin coupling interactions with 61Ni. In the same study, the T1 value of 0.218 s was found for the 61Ni nucleus in Ni(CO)4 at 25
C, indicating efficient relaxation of 61Ni via quadrupolar relaxation. Note that even though the compound is symmetric, and the overall electric field gradient should be zero, asymmetric vibrations can still produce asymmetric environments at the nucleus and enable quadrupolar relaxation.67 No further relaxation studies or temperature-dependent chemical shift measurements were reported. Despite the aforementioned difficulties, the ranges of 61Ni NMR chemical shifts, coupling constants, relaxation times, and the linewidth still offer an unexplored area for assessing the viability of the natural abundance of 61Ni NMR as a structural probe.

9.22.5.2.9

63/65

Cu

Copper has two NMR active isotopes, 63Cu and 65Cu both of which have a nuclear spin of I ¼ 3/2 and a large natural abundance: 69.1 and 30.9%, respectively. The nuclear spin of 63Cu facilitates the quadrupole relaxation of Cu(I) containing diamagnetic species in lower symmetry environments. This leads to broader resonance lines; thus, it is difficult to detect the copper resonance signal for variable temperature studies. Reasonably narrow lines could only be observed in the solution of copper (I) complexes with regular tetrahedral symmetry and diagonal and trigonal planar copper complexes are known to be generally NMR silent.113 The common oxidation state of Cu(II) is not known for these species, presumably because of the open-shell nature of this ion. Connor et al. reported a 63Cu NMR study of the interaction between Cu(I) ions in [Cu(NCMe)4](BF4) and diarylazo complexes in acetonitrile.114 In the studied complexes, the 63Cu signal is broadened both by exchange contributions to the relaxation rate and by the presence of species of low point symmetry. No temperature-dependent studies of the chemical shift were reported. Despite the challenges associated with this nucleus, some information about the variable-temperature chemical shift behavior is known. Zepf et al. investigated the behavior of the 63Cu NMR signal in the tetrahedral coordinated Cu(I) complexes, (in the form of [CuL4]X (L ¼ CH3CN), or P(OC2H5)3, X ¼ ClO4, BF4 or p-CH3C6H4-SO3) as a function of temperature, solvent, and anion.[115] The temperature dependence of the 63Cu signal was found to vary significantly across the samples. The temperature-dependence of the sensitivities was reported as 0.75 ppm
C 1 for the tetrakisacetonitrile complex, and 0.1 ppm
C 1 for the organophosphite complexes (Fig. 19). In all complexes, the linewidth increased as temperature lowered, which is expected for the relaxation processes governed by the quadrupolar relaxation mechanism. The deviations from a perfect tetrahedral environment cause the linebroadening in both complexes. In the following reports, the chemical shifts in cuprous complexes including the observation of indirect spin-spin-coupling to coordinated 31P nucleus.116,117 In these complexes, the lack of a copper signal is attributed to a strong quadrupole interaction due to a residual electric field gradient at the 63Cu nucleus. The reasons responsible for this asymmetric charge distribution were stated as a slight distortion from regular tetrahedral geometry and strong metal to ligand back donation might influence the charge distribution. These reports also lack the temperature-dependent chemical shift and relaxation studies. This scarcity of knowledge in the 63/ 65 Cu complexes makes these nuclei difficult to utilize for desired temperature sensing applications.

9.22.5.2.10

67

Zn

Zn is a challenging nucleus for NMR. Indeed, the first NMR measurements of 67Zn were made in 1953 by Weaver et al.,118 and since then not many examples have been reported. The reason for this dearth is the relatively small NMR signal of 67Zn which has a natural abundance of 4%, a small nuclear magnetic moment and a nuclear spin of I ¼ 5/2. The 67Zn MMR signal in a 1 m aqueous

67

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Transition metal nmr thermometry

Fig. 19 (a) Structures of [Cu(NCCH3)4]þ and [Cu(P(OCH2CH3)3)4]þ, two Cu(I) complexes studied for temperature-dependent 63Cu NMR properties. Orange, red, blue, gray, and white spheres represent Cu, O, N, C, and H atoms, respectively. (b) 63Cu NMR peak positions for both complexes. Data were collected at 23.9 MHz (100 MHz 1H spectrometer). Samples were the ClO4 salts of the complexes in a and collected in CH3CN (for [Cu(NCCH3)4]þ) and CHCl3 (for [Cu(P(OCH2CH3)3)4]þ). Constructed with data from Kroneck, P.; Kodweiß, J.; Lutz, O.; Nolle, A.; Zepf, D. 63 Cu NMR Studies of Copper (I) Complexes in Solution: Influence of Anion, Solvent and Temperature on the Linewidth and Chemical Shift of the Copper Resonance. Z. Naturforsch. A 1982, 37, 186–190; Gill, D. S.; Singh, R.; Rana, D. S.; Wagler, J.; Kroke, E. Preparation, Characterization, X-Ray Structure Determination and Solution Properties of some Novel Copper(I) Bisulfate and Sulfate Salts and Their Stable Derivatives. Z. Naturforsch. B 2011, 66, 1042–1048; Fuchs, R.; Klüfers, P. Heteronuclear Co-Ordination Compounds With Metal-Metal Bonds, V(I), Reactions With [(NH3)2CuCo(CO)4]: Synthesis and Structure of [(PPh3)2CuCo(CO)4], [Cu{P(OMe)3}4][Cu{Co(CO)4}2] and (Ph3P)2N[Cu{Co(CO)4}2]. Z. Naturforsch. B 1991, 46, 507–518.

solution of a Zn salt is about 10 6 times weaker than the 1H signal in a solution with the same magnetic field. The chemical shift range of the 67Zn nucleus varies is ca. 3000 ppm. In addition to the low intrinsic sensitivity, solution-state 67Zn NMR is further hampered by the fact that molecular tumbling motion always induces efficient 67Zn quadrupole relaxation, resulting in short lifetimes and broad NMR lines, consequently making the 67Zn experiments remarkably difficult. With regard to the potential for

Fig. 20 Example variable-temperature 67Zn NMR peak positions of ZnCl2 dissolved in H2O. Concentrations (in molal) are depicted for each version, as well as the structure of the assigned ZnCl42 species with variable-temperature shift. Data were collected at 4.8 MHz (ca. 77 MHz 1H). Constructed with data from Epperlein, B. W.; Krüger, H.; Lutz, O.; Schwenk, A. Fourier Transform Nuclear Magnetic Resonance Studies of 67Zn. Z. Naturforsch. A 1974, 29, 1553–1557; Hennings, E.; Schmidt, H.; Voigt, W. Crystal Structures of ZnCl2$2.5H2O, ZnCl2$3H2O and ZnCl2$4.5H2O. Acta Cryst. E 2014, 70, 515–518.

Transition metal nmr thermometry

767

temperature dependence, the relevant energy gaps, like Ni(0) and Cu(I), are metal-to-ligand charge transfer transitions, because the Zn(II) ion is d10. To the best of our knowledge, only one report demonstrates the extent of the temperature dependence of the 67Zn chemical shift.119 In this study, Zn(II) salts dissolved in water revealed the following Dd/DT values: ZnBr2, 0.61; ZnCl2, 0.70, and Zn(ClO4)2, 0 ppm
C 1 (Fig. 20). These measurements are presumably of aqua complexes of these species, e.g., ZnCl2(H2O)n, but challenging to directly assign to ligand field considerations owing to the lack of characterization. Interestingly, there appears to be a substantial concentration dependence, up to ca. 0.2 ppm
C 1, on Dd/DT, which is not well understood. There is also a dependence of the 67Zn chemical shift on H2O/D2O,120 analogous to the effect of H/D exchange on amine complexes of 59Co.48,50 and though, unlike for 59 Co, the effect on temperature dependence or determination of the relaxation times has not been studied yet. For increasing temperature, a linear increase of the chemical shift and a nonlinear decrease of the linewidth for zinc halide solutions were reported,119 suggesting a weak utility of this nucleus for thermometry. The inconsistency in the trends in the change of the linewidth (along with the inherit line broadening due to the quadrupolar mechanism) might prevent high-resolution thermometry studies. Indeed, due to the linewidth values being very sensitive to the slight variations in concentration, temperature, pH, etc., a linear change in the temperature is required for the most accurate measurements but would be rapidly convoluted with many other changing chemical factors in a thermometry setting. Additionally, Zn2þ ions are vital in biological chemistry.121,122 Considering its importance, and the potential utility of Zn NMR for studying the Zn(II) species in solution, more systems should be developed for structural studies of controlling parameters contributing to temperature-dependent NMR parameters of 67Zn nucleus to develop guidelines for its applications in thermometry.

9.22.6

Conclusion and future directions

The use of magnetic resonance imaging (MRI) for biomedical diagnosis and physiological study is one of the most powerful applications of nuclear magnetic resonance. Thermometry may seem like a relatively straightforward or unimportant technique. Afterall, in the coronavirus pandemic many people became highly familiar with at-a-distance thermometry via handheld IR thermometers. Yet imaging the interior of the body is important for several cancer treatments, and even now, we are learning new and unusual aspects of temperature management inside the body (e.g., that the brain operates at temperatures of up to 40
C).6 The foregoing chapter illustrated what is known about the variable temperature response of metal-nucleus NMR and how it related to aspect of physical structure and electronic structure in the molecule surrounding the metal ion. But it is worth noting that the extent of what is known is clearly eclipsed by what is not! Indeed, for a few nuclei, the only solution-phase variabletemperature NMR data for some nuclei are limited to a mere mention in a manuscript, and any other variable-temperature data are restricted to the solid phase. Hence, to the novice who reads this chapter, the authors implore you see the opportunity here and devise your own questions in the area and explore them. There is an entire exciting area of research here with many, many questions still in need of answering. Below we highlight two exciting areas that we think are worth diving in deeper detail on. But again, we implore the reader to take on the mantle and find new areas beyond these! First, we note that a large part of the foregoing discussion was based on chemical-shift thermometry, and there we focused on the temperature sensitivity of a specific contribution to that shift, the paramagnetic shift sp. But that scope is fairly limited in the grand scheme of the fielddindeed, there are many magnetic interactions that can potentially shift the NMR frequency of a metal ion. One of these interactions is the electronuclear hyperfine interaction. The hyperfine interaction between unpaired electrons on metal ions and light-element nuclei on the ligand shell (e.g., 1H or 19F) is relatively well documented to produce strong environmental sensitivities.123–126 Indeed, this type of interaction has produced relatively enormous sensitivities, e.g., 14 ppm
C 1 for 1H and 31 ppm
C 1 for 31P.78,127 That same interaction has likewise demonstrated unprecedented Dd/DT values for metal ions: 150 ppm
C 1 for a select few Co complexes.7 These latter values are the highest for any studied nucleus! It would be worth expanding this area of study. Second, we also note that nearly all of the examples in this chapter were species that contained only one metal ion. Calibration is necessary for applying these species for thermometry using signal intensity as potential readout mechanism, a condition best avoided in favor of minimizing analysis time.128 We propose investigating multinuclear compounds, wherein more than one metal nucleus responds to radio frequencies within a reasonably close window and do so differently. In this case, one can exploit the difference in signals as a method of a thermometry with an internal standard. A system of this type could be, e.g., a dinuclear complex with two Co(III) ions with slightly different geometries. Titanium is an intriguing option because the two isotopes of titanium, 47Ti and 49Ti, appear within the same chemical shift window.83 As these nuclei possess different masses, they may have different temperature responses. Finally, if tuned just right, one could employ heteronuclear systems of completely different elements. Magnetic nuclei of different elements typically exhibit NMR spectra that are in distinct frequency windows. For example, one does not observe a 19F NMR signal when scanning the typical 1H window. For 59Co and 121Sb, however, the peaks show up in the same window, ostensibly because of the enormous width of possible d values for 59Co.129 Molecules including both these nuclei or other appropriately chosen matches of nuclei would be promising next ventures.

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Acknowledgements We thank the generous support of the National Science Foundation (CAREER award 2047325), the National Institute of Biomedical Imaging and Bioengineering (R21-EB027293), and the Research Corporation for Scientific Advancement (27663).

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Piotr Garbacz and Włodzimierz Makulski, University of Warsaw, Warsaw, Poland © 2023 Elsevier Ltd. All rights reserved.

9.23.1 9.23.1.1 9.23.1.2 9.23.1.3 9.23.1.4 9.23.2 9.23.2.1 9.23.2.2 9.23.2.3 9.23.2.4 9.23.3 9.23.3.1 9.23.3.2 9.23.3.3 9.23.3.4 9.23.3.5 9.23.3.6 9.23.3.7 9.23.4 References

NMR spectrum of a gaseous sample Density-dependence of gas-phase NMR spectrum Nuclear magnetic shielding Nuclear relaxation Indirect spin-spin coupling Applications of gas-phase NMR studies Determination of nuclear magnetic dipole moments Validation of results of state-of-the-art quantum mechanical computations Absolute shielding scales Hyperpolarization: Magnetic resonance imaging Gas-phase NMR of particular nuclei Noble gases Boron Silicon and germanium Nitrogen and phosphorus Oxygen and sulfur Halogens Heavy nuclei: Tin, tungsten and lead Conclusions

772 772 772 774 775 777 777 777 777 778 778 778 780 780 780 780 781 783 785 785

Abbreviations EFG Electric field gradient (V/m2) FWHM Full width at half maximum (Hz) IECS Isotope effects on chemical shifts J Indirect spin-spin coupling (Hz) MRI Magnetic resonance imaging NA Natural abundance NMR Nuclear magnetic resonance spectroscopy NQM Nuclear electric quadrupole moment (m2 or barn, where 1 b ¼ 10 28 m2) RF Radiofrequency S/N Signal-to-noise ratio T1 Spin-lattice (longitudinal) relaxation time (s) T2 Spin-spin (transverse) relaxation time (s) d Chemical shift (ppm; dimensionless) m Nuclear magnetic dipole moment (J/T) s Nuclear magnetic shielding (ppm; dimensionless)

Abstract The chapter presents the basis of the gas-phase NMR spectroscopy of nuclei other than 1H and 13C. It is devoted to features specific to gas-phase investigations of nuclear shielding, spin-spin coupling, and nuclear relaxation. These studies provide NMR parameters corresponding to the state of isolated molecules, enable the precise determination of nuclear magnetic moments, and provide information on NMR isotope substitution effects. Moreover, NMR gas-phase studies are considered from the perspective of applications, e.g., in porous materials and as case studies of particular elements: noble gases, halogens, oxygen and sulfur, boron, nitrogen and phosphorus, silicon, germanium, tin, and heavy metals such as lead and tungsten.

Comprehensive Inorganic Chemistry III, Volume 9

https://doi.org/10.1016/B978-0-12-823144-9.00046-7

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9.23.1

Gas-phase NMR of nuclei other than 1H and

13

C

NMR spectrum of a gaseous sample

Nuclear magnetic resonance (NMR) spectra may be observed in any phase due to a minimal coupling between nuclear and molecular degrees of freedom. However, in most cases, motional averaging affects spectra depending on the sample phase. For instance, the 31P NMR line of solid black phosphorus is more than a hundred times wider than that of P4 vapor for which FWHM z 100 Hz.1,2 The latter is noticeably broader than the linewidth observed in the liquid-state, i.e., the 31P NMR signal of white phosphorus dissolved in CS2 has a width of several Hz.3 Even more dramatic influence of the sample phase on NMR spectrum acquisition is observed due to variation of the time required for the return to the equilibrium state after radiofrequency excitation quantified by the T1 relaxation time. Nuclear relaxation of gaseous samples is typically fast, e.g., about 5 ms for phosphorus vapor, compared to liquid and solid-state state, e.g., T1 of solid black phosphorus reaches several tens of seconds. Other factors that impact the applicability of gas-phase NMR are that, in gases, typically the molar density is small (a fraction of mol/L1 under atmospheric pressure), and interactions between molecules are reduced compared to the liquid and solid states. As in solution, the molecules in the gas phase are subjected to fast random motion which results in the averaging of anisotropic nuclear interactions, consequently resulting in that most of the NMR spectra consisting of Lorentzian lines. For a broad review of NMR studies performed in the gas phase see Refs. [4–8] and references therein to original studies.

9.23.1.1

Density-dependence of gas-phase NMR spectrum

The density dependence of the gas-phase NMR spectrum may be briefly described as follows. In principle, studies in the region of pressure much below 1 bar (in the limiting case approaching vacuum) would give conditions well-suited for determining NMR parameters of an isolated molecule. However, at this region of sample densities, the sensitivity is low due to the low density of molecules (at least a thousand times lower than when the gas is liquefied). Additionally, a significant broadening of the NMR lines is observed because of the nuclear spin-rotation relaxation. Therefore, experimental studies in this region of sample densities are the most difficult. The lines become narrower when a pressure reaches a few bars, and the observed chemical shift varies linearly with pressure due to binary molecular collisions.9 The density-dependence slope of the chemical shift is determined by the magnetic susceptibility of the sample and the interaction-induced shielding. Depending on the system under study, one of these two factors may prevail, e.g., very high sensitivity to the electronic environment of 129Xe renders the magnetic susceptibility effect negligible compared to the interaction-induced shielding. In contrast, for 3He the magnetic susceptibility contributes significantly to the slope of shielding density dependence. Therefore, it is much easier to determine the NMR parameters by extrapolating the spectral parameters to the zero-density limit using the medium-pressure range, rather than from a low-pressure sample. At pressures of dozens of bars, the NMR line width may become comparable with typical line widths observed in the liquid state. Especially in the region of supercritical conditions, NMR lines become narrower. For nuclear relaxation suppression, mainly dissolution in supercritical CO2 was applied. Studies under these conditions were reviewed in Ref. [10]. In the high-pressure regime, the density dependence of the chemical shift is non-linear because of increasing contributions of multi-body collisions. In extreme cases, such as 19F NMR in perfluoro-n-hexane dissolved in CO2,11 the chemical shift does not vary with the gas density monotonically, i.e., it has a local minimum. The density-dependence of the frequency, width, and multiplet structure of NMR peaks observed in the gas-phase are described in more detail in the following subsections. Let us notice that the gas-phase NMR parameters may also be obtained independently from molecular beam experiments and high-resolution microwave spectroscopy.12

9.23.1.2

Nuclear magnetic shielding

The spin-precession frequency is a quantity, which depends on the strength of the magnetic field, whereas the property that depends only on the molecule’s electronic structure is nuclear magnetic shielding; thus, we will focus only on the latter. The magnetic shielding of a nucleus X, sA(X), is related to its resonance frequency, nA(X), in a molecule A by the equation:  m
hnA ð X Þ ¼ X 1  sA ð X Þ B0 ; (1) IX where mX and IX are respectively the nuclear magnetic dipole moment of the nucleus X (usually expressed in nuclear magnetons, i.e., 1 mN ¼ 5.050783699  10 27 J/T) and its spin number; B0 is the magnetic field strength (T), h ¼ 6.62607015  10 34 J sdthe Planck constant (seep Ref. [13] for the current values of physical constants). In Eq. (1), the total length of the nuclear magnetic ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi moment vector mX is ðI þ 1Þ=I times larger than its projection, i.e., mX, commonly referred to in the literature as “nuclear magnetic moment.” In the following text, the term nuclear magnetic moment will be used as a synonym for its projection. The relationship between magnetic shielding (dimensionless; 1 ppm ¼ 10 6) and chemical shift, dA(X), is dA ð X Þ ¼ sref ð X Þ  sA ð X Þ;

(2)

where s (X) is magnetic shielding of the nucleus X in a reference molecule. Eq. (2) is valid when s (X)  1. ref

A

1 Commonly used in older literature a non-SI unit of the gas density is amagat (amg), where 1 amagat ¼ 44.615 mol$m 3, i.e., the moles number of ideal gas atoms per unit volume at the pressure p ¼ 101.325 Pa and temperature T ¼ 273.15 K.

Gas-phase NMR of nuclei other than 1H and

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C

773

Let us consider the case of a pure gas A. The dependence of shielding sA(X) of the nucleus X in the molecule A on the density 9A is intractable. To obtain a closed-form expression, we take advantage of the fact that the shielding sA(X) weakly depends on the gas density 9A. The shielding sA(X) written as the power series in the density 9A (in mol/L or amg) is14:
sA X; 9A Þ ¼ sA0 ð X Þ þ sAA ð X Þ9A þ sAAA ð X Þ9A 2 þ .: (3) 1 2 Each coefficient of the nuclear shielding power expansion in Eq. (3) may depend on temperature, e.g., usually s1A  A decreases with increasing temperature. For instance, for pure 129Xe at room temperature, these coefficients are s0Xe(129Xe)¼ 7033.3(100) ppm,15 s1Xe(129Xe)¼  0.548(4) ppm/amg, and s2Xe(129Xe)¼  0.169(20)  10 3 ppm/amg2.16 The density-dependence of xenon-129 nuclear magnetic shielding and resonance frequency is illustrated in Fig. 1. The successive terms in Eq. (3) have the following physical interpretation: s0A is the nuclear magnetic shielding of X in the molecule which does not interact with other molecules (i.e., equivalent to an isolated molecule), s1A  A9A is the interaction-induced contribution to magnetic shielding due to collisions between the molecule A with other molecule A, and s2A  A  A is the contribution caused by three-body collisions of A molecules. In the microscopic picture, near room temperature and atmospheric pressure, the shielding sA(X) varies on the timescale of picoseconds: most of the time, the molecule does not interact with other molecules, and shielding of the nucleus X is s0. During the collision of two molecules, the gaseous dimer A-A forms, the shielding of which contributes to the coefficient s1A  A. Much less probable are collisions involving more than two molecules. Thus, if the density of gas does not exceed approx. 1 mol/L (20 bar) then higher-order terms in Eq. (3) are usually not observed, i.e., the coefficients starting from s2A  A  A are negligible. At higher densities, the density dependence becomes typically non-linear, and the unambiguous assignment of the contributions of multi-body interactions is not straightforward. In many cases, gas-phase data are reported in the zero-density limit. The most favorable situation is when gas A is a minimal admixture to gas B, which serves as a solvent (a buffer/carrier gas). In this situation in Eq. (3) higher terms may be omitted, and one finds that
ð X Þ9B ; (4) s X; 9A ; 9B Þ ¼ sA0 ð X Þ þ sAB 1 where s1A  B(X) is the interaction-induced shielding of the nucleus X in the A-B dimer. The frequencies of the collisions are proportional to the gases densities, thus in Eq. (4), shielding of the A-B dimer contributes to a weight of 9B. One should take caution using the literature interaction induced shielding s1A  B(X), since depending on the convention used, the contribution of the bulk molar magnetic susceptibility of the gas B, cB, may or may not be taken into account. The slope of the experimentally determined density dependence of shielding sA(X) is sAB ð X Þ  13cB (cB expressed in SI units, i.e., in L/mol) under 1 the assumption that the sample is an infinite cylinder whose axis is oriented along the magnetic field B0 (Fig. 2). For an infinite

Fig. 1 Nuclear magnetic shielding and resonance frequency of pressurized 129Xe (A). The linear in density component before (B) and after (C) the correction for the bulk magnetic susceptibility of 129Xe. The dashed line is an extrapolation of magnetic shielding from the medium pressure region to the zero-density point. Figure based on virial expansion coefficients reported in Refs. [15, 16].

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C

Fig. 2 The high-pressure (HP) cell placed in the homogeneous external magnetic field B0 (A). The horizontal cross-section and the magnetic field B0 are along the symmetry axis of the HP cell; the vertical cross-sections are at the height of the receiver coil. The magnetic field is distorted because of the magnetic susceptibility of the HP cell and the sample, which is most notable at the ends of the HP cell. At the height of the receiver coil, the magnetic field in the region where neon is placed is homogeneous and reduced almost by the same factor as for the infinite cylinder, i.e., it is smaller by 13cNe B0 . The picture is based on the results of the finite element computations performed in the COMSOL computer program and magnetic susceptibilities of materials taken from Ref. [17].

cylinder oriented perpendicularly to the magnetic field, the correction is þ 16cB , and it vanishes for a spherical sample. See Ref. [18] for other examples and the formula used to calculate the bulk magnetic susceptibility correction for any given sample shape. Let us exemplify the procedure of finding interaction-induced shielding from the experimental data on the case of studies of 3He dissolved in carbon dioxide.19 The measured slope of the nuclear shielding density dependence is þ 84.7 ppm mL/mol. The estimated bulk magnetic susceptibility correction is 13cB ¼  93:2 ppm mL/mol (the minus sign means that CO2 is diamagnetic). Thus, the interaction-induced coefficient is s1He  CO2(3He) ¼  8.5 ppm mL/mol, which means that the 3He-CO2 interaction induces deshielding of helium-3 nucleus. As for this system and also for most of the studied molecules, magnetic shielding decreases with gas density, i.e., the interaction-induced shielding s1A  B has the negative sign. Heavier nuclei in molecules with lone pairs may exhibit a positive slope of the shielding-density dependence as it is in the case of shielding of nitrogen-15 in CH3CN and HCN.20,21

9.23.1.3

Nuclear relaxation

Depending on the gas pressure, the relative contributions of the intrinsic nuclear relaxation, e.g., the formation of Xe2 van der Waals dimers in the case of xenon gas, and extrinsic nuclear relaxation, e.g., collisions with the walls of the glass container in which the xenon gas is sealed, may prevail. For instance, 129Xe intrinsic nuclear relaxation is caused by the spin-rotation and chemical shift anisotropy relaxation mechanisms.22,23 The nuclear relaxation rate depends on the gas pressure in a way similar to the relaxation rate dependence on the temperature for liquids, i.e., the dependence of T1 on temperature/pressure resembles a V-shape. The relaxation rate in the gas phase is the most efficient if the spin precession frequency matches the frequency of fluctuations of NMR interactions. The description of the appropriate theoretical treatment of nuclear relaxation in the gas phase is given in Ref. [24] and exemplified there in the case of the hydrogen-rare gas system. Qualitatively, the relationship between nuclear relaxation rate and pressure may be described as follows. For a single molecule in a vacuum, nuclear relaxation is suppressed. At the low-pressure limit, the nuclear relaxation rate increases with pressure, e.g., the longitudinal relaxation times of 19F nuclei in the spherical top molecules SiF4 and CF4 below atmospheric pressure do not exceed a few milliseconds at a temperature of 293 K.25 This pressure region was rarely explored experimentally due to decreased NMR signal intensities in such dilute samples. When the frequency of collisions becomes comparable with the spinprecession frequency, the nuclear relaxation rate reaches a maximum. For instance, the frequency of collisions between molecules is of the order of 1 GHz at standard conditions. For higher pressures, its efficiency decreases (Fig. 3). Most gas-phase NMR studies have been conducted in this pressure region. The widths of NMR lines may become as narrow as in the liquid phase, i.e., they have a width of a few Hz, for pressures ranging to several dozen bars. This narrowing is clearly visible

Gas-phase NMR of nuclei other than 1H and

13

C

775

Fig. 3 The increase of the NF3 pressure makes the multiplet structure observed in 19F NMR, i.e., 1:1:1 triplet of 14NF3 if relaxation effects on the NMR lineshape are neglected, becomes visible. The sample densities in spectra A, B, and C are 1.71 mol/L, 1.26 mol/L, and 0.628 mol/L, respectively. 19F NMR chemical shift is given relative to liquid CFCl3.

when the buffer gas is applied in supercritical conditions. In the region where longitudinal relaxation time (T1) is proportional to the gas density, the dependence of the nuclear relaxation on temperature T, e.g., T1/r, is proportional to 1/Tn. The exponent n depends on the dominating mechanism of relaxation, e.g., spin-rotation relaxation has n z 1.5 (e.g., 19F in CF426; 15N in 15N2O27).

9.23.1.4

Indirect spin-spin coupling

Gas-phase NMR studies of the indirect spin-spin coupling were reviewed in Ref. [28]; see also particular studies reported in Refs. [29–31]. For the indirect (scalar) spin-spin coupling between nuclei X and Y in the molecule A, an analogous equation to Eq. (4),
(5) J X; Y; 9B Þ ¼ J0 ð X; Y Þ þ J1AB ð X; Y Þ9B ; has applicability limited to the case of very well-resolved spectra since the motional averaging of the spin-spin coupling tensor J affects the multiplet splitting in a non-trivial way. In general, the separation between peak maxima is smaller than J0(X, Y) irrespective of the sign of J1A  B(X, Y). The theoretical basis for the analysis of NMR lines perturbed by nuclear relaxation processes is described in Ref. [32]. This behavior was firstly observed and described by Pople in the 14NH3 molecule.33 Rapid molecular reorientation and fast quadrupole 14N relaxation result in changes of the lineshape of the 19F signal of 14NF3, which is shown in Fig. 3. If we neglect the influence of the nuclear relaxation on the NMR signal, then the anticipated multiplet components widths are 1:1:1. However, the observed multiplet at high pressure consists of three partially overlapping lines of widths 3/2:1:3/2 because of nuclear quadrupole relaxation. Another example is the 1H NMR spectrum of PH3 that is given by the formula SðuÞ ¼ WM1 W T ; where

(6)

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Gas-phase NMR of nuclei other than 1H and

13

C

0 B B B B B B B B B B B B B 0 B B B B X; Y; 9B Þ B 0 u þ J M ¼ ıB B @ B B B B B B B B B B B B B X; Y; 9B Þ B B200u  J B B 1 B B 0 1 B B B B C a b B C B A; B B2C þ @ @ @ A b a

(7)

and ı is the imaginary unit and W ¼ (1, 1). The first component of the matrix M describes the unperturbed spectrum, while the second component describes the effect of the nuclear relaxation on the spectral line shape S(u). Parameters a and b vary with the gas density, and they depend on the T2 relaxation time of protons and the T1 relaxation of the phosphorus nucleus. Therefore, the accurate determination of the spin-spin coupling J0(X, Y) of the non-interacting molecule requires finding the best fit of the function S(u) to the experimental data. The multiplet splitting variation with the gas density may be qualitatively described as follows (Fig. 4). There are almost no collisions at very low densities; thus, nuclear relaxation is suppressed. In the limiting case of sample density, which reaches the zerodensity point, the separation between multiplet components equals J0(X, Y). Then, when the pressure increases, the multiplet collapses, and only a single line is observed. For higher pressures, the multiplet structure appears again, and at the low-pressure limit, the splitting is proportional to 1/9B2. The influence of nuclear relaxation on the apparent value of J0(X, Y) is twofold. The peaks broaden, and the multiplet components phases are shifted, i.e., a dispersion component becomes present. At the high-pressure limit, the binary collisions introduce an additional interaction-induced term which is proportional to 9B, i.e., the second term in Eq. (5). The differences between the multiplet splitting and the spin-spin coupling constant J0(X, Y) may reach several percent

Fig. 4 The variation of the doublet splitting with the pressure of the gaseous sample (the red line) and its linear extrapolation from the highpressure region (the blue line). When the pressure is low, the doublet collapses (A). In the mid-range of pressures, the distorted line shape by the nuclear relaxation is observed. It consists of absorption and dispersion components which make the splitting smaller than if relaxation would be not present (B). At the high-pressure range, the variation of the splitting is dominated by the contribution induced by intermolecular interactions (C). The slope of the splitting pressure dependence is vastly exaggerated compared to the effects of nuclear relaxation on the doublet splitting. Thus, in the majority of cases, the doublet splitting does not exceed J0(X, Y) even though J1A  B(X, Y) > 0.

Gas-phase NMR of nuclei other than 1H and

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C

777

even for resolved multiplets. For instance, the doublet observed in 31P NMR spectra of a neat gaseous phosphine has a splitting which is reduced by nearly 20% compared to the value of the 1J(31P, 1H) indirect spin-spin coupling constant.34

9.23.2

Applications of gas-phase NMR studies

9.23.2.1

Determination of nuclear magnetic dipole moments

The measurements of magnetic dipole moments of nuclei by NMR spectroscopy have high precision and accuracy (up to eight significant digits). These measurements are very well suited for studies of stable isotopes and those for which decay is slow. See Ref. [35] for a compilation of results obtained by applying different methods of nuclear magnetic dipole moment determination. The studies are usually conducted using a nucleus of known magnetic moment in a molecule which nuclear magnetic shielding can be calculated by quantum mechanical computations. For heavy nuclei, the inclusion of the correction for nuclear magnetic shielding may significantly influence the accuracy of nuclear moment determination, e.g., sPb(CH3)4(207Pb) exceeds 10,000 ppm. The sample may be a molecule that contains a proton (1H) as a reference nucleus and the nucleus for which the magnetic moment is determined, e.g., for 31P  PH3, 14/15N  NH3, 10/11B  BF3, 29Si  SiH4. The other option is to introduce a noble gas to the sample, such as 3He, and to use it as a reference. Since in both cases the sample is macroscopic, all nuclei are subjected to an applied magnetic field of the same strength; thus, one can use Eq. (1) for the reference nucleus Y and the studied nucleus X. Eliminating the field B0, one obtains 
nX 1  sA ðY Þ IX $ mðY Þ: mð X Þ ¼ $ (8) nY ð1  sA ð X ÞÞ IY The magnetic moments of a series of nuclei were determined, e.g., m(29Si) ¼  0.555052(3) mN,36 m(10B) ¼ 1.8004636(8) mN,37 m( P) ¼ 1.130925(5) mN,38 m(15N) ¼  0.283057(1) mN,39 and m(21Ne) ¼ 0.6617774(10) mN40 using this method. 31

9.23.2.2

Validation of results of state-of-the-art quantum mechanical computations

Gas-phase NMR provides spectral parameters such as nuclear magnetic shieldings, indirect spin-spin coupling constants, and electric field gradients, which can be easily compared with quantum mechanical computations. In the perturbative theoretical approach, the NMR spectral parameters are first computed for the equilibrium geometry of the molecule, then corrected for vibrations and rotations, e.g., applying the zero-point vibration correction and averaging over the Boltzmann distribution. Using gas-phase NMR data, one can separate these corrections, e.g., by studying isotope effects and comparing them with quantum chemical computations. For small molecules, experimentally determined nuclear magnetic shielding agrees with that computed using the coupledcluster singles and doubles method within  1 ppm for 15N,41  2 ppm for 19F,42  5 ppm for 17O43 and 31P.41

9.23.2.3

Absolute shielding scales

Absolute shielding scales are in contrast to chemical shift scales, where the reference choice is mainly arbitrary and primarily motivated by the sharp and strong NMR signal of the studied nucleus in the reference molecule, based on the physical quantity, namely, nuclear magnetic shielding. E.g., chemical shifts of fluorine in NF3 and HF measured relative to CFCl3 have opposite signs. However, it does not follow from this that 19F is shielded in one case and in the other is deshielded. Rather, the electrons in these molecules reduce the strength of the field near the nucleus in both cases since sHF(19F) > sCFCl3(19F) > sNF3(19F) > 0. The absolute shielding scales utilize the magnetic shielding of at least one reference compound. For the determination of the nuclear shielding in the molecule on which the scale is based, one may use different measurable quantities: (i) spin precession frequencies, (ii) spin rotation constants, (iii) nuclear relaxation times.44 Using these methods, absolute shielding scales of 19 45,46 15 F, N,47 77Se and 125Te,48 and 29Si49 were established. Eq. (1) considered from a different perspective than described in Section 9.23.2.1 may be used to establish an absolute shielding scale from spin precession frequencies if the nuclear moments are known with sufficient precision from other independent measurements. Taking as an example 3He, one can use the highly accurately computed nuclear magnetic shielding of the helium-3 atom, e.g., s(3He) ¼ 59.96743(10) ppm,50 and then find nuclear shielding of any other nucleus X by measuring the resonance frequencies of 3He and X in the studied molecule. In this way, instead of using a different standard for each nucleus, only one uniform scale for all nuclei is established. In practice, it is more convenient to determine the frequency ratio 3He/2H lock signal of the spectrometer, which avoids the necessity of equipping the NMR spectrometer with the probe which may be tuned to the 3He resonance. The 3He resonance lies halfway between the high and low bands used in most of NMR spectrometers. Details of this approach and the experimental procedure are given in Ref. [51]. An alternative procedure for the determination of absolute shielding scales is based on the Ramsey–Flygare relationship,52,53 which for heavy nuclei requires the inclusion of relativistic corrections. The Ramsey–Flygare relationship allows one to find the nuclear shielding based on the spin-rotation constant. Recent developments in absolute shielding scales for NMR spectroscopy and relativistic effects on nuclear magnetic shielding are given in Ref. [54].

778 9.23.2.4

Gas-phase NMR of nuclei other than 1H and

13

C

Hyperpolarization: Magnetic resonance imaging

The tiny difference between spin state populations, typically at most 10 4, observed at room temperature makes NMR sensitivity small compared with optical spectroscopies such as UV-VIS. However, this unfavorable factor may be significantly reduced if the difference between the spin populations is enhanced by the application of hyperpolarization techniques such as spin-exchange optical pumping (SEOP), dynamic nuclear polarization (DNP), or parahydrogen induced polarization (PHIP).55 In noble gases (3He, 129/131Xe), SEOP allows one to obtain enhancements of the signal reaching four orders of magnitude. When one of the reagents is a gas, usage of PHIP permits the transfer of the nuclear polarization from para-H2 to the studied gaseous compound56 and to conduct studies of heterogeneous catalysis.57 The NMR signal of hyperpolarized gaseous compounds has been used in magnetic resonance imaging, e.g., in studies of 19F MRI with the aid of perfluoropropane.58,59 See also Section 9.23.3.1 for further details relevant to the noble gases.

9.23.3

Gas-phase NMR of particular nuclei

NMR spectroscopy is capable of observing almost all elements (at least one isotope for a given element occurring naturally). However, the number of studied inorganic compounds in the gas phase by NMR is mainly determined by the physical properties of volatile compounds formed by a particular element and the nuclear properties of a chosen isotope of that element. Compared with the gas-phase NMR studies of the proton and carbon, which are present in numerous, primarily organic compounds, the gasphase NMR of other elements is more limited by the cardinality of available samples (Fig. 5). Noble gases were studied primarily by gas-phase NMR besides helium, which was also studied extensively by the liquid-state NMR due to quantum properties of 3He revealing at cryogenic temperatures. Since many hydrides and fluorides have low boiling points, their studies are a substantial part of the gas-phase NMR of inorganic compounds. Usage of these compounds is convenient since 1H and 19F are abundant and high-gyromagnetic ratio nuclei. Therefore, if they are present in the molecule, one may use polarization transfer to increase the magnetization of other nuclei in that molecule. This especially applies to p-block elements. In contrast to non-metals and semimetals, the number of volatile compounds of s- and d-block elements is limited, and NMR spectra of their inorganic compounds have been recorded mainly in solutions of their salts. Measurements of quadrupole nuclei, i.e., those of the spin number higher than ½, in the gas phase are challenging tasks. This mainly applies to compounds which do not have high symmetry (e.g., tetrahedral or octahedral). In this case, the quadrupole relaxation mechanism broadens the lines, which becomes a severe obstacle, especially considering the low density of observed nuclei in the gas phase. Another issue is the value of the gyromagnetic ratio of the isotope, which, if it is low, makes the gas-phase studies difficult.

9.23.3.1

Noble gases

The stable isotopes of noble (rare) gases which NMR can observe are 3He, 21Ne, 83Kr, 129Xe, and 131Xe. Typically, nuclei of noble gases relax slowly, e.g., at room temperature, the relaxation time for a 3He density of 10 amagats is 74.4 h60 and 129Xe under sufficiently low pressure has a T1 relaxation time that may reach nearly 100 h.61 Consequently, their gas-phase NMR lines are sharp, and

Fig. 5 The periodic table of gas-phase NMR spectroscopists. The elements are ranked according to the difficulty of their NMR spectral acquisition: ① easy-to-measure, i.e., natural abundance at least 10%, gyromagnetic ratio at least 20% of gH, spin-1/2; ② moderate-to-measure, i.e., between the first and the last group; ③ hard-to-measure, i.e., natural abundance smaller than 1%, presence of a quadrupole moment, gyromagnetic ratio smaller than 5% of gH. Elements that were studied in detail by gas-phase NMR spectroscopy are boldfaced. The safety issues of gas-phase sample handling, such as samples of mercury and lead compounds, are the primary factors limiting their gas-phase NMR studies.

Gas-phase NMR of nuclei other than 1H and

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their observed full widths at half maximum, which do not exceed 1 Hz, are mainly due to inhomogeneity of the magnetic field (Fig. 6). In the case of xenon-131, collisions between the noble gas atoms and the inner surfaces of the container in which the gas is placed may affect the shape of the NMR line.62 The interaction-induced shielding of pure noble gases varies from a fraction of ppm $ mL$ mol 1 for helium-3 to several thousand for xenon (Table 1). High sensitivity to variation of the electronic environment of 129/131Xe makes it an excellent probe for studies of microporous materials, e.g., their interactions with gases and diffusion in the material.65 For instance, one may infer the size and shape of cavities and the presence of paramagnetic centers from the NMR spectra of a noble gas introduced to porous materials.66–71 The variation of the noble gases’ chemical shifts with temperature has also been used to study liquid crystals.69 3He, 21Ne, 83Kr, and 129Xe gas-tosolution shifts follow the breadths of their chemical shift ranges, e.g., in CCl4 these shifts are respectively e0.406 ppm, e15.7 ppm,

Fig. 6 NMR spectra of noble gases. The conditions of measurements were: p ¼ 20–30 bar, T ¼ 300 K, B0 ¼ 11.74 T. The lineshape of the NMR spectrum is due to collisions between the gas atoms and the glass ampoule surface in which the gaseous sample was sealed.

Table 1 Element a (nX) 3

He

21

Ne

83

Kr

131

Nuclear parameters of noble gases determined from gas-phase NMR. Nuclear magnetic moment (mN)

Second virial coefficient of shielding s1X  X (ppm mL mol 1)

References

2.127,625,308(25)

0.37(12)

19,63

þ0.661,777,4(10)

82(1)

40

0.970,729,7(32)

3380.6(300)

64

129

0.777,961(16)

13,506(100)

15

131

þ0.691,845,1(70)

13,621(100)

15

Xe Xe

a40

Xe

Ar and 222Rn are radioactive isotopes, and they are not included in the table. From Makulski, W. and Garbacz, P. Gas-Phase21 Ne NMR Studies and the Nuclear Magnetic Dipole Moment of Neon-21. Magn. Reson. Chem. 2020, 58, 648–652.

