Electron Paramagnetic Resonance: Volume 27 (ISSN) [1 ed.] 9781839161711, 9781839162534, 9781839163173, 183916171X

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Electron Paramagnetic Resonance Volume 27

A Specialist Periodical Report

Electron Paramagnetic Resonance Volume 27 A Review of the Recent Literature. Editors Victor Chechik, University of York, UK Damien M. Murphy, Cardiff University, Cardiff, UK Bela E. Bode, University of St Andrews, UK Authors K. Ackermann, University of St Andrews, UK B. E. Bode, University of St Andrews, UK Maruan Bracci, University of Zaragoza, Spain Paolo Bruzzese, Universita¨t Leipzig, Germany Antonino Famulari, University of Zaragoza, Spain David Fioco, Cardiff University, UK Andrea Guidetti, University of Antwerp, Belgium Andrew M. Hartley, University of Leeds, UK Oleksii Laguta, Brno University of Technology, Czech Republic Benjamin J. Lane, University of Leeds, UK Yu-Kai Liao, University of Turin, Italy Yue Ma, University of Leeds, UK Andriy Marko, Brno University of Technology, Czech Republic Daniel O. T. A. Martins, University of Manchester, UK Eufemio Moreno-Pineda, Universidad de Panama´, Panama´ Damien M. Murphy, Cardiff University, UK Petr Neugebauer, Brno University of Technology, Czech Republic M. Oranges, University of St Andrews, UK Christos Pliotas, University of Leeds, UK Leonora Podvorica, University of Turin, Italy Seyedeh Fardokht Rezayi, Cardiff University, UK Vinicius T. Santana, Brno University of Technology, Czech Republic ˇedivy´, Brno University of Technology, Czech Republic Matu ´ ˇs S

IIenia Serra, University of Antwerp, Belgium Antonı´n Sojka, Brno University of Technology, Czech Republic Pierluigi Stipa, Universita` Politecnica delle Marche, Italy Kavipriya Thangavel, Universita¨t Leipzig, Germany M. Tseytlin, West Virginia University, USA Floriana Tuna, University of Manchester, UK Bolin Wang, University of Leeds, UK J. L. Wort, University of St Andrews, UK

ISBN: 978-1-83916-171-1 PDF eISBN: 978-1-83916-253-4 EPUB eISBN: 978-1-83916-317-3 DOI: 10.1039/9781839162534 ISSN: 1464-4622 A catalogue record for this book is available from the British Library r The Royal Society of Chemistry 2021 All rights reserved Apart from fair dealing for the purposes of research for non-commercial purposes or for private study, criticism or review, as permitted under the Copyright, Designs and Patents Act 1988 and the Copyright and Related Rights Regulations 2003, this publication may not be reproduced, stored or transmitted, in any form or by any means, without the prior permission in writing of The Royal Society of Chemistry or the copyright owner, or in the case of reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency in the UK, or in accordance with the terms of the licences issued by the appropriate Reproduction Rights Organization outside the UK. Enquiries concerning reproduction outside the terms stated here should be sent to The Royal Society of Chemistry at the address printed on this page. Whilst this material has been produced with all due care, The Royal Society of Chemistry cannot be held responsible or liable for its accuracy and completeness, nor for any consequences arising from any errors or the use of the information contained in this publication. The publication of advertisements does not constitute any endorsement by The Royal Society of Chemistry or Authors of any products advertised. The views and opinions advanced by contributors do not necessarily reflect those of The Royal Society of Chemistry which shall not be liable for any resulting loss or damage arising as a result of reliance upon this material. The Royal Society of Chemistry is a charity, registered in England and Wales, Number 207890, and a company incorporated in England by Royal Charter (Registered No. RC000524), registered office: Burlington House, Piccadilly, London W1J 0BA, UK, Telephone: þ44 (0) 20 7437 8656. Visit our website at www.rsc.org/books Printed in the United Kingdom by CPI Group (UK) Ltd, Croydon, CR0 4YY, UK

Preface DOI: 10.1039/9781839162534-FP007

The topics described in the current Volume 27 of the EPR Specialist Periodical Report Series have been selected to reflect particularly exciting and timely examples of the applications and developments in EPR spectroscopy. We have again aimed to reflect the widespread applications of EPR in chemistry and the cognate fields of physics, material science, biology, and medicine – and to provide updates for specialists as well as overviews for non-experts who may wish to better understand the scope of the technique. We have also intended to balance the different types of articles in this volume from relatively well-established fields to the latest instrument developments, in order to demonstrate not only the diversity of research fields in which EPR is used but additionally the wealth of information that can be extracted from the advanced pulsed capabilities. This information includes not just the simple detection and quantification of a free radical or paramagnetic ion, but also the detailed insights into the structure, conformation and dynamics of the spin system on length/time scales not easily accessible by other techniques. For all these reasons, EPR has and will continue to be the most powerful technique to inform, study and interrogate paramagnetic species in almost any sample system. In the current Volume of this SPR series, we have commissioned a diverse but exciting series of Chapters that illustrate and exemplify some of the current applications and developments of EPR. In Chapter 1, Murphy and co-workers provide an overview on the applications of EPR to examine open-shell paramagnetic species of relevance to heterogeneous, homogeneous and enzymatic catalysis, giving recent examples which best demonstrate the power of the technique to uncover complex reaction pathways. In Chapter 2, Bode and co-workers offer a timely perspective on the investigation of biomolecular binding events, by comprehensively showing the multitude of ways in which EPR can detect and quantify interactions, whilst intimately coupling structural information and binding events within the biological structural context. EPR has long been used to study membrane proteins including investigations of conformation, folding, oligomerisation and dynamics, and this theme is picked up in Chapter 3 by Pliotas, who focuses on the applications of pulsed EPR in this area, coupled with experimental consideration and supporting computational tools, including illustrative work on mechanosensitive ion channels. Nitroxides (as spin labels) and nitrones (as spin traps) have a long history in the field of EPR over many decades, so Stipa provides a comprehensive review covering their most recent applications for EPR spectroscopy in Chapter 4. Another incredibly important application area of EPR, lies in the field of quantum computing, so in Chapter 5 Tuna gives an overview of the latest advances in the design and testing of molecular electron spin systems with Quantum Information Processing (QIP) attributes, thereby highlighting the tremendous progress made in electron spin manipulations driven by pulse EPR spectroscopy. Finally, in Electron Paramag. Reson., 2021, 27, vii–viii | vii  c

The Royal Society of Chemistry 2021

Chapters 6 and 7, attention is focussed on the development and instrumentation aspects of EPR. In Chapter 6, Tseytlin presents the latest developments in CW rapid scan EPR, highlighting the recent practical progress that has been achieved, complemented by the important algorithms and instrument developments that enable measurement of undistorted EPR spectra with enhanced sensitivity. Volume 27 is then nicely rounded off in Chapter 7, as Neugebauer discusses the latest developments in high-frequency EPR with a special focus on experiments in frequency domain compared to traditional field domain EPR, highlighting the possibility of accessing very short relaxation times by implementing frequency rapid scans. From these excellent series of Chapters, we hope that both the expert EPR practitioner and novice user will value these timely reviews, offering a broad perspective on the latest developments in the field. Finally, we are most indebted to all of our reporters for their excellent, prompt and efficient cooperation in the production of this Volume, and the staff at the Royal Society of Chemistry for their continued and professional editorial support. Bela E. Bode (St Andrews), Victor Chechik (York) and Damien M. Murphy (Cardiff)

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Author biographies DOI: 10.1039/9781839162534-FP009

Katrin Ackermann obtained a degree in biochemistry from the Goethe University in Frankfurt (DE), where she prepared her thesis on liquid-state protein NMR. For her postgraduate studies she worked on diurnal rhythms in human post-mortem tissues at the Anatomy in Frankfurt. She continued to work in the field of human chronobiology during two postdoctoral stays at the University of Surrey (UK) and at the Erasmus University in Rotterdam (NL), before joining the University of St Andrews in 2012 and starting to work with EPR. Her projects in the Bode group are centred on EPR applications for structural biology.

Bela E. Bode received his PhD from the Goethe University in Frankfurt working on quantitative aspects of nanometre distance measurements by pulse electron paramagnetic resonance with Prof. Schiemann and Prof. Prisner. He joined Prof. Matysik at Leiden University exploring optical methods in NMR first as a Humboldt-Fellow later as Marie-Curie Fellow. In 2011 he moved to St Andrews to start his independent career. Bela’s research involves methodology and applications of EPR spectroscopy with special interest in biomedical science and catalysis. Outside the lab Bela loves to explore the Kingdom of Fife and the rest of Scotland.

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Maruan Alberto Bracci is a PhD student enrolled in a joint project between the University of Zaragoza and Antwerp, under the H2020-MSCA ‘‘PARACAT’’ program. He received a Master Double Degree in Chemistry and Advanced Chemical Methodologies from the University of Camerino, Italy, and the University of Catamarca, Argentina. His research interests are focused on the development and the optimization of methods for trapping and stabilizing short-lived reaction intermediates of peroxidases and other heme enzymes, using hyperfine EPR techniques to understand the structure-function relations in these systems.

Paolo Cleto Bruzzese is a PhD student in the EPR group at the University of Leipzig currently involved in a Marie Sklodowska Curie action called PARACAT as an early stage researcher. He obtained his Master’s degree at the University of Torino in Chemistry in 2018. His research interests focus on the determination of geometrical and electronic structure of reactive Cu(II) ions in zeolites by combining EPR techniques and DFT computations on complex models. He is particularly interested in the characterization of Cu species responsible for the methane to methanol conversion process (MTM) in zeolites materials.

Victor Chechik is a Reader at the University of York (UK). After completing PhD studies in physical organic chemistry in Russia in 1993, he was a postdoc in the groups of Charles J. M. Stirling (University of Sheffield) and Richard M. Crooks (Texas A&M University), working on self-assembled monolayers and monolayer-coated nanoparticles. He only discovered the power of EPR spectroscopy when he started at York in 1999. His research interests have since included free radical chemistry, detection of shortlived radical intermediates, mechanisms of radical reactions, stable free radicals as labels and probes for supramolecular assemblies, and of course EPR spectroscopy.

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Antonino Famulari obtained his Bachelor’s and Master’s degree in Chemistry at the University of Messina, Italy. Currently, he is undertaking his PhD as part of the, Marie Sklodowska-Curie Actions funded, project PARACAT as an early stage researcher at the University of Zaragoza. His research interest focuses on understanding the reaction mechanism and the nature of reactive intermediates of cytochromes P450 in two bacterial model enzymes: the CYPBM3 and the CYP116B5.

David Fioco is currently part of the Cardiff University EPR group and PARACAT programme, a Horizon 2020 project funded by a Marie Skłodowska-Curie grant agreement. He obtained his Bachelor’s degree in ` La Sapienza di Chemistry at ‘‘Universita Roma’’ and his Master’s degree in Chemistry ` di Pisa’’. Within the from ‘‘Universita PARACAT project he is investigating the photochemistry of Cr based complexes of relevance for olefin oligomerization.

Andrea Guidetti is a PhD student at the BIMEF group of the University of Antwerp since 2019, as a member of the EU-funded PARACAT project. He obtained his master’s degree in Chemistry at the University of Padua in 2017. His current research interests involve the use of EPR and other spectroscopic methods to gain mechanistic insight of photocatalytic processes which employ earth-abundant metal complexes and organic dyes as photosensitizers, in collaboration with the ORSY group at the University of Antwerp.

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Andrew Hartley is a post-doctoral research associate in the Astbury Centre for Structural Molecular Biology at the University of Leeds. He graduated from the Liverpool with a degree in Genetics, and completed his PhD at Cardiff University in 2010, in the laboratory of Dafydd Jones. He then moved to ´chal Birkbeck to work with Amandine Mare as a post-doc working on cytochrome c oxidase, where he solved the structure of respiratory supercomplexes in yeast mitochondria by cryo-EM. In 2019 he moved to the lab of Christos Pliotas at Leeds University, to characterise mechanosensitive ion channels by Pulsed EPR ad CryoEM.

Dr Oleksii Laguta obtained his MSc diploma in physics at the National University of Kyiv (Ukraine) in 2013. In 2016, he received PhD in Lasers, Molecules, Atmospheric Radiation from the University of Lille (France). After that, he moved to Stuttgart to work as a postdoctoral research fellow in the group of Petr Neugebauer (AG van Slageren, Stuttgart University) on the development of frequency domain rapid-scan HFEPR. Since 2019, he is a junior researcher at the Central European Institute of Technology in Brno, Czech Republic. Currently, he studies fast spin dynamics at (sub)millimetre wave range using rapid-scan EPR with his own project under Marie Sklodowska Currie Action – IMPROVE program.

Benjamin J. Lane obtained a BSc (Hons) in Biochemistry from the University of St Andrews in 2018. Ben then joined the Wellcome Trust PhD Programme at the Astbury Centre for Structural Molecular Biology within the University of Leeds. Following rotation projects investigating various aspects of membrane proteins, Ben joined the groups of Christos Pliotas and Stephen Muench. His project focuses on understanding the structural basis for functional multimodality in mechanosensitive ion channels using cryo-electron microscopy and electron paramagnetic resonance (EPR) spectroscopy. xii | Electron Paramag. Reson., 2021, 27, ix–xx

Yu-Kai Liao studied Mathematics and Physics at the National Tsing Hua University, Taiwan, followed by a Master’s degree in Physics at the University of Leipzig, Germany, working on EPR investigations on paramagnetic ions incorporated into metal sites in metal-organic frameworks (MOFs). He is currently undertaking his PhD study at University of Turin, focussing on the mechanism of the Phillips catalyst by studying the role of Cr species as active sites under different olefin polymerization conditions.

Yue Ma received her BSc degree in Biochemistry from the University of Bristol in 2017. Since then, she has been a PhD student under the supervision of Christos Pliotas studying the structural and dynamic behaviour of a challenging eukaryotic mechanosensitive membrane protein. Her project utilizes site-directed spin labelling combined with electron paramagnetic resonance (EPR) spectroscopy to investigate the in-lipids structural transitions of membrane proteins in response to external stimuli. She aims to reveal the universal gating mechanism that potentially exists among mechanosensitive channels and the role that lipids play during channel gating.

Dr Andriy Marko is currently a senior researcher at the Central European Institute of Technology (CEITEC) in Brno (Czech Republic). Also, he is a fellow of Marie Sklodowska Currie Action – IMPROVE program with an own project related to the theory of frequency rapid scan Electron Paramagnetic Resonance (EPR). Generally, his scientific interests are focused on the theory of magnetic resonance and simulation and interpretation of experimental data. Andriy Marko has studied physics at the Ivan Franko Lviv University (Ukraine) and graduated in 1998 with diploma thesis devoted to the description of relativistic particle interactions. In 2005, he obtained his PhD from the University of Saarland (Germany) with the thesis related to Nuclear Magnetic Resonance (NMR) applications to the studies of liquid diffusion Electron Paramag. Reson., 2021, 27, ix–xx | xiii

through porous media. In 2006, Andriy Marko joined the EPR research group of prof. Prisner as a postdoc at the Goethe University Frankfurt (Germany). There, his research work was focused on the theoretical analysis and interpretation of pulsed dipolar EPR data for the determination of structure and dynamics of complex biological macromolecules.

Daniel O. T. A. Martins obtained his BSc (Hons) in Chemistry from Fluminense Federal University (2017) and MSc from the ˜o Paulo, Brazil (2020). He was University of Sa awarded a ‘Science without Borders’ exchange scholarship, studying for one year at the University of Manchester (UK), and did research placements at the UK National EPR Facility, and University of Ottawa (Canada). He was awarded a University of Manchester Presidential Scholarship and started his PhD under the supervision of Dr Floriana Tuna and Professors Eric J. L. McInnes and Richard E. P. Winpenny, working on quantum information processing with molecular spin systems.

Eufemio Moreno-Pineda obtained his BSc in Chemistry from the University of Panama. He then moved to Manchester (2011) to pursue MSc and PhD studies on molecular nanomagnets, supervised by Dr Floriana Tuna, and Professors Eric. J. L. McInnes and Richard E. P. Winpenny. He subsequently completed a postdoctoral stay at the National EPR Facility in Manchester, before moving to Karlsruhe (2015), Germany, to do postdoctoral studies on SMMs for Quantum technologies at the Institute of Nanotechnology in KIT under the supervision of Professors Mario Ruben and Wolfgang Wernsdorfer. Currently he is lecturer at the University of Panama.

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Damien M. Murphy is Professor of Physical Chemistry at Cardiff University. After obtaining his Chemistry degree from the Dublin Institute of Technology in 1990, he moved to the University of Turin to undertake his PhD in EPR of surface defects on polycrystalline materials. Following successive post doctoral appointments at the ´ P. et M. IST, Lisbon (1994) and Universite Curie, Paris (1995), he was appointed to a permanent academic position in Cardiff University, School of Chemistry, where he is currently a Full Professor and Head of School. He is a Fellow of the RSC (FRSC), Fellow of the Learned Society of Wales (FLSW) and a former Royal Society Wolfson Research Award holder. His research interests are broadly focused on the applications of advanced EPR methods for catalysis research.

Dr Petr Neugebauer is research group leader and founder of the Magneto-Optical and THz Spectroscopy (MOTeS) group at the Central European Institute of Technology (CEITEC), Brno, Czech Republic. The group focuses on the development of High Frequency Electron Paramagnetic Resonance (HFEPR) spectroscopy, especially frequency rapid scan above 100 GHz (ERC starting grant), HFEPR applications to molecular magnetism and thin film materials, amongst others. He received his diploma in Physical Engineering in 2005 at Brno University of Technology, Czech Republic, and in 2010 obtained a PhD degree (Marie Curie fellowship) in Physics of Condensed Matter and Radiation at Grenoble High Magnetic Field Laboratory (GHMFL) and Grenoble University, France, working under the supervision of Dr AnneLaure Barra on the development of HFEPR. After the PhD, he joined the group of Prof. Thomas F. Prisner for a two-year postdoctoral stay (Stipendium: Center of Excellence Frankfurt) at the Center for Biomolecular Magnetic Resonance at Goethe University, Germany. In Frankfurt, he was focused on pulsed HFEPR and liquid state Dynamic Nuclear Polarization (DNP). Consequently, he joined Prof. Joris van Slageren at University of Stuttgart, Germany, where he continued in the development of HFEPR spectroscopy for an additional 5 years (German priority program SPP1601: New Frontiers in Sensitivity for EPR Spectroscopy: From Biological Cells to Nano Materials). He is a member of the International EPR ¨rttemberg. Society and Elite Program of Baden-Wu

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Maria Oranges received her Bachelor and Master degrees in Chemistry from the University of Calabria in Italy. For her final project, she characterised spin labelled DHPC bilayers studying the phase behaviour and flexibility by CW-EPR, and polarity profiles and water accessibility by three-pulse ESEEM. In September 2016 she moved to Scotland joining the group of Dr Bela Bode where she has just completed her PhD studies. Her research was related to distance measurement-based EPR methods for studying multimerisation equilibria and orientational correlations between spin centres. Now, she will carry on doing more EPR research as postdoc at the Weizmann Institute.

Christos Pliotas obtained a BSc in Physics at the University of Athens and an MSc under the supervision of DJ Lurie at the University of Aberdeen. He then completed a PhD at Aberdeen specialising in membrane proteins, before moving to St Andrews with James Naismith FRS and Olav Schiemann. There, he employed PELDOR/DEER on the seven-spin channel MscS addressing its debated conformation. He was the recipient of a Royal Society of Edinburgh Fellowship and a principal investigator at St Andrews. Christos moved with his group to the Astbury Centre at the University of Leeds, where he applies pulsed EPR methodologies on complex membrane proteins.

Leonora Podvorica is a PhD student enrolled in a joint PhD program between the University of Turin and Antwerp within the PARACAT project. She obtained her Bachelor degree in Chemical Engineering and her Master degree in Analytical and Environmental Chemistry at the University of Pristina ‘‘Hasan Prishtina’’, Kosovo including 5 months at the University of Umeå, Sweden. The main focus of her current research comprises the exploring of the paramagnetic active species in Ziegler-Natta catalysts (role of activator, nature of the metal-alkyl bond) and the role of coordinated Lewis bases. xvi | Electron Paramag. Reson., 2021, 27, ix–xx

Seyedeh Fardokht Rezayi is a current PhD student in the EPR group at Cardiff University and one of the early stage researchers in PARACAT project. She obtained her Bachelor and master degree in Chemistry from Iran. Currently, her research interest focuses on the application of earth abundant metals for small molecule activation and C–C cross coupling. She is interested in characterizing the paramagnetic states, spin transitions and the effect of coordinated ligands on the catalytic activity of the paramagnetic metal centres.

Dr Vinicius Santana received his PhD in ˜o Paulo applied physics at the University of Sa (Brazil) in 2016 working with exchange coupled molecular compounds using EPR spectroscopy supervised by Prof. O. R. Nascimento. Currently, he is a Junior Research Fellow at the Central European Institute of Technology of the Brno University of Technology (Brno/ Czechia) and a team member of the Magnetooptical and THz spectroscopy group led by P. Neugebauer, where he participated in the setup of a HFEPR spectrometer and works with applications of this technique for the investigations of molecular spin systems and solid-state magnetic materials. In 2018, he obtained the prestigious individual grant Marie SklodowskaCurrie Action – IMPROVE. He is a member of the international EPR society. ´ˇs ˇ Matu Sedivy´ studied microelectronics at the Faculty of Electrical Engineering and Communication Brno University of Technology (FEEC BUT), Czech Republic, and obtained master’s degree in 2017. Currently, he is a PhD student at FEEC BUT and member of a magneto-optical and terahertz spectroscopy research group at the CEITEC BUT. He cooperates on technical improvements of a custom build HFEPR spectrometer and he is a main developer of automation software for the HFEPR spectrometer. His research is focused on a study of semiconductors doped by paramagnetic centres via frequency domain rapid-scan HFEPR technique. Electron Paramag. Reson., 2021, 27, ix–xx | xvii

Ilenia Serra is a PhD student working in a joint project between the University of Antwerp and the University of Zaragoza, in the H2020 Marie Skłodowska Curie Action ‘‘PARACAT’’. She obtained her Master degree in Industrial Biotechnology at the University of Modena and Reggio Emilia, Italy (2018). During the preparation of her Master’s thesis, she spent three months as a training student at the University of York, where she used EPR spectroscopy to study copper-enzymes. Her research interest within the PARACAT program focuses on the spectroscopic investigation of chlorite dismutases and heme-containing peroxidases.

Antonı´n Sojka received his BSc degree from the Brno University of Technology (Brno, Czech Republic) in 2015. He continued his study at the same university, where he obtained in 2017 an MSc degree in physical engineering. Since 2017, he is a Ph.D. student at Central European Institute of Technology in Brno, where he is developing a novel Terahertz high field Electron Paramagnetic Resonance Spectrometer under the leadership of Petr Neugebauer. His research is focused on developing frequency-domain rapid-scan EPR to study short relaxation times (Bns), which are not able to be observe by conventional pulse EPR spectrometers.

Pierluigi Stipa graduated at Bologna University with a thesis on the synthesis of stable indolinic nitroxides from nitrones under the guidance of Prof. Lucedio Greci in ` Politecnica 1983, then joined Universita delle Marche. Among the founders of G.I.R.S.E (Italian Federation of EPR spectroscopists) in 1987, spent his postdoc with ´ des the S.R.E.P (Structure et Reactivite Especes Paramagnetiques) research group directed by Prof. Paul Tordo at Marseilles University. Currently is full professor of Chemistry, and his scientific interests have always been focused on organic free radical chemistry, EPR Spin Trapping, Nitroxide synthesis and applications as antioxidants in polymers and biological systems. xviii | Electron Paramag. Reson., 2021, 27, ix–xx

Kavipriya Thangavel, is one of the early stage researchers in the PARACAT- MSCA program, and currently undertaking a joint doctoral program on the EPR investigations of high spin bimetallic MOFs at the Universities of Leipzig, Germany and Cardiff, UK. She obtained her MSc degree in Physics from the Bharathiar University (2016), India. Later, she graduated her MPhil in Physics from the University of Madras (2017), India. Afterwards, she joined the Department of Physics, Indian Institute of Technology Madras (IITM), India as a Junior Research Fellow and worked in the field of low temperature magnetism (2018–2019).

Mark Tseytlin, currently an Assistant Professor of Biochemistry at West Virginia University, has received a Ph.D. degree in physico-mathematical sciences from the Russian Academy of Sciences in 2002, where he conducted independent research until immigration to the US in 2008. In America, he worked in several leading EPR groups at the U. of Denver, Dartmouth College, and the U. of Chicago (as Visiting Scholar). Dr Tseytlin’s area of expertise is in the development of novel technologies for EPR imaging and spectroscopy, including theory, software, and instrumentation.

Floriana Tuna obtained her PhD in 1997 from the Physical Chemistry Institute of the Romanian Academy in Bucharest. Following a DAAD fellowship at the University of Heidelberg (Germany), a CNRS postdoctoral stay at ICMCB Bordeaux (France), and a Marie Curie Individual Fellowship at the University of Warwick (UK), she joined the University of Manchester Molecular Magnetism team, and later the EPSRC UK National EPR Facility progressing to Senior Research Fellow. She was awarded a Leverhulme Trust (UK) Fellowship and the Romanian Academy ‘Ilie Murgulescu’ Prize for excellence in research, publishing to date over 300 high-impact papers on magnetochemistry and EPR. Electron Paramag. Reson., 2021, 27, ix–xx | xix

Bolin Wang is a PhD student under the supervision of Christos Pliotas in the Faculty of Biological Sciences at the University of Leeds. He studied Biotechnology and Structural biology at Zhengzhou University and the Chinese Academy of Sciences, where he received his bachelor’s and master’s degrees. His research focuses on the gating mechanisms of mechanosensitive ion channels using a combination of methodologies including cryo-electron microscopy (cryo-EM), electron paramagnetic resonance (EPR) spectroscopy, and molecular dynamic (MD) simulations.

Joshua L. Wort received his Master of Science in Biochemistry in 2016 from University College London. Here, while working with Dr C. M. Kay, he applied EPR to investigate both the catalytic cycle of the chaperone Hsp90, and later the mechanism of polymerisation in a-1 antitrypsin. Subsequently, he took a summer internship at the CNRS in Marseilles studying the Molybdate enzyme Arsenite oxidase via CWEPR. He is currently undertaking his PhD at the University of St Andrews with Dr B. E. Bode, wherein quantitative pulse dipolar EPR methods are benchmarked and applied to biological model systems.

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CONTENTS

Cover

Preface

vii

Bela E. Bode, Victor Chechik and Damien M. Murphy Author biographies

ix

Paramagnetic species in catalysis research: a unified approach towards (the role of EPR in) heterogeneous, homogeneous and enzyme catalysis

1

Maruan Bracci, Paolo Cleto Bruzzese, Antonino Famulari, David Fioco, Andrea Guidetti, Yu-Kai Liao, Leonora Podvorica, Seyedeh Fardokht Rezayi, IIenia Serra, Kavipriya Thangavel and Damien M. Murphy 1 Introduction 2 Heme enzymes as biocatalysts 3 Catalysts for polymerisation 4 Microporous systems 5 Homogeneous systems for small molecule activation 6 Summary and perspectives Acknowledgements References

1 2 15 24 30 37 38 38

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The Royal Society of Chemistry 2021

Advanced EPR spectroscopy for investigation of biomolecular binding events Joshua L. Wort, Maria Oranges, Katrin Ackermann and Bela E. Bode 1 Introduction 2 Characterising binding equilibria via EPR 3 Case studies 4 Summary Abbreviations Acknowledgements References Using pulsed EPR in the structural analysis of integral membrane proteins Andrew M. Hartley, Yue Ma, Benjamin J. Lane, Bolin Wang and Christos Pliotas 1 2 3 4 5

Introduction PELDOR distances measurements on membrane proteins Sample preparation for EPR Electron spin echo envelope modulation (ESEEM) Combining molecular dynamics simulations with pulsed EPR Acknowledgements References

Recent contributions of EPR to nitrone and nitroxide chemistry

47

47 49 57 65 66 67 67 74

74 76 83 90 94 98 98

109

Pierluigi Stipa 1 Introduction 2 Nitrones 3 Nitroxides 4 Concluding remarks Acknowledgements References

Molecules as qubits, qudits and quantum gates Eufemio Moreno-Pineda, Daniel O. T. A. Martins and Floriana Tuna 1 2 3 4 5

Introduction Qubits Molecular electron spin qubits Scaling up electron spin qubits into MOFs Quantum gates

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109 109 118 138 140 140

146

146 148 154 159 161

6 Multilevel qubits (qudits) 7 Conclusions and perspectives Acknowledgements References

Continuous-wave rapid scan EPR

168 181 182 182

188

Mark Tseytlin 1 Introduction 2 Underlying concepts 3 Instrumentation 4 Summary and future directions References

188 190 204 211 211

High-frequency EPR: current state and perspectives ˇedivy´, Oleksii Laguta, Andriy Marko, ´ˇs S Antonı´n Sojka, Matu Vinicius T. Santana and Petr Neugebauer

214

1 Introduction 2 Instrumentation 3 Theoretical basics 4 Applications 5 Frequency rapid scan EPR at high magnetic fields 6 Conclusion Acknowledgements References

214 218 226 229 238 243 245 245

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Paramagnetic species in catalysis research: a unified approach towards (the role of EPR in) heterogeneous, homogeneous and enzyme catalysis Maruan Bracci,a Paolo Cleto Bruzzese,b Antonino Famulari,a David Fioco,c Andrea Guidetti,d Yu-Kai Liao,e Leonora Podvorica,e Seyedeh Fardokht Rezayi,c IIenia Serra,d Kavipriya Thangavelb and Damien M. Murphy*c DOI: 10.1039/9781839162534-00001

Paramagnetic (open-shell) systems, including transition metal ions, radical intermediates and defect centres, are often involved in catalytic transformations. Despite the prevalence of such species in catalysis, there are relatively few studies devoted to their characterisation, compared to their diamagnetic counterparts. Electron Paramagnetic Resonance (EPR) is an ideal technique perfectly suited to characterise such reaction centres, providing valuable insights into the molecular and supramolecular structure, the electronic structure, the dynamics and even the concentration of the paramagnetic systems under investigation. Furthermore, as EPR is such a versatile technique, samples can be measured as liquids, solids (frozen solutions and powders) and single crystals, making it ideal for studies in heterogeneous, homogeneous and enzyme catalysis. Coupled with the higher resolving power of the pulsed, higher frequency and hyperfine techniques, unsurpassed detail on the structure of these catalytic centres can be obtained. In this Chapter, we provide an overview to demonstrate how advanced EPR methods can be successfully exploited in the study of open-shell paramagnetic reaction centres in heterogeneous, homogeneous and enzymatic catalysts, including heme-based enzymes for use in biocatalysts, polymerisation based catalysts, supported microporous heterogeneous catalytic centres to homogeneous metal complexes for small molecule actions.

1

Introduction

Within the chemical sciences, catalysis remains a vitally important field of research. Indeed, continued developments in new or improved catalysts is essential to meet the future challenges in delivering the raw materials or products underpinning fuels, water and the environment, healthcare, energy, food, and resources sustainability. In all cases, catalysts will be necessary since they offer an extremely energy efficient means of providing these valuable chemicals. Despite their phenomenal success, further enhancements and improvements in their efficiency requires a greater understanding of how they operate, and more a

Department of Condensed Matter Physics, Faculty of Sciences, University of Zaragoza, Calle Pedro Cerbuna 12, 50009, Zaragoza, Spain b Felix Bloch Institute for Solid State Physics, Universita¨t Leipzig, Linne´str. 5, 04103 Leipzig, Germany c School of Chemistry, Main Building, Cardiff University, Cardiff CF10 3AT, UK. E-mail: MurphyDM@cardiff.ac.uk d BIMEF Laboratory, Department of Chemistry, University of Antwerp, Belgium e Department of Chemistry, University of Turin, Via Giuria 9, 10125-Torino, Italy Electron Paramag. Reson., 2021, 27, 1–46 | 1  c

The Royal Society of Chemistry 2021

specifically on the mechanistic pathways responsible for converting reactants into products. This inevitability requires the application of advanced techniques that can probe the catalytic reaction, ideally with spatial or temporal resolution, under reaction conditions. However, another equally insightful direction for understanding reaction profiles, is to detect, characterize and monitor the various reaction intermediates involved in the step-wise catalytic cycle. Indeed, chemical reactions are ultimately controlled by two fundamental parameters, namely energy (including free and activation energy) and angular momentum (involving the spin) of the reactants and products. As a consequence of this, reactivity patterns often depend critically on the presence of paramagnetic (open-shell) intermediates. Elucidating the role and influence of such open-shell intermediates in any catalytic cycle is presently one of the most challenging endeavours in this field of research, both from an experimental and theoretical perspective. The rewards for undertaking such research endeavours are considerable if the many successful (but also generally expensive and toxic) noble metal based catalysts can be replaced by (generally cheap and non-toxic) earth abundant metals. Certainly, in the case where paramagnetic centres are involved, Electron Paramagnetic Resonance (EPR), and the associated advanced range of pulsed, hyperfine or high frequency techniques, are without doubt essential for investigating and fully interrogating the paramagnetic component of the reaction system. Nevertheless, the technique is still largely underexploited in the field of catalysis research, since it often requires highly specialised equipment and expertise to collect and interpret the data. In this Chapter, we will therefore illustrate the outstanding success of EPR to uncover new chemical secrets in the field of catalysis, by focusing more broadly on homogeneous, heterogeneous and enzymatic based catalysts. Within this broad domain of catalysis research, we will cite specific examples ranging from heme-based enzymes for use in biocatalysts, to homogeneous and supported polymerisation systems (including Ziegler-Natta, Philips and oligomerisation based catalysts), to microporous heterogeneous systems (such as zeolites and metal organic frameworks) to homogeneous complexes active in small molecule actions (such as homogeneous catalytic centres, systems for catalytic alcohol oxidation to C–C cross coupling). Despite the varying nature of the catalytic active site in all these systems, the analytical approach offered by EPR to interrogate the active species, remains unifying, simple and similar; in all cases, we seek to probe the nature of the local paramagnetic system and it’s longer range interactions with the surrounding nuclei through the spin Hamiltonian and where possible compare this to computational data. Through this approach, detailed insights into the mechanism and active intermediates involved in the reaction cycle can be examined with unsurpassed detail.

2

Heme enzymes as biocatalysts

In recent times, the increasing demand for a reduction in the environmental impact of industrial processes has resulted in the search for 2 | Electron Paramag. Reson., 2021, 27, 1–46

greener alternative processes. The field of biocatalysis has attracted increasing popularity, particularly with the advent of modern biotechnology. The term biocatalysis refers to the use of enzymes, or entire microorganisms, to perform industrially relevant chemical transformations, an activity whose origins dates back to the beginning of the 20th century. Biocatalysis is generally considered as sustainable process because of their many distinctive characteristics, including non-toxicity, mild reaction conditions, compatibility with aqueous solvents, and ability to generate pure products due to their high (enantio-) selectivity. However, some challenges remain with respect to the widespread utilisation of these biocatalysts, including their stability and reusability, the costs associated with downstream processing, and the time-to-market pressure which often favours more consolidated methods.1,2 Within this field, a well-known and diverse group of biocatalysts is based on the heme enzymes. They belong to the larger class of heme proteins, which are widespread biomolecules in nature, holding a diverse range of functionalities. For example, the versatility of the heme group is often exploited in activities such as oxygen storage and transport, electron transfer, signal transduction and catalysis.3 For the purpose of this section, the following discussion will focus on the latter aspects of their function. In the IUPAC Compendium of Chemical Terminology, ‘‘heme’’ is defined as a macrocyclic system containing an iron centre coordinated to a porphyrin ring which acts as a tetradentate ligand, and to one or two additional axial ligands.4 The reactivity of heme enzymes is governed both by the chemistry at the heme iron centre, and the interaction of the prosthetic group with the protein moiety. Biological redox reactions involve electron transfer processes, for which efficiency is optimised when the free energy driving force (DG) is maximised and the reorganisation energy (l) is minimised, in accordance with Marcus’s theory.5 In heme systems, the electron delocalisation over the porphyrin ring reduces the need for re-ordering in the local structure. As a result, the thermodynamics is defined by the redox potential of the couple donor-acceptor, which in the case of heme enzymes, is regulated by the protein matrix.6 Among the representative heme-types found in biology (labelled a, b, c, d1), the best studied is probably the heme b (iron protoporphyrin IX), common to the oxygenase and peroxidase families (Fig. 1). These two broad classes of heme enzymes, which oxidise substrates utilising dioxygen and hydrogen peroxide respectively,7 will be discussed later. The iron centre in heme systems can be found in various oxidation states, the most common of which are Fe21, Fe31 and Fe41. The first two states are commonly found in two different spin configurations, either high-spin or low-spin, depending on the distribution of electrons in the d-orbitals, whose degeneracy is removed by the ligand field splitting. The Fe41 oxidation state is of notable importance for the catalytic mechanism of many heme enzymes, existing in transient states, which are formed during the turnover cycle upon binding of the activator substrate. Indeed, the key intermediates in the reaction cycle are often described as Fe41-oxo species, known as Compound I and Compound II. The former stores two oxidising equivalents, one on the iron, and one in the form of a free radical. Electron Paramag. Reson., 2021, 27, 1–46 | 3

Fig. 1 Schematic structure of heme b. Table 1 Electronic configurations of iron in heme systems.