780

Gas-phase NMR of nuclei other than 1H and

13

C

e109.8 ppm, and e222 ppm, and linearly correlate with each other.70 Moreover, the signals recorded from noble gas samples may be enhanced several thousand times using laser optical pumping and spin-exchange in comparison with the signal recorded at thermal equilibrium.72 Most studies have used hyperpolarized xenon but other gases, such as 3He, can be successfully hyperpolarized. Hyperpolarized gaseous xenon NMR finds applications in medical diagnostics, i.e., magnetic resonance imaging of lungs.73 NMR of noble gases is also used in studies of fullerene chemistry.74

9.23.3.2

Boron

Boron has two naturally occurring NMR active nuclei: 10B (NA: 19.9%; I(10B) ¼ 3) and 11B(NA: 80.1%; I(11B) ¼ 3/2). Both are quadrupolar and consequently have broad signals. Gas-phase studies of BF3 were reported in Refs.30,37,75 Absolute shielding scales of 10B and 11B based on the BF3 molecule, which may be pressurized up to 50 bar, gave s(BF3OEt2, liquid) ¼ 110.8 ppm in 10B NMR and 110.9 ppm in 11B NMR studies for this secondary reference. Moreover, 10B and 11B magnetic moments were determined using the resonance frequency of 3He introduced as a small admixture to the BF3 samples. The 11B NMR spectra of gaseous boron trifluoride show a characteristic 1:3:3:1 (quartet) multiplet due to spin-spin coupling with 19F nuclei. The indirect spin-spin coupling 1J0(11B,19F) in BF3, corrected for the intermolecular interactions, is 16.40 Hz at 300 K.75

9.23.3.3

Silicon and germanium

Si nuclei possess favorable intrinsic nuclear properties: a ½ spin number, a fairly high nuclear magnetic moment, and 4.70% natural abundance. The first gas-phase experiments were focused on studies of spin-rotation relaxation in SiH4 and SiF4 and provided the silicon absolute shielding scale.49 The revisited shielding scale of 29Si, based on the precise measurements of 1H and 29Si spectra in gaseous silane complemented by ab initio calculations, is described in Ref. [36]. The 29Si gas-to-liquid shift of Si(CH3)4 is tiny and equals  60 ppb.76 Extrapolated to the zero-density point 29Si nuclear magnetic shielding for Si(CH3)4, SiF4, and (SiF3)2O is 482.85 ppm,36 488.15 ppm,31 and 487.95 ppm,31 respectively. The indirect spin-spin coupling in silane is 1 J0(29Si, 1H) ¼  201.01(2) Hz.77 In contrast to 29Si, 73Ge gas-phase NMR spectroscopy is challenging because of an electric quadrupole moment (Q(73Ge) ¼  0.18  10 28 m2, I(73Ge) ¼ 9/2) and a low resonance frequency, i.e., 73Ge resonance frequency is about 3.5% of that of the proton, often beyond the capabilities of most NMR spectrometers. Thus, 73Ge gas-phase NMR studies are much more limited than those for silicon. See, for example, the studies of GeH476 and Ge(CH3)478 in Kr and Xe as buffer gases. The extrapolated zero-density point indirect spin-spin coupling in GeH4 is 1J(73Ge,1H) ¼  96.97(2) Hz.77 29

9.23.3.4

Nitrogen and phosphorus

Oxides, hydrides, and fluorides of nitrogen may be easily observed by gas-phase NMR. The less abundant isotope of nitrogen, 15N (NA: I(15N) ¼ 0.3%), gives sharp lines in contrast to the broad resonances of the more abundant and quadrupolar 14N (NA: I(14N) ¼ 99.6%). Phosphorus-31, with a relatively large gyromagnetic ratio, is also a good nucleus for gas-phase NMR studies (NA: 100%, I(31P) ¼ 1/2), but the number of its volatile compounds is more limited than in the case of nitrogen. Several compounds of nitrogen and phosphorus were studied in the gas phase, e.g., N2,79–81 NH3,82 N2O,27 and PH3.34,83 The nuclear properties of nitrogen compounds may be exemplified in molecular nitrogen. The reported value of the nitrogen shielding density dependence coefficients s0N2(14N) and s1N2  N2(14N) are respectively e63.4(2) ppm and ¼  112.6(8) ppm $ mL/mol.81 The indirect spin-spin coupling in the nitrogen molecule is 1J(15N, 14N) ¼ 1.8(6) Hz. The shift of 15N shielding due to 15N/14N substitution of the second nitrogen is 60.1(2) ppb.79 For 15N217O the spin-spin coupling 1J(17O, 15N) determined based on the multiplet splitting observed in a neat gas pressurized to 50 bar is 51.47 Hz (Ref. [5], p. 176). In the molecule of PH3, the indirect spin-spin coupling 1J0(31P, 1H), corrected for nuclear relaxation, is 176.18(2) Hz; its second virial coefficient is 1J1(31P, 1H) is 0.705(9) Hz L mol 1.34

9.23.3.5

Oxygen and sulfur

Oxygen-17 and sulfur-33 nuclear magnetic properties are similar; however, 33S gas-phase NMR spectra are significantly more challenging to record than 17O NMR because the quadrupole moment of sulfur-33 is almost 25 times larger than that of oxygen-17. Moreover, the low natural abundance of both 33S (0.76%) and 17O (0.038%) makes isotopic enrichment usually necessary to obtain gas-phase spectra with an acceptable signal-to-noise ratio. Several examples of shielding of volatile compounds of 17O and 33S are shown in Table 2. One of the most favorable compounds for observation of 33S NMR is sulfur hexafluoride. SF6 is a highly symmetric octahedral molecule; therefore, the electric field gradient at the sulfur nucleus vanishes. Consequently, quadrupolar line broadening is not observed, and the full width at half maximum of the 33S line is about 1 Hz (Fig. 7A). On the other hand, the lowering of the nuclear site symmetry in COS and SO2 dramatically broadens the 33S NMR line (Fig. 7B and C). When a fluorinated hydrocarbon such as CH3F or CHF3 is used as a buffer gas, water occurs as single molecules in contrast to the neat liquid. The use of CH3F or CHF3 permits a relatively high water content in the sample and prevents the fast exchange of protons

Gas-phase NMR of nuclei other than 1H and Table 2

13

C

781

Nuclear magnetic shielding for molecules containing oxygen-17 and sulfur-33.

Molecule

Nucleus

s0/ppm a

s1 /(ppm $mL/mol)

1

17

C O 12 17 C O2 14 17 N2 O 17 12 32 O C S 33 19 S F6

17

36.16(4)b 350.13(10) 64.97(10) 106.38(20) 200.15(10) 175.90(10)

1339(40)b,84 119(12)5,p.159 432(12)5,p.159 335(25)5,p.159 720(12)5,p.159 132(7)86

H217O 12 17

O O 17 O 17 O 17 O 33 S

a17

O shielding of isolated molecules relative to neat water at 300 K: Gaseous solution in xenon.

Spin-spin coupling /Hz 1

J(17O,1H) J(17O,13C) 1 17 13 J( O, C) 1 17 14 J( O, N) 1 17 14 J( O, N) 1 33 19 J( S, F) 1

e78.2284 16.485 16.185 51.475,p. 179 35.85,p. 179 e250.955,p.179

33

S relative to 2 M aqueous Cs2SO4 solution at 298 K.

b

that would hinder observation of indirect spin-spin coupling with oxygen-17. The water vapor 17O NMR spectrum clearly exhibits 1 H/2H isotope substitution effects on 17O nuclear shielding (Fig. 8). The indirect spin-spin coupling 1J(17O, 1H) in the isolated water molecule, e78.2(1) Hz,84 is almost the same as that for water encapsulated in fullerene, e77.9 Hz,87 and in 0.1% water solution in hexane, e78.70(2) Hz.88 However, it differs noticeably ( 10 Hz) from the value obtained for a liquid phase, which is 90(2) Hz.89

9.23.3.6

Halogens

Most gas-phase studies of halogens (19F, 35/37Cl, 79/81Br, 127I) have been devoted to fluorine. The lack of quadrupole moment and high gyromagnetic ratio makes 19F an easy-to-study nucleus by gas-phase NMR. Moreover, due to the high sensitivity of 19F shielding on the electronic environment, measurements of these spectra are very convenient in studies of subtle NMR effects such as isotope shifts. Large quadrupole moments of the heavier halogens result in a limited number of gas-phase NMR studies. The exception is hydrogen chloride for which gas-phase NMR studies led to the establishment of the 35Cl and 37Cl absolute shielding scales and their magnetic dipole moments: m(35Cl) ¼ þ 0.821721(5) mN and m(35Cl) ¼ þ 0.683997(4) mN.90 19 F NMR spectra in the gas phase were utilized to measure isotope effects on chemical shifts (IECS) in SiF4 and (SiF3)2O31 and in 37 BF3. The origin and general rules governing both phenomena are described in more detail in Refs. [1,91]. IECS of a nucleus X can be written in terms of the chemical shifts or nuclear magnetic shielding differences:

Fig. 7 33S NMR spectra of gaseous sulfur compounds: (A) SF6 (1.0 mol/L; room temperature), (B) SO2 (0.28 mol/L at 333 K), and (C) COS (0.80 mol/L at 323 K). Their chemical shifts, measured relative to the 2.0 M Cs2SO4 in D2O, are respectively 176.09 ppm, 357.76 ppm, and  457.65 ppm.

782

Gas-phase NMR of nuclei other than 1H and

13

C

Fig. 8 17O NMR spectrum of water vapor in the CHF3 buffer recorded at the density of 1.49 mol/L and temperature of 300 K. (A) and after its deconvolution shown in the reversed orientation (B). The signals from left to right are attributed to H217O, HD17O, and D217O, respectively. The spectrum was 1H-decoupled; thus, the coupling between 1H and 17O is not visible in the spectrum. n

DX



m=M





 Y ¼ dX M Y  dX m Y ¼ sX m Y  sX M Y :

(9)

Conventionally, M is the heavier isotope, and m is the lighter isotope of the element Y separated by n bonds from the nucleus X. In this convention, the isotope effects for n ¼ 1 are usually negative, i.e., the substitution of the lighter isotope by the heavier one decreases the resonance frequency of the nucleus X. One can rationalize this tendency by considering that (i) magnetic shielding decreases with the bond length,92 and (ii) the substitution of a nucleus by its heavier isotope lowers the vibrational ground state making the mean bond length shorter. Let us exemplify the secondary isotope effects, i.e., those due to substitution adjacent to the nucleus of interest in the molecule (n ¼ 1), in the case of sulfur hexafluoride.93 The 19F NMR spectrum of gaseous SF6 shown in Fig. 9 consists of well-resolved signals of 32SF6 (NA: 94.99%), 33SF6 (NA: 0.75%), and 34SF6 (NA: 4.25%). The 19F signal of 33SF6 is a quartet (1:1:1:1) because of coupling with a sulfur-33 nucleus with the spin number 3/2. The isotope effects on 19F due to sulfur nucleus substitution are: 1D19F(32/ 33 S) ¼  28 ppb, 1D19F(32/34S) ¼  51 ppb, 1D19F(32/36S) ¼  100 ppb (1 ppb ¼ 10 9). The last value was measured for the liquid SF6 sample since the signal of 36SF6 (NA: 0.01%) even in this case is barely visible. These isotope effects depend on the mass factor mM m in a linear manner. A similar dependence was observed in SeF6 and TeF6 molecules.94 In the case of a large relative change of isotope mass under substitution, e.g., 2H/1H, the secondary isotope effect on 19F shielding may result in dramatic shifts. For CH3F observed at p ¼ 20 bar, the substitution of two and three protons by deuterons, respectively, shifts the fluorine shielding by  1175 and  1735 ppb95 (see Fig. 10). Let us notice that the isotope substitution mainly affects the magnetic shielding extrapolated to the zero-density limit. It has almost no effect on the interaction-induced shielding, i.e., the slope of the shielding-density dependence. See Fig. 11 for an example of 19F magnetic shielding in NF3.

Gas-phase NMR of nuclei other than 1H and

13

C

783

Fig. 9 19F NMR spectrum of SF6 acquired in the gas-phase at room temperature and at a pressure of 26.0 bar. The upper trace shows the magnification of the quartet attributed to 33SF6. The lower trace shows an intense peak due to 32SF6 with a small peak on its right shoulder that is attributed to 34SF6. The chemical shift is referenced to neat CFCl3.

Several examples of 19F nuclear magnetic shielding determined by gas-phase NMR are shown in Table 3, including sevoflurane, desflurane, and halothane, which belong to the popular general inhalation anesthetic often in gaseous mixtures with xenon for the maintenance of anesthesia.

9.23.3.7

Heavy nuclei: Tin, tungsten and lead

In the following text, the term heavy nucleus refers to a nucleus that belongs to the 6th period of the periodic table, in contrast to the convention used in physics, where heavy nuclei are transuranium unstable nuclides with a Z number greater than 87. The measurement of heavy nuclei gas-phase NMR is typically challenging and limited by the small number of available stable compounds that are gases or volatile liquids at laboratory conditions. Tin has a very wide chemical shift range of approximately 6000 ppm and has three NMR-active isotopes: 115Sn (NA: 0.34%), 117 Sn (NA: 7.68%), and 119Sn(NA: 8.59%). The chemical shift reference, Sn(CH3)4, is well-suited for gas-phase NMR experiments (boiling point 74–76  C). The absolute shielding of neat liquid tetramethyltin is s(117/119Sn) ¼ 2181(200) ppm and was determined from relaxation studies and spin-rotation constants of Sn(CH3)4.97 The magnetic moments of tin isotopes m(119Sn) ¼  1.0447773mN, m(117Sn) ¼  0.9983147mN, and m(115Sn) ¼  0.9166864mN, were determined from gas-phase 117/119Sn NMR spectroscopy of Sn(CH3)4 mixtures with CO2 and N2O gases at 300 K.98 Tungsten has a limited number of volatile compounds, moderate natural abundance, and low gyromagnetic ratio, making it a challenging nucleus for gas-phase NMR studies. One of the favorable compounds of tungsten for gas-phase NMR is its hexafluoride, whose partial pressure reaches a fraction of the atmospheric pressure at room temperature. 183W gas-phase NMR spectra of WF6 were observed (i) applying CF4 under pressures up to 35 bar as the buffer gas that narrows its spectral lines and (ii) using the insensitive nuclei enhanced by polarization transfer, i.e., the INEPT pulse sequence, from 19F to 183W nuclei for increasing the signal-tonoise ratio. The nuclear dipole moment of 183W determined using the calculated magnetic shielding with relativistic corrections, s0(183W) ¼ 6221.0 ppm,99 is m(183W) ¼ 0.116953(18) mN.100 In WF6, the effect of intermolecular interactions on nuclear magnetic shielding of 183W is noticeable since its gas-to-liquid shift is Dsgl(183W) ¼  18.4 ppm. Lead, in particular its 207Pb isotope nucleus, has medium NMR sensitivity and a large range of chemical shifts exceeding 10,000 ppm; thus, despite its toxicity, it is well-suited for gas-phase NMR studies. 207Pb in volatile tetramethylead, Pb(CH3)4,

784

Gas-phase NMR of nuclei other than 1H and

13

C

Fig. 10 19F NMR spectrum of CH3F isotopologues recorder at the pressure of 20.4 bar. These are from the left to the right side, CH3F (A), CDH2F (B), CD2HF (C), and CD3F (D). The chemical shift is referenced to neat CFCl3.

Fig. 11 The density dependence of 19F magnetic shielding for 14NF3 and 15NF3 measured at the natural abundance of nitrogen for neat gaseous nitrogen trifluoride. The slope of the dependence without the correction for the bulk magnetic susceptibility is within the experimental uncertainty the same for both nitrogen isotopes and equals 192(12) ppm mL/mol.

Gas-phase NMR of nuclei other than 1H and Table 3

19

F compound

Desflurane

Halotane

C

785

F absolute nuclear magnetic shielding of selected compounds.

19

Sevoflurane

13

Solvent gas (CF3)2CHOCH2F (CF3)2CHOCH2F CF3CHFOCHF2 CF3CHFOCHF2 CF3CHFOCHF2 CF3CHFOCHF2 CF3CHBrCl

Xe 269.874(4) 353.073(7) Xe 280.657(4) 342.116(9) 280.929(9) 282.320(9) Xe 272.671(5)

CO2 269.884(7) 353.074(8) N2 O 280.656(4) 342.117(8) 280.937(9) 282.315(9) SF6 272.682(5)

References This work 96

96

was investigated by gas-phase NMR in mixtures with Xe and SF6. The 207Pb nuclear magnetic moment based on the extrapolated to zero-density limit 207Pb resonance frequency of the Pb(CH3)4 molecule yielded m(207Pb) ¼ 0.59064 mN.101

9.23.4

Conclusions

Gas-phase NMR spectroscopy offers a unique insight into intermolecular interactions and the determination of spectral parameters with high precision. This is mainly achieved because, compared with condensed phases, the strength of interactions between molecules and atoms in the vapor is reduced. On the other hand, the relatively low density of the gases makes gas-phase NMR studies challenging, especially in the case of fast nuclear relaxation and low-gamma nuclei. Several experimental strategies were developed to overcome the low S/N ratio in the gas phase, such as applying high pressure and hyperpolarization. In general, the dependence of the NMR signal on the pressure is complex except for the pressures from a few to roughly 20 bar, in which the dependence of the nuclear magnetic shielding (equivalently: chemical shift) on the gas density is linear. Gas-phase NMR studies are primarily devoted to volatile hydrides and fluorides, and noble gases. The studies in gas-phase provided nuclear magnetic dipole moments, permitted validation of results of state-of-the-art quantum mechanical computations, and enabled establishing absolute shielding scales for many nuclei besides 1H and 13C, e.g., 10B, 11B, 14N, 15N, 17O, 19F, 29Si, 31P, 33S, 35Cl, 37Cl, 73Ge, 117Sn, 119Sn, 183W, and 207Pb.

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Chem. 2014, 86, 6192–6196. 58. Couch, M. J.; Ball, I. K.; Li, T.; Fox, M. S.; Littlefield, S. L.; Biman, B.; Albert, M. S. Pulmonary Ultrashort Echo Time 19F MR Imaging with Inhaled Fluorinated Gas Mixtures in Healthy Volunteers: Feasibility. Radiology 2013, 269 (3), 903–909. 59. Halaweish, A. F.; Moon, R. E.; Foster, W. M.; et al. Perfluoropropane Gas as a Magnetic Resonance Lung Imaging Contrast Agent in Humans. Chest 2013, 144 (4), 1300–1310. 60. Newbury, N. R.; Barton, A. S.; Cates, G. D.; Happer, W.; Middleton, H. Gaseous 3He Magnetic Dipolar Spin Relaxation. Phys. Rev. A 1993, 48, 4411–4420. 61. Anger, B. C.; Schrank, G.; Schoeck, A.; Butler, K. A.; Solum, M. S.; et al. Gas-Phase Spin Relaxation of 129Xe. Phys. Rev. A 2008, 78. 043406-1–043406-10. 62. Meersmann, T.; Haake, M. Magnetic Field Dependent Xenon-131 Quadrupolar Splitting in Gas and Liquid Phase NMR. Phys. Rev. Lett. 1998, 81, 1211–1214. 63. Jackowski, K.; Jaszunski, M.; Kamienski, B.; Wilczek, M. NMR Frequency and Magnetic Dipole Moment of 3He Nucleus. J. Magn. Reson. 2008, 193, 147–149. 64. Makulski, W. 83Kr Nuclear Magnetic Moment in Terms of that of 3He. Magn. Reson. Chem. 2014, 52, 430–434. 65. Ito, T.; Fraissard, J. 129Xe NMR Study of Xenon Adsorbed on Y Zeolites. J. Chem. Phys. 1982, 76, 5225–5229. 66. Demarquay, J.; Fraissard, J. 129Xe NMR of Xenon Adsorbed on Zeolites: Relationship between the Chemical Shift and the Void Space. Chem. Phys. Lett. 1987, 136, 314–318. 67. Terskikh, V. V.; Moudrakovski, I. L.; Breeze, S. R.; et al. A General Correlation for the 129Xe NMR Chemical Shift  Pore Size Relationship in Porous Silica-Based Materials. Langmuir 2002, 18, 5653–5656. 68. Jameson, C. J.; de Dios, A. C. Xe Nuclear Magnetic Resonance Line Shapes in Nanochannels. J. Chem. Phys. 2002, 116, 3805–3821. 69. Jokisaari, J. NMR of Noble gases dissolved in liquid crystals. In NMR of Ordered Liquids; Burnell, E. E., de Lange, C. A., Eds., Springer: Dordrecht, 2003; pp 109–136. 70. Jokisaari, J. NMR of Noble Gases Dissolved in Isotropic and Anisotropic Liquids. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 1–26. 71. Garbacz, P.; Jackowski, K. NMR Shielding of Helium-3 in the Micropores of Zeolites. Micropor. Mesopor. Mat. 2015, 205, 52–55. 72. Albert, M.; Cates, G.; Driehuys, B.; et al. Biological Magnetic Resonance Imaging Using Laser-Polarized 129Xe. Nature 1994, 370, 199–201. 73. Goodson, B. M. J. Magn. Reson. 2002, 155, 157–216. 74. Saunders, M.; Jimenez-Vazquez, H. A.; Bangerter, B. W.; Cross, R. J.; Mroczkowski, S.; et al. 3He NMR: A Powerful New Tool for Following Fullerene Chemistry. J. Am. Chem. Soc. 1994, 116, 3621–3622.

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75. Jackowski, K.; Makulski, W.; Szyprowska, A.; Antusek, A.; Jaszunski, M. Temperature Dependence of the 1J(11B-19F) Spin–Spin Coupling in BF3 Molecule. Magn. Reson. Chem. 2009, 47, 857–861. 76. Makulski, W.; Jackowski, K. 1H, 13C and 29Si Magnetic Shielding in Gaseous and Liquid Tetramethylsilane. J. Magn. Reson. 2020, 313, 106716-1  106716-6. 77. Antusek, A.; Ke˛ dziera, D.; Jackowski, K.; Jaszunski, M.; Makulski, W. Indirect Spin-Spin Coupling Constants in CH4, SiH4 and GeH4 – Gas-Phase NMR Experiment and Ab Initio Calculations. Chem. Phys. 2008, 352, 320–326. 78. Nazarski, R. B.; Makulski, W. 1JCH Couplings in Group 14/IVA Tetramethyls from the Gas-Phase NMR and DFT Structural Study: A Search for the Best Computational Protocol. Phys. Chem. Chem. Phys. 2014, 16, 15699–15708. 79. Friedrich, J. O.; Wasylishen, R. E. The Nuclear Shielding Derivative and Spin–Spin Coupling in Nitrogen. J. Chem. Phys. 1985, 83, 3707–3708. 80. Jameson, C. J.; Jameson, A. K.; Smith, N. C. 15N Spin Relaxation Studies of N2 in Buffer Gases. Cross sections for molecular reorientation and rotational energy transfer. J. Chem. Phys. 1987, 86, 6833–6838. 81. Garbacz, P.; Misiak, M.; Jackowski, K. Interactions between Nitrogen and Oxygen Molecules Studied by Gas-Phase NMR Spectroscopy. Chem. Phys. Lett. 2018, 699, 194–198. 82. Jameson, C. J.; de Dios, A. C.; Jameson, A. K. Nuclear Magnetic Shielding of Nitrogen in Ammonia. J. Chem. Phys. 1991, 95, 1069–1079. 83. Jameson, C. J.; de Dios, A. C.; Jameson, A. K. The 31P Shielding in Phosphine. J. Chem. Phys. 1991, 95, 9042–9053. 84. Makulski, W.; Wilczek, W.; Jackowski, K. 17O and 1H NMR Spectral Parameters in Isolated Water Molecules. Phys. Chem. Chem. Phys. 2018, 20, 22468–22476. 85. Wasylishen, R. E.; Friedrich, J. O.; Mooibroek, S.; Macdonald, J. B. Isotope Shifts and Spin–Spin Coupling Constants in the 13C and 17O NMR Spectra of Carbon Monoxide and Carbon Dioxide. J. Chem. Phys. A 1985, 83, 548–551. 86. Jackowski, K.; Wilczek, M.; Makulski, W.; Kozminski, W. Effects of Intermolecular Interactions on 33S Magnetic Shielding in Gaseous SF6. J. Phys. Chem. A 2002, 106 (12), 2829–2832. 87. Elliott, S. J.; Bengs, C.; Kouril, K.; Meier, B.; Alom, S.; et al. NMR Lineshapes and Scalar Relaxation of the Water-Endofullerene H2 17O@C60. ChemPhysChem 2017, 19, 251–255. 88. Wasylishen, R. E.; Friedrich, J. O. Deuterium Isotope Effects on Nuclear Shielding Constants and Spin-Spin Coupling Constants in the Ammonium Ion, Ammonia, and Water. Can. J. Chem. 1987, 65, 2238–2243. 89. Burnett, L. J.; Zeltmann, A. H. 1H–17O Spin-Spin Coupling Constant in Liquid Water. J. Chem. Phys. 1974, 60, 4636–4637. 90. Jaszunski, M.; Repisky, M.; Demissie, T. B.; Komorovsky, S.; Malkin, E.; et al. Spin-Rotation and NMR Shielding Constants in HCl. J. Chem. Phys. 2013, 139, 234302. 91. Jameson, C. J. Fundamental Intramolecular and Intermolecular Information from NMR in the Gas Phase. In Gas Phase NMR. Experiment, Theory and Applications, RSC, 2016. 92. Jameson, C. J.; de Dios, A. C. The Nuclear Magnetic Shielding as a Function of Internuclear Separation. J. Chem. Phys. 1993, 98, 2208–2217. 93. Makulski, W. Isotope Effects on the 19F NMR Chemical Shifts in Sulfur Hexafluoride. Mol. Phys. Rep. 2001, 33, 82–86. 94. Jameson, C. J. Rovibrational Averaging of Nuclear Shielding in MX6 – Type Molecules. J. Chem. Phys. 1986, 85, 5484–5492. 95. Jackowski, K.; Kubiszewski, M.; Makulski, W. 13C and 19F Nuclear Shielding and Spin-Spin Coupling in Gaseous Fluoromethane-d3. J. Mol. Struct. 2002, 614, 267–272. 96. Macia˛ ga, E.; Makulski, W.; Jackowski, K.; Blicharska, B. Multinuclear NMR Studies of Gaseous and Liquid Sevoflurane. J. Mol. Struct. 2006, 785, 139–142. 97. Laaksonen, A.; Wasylishen, R. E. An Absolute Chemical Shielding Scale for Tin from NMR Relaxation Studies and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1995, 117, 392–400. 98. Makulski, W. Tetramethyltin Study by NMR Spectroscopy in the Gas and Liquid Phase. J. Mol. Struct. 2012, 1017 (2012), 45–50. 99. Ruud, K.; Demissie, T. D.; Jaszunski, M. Ab Initio and Relativistic DFT Study of Spin–Rotation and NMR Shielding Constants in XF6 Molecules, X ¼ S, Se, Te, Mo, and W. J. Chem. Phys. 2014, 140, 194308-1–194308-7. 100. Garbacz, P.; Makulski, W. 183W Nuclear Dipole Moment Determined by Gas-Phase NMR Spectroscopy. Chem. Phys. 2017, 498–499, 7–11. 101. Adrjan, B.; Makulski, W.; Jackowski, K.; Demissie, T. B.; Ruud, K. NMR Absolute Shielding Scale and Nuclear Magnetic Dipole Moment of 207Pb. Phys. Chem. Chem. Phys. 2016, 18, 16483–16490.

9.24

Applications of NMR spectroscopy in cultural heritage science

Molly Wagnera, Jaclyn Catalanob, Valeria Di Tullioc, Roberta Pigliapochid, Nicholas Zumbulyadisa,e, Silvia A. Centenod, and Cecil Dybowskia, a Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, United States; b Department of Chemistry and Biochemistry, Montclair State University, Montclair, NJ, United States; c “Segre-Capitani” Nuclear Magnetic Resonance Laboratory, ISB-CNR, Rome, Italy; d Department of Scientific Research, The Metropolitan Museum of Art, New York, NY, United States; and e Independent Researcher, Rochester, NY, United States © 2023 Elsevier Ltd. All rights reserved.

9.24.1 9.24.1.1 9.24.1.2 9.24.2 9.24.2.1 9.24.2.1.1 9.24.2.1.2 9.24.2.1.3 9.24.2.1.4 9.24.2.1.5 9.24.2.2 9.24.2.2.1 9.24.2.2.2 9.24.2.2.3 9.24.2.3 9.24.2.3.1 9.24.2.3.2 9.24.2.3.3 9.24.2.3.4 9.24.2.3.5 9.24.2.4 9.24.2.4.1 9.24.2.4.2 9.24.2.4.3 9.24.2.4.4 9.24.2.5 9.24.2.5.1 9.24.2.5.2 9.24.2.6 9.24.2.6.1 9.24.2.6.2 9.24.2.7 9.24.2.8 9.24.2.8.1 9.24.2.8.2 9.24.2.9 9.24.2.10 9.24.3 Acknowledgments References

Introduction Science and cultural heritage How does NMR spectroscopy provide a unique perspective? Case studies Stone and ceramics Porosity, water absorption, and distribution Cleaning methods Salts and pollutants Solid-state NMR characterization and provenance Pottery Paintings Wall paintings Canvas paintings Cleaning treatments Paints and their constituent parts Drying oils Mock films Heavy-metal soaps Maya blue Synthetic materials Biological remains and materials Mummies Bone Leathers Parchment Paper Model samples of paper Paper artifacts and conservation treatments Wood Wood artifacts Violins Textiles Resins, gums, and other plant products Amber, copals and jet Rubber and latex Synthetics Other substances associated with human life Conclusions

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Abstract Nuclear magnetic resonance spectroscopy has advanced our understanding of cultural heritage objects. Solution NMR, solid state NMR, unilateral NMR, magnetic resonance imaging (MRI) and other MR techniques have been used on a wide variety of materials such as stone, ceramics, paintings, biological remains, paper, wood, textiles, resins, gums, and synthetic materials. This review highlights NMR studies that provide structural and chemical identification, moisture content and distribution, uncovers artistic techniques, determines geographical origins, identifies constituent materials of an object and helps to

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determine the best cleaning or treatment method for conservation. In addition, physical and chemical transformations and structural modifications due to deterioration of an object can be monitored by NMR methods, and this information provides conservators with clues as to the most appropriate methods of preservation of a unique artifact. With the continued development of NMR pulse sequences, probes and sensors, the sensitivity and utility of NMR spectroscopy in cultural heritage continues to grow.

9.24.1

Introduction

9.24.1.1

Science and cultural heritage

Cultural heritage objects are dual-natureddthey are both something and about something.1 Physical science can provide meaningful information on certain questions that aid in the understanding and clarification of their material composition, region, method and date of creation, and authenticity. Although these attributes do not necessarily address their philosophical nature or the thoughts and opinions of their creators, they do connect the objects to the web of human history and provide insight into their relation to humanity. Cultural heritage objects may be quite complex as they can be composed of multiple materials structured in complex ways and some of these materials may have been altered due to aging, environmental factors, human interaction and/or cleaning or restoration treatments. Scientific methods can aid in answering many questions about cultural heritage objects. Nondestructive and noninvasive techniques are preferred when analyzing an object. If an object cannot be directly studied, models that simulate the object and its environment as closely as possible are used instead. Micro-sampling is only done when pertinent questions remain after exhausting all noninvasive testing options and the condition of the work allows for such sampling.2 Vibrational spectroscopic techniques such as Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy are easy to use, highly sensitive, require minimal or no invasive sampling and are routinely used for the characterization and identification of the molecular composition of cultural heritage objects.3–10 X-ray-based techniques including powder and single-crystal diffraction, X-ray fluorescence (XRF), and X-ray absorption near-edge structure (XANES) also provide valuable information, particularly regarding inorganic compounds, but may also be quite useful in the case of organic materials, and their distributions in objects.11–23 The use of macro-XRF mapping, full-field XRF imaging, and hyperspectral imaging of historical paintings has been covered in great detail.24 Scanning electron microscopy (SEM) and optical microscopy are used for inspecting objects of cultural interest.25,26 Chromatographic and/or mass spectrometric techniques, such as gas chromatography-mass spectrometry (GC-MS), pyrolysis-GC-MS, secondary ion mass spectrometry (SIMS), high performance liquid chromatography (HPLC), direct temperature-resolved mass spectrometry (DTMS) and related methods have also been used in cultural heritage studies.27–32 Most studies utilize a combination of techniques to answer specific questions about an object.

9.24.1.2

How does NMR spectroscopy provide a unique perspective?

Nuclear magnetic resonance (NMR) spectroscopy has been a powerful tool in chemistry since its inception in the mid-20th century; however, its application to studies in cultural heritage science is relatively recent. From its introduction as a tool for chemical analysis, NMR spectroscopy has been widely used to analyze samples in the liquid phase. Many materials of interest in cultural heritage cannot be solubilized without damaging the sample irreversibly, or modifying its molecular structure, which sets a limit on the application of liquid-state NMR spectroscopy to such objects. The advent of techniques that increase sensitivity, such as cryogenically-cooled probes (cryoprobes) or microprobes, has reduced sample size requirements and enabled a wider application of NMR spectroscopy in cultural heritage science.32,33 The development of NMR spectroscopy to address solid materials, such as high-power decoupling, magic-angle spinning (MAS), and cross-polarization to enhance sensitivity, and the more general trend of applying NMR spectroscopy to nuclei other than 1H and 13C has benefitted the study of a wide variety of cultural heritage studies with the technique.34,35 The use of unilateral NMR sensors has also increased the utility of NMR in certain cultural heritage studies. One particular advantage is that these sensors are portable and noninvasive. They can be used on arbitrarily sized artifacts in situ, obviating the need to move potentially fragile objects or allowing the study of immovable objects such as frescoes.36–39 The power of using the technique, however, is offset by the characteristic inhomogeneous magnetic field used, which typically eliminates detection of the chemical shift of nuclei for identifying specific chemical species. However, with careful set up and experimentation, unilateral NMR can be utilized as a form of high-resolution spectroscopy.40–42 Several reviews have focused on the applicability of the technique, particularly for samples that are difficult to study with traditional methods, such as fixed objects like frescoes and wall paintings or objects with specific environmental needs like continual cold storage.43–46 The portability and nondestructive nature of the unilateral NMR sensors are extremely appealing for cultural heritage studies. Although the application of the technique to cultural heritage is relatively recent, its applications and technological developments are continually growing. These developments include scan depths ranging from a few microns up to a few centimeters depending on the probe head chosen, giving one reasonable high depth resolution.47 Magnetic resonance imaging (MRI) can also be applied to cultural heritage studies, especially those involving human remains or other bone artifacts, as discussed in Section 9.24.2.4. Developments in MRI methods, previously limited to hydrated or rehydrated tissue, have allowed the study of human tissue morphology without necessitating the damaging rehydration step.48 These images

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provide invaluable information including soft-tissue differentiation, both to those looking to not only the preservation and conservation of these objects but also the paleopathology that can be discerned only from such imagery. In this review, we aim to illustrate the utility of NMR-based techniques in cultural heritage science to a broad array of cultural heritage objects, focusing on inorganic components and the effects of water and atmospheric moisture. Case studies of all of the aforementioned NMR techniques are discussed in detail throughout Section 9.24.2 which has been divided by type of material. While our intention was to cover as many of the numerous applications of NMR techniques to the field of cultural heritage the exponential growth of the applications of NMR spectroscopy to this field during the past decade precludes an exhaustive coverage of the topic. As an example, the application of NMR techniques to lead-based paints has been covered in great detail.49 Several reviews focusing specifically on the applicability of NMR techniques in cultural heritage studies have appeared.50,51

9.24.2

Case studies

9.24.2.1

Stone and ceramics

This section covers both natural stones as well as ceramic materials. These materials, while very different in composition and construction, are studied with similar methodologies. For this review, these materials have been grouped together under one heading and arranged by experimental goals and NMR methods. Porous materials, such as stone, mortar, brick, and concrete (as well as wood and paper, covered in later sections) absorb and release water in response to temperature and humidity fluctuations in their environment. The properties of these porous materials are affected by the moisture content that may lead to the degradation of these materials in a number of ways. First, rainwater acts as a transport of environmental pollutants (e.g., acid rain) that can react with the constituent components of an object, resulting in decay.52 Second, wet-dry cycles encourage solubilization, crystallization, and migration of salts inside porous structures, a process that may result in efflorescence and sub-fluorescence of salts throughout and on the surface of materials, thus potentially weakening the internal structure or ruining the esthetics of an object.53 Third, objects subjected to temperatures below the freezing point of water may be physically damaged by the pressure exerted by the expansion of ice crystals in the pores, resulting in micro- or macro-fractures.54 Fourth, moisture also encourages biological growth that can affect the esthetic and structural properties of an object.55 Climate change and increasing atmospheric pollution have increased the rate of these inexorable processes.53,56 Therefore, consolidation treatments are often necessary to prevent further damage. These treatments aim to reestablish the integrity of the original material, while still allowing for the necessary water vapor exchange and avoiding any visual or mechanical alteration to the object. To assess the damage and to provide the most effective treatment, scientific investigations of various aspects of the object are essential. Quantification of moisture inside a stone, pore distribution, variation in distribution over time, the effect of treatment(s) on the porosity, or the depth of penetration of a treatment are all areas that must be explored to address environmentally driven deterioration of these cultural artifacts.57,58 NMR spectroscopic analysis is exceptionally helpful in such investigations.

9.24.2.1.1

Porosity, water absorption, and distribution

Low-resolution 1H NMR analysis, both spatially resolved (tomography) and unresolved (relaxometry), has been widely used to study heterogeneous solid-liquid systems, particularly those characterized by high surface/volume ratios.57 Conventional MRI allows visualization of water dispersion and diffusion through porous media.57 This technique provides information on penetration depth, as well as the distribution of water before and after conservation treatments. These low-resolution NMR techniques require the sample to be contained within the magnetic field. An early study in 1995, performed on a home-built NMR instrument, assessed moisture content in fired-clay bricks.59 Other imaging techniques could not be used due to the large amount of paramagnetic material present in the bricks. Fire-clay bricks are typically composed of aluminum oxide, silicon oxide and other various oxides including iron (III) oxide. One-dimensional moisture concentration profiles were obtained for multiple types of fired-clay bricks and other porous building materials and used to determine the moisture transport in the systems, which could be modeled as a diffusive process. The diffusivity was found to be described as an exponential function of the moisture content of the brick, whereas absorption in other materials like gypsum (CaSO4$2H2O) and mortar could not be modeled as an exponential function of moisture content via this method due to their low iron content. This was the first NMR study done on fire-clay bricks and the methods determined here can be used to quantitatively determine moisture content in other brick samples.59 Hydrophobic treatments for stone artifacts are needed to decrease the uptake of water and the wettability of the stone yet must allow for vapor leakage and avoid modifying the visual image of the object. It is essential to test if the protective treatments work in prevention or retardance of water uptake. The following examples discussed briefly below have shown that NMR can aid is evaluating protective treatments by assessing water content and dynamics in stone samples. The effectiveness of Paraloid B72Ò (a 70/30 ethyl methacrylate/methyl acrylate copolymer) and Silirain 50Ò (an alkyl alkoxy silane oligomer) as consolidation treatments on biocalcarenite (Lecce Stone) exposed to liquid water has been monitored in several studies by MRI.57,60,61 The kinetics of capillary water uptake of the treated samples were monitored via MRI. The saturation depth of the water, and therefore the penetration depth of the treatment, can be determined when water is imbibed via the untreated face of the samples. Treatment efficiency can also be determined by testing water uptake via the treated faces.61 Another interesting example is found in reports of water monitoring in marbles from Candoglia and Carrara and travertine samples in treatments with Fluorophase (a fluorinated copolymer of vinylidene and esafluoropropene), Hydrophase (protective compound constituted by alkylsiloxane chains), and Paraloid B72Ò. The MR

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images provided a non-destructive determination of water ingress and a visual comparative method to evaluate treatment effectiveness and assess material inhomogeneity without the need to destroy the sample. MR images of stone samples before and after treatment provided visual maps to the treatments ability to penetrate the stones infrastructure and repel water. These measurements show the utility of MRI for studying the absorption and drying kinetics of water in porous samples.62,63 A combination of MRI and 1H relaxometry was used to monitor consolidation of dolomite via calcium hydroxide nanoparticles.64 The three-dimensional MRI results provided a visual comparison of pore sizes in specimens before and after treatment. NMR relaxometry data showed a shift in the longitudinal or spin-lattice relaxation (T1) distribution curve towards shorter times with treatment. The results indicated a general decrease in pore size after treatment, indicating that the consolidation treatments had been effective in reducing free volume that would trap water.64 When sample size is too large, such as in the case with most stone buildings and artifacts, and core removal is either not possible or a last resort, unilateral NMR studies provide information on moisture content and distribution in these samples. Unilateral NMR studies have been exceptionally useful for stone-based cultural heritage artifacts such as large buildings and walls. They have been shown to be comparable to standard NMR techniques for measuring parameters such as proton spin density, T1 and transverse (T2) relaxation times, and diffusion coefficients.36,65 The apparent relaxation time distribution within any porous media is affected by pore surface relaxation and internal field gradients in porous materials. Provided that the signal decay is dominated by the surface relaxation and the material is saturated by low-viscosity fluids, the decay curve associated with water in a single pore is a single exponential with a decay constant proportional to the pore size, with water in small pores displaying relaxation times shorter than that in large pores. Therefore, the 1H NMR signal in a porous material can be related to the material’s porosity and pore-size distribution as relaxation times of water are sensitive to the pore size and changes in the pore structure.47,51 One study demonstrated that unilateral NMR sensors can readily characterize the pore-size distribution of water-filled pores of sandstone, historical brick, and samples in various states of consolidation.66 The technique was shown to be comparable to traditional mercury intrusion porosimetry (MIP), but with the added benefit of removing the environmental impact of mercury use and eliminating the need to remove samples from the objects of study. Unlike MIP, unilateral NMR measurements allow analysis of samples containing ferromagnetic contamination, such as historical brick materials. In the study, distributions determined by unilateral NMR techniques better matched those obtained with MIP than those obtained via traditional low-field NMR measurements, presumably due to the statistical unlikelihood of large contaminant volumes in smaller sampling sizes. Unilateral NMR measurements sample in small, thin sensitive volumes that are statistically less likely to encounter the few large paramagnetic impurities that are found in the sample. In contrast, traditional low-field NMR is a bulk sampling technique thus increasing the statistical chance that the few impurities can affect the signal of the whole sample. Similarly, another study67 compared unilateral NMR techniques to MIP and low-field NMR techniques for characterizing pore size, using samples with imperfect surfaces or containing impurities. Comparison of MIP pore distributions with distributions derived from unilateral NMR T1 relaxation data demonstrated that the inhomogeneous field of the unilateral NMR device did not result in noticeably different distributions. However, T2 data were more complex and were affected by the magnetic field gradient inherent in materials containing para- or ferromagnetic impurities.67 In experiments done in a homogeneous field, the distribution of T2 times is a map of the pore-size distribution, whereas in the inhomogeneous field of a unilateral NMR sensor the distribution of T2 times cannot be directly related to the pore-size because the decay of the Carr-Purcell-Meiboom-Gill (CPMG) echo envelope is affected by diffusion and flip-angle distribution in the pulse sequence, such that only T2eff can be observed. Unilateral NMR has been utilized to determine porosity in water-saturated limestone and sandstone drill by normalization of the CPMG signal to 100% porosity and the integrals of the T2eff distribution curves normalized to pure water. The results were comparable values to those attained in a homogeneous field, with the advantages that samples did not need to be machined nor did they require a volume calibration and the sensor is portable.68 The effect of combined use of tetraethoxysilane (TEOS) and colloidal nanoparticles of silica and polytetrafluoroethylene on tuff stone has been assessed by unilateral NMR.69 Tuffs are of particular interest, as this volcanic stone is used widely in buildings, monuments, sculptures, and artifacts around the world. Tuff stone is heterogenous, composed of at least 75% volcanic ash and varies in composition and grain size but deterioration such as scaling, flaking and cracking effect all the stones. Its high porosity permits deep penetration of water, which may cause extensive damage. The unilateral NMR-derived diffusion measurements allowed estimates of the tortuosity and average surface-to-volume ratios of pores for the samples before and after treatments. The data showed a decrease in average pore radius for all treatments, with the nSiO2-nPTFE treatment showing the highest reduction of 47%. T2 distributions provided information regarding the water distribution in pores of various sizes. The presence of multiple peaks confirmed the heterogeneous nature of tuffs. All samples displayed a smaller percentage of water in larger pores after treatment indicating that the consolidation treatments were effective at reducing the average pore size of the material.69 Solid-state 29Si and 27Al MAS NMR spectroscopies have been applied to the investigation of degradation and conservation of building stones from La Basilica Colegiata de Nuestra Señora de Guanajuato, a UNESCO World Heritage Site in Central Mexico.70 The church was constructed from pink quarry, a material composed of quartz and feldspar-based (aluminosilicates) materials. NMR spectra were taken before and after consolidation with TEOS. Interestingly, several TEOS-treated samples seemingly “recovered” signal and appeared to be like the 29Si spectra of the untreated, undegraded stone showing a reversal of the decomposition of albite, which was in agreement with XRD patterns. The 27Al spectra also indicated a change after TEOS treatment, with the octahedral signal (albite) decreasing in intensity and becoming more shielded, suggesting a structural change in the material this is also noted by a change in the XRD pattern. Both the 29Si and the 27Al NMR results indicate a shift back towards the original, undegraded material. While these results are promising, several samples were too far degraded to show full “recovery” of the NMR resonances; however, these samples did show increased mechanical strength after TEOS treatment. Though not entirely conclusive, the results indicate the

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potential for TEOS consolidation treatments to regenerate some of the mechanical and structural properties of the degraded materials. The results also suggest the potential of solid-state NMR analysis to monitor degradation and consolidation processes.70 An assessment of signal intensities from CPMG echo envelopes measured with the unilateral NMR technique for saturated samples of Lecce stone and Yellow tuff, as well as bulk water, were used to calculate the open porosities of the stone samples.71 These were found to be 41% and 68% for Lecce stone and Yellow tuff, respectively. Interestingly, the open porosity for Lecce stone was comparable to that determined by traditional MIP; however, the open porosity for the tuff was substantially larger than the value determined by MIP. The discrepancy between the two techniques was attributed to the fact that MIP measures pore entry size while NMR measures the pore body. The presence of “ink bottle” pores (pores with small openings and large bodies) could therefore result in an underestimation of the porosity by MIP. NMR would be able to measure such pores thus highlighting the potential utility of unilateral NMR spectroscopy over MIP in determining porosity of porous samples. It should, however, be noted that an unsaturated sample could also provide an underestimation of the porosity by NMR.71 NMR techniques can monitor kinetics of water movement in and around stone samples. By assessing the depth and rates of water penetration in the samples, conclusions regarding preservation, conservation, and/or consolidation methods can be drawn. Additionally, the methods can be applied in the same manner to the cleaning gels and/or the gel-stone interfaces during treatment. One study showed that unilateral NMR techniques is comparable to MRI in monitoring kinetics of water uptake in Pale Finale samples treated with a conventional treatment, of copolymer Paraloid B72Ò, or acrylic monomers with an initiator AIBN to form the polymer within the pores.72 These treatments are applied as monomeric solutions introduced inside the porous network by capillary action. The solution is then polymerized either by frontal or in situ methods. Pale Finale is a type of calcareous sedimentary stone with shells widely used in buildings in northern Italy, was chosen for this study due to heterogeneous porosity and common use in cultural heritage objects. As with the previously discussed studies, T2 distributions measured with the unilateral NMR sensor provided information regarding the pore size distributions in the samples. Interestingly, the results of the study suggested that water-saturated samples treated with Paraloid B72Ò displayed signal intensities close to those of the untreated stone, indicating that treatment with Paraloid B72Ò does not affect water uptake. The monomer treatments forming polymers in situ, on the other hand, all displayed decreased NMR signal intensities when compared to untreated samples, indicating decreased water uptake after treatment.72 Unilateral NMR 1H depth profiles encode the amplitude of the proton signal as a function of depth scanned.73 Because the signal amplitude is directly proportional to the amount of water, comparisons of normalized amplitudes provide information about the amount of water absorbed by a sample as a function of treatment.74 One study75 reports unilateral NMR measurements of depth profiles of water in sandstone (10% porosity) and calcarenite (35% porosity) specimens for various times of application of a hydrophobic treatment: dimethylsiloxane in white spirits (a mixture of saturated aliphatic and alicyclic C7 to C12 hydrocarbons). This study was the first to report additional parameters that could be determined by unilateral NMR to access the conservation treatments including hydrophobic efficiency, penetration depth, and angles describing change of slope in depth profiles. The hydrophobic efficiency is determined by the loss of proton density as a function of depth. The penetration depth was determined by fitting the depth profiles and from calculating angles of the inflection in the slope in the depth profiles information regarding sample inhomogeneity can be determined. The sandstone samples showed decreasing amplitude of the NMR signal with increasing treatment time at 1 mm from the surface, whereas the signal at 5 mm was equivalent to the untreated stone, indicating that the hydrophobic effects of the treatment were not felt at 5 mm depth. The calcarenite samples showed substantially better hydrophobic efficiency than the sandstone samples at the longer treatment exposure times at depths of 1- and 5-mm. Fig. 1 shows one-dimensional depth profiles. Depth profiles of the sandstone samples (Fig. 1A and B) display lower amplitudes for the first 3 mm of sample. At greater depths, the signal is comparable to the untreated sample. Measurements of the calcarenite samples did not provide information regarding treatment effects on the penetration depth of water because the signal was very low across the entire specimen due to the effectiveness of the treatment (Fig. 1C). To gain further insight, the sample was flipped and allowed to absorb water through the untreated side which provided a better visualization of the penetration depth of the treatment (Fig. 1D). Transverse relaxation times (T2) of the treated and untreated samples measured by the unilateral NMR technique gave porosity information for the samples. Three T2 values were found for all samples, corresponding to water in small (short T2), medium, and large pores (long T2). Changes in the distribution functions provided information on the change in porosity due to the various treatments, showing that after treatment there was a loss of water in medium and large pores.75 A unilateral NMR to study of hydrophobic treatments on samples of sandstone and limestone was compared to results from gravimetric analysis to further validate unilateral NMR as an effective technique to measure water adsorption compared to traditional techniques that use micro-destructive core-sample extraction.76 Average hydrophobic efficiency and the water absorption coefficient measured by unilateral NMR were shown to indicate effectiveness of a hydrophobic treatment and were in agreement with gravimetric analysis. Importantly, the NMR measurement was carried out in situ, without necessitating the removal of a core sample. Hydrophobic depth, on the other hand, traditionally requires measurement of water ingress from the untreated side, which is more difficult, if not impossible, to monitor in situ without destructive methods. The authors of the study noted that the unilateral NMR hydrophobic depth measurement is still valuable in a laboratory setting, as it allows more precise determination of treatment depth than the traditional visual approach done with extracted core samples. Therefore, for model samples, hydrophobic depth can be determined with great precision in the laboratory without necessitating core sample removal.76

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Fig. 1 Depth profiles of sandstone (A and B) and calcarenite (C–E). (A and C) Involved water absorption from the treated face. (D) Involved water absorption from the untreated face. (B and E) Show mathematical fitting of the experimental data visible in A and D, respectively. Reproduced with permission, from Di Tullio, V.; Proietti, N.; Capitani, D.; Nicolini, I.; Mecchi, A. M., NMR Depth Profiles as a Non-invasive Analytical Tool to Probe the Penetration Depth of Hydrophobic Treatments and Inhomogeneities in Treated Porous Stones. Anal. Bioanal. Chem. 2011, 400 (9), 3151–3164.

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9.24.2.1.2

Cleaning methods

Unilateral NMR water-monitoring has been used in assessing agar gels as cleaning agents for stone materials.77 Gelling agents provide better extraction of contaminants than traditional solvent methods by mitigating solvent evaporation at the surface and encouraging penetration into the pores. Semi-rigid gels, such as agar, have the added benefit of inherent stiffness that simplifies their removal from the stonework and minimizes the potential for residual matter being left behind. Gels can be made with varying percentages of agar in water with or without additional chemicals to tailor the cleaning agent to the substrate. For example, gels with and without EDTA (ethylenediaminetetraacetic acid) were investigated to remove copper stains (caused by precipitation of copper salts) from stone. Formation of salts on the stones can lead to deterioration caused by salt crystallization pressure inside a porous material. However, studies are also needed to make sure the effects of the treatments do not cause more damage leaving trapped water in the stone. In this study77 the release of water from agar gels to the pores of Noto calcarenite (36.2% porosity) was investigated via unilateral NMR depth profiling. The amplitude of the 1H depth profile of the stone samples shows the water uptake at distances of up to 20 mm from the surface. (Fig. 2) In A, the gel with the lowest weight percent of agar (1%) demonstrated a rapid ingress of water across the entire 20 mm sample depth. In B, the intermediate weight percent gel (3%) also showed water ingress across the entire sample depth, but at a much slower rate. In C, the largest weight percent gel (5%) did not allow complete penetration even after many hours of contact of water with the stone. It is clear from these results that the kinetics of water absorption at the gel-stone interface is mediated by the amount of agar in the gel. The amplitude of the signal is

Fig. 2 1H depth profiles obtained via unilateral NMR techniques for Noto calcarenite stone samples after contact with 1% (A), 3% (B), or 5% (C) agar gels after 30 (black), 60 (white), and 240 (gray) minutes. The depth profile for the dry stone is displayed as grey squares in box A. Reproduced with permission from Canevali, C.; Fasoli, M.; Bertasa, M.; Botteon, A.; Colombo, A.; Di Tullio, V.; Capitani, D.; Proietti, N.; Scalarone, D.; Sansonetti, A., A Multi-Analytical Approach for the Study of Copper Stain Removal by Agar Gels. Microchem. J. 2016, 129, 249–258.

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reduced as the agar concentration is increased, indicating that the total absorption of water decreases with increasing agar concentration.77 To evaluate water in the gels during desorption, T2eff measurements of the gels were taken after the agar gel was in contact with the stone for 0, 30, 60, and 240 min. All samples demonstrated biexponential T2 decay with the longer relaxation time attributed to “free” waterdwater that is able to move freely across the gel-stone interface, and the shorter relaxation time attributed to “bound” water, i.e., water affected by hydrogen bonding and/or chemical exchange with the agar matrix. The mobility of “free” water was found to decrease with increasing agar concentration and with increasing time. This observation was explained as a result of shrinking free space among the agar chains in the gel matrix, either by the initially higher concentration of agar chains or by the decreasing space between chains as the water from those spaces move into the stone matrix. The gels with additives such as EDTA were shown to remove hydrated copper sulfate and brochantite (Cu4SO4(OH)6) by inductively coupled plasma atomic emission spectroscopy (ICP-AES).77 Unilateral NMR techniques have been utilized to determine that total open porosity, average pore size, tortuosity and water release from gellan gum gels into multiple stone substrates.71 Diffusion of water in the gels and the distribution of two different stones with different porosities, Lecce stone (41% porosity) and yellow tuff (68% porosity). The effect of using gellan gum gels (linear, anionic heteropolysaccharide produced by the microorganism Sphingomonas elodea) for cleaning of stones were also studied.71 1H depth profiles taken of the stone samples after various times of exposure to 1.5% and 3% gel concentrations indicated that Lecce stone was saturated by water faster and deeper than the yellow tuff, showing that in addition to porosity composition of the stone is also important. 1H depth profiles for the gels showed gel deformation during the water absorption by the stone. The gel deformed faster when applied to yellow tuff than to the Lecce stone. All results indicated that the release of water by the gel and its subsequent absorption by the stone substrate were affected by the gel’s properties, as well as the porosity and composition of the support.71 There have been many polymers used as consolidants and/or water repellants in the conservation of stone structures, with the intent of preventing further damage. However, numerous products have failed to work without consequence and have caused additional problems for conservators, such as yellowing or physical damage. It is thus important to analyze their removal from an object. 1 H and 13C solution NMR spectroscopies, in conjunction with a number of other techniques, have been used to quantify the relative efficiency of several nanocontainer aqueous systems (in comparison to acetone) for the removal of two consolidation treatments, Paraloid B72Ò and Dri-Film 104Ò (partially prepolymerized alkoxy silane), both fresh and aged.78 Three removal treatments were tested via cellulose poultices containing acetone or sodium dodecyl sulfate in a microemulsion or as a micellar solution. Direct application of solvents, while often effective for the removal of previous conservation treatments, can also affect the underlying substrate directly or allow for the solubilized substance to diffuse further into the object being conserved. Additionally, the use of copious amounts of organic solvents has a high environmental impact. It is therefore of great interest to find a system that both minimizes the amount of solvent used and allows for full impact to remove the previous treatment. Nanocontainers provide a potential system that uses minimal solvent but is still able to solubilize the substance needing to be removed. NMR analyzes of the soluble fractions of the applied materials indicated that traditional acetone treatment removed a greater quantity of polymer than using the two nanocontainer treatments, although extracted materials from all treatments showed evidence of polymer removal. These observations agree with the strong “absolute” removing power of acetone, but the lower content in the nanocontainer systems could be partially attributed to incomplete extraction. Additionally, as the complete removal of the polymer is not always advisable due to potential weakening of mechanical properties in the structure or dispersion of the solubilized polymer, the nanocontainers may represent a reasonable “green” choice for treatment.78 1 H solution NMR spectroscopy was used to identify waxes used as protective coatings on eight different stone surfaces and to evaluate the efficiency of three solvents/solvent mixtures in removing the waxes from the surfaces.79 1H NMR data for paraffin and beeswax samples showed distinct spectra that could be used to identify each material and thus guide conservation treatments. For example, the study identified the surface coatings on a 16th century marble statue, Madonna with Child by Antonello Gagini (1503). The color and distribution of the coating varied across the surface of the sculpture and was believed by restorers to be a mix of both beeswax and paraffin. Several samples were taken across the surface of the statue and, contrary to the restorers’ hypotheses, the 1H NMR data indicated they were exclusively beeswax. Preliminary 1H NMR analysis of the solvent solutions tested for wax removal. The results indicated that beeswax is generally easier to remove from stone surfaces than paraffin, especially with a solvent mixture of cyclohexane and ethyl acetate, with up to 99% removal. In addition, removal of waxes from an object was dependent on the porosity of the stone sample.79

9.24.2.1.3

Salts and pollutants

The presence of atmospheric pollutants is a known source of degradation of stone objects.53,54,80 The absorption and desorption of water facilitates the transport of deliquescent salts and reactive atmospheric compounds, as well as soluble minerals in the stone. The presence of deliquescent salts promotes water adsorption. Calcareous stone is particularly prone to degradation by reaction with the acidic products of atmospheric pollutants, such as SOx, NOx, CO2, and water.80 These reactions convert the relatively insoluble CaCO3 into soluble Ca(NO3)2 and CO2. Unilateral NMR techniques have been employed to monitor the kinetics of water absorption and condensation in samples of Lecce stone artificially polluted with known concentrations of Ca(NO3)2 , 4H2O.80 Gravimetric data indicate that the artificially polluted samples have larger increases in absorbed water mass as compared to unpolluted samples and the same results were shown by unilateral NMR. T2 distributions taken for the untreated and two treated samples at varying times up to 12 days exposure to 80%

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relative humidity. The distribution for an untreated sample increases slightly in amplitude over time but it remains centered at short values of T2 values, as expected for water having van der Waals interactions at the surface (Fig. 3A). On the other hand, the distributions for the polluted samples (Fig. 3B and C) exhibit very different behavior with increasing sorption times and increasing pollution exposure, the signal amplitude increases significantly and the distributions shift towards longer values of T2, suggesting increasing amounts of mobile water in the samples treated in this manner. (Fig. 3) At short sorption times, the presence of salt influences the kinetics but not the mechanism of water adsorption as evidenced by the fact that the T2 values of the polluted and non-polluted samples are nearly indistinguishable. At longer sorption times, however, the T2 distribution curves for the polluted samples, though markedly similar to each other, vary greatly from the unpolluted sample indicating that the presence of the salts has affected the water condensation mechanism and kinetics. Although a mathematical model is not possible in these complex systems, there is an increase both in quantity and mobility of water in the polluted samples, which could be used as in situ references for insight on pollutants in real porous stone objects.80 Low-resolution liquid-state NMR spectroscopy has been utilized to analyze the formation of salt crystals in porous structures. Salt crystallization may occur at the surface in a process known as efflorescence, or below the surface in a process that results in mechanical stress which ultimately weakens the structure and results in possible delamination, chipping, or disintegration. A study in 200281 looked at the drying of a NaCl solution on brick samples. Cylindrical samples of brick, saturated with solution, and sealed on all sides except the top, were moved vertically through the magnet. 5% RH air was blown over the top face to induce crystallization at the surface. 1H and 23Na solution NMR were used to follow the concentration of the salts in solution, with an echo time chosen to avoid incorporating any detection of crystalline material in the signal.81 23Na solution NMR on a home built magnet was used to determine the solubility inside a porous material of two solutions of sodium salts, Na2SO4 and Na2CO3, known to cause damage to items of cultural heritage to investigate the mechanical stress of crystallization inside a pore. Experiments were conducted in a model porous system that possessed well-determined pore-size distributions, with the intent to induce supersaturation inside the pore of the solutions and crystallization by change of temperature. Na2CO3 showed supersaturation for small (< 30-nm) pores, showing that crystallization in the pore was higher than crystallization in the bulk under the same conditions and the crystallization within the pore exerted a pressure (4 MPa). For Na2SO4 the 23Na NMR results within the pores match the NMR results for the bulk solution and both matched the metastable crystal form Na2SO4 ,7H2O. Due to this crystal form, no crystallization pressure was exerted, and sodium sulfate would not be a cause of mechanical stress below the surface.82 The same conclusions were drawn by a more complete study by the same authors.83 These studies highlight the fact that the tensile strength of many building materials is around 3 MPa. Thus, the crystallization pressures found in studies indicate damage is possible from crystal formation in pores with diameters of less than 30 nm.83 Another study examined Na2SO4 weathering of samples of fired-clay brick, Indiana limestone (mean pore size of 60 mm), and Cordova limestone (bimodal mean pore sizes of 0.60 and 50 mm).84 A combination of 1H and 23Na low resolution and non-destructive NMR spectroscopies were used together with an optical displacement sensor to measure the concentration of the weathering solution and the expansion caused by crystallization, respectively, to determine which crystal phase of Na2SO4 was responsible for the physical damage that occurred during wetting-drying cycles. The initial drying cycle showed evidence of thenardite (anhydrous Na2SO4) crystallization and physical expansion. After rewetting with a sodium sulfate solution, competition between the dissolution of thenardite and formation of mirabilite (Na2SO4 $ 10H2O) keeps the solution highly saturated with mirabilite, resulting in a high crystallization pressure, and thus significant expansion as soon as the sample is rewetted. The Cordova limestone experienced disintegration after one wetting-drying cycle. Indiana limestone cracked after two cycles. The fired-clay brick cracked after three cycles. The wetting-drying-rewetting cycles are the fundamental cause of damage in these samples.84

9.24.2.1.4

Solid-state NMR characterization and provenance

Solid-state NMR techniques have been shown to be quite useful for studying crystalline or amorphous solids. In addition to their ability to analyze a variety of materials through various nuclear species, solid-state NMR measurements are particularly sensitive to molecular structure, which is often used as a structural fingerprint. Measurement of nuclei like 207Pb, 67Zn, 35Cl, 37Cl, and 51V (and others) provide information on local structure that may define structure or chemical species. Six white marbles from varying geographic regionsdCarrara (from Italy), Göktepe (from Turkey), Pentelic (from Greece), SaintBéat (from France), Estremoz Anticline (from Portugal), and O-Incio (from Spain)dwere analyzed using 13C solid-state NMR.85 Four archeological artifacts of known origin validated the methodology: a portrait of Roman Emperor Hadrian (H) from 130 AD; an unknown female portrait (F) from the first-to-second century AD; the lid of a sarcophagus dedicated to Ithacius (SI); and a contemporary reproduction of a sphinx (S) made of Carrara marble. All samples showed a 13C NMR profile (Fig. 4) indicating defects in the primary component of marble, calcite (CaCO3). The substitution for Ca2þ in the crystal lattice of calcite by secondary elements, such as Mg, Mn, and Fe, affect the crystalline structure of the sample, thereby producing distinctive effects observable in 13 C NMR spectra, for example broadening of the 13C NMR signal. A correlation was made between the area of the resonance and the Fe content due to the paramagnetic influence on T1. These defects and their resulting NMR profiles are associated with geographic regions. By comparing the spectra of the archeological artifacts to those of the quarried marbles, the authors were able to ascertain or confirm the geographical origin of each marble. The results indicate that solid-state NMR spectroscopy is a useful tool in the analysis of white marble, especially in regard to its geographical origins, with minimal sampling.85 Another 13C solid-state NMR study used the paramagnetic composition for marble identification, but also used paramagnetic composition in 29Si and 27Al NMR spectra to identify chert samples.86 The 13C NMR spectroscopy was particularly useful for distinguishing samples from neighboring quarries in a single district, in this case the Garonne river in the Saint-Béat district of France.

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Fig. 3 T2 distributions for Lecce stone with (A) no pollution, (B) 0.63 wt%, and (C) 1.22 wt% artificial pollutant solution of Ca(NO3)2. Reproduced with permission from Casieri, C.; Terenzi, C.; De Luca, F., Noninvasive Monitoring of Moisture Uptake in Ca(NO3)2-Polluted Calcareous Stones by1HNMR Relaxometry. Magn. Reson. Chem. 2015, 53 (1), 15–21.

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The individualized characteristics permitted discrimination of the marble sources in a relatively small geographic areas, a rather difficult task by other archaeometric methods typically applied to marbles. 29Si NMR was used to characterize the silicon species and quartz (SiO4), and 27Al NMR techniques targeting aluminosilicates were similarly useful in chert provenance. Variation in the signal area for the quartz was attributed to magnetic susceptibility arising from the effects of paramagnetic impurities on T1 relaxation, as with the marble samples.86 Aluminum content in cherts is minimal (< 1%) but the ratio of tetrahedral Al(IV) to octahedral Al(VI) coordination determined via 27Al NMR spectroscopy is a reasonable geographic discriminator.86 An instrumental analysis, including solid-state NMR techniques, of stones from the pyramid of Cheops (the Great Pyramid of Giza) assessed the possibility that the stones were molded rather than carved and transported.87 The generally accepted theory is that the construction blocks were carved by hand, moved, and then hoisted into place. A recent theory suggests that the blocks were molded in place, rather than carved and transported. 27Al and 29Si solid-state NMR spectroscopy and proton-induced gamma/X-ray emission (PIGE/PIXE) were used to assess whether the blocks might have been molded. Spectra of a synthetic molded geopolymer were compared to samples taken from the pyramid. Some tetrahedral aluminum common in the geopolymer was found in the pyramid samples, which shows the possibility that the blocks were molded, but further study is needed.87 27 Al and 29Si solid-state NMR analyzes have also been used to identify and classify ancient mortar samples which contain aluminum silicates with the intent of understanding the long-term stability of the historical constructions.88 The chemical compo-

Fig. 4 13C-NMR spectra of the six marble samplesdGöktepe (yellow), Pentelic (purple), Saint Béat (green), O Incio (red), Carrara (blue) and Estremoz Anticline (black)dand the four archaeological items (dark gray). Reproduced with permission from Gutiérrez Garcia-M, A.; Savin, M. C.; Cantin, N.; Boudoumi, S.; Lapuente, P.; Chapoulie, R.; Pianet, I., NMR as a new tool for cultural heritage application: The provenance of ancient white marbles. Archaeometry 2019, 61 (4), 795–808.

sitions of samples from areas in the Czech Republic including the Znojmo Rotunda (dated to the 11th century), a bridge dated to the 12th century, and remnants of Svojsín, an old fortress dated to the 11th century. Were determined by X-ray fluorescence (XRF) analysis. The firing process used in the creation of mortars determines the various silicon-containing compounds present in the samples, resulting in broad NMR spectra covering the range of all silica structure units. The 27Al MAS spectra provided better

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evaluation points for the mortar samples. After slow heating to temperatures between 750  C and 950  C, the aluminum ion coordination to oxygen changes from a natural octahedral coordination to a pentahedral coordination and a tetrahedral coordination. Similar to a previous study,86 a comparison of the integrals of the NMR peaks for the octahedral Al(VI) and tetrahedral Al(IV) coordination provided insight into the origin and preparation of the ancient mortars.88 Aluminum in the tetrahedral coordination to oxygen enables it to form along silica chain structures and form a stable poly-condensed component aiding in the stability of ancient mortars.

9.24.2.1.5

Pottery

Fired clay ceramics have been an important source of building materials and pottery in many cultures throughout time. Understanding their origin and production method can provide historians with invaluable information regarding the technology and trade of past civilizations. A multi-technique study applied electron paramagnetic resonance (EPR) spectroscopy, SEM, PXRD, and NMR spectroscopy to clarify the structure of clay and assess the structural changes imparted during the firing process.89 27Al MAS NMR spectra were taken for samples of Deruta clay fired at various temperatures. Triple quantum magic angle spinning (3Q MAS) 27Al spectra were obtained to refocus the second-order quadrupole effects and better resolve the spectra. The resolved spectra showed three aluminum environments: two tetrahedral and one octahedral coordinations. The signal for the octahedral coordination decreased as firing temperature increased until it disappeared around 850  C. The work has laid a foundation for potentially “fingerprinting” clays via combination of the applied techniques, including NMR spectroscopy.89

9.24.2.2

Paintings

Rock art or cave paintings predate written history by thousands of years.90 The practice of applying color in the form of pigments or pigmented paint to a solid surface has expanded greatly since our prehistoric beginnings to include a multitude of solid supports, including canvas, wood, paper, cardboard, metal, stone, glass, animal skins, plaster, etc.91 This section focuses on how NMR can be used to analyze paintings on different types of supports.

9.24.2.2.1

Wall paintings

Frescos are often large and immobile, making them rather difficult to preserve and conserve, necessitating in situ conservation and study.92,93 Their constituent parts in addition to the paints (plasters and mortars) add an additional layer of complexity to their conservation. As discussed in Section 9.24.2.1, stone and masonry are porous materials easily penetrated by moisture that can wreak havoc on fragile systems. Moisture is one of the biggest problems in the conservation of wall paintings. Water penetration into the paintings and their underlying support may cause physical damage such as fractures, stresses, or cracks, or it may facilitate chemical or biological degradation via salt formation and intrusion, atmospheric pollutants, or bacterial growth.54 Color leaching or fading is a concern when it comes to painted artifacts.94 Understanding the distribution and movement of water through these artifacts provides invaluable information on their restoration and conservation. Unilateral NMR techniques provide a particularly useful method for studying these objects due to its portability, non-destructive nature, and ability to measure water content. As discussed in Section 9.24.2.1, the signal detected by unilateral 1H NMR is directly proportional to the water content of the object under study. Depth profiling may also be used to differentiate among the wall, support, and paint layers. For example, in an early study, Hahn-echo measurements of a late 16th century fresco in Florence, Italy, investigated the outer layer of plaster and the lime (hydrated calcium oxide) mortar behind the fresco.95 The Hahn-echo experiment implements a p2 pulse, followed by a p pulse after a set delay, resulting in a refocusing of the signal known as an echo. These measurements provide an indication of the humidity of the sample, where a strong signal indicates a well conserved fresco. Measurements taken at the surface in areas of visible degradation exhibited a decrease in the intensity of the Hahn-echo compared to non-degraded areas. Hahn-echo measurements could not be used to probe the humidity in areas of salt efflorescence due to the hygroscopic nature of the salts. Instead, relaxation (T2) decays of protons in areas with visible salt efflorescence measured with CPMG sequences was better able to probe the deterioration in these areas since areas affected by salt efflorescence had broader T2 distributions centered on longer values than areas where it was not present due to hydroscopic nature of the salts.95 Another study46 utilized unilateral NMR to assess the protectiveness and effectiveness of consolidation treatments on model plaster specimens (where lime and silica sand were used as aggregate) saturated with water.46 1H depth profiles and T2eff distributions were found for each sample and each technique allowed for calculation of average loss of water and the total open porosity, respectively. The results indicated that the effectiveness of a treatment depends on both the hydrophobic nature of the treatment and its application method.46 Several sites in ancient Herculaneum, near Naples, Italy, were analyzed using unilateral NMR technology due to the sites’ importance in cultural heritage and the amount of deterioration and decay present.96 Three of those sites are discussed in the following paragraphs. The moisture content of several points across the famous mosaic of Neptune and Amphitrite were assessed in spring and fall to determine if seasonal changes had an effect on moisture content. One point in the mosaics can be described as having two regions: region 1 at a depth of 0 to 6–7 mm corresponding to the tesserae tiling and the mortar between them and region 2 at a depth of greater than 7 mm corresponding to the binding mortar embedding the tesserae. The moisture content of the region 1 did not appear to vary between seasons; however, the region 2 did show fluctuations consistent with wetter springs and dryer falls.

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Unilateral NMR studies were also performed in the House of the Black Room, a luxurious residence aptly named for its large room decorated with pillars and chandeliers painted with a black background.96 Early excavation and organic-based conservation treatments had led to increased wall degradation causing efflorescence on the surface or just below the paint layer. Depth and T2eff profiles acquired for the wall having visible salt efflorescence showed similar signals in the areas of consolidation treatment as compared to areas where the treatment had been removed, suggesting that the early treatment had not been entirely removed and that moisture exchange was hindered. The study also looked at ammonium oxalate and barium hydroxide treatment methods and showed that ammonium oxalate leads to lower moisture content, while barium hydroxide lead to higher moisture content.96 Unlike the other sites at Herculaneum, the Villa of the Papyri has been exceptionally well preserved and is maintained at 96% relative humidity to direct moisture migration into the walls and thus prevent salt crystallization.96 Unilateral NMR analyzes of this room indicated two different stratigraphies in different walls. One wall was dated from before the earthquake of 62 AD and the other rebuilt after the earthquake. Depth profiling and T2 distributions showed differences in the complexity and thickness of the mortar prepared for the wall painting. In addition, XRF data indicate the use of two red pigments, cinnabar (HgS) and iron oxide, corresponding to the two stratigraphies identified by unilateral NMR measurements. The iron oxide is cheaper red pigment that was used in the restoration.96 Unilateral NMR was used to assess the drying behavior and influence of consolidants on fresco and secco paintings made in accordance with historical practices.97 The NMR results indicated that the painting method has a direct influence on the water transport properties at the surface layer. Absorption coefficients quantified with NMR results were obtained for two depths in fresco and secco samples before and after treatment with Ba(OH)2 or ammonium oxalate. The smaller particles in the outer layer created a tighter pore network more subjected to capillary action than the larger pores of the inner layers. Variations in the diffusion coefficients between treatments were substantially more noticeable for the fresco samples. The effect of salt, particularly NaCl, on the molecular dynamics through an entire model sample (tuff stone base and three layers of mortar) were also monitored. The salttreated samples display slower diffusion, likely stemming from an increased viscosity of the supersaturated salt solution and from the reduced pore sizes caused by salt crystallization.97 Because the unilateral NMR sensor is mobile, entire surfaces of objects or walls can be scanned. Combining the one-dimensional spectra obtained via the unilateral sensor with carefully monitored x-y coordinate data, two-dimensional “maps” of the surface can be generated.47 One study utilized unilateral NMR procedures to map the water content in a set of 16th century wall fresco paintings in the Serra Chapel, Rome, Italy.98 The left side of the painting is more deteriorated cause loss of paint than the right side (Fig. 5A), with the hypothesis that the cause of the difference is due to moisture rising from the ground on the left side of the chapel. Hahn echo NMR results where the signal is related to water content were displayed visually as a 2D contour plot, shown in Fig. 5B. Earlier conservation efforts had added to the degradation of these paintings. The application of linseed oil, animal glues, and waxes hindered the ability of the plaster to exchange moisture with the environment and, as a result, trapped moisture and moisturedriven contaminants against the painting surface. Soluble salts have been continually hydrated and crystallized against the paint film, resulting in detachment, microfractures, and visible efflorescence. T2 values measured by CPMG in areas of high salt content were markedly shifted to longer values in comparison to the areas without salt. The authors attributed this observation to the increased moisture content in these areas due to the hygroscopic nature of the salts.98 To further validate the usefulness of 2D contour maps of Hahn echo signals by unilateral NMR, the technique was used in an emergency intervention on the late 15th century wall paintings of San Rocco church in Milan, Italy. Unilateral NMR was used in addition to infrared thermography (IRT) and gravimetry to identify and conserve the rapidly degrading images.99 IRT determined the northern wall painting was most affected by the presence of water. Unilateral NMR was utilized to obtain detailed information regarding the moisture distribution in the plaster and underlying wall in this area. 2D contour maps of Hahn echo signals provided a visual representation of the water distribution throughout the wall and showed that two wet areas separated by a dry area. One wet area at the bottom of the wall due to the slope of the garden soil and the other higher wet area was due to solubility of hygroscopic salts. Gravimetric analyzes confirmed the findings of the calibrated NMR map of water. The comparison demonstrated that unilateral NMR is an efficient tool for analyzing the quantitative moisture content and distribution in wall paintings in situ without necessitating drilling samples.99 Moisture distribution mapping was also performed on the wall painting St. Clement at mass and the legend of Sisinnius located on a sublevel of St. Clement Basilica in Rome, Italy.100 The painting dates back to the early 11th century, providing one of the earliest examples of the passage from Latin to Italian. The presence of flowing water under the Basilica produced unfavorable conditions for the preservation of this historical object. The consistently high humidity and cool temperatures also limited the use of techniques such as IRT. Destructive sampling in such techniques as gravimetry were not allowed on such a priceless artifact. In this case, a unilateral NMR study using Hahn-Echo 2D distribution maps provided moisture distribution maps at depths of 0.1 and 0.5 cm in the affected wall that could be used to evaluate the water damage, allowing a treatment plan to be defined.100 Unilateral NMR studies were subsequently used to monitor capillary rise of water from the ground below four and 7 months after the preventative treatment. The surface scans (0.1 cm) were highly dependent on environmental conditions, presence of salts or biological deterioration, whereas measurements made at a depth of 0.5 cm showed a clear decrease in water content due to the capillary rise, at both 4 and 7 months after treatment.101 Analysis of depth profiles obtained via unilateral NMR techniques provide information on the stratigraphy of samples.102 Differences in pigments, binders, age, and moisture content can affect the 1H signal from unilateral NMR measurements.103 These variations give insight into the constituent layers of an object without necessitating the removal of a cross-section or core sample. Additionally, the mobility of the technique, as discussed with the 2D mapping, provides information about objects as a whole

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Fig. 5 (A) Photographs of the set of paintings in the Serra Chapel with (B) corresponding Hahn echo distributions maps. Red areas indicate areas of low moisture. Blue areas indicate areas of high moisture. Reproduced with permission from Proietti, N.; Capitani, D.; Rossi, E.; Cozzolino, S.; Segre, A. L., Unilateral NMR Study of a XVI Century Wall Painted. J. Magn. Reson. 2007, 186 (2), 311–318.

rather than the localized information provided by cross-sections or core samples. At the same time the NMR result guided conservators to targeted areas for further study.44 The stratigraphy of wall paintings was assessed via unilateral NMR depth profiling to determine the applicability of the technique for nondestructive studies of layered samples, particularly in regards to “hidden” paintings.93 Depth profiles of model samples and

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Applications of NMR spectroscopy in cultural heritage science

real samples of the walls in Villa Palagione and the Seminario Vescovile di Sant’Andrea were obtained. The Villa Palagione dates back to the late 16th century and, after a period of disrepair, was restored in the late 20th century with modern materials. Oral and photographic accounts indicated that a number of the walls were originally covered in paintings, and that these original paintings remained under the modern restorations. NMR profiles taken in several locations on the walls of the Villa showed different layers of paints and mortar, confirmed by XRF and visual inspection of removed wall sections. The walls of the Seminario Vescovile di Sant’Andrea provided a unique opportunity as “hidden” paintings were discovered during an early 21st century restoration of the exterior courtyard. Some of the contemporary materials covering the paintings were removed, but others remained in place providing samples of both the “hidden” and uncovered material without necessitating further alteration of the site.93

9.24.2.2.2

Canvas paintings

Unilateral NMR techniques are also applicable to paintings on canvas surfaces. Unilateral NMR has been used, in conjunction with neutron radiography, to observe the spatial and temporal moisture distribution in reconstructed layered oil paintings on canvas.104 The results indicated that the linen of the canvas absorbs the highest proportion of moisture, resulting in image maps of water that match the weave-pattern of the canvas. The diffusion of water and polyethylene glycol (PEG) solutions into and through the oil paint layer was monitored using two unilateral NMR techniques, MoUSE (Mobile Universal Surface Explorer, Magritek, Aachen, Germany) and a home-built device called GARField (Gradient At Right angle to Field). The profiles obtained via the MoUSE demonstrated water uptake in the canvas and the ground (CaCO3) layers, but the maps did not have sufficient resolution to define the process in the oil paint layer. The GARField technique, on the other hand, permitted sampling in the oil paint and ground layers, with spatial resolution of 5 mM. The combined results indicated that the majority of the absorbed water was contained in the polymeric matrix, and a small, but significant, portion was able to penetrate the pores of the ground layer.104 Unilateral NMR has been compared to the traditional method of microsample cross-section removal and subsequent analysis to assess the stratigraphy of canvas paintings.102 SEM was used to validate the NMR results, as seen in Fig. 6. The unilateral NMR technique was used to profile several pieces from the Galleria Nazionale dell’Umbria in Perugia, Italy, and was shown to differentiate between the layers of the painting Adorazione dei Magi, as well as variations of thickness in the layers in different sampling spots. The study indicated the potential for unilateral NMR mapping to provide a 3D stratigraphy map of entire paintings, providing valuable information of the painted environment as a whole, rather than the localized information provided by small cross-sections.102 Another study focused on investigating both signal intensity and T2 distributions in model painted canvases prepared with different pigments and binders via unilateral NMR.105 Two pigments, yellow ochre and English red, in either linseed oil or egg yolk were applied to linseed-oil- or animal-glue-based ground layers on canvas. Micro-destructive cross-sections were removed and studied in an optical stereomicroscope. T2 and depth profiles were taken for each sample. English red is composed of iron oxide which creates paramagnetic effects notable by the reduction of intensity in the T2 maps of both the egg-yolk and linseed-oil samples containing the pigment. Yellow ochre is composed of ferric oxide also exhibits paramagnetic properties, but to a lesser degree than English red. Comparisons of the stereomicroscope images with the normalized NMR signal intensities and T2 maps for the linseedoil-based samples in Fig. 7 demonstrate that differentiation between layers is possible by both techniques. The study emphasizes that the stereomicroscopic images are based on the visual 2D geometry of the surfaces of the layers, whereas the NMR images are determined by the sensitive volume of the sampling area. In the NMR technique, the effects of layer irregularities are mediated, and the resulting signal contains information on possible infiltration of binders between adjacent layers. The combination of the signal intensity and relaxation times reflect both the individual layers, as well as their possible intersection, which is of great importance for paintings on canvas because these works regularly contain irregularities and overlapping layers.105

9.24.2.2.3

Cleaning treatments

Water penetration and dynamics of water with different salt concentration in waterborne acrylic paint films containing titanium white were for the first time studied in situ with unilateral NMR techniques in regard to washing off surface grime.106 The adsorption of water with different concentrations of salt was measured before and after washing. The unwashed samples swelled considerably on application of water. The washed samples exhibited less swelling, likely due to the missing hydrophilic action of the surfactants removed by washing. Additionally, the washed samples absorbed less water with increasing salt concentrations due to the decrease in osmotic pressure between the salt solutions and the polymer network. The self-diffusion coefficients of water in the washed and unwashed samples varied only slightly from sample to sample, indicating that the diffusion of water is not strongly influenced by surfactants or size of the salt ions Water penetration and dynamics in waterborne acrylic paint films containing titanium white have also been studied with unilateral NMR techniques. The paint films were exposed to water and salt solutions of various concentrations before and after washing.106 The effect of cleaning treatments on wall paintings has also been addressed by NMR studies.107 The study evaluated the degradation of a 16th century wall painting in the Tarquinia cathedral in Rome, Italy. Understanding the constituent components, the current level of degradation, and the effects of previous restoration treatments were all necessary to provide the best treatment for the samples. 13C CPMAS NMR spectra were used to identify the translucent layer covering the wall surface. The NMR results indicated the presence of mostly beeswax with traces of starches or plant gums. A subsequent unilateral NMR study assessed the effectiveness of a microemulsion and a solvent gel for removing the beeswax layer by assessing depth profile stratigraphy before and after cleaning. The solvent gel was found to remove 17% of the beeswax, while the microemulsion was found to remove 92%. Unilateral NMR studies were also used to measured water uptake at the wall and the amount of water released by two hydrogel/bacteria

Applications of NMR spectroscopy in cultural heritage science

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Fig. 6 (Left) Unilateral NMR depth profiles and (Right) SEM images of model paintings containing a gypsum and animal glue primer and (A and B) verdigris (copper acetate) or (C and D) cobalt blue pigments. Reproduced with permission from Presciutti, F.; Perlo, J.; Casanova, F.; Glögger, S.; Costanza, M.; Blümich, B.; Brunetti, B.G.; Sgamellotti, A., Noninvasive nuclear magnetic resonance profiling of paint layers. Appl. Phys. Lett. 2008, 93, 033505.

cleaning systems, Carbogel and Vanzan NFC gel, for removal of salt efflorescence. Carbogel was found to be the better support for this purpose; however, the presence of hydrophobic beeswax impeded water uptake at the wall for both gels.107 Another study108 looked at a series of thickened or gelled cleaning methods for acrylic paint films containing titanium white or Hansa yellow (organic) pigments. Unilateral NMR techniques, spatial resolved profiles of the T2eff and relative volume of water in the top layer or paint film, were used to monitor the rate of diffusion and penetration depth of water in the samples, as well as quantitatively determine the amount of water which had swelled the paint during treatment, gel vs. swab method. The study found that young paint samples ( 4 weeks old) absorbed much more water than their aged counterparts. Although the young samples absorbed similar quantities of water, a stark contrast is noted between samples with different pigments after 2 years of aging, at which point the Hansa yellow absorbed twice as much water as a comparable titanium white film. Acrylic paint films often have additional additives, so the difference could be more complex than the pigment itself. The majority of the cleaning methods tested resulted in more water uptake than traditional swab cleaning method.108 Water penetration on both acrylic- and vinyl-based titanium oxide paints during simulated cleaning with triammonium citrate (TAC) in both aqueous and hydroxypropylcellulose (KlucelÒ G) gel forms was monitored by unilateral NMR procedures.109 The use of TAC had been shown in previous studies to decrease water penetration into acrylic paint films. A broadening of the NMR signal at the air-sample interface after treatment demonstrated the swelling phenomena in both the free and gelled TAC solutions for both paint samples. The relaxation decay for the vinyl sample after 10 min of gel exposure appeared more intense than the decay of a sample treated for 2 min, indicating a potential delay of water penetration into the sample. This agrees with the corresponding depth profiles utilized to assess the swelling of the paint films after solvent application. The vinyl samples dried faster than the

804 Applications of NMR spectroscopy in cultural heritage science

Fig. 7 (Left) Stereomicroscopic images, (Middle) normalized NMR signal intensities, and (Right) T2 distributions for linseed-oil ground, egg yolk paints with (A) yellow ochre and (B) English red pigments. Images and distributions have been graphically matched for ease of comparison. Reproduced with permission from Brizi, L.; Bortolotti, V.; Marmotti, G.; Camaiti, M., Identification of Complex Structures of Paintings on Canvas by NMR: Correlation Between NMR Profile and Stratigraphy. Magn. Reson. Chem. 2020, 58 (9), 889–901.