High spin Low spin

Fe21

Fe31

Fe41

S¼2 S¼0

S ¼ 5/2 S ¼ 1/2

— S¼1

After one-electron reduction, the free radical is lost, resulting in the formation of Compound II.8 A summary of the variable oxidation and spin states occurring in heme system are listed in Table 1. In heme proteins, the metal centre commonly adopts an pseudo octahedral coordination mode, with four equatorial nitrogen atoms from the porphyrin ring and a protein residue as proximal axial ligand in the fifth position, typically a histidine, cysteine or tyrosine. The sixth axial position can either be occupied by another endogenous ligand, an external molecule (such as water), or even left free (uncoordinated) to promote substrate binding. Coordination by the porphyrin ring places the iron d-orbitals in an intermediate ligand field, close in energy to the ‘low-spin to high-spin’ transition, so that the spin state is sensitive to the nature of these axial ligands. A ‘‘strong’’ ligand will cause a splitting of the eg and t2g orbitals, larger than the pairing energy that is necessary to keep two electrons in the same orbital. Only the lower energy t2g orbitals will be occupied, leading to a low-spin configuration. Alternatively, a ‘‘weak’’ ligand will have an orbital energy separation small enough to prefer the occupancy of the eg orbitals, thus contributing to a high-spin configuration.9 Since almost all of these iron states are paramagnetic, EPR spectroscopy is one of the most suitable techniques for the investigation of heme-based systems. Moreover, even if proteins are large, complex molecules, the EPR characterisation method is still reliable as it focuses specifically on the paramagnetic active site, where the unpaired electrons reside. In metalloproteins possessing iron centres with multiple unpaired electrons (S41/2), the zero-field splitting (ZFS) term can be much larger than the X-band microwave quantum. In the case of high spin Fe31, the observed EPR spectrum is derived exclusively from transitions within the Kramers doublets, and it can be treated as an effective S ¼ 1/2 system10 (Fig. 2). However, for a more accurate description of the 4 | Electron Paramag. Reson., 2021, 27, 1–46

Fig. 2 Illustrative continuous wave (CW) EPR spectra of high-spin Fe31 (S ¼ 5/2) heme based centres simulated using the Easyspins package, with g>effE6, g8effE2 for the axial case (left); gxeffE6.4, gyeffE5.2, gzeffE2 for the rhombic case (right).

spin system, two independent parameters denoted as the tetragonal zerofield splitting (D) and rhombic zero-field splitting (E) terms, can be derived from the principal values of the D tensor, which describe the zero-field splitting interactions in the spin Hamiltonian. The defined ratio Z ¼ E/D (with 0oZo1/3) is called the rhombicity term, and is commonly used in the simulations of X-band CW EPR spectra of heme proteins with high spin multiplicity since they depend, to a good approximation, on this single parameter.11 Another example of high-spin iron is Fe21 with S ¼ 2, characterised by four unpaired electrons. Despite being an EPR-active species in principle, very few examples of high spin ferrous heme have been reported in literature.12,13 The detection of this non Kramer ion is impeded by the large ZFS which removes the Dms ¼  1 levels above the accessible microwave energy i.e. the allowed transition. At X-band, only at very low applied magnetic fields can a broad structureless feature be detected. For these reasons it is generally assumed that the high-spin ferrous complexes are EPR silent at X-band.12 Low-spin Fe31 (S ¼ 1/2) is commonly found in heme structures possessing strong axial ligands. In contrast to the high-spin states, this spin state can be represented by a simpler spin Hamiltonian, in which the zero-field splitting terms are absent, and thus a more readily interpreted EPR spectrum (Fig. 3). The g-values for low-spin ferric heme proteins are very often interpreted with a crystal field model that correlates them to the relative energy splitting of the iron t2g orbitals,14,15 and therefore the corresponding spin distribution. How, and to what extent the electron system is affected by the axial substituents, can be related to the nature of the axial ligands and the active-site geometry.16–18 A different case of low-spin iron occurs in its reduced state (Fe21, S ¼ 0), although this species is not paramagnetic, having six paired electrons in the outer valence shell which fully occupy the t2g orbitals due to the large separation from the ligand field. It is clear that whilst iron heme proteins possess diverse and variable electron configurations that may be challenging to study, they nevertheless offer highly desirable application in modern catalysis. In the following sections, more Electron Paramag. Reson., 2021, 27, 1–46 | 5

Fig. 3 Illustrative CW EPR spectrum of a low-spin Fe31 (S ¼ 1/2) heme based centre simulated using the Easyspins package with gz ¼ 2.42, gy ¼ 2.25, gx ¼ 1.92.

specific examples will be presented to demonstrate their applicability and reaction versatility as aerobic oxidation catalysts, and importantly how EPR can be exploited to understand their reaction cycles. 2.1 Compound I in heme systems Although a great deal of uncertainty exists around the first reactive intermediate in heme-based systems, most of the literature reports concur that the catalytic activity starts with the species commonly (but not always) referred to as Compound I.19 For example, in peroxidases, Compound I is responsible for a diverse assortment of industrially relevant reactions including enantioselective epoxidation of olefins, oxidation of amines, alcohols and sulphides, as well as peroxidase-catalysed polymerisation of aromatic molecules. For this reason, peroxidases have historically received greater attention for their potential application in the field of biocatalysis.20 In P450s for example, vide infra, it performs oxygenation reactions, whilst in catalases, it facilitates peroxide disproportionation. This serves to defend aerobic organisms by breaking down toxic hydrogen peroxide into water and molecular oxygen.21 During the catalytic cycle, all these enzymes oxidise the iron above the ferric Fe(III) resting state to form Compound I, a high-valent iron(IV)–oxo intermediate8 (see Scheme 1 below). The formation of this intermediate occurs following the heterolytic cleavage of the substrate O–O bond, which leads to the storage of two oxidising equivalents, one that resides in iron(IV), and another one somewhere in the protein. Several

Scheme 1 6 | Electron Paramag. Reson., 2021, 27, 1–46

observations indicate that it could reside on the porphyrin ring, or in a tryptophan (Trp), tyrosine (Tyr) or cysteine (Cys) residue of the protein, more commonly in the form of a cationic free radical.7 In Scheme 1, R can be a hydrogen or an organic group, whereas the labels TT TT represent the porphyrin ring and proximal ligand (His, Tyr or Cys), with oxygen representing the sixth ligand. Numerous techniques have been used to unravel the complexities surrounding the characterisation of Compound I, but it remains a challenging task in part due to the transient nature of this intermediate and its correspondingly high reactivity. EPR plays a crucial role in characterising such intermediates, largely because both oxidising equivalents of Compound I form paramagnetic states readily detected by the technique. To date, several CW EPR spectra of Compound I with distinct features have been reported in the literature for different systems. They are usually described by a model consisting of two interacting spin systems, one from the heme iron (S ¼ 1) and one from a free radical (S ¼ 1/2). The spin distribution on the oxo-ferryl moiety is generally modelled by taking into account an almost purely axial zero field splitting, which is sensitive to the ligand environment. The main interaction between the iron and the free radical, is the so-called exchange interaction, a weak spin–spin interaction that is caused by the partial overlap of the wave functions of the two paramagnetic centres. This interaction varies in strength and sign, which is highly dependent on the electron distribution of both species. This ultimately determines the net spin state of Compound I.19,22–25 It should also be noted that, although the ZFS is very sensitive to the molecular structure, the magnitudes reported for Fe(IV) ¼ O in heme enzymes are usually much larger than the energy of the MW quantum (especially at X-band), thereby shifting the transitions outside the accessible magnetic field range.26 Whilst the oxo-ferryl moiety is EPR silent, the electronic levels of Fe(IV) affect the relaxation properties of the interacting radical species. CW EPR relaxation studies have therefore been used to obtain the ZFS parameters of Fe(IV) ¼ 0 in some enzymes.22,27 When the radical resides on the porphyrin ring, or on a residue close enough to the iron centre, then the EPR spectrum of Compound I appears broad and can be interpreted by considering the exchange interaction.28,29 On the other hand, if the radical resides on an amino acid (this intermediate is variously referred to as Compound ES, Compound I* or Compound-IB30–33), and is sufficiently remote from the iron centre, then no orbital overlap occurs. As a consequence, the exchange interaction is negligible and the shape of the EPR spectrum is dominated by the non-coupled organic radical contribution.30 Interestingly, the nature of the amino acid in which the radical is stored can be determined from the CW EPR spectrum assuming some of the characteristic hyperfine interactions can be resolved by suitable techniques. In most reported cases, the small hyperfine interactions between the electron spin and magnetic nuclei in Compound I, are completely unresolved in the CW EPR spectra. In these cases, more advanced hyperfine spectroscopies are required to resolve these small interactions. For example, CW and pulsed Electron Nuclear DOuble Resonance Electron Paramag. Reson., 2021, 27, 1–46 | 7

(ENDOR) spectroscopies have been used to fully characterize the location of the free radical and spin distribution on the active site in heme enzymes.34–36 The ENDOR technique, combined with isotopic substitutions of Compound I in Horseradish Peroxidase, has provided detailed insights into hyperfine couplings between the free radical and 1H, 14N nuclei which originate from the porphyrin ring, indicating that the ferryl moiety is not protonated. Using 17O labelling, it was found that the oxygen from the peroxide is transferred to the iron(IV)-oxo species where one of the oxidizing equivalent is stored.37,38 In addition to this information on spin-distribution, complimentary information on local structural aspects, can also be derived from the resolved hyperfine data. For example, using multi-frequency EPR and ENDOR, the 1H hyperfine coupling observed in a Trp radical-type Compound I of peroxidase, was used to calculate the dihedral angles of the aromatic radical and thus, with the aid of crystallographic structures, DFT and site directed mutagenesis, identify the exact position of the radical in the protein.39,40 It is known that a multitude of factors can tune the reactivity of Compound I. Such factors can include the nature and distance of the iron proximal ligand to the metal centre, which can be a histidine (as in peroxidases), a cysteine (as in P450s) or a tyrosine (as in catalase). Another important factor is the polarity of the protein cavity, to which the oxygen of Compound I is exposed, and where the reaction with the substrates can occur. This was determined by several amino acid residues, which were more or less conserved among the different proteins. The reactivity can also be influenced by the propionate groups of the heme, which are used to anchor this prosthetic group to the protein moiety. These are expected to destabilise the cationic radical hosted in the porphyrin if they are not involved in polar bonds. Finally, the network of hydrogen bonds that involves the entire active site, and its geometry, is also known to play a fundamental role that affects the reactivity.41–43 These factors appear to depend on where the radical is located, which is crucial for the reaction mechanism involving the intermediate. The power of EPR to characterise these heme-based systems is certainly enhanced by complementary QM/MM calculations. The ab initio calculation of the electronic density, confined to the active site, enables one to compute magnetic-resonance parameters including the g tensor, and A tensors for remote surrounding nuclei. Usually, several models are required to fully describe the spin system, taking into account different regions of the proteins, spin distributions, hydrogen bonds, etc. However, only by comparison with experimental data, such as EPR, is it possible to validate and determine the accuracy of the computed model. One of the standard outputs of the calculations are the hyperfine constants that can be directly compared with the experimental parameters obtained by advanced hyperfine techniques.44,45 It is clear that to understand the mechanism of these heme-based catalysts, it is fundamentally important to determine the electronic distribution, and the nature of the reactive intermediates. In the future, further studies involving hyperfine spectroscopies will be required to better understand the role of these paramagnetic spin states in the reactivity of 8 | Electron Paramag. Reson., 2021, 27, 1–46

compound I. The experimental results, coupled with theoretical calculations, will serve to clarify the nature of these intermediates. This endeavour remains challenging however, owing to the difficulties of isolating and stabilising Compound I on such short timescales. In these cases, a rapid freeze-quench approach is required. The purity of the enzyme is also sometimes overlooked as an important parameter, crucial to aid in the characterisation of such proteins. A good example, which has puzzled the scientific world for decades, is the isolation of compound I from P450. This was achieved by focusing on an extremely high purification of the enzyme which crucially influences the stability of the intermediate.46 In summary, EPR can certainly provide a highly informative insight into the electronic structure of the heme-based systems. In most cases, valuable information can be obtained by straightforward CW EPR measurements at X-band (9.5 GHz) microwave frequencies, whilst the most fruitful array of information can only be revealed using the more advanced pulsed EPR techniques, including high-field EPR, ENDOR, ESEEM and HYSCORE capabilities. 2.2 Chlorite dismutases Heme peroxidases are oxidoreductases which feature a heme prosthetic group in their active site. According to a recent phylogenetic classification,47 within the peroxidase-chlorite dismutase superfamily is the heme b containing enzyme chlorite dismutase (Cld), which catalyses the decomposition of chlorite (ClO2) into chloride (Cl) and molecular oxygen (O2). First described in 1996 by Van Ginkel and co-workers,48 chlorite dismutases were initially found in perchlorate-reducing bacteria (PCRB), which are facultative anaerobes utilising perchlorate (ClO4) and chlorate (ClO3) as the final electron acceptors in the absence of oxygen. Considerable interest remains in the chlorite dismutases because of their unique ability to catalyse the formation of an oxygen–oxygen bond, and their biotechnological potential in the field of bioremediation, particularly in relation to the rising levels of chlorite concentrations in drinking water and soil.49 Chlorite dismutases are currently classified into two lineages, namely Clade I containing homohexa- and pentameric-enzymes, and Clade II comprising the less well characterised dimeric representatives. Notwithstanding the overall structural differences between these two Clades, the active-site architecture and the crucial amino acids can be essentially superimposed. A fully conserved histidine acts as fifth proximal ligand for the ferric heme iron, whilst at the distal site a conserved flexible arginine is also the only charged residue in a completely hydrophobic pocket.50 Crystal structures of chlorite dismutases demonstrated that this residue can adopt two different conformations, denoted as ‘‘in’’ when pointing towards the iron or ‘‘out’’ when pointing away from the heme. It has been suggested that the arginine could either be involved in substrate recognition, or in preventing the transiently formed intermediates to escape from the active-site,51 but its role needs to be further elucidated. In the resting state of chlorite dismutases, a water molecule generally acts as a weak distal ligand for the heme iron. This is supported by UV–visible Electron Paramag. Reson., 2021, 27, 1–46 | 9

spectroscopy, which shows that at neutral pH, chlorite dismutases possess the typical spectral features of a penta-coordinated high-spin iron centre.50 Due to the paramagnetic nature of Fe31, more detailed insights into the active site configuration can be obtained by means of EPR spectroscopy, which has been extensively applied in numerous studies on chlorite dismutases. In particular, CW X-band EPR spectroscopy in frozen solution revealed that chlorite dismutases from Clade I typically exhibit rhombically distorted high-spin spectra at neutral pH.52–55 In contrast, the few representatives from Clade II investigated so far, are characterised by purely axial high-spin signals.55–57 Minor contributions from low-spin components were also detected by EPR at pH ¼ 7. In some cases, the low-spin signals observed at neutral pH were assigned to an imidazole adduct (strong ligand), derived from protein purification procedures involving a His-tag affinity step.58 However, this could be ruled out for recombinant chlorite dismutases, which were purified without the use of imidazole; in these systems low-spin components of uncertain origin are often observed.55,59 Chlorite dismutase activity has been shown to be critically influenced by pH, having an optimum activity between 5.0 – 5.5, and a significant decrease in the reaction rate at higher pH values.51,56 EPR spectroscopy was also exploited in pH-dependence studies, revealing the formation of hydroxide-ligated heme iron at alkaline pH,53,57,59 which could contribute to slowing of the turnover rate. The reason for this dramatic change upon pH variation, is only one of many unresolved questions involved in the catalytic cycle of chlorite dismutases. An in-depth analysis of the numerous proposed pathways cannot be adequately treated in this Chapter, although a general description will be presented here to highlight how EPR spectroscopy can provide unique mechanistic insights into how these enzymes operate. A commonly accepted reaction mechanism is presented in Fig. 4. In this mechanism, the anionic substrate initially binds to the ferric resting state of the enzyme (labelled step 1), forming an Fe31-ClO2 complex (step 2). During this step, the flexible arginine is believed to move from

Fig. 4

Schematic illustration of the proposed catalytic cycle for chlorite dismutases.

10 | Electron Paramag. Reson., 2021, 27, 1–46

the ‘‘out’’ to the ‘‘in’’ conformation. Then, the cleavage of the chlorite molecule occurs (step 3), with a subsequent rebinding step (step 4), before the products are released (step 5).50 The main uncertainty concerning this reaction is whether chlorite is cleaved via a heterolytic or homolytic mechanism, resulting in oxidation of the heme iron to a Compound I or Compound II species respectively; with subsequent formation of either hypochlorite (ClO) as intermediate in the first case, or chlorine monoxide (ClO ) in the second case. So far, homolytic cleavage has been supported by computational studies,60,61 whilst biochemical evidences have favoured the heterolytic pathway.51,62 Nevertheless, recent investigations on a dimeric Clade II chlorite dismutase,32 showed the apparent direct transition from the resting state, to a Compound II species in the range of pH 5–9, while the formation of a Compound I species was postulated as a side reaction at acidic pH. As expected from this mechanism, a transient radical is formed either on the porphyrin p-cation, or on the substrate intermediate. In addition, the decay of the porphyryl radical to a protein-based radical (Compound I*), due to internal electron transfer to a nearby amino acid, has also been proposed for a pentameric Cld.54 The identification and exact nature of the transient radical is not trivial to characterise, and for this reason EPR spectroscopy has played a pivotal role is these studies, since radicals of different origin exhibit distinct spectral features in frozen solution. The major hindrance to studies of these reaction intermediates is the time-scale limitation. Stopped-flow UV–vis spectroscopy showed that the dominant transient species is formed within a few milliseconds from the addition of chlorite, and that it persists as long as chlorite is available, which is on the order of a few seconds using the experimental conditions applied until now.32,51 Due to technical aspects associated with sample preparation times for EPR analysis, little data is available on the reaction of chlorite dismutases with their substrate. In fact, only two examples of EPR analysis on the turnover of these enzymes have been reported to date. In the work of Lee et al.,54 on chlorite dismutase from Dechloromonas aromatica, the protein sample containing chlorite was flash-frozen in liquid nitrogen within one second. The authors observed the complete loss of spectral features associated with the ferric enzyme, and the concomitant appearance of a broad and a sharp signal. These were assigned to an S ¼ 3/2 porphyrin p-cation radical (Compound I), and a tryptophanyl radical, respectively. In a more recent study by Hofbauer and co-workers,51 the pentameric enzyme from Candidatus nitrospira defluvii was mixed with different amounts of chlorite, but in this case the reaction was allowed to go to completion before the sample was analysed using EPR. With increasing concentrations of chlorite, the high-spin signal of the resting state progressively disappeared, with no concomitant formation of low-spin species. At very high excess of chlorite (42500-fold), a protein radical was observed. These results were consistent with the hypothesis of an irreversible enzyme inactivation mechanism, also supported by UV–visible spectroscopy. It is clear that EPR spectroscopy remains invaluable in studies of chlorite dismutases. Using less active variants, which can be obtained with relative ease by site-directed mutagenesis, working under different Electron Paramag. Reson., 2021, 27, 1–46 | 11

pH conditions and sample preparations using a freeze-quench apparatus, some of the existing technical limitations encountered in this field can be overcome, revealing new insights and discoveries into this fascinating series of enzymes. 2.3 Cytochromes P450 Another exceedingly important member of the heme superfamily63 of enzymes is CYP450.64 The name for these enzymes is derived from the spectral properties of the cytochrome (CY) and heme-pigment (P) which displays a shift of the typical Soret optical absorption band maximum to 450 nm in the Fe21–CO bound state.65 From a functional viewpoint, CYP450s are versatile and ubiquitous monooxygenases which principally catalyse hydroxylation of nonactivated hydrocarbons.66 This elementary reaction delivers different results, such that some organisms use it as a way to degrade and digest carbon,67 whilst others (such as mammals) use it to metabolize endogenous chemicals, and purify the organism from xenobiotics like drugs and medicines.68 The remarkable functional diversity also extends to biosynthesis of steroids and epoxidation of olefins.69,70 By exploiting a concerted electron and proton transfer mechanism, operating at the active site of the protein, an oxygen atom from dioxygen can be attached with high specificity to a very wide range of substrates, as represented by the reaction: R–H þ O2 þ 2e þ 2H1-R–OH þ H2O An electron flow is established from an electron donor, normally NAD(P)H, and directed through other cofactors, located in the physiological partners or other domains of the protein, to the heme containing P450 domain. From a structural viewpoint, the iron atom located at the centre of the heme is the main protagonist of the active site. It can coordinate six ligands in an octahedral environment. The metal binds to four nitrogen atoms from the pyrroles of the porphyrin ring, and invariably a cysteine, through a thiolate coordination bond connected to the protein. The sixth axial position is open to the substrate pocket where the reaction takes place, and the occupancy of this site changes sequentially throughout the catalytic cycle, from a water molecule in the resting state, to an empty vacancy when the substrate binds to an oxygen molecule in the catalytic cycle. The general catalytic cycle of P450 enzymes is illustrated in Fig. 5. Crucially, several different paramagnetic intermediates are generated throughout the cycle. EPR spectroscopy has therefore become an essential technique for interrogating the catalytic cycle. The primary states, and their associated paramagnetic species, include: The resting state (1). The ferric iron is a d5 paramagnetic ion, and CW EPR can thus provide detailed information on the electronic configuration and orbital geometry, including the obvious confirmation of the low spin (S ¼ 1/2) configuration. CW ENDOR and Pulse EPR experiments have revealed numerous weak hyperfine interactions of the ferric heme centre, mainly nitrogen and hydrogen nuclei from the porphyrin and 12 | Electron Paramag. Reson., 2021, 27, 1–46

Electron Paramag. Reson., 2021, 27, 1–46 | 13

Fig. 5 General CYP450 catalytic cycle.

axial substituents. In fact, evidence of iron-water binding in the resting state was provided by ENDOR and four-pulse ESEEM techniques, that gave a direct measure of the anisotropic hyperfine interaction for the water protons.71,72 The study of these hyperfine interactions also revealed the orientation of the orbital geometry in in the resting state of P450s. The substrate-bound ferric state (2). When the enzyme binds the substrate close to the distal site, the water molecule is subsequently displaced, and the five-coordinated iron changes electron configuration to high-spin (HS) or to a mixture of HS and LS states.17 The EPR spectrum is very sensitive to changes in the coordination number or geometry of the iron, and therefore the technique has been used to detect changes in the heme pocket by substrate binding.73 Also, the decrease in linewidth of the ferric iron EPR signals in the bound-state, can be interpreted as a structural stabilisation brought about by substrate binding. Conformational enzyme changes of P450cam was detected using DEER experiments by exploiting the distance distributions between two spin labels, attached at the surface of the enzyme, on opposite sides of the substrate access channel.74 Ferrous dioxygen and Ferric superoxide states (3)/(4). When the first electron is transferred to the FeIII centre, it causes reduction to FeII which was discovered to be the rate determining step of the cycle.75 Although the iron in this state could be paramagnetic, only a few studies have been performed to date in such systems, owing to technical challenges (discusssed vide infra). This species has been observed and characterised using X-ray spectroscopy.76 Peroxo-Ferric and Hydroperoxo intermediates (5)/(6). Following the addition of a second electron to the centre, a peroxo-ferric species is formed. The transfer of a proton to the dioxygen moiety then produces a hydroperoxo intermediate. Detailed and numerous EPR studies on these intermediates have shed light on their characteristic electron configuration, and chemical nature. These intermediates are very hard to accumulate in the natural cycle, and therefore various research groups have exploited techniques including cryoreduction and annealing, in order to monitor changes to the iron system and ligand binding.35,77 Compound I (7). After a second proton transfer, a water molecule is subsequently released from the active site leaving an FeIV ¼ O intermediate, which is referred to as Compound I and represents the true catalytic species of the whole cycle. This intermediate has been observed recently, by CW EPR and other techniques, in several members of the family using the peroxide shunt, which reacts with the resting state with peroxides/peracids.78 The electronic characteristics of this species have been described vide infra in section 2.1. Rebound mechanism and product (8)/(9). Once Compound I has formed, it catalyses the hydroxylation reaction through a mechanism that is still poorly understood and widely debated, even if many scientist agree on a rebound-type mechanism. In this iron state, a hydrogen atom is removed from a certain position on the substrate, and bound to oxygen followed by the formation of an hydroxyl group, which rebinds rapidly to the radical substrate forming the product.79 14 | Electron Paramag. Reson., 2021, 27, 1–46

In all stages of the catalytic cycle, EPR has undoubtedly played an essential role in deciphering the nature of the chemical intermediates, and the catalysis occurring in these proteins. However, many unanswered questions remain. In recent years, there is emerging evidence and interest focusing on the use of CYP450 enzymes not just as monooxygenase, but as peroxygenases by using the peroxide shunt.80 Indeed, as it can be seen in Fig. 5, the catalytic cycle of CYP450 can be productive using hydrogen peroxide. Through this path, Compound I can be obtained directly from the resting state of the protein. The advantage of this reaction is that catalysis is performed without using expensive electron donors, such as NAD(P)H and without involvement of other protein partners and oxygen, but simply using hydrogen peroxide or peracids as their substitutes. Unfortunately, despite their great potential, these substrates are strong oxidants. Following a number of catalytic cycles, irreversible damage occurs to the cytochromes, which in turn greatly reduces their activity. Recently, several CYP450s were discovered that can undertake the catalysis using H2O2 without damage, namely a CYP450 enzyme called CYP116B5.81 This cytochrome shows remarkable stability in the presence of peroxide, and a peroxygenase-like reactivity. This behaviour is quite peculiar. For instance, in CYPBM3,82 a cytochrome with which it shares almost the same electron transfer topology, showed the classic CYP450 behaviour of undergoing damage from interaction with peroxides. Reaction assays, where the interaction between H2O2 and these two comparative proteins was studied, revealed that as the concentration of H2O2 increased from 0 mM to 5 mM, the activity of CYPBM3 decreased by 80%, whilst that of CYP116B5 only decreased by 10%.83 All this ensures that CYP116B5 may find interesting potential use in biocatalysis as a highly performing, reliable, cheap and eco-friendly catalyst. For all these reasons, a better understanding of the behaviour and reactivity of CYP450 enzymes is crucial to underpin future developments in catalysis. A considerable amount of research has already been undertaken on these systems, whilst new emerging discoveries on species such as CYP116B5, demonstrate the wealth and potential yet to be uncovered in this important class of enzymes. EPR spectroscopy will thus continue to play a pivotal role in studying these underpinning paramagnetic mechanisms.

3

Catalysts for polymerisation

The exceedingly successful catalytic activities and functions, delivered by enzymes, are of course well known. Indeed, the success and specificity achieved by enzymes is unparalleled and unmatched by any synthetic catalysts. However, one area of synthetic catalysis where yields and turnovers are quite remarkable, is in the field of polymerisation. This is best exemplified from the widespread successful use of Ziegler-Natta and Phillips based catalysts for olefin polymerisation, and also more recently for Cr based catalysts used in oligomerisation. In these catalysts, paramagnetic intermediates or oxidation states are frequently involved and central to the catalytic cycle. As a result, EPR once again has become an Electron Paramag. Reson., 2021, 27, 1–46 | 15

indispensable tool for the characterisation, and thus improvement of these catalytic reactions. In general, polymerisation and oligomerisation catalysts behave in very different ways, but ultimately they do share a few common traits. An ethylene molecule, or another olefin (such as propylene), will usually coordinate to the metal centre using the electron density of the double bond (this 2 electron, 3 centre bond has a hapticity number of Z2). In this position, the molecule has a greater chance to interact with another olefin. The ability of the metal centre to thereby switch between oxidation states, crucially enables the coordinated reagents to undertake insertion reactions, such as oxidative coupling. Each insertion step extends the growing chain by one unit. Ziegler Natta catalysts for ethylene or propylene polymerization can grow linear chains of thousands of carbon atoms, while in the case of the chromium catalysts for ethylene oligomerization the chain growth occurs through the formation of a metallacycle. Ring geometry restrictions typically limit the maximum length to 2, 3 or 4 monomers. Analogous to the role played by EPR in the characterisation of enzymes, local information of the paramagnetic metal sites in the polymerisation and oligomerisation reaction centres can be revealed with exquisite detail. One of the most relevant paramagnetic metal ions in olefin polymerization is Ti31, whereas paramagnetic Cr11/31 states are crucially important in oligomerisation processes. The distortion of the local geometry of paramagnetic metal centres in the activated, and reactive catalysts, is manifested through the spin Hamiltonian parameters, including the g tensors for Ti31 and low spin Cr11, and the additional ZFS terms for the Cr31 centres. For systems with half-integer spin (Kramers species), the experiment can be readily performed at conventional microwave frequency (9.5/34 GHz for X-/Q-band), whereas the ‘‘EPRsilent’’ integer spin systems (non-Kramer species) require high-field/ high-frequency EPR (HFEPR) measurements to fully interpret the paramagnetic state. Other advanced EPR techniques, including ENDOR, ELDOR detected NMR, ESEEM, and HYSCORE, have been successfully used to probe the other nuclei in the coordination sphere. The results combined from these techniques can provide an unrivalled view of the structures and chemical bonds between metal sites and ligands, which will be illustrated in the following sections. 3.1 Ziegler-Natta catalysts Ziegler – Natta catalysts (ZNC) represent one of the most important discoveries within the polymerisation industry. Their discovery by Karl Ziegler in 1954 lead to a breakthrough in the synthesis of ethylene at room temperature, and enabled Giulio Natta to polymerise propylene into crystalline polypropylene for the first time in 1954. ZNC can be based on homogeneous (including Ti, Zr and Hf complexes) and heterogeneous (including Ti complexes) catalysts. The characterisation of the heterogeneous ZNC is exceedingly challenging, compared to their homogeneous counterparts bearing a single active site,84,85 in part owing to the presence of multiple active sites. The distribution and heterogeneity of the active sites, can then be discriminated using EPR, since as stated 16 | Electron Paramag. Reson., 2021, 27, 1–46

above, the spin Hamiltonian parameters are sensitive to changes in the local coordination environment around the metal centre. In heterogeneous ZNC the reactions occur at specific active sites formed by TiCl4 located on the surface of a highly active MgCl2 support (SiO2, TiO2, MgO, and Al2O3 supports have also been reported86), and activated using a suitable co-catalyst consisting of a main group metal alkyl (generally an aluminum alkyl). The active sites are presumed to be paramagnetic Ti31 species featuring a metal–carbon bond, generated by the reduction of the supported Ti41 centre by the co-catalyst.85 The over-reduction of Ti41 to Ti21 and Ti1 has also been reported.87 Lewis bases are added to the system as additional components, not only to improve the activity of the catalyst, but also to enhance and control the stereoregularity that primarily affects the crystallinity of the polymer.88,89 The presence of a large number of potentially active components in the catalyst, complicates the detailed microscopic understanding of the inner working mechanism of these heterogeneous ZNCs. The activity, selectivity and specificity of the catalyst’s active site are determined from each of the individual components, and even subtle changes in the coordination sphere of the active sites can lead to substantial changes in the catalytic performance. A thorough characterisation of these catalysts at the molecular level, in terms of electronic, chemical, and structural properties is required, although complicated by the heterogeneity of the support, the low concentration of the active sites, and the ease of contamination. Nevertheless, EPR and the advanced hyperfine techniques can provide the desired information, particularly when complimented using suitable computational work.90 The paramagnetic Ti31 center, bearing a simple d1 electron configuration (S ¼ 1/2), is most readily characterised by EPR spectroscopy.90 CW and Pulse EPR techniques then provide a unique insight into the geometric, electronic structure, and the surrounding environment of the paramagnetic Ti31 active sites. Such information is extracted through the electron Zeeman interaction (characterized by the g matrix) and the hyperfine interactions of the unpaired electron with local spin active nuclei 47Ti and 49Ti, and more remote surrounding nuclei in the first and even second coordination spheres, including 1H, 17O, 27Al and 35,37Cl nuclei.90–92 Representative examples that illustrate how the coordination environment of Ti31, with ethylene association in model systems can be investigated by EPR, have been reported recently.92–94 Most of the published EPR spectra include overlapped signals arising from different Ti31 species with either axial (g>4g8 and g>og8) or rhombic (gxagyagz) g values ranging from 1.89 to 1.99. The deviations in the g values may be attributed to a different genesis, all of which are related to the influence of the chemical environment on the paramagnetic species. Some of the most common reasons, for the slight deviation of the g values in the ZNC, include the localisation of Ti31 species at different surface terminations of MgCl2 support (lateral cut 110 and 104), the nature of Lewis bases and even the nature of the co-catalyst used in the activation process.92,95,96 Brant et al.,96 described an EPR investigation on a model ZNC prepared by the deposition of alkylmagnesium butoxide (AMB) and titanium Electron Paramag. Reson., 2021, 27, 1–46 | 17

tetrachloride onto a silica support. Their work did not provide much insight regarding the structures of the active sites themselves, responsible for the reported g values (g ¼ 1.99, 1.957, 1.951), except for a signal at g ¼ 1.895, but they provide an important correlation between Ti spin concentrations and different Ti/Mg ratios. Increasing the Ti–Mg ratio was found to lead to higher signal intensities for the lower g values and higher activity of the catalyst in ethylene polymerization, while decreasing Ti–Mg ratio lead to higher signal intensity for higher g-values. Using a wet chemical route, they demonstrated that the amount of Ti31 and Ti21 formed after the reduction of Ti41 was 95% and 0.8% respectively. However, the total amount of EPR active Ti31 detected only represented 10–20% of all the titanium, suggesting the presence of considerable quantities of EPR silent Ti31 centres.95 The exact identity of these EPR silent Ti31 species remains unclear, but it is likely attributed to clustered organisations of titanium active sites, which results in antiferromagnetically – EPR silent-coupled states.97 In a series of papers, Koshevoy and co-workers99–101 detailed an EPR investigation of super-active supported titanium-magnesium catalysts, with a low titanium content (r0.1 wt.%), which was activated with aluminum trialkyls of different composition. The formation of isolated Ti31 species, with slightly different g values, was reported which corresponded to commonly reported g values for ZNC. The EPR active Ti31 species in these systems represented 40–70% of the total titanium content, higher than for conventional catalysts. The content of EPR active Ti31 species was found to rely on the composition of the co-catalyst, and was correlated to the activity of the catalyst in ethylene polymerization and ethylene copolymerization with a-olefins.98–100 Morra et al.,93 investigated an industrial catalyst consisting of TiCl4/ MgCl2/dibutylphthalate, activated by triethylaluminum (TEA). The presence of three distinct EPR-active Ti31 species was reported, two of them being more dominant than the third. The measurements were performed using a combination of multi-frequency (X, Q, and W band) CW and pulse EPR techniques (including HYSCORE and ELDOR-detected NMR). The g values extracted from the X- and W-band spectra were reported as g1 ¼ 1.93, g2 ¼ 1.88 and g3 ¼ 1.89 for the first species 1 (with 76% abundance), g1 ¼ 1.96, g2 ¼ 1.94 and g3 ¼ 1.89 for the second species 2 (with 23% abundance) and finally g1 ¼ 1.97, g2 ¼ 1.96 and g3 ¼ 1.96 (with only 1% abundance) for the third species 3. From the Q-band HYSCORE spectra, a hyperfine coupling between Ti31 and 35,37Cl was observed, suggesting a direct coordination of Cl nuclei to the two more abundant Ti31 species. The catalyst was subsequently exposed to molecular oxygen, to demonstrate the reactivity and the accessibility of the EPR active sites. A decrease of the Ti31 signal intensity was observed immediately, due to oxidation to the EPR silent Ti41 centre along with the concomitant appearance of surface superoxide (O2) signal. The latter superoxide signal was used as a spin probe to reveal the presence of Al nuclei, originating from the co-catalyst, in close proximity to the Ti31 species. Moreover, a hyperfine interaction with 1H nuclei was resolved in X-band HYSCORE measurements, translating into an O2. . .H distance of 18 | Electron Paramag. Reson., 2021, 27, 1–46

0.33 nm. Finally, analysis of the Q-band HYSCORE revealed that the large isotropic (Fermi contact) hyperfine interaction with 27Al, indicated that the O2 radical is stabilized on the Ti41 centre and experiences a direct interaction with the 27Al nucleus of the co-catalyst.92 Advanced EPR studies were also used to provide meaningful information on the nature of paramagnetic metal-olefin complexes. These experiments, performed on ZNCs, revealed important information on the p-coordination mode of the olefins at the paramagnetic center, and thus in turn informed on how the stereoselectivity of the catalyst is directed. In particular, standard HYSCORE and SMART-HYSCORE experiments (the latter providing higher sensitivity and an absence of any blind spots), in combination with DFT calculations, were performed by Morra et al.95 The study was performed on mono-ethylene complexes with trivalent titanium centres, produced by adsorption of C2H4 and 13C-enriched C2H4 on reduced TiAlPO-5 zeotype materials. This study provided experimental proof for the p-coordination of ethylene to the paramagnetic Ti31 centre, in addition to the electronic and geometric structure of the ethylene-Ti31 intermediate complex. The HYSCORE spectrum revealed the presence of two distinct 13C couplings, confirming that the two carbon nuclei of ethylene are inequivalent, with C2 displaying a larger coupling to the Ti compared to C1. This affirmed an asymmetry in the spin density delocalisation between the two carbons of ethylene. From this study, it was shown that the reactivity of the ethylene molecule and the stereoselectivity of the catalyst are as a consequence of the electronic effects.94 Another study was performed by Allouche et al.,94 using HYSCORE in combination with X-ray crystallography and DFT calculations, to investigate two model systems of low coordinated bis(alkoxide) Ti31 alkyl complexes formed upon ethylene polymerisation. In this study, they provided structural assignment for (  Si2O)(  SiO)2Ti31–R surface species as key intermediates in the ethylene polymerisation activity of the silicasupported titanium hydrides. From the CW EPR spectra, they observed rhombic g tensors for both complexes, bearing different degrees of g-anisotropy. After the reaction of the complexes with 13C-labelled ethylene, weak 1H couplings were observed in the HYSCORE spectra to the first coordination sphere of Ti31, and the closest proton to the Ti31 centre was found to be from the Ca carbon of the alkyl ligand. The HYSCORE spectra also showed the characteristic 13C hyperfine coupling.93 Whilst most of the reported systems to date are based on the paramagnetic 3d1 Ti31 oxidation state, the 3d2 configuration of Ti21 can also be paramagnetic, when present as a high spin triplet state (S ¼ 1); however very few EPR studies of Ti21 are reported.96 Nevertheless, some studies have employed an indirect route to study Ti21 with EPR, using selective oxidising reactions of Ti21 to Ti31, using water or pentafluorochlorobenzene: 2Ti21 þ 2H2O-2Ti31 þ 2OH þ H2 TiCl2 þ C6F5Cl-TiCl3 þ C6F5 In other studies, EPR has also been used to identify and study the organic radicals formed after activation of the pre-catalyst with the Electron Paramag. Reson., 2021, 27, 1–46 | 19

co-catalyst. The origin of the organic radicals is generally found to be due to the presence of internal and external electron donors.101 Clearly, as described above, EPR offers a powerful means to characterise the active sites on ZNC and their surrounding environment. Whilst most of these studies have utilized the more readily available CW EPR method, the advantages offered from pulsed EPR techniques offers a far greater step forward in terms of the information that can be extracted from the unresolved hyperfine interactions on the structure of the active sites. 3.2 Phillips based systems The Phillips catalyst was discovered by J. P. Hogan and R. L. Banks at Phillips Petroleum in the 1950s.102 It is a Cr-based catalyst used for ethylene polymerisation and its use is so widespread that it accounts for over 40% of the high-density polyethylene (HDPE) commercially available. Despite being successfully utilised in large scale industrial operations for the past 60 years, it may be rather surprising to learn that there are still many unanswered questions concerning the mode of operation of the catalysts.103–105 In particular, the oxidation state and geometry of the active site is still poorly understood, whilst some of the fundamental steps involved in the polymerisation mechanism remain elusive. These questions remain unresolved for several reasons. First, only a small fraction of the Cr-sites are actually active, such that many studies have actually reported upon indirect Cr-species. Second, the Phillips catalyst itself represents a rather complex arrangement of chemical entities, which are sensitive to the experimental conditions. As a result, experiments conducted in different research laboratories may have employed slightly different conditions, giving rise to slightly different distribution of centres within the catalyst. Third, most laboratory studies were conducted on high vacuum lines which often do not reproduce the experimental conditions employed in industrial applications, and therefore the observer is actually reporting on different states of the catalyst. In general terms, the Phillips catalysts are prepared by dispersing hexavalent chromium ions onto the surface of porous inorganic materials.105 The catalyst is then activated by calcination in an oxidising atmosphere at temperature above 600 1C. After the activation step, Cr61 will be the dominating Cr species, with a minor proportion of Cr51 species.106 There are two common forms of the Phillips catalyst, namely the oxidised form and the reduced form. The oxidised form is based on the aforementioned Cr61 precatalyst. It can react with ethylene at T4100 1C, and initiate polymerisation after the induction time. During the induction period, the chromium is reduced to lower oxidation state, predominantly Cr21, before forming the Cr-R active sites (for which the oxidation state is uncertain). The small amount of Cr51 centres (with S ¼ 1/2), can be investigated by X-/Q-band EPR, and these usually reveal an axial set of g values when grafted on alumina support. On the other hand, two Cr51 centres with axial and rhombic g values were reported for the silica grafted material.107,108 Upon ethylene polymerisation, high spin Cr species, characterized by signals with geffB4.3, can also be detected. 20 | Electron Paramag. Reson., 2021, 27, 1–46

These were attributed to Cr31 species (S ¼ 3/2) with large ZFS parameters,108 and illustrate the complexity of speciation in these catalysts. By comparison, the reduced form of the Phillips catalyst can be obtained by further reducing the oxidised form with CO. At 350 1C, the Cr61 sites can be quantitatively converted to Cr21. After this reduction, the catalyst is active for polymerisation with ethylene at room temperature, without an induction time. EPR investigations of these catalysts showed that only a small amount of Cr51 remained as an impurity after the reduction.108–110 The non-Kramers Cr21 species (S ¼ 2) was investigated using high field EPR at 106/212/317 GHz, and was reported to have a very small rhombicity for the ZFS tensor.109 Upon ethylene polymerisation, two research groups reported different observations, albeit under slightly different conditions. In one case, the X-/Q-band spectrum was reported to be unaltered following ethylene exposure at room temperature,108 and assumed that no Kramers species was involve in the polymerisation. However, in another study the polymerisation reaction was performed at T ¼ 80 1C and the authors reported the appearance of Cr31 signals, characterised by the broad linewidth, centred at gB1.98 with axial symmetry, together with the loss from Cr21 signals.109,110 Therefore, it was concluded that the Cr21 sites were oxidised to organo-Cr31 species by ethylene, which initiated the polymerisation. As described above, both forms of the Phillips catalysts require a reduction step forming the Cr21 centres. The polymerisation mechanism is then proposed to operate via a two electron redox process involving Cr21 and Cr41, or a one electron redox process involving Cr21 and Cr31. To delineate which mechanism is operative, considerable efforts in surface organometallic chemistry (SOMC) and supported homogeneous catalysis (SHC) have created systems bearing surface chromium sites with welldefined oxidation state and nuclearity on a silica-/alumina surface.111 ´ret and colleagues.112,113 In This is exemplified by the research from Cope 31 31 their studies, Cr -siloxide and Cr -amide were grafted onto the silica surface. In the case of the Cr31-siloxide, two high spin Cr31 species with geffB4.9 were detected in the X-band EPR spectrum, together with hyperfine couplings to 29Si at 2.99 MHz identified in the HYSCORE experiment. On the other hand, the grafted Cr31-amide produced an EPR signal with with geffB2, attributed to low spin Cr31 (S ¼ 1/2) whilst the HYSCORE spectrum revealed a hyperfine coupling to 14N at 1.05 MHz. Bearing in mind the limitations stated earlier, it is crucial to investigate the complex Phillips catalyst with a plethora of analytical and spectroscopic techniques, if the mechanism is to be truly understood. As shown above, EPR is one such spectroscopic technique that can provide detailed information on the local geometry of the Cr species and even the surrounding environment using advanced technique such as HYSCORE. Kramers species including Cr31 and Cr51 can be investigated at conventional microwave frequencies employed in EPR (i.e., X-/Q-band), whilst higher microwave frequencies are needed to investigate the non-Kramers species like Cr21 and Cr41. The potential opportunities afforded by pulsed EPR are undoubtedly yet to be explored, but owing to the complex speciation and distribution of spin active centres in these catalysts, it will always Electron Paramag. Reson., 2021, 27, 1–46 | 21

remain challenging to fully characterise the paramagnetic centres in these catalysts. Nevertheless, EPR will remain a vitally important tool in the arsenal of techniques used to study the Philips Catalysts. 3.3 Oligomerisation based systems Oligomerisation is a similar process to polymerisation, but aimed at assembling shorter molecular chains and preferably with a well defined chain length. One of the commonly employed processes is the oligomerisation of ethylene, as it is the simplest of all building blocks (monomers) available. The products of ethylene oligomerisation are called linear a-olefins (LAO), which can be as short as 1-butene, but do not have a specific maximum chain length limit. 1-hexene and 1-octene are the most desirable product chain lengths for this type of reaction. Chromium-based catalysts, in conjunction with aluminium co-catalysts, have proven to be highly effective for this reaction, and the Phillips trimerisation system (not to be confused with the above Philips polymerisation catalyst) is currently used to produce large quantities of 1-hexene.114 More recently,115 it was discovered that the chromium based organometallic complexes, based around the general structure [Cr(CO)4(Ph2PN(i-Pr)PPh2)]1 have excellent oligomerisation activity and, like the previous catalysts already employed in industry, is activated using a large excess of a co-catalyst, such as triethylaluminium (TEA) or methylaluminoxane (MAO). The co-catalyst is used to remove the carbonyl ligands in the complex. However, a wide variety of species are formed during this activation step and indeed the catalytically active species remain uncertain, whilst the full scope of the secondary reactions induced by these agents remains uncertain. Following the activation of the catalyst, two ethylene molecules bind to the Cr metal centre. At first the substrate is thought to bind through the double bond, whilst in the second stage, two ethylene molecules undergo oxidative coupling, which alters the oxidation state of the chromium centre by þ2. Chain growth occurs in consecutive insertion stages after the formation of the first 5-membered ring. As additional ethylene molecules are inserted, larger 7- and 9- membered rings are formed, with the metal centre acting as one of the vertices. The specific metal complex used, including the choice of phosphine ligands and the reaction conditions, can all be tuned to selectively produce 1-butene, 1-hexene or 1-octene. Similar to the case described vide infra for the Phillips based catalyst, the redox states of chromium that are operative in the catalytic cycle for the oligomerisation systems are also unknown. A two electron redox couple is believed to occur in the chromium oligomerisation catalyst, involving either Cr11 and Cr31 (both paramagnetic) or involving Cr21 and Cr41.114 Indeed chromium possess several accessible oxidation states, ranging from 0 to VI, and many of these are paramagnetic. The low spin states involving Cr11, Cr31 or Cr51, are not affected by ZFS, and are therefore relatively easy to study at conventional microwave frequencies used in EPR. As stated earlier, the high spin states can be more problematic to characterise, unless the user has access to high field EPR measurements. 22 | Electron Paramag. Reson., 2021, 27, 1–46

Nevertheless, the sheer abundance of potential paramagnetic centres involved in the oligomerisation catalysts has meant that EPR has played a crucial role in the characterisation of such systems, especially when used in conjunction with other techniques and computational chemistry.114 As previously explained, large quantities of aluminium based cocatalysts are required to activate the chromium pre-catalyst. There are numerous reasons why this abundance of co-catalyst is far from ideal. First, from a pure atom economy perspective, it makes the reaction less efficient by adding to the reagents whilst also requiring later separation from the clean product. Second, there are many by-products which are not believed to be catalytically active. And finally, the exhausted salts are an environmental hazard which cannot easily be disposed of nor recycled.115 To date, a number of EPR studies have been conducted using X-band CW techniques116,117 to determine the oxidation states and structure of the Cr31 based catalyst [Cr(acac)3(Ph2PN(i-Pr)PPh2)]3, both during the activation step with Al agents, and during the actual oligomerisation. By comparison, other groups have studied the Cr11 based catalyst, [Cr(CO)4(Ph2P(CH2)3PPh2)]1 and [Cr(CO)4(Ph2PN(i-Pr)PPh2)]1, following activation with TEA.117 When low levels of TEA are used a Cr(I) bis-arene complex, [Cr(Ph2P(CH2)3PPh2-bis-Z6-arene)]1 was formed, as revealed by EPR and DFT. This bis-arene complex was proposed to form via intramolecular rearrangement and co-ordination of Cr11 to the phenyl groups of the phosphine ligand in aliphatic solvents, following loss of CO. It was thought that this prevents release of Cr11 ions into solution. On the contrary, when aromatic solvents were employed such as toluene, a bis-tolyl complex was preferentially formed. The same group also studied the activation when higher levels of TEA were employed.118 It was clear that the TEA was responsible for the complete removal of all CO groups from the Cr11 complex and this reaction occurs via a dominant pathway involving a series of Cr11 intermediates, including a cis-[Cr(CO)3(Ph2PN(i-Pr)PPh2)]1 complex and a ‘piano-stool’ type complex [Cr(CO)2(Ph2PN(i-Pr)PPh2)]1. Each of these paramagnetic complexes produced a distinctive set of spin Hamiltonian parameters as characterised by CW EPR, and verified by DFT. It was clear that the distribution and nature of the Cr11 intermediates was highly sensitive to the experimental conditions employed, including the quantity and manner of TEA addition. Hence similar to the case described earlier for the characterisation of the Phillips catalyst, different results can be obtained from different laboratories, if the experimental conditions are not identical.119 Owing to the problems associated with using the aluminium based co-catalysts, some work has also been conducted to examine whether UV photolysis can be successfully employed to remove the carbonyl ligands in these catalysts. A CW EPR study was therefore recently reported on the UV activation of a [Cr(CO)4(Ph2P(CH2)3PPh2)]1 complex.120 In general there is very little literature on the photochemistry of Cr11 systems,120 despite the copious amount of literature available on the analogous Cr0 complexes; this is likely due to the air sensitive nature of the Cr11 systems. UV photolysis of the [Cr(CO)4(Ph2P(CH2)3PPh2)]1 complex breaks both the Cr–CO and Cr–P bonds, ultimately leading to the formation of a Electron Paramag. Reson., 2021, 27, 1–46 | 23

dicarbonyl [Cr(CO)2(Ph2P(CH2)3PPh2)2]1 complex and a mer-[Cr(CO)3(Ph2P(CH2)3PPh2)2]1 complex which is an intermediate observed only at low temperature. The spatial symmetry of the starting complex (g1 ¼ 1.988, g2 ¼ 2.066, g3 ¼ 2.066) and the final complex (g1 ¼ 1.968, g2 ¼ 2.024, g3 ¼ 2.024) were both axial, while the intermediate complex was rhombic (g1 ¼ 1.984, g2 ¼ 2.026, g3 ¼ 2.050), bearing a non-chelating P atom. The ability to monitor symmetry changes can be invaluable in the study of reaction intermediates and isomerisation studies.

4 Microporous systems Catalysis by microporous systems such as activated carbons, zeolites, metal organic frameworks and alumina phosphates is very widespread with industrially relevant processes including fossil fuel refining and the production of valuable chemicals.121 One of the most important features of these catalysts lies in their crystalline structure. The presence of pores and channels of molecular dimensions can provide some degree of shape selectivity of reactants, intermediates and products within the framework.122 Moreover, the large internal surface area and void volumes provide the perfect environment for the coordination of active transition metal centers, which are usually the main actors of the catalytic cycle. The high dispersion of the sites makes the microporous materials suitable as single-site catalysts, capable of filling the gap between homogenous and heterogeneous catalytic science.123 EPR spectroscopy has been widely used to investigate catalytically active microporous systems.124,125 In most cases, the active species is a transition metal ion in a paramagnetic valence state, associated with the microporous framework. CW and pulse EPR experiments provide a detailed description on the electronic state of the active sites and their surrounding environment. This exquisite information, when combined with data from other techniques, can enable one to determine the location and geometry of the active site, which is fundamental for a better understanding of the catalytic process. Furthermore, owing to the high sensitivity of the technique, the EPR signal can provide quantitative information on the amount of paramagnetic species present in the microporous material, even at very low concentrations. Although EPR spectroscopy can only detect species bearing unpaired electrons, valuable insights into the geometry, accessibility and reactivity of diamagnetic centres may be indirectly probed using suitable paramagnetic spin probes, that fit into the framework and interact with the species of interest. Such paramagnetic spin probes that have been successfully exploited in studies of microporous materials include nitroxides,126 nitric oxide (NO)127,128 and superoxide (O2).129 It should also be mentioned that the advent of in situ and operando techniques has provided another opportunity to monitor the catalytically relevant species in microporous materials under nominally active conditions, including the identification of transient radical intermediates and the analysis of photocatalytic efficiency, via light illumination and electrocatalytic performance.130,131 This also provides further insights and clarity into the 24 | Electron Paramag. Reson., 2021, 27, 1–46

reaction mechanisms that can lead to improved catalyst design.132 Nonetheless, the intrinsic practical difficulties of in situ methods have limited its approach to CW EPR measurements; pulse EPR has still not been employed for the study of microporous catalysts in reactive estate under such in situ conditions.125 In this section of the Chapter, we will present some of the most important examples pertaining to the applications of EPR in the study of microporous single-site catalysis. In particular, we will focus on two of the most representative classes of these materials, namely Zeolites and Metal Organic Frameworks (MOFs). The former class represent the largest group of microporous materials, and are indeed the most widely exploited from an industrial perspective for more than 40 years.133 The latter class have recently been introduced into the catalysis field due to their high degree of flexibility, functionality and hydrothermal stability for organic and inorganic components.134 4.1 Zeolites Zeolites and zeotype materials are aluminosilicate, aluminophosphate and silico-alumino-phosphate microporous systems characterized by a regular three-dimensional framework of channels and cages.135 The fundamental building unit of all zeolites is the tetrahedral site (T site) usually composed by a Si41 atom coordinated to four oxygen atoms. The T sites are commonly substituted by Al31, P51, Ga31 or even a small number of transition metal ions. The tetrahedral units are connected to each other through the oxygen atoms, and are able to arrange themselves in different ways, to create a huge variety of structures with different framework topologies. Typically, the Al atoms substitute the siliceous positions and generate an anionic charge inside the solid which has to be compensated by extra-framework cations. In natural zeolites, these are usually alkali or alkaline-earth ions which occupy the microporous space. Since they are not covalently bound to the framework, the charge-balancing cations can be partially or totally exchanged by other different cations. Whereas the acidic properties of synthetic zeolites have been exploited since the 1960s on large industrial scales, for example in crude oil refining,136 the interest in transition metal ion (TMIs) exchanged zeolites and zeotypes as redox catalyst has grown over the past 20 years. The introduction of Co, Cu, Fe, Ti, Ni, Rh and Pd as counterions inside the zeolitic framework has proven to be very promising in industrially relevant oxidation and reduction reactions.137,138 As most of these TMIs are paramagnetic, EPR spectroscopy has been extensively used in the characterisation of such exchanged zeolites for several decades.132 On the one hand, it is a powerful tool enabling the user to extract information on the location, structure and dispersion of the paramagnetic TMIs in zeolite catalysts. On the other hand, thanks to recent technological advances, the application of in situ investigations has also made it possible to monitor catalytically active species under conditions close to those of the operating reaction conditions.139,140 Perhaps on the of the most widely studied paramagnetic TMI in exchanged zeolites has been Cu21, and numerous EPR studies have been Electron Paramag. Reson., 2021, 27, 1–46 | 25

devoted to this over the years.141 The identification of the local environment around the Cu21 exchanged sites is an important prerequisite for understanding their catalytic activity. Normally, for a particular zeolite, more than one copper species coexists in the material, depending on the hydration state and Si/Al ratio. After the removal of water, the Cu21 ions are strongly bound to the oxygens of the framework and the difference among the sites are mainly related to the Al distributions.142 The presence of Al pairs, as opposed to isolated Al sites around the cupric species, affect the redox and/or acidic properties for a specific Cu site and, thus, the activity of the catalyst.143 The hyperfine coupling constants and g values directly obtained from the CW EPR spectrum are strongly affected by the local environment for a specific copper ion.144 In fact, for a given coordination sphere, the Cu21 complex, which suffers from a lower ligand field splitting parameter (DLF) and less negative total charge on the copper, will also produce higher g8 and lower A8 values.145 The pioneering work of Peisach and Blumberg demonstrated this empirical correlation between the EPR parameters for several Cu21 containing biological systems.146 Later on, these models were successfully used for the interpretation of copper exchanged zeolites139 (Fig. 6). An example of how these plots can be interpreted is given in Fig. 6. All of the dehydrated zeolites are almost perfectly located on the antidiagonal of the plot. This means that generally, for the same coordinating atom type and number (e.g. 4 equatorial oxygen donor atoms), a Cu21 ion surrounded by a more negative coordination sphere is found in the upper-left part of the plot, whereas in the opposite case, it is found in the lower-right. Thus, the information extracted from the Peisach–Blumberg model is fundamental for the assignment and understanding of the Cu21 sites. For instance, Cu-MFI hosts two distinct copper species named as MF1 and MF2 in Fig. 6. MF2 was assigned to a six-membered ring site with two Al whereas MFI1 was assigned to a six-membered ring site in which one Al is inside the ring while the other one bridges the ring.139 Since the latter

Fig. 6 Peisach-Blumberg plot for different Cu-exchanged zeolites. The data for hydrated Cu zeolites are given with squares and they refer to low temperature measurements. Adapted from ref. 144 with permission from Springer Nature, Copyright 2016. 26 | Electron Paramag. Reson., 2021, 27, 1–46

environment produces a more negative charge on the Cu21 ion, the parameters related to this site appear in the higher left hand part of the plot. Regarding the hydrated Cu-zeolites, their position on the bottom right hand side is due to the different number and nature of ligands around the copper (i.e., water molecules instead of framework atoms). Despite the enormous potential offered by in situ EPR spectroscopy,147 many limitations and difficulties remain. The advent of specific experimental assembles/setups has facilitated some limited exploitation of the approach to study zeolite catalysts under almost operando conditions. Examples include the analysis of TMIs in zeolites after adsorption of different reactants or probe molecules,148 after treatment at temperatures or pressures typical of a specific reaction,149 or for the identification of ¨ckner radical intermediates.150 Of particular note is the work by Bru et al.,150 on Fe-ZSM-5 zeolites. It was found that these catalysts are able to oxidise benzene to phenol in the presence of N2O at room temperature.151 The active species responsible for the oxidation process was attributed to a so-called a-oxygen species, formed on the iron sites of the ZSM-5 material after contact with N2O. The radical anionic nature of the a-oxygen was experimentally confirmed by in situ EPR results. After a pre-treatment of Fe-ZSM-5 at 973 K in Ar, the Fe31 single site EPR signal disappeared because of the reduction to Fe21, which is effectively EPR silent at conventional microwave frequencies. The subsequent oxidation at 523 K in an N2O/Ar flow regenerated the iron signal, together with a radical line at g ¼ 2.018. This signal was assigned to an O  radical anion, formed by electron transfer from Fe21 to N2O.150 It was also proved that only N2O is able to create the a-oxygen centre because no radical line was observed when O2 was used as oxidant. It is certainly clear that EPR spectroscopy is a powerful technique for providing a detailed and informative description on the active sites of TMI exchanged zeolites, including geometry and electronic structural data. Moreover, the application of in situ EPR approaches allows one to monitor fundamental changes to the nature of the catalytically TMI sites, under operative conditions and/or identify specific radical species formed from certain reactants. 4.2 Metal organic frameworks In recent years, Metal Organic Frameworks (MOFs) have started to gain considerable attention as the most prominent class of microporous materials for applications in gas storage and separation, liquid purification, catalysis, sensing, electrochemical energy, super-capacitors, and heat storage owing to their unique structural diversity and tunability.152–157 The ultrahigh porosity, tuneable pore nature, enormous internal surface (1000 – 10 000 m2 g1) and volume area, very low density and crystal integrity are just some of the bespoke properties of MOFs which provide a pathway towards a potentially unique role in the field of heterogeneous catalysis.153–155 The high surface area of MOFs also creates large accessible volume space with a large number and variety of active sites for catalysis.153 In addition to this, another important property of MOFs is the so-called Electron Paramag. Reson., 2021, 27, 1–46 | 27

‘breathing effect’, where the porous nature of the MOF can be manipulated to reversibly change from narrow to large pore transformations without any topological framework distortion.157 Furthermore, MOF materials can also be functionalised for bespoke catalytic applications via the modification of coordinatively unsaturated active sites, the encapsulation of guest species in pores, or by coating with functional materials.153,158,159 Although MOFs are essentially based on a cage-like complex structure, they are composed of two simple hybrid building blocks through ion-covalent bonds. The first is the metal clusters, or secondary building units (SBU), and the second is the organic linkers.154,157,160 The appropriate choice of MOF components dictate the physical and chemical properties of the resulting material, including porosity, chemical and thermal stability, magnetic susceptibility, conductivity, etc.154,157,160 The first MOF, developed by Yaghi et al.,161 was namely MOF-5 with a relatively simple structure. Later developments expanded the complexity of the chemical composition, to include more than one linker and/or hetero bimetallic species using a variety of synthesis techniques including hydrothermal, solvothermal, electrochemical, mechanochemical, sonochemical, and microwave assisted techniques, along with other post-synthesis modification methods adopted by several groups.160,162 Furthermore, chemists have also successfully synthesised highly complex and interesting multi-component MOFs which contain multiple SBU and organic linkers within a single framework.162 Once again, owing to the likely presence of paramagnetic centres in these MOFs, unsurprisingly EPR has played an important role in the characterisation of such materials (as summarised in Fig. 7). Most notably, Kultaeva et al.,163 correlated the magnetic properties of a copper-based MOF, labelled [Cu(prz-trz-ia)], through the temperature-dependent magnetisation results of SQUID magnetometry along with multi-frequency EPR results. It is interesting to note that, the temperature-dependent magnetic

Fig. 7 EPR as a tool to study different properties of MOFs. 28 | Electron Paramag. Reson., 2021, 27, 1–46

behaviour extracted from the EPR results and the magnetic susceptibility data from the SQUID experiments provided a negative value of the paramagnetic Curie temperature (yp) due to the antiferromagnetic interaction between the cupric ions. An isotropic exchange coupling constant, J1, of antiferromagnetically coupled cupric ions was extracted from the SQUID (26 cm1) and EPR (23 cm1) results, which agreed well with the DFT calculations. Recently, Bitzer et al.,164 used EPR along with the X-ray diffraction and X-ray absorption spectroscopy to study the incorporation of Fe31 ions into another copper-based MOF, labelled CuBTC, with paddlewheel units. The presence of Fe31 – Cu21 paddlewheels have been successfully confirmed from the strong magnetic interactions among the Cu21- Fe31 species with a g value of 2.023. Using a variety of EPR methods, Mendt et al.,165–167 also explored the structural phase transition of MIL-53(Al/Cr),165 adsorption of CO2 over the MIL-53(Al/Cr)166 under pressure, and the low temperature NO binding in the MIL-100(Al).167 Although several excellent literature reviews and papers have been published that deal with the catalytic applications of MOF for a varied host of reactions,153,160,168,169 and whilst many EPR publications have focused on heterogeneous catalysis,90,170 there are fewer articles devoted to the combined EPR study of catalytic applications in MOFs. Currently, EPR is finding considerable success in the studies of charge generation, pathways to charge transfer, broad band absorption in photocatalytic activity, and mechanistic origins of electrocatalysts in MOF materials. For example, Nasalevich et al.,131 investigated the photocatalytic potential of NH2 functionalized, d0 metal based MIL-125(Ti), UiO-66(Zr) and UiO-66(Hf) MOFs through X-band EPR under UV illumination. The Ti31 (S ¼ 1/2) ions were generated in the photoexcited state, only in the NH2-MIL-125(Ti) material upon UV illumination as a result of ligand-metal charge transfer(LCMT). Also, a transient weak signal found in the NH2-UiO-66(Zr) and NH2-UiO66(Hf) materials, was attributed to the highest occupied crystalline orbital (HOCO) – lowest unoccupied crystalline orbital (LUCO) transition of a radical in the framework and no LCMT was observed. The EPR results were also in accordance with the computational results. Horiuchi et al.,171 also performed X-band in situ EPR studies on amino functionalised Ti-MOF under the visible light irradiation. Once again, paramagnetic Ti31 ions were produced from the diamagnetic Ti41 centres via LCMT with reported spin Hamiltonian parameters gxx ¼ 1.980, gyy ¼ 1.953, gzz ¼ 1.889. The presence of Ti31 ions was confirmed by exposure of the material to air, at which point the paramagnetic Ti31 centres were immediately oxidised back to the original Ti41 centres. In another study, Chen et al.,130 investigated the NNU-28(Zr) MOF under the continuous visible light illumination using in situ X-band EPR to study the photocatalytic activity of CO2 reduction with formate formation. Firstly, the anthracene-based ligand in the NNU-28 material was found to act as a photo-reducing component of CO2, which was confirmed by the strong EPR signal of an anionic radical (g ¼ 2.003) under visible light irradiation, whereas the ligand itself in the absence of any irradiation, gave a weak signal with the same g value. The authors found two more Electron Paramag. Reson., 2021, 27, 1–46 | 29

additional signals at g ¼ 2.009 and g ¼ 2.030 during the in situ EPR measurements of NNU-28(Zr) upon continuous visible light illumination, which were not related to the ligand. These new signals were attributed to the LCMT process of Zr6 oxo clusters, thereby revealing the existence of a dual catalytic pathway as confirmed by the EPR. Zhao et al.,172 investigated the electrocatalytic performance of mixed CO0.6Fe0.4-MOF-74 and compared their results with Co-MOF-74 (Co21, S ¼ 3/2) and Fe-MOF-74 (Fe21, S ¼ 2) materials for the oxygen evolution reaction (OER) by means of X-band EPR. The EPR data revealed that the Co0.6Fe0.4-MOF-74 has more open metal clusters compared to the single metal counterparts. Ji et al.173 have also investigated the Lewis acidic nature of MOFs, including ZrOHBTC and ZrOTf-BTC, to better understand the catalytic performance of the materials. The difference between the gzz values from the Zr(O ) active species of ZrOH-BTC and ZrOTf-BTC, was revealed by EPR owing to the difference in Lewis acidity of those MOFs. The gzz value of 2.0310 for ZrOTf-BTC was shown to arise from the energy splitting (DE ¼ 0.99 eV) between the px* and py* orbitals which is comparable to the DE (1 eV) of benchmark homogeneous Lewis acid catalyst Sc(OTf)3.