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acrylic samples, with the CPMG echo decay curves resembling those of the dry samples at 4 h of drying for the vinyl and 8 h of drying for the acrylic sample, as shown in Fig. 8. The penetration of water into both types of synthetic paint films was not slowed by the application of the TAC solution or gel.109 In the same study, the potential use of the unilateral NMR technique to monitor removal of varnishes from surface of oil or tempera paints was addressed. The removal of a varnish from a paint sample of lead white in linseed oil or egg tempera by means of ligroin (solvent of C7 and C8 hydrocarbons) was seen to be similar to the changes observed in the TAC studies, with swelling and solvent penetration seen in the NMR data. Distinguishing between the varnish and underlying paint layers with this technique proved difficult because of the similar proton content of the layers and the limited spatial resolution. Some varnish removal was noted by a decrease in NMR depth profile thickness, confirmed by optical microscopy and FTIR analysis.109 1 H depth profiles were used to study two paintings by Giuseppe Capogrossi (Surface 538 and Surface 553).110 The depth profiles showed the thickness of the paint layer and the heterogeneity of the different pigments. The linseed oil matrix of the painting (full of hydrogen nuclei) allowed for measurement of the proton density along the paint layer. Linseed oil is triglyceride of saturated and unsaturated fatty acids. Two areas had a greater thickness due to a varnish in one area and a repainted black paint area in another. In addition, T2eff distributions before and after water-based cleaning treatments in two paintings were measured. The paintings before treatment showed similar T2eff distributions to those in model studies on lead-white paint, with three T2eff values being found. Slightly lower values of the relaxation times, as compared to the model samples, were attributed to the increase in crosslinking from natural aging of the paintings. Three hours after treatment, however, the longer T2eff values associated with more mobile fractions of the paint matrix had shifted to even longer times, indicating that the presence of water greatly affects the paint matrix.110 1 H HR-MAS spectroscopy was used to characterize organic materials in paintings.110 Samples of a 10-year aged laboratory sample of lead carbonate in linseed oil were compared to a sample from a 17th century wall painting in the National Gallery of

Fig. 8 CPMG echo decays for acrylic (A and B) and vinyl (C and D) paint films treated with free (A and C) and gelled (B and D) solutions of TAC. Reproduced with permission from Moretti, P.; Cartechini, L.; Miliani, C., Single-Sided NMR: A Non-invasive Diagnostic Tool for Monitoring Swelling Effects in Paint Films Subjected to Solvent Cleaning. Anal. Bioanal. Chem. 2020, 412(5): 1063-1075.

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Modern Art, Rome, Italy. The sample was placed in a rotor with deuterated DMSO. Although the spectra were quite similar, that of the wall sample had sharper resonances indicating a higher solubility of the constituent components. This effect was attributed to hydrolysis of the linseed oil matrix over time and the increased solubility of free fatty acids in DMSO. 1H-1H TOCSY experiments indicated the presence of both saturated and unsaturated fatty acids for the model sample, implying incomplete polymerization. 1H HR-MAS NMR analysis was also applied to three different varnishes: shellac (sequiterpenoid resin), sandarac, and colophony (diterpenoids resins). The results showed that these binders/varnishes give well-resolved NMR spectra to identify components in the material. This is important because overtime these varnishes discolor and degrade, and information gained from these studies can be helpful in treatment and removal of varnishes.110

9.24.2.3

Paints and their constituent parts

NMR techniques have long been essential parts of the chemist’s toolbox for identification of compounds. Understanding the chemical composition of paints and the related degradation processes is essential to facilitating the best restoration, conservation, and preservation practices in dealing with cultural objects. Pigments are usually fine powders of either organic or inorganic compounds.111–113 Binding media are usually materials such as vegetable gums, proteinaceous materials such as egg yolk, egg white, or casein, waxes, synthetic polymers, or drying oils.114 Paints may be directly applied to a surface, but the use of a ground is often necessitated to create more uniform starting surfaces.91

9.24.2.3.1

Drying oils

9.24.2.3.2

Mock films

1D and 2D solution NMR techniques have been applied to the study the organic components of oil paintings,115 particularly pure drying oils such as linseed oil, boiled linseed oil, poppy oil, as well as model paints containing various pigments. For example, in one study, the NMR-determined chemical composition of the “mobile” phase of several paint samples and how the paints degraded.115 To provide an analytical standard for linseed oil, egg tempera, and acrylic polymer to assess degradation of painted cultural heritage objects and to assess the validity of the technique in identifying these binding media, 1H-1H COSY and 1H-13C qHMQC (quantitative heteronuclear single quantum coherence) techniques were used to complete total peak assignment for the binders which provided identification of polymeric constituents.116 The methyl groups of cholesterol have been similarly used as an identifier of egg yolk in 1D and 2D solution NMR spectra 1H spectra.117 2D techniques such as 1H-13C qHMQC (Fig. 9) provided evidence of egg yolk in a significantly degraded sample from an early 19th century Greek icon “Evangelismos.” Characteristics peaks of the egg yolk are absent from oil paintings shown in Fig. 9D. For younger samples, it was shown that semiquantitative data on composition of egg yolk in egg tempera or in a mixed binding medium could readily be obtained with these techniques. In older samples, a quantification was not possible, but it was possible to identify cholesterol or cholesterol oxidation products with 1D or 2D NMR techniques.117 1 H solution NMR spectroscopy has been used to investigate the cross-linking processes of drying oils commonly used as binders.118 The study followed established protocols for studying the cross-linking processes of drying oils but expanded the sampling to include art-relevant oil binders such as linseed oil, poppy oil, and walnut oil. 1H spectra of the oils were obtained before and after heating to 60  C under either a nitrogen or oxygen atmosphere. Variations in the spectra were noted for the samples heated under oxygen, but no change was noted for those heated in nitrogen, confirming the importance of oxygen in the drying process. A comparison of the 1H solid-state spectra of the CDCl3-swollen insoluble fraction and the CDCl3-extracted liquid fraction showed few differences in three paint samples. The spectroscopy could not conclusively differentiate different drying oils from one another, but it did identify and distinguish drying oils from other binders in aged paint films.118

Unilateral NMR has been used to measure proton T2 values of paint films. Increasing rigidity in paint films leads to decreased T2 values.119 Films with high degrees of internal intermolecular motion display longer T2 values. However, paintings are complex and multilayered consisting of a support, ground layer, and multiple pigments mixed with a binder. In addition, the aging and curing factors of a painting are affected by a number of parameters including temperature fluctuations, UV irradiation, humidity, and treatments. Therefore, interpretation of T2 values from paintings need to account for all these factors. The relaxometry of both artificially and naturally aged mock linseed-oil-based paint samples was examined with unilateral NMR experiments for five pigments, red pigment (organic), zinc white (zinc oxide), indigo blue (organic dye), cobalt green (cobalt and zinc oxide) and Bristol yellow (mixed pigment).119 T1-T2 correlation experiments were performed and the data collected was used to extract the one-dimensional data for T1 and T2. Both T1 and T2 data of the drying and aging process of the fresh films with red pigment indicate an initial induction period followed by a mono-exponential decay. The initial induction period is due to the hardening of the surface layer which impact the aging of the layers underneath. The effect of pigment type and concentration on the relaxation times was also investigated after the samples aged for 2 months, as shown in Fig. 10. There is not a linear relationship between pigment concentration and either relaxation time, but a general trend that increasing pigment concentration either decreases T1 and T2 or it remains the same. This is in agreement with practice that adding pigment increases the firmness of the paint. Pigment mixtures (not shown) of higher order exhibited complex trends in relaxation time with pigment concentration. In order to determine if T1-T2 correlation experiments can be used to determine the date of a painting, naturally aged samples dated between

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Fig. 9 1H-13C qHMQC of four samples in deuterated acetone: (A) pure cholesterol; (B) 19th century Greek Icon “Evangelismos”; (C) 2-year aged egg yolk binding media; (D) sample from Portrait of a Young Man, oil painting from early 20th century. The arrows on B, C indicate the resonance characteristic of cholesterol, notably absent in the oil painting. Reproduced with permission from Sfakianaki, S.; Kouloumpi, E.; Anglos, D.; Spyros, A., Egg Yolk Identification and Aging Inmixed Paint Binding Media by NMR Spectroscopy. Magn. Reson. Chem. 2015, 53 (1), 22–26.

1914 and 1951 were used. The data suggested a weak trend between age of sample and relaxation time. However, due to the complex nature of the genuine artworks, further studies would be necessary for NMR relaxometry to be a stand-alone technique for age determination in paint films.119 Another study examined the relaxometry of water-mixable oil paints that often contain an added emulsifying agent to allow water to be miscible in the paint matrix to see its effect on the curing process.120 NMR relaxometry performed on a set of samples containing both traditional oil and water-mixable oil paints displayed T2 values for each group that, though similar, showed separate trends. Specifically, the water-mixable oil paints displayed generally longer relaxation times than the traditional oil paints, indicating that the two paints form different physical and chemical environments during the curing process. The shorter T2 values of the traditional oil paints is indicative of reduced isotropic motion and a higher degree of cross-linkage than the water-mixable counterparts. These results suggest that the added emulsifier reduces the curing rate of these films relative to films without the added emulsifier.120

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Fig. 10 (A) T1 and (B) T2 relaxation times of paint samples with varying pigment types and concentrations. Reproduced with permission from Busse, F.; Rehorn, C.; Küppers, M.; Ruiz, N.; Stege, H.; Blümich, B., NMR Relaxometry of Oil Paint Binders. Magn. Reson. Chem. 2020, 58 (9), 830– 839.

9.24.2.3.3

Heavy-metal soaps

The formation of heavy-metal carboxylates, or soaps, is a severe degradation process affecting oil paints with heavy metal pigments, such as those of lead, zinc, cadmium, and copper.121 Saponification of triglycerides in the paint matrix has been noted in numerous painted artifacts, particularly in oil paintings.49,122 For example, heavy-metal soaps form by saponification of heavy-metal-containing pigments, such as lead white and lead-tin yellow, with free fatty acids (FFAs) in the binding medium or in protective coatings.123 The formation of soaps is accompanied by irreversible damage to the painted works, such as the development of hazy films, protrusions, cracks, flaking and delamination.121 A thorough understanding of their composition and formation is necessary to prevent and monitor these degradation processes. The mobility of water in oil-based films is believed to affect the saponification process, and thus the characterization of diffusion and transport of water in such environments is an important clue to understanding the underlying chemical processes. Such processes in oil paint films have been interrogated by a combination of unilateral and high-resolution 1H NMR techniques.124 Unilateral measurements of T1 and T2eff for protons in a paint of lead white in linseed oil. The authors addressed question of thickness and humidity as modifiers of paint behavior. T2eff distributions were fit with three or more distinguishable components, classified as short, T2A (0.15–0.2 ms) affecting the majority of the spins; intermediate, T2B (0.55–0.8 ms) affecting roughly 30% of the spins; and long, T2C (3–4 ms) affecting 5–15% of the spins. This was similar to what was seen in the Giuseppe Capogrossi’s paintings (Surface 538 and Surface 553) discussed above.110 T2A was assigned to the protons in the rigid polymer network. T2B was assigned to the mobile regions of the polymer network such as terminal methyl groups. T2C was assigned to residual fatty acids either partially or entirely unpolymerized in the network. In substantially cross-linked paints, this relatively mobile faction was attributed to the products of hydrolysis of ester bonds in the network. For samples exposed to 90% RH, an additional component T2E ( 30 ms) was seen after 1 week of exposure; it was attributed to freely moving water molecules in the pores of the sample. At the longest exposure times (5 weeks) another component, T2D ( 10 ms), was seen in 200- and 500-mm thick samples. The values of T2B and T2C shifted significantly to 1 ms and 4 ms, respectively, over the first few weeks of exposure, indicating that the paint films absorb substantial quantities of water if exposed to high humidity (Fig. 11). To characterize the water absorption capacity of the paint films, they were directly exposed to a water, rather than to water vapor. The T2eff components vary with exposure time to water, in a manner similar to those in the relative-humidity studies, but on a much shorter timescale. T2B and T2C values shift substantially in the first 24 h of exposure. After 72 h, the distributions begin to show longer T2eff values associated with water protons and a decrease in the T2C values. It was hypothesized that this was due to the formation of ionic or polar aggregates.124 Similar exposure tests to films of pure linseed oil demonstrated differences between an oil matrix and a pigment-oil matrix.124 Before and after 120 h of direct water exposure, the T2eff distribution of the pure linseed oil showed three components. No component assignable to water-associated protons was noted, which indicated that the presence of pigment drastically changes the wettability of the matrix. 1H HR-MAS-based self-diffusion measurements of each unique component in the 1H NMR spectrum indicated that the diffusion coefficient in these systems is a function of diffusion length.124 Lead stearate, lead palmitate and lead azelate were shown to implicated in soap formation by other spectroscopic methods. Although a crystal structure existed for lead azelate, a crystal structure for lead stearate or palmitate was not obtainable due to the high insolubility of these lead soaps. In an application of NMR spectroscopy to address this problem and determine structural information about lead soaps, a series of five lead carboxylates with varying carbon chain lengths were analyzed by solid-state 13C and 207Pb NMR methods to elucidate structural and chemical information.125 The study was the expand to include a series of eight

Applications of NMR spectroscopy in cultural heritage science

Fig. 11 T2eff distributions (Left) and values as a function of time (Right) for lead white-linseed oil paint films exposed to varying RH values, as denoted on the individual graphs. Reproduced with permission from Di Tullio, V.; Zumbulyadis, N.; Centeno, S. A.; Catalano, J.; Wagner, M.; Dybowski, C., Water Diffusion and Transport in Oil Paints as Studied by Unilateral NMR and 1H High-Resolution MAS-NMR Spectroscopy. ChemPhysChem 2020, 21 (1), 113–119.

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lead carboxylates was studied by solid-state 13C and 207Pb NMR techniques.122 Wide-band-uniform-rate-smooth-truncation (WURST) CPMG 207Pb was used due to the enhancement in signal and the large span of the 207Pb signal. WURST CPMG spectra of these materials indicate that the lead centers in the carboxylates fall into two spectroscopic groups. The first group has a large (> 2000 ppm) spectral span indicative of a less symmetric arrangement around the lead center, as seen in Fig. 12E–H. The second group has a smaller (< 1000 ppm) spectral span, indicative of a less asymmetric electronic (holodirected) local environment of the center.125 This difference in structure between the two classes was confirmed by comparison of single-crystal X-ray crystallographic structures of lead nonanoate with data for lead heptanoate.122 The significance of this was that solid-state NMR was able to be used to determine the a structural model for lead palmitate and lead stearate. The coordination geometry of these lead carboxylates was further investigated by NMR and X-ray crystallography. An expanded series of eight lead carboxylates was studied by solid-state 13C and 207Pb NMR techniques.122 As in the first study, the carboxylates were found to fall into two categories. In the 13C spectra, the long-chain ( 9 carbons) carboxylates exhibited resonance doubling of the a-carbon, with chemical-shift differences of 1.13–1.25 ppm. The short-chain (< 9 carbons) carboxylates exhibited a similar doubling, but with chemical-shift differences of only 0.50–0.69 ppm, as seen in Fig. 12) The difference in the 207Pb NMR properties

Fig. 12 (Left) 207Pb WURST-CPMG spectra and (Right) 13C spectra for (A) lead octadecanoate, (B) lead hexadecanoate, (C) lead undecanoate, (D) lead decanoate, (E) lead nonanoate, (F) lead octanoate, (G) lead heptanoate, and (H) lead hexanoate. Reproduced, with permission, from Catalano, J.; Murphy, A.; Yao, Y.; Yap, G. P. A.; Zumbulyadis, N.; Centeno, S. A.; Dybowski, C., Coordination Geometry of Lead Carboxylates Spectroscopic and Crystallographic Evidence. Dalton Trans. 2015, 44 (5), 2340–2347.

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811

is most notable in the d11 and d22 components of the chemical-shift tensor. d33 values were similar for all of the lead carboxylates. d11 and d22 are substantially more shielded in the longer chain carboxylates and are indicative of a more holodirected coordination around the lead center. This difference in structure between the two classes was confirmed by comparison of single-crystal X-ray crystallographic structures of lead nonanoate with data for lead heptanoate.122 13 C and 207Pb NMR, as well as PXRD data of mixtures of lead carboxylates relevant to soap formation have been reported.126 The 13 C spectra showed significant broadening for the mixtures, as well as new signals indicative of the formation of a disordered phase. PXRD data indicated that unit cell parameters were a function of the C16/C18 ratio in the mixture.126 A variety of NMR methods have been used to obtain information on the reactivity of pigments with free fatty acids. A combination of 13C, 207Pb, and 119Sn solid-state NMR analyzes gave information on the reactivity of lead-tin yellow I with free palmitic acid.123 Before this study, it was hypothesized that an impurity in lead-tin yellow and not lead-tin yellow itself was implicated in soap formation. An extensive review of the use of NMR spectroscopy to investigate structure, reactivity, and dynamics of lead soap formation in paintings was published in 2020.49

9.24.2.3.4

Maya blue

Maya blue is found in artifacts that originate in Central America and is aptly named for its prominent use in the Mayan wall paintings at Chichén Itza in the Yucatan Peninsula, Mexico.127,128 The pigment is composed of the clays palygorskite, [(Mg,Al)4(Si)8(O,OH,H2O)26 ,nH2O] and sepiolite with dilute (< 5%) quantities of the organic dye indigo, C16H10N2O2.112,129 It has incited great fascination in the art community as the color, although the material is often present in very dilute concentrations, is vibrant, lustrous and exceptionally durable.128,130 Several studies have been performed to assess the durability and brilliance of the pigment. The interactions of the clays with the organic dye were assessed via several NMR techniques.127 Solid-state 29Si CPMAS NMR was used to determine if the dye intercalated the material (sepiolite) upon heating. The spectra for samples with and without the dye were similar for both the hydrated and dehydrated samples. A recovery of the original hydrated 29Si NMR spectrum would be expected for samples with small molecules penetrating the crystal lattice, as is seen with solvents such as acetone and pyridine131; however, this was not noted for the dye, indicating that the molecule is not intercalated in the clays. 13C CPMAS NMR showed that there was a crystallographic change in the indigo upon mixing with sepiolite. In addition, there is a small shift in the carbonyl residue for the sepiolite-indigo adduct, indicating the indigo molecules interact with the surface silanol groups instead of within the pores where a larger chemical shift would be observed. Both 29Si and 13C CPMAS NMR results indicate surface coverage of the dye.127 A combination of computational molecular mechanics, NMR, FTIR, and Raman spectroscopies were utilized to assess the stability of the palygorskite-indigo complexes.128 Molecular mechanics calculations were used to model the superstructure of the complex and indicated that the dye can permeate the structure of the clay once water inside the channels (zeolitic) is removed by heating. Hydrogen bonding of the dye to structural water molecules (tightly bound water coordinated to the magnesium and aluminum in the palygorskite framework) was confirmed by the blue-shift in the IR bending mode of the structural H2O and the red-shift of the Raman C]O stretching mode. 1H MAS NMR for both freshly synthesized indigo and original Maya blue show spectra with similar features to palygorskite with notable additions of a shoulder at 13.0 ppm and a broad hump at 17.8 ppm. The shoulder suggests an interaction between the dye N-H group and an oxygen atom of the clay structural water. The shift of the N-H group (10.7 in pure indigo) to 13.0 in the Maya blue suggests the formation of a weak H-bond also supported by the Raman data. The broad feature at 17.8 ppm is not present in the spectra for either the pure dye or clay suggesting the presence of a strong H-bong acting between the indigo carbonyl group and the clay structural water, also confirmed by Raman data.128 Further solid-state NMR studies of indigo and its derivatives were completed to determine the distribution and interactions of the derivatives in the palygorskite framework.129 13C-1H dynamic nuclear polarization (DNP) can resolve the signals from three organic moleculesdindigo, dehydroindigo (C16H8N2O2), and indoxyl (C8H7NO). DNP utilizes the Boltzmann polarization of the electron spin reservoir of a polarizing agent to boost the NMR signal of the nucleus being studied. It is a particularly valuable technique for experiments with low-sensitivity samples. 2D 13C-1H DNP-heteronuclear correlation (HECTOR) NMR experiments show signals from 13C nuclei that are dipole-dipole coupled to nearby (< 1 nm) 1H nuclei in the palygorskite framework. The 13 C signals in the 114–136 ppm region of the larger indigo/dehydroindigo molecules correlate with the 1H signals in the 10.4– 13.5 ppm region associated with strongly H-bonded -OH moieties, indicating that the organic molecules participate in strong hydrogen bonds in Maya blue, likely involving the carbonyl oxygen atoms and structural water molecules, similar to the conclusions by Giustetto et al.128 The indoxyl, on the other hand, has 13C signals around 99–106 ppm that are correlated with 1H signals at 4.6 ppm corresponding to zeolitic water, and at 7.5–8.5 ppm attributed to overlapping contributions from the aromatic moieties on the organic molecules and weakly H-bonded -OH species. DNP polarization buildup curves, which are dependent on the distance of the organic molecule from the palygorskite particle surface, also indicate that the indoxyl molecules are located predominantly in the interior of the network, while the indigo/dehydroindigo molecules are predominantly near the surface.129 A comparison of Maya blue made with synthetic and natural indigo has also been completed using various NMR techniques.130 27 Al and 29Si spectra of the freshly made Maya blue samples show little difference between the natural and synthetic indigo-based Maya blue; however, upon artificial aging the 29Si spectra of the natural-based Maya blue samples are broader than either their respective fresh samples or the synthetic samples. Additionally, the small feature at  85 ppm, originally present in all of the spectra, is entirely gone after aging. Similarly, the 27Al spectra also show broadening and asymmetric line shapes for the natural-based samples. 129Xe NMR spectroscopy can be used to assess pore dimensions and porosity within a microporous material via the

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following linear relationship: d(r) ¼ d0 þ dS þ d1r. d0 is the reference, dS is related to the mean free path of a xenon atom within a pore, d1 is the coefficient describing the effect of the xenon-xenon collisions, and r is the density of the xenon. A graph of d ¼ f(r) is related to the free porous volume of the sample. Graphs of the synthetic-based samples showed little to no variation in their slopes after aging, indicating no change in porosity. The graphs of the natural-based samples, in contrast, show a substantial increase in slope after aging. Additionally, samples with higher pigment concentration display a greater increase in the slope. Both results indicate that indoxyl in the natural pigment can permeate the clay pores and affects the porosity of the clay framework, which leads to an increased stability and durability of the natural versus synthetic pigment. Indoxyl can then be oxidized into indigo in the pores.130

9.24.2.3.5

Synthetic materials

Synthetic materials such as alkyd resins represent a relatively new family of paints that need to be studied, with artists like Pablo Picasso and Jackson Pollock utilizing these resin paints in their works.132 Alkyd resins, first used in the early 20th century, consist of a polybasic acid, a polyol, and a source of fatty acids. Use of FTIR along with 1D and 2D solution NMR of chloroform extracts made it possible to study the drying process of model alkyd resins and French ultramarine.133 The experiments focused mainly on changes occurring at or in the vinyl and diallyl protons during the drying and curing process which was marked by a decrease in the NMR resonance intensities associated with the vinyl bond position in both the 1H and 13C spectra. The films were considered to be fully polymerized after 10 weeks; the signal of protons in double bonds decreased by nearly a third within the first 48 h, indicating that the early stages of drying result in dramatic changes in the films. The authors concluded that the drying process was twofold: (1) physical drying by solvent evaporation, which occurs mainly in  96 h; and (2) chemical curing, which proceeds in  70 days.133 Increasing pigment concentration in acrylic paints is known to increase rigidity of the material, and thus decrease T2 relaxation times.134 Inverse Laplace transformation analysis of each of four different pigment/binder emulsions was used to probe the relationship between pigment concentration and T2. The four pigments were phthalo blue (C32H16CuN8), alizarin crimson C14H8O4), ivory black (primarily Ca5(OH)(PO4)3 with 5% C(s), and titanium white (TiO2). Most samples displayed biexponential T2 behavior with two T2 values differing by an order of magnitude. The longer T2 value was attributed to the “free” polymer, or the polymer not crosslinked or adsorbed on pigment particles. The smaller T2 value was attributed to the polymer adsorbed on pigment particles. The value of the smaller T2 was hypothesized to be affected by pigment type and particle size which was informed by SEM-EDS. Smaller pigment particles, having greater surface areas for polymer absorption, tend to show a decrease in the relaxation time and an increase the proportion of protons having smaller T2. Chemical composition of the pigment was found to affect adsorption of the base polymer. Organic pigments can potentially adsorb more of a hydrophobic polymer than inorganic, hydrophilic pigments. Either of these two explanations is consistent in rationalizing the NMR results for ivory black, an inorganic pigment with a large specific surface area, which showed long T2 values in all tested samples.134

9.24.2.4

Biological remains and materials

Cultural heritage encompasses more than objects specifically created by humanity; our heritage includes the remains of humanity as well. Understanding the alterations of inorganic and biological tissues after burial is also of importance in cultural heritage and provides invaluable information regarding past generations. Bones and dentine, both human and animal, are composite inorganic and organic materials, the analysis of which provides information regarding diet, lifestyle, and traditions of generations past. The analysis of their transformation through post-mortem physio-chemical processes is of great importance in describing the life and lifestyle of generations of humans. Analysis of mummified human remains provides examples of the numerous problems when dealing with these extremely culturally and physically sensitive objects. Mummies and other human remains have the added complexity of being exactly that, human remains.135–137 Any treatment or study done on these objects must take into consideration the nature of the subject and, for example, ensure that the science does not create desecration of a human resting place, among other considerations. Noninvasive procedures are therefore of great importance when dealing with human remains. Imaging methods, such as MRI in particular, have been developed specifically for investigating biological systems, but the lack of moisture in historical samples has often limited the use of MRI. Rehydration may sometimes be considered, but this is fraught with physical and cultural problems.48 Indeed, early attempts at MRI studies without rehydration failed. While MRI analysis was theoretically possible on some frozen or wet samples, such as the natural glacier mummy, Iceman, and in the case of bog bodies, these samples are often too fragile or unable to be analyzed as particular storage conditions (e.g., cold storage for Iceman) are needed for their preservation.138

9.24.2.4.1

Mummies

MRI has been applied to characterize a well-preserved medieval Korean mummy from the 17th century to test the quality of the MRI images that could be obtained.139 Due to the relatively highly hydrated state of the mummy, the images obtained were quite useful; the MRI technique easily provided visualizations of individual organs. The MRI image of the spinal column of this individual proved particularly enlightening. The high signal intensities of the T1- and T2-weighted images allowed for visualization of the intervertebral fibrocartilage that likely would not have been seen in a CT scan. Only the T2-weighted scans allowed for visualization of the nucleus pulposus (the inner core of the vertebral disc). The combination of these images indicated that the individual suffered from a vertebral diseasedspinal stenosis caused by diffuse disc bulgingdthat would not have been diagnosable from CT images alone thus demonstrating the special utility of MRI in archeological analysis, especially of hydrated or “wet” samples.139

Applications of NMR spectroscopy in cultural heritage science

813

Historical pathology is a valuable tool in understanding the evolution, epidemiology, and etiology of diseases and syndromes throughout time. It also allows for the interpretation of ancient living conditions, medical practices, and human evolution and response to disease. Paleo diagnostic techniques often yield limited information. Advancements in the techniques allow for greater information to be gathered from the samples and thus further our knowledge of ancient pathology and medicine. MRI techniques have been compared to traditional CT techniques in several studies, with mixed results. One study examined a series of Egyptian and Peruvian mummies with both traditional CT imaging and MRI.140 In this particular study, the MRI images were quite detailed as compared to the CT images. Another study successfully utilized a combination of X-ray, CT, and MRI imaging to diagnose a case of Hand-Schuller-Christian’s disease in an Egyptian mummy. The MR imaging proved valuable for evaluation of the intervertebral disc spaces necessary to distinguish the presence of Langerhans cell histiocytosis (the disease family that encompasses Hand-SchullerChristian disease), which is not possible with the other techniques. The MR imaging was therefore instrumental in ruling out problems such as myeloma, osteonecrosis, or spondylitis in this particular case.141 Low proton densities and short T2 values in “dry” samples lead to blurry tissue contours and low signal-to-noise ratios in MRI experiments. Developments such as multiple scanning, use of pulse sequences to accentuate sensitivity, and adjustment of MRI parameters are essential to expand the use of the technique to “dry” samples. In one report, for example, the use of three shortecho-time pulse sequences was assessed by examining their utility in imaging a mummified hand.142 Three different methods of 1 H-MRI were tested in this study: ultrashort echo time (UTE) frequency-encoded pulse sequences; single point imaging (SPI) phase-encoded pulse sequences; and Pointwise encoding time reducing with radial acquisition (PETRA), a hybrid technique. All techniques were tested at two clinical magnet strengths, 1.5 and 3 T with the intent to optimize the images of bone, cartilage, and tendons. The image produced by each technique, and the sample from which they were taken, are shown in Fig. 13. All the MR images show tissue differentiation, and allow anatomical identification of larger structures, but small details are difficult to visualize due to image blurring. The study shows the feasibility of MRI as an imaging tool for archeology of dry samples, but further development of instrumentation and pulse sequences to overcome inherent limitations are necessary to provide wider use of the technique with these kinds of samples.142

Fig. 13 (Above) Mummified hand, Egyptian origin. The yellow line indicates the location of the imaging. (Bottom) 1.5 and 3T spatial NMR images from the three short-echo-time techniques and a CT standard image. The CT image possesses labels for anatomically important structures metacarpals (I-V) with spongy (A) or cortical (B) bone, tendons (2,3), muscles (4), and skin (5). Reproduced with permission from Özen, A. C.; Ludwig, U.; Öhrström, L. M.; Rühli, F. J.; Bock, M., Comparison of Ultrashort Echo Time Sequences for MRI of an Ancient Mummified Human Hand. Magn. Reson. Med. 2016, 75 (2), 701–708.

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Soft-tissue differentiation is limited by traditional CT scans, and rehydration of ancient samples is morphologically altering and often destructive. The development of new MRI pulse sequences allows for visualization of tissues previously unseen or in greater detail than allowed in other methodologies. One complication faced by MRI imaging of mummified tissue is the conversion of normal hydrated tissues to adipocerous (waxy) tissue. T1-weighted 1H MR images were obtained from the adipocerous tissue of an Egyptian mummy brain (3000 years old),143 and internal structures could be distinguished using fast imaging techniques. Taking into account the fast T1 and fast T2 in the experimental setup, the images showed the presence of substantially more bound water than expected.143 Images of soft tissue, bone, and embalming materials have been analyzed using a 3D ultra-short-echo-time technique144 to investigate the subchondral bone and collagen-type-1-rich tissues in Peruvian and Egyptian mummies without the need for rehydration.145 In particular, subchondral bone (bone found just below cartilage) and cartilage-rich tissues were much brighter on MR images than the CT scans. Additional structures including arteries, ligaments, bone marrow, meninges, and teeth could be visualized on the MRI scans that we not visible with the CT scans.145 The ongoing development of ultra-short echo time techniques continues to expand the utility of MRI in the paleo diagnostic and archeological fields. Ancient Egyptian mummification involved dehydrating the body with natron, a blend of sodium salts such as NaCl, Na2SO4, NaHCO3, and Na2CO3 ,10 H2O. It is therefore reasonable to assume that remains mummified in this manner should possess a substantial amount of sodium that might be analyzed with 23Na MRI spectroscopy. One study146 successfully obtained images of a mummified finger with both 1H and 23Na MRI. Comparison of the MR images with a CT images indicated that the 1H signal corresponded significantly with skin and dry tissue while the 23Na signal corresponded with bone. It was proposed that the sodium signal arose from an exchange in the tissue that occurs during the mummification process, as the signal was not present in the spectrum of another historical, non-mummified bone. The images in this study were not perfect, as the sample had areas that could not be imaged; however, the study emphasized the possibilities of using the combined multinuclear approach in studying this type of sample.146

9.24.2.4.2

Bone

Unilateral NMR techniques have been demonstrated to differentiate bandages, bone, nail, and flesh by comparing the T2-weighted density profiles for each sample.138 Depth profiles of various soft and hard tissue layers in both modern and ancient samples are shown in Fig. 14. Although the skull bone of Iceman is closer in age to the older skull, the higher signal noted in the skull bone of Iceman indicate that the bone is filled with water. Similarities can be seen among the signal shape and intensity of a frozen modern cadaver and the Iceman. A similar comparison between signal intensity and shape is also seen for the modern cadaver and the modern skull, as well as for the mummy and the old skull. The decreased signal in the mummy and old skull are attributable to the partial decay of the bone structure over several centuries resulting in lower signal. The study suggested that water content which can be used as a marker of both sample integrity and age, as well as a method of differentiation between skin, bone, and bandages. Additionally, the study notes that unilateral NMR provides a unique methodology for monitoring the decomposition of Iceman as the state of his ongoing degradation is under debate.138 Bone and teeth are composite materials consisting of organic compounds such as collagen and minerals, primarily hydroxyapatite Ca10(PO4)6(OH)2. Analysis of both human and animal bone can provide valuable information for archeologists and conservators. In 1995, 13C and 1H solid-state NMR spectroscopy in combination with X-ray diffraction (XRD), examined the composition of a 15,000-year-old bovine knuckle found in the La Riera Cave, Asturias, Spain. The results indicated a decreased content of carbonate, 0.5% compared to the 3–5% content of modern bones, and the presence of calcinated hydroxyapatite, calcite, CaCO3, and calcium phosphate hydrate, Ca3(PO4)2 , XH2O. The combined XRD and NMR techniques indicated that diagenesis involved the conversion of original bone material into calcium phosphate hydrate, calcite, and calcinated hydroxyapatite. These results have great impact on the standardization of bone dating. For example, modified carbonate content affects the interpretation of carbon-14 dating, which is often used to date and make assessments regarding the diet of the bone source.147 A combination of solid-state 13C and 1H NMR spectroscopy, accompanied by XRD and FTIR spectroscopy, has been applied to assess diagenesis (in this case postmortem chemical and physical processes) of bones in the tombs in the necropolises of Posedonia in Southern Italy.148 The tombs in the area were dated between the 7th century BCE and the 2nd century CE by archeologists, providing a range of aged samples to compare to a modern bone and pure hydroxyapatite. All of the ancient samples were analyzed before and after mechanical abrasion to remove surface contaminants, drying to remove surface hydration, and acetic acid treatment to evaluate diagenesis progress. The acetic acid treatment was necessary to remove absorbed calcite which is deposited on bones by ground water. After the treatments, the 1H MAS NMR spectra of all ancient samples showed varying similarity to that of pure hydroxyapatite, with the oldest bone sample strongly resembling the pure sample. The 1H MAS NMR spectrum of the modern bone showed several peaks indicative of type-1 collagen. The 1H spectra of the 1st-2nd century AD samples showed evidence of organic compounds, with one of the samples showing a significant shoulder in the same region as the modern bone; however, it is clear that the organic portions have degraded over time, shown by the broadening of the peak. The presence and eventual full degradation of organic fractions is a time dependent process that could provide a rapid dating method for archeologists with a simple comparison of 1H MAS NMR spectra. In addition to bone samples, a 4th-3rd century BCE tooth taken from one of the tombs was also tested to compare the resilience of tooth enamel to that of bone. This sample was not treated with acetic acid because no observed calcite was shown in the 1H MAS NMR spectrum. 1H spectrum showed only a narrow peak related to a highly crystalline material, and low hydration water. 13C MAS-NMR analysis confirmed the lack of signal associated with adsorbed calcite. Both NMR studies indicated that tooth enamel is more resistant to diagenesis than bone which could provide more accurate dating information in future studies.148

Applications of NMR spectroscopy in cultural heritage science

815

Fig. 14 1H NMR depth profiles of several old (mummy, old skull, Iceman) and modern (cadaver, modern skull, F.J. Rühli) samples. Reproduced with permission from Rühli, F. J.; Böni, T.; Perlo, J.; Casanova, F.; Baias, M.; Egarter, E.; Blümich, B., Non-invasive Spatial Tissue Discrimination in Ancient Mummies and Bones In Situ by Portable Nuclear Magnetic Resonance. J. Cult. Herit. 2007, 8 (3), 257–263. 1 H, 13C, and 31P magic-angle spinning (MAS) NMR technique identified parameters to assess degradation of several bone samples from ancient remains in Sedlec, Czechia.149 1H MAS spectra indicated that the organic fraction in these samples was rather high, albeit still lower than fresh bone. Lower signals from bound water, the organic matrix, and structural hydroxyl groups were indicative of degradation. The 31P spectra displayed a decrease in the signal of sharp crystalline apatite and an increase in the broad component attributed to the amorphous hydrated surface layer of the mineral platelets, suggesting increased degradation of an object. The presence of humic and/or fulvic acid, as seen by 1H NMR analysis, implied multiple diagenetic pathways as described in previous literature.150 1H-13C CP MAS studies were inconclusive for the identification of humic compounds as these spectra were dominated by signals by the organic faction and prevented the isolation of the resonance of the inorganic carbon. Although most of the samples in this study displayed minor signs of degradation, the samples taken from bones found in contact with the walls or moist soil showed accelerated degradation, suggesting the role of water and moisture in the decay processes.149 Solid-state 31P and 13C NMR techniques have been used to assess the inorganic and organic components of elephant ivory from a shipwreck of a 17th century Dutch trading vessel off the western coast of Australia.151 This study provided the first detailed analysis

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of archeological ivory that had been exposed to a marine, rather than terrestrial or freshwater, environment for an extended timeframe. The 31P NMR results indicated a phosphorous content consistent with modern ivory and of archeological bone samples as a whole; however, differences in sideband number and intensity indicated local structural differences among the various sampling points when the material is exposed to the marine environment. Elemental analysis and FTIR measurements indicated that iron had replaced calcium in the interior bone matrix, forming vivianite (a hydrated iron phosphate). The increased line broadening and sidebands in 31P NMR spectra of samples from these areas were consistent with a disordered phosphorous environment or the inclusion of paramagnetic compounds in these interior samples. 13C NMR results showed that very little or no organic material remained in the waterlogged tusk. In contrast, FTIR data showed absorptions suggestive of carbonate groups associated with biological apatites indicating the presence of some organic matter in these areas. Either the concentrations of the organic factions in these areas are too low to detect by NMR or their relaxation times precluded their detection with the utilized experimental techniques. The exposure to a marine environment with copious neighboring iron artifacts, such as that of a shipwreck, clearly impacted the degradation of the tusk.151