5

Homogeneous systems for small molecule activation

Homogeneous photocatalysis is a fertile field of research that is gathering more and more momentum in the chemical research world. This is because activation via light irradiation gives access to many different reaction pathways, which are sometimes difficult to achieve via other more conventional synthetic methods, and usually with high selectivity for the products.174 Most of these characteristics are due to the transient nature of the active forms involved in these reactions, as the irradiation of the chromophores generates high-energy species, such as ionic radicals and excited states, which differ greatly in their capabilities from their precursors.175 This of course presents a significant obstacle in determining the nature of these intermediate species, as their high reactivity often comes at the cost of the overall lifetime of the compound. Consequently, understanding the mechanism of reaction for this type of process is quite challenging. Catalysis is known for its crucial role in the modern chemical industry, and due to the progressive tendency to eliminate expensive and toxic noble metals, in favour of the more abundant and less toxic first-row transition metals, the analysis and interests in open-shell (radical type, paramagnetic) complexes is growing significantly.176 Indeed, the efficiency of the platinum group metals (PGMs) is unsurpassed compared to the first-row transition metals; nevertheless, this has not deterred many international research groups in actively exploring new ways to exploit these latter metals, to deliver reactions akin to enzyme based systems. For example, the oxidation of alcohols to aldehydes, ketones, and carboxylic acids is perhaps one of the most widely used class of oxidation reactions in organic chemistry, and homogeneous palladium-catalysed systems are very effective for these selective oxidation of organic molecules primarily based on the two-electron redox reactions.177 However, 30 | Electron Paramag. Reson., 2021, 27, 1–46

more recently, copper catalysts have demonstrated some potential in these types of reactions. Copper is highly desirable for such reactions as it is far cheaper, and less toxic, compared to palladium. Indeed, Cucontaining enzymes (oxidases) can mediate a wide variety of essential oxidation reactions in nature, from outer-sphere electron transfers (e.g., laccases) to dehydrogenation (e.g., galactose oxidase).178 So the potential opportunities for using homogeneous Cu-based catalysts is obvious, and whilst they have been successfully applied to numerous aerobic oxidation reactions,179–181 the mechanism by which these Cu-mediated reactions operate are not well understood, unlike the PGM counterparts.177 The activation of so-called inert bonds like carbon-carbon (C–C) bonds is another reaction of extreme importance in organic chemistry. In conventional organic transformations, relatively inert C–H, C–O and C–C bonds must be altered to the analogous activated C–X (X ¼ I, Br, Cl) or C–OR functionalities, which involve more elaborate synthetic routes and invariably result in the generation of by-products. Therefore, in modern chemistry, transition metal catalysed highly selective C–H, C–O, and C–C functionalisation is also growing in momentum.182 Despite the prosperous advances made in transition metal catalytic and photocatalytic methodologies, there is still a lack of understanding on how these catalysts operate, and as paramagnetic species are frequently involved, the traditional analytical tool of synthetic chemists, NMR, cannot be easily applied. For this reason, EPR is essential when probing the single electron transfer events typical of first-row transition metals. The paramagnetic pre-catalyst, the activated catalyst itself, or the subsequent reactive intermediates, can all be investigated for valuable insights into the formal oxidation state of the metal and the effect of ligand structure on the catalytic activity.183 5.1 Homogeneous photocatalytic centres EPR has been widely used to understand the mechanism of heterogeneous photochemical systems.184–186 However, the use of EPR to study homogeneous photocatalysis is still comparatively sparse. The most commonly employed transition metal catalysts used in homogeneous photocatalysis are based on ruthenium and iridium.175 The [Ru(bpy)3]21 (bpy ¼ 2,2 0 -bipyridine) complex, in particular, is an extremely popular sensitiser and has been extensively studied and employed as a means to harness light energy.187 The ground state of the complex is EPR silent, although most of the photoinduced excited states are not. Wang et al.,187 for instance, reported how this ruthenium complex can be used to promote a light-driven water oxidation by a di-nuclear cobalt complex, [(TPA)Co(m-OH)(m-O2)Co(TPA)](ClO4)3.188 In the presence of an electron acceptor, Na2(S2O8), and at a pH maintained at 8 via a borate buffer, this system revealed the evolution of oxygen at a turnover frequency of 1.4. X-band CW EPR at low temperature (10 K) was then used to follow the evolution of the system after irradiation; while the initial mixture is EPR silent, as the Co31/Co31 complex does not possess any unpaired electrons, after a single laser flash at 532 nm the system developed a signal with g ¼ 2.03 which is consistent with a mixed valence S ¼ 1/2 di-nuclear Co31/Co41 state.189,190 Further irradiation resulted in a gradual decrease Electron Paramag. Reson., 2021, 27, 1–46 | 31

in the intensity of this signal, and eventually the appearance of a broad spectral feature, composed of many different signals between 250 and 295 mT. The two main signals appear to be characterised with g values of 2.33 and 2.42 respectively. The signals with gE2.3 have been reported to be evidence for [Co(IV)(O)] species in cobalt oxide films.191 Since lightscattering experiments eliminated the possibility that the complex degrades into nanoparticles during the process, the first signal was suggestive of a Co41(O)/Co41(O) complex, but the low intensity makes a definitive assignation of the signal rather difficult. Based on these observations, the proposed mechanism showed that evolution of the complex between different di-nuclear structures with the two metallic centres progresses between oxidation states. The time evolution of the paramagnetic species can also reveal interesting information. Hollmann et al.,191,192 carried out in situ EPR measurements to gain mechanistic insight into a novel photocatalytic system,192,193 employing an iridium complex [Ir(ppy)2(bpy)]1 (ppy ¼ 2phenylpyridine), as a photosensitiser for the water-reduction catalyst [Fe3(CO)12], along with triethylamine as a sacrificial reductant for the chromophore. The first step of the reaction is the excitation of the photosensitiser and its subsequent quenching by triethylamine, which generates the reduced form of the iridium compound. The [Ir(ppy)2(bpy)]1 complex is a low spin d6 species and therefore EPR silent. However, after irradiation at 300 K in the presence of the reducing agent, the formation of the reduced species gives rise to an intense isotropic signal at g ¼ 1.984. The absence of such a signal in the pure solvent (tetrahydrofuran), or in a mixture of the solvent and water, suggests that the irradiation and the sacrificial reductant are both necessary to initiate the reaction. After reaching a maximum intensity after 20 minutes of irradiation, the signal rapidly decreased due to the degradation of the ligands. The reduced form of the iridium complex then reacted with the iron pre-catalyst, to form the active species of the water-reduction cycle, which generated hydrogen from the water protons. The only intermediate that had been previously detected was [HFe3(CO)11], which was presumed to be the active catalytic species.194 When the full reaction mixture, including the iron catalyst, was analysed using EPR, the iridium signal was not observed, due to the fast electron transfer to [Fe3(CO)12] that greatly reduced the reduced photosensitiser lifetime. The second catalytic cycle was more difficult to observe via EPR, due to the prevalence of EPR silent species. After addition of the iridium photosensitiser, a non-irradiated sample displayed three narrow radical signals. Each one of these signals was assigned to a specific di-nuclear iron radical complex, [Fe3(CO)12]  (g ¼ 2.0016), [Fe3(CO)11]  (g ¼ 2.0497), and [Fe2(CO)8]  (g ¼ 2.0385), which accounted for about 94% of the all iron present in the starting solution. After irradiation these signals were replaced by a triplet signal with g ¼ 2.0433 consistent with the formation of a [H2Fe2(CO)7]  species, accounting for just 3% of the total iron content. Experiments conducted with a 420 nm cut-off filter, which excludes the UV component of the irradiating light, showed a nearcomplete suppression of these radical signals without a corresponding 32 | Electron Paramag. Reson., 2021, 27, 1–46

reduction of hydrogen production, proving that these species are decomposition products, and are not involved in the reaction mechanism. The low intensity of the EPR signals in these reactions suggest that the main species involved are diamagnetic. This observation was confirmed by in-situ Raman spectroscopy and DFT calculations, suggesting the [HFe3(CO)11] species is the main component present during the reaction, demonstrating the importance of a combining a variety of characterisation techniques in order to achieve a comprehensive approach to mechanistic investigations. An important tendency in the current research on photochemical systems is the shift towards earth-abundant metals and organic dyes, which would greatly increase the practicality and the green potential of the photochemical processes.195 Ruthenium and iridium, while well-known and extensively studied, are rare metals, and as such are severely limited in their application. As an example, several noble-metal free alternatives have been studied as photosensitisers for the previously cited iron-based waterreducing carbonyl complex, such as copper(I) complexes, zinc porphyrins and organic dyes.196–198 Many of these catalytic cycles involve radicals with very short lifetimes, which require the use of radical traps for detection, thus adding another layer of complexity to the study.199 Thorough EPR investigations of these systems is often further complicated by poorly understood reactivities and detection issues. For example, copper (I) based complexes, such as [Cu(dap)2]1 (dap ¼ 2,9-bis(p-anisyl)-1,10-phenanthroline), have been successfully employed in a wide variety of photoredox reactions.200–203 As copper-based photocatalytic processes are relatively new, these systems have seldom been subjected to detailed mechanistic analyses. EPR could offer a promising avenue of research in this field, since the complex should evolve to a Cu21 site at some point during the catalytic cycle.204,205 Furthermore, complexes presenting M–N bonds, such as metal porphyrins, have also been successfully investigated using pulsed EPR techniques, such as ESEEM and HYSCORE, revealing detailed structural information on the system.206,207 Thus, despite the obvious challenges, it is easy to see how these methodologies could be fruitfully adapted to this, and other novel photocatalytic systems, in order to obtain more important mechanistic insights and further expand this field of research. 5.2 Catalytic alcohol oxidation The catalytic oxidation of alcohols is a very important industrial process, and the reaction mechanism is often dominated by the involvement of free radicals and paramagnetic transition metal species. Understanding the nature of these intermediates is therefore essential in order to ascertain the underlying catalytic cycle, and as illustrated earlier for other important reactions, EPR provides an ideal method of choice to unravel the crucial low energy reaction pathways provided by the catalyst.183 Considering the dominance of paramagnetic species in copper-containing alcohol oxidation catalysts, Stahl et al., recently explored the mechanism of aerobic alcohol oxidation with Cu/nitroxyl systems.208–211 In a series of studies, the authors evaluated the performance of various Cu/nitroxyl catalytic systems containing Cu/TEMPO (where TEMPO ¼ 2,2,6,6-tetramethylpiperidine-N-oxyl) Electron Paramag. Reson., 2021, 27, 1–46 | 33

and Cu/DBED, DMAP (where DBED ¼ N-N 0 -di-tert-butylendiamine, and DMAP ¼ p-(N,N-dimethylamino) pyridine).210,212 Combined EPR, UV–vis and cyclic voltammetry (CV) indicated a two-stage catalytic mechanism involving catalyst oxidation, in which Cu11 and TEMPO-H are react with O2 and substrate oxidation, mediated by Cu21 and the nitroxyl radical via a Cu21-alkoxide intermediate.210 Since the research was based on the comparison of both aliphatic and aromatic alcohols, interestingly, the observations suggested that the resting state of the catalyst varied depending on the identity of alcohol substrate. With aromatic alcohols such as ph-CH2OH, EPR revealed that the majority of the catalyst is present as Cu11, whereas with an aliphatic substrate like Cy-CH2OH, both Cu11 and Cu21 co-exist during the reaction and their ratios change as the substrate oxidation progresses. Another related homogenous catalyst system entailing [Cu(MeCN)4]PF6, N-N 0 -di-tert-butylendiamine (DBED) and p-(N,N-dimethylamino)pyridine (DMAP) was shown to be capable of mediating efficient aerobic oxidation of alcohols.212 This catalytic system was correlated with an oxidative self-processing step and EPR spectroscopy evidenced the build-up of organic nitroxyl species which could be generated during steady-state turnover, from DBED with the EPR signal of an organic radical g ¼ 2.0023 clearly visible, accompanied by a hyperfine coupling of A ¼ 85 MHz. The signal increased in intensity during the steady-state period of the reaction, and was assigned to the EPR spectra of the nitroxyl radical TEMPO and (9-azobicyclo[3.3.1]nonane N-oxyl) ABNO.213,214 Analysis of the extracted aliquots of the Cu/DBED/DMAP catalyst system revealed an EPR spectrum with axial symmetry based on the parameters g84g>, gxx ¼ 2.03, gyy ¼ 2.07, gzz ¼ 2.26 and A8 ¼ 553 MHz. Both galactose oxidase (GAO) and Cu/nitroxyl systems have been well investigated and different catalytic pathways have been proposed based on EPR spectroscopy, kinetic analyses and computational studies. Concurrently in both oxidation methods, the formation of Cu21-alkoxide intermediates has been confirmed in several cases.215,216 In an effort to understand the structure of the intermediates, Stoll et al., prepared a CuIIalkoxide complex, labelled TptBuCuII(OCH2CF3), where TptBu ¼ hydrotris(3-tert-butyl-pyrazolyl)borate which was abbreviated to CuII-O(TFE).215 The authors characterised the electronic structure of the complex using powder and single crystal EPR, and confirmed the expected trigonal monopyramidal coordination geometry. Their study revealed the identity of single occupied molecular orbital (SOMO) as dx2–y2 and its orientation within the CuII–O(TFE) complex, in a plane normal to the Zg axis and nearly normal to the long Cu–Naxial bond. The compound produced a distinctive EPR spectrum, possessing axial symmetry and large Dg shift producing gzz ¼ 2.44 with a small copper hyperfine coupling of Cu Azz ¼ 120 MHz.217 In addition to probing the interaction of the unpaired electron with copper nuclei, ENDOR measurements were also used to ascertain the magnitude of the interaction between the unpaired electron and nearby spin active nuclei (1H,19F,14N). With these investigations, they quantified the extent of delocalization of the unpaired electron onto the TPtBu and triflourethoxide ligands and found much of the spin population 34 | Electron Paramag. Reson., 2021, 27, 1–46

is based on the Cu21 ion (E 68%) with no more than 15% on the oxygen of the alkoxide ligand. Bosch et al., explored the electron structure and reactivity of a copper complexes bearing bidentate redox-active ligands consisting of H-bonding donor groups.218 A combination of single-crystal X-ray, EPR, UV–vis and CV techniques were combined to probe the catalytic mechanism of this complex, which had some pronounced differences with the common GAO model systems, in which O2 reduction occurs at the same time as oxidation of the substrates.219 In their initial study, the molecular structure of the complex was analysed by single-crystal crystallography. This revealed that the molecular structure depended on the coordinating ligand and solvent used in crystallisation, including a square-planar or twisted pseudo-tetrahedral geometry. The redox chemistry of copper complexes was then probed by CV and UV–vis spectroscopy, and the results were corroborated by EPR spectroscopy. The EPR data obtained in these oxidation/reduction experiments confirmed the axial symmetry of the complex, with g> ¼ 2.05, g8 ¼ 2.21 and A8 ¼ 154 G. The addition of a second equivalent of Fc1 generated a copper species which was EPR silent, due to its associated two o-benzosemi-quinonediiminato radical ligands, in which the metal ion and the ligand radicals were antiferromagnetically coupled due to the nonplanar geometry (i.e., D2d geometry), and was concomitant with the appearance of an EPR signal at g ¼ 1.99. Several papers have also been published recently describing the role of EPR to study the catalytic oxidation reactions of various Cu complexes.220–222 In most of these Cu21 complexes, EPR was primarily used to identify the oxidation state of the central metal ion, the coordination environment surrounding the active site and also to gain insights into the alcohol oxidation mechanism. 5.3 C–C cross-coupling The carbon-carbon cross-coupling reaction is one of the most important chemical transformations in synthetic organic chemistry. Among the transition-metal catalysts employed for this reaction, nickel- and iron-based systems have been very successful in important reactions such as the Heck, Himaya, Kumada, Negishi, Suzuki-Miyaura, Sonogashira and Still coupling reactions. Iron is particularly attractive for these reactions because is is very abundant, and also easily switched among several oxidation states in catalytic cycles.223 Different spectroscopic methods, including EPR, 57Fe ¨ssbauer, and magnetic circular dichroism, have revolutionised the Mo ability to delineate the underlying iron and nickel speciation.224 The driving force in this field, in recent years, has focused on the choice of ligands employed to stabilise the active oxidation states, such as N-heterocyclic carbenes (NHCs) and bisphosphines, and these ligands have also been found to improve the overall selectivity in cross-coupling reactions.225–228 For example, Whittlesey et al.,224,228,229 designed a series of air-sensitive [NiI(PPh3)(NHC)X] complexes (X ¼ Br, Cl) using bulky NHC ligands. They investigated the effect of sterically demanding substitution at the central heteroaromatic ring which is required to stabilise the low-coordinate and low-valent Ni11 complex and to avoid any intermolecular Electron Paramag. Reson., 2021, 27, 1–46 | 35

reactions.225,229,230 The authors used a combination of CW and pulsed EPR spectroscopy, with complimentary DFT calculations, to extract information about the fundamental properties (structure and bonding) and catalytic efficiency of the complex in the Kumada coupling of aryl-flourides and aryl-chlorides. The EPR spectra revealed a rhombic symmetry for the low coordinated Ni11 systems, with a large super-hyperfine coupling to the 31P and 79,81Br nuclei. All complexes displayed an unusual trend in the g values (g3–g2og2–g1) which is in contrast with the observations for other three coordinated complexes, such as [Ni (PPh3)3][BF4], [Ni (PPh3)2X] (X ¼ Cl, Br) and [Ni-(N^N)R(L)] (in which (N^N)R ¼ R-substituted bulky b-diketiminate and L ¼ PCy3 or 1,1-bis(diphenylphosphino) (dppm)). This trend was accounted for due to the NHC ligand influence on the g tensor, which must in turn supersede the effects of the vibronic interactions. The spin Hamiltonian parameters of these complexes were all found to be influenced by the changes in NHC ring size, the choice of the substituent (mesityl or tolyl) and the choice of halide. Furthermore, DFT calculations revealed a mixed SOMO of 3dz2 and 3dx2–y2 character which is highly dependent on the complex geometry.230 In another example, Apfel et al.,230,231 showed that Ni and Fe complexes bearing the Triphos(2-((diphenylphosphaneyl)methyl)-2-methylpropane1,3-diyl)bis(diphenylphosphane) and TriphosSi(((methylsilanetriyl)tris(methylene))-tris(diphenylphosphane)) ligands are potential noble metal-free alternatives for the C–C cross-coupling of aryl iodides and alkynes.231,232 Owing to the high steric hindrance of the Triphos ligand, such Ni complexes did not show any disproportionation of the respective Ni11 complexes to Ni0 and Ni21, and also no evidence of any dimerisation to form the di-nickel complex. The Kumada cross-coupling abilities of these complexes were also studied by Apfel et al.223 The precatalyst is based on the EPR silent Ni21 complex, which reverts to Ni11 following addition of a Grignard reagent to the solution. EPR analysis of the reaction medium revealed small changes to the hyperfine pattern, accompanied with a broadening of the g values after the addition of an aryl-iodides, and also suggested the formation of least one additional Ni21 species during the catalytic cycle. In addition to nickel, iron has also attracted considerable attention for its role in cross coupling reactions. Bedford et al., designed and evaluated different iron based catalytic systems, using EPR amongst other techniques, to probe the reaction mechanism.233,234 In particular, the efficiency of the iron-phosphine catalyst, based upon the relatively easily accessible bis(diphenylphosphino) ethane (dppe) ligand was investigated.233 The dppe-based catalysts demonstrated excellent reactivity in reactions compared to the dpbz-based class of ligands (dpbz ¼ 1,2-bis(diphenylphosphino)benzene). To understand the basis for the similarity in performance, the study focused on the molecular and electronic structures of Fe11–dppe species. The application of DFT calculations, X-ray crystal structure, and EPR studies confirmed that this low valent iron state adopted a distorted trigonal bipyramidal structure with a low spin (S ¼ 1/2) character. In both complexes, the Mulliken spin density was mostly localised on the iron centre, with only a small contribution from the 36 | Electron Paramag. Reson., 2021, 27, 1–46

ligating P and halide atoms. The complexes all possessed a rhombic g tensor, consistent with the low spin character of the Fe11 centre, with spin Hamiltonian parameters of g1 ¼ 2.038, g2 ¼ 2.051 and g3 ¼ 2.132 for Fe11-dppe with a Br substituent; and g1 ¼ 2.047, g2 ¼ 2.066 and g3 ¼ 2.167 for Fe11-dppe with the Cl substituent. The EPR spectra also revealed more complicated interactions arising from overlapping super-hyperfine features emanating from 31P and 35,37Cl/79,81Br nuclei. In addition to these super-hyperfine interactions, underlying quadrupole interactions responsible for the unusual linewidth effects, were also observed. The progress towards an improved mechanistic understanding of iron and nickel catalysed cross-coupling reactions has dramatically improved over the last decade. EPR has been instrumental in leading this revolution of understanding the role of first-row earth abundant metals in C–C cross coupling catalysis. Significant improvements in the use of iron and nickel species that afford greater stability and selectivity, bearing simple salts like ferric salts,235,236 or ligands such as bisphosphine,237 and NHC,225,238,239 is yet to be achieved.

6

Summary and perspectives

In the past, certain catalysts dominated the manufacturing industry, from aluminosilicates used for catalytic cracking, to iron and its historical use in the Haber process, to vanadium for sulfuric acid production to platinum and alumina used as versatile bifunctional catalysts to nickel for synthesis gas production. So many of the materials and products we depend upon, such as fuels, fragrances, fertilizers, foodstuffs, pharmaceuticals and fabrics, continue to involve catalysts that were developed over the decades. Just as important, many fundamental molecules and chemicals used for the manufacture of numerous commodity chemicals also rely upon a catalyst, such as benzene, toluene, xylene, terephthalic acid and propylene. Despite this success and dependency, there remains an urgent need to develop new catalysts that can transform or upgrade the readily available raw materials in a sustainable and environmentally friendly manner. This challenge facing the catalysis community is significant and considerable; for example, how can we use cheap abundant elements employing molecular oxygen as an oxidation at ambient conditions in a single pot reaction with no waste. With all these considerations in mind, more and more attention is returning to the role of first row transition metals for catalytic reactions that were previously considered impossible to deliver. And as we explore this potential landscape with the benefit of modern and more powerful analytical techniques, along with improved computational power, we are beginning to see the growing influence and evidence for the involvement of paramagnetic (open shell) centres and free radicals. The dominant and most successful characterisation technique in catalysis over the decades has undoubtedly been NMR, but when paramagnetic systems are in play, these quintessential tools have some limitations. Nevertheless, this is the realm where EPR can contribute and offer it’s enormous wealth of information on the paramagnetic states, akin to the diamagnetic states Electron Paramag. Reson., 2021, 27, 1–46 | 37

comprehensively explored by NMR. The involvement of a paramagnetic state should not therefore hinder nor limit the developments of new catalytic processes, merely because they are hard to study, and instead involve the substantial EPR tool-kit to uncover the nature of the active sites involved in the reaction pathways. In this Chapter, we have therefore tried to exemplify and reveal not only how widespread the paramagnetic state is in very different types of catalytic reactions, but also how much information can be extracted from the EPR data. Regardless of the nature of the catalyst, from heterogeneous to homogeneous to enzymatic, the EPR method can still provide local and longer range information on these open-shell states. If we are to assist the catalysis community in meeting the challenges of developing the next generation of environmentally friendly catalysts, then EPR will be one of the essential characterisation methods required to shed light on the inevitable involvement of the free radical and paramagnetic centres.

Acknowledgements The authors gratefully acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 813209 entitled PARACAT. The authors would also like to thank the PARACAT academic supervisors, Profs. ´s Garcı´a Rubio, and Sabine Van Doorslaer, Mario Chiesa, Andreas Poeppl, Ine for constructive discussions and feedback in preparing this Chapter.

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46 | Electron Paramag. Reson., 2021, 27, 1–46

Advanced EPR spectroscopy for investigation of biomolecular binding events Joshua L. Wort, Maria Oranges, Katrin Ackermann and Bela E. Bode* DOI: 10.1039/9781839162534-00047

The emergence of systems biology in the post-genomic era has led to investigating increasingly complex macromolecular assemblies, emphasising holistic approaches in structural biology. This changing philosophy is prefaced on the understanding that pathologies are often borne-out of dysregulated, multifaceted interactions within wider biological networks. However, while accurate characterisation of such biomolecular interactions in a biologically valid context is important, this dramatically increases the experimental complexity. In this purview, electron paramagnetic resonance (EPR) is particularly appealing because it is one of few techniques not overwhelmed by the increasing complexity of biomacromolecules in their native context or supramolecular networks. In a variety of ways EPR can additionally detect and quantify interactions, intimately coupling structural information and binding events within the biological or structural context.

1

Introduction

For more than sixty years the postulate that all biomolecular function is encoded by structure has been successfully explored, providing great insight largely by means of X-ray crystallographic structure determination. The structure-function paradigm has become a central dogma of structural biology.1,2 The development of systems biology3 over the last decades has heralded a transformative change in how this structurefunction relationship is investigated. As more and more examples have emerged where interactions in multi-component systems can lead to emergent properties, it has become evident that the reductionist approach of studying isolated biomolecules can be sub-optimal. This has propelled integrative biochemical and biophysical strategies which preserve biological validity under experimental conditions and facilitate measurement within biological context. Furthermore, acknowledgement of the interplay between the cellular environment4 and machinery makes measurement in situ or in vivo especially appealing. Perhaps the best-known example of an emergent property is the cooperativity of oxygen binding afforded by Haemoglobin quaternary structure.5 More generally, non-covalent interactions are crucial in modulating reversible, tuneable responses to stimuli and environmental stressors. The scope of these non-covalent interactions is ubiquitous and their significance in human health and disease is crystallised by dysregulation causing neurodegenerative amyloidogenic pathologies. Select examples include: a-synuclein, and amyloid-b (Ab) aggregate formation EaStCHEM School of Chemistry, Biomedical Sciences Research Complex, and Centre of Magnetic Resonance, University of St Andrews, North Haugh, St Andrews, KY16 9ST UK. E-mail: [email protected] Electron Paramag. Reson., 2021, 27, 47–73 | 47  c

The Royal Society of Chemistry 2021

in Parkinson’s,6 and Alzheimer’s diseases,7 respectively, and Huntingtin misfolding in Huntington’s disease.8 Many of these interactions make ideal therapeutic targets for small-molecule drug design, which reinforces the need to characterise their binding equilibria. Techniques commonly used to study non-covalent interactions include isothermal titration calorimetry (ITC), surface plasmon resonance (SPR), and biolayer interferometry (BLI). ITC is label-free and performed in solution, but is calorimetric which can limit sensitivity, and makes detection of low-affinity interactions difficult. Analysis of complex binding equilibria by ITC is vulnerable to overfitting, though this is being addressed in the field.9 SPR is also label-free, can be used for thermodynamic and kinetic10 characterisation with higher sensitivity11 than ITC, but requires immobilisation. Similarly, BLI requires ligand immobilisation, has lower accuracy and reproducibility than SPR, but is easily adapted to a 384-well plate format facilitating high throughput.12,13 An important consideration is that none of these methods provide any structural information. Size exclusion chromatography mass spectrometry (SEC-MS) is also appealing as a high-throughput method used in ligand-screening,14 and ion-mobility mass spectrometry (IMMS) has been used in conjunction with infrared spectroscopy to report coarse aggregate structure.15,16 Indirect structural information can be inferred using Hydrogen–Deuterium exchange mass spectrometry (HDX-MS),17,18 which has been coupled with NMR and SPR to validate protein-ligand19 and protein–protein20 interactions, respectively. Native mass spectrometry techniques such as laser induced liquid bead ion desorption (LILBID)21,22 allow non-covalent interactions to be studied directly, though structural information is limited to oligomeric state.23 Furthermore, mass spectrometry methods require measurement in the gas-phase. Alternatives which provide information about quaternary structure and can inform binding equilibria in solution-state include: small-angle X-ray scattering (SAXS),24 sedimentation velocity analytical ultracentrifugation (SV-AUC),25 and dynamic light scattering (DLS).26 Circular dichroism (CD) is sensitive to secondary structural changes upon ligand or protein binding,27 which can report sub-populations in binding equilibria.28 However, it should be appreciated that this is not always possible if the ligand binding event is not coupled to a structural change, in which case it can be complemented by differential scanning fluorimetry (DSF).29,30 In recent years, techniques such as nuclear magnetic resonance (NMR),31 ¨rster resonance energy cryo-Electron Microscopy (cryo-EM),32 and Fo transfer (FRET)33 have found increasing utility as methods for investigating macromolecular binding events.34–39 The combination of atomistic structural constraints and binding information is especially useful to provide mechanistic insight.40–42 Solid state NMR (ssNMR) is useful for studying large systems in a native context, isotope labelling can provide insight of individual components within a complex, without concerns of sizelimitation.43 However, owing to the incomplete averaging of anisotropies ssNMR has broader linewidths than liquid-state NMR. The latter is more frequently used in a biological context. Nevertheless, the opportunity to enhance solid-state NMR signals via dynamic nuclear polarisation (DNP) allows interrogation of systems of tremendous complexity.44 48 | Electron Paramag. Reson., 2021, 27, 47–73

Cryo-EM is increasingly used to study biomolecular assemblies that are non-permissive to crystallisation. Generating an ensemble of threedimensional structures, cryo-EM has utility in characterising heterogeneous sub-populations, which is often not possible using X-ray crystallography. Additionally, sample preparation on a shorter timescale than crystallisation provides greater sensitivity to weak non-covalent interactions between molecules. A recent example involved the trapping of the a2b2 ribonucleotide reductase holo-complex,39 where slowing the dissociation rate to the minute time-scale allowed detection of the complex via cryo-EM. However, the required technical expertise and access to facilities can be limiting. FRET is appealing in complex systems with multiple components, as ‘multi-colour’ approaches using different fluorophore labels for the components of heteromultimers mean interactions between specific partners can be followed in vivo.45,46 Even so, FRET is commonly limited to pairwise distances, but can provide long-range distance constraints with single molecule sensitivity at ambient conditions.47 However, FRET requires the use of pairs of large labels, which can perturb native structure and binding interactions and gives rise to uncertainties in the orientation factor needed for accurate distance extraction. One technique which has developed very promising methodologies for the study of biomolecular binding and interactions is electron paramagnetic resonance (EPR) spectroscopy. EPR is a methodology exclusively and exquisitely sensitive to paramagnetic centres with unpaired electron spins. Especially the more recent pulse techniques are ideally suited to bridge the disconnect between local atomistic structural information and lower resolution topologies. Particularly, pulse dipolar EPR (PD-EPR) can provide longerrange distance information than typically accessible by NMR, in favourable cases exceeding 100 Å.48 While the sensitivity of PD-EPR is not yet comparable to optical methods, the often required labelling is commonly less structurally perturbative than in FRET; spin labels are significantly smaller than comparable fluorophores. Thus, the contribution of PD-EPR to structural biology has been profound, and several excellent reviews exist.49–54 In this purview, PD-EPR is useful for coupling structural information and binding events. Here, the state-of-the-field of EPR applied specifically to non-covalent interactions and associated binding equilibria is reviewed. The review proceeds in three main sections: i) continuous-wave EPR (CW-EPR), ii) pulse EPR spectroscopic methods of monitoring binding equilibria, and iii) critical analysis of exemplary case studies, highlighting different methodological aspects.

2

Characterising binding equilibria via EPR

2.1 Continuous-wave EPR Continuous-wave EPR is sensitive to binding equilibria through changes in spectral line-shape. Broadly, this manifests by three main mechanisms (see Fig. 1): i) altered molecular dynamics (i.e., changes in the rotational correlation time tc) or relaxation behaviour upon complexation, resulting Electron Paramag. Reson., 2021, 27, 47–73 | 49

Fig. 1 Monitoring of interactions via CW-EPR. The minor circular sector represents a monovalent ligand, the major circular sector represents a protein, and the square tag represents a paramagnetic spin label. The left-hand side (LHS) of each reaction scheme is represented by the grey EPR spectra, while the right-hand side (RHS) of each reaction scheme is represented by the black EPR spectra.

in inhomogeneous or homogeneous line broadening, respectively, ii) introduction of new interactions (often dipolar coupling of unpaired electron spins), leading to line splitting or broadening, and iii) structural changes inducing altered spin Hamiltonian parameters, yielding differential spectral line-shapes amongst bound and unbound subpopulations. One should bear in mind that these methods are indirect reporters of macromolecular interactions; the spectral line-shape is a convolution of homogenous and inhomogeneous line-broadening and accurate analysis relies on components being separable.55 Changes in tc have been used to monitor binding events between protein monomers56 and between nucleic acids and small molecules.57,58 This method allows interactions to be followed under native conditions,59 in vivo60 and in real-time to provide insight into kinetics.61,62 It was possible to extract quantitative kinetics in the cyanobacterial circadian clock in vitro in a real-time CW-EPR assay63 over several days, studying the circadian assembly and disassembly of its components based on changes in tc. Quantifying tc is useful in spin-labelled systems interacting with a diamagnetic partner (where the effects of potential dipolar broadening are absent), and in epitope mapping64 when coupled with mutational analysis. However, labels with high intrinsic flexibility are insensitive probes to monitor changes in molecular backbone dynamics. Introducing artificial amino acids with paramagnetic moieties rigidly fixed to their backbone structure can improve sensitivity,65 although it can be impracticable in large peptides. Furthermore, this method is dependent on both the paramagnetic species, and the chosen frequency-band; spin labels with greater anisotropy can provide sensitivity to faster timescales when measured at higher frequencies.66 50 | Electron Paramag. Reson., 2021, 27, 47–73

Solution-state nitroxide-based CW-EPR performed at X-band is typically sensitive to rotational correlation times on the scale of 1011–107 seconds, before being well into the isotropic and rigid limits, respectively. Dipolar line-broadening is another method to monitor binding interactions via CW-EPR,67 particularly between multiple spin-labelled or paramagnetic species, and occurs in systems where electron spins are coupled through space. Thus, dipolar line-broadening is appealing in monitoring oligomerisation,68–70 or in systems with known conformational changes upon ligand binding, that bring spin labels into a distance range between 8 and B25 Å. However, this approach requires measurement of both coupled and uncoupled spin systems to accurately assess the dipolar line-broadening, which requires control samples and can be practically difficult in homo-multimers. When monomeric subunits cannot be measured in isolation, appropriate diamagnetic spin dilution can provide a statistical label distribution and facilitate measurement of the singly labelled homo-multimer.71 The Spin Hamiltonian parameters provide a phenomenological means to monitor structural and electronic changes, manifest as altered system parameters since they describe all the interaction energies in a spin system. More broadly, simulation of distinct spectral components is a powerful method to quantitatively assess linear weighted contributions of sub-populations to composite spectra; this approach has been used extensively to monitor metal ion binding within proteins.72 Furthermore, dissociation constants have been determined for both protein–protein73 and protein–ligand74 interactions based upon spectral changes, by deconvolution of experimental spectra into bound and unbound populations. A common electronic structural change is altered ligand field symmetry; the increased zero-field splitting of MnII upon coordination by MnxG was used to monitor kinetics of binding.75 Changes in spectral parameters are especially useful reporters of interactions if coupled with robust multi-frequency simulations.76 However, this methodology can be vulnerable to overfitting, therefore in systems with more than two components, additional biophysical techniques may be necessary to validate spectral simulations.77 In the extreme case, charge transfer processes can remove paramagnetic centres and thus abolish the spin Hamiltonian altogether, resulting in a quenching of the spectral line. This has proved instructive in elucidating mechanistic understanding in protein redox chemistry.78,79 While dipolar coupling is often analysed via convolution with a dipolar broadening function with a different susceptibility to experimental noise than direct superposition of spectral components, the robustness of all three approaches will greatly improve given spectral differences between bound and unbound components are sufficiently large to be resolved. In cases where this is ill met there is a potential risk of overfitting. In conclusion, CW-EPR is a valuable method to probe biomolecular interactions, and can provide structural, kinetic and thermodynamic insight. However, in most cases CW-EPR only allows indirect measurement of binding events. Furthermore, quantitative analysis of CW-EPR spectra is often constrained by parametric models and thus relies on a priori knowledge of the system. This is a significant limitation, Electron Paramag. Reson., 2021, 27, 47–73 | 51

particularly because observing binding directly removes dependence on such parametric models and is more robust and facile than indirect detection; pulse EPR methods have subsequently found increased appeal as additional tools for investigating binding events. 2.2 Pulse EPR spectroscopy Pulse EPR spectroscopic methods allow direct measurement of binding events by isolating specific terms in the spin Hamiltonian (see Fig. 2). This typically involves two spin coupling regimes: i) hyperfine couplings arising from electron–nuclear interactions, and ii) dipolar couplings arising from electron–electron interactions. Hyperfine spectroscopy methods may provide direct evidence of binding events in the frequency domain by virtue of nuclear Larmor precession, and the relative intensities of the frequency peaks. On the other hand, dipolar spectroscopy can provide direct evidence of binding in the time domain, manifesting in the modulation depth (D) (i.e., the percentage of electron spins coupled through space contributing to the signal). Additionally, dipolar spectroscopy can also give indirect evidence of interactions in the distance domain, via a conformational change coupled to the binding event. 2.2.1 Electron–Nuclear spin coupling. Electron–nuclear interactions can provide valuable insight into ligand binding environment and ternary complex formation via fingerprinting of the coordinating nuclei. This hyperfine coupling is typically probed by two main strategies: i) electron spin echo envelope modulation (ESEEM)80,81 that is most

Fig. 2 Monitoring of interactions via pulse EPR. The minor circular sector represents a monovalent ligand, the major circular sector represents a protein, and the square tag represents a paramagnetic spin label. In the Hyperfine Couplings section (top left), the LHS of the reaction scheme is represented by the grey ESEEM spectra, while the RHS of each reaction scheme is represented by the black ESEEM spectra. In the Distance Distributions section (top right), the LHS of the reaction scheme corresponds to the shorter distance, while the RHS of the reaction scheme corresponds to the longer distance. In the Modulation Depths section (bottom left), each row of the reaction scheme corresponds to cases I-III, respectively. 52 | Electron Paramag. Reson., 2021, 27, 47–73

sensitive for weak coupling interactions to quadrupolar nuclei and at low fields owed to reliance on forbidden transitions, and ii) electron– nuclear double resonance (ENDOR)82,83 for strongly coupled nuclei often attractive at higher frequency due to dispersion of nuclear frequencies. Therefore, ESEEM and ENDOR offer complementary information in different regimes of hyperfine couplings. An additional technique is electron–electron double resonance (ELDOR)-detected NMR (EDNMR),84,85 which is also sensitive to strong-coupling interactions but has improved sensitivity compared to ENDOR.86 ESEEM has been used extensively to characterise metal ion binding within proteins. The nitrogen ESEEM modulation depth quantified the binding affinity of CuII-iminodiacetic acid (IDA) for a-helical and b-sheet double-histidine motifs in Streptococcus sp. G. protein G, B1 domain (GB1) and confirmed double histidine coordination.87 Furthermore, a combination of ESEEM and hyperfine sub-level correlation (HYSCORE) spectroscopy was used to investigate the influence of pH upon CuII binding to the active site of D. melanogaster Lysyl Oxidase (LOX).88 Results indicated that under high pH conditions (pH 9.3) the CuII is uniformly coordinated in an environment containing a single histidine residue, but under physiological pH (pH 7.5), the CuII is instead coordinated in two equivalently populated environments containing one and three histidine residues, respectively. A novel MnII binding site in human Calprotectin, coordinated by six histidine residues was characterised using two-, three- and four-pulse ESEEM.89 Quantification of the 15N four-pulse ESEEM combination peak showed that the MnII binding equilibrium could be shifted from multiple lower affinity sites to the high-affinity hexa-histidine site, upon addition of CaII. Conversely, ENDOR is an appealing strategy to investigate interactions within nucleotides, especially at Q- and W-band frequencies where the coupling originating from 31P in the phosphate backbone is too large to be detectable by routine ESEEM measurements. ENDOR is also increasingly combined with EDNMR because of improved sensitivity, and an absence of blind spots in the EDNMR spectrum. Additionally, quantitation of peak intensities is more straightforward when compared to both ENDOR and ESEEM, and therefore EDNMR is a powerful tool that has been appropriated to directly quantify equilibrium sub-populations.90 However, while EDNMR is useful in the study of interactions with low-g quadrupolar nuclei, the improved sensitivity compared to ENDOR is compromised by a loss in the line-shape information and subsequent resolution (i.e., the central hole can mask signals manifesting from low frequencies). Notably, 31P hyperfine couplings can provide insight into the catalytic cycles of systems with ATPase activity, particularly those amenable to substitution of diamagnetic divalent metal cofactors with paramagnetic analogues. For example, substituting a MgII cofactor for paramagnetic MnII in the chaperone Heat Shock Protein 90 (Hsp90)91 allowed investigation of the ATP hydrolytic cycle using 31P ENDOR. While the ATP-bound state had been studied extensively, the ADP-bound (posthydrolytic) state has been identified to be involved in recruitment and chaperoning of client proteins, and was found to be in a ‘compact’ Electron Paramag. Reson., 2021, 27, 47–73 | 53

configuration in solution. This approach has been suggested as broadly applicable to other systems utilising MgII cofactors and driven by ATP-hydrolysis. In another study, a combination of ENDOR and EDNMR allowed identification of different nucleotides coordinated to a MnII cofactor in the nucleotide binding site of a pair of ABC exporters, homodimeric MsbA and heterodimeric BmrCD, and revealed how their ATP turnover kinetics differed.92 These results support the postulated mechanistic divergence of ABC exporters in dependence of their nucleotide-binding domains with slower sequential ATP-hydrolysis in heterodimeric exporters, compared to homo-dimeric exporters. 2D EDNMR was used to correlate 31P and 13C cross-peaks,93 combined with 13 C ENDOR to detect a ternary complex of a synthetic tetracycline (TC) RNA aptamer, TC and MnII. 2.2.2 Electron–Electron spin coupling 2.2.2.1 Direct measurements of binding equilibria. It was recognized as early as 1984 that PD-EPR could principally be used to assess multimerization via spin-counting.94 Here, we can define the modulation depth95 (D) mathematically and relate this to the number of coupled electron spins (N): D ¼ 1  (1  lf )N1

(1)

where l and f are the inversion efficiency of the pump microwave pulse, and the labelling efficiency, respectively. Importantly, for a constant labelling efficiency, as inversion efficiency increases (e.g., in the relaxation induced dipolar modulation enhancement (RIDME) experiment,96,97 where lmax ¼ 0.5, for S ¼ 1/2 systems) modulation depths become non-linear. Furthermore, it should be noted that while this relationship is conceptually valid for all PD-EPR experiments, it has only been empirically validated for the 4-pulse pulse electron–electron double resonance (PELDOR) experiment.98 Since this time, PD-EPR has been used to disentangle competing structural models,99,100 metal–ligand binding,101,102 and cooperativity of binding.103,104 Modulation depth quantification is arguably the most direct way to investigate binding equilibria via PD-EPR, and one of the most sensitive. Considering a binary interaction between quantitatively labelled macromolecules that each contain identical paramagnetic moieties, only dipolar-coupled electron spins (i.e., the fraction of molecules that form an intermolecular complex) will modulate the detected echo, representing the weighted contributions of signals arising from macromolecules in the free and intermolecularly bound states. This fraction is reported by the modulation depth. By systematically titrating the binding partners (e.g., ligand against a fixed protein concentration) the equilibrium can be characterised. There are several examples of using PELDOR modulation depths to determine association constants in monomer-dimer, or more complex equilibria,105–110 or to infer respective affinities.111 PELDOR has also been used to investigate stoichiometry of binding,112 and the stability of nucleic acid complexes.113 54 | Electron Paramag. Reson., 2021, 27, 47–73

The strengths of this approach to investigate macromolecular interactions directly, compared with indirect methods are multifaceted. Modulation depth quantification is more robust than quantification of populations from PD-EPR distance distributions because it is not predicated on detectable conformational changes upon ligand binding. Perhaps more significantly, the probability of false-positive errors (i.e., modulation of the detected echo when interaction does not occur) can be minimised by measuring negative control samples where the interaction is knocked out. However, false-positive errors are feasible as the result of sub-optimal estimation of the background function; the necessity for high-quality time domain data is therefore crucially important in modulation depth quantitation. Additionally, from a simply qualitative perspective modulation depth can provide a Boolean assessment of interactions in the system under investigation. This is rarely possible using indirect methods such as CW-EPR, outwith charge transfer or quenching reactions (see Section 2.1). The potential of modulation depths to report equilibrium populations is broadly leveraged on two factors: i) accurate background correction to faithfully separate the modulated and unmodulated components of the detected echo from the echo decay and ii) to robustly separate and quantify the modulated and unmodulated contributions neither should be vanishingly small as the sensitivity to changes would diminish within experimental noise. While the PELDOR background is best understood, achievable modulation depths are frequently constrained by low inversion efficiency (l) of rectangular microwave pulses, particularly in paramagnetic centres with broad spectral lines such as many metal ions. This is frequently remedied through application of shaped-pulses and arbitrary waveform generators (AWGs).114,115 Nevertheless, single-frequency techniques such as RIDME,96,97 double quantum coherence (DQC) filtered EPR116 and single-frequency technique for refocusing (SIFTER)117 can yield significantly improved sensitivity. Although this has not been shown comprehensively for all methods discussed, conceptually all signals will be superpositions of modulated and unmodulated echoes, representing bound and unbound components. Thus, there is significant scope to increase sensitivity to weak binding events by single-frequency methods. A potential caveat of quantifying modulation depths to monitor macromolecular interactions is that both interacting species must contain a paramagnetic moiety, otherwise the modulation depth will remain constant. Particularly in the case of small molecule effectors, introducing paramagnetic moieties or using analogues can risk structural perturbation and disrupt the interaction. Additionally, in multibody systems modulation depths may not resolve all distinct pairs of interacting species. It may then be desirable to correlate modulation depths between individual sets of spin-pairs, which can be accomplished through spin labelling with spectroscopically orthogonal paramagnetic moieties. These spin labels have distinct spectroscopic properties, such as not fully overlapping EPR spectra, or different relaxation behaviours. Such orthogonality allows each type of spin label to be addressed selectively, and their respective contributions to a modulated signal can be separated Electron Paramag. Reson., 2021, 27, 47–73 | 55

by an appropriate choice of experiment parameters. However, this is often a laborious process, and may require additional sample preparation and control measurements. Instead, in favourable cases118,119 all permutations of the interacting species yield unique and detectable distances, and sub-populations can be quantified in the distance domain without the need for spectroscopically orthogonal labels. 2.2.2.2 Indirect measurements of binding equilibria. PD-EPR can also be used to monitor binding equilibria indirectly in the distance domain. The dipolar evolution function can be transformed into a distance distribution by regularisation procedures and shifts in peak intensities can provide a proxy for direct detection of free and bound sub-populations. Of course, this presupposes that the interaction under investigation is coupled to a conformational or structural transition on a scale detectable by PD-EPR, which is a dichotomous problem; differences between conformational sub-ensembles should be as large as possible but not outwith the range of reliable distance detection. In favourable cases it will be possible to extract orientation information in addition to the distances.120,121 The coupling of conformational transitions with ligand binding or protein–protein interactions is a common motif in evolution to modulate binding affinity. For the modulation depth to be a sensitive reporter of binding interactions, they must involve (at least) pairs of paramagnetic species; otherwise the modulation depth remains constant. Therefore, shifts in distance distribution peaks can be advantageous in monitoring diamagnetic ligand or metal ion binding events, where the modulation depth is otherwise unchanged. Several studies have successfully interpreted conformational equilibrium populations from integrated distance distribution peaks in synthetic model systems,122 globular proteins,123 transmembrane ion transporters,119,124–126 and signal transduction proteins.127,128 An additional benefit of this approach is that it can be used to quantify populations of multiple conformational states from a single series of measurements. Furthermore, monitoring binding equilibria in the distance domain affords structural insight, while modulation depth alone does not. For N-degree singly spin-labelled homo-multimers, this yields at least N-fold coupled unpaired electron spins and causes deviations from the spin-pair approximation in the standard Tikhonov regularisation kernel of DeerAnalysis,129 a commonly used software in the processing of PD-EPR data. Multi-spin effects manifest from this interaction as sum and difference combination frequencies130 being mapped to the distance domain. Significantly, these peaks do not correspond to distances between spin labels in physical space, and so are referred to as ghost peaks.131 This phenomenon can often complicate distance distribution analysis owing to an artificial peak broadening and suppression, particularly at longer distances.132 This is problematic in both systems with multiple conformational states and where structural models are not available. Several strategies have been developed to suppress multi-spin effects at the level of sample preparation,133,134 data acquisition,135–137 and in post-processing.131 However, ghost peaks can also be diagnostic of complex 56 | Electron Paramag. Reson., 2021, 27, 47–73

formation in the distance domain, as was demonstrated for ternary complexes of metal ions and nitroxide terpyridine ligands.104 Furthermore, the oligomeric state of the Anabaena Sensory Rhodopsin (ASR) was confirmed as trimeric138 by comparing experimental and simulated dipolar evolution functions with N coupled electron spins (vide supra, regarding spincounting via PD-EPR). Very recently oligomerisation degree could be derived by multi-quantum counting in trityl labelled model multimers.139 However, quantification of distance distribution peaks is often less stable than direct analysis of time-domain data, owing to the need for a subjective regularisation step. Additionally, arbitrary selection of integration boundaries of distance peaks is likely to compound this problem and may result in confirmation bias by the user. In this case, model-free multi-Gaussian fitting is a viable option to circumvent the need for a regularisation step.140–143 Furthermore, several recent studies have concerned how to streamline dipolar EPR data processing and optimise the regularisation parameter.144–146 As mentioned above, high-quality timedomain data is necessary to ensure distance distribution peaks can be integrated reliably, and quantification is predicated on the assumption that binding events are coupled to detectable conformational transitions, a condition not well met for all systems.

3

Case studies

The previous sections have introduced different EPR methodologies, and their place in the wider framework of studying macromolecular non-covalent interactions. Having addressed some of their respective limitations and advantages allows for analysis of recent illustrative examples from literature in the subsequent discussion. Therefore, in the scope of this review non-covalent interactions can be broadly studied by EPR using four main strategies: i) altered CW-EPR spectral lineshape, ii) quantification of electron–nuclear couplings, iii) quantification of modulation depths, and iv) quantification of distance distribution peaks. Furthermore, we largely limit our discussion of interacting species to protein and nucleic acid macromolecules. 3.1 Altered CW-EPR spectral lineshape A particularly significant branch of non-covalent interactions involves the study of protein misfolding events and pathological protein fibrillation; understanding the structural alterations that accompany these deleterious transitions is of paramount importance in developing targeted therapeutic drugs. In this regard, CW-EPR has proved especially useful as a tool to probe the associated kinetic and dynamic processes with individual monomer resolution. For instance, aggregation kinetics of Dtau-187 were investigated using rotational correlation times, and linear combinations of mobile, immobile and spin-exchanged components.70 Importantly, the spin-exchanged component was absent for residues 400C and 404C throughout the aggregation process indicating that the C-terminal region of the protein remains flexible. In another study, three-component simulations of CW-EPR spectra suggested the Electron Paramag. Reson., 2021, 27, 47–73 | 57

proliferation of amyloid-b plaques is mediated by the concentration of sodium-dodecyl sulphate (SDS), indicating incorporation of detergent molecules into the aggregates.147 Spin labels with high intrinsic flexibility can be ill-suited to report changes in molecular backbone dynamics upon binding or oligomerisation. Indeed, this emphasizes the need for highly rigid spin labels with short tethers, where motion is not dominated by rotation about bonds linking the paramagnetic moiety to the protein backbone. An example is the artificial amino acid 2,2,6,6-tetramethyl-N-oxyl-4-amino-4-carboxylic acid (TOAC) quantitatively incorporated into amyloid aggregates using solid phase peptide synthesis (SPPS) to approximate the number of monomers in the aggregates by monitoring a respective increase in the rotational correlation time and spectral simulation.65 Importantly, in this example the model peptide was only 13 amino acids long and therefore TOAC could be directly incorporated during synthesis. This strategy is not amenable to all systems and genetically encoded spin-labels that selfassemble are sometimes preferable to improve labelling efficiency in larger peptides, however these often cannot compete with TOAC rigidity. Genetically encoding a motif for self-assembling spin-labelling was initially demonstrated for CuII binding to a double histidine motif in nitroxide-labelled T4 lysozyme,148 and later in the membrane protein Lactose Permease to confirm the a-helical packing structure.149 An illustrative example of how CW-EPR has also been appropriated for the optimisation of genetically encoded double-histidine based spinlabels is a study by Lawless et al.87 (see Fig. 3). Here, the formation of the CuII-IDA chelate for labelling of engineered double-histidine motifs was monitored by shifts in the A8 and g8 components between the free CuII and CuII-IDA complex. The authors could show that adding a stoichiometric amount of IDA only resulted in B65% complexation, even at 500 mM CuII concentration. Instead, complexation of 480% could be achieved by adding 2 molar equivalents of IDA, and complexation formation plateaued at higher equivalents. CW-EPR has also been used in the characterisation of protein–protein56,60,69 and protein–nucleic acid

Fig. 3 (A) CW-EPR spectrum of CuII with one equivalent of IDA in water (solid) which clearly shows two components. Spectrum was simulated (dotted) by the addition of two individual spectra: CuII-IDA in N-ethyl morpholine buffer (inset black) and free CuII in water (inset grey). (B) The percentage of the bound CuII-IDA complex versus equivalents of added IDA. At one equivalent of IDA, onlyB65% of CuII is bound to IDA. The concentration of CuII was 500 mM. Reproduced from ref. 87 with permission from the Royal Society of Chemistry. 58 | Electron Paramag. Reson., 2021, 27, 47–73

interactions,62 small molecule binding events,59,61,74,150 the validation of predicted in silico trends in affinity based on structural modelling,64 and determination of Michaelis constants.151 Development of a bifunctional spin label also allows immobilisation and surface–ligand binding studies in proteins.152 Importantly, Lawless et al. could show that while formation of bis-IDA complex was favoured at excess IDA concentrations, in presence of another coordinating ligand such as imidazole, formation of the biscomplex was inhibited. This is significant because only the monocomplex of CuII-IDA can effectively coordinate to double-histidine motifs, while the bis-complex has all four equatorial coordination sites occupied and free CuII will bind the conjugate bases of acidic amino-acid residues non-discriminately. The authors also estimated apparent dissociation constant (KD) values from CW-EPR for the interaction between CuII-IDA and two configurations of double histidine motifs. However, it should be noted that all measurements were performed at 500 mM protein concentration, meaning these apparent KD values are likely only lower-bound estimates of affinity. This emphasizes the need for caution when using CW-EPR to determine KD in the absence of other complementary approaches that can yield more complete thermodynamic information. An example of using a combination of CW-EPR, ENDOR and UV–vis spectroscopies to determine both kinetic and dissociation constants is a recent study of the cytochrome P450 enzyme CYP121.153 3.2 Quantification of Electron–Nuclear couplings Hyperfine spectroscopy is a particularly valuable toolbox in characterising the binding environment of small molecule effectors and can yield insight into both inner and outer coordination-sphere interactions of paramagnetic metal ions. Significantly, this allows hyperfine spectroscopy to bridge the local and long-range structural information provided by CW-EPR and PD-EPR methods, respectively. For instance, a combination of ESEEM and CW-EPR was used to investigate the MnII/MnIV redox cycle of the multi-copper oxidase MnxG protein.75 Here, three populations of MnII-containing species were detectable in the reaction mixture, and quantification of 14N and 2H ESEEM modulation depths calibrated against other systems with known coordination environments allowed counting of the nitrogenous and solvent coordinating ligands, respectively. The multi-copper oxidase complex performs a two-electron oxidation of MnII to MnIV and assistance of the binding site in tuning the MnII redox potential is postulated. The coordination environment of MnII in the MnxG protein was shown to contain two solvent water molecules and one histidine residue. Additionally, the observation of a weakly exchange-coupled MnII–MnII dimer by CW-EPR allowed proposing mechanistic details for MnII binding and oxidation. Another example of quantifying ESEEM and ENDOR to determine distinct binding environments for sub-populations in frozen solution was shown by Gagnon et al.89 (see Fig. 4). Here, the human MnII-sequestering protein Calprotectin was shown to coordinate MnII via a novel Electron Paramag. Reson., 2021, 27, 47–73 | 59

Fig. 4 4-pulse ESEEM spectra of MnII- and CaII-bound mixed 14N/15N-labelled DHis3Asp with 0.9 molar equivalents of MnII. The inset is a graph of maximum intensity of the combination peak versus the number of 15N ligands. The black asterisk represents the intensity of the 15N sum combination line measured for 15N-labelled MnII-calprotectin in the absence of CaII and was not used in the calculation of the best fit line. The number of 15 N ligands for this point was calculated using the linear relationship determined from the best-fit line. All samples contained 200 mM DHis3Asp, 2 mM CaII and 180 mM MnII at pH 7.5 (80% (v/v) 75 mM HEPES, 100 mM NaCl, 20% (v/v) PEG 200). Reproduced from ref. 89 with permission from American Chemical Society, Copyright 2015.

hexa-histidine high-affinity binding site. Residues H103 and H105 of the C-terminal tail were speculated to be mechanistically significant in the exclusion of solvent water from the binding site, and quantification of 2 H ESEEM modulation depths indicated one or two inner-sphere deuterons in H105A and H103A constructs, respectively. Therefore, this study demonstrates the power of hyperfine spectroscopy and EPR more broadly to intimately couple structural and thermodynamic insight. Hyperfine spectroscopy has been used extensively in many other systems to investigate non-covalent interactions.88,90–93 Additionally, Calprotectin is a heterodimer of S100A8 and S100A9 subunits and isotopic enrichment with 15N eliminated the quadrupolar interaction inherent for naturally abundant 14N; this allowed quantitative determination of the number of coordinating nitrogenous ligands based on the intensity of the 15N combination peak in 4-pulse ESEEM. 4-pulse ESEEM was also used to monitor MnII-Calprotectin speciation in the absence of CaII; interestingly MnII binding became promiscuous: the 15N combination peak intensity corresponded to coordination by 2.6 nitrogen ligands, as opposed to 6 nitrogen ligands in presence of CaII, suggesting approximately 50% occupancy of the high-affinity hexa-histidine site. Furthermore, 2H ESEEM modulation depths in the absence of CaII could be fitted as a linear combination of ESEEM signals from hexaaqua-MnII and of MnII-Calprotectin in presence of CaII, and so the authors concluded that CaII was necessary to promote specific and high-affinity MnII-binding and sequestration. 60 | Electron Paramag. Reson., 2021, 27, 47–73

3.3 Quantification of modulation depths Hetero- and homo-oligomerisation events represent another class of noncovalent interactions that are encountered frequently across all domains of life.154 These interactions are crucially important in the evolution of novel functionality and activity in complex multicomponent systems155 and the cellular machinery.156 Membrane ion channels are a notable example where oligomerisation has facilitated incredible diversification of protein function and are particularly interesting as potential drug targets. Indeed, over 60% of all current therapeutics target membrane protein interactions.157 Determination of the oligomeric state of a system can therefore provide mechanistic insight and is accessible through modulation depth quantitation and spin-counting using PD-EPR. For instance, three-pulse PELDOR indicated that the peptaibol Alamethicin exists in equilibrium between monomers, dimers and pentamers;158 this oligomeric polydispersity facilitates formation of differently sized ion channels in bacterial membranes, causing lethal ion permeation. An inhibitor-based spin label was used to investigate the dimerisation mode of the receptor tyrosine kinase epidermal growth factor receptor.159 The protein was predicted to form asymmetric (active) and symmetric (inactive) dimers in solution, based on crystallographic data. Results suggested that interface mutations inhibited formation of the active dimer, and caused adoption of a monomeric state, as opposed to the predicted symmetric dimers. Another illustrative demonstration of quantifying modulation depths to directly determine the mechanism of oligomerisation in an ion channel protein is a study by Georgieva et al.106 (see Fig. 5). Here, Influenza A M2 transmembrane domain (TMD) was shown to exist in an equilibrium of tightly interacting dimers, and weakly interacting functional tetramers (as dimers-of-dimers). The efficiency of the TMD self-association was shown to be influenced by the protein-to-lipid ratio; increasing this ratio led to monotonically increasing PELDOR modulation depths. However, at all protein-lipid ratios the observed modulation depths were consistently lower than predicted for complete tetramerisation, instead indicating polydispersity with dimeric species dominating at very low protein-to-lipid ratios. Modulation depth quantification has been applied successfully to study many other complex protein105,107–109,160,161 and nucleic acid111,113 conformational and thermodynamic equilibria. Importantly, this study also showcases the utility of modulation depth quantification for studying subtle changes in equilibrium populations under disparate sample conditions, namely at pH 5.5 compared with pH 8.0. The authors performed a global fit of both pH series and could therefore differentiate between the proposed monomer-to-tetramer kinetic scheme, and a tandem model in which a monomer-to-dimer transition is followed by a consecutive dimer-to-tetramer transition. More recently, the hydrolytic cycle of HSP90 was also investigated by modulation depth quantitation in presence of ATP (pre-hydrolysis state), ATP and Vanadate (trapped high-energy state), and ADP (post-hydrolysis state). The authors could nicely reconcile increasing modulation depths throughout the cycle with KD values taken from literature.91 Electron Paramag. Reson., 2021, 27, 47–73 | 61

62 | Electron Paramag. Reson., 2021, 27, 47–73 Fig. 5 Concentration profiles of M2TMD21–49 monomers, dimers and tetramers as a function of protein-lipid (P:L) and protein-detergent (P:D) molar ratios. DEER signal modulation depth concentration profiles (filled squares) are plotted in the top row vs. M2 molar fraction for DOPC/POPS lipid mixture in (A) and (B) and b-DDM in (C). The fits of these experimental data to the equilibrium model based on tandem monomer-to-dimer-to-tetramer vs. that for monomer-to-tetramer model (for 89lipid and detergent at pH 5.5) are plotted in solid red and dashed green lines, respectively in (A) and (C) upper panels. Clearly, the tandem model is necessary to describe the M2TMD assembly pathway. Respective equilibrium constants, k2d, k4d for the tandem model are 15106 molar fraction and 448106 molar fraction, pointing to strong binding for dimers but relatively weaker bound tetramers. In b-DDM these constants both are weak and close to each other, being 264106 and 644106 molar fraction. Concentration profiles of populations for M2TMD21–49 monomers (M), dimers (D), and tetramers (T) are plotted in (A) and (B) lower panels for DOPC/POPS lipid membranes at pH’s 5.5 and 8, respectively, and for b-DDM in (C) lower panel. The populations of each fraction are expressed as M2 percentages of total M2TMD21–49 monomer concentration, CM2TMD ¼ CM þ CD þ CT. Here CM2TMD is expressed as M2 molar fraction, 1/(1 þ A/P) where A/P is amphiphile-to-protein molar ratio. Reproduced from ref. 106 with permission from Springer Nature, Copyright 2015.

Lastly, one advantage of using modulation depth quantitation compared to ITC, SPR and other more established techniques to monitor complex equilibria is the additional distance information allowing to assign the quantitative interaction to structure in addition to the potential for obtaining multiple modulation depths from a single sample when using orthogonal labelling. In contrast, ITC and SPR typically provide only a single observable into which all interactions are subsumed which requires careful experiment design to prevent over-fitting. Introducing the dipolar interaction through a spin label that is not contributing to the detected echo (e.g., in RIDME or PELDOR with orthogonal labels) can provide information on practically non-saturable or nonspecific binding events, which can be notoriously difficult and expensive to analyse using other techniques. 3.4 Quantification of distance distribution peaks Small molecule effectors are ubiquitous throughout nature, modulating the relationship between macromolecular structure and function. From a thermodynamic perspective enthalpically unfavourable ligand binding can achieve net free-energy gain through coupling with a structural transition that increases the entropic component of the free-energy landscape, and vice versa. Therefore, PD-EPR is well-suited to monitor such binding events in the distance domain. For instance, a thermophilic cytochrome P450 family protein (CYP119) undergoes a disordered-toordered transition upon binding of lauric acid, which could be followed as changes in the PELDOR distance distribution.162 Along the same concept, the influence of preventing lipid penetration into nano-pockets of the mechanosensitive ion channel MscL was investigated by PELDOR through sulfhydryl modification, and the channel conformation was monitored. Results suggested that lipids behave as negative allosteric modulators, wherein their absence within the nano-pockets lowers the activation energy to channel opening.163 Disordered-to-ordered transitions are also common motifs in nucleic acid interactions, as the tertiary structure of the synthetic tetracycline RNA riboswitch was shown to be stabilised in presence of MgII using PELDOR, independent of the tetracycline ligand.93 The distribution width decreased with increasing MgII concentration, indicating transition from an ensemble of metastable states to a global energy minimum. A similar reduction in conformational flexibility was monitored by PELDOR in the DNA cocaine aptamer upon ligand binding.164 Another example for quantifying equilibrium populations from the distance domain is a study by Glaenzer et al. (see Fig. 6). Here, neuraminic acid binding to a tripartite ATP-independent periplasmic (TRAP) transporter protein was shown to trigger the open-to-closed transition of the channel.119 A KD was determined for the interaction from integration of PELDOR distance distribution peaks, which was consistent with previous ITC data. Notably, the time-domain data could also be fitted as a linear combination of free and ligand bound states and could show the resulting simulations agreed nicely with experiment. Electron Paramag. Reson., 2021, 27, 47–73 | 63

Fig. 6 Open-close transition of VcSiaP followed by PELDOR spectroscopy. (A) PELDOR time-traces of VcSiaP Q54R1/L173R1 titrated with the indicated amounts of Neu5Ac (black traces). Fits resulting from linear combinations of the 0 mM (open) and 600 mM (closed) Neu5Ac time traces using the equation y ¼ aopen þ (1  a)closed are shown as superposed curves. Note that small differences in modulation depths were corrected by scaling the time traces to a modulation depth of 100% before the fitting procedure. The fitting results were then back-scaled to the original modulation depth. (B) Distance distributions (DeerAnalysis 2016) corresponding to the time-traces shown in (A). The distributions were normalised, so that their integral equals one. The error bars were calculated using the evaluation procedure from DeerAnalysis 2016. (C) Binding isotherm of the VcSiaP Q54R1/ L173R1Neu5Ac interaction. (Black dots) Calculated VcSiaP/Neu5Ac concentrations. (Solid qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi red line) Fit of the equation y ¼

ðPtot þLtot þKD Þ 

ððPtot þ Ltot þ KD Þ2  4  Ptot  Ltot Þ

to 2 the data points. Ptot is the total concentration of VcSiaP, Ltot is the total amount of Neu5Ac and KD is the dissociation constant. A KD of 0:8  0:4 mM was determined. Reproduced from ref. 119 with permission from Elsevier, Copyright 2016.

Importantly, this circumvented the Tikhonov regularisation step; the authors note that for the same time-domain data, this processing influences distribution shape and width in dependence of the selected regularisation parameter (a). By fitting the time-domain data directly, this removed the dependence of the calculated integrals upon the regularisation parameter, and additionally indicated no intermediate states in the energy landscape. Analysis of distance distribution peaks from PD-EPR has 64 | Electron Paramag. Reson., 2021, 27, 47–73

been used successfully to investigate conformational and binding equilibria in protein systems,123,125–127,140,165–167 as well as in protein–nucleic acid,168–171 and ligand–nucleic acid172 interactions. Perhaps most significantly for this study is that previous ITC studies had not detected any binding of neuraminic acid for a R125A construct. However, PELDOR was sufficiently sensitive to detect weak ligand binding. This suggests that PD-EPR may be especially suited to monitor weak binding interactions in concentration regimes where ITC is insensitive or impractical. An additional consideration beyond the scope of the initial study is the influence of temperature upon binding equilibria; this is most likely relevant for diffusion-limited high-affinity interactions, since even under snap-freezing conditions, the cooling rate is still comparatively slow. A recent study illustrated this point by comparing dissociation constants estimated from PD-EPR measurements in frozen solution and ITC measurements at room-temperature.102 Results indicated the affinities reconciled if the ITC-derived value was extrapolated to cryogenic temperatures, 50–60 K below room-temperature where chemical dynamics freeze out. A further implication is that endothermic reactions may not be accessible under cryogenic EPR conditions, though this consideration could be overcome by measuring at ambient temperature (by altering the matrix composition or using different spin labels). It is also worth noting that this strategy is often leveraged on the availability of high resolution cryo-EM or X-ray crystal structures to inform construct design. More broadly, the approach is also limited by the ability to resolve distinct conformers in the distance distribution in dependence of the rotameric freedom of the attached spin labels and is particularly challenging in systems with subtle conformational transitions.173 The development of highly rigid genetically encoded doublehistidine motifs to coordinate CuII-chelate labels has been shown to dramatically improve precision of distance determination in proteins and can potentially ameliorate this resolution issue.174

4 Summary In closing, this chapter has explored how different EPR methods have been applied to investigate non-covalent interactions, and the interplay between their structural and thermodynamic characterisation. More specifically, the advantages and limitations of CW-, pulse hyperfine, and PD-EPR spectroscopies are discussed and compared with other biochemical and biophysical techniques. Coupling of structural and thermodynamic information in complex biomolecular systems is increasingly important from the perspective of societal health: i) to ameliorate the increasing incidence of amyloidogenic pathologies in an aging society, and ii) to streamline the development pipeline of novel therapeutics and antibiotics. The advanced EPR spectroscopic toolbox is well-positioned to address such burgeoning issues, by access to structural information across multiple distance regimes, and to binding information either directly or indirectly. However, critical analysis of recent literature also demonstrates the need for caution in interpretation of thermodynamic information extracted Electron Paramag. Reson., 2021, 27, 47–73 | 65

using EPR spectroscopies, such as the challenges inherent in comparing thermodynamic data between cryogenic and ambient temperature regimes. Therefore, the complementarity of advanced EPR techniques with other methods cannot be overlooked and represents an integrative and holistic strategy for characterisation of systems in frozen solution. Excitingly, recent advances in method development such as the improvement of measurement sensitivity through the increased adoption of AWGs, and design of redox-stable spin labels175–177 also highlight the possibility of in situ applications.178,179 Thus, the importance of advanced EPR methods is likely to continue to increase in the future, where biomolecular interactions can be studied in the native cellular environment. Finally, this further emphasises the appeal of EPR to investigate, with high biological validity, pathologically relevant macromolecules.

Abbreviations ASR AWG BLI CD CW-EPR DLS DQC DSF EDNMR ELDOR ENDOR EPR ESEEM FRET GB1 HDX-MS Hsp90 HYSCORE IDA ITC IMMS LHS LILBID LOX NTA PD-EPR PELDOR RHS RIDME SAXS SEC-MS SIFTER SPPS

Anabaena sensory Rhodopsin Arbitrary waveform generator Biolayer interferometry Circular dichroism Continuous-wave EPR Dynamic light-scattering Double quantum coherence Differential scanning fluorimetry ELDOR-detected NMR Electron–Electron double resonance Electron–Nuclear double resonance Electron paramagnetic resonance Electron-spin echo envelope modulation ¨rster resonance energy transfer Fo Streptococcus sp. G. protein G B1 domain Hydrogen–Deuterium exchange mass-spectrometry heat shock protein 90 Hyperfine sublevel correlation Iminodiacetic acid Isothermal titration calorimetry Ion-mobility mass spectrometry Left-hand side Laser-induced liquid bead ion desorption Lysyl Oxidase Nitrilotriacetic acid Pulse dipolar EPR Pulse electron–electron double resonance Right-hand side Relaxation induced dipolar modulation enhancement Small-angle X-ray scattering Size-exclusion chromatography mass-spectrometry Single-frequency technique for refocusing dipolar couplings Solid phase protein synthesis

66 | Electron Paramag. Reson., 2021, 27, 47–73

SPR ssNMR SV-AUC TC TMD TOAC TRAP

Surface plasmon resonance Solid-state NMR Sedimentation velocity analytical ultracentrifugation Tetracycline Transmembrane domain 2,2,6,6-tetramethyl-N-oxyl-4-amino-4-carboxylic acid Tripartite ATP-independent periplasmic

Acknowledgements We gratefully acknowledge studentship support by UKRI for JLW (BB/ M010996/1) and MO (EP/N509759/1) and funding by the Leverhulme Trust (RPG-2018–397). The EPR instruments have been supported by previous Wellcome Trust [099149/Z/12/Z] and UKRI equipment grants (BB/R013780/1).

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Using pulsed EPR in the structural analysis of integral membrane proteins Andrew M. Hartley,y Yue Ma,y Benjamin J. Lane,y Bolin Wangy and Christos Pliotas* DOI: 10.1039/9781839162534-00074

Pulsed EPR methods, such as PELDOR (or DEER) and ESEEM have emerged as powerful tools for assessing membrane protein conformation, folding, oligomerisation and dynamics. PELDOR distance measurements can provide quantitative information on the conformational equilibria of membrane proteins, dovetailing well with techniques such as X-ray crystallography and cryo-EM. ESEEM spectroscopy can offer deuterium (or solvent) accessibility quantification at a single residue level. An inherent limit placed on membrane protein studies is the need to remove the protein from its natural membrane environment. However, recent developments in the membrane protein field provide lipid scaffolds that mimic that environment, to limit the impact of protein solubilisation and offer flexibility of choice in lipid composition, a key factor in the functional integrity of membrane proteins. Additionally, computational tools can be used to aid spin-labelling experiments, or tailored to incorporate experimentally derived PELDOR distance restraints to reveal the complete conformational ensemble of membrane proteins. In this chapter, we will focus on the application of pulsed EPR in the study of membrane proteins, highlighting case studies including our work on mechanosensitive ion channels. We will discuss experimental considerations, and introduce some of the computational tools that can be used in combination with pulsed EPR methods.

1

Introduction

Early forms of electron paramagnetic resonance (EPR) spectroscopy used paramagnetic centres naturally present in the particular protein of interest, such as metal ions, haems, or iron-sulphur clusters. However, the introduction of site-directed spin-labelling (SDSL) techniques1 enabled the investigation of proteins without requiring these natural paramagnetic co-factors. Additionally, SDSL opened up new avenues of experimentation that could exploit multiple labels on a single protein, which could be accurately quantified using EPR and other methods.2 PELDOR (Pulsed ELectron–electron DOuble Resonance – also known as DEER – Double Electron–Electron Resonance) spectroscopy is one such technique, and one that is able to measure distances between two (or more) identical paramagnetic spin labels into the nanometre range.3–5 PELDOR is at its most powerful, especially in the study of complex membrane proteins (MPs), when combined with a second technique, most frequently X-ray crystallography, but increasingly with cryo-electron microscopy (cryo-EM) or in silico molecular dynamics simulations. Traditional structural techniques such as X-ray crystallography can provide atomic resolution information on MP structure, however they represent Astbury Centre for Structural Molecular Biology, School of Biomedical Sciences, Faculty of Biological Sciences, University of Leeds, Leeds, United Kingdom. E-mail: [email protected] y Authors contributed equally to this work. 74 | Electron Paramag. Reson., 2021, 27, 74–108  c

The Royal Society of Chemistry 2021

only snapshots of static MPs, and do not inform on protein dynamics. Additionally, when considering X-ray crystallographic data alone, crystal packing can lead to ambiguities regarding the precise oligomerisation state of a protein, or can cause helical distortions that influence the interpretation of protein conformation. PELDOR can supplement data from X-ray crystallography by determining any conformational changes that may occur, or confirming protein oligomerisation. Cryo-EM can also alleviate many of the shortcomings of X-ray crystallography. The lack of crystal packing removes oligomerisation ambiguities, and it is possible to obtain information on multiple conformational states of a protein within a single experimental dataset. However, cryoEM can be a time-consuming, costly, and data-intensive technique, and access to state-of-the-art microscopes is still limited. Additionally, high resolution is not guaranteed, so atomic structural details of proteins can be missed, even in the largest of datasets. PELDOR can provide structural and dynamic insights into the conformational ensemble of a system, which can then be linked to function, that X-ray crystallography and cryo-EM cannot. Sample preparation for PELDOR (see Section 3) is no different than for X-ray crystallography or cryo-EM beyond the requirement for site-directed spin-labelling. PELDOR offers very high resolution, demonstrated by X-ray structures of spinlabelled MPs,5,6 and distances up to 160 Å have been recorded on fully deuterated, soluble proteins.7–9 PELDOR is an increasingly popular technique, and has been used on MPs for a variety of purposes, from assigning protein conformation and/or oligomerisation, to determining the impact of agonist/antagonist binding on protein structure. Electron Spin Echo Envelope Modulation (ESEEM) spectroscopy is another pulsed EPR technique, and measures the interaction of electron spins with surrounding nuclei at distances of up to 5–9 Å. In the case of biomolecules, ESEEM spectroscopy has been particularly useful in measuring the accessibility of spin-labelled residues to solvent and lipids, and has allowed structural biologists to probe the local secondary structure of MPs.5,10–14 ESEEM could therefore be used alongside PELDOR and/or other structural methods to provide information about the local environment of the labelled residue. In Section 4 we will review recent applications of ESEEM in the study of biomolecules, with a focus on MPs. In both PELDOR and ESEEM, the same MPs can be used: they need only be pure, efficiently spin-labelled, and functional, and they can be prepared in multiple solution conditions to enable functional and structural comparisons. Indeed, pulsed EPR experiments including PELDOR and ESEEM can be performed in an unsurpassed variety of conditions, some of which may be unsuited to other biophysical methods. In the case of MPs, distance (PELDOR) and solvent accessibility (ESEEM) measurements can be performed in a variety of lipid membrane mimics, which can resemble their native membrane environment, or be tailored to suit their structural and functional needs. In special circumstances, lipid membrane mimics can facilitate the tuning of biophysical parameters such as membrane curvature, tension and fluidity. Lipid bilayer mimics range from curved liposomes to flat MSP nanodiscs of defined size,15 SMALPs,16 and Electron Paramag. Reson., 2021, 27, 74–108 | 75

adaptable or heterogeneous scaffolds such as saposins17 and bicelles.5,18 Sample considerations and the range of lipid mimics available for EPR measurements of MPs will be discussed in Section 3. In recent years, computational tools that enable the implementation of sophisticated molecular dynamics (MD) simulations have been specifically developed to serve the needs of the unique properties and landscape of MPs.19 Other computational tools enable an accurate description of spin label rotamers when covalently attached to a cysteine residue.20 We previously combined these two tools in the study of integral MPs,11 and monitored interactions between lipids and spin-labelled MPs, assessing the effect of the introduced cysteine modification on their local and global structures. In Section 5 we will describe that when these MD tools are combined with experimentally-derived EPR distance (PELDOR, or DEER) and accessibility (ESEEM) restraints, they constitute a powerful methodology platform for addressing MP conformation, folding and oligomerisation, and resolving the ensemble of structural dynamics for complex integral MPs.