9.24.2.4.3

Leathers

Animal hides are of great interest in cultural heritage. Leather objects and clothing provide invaluable information about the cultures that produced them. Understanding original tanning and production processes gives insight into their origin and use, as well as providing information useful in conserving them. T2-weighted MRI maps, unilateral depth profiles and 1H solid state NMR have been reported for six-year-aged untreated, salix (Willow bark extract)-treated, and cod-liver-oil-treated samples of reindeer skin to assess the tannin fixation into the collagen lattice.152 Salix is composed of condensed tannins also called proanthocyanidins and hydrolysable tannins compared to cod-liver oil which is composed of high percentage of long-chain unsaturated fatty acids. T2-weighed MRI maps showed the untreated sample had an intermediate proton relaxation time of roughly 8 ms, whereas the salix-treated sample had a substantially shorter relaxation time of roughly 2 ms, indicating a more rigid sample. Conversely, the codliver-oil-treated sample had a longer relaxation time of roughly 12 ms, indicating a more flexible sample. Additionally, depth profiling of the samples conducted by unilateral NMR showed a variation in relaxation times between the treated surface and the inner layer for the salix-treated samples, indicating that the cross-linking process propagated through the skin, and was not uniform through the entire sample. Depth profiling for the cod-oil-treated samples, on the other hand, show more consistent relaxation behavior indicating that the oil has penetrated the whole skins sample. These results indicate that tannin-collagen interactions stemming from the salix-treatments result in more rigid and less homogeneously treated samples than either the untreated samples or the samples treated with the cod-liver oil.152 These techniques create a unique pair of complimentary tools to address the differences in vegetation- and oil-treated samples and can provide targeted insight into their preservation and conservation. 1 H solid-state NMR was also utilized to assess aging of the reindeer skin samples and confirmed the unilateral results that vegetable tannin crosslinking with collagen was more effective than that of the cod liver oil.152 1H NMR spectra, normalized for sample weight, showed an increase in signal intensity for samples of reindeer skin treated with salix or cod liver oil compared to the untreated samples. Both treated samples showed a decrease in intensity with aging time; however, even after 6 years of aging, the cod liver oil samples displayed intensities greater than those of an untreated sample. The substantial decrease in the salixtreated samples is explained by the increased immobilization of protons due to the crosslinking of the tannin with the collagen in the skin.152 A combination of 13C solid-state NMR and EPR techniques was used to evaluate samples of several leather shoe soles dating from the 13th–18th century compared to modern leather samples.153 The historical samples in this study had been exposed to water-logged conditions before their excavation in Lyon, France. 1H-13C CP-MAS NMR spectroscopy was used to observe the rigid polymers associated with collagen and tannin moieties. Single-pulse 13C magic-angle-spinning (SP-MAS) spectroscopy allowed the authors to observe lubricants used to soften the leather. The 13C CP-MAS spectra of the archeological samples were typical of pure collagen. The presence of vegetal tannins or lubricants in the archeological samples could not be determined via the SP-NMR studies, indicating that either the substances had completely leached from the soles over time or the samples were not treated with vegetal tannins or lubricants. A modern piece of vegetable-tanned and oil-lubricated leather was put through a 2-week water extraction to simulate the water-logged conditions of the archeological samples and the resulting spectra displayed a complete loss of the signal from the oil lubricant and a roughly 10% decrease in signals associated with tannins supporting the hypothesis that the water-logged conditions led to substantial leaching of the original compounds. Interestingly EPR results for the waterlogged archeological samples indicated significant amounts of Fe and Mn oxides that are not present in the modern samples possibly indicating a transfer from surrounding sediment deposits. The surprisingly good state of conservation of the artifacts was attributed to a combination of the conditions in which the artifacts had been aged and a potential stabilization of the collagen moiety by metal oxides leeched from the local area.153 13 C solid-state NMR techniques were employed to examine seven tanning compounds – condensed vegetable tannins (mimosa and quebracho), hydrolysable vegetable tannins (chestnut and tara) inorganic tanning (chromium (III) and aluminum (III)), and glutaraldehyde in their pure forms and in treated leathers- to assess their NMR characteristics and the spectroscopic changes of the protein structures associated with the tanning processes.154 All of the vegetable tanning agents had distinctive spectroscopic signatures, especially in the range of 70–165 ppm. The inorganic compounds have less distinguishable 13C NMR fingerprints. In the case of the Cr(III)-tanned samples the strongly paramagnetic center affected the 13C NMR resulting in decreased signal intensity for the nuclei closest to the paramagnetic center, although the complexity of the collagen moiety makes it impossible to determine the specific amino acid residues at which the chromium interaction occurs. 27Al solid-state NMR analyzes provided additional

Applications of NMR spectroscopy in cultural heritage science

817

information regarding the aluminum (III) tanning agent as the quadrupolar nature of the 27Al nucleus is responsive to changes in the geometric coordination of the complex. These spectra indicated an octahedral coordination for the aluminum center with six oxygen ligands, rather than the more common tetrahedral coordination. The glutaraldehyde tanning showed no clear signal in the 13 C NMR spectrum that could be attributed to the tanning agent.154 Unilateral NMR technique in tandem with thermal microscopy have been used to characterize the behavior of the collagentannin complex in tanned leathers.155 Previous unilateral NMR studies had been reported that assessed water dynamics in collagen fibers156 and the effect of cross-linking in the collagen fibers on the water dynamics.157 In this study, the authors expanded the investigation to address the effect of artificial aging via dehydrothermal and light-irradiation treatments. Samples of cow and sheep leather were treated with condensed (mimosa and quebracha) and hydrolyzable (chestnut) tannins and subjected to artificial aging at 70  C and 30% relative humidity for up to 64 days. Unilateral NMR CPMG decays for the wet collagen samples could be fit with bi- or tri-exponential functions to obtain relaxation values T2eff_short (bound water), T2eff_intermediate (weakly bound water), and T2eff_long (free [lattice] water). Dry samples could only be fit with mono- or bi-exponential functions corresponding to the shortest and longest T2eff components. T2eff_long values for both calf and sheep leather depended on the tannin type, although the distinction between the condensed and hydrolysable tannins was more pronounced in the sheep leather, likely indicating a morphology difference between the collagens. Interestingly, T1 values were useful for differentiation between the effects of the different tannin types in the calf leather, but not in the sheep leather. Both the T1 and T2eff_long values could be used to infer animal origin of a skin sample and changes in water dynamics due to heat and light exposure. Both techniques indicated change in water dynamics and collagen structure, when the material was de-tanned, e.g., when the tannin matrix was depleted.155 A large database of solid-state 13C NMR and FTIR spectra of both newly manufactured and historical collagen-based materials including tanned leathers, hides, and parchments, has been compiled to facilitate the interpretation of ancient leathers.158 In leathers, the collagen matrix is affected by the tanning agent. 13C NMR spectroscopy is advantageous for analysis of the tannincollagen matrix, as the NMR signals associated with collagen and tannins do not overlap, whereas the FTIR spectra of these kinds of materials show significant overlap. Micro-differential scanning calorimetry (DSC) of the samples was also performed to quantify collagen populations with distinct hydrothermal stabilities and characterize the overall thermal behavior of the historical leathers. The characterization of historical samples is complex and often impossible via a single method. The combined use of solid-state NMR spectroscopy, FTIR spectroscopy, and micro-DSC provided a useful basis for evaluating the deterioration of historical objects, with each technique providing important information.158

9.24.2.4.4

Parchment

Solid-state NMR techniques have been applied by several research groups to assess historical parchment samples.159,160 Unlike leather, parchment is not tanned, but rather only treated to remove the hair from the pelts. Consequently, this process leaves the parchment especially vulnerable to changes in humidity. Collagen can degrade into a less ordered structure in a process called gelatinization, which may cause further degradation of the sample as gelatin is more susceptible to added hydrolysis of peptide bonds when exposed to atmospheric water. One study159 utilized mathematical fitting, integration, and normalization of 1H wide-line NMR spectra to find the ratio of the narrow component (related to bound water) and the broad component (related to collagen) to determine the amount of degradation of parchment samples. Water content in the parchment samples was found to decrease with increasing age of the sample and was attributed to the partial hydrolysis of peptide bonds in the collagen matrix, a fact confirmed by high-performance liquid chromatography (HPLC). The study also examined the 13C CP-MAS NMR spectra of the samples. An analysis of the line broadening of the samples in comparison to the line broadening of pure collagen and gelatin provided a method of evaluating the degradation of the parchment samples with younger samples showing more narrow lines and older samples showing broader lines due to the gelatinization of collagen. Peaks in 13C spectra could also be assigned to polymorphs of chalk, CaCO3, which is known to be used in the preparation of some historical parchments.159 Solid-state 1H and 13C NMR analyzes were used to investigate water and lipid content in fragments of the Dead Sea Scrolls.160 After their discovery in the mid-1900s, the scrolls have begun to deteriorate. Unrolling, cleaning, reading, and general handling of the scrolls have exposed them to pollution, light, and moisture. Previous studies and conservation efforts have left residues of synthetic glues, castor oil, and glycerol on the scrolls. Current conservation efforts are aimed at removing traces of previous treatments, as well as addressing the natural deterioration inherent for parchment. The 1H solid-state static NMR spectrum of the Dead Sea Scroll fragments shows two components: a narrow component attributed to water and a broad component attributed to the collagen hydrogen atoms. It was noted that the water component, however, had a broader linewidth with respect to previously reported values for historical parchments159 indicating a higher degree of water bonding with the collagen moiety. Integral analysis of these two components indicated a lower water content and the increased water interactions with the protein network for the Dead Sea Scroll fragment were indicative of partial hydrolysis. This was in agreement with unilateral NMR measurements of fragments of the Dead Sea Scrolls displayed a very short T1 component around 8.7 ms compared to modern parchment 45 ms. 13C CP-MAS NMR spectra of both modern parchment and the Dead Sea Scrolls (Fig. 15) show exceptional agreement, with the Dead Sea Scrolls exhibiting additional features associated with a lipid fraction, likely from animal fat that wasn’t completely removed during the preparation process.160 The deterioration of a set of 14th–16th century parchment samples taken from book bindings in a collection in Turin, Italy was studied by multiple techniques, including unilateral NMR, differential scanning calorimetry (DSC), scanning electron microscopy (SEM), and FTIR spectroscopy in an attempt to quantify the degradation processes.161 The techniques were able were able to determine a number of thermodynamic, chemical, and structural markers that were proposed to describe deterioration pathways. For

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Applications of NMR spectroscopy in cultural heritage science

Fig. 15 13C CPMAS spectra for a modern goat parchment and a sample from the Dead Sea Scrolls. Indicators at 14.9, 33.1, and 185.1 ppm indicated peaks unique to the Dead Sea Scrolls and were attributed to a lipid faction. The shoulder at 170 is indicative of a carbonate group and was associated with the liming treatment process. Reproduced with permission from Masic, A.; Chierotti, M. R.; Gobetto, R.; Martra, G.; Rabin, I.; Coluccia, S., Solid-State and Unilateral NMR Study of Deterioration of a Dead Sea Scroll Fragment. Anal. Bioanal. Chem. 2012, 402 (4), 1551–1557.

example, the unilateral NMR results indicated that gelatinization produces disordered structures that correspond to shorter T1 values and that hydrolysis pathways lead to longer T1 values.161 These results provided a thorough exploration of a small historical sample group; however, the results indicated that the combination of techniques can provide a useful method for determining the state of deterioration for historical parchment. 13 C CPMAS spectra were taken of parchments made of goat, sheep, and cow hides for the database of collagen-based materials discussed in the section concerning leathers.158 As in other studies, peaks of amino acid residues as well as peaks associated with polyforms of CaCO3 were found in all samples. The sheepskin parchment exhibited additional peaks attributed to the CH3 and (CH2)n moieties of lipids. A semi-quantitative analysis of fat content was made by comparing the ratio of the peak areas of lipids and collagen. Calf and goat parchments had ratios in the range of 0.2–0.3, while the sheep parchment was found to have a ratio of 1.7, indicating a substantially higher fat content. The only significant difference among the 13C NMR spectra of parchment, hide powder, and pure gelatin is a broadening of the lines in the gelatin spectrum.158

9.24.2.5

Paper

The composition of paper is dependent on the manufacturing/sizing process and the source of the raw materials used in its preparation.162 Antique paper and modern papers deemed “high quality” are made from rags and are composed of long linear cellulose fibers with the possible addition of sizing agents. Around the second half of the 19th-century wood pulp replaced the rag as the base material for the paper composition.163 Wood pulp, unlike the rag, contains shorter cellulose fibers as well as additional components such as hemicellulose, lignin, coloring agents, or fillers.164,165 Electron paramagnetic resonance (EPR) data on historical samples indicate the presence of some paramagnetic impurities, from the manufacturing process or from ink contamination. 13C solidstate NMR spectroscopy has been used to fingerprint the organic components of paper166 and can differentiate between crystalline cellulose and amorphous cellulose.167

9.24.2.5.1

Model samples of paper

A carefully balanced water content is necessary to maintain structure and flexibility in paper. Paper consists of cellulose and water, where the water exists in pores and not the cellulose matrix which contains crystalline and amorphous regions. Solid-state 1H-13C CPMAS and wide-line separation (WISE) 2D 1H-13C NMR techniques have been used to determine the morphology of paper.164 Dipole-filtered 1H- 13C CPMAS experiments were utilized to determine if the water pools within the paper morphology were found within the crystalline cellulose or the amorphous cellulose region. By modulating the mixing time and monitoring the 13C signals for the crystalline and amorphous cellulose regions, it was determined that the 1H signal of the water selectively cross-polarized the signal of the amorphous cellulose region, thus indicating that the water pools are surrounded by the amorphous cellulose and not the crystalline cellulose. 2D WISE NMR experiments display, for every resolved carbon resonance, a wide-line proton spectrum which reflects the size of the dipolar coupling of the protons in proximity to the respective carbon. With variations in the mixing time, information on the spin-diffusion of the proton spin pools can be determined. Both methods indicated that the pools of water average 1.5 nm in diameter. The distance between such pools was found to be on the order of 3 nm, which agrees with data from transmission electron microscopy.164 From this study, NMR was able to provide structural information on the water-cellulose matrix and the techniques can be used on cellulose-based artifacts to aid in their continual preservation and conservation efforts.

Applications of NMR spectroscopy in cultural heritage science

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There are multiple possible degradation pathways for cellulose-based paper products. One concern is the darkening or yellowing of pages due to oxidation of alcohols to formation of double bonds and carboxylic acids. Unlike previous studies that used XPS (Xray photoelectron spectroscopy) to look at carbon oxidation on the surface of the paper, NMR has the advantage to analyze the changes of the bulk sample.13C CPMAS NMR spectroscopy was utilized to study carboxylic acid content in historical paper samples after treatment with just water, water and deacidifying solutions of Ca(HCO3)2, Mg(HCO3)2, or Ca(OH)2, or a reducing reagent of borane tert-butylamine for 1 h. Carboxylic acid content was determined by comparing the normalized area of the peaks in the range 140–220 ppm. Decreased content was equated with better cleaning power. The results indicated that the best cleaning method was treatment with deionized water, which was able to remove the soluble portions of the cellulose containing the oxidized carbonyl groups, while the other tested showed an increase in the number of carbonyl carbons compared to the water sample. However, the water method alone is not able to reduce the oxidized carbonyl groups or neutralize the acids.168 13 C CPMAS spectra of paper samples after artificial aging via oxidative treatment with sodium metaperiodate showed a general broadening of all cellulose resonances, with substantial broadening at increasing exposure times, indicating a substantial decrease in crystalline cellulose and a corresponding increase in amorphous cellulose.169 While paper degradation is a complex set of phenomena, most processes including the acid hydrolysis of cellulose encompassed by this study are demarked by a loss of water in the sample. NMR relaxometry data were also obtained for the samples, both by conventional 1H low resolution NMR and by unilateral NMR to assess the water content in the samples pre- and post-artificial aging. T2 relaxation data can be correlated with water confined in the pores of the cellulose matrix. Both relaxometry methods determined significant T2 shortening with aging; however, the unilateral NMR studies did not necessitate the removal of any sample to perform the experimentation. While the amount of sample needed for 1H NMR relaxometry is rather low, the removal of samples of any size from objects of cultural heritage is strictly avoided. The agreement of the results of the two techniques indicated that unilateral NMR could be an exceptional tool for studying the degradation and aging of paper and cellulose based artifacts.169 A multi-analytical approach has been applied to monitor the degradation of paper and papyrus samples by weathering (heat and/or light) and chemical (oxidation by sodium metaperiodate) aging.170 Papyrus is mainly composed of cellulose, but it naturally contains a high degree of lignin. Newsprint paper, also considered in this study, is composed of mechanical pulp and waste paper that has been blanched and de-inked. Deconvolution of the 13C CPMAS NMR spectra before and after weathering allowed a quantitative evaluation of the modifications in the cellulose and lignin. A quantitative evaluation of the following integrals provided insight in the change of the cellulose matrix: the ratio between the peaks at 89.7 and 83.7 ppm provided the crystalline/amorphous cellulose ratio; the broad shoulder between 90 and 100 ppm provided insight on the amount of oligomeric material. A broadening of the resonances in aromatic and methyl regions was also noted and indicated that weathering was more prominent for the lignin component and chemical aging was more prominent for the cellulose component of the samples. The presence of lignin in both the papyrus and newsprint enhanced the effect of the weathering processes compared to pure cellulose paper. 1H low-resolution NMR relaxometry, measured via conventional and unilateral NMR experiments, showed a shift to shorter values of T2 with increased weathering indicating a decreased water content and destabilization of the samples after the aging processes. While the results of this study only address artificial aging, they can be used as a potential diagnostic steppingstone for investigating the degradation process in naturally aged specimens.170

9.24.2.5.2

Paper artifacts and conservation treatments

The unilateral NMR MoUSE was used in another study165 to assess the states of samples from 17th century books in various degrees of degradation. As the level of degradation increased, the relaxation distribution shifted to shorter times, consistent with the degradation of paper being associated with a loss of water.165 13 C CPMAS NMR spectroscopy has also been used to follow the enzyme degradation of cellulose in paper samples inoculated with Clostridium cellulolyticum before and after treatment with two commercially available waterborne polyurethanesdpolyesterbased PES995 and polycarbonate-based PC954. Damage of the cellulose structure was not noted in the NMR spectra until 10 days of exposure by showing a broadening in all the peaks and the ratio in intensity of the amorphous and crystalline peaks increased, showing an increase in the amorphous content. Samples were completely degraded after 15 days of exposure and could not be measured. The 13C NMR spectra for the samples treated with polyurethanes are shown in Fig. 16 and the amorphous and crystalline peaks of cellulose are labeled. Both of the polyurethane treatments protected the paper from enzymatic attack; however, the broadness of the resonances present after day 10 of exposure is more notable in the spectra for the PES995-treated sample indicating that the polycarbonate-based treatment has slightly better protecting power. However, even after 30 days of exposure the samples were still protected showing the effectiveness of both treatments against enzyme degradation.171 Paper samples with sol-gel composed of varying siloxane precursors including tetraethoxysilane, methyl triethoxysilane, dimethyl diethoxysilane, and trimethyl monoethoxysilane, were assessed to determine the applicability of siloxane matrices as a potential conservation treatment of paper artifacts.163 These treatments can be easily applied with a dip coat at room temperature. Additionally, the great functionality of silanes leads to the potential that the combination of hydrophobicity, anti-fungal, and flam retardancy can all be achieved with a single treatment. In the case of this study, it was proposed that the increasing number of methyl groups and thus increasing the hydrophobicity should enhance the protecting power in all three aforementioned categories. 29Si solid-state NMR spectroscopy was used to quantify the amount and degree of condensation for the treatments on paper sheets treated with the siloxanes. The degree of condensation was measured by the number and type of SieOe bonds determined by the shift and integration of the various 29Si resonances. While relatively high degrees of condensation were found for the majority of the treatments indicating good coverage of the treatment, the nature of the trimethyl monoethoxysilane precursor prevented

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Fig. 16 13C CPMAS solid-state NMR spectra for (A) untreated paper samples and paper samples treated with (B) polycarbonate-based PC954 and (C) polyurethane-based PES995 both (a) before and after (b) 2 days, (c) 5 days, (d) 10 days, (e) 15 days, and (f) 30 days of exposure. After 15 days of exposure, the untreated paper (A) was entirely destroyed. Reproduced with permission from Boileau, C.; Tardif, C.; Castro, K.; Proietti, N.; Vicini, S.; Madariaga, J. M.; Carvalho, M. L.; Princi, E., Efficacy of Waterborne Polyurethane to Prevent the Enzymatic Attack on Paper-Based Materials. J. Appl. Polym. Sci. 2009, 113, 2030–2040

condensation due to steric hinderance and thus the treatment was not successful. Contact angle measurements to determine the hydrophobicity of the samples showed that the increasing the number of methyl groups did increase the hydrophobicity of the paper. 13C solid-state NMR spectroscopy indicated that none of the treatments were found to affect the cellulose network and shows that these treatments could be used to protect paper artifacts. However, further studies are needed to determine other factors, such as ink solubility, reversibility, and breathability of the siloxane treatments; however, the results found in this study indicate a potential treatment option for paper artifacts.163 Acrylic copolymers have been suggested as a potential consolidation and protection treatment for paper-based objects. Early efforts in polymer-based conservation often did significant damage to the paper.172 A multi-technique study to assess the suitability of grafting copolymers of vaporized acrylic monomers on paper preservation has been reported. Artificial aging via oxidation of the paper samples was performed by sodium metaperiodate and monitored by 13C CPMAS spectroscopy. Little or no evidence of increased amorphous cellulose was noted in the spectrum after 2 h of oxidation. The spectrum of the untreated sample obtained after 5 days of oxidation, on the other hand, showed marked broadening of the cellulose signals. 13C CPMAS spectra were also obtained after the copolymer application, to infer any changes wrought in the cellulose matrix by the polymerization. No effects on the samples were noted after the application and polymerization of any of the polymers. Spin-lattice relaxation values T*1 (1H) and T*1 (13C), obtained via mathematical interpolation of the cross-polarization kinetics, showed that T*1 (1H) is averaged by spin diffusion and thus sensitive to macroscopic variations. T*1 (13C) is sensitive to local motions and thus sensitive to site-specific motions. A comparison of these values for the untreated paper and paper with polymer grafts indicated that the poly (methyl methacrylate) was in close contact with the cellulose chains indicating a successful treatment method. These polymers are resistant to biological attack and can be modified to obtain desired properties, such as the addition of a fluorinated termonomer to increase water repellence. Future work is needed to further develop these additional properties, but this study provides a baseline for the grafting of polymeric materials on cellulosed based artifacts.173 Unilateral NMR techniques have been utilized to assess the relative distribution of amorphous and crystalline cellulose in paper artifacts.174,175 T1 and T2 data were obtained from the musical manuscript Codex Major dating from the early 17th century and held in the library of the Palazzo Altemps, Rome, Italy.174 Four areas of the Codex were chosen for study: edges of pages clear of writing; areas of dark shadow, attributed to likely dispersal of ink after exposure to moisture; and two areas with ink (iron-gal) writing, either with or without visible corrosion. Various NMR measurements were taken in each of the areas, including inversion-recovery measurement of T1, and determination of the decay under a CPMG sequence. T1 and T2 relaxation times for the paper areas match those values reported in the literature for good quality paper. Shorter relaxation times are noted for the areas with visible ink corrosion (care for paramagnetic impurities were taken into account); however, the damage, attributed to likely acidic ink induced hydrolysis, seems confined to these areas. The results indicated that state of the paper is relatively healthy as determined by ratio of cellulose to water and thus the overall state of the Codex is rather good. The T1 values do not indicate overall acidification of the paper. The dimensions of the water pools contained in the cellulose network were within reason. The unilateral NMR sensor allowed for the assessment of the Codex without the need for any invasive sampling.174,175

Applications of NMR spectroscopy in cultural heritage science

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The Atlas Major, a collection of maps from the mid-17th-century compiled by William and Joan Bleau were highly prized for their grand embellishment, rich colors, and overall esthetic quality. Unilateral NMR was used to assess the degradation of a map showing the territory of Vicenza, Italy.176 The map was in rather poor condition due to oxidation, physical damage, and the presence of adhesive strips on the backside. Although the polychromy of the piece was preserved relatively well, the inks of the page had faded substantially. Proton T1 spin-lattice relaxation times measured at various places on the map were found to be characteristic of ancient paper. T1 values in some areas of the map were found to be much shorter than relaxation times in other areas, an observation attributed to the presence of paramagnetic impurities in certain places. The presence of Cu and Fe in these areas was confirmed by XRF. T2 values were short on average ( 0.3 ms), although some regions displayed significantly longer ( 0.6– 0.8 ms) values attributed to the presence of organic materials from previous restorations or possibly from the adhesives on the backside of the piece.176 A similar study was conducted on an 18th-century Dutch map describing a battle in the War of Polish Succession, 1733–1738.177 Like the Bleau map, this map was in a poor state of conservation due to oxidation, physical damage, adhesive contamination on the backside, and grease contamination from years of handling. Similarly, the polychromic regions were in a decent state of conservation, but the inks had faded considerably. A multi-analytical approach was needed to assess the state of preservation and degradation of the piece. Unilateral NMR was used to measure T1 and T2 values at two sets of points. The first set compared areas with and without foxing (brown spots) Fig. 17A. Both spots displayed a biexponential decay with equivalent values for the longest T1 component; however, the shorter component was smaller by nearly a factor of two for protons in the area with the foxing. This was attributed to, as confirmed by XRF, the presence of Cu and Pb. The second set of points compared areas of differing color green and white (Fig. 17B). These points also exhibited a biexponential spin-lattice decay. The shorter of the two components differed between regions. Components associated with protons in the green area were shorter than those associated with the white area by more than a factor of two. As in the other study, this difference was attributed to, as confirmed by XRF, the presence of paramagnetic impurities in the green ink. Aperiodic Saturation recovery sequence for measuring T1 and T2 distributions for both data sets can be seen in Fig. 17.177 Unilateral 1H NMR techniques have been applied to assess the enzymatic attack of Aspergillus Niger on paper.178 Relaxometry of any kind of paper sample yields three T2 components generally described as a slow relaxing component of  9 ms, an intermediate component between 0.1 and 0.5 ms, and a fast relaxing component on the order of 0.05–0.1 ms. The analysis of CPMG decays

Fig. 17 (A) T1 relaxation results obtained using an Aperiodic Saturation recovery and (B) T2 relaxation time distributions for (Left) areas with and without foxing and (Right) Areas of different color. Reproduced with permission from Castro, K.; Proietti, N.; Princi, E.; Pessanha, S.; Carvalho, M. L.; Vicini, S.; Capitani, D.; Madariaga, J. M., Analysis of a Coloured Dutch Map From the Eighteenth Century: The Need for a Multi-Analytical Spectroscopic Approach Using Portable Instrumentation. Anal. Chim. Acta 2008, 623 (2), 187–194.

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indicated that the intermediate T2 component shifted dramatically with enzymatic attack, shortening from the 0.3–0.4 ms in control samples to approximately 0.1 ms in the attacked samples. This intermediate component is attributed to water located within the small pools dispersed throughout the amorphous phase of the cellulose matrix. The drastic change in the relaxation times of this component imply that the enzymatic attack occurs near these water pools. Unilateral NMR was able to reveal even mild enzymatic attack that was not observable with other methods.178 Consolidants and protectants that reduce acidity in the cellulose environment are of great interest, as acidic environments both promote the chemical degradation of cellulosic materials and the growth of fungi.179,180 Liquid-state 1H NMR spectroscopy was used to characterize polymerized polyamidoamines assessed for their potential as protectants and as deterrents of fungal growth on cellulose-based samples.179 Unilateral NMR 2D T1-T2 correlation maps were used to assess the neutralization properties of alkaline nanoparticles dispersed in a variety of solvents. These maps produce distribution contour maps with two main spots below the T1 ¼ T2 (bulk water) line. The “lower” spot (the spot with the lower T2 values), which was unaffected by aging or acidification, is related to water trapped inside the fibrils of the amorphous. The “upper” spot (the spot with the higher T2 values), which was affected by aging and acidification, are related to more mobile water located near the surface of the fibrils or close to the fibril surface. In addition, NMR diffusive diffraction measurements assessed the mobility of water in the samples by analyzing the pulsed field gradient stimulated echo (PFG-STE) signal to obtain information on the restricted motion. When signal attenuation is plotted

as a function of q ¼ gdG 2p (where g is the gyromagnetic ratio, d is the diffusion pulse duration, and G is the gradient vector), the resulting graph and the non-monotonic behavior (q dips) of the resulting data can be used as an indirect probe of restricted geometry.181 Due to the complexity of the heterogenous pore system, only the smallest q dip corresponding to the largest confining structure is detectable with this method to some certainty. The results of both NMR experiments showed artificially aged samples by heat and humidity demonstrated slightly decreased T2 values associated with a decrease in the confining size of water due to the random cleavage and increased intrafibre hydrogen bonding of the cellulose chains. The hydrolysis in the acid-treated samples was a factor in opening the structure of the cellulose, resulting in significantly longer relaxation times and larger confinement size for water when compared to data on reference samples. Artificial aging of the acidified samples produced shorter T2 relaxation times than the strictly acidified samples indicating a substantial effect on the cellulose structure. While depolymerization of the cellulose is irreversible, treatment with calcium hydroxide nanoparticles hampered further depolymerization even during harsh artificial aging treatments as evidenced by T2 values and confinement size returned to values similar to those of reference samples. Overall, the NMR measurements indicated a restructuring recovery of the cellulose network by treatment with alkaline nanoparticles even after acidification and in strong artificial aging environments.180 Unilateral NMR measurements have been applied to monitor the action of surface enhanced Raman spectroscopy (SERS) active gels on artworks.182 These gels are designed to enhance scattering in Raman measurements. Characterization of their interaction with the surfaces to which they are applied must be considered in understanding the nature of the scattering. Unilateral NMR examination of such materials has provided the ability to profile the gels and the underlying matrix on which they have been applied, allowing assessment of the penetration depth and any modifications to the underlying matrix. The studied gels included multiple viscosities of glucose-reduced citrate-capped silver colloids suspended in methylcellulose or gelatin on a madder lake encaustic wax on colored paper substrates. NMR MoUSE data indicated that the original methylcellulose gel penetrated roughly 60 mm into the underlying paint layer of the encaustic wax sample. Upon removal of the gel, the overall paint layer was reduced by 60–70 mm. The optimized methylcellulose gels with added sodium citrate, however, did not show any notable penetration or detachment of paint within the 20-mm tolerance of the instrument upon removal. When applied to archival paper, the signal of the gels engulfed the signal of the paper. The lowest viscosity methylcellulose gel completely penetrated the sample and was unable to be removed. The gelatin-based gels proved more useful for paper samples and could be removed from the surface; however, the NMR profiles indicated the absorption of water from the gels into the paper leaving residual signal even after the gels had been removed. The unilateral NMR experiments provided the opportunity to find the most applicable gel for both SERS applications and analysis of historical objects.182

9.24.2.6

Wood

Like paper, wood artifacts are composed of cellulose, hemicellulose, lignin, and water. Unlike paper artifacts that present in thin sheets, wooden artifacts often involve a significant third dimension that must be considered during their preservation and conservation efforts. Numerous NMR studies have been applied to wood samples in areas other than cultural heritage. Although these studies may provide insights into questions in cultural heritage, they are beyond the scope of this review.183–190

9.24.2.6.1

Wood artifacts

An important aspect of the treatment of wooden artifacts is the penetration capabilities of water and consolidation solutions. MRI has been used to provide spatial images to address the water content and movement in a wooden sample, for example in the analysis of ingress of D2O into a waterlogged archeological oak timber taken from the shipwreck of the Mary Rose.191 Wood possesses a complex structure during tree growth resulting in a heterogeneous microporous structure of connected cells. Several facets of the wooden timber were tested in order to assess the uptake of D2O at varying depths in the sample. It was noted that diffusion coefficients at the surface were higher than those for water in the interior of the timber. The observation was attributed to increased porosity due to higher degradation on the sample’s exterior.191

Applications of NMR spectroscopy in cultural heritage science 13

823

C CPMAS has been applied to evaluate the degree of degradation of several waterlogged samples obtained from a 16th century wreck in Zakynthos, as well as to studies of olive endocarps dated to 300 BCE from a well in Pella, Greece.192 A wooden sample from the wreck was compared to a modern sample of Hungarian oak, Quercus conferta. The 13C spectra of the specimen and the modern sample were quite similar, with the exception of peaks assigned to the methyl and carboxylic carbons of hemicellulose present in the modern sample, but not in the historical sample. The olive endocarps were compared to two modern samples of Olea europaea, and the spectra differed only in the presence of the peaks ascribed to hemicellulose, as well as a peak assigned to the methylene groups of fatty acids and tannins. The comparison of the hazelnut exocarps found aboard the wreck and modern hazelnut exocarps also showed only variations in the peaks attributed to the methyl and carboxylic carbons of hemicellulose. All of the materials examined indicated a preferential loss of hemicellulose during the initial stages of decay. While a preferential loss of hemicellulose has been noticed in certain types of biological deterioration, such as that caused by brown or white rot fungi, these types of biodeterioration require an oxygen-rich environment. Additionally, cellulose and hemicellulose are attacked simultaneously for many forms of biodeterioration. The oxygen-restricted environment of these samples, as well as the lack of evidence of biological deterioration on the crystalline/amorphous cellulose and depletion of hemicellulose suggested preferential chemical lysis of the hemicellulose as the degradation pathway for these samples.192 Liquid-state 13C NMR spectroscopy was used to identify the alcohol and phenol groups and 2D HSQC NMR spectroscopy was used to identify and quantify the principal intermonomeric units in acetylated lignin extracts from samples of archeological wood from the San Rossore Roman harbor in Pisa, Italy, and from a shipwreck in the waters of Tantura Lagoon in Haifa, Israel.193 Lignin possess a complex structure cross-linked in multiple dimensions by a variety of bonds, such as ether and CeC bonds, between the monomeric units. The NMR results indicated that the chemical structure of the lignins was not heavily modified by exposure to waterlogging conditions. The assignment of signals in the HSQC spectra were based on the chemical shift data obtained from milled wood lignin reported in the literature. The presence of arylglycerol-b-aryl ether, dibenzodioxocine, and pinoresinol indicated that the chemical structure of lignin was not heavily modified and the intermonomeric bonds are still present even after significant water exposure. Quantitative 13C NMR was also used to assess the sample and was used to confirm the oxidative process noted by the high amount of the arylglycerol-b-aryl ether intermonomeric unit. It was also noted that the oxidation occurred at the carbon in a benzylic position. 31P spectra were acquired with non-acetylated samples to further elucidate evidence of the oxidative effect. The presence of alcohol and carboxylic groups in the 31P spectrum of the San Rossore sample indicated the cause of the oxidative process was likely white rot fungi.193 Samples of ancient larch and fir from the Castle of Valentino in Turin, Italy, have also been studied by 1H low resolution NMR techniques.194 The Fourier transform of the free-induction decay (FID) displayed a broad component due to protons in the rigid polymeric matrix and a narrow component due to water. Lowering the temperature of measurement and monitoring the effect on the water resonance provided information regarding the porous structure of the sample. The historical samples were found to have small pore distributions (typical sizes of  1 nm). Dipolar filtering of the 13C CPMAS spectra allowed determination of the relative locations of the water pools and lignin. A model was proposed based on the NMR data that water pools are surrounded by thin layers of amorphous cellulose or lignin, and the crystalline cellulose surrounds the amorphous cellulose domains.194 These results are similar to what was seen in paper.164 Solid-state NMR analysis was also applied to specify the state of preservation of several wood Viking artifacts in the Oseberg collection in Norway.195 The samples in this study were treated in 1904 when standard practice was to treat all wooden objects with alum to strengthen their structure. Unfortunately, these earlier conservation treatments resulted in highly acidic, fragile systems. Two fragments of the alum-treated wood were studied, along with a non-alum-treated historical sample taken from the Oseberg ship. 31P solid-state NMR can yield information about the quantity and relative ratios of phenolic and other lignin functionalities in a sample. A 31P label must be introduced to the sample, generally by solvation in pyridine and phosphitylation by 2chloro-4,4,5,5,-tetramethy-1,3,2-dioxaphospholane (2-Cl-TMDP).196 The 31P NMR spectra indicated a loss of polysaccharides and an increase in carboxylic functionalities in the samples treated with alum resulting in spectra resembling that of pure lignin. The 31P spectra of the untreated Osberg sample was dominated by the bimodal peak related to the derivatization of primary and secondary hydroxyl groups of cellulose and hemicellulose, with only minor peaks in the regions pertaining to phenols and carbocyclic acids resembling the reference structure of sound wood. The 2D-HSQC spectra for the alum-treated samples nearly matched that of lignin. The presence of the crosspeak related to methyl esters supported the suggestion that a significant quantity of acidic functionalities was present which had also been noted in the 31P spectra. Although both alum-treated samples showed peaks suggesting degradation, the non-alum treated sample from the Osberg ship had peaks assigned to cellulose, hemicellulose, and lignin, indicating a good state of preservation.195 13 C CPMAS and unilateral NMR were used to fingerprint wood of an Egyptian XXV-XXVI dynasty sarcophagus.197 The sarcophagus had been sold to the Museo del Vicino Oriente of the Sapienza University of Rome by a private collector. Limited information was known about the history of the sarcophagus and a multi-analytical study was carried out to determine the constitutive elements and assess the state of conservation the sarcophagus. Unilateral NMR was used to assess the preservation state of the wood by assessing the T2 relaxation values with longer values being associated with better preserved wood. Both the interior and exterior of the sarcophagus exhibited biexponential trends; however, exterior values were consistently shorter indicating a more advanced state of decay on the outside of the sarcophagus. 13C CPMAS spectra were used as a fingerprint for wood type. The ratio between the resonances at 152.6 ppm and 147 ppm serves as a quick identification as hardwood (> 1) or softwood (< 1). The wood was identified as a softwood with a ratio of 0.48. 13C CPMAS was also utilized to identify a white milky substance found on the interior of the

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sarcophagus. The substance was determined to be polyvinyl acetate, a synthetic resin commonly used in the restoration of Egyptian antiquities and provided insight into the undocumented conservational history of the piece.197

9.24.2.6.2

Violins

Liquid and solid-state NMR analyzes have been used to assess various varnishes and varnish mixtures common to the violin-making process.198 The tonality of certain violins such as those of Antonio Stradivari has been thought to be a property of a secret production method that has been lost to time. Several studies have been conducted in an effort to elucidate the secrets behind history’s greatest violins. 1H NMR spectra of linseed oil and colophony, though complicated, can be unambiguously assigned.198 Blends of the mixtures exhibited overlapping signals with intensities in proportion to the relative ratios in the mixtures. 2D NOESY spectra of the mixtures before drying showed no cross peaks between the two, indicating the fractions are poorly linked before drying. 13C solid-state NMR spectra showed the formation of a hybrid ester species obtained by a reaction between diterpenic carboxylic acids of colophony and the triglycerides of the oil. Analysis of solid-state spin-lattice relaxation times in the rotating frame (T1r 1H) provided information on the miscibility of the colophony and linseed oil. These relaxation times are dominated by the spin diffusion phenomenon with the value for similar protons averaging out to a unique value. Matching T1r values for different species indicates a strong coupling, and therefore a highly miscible blend. The T1r 1H for the linseed oil/colophony mixture suggested that a 75/25 wt % linseed oil/colophony produced the most homogeneous coating.198 13 C solid-state NMR spectroscopy has been used to characterize wood samples from four Stradivari instruments and one Guarneri instrument, in an attempt to discern the unique compositions of these Cremonese masterpieces. Results indicated that the historic maples used in the Cremonese instruments showed significant reduction in the signals related to hemicellulose. Additionally, weak correlations between methoxy and aromatic carbons indicated the oxidation of lignin. The crystallinity of cellulose by NMR spectroscopy was found to be relatively unaltered for the historical samples, in agreement with X-ray scattering experiments.199 Unilateral NMR MoUSE profiles were obtained for mock samples and for five historical violins in the Museo del Violino, in Cremona, Italy. Proton density profiles of the wood were largely similar, with only small variations attributed to differences in the wood texture.200 The sample was expanded to include 10 violins from the Ashmolean Museum in Oxford, England. Depth profiles taken at the point of least curvature for the Oxford violins and at up to three positions for the Cremonese violins, based on thickness of the varnish and curvature of the piece, were obtained. (Violins are, even in areas of low curvature, curved objects, which affects the spatial resolution of unilateral NMR measurements. Structures thinner than 0.2 mm could not be resolved.) The results of the depth profiles were consistent across the majority of the samples at the Ashmolean Museum, as the violins all displayed wood stiffness higher than that of fresh maple, likely from decreased amounts of bound water in the samples. Interestingly, one of the studied violins from the Oxford collection (the Lupot 1816) showed lower stiffness at both the inner and outer surfaces of the back plate, attributable to a possible unknown treatment of both the inner and outer surfaces of the plate. A stark contrast was noted between the Oxford samples and the samples from the Museo de Violino (Fig. 18). Differences in T2 distributions and depth profiles suggested differences in preservation state of the instruments. Interestingly, two of the sample violins in the Italian collection (the Amati 1658 and Stradivarius 1715) have sampling spots with longer T2 values than those expected for healthy woods, which might be attributable to potential degradation, either chemical or mechanical in nature.201

9.24.2.7

Textiles

Cellulose is also an important component of textiles made from cotton and flax (linen). The polymerization of cellulose in these materials is characteristic of the starting plant material and the treatments done during the spinning, weaving, and finishing processes.202 As with the paper samples discussed in Section 9.24.2.5, 13C CPMAS NMR experiments have been used to follow the artificial oxidation of cotton and linen samples with sodium periodate.203 The effects of degradation were quite pronounced at longer times and with more concentrated exposures to the periodate as was noted by the increased broadening of cellulose resonances as well as an increases in the amorphous cellulose resonances in the 13C NMR spectra with increased exposure time. The degradation was attributed to the increasing amorphous material and the formation oligomers. Linen samples, due to their content of lignin (which is not present in cotton), were found to be substantially more affected by these oxidative processes and exhibited greater increases in the amorphous cellulose resonances and greater overall broadening after artificial oxidation.203 Polymer grafting has also been tested on textile samples as with the paper samples previously discussed.172 Solid state 13C CPMAS NMR was used to evaluate the grafting potential of two acrylic monomersdethyl acrylate and methyl methacrylatedfor their potential as a conservation and preservation method for cellulose-based textiles. Artificial aging of the samples was performed with sodium periodate to model natural aging. Natural aged cotton samples were also tested. Successful grafting necessitates no change to the material aspect of the sample while simultaneously achieving a high percentage of polymer coating adhered to the substrate with physical forces. This adherence can be determined via cross-polarization NMR. By varying the contact time and comparing the intensities of the anomeric carbon of the substrate and the carbonyl carbon of the polymer, a determination on whether grafting was successful (i.e., the spin-lattice relaxation time, T1r(1H) values for these resonances were within tolerances of each other) or was unsuccessful (i.e., the T1r(1H) values for these resonances were dissimilar). Similarities in the T1r(1H) values for poly(methyl methacrylate) and the cellulose of the textiles indicated that grafting took place on the surface or within the cellulose network. Ethyl acetate grafting necessitated additional single pulse excitation 13C experiments with recycle delays of 500 s to

Applications of NMR spectroscopy in cultural heritage science 825

Fig 18 Unilateral NMR results for the ten violins in the Museo del Violino. The leftmost column shows the relaxation contrast corresponding to wood stiffness for all measurements as well as a small colorcoordinated graphic to show sampling spots. The next columns are arranged in pairs of two images (Left) T2 relaxation time distributions, and (Right) hydrogen density corresponding to wood density that correspond to the colored spots in the graphic in the first column. Reproduced with permission from Blümich, B.; Baias, M.; Rehorn, C.; Gabrielli, V.; Jaschtschuk, D.; Harrison, C.; Invernizzi, C.; Malagodi, M., Comparison of Historical Violins by Non-destructive MRI Depth Profiling. Microchem. J. 2020, 158 (June), 105219–105219.

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obtain semi-quantitative data as the previous methodology resulted in inhomogeneous data. Both 13C NMR methods proved useful for assessing the grafting potential of the acrylic monomers on the textile substrates.172 Solid-state NMR procedures can identify the structure of silks, a biopolymer composed of fibroin and water,202 as seen by 13C CPMAS NMR of three samples from a 12th century Japanese tomb.204 Splitting in the region ascribed to the peptide bond was attributed to variations in the secondary structure, i.e., forms Silk I (random coil) and Silk II (anti-parallel b-sheets). The relative amounts of the two forms had a non-linear dependence on age.204 1H cryoporometry and solid-state 13C CPMAS NMR spectroscopy were used to characterize the microstructure of fresh and historic silk samples.205 Cryoporometry utilizes the Gibbs-Thompson equation 1000 K sl T0 (DT ¼ T0  T ¼ R2s DH ¼ T0  X ¼ R where T0 is the normal melting point, T is the melting point of the confined solid of dimenf rs

sion R, X is the inverse temperature, ssl is the surface energy at the solid-liquid interface, DHf is the bulk enthalpy of fusion, rs is the mass density of the crystal solid, and K is a constant that depends solely on the physical properties of the liquid) which expresses the melting point depression of a liquid confined within a small pore. Pore size distributions can be estimated from measurements of liquid, in this case water, as a function of temperature. Assessing the 1H FID signal amplitude for the two components (a fast decay due to fibroin and a slow decay ascribed to water) as a function of temperature provided information on the water pore-size distributions of each sample. Interestingly, the historic silk showed evidence of pore sizes larger than 2 nm, suggesting an increase in micro-voids throughout the sample during aging. While the basic spectral shape remains the same, the 13C CPMAS spectra of the historic silks showed a general reduction in signal intensity when compared to that of fresh silks. Deconvolution of the peak centered at  20 ppm reflects a significant decrease in the percentage of random coil silk in the historic samples. A decrease in the random-coil conformation correlated with the change in pore size from the 1H data, suggesting that amorphous regions of the textile gradually loosened with increased deterioration.205 Sodium borohydride is a reductive bleaching agent that can restore oxidized cellulose functionalities to the original hydroxyl groups and has been suggested as an alternative solution to oxidative bleaching solutions.206 Solid-state 13C CPMAS NMR spectroscopy has shown that sodium borohydride washing of modern and ancient textile samples resulted in decreased hemicellulose content but had no effect on the cellulose crystallinity. Maintaining the cellulose crystallinity is necessary for maintaining the integrity of the textile being treated. Conservation treatments of historical textiles frequently included treatments with aqueous solutions for removal of stains.207 However, no treatment is without risk. Oxidative bleaching achieves the goal of stain removal and brightening of the textiles but is difficult to control and can produce long-term effects that add to the overall degradation of the textile.206

9.24.2.8 9.24.2.8.1

Resins, gums, and other plant products Amber, copals and jet

Amber is a fossilized resin found in decorative objects and jewelry. Knowledge of its chemical structure provides information on its geographic and biological origins; however, its relative insolubility and lack of crystallinity make the substance difficult to analyze. 13 C solid-state NMR spectra have provided information on the carbon functionalities of amber samples from a multitude of geographical locations. For example, spectra of four Baltic ambers from different locations essentially had identical spectra.208 Studies of broader European ambers indicated that samples could be divided into two groups distinguishable from each other mainly by the presence the exo-methylene resonances for the Baltic or lack of for the southern European ambers.209 Samples of amber from the Dominican Republic were analyzed in a similar manner. Unlike the regional consistencies found in the European samples, spectra of the Dominican samples displayed a significant variation in carbon functionalities, particularly in the methylene peak, the ether/ester peaks, and the alkene carbon resonances which show extreme variation from sample to sample.210 Amber samples from several locations across Mexico produced almost identical spectra, even though the samples varied greatly in color.211 These spectra were distinguishable from the Baltic and Dominican ambers, although similarities with the latter were noted. Cretaceous amber from Canada and the eastern coast of the United States showed nearly identical spectra.212 Samples from the western United States exhibited very weak or absent exo-methylene signals. The small or absent exo-methylene and the considerable carbonyl resonance without the ester resonance distinguished these ambers from those of the Baltic, Mexican, and Dominican sources. A sample of amber from the central United States (Arkansas) contrasted greatly with the other North American samples, with the exo-methylene resonance and the resonance at 145 ppm entirely missing, and a sharp resonance at 150 ppm appearing.212 Ambers from New Zealand and Australia have also been characterized by NMR.213 The vast majority of samples from New Zealand were found to be similar to those found in the northern parts of North America and were attributed to Agathis. Samples from Australia and Papua New Guinea showed similarities with the amber found in the central United States.213 A series of ambers dated to the Cretaceous Period (ages ranging from roughly 60–110 million years) from Greenland, Lebanon, Israel, Jordan, Canada, the United States, France, and Switzerland and a Triassic sample (aged at roughly 220–230 million years) from Bavaria were compared by 13C solid-state NMR spectroscopy. The study noted the remarkable similarities among the samples, particularly given their geographic dispersion. The exo-methylene resonance was notably absent from the spectra of all samples. The samples were generally grouped into five categories, based on similarities in their spectra. Overall, the similarity of the spectra indicated a common paleobotanical source with wide geographical distribution during the Triassic and Cretaceous eras.214 Several studies have sought to isolate novel organic compounds from amber samples.215,216 1D and 2D solid-state NMR techniques have been used to isolate and provide structural refinement for unique compounds in ambers, which could result in the specific identification of the original source of the material. 1H, 13C, and HSQC NMR experiments on amber from the Oise River area of Paris, France, showed the presence of two methyls, nine methylenes, four methines, and four quaternary carbons. The

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spectral features indicated a tricyclic diterpene as the basic structure. Comparison to modern flora indicated a potential source of the Oise amber: Hymenaea oblongifolia. Interestingly, this species is currently only found in the Amazon rainforest and implies the presence of a tropical climate in the Paris basin in past epochs.215 Kujigamberol, a new dinorlabdane diterpenoid compound was isolated from amber found in the Kuji region of Japan and the structure was determined by NMR techniques. It is different than diterpenoids isolated from Baltic ambers.216 Copals are hardened, but non-fossilized, resins that have aged for generally under a million years. Both copals and ambers can be identified and distinguished by a variety of NMR techniques. Younger copals tend to show a large number of resonances, especially in the region between 0.0 and 2.0 ppm.217 Colombian copalites were found to produce similar spectra to resins obtained from the genus Hymenea in solid-state NMR studies.218 13 C NMR CPMAS experiments have been used to identify and distinguish two types of jet, English and Spanish, from other carbonaceous materials and black materials commonly confused with jet.219 Jet, like amber, has been highly sought after as a decorative gemstone in both ancient and modern societies. It is carbonaceous in nature, composed of highly compressed wood that has been under anaerobic and reducing conditions for millennia. In this investigation, two jet samples showed remarkably similar spectra, with broad resonances in the aliphatic and fine structure visible in the aromatic regions. The English samples displayed a prominent shoulder on the low-frequency side of the aliphatic region that can be used to differentiate the two jets. The spectra of both jet samples are significantly different from spectra of other dark materials such as peat, horn, glass, onyx, vulcanite, bakelite, and epoxy resins, all of which can easily be confused with jet by a visual inspection.219 The 13C CPMAS NMR spectra of the two jet bead samples found at an archeological excavation of the Maya community at Tipu, Belize, matched the spectrum of Spanish jet.220 The 13C CPMAS NMR spectra for amber beads found at the same archeological excavation were not consistent with Mexican amber, but rather found to be characteristic of Baltic amber indicating a decisively European source of the beads.220Both the jet and amber artifacts mentioned previously were found near the graves of relatively young children. It is historically known that Christian priests focused conversion efforts on the younger members of the New World societies, and the decisively European source of the beads could indicate that these were potentially part of gifts given to the local children by the European missionaries in the area.220

9.24.2.8.2

Rubber and latex

An extensive study with NMR spectroscopy to collect a library of chemical signatures of angiosperms and gymnosperms that produce resins, gums, latexes, and other useful plant exudates has been reported.221 While the extrudates of numerous plants look similar on a macroscopic level, they have unique chemical signatures that can be identified by NMR. Identification of family, genus, or even species of the original plant matter used in the making of such exudates can provide researchers with knowledge into the geographical origin and processing history of the product. Additionally, such knowledge can guide the cleaning or conservation of objects containing such compounds. The study reported results for 65 species from 20 plant families and provided information for uniquely identifying features of individuals and groups of plants. The study an exceptional effort to relate chemical structure to plant taxonomy which allows for unambiguous classification of unknown exudate samples to be characterized as resins, gums, gum resins, or latex.221 13 C CPMAS NMR and 13C MAS NMR spectroscopy have been used to characterize the molecular structure of modern and ancient rubbers and latexes.222 Rubbers are polymeric plant extrudates popular for their flexibility and elasticity. One of the earliest known applications of rubber was by ancient Mesoamerican peoples. Rubber had a sacred place among the Maya and a game played with a solid rubber ball was a central part to their origin story, the Popol Vuh. Although many of these ancient rubber artifacts have been lost, a few have been recovered, including a set of 12 solid rubber balls at the Manatí site, Mexico. Both ancient and modern samples showed the five characteristic nuclear magnetic resonances associated with natural latexes and rubbers. Treatment of the natural latex with a liquid extracted Ipomoea alba, a species of morning glory vine, was necessary to avoid a brittle and non-elastic material after drying. 13C MAS spectra before and after processing with I. alba indicate the treatment both concentrates and purifies the natural latex into rubber.222 Solid-state NMR techniques have been used to assess the degradation in model rubber samples and a 5-year-old artist “test” piece.223 Natural rubber products have been utilized in many modern works of art. Unfortunately, these products degrade relatively quickly due to their vulnerability to the effects of light and oxygen. High-resolution 1H MAS NMR spectra of two modern samples and the artistic piece, while not entirely resolvable due to extreme broadening of a dense proton network, were resolved into several peaks that showed variance among samples. 13C MAS NMR spectroscopy utilizing a DEPTH experiment gave better spectral resolution than the proton spectroscopy. The spectrum acquired on the artistic piece at a spot that was not visibly degraded was similar to the spectrum of a fresh sample, while the spectrum of another site that showed visible signs of degradation displayed substantial reduction in the isoprene peak and other signs of oxidation. 1H-13C CPMAS spectra of the degraded site displayed several additional broad signals compared to those of the fresh/non-degraded site, indicating that several processes are associated with the degradation process, rather than just the chain scission at the double bond, as had been deemed the primary path in strictly laboratory studies.224,225 The NMR spectra of the UV-irradiated samples showed evidence of chain scission, while the naturally aged test sample displayed evidence of oxidation.223 Unilateral NMR relaxometry with multivariate data analysis was used to map the degradation of the rubber mask assessed in the previous study.226 The relaxation decays for 53  10  10  0.1 mm fields were assessed by unilateral NMR methods, of fresh model samples of rubber and of two visibly different spots on the 5-year-old “test” piece were biexponential,223 attributable not to different chemical sites, but to different forms of polyisoprene. The less visibly degraded spots displayed relaxation times similar,

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although distinct, to those of a fresh test sample, while a visibly degraded edge spot relaxed much faster. Principal component analysis indicated that the overall sample was quite good as most of the scores cluster close to the score for fresh latex. Unilateral NMR experiments were also used to monitor early degradation induced by UV irradiation in the fresh rubber samples, with spatial resolution not possible with solid-state techniques that are dominated by the bulk signal. Relaxation decays of urethane rubber samples were measured at 100, 200, and 300 mm after 60 days of artificial UV aging at 254 nm to assess the extent to which the degradation of the material could be determined via unilateral NMR assessed by principal component analysis. A strong association was observed by comparing the depth and predicted depth in the partial least square regression method. The statistical analysis indicates that the study could discriminate between the relaxation decays measured at different depths and could therefore potentially be used to map the degradation of these types of artistic materials.226

9.24.2.9

Synthetics

The increasing use of synthetic polymeric materials in art is another area in which NMR methods might aid the conservator. For example, unsaturated polyester resins reinforced with fiberglass have been used to create rigid, 3D shapes and sculptures.227 Two late 20th-century art installations, The Last Milk Platform by Jan-Erik Andersson and Cocotte with Two Dogs by Kari Tykkylainen, have been studied by 1D and 2D high-resolution solution NMR spectroscopic methods, in an attempt to understand the natural aging of the two pieces.227 Acetone-extracts of the two pieces and of two cured and aged reference samples were analyzed with 1D and 2D 1H NMR spectroscopy. The spectra displayed a diverse mix of chemical speciesdsuch as oligomeric unsaturated polyester chains that contain phthalic and diol units, including phthalate and isophthalate and esterified 1,2-propylene glycol; as well as crosslinkers like styrene and its byproducts benzaldehyde and benzoic acid, plasticizers like dimethylphthalate; aliphatic esters that were included in the peroxide initiator; and degradation productsdwhich indicated the utility of NMR to identify the chemical composition of the unsaturated polyester resins, and to assess their state of conservation and degradation.227 In addition to providing essential information on the preservation of animal-derived products, solid-state NMR can also give great insight into mistaken identities.228 For example, a small box in the collections of the Portuguese Museum of Ancient Art was thought to be made of tortoise shell with gold encrustations. The formation of a hazy white film and surface warping resulted in a rapid analysis for preservation. The 1H and 13C NMR of the object indicated the presence of four organic compounds characteristic of cellulose acetate, and not of tortoise shell.228 A set of 50 of the most commonly utilized thermoplastic resins, as well as natural latex rubber and a urethane rubber, were measured by unilateral NMR analysis, using principal component analysis to establish an unambiguous and model-free large data set of relaxation decays. Having an established database permits easier analysis of artworks and their state of degradation by conservators.

9.24.2.10 Other substances associated with human life Various organic substances have been used in the preservation and decoration of bodies for centuries. Like the bodies themselves, these substances are prone to degradation and changes such as cracks, color changes, and chemical alteration over time. Analysis of these materials can provide insight into the lives of past generations, including trade, food processing and storage, cosmetics, etc. An early application of NMR methods of such substances was the 1974 analysis of a dark liquid found in a sealed glass flask, dated from between 600 and 400 BCE.229 The sample was identified by 1H liquid-state NMR spectroscopy to be predominantly oleic acid, potentially from hydrolyzed olive oil. 1H liquid-state NMR was also used to identify a solid residue from a 3rdcentury CE pilgrim flask as a mixture of myristic and palmitic acids.229 Another study utilized 1H liquid-state NMR spectroscopy to analyze and identify resin samples from 22 Hellenistic amphorae found in Apollonia Pontika (southeast Bulgaria). A comparison with contemporary samples indicated that the amphorae were used to transport retsina, a pine resin wine.230 1 H and 13C liquid-state NMR examination has been performed as part of a compositional analysis of historical beer samples. The study indicates that the changes in carbohydrates and carbohydrate-adducts may be markers for aging or reflect changes in the historical brewing processes. Fig. 19 shows the 1H-13C HSQC spectra of three beers from the late 19th and early 20th century and a modern sample. The carbohydrate contents of the bottles indicate an increase in product stability as scientific brewing practices proliferated at the turn of the century. Two-dimensional NMR spectroscopy shows that the oldest of the samples has signs of enzymatic degradation, while the youngest of the samples has better preservation of the malto-oligosaccharides. The analysis of these samples also gives information on the evolution of cereals in the brewing process.231 Residues found on prehistoric pottery samples from archeological sites have been analyzed by 13C and 15N MAS NMR spectroscopy to provide data on the diet and cooking methods of ancient peoples.232 One study observed encrusted material found on round pots and plates found around Southern Indian Black Lake and Kame Hills, Canada. Ratios of 13C/12C are indicative of variations in photosynthesis. Plants that utilize a C4 pathway, such as maize, are approximately 14% enriched compared to plants that utilize C3 pathways. Similarly, 15N/14N ratios in animals show that herbivores are  3% enriched in comparison to plants, and carnivores are a further 3% enriched compared to herbivores. With this knowledge, it is possible to use the isotopic ratios of the encrusted samples to infer materials humans used in these dishes. The majority of the dishes contained traces of meats, fish, and fats and little to no traces of vegetation.232 Another study utilized 13C solid-state NMR and FTIR spectroscopies to analyze residues found on several samples of Roman Iron Age pottery from the Netherlands.233 Comparisons of the aromatic and aliphatic signals, especially the areas associated with

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Fig 19 1H-13C HSQC spectra of historic and modern lager samples. Highlighted signal areas include: starches in Bottle 1, A; b-glucan and b-xylan in Bottle 2, A; And other differences noted from the modern sample in Bottle 3, A. B figures indicate further differences in mono- and disaccharide compositions of the beers. Reproduced with permission from Walther, A.; Ravasio, D.; Qin, F.; Wendland, J.; Meier, S., Development of Brewing Science in (and Since) the Late 19th Century: Molecular Profiles of 110–130year Old Beers. Food Chem. 2015, 183, 227–234.

proteins, collagen, polysaccharides, and lipids, led to samples being classed in one of four categories: highly condensed chars characteristic of cellulose and carbohydrate materials, mildly condensed chars characteristic of proteinaceous materials, non-aromatic residues assigned to unheated proteinaceous material (possibly indicating a waterproofing method for the ceramic), and soots characteristic of smoke condensates from wood fires. NMR techniques can provide valuable information about samples, particularly samples that have experiences some level of thermal degradation that cannot be obtained by other methodologies. The combination of these results with the results of other techniques, such as FTIR or mass-spectrometry, can provide further information into the use of the ancient pottery and thus better information into the different aspects of past societies.233 13 C liquid-state NMR spectroscopy has been used to identify the composition of medieval seals on documents in British collections.234 The Royal seals of King Stephen (1135–54), King John (1199–1216), and King William IV (1830–37) and an unprovenanced personal medieval seal were compared to ancient (14th century) and modern beeswax, colophony (rosin), and shellac. The modern and ancient beeswax showed remarkably similar spectra, with only notable differences around the area of  130 ppm (alkene or aromatic carbons) which was reduced in the ancient sample likely due to a decrease in saturation from oxidation. The similarities in the spectra indicated an overall long-term stability in the chemical nature of the beeswax. The majority of the seals showed the characteristic spectral fingerprint of beeswax. One, however, the seal of King William IV, indicated a composition more closely matching that of a mixture of beeswax and rosin as indicated by the more complicated resonances found in the 130– 150 ppm region. It should be noted that the spectral resonances do not perfectly match those of modern rosin and further studies would be needed to fully determine if the signals are those of a degraded form of the substance.234 Lipids have been widely used throughout human history as cosmetics, medicines, and clothing treatments.235 1H and 31P liquidstate NMR techniques have been used to analyze the lipid fraction in historic 17th–18th-century ointment samples from the Aboca Museum of San Sepolcro in Tuscany, Italy. Standards of olive oil, almond oil, palm oil, pig suet, colophony, pine resin, and beeswax, as well as model ointments prepared with historical recipes, were tested. Cholesterol and its derivatives, glycerophospholipids, cholines, and triglycerides were easily detected by 1H NMR. 31P NMR, after solvation in a mixture of pyridine and CDCl3 and

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the addition of 2-chloro-4,4,5,5,-tetramethyl-1,2,3-dioxaphospholane, provided information regarding hydroxyl groups and permitted the quantification of the different alcohol and free carboxylic acid moieties. After analysis of the standards, the presence of beeswax, pig suet, pine resin, olive oil, and cacophony in the ancient samples were confirmed. Additional peaks indicated the possible presence of linoleic and lactic acids, as well as oxidation and hydrolysis products likely present from the degradation of the samples.235 Tars and pitches associated with historical shipbuilding have been analyzed by NMR methods.236,237 Tars derived from Scotch pine, Norwegian Pine, coal, peat, and crude oil can be differentiated from each other spectroscopically (both 1H and 13C), allowing the identification of the origin of materials obtained from various shipwrecks and other wooden archeological samples.

9.24.3

Conclusions

Numerous applications of NMR methods for the study and conservation of cultural heritage have been reported. NMR spectroscopy is a tool widely applicable to identification of materials. It has been used successfully to answer questions about numerous aspects relating to the materiality of objects of cultural heritage significance. From structural and chemical identification to moisture content and distribution, these experiments shed light on the techniques, geographical origins, and constituent materials of an object and on the processes to which it may have been subject in its life. Physicochemical transformations and structural modifications can be monitored by NMR methods, and this information can provide conservators with clues as to the most appropriate methods of preservation of a unique artifact. Importantly, the wide variety of NMR techniques available to analyze materials and the continual development of new techniques, instrumentation, and data-processing methods provide ever-improving means to address problems of identification and differentiation essential to answering questions in the field of cultural heritage. The development of solid-state NMR techniques and the general availability of these techniques has important applications of NMR spectroscopy in cultural-heritage science. A disadvantage of NMR spectroscopy has been its relative insensitivity, requiring relatively large samples for study. However, the use of cryoprobes and microprobes, the development of hyperpolarization techniques, ultrafast 1H-MAS and the advent of NMR spectrometers operating at GHz frequencies has continued to minimize the size and amount of sample needed to obtain useful information from NMR spectra. As these developments continue, it is expected that the kinds of microscopic samples that are the staple of conservation science will be analyzable with NMR techniques. The relatively new area of unilateral NMR sensors that allow “NMR analysis at a distance” has added to the utility of the technique in cultural heritage. Removal of samples from an object is often unnecessary with unilateral NMR analysis, and the portability inherent to the technique permits the study of objects like frescoes, which are not movable. Although high-resolution spectra are not obtainable with the unilateral technique, the applications are ever-growing. Continual development of the sensors and processing software, and a desire for portable, non-invasive measurements will certainly drive the technique beyond the applications described in this review. The development of commercial instrumentation that addresses nuclei other than 1H and 13C is another advance in NMR spectroscopy that directly affects cultural-heritage science. Many solids of interest to conservation scientists are inorganic, which are often devoid of common nuclei like 1H and 13C seen in organic materials. NMR spectroscopy of nuclei like Pb, Cd, Zn, O, and others can often provide information to answer questions about primarily inorganic objects. As one can glean from the examples in the review, NMR spectroscopy has already demonstrated its utility in a wide variety of studies in cultural-heritage science. The further exploitation of NMR techniques, as developments in NMR technology continue, will only expand these contributions to answer questions that currently seem unanswerable with the technique.

Acknowledgments The work in this article was supported, in part, by the USA National Science Foundation under grants DMR-1608594 and DMR-1608366 to The Metropolitan Museum of Art and the University of Delaware.

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9.25

Advances in the computation of nmr parameters for inorganic nuclides

Sean T. Holmesa,b, Fahri Alkanc, and Cecil Dybowskid, a Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, FL, United States; b National High Magnetic Field Laboratory, Tallahassee, FL, United States; c Department of Nanotechnology Engineering, Abdullah Gül University, Kayseri, Turkey; and d Department of Chemistry and Biochemistry, University of Delaware, Newark, DE, United States © 2023 Elsevier Ltd. All rights reserved.

9.25.1 9.25.2 9.25.3 9.25.4 9.25.4.1 9.25.4.2 9.25.4.3 9.25.4.4 9.25.4.5 9.25.4.6 9.25.4.7 9.25.5 Acknowledgments References

Introduction Modeling magnetic shielding tensors Calculating NMR parameters of solids Theoretical calculations applied to particular elements Fluorine Cadmium Tin Tellurium Mercury Lead Platinum Summary

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Abstract In this article, we discuss practical aspects of the computation of NMR parameters of inorganic nuclides, as well as insights afforded by such calculations into the characterization of molecular-level structure and dynamics and the validation of theoretical models. An emphasis is placed on calculation of the magnetic shielding tensors of solids using cluster-based models that account for intermolecular interactions. In particular, the use of valence modification of terminal atoms using bond valence theory (VMTA/BV), which reduces net charges on clusters through terminal pseudoatoms with nonstandard nuclear charges, is demonstrated to be a robust technique for calculations on nuclei in network solids. Clusterbased calculations, including those that employ the VMTA/BV method, afford a unique opportunity to calculate magnetic shielding tensors for nuclei in solids by using density functional theory approximations beyond the generalized gradient approximation and by incorporating relativistic effects at the spin-orbit level. These developments are spurred by use of the zeroth-order regular approximation (ZORA), which provides a robust method of accounting for relativistic effects (up to the spin-orbit level) experienced by valence electrons. Calculations of NMR parameters are discussed for fluorine, cadmium, tin, tellurium, mercury, lead, and platinum, all of which have seen significant advances in recent years. These examples highlight the importance of such factors as coordination geometry, oxidation state, relativistic effects, and density functional approximations on computed magnetic shielding tensors.

9.25.1

Introduction

Recent years have witnessed significant advances in the computation of NMR parameters of inorganic nuclides, which have opened large sections of the Periodic Table to study.1–5 These advances have been driven by a combination of theoretical advances (e.g., improved density functional approximations, basis sets, relativistic methods, etc.) and robust protocols for calculations applied to a large variety of systems. As computational and experimental NMR methods continue to advance, it is expected that calculations of NMR parameters will continue to play an essential role in the characterization of materials. In this article, we revisit some of the seminal theoretical work, significant recent developments, and applications of NMR calculations, with an emphasis on the calculation of magnetic shielding tensors in solids. Comparison of computed and experimental values, including the principal components of chemical shift tensors (which are most typically available from the analysis of powder samples), reveals that a fuller understanding of the impact of different computational approaches is often not apparent when considering the isotropic chemical shift alone. Additionally, the analysis of solids, particularly network solids, permits calculations of magnetic shielding tensors in systems with a richer variety of coordination geometries, coordination numbers, and oxidation states than is typically observed from studies on isolated small molecules. These observations afford deeper insights into the chemistry of materials, such as the influence of coordination geometry, oxidation state, and relativistic effects on magnetic shielding, as well as the interplay between these factors. Furthermore, the insights presented in calculations of magnetic shielding tensors in solids can be applied with greater confidence to further computational studies on isolated or solvated molecules.

Comprehensive Inorganic Chemistry III, Volume 9

https://doi.org/10.1016/B978-0-12-823144-9.00020-0

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Advances in the computation of nmr parameters for inorganic nuclides

One recent significant advance in the computation of NMR parameters has been the ability to calculate chemical shifts for systems containing heavy atoms accurately. NMR calculations for heavy 6th-period elements such as lead, mercury, and platinum, pose extra challenges for theoretical chemists, as compared to lighter elements like carbon or fluorine. Apart from the necessity of using a large number of basis functions to describe the larger number of electrons, accurate predictions of NMR parameters for these elements requires some level of relativistic treatment of the electronic structure. In fact, relativistic computational chemistry methods have often been benchmarked in terms of their accuracy in predicting NMR parameters of heavy atoms. When additional heavy atoms are present in a system, relativistic effects are often further modulated through the heavy-atom-on-heavy-atom (HAHA) mechanism. Large ranges of experimental isotropic chemical shifts (ca. 10,000 ppm) and chemical shift anisotropies (ca. 5000 ppm) are not uncommon for the NMR-active nuclei of such elements, a fact that provides an excellent opportunity for theoretical chemists to compare predictions with experimental results. In contrast, the importance of relativistic effects on the magnetic shielding of 5th-period elements is less firmly established, as many studies have presented conflicting reports on their influence. To date, the majority of these studies has focused on isolated molecules or molecules in solution; however, recent advances in computational protocols have extended studies to the characterization of solids.6–8 These studies on solids demonstrate that the inclusion of relativistic effects is often essential for systems containing cadmium, tin, and tellurium, while also suggesting explanations for conflicting results of early calculations. Additionally, relativistic effects sometimes influence the magnetic shielding of light atoms when additional heavy atoms are present in the system through the heavy-atom-on-light-atom (HALA) mechanism.9 Extensive overviews of the effects of relativistic interactions on NMR parameters exist.10–13 Aside from benchmarking, NMR calculations have accompanied experimental studies to correlate various molecular and structural properties with the observed NMR parameters of these challenging nuclei. In general, calculations of magnetic shielding tensors of heavy atoms are less common in the literature, as a theoretical framework for such computationsdwhich must incorporate both periodic boundary conditions and spin-orbit coupling explicitlydis not currently available. Therefore, calculations frequently employ a cluster methodology to mimic the solid-state environment around the NMR nucleus. Calculations on cluster models also afford opportunities to assess the impact of other aspects of electronic structure modeling that are difficult or impossible to implement efficiently in periodic-structure codes, including DFT approximations beyond the generalized gradient approximation (GGA). In this respect, the use of hybrid DFT functionals, which introduce an admixture of Hartree-Fock exchange (HFX), can substantially increase agreement with experimental values, although their use involves substantially increased computational costs, especially when combined with relativistic methods that include spin-orbit coupling. The benefits afforded by the use of hybrid functionals have been documented extensively for calculations of magnetic shielding tensors of nuclides commonly found in organic molecules,14–19 but these observations are only beginning to be generalized to inorganic nuclides across the Periodic Table. In this article, we highlight recent advances in the computation of NMR parameters of inorganic nuclides, with an emphasis on magnetic shielding tensors in solids. To this end, we begin with a short discussion on modeling the relationships between experimental and calculated NMR tensor parameters, and methods for quantifying the accuracy of such calculations. Next, we discuss computational protocols for modeling solid-state effects on NMR parameters, with an emphasis on robust cluster-based calculations and the performance of cluster models relative to periodic-structure calculations. Finally, we review the calculation of the magnetic shielding tensors of fluorine, cadmium, tin, tellurium, mercury, lead, and platinum, all of which have been the subjects of multiple recent investigations. These examples provide insights into various aspects of the computation of NMR parameters, including the modeling of solids with periodic-structure and cluster-based approaches, the importance of relativistic approximations, and the choice of DFT functional, as well as chemical insights such as the influences of oxidation number and coordination geometry on chemical shifts, for example.

9.25.2

Modeling magnetic shielding tensors

Before beginning a discussion of the calculation of magnetic shielding tensors of inorganic nuclides in solids, we provide the conventions used to define and quantify relationships between experimental chemical shift tensors and calculated magnetic shielding tensors. These conventions are used subsequently to assess cluster models for calculations on solids, as well as to explore the accuracies of computational methodologies for computing NMR parameters of inorganic nuclides. The relationship between the calculated principal components of magnetic shielding tensors (siiv,exp) and the experimental principal components of chemical shift tensors (diiv,calc) can be modeled using least-squares linear regression through the following expression: v;exp

sii

¼ Adv;calc þB ii

(1)

In this expression, the index v denotes the nuclear site (v ¼ 1, 2, ., N), the index N denotes the total number of nuclear sites, the index i denotes the principal component of the magnetic shielding (or chemical shift) tensor (i ¼ 1, 2, 3), A represents the slope of the correlation line, and B represents the interpolated shielding of the chemical shift reference. The reference for the elements discussed in this article are CFCl3 (l) for fluorine, 0.1 M Cd(ClO4)2 (aq.) for cadmium, Sn(CH3)4 (l) for tin, Te(CH3)2 (l) for tellurium, Hg(CH3)2 (l) for mercury, Pb(CH3)4 (l) for lead, and 1.0 M PtCl62 (aq.) for platinum. The strengths of the linear-regression models

Advances in the computation of nmr parameters for inorganic nuclides

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are quantified through coefficients of determination, R2. For comparison with experimental values, calculated magnetic shielding tensors can be converted to the chemical shift scale (diiv,calc) through the following expression: dv;calc ¼ ii

B  sv;calc ii j Aj

(2)

It is also common to convert to the chemical shift scale by assuming an ideal slope of A ¼  1.0. Agreement between the experimental and calculated principal components of the chemical shift tensor of nuclear site v is quantified through the residual: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 3   u1 X v;calc v;exp 2 (3) residual ¼ t dii  dii 3 i¼1 Similarly, the agreement between the experimental and calculated principal components of the chemical shift tensors for an ensemble of N nuclear sites is quantified through the rms error: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N X 3   u 1 X v;exp 2 rms error ¼ t dv;calc  dii (4) 3N v¼1 i¼1 ii The agreement between calculation and experiment may also be assessed by expressing experimental values on an absolute shielding scale.20–22 In such cases, the agreement between calculation and experiment is quantified by analogous expressions for the residual and rms error. Similarly, comparison can be made using the reduced chemical shift, which expresses experimental chemical shift principal components relative to the isotropic chemical shift, and calculated magnetic shielding principal components relative to the isotropic magnetic shielding (i.e., Ddii ¼ dii  diso ¼ siso  sii).

9.25.3

Calculating NMR parameters of solids

Calculations of NMR parameters in solids often require the inclusion of intermolecular effects to achieve reasonable agreement with experimental values.23 Perhaps the most popular approach in recent years for calculating NMR parameters such as magnetic shielding tensors in solids has been plane-wave DFT, with the gage-including-projector-augmented-wave (GIPAW) method of Pickard and Mauri.24 In this method, the wave function is expanded in a basis of plane waves, whereas core-valence interactions are described through pseudopotentials.25 Yates et al. have discussed the implementation of scalar-relativistic pseudopotentials in such calculations.26 Implementations of GIPAW using norm-conserving and ultrasoft pseudopotentials are available in such codes as CASTEP and QUANTUM ESPRESSO.27,28 Plane-wave DFT calculations have also been applied extensively for the calculation of EFG tensors, as highlighted by the work of Profeta et al.29,30 Although a general review of the applications of plane-wave DFT for the calculation of NMR parameters is outside the scope of this article, the reader is referred to the recent review by Bonhomme et al. for a more complete discussion.31 Despite the successes of periodic-structure methods such as GIPAW for the calculation of NMR parameters, these methods suffer from several factors that limit their general applicability to calculations for nuclei across the Periodic Table. One significant limitation is that hybrid density functionals (e.g., B3LYP, PBE0, etc.), which include an admixture of HFX, are difficult to implement in periodic-structure codes; as such, GIPAW calculations are often limited to pure DFT methods such as those that employ the GGA. Additionally, GIPAW lacks all-electron methods for describing relativistic effects, including spin-orbit coupling. Together, these limitations have led to a resurgence of cluster-based techniques for computing NMR parameters in solids. The construction of clusters that properly represent the local environment of an NMR-active nucleus is a significant challenge. These challenges differ depending on the nature of the crystal structure of the material, with different computational methods being necessary for molecular and network solids. For molecular solids, clusters can be constructed in which a central molecule containing the NMR-active nucleus is surrounded by shells of peripheral molecules. It is often possible to decrease the computational cost for such systems by employing a lower level treatment of the electronic structure for the peripheral atoms, including the use of smaller basis sets or the frozen-core approximation.32 The calculation of magnetic shielding tensors for molecular solids is strongly influenced by cluster size, which is readily demonstrated through the calculation of the mercury magnetic shielding tensors of Hg(SCN)2 and Hg2Cl2 using clusters of different sizes (Fig. 1A and B).32 The results demonstrate that the differences in the computed principal components range between 345 and 1594 ppm, depending on the cluster size (Table 1). On the other hand, the comparison of large clusters with extended clusters, only shows a deviation of less than 1%. These results indicate that calculated chemical-shift tensors show a strong convergence with increasing cluster size. The correlations between experimental and calculated values for small and large clusters (Fig. 1C and D) reveal that a reasonably quantitative agreement between theory and experiment can be obtained by employing large cluster models for the solid state. The simplest approach for constructing a cluster to represent the structure of a network solid is to build a cluster of atoms with an overall net charge. These clusters must be kept small because the net charge increases rapidly as the number of atoms in the cluster

840

Advances in the computation of nmr parameters for inorganic nuclides

(A)

Extended cluster

Large cluster

Small cluster (B)

(C)

(D)

12500

12000

Calculated Shielding (ppm)

Calculated Shielding (ppm)

13000

11000 10000 9000 8000 7000 –4500 –3500

–2500 –1500

–500

500

11500

10500

9500

8500

7500 –4500

Experimental Chemical Shift (ppm)

–3500

–2500

–1500

–500

500

Experimental Chemical Shift (ppm)

Fig. 1 Examples of different cluster models for (A) Hg(SCN)2 and (B) HgCl2, and the comparison between experimental principal components of mercury chemical shift tensors and calculated principal components of mercury magnetic shielding tensors for (C) a small cluster model and (D) large cluster model for mercury-containing solids. This figure is adapted from Alkan, F.; Dybowski, C. Calculation of Chemical-Shift Tensors of Heavy Nuclei: A DFT/ZORA Investigation of 199Hg Chemical-Shift Tensors in Solids, and the Effects of Cluster Size and Electronic-State Approximations. Phys. Chem. Chem. Phys. 2014, 16, 14298–14308, https://doi.org/10.1039/C4CP01682C. Copyright 2014, PCCP owner societies. Table 1

Comparison of calculated principal components of the mercury magnetic shielding tensor using various sizes of cluster models.a

Model clusters Hg(SCN)2 Small cluster Large cluster Extended cluster Hg2Cl2 Small cluster Hg(1) Small cluster Hg(2) Large cluster Hg(1) Large cluster Hg(2) Extended cluster Hg(1) Extended cluster Hg(2)

s11 (ppm)

s22 (ppm)

s33 (ppm)

siso (ppm)

U (ppm)

k

7505 7860 7869

8998 8554 8554

12,511 11,670 11,648

9671 9361 9357

5006 3810 3779

0.40 0.64 0.64

7683 7683 8058 8028 8089 8088

7683 7683 8058 8028 8090 8088

13,203 13,203 11,609 11,609 11,531 11,530

9523 9523 9242 9222 9237 9235

5520 5520 3551 3581 3442 3442

1.00 1.00 1.00 1.00 1.00 1.00

The isotropic magnetic shielding, span, and skew are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and k ¼  3(s22  siso)/U, respectively. Adapted from Alkan, F.; Dybowski, C. Calculation of Chemical-Shift Tensors of Heavy Nuclei: A DFT/ZORA Investigation of 199Hg Chemical-Shift Tensors in Solids, and the Effects of Cluster Size and Electronic-State Approximations. Phys. Chem. Chem. Phys. 2014, 16, 14298–14308. a

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increases, which often has the practical effect of preventing self-consistent field (SCF) convergence. This small-cluster approach has been used to calculate the fluorine magnetic shielding tensors of a number of systems.33–37 Several approaches have been proposed to deal with the problem of SCF convergence resulting from large net charges on clusters. One approach is to saturate the dangling bonds on the terminal atoms with additional hydrogen atoms (denoted hydrogen addition, or HA). For example, Tossell et al. have used the HA approach to calculate nitrogen magnetic shielding in Si3N4, C3N4, P3N5, and h-BN,38,39 as well as the sodium magnetic shielding of silicates and aluminosilicates.40 Valerio et al. and Brouwer et al. calculated silicon and/or aluminum magnetic shielding tensors in several zeolites,41–44 whereas Koller et al. calculated sodium magnetic shielding and electric field gradients (EFGs),45 and Holmes et al. calculated calcium magnetic shielding and EFG tensors in calcium complexes.46,47 The HA approach has been applied to the calculation of the magnetic shielding tensors of heavy atoms such as mercury and lead.32,48,49 However, there are problems with the HA method, including ambiguities regarding the proper number and placement of terminal hydrogen atoms, and frequent difficulties associated with SCF convergence. Another approach to deal with the problem of excess charge on a cluster is the embedded-ion method (EIM) or related formalisms. In the EIM method, clusters are embedded in an array of classical point charges placed at the crystallographic origins of the absent atoms. The charges are generally produced through a self-consistent algorithm. The EIM approach was used by Stueber et al. to calculate the carbon magnetic shielding tensors of several ionic compounds.50 Similar techniques were used by Weber and Schmedt auf der Günne to calculate the fluorine isotropic shielding in NaF, as well as the phosphorus magnetic shielding tensors of four magnesium phosphates51 and related systems.52 Bjornsson and Bühl calculated magnetic shielding and EFG tensors of vanadium and ruthenium complexes.53 Dittmer et al. have demonstrated that EIM methods can be extended to double-hybrid DFT and post-Hartree-Fock methods.54 Nonetheless, calculations using the EIM termination scheme can still suffer from difficult SCF convergence, arising from the interface between the quantum mechanical and electrostatic regions and with charge on the quantum region of the cluster. The valence modification of terminal atoms using bond valence theory (VMTA/BV) approach was introduced by Alkan and Dybowski as a robust method for calculating the magnetic shielding tenors of atoms in network solids.55 In this approximation, pseudoatoms with altered nuclear charges (Zmod) replace the terminal atoms of the cluster, with the effect of reducing the overall charge of the cluster, and allowing meaningful SCF convergence. The value of Zmod is given by the following: Zmod ¼ Znuc þ DS

(5)

Here, Znuc is the unaltered formal charge of the nuclei of the terminal atoms of the cluster, and DS represents missing bond strength of the terminal atoms in the cluster, as compared to the same site in the actual crystal structure. The value of DS for a terminal atom in a cluster is given by the following: X R  Rk  (6) DS ¼ V  exp k0 bk k In this equation, V is the unaltered valence of the terminal atom. The exponential term in this expression is the bond-valence relation introduced by Brown, in which Rk is the bond length between two atoms in a pair containing the terminal atom, and Rk and bk are the bond-valence parameters for the two atoms.56 The utility of the VMTA/BV method is illustrated through calculation of the cadmium magnetic shielding tensor using the 3rdcoordination-shell cluster of CdF2 (Fig. 2). For clusters centered on cations such as Cd2þ, clusters must be expanded up to oddnumbered coordination shells (i.e., up to the 1st, 3rd-, or 5th-coordination shells) such that the terminal atoms of the cluster are all anions (i.e., fluorine atoms for the cluster of CdF2) for which the values of Zmod are more positive than the values of Znuc. The 3rd-coordination-shell cluster of CdF2 consists of 13 Cd2þ ions and 56 F ions; with standard nuclear charges, this results in a net charge of  30 a.u., which makes SCF convergence impossible. Using the VMTA/BV approach, the charges on the terminal fluorine atoms are modified to Zmod ¼ 9.75 and 9.50 a.u., depending on the amount of missing coordination for the terminal fluorine; use of the VMTA/BV method reduces the total charge on the cluster to 0.00 a.u., and allows the SCF cycle to converge rapidly for this cluster, resulting in a meaningful calculation of the cadmium magnetic shielding tensor. The lead magnetic shielding tensors of a-PbO and b-PbO have been calculated using several termination protocols, including HA and VMTA/BV, as well as the VMTA approach, wherein the charges of the terminal oxygen atoms are increased by þ 1 a.u. (Table 2).55 For both materials, the values of the principal components of the lead magnetic shielding tensors depend on such factors as the size of the cluster and the method of termination. There are marked differences between the termination schemes for calculations on 1st-coordination-shell clusters, which can be as large as 2000 ppm for certain principal values. In contrast, calculations on 3rd- and 5th-coordination-shell clusters differ less markedly between termination schemes. For 5th-coordination-shell clusters, the agreement between the HA, VMTA, and VMTA/BV termination approaches is within 50 ppm, demonstrating that for the lead atoms in these materials, the three methods of termination each work well with sufficiently large clusters. Calculations on large clusters generally result in better agreement with experimental values, as illustrated by the smaller values of the residuals. These errors are in the range of 473–1069 ppm for 1st-coordination-shell clusters, whereas the residuals fall into the ranges of 137– 367 ppm and 144–158 ppm for 3rd- and 5th-cordination-shell clusters, respectively. The local symmetry of the electronic structure around an NMR-active nucleus influences the principal values of the NMR interaction tensors. These effects can be demonstrated in cluster-based calculations of the lead magnetic shielding tensor of a-PbO by perturbing the local point group symmetry of the lead atom by including additional atoms (up to the 7th-coordination shell) along the x-axis, as illustrated by the perturbed 5th-coordination-shell cluster in Fig. 3.55 The single crystallographically-distinct lead atom in a-PbO sits at a site of C4v local point group symmetry and features a chemical shift skew of k ¼ 1.00. There are large differences in the calculated lead magnetic shielding tensors between clusters in which the