2 PELDOR distances measurements on membrane proteins In this section we will review the recent applications of PELDOR (or DEER) distance measurements on integral MPs, including transporters (such as ABC transporters and multi-drug transporters), GPCRs, ion channels (such as potassium and mechanosensitive channels), and outer MPs. Table 1 shows a list of MPs that have been used in PELDOR studies (Table 1). 2.1 Transporters Membrane transporters encompass an incredibly diverse family of proteins that sample the full spectrum of protein structure, and utilise an array of mechanisms to fulfil their role within the membrane. These proteins, often consisting of large, flexible domains, are ideally suited to PELDOR applications, which has been used on a number of membrane transporters to great effect. 2.1.1 ABC transporters. ABC (ATP-binding cassette) transporters are large, dimeric, MPs that couple the hydrolysis of ATP in cytoplasmic ATP-binding domains to the transport of biomolecules through their transmembrane domains. Much of the knowledge of these proteins comes from crystal structures, however the mechanisms by which the energy produced by ATP-hydrolysis is transduced to the transmembrane domains is unclear for many ABC transporters. PELDOR has been applied to numerous ABC transporters to elucidate oligomerisation states or conformational changes that underpin transport or energy transduction mechanisms, including TAP (ABC-transporter associated with antigen processing),21 TAPL (TAP-like),22 McjD,23 MsbA,24–28 and BtuCD-F.29,30 PELDOR has been applied extensively to certain ABC transporters, and has contributed much to the understanding of these proteins. MalFGK2, an ABC transporter responsible for the import of maltose, contains two transmembrane subunits, MalF and MalG, a cytoplasmic nucleotidebinding domain (MalK2), and a periplasmic maltose-binding domain 76 | Electron Paramag. Reson., 2021, 27, 74–108

Table 1 Membrane proteins studied by PELDOR. Protein family

Ref.

Protein

Ref.

ABC transporters TAP TAPL MalE-FGK2 McjD Multidrug P-glycoprotein transporters EmrE NorM LmrA TmrAB Secondary transporters SLC26 LeuT NhaA PepTSo PepTSt Mhp1 ExbB ExbD TonB GPCRs Rhodopsin Rhodopsin-arrestin Gloeobacter rhodopsin Channel-rhodopsin 2 b2-adrenergic receptor Ion channels KcsA GLIC mVDAC1 NavSp1 KvAP KCNE1 MscL Photosynthetic LHCII proteins Photosystem I

Protein

21 22 31–34 23 48–51 40 43,44 46 211 69,213 62–65 215 216 216 217 126 126 121,127,220 72–74,77,78 75,76 79

TM287/288 MsbA BtuCD-F

35–39 24–28, 144, 210 29, 30

LmrP BmrCD MdfA

41, 42 47 45

GltPh FeoB OxlT PutP BetP vSGLT CaiT LacY ClC-ec1

52–54, 212 66 214 55–58 59–61 67 68 218 219

Mitochondrial proteins

111–113 107 108 118 117 116 231,232 236–238 243 245,246 249–251 253

Bax V-ATPase F0-F1 ATP synthase Outer membrane Omp85 proteins OmpA Wza Peptides Colicin A Melittin Sticholysin I a-synuclein WALP peptides Receptors SRII/HtrII

Others

GluA2 (AMPA) TCRa (peptide) HIV-1 gp41 Sec translocon

Bacterio-rhodopsin 221 Sensory rhodopsin 80 Proteo-rhodopsin 81

82 70

AT1R

71

83–87 223,224 109 88 90 91,92 11,14,94,97 98–102 104

CorA ELIC VDAC2 BacNav HCN2 M2 MscS Photosystem II Photosynthetic reaction centre Bak Complex I HsDHODH FecA BtuB FhuA Gramicidin A Alamethicin Zervamicin K and E peptides b-peptides GluN1-GluN2B (NMDA) EGFR

84, 222 224 110 89 225 226–228 18, 93–96 105 103

YgaP GlpG

133 254

132 193 134 135

114, 115 106 229 119 120, 122–125, 230 121, 220 233–235 234, 239–242 234, 244 247, 248 252 130, 131 128, 129

Electron Paramag. Reson., 2021, 27, 74–108 | 77

(MalE).31 PELDOR spectroscopy has been used to monitor structural changes in MalK2 upon ATP binding,31 MalE binding and inter-domain structural changes upon ATP binding,32 the impact of substrate presence on MalE binding,33 and the effect of inhibitor binding to MalK2.34 All these studies have provided valuable insights in the molecular motions that underpin energy transduction in the MalFGK2 complex, and the effect of substrate, nucleotide, and inhibitor binding on an ABC transporter. TM287/288 is a hetero-dimeric ABC transporter that has been the subject of multiple PELDOR studies. PELDOR was used alongside X-ray crystallography to determine that the asymmetric nucleotide-binding domains remain in contact in the apo state,35 in contrast to many heterodimeric ABC transporters. In addition, PELDOR has been used to understand the structural changes that occur between outward-facing, occluded, and inward-facing conformations in a variety of physiological conditions, and in response to ATP binding.36,37 Finally, TM287/288 has also been used as a model to explore inter-spin distances measured by the introduction of ‘‘sybodies’’38 and nanobodies.39 2.1.2 Multi-drug transporters. Multi-drug transporters represent a broad sub-class of transporters that are responsible for the uphill export of toxic compounds. To do this, multidrug transporters use a variety of energy sources, such as proton translocation or ATP hydrolysis, and protein structure and transport mechanism vary widely between these subgroups. The conformational changes that occur in small, dimeric (or pseudodimeric), proton-coupled multi-drug transporters upon substrate binding and/or protonation have been analysed by PELDOR in several different protein models, including EmrE,40 LmrP41,42 and NorM,43,44 and the solution structure of MdfA was characterised using a dual spinlabelling approach.45 Multidrug transporters that harness the energy from ATP hydrolysis are typically larger, and exhibit similar structures to the ABC-transporters discussed earlier. PELDOR has been used to study the conformational dynamics of the homo-dimeric LmrA,46 and the hetero-dimeric BmrCD,47 as well as P-glycoprotein, a key protein involved in drug resistance in cancer.48–51 2.1.3 Secondary transporters. Secondary transporters couple substrate transport across the membrane to ion translocation. They exhibit a structural diversity matched by the substrates they transport, and as such, understanding of their transport mechanisms is limited despite the existence of many crystal structures. PELDOR has been applied to a number of these proteins from a variety of organisms to help understand the individual mechanism of each protein, and any features that may be shared between them. The trimeric sodium-coupled aspartate transporter from Pyrococcus horikoshii (GltPh) has been the subject of several PELDOR studies, all focussed on conformational heterogeneity, in the presence and absence of ligands.52–54 The proline transporter from Escherichia coli (PutP) is another secondary transporter that has been studied by PELDOR, including one of the first on a MP.55 Since then, PELDOR has been used 78 | Electron Paramag. Reson., 2021, 27, 74–108

to systematically study the molecular motions of PutP structural motifs, and their role in gate dynamics.56–58 Osmotic activation of the betaine transporter from Corynebacterium glutamicum (BetP) has also been studied using PELDOR,59 and computational methods have been used to interpret observed differences to crystal structures.60 By using a novel seven-pulse sequence, distances of up to 6 nm have been measured in BetP.61 LeuT, a bacterial leucine transporter has been frequently used as a model for the human dopamine transporter (hDAT), recently implicated in autism spectrum disorder.62,63 PELDOR studies on ligandinduced conformational dynamics revealed structural intermediates and motifs in its alternating-access model,64,65 and studies on LeuT proteins harbouring mutations identified from hDAT genomic studies revealed their impact on protein structure and function.62,63 Other secondary transporters that have been the subject of recent PELDOR studies include FeoB,66 vSGLT,67 CaiT,68 and SLC26.69 2.2 GPCRs G-protein coupled receptors (GPCRs) are a large family of proteins responsible for transferring inter-cellular signals across the membrane by binding extracellular substrates and interacting with intracellular G proteins. Crystal structures of the b2-adrenergic receptor revealed two distinct conformations, one active and one inactive, but PELDOR studies were able to reveal conformational heterogeneity and an equilibrium of inactive and active conformations existing concurrently.70 Ligandinduced conformational changes were studied by PELDOR in the angiotensin II type I receptor (AT1R), revealing four distinct conformations that exist in different equilibria in response to different agonists.71 Rhodopsin is a GPCR that is activated by light via its co-factor retinal, causing the binding of the G protein, subsequently followed by binding of arrestin and signal inhibition. Rhodopsin has been a model system for the study of GPCRs, and as such, several PELDOR studies of rhodopsin have been focussed on light-activation or arrestin binding. PELDOR studies on a suite of label pairs on the cytoplasmic face of the protein revealed specific motions of transmembrane helices in response to light activiation,72 but a similar experiment on rhodopsin in nanodiscs suggested light-activation within a lipid environment results in multiple active conformations.73 PELDOR was then used to characterise rhodopsin binding to a Gi protein74 and arrestin,75,76 and found that Gi binding differed to that of Gs binding, and that arrestin is recruited by phosphorylation of the rhodopsin C-terminus. Additionally, PELDOR has been used to investigate the oligomerisation of rhodopsin in rod outer-segments. AFM experiments suggested rhodopsin forms ordered rows of dimers in vivo, and PELDOR was used on in vitro reconstituted dimers to determine the dimer interface.77 However, an earlier study using PELDOR on rod outer-segments suggested rhodopsin distributed randomly within the membrane.78 Rhodopsin proteins are present across a wide variety of species, and some of these have been subjects of PELDOR studies themselves. Gloeobacter rhodopsin is a cyanobacterial rhodopsin with potential applications in synthetic biology, and PELDOR was used to investigate its Electron Paramag. Reson., 2021, 27, 74–108 | 79

pH-dependent oligomerisation state.79 The oligomeric states of Anabaena sensory rhodopsin80 and proteorhodopsin81 were also determined by PELDOR. Channelrhodopsin belongs to a subfamily of rhodopsin and functions as a light-sensitive cation channel. PELDOR studies on slowphotocycling variants revealed conformational changes occurring in the protein that were not previously described in channelrhodopsin.82 2.3 Ion channels Ion channels are structurally and functionally diverse and play crucial roles in a huge variety of cell types, tissues and organisms. 2.3.1 Potassium ion channels. KcsA is a prokaryotic pH-gated potassium channel that exhibits a complicated mechanism of gating, combining a proton-dependent gate on the cytoplasmic side and a protonindependent gate in the outer vestibule, and PELDOR has been proven as a valuable tool in addressing its complex gating mechanism.83,84 In KcsA, C-type inactivation (caused by a prolonged stimulus), and gate opening have both been associated with the conformation of the outer vestibule and occupancy of the selectivity filter, and cw-EPR was used to monitor the effect of Cd21 binding in the outer vestibule.85 Metal bridges were found to form in the outer vestibule during inactivation, caused by structural rearrangements that brought individual subunits of the tetrameric protein closer together. In a subsequent study, PELDOR was used in combination with other spectroscopic techniques to determine that these structural changes were not caused by large-scale backbone rearrangements, but rather by local dynamics and hydrogen-bonding networks.86 PELDOR was also used to monitor the extent of channel opening at the inner gate in response to pH, and found that opening occurred around pH 4, in good agreement with previous calculations of its pKa.87 2.3.2 Voltage-gated ion channels. The regulation of voltage-gated ion channels has also been studied in numerous protein models using PELDOR. Bacterial voltage-dependent sodium channels consist of six transmembrane helices and a four-helix cytoplasmic C-terminal domain. PELDOR studies on the pore domain88 and C-terminal domain89 revealed conformational flux in both, with mechanistic and regulatory consequences. Conformational changes in the voltage-sensing domain of a potassium channel have also been observed by PELDOR.90 The function of some voltage-gated ion channels is also modulated by peripheral proteins, and one example is KCNE1, a small, single transmembrane helix protein the structure of which has been examined in lipids by PELDOR.91,92 2.3.3 Mechanosensitive ion channels. Mechanosensitive ion channels are non-specific ion channels that gate in response to increased tension in the lipid bilayer. In bacteria, there are two families of mechanosensitive ion channels, MscL (mechanosensitive ion channel of large conductance) and MscS-like (mechanosensitive ion channel of small conductance-like), which differ in protein structure and oligomerisation state. MscS-like channels are heptameric and gate at much lower pressure thresholds 80 | Electron Paramag. Reson., 2021, 27, 74–108

than MscL, and with lower conductances. They all share a minimal domain towards their C-terminal end that corresponds to the full-length MscS protein. Systematic PELDOR studies on MscS have revealed the presence of unique hydrophobic pockets within the transmembrane domain in detergent93 and in lipid bilayers,18,93 which were later confirmed by X-ray crystallography.5,6 The high resolution of this spinlabelled MP structure confirmed PELDOR measurements recorded in an earlier study that determined the protein was heptameric, and in an open state.5,6,93 The homomeric nature of MscS can cause difficulties in PELDOR due to multi-spin effects, and as such, MscS is an ideal model for examining methodological and computational methods that can alleviate these difficulties.94–96 MscL is a pentameric ion channel, and a smaller protein than MscS. However, PELDOR studies revealed similar pressure-sensitive pockets within the transmembrane helices, and site-directed spin-labelling of selected residues perturbed lipid exchange between these pockets and the membrane, resulting in conformational changes in the absence of membrane tension.11 These distance measurements demonstrated for the first time the strength of the PELDOR methodology, by simultaneously triggering and monitoring channel conformation in both liposomes and nanodiscs.11 PELDOR has also been used to demonstrate MP folding in an engineered strain of E. coli using MscL as the model.97 Finally, PELDOR was used to identify and compare substantial structural differences within pressure-sensitive and mechanical gating regions of two MscL orthologues in lipid nanodiscs, revealing the cause of significant functional discrepancies between these two channels, otherwise considered structurally highly similar.14 2.4 Photosynthetic and mitochondrial proteins Photosynthetic proteins capture energy from light, and transfer it into an energy currency the cell can utilise. In plants, the major light-harvesting chlorophyll a/b complex (LHCII) absorbs light energy, which is then transformed into ATP by the photosynthetic reaction centres. LHCII forms a trimer, with each protein consisting of four transmembrane helices and an N-terminal domain. The transmembrane domain absorbs light energy via its 8 chlorophyll a chromophores, 6 chlorophyll b, and 4 carotenoids. PELDOR studies revealed a very stable transmembrane core, with little motility, a requirement for efficient energy transfer between chromophores.98 Flexibility was observed in the N-terminal domain and the luminal loop,98,99 and the N-terminal domain was found to exist in two distinct conformations, with implications in protein oligomerisation and localisation.100 Protein folding has also been studied in LHCII by PELDOR, and by spin-labelling different parts of the protein, a timetable of folding events was proposed.101,102 Light induced conformational changes in photosynthetic proteins and their impact on chromophore-chromophore orientation has been studied in several systems. PELDOR studies on the reaction centre of Rhodobacter sphaeroides determined the protein underwent no conformational changes upon light-induced reduction,103 and a similar experiment on photosystem I Electron Paramag. Reson., 2021, 27, 74–108 | 81

from Synechocystis reached the same conclusion.104 PELDOR has also been used to study the oxygen-evolving complex of photosystem II.105 Mitochondria are primarily responsible for energy production in eukaryotes, and possess a diverse proteome to fulfil this role. An electron transport chain comprising several protein complexes couples electron transport to the formation of a proton gradient across the inner mitochondrial membrane, which is then used to drive ATP synthesis. Several proteins of the electron transport chain have been studied by PELDOR, including complex I106 and ATP synthase,107 as well as a bacterial ATPase.108 The voltage-dependent anion channel (VDAC) is a mitochondrial outer MP responsible for the exchange of ions between the cytoplasm and the mitochondria. During apoptosis the protein forms dimers, the formation and structure of which have been characterised by PELDOR in two organisms, murine VDAC109 and zebrafish.110 Although not a mitochondrial protein, Bax and Bak insert within the mitochondrial outer membrane and form homo-oligomers, permeating the mitochondria leading to apoptosis. PELDOR studies on Bax in detergent and lipid environments revealed the presence of multiple Bax homooligomers (up to 10),111 and subsequent studies described the homodimer interface, as well as an inter-dimer interaction domain.112 By employing multiple, orthogonal spin-labels, inter-dimer distance distributions were recently observed.113 Similar studies on Bak have also described an intra-dimer interface, and an inter-dimer interface.114,115 2.5 Outer membrane proteins Outer MPs in gram-negative bacteria are typically b-barrel pores that interact with proteins in the periplasm and/or inner membrane. Several outer MPs have been studied by PELDOR, including Wza,116 OmpA117 and Omp85.118 BtuB, FecA and FhuA are all TonB-dependent outer MPs, interacting with the periplasm-spanning TonB protein via a Ton box in their periplasmic domains. PELDOR studies on the Ton boxes of FecA and BtuB revealed substrate-induced Ton box disorder, facilitating interactions with TonB.119,120 Equivalent experiments on FhuA did not observe an increase in Ton box exposure, nor increased order upon TonB binding, suggesting TonB-dependent outer MPs do not share a single mechanism.121 Further experiments on BtuB observed allostery between the Ton box and extracellular loops, suggesting a link between TonB binding and the initiation of transport.122 The native form of outer MPs is typically cysteine-free, which entertains the possibility of performing in-cell PELDOR experiments. Such experiments have been performed on Escherichia coli BtuB in native, asymmetric outer membranes and whole E. coli cells,123–125 yielding comparable results to purified proteins, representing an exciting step in the evolution of PELDOR methodologies. PELDOR has also been used to study the Ton complex apparatus at the bacterial inner membrane as well, determining the oligomeric structure of the proteins within the Ton complex,126 and the conformation of TonB itself.127 82 | Electron Paramag. Reson., 2021, 27, 74–108

2.6 Receptors The epidermal growth factor receptor (EGFR) presented a problematic model system for PELDOR studies; removal of native cysteines resulted in an inactive protein, indicating structural changes caused by the mutations.128 To overcome this limitation, a spin-labelled inhibitor was used, derived from an existing EGFR inhibitor. PELDOR studies using the novel spin-labelled inhibitor revealed intra-dimer distances that correlated with an active, asymmetric dimer conformation. Distance measurements on mutants with an impaired ability to form the asymmetric dimer revealed a monomeric form of the protein, rather than the inactive, symmetric dimer.128,129 NMDA (N-methyl-D-aspartate) receptors are clinically relevant proteins, but little is known of their conformational transitions between states, or the structural effects of agonists and inhibitors. PELDOR studies of the hetero-tetrameric GluN1-GluN2B NMDA receptor revealed the different structural effects of agonist and inhibitor binding on the ligand-binding domain, and the effect of allosteric inhibitor binding in the N-terminal domain.130 PELDOR was also used to show that deletion of the N-terminal domain resulted in two populations of ligand-binding domain conformations.131 PELDOR experiments on the GluA2 ionotropic glutamate receptor in multiple states revealed large-scale conformational changes in multiple protein domains upon agonist binding and desensitisation.132 2.7 Others The solution NMR structure of YgaP, a membrane-bound sulphurtransferase, revealed that it exists as a dimer and that the dimer interface is formed by its two transmembrane helices.133 Parallel PELDOR studies confirmed this dimeric structure, and observed conformational changes within a transmembrane helix in response to thiocyanate (SCN) binding, suggesting a potential role in SCN transport.133 The HIV-1 viral envelope protein Env is formed by two polypeptides, gp120 and gp41, and it is conformational changes in gp41 that result in viral membrane fusion. Even though Env is known to exist as a homotrimer of heterodimers, there remains confusion over the oligomeric state of the transmembrane domain of gp41. PELDOR was used alongside a suite of biophysical tools to determine that the gp41 transmembrane domain exists as a monomer in lipid bilayers, and that trimerisation is likely initiated by other domains of gp41.134 The Sec translocon, comprised of SecYEG and the ATPase SecA, transports proteins across the membrane. PELDOR measurements on SecYEG revealed conformational changes occurring during ATP hydrolysis by SecA, providing experimental evidence for a more detailed molecular dynamics simulation.135

3

Sample preparation for EPR

In this section, we will describe the basic sample requirements for in vitro EPR studies. We will briefly describe methods of spin-labelling, and Electron Paramag. Reson., 2021, 27, 74–108 | 83

discuss the variety of reconstitution methods and materials available. We will also introduce deuteration as a method for increasing the maximum distance limit by extending the phase memory time. For a successful in vitro EPR experiment, the sample requirements are simple: the protein must be pure, functional, efficiently spin labelled (460%) and at a spin concentration of around 100–200 mM in a 40 mL volume. Lower concentrations may also be used (i.e.410 mM), but we always aim for long time traces with excellent signal-to ratio and a spin concentration below 100 mM could result in low sensitivity, and reduced signal-to-noise ratio. Preparation of purified MPs for in vitro biochemical and biophysical analyses is a difficult and costly process, and low yield is a common issue, as larger cell cultures are required to extract sufficient MP quantities. Considering the expense of detergents and other materials required for MP purification, the optimisation of gene constructs and cell growth conditions is recommended prior to any attempts at large scale protein production and in vitro analysis. The remainder of this section will mainly focus on sample preparation for in vitro pulsed EPR studies of integral MPs, including the selection of labelling sites, a brief practical guide to labelling proteins, and a comparison of available lipid bilayer scaffolds for MPs, which could resemble their unique native membrane environment. 3.1 Selecting spin-labelling sites PELDOR is at its most powerful when a structure of at least one conformational state of a protein is available. That way, it is possible to predict which residues may undergo putative conformational changes, and design spin-labelled proteins for analysis. Additionally, the in silico distance measurements by software such as PyMOL within the known structures provide required control measurements, which can be used to ascertain the validity of any distance distributions measured by PELDOR. That being said, the introduction of the MTSSL spin label can contribute significantly to any expected distances, so it is essential that the MtsslWizard plug-in136 in PyMOL, or MMM137 software, is used to predict the expected distances between two labelling sites (see Section 5). These in silico modelling tools allow users to readily calculate the conformational space of a spin label incorporated at the target site. The most popular spin label, S-(1-oxyl-2,2,5,5-tetramethyl-2,5-dihydro1H-pyrrol-3-yl)methyl methanesulfonothioate (MTSSL), will be used as an example for explaining the rationale governing labelling site selection. MTSSL is a small chemical (as small as a phenylalanine residue and much smaller than commonly used FRET fluorophores), which is covalently attached to cysteine residues within the target protein via a disulphide bond. As MTSSL is small, it is expected to cause low perturbation of the target site, nevertheless, this should be tested. Below are several suggestions for designing MTSSL labelling sites:  Exposed native cysteines should be mutated to serine or alanine. Buried cysteines, or cysteines forming stable disulphide bonds may be kept, but spin label accessibility to these cysteines must be tested before 84 | Electron Paramag. Reson., 2021, 27, 74–108

such a construct is considered as ‘‘cysteine-free’’. Furthermore, any such construct should be tested for function prior to re-engineering cysteines back into selected sites for labelling  Labelling of key residues which are known to be important for protein function, and highly conserved residues, should be avoided  Spin labels should be added to relatively rigid protein regions, such as a-helices, rather than flexible loops to avoid excessive spin label conformational flexibility, which may hinder accurate PELDOR distance measurements due to broadening of the distance distribution  The polarity of the chosen spin label should be also considered. For instance, MTSSL is hydrophobic and has a preference for hydrophobic cavities on the protein surface  Extracellular and intracellular MP regions are generally more accessible to spin labels than transmembrane domains  Control sites in structured regions that are not expected to undergo conformational transitions are crucial to demonstrate changes for domains which present changes in their tertiary structure 3.2 Adding spin labels Once a target residue has been selected, and the mutated protein is shown to be functional, the spin label is normally incubated with the purified MPs in 10-fold excess for at least two hours before using dialysis or gel filtration to remove the excess spin label. For particularly sensitive MPs, an on-column spin-labelling method is recommended. Rather than using dialysis, 10–20 bed volumes of wash buffer can strip away any unattached spin labels from the proteins whilst they are attached to the affinity column. This on-column spin-labelling method has been described in detail elsewhere.5 For temperature sensitive proteins, the spin label can be incubated with the protein for longer periods (3 hours or even overnight) at 4 1C to increase the labelling efficiency. 3.3 Reconstitution in lipid bilayers A wide variety of detergents have been developed to extract MPs from native cell membranes and solubilise them.138,139 Detergents have been successfully applied to in vitro structural and functional studies of MPs and continue to be the predominant choice. Though the detergent micelles are amphipathic, they generally constitute poor lipid mimics. Lipids play an important role in the structural integrity and protein-lipid interactions of MPs, which may denature or lose function in detergent micelles.140,141 Therefore, reconstituting MPs into a lipid-bilayer mimic is often an essential measure, as it allows the study of MPs within a native membrane environment. Table 2 lists the most commonly used lipidbilayer scaffolds such as liposomes, nanodiscs and bicelles, and two newly developed scaffolds, SMALPs and Salipro nanoparticles (Table 2). 3.3.1 Liposomes. Liposomes can accurately replicate the curvature and fluidity of cell membranes due to their spherical shape. Their large, curved, surface area suits the study of large MPs with extended Electron Paramag. Reson., 2021, 27, 74–108 | 85

86 | Electron Paramag. Reson., 2021, 27, 74–108

Table 2 Lipid scaffolds for in vitro membrane protein studies, including pulsed EPR techniques.a Lipid bilayer scaffold Liposome

Schematic view

Diameter 20 nm–100 um

Building material Lipids

Protocol C. Kapsalis et al.

Case studies 11

MscL11 TM287/28835 Bax113 Sensory rhodopsin80

Nanodisc

9.8 nm–17 nm

Lipids, membrane scaffold protein

C. Pliotas5

LmrP41 P-glycoprotein50 BmrCD47 MscS18 MscL11,14

SMA lipid particle (SMALP)

10 nm–30 nm

Styrene

S. C. Lee et al.16

KCNQ1153

maleic acid

Salipro nanoparticle

Highly adaptive

Lipids,

KCNE192

A. Flayhan et al.17

N/A

saposin A

Electron Paramag. Reson., 2021, 27, 74–108 | 87

Bicelle

10 nm–100 nm

DMPC and CHAPSO/DHPC

C. Pliotas5

MscS18 mVDAC1109 McjD23

a The schematic views of liposomes and bicelles are cross-sectional views, the remainder are front views. The alignment of saposin A proteins is taken from structure 6D80.155 Cyan bonds represent lipids, green bonds represent CHAPSO.

transmembrane domains that are regulated by membrane curvature, such as the PIEZO mechanosensitive channels,142 and provides a platform for protein–protein interaction studies within membranes. There are many PELDOR studies of MPs performed within liposomes,11,35,80,113 as they are relatively easy to make compared with other bilayer mimics that require scaffold proteins or peptides. In addition, liposomes offer great flexibility in adjusting lipid composition, which can be readily tailored for each protein. In a recent EPR study, the membrane channel MscL was reconstituted in liposomes of a composition resembling the native protein environment, and PELDOR measurement concluded that MscL adopted a closed conformation in the presence of the curved liposomal membrane.11 However, MPs can be inserted into liposomes in either orientation, which can increase the complexity of data analysis. Another concern of liposomes in EPR studies is the spin echo dephasing time (Tm). The Tm of reconstituted proteo-liposomes was found to be significantly shorter than for detergent-solubilised proteins.143 The Tm of nitroxides in reconstituted liposomes can be less than 1 ms at 50 K,83 which can limit measurement reliability for distances longer than 3 nm, as well as decreasing the signal-to-noise ratio.83 Short dephasing times can be avoided through a reduction of spin gathering in liposomes.143 This can be achieved by either increasing the lipid to spin-labelled protein ratio,28,144 by mixing spin-labelled proteins with non-labelled proteins,83,120 or by sparse labelling approaches that introduce diamagnetic labels along with paramagnetic ones.94 The deuteration of lipids and buffers is another solution (see Section 3.4), but this is an extensive undertaking, and only becomes useful when the spin clustering is substantially reduced.143 A further way to avoid spin clustering is to reconstitute proteins into a single discoidal lipid bilayer mimic, such as nanodiscs. 3.3.2 Nanodiscs. Nanodiscs are a popular membrane mimic that enables the biophysical characterisation of MPs in vitro.15,145 Membrane scaffold proteins (MSPs) are engineered amphipathic proteins that take advantage of the structural features of apo-lipoprotein A-1,145 and form two belt-like scaffolds that encircle a phospholipid bilayer along with the reconstituted MP, forming a soluble complex nanoparticle. MSP proteins contain no cysteines in their native form, so target proteins can be labelled with cysteine-reactive labels (such as MTSSL) before, during, or after MP reconstitution into nanodiscs. The length of the MSPs used for reconstitution determines the diameter of the nanodiscs, which can range from 9.8 nm to 17 nm.146 The size of the nanodisc can be tailored to the MP under study, and the lipid composition can also be varied to a certain extent. Studies have shown that the activity of detergent solubilised MPs is enhanced when they are reconstituted into nanodiscs47 and in other cases their conformational equilibrium is altered.41 On the other hand, lipid composition and lipid-to-MSP ratio optimisation is required, which 88 | Electron Paramag. Reson., 2021, 27, 74–108

can be a lengthy process, while extra steps are required for the purification of MSP proteins.15 In previous studies, nanodiscs were used in the study of two distinct mechanosensitive ion channels, the heptameric MscS18 and pentameric MscL.11,14 In these studies, PELDOR distance measurements were recorded in nanodiscs, and showed that both MscS and MscL adopt a closed conformation due to bilayer compression induced by the surrounding lipids forming the nanodiscs.11,18 3.3.3 SMA lipid particles (SMALPS). Styrene maleic acid (SMA) copolymers can insert into crude membranes and extract native ‘‘nanodiscs’’ containing target proteins, which can then be purified.147 The major advantage of using SMA is that detergent solubilisation (‘‘detergent-free’’ method) and protein reconstitution is not required.16,148 Furthermore, the membrane proteins can co-purify with their native lipids, which may be important for their function and can be identified by mass-spectrometry. The size of the SMALP depends on the ratio of styrene to maleic acid, and varies from 10–30 nm in width.149 For example, a 2 : 1 styrene:maleic acid ratio (B10–15 nm width) has been used to solubilise AcrB, which is 360 kDa and contains 36 transmembrane helices.150 However, SMALPs are intolerant to divalent cations and a pH below 7.151 Additionally, protein extraction using SMA can result in a lower MP yield, and SMA has been found to inhibit the function of some MPs.152 Therefore, optimised extraction protocols, and functional assays, are necessary for SMA MP extraction. In two recent PELDOR studies of SMALP-reconstituted MPs, the Tm was improved by two-fold compared to proteo-liposomes, and was similar to the Tm of the protein in detergent micelles.91,153 3.3.4 Saposin-lipoprotein (Salipro) nanoparticles. The size limitations of nanodiscs and SMALPs may be overcome by using saposin A peptides. Unlike MSP nanodiscs, saposin A can adapt to MP size and form homogeneous disc-like nanoparticles by incorporating a different number of saposin A protein peptides into a saposin A-lipoprotein (Salipro) nanoparticle.17,154 Salipro nanoparticles have been shown to maintain the structural and functional integrity of proteins by cryoEM,154–156 solution NMR,157 and in vitro functional studies.158,159 Although no EPR studies on Salipro nanoparticles have yet been reported, it is a promising method for studying molecular interactions within large protein complexes in native-like lipid environments. That being said, saposin A contains six native cysteine residues, which form three potential disulphide bridges.160 To avoid unspecific labelling, and disruption of saposin A, it is recommended that spin-labelling of the target MP is completed prior to reconstitution, if using a cysteine reactive spin label such as MTSSL. Additional saposin A purification steps are also required prior to reconstitution.17 3.3.5 Bicelles. Bicelles were introduced for solid-state NMR studies of membrane-associated molecules.161 Bicelles are discoidal lipid bilayers without polymeric chains or amphipathic proteins to encompass them. The planar regions of bicelles are composed of ‘‘long-chain’’ Electron Paramag. Reson., 2021, 27, 74–108 | 89

phospholipids such as DMPC, and the edges are bordered with either a zwitterionic detergent (e.g. CHAPSO), or short-chain phospholipids (e.g. DHPC) to shield the hydrophobic lipid tails from the aqueous solution. The size of the bicelle is dependent on the molar ratio of long-chain lipids to short-chain lipids/detergent (q), and the total lipid concentration (CL). Specifically, large bicelles with a high total lipid concentration (q43, CL of 15–25% w/w) can align in magnetic fields at temperatures above the transition temperature of the long chain phospholipid used to form the planar bilayer.162 This bicelle property has been used to probe the topology of integral membrane peptides, and to determine the helical tilt of peptides with respect to the bilayer surface.163,164 However, the magnetic alignment of bicelles requires EPR measurements to be recorded at temperatures higher than 298 K,165 which is not appropriate for temperature sensitive MPs. Bicelles are therefore randomly distributed (in respect to external applied magnetic fields) in typical PELDOR conditions (temperatures below 100 K). Unlike other scaffolds discussed above, there are limited options for bicelle composition, particularly the long-chain lipids. Phospholipids with the same chain length as DMPC but a different headgroup can be added to enhance variability.162 Bicelles have been successfully used in PELDOR studies, including the MscS gating mechanism,18 dimer formation of mVDAC1,109 and conformational changes of McjD.23 3.4 Extending spin echo dephasing time through protein and solvent deuteration Spin echo dephasing time (Tm) limits the maximum distance measurements possible by PELDOR. Tm is affected by instantaneous and spectral diffusion, and hyperfine interactions between unpaired electrons and nearby protons, such as those from the methyl groups of amino acids, alkyl chains of lipids, and solvents.8 These hyperfine interactions reduce the Tm to around 0.6–2 ms for membrane buried sites,166 which limits the maximum PELDOR distance measurements to 4 nm.8 Deuteration can eliminate the hyperfine interactions and extend the Tm, as deuterium has a 6.5-fold smaller gyromagnetic ratio than protons.8 Using deuterated solvents and cryoprotectants can extend the Tm, while full protein deuteration can further increase the relaxation time,8,9,167 allowing distances of up to 160 Å in soluble proteins to be measured.7 However, this approach has not been applied to integral MPs yet, and is expected to offer great advantages in the study of large (BMDa), multimeric MPs, where long distances over 10 nm are commonly present. Full protein deuteration is costly, but it offers a significant increase in sensitivity, enabling PELDOR recording at shorter averaging times and lower protein concentrations compared to nondeuterated protein samples.9

4 Electron spin echo envelope modulation (ESEEM) In this section we will introduce ESEEM spectroscopy, and discuss recent applications of the technology to the study of MPs. 90 | Electron Paramag. Reson., 2021, 27, 74–108