842

Advances in the computation of nmr parameters for inorganic nuclides

Pseudofluorine 1 Zmod = 9.75 a.u

(A)

(B) 1.E+03 1.E+02 1.E+01

SCF Error

1.E+00

Standard charges VMTA/BV charges

1.E-01 1.E-02 1.E-03 1.E-04

Convergence threshold

1.E-05 1.E-06

Pseudofluorine 2 Zmod = 9.50 a.u

0

10

20

30

40

50

60

SCF Cycle

Fig. 2 (A) The 3rd-coordination-shell cluster of CdF2 with pseudofluorine atoms and VMTA/BV values of Zmod. (B) Illustration of the SCF convergence for the cluster models of CdF2 in which the cluster features standard nuclear charges on the terminal atoms, or charges that are modified according the VMTA/BV approach.

proper local symmetry is fully realized, and those that are perturbed from their correct symmetries (Table 3). These effects are most noticeable in 1st-coordination-shell clusters, for which the perturbed cluster alters the skew to k ¼ 0.72, and much less noticeable in 5th-coordination-shell clusters, where the skew retains the correct value of k ¼ 1.00. This result, along with results regarding the importance of cluster size, demonstrate that the lead magnetic shielding tensor of a-PbO is fully converged in calculations featuring Table 2

a-PbO Exp. 1-HA 1-VMTA 1-VMTA/BV 3-HA 3-VMTA 3-VMTA/BV 5-HA 5-VMTA 5-VMTA/BV b-PbO Exp. 1-HA 1-VMTA 1-VMTA/BV 3-HA 3-VMTA 3-VMTA/BV 5-HA 5-VMTA 5-VMTA/BV

Principal components of lead magnetic shielding tensors and reduced chemical shifts for various cluster models of a-PbO and b-PbO.a,b s11 (ppm)

s22 (ppm)

s33 (ppm)

siso (ppm)

Dd11 (ppm)

Dd22 (ppm)

Dd33 (ppm)

U (ppm)

Residual (ppm)

– 9400 7385 9451 6204 5861 5914 5935 5936 5914

– 9400 7385 9451 6204 5861 5889 5935 5936 5915

– 10,645 9681 11,269 8918 8870 8827 8922 8906 8900

– 9815 8151 10,057 7109 6864 6868 6931 6926 6910

1100 415 765 606 905 1003 981 995 990 996

1100 415 765 606 905 1003 979 995 990 994

2200 830 1531 1212 1809 2006 1960 1991 1980 1990

3300 1244 2296 1818 2714 3010 2940 2986 2970 2986

– 969 473 699 276 137 170 148 156 148

– 9125 7109 8630 5956 5747 5655 6136 6098 6100

– 9533 7525 9283 6406 6228 6197 6150 6172 6150

– 10,871 9537 11,516 9270 9273 9352 9630 9593 9581

– 9843 8057 9810 7211 7083 7068 7305 7288 7277

1293 718 948 1180 1255 1335 1413 1169 1190 1177

1233 310 532 527 805 855 871 1155 1115 1127

2527 1028 1480 1706 2059 2190 2284 2324 2305 2304

3820 1746 2428 2886 3314 3525 3697 3493 3495 3481

– 1069 754 629 267 294 261 144 157 158

The isotropic magnetic shielding, span, and reduced chemical shift are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and Ddii ¼ dii  diso ¼ siso  sii, respectively. b The residual is defined in Eq. (3). Adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026. a

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Fig. 3 Perturbed 5th-coordination-shell cluster of a-PbO. The added coordination in the x-direction is shown in red circles, whereas the central Pb atom is highlighted. This figure is adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026, https://doi.org/10. 1039/C5CP03348A. Copyright 2015, PCCP owner societies. Table 3

1-symb 1-pertc Difference 3-symb 3-pertc Difference 5-symb 5-pertc Difference

Principal components of the lead magnetic shielding tensors of symmetric and perturbed 1st-, 3rd-, and 5th-coordination-shell clusters of a-PbO. s11 (ppm)

s22 (ppm)

s33 (ppm)

sisoa a (ppm)

U a (ppm)

ka

9451 8183 1268 5887 5734 153 5914 5906 8

9451 8578 873 5889 5875 14 5915 5909 6

11,269 10,964 305 8827 8737 90 8900 8888 2

10,057 9241 816 6868 6782 86 6910 6901 9

1818 2781  963 2940 3004  64 2986 2982 4

1.00 0.72 0.28 1.00 0.91 0.09 1.00 1.00 0.00

The isotropic magnetic shielding, span, and skew are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and k ¼  3(s22  siso)/U, respectively. b Symmetric cluster. c Perturbed cluster. Adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026. a

the 5th-coordination-shell cluster; perturbations to local structure that occur at greater distances have little impact on the calculated magnetic shielding tensors. The VMTA/BV approach provides values of Zmod ¼ 9.5 and 9.0 for the two types of terminal atoms in cluster models of a-PbO.55 Modification of the values of Zmod for these two sites results in an overall net charge on the cluster (Table 4). The values of the isotropic magnetic shielding and span are linearly correlated with the net charge on the cluster (Fig. 4). For small 1stcoordination-shell clusters, the variation in the magnetic shielding tensor is large; for example, varying Zmod by 0.4 a.u. alters the isotropic magnetic shielding by ca. 2000 ppm and the span by ca. 1000 ppm. These effects are much smaller for large 5thcoordination-shell clusters, where varying the value of Zmod by the same amount alters the isotropic magnetic shielding by 55 ppm and the span by 157 ppm. The modification of the values of Zmod on the terminal oxygen atoms from ideal conditions is partially compensated through delocalization of charge onto the other atoms in the cluster.55 For the 5th-coordination-shell clusters in Table 4, there is a positive correlation between the total charge on the cluster and the Mulliken charge on the central lead atom. This observation accounts for the change in the magnetic shielding tensors as the values of Zmod are altered from the ideal values. The values of s11 and s22 are

844 Table 4

Advances in the computation of nmr parameters for inorganic nuclides Dependence of the calculated lead magnetic shielding tensor of a-PbO on the total charge on a cluster extended to the 5th-coordination shell.

Zmod on O1 and O2

Total charge on cluster

Mulliken charge on Pb

s11 (ppm)

s22 (ppm)

s33 (ppm)

siso (ppm)

U (ppm)

9.3, 8.8 9.4, 8.9 9.5, 9.0 9.6, 9.1 9.7, 9.2

4.0 2.0 0.0 2.0 4.0

1.344 1.364 1.381 1.395 1.408

6005 5957 5914 5874 5839

6006 5959 5915 5876 5841

8959 8928 8900 8873 8848

6990 6948 6910 6874 6843

2954 2971 2986 2999 3009

Adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026.

Fig. 4 The effect of Zmod on (A) isotropic shielding and (B) span for models that extend through the 1st- (blue), 3rd- (red), and 5th- (black) coordination shell for a-PbO. DZmod is the deviation of Zmod from the optimal values determined by the VMTA/BV method. This figure is adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026, https://doi.org/10.1039/C5CP03348A. Copyright 2015, PCCP owner societies.

more strongly affected by the choice of Zmod, suggesting that the delocalization of charge and concomitant electron density most influences orbitals oriented within the 1–2 plane, rather than orbitals oriented perpendicular to this plane. A recent study compared the calculation of silicon and phosphorus magnetic shielding tensors as computed using the VMTA/BV and GIPAW approaches.57 Representative clusters used in the study are illustrated in Fig. 5. This study implemented locally-dense basis sets in the cluster-based calculations of silicon and phosphorus magnetic shielding tensors to decrease the overall cost of the

Mg2SiO4

Mg3(PO4)2

Fig. 5 Illustration of 3rd-coordination-shell clusters of MgSiO4 and Mg3(PO4)2. The TZ2P region is shown in ball-and-stick model and the TZP region is shown as a wireframe model. This figure is adapted from Holmes, S. T.; Alkan, F.; Iuliucci, R. J.; Mueller, K. T.; Dybowski, C. Analysis of the Bond-Valence Method for Calculating 29Si and 31P Magnetic Shielding in Covalent Network Solids. J. Comput. Chem. 2016, 37, 1704–1710, https://doi.org/10.1002/jcc.24389. Copyright 2016, Wiley Periodicals, Inc.

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calculation; in particular, the central XO4 (X ¼ Si, P) structural units were given the larger TZ2P basis set, whereas all additional atoms were given the smaller TZP basis set. Calculations of silicon and phosphorus magnetic shielding tensors using 3rd- and 5th-coordination-shell clusters are generally in agreement, with principal components differing by only 1–2 ppm in most cases.57 This observation demonstrates that 3rdcoordination shell clusters are sufficiently large to model the magnetic shielding tensors (Table 5). In contrast, differences in the principal components between 1st- and 3rd-coordination-shell clusters are as large as ca. 50 ppm. The lowest residuals between calculation and experiment are generally observed for calculations expanded to the 3rd- and 5th-coordination shell. The only exception to this trend is the low residual observed for the 1st-coordination-shell cluster calculation for Na2SiO3; this is likely the result of error cancelation, as indicated by a calculated span that deviates significantly from the experimental span, as well as from spans calculated using larger clusters. Silicon and phosphorus magnetic shielding tensors were calculated for an ensemble of materials using the VMTA/BV and GIPAW approaches (Fig. 6).57 The magnetic shielding tensors are more strongly shielded when calculated using the VMTA/BV approach, rather than the GIPAW approach. The mean absolute deviations between the two protocols are 21.4 and 38.0 ppm, for silicon and phosphorus, respectively. For silicon, the residual between calculated and experimental magnetic shielding tensors is 46.4 ppm for the GIPAW approach and 25.3 ppm for the VMTA/BV approach. For phosphorus, the residuals are 49.9 ppm for the GIPAW approach and 13.3 ppm for the VMTA/BV approach. However, use of the VMTA/BV approach provides a method of calculating magnetic shielding tensors using a hybrid functional. When a hybrid functional is employed, residuals fall to only 11.1 ppm and 6.3 ppm for silicon and phosphorus, respectively. The VMTA/BV approach can also be applied to the calculation of the magnetic shielding tensors of anionic sites such as fluorine, as indicated by clusters representing NaF and CaF2 (Fig. 7).58 When the central atom of the cluster is anionic, clusters are expanded to include even-numbered coordination shells (i.e., up to the 2nd- or 4th-coordination shells) so that the terminal atoms on the clusters are always anions that can be treated with the VMTA/BV approach in a manner analogous to those in which the central atom is cationic (Vide supra). Calculated fluorine magnetic shielding tensors are presented in Table 6 for 2nd- and 4thcoordination-shell clusters of MgF2, AlF3, and ZnF2. There are modest differences between the principal components of the fluorine magnetic shielding tensors determined for the two sizes of clusters. Additionally, the calculated isotropic fluorine magnetic shielding for the 4th-coordination-shell clusters is in better agreement with experiment, indicating that larger clusters are necessary to model solid-state effects fully.

9.25.4

Theoretical calculations applied to particular elements

9.25.4.1

Fluorine

DFT calculations of fluorine magnetic shielding tensors often lead to large deviations from experiment and the results of advanced ab initio calculations.59 Several studies have reported that the slope describing the linear relationship between calculated magnetic Table 5

Principal components of experimental and computed magnetic-shielding tensors, isotropic magnetic shielding, and span for 1st-, 3rd-, and 5th-coordination-shell clusters for SiO2, Na2SiO3, Mg2P4O12 (P1), and Mg2(PO4)2 determined with VMTA/BV theory.a-c

Material SiO2 Experimental 1st-coordination-shell cluster 3rd-coordination-shell cluster 5th-coordination-shell cluster Na2SiO3 Experimental 1st-coordination-shell cluster 3rd-coordination-shell cluster 5th-coordination-shell cluster Mg2P4O12 (P1) Experimental 1st-coordination-shell cluster 3rd-coordination-shell cluster 5th-coordination-shell cluster Mg3(PO4)2 Experimental 1st-coordination-shell cluster 3rd-coordination-shell cluster 5th-coordination-shell cluster a

s11 (ppm)

s22 (ppm)

s33 (ppm)

siso (ppm)

U (ppm)

k

Residual (ppm)

471.1 440.7 447 447.5

475.5 441.5 450.3 449.9

477.6 442.5 456.4 459.2

474.7 441.6 451.2 452.2

6.5 1.8 9.4 11.7

0.37 0.17 0.29 0.59

– 33.2 23.6 22.7

388.2 401.4 357.9 363.9

429.4 432.8 395.9 398.1

519.1 483.8 499 495

445.6 439.3 417.6 419

130.9 82.4 141.1 131.2

0.37 0.24 0.46 0.48

– 21.8 28.5 26.8

272.5 240.8 262.6 258.7

329.4 280.6 317.3 316.8

487 403.6 479.4 489.9

363 303.8 353.1 355.1

214.5 162.9 216.8 231.2

0.47 0.43 0.50 0.50

– 58.7 10 10.9

315.7 293.7 303.4 305.4

325.7 303.7 317.5 313.5

344.2 327.1 331.3 336

328.5 308.2 317.4 318.3

28.5 33.4 27.9 30.6

0.29 0.40 0.01 0.47

– 20.5 11.3 10.4

Silicon and phosphorus magnetic shielding tensors were calculated using the PBE functional. The isotropic magnetic shielding, span, and skew are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and k ¼  3(s22  siso)/U, respectively. c Experimental chemical shifts were converted to the shielding scale using the values for the shielding of the reference systems (see refs. 21 and 22). Adapted from Holmes, S. T.; Alkan, F.; Iuliucci, R. J.; Mueller, K. T.; Dybowski, C. Analysis of the Bond-Valence Method for Calculating 29Si and 31P Magnetic Shielding in Covalent Network Solids. J. Comput. Chem. 2016, 37, 1704–1710. b

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Fig. 6 Plots illustrating the relationships between calculated and experimental principal components of magnetic shielding tensors. (A) Siliconcontaining materials; (B) phosphorus-containing materials. Values obtained using the GIPAW approach are shown in red, and values obtained using the cluster-based VMTA/BV approach are shown in blue. The best-fit lines are shown in black. This figure is adapted from Holmes, S. T.; Alkan, F.; Iuliucci, R. J.; Mueller, K. T.; Dybowski, C. Analysis of the Bond-Valence Method for Calculating 29Si and 31P Magnetic Shielding in Covalent Network Solids. J. Comput. Chem. 2016, 37, 1704–1710, https://doi.org/10.1002/jcc.24389. Copyright 2016, Wiley Periodicals, Inc.

Fig. 7 2nd-coordination-shell clusters for (A) NaF and (B) CaF2. Terminal atoms treated with VMTA/BV model are indicated by a yellow halo around the atom. This figure is reproduced from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19 F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752, https://doi.org/10.1021/acs.jctc.7b00555. Copyright 2017, American Chemical Society. Table 6

Comparison of calculated principal components of fluorine magnetic-shielding tensors and isotropic magnetic shielding using 2ndcoordination-shell and 4th-coordination-shell clusters for MgF2, AlF3, and ZnF2.a-c

Material MgF2 Experimental 2nd-coordination shell cluster 4th-coordination shell cluster AlF3 Experimental 2nd-coordination shell cluster 4th-coordination shell cluster ZnF2 Experimental 2nd-coordination shell cluster 4th-coordination shell cluster a

s11 (ppm)

s22 (ppm)

s33 (ppm)

siso (ppm)

U (ppm)

k

– 382 369

– 408 393

– 429 410

382 406 391

– 47 41

– 0.13 0.15

– 337 338

– 348 340

– 425 409

362 370 362

– 88 71

– 0.75 0.93

– 398 390

– 428 407

– 445 429

391 424 409

– 47 39

– 0.26 0.15

Fluorine magnetic shielding tensors were calculated using the PBE0 functional with a 50% HFX admixture. The isotropic magnetic shielding, span, and skew are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and k ¼  3(s22  siso)/U, respectively. c Experimental chemical shifts were converted to the shielding scale using the values for the shielding of the reference systems (see ref. 20). Adapted from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752. b

Advances in the computation of nmr parameters for inorganic nuclides

847

shielding and experimental chemical shift deviates substantially from the ideal value of A ¼  1.0 by as much as ca. 40%.15,34–36,60– 63 The first example of a DFT calculation of fluorine magnetic shielding was provided by Schreckenbach and Ziegler for the F2 molecule; this study reports that standard DFT approximations underestimate the energy of the HOMO-LUMO (p / s*) transition, which results in a large overestimation of the paramagnetic contribution to the magnetic shielding.64 Fukaya and Ono report that the magnitudes of these errors depend on the types of atoms bonded to fluorine, such that predictions of chemical shifts for sulfur-, oxygen-, and nitrogen-containing molecules are generally less accurate than those of fluorocarbons, for example.65 Both periodic-structure and cluster-based models have been employed successfully to calculate fluorine magnetic shielding tensors in solids. Studies using the periodic-structure method have focused primarily on NMR crystallography.60,66–77 Studies involving cluster-based models have explored the proper construction of clusters, the role of different types of DFT functionals basis sets, and relativistic effects.33–35,37,58,78,79 Several studies have used periodic-structure calculations to explore the origin of fluorine magnetic shielding, as well as to determine computational protocols that result in accurate predictions of chemical shifts. Sadoc et al. explored the implementation of empirical corrections to GIPAW calculations of the fluorine isotropic magnetic shielding of metal fluorides.61 In their study, the local potentials of unoccupied calcium 3d, scandium 3d, or lanthanum 4f ultrasoft pseudopotentials were artificially shifted to higher energies, which decreases the covalent character of the metal-fluorine bond by reducing the interaction between the unoccupied metal d or f states and occupied fluorine p states (Fig. 8). Laskowski and Blaha applied the periodic augmented-plane-waveplus-local-orbital (APW þ lo) technique to study the relationships between magnetic shielding and electronic structure in MF (M ¼ Li, Na, K, Rb, Cs) systems.62 They concluded that the variation of fluorine isotropic magnetic shielding in these systems is related to (i) the interaction between fluorine valence p states and metal semi-core p states, as well as the hybridization of these states, and (ii) the position of the unoccupied metal d states. A study by Laskowski et al. explored the use of the GGA þ U scheme to shift the unoccupied metal d states of alkali and alkaline-earth metal fluorides; although this method has the potential to bring calculated shielding into agreement with experiment, separate adjustment of the value of U is required for every system.63 The authors also explored the use of a hybrid functional to calculate the fluorine shielding of the same systems; in particular, they found that the best results for these systems are found when using the PBE0 functional with a smaller HFX admixture than. Alkan et al. assessed the calculation of fluorine magnetic shielding tensors in organic and inorganic materials using periodicstructure and cluster-based calculations.58 The analysis was applied to 12 fluorine sites in organic systems (CFCl3 and 11 aromatic systems) and 12 metal fluorides (i.e., LiF, NaF, CaF2, ZnF2, RbF, SrF2, CdF2, CsF, BaF2, LaF3, HgF2, and PbF2). The fluorine magnetic

(A)

(B)

50

LaF3

0

–100 CaF2 All compounds without CaF2 ScF3 and LaF3

–150

Shift 3d Ca / eV

–250

Linear regression for all compounds GISO = -0.70(4) VISO + 57(8) ; R2 = 0.96 0

50

100

CaF2

2

200 250 150 VISO Calculated (ppm)

4

300

350

400

200

250

300

350

150

200

250

100

150

200

ScF3

2

0 50 (D) 6

GISO = -0.80(3) VISO + 89(9) ; R2 = 0.98 –200

4

0 150 (C) 6

ScF3

–50

Shift 3d Ca / eV

VISO Experimental (ppm)

Shift 3d Ca / eV

6

4

100

LaF3

2 0

0

50

VISO Calculated (ppm)

Fig. 8 (A) Experimental isotropic fluorine chemical shifts versus calculated isotropic magnetic shieldings. The solid line represents the linear regression when considering all compounds and the dashed line represents the linear regression when considering YF3 and alkali and alkaline earth compounds without CaF2. The arrows represent the change in siso when applying a shift on the 3d orbitals of Ca and Sc and on the 4f orbitals of La. The panels on the right side report the siso evolution with the applied shifts on the 3d orbitals of Ca (B) and Sc (C) and on the 4f orbitals of La (D). This figure is reproduced from Sadoc, A.; Body, M.; Legein, C.; Biswal, M.; Fayon, F.; Rocquefelte, X.; Boucher, F. NMR Parameters in Alkali, Alkaline Earth and Rare Earth Fluorides From First Principle Calculations. Phys. Chem. Chem. Phys. 2011, 13, 18539–18550, https://doi.org/10.1039/ C1CP21253B. Copyright 2011, PCCP owner societies.

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shielding tensors were calculated using the GIPAW method, as well as with a cluster-based approach using various combinations of functionals, basis sets, and relativistic corrections (Table 7). For the fluorocarbons, the best agreement between calculation and experimental 19F chemical shift tensors is observed for cluster-based calculations using the hybrid PBE0 functional with a 50% HFX admixture (i.e., PBE0 (50%)), which outperforms GIPAW calculations and cluster-based calculations using GGA functionals;58 these calculations result in the linear-regression parameter A ¼  1.00, indicating that the systematic errors reported in many previous studies are not present. In contrast, calculations using GGA functionals result in much poorer agreement with experiment and very little variation between different classes of triple-zeta basis sets (i.e., TZ2P, cc-PVTZ, and pcSseg-3). For each material, the 19F nucleus becomes more shielded as the HFX admixture in the hybrid functional is increased; this is likely a signal of the increased HOMO-LUMO gap that results in the hybrid calculations, which reduces the magnitude of the negative paramagnetic contribution to the shielding. Additionally, the span of the fluorine magnetic shielding tensors varies with the HFX admixture and the hybridization of the directly-bonded carbon atom; for the sp2-hybridized aromatic systems, the span decreases with increasing proportion of HFX, whereas for the sp3-hybridized CFCl3, the span increases. For inorganic solids, the best agreement is also obtained with cluster-based calculations using a the PBE0 (50%) functional.58 These result in linear-regression parameters of A ¼  1.06 and B ¼ 204 ppm, whereas comparable calculations using the PBE functional result in values of A ¼  1.38 and B ¼ 86 ppm. The use of hybrid functionals results in higher predicted values of the fluorine shielding in every case; however, the size of this change (relative to the GGA functional PBE) is strongly system-dependent, with larger effects observed for fluorine atoms bonded to metal sites with higher atomic numbers. For example, the difference between the calculated PBE and PBE0 (50%) fluorine shielding for MgF2 is 16 ppm, whereas differences between 112 and 125 ppm are observed for the three fluorine sites in LaF3. The differences in predicted shielding between these functionals can be rationalized by considering variations in the calculated HOMO-LUMO gap, and the natures of these orbitals. For MgF2, the HOMO-LUMO gap increases in calculations using the PBE functional as compared to the PBE0 (50%) functional by 6.3 eV. For LaF3, that increase is between 8.1 and 8.6 eV. However, one calculates a large difference in shielding of 72 ppm for CaF2 with these two methods, even though the increase in the HOMO-LUMO gap similar to that observed for MgF2. This observation suggests that the types of orbitals also affects the results of the calculations. For CaF2, the large change in fluorine shielding (relative to MgF2) is explained by the observation that the LUMO level originates from Ca atomic d-states for PBE calculations, but from Ca s-states for PBE0 (50%) calculations. Similar effects are observed for other Group II metal fluorides, except for MgF2, which does not have access to low-lying metal d-states. When fluorine atoms are bonded to heavy atoms, relativistic effects can influence the fluorine magnetic shielding tensors through the HALA mechanism.9 To explore this effect further, Alkan et al. calculated fluorine isotropic magnetic shielding for the metal fluorides using non-relativistic DFT calculations and relativistic DFT calculations employing the ZORA Hamiltonian as expanded to include up to scalar or spin-orbit terms (Fig. 9).58 For non-relativistic calculations, there are large systematic deviations from experimental chemical shifts that are reflected by the linear-regression parameter A ¼  1.31 and B ¼ 162 ppm. In contrast, the ZORA/SC and SO calculations that include relativistic effects result in nearly identical linear-regression parameters, with scalar calculations yielding values of A ¼  1.06 and B ¼ 204 ppm, and SO calculations yielding values of A ¼  1.06 and B ¼ 205 ppm.

Table 7

Statistical data for the relationships between calculated principal components of fluorine magnetic shielding tensors and principal components of fluorine chemical shift tensors for 12 fluorocarbon sites and 12 metal fluorides.a

Methodology Fluorocarbons Cluster Cluster Cluster Cluster Cluster GIPAW Metal fluorides Cluster Cluster Cluster GIPAW a

Functional

Basis set

A

B (ppm)

R2

PBE PBE0 (25%) PBE0 (50%) PW91 PW91 PW91

TZ2P TZ2P TZ2P cc-pVTZ pcSseg-3 –

1.15 1.07 1.00 1.16 1.17 1.20

129 161 189 132 127 115

0.984 0.988 0.988 0.986 0.986 0.987

PBE PBE0 (25%) PBE0 (50%) PBE

TZ2P TZ2P TZ2P –

1.39 1.18 1.06 1.38

106 164 204 86

0.967 0.985 0.985 0.965

The definitions of the linear-regression parameters are given in Eq. (1). Adapted from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752.

Advances in the computation of nmr parameters for inorganic nuclides

(B)

(A)

350

250

150

450 Calculated Shielding (ppm)

Calculated Shielding (ppm)

Calculated Shielding (ppm)

(C)

450

450

350

250

150

50 -300 -200 -100 0 100 Experimental Shift (ppm)

50 100 -300 -200 -100 0 Experimental Shift (ppm)

849

350

250

150

50 -300 -200 -100 0 100 Experimental Shift (ppm)

Fig. 9 Effects of level of inclusion of relativity on the correlation between the calculated fluorine isotropic magnetic shielding and experimental isotropic chemical shift. Calculated values were obtained at the (A) non-relativistic, (B) ZORA/SC, and (C) ZORA/SO levels. All calculations used the PBE0 functional with a 50% admixture of HFX. This figure is reproduced from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752, https://doi.org/10.1021/acs.jctc.7b00555. Copyright 2017, American Chemical Society.

The substantial reduction of the error in the value of A for the relativistic calculations reveals that inclusion of such effects is necessary to achieve good agreement with experimental chemical shifts for metal fluorides. Relativistic contributions to fluorine isotropic magnetic shieldings are dominated by scalar effects (Table 8).58 For systems that contain only light atoms (i.e., LiF, NaF, CaF2, and ZnF2), relativistic contributions (DsSC þ SO) are small, whereas for systems containing heavy atoms (i.e., CsF, BaF2, LaF3, HgF2, and PbF2), these contributions can be as large as ca. 77 ppm. For the intermediate systems RbF, SrF2 and CdF2, relativistic effects are noticeable, but still less than 10 ppm in all cases. The inclusion of relativistic effects results in additional shielding of the fluorine nucleus for all systems except the Group XII metal fluorides (Vide infra). Table 8

Calculated fluorine isotropic magnetic shielding computed at the non-relativistic level, as well as the ZORA/SC and SO corrections to the shielding.a-c

System

siso (non-relativistic) (ppm)

DsSC (ppm)

DsSC þ SO (ppm)

F LiF NaF CaF2 ZnF2 RbF SrF2 CdF2 CsF BaF2 LaF3 (F1) LaF3 (F2) LaF3 (F3) HgF2 PbF2 (F1) PbF2 (F2)

481 411 432 310 424 297 294 421 219 214 193 118 138 443 136 176

0 0 0 1 3 7 7 6 22 26 34 47 46 23 71 71

3b 2 3 4 (3) 2 (1) 8 (1) 8 (1) 6 (0) 20 ( 2) 25 ( 1) 36 (2) 46 ( 1) 44 ( 2) 30 (7) 77 (6) 77 (5)

a

All calculations were performed using the PBE0 functional with a 50% admixture of HFX. The spin-orbit-only contributions to fluorine magnetic shielding are shown in parentheses. c In principle, the spin-orbit contributions should vanish due to the spherical symmetry of the F anion. For this reason, the calculated spin-orbit contribution to the fluoride ion should be treated as the numerical uncertainty for the discussion on spin-orbit contributions to the fluorine magnetic shielding in the other systems. Adapted from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752. b

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Advances in the computation of nmr parameters for inorganic nuclides

The effects of SO coupling are small, with the largest contributions of ca. 5–7 ppm observed for systems containing heavy atoms, such as HgF2 and PbF2. In general, the SO contribution to magnetic shielding tensors through the HALA mechanism is related to the s-character of the heavy atom-light atom bond; therefore, the small SO effects observed for the metal fluorides likely reflect the limited s-character of the metal-fluorine bond. Fig. 10 shows the relationship between the relativistic contribution to the fluorine isotropic magnetic shielding and the atomic number of the cation to which the fluorine atom is bonded.58 The absolute values of the relativistic contributions tend to increase with increasing atomic number. However, relativistic contributions to the Group XII metal fluorides MF2 (M ¼ Zn, Cd, Hg) are uniquely negative. For these systems, the LUMO levels originate mainly for the metal s states, which undergo contraction under the influence of scalar interactions. This mechanism results in a decrease in the HOMO-LUMO gaps, influencing the sign and magnitude of the relativistic contributions, compared to the other systems. Relativistic effects are evident in the calculation of principal components of fluorine magnetic shielding tensors for systems containing heavy atoms, such as PbF2 and LaF3 (Table 9).58 Large differences are observed between non-relativistic calculations and those performed at the ZORA level, as extended to include up to SC or SO terms; differences in individual principal components are as large as 92 ppm. In every case, inclusion of relativistic effects results in a decrease of the span of the magnetic shielding tensor. Comparable to results for isotropic magnetic shielding, the effects of SO coupling are small for the principal components, with SO contributions ranging between 0 and 7 ppm.

9.25.4.2

Cadmium

Most studies of cadmium magnetic shielding have been devoted to isolated molecules. The first of these reports by Nakatsuji et al. presented HF calculations of the cadmium magnetic shielding in several gas-phase complexes, proposed that the variation in shielding among these complexes is proportional to the p-donating ability of the ligands, and demonstrated that the calculations reproduce qualitative trends in experimental isotropic 113Cd chemical shifts.80,81 A subsequent analysis by Ellis et al. was unable to reproduce the experimental trend in the 113Cd chemical shifts of Cd(CH3)2 and Cd(C2H5)2, and concluded that the apparent agreement between calculation and experiment in earlier studies was partially the result of error cancelation, due to the use of insufficiently large basis sets, and the neglect of electron correlation and/or relativistic effects.82 Higashioji et al. explored the importance of basis set effects on the calculation of cadmium magnetic shielding.83 Later studies provided non-relativistic DFT calculations of cadmium magnetic shielding tensors in isolated molecules and the materials Cd(NO3)2$4H2O and Cd(acetate)2$2H2O.84–88 Several studies have explored the influence of relativistic effects on cadmium magnetic shielding tensors, although conflicting results regarding their significance are reported. A study by Roukala et al. calculated cadmium magnetic shielding for the isolated systems Cd(CH3)2 and Cd(H2O)62þ using several relativistic methods, including the quasi-relativistic Breit-Pauli perturbation theory (BPPT) and Dirac-Hartree-Fock (DHF) theory.89 They determined that relativistic contributions to cadmium magnetic shielding tensors are substantial, although the sizes of these contributions differ appreciably between the BPPT and DHF methods. Li et al. combined molecular dynamics simulations and BPPT/DFT calculations to compute the shielding of the Cd2þ ion in aqueous solution.90 The authors concluded that SO contributions to cadmium magnetic shielding tensors tend to be of similar

Fig. 10 Absolute value of the contribution of relativistic effects (SC þ SO) to isotropic magnetic shielding of fluorine-containing solids as a function of the atomic number of the cation (M) in MFn (M ¼ Li, Na, Ca, Zn, Rb, Sr, Cd, Cs, Ba, La, Hg, Pb; n ¼ 1, 2, 3) systems. Group XII metal fluorides ZnF2, CdF2, and HgF2 are shown as blue points. This figure is reproduced from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752, https://doi.org/10.1021/acs.jctc.7b00555. Copyright 2017, American Chemical Society.

Advances in the computation of nmr parameters for inorganic nuclides Table 9

Comparison of the calculated principal components of fluorine magnetic shielding tensors and spans of fluorine atoms in LaF3 and PbF2 at the non-relativistic, ZORA scalar relativistic, and ZORA spin-orbit levels of theory.a,b

Material

s11 (ppm) s22 (ppm) s33 (ppm) siso (ppm) U (ppm) k

LaF3 (F1) Non-relativistic Scalar Spin-orbit LaF3 (F2) Non-relativistic Scalar Spin-orbit LaF3 (F3) Non-relativistic Scalar Spin-orbit PbF2 (F1) Non-relativistic Scalar Spin-orbit PbF2 (F2) Non-relativistic Scalar Spin-orbit

107 153 153

180 216 218

292 311 315

193 227 229

185 158 162

0.21 0.20 0.20

10 72 69

172 212 212

172 213 213

118 166 165

162 141 144

1.00 0.99 0.99

30 89 85

192 231 230

192 232 231

138 184 182

163 143 146

0.99 0.99 0.99

118 193 197

122 197 202

168 233 240

136 208 213

51 40 42

0.82 0.80 0.79

126 214 219

188 256 261

214 272 279

176 247 253

87 58 60

0.41 0.45 0.40

851

a Fluorine magnetic shielding tensors were calculated using the PBE0 functional with a 50% HFX admixture. b The isotropic magnetic shielding, span, and skew are defined as siso ¼ (s11 þ s22 þ s33)/3, U ¼ | s11  s33 | and k ¼  3(s22  siso)/U, respectively. Adapted from Alkan, F.; Holmes, S. T.; Dybowski, C. Role of Exact Exchange and Relativistic Approximations in Calculating 19F Magnetic Shielding in Solids Using a Cluster Ansatz. J. Chem. Theory Comput. 2017, 13, 4741–4752.

magnitude for different systems, and are therefore mutually canceled upon conversion to the chemical shift scale. Casella et al. calculated the cadmium magnetic shielding tensors in numerous coordination compounds using non-relativistic methods, as well as with the ZORA with the Hamiltonian expanded to include up to SC or SO terms.91 They concluded that the inclusion of relativistic effects, at either the ZORA/SC or SO level, does not lead to better agreement with experiment than is possible with non-relativistic DFT calculations. Additionally, Jokisaari et al. reported relativistic contributions to the cadmium-X (X ¼ H, C) scalar coupling tensors for Cd(CH3)2.92 A recent study by Holmes and Schurko has assessed several issues in calculating the cadmium magnetic shielding tensors of 30 cadmium sites in 27 materials;6 these considerations include comparisons of (i) calculations using the periodic-structure GIPAW approach and a cluster-based approach, (ii) relativistic DFT calculations performed with the ZORA Hamiltonian, as extended to include up to SC or SO terms, and (iii) several density functional approximations, including GGA and hybrid methods (Fig. 11 and Table 10). BLYP/GIPAW and cluster-based calculations performed at the BLYP/ZORA/SC level reveal that cluster-based and GIPAW approaches (using either ultrasoft or norm-conserving pseudopotentials generated on the fly), produce very different values for the cadmium magnetic shielding tensors. None of these methods results in good agreement with experimental principal components of chemical shift tensors, suggesting that more advanced computational methods are necessary for calculating cadmium magnetic shielding tensors accurately. The relationship between calculated principal components of the cadmium magnetic shielding tensors and the experimental principal components of cadmium chemical shift tensors yields values of A ¼  0.38 and B ¼ 4490 ppm for GIPAW calculations using ultrasoft pseudopotentials, values of A ¼  1.07 and B ¼ 3670 ppm for GIPAW calculations using norm-conserving pseudopotentials, and values of A ¼  1.17 and B ¼ 3670 ppm for the cluster-based calculations. The cluster-based calculations resulted in the lowest rms error of 71 ppm, whereas the two sets of GIPAW calculations resulted in rms errors of 168 ppm and 86 ppm, respectively. Comparable results were obtained using other GGA-type functionals (i.e., PBE, PW91, and RPBE). The comparison of ZORA/SC and SO calculations reveals that the inclusion of SO terms increases the shielding of the reference state by ca. 540 ppm. Whereas calculations performed at the BLYP/ZORA/SC level result in linear-regression parameters of A ¼  1.17 and B ¼ 4209 ppm, BLYP/ZORA/SO calculations result in values of A ¼  1.09 and B ¼ 3670 ppm. However, ZORA/ SC and SO calculations result in similar rms errors of 71 ppm and 76 ppm, respectively. The influence of spin-orbit coupling is

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Advances in the computation of nmr parameters for inorganic nuclides

Fig. 11 Correlations between calculated principal components of cadmium magnetic shielding tensors and experimental cadmium chemical shift tensors, as calculated at the (A) BLYP/GIPAW/USPP, (B) BLYP/GIPAW/NCPP, (C) BLYP/ZORA/SC, (D) BLYP/ZORA/SO, (E) B3LYP/ZORA/SO, and (F) BH&HLYP/ZORA/SO levels. Results are shown for 30 cadmium sites. The results in panels C–F were calculated using cluster-based models of the materials. This figure is adapted from Holmes, S. T.; Schurko, R. W. A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations. J. Chem. Theory Comput. 2019, 15, 1785–1797, https://doi.org/10.1021/acs.jctc.8b01296. Copyright 2019, American Chemical Society.

evident in systems featuring cadmium-selenium or cadmium-iodine bonds. For calculations performed at the BLYP/ZORA/SC level, large errors are evident in each principal component of the magnetic shielding tensor, whereas for calculations performed at the SO level, large errors are only evident in values of s33 of iodine-containing systems. Spin-orbit contributions to the individual principal components of the cadmium magnetic shielding tensors can be as large as ca. 1100 ppm in such systems, demonstrating the importance of HAHA effects. In contrast, for cadmium sites featuring bonds to light atoms only, the spin-orbit effects on the principal components of the magnetic shielding tensors are between 468 and 593 ppm; this narrow distribution of spin-orbit contributions

Table 10

Statistical data for the relationships between calculated principal components of cadmium magnetic shielding tensors and experimental principal components of cadmium chemical shift tensors.a

Methodology

A

B (ppm)

R2

rms error (ppm)

BLYP/GIPAW/USPP BLYP/GIPAW/NCPP BLYP/ZORA/SC BLYP/ZORA/SO B3LYP/ZORA/SO BH&HLYP/ZORA/SO

0.38 1.07 1.17 1.09 1.10 1.06

4490 4106 3670 4209 4276 4368

0.72 0.91 0.94 0.93 0.96 0.98

168 86 71 76 54 41

a

The definitions of the linear-regression parameters are given in Eq. (1). Adapted from Holmes, S. T.; Schurko, R. W. A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations. J. Chem. Theory Comput. 2019, 15, 1785–1797.

Advances in the computation of nmr parameters for inorganic nuclides

853

may explain why several earlier studies suggested that the inclusion of spin-orbit terms does not impact the accuracy of such calculations.90,91 DFT calculations of cadmium magnetic shielding tensors are also influenced by the choice of functional. In particular, the use of hybrid functionals such as B3LYP and BH&HLYP, combined with the effects of spin-orbit coupling, results in better agreement with experimental cadmium chemical shift tensors than any other examined combination of methods.6 Whereas BLYP/ZORA/SO calculations result in a rms error of 76 ppm, calculations performed with the B3LYP or BH&HLYP functional result in errors of 54 ppm and 41 ppm, respectively. The importance of hybrid functionals is most evident in cadmium sites featuring additional heavy atoms, such as selenium or iodine (Table 11). Hybrid functionals such as BH&HLYP result in an increase in magnetic shielding between 68 and 257 ppm for all principal components (relative to BLYP), except for the values of s33 in systems containing cadmium-iodine, which are decreased between 178 and 216 ppm, brining all three principal components into good agreement with experiment.