ESEEM is a pulsed EPR technique used to study hyperfine interactions in a paramagnetic system.5,11,168,169 The technique looks at the modulation of an electron spin echo by nuclei at distances of up to 5–8 Å.170,171 This modulation causes a periodic alteration of the electron spin echo amplitude, which can be used to determine hyperfine and nuclear quadrupole parameters.168,169 Historically, ESEEM has been an important method for the investigation of radical formation and the electronic structure of paramagnetic species. In the case of biomolecules, the technique has been powerful in the study of metal centres and the catalytic mechanisms of metalloproteins.172 More recently, by measuring the accessibility of spin-labelled residues to solvent and lipids, ESEEM spectroscopy has allowed structural biologists to probe the local secondary structure of MPs.5,10 ESEEM has also provided supporting evidence for the occurrence of conformational changes in the presence of specific triggers in MP channels.11,14 ESEEM can provide valuable information when combined with PELDOR, as solvent accessibility measurements can offer important insights into the local environment of residues inaccessible by PELDOR.12,170,173 As sample preparation is identical to PELDOR and the technique has comparatively faster data acquisition times, the role of ESEEM measurements in developing the structural understanding of MPs is crucial. Several different pulse schemes can be used to observe nuclear modulation effects,174 however two-pulse ESEEM (2pESEEM) and threepulse ESEEM (3pESEEM) are the most common. Several advantages are associated with 3pESEEM experiments, including the slower decay of time traces and the ability to suppress signal contribution from specific nuclei (e.g. deuterium or proton).5 4.1 General applications of ESEEM for the study of biomolecules Most biomolecules are naturally EPR silent, lacking the paramagnetic centres that make systems amenable to EPR spectroscopy. Initial investigations of biomolecules using ESEEM were restricted to metalloproteins with paramagnetic metal ion co-factors and free-radical enzyme intermediates. However, the development of site-directed spin-labelling (SDSL) revolutionised biological EPR, allowing the application of the technique to most proteins.175,176 Several paramagnetic metal species can be found in biological systems including ions of copper, cobalt, iron, manganese, molybdenum, nickel, and vanadium, and these ions can play structural roles, but more commonly are involved in catalysis and electron transfer.177 All metalloproteins involved in electron transfer chains have redox states with unpaired electrons, and ESEEM has been widely applied to studies of these biological paramagnetic metal centres. ESEEM spectroscopy has been applied to the study of metal-binding sites and co-ordination, the formation of radicals in catalysis, and metalloenzyme mechanisms. One of the earliest studies that highlighted the power of ESEEM techniques was its use in understanding Cu(II) sites and associated ligands of Stellacyanin.178 Since then, ESEEM has been applied to a variety of metalloproteins, including its use in identifying the coordinating ligands of a metal ion site (Mn21-substituted) in the Electron Paramag. Reson., 2021, 27, 74–108 | 91

hammerhead ribozyme,179 the study of the deuterium exchange rate of water molecules coordinating a metal site in cytochrome c oxidase,180 and determining the type of interstitial atom in the MoFe cluster of a nitrogenase.181 ESEEM has also been used to probe enzymatic mechanisms and radicals, examples of which include the involvement of pyridoxal 5’-phosphate in the catalytic mechanism of lysine 2,3-aminomutase,182 catalytic intermediates in the mechanism of methylamine dehydrogenase,183 and investigations of the photosystems.184,185 4.2 Application of ESEEM to the study of membrane protein structure A wide range of MPs have been studied by combining SDSL with cw-EPR, PELDOR and ESEEM methodologies to develop the understanding of MP structure and dynamics.186 ESEEM spectroscopy is particularly useful in investigating the local secondary structure and local interactions of MP domains in both aqueous and membrane environments. The accessibility of spin-labelled residues to deuterium (solvent) and protons (residues and acyl chains) can provide important insights into the dynamics and local environments of proteins. Exposure of specific residues to phospholipid headgroups can be monitored using 31P ESEEM, allowing lipid localisation. This can be used in conjunction with 31P NMR to identify and quantify the lipid species associated with a protein.11 The study of the potassium channel KcsA is an excellent example of the application of ESEEM spectroscopy to investigate several aspects of protein structure and function.12 Deuterium 3pESEEM experiments demonstrated that solvent (D2O) permeation into the membrane along the surface of an external transmembrane helix decreased with increasing depth of the protein in the membrane.12 Nine residues along the outer surface of the helix were spin-labelled and the spectral density at each was measured in reconstituted proteins. For comparison, spectral density at different immersion depths in empty vesicles was determined using spin-labelled phospholipids, labelled at different positions along the alkyl chain.12 KcsA did not appear to disrupt the lipid packing in the membrane, as water permeability along its outer helix did not increase above the levels observed in the empty vesicles. Additionally, 31P ESEEM was used to investigate protein-lipid interactions.12 The Pliotas group has utilised EPR spectroscopy to characterise structural differences between the closed and sub-conducting state(s) of the mechanosensitive channel MscL.11,14 ESEEM spectroscopy performed on a subconducting state of the channel, stabilised by an L89W mutation located at the entrance of a pressure-sensitive lipid pocket, supported a rotation of TM2 helix following channel expansion.11 Solvent accessibility measurements of a spin-labelled residue on TM2 (L72R1) in the absence of the L89W mutation showed very little modulation of the echo. This suggested that the residue was not accessible to solvent. Following stabilisation of the MscL sub-conducting state, L72R1 was found to be seven-fold more accessible to solvent. Therefore, ESEEM spectroscopy is a valuable tool for monitoring conformational changes of proteins. ESEEM has also been used to investigate the light-harvesting MP complex, LHCII. Water accessibility measurements by ESEEM 92 | Electron Paramag. Reson., 2021, 27, 74–108

highlighted that the conformational state of the LHCII N-terminal domain is different in solubilised monomers in comparison to trimeric LHCII crystals.173 Subsequent studies followed the folding of LHCII by PELDOR and ESEEM spectroscopy.101,187 Sites for spin-labelling were guided by PELDOR and rotamer library simulations, and ESEEM spectra recorded at different time points during protein folding showed a decreasing deuterium peak.187 The decreasing exposure of the reference residue to heavy water showed that folding of the protein was completed after 1800 s. It should be noted that termination of folding by flashfreezing and EPR sample preparation is a slow process, meaning the methodology can only be applied to proteins folding on the scale of tens of seconds to minutes.187 However, it remains that ESEEM spectroscopy can supplement other techniques, such as PELDOR, circular dichroism, and fluorescence-based techniques, to understand the folding process and kinetics of proteins. Studies have also demonstrated the use of ESEEM in determining the local secondary structure and topology of membrane peptides in a lipid environment. The presence of a-helices in both transmembrane and soluble regions were detected on the membrane peptide KCNE1 in both detergent micelles and lipid-based bicelles using ESEEM spectroscopy.10 Due to the characteristic structure of an a-helix, the interaction of spin labels and deuterated amino acids 3–4 residues distant will result in deuterium Larmor peaks in the ESEEM frequency domain spectra.10 A spin-label that is placed two amino acids from a deuterated valine will produce no 2H peak. The presence of 2H peaks from spin-labels 3–4 amino acids apart, and the absence of a peak when the label is two residues away, demonstrated local a-helical structure.10 The methodology was enhanced further by using 2 H-labeled leucines rather than valines as above, resulting in a four-fold increase in observed 2H modulation depth.188 Another study used ESEEM to investigate interactions between antimicrobial peptides and the membrane, helping researchers to understand the location of peptide regions following binding.170 Many studies have used ESEEM methodologies to study a variety of small membrane peptides including the acetylcholine receptor M2d peptide,188–191 a ubiquitin peptide,192 model amphipathic peptides,13 and the core peptide of the T-cell receptor TCRa transmembrane domain.193 In general, there is no size limitation for the study of proteins using ESEEM methodologies, so the technique is applicable to larger protein systems. 4.3 Experimental considerations While most PELDOR applications move to Q-band (34 GHz) due to increased sensitivity, the ESEEM effect is reducing with increasing frequency, and X-band (9 GHz) remains the most versatile and appropriate for performing the ESEEM experiments. There is greater flexibility with temperature in ESEEM as measurements can be performed at 50 K or 80 K, with similar data quality for nitroxide spin labels. ESEEM sample preparation is the same as discussed earlier for PELDOR, as ESEEM and PELDOR measurements can be conducted on the same sample in similar cavities. The spin-labelled proteins are frozen, so are not susceptible to Electron Paramag. Reson., 2021, 27, 74–108 | 93

protein denaturation, allowing them to be stored and re-measured as necessary. To determine solvent accessibility, a specific t value can be used to suppress the proton signal in a 3-pulse ESEEM experimental setup. For our experiments, time-domain traces from measurements are background-corrected, apodized with a hamming window and zero-filled before Fourier transformation. Either the modulation depth in the time domain or the amplitude of the deuterium peak in the frequency domain is then used to ascertain accessibility to water 2H nuclei. Volkov et al. have previously discussed different methodologies and considerations for water accessibility measurements using ESEEM.173 The step-by-step process of conducting an ESEEM experiment is beyond the scope of this chapter, but has been described elsewhere.5 Structural investigations of MPs by ESEEM spectroscopy require SDSL to be considered within the context of the research question. Crystal and cryo-EM structures of proteins can allow the prediction of the water and/or lipid accessibility of a specific residue. In the absence of a high-resolution structure, successful spin-labelling of a protein is often a case of trial and error, which can make the process time consuming and laborious. Hydrogen–deuterium exchange mass-spectrometry (HDX-MS) can be a valuable tool in the efficient selection of labelling-sites. The technique offers fast mapping of MP domains that experience larger changes in their relative accessibilities between different states. Previous studies have demonstrated the application of HDX-MS to membrane proteins.135,194 In HDX-MS, exchange of protons on the protein, with deuterium in a deuterated solvent, generates accessibility information that can be used to investigate the structure and dynamics of the protein. Differences in the rate of exchange between two states (e.g. open and closed) at the peptide level, enables the identification of protein regions that potentially undergo conformational changes. However, the resolution of HDX-MS is limited, it requires the presence of a state reference, and does not provide any quantitative information regarding the level of relative solvent exposure. That being said, the results from HDX-MS experiments can subsequently be used to aid the selection of labelling sites to further probe local interactions using ESSEM. ESEEM offers single residue resolution, does not require a reference system, and allows for semi-quantitative analysis of the degree of accessibility of different residues.

5 Combining molecular dynamics simulations with pulsed EPR In this section, we will introduce molecular dynamics (MD) simulations and their uses in combination with pulsed EPR methodologies. PELDOR and ESEEM are powerful techniques in MP structural biology, however they both require prior knowledge of protein structure to determine optimal labelling sites, and to interpret results. The two most commonly used computational tools for the design of labelling sites and in silico distance predictions are MtsslWizard136,195 and MMM.196 Both software tools are quick and simple to use and have been implemented in recent studies of MP channels.11,14,18,93 However, there are certain 94 | Electron Paramag. Reson., 2021, 27, 74–108

limitations that must be considered when using either software for designing PELDOR experiments. Both MtsslWizard and MMM do not consider rotamer orientation preference often induced by the local MP environment. In particular, one has to consider highly hydrophobic transmembrane domains where the presence of detergent used for membrane extraction, and/or lipids (either native or exogenously added), may impact side-chain rotamer orientation. Importantly, the overwhelming majority of X-ray crystal structures do not resolve such molecules, and structural models available in the PDB are devoid of lipids or detergent, thus these molecules are not taken into consideration during in silico spin-labelling approaches. Rotamers with preferred orientations, or highly flexible spin-labelled residues, can lead to multimodal or broad distance distributions respectively, which could lead to uninterpretable data. The vast majority of X-ray crystal structures represent only a single conformation for a given MP and MD simulations, combined with distance restraints generated by PELDOR, could be used to observe the whole conformational ensemble of MP dynamics. MD simulations use Newton’s second law of motion to mimic MP behaviour under controlled conditions and in defined timescales. Using MD simulations, various attributes of proteins (or specific residues) can be explored, such as solvent accessibility and mobility, and intra-protein distance distribution determination could be offered. Therefore, MD simulations could be used in parallel with PELDOR to aid the choice of labelling sites, and support experimental laboratory work on protein dynamics.197 MD simulations can also be used to validate the analysis of PELDOR distance distributions.198 Another important function of MD simulations is to facilitate the interpretation and analysis of the experimental PELDOR results, which is well demonstrated in the study of ABC transporters199 and MscL.11 5.1 MD simulation set-up MTSSL, the most widely used spin label, has a length of 7–8 Å, and this must be accounted for in MD simulations, since using the Ca atoms to measure the distances would introduce significant errors. MD simulations can be performed within a range of native membrane lipids and/ or detergents, which is highly advantageous in the study of MPs. It is important that distance modelling should be performed in conditions consistent with those used in the in vitro experiments. The general pipeline for MD simulations of spin-labelled MPs is illustrated in Fig. 1. The easiest way to set up the MD simulation is to use the CHARMM-gui web server.20 It provides a selection of a variety of lipids, and tools to mutate residues and attach spin labels. If a more comprehensive control of the system is desired, a bespoke system can be built using other software packages and force fields. Force fields such as gromacs,200 OPLS,201 AMBER202 and CHARMM203 describe all required MTSSL parameters. The first step for setting up an MD simulation of a spin-labelled MP is to prepare a spin-labelled PDB file of the target protein, which can be implemented using the CHARMM-gui web server,20 MtsslSuite,195 or MMM.196 Electron Paramag. Reson., 2021, 27, 74–108 | 95

96 | Electron Paramag. Reson., 2021, 27, 74–108 Fig. 1 Representative MD simulation pipeline, using the study of TbMscL as an example. A. General MD simulation pipeline of spin-labelled membrane proteins. B. Structure of the closed pentameric TbMscL (PDB ID: 2OAR) with the MTSSL at residue L89 (L89R1). One subunit is highlighted in blue and the MTSSL labels are represented in red. C. Side view and top view of MscL embedded in a DMPC lipid bilayer. D. Comparison of PELDOR distance distributions of L89R1 in DDM, DMPC nanodiscs, a MtsslWizard prediction and a MD simulation of L89R1).

5.2 MD simulations in the analysis of MP channels An example of how MD simulations can be used in combination with PELDOR for the study of MPs has been recently reported.11 MscL was labelled with MTSSL at thirteen different sites spanning all protein domains, and PELDOR distances were measured on pentameric MscL, both in detergent and lipid nanodiscs.11 Whilst distances for most of the sites were similar in both conditions tested, and in agreement with the closed state X-ray structure of MscL (PDB 2OAR), L89R1 presented a significant distance increase in detergent compared to the expected modelled distances (Fig. 1). The longer distances indicated that MscL was in an expanded conformation, representing a sub-conducting channel state. In contrast, when PELDOR was performed on L89R1 reconstituted in lipid nanodiscs (DMPC), both distances generated for a five-spin system, such as MscL, decreased. To investigate the reasons behind this conformational change induced by the presence of lipids, atomistic MD simulations of the closed MscL state (in DMPC lipids) with L89 mutated to a cysteine and spinlabelled with MTSSL were run for 100 ns. The inter-spin distances derived by the MD simulations were shorter than the experimental distances observed for L89R1 in DDM and consistent with those in DMPC nanodiscs (Fig. 1). This study provided the first experimental demonstration of the ‘‘lipid moves first’’ model, which describes a mechanism for mechanical regulation in MP channels.6,204 This observation also highlights that when designing spin-labelling sites within the transmembrane region of MPs, lipids should be taken into consideration in any associated distance modelling, and thus data analysis and interpretation. 5.3 Sophisticated MD simulations MTSSL has five, not fixed by the structure, dihedral angles and it is complex to model all of its possible conformers.205 To deal with the long timescales required to explore all rotameric ensembles, different strategies may be applied. Dummy spin labels have been developed to reduce the complexity of MTSSL, so the conformational ensembles can be explored faster than actual MTSSL.206 Annealing MD simulations and the Colvars module in NAMD can also be used to reduce the time required to explore all the MTSSL ensembles by introducing multiple spin labels that cannot be perceived by each other.207 Simulated scaling (SS) MD simulation was also demonstrated to be useful, as it samples the MTSSL rotamers significantly faster.205 PELDOR is able to determine conformational changes within MPs without the need for solving additional structures by X-ray crystallography or cryo-EM, while offering atomic resolution.5,6 However, additional structural information is sometimes required to fully interpret results from PELDOR experiments. In these cases, MD simulations can be employed to predict, model or assign conformational MP states from PELDOR-derived data. And in cases where PELDOR distance distributions are found to differ from those expected in a structure, these experimental distance measurements could be implemented in distance-restrained MD simulations to guide protein movement (or state transition) from an initial structural model, to the conformational state(s) observed by PELDOR.208,209 Electron Paramag. Reson., 2021, 27, 74–108 | 97

Acknowledgements This project was supported by a BBSRC grant to C.P. (BB/S018069/1). C.P. also acknowledges support in the form of PhD studentships from the Wellcome Trust (219999/Z/19/Z) for B.J.L. and the Chinese Scholarship Council for Y.M. and B.W.

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Recent contributions of EPR to nitrone and nitroxide chemistry Pierluigi Stipa DOI: 10.1039/9781839162534-00109

The present contribution provides an overview of the latest research studies in which Nitrones and Nitroxides are involved in the applications of Electron Paramagnetic Resonance Spectroscopy (EPR) in different fields. Due to the free radical nature of Nitroxides (Aminoxyls), their use in EPR investigations is rather straightforward, while for Nitrones (N-oxides) it relies instead on their use as ‘‘radical scavengers’’, and/or by their use in the EPR Spin Trapping technique. Since the chemistry of both Nitrones and Nitroxides have been extensively described elsewhere, this contribution would only represent an update on some of their most recent application involving EPR spectroscopy.

1

Introduction

The relationship between Nitroxides (Aminoxyls) and Electron Paramagnetic Resonance (EPR – also known as ESR: Electron Spin Resonance) is straightforward, because of their paramagnetic properties due to their free radical nature. EPR studies of Nitrones (N-oxides) rely instead on their use as antioxidants acting as ‘‘radical scavengers’’, or on the EPR Spin Trapping technique, where they are transformed in the corresponding nitroxides by radical addition and detected by EPR. In addition, Nitrones could also represent the synthetic precursors of Nitroxides. Since the chemistry of both Nitrones and Nitroxides have been extensively described elsewhere, only some introductory notes are reported at the beginning of the corresponding sections. In fact, this contribution aims to report some of the most recent application of Nitrones and Nitroxides involving EPR spectroscopy in the time span from 2016 till the beginning of 2020. However, within this (limited) period, hundreds of papers are available and worthy of mention, so their absence here is not due to their quality but only to (my) personal limits. The chapter is organised in 2 main sections, namely Nitrones and Nitroxides, each of them further divided into subsections depending on some specific applications.

2

Nitrones

2.1 Nitrones as spin traps Electron Paramagnetic Resonance (EPR) Spin Trapping represents one of the most specific and reliable techniques for the detection and identification of short-lived free radicals, whose lifetime is too short for the direct detection by EPR. This technique, widely used since its introduction at the end of 1960,1–3 employs a suitable diamagnetic molecule (a Spin Trap), which can quickly react with short-lived free radicals to ` Politecnica delle Marche, S. I. M. A. U. Department – Chemistry Division, Universita Via Brecce Bianche 12, I-60131, Italy. E-mail: p.stipa@staff.univpm.it Electron Paramag. Reson., 2021, 27, 109–145 | 109  c

The Royal Society of Chemistry 2021

form relatively long-lived radicals (Spin Adducts), whose EPR signals are persistent enough to be recorded and analysed: the identity of the radical formed can be obtained from the Spin Adduct EPR spectral parameters, namely the hyperfine coupling constants (hfccs) and g-factors, characteristic of the type of initial radical trapped. In this context, Nitrones (N-oxides) are very efficient Spin Traps4,5 being able to undergo fast radical additions with all kinds of radicals, C-centred as well as O-centred ones, to yield nitroxides (aminoxyls) as Spin adducts, probably the most persistent organic free radicals in liquid solutions. The use of nitrones as Spin Traps is due to the reactivity of the Carbon–Nitrogen double bond, which rapidly undergoes addition of a transient free radical to yield the corresponding Nitroxide (Scheme 1 – Path A). However, one of the most common drawbacks in this use of Nitrones is represented by the addition of a Nucleophile, often present in the reaction medium, followed by oxidation to still give a nitroxide as a final product, but in this case not representative of the reaction mechanism under study6 (Scheme 1 – Path B). Among all the commercially available nitrones, N-tert-butylbenzylideneamine N-oxide (PBN) and 5,5-dimethyl-3,4-dihydro-2H-pyrrole N-oxide (DMPO) are probably the most popular, but their use is not without limitations (see Scheme 2). For example, PBN and its analogues give Spin Adducts with similar EPR spectra, generally consisting of a triplet of doublets, with a relatively small variation in the doublet splitting depending on the radical trapped, and this may constitute a source of misinterpretations in Spin Trapping experiments (see Fig. 1).7 On the other hand, the use of DMPO is limited

.

+ R2

N

R1

O

or N+

R1

+ R2(+H+)

O-

nitrone

B

A R1 ox R1 N O•

N

R2 O- (H+)

(-H+)

R2

nitroxide

Scheme 1 Path A: Spin Trapping; Path B: nucleophilic addition followed by oxidation.

R

But

R

H

N+ H

N

O-

O R = Phenyl- : PBN; R = H : EBN; R = Pyridil-1-Oxide : 4-POBN

R = Me : DMPO; R = CONH2 : AMPO; R = CO2Et : EMPO; R = P(O)(OEt)2 : DEPMPO

Scheme 2 Chemical structure of the most popular Nitrone spin traps. 110 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 1 Typical EPR spectra of most common Nitrone Spin Adducts.

by its sensitivity to nucleophilic attack (by water), and the relatively low stability of its superoxide Spin adduct which decomposes rapidly.8 Moreover, the presence of a-hydrogens to the nitrone function as in DMPO is an important factor, because it is known that the corresponding aminoxyls are unstable and may disproportionate to the corresponding nitrone and hydroxylamine;9,10 in addition, it has been observed that electron-withdrawing substituents close to the N–O function could stabilize Spin Adducts,11 in particular those arising from superoxide trapping. By taking into account all these reasons, continuous effort has been devoted to the synthesis of other nitrones,12–15 including PBN and DMPO analogues,16,17 to be used in Spin Trapping experiments in order to minimize the above-mentioned drawbacks (Fig. 2). 2.1.1 In biological systems. Although EPR Spin Trapping represents a general technique useful to point out if a transient free radical is involved in the course of a chemical transformation, in the last decades it has found increasing applicability in the study of biological systems, as a large amount of human disease states has been ascribed to ‘‘unbalanced’’ production of mainly O-centred radicals (Reative Oxygen Species – ROS) but also of N-centred ones (Reative Nitrogen Species – RNS).18 These species, normally produced by cells in view of a ‘‘redox homeostasis’’,19 in some circumstances may induce stress leading to disruption of cellular functions. Such situation is defined as ‘‘oxidative stress’’ and is characterized by enhanced production of ROS, with the Electron Paramag. Reson., 2021, 27, 109–145 | 111

112 | Electron Paramag. Reson., 2021, 27, 109–145 Fig. 2 Experimental (black) and simulated (red) liquid solution EPR spectra of benzoxazine nitrones spin adducts 1–5(a–g). Adapted from ref. 13 with permission from American Chemical Society, Copyright 2007.

simultaneous impairment of cellular defence mechanisms.20 The process usually starts form a one-electron reduction of molecular oxygen, likely taking place in mitochondria, to form the Superoxide Radical Anion O2 which, in turn, may give rise to Hydroperoxyl (HOO ) as well as Hydroxyl Radicals (HO ). The presence of such species, as well as the increase of their concentration in these situations, have been well documented by means of EPR Spin Trapping experiments (see Fig. 1). As a typical example concerning human health, Alzheimer’s disease is characterized by many concomitant factors, mainly by Amyloid-b (A-b) deposits, cholinergic deficit and extensive metal-induced (copper, iron) oxidative stress. It has been recently demonstrated that in the presence of tacrine-7-hydroxycoumarin hybrids, the use of DMPO as a Spin Trap can significantly suppress the formation of HO radicals. This can be likely ascribed to the formation of a Cu(II)-coumarin complex which prevents the Cu(II)-catalysed decomposition of hydrogen peroxide, in turn alleviating the effects of oxidative stress-induced damage.21 However, the Spin Trapping activity of Nitrones is not limited to ROS scavenging. As an example, during oxidative stress, ROS can abstract hydrogen atoms also from Glutathione (GSH) to form the corresponding thiyl radical (GS ). Since GSH is the most abundant cellular thiol, this process is viewed as a toxicological event and GS can in turn abstract H-atoms from cellular molecules, react with sulfhydryls to form disulfides, and add to double bonds.22 The detection of GS in a biological milieu is difficult for its short half-life, and the corresponding DMPO adduct is not very persistent as well. However, by using EBN as Spin Trap (see Scheme 2) and generating GS via photolytic cleavage of the S–N bond of S-nitrosoglutathione (GSNO),23 it has been possible to obtain a persistent EPR signal attributed to the corresponding GS-EBN adduct, whose half-life was significantly improved in the presence of cyclodextrins (see Fig. 3).24 Moreover, concerning the anti-cancer effect attributed to anti-diabetic biguanide drugs metformin (N,N-dimethylbiguanide), buformin (1-butylbiguanide), and phenformin (1-phenethylbiguanide), it has been demonstrated that these drugs dramatically enhanced oxidative DNA damage under oxidative condition by a Fenton-like reaction involving hydrogen peroxide and Cu(ll). When these experiments were carried out in the presence of DMPO or 4-POBN (see Scheme 2) as Spin Traps, it has been shown that nitrogen-centred radicals (see Fig. 4) were generated from biguanides and that the concentration of these radicals was decreased by the addition of DNA. This may suggest a possible mechanism through which these drugs could exert their anti-cancer effect.25 Another interesting application of Nitrones in biological system is represented by Immuno Spin Trapping. This technique is based on the reaction of amino acid and DNA base-derived radicals with the Spin Trap 5,5-dimethyl-1-pyrroline N-oxide (DMPO) to form protein- and DNA-DMPO nitroxide radical adducts, respectively. These adducts can be detected by different techniques, including immunochemistry using specific anti-DMPO nitrone antibodies, regardless of their oxidative/ reductive state,26 hence circumventing the typical nitrones drawbacks in Electron Paramag. Reson., 2021, 27, 109–145 | 113

Fig. 3 Spin-trapping of photolytically generated thiyl radicals by EBN. Reactions were carried out at 25 1C in 0.1 M phosphate buffer (pH 7.4) containing EBN (50 mM) and S-nitrosothiol (5 mM). A 1- EPR spectra of GSNO and EBN prior to (light off; black trace) and after illumination (light on; red traces); 2-computer simulation of the EPR spectrum of EBN/ SG; 3- EPR-monitored decay of EBN/ SG (light off). Consecutive spectra were recorded with time intervals of 30 s (1) and 150 s (3). Arrows indicate the directions of the spectral changes. B-EPR spectra were recorded after illumination of S-nitrosothiols and EBN for 5 min; 1-S-nitroso cysteine and EBN; 2-S-nitroso N-acetyl-D-penicillamine and EBN; 3-S-nitroso 2-methyl-2-propanethiol and EBN. Reproduced from ref. 24 with permission from Springer Nature, Copyright 2016.

living systems. This method has been used to determine the distribution of free radicals in cells and tissues and even in living animals;27 when coupled with Magnetic Resonance Imaging, the contrast agent could be represented by the DMPO-radical adducts (nitroxides) themselves.28 Concerning these systems, membranous organelles represent probably the major endogenous sources of reactive oxygen and nitrogen species within cells and, when present in high levels, these species can cause macromolecular damage and disease. In these cases it is useful to understand if nitrone Spin Traps could be selectively targeted to intracellular membranes. This possibility has been recently investigated using a bioorthogonal imaging approach. To test localization with authentic membranes in living cells, fluorophores were introduced via strainpromoted alkyne-nitrone cycloaddition (SPANC), using the cyclic 114 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 4 EPR spectra of spin-adducts of POBN (left) or M4PO (right), derived from biguanides in the presence of Cu(ll) and H2O2. Arrows indicate MnO signals. Adapted with permission from S. Ohnishi, H. Mizutani and S. Kawanishi, The enhancement of oxidative DNA damage by anti-diabetic metformin, buformin, and phenformin, via nitrogen-centered radicals, Free Radical Res., 2016, 50, 929–937. Reproduced from ref. 25 with permission from Taylor & Francis.

Fig. 5 Membrane-specific diC12PO as s spin trapping agent (left), its cycloadduct with DBCO-Rhod and demonstration of its presence in bovine aortic endothelial cells by means of confocal microscopy (right). TOC Reproduced from ref. 29 with permission from The Royal Society of Chemistry.

nitrone 5-dodecylcarbamoyl-5-N-dodecylacetamide-1-pyroline-N-oxide (diC12PO). In this study, a cycloadduct of dibenzylcyclooctyne-PEG4-5/ 6-sulforhodamine B (DBCO-Rhod) with diC12PO was prepared and its presence in bovine aortic endothelial cells was demonstrated by means of confocal microscopy29 (see Fig. 5). 2.1.2 In catalysis and photocatalysis. Despite the large amount of studies carried out in the last decades involving EPR Spin Trapping in biological systems, a significant increase has also recently been recorded in the number of papers dealing with the use of Nitrone Spin Traps in Catalytic and Photocatalytic processes, where the understanding of the reactions mechanisms becomes of primary interest also for synthetic purposes.30 As a typical example, an atomically dispersed Fe–N–C catalyst has been prepared, and its efficacy in the selective oxidation of the Electron Paramag. Reson., 2021, 27, 109–145 | 115

Fig. 6 Selective oxidation of hydrocarbon C–H bonds. The spectrum was recorded after 1 min. upon introducing DMPO to the reaction system. Ethylbenzene was used as the substrate. Reproduced from ref. 31 with permission from American Chemical Society, Copyright 2017.

C–H bond of a variety of substrate tested. The selectivity of the corresponding reaction products reached as high as 99%, and EPR Spin Trapping experiments gave a significant contribution in proposing a possible mechanism,31 since DMPO was able to Trap hydroxyl, ethyl, tert-Butylperoxyl radicals, as well as the oxidation product of DMPO itself formed during these reactions has been detected (see Fig. 6). Similarly, it is known that some gold(I) complexes act as photocatalysts and efficiently generate carbon-centred radicals from organic halides.32 In the presence of some of these complexes, always for synthetic purposes, it was possible to point out the formation of the  CF2P(O)(OEt)2 radical by means of EPR Spin Trapping with DMPO33 in the photoredox difluoroalkylation and perfluoroalkylation of hydrazones involving a C(sp2)-H, to yield gem-difluoromethylated and perfluoroalkylated hydrazones as highly functionalized and versatile molecules. For similar reasons, since hydrogen peroxide is a promising high-energy product for various applications, including environmental remediation, organic synthesis, and fuel cells,34,35 hollow MoO3/SnS2 heterostructured nanotubes for efficient light-driven H2O2 production have been prepared (see Fig. 7), and their efficiency tested also by means of EPR Spin Trapping with DMPO, by measuring the increase of the intensity of the signal due to the corresponding O2 and HO adducts with solar light irradiation.36 In addition, the HO radical represents also a key intermediate in the voltammetric detection of hydrogen peroxide.37 Concerning energy production and storage, aprotic sodium-oxygen (Na-O2) batteries usually have the advantages of low-cost elements, low charge overpotential and high reversibility; a solution-mediated superoxide transport is operating in these systems, although the nature of this mechanism is not fully understood. In this context, the HOO radicals involved were trapped by 116 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 7 Schematic illustration of H2O2 production with a two-channel pathway. Reproduced from ref. 36 with permission from the Royal Society of Chemistry.

Fig. 8 Schematic illustration of the Na/O2 cell and in situ electrolyte extraction during cycling to spin trap either hydroperoxyl radicals as the DMPO-OOH adducts at 210 K and/or carbon-based radicals. Reproduced from ref. 38 with permission from American Chemical Society, Copyright 2016.

reacting with DMPO at different electrochemical stages, also allowing to monitor their production and consumption during cycling38 (see Fig. 8). By adding large amounts of water to the electrolyte, the ESR spectrum became typical of trapping carbon-centred radicals, probably arising from H-abstraction to the electrolyte by the HOO radicals formed. However, in many recently published papers, EPR Spin Trapping is involved in the course of several catalytic and photocatalytic processes of environmental interest, such as the degradation of pollutants from soils (i.e. Atrazine39 and Tetracycline40 removal), which is mainly achieved via the production of HO radicals.41 In this field, the ultrasound activation of Persulfate as an oxidant in aqueous solution, to be used in contaminated Electron Paramag. Reson., 2021, 27, 109–145 | 117

Fig. 9 Experimental setup for in situ EPR measurements of sonicated solution. 1: Transducer; 2: Horn; 3: Argon gas inlet; 4: Reactor; 5:  OH; 6: SO4 ; 7: DMPO; 8: Peristaltic pump; 9: EPR spectrometer; 10: Aqua-X tube; 11: Spectrum. Reproduced from ref. 42 with permission from American Chemical Society, Copyright 2017.

soils, has been investigated. The oxidant effect is ascribed to the formation of the sulphate radical anion (SO4 ), a strong oxidant probably formed at the water interface of the cavitation bubbles induced by sonication. The experiment setup is shown in Fig. 9, while the reaction mechanism, studied by means of EPR Spin Trapping with DMPO, is reported in Fig. 10 together with the corresponding measured rate constants:42

3

Nitroxides

The chemistry of Nitroxides has been extensively described elsewhere,43–50 and this contribution, as already stated in the Introduction Section of the Chapter, would represent only an update on some of the most recent applications involving EPR. However, a brief introduction is reported hereafter for the non-specialised readers. Nitroxides (Aminoxyls) constitute a broad family of organic free radicals, where the unpaired electron is mainly localized on the threeelectron p bond between an oxygen atom and a fully substituted nitrogen. Depending on the substituents or whether the N–O group is part of a cycle, some of these radicals could be very persistent (kinetically), while others are stable compounds (thermodynamically), which could be stored for years in their solid state (see Scheme 3) and, in some cases, are commercially available. 118 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 10 Experimentally Determined Rate Constants. aMs1, s1, and M1s1 are units for zero-, first-, and second-order reaction rate constants, respectively. bk values are corrected for reactions at the bubble–water interface (effective temperature of B340 K), whereas kobs values are EPR measured values in sonicated solution purged with argon (Temperature ¼ 293 K and pH 7.4). Adapted from ref. 42 with permission from American Chemical Society, Copyright 2017. X R2 N

.

O

DIALKYLS

R1 R2

R3 N

.

R4

O piperidinic (TEMPO Deriv.)

-O

R

R R1

R1 N

N

O

O

.

pyrrolidinic (PROXYLS)

.

pyrrolinic

R2

O

R1 R2

N

.

R5

N+

R

R3 N

.

.

N O

R4

O

O oxazolidinic (DOXYLS)

imidazolinic (NITRONYLS)

isoindolinic

Scheme 3 Chemical structure of the most popular nitroxides.

.

+

N

N

. O

O-

Scheme 4 The two mesomeric forms of nitroxides: the form with separate charges is favoured by polar solvents, hence for a given nitroxide larger aN are expected than in apolar solvents.

However, since the spin density is mainly located on the N–O function, the EPR spectra of nitroxides are characterised by the nitrogen three lines (eventually further split) with characteristic hyperfine coupling constant values (aN hfccs). These values depend on the structure of the nitroxide and its geometry,51 but also on the solvent used. In fact, Nitroxides are probably the most persistent organic free radicals in liquid solutions, and in terms of valence bond theory, the N–O group could be represented by the two mesomeric structures reported in Scheme 4. The contribution of each form depends on the stabilization contribution from solvent polarity, modulating the aN value attributable to the corresponding different spin density at nitrogen atom. A similar solvent dependence has also been reported for g-factors, although in general Electron Paramag. Reson., 2021, 27, 109–145 | 119

their value is included in a narrow range between 2.0050 and 2.0060.52 Concerning stability, it mainly depends on the presence of hydrogen atoms in b position with respect to the N–O group, for the possibility to undergo disproportionation reactions; also b-fragmentations must be taken into account, in particular in the presence of crowded N–O neighbours (see Scheme 5).53,54 Other peculiarities of the N–O bond are represented by its length and energies, which are considered midway between those characteristics of a single (N–OH) and a double (NQO) bond.55 However, the chemistry of nitroxides is mainly characterised by reactions involving their free valence. Although self-reactions are not known for nitroxides they, as all free radicals, can undergo couplings with other free radicals: the corresponding rate constants with C-centred radicals are sometimes in competition with those characterising the recombination (self-reactions) of these latter species,56–59 as well as their reaction with molecular oxygen, explaining of the use of Nitroxides as antioxidants in polymers and in biological systems.60–65 In this last environment, the possibility of H-abstraction reactions from different substrates plays an important role representing an important limitation, as nitroxides may behave as pro-oxidants. In addition, their reactivity with ‘‘electrophilic’’ radicals, such as O- and N-centered ones, is still not definitively established, except in the case of aromatic aminoxyls, where the delocalization of the unpaired electron in an aromatic p system is allowed,66,67 as in indolinonic,68–72 quinolinic73 and benzoxazine nitroxides54 (see Fig. 11). Nitroxides are also redox active species and can undergo one-electron reduction or oxidation (see Scheme 6). In the presence of protonating agents, the anion could be transformed into the corresponding hydroxylamine (N–OH) and the process could become irreversible, while the oxidation to oxoammonium cation is reversible for most nitroxides. These properties open up to a wide number of their applications, ranging from material science to catalysis, as well as in biological systems. In the latter case nitroxides are considered as mimes of Superoxide Dismutase (SOD), an enzyme able to transform the superoxide radical anion produced within cells into hydrogen peroxide,74,75 and different possible mechanisms have been proposed (see Fig. 12). However, the direct involvement of HOO , as the protonated form of O2 , cannot be excluded,76 as confirmed by proper Density Functional Theory (DFT) calculations.77 The applications of nitroxides here reported could be roughly grouped based on their properties: i) chemical, i.e. directly involving the unpaired electron; ii) magnetic, focussing on such a ‘‘physical’’ aspect; iii) spectroscopic, mainly concerning the study of the corresponding EPR signals dependence by their molecular environment (Spin Probes and Spin Labels). 3.1 Chemical behaviour The nitroxides applications directly involving the unpaired electron may include those depending on their ability to react with other radicals, such as the C-centred ones as, for example, in the Nitroxide Mediated Polymerization (NMP), but also on their redox activity (see Scheme 6), which allows their use either in the design of new batteries and as antioxidants. 120 | Electron Paramag. Reson., 2021, 27, 109–145

2

C

N

.