9.25.4.3

Tin

Multiple studies have investigated the significance of relativistic effects on the calculation of tin magnetic shielding tensors. Kaneko et al. investigated the isotropic magnetic shielding of tin tetrahydride and tetrahalides using HF calculations with spin-orbit effects included through effective core potentials.93 They found that calculated values are in good agreement with experiment only when spin-orbit effects are included in the calculations, especially for those systems in which the tin atoms are bound to additional heavy atoms such as bromine or iodine. Melo et al. used the relativistic polarization propagator approach (RelPPA) to explore the origin of trends in the magnetic shielding of molecules SnXH3 (X ¼ H, F, Cl, Br, I) and SnXYH2 (X, Y ¼ F, Cl, Br, I),94 whereas Maldonado and Aucar studied SnX4nYn (X, Y ¼ H, F, Cl, Br, I).95 Broeckaert et al. calculated the isotropic magnetic shielding of a series of isolated molecules using the DFT/ZORA/SO approach.96 Demissie compared non-relativistic calculations of tin magnetic shielding and tinX (X ¼ H, C) scalar couplings with those performed using the ZORA and quasi-relativistic Douglass-Kroll-Hess (DKH) Hamiltonians.97 Malkin et al. used 4-component relativistic calculations to revise the absolute shielding of the 119Sn chemical shift reference system Sn(CH3)4.98 Bagno et al. calculated the tin isotropic magnetic shielding and tin-X (X ¼ H, C) scalar coupling constants for a series of Sn4þcontaining small molecules using the ZORA approach.99 Their study demonstrated that the effects of spin-orbit coupling dominate when the tin atoms are directly bonded to additional heavy atoms such as bromine or iodine. However, when no additional heavy atoms are present, calculations of tin magnetic shielding and scalar coupling constants, with and without the inclusion of spin-orbit Table 11

Experimental and calculated cadmium chemical shift tensors for sites featuring cadmium-iodine or cadmium-selenium bonds.a d11 (ppm)

d22 (ppm)

d33 (ppm)

diso (ppm)

U (ppm)

k

rms error (ppm)

268 606 238 317

186 529 197 219

47 175 380 6

167 437 18 177

221 431 618 323

0.26 0.64 0.87 0.39

– 275 292 80

291 592 243 334

175 555 129 159

122 135 272 65

196 427 33 186

169 457 515 269

 0.37 0.84 0.56  0.30

– 280 231 42

683 805 771 716

663 790 736 702

540 780 511 569

629 792 673 662

143 24 260 147

0.72  0.20 0.73 0.81

– 172 68 34

752 803 711 770

570 761 589 625

93 87 125 120

472 550 475 505

659 716 586 650

0.45 0.88 0.58 0.55

– 114 32 37

733 772 673 756

547 728 536 584

100 57 90 119

460 519 433 486

633 715 583 638

0.41 0.88 0.53 0.46

– 110 36 27

n

CdI2(C5H4NCOOPr )2 Exp. BLYP/ZORA/SC BLYP/ZORA/SO BH&HLYP/ZORA/SO CdI2(C5H4NCOOMe)2$MeOH Exp. BLYP/ZORA/SC BLYP/ZORA/SO BH&HLYP/ZORA/SO Cd[N(Pri2PSe)2]2 Exp. BLYP/ZORA/SC BLYP/ZORA/SO BH&HLYP/ZORA/SO CdSe2N2C40H54 (Cd1) Exp. BLYP/ZORA/SC BLYP/ZORA/SO BH&HLYP/ZORA/SO CdSe2N2C40H54 (Cd2) Exp. BLYP/ZORA/SC BLYP/ZORA/SO BH&HLYP/ZORA/SO

The isotropic magnetic shielding, span, and skew are defined as diso ¼ (d11 þ d22 þ d33)/3, U ¼ | d11  d33 | and k ¼ 3(d22  diso)/U, respectively. Adapted from Holmes, S. T.; Schurko, R. W. A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations. J. Chem. Theory Comput. 2019, 15, 1785–1797. a

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Advances in the computation of nmr parameters for inorganic nuclides

coupling terms, yield similar results, suggesting that spin-orbit effects are not significant in these systems. Several studies have used plane-wave DFT methods with relativistic pseudopotential approximations to calculate tin magnetic shielding tensors. Mitchell et al. used the GIPAW approach to calculate the isotropic magnetic shielding of stannate pyrochlores and other tin-containing materials with various oxidation states.100 Aliev et al. studied the tin magnetic shielding tensor of SnO2.101 Lucier et al. calculated the magnetic shielding tensors of two Sn2þ-containing complexes.102 Other studies have reported that non-relativistic calculations also result in good agreement with experiment in certain cases.103–108 Together, these results suggest that the nature of relativistic effects on tin magnetic shielding tensors depends on a complex set of factors including oxidation state, coordination geometry, and the type of atoms bonded to tin. Alkan et al. calculated the tin magnetic shielding tensors of 12 tin sites with different oxidation states and coordination geometries; these include the Sn2þ-containing systems SnO, SnHPO4, SnHPO3, SnC2O4, SnSO4, and BaSnF4, and the Sn4þ-containing systems SnO2, Ca2SnO4, SnS2, Pb2SnO4, Na6Sn2S7, and Sr2SnO4 (Table 12 and Fig. 12).8 Several computational protocols are discussed, including the comparison of the results of (i) periodic-structure and cluster-based approaches performed with the PBE functional and relativistic effects included at the ZORA/SC level, (ii) ZORA/SC and ZORA/SO approaches combined with the PBE functional, and (iii) the GGA PBE and hybrid PBE0 functionals combined with relativistic effects at the ZORA/SO level. Calculations performed at the PBE/GIPAW and PBE/ZORA/SC levels result in very different linear-regression parameters for Sn2þ- and Sn4þ-containing systems.8 In both sets of calculations, the slope of the correlation line deviates significantly from the ideal value of  1.00, and the interpolated values of the shielding of the reference system differs between the two subsets of tin atoms by as much as 400 ppm. PBE/GIPAW calculations result in linear-regression parameters of A ¼  0.71 and B ¼ 3019 ppm for the Sn2þ-containing systems, and values of A ¼  1.08 and B ¼ 2869 ppm for the Sn4þ-containing systems. Similarly, PBE/ ZORA/SC calculations result in linear-regression parameters of A ¼  0.77 and B ¼ 2745 ppm for the Sn2þ-containing systems, and values of A ¼  1.00 and B ¼ 2338 ppm for the Sn4þ-containing systems. In contrast, calculations performed at the PBE/ ZORA/SO level result in comparable linear-regression parameters for tin sites with different oxidation states. For the Sn2þ-containing systems, these values are A ¼  0.99 and B ¼ 2849 ppm; for the Sn4þ-containing systems, these are A ¼  0.99 and B ¼ 2875 ppm. For the Sn2þ-containing systems, PBE/GIPAW calculations result in consistently large residuals, ranging between 229 and 314 ppm.8 These errors are most apparent in the calculated values of s33. The PBE/ZORA/SC calculations result in somewhat lower residuals of 124–250 ppm, although the agreement with experiment is still poor. Both the PBE/GIPAW and PBE/ZORA/SC calculations result in spans that are 200–500 ppm smaller than the experimental values. However, the residuals are typically under 100 ppm for calculations performed at the PBE/ZORA/SO level, while also resulting in spans that are in closer agreement with experiment. For the Sn4þ-containing systems SnO2, Ca2SnO4, Pb2SnO4, and Sr2SnO4, the agreement with experiment tends to be better for all computational protocols than observed for the Sn2þ-containing systems.8 PBE/GIPAW calculations result in residuals of 41– 159 ppm, whereas PBE/ZORA/SO calculations result in residuals of 16–139 ppm. For SnS2 and Na6Sn2S7, only calculations performed at the PBE/ZORA/SO level result in good agreement with experiment. The 1st-coordination shell around the tin atom consists of sulfur atoms for these systems (rather than oxygen atoms), and the SO contributions to the magnetic shielding tensors Table 12

Linear-regression parameters for the linear relations between calculated magnetic shielding tensors and experimental chemical shifts of tin-containing solids.a

Method Sn2 þ-containing systems PBE/GIPAW PBE/ZORA/SC PBE/ZORA/SO PBE0/ZORA/SO Sn4 þ-containing systems PBE/GIPAW PBE/ZORA/SC PBE/ZORA/SO PBE0/ZORA/SO All Sn-containing systems PBE/GIPAW PBE/ZORA/SC PBE/ZORA/SO PBE0/ZORA/SO a

A

B (ppm)

R2

0.71 0.77 0.99 1.04

3019 2745 2849 2981

0.95 0.91 0.98 0.99

1.08 1.00 0.99 1.05

2869 2338 2875 3023

0.89 0.92 0.94 0.97

0.77 0.92 0.98 1.03

3001 2499 2867 3003

0.90 0.85 0.97 0.99

The definitions of the linear-regression parameters are given in Eq. (1). Adapted from Alkan, F.; Holmes, S. T.; Iuliucci, R. J.; Mueller, K. T.; Dybowski, C. Spin-Orbit Effects on the 119Sn Magnetic-Shielding Tensor in Solids: A ZORA/DFT Investigation. Phys. Chem. Chem. Phys. 2016, 18, 18914–18922.

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855

Fig. 12 Correlations between calculated principal components of tin magnetic shielding tensors and experimental tin chemical shift tensors for 12 tin-containing solids, as determined with different methodologies. Computed magnetic shielding tensors were obtained using (A) the PBE/GIPAW method, (B) the PBE/ZORA/SC method, and (C) the PBE/ZORA/SO method. Sn2þ sites are shown in red; Sn4þ sites are shown in blue. This figure is reproduced from Alkan, F.; Dybowski, C. Effect of Co-Ordination Chemistry and Oxidation State on 207Pb Magnetic-Shielding Tensor: A DFT/ZORA Investigation. J. Phys. Chem. A 2016, 120, 161–168, https://doi.org/10.1039/c6cp03807g. Copyright 2016, PCCP owner societies.

are larger due to the presence of the heavier atoms. Calculations on SnS2 and Na6Sn2S7 result in residuals of 226–186 ppm at the PBE/GIPAW level, 286–199 ppm at the PBE/ZORA/SC level, and only 13–29 ppm at the PBE/ZORA/SO level. Differences between principal components of magnetic shielding tensors calculated at the PBE/ZORA/SO and PBE/ZORA/SC levels (Dsii) elucidate the effects of SO coupling (Fig. 13A).8 Spin-orbit effects on magnetic shielding tensors depend on the oxidation state of the tin atom. For Sn2þ-containing systems, SO contributions are most evident in values of s33 (Ds33 ¼ 500 ppm on average), whereas values of Ds11 and Ds22 are between 154 and 260 ppm. In contrast, for Sn4þ-containing systems, the SO

(A)

VZORAJSO – VZORAJScalar (ppm)

'V11 'V22

600

'V33 400

200

0

O Sn

O4

S

P nH

O3

P nH

S

4 O1 O4 F 4 nO 2 O 4 nO 2 nO 4 O4 SO Sn n 4 Sn C2 Sn S S n S S n a 2 2 S 6 S B Sr 2 Pb Ca Na

(B)

V11

V33

(C)

V11

V33

Fig. 13 (A) The difference (Dsii) in principal components of tin magnetic shielding tensors calculated with the ZORA/SO method and the ZORA/SC method. All calculations model the solid-state environment with the cluster-based VMTA/BV approach. Magnetic shielding calculations used the PBE functional. The orientations of tin magnetic shielding tensor axes along with MOs associated with the “lone pair” for (B) SnO and (C) BaSnF4. This figure is reproduced from Alkan, F.; Dybowski, C. Effect of Co-Ordination Chemistry and Oxidation State on 207Pb Magnetic-Shielding Tensor: A DFT/ ZORA Investigation. J. Phys. Chem. A 2016, 120, 161–168, https://doi.org/10.1039/C6CP03807G. Copyright 2016, PCCP owner societies.

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Advances in the computation of nmr parameters for inorganic nuclides

contributions to each principal component are more uniform, with Dsii varying between 435 and 654 ppm. The orientation of the principal axes of the magnetic shielding tensors in two Sn2þ-containing systems are shown in Fig. 13B and C. The principal axis of the most shielded component (s33) is aligned with the symmetry axis of the lone-pair molecular orbital, which results primarily from tin 5 s and 5p atomic states. Similar dependences on oxidation state and coordination geometry are also apparent in the calculation of lead magnetic shielding tensors (Vide infra); however, values of Dsii tend to be around 2000–3000 ppm due to the presence of the heavier lead atom in the latter case.109 Tin magnetic shielding tensors have been calculated using the hybrid functional PBE0 in combination with the ZORA/SO Hamiltonian.8 In general, the PBE0/ZORA/SO-calculated principal components of tin magnetic shielding tensors are 100– 200 ppm more shielded than those obtained with the PBE functional. The results of these calculations for all tin-containing materials are described with linear-regression parameters A ¼  1.03 and B ¼ 3003 ppm. These calculations result in a modest reduction in scatter about the best-fit line, relative to comparable calculations employing the GGA PBE functional, leading to residuals that are below 100 ppm for each tin site.

9.25.4.4

Tellurium

The majority of studies on the calculation of tellurium magnetic shielding tensors have focused on isolated molecules or molecules in solution, rather than on solids. Ruiz-Morales et al. reported calculations of the shielding of organic and inorganic tellurides with relativistic effects incorporated at the scalar level.110 Although the work reproduced experimental trends in the variation of chemical shifts with the nature of attached ligands, it also showed deviations from experiment dependent on the tellurium oxidation state. In another study, Hada et al. employed a quasi-relativistic method that included spin-orbit contributions. They found that such terms increase the calculated isotropic magnetic shielding by as much as ca. 600 ppm.111 Hayashi et al. used the ZORA approach, including SO terms, to calculate the shielding of several tellurium-containing small molecules.112 Pietrasiak et al. used the same approach to calculate the shieldings of several perfluoroalkyl aryl tellurides, and discussed trends in shielding in terms of natural localized molecular orbitals.113 Several studies have used the ZORA/SO method and/or four-component relativistic methods to examine the role of vibrational corrections and solvent interactions on the shielding of tellurium-containing molecules in solution.114,115 Together, these studies demonstrate that spin-orbit contributions to tellurium magnetic shielding tensors are large, and inclusion of them is necessary to obtain significant agreement with experimental values. Several studies employed periodic-structure calculations and relativistic pseudopotentials to calculate tellurium magnetic shielding in solids. Bashi et al. used the full potential linearized augmented plane wave(FP-LAPW) method to calculate magnetic shieldings in solids of the form XTe3O8 (X ¼ Ti, Zr, Sn, Hf). They concluded that the shielding depends on the nature of valence MOs arising from the X p and d states.116 In further work, Bashi et al. used the same method to calculate the magnetic shielding in X2TeO3 (X ¼ Na, K, Ag) and PbTeO3.117 Garaga et al. used the GIPAW approach to calculate the magnetic shielding tensors of tellurium oxides.118 The latter study noted systematic errors in the calculations of the magnetic shielding tensors for tellurium sites featuring the 4þ oxidation state. In contrast, Demko and Wasylishen used the ZORA/SO method to compute the shielding of Te[N(iPr2PSe)2]2 using an isolated molecule approach (N.B. The authors also calculated shielding for analogous solids containing cadmium, mercury, and platinum).119,120 Alkan and Dybowski calculated the tellurium magnetic shielding tensors of 15 tellurium sites that feature various oxidation states and coordination geometries.7 The calculations used a cluster-based approach to examine the importance of relativistic effects through use of the ZORA Hamiltonian, and also compare various GGA and hybrid functionals. Fig. 14 shows the relationships between experimental principal components of tellurium chemical shift tensors and calculated principal components of tellurium magnetic shielding tensors, as calculated at the PBE/ZORA/SC and PBE/ZORA/SO levels.7 The

(A)

(B)

Calculated Shieding (ppm)

Calculated Shieding (ppm)

4500

3500

2500

1500

500 –1500

–500

500

1500

2500

Experimental Chemical Shift (ppm)

4500

3500

2500

1500

500 2500 500 1500 –1500 –500 Experimental Chemical Shift (ppm)

Fig. 14 The correlation between experimental principal components of tellurium chemical shift tensors and calculated principal components of tellurium magnetic shielding tensors, as calculated at the (A) PBE/ZORA/SC and (B) PBE/ZORA/SO levels. This figure is reproduced from Alkan, F.; Dybowski, C. Spin-Orbit Effects on the 125Te Magnetic-Shielding Tensor: A Cluster-Based ZORA/DFT Investigation. Solid State Nucl. Magn. Reson. 2018, 95, 6–11, https://doi.org/10.1016/j.ssnmr.2018.08.005. Copyright 2018, Elsevier.

Advances in the computation of nmr parameters for inorganic nuclides

857

PBE/ZORA/SC calculations result in linear-regression parameters of A ¼  0.81 and B ¼ 2739 ppm, whereas PBE/ZORA/SO calculations result in parameters of A ¼  1.02 and B ¼ 3415 ppm. In addition to resulting in a value of A closer to the ideal case, PBE/ ZORA/SO calculations also result in lower residuals for the majority of systems, with an average residual of 105 ppm. In contrast, PBE/ZORA/SC calculations result in an average of 276 ppm. The Te4þ-containing systems feature large spans, ranging between ca. 500 and 1600 ppm. For these sites, PBE/ZORA/SC calculations consistently underestimate the spans by several 100 ppm, whereas PBE/ZORA/SO calculations result in much better agreement with experimental values. Differences between the principal components of tellurium magnetic shielding tensors calculated at the PBE/ZORA/SC and PBE/ ZORA/SO levels of theory illustrate the importance of spin-orbit coupling (Fig. 15).7 For Te4þ-containing systems (TeO2, b-TeO2, Na2TeO3, and MgTe2O5), spin-orbit effects are most apparent in the principal component s33, for which the values of Ds33 are ca. 500 ppm. In contrast, the spin-orbit contribution to the values of s11 and s22 fall between 50 and 383 ppm. This difference accounts for underestimations of the spans of Te4þ-containing systems for calculations performed at the PBE/ZORA/SC level. For the Te6þ-containing system Te(OH)6, which features holodirected coordination geometries for the two tellurium sites, values of Dsii are ca. 550 ppm for each principal component, which is why both PBE/ZORA/SC and PBE/ZORA/SO calculations result in similar values of the span. Spin-orbit contributions are largest for the magnetic shielding tensors of the Te2þ-containing system ((CH3)2SnTe)3, with values of Dsii ranging between 600 and 800 ppm. The large values of Dsii likely reflect the oxidation state of the tellurium atom, as well as HAHA effects resulting from tin-tellurium bonds. Fig. 16 illustrates the effect of spin-orbit coupling on the electronic structure of the Te4þ-containing system TeO2.7 For these cluster-based calculations, the HOMO level originates predominately from linear combinations of tellurium s and p atomic states, and can be viewed as a lone pair centered on the tellurium atom. The principal component of the tellurium magnetic shielding tensor s33 aligns along the axis of this molecular orbital. The LUMO through LUMO-2 levels originate from tellurium p states. Although the nature of the HOMO level does not experience any significant change under the influence of spin-orbit coupling, the LUMO through LUMO-2 levels exhibit mixing and energy changes similar to the P3/2 and P1/2 splitting of atomic p states. These results demonstrate that the underestimation of the values of the span of Te4þ-containing system at the PBE/ZORA/SC level of theory arises from an incorrect description of the interaction between the tellurium lone pair and the unoccupied MOs originating from tellurium p states. Calculated tellurium magnetic shielding tensors are influenced by the choice of density functional approximation (Table 13).7 For the GGA functionals (i.e., PBE, PB86, and BLYP), the values of the linear-regression parameters are similar, with differences in the value of B of ca. 100 ppm. For calculations performed using the hybrid functionals PBE0 and BH&HLYP, the agreement with experiment is strong, as indicated by the high values of R2, although the values of A deviate from the ideal value of  1.00 by at least 9%. Calculations using hybrid functionals result in higher values of B than obtained from GGA functionals. The linear-regression parameters depend on the HFX admixture in the functional. The PBE0 functional, which features a 25% HFX admixture, is characterized by values of A ¼  1.09 and B ¼ 3662 ppm. The BH&HLYP functional, which features a 50% HFX admixture, has a value of A ¼  1.14, which deviates more severely from the ideal case, as well as a more shielded value for the reference system of B ¼ 3798 ppm.

9.25.4.5

Mercury

Among the heavy 6th-period elements, mercury has been the most comprehensively studied in early benchmark investigations of relativistic effects on magnetic shielding. These reports often employed the HgX2 (X ¼ CN, Cl, Br, etc.) series of small molecules for

VZORAJSO – VZORAJScalar (ppm)

1000

'V11 'V22

800

'V33

600 400 200 0 Te

O2

eO

T E-

O3

2

Te

N

a2

M

e gT

O5

te

2

Si

H

(O

Te

) 6,

I

te

Si ,

H) 6

eI

, e) 3

eI

sit

, e) 3

sit

I

nT nT ) 2S ) 2S 3 H {(C {(C

(O

Te

II

H3

Fig. 15 The difference between the principal components for the tellurium-containing materials at the PBE/ZORA/SC level of theory and at the PBE/ ZORA/SO level of theory. This figure is reproduced from Alkan, F.; Dybowski, C. Spin-Orbit Effects on the 125Te Magnetic-Shielding Tensor: A ClusterBased ZORA/DFT Investigation. Solid State Nucl. Magn. Reson. 2018, 95, 6–11, https://doi.org/10.1016/j.ssnmr.2018.08.005. Copyright 2018, Elsevier.

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Advances in the computation of nmr parameters for inorganic nuclides

Fig. 16 (A) The comparison of electronic structure for TeO2 with or without the inclusion of ZORA/SO terms, and the illustration of (B) the LUMO level and (C) the HOMO level calculated at the PBE/ZORA/SO level of theory. This figure is reproduced from Alkan, F.; Dybowski, C. Spin-Orbit Effects on the 125Te Magnetic-Shielding Tensor: A Cluster-Based ZORA/DFT Investigation. Solid State Nucl. Magn. Reson. 2018, 95, 6–11, https://doi.org/10. 1016/j.ssnmr.2018.08.005. Copyright 2018, Elsevier. Table 13

Linear-regression parameters between experimental principal values of tellurium chemical shift tensors and calculated principal components of tellurium magnetic shielding tensors, as calculated using the ZORA spin-orbit Hamiltonian.a

Functional

A

B (ppm)

R2

PBE BP86 BLYP PBE0 BH&HLYP

1.02 1.02 1.01 1.09 1.13

3415 3371 3301 3662 3798

0.986 0.987 0.988 0.992 0.995

a

The definitions of the linear-regression parameters are given in Eq. (1). Adapted from Alkan, F.; Dybowski, C. Spin-Orbit Effects on the 125Te Magnetic-Shielding Tensor: A Cluster-Based ZORA/DFT Investigation. Solid State Nucl. Magn. Reson. 2018, 95, 6–11.

simplicity of computation and comparison between methods. The seminal work of Wolff et al. using the ZORA Hamiltonian found good agreement between experimental and calculated isotropic magnetic shieldings (Fig. 17A), the average deviation between calculation and experiment being 163 ppm.121 These studies demonstrated the importance of inclusion of the spin-orbit term in theory for accurate predictions of magnetic shielding for heavy atoms. In a report that included experimental and theoretical work, Jokisaari et al. investigated the performance of ZORA for the prediction of isotropic and anisotropic components of the mercury shielding tensor in methylmercury halides.122 Their work showed an overall good agreement with the experiment when the effects of spin-orbit terms are included in the computation of the shielding tensor. In other theoretical work,123–126 Nakatsuji and coworkers compared the performance of non-relativistic calculations with calculations involving the quasi-relativistic DKH Hamiltonian. Their results clearly show the necessity of inclusion of both scalar and spin-orbit relativistic effects for both qualitative and quantitative agreement with experiment (Fig. 17B). In addition, the largest deviations between non-relativistic and relativistic cases were observed for the HgI2 and HgBr2, indicating the importance of relativistic effects by HAHA effects. Arcisauskaite et al.127 compared the performance of linear response elimination of the small component (LR-ESC), ZORA and 4component relativistic methods to the non-relativistic case for mercury magnetic shieldings and chemical shifts (Table 14). Their study shows that absolute shieldings calculated by the 4-component method and the ZORA method differ by ca. 2000 ppm, whereas calculated chemical shifts differ by less than ca. 60 ppm. In the case of non-relativistic or LR-ESC results, large deviations from the 4-component results are observed for chemical shifts, mainly due to the absence of spin-orbit contributions. The poor performance of ZORA for absolute shieldings has been shown to result from substantial errors introduced in the contributions

Advances in the computation of nmr parameters for inorganic nuclides

(A)

(B)

-1000

1000

calc.

non-relativistic

exp.

-1500

Experiment (ppm)

Chemical Shift (ppm)

859

-2000 -2500

DKH -1000

-3000

-3000 -3500 HgCl2

-5000 -5000 HgCl2(NH3)2

HgBr2 HgBr2(NH3)2

Hgl2

Hgl2(NH3)2

-3000 -1000 Theory (ppm)

1000

Fig. 17 (A) Comparison of experimental and ZORA/SO calculated isotropic mercury chemical shifts. (B) Comparison of non-relativistic and DKH levels of theory on the correlation of theory and experiment for isotropic mercury chemical shifts. (A) This figure is adapted from reference Wolff, S.K.; Ziegler, T.; van Lenthe, E.; Baerends, E.J. Density Functional Calculations of Nuclear Magnetic Shieldings Using the Zeroth-Order Regular Approximation (ZORA) for Relativistic Effects: ZORA Nuclear Magnetic Resonance. J. Chem. Phys. 1999, 110, 7689–7698, https://doi.org/10.1063/1. 478680. Copyright 1999, American Institute of Physics. (B) This figure is adapted from Fukuda, R.; Hada, M.; Nakatsuji, H. Quasirelativistic Theory for Magnetic Shielding Constants. II. Gauge-Including Atomic Orbitals and Applications to Molecules. J. Chem. Phys. 2003, 118, 1027–1035, https:// doi.org/10.1063/1.1528934. Copyright 2003, American Institute of Physics. Table 14 Molecule

Comparison of calculated mercury magnetic shieldings and chemical shifts with different levels of relativistic theory. Non-relativistic

Magnetic shielding (ppm) 6122 Hg(CH3)2 HgCl2 7203 HgBr2 7195 6791 HgI2 Chemical shifts (ppm) HgCl2 1087 HgBr2 1079 HgI2 673

LR-ESC

ZORA

4-Component

8533 10,010 10,355 10,403

7967 9948 11,179 12,185

10,015 12,049 13,254 14,265

1489 1838 1886

1996 3237 4251

2055 3271 4292

Adapted from Arcisauskaite, V.; Melo, J. I.; Hemmingsen, L.; Sauer, S. P. A. Nuclear Magnetic Resonance Shielding Constants and Chemical Shifts in Linear 199Hg Compounds: A Comparison of Three Relativistic Computational Methods. J. Chem. Phys. 2011, 135, 044306.

of the innermost core levels to the magnetic shielding, whereas contributions from valence shells show very good agreement with the results of 4-component calculations.128 As the errors introduced by core levels mostly cancel when theoretical chemical shifts are evaluated, ZORA is expected to perform well for calculated chemical shifts. These findings are further supported by the work of Wodynski et al., where ZORA has shown to reproduce only 75–79% of the absolute shielding values of the 4-component results for the 6th-period elements.129 Roukala et al. report that BPPT calculations, similar to ZORA, significantly underestimate the absolute shielding of 199Hg nuclei, whereas errors in chemical shifts are much smaller compared to the 4-component relativistic level of theory.89 In another important study, Autschbach showed the importance of including the exchange-correlation functional response for both chemical shifts and absolute shieldings of mercury.130 More recently, Yoshizawa and Hada employed the exact two-component relativistic method to predict the absolute shieldings of small molecules of the form HgX2 (X ¼ CH3, Cl, Br, I).131 Unlike the results of quasi-relativistic methods (i.e., ZORA, BPPT, LR-ESC), their results with exact two-component methods deviate only by 20–48 ppm from 4component relativistic results. Overall, these findings suggest that quasi-relativistic methods are computationally-inexpensive alternatives to the full 4-component formalism for the calculations of 199Hg chemical shifts. However, for the accurate prediction of absolute shieldings, the 4-component method or the exact 2-component relativistic method should be employed. As previously discussed, calculations of mercury magnetic shielding tensors have a marked dependence on cluster size. Taylor et al.132 employed the ZORA Hamiltonian and the cluster approach for the prediction of the principal components of the 199Hg chemical shift tensor of HgCl2. Their results indicate that a more accurate description of the chemical shift tensor can be obtained by using a large cluster model adapted from the crystal structure. Alkan and Dybowski explored relativistic effects on principal

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components of mercury magnetic shielding models using cluster models.32 Calculations with large cluster models show that there is a ca. 40% deviation between theory and experiment when non-relativistic DFT techniques are employed, and only a slight improvement can be obtained when only scalar relativistic effects are included in the ZORA Hamiltonian. In comparison, ZORA calculations with the inclusion of spin-orbit coupling show a deviation less than ca. 3% from ideal agreement. For the calculated span, nonrelativistic and scalar-relativistic calculations underestimate experimental values by ca. 1500 ppm in some cases, whereas calculations that include spin-orbit coupling show closer agreement with experiment for the calculated spans as well. The effects of spin-orbit coupling are most pronounced in calculations on HgBr2 and HgI2, demonstrating the importance of the HAHA mechanism in systems containing additional heavy atoms.

9.25.4.6

Lead

Similar to the case of mercury, lead is a 6th-period element that has attracted a number of theoretical NMR studies. In early benchmark work, Ziegler and coworkers investigated the performance of ZORA for calculating lead magnetic shieldings.133 Their results indicate that both paramagnetic and spin-orbit contributions become comparably important for lead chemical shifts to achieve meaningful correlations with experiment. For the PbX4 (X ¼ Br, I) series, spin-orbit contributions become even more significant than the paramagnetic contribution as a result of HAHA effects. Similarly, Le Guennic and Autschbach indicated the importance of spin-orbit contributions and HAHA effects for the calculated magnetic shielding tensor of in PtPb12 2.134 Aucar and coworkers benchmarked the relativistic and electron-correlation effects for XY4nZn (X ¼ Sn, Pb; Y, Z ¼ H, F, Cl, Br, I).95,135 Their results showed that the differences in absolute shielding between non-relativistic and 4-component relativistic calculations vary between 6000 and 12,000 ppm where the largest deviations between the two levels of theory are recorded for PbI4. In comparison, the scalarrelativistic LR-ESC method yields lead absolute shielding values that are ca. 20% smaller (3000–4000 ppm) than those obtained from 4-component calculations. The inclusion of correlation effects with the random phase approximation (RPA) provides more reliable results, as compared to standard DFT methods (B3LYP, PBE0 and BLYP). Based on these calculations, the authors proposed an absolute magnetic shielding of 14,475.1  500.7 ppm for Pb(CH3)4.95 Adrjan et al. also studied the absolute shielding scale of lead by employing theoretical calculations and gas-phase NMR measurements.136 They have obtained 10,799.7 ppm for the same reference shielding. In a very recent study, Franzke and Weigend implemented an efficient scalar-relativistic exact twocomponent theory for magnetic shielding calculations.137 In this case, the calculated absolute shielding was 5435 ppm, showing a large deviation from previously obtained 4-component results that included the spin-orbit contributions. While benchmark calculations of lead absolute shieldings or chemical shifts in gas or solution are not as numerous as those for mercury, lead is the most thoroughly investigated 6th-period element in the solid state both experimentally and theoretically, thanks to its rich and versatile coordination chemistry.138 To date, most quantum chemical investigations have utilized clusterbased approaches to model the solid-state environment, along with the ZORA Hamiltonian to account for relativistic effects. In one such study, Schurko and coworkers investigated the Pb2þ coordination environment in (2,6-Me2C6H3S)2Pb adducts using 207 Pb solid state NMR measurements and ZORA calculations.139 They showed that relativistic ZORA calculations adequately reproduce the experimental values for the principal components of the chemical shift tensor. In terms of the chemical shift anisotropy, non-relativistic values were found to be ca. 2000 ppm smaller than experiment, whereas significant improvements were obtained for calculated chemical shift anisotropies when the ZORA Hamiltonian was employed. In a similar experimental and theoretical study, Greer et al. investigated the lone-pair activity of lead in a series of Pb2þ coordination polymers.140 Although the ZORA results employing molecular clusters exhibited qualitatively good agreement of the calculated principal components with experiment, the deviations between theory and experiment were as large as ca. 1000 ppm, indicating possible room for improvement. In this case, the authors argued that some of the large deviations resulted from the use of a cluster approach. Lead magnetic shielding calculations using cluster models, and relativistic effects through the ZORA method, have also been employed to differentiate between the effects of the chemical shift and Knight shift interactions in semiconductors,49 or to assign the crystallographically inequivalent nuclei in the solid-state NMR spectra of materials with complex molecular-level structures.48 Dmitrenko et al. investigated the lead magnetic shielding tensor of Pb2þ and Pb4þ halides by employing the ZORA Hamiltonian and small anionic model clusters, obtaining reasonable agreement between theory and experiment.141 The authors also suggested that the spin-orbit contributions to the magnetic shieldings are different in magnitude for PbX2 and PbX4 (X ¼ F, Cl, Br, I) systems. In a series of benchmark studies,55,109 Alkan and Dybowski investigated the effect of different cluster models, density functionals, and relativistic approximations for a suite of lead-containing network solids. The description of the various cluster models was discussed in the previous section (Vide supra). For these systems, ZORA/SC calculations show reasonable qualitative agreement with experiment (Fig. 18A); however, the slope of the correlation line shows a deviation of ca. 65% (i.e., A ¼  0.365) from ideal agreement. In comparison, the same deviation reduces to ca. 13% (i.e., A ¼  0.869) when the ZORA/SO Hamiltonian is employed. Further improvement is achieved when hybrid functionals such as B3LYP are employed instead of GGA functionals, resulting in a correlation with experiment with a slope approaching the ideal value of  1.00 (Fig. 18B). An important consideration for the prediction of magnetic shieldings in lead-containing compounds is the influence of coordination geometry around the lead atom.109 For hemidirected lead sites, the spin-orbit contribution is much larger for the s33 component, relative to s11 or s22 (Fig. 18C). The principal axis of the s33 component of the lead magnetic shielding tensors of hemidirected lead atoms tend to align near the symmetry axis of the lone pair, which results from the linear combination of lead 6s and 6p states. This result indicates that the spin-orbit contribution to the magnetic shielding anisotropy or span is significant

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Fig. 18 The correlation between experimental principal components of lead chemical shift tensors and calculated principal components of lead magnetic shielding tensors, as computed at the (A) BP86/ZORA/SC (red) and BP86/ZORA/SO (blue) levels. (B) The correlation between experimental and calculated principal components for hemi (blue) and holo-directed (red) lead-containing solids at the B3LYP/ZORA/SO level. (C) The difference between principal components as calculated with the ZORA/SO and ZORA/SC Hamiltonians. Compounds 1–8 correspond to hemidirected lead sites whereas 9–14 correspond to holo-directed lead sites. (A and B) This figure is adapted from Alkan, F.; Dybowski, C. Chemical-Shift Tensors of Heavy Nuclei in Network Solids: A DFT/ZORA Investigation of 207Pb Chemical-Shift Tensors Using the Bond-Valence Method. Phys. Chem. Chem. Phys. 2015, 17, 25014–25026, https://doi.org/10.1039/C5CP03348A. Published by the PCCP owner societies.(C) This figure is adapted from Alkan, F.; Dybowski, C. Effect of Co-Ordination Chemistry and Oxidation State on 207Pb Magnetic-Shielding Tensor: A DFT/ZORA Investigation. J. Phys. Chem. A 2016, 120, 161–168, https://doi.org/10.1021/acs.jpca.5b10991. Copyright 2016, American Chemical Society.

for hemidirected lead-containing solids. On the other hand, the spin-orbit contribution is more uniformly distributed among the principal components of holo-directed lead-containing systems.

9.25.4.7

Platinum

The calculation of platinum magnetic shielding has attracted significant interest due to the large range of 195Pt chemical shifts (ca. 15,000 ppm) and the importance of relativistic effects. In an early study, Gilbert and Ziegler used BPPT and ZORA relativistic corrections at the spin-orbit level to compute the platinum magnetic shielding in Pt2þ-containing isolated molecules.142 Their results demonstrated that paramagnetic and spin-orbit terms have comparable significance for the calculation of platinum magnetic shielding tensors, and that spin-orbit terms cannot be neglected, as illustrated by calculations on the series of complexes PtX2(PMe3)2 (X ¼ Cl, Br, I) performed at the scalar and spin-orbit levels (Fig. 19). Likewise, Krykunov et al. explored the origins of platinum magnetic shielding in isolated molecules by quantifying the magnitudes of paramagnetic and spin-orbit contributions.143 Penka 2 complexes, and noted their sensitivity Fowe et al. used the ZORA/SO Hamiltonian to calculate the magnetic shieldings of PtClnBr6-n toward changes in bond lengths, among other structural factors.144 Burger et al. used DFT/ZORA calculations to explore the

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0

-500

-1000 G(ppm) -1500 Expt - Pauli Spin-Orbit - Pauli Scalar -2000 cis-PtCl2(PMe3)2

cis-PtBr2(PMe3)2

trans-PtCl2(PMe3)2

cis-Ptl2(PMe3)2

trans-PtBr2(PMe3)2

trans-Ptl2(PMe3)2

Fig. 19 Plot of experimental and calculated platinum chemical shifts for a series of PtX2(PMe3)2 (X ¼ Cl, Br, I) complexes, showing the need to include spin-orbit relativistic effects. This figure is reproduced from Gilbert, T. M.; Ziegler, T. Prediction of 195Pt NMR Chemical Shifts by Density Functional Theory Computations: The Importance of Magnetic Coupling and Relativistic Effects in Explaining Trends. J. Phys. Chem. A 1999, 103, 7535–7543, https://doi.org/10.1021/jp992202r. Copyright 1999, American Chemical Society. 145 variations in magnetic shielding among PtXnY62 Autschbach and Zheng provided platinum  n (X, Y ¼ F, Cl, Br, I) complexes. 2þ 3þ 4þ magnetic shieldings for several Pt , Pt , and Pt complexes using 2-component DFT calculations, and analyzed the results in terms of the contributions of natural localized molecular orbitals and natural bond orbitals.146 Their analysis proposed a “d-orbital rotation model,” as well as identified the following factors as being critical for understanding the variation in platinum chemical shifts among various nuclear environments: (i) differences between (pseudo-) square-planar and (pseudo-) octahedral coordination geometries; (ii) the extent of delocalization of the non-bonding Pt 5d lone pair orbitals; (iii) the delocalization of the Pt–ligand bonds; and (iv) the occupancy of the antibonding Pt–ligand s* orbitals. In another study, Sutter and Autschbach provided a theoretical analysis of several azido platinum complexes using the ZORA method.147 In this study, they explored HALA effects through calculations of nitrogen magnetic shielding, and also provided calculations of nitrogen EFG tensors and platinum-nitrogen scalar coupling constants. Together, these studies demonstrate that inclusion of relativistic effects at the spin-orbit level is essential for calculation of platinum magnetic shielding tensors, as well as the magnetic shielding of other atoms in systems containing platinum. Several studies have provided calculations of isotropic platinum magnetic shieldings of solvated complexes. For example, Autschbach and Le Guennic calculated the platinum magnetic shieldings of [(NC)5Pt-Tl(CN)n]n  (n ¼ 0–3) and [(NC)5Pt-TlPt(CN)5]3 complexes.148 Their results, obtained at the ZORA/SO level, found that good agreement with experiment is achieved using an explicit first solvation shell of solvent molecules, with longer-range bulk solvent effects modeled with the conductorlike screening model (COSMO). Similarly, Sterzel and Autschbach explored solvation effects on [PtCl6]2, [PtCl4]2, and [Pt2(NH3)2Cl2((CH3)3CCONH)2-(CH2COCH3)]Cl complexes.149 This study found that explicit quantum mechanical treatment of the first solvation shell and bulk solvent effects treated with the COSMO method leads to good agreement with experiment. Truflandier and Autschbach calculated the platinum magnetic shieldings of five anionic complexes in aqueous solution.150 This study utilized ab initio molecular dynamics simulations to derive a large number of snapshot structures representing the local environment of the platinum complexes and interacting water molecules (Fig. 20). A similar study by Truflandier et al. used ab initio molecular dynamic simulations to calculate the platinum magnetic shielding of cisplatin derivatives in aqueous solution.151 Several other studies report computation of platinum magnetic shielding tensors in solids. For example, Lucier et al. used GIPAW and isolated-molecule methods to calculate the magnetic shielding tensors of several Pt2þ-containing anti-cancer drugs.152 They found that GIPAW calculations, and isolated molecule models combined with the ZORA Hamiltonian, typically result in substantial errors in the principal components of the magnetic shielding tensors. These errors are especially apparent in the unique principal component s11, which is oriented perpendicular to the plane containing the square-planar platinum atom. Tang et al. calculated the magnetic shielding tensors of two platinum complexes using an isolated-molecule protocol, combined with non-relativistic and ZORA approaches.153 This study provided a detailed molecular orbital analysis to discern the origin of variation in magnetic shieldings of these complexes. Mastrorilli et al. and Todisco et al. used the ZORA Hamiltonian, together with gas-phase optimized molecules, to calculate the magnetic shielding tensors of platinum atoms in various oxidation states.154,155 In addition, the authors calculated platinum-phosphorus primary scalar coupling constants, as well as explored HALA effects on phosphorus magnetic shielding tensors. Roukala et al. used a combination of periodic-structure and isolated-molecule calculations to predict the

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Fig. 20 Evolution of the platinum magnetic shielding in [PtCl4$12(H2O)]2 during the ab initio molecular dynamics (blue) and the corresponding distribution of platinum magnetic shielding accumulated over 128 configurations (black). The green solid line and black dashed line are Gaussian and polynomial fits. The average shielding and standard deviation are indicated by the down triangle and the horizontal bar, respectively. This figure is reproduced from Truflandier, L. A.; Autschbach, J. Probing the Solvent Shell with 195Pt Chemical Shifts: Density Functional Theory Molecular Dynamics Study of PtII and PtIV Anionic Complexes in Aqueous Solution. J. Am. Chem. Soc. 2010, 132, 3472–3483, https://doi.org/10.1021/ ja9096863. Copyright 2010, American Chemical Society.

platinum magnetic shielding tensors of several bis(dialkyldithiophosphato) Pt2þ complexes.156 In particular, the authors used lowlevel plane-wave DFT calculations to refine the crystal structures and to evaluate the size of intermolecular effects. They performed additional isolated-molecule calculations at the PBE0/ZORA/SO level, which, together with the refinement, led to overall satisfactory agreement with experimental results. The authors calculated secondary platinum-phosphorus scalar coupling constants and phosphorus magnetic shielding tensors in the same complexes. Calculations of platinum magnetic shielding tensors have been crucial establishing inorganic crystal structures in NMR crystallographic investigations. A study by Lucier et al. proposed a complete crystal structure for Magnus’ pink salt, [Pt(NH3)4][PtCl4], based on DFT/ZORA calculations of platinum magnetic shielding tensors, among other techniques.157 This study demonstrates that, in the solid state where many square-planar Pt2þ complexes pack in a columnar fashion, Pt-Pt metallophilic interactions influence the electronic structures of the platinum atoms; proper modeling of these intermolecular interactions is essential in such cases, making calculated platinum magnetic shielding tensors an important metric for assessing the quality of proposed crystal structures.

9.25.5

Summary

Calculation of the NMR parameters of inorganic nuclides continues to play an important role in the characterization of materials and the benchmarking of theoretical models. In this article, we discussed recent advances in computational methods and their application to these difficult chemical systems. Many of the insights for these solid systems were possible through the development of robust cluster-based models to account for solid-state effects on NMR parameters. These methods can be applied to calculations on network solidsda development that may have wide-ranging applications in solid-state NMR studies of materials. In addition, the calculation of magnetic shielding tensors of fluorine, cadmium, tin, tellurium, mercury, lead, and platinum were discussed. These examples illustrate the importance of computational considerations such as the use of DFT approximations beyond generalized gradient approximation, as well as the importance of relativistic effects at the spin orbit level on systems containing heavy atoms to calculations of the many inorganic nuclei. These and further developments of the methodologies described here can be expected to allow calculation of NMR parameters for nuclei across the Periodic Table.

Acknowledgments CD acknowledges the support of the US National Science Foundation during the preparation of this review through grant DMR-1608366.

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