C

O H

C

N

C

OH H Disproportionation

Scheme 5

+

C

N+ O-

C

;

C

N

.

C

C

N+

C

+

R

.

O-

O R Fragmentation

Disproportionation of a nitroxide with b-hydrogen atoms (left) and b-fragmentation of hindered nitroxides (right).

Electron Paramag. Reson., 2021, 27, 109–145 | 121

Fig. 11 Optimized geometry (a) and SOMO plot (b) (positive values in red and negative in green) of benzoxazine nitroxide 3-Benzyl-3-phenyl-2H-benzo[1,4]oxazin-4oxyl computed at the B3LYP/EPR-III level, showing the arbitrary atom numbering. Reproduced from ref. 54 with permission American Chemical Society, Copyright 2011.

+H

N

- H+ OH

. O-

N

+ H+ hydroxylamine

- e-

N

.O

+e anion

-H

nitroxide

- e+ e-

+

N

O

oxoammonium

.

Scheme 6 Redox properties of nitroxides. In the presence of protonating agents, the anion could be transformed in the corresponding hydroxylamine (N–OH), also formed through an alternative (HAT) pathway (in red).

Fig. 12 Nitroxides as SOD mimics. Both proposed mechanisms (1) and (2) are two-steps processes. Mechanism (3) is an alternative proposed on the basis of the addition of hydroperoxyl radical to nitroxide followed by decomposition of the corresponding adduct.

However, their employment as catalysts is also intriguing, and continuous efforts are devoted towards the synthesis of new derivatives. 3.1.1 Nitroxide mediated polymerization (NMP). Among the more recent techniques available for the Controlled (living) Radical Polymerization, Nitroxide Mediated Polymerization (NMP) is probably one of the most convenient. It allows to prepare well-defined polymers and copolymers, with predictable molecular masses and narrow molecular weight distributions.78 NMP is based on the reversible trapping of a reactive propagating (C-centred) radical by a suitable nitroxide to yield a dormant species (alkoxyamine): rapid exchange between the active and dormant forms allows the polymer to grow while minimizing the frequency of bimolecular termination reactions (see Fig. 13). Nitroxides, and in particular the corresponding alkoxyamines, play an extremely important role because the living character of a polymer depends on the temperature dependent equilibrium involving the alkoxyamine C–O bond homolysis. Many studies have been carried out in order to understand the factors modulating the alkoxyamine thermal decomposition, as the persistency of the released radicals (The Persistent Radical Effect),79 the (steric) strain in proximity of the breaking bond, but also polar effects eventually affect the breaking bond energy.80–84 Recently the relationship between the steric and polar effects in alkoxyamines has been studied: it has been 122 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 13 General scheme for Nitroxide Mediated Polymerization. The propagating chain represents the growing C-centred radicals scavenged by nitroxides according to kc, the radical coupling rate constant, to give (macro) alkoxyamines. The C–O bond undergoes thermal cleavage, according to kd, the alkoxyamine decomposition rate constant, to give back the nitroxide and the C-centred radicals. The polymerization control depends on the kc/kd ratio.

found that, with few exceptions of some cyclic nitroxides, the steric effect is described by the ‘‘sum’’ of the bulkiness of the groups present at the a-carbons. This was expected for ‘‘normal’’ steric effect, but in the case of acyclic nitroxides these effects are somehow levelled. A sterically hindered commercially available N-alkoxyamine has been investigated as a stabilizer in the context of photo-oxidative stability of calcium carbonate reinforced polypropylene (CCPP).85 The samples, prepared by melt compounding and exposed to artificial accelerated photo-ageing, showed that the deterioration of neat CCPP takes place very rapidly in comparison with the composites containing the studied alkoxyamine; however, in order to obtain a significant efficiency, alkoxyamine amount should reach at least the 0.5 wt%. Moreover, in the last decade many efforts have been produced toward the production of hydrogels, due to the large number of their potential applications. In particular, injectable hydrogels, liquid materials at room temperature but able to gel in situ within human body, have become highly interesting biomaterials in tissue engineering and drug/vaccine delivery, due to their minimally invasive character. Recently, an amphiphilic poly(D,L-lactide)-b-poly(NIPAAm-co-polyethylene glycol methacrylate) (PLA-b-P(NIPAAm-coPEGMA)) copolymer has been prepared through a combination of ring-opening (ROP) and NMP. Such a material undergoes gelation in aqueous solution near 30 1C, and is also characterised by good biodegradability, since a complete mass loss was observed under physiological conditions within a few days upon PLA hydrolysis.86 In addition, providing proper modifications in order to obtain light-sensitive alkoxyamines, the C–O bond homolysis could also be light-induced, giving rise to a nitroxide-mediated photopolymerization process. Recently, by following this principle, a first polymer layer has been produced by UV irradiation on a first monomer, and in a second step another monomer has been polymerised forming a covalent bond to the first one by Laser Direct Writing (LDW) generating polymer microstructures (see Fig. 14).87 Another method able to cleave alkoxyamine C–O bond involves electrochemical processes: in a recent study, designed to shade light on possible (catalytic) effects of external electrostatic fields, alkoxyamine decomposition has been obtained by anodic oxidation.88 However, in this case the fragmentation yielded a carbocation, instead of a C-centred Electron Paramag. Reson., 2021, 27, 109–145 | 123

Fig. 14 A schematic example of Laser Direct Writing by means of Nitroxide Mediated Photopolymerization (NMP2) process. Reproduced from ref. 87 with permission American Chemical Society, Copyright 2020.

radical, together with the expected nitroxide. The mechanism postulated, also supported by high level theoretical calculations, foresees the formation of a transient alkoxyamine radical cation, which irreversibly decomposes in the abovementioned products. 3.1.2 Redox activity of nitroxides. Nitroxides are interesting redoxactive species. Both oxidation and reduction potentials depend on the substituents linked to the N–O function and the ring size. Recently, in order to replace the current devices for energy production/storage, many studies have been carried out on the possibility to use nitroxides in the battery’s architecture, since previously they have been successfully used as electrodes in all-organic radical batteries. However, an important drawback of these batteries is represented by the reduced redox potentials, in comparison to those of the widely used lithium-ion batteries, making their energy-producing capacity often inadequate for use as a primary battery. In addition, nitroxide radicals can give rise to side reactions with electrolytes traditionally used, based on molecular solvents, yielding a series of undesirable and irreversible by-products, significantly reducing the life of these batteries. Since ionic liquids have demonstrated their ability to reduce the reactivity of radicals through strong intermolecular interactions, their use as electrolytes has been investigated from the theoretical point of view in a recent study. The results obtained, showed a significant increase in the redox potential of TEMPO chosen as a model nitroxide, from the measured value of 2.2 eV in aqueous media to 5.5 eV, likely due to the stabilization of the anionic form of TEMPO by ionic liquids.89 It should in fact be 124 | Electron Paramag. Reson., 2021, 27, 109–145

Fig. 15 Alternative catalytic cycle proposed for the antioxidant activity of nitroxides in the presence of protonating agents. Reproduced from ref. 92 with permission from American Chemical Society, Copyright 2016.

noted that the one-electron reduction of nitroxides is sometimes an irreversible process, especially in the presence of protic solvents (see Scheme 6). However, the development of new redox polymers is of increasing interest, and a strategy seems to be represented by the combination of nitroxides with the backbone of a conjugated conductive polymer. In line with that, poly(3,4-ethylenedioxythiophene) (PEDOT)90 and 2,7-bisthiophene carbazole (2,7-BTC)91 backbones have been successfully used in combination with TEMPO. Directly connected with the redox activity of nitroxides is their use as antioxidants. Concerning the possible mechanism involved, the importance of the presence of protonating agents acting as a catalyst has been recently outlined.92 The proposed sequence, alternative to that commonly accepted, foresees the protonation of the nitroxide (TEMPO in this case) to yield its (protonated) hydroxylamine, which in turn undergoes H-abstraction by a peroxyl radical to form the corresponding oxoammonium ion; this latter species regenerates the starting nitroxide, as a result of an electron transfer process with an alkyl radical, eventually formed by alkoxyamine decomposition (see Fig. 15). Concerning biological systems, the concept of ‘‘redox status’’ of the whole organism (organ or cell) has been introduced in view of their bioreductive capacity towards ROS action. Since these species are constantly generated in living cells, their overall effect is determined by the rate of their production, the concentration and the activity of the antioxidants present. In this context, many factors play an important role in enhancing the oxidative damage of cells and tissues, either by decreasing Electron Paramag. Reson., 2021, 27, 109–145 | 125

the antioxidant capacity (redox buffer capacity)93 or increasing the rate of ROS production, so introducing an oxidative stress condition, which is implicated in many pathological situations. From this point of view nitroxides have shown promising potential as therapeutic antioxidants,94 although there are controversial opinions based on their tendency to be reduced in vivo to hydroxylamine, thus acting as pro-oxidants. Despite that, it has been demonstrated that TEMPO inhibits hydroxyl radical production (by up to 90%) from the Fenton-like reaction between Fe(II)-citrate with hydrogen peroxide,95 as this reaction may represent one of the mechanisms able to induce oxidative stress and pathological conditions. In this case the inhibition was due to oxidation of the Fe(II)-citrate by TEMPO when their stoichiometric ratio is of 1.0 : 1.1. Concerning lipid peroxidation occurring in biological membranes, a series of lipid-functionalized nitroxides having a pyrroline nitroxide moiety, linked either to a glycerol or to a steroid unit, has been synthesized (see Fig. 16): their penetration depth in phospholipid bilayers has been determined by EPR spectroscopy,96 and it was also possible to build a kind of ‘‘molecular ruler’’ within the bilayer with the aid of proper Molecular Dynamics calculations.97 These derivatives showed an interesting antioxidant activity depending of their penetration depth, despite their very similar redox potentials since all of them bear the same nitroxide moiety. However, the mechanism through which nitroxides can act as antioxidants represents a complicated task, because their redox properties and ability to scavenge free radicals could operate at the same time. As a result, it has been found that the aromatic nitroxides of the indolinonic and benzoxazinic series, which also are able to trap O-centred radicals, are more efficient antioxidants with respect to TEMPO in biological systems, in line with their corresponding nitrones which are more effective than PBN.98 A typical situation in which a ROS overproduction has been found, and easily reproducible on the lab scale allowing its study, is represented by Ischemia-Reperfusion. This practice represents a therapy used to treat acute ischemic stroke, but the resulting ROS generation causes injury, which aggravates infarction. As an example, in order to achieve an effective and non-toxic antioxidant, novel core–shell type nanoparticles containing 4-amino-TEMPO have been developed and their ability to scavenge reactive oxygen species were investigated, finding that they confer neuroprotection in induced cerebral acute ischemic stroke in mice.99 In this study, ROS production has been evaluated at first by means of EPR Spin Trapping then, always by means of EPR, the nitroxide containing nanoparticles have been detected in endothelial cells around the ischemic lesion. As a result, infarction size and neurological scale were significantly decreased after this treatment, preserving the endothelium in the ischemic brain and neuronal apoptosis, while superoxide production, and gene oxidation, were significantly suppressed. Nitroxides can also be used as biomarkers in biological systems. This application comes from the typical H-abstraction reaction by which the nitroxide N–O group is reduced to the corresponding N–OH one (Scheme 6 in red) to give an EPR silent hydroxylamine. This reaction is in 126 | Electron Paramag. Reson., 2021, 27, 109–145

Electron Paramag. Reson., 2021, 27, 109–145 | 127

Fig. 16 Pyrroline derived liponitroxides and their penetration depth within a phospholipid (egg-PC-like) bilayer. Adapted from ref. 97, https://pubs.acs.org/doi/10. 1021/acsomega.8b03395, with permission American Chemical Society, Copyright 2019.

general very fast, occurring as a nitroxide is introduced in a functional biological system (a cell, for example) by the action of (mainly) ascorbic acid and/or other reducing agents. The nitroxide EPR signal intensity decay recorded in these cases depends not only on the nature of the nitroxide employed, such as its susceptibility to reduction and lipophilicity, but also on its redox activity and accessibility in the tissue of interest. As previously shortly mentioned (in Section 2.1.1), many studies have suggested that oxidative damage induced by ROS is an important mechanism in the Alzheimer’s disease progression, and that oxidative stress could further impair mitochondrial function. By using proper transgenic mice (overexpressing AbPP/Ab in neurons), the ROS production may be estimated by recording the nitroxide EPR signal intensity increase as a consequence of the formation of methoxycarbonyl-Proxyl (MCP) by in vitro oxidation of CMH, the corresponding hydroxylamine (see Scheme 7). On the other hand, in vivo EPR measurements have been performed by following the MCP signal decay due to its reduction to CMH. With the aid of other type of measurements, it has been found that oxidative stress and mitochondrial dysfunction appeared in the early onset of Alzheimer’s disease, and that increased ROS levels were associated with defects caused by mitochondrial dysfunction.100 Since oxidative stress usually starts form the formation of Superoxide Radical Anion O2 , likely taking place in mitochondria, they represent an attractive target and specific nitroxides have been developed, mainly by introducing a triphenylphosphonium moiety.101 This practice has been also exploited for the synthesis of the corresponding hydroxylamines,102,103 as they act as very sensitive EPR Probes for superoxide, being rapidly converted into their corresponding EPR active nitroxides. The nitroxide/hydroxylamine couple is involved in many processes, as for example the activation of C–H bonds in hydrocarbons in a photocatalytic process: when N-Hydroxyphthalimide (NHPI) is absorbed on a a-Fe2O3 surface, a separation of hole (h1) and electron (e) is easily produced after 455 nm light irradiation, resulting in NHPI oxidation to the corresponding nitroxide PINO (see Scheme 7). The half-life time of this confined radical has been measured by in situ electron paramagnetic resonance (EPR), right after the light was turned off, since the nitroxide is able to abstract an H atom from an hydrocarbon C–H bond: the C-centred

O

O

C OMe

C O

O (CH2)11 X P(Ph)3

X

X

.

H = N-O : MCP H = N-OH : CMH

Br -

H = N-O. : Mito-CP H = N-OH : Mito-CMH

O H = N-O. : PINO H = N-OH : NHPI

Scheme 7 MCP (3-methoxycarbonyl-2,2,5,5-tetramethyl-pyrrolidine-1-oxyl) and its mitochondria specific derivative Mito-CP, together with their corresponding hydroxylamine CMH (1-hydroxy-3-methoxycarbonyl-2,2,5,5-tetramethylpyrrolidine). PINO (PhthalimideN-oxyl) and the corresponding hydroxylamine NHPI (N-Hydroxyphthalimide). 128 | Electron Paramag. Reson., 2021, 27, 109–145

radical produced rapidly reacts with molecular oxygen to form peroxides, which decompose leading to alcohols and carbonyl derivatives.104 3.1.3 Recently synthesized nitroxides. The ease with which nitroxides can be reduced to the corresponding hydroxylamine could represent a limitation for their use in vivo, mainly attributed to the fast reaction with ascorbic acid, or other reducing agents present in specific physiological compartments. To circumvent this issue, an interesting approach is based on the synthesis of sterically hindered nitroxides, where the methyl groups often present in a-position with respect to the N–O function are replaced by ‘‘bulkier’’ groups, for example ethyl or cyclohexyl substituents, in isoindoline,105–107 imidazoline,108 pyrroline,109,110 pyrrolidine,111 as well as piperidine112 nitroxides (see Scheme 8). However, the synthesis of new stable nitroxides has been also oriented towards derivatives easily detectable even after losing their paramagnetic features, eventually arising from redox reactions or C-centred radicals scavenging. This goal has been obtained by bonding a BODIPY fluorophore to nitronyl- piperidine and pyrroline type nitroxides, and more recently to isoindoline nitroxides.113 Fluorinated nitroxides have also been prepared by different approaches. Among these, it is interesting the synthesis of derivative 1 (see Fig. 17) obtained from the lithiation of the corresponding nitronylnitroxide, followed by addition of perfluorobenzonitrile with substitution of its para-fluorine atom. Further reduction of the reaction product yielded derivative 2.114 O

O

R

R

R

R

N

. N O N

N

O

O

.

.

N

N

N

O

O

O

.

.

.

Scheme 8 Sterically hindered nitroxides with resistance to reduction for in vivo applications.

Fig. 17 Experimental EPR spectrum (black) of nitroxide 1 recorded at room temperature in a degassed dilute toluene solution and its simulation (red). Adapted from ref. 114 with permission from American Chemical Society, Copyright 2017. Electron Paramag. Reson., 2021, 27, 109–145 | 129

Scheme 9 Blood–Brain Barrier crossing nitroxides, accumulating after hydrolysis (A) or by nicotine acetylcholine receptor interactions (B).

Other interesting fluorinated nitroxides have been synthesized and successfully employed as Spin Probes in the study of halogen bond formation.114 Moreover, since EPR signal linewidth is very sensitive to molecular oxygen, appropriate nitroxides could be exploited as probes for fine estimation of O2 concentration in biological tissue by direct linewidth measure in nitroxide EPR spectra. In this field, the determination of O2 content in brain becomes crucial, but requires that the ‘‘probe’’ can cross the Blood–Brain Barrier (BBB), as for nitroxides reported in Scheme 9. These derivatives can cross the BBB, where esterase enzymes hydrolyse the ester groups to the corresponding carboxylates. This allows both higher accumulation in brain tissue at physiologic pH and greater resistance to bioreduction.115 Moreover, in order to improve the signal-to-noise ratio (S/N) of EPR spectra, perdeuterated analogues, eventually also with 14N replaced by 15N, have been prepared: the latter ones were 2-fold more sensitive in vivo than the normo-isotopic corresponding nitroxides116 due to the consequent increased signal intensity. Crossing BBB represents also an important prerequisite for the use of nitroxides as contrast agents in brain Magnetic Resonance Imaging (MRI). For this purpose, to favour their accumulation in brain tissue, nitroxides bearing a nicotine acetylcholine receptor ligand have been prepared and successfully tested (see Scheme 9).117 However, other nitroxides have been recently synthesized, mainly for their use in Spin Labelling and in Dynamic Nuclear Polarization and will be treated in the following dedicated sections. 3.2 Magnetic properties Magnetic resonance in general represents a powerful tool for noninvasive investigation of biological systems, as it allows performing spatially resolved spectroscopic measurements. For instance, EPR Imaging is based on the use of paramagnetic probes able to distribute in a targeted biological district. This has opened a wide research area aimed to propose suitable nitroxides, trying to promote their possibility to concentrate in specific tissues, and to overcome some typical drawbacks of their use, such as for example their tendency to be reduced in vivo. As an example, in a study where tissue oxygenation and pH of ischemic rat heart have been monitored by EPR Imaging, a suitable PROXYL derivative, perdeuterated and with 15N replacing the 14N isotope, also bearing a carboxylic group at both C-3 and C-4, has been successfully employed as an O2 probe, while a nitroxide radical linked to a glutathione residue (RSG) has been used for pH evaluation.118 130 | Electron Paramag. Reson., 2021, 27, 109–145

On the other hand, since Nuclear Magnetic Resonance Imaging (MRI) is based on water proton resonance and requires low energy frequency irradiation, it offers a much higher versatility and ease to use in clinical medicine compared to EPR. However, the very low sensitivity of MRI represents probably its main limitation, because of the low magnetic energy of nuclear spins compared to thermal energy at room temperature. To solve this problem, along with improving instrumentation, appropriate derivatives to be used as ‘‘contrast agents’’ to enhance sensitivity have been extensively studied, with recent focus on spin polarization transfer processes. Among these methods, Dynamic Nuclear Polarization (DNP) appears to be the most versatile, as it allows a large number of applications both in solid and in liquid states. This technique is based on the presence of paramagnetic centres in the sample at low concentration to avoid broadening of the NMR spectrum, and on irradiation close to the frequency of the EPR transition: the large polarization of the electron spin system produced is transferred to the nearby nuclei through the dipolar interaction between the electron and nuclear spins, obtaining a huge enhancement of the S/N ratio of the NMR signal. In this field, nitroxide radicals play an important role for their strong dipolar coupling to water, versatility and very low toxicity at the concentration used for in vivo applications if compared to some lanthanide derivatives. Therefore, a lot of work has been (and still is) devoted in order to obtain more and more suitable molecules, characterised by their corresponding Enhancement Factor (e). The DNP enhancement of 1H signals was also monitored as a function of microwave frequency, microwave power, nitroxide concentration (TEMPO), and temperature,119 and the results interpreted in terms of electron spin–lattice relaxation times, experimental MW irradiation parameters, and the electron spectral diffusion (eSD) model.120 A larger improvement can be obtained by increasing the number of paramagnetic centres per molecule, and for this reason dinitroxides represent very interesting candidates. However, in these derivatives one must consider the electron spin–spin exchange coupling between unpaired electrons localized on different centres, that depends on their distance, and the corresponding relaxation parameters. One of such works reports a study carried out upon 18 different dinitroxides derived from bTurea,121 showing a correlation between e and the structure of the derivatives in terms of solubility, average distance between the paramagnetic centers, relative orientation of the nitroxide moieties and electron spin relaxation times. However, in the presence of dinitroxides, a reverse cross-effect mechanism could occur, that can deplete the polarization; this can be avoided by using a polarizing agent composed of a narrow-line component, such as a trityl (triphenylmethyl) radical, tethered to a (broad-line) TEMPO nitroxide, as demonstrated in a magic-angle spinning (MAS) NMR study.122 In a further study a family (the AsymPol family) of highly efficient polarizing agents composed of asymmetric bis-nitroxides has been introduced, in which a piperidine-based nitroxide and a pyrrolinic or a pyrrolidinic one are linked together.123 In addition, these derivatives show a relatively short linker between the two nitroxide moieties, which generates an advantageous intramolecular electron dipolar J-exchange interaction, and a conjugated Electron Paramag. Reson., 2021, 27, 109–145 | 131

carbon–carbon double bond in the 5-membered ring, to improve the rigidity, has been introduced; moreover, phosphate groups to yield highly water-soluble dopants have been added, and methyls were replaced by spirocyclohexyl groups to slow down the electron spin relaxation. Interesting suggestions came from a study in which radical-embedded covalent organic frameworks have been prepared and tested as DNP agents: PROXYL type nitroxides have been covalently reticulated, homogeneously distributed, and rigidly embedded into the crystalline and mesoporous frameworks with different concentrations, recording excellent performance in solid-state NMR.124 The origin of magnetic interactions in di- and polynitroxides can be either ferromagnetic or antiferromagnetic, depending on their conformation and on the coupling between the radical sites: the net magnetic behaviour, as well as the properties of the resulting material could be very different, influencing its applications. On these bases, a study of the magnetic and electrochemical properties of a flexible TEMPO-substituted disulfide diradical has been performed. EPR studies indicated a strong intramolecular spin-exchange interaction between the two nitroxide groups in solution, that depends on the temperature and solvent; in dilute frozen solution an intramolecular dipolar interaction between the two radicals is likely present, attributed to a syn-like conformation adopted. In addition, antiferromagnetic interactions have been observed, and the magnetic and electrochemical properties in solution were preserved in its self-assembled monolayer by chemisorption on an Au(111) substrate, also showing a dependence of the EPR spectra on the magnetic direction.125 All these results should contribute to a better understanding of the magnetic interactions in these systems, in order to facilitate the design of surface molecular devices. In fact, the magnetic properties of nitroxides have been exploited also in the chemistry of materials. In this field, graphene represents an interesting material with outstanding electrical and mechanical properties, and its corresponding nanoribbons exhibit half metallicity and quantum confinement. Due to their possible interest in spintronic and quantum computing devices, magnetic edges in graphene nanoribbons have been extensively studied from a theoretical point of view, since experimental investigations have been hampered for the chemical instability of graphene terminations. In a recent study, graphene nanoribbons have been functionalized with stable nitronylnitroxides, allowing its unpaired p electron to overlap with the p system of the aromatic backbone;126 the corresponding DFT calculations performed revealed a (sizeable) spin density injected into the graphene backbone, which creates localized non-dispersive states, and a magnetic dispersive edge state, confirmed by further multifrequency EPR spectroscopy. The results obtained indicate that these materials could represent ideal candidates in quantum nanoelectronics devices. 3.3 Nitroxides as spin probes and spin labels Nitroxide radicals can be also regarded as efficient ‘‘probes’’, since their EPR parameter values, such as hfccs, g-factor and lineshape showed dependence on their structure, conformations and environmental 132 | Electron Paramag. Reson., 2021, 27, 109–145

interactions. In particular, the anisotropy in the g and A tensors are such that when the probe can rotate rapidly, as for example in low-viscosity organic solvents at room temperature, the CW EPR spectrum is narrowed revealing only giso and Aiso contributions. However, if the tumbling dynamics of the system is slowed, by lowering temperature, increasing viscosity, or if the probe is linked to a larger, more slowly diffusing molecule, changes in the nitroxide signal lineshape are produced. Moreover, since changes in the microwave frequencies are sensitive to rotational correlation times (tc) in the nanosecond region, altering the microwave frequency will alter the timescales measured, and higher frequencies will offer enhanced resolution. All these features, coupled with nitroxides chemical stability and the high sensitivity of EPR spectroscopy, which allows to record signals with an excellent S/N ratio up to micromolar concentrations, are responsible of the development of the use of these derivatives as Spin Probes and Spin Labels. In fact, in the last decades, a large number of nitroxides have been synthesized as suitable probes for different applications. The majority of studies have been mainly focused on tuning their distribution within biological compartments and/or to minimizing their tendency towards reduction.97,127–129 However, in the last few years, the interest in the study of supramolecular systems has increased, and therefore the use of nitroxides as Spin Probes in host–guest chemistry.130–132 In this regard, the interactions of the guest nitroxides have been studied in different host systems, such as cyclodextrins, calixarenes, and cucurbiturils, but also micelles, metal organic frameworks and porous based materials. Recently, a new pyrrolidine nitroxide embedded in a crown ether (see Fig. 18) has been synthesized and used as a ‘‘wheel’’ in a bistable [2]rotaxane, containing both dialkylammonium and 4,4 0 -bipyridinium recognition sites.133 In this case the nitroxide is directly involved in the recognition process between the two sites, due to two different interactions and thus acting as an EPR probe, but this feature can be also used to detect the shuttling

Fig. 18 C: nitroxide crown ether in ref. 133; D: mixed trityl-nitroxide biradicals in ref. 135. TEMPONE: 4-oxo-TEMPO; bTbk: bis-TEMPO-bis-ketal. Electron Paramag. Reson., 2021, 27, 109–145 | 133

process of the paramagnetic wheel within the rotaxane moiety. More recently a study has been reported where the nitroxide 4-oxo-TEMPO (TEMPONE), and the dinitroxide bis-TEMPO-bis-ketal (bTbk) (see Fig. 18) have been used as hosts in CB[7] and CB[8] cucurbiturils, respectively.134 In the complexation between TEMPONE and CB[7], the EPR sequence obtained by incrementing concentrations of cucurbituril suggested a perpendicular position of the nitroxide group with respect to the C7 axis of the host. However, in the interaction between bTbk and CB[8] the EPR results suggest a shuttling process, since the nitroxide is too large to be fully included within the host as in the previous case, also confirmed by the 1H NMR spectra on the reduced dinitroxide analogue. In another study involving cyclodextrins, diradicals have been employed, but in this case one of the two radical centres is represented by a trityl derivative (see Fig. 18).135 In the host–guest complexes where the nitroxide and linker parts could interact with the cyclodextrins’ cavities, a suppression of the intramolecular through-space spin–spin exchange coupling has been recorded, thus allowing the determination of the through-bond spin– spin exchange coupling. The effect of the linkers in these biradicals on the host–guest interactions was also investigated: the biradicals with shorter linkers were characterised by a higher through-bond spin–spin exchange coupling. In a recent paper the host–guest interactions between nitroxides and self-assembled supramolecular coordination cages have been reported. The study has been carried out using TEMPO and PROXYL derivatives as guests and cage structures having the general formula [M8L12][X]16, where M ¼ Co21 or Cd21, L ¼ C28H22N6, and X ¼ ClO4 or Cl (see Fig. 19) in water and acetonitrile as solvents.136

Fig. 19 Schematic representation of the cage structures C1w ([Co8L12][Cl]16) and C2org ([Cd8L12][ClO4]16), highlighting the approximately cubic shape. Only 2 of the 12 ligands are depicted, illustrating the bis-bidentate binding of the ligand to the metal atoms. The ‘‘w’’ and ‘‘org’’ endings represent solvents (water and acetonitrile). Adapted from ref. 136 with permission from American Chemical Society, Copyright 2020. 134 | Electron Paramag. Reson., 2021, 27, 109–145

Besides the different interactions recorded, host–guest complex formation resulted in all cases in significant decrease in the molecular tumbling rate of the guests, with tumbling becoming strongly anisotropic. In addition, the polarity of the cage environment in both solvents was found to be intermediate if referred to the properties of both solvents used, although very small changes of B0.3 Gauss in hyperfine value have been recorded. In order to get a deeper insight and/or perform specific measurements, the Spin Probe could be directly bonded to a targeted substrate, thus ‘‘labelling’’ it with a paramagnetic species enabling its investigation using EPR spectroscopy.137,138 Of course, the use of the Spin Labels should fulfil the same criteria as Spin Probes and, being directly bonded, should not introduce any possible structural distortion of the system under study. By far the largest family of Spin Labels are based on nitroxides, mainly of the five- or six-membered heterocyclic families, therefore a ‘‘Spin Label’’ can be defined as a derivative of the parent nitroxide properly modified to enable its incorporation into a larger framework, and thus used as a probe. This difference with respect to a simple ‘‘Spin Probe’’ allows their use in the measurement of the distance between two stable free radicals labelling specific molecules, by means of continuous wave (CW) or pulsed techniques, always retaining the possibility to probe the local environment, such as its accessibility and dynamic mobility.139 Concerning distance measurements, which for nitroxides have an effective range of 0.5 to 8.0,140–142 the availability of pulsed EPR spectrometers allowed the development of techniques based upon proper pulse sequences. For example, the pulsed EPR experiment known as double electron–electron resonance (DEER),143 or pulsed electron double resonance (PELDOR),144 has become a useful method for measuring nanometre distances between pairs of nitroxides. This experiment takes advantage of two microwave frequencies, and its 4-pulse version measures the dipolar coupling frequency as a modulation on a refocused echo. For the 5- and 6-membered heterocyclic nitroxides with four methyl groups on both carbons linked to the N–O function, the balance between the T1 (longitudinal) and Tm (spin coherence) relaxation times with the Boltzmann distribution is often optimal at around 50 K. However, it has been found that the use of deuterated solvents lengthens the Tm time, since 2H has a lower magnetic moment than 1H, reducing the rate of relaxation through spin diffusion. Moreover, the alternative isotope substitution of 15N at the N–O moiety has been applied to allow orthogonal labelling using two Spin Labels. The DEER technique is also capable to extract orientational information between the labels when the nitroxides used possess a welldefined and narrow distribution of conformations with respect to one another. Taking advantage of the increasing knowledge in synthetic organic chemistry, it is possible to ‘‘graft’’ the Spin Label to a specific position within the system to get more specific information concerning the system under study. The resulting so called ‘‘Site Directed Spin Labelling’’ (SDSL) makes use of nitroxides bonded at specific sites within a molecule, usually through covalent bond formation, but also Electron Paramag. Reson., 2021, 27, 109–145 | 135

through non-covalent interactions. However, although this technique can be applied in every type of context, has had its greatest diffusion in biomolecular systems.145 In these cases, this technique has mainly taken advantage of the specific reactivity of cysteine residues. Alternatively, ‘‘click’’ chemistry offers major benefits by providing a fast and highly selective, biocompatible reaction between azide and alkyne groups. As an example, a biocompatible and highly specific coupling method has been reported, with the potential for Spin Labelling in quantitative yields in intracellular environments. This approach has a general character and should be applicable to nitroxides, but also to different types of Spin Labels, in order to study the conformation and dynamics of diamagnetic biomolecules in vivo by DEER. It consists of chemical reactions where PROXYL-like nitroxides, bearing a methyleneazide group in position 3, were allowed to react with ‘‘unnatural’’ amino acids, based on lysine bearing a carbamate linked to a strained cyclic octyne and bi-cyclic nonyne or propargyl groups; as an alternative, the alkyne functionality could be present in the nitroxide and react with azido phenylalanine.146 The resulting labels (see Scheme 10) have been successfully tested in vitro as well as in vivo. However, concerning labelling procedures, probably the most used ones take advantage of the -SH cysteine group reactivity to give uncleavable S–C bonds. Two different gem-diethylfunctionalized nitroxides Spin Labels, with a iodoacetamide and a maleimide groups (see Scheme 10), have been used and compared considering their labelling efficiency, side chain dynamics and interspin distances, as well as their resistance to reducing agents in cells.110 The utility of having two distinct functional groups specific for cysteines (possibly at pH close to 7.5 because at different pH values other amino acids could be labelled) connected to proteins via S–C bonds, could be explained by the following considerations. First, each protein site has its distinct properties in terms of label accessibility, sensitivity to point mutation, steric constraints, electrostatic properties, water-membrane exposure, and so on; therefore, to maximize the success of the labelling strategies, it is advantageous to have chemically diverse functional groups, and Spin Labels of different size and flexibility. In addition, maleimide groups present some drawbacks: their thiol adducts can undergo a slow reverse Michael addition with the release of the Spin Label; the succinimidyl thioethers can undergo an irreversible pHdependent hydrolysis; finally, the addition of the cysteine -SH group to the maleimide ring forms a chiral center with the formation of two isomers, introducing difficulties in the distances interpretation. Both Spin Labels are suitable for labelling accessible cysteines in proteins, providing valuable mobility information by CW EPR and interspin distances by DEER spectroscopy; interestingly, an increase in bioreduction resistance was recorded due to the gem-diethyl functionalities. On the other hand, these methods show several potential drawbacks, such as need of a good expertise in synthetic organic chemistry, exposure of the Spin Labels to reagents with potential (partial) reduction, and incomplete labelling by side reactions between the Spin Label and other functional groups of the nucleic acids producing non-specific labelling. 136 | Electron Paramag. Reson., 2021, 27, 109–145

NH2

O Y

X

N

N

O

N N

N

.

O OH

H

H N

O

E

O

X

N

O

N

N

O

O

G

H

.

.

OH

N O

O

O

N N

Y

N

I

.

F

NH2

Electron Paramag. Reson., 2021, 27, 109–145 | 137

.O

.

.

N

N O

N O

N

O

I

N+

N

O

J

N+

N

O

N+

K

Scheme 10 Combinations of spin labels, unnatural amino acids (UAAs) and side chains from ref. 146: E, from carbamate þ propargyl-lysine; F, from ethynylnitroxide þ azido phenylalanine. Gem-diethyl-functionalized nitroxides spin labels, from ref. 110: functionalised with iodoacetamide (G) and a maleimide (H) group. Tetramethylrosamine derived spin labels from ref. 147: with pyrroline (I), piperidine (J) and isoindoline (K) functionalised nitroxides.

These issues could be circumvented if noncovalent interactions can be employed. An example of SDSL of unmodified RNA has been reported, where pyrrolidine-, piperidine- and isoindoline-nitroxide derivatives of tetramethylrosamine were shown to bind with high affinity to the malachite green (MG) aptamer (see Scheme 10), as confirmed by CW EPR, PELDOR and fluorescence spectroscopy.147 While Tm in nitroxides is rather small even upon strict immobilization,128 Tm in triarylmethyl radicals (TAM) is significantly longer allowing long-range distance measurements. Thus, TAM/nitroxide labelling has been employed in orthogonal Spin Labelling, which in general represents an important approach for studying biomolecules and their complexes.148,149 Among pulse dipolar EPR spectroscopy techniques, the Relaxation Induced Dipolar Modulation Enhancement (RIDME)150,151 was employed in a recent study in conjunction with such an approach, allowing the measurements in orthogonally labelled double stranded DNA, using TAM as a slowly relaxing label and nitroxide as a fast relaxing partner spin, and demonstrating that at room temperature the results obtained are close to those with PELDOR on the same sample but at low-temperature.152 Concerning distance measurements, ‘‘triple’’ Spin Labelling has also been reported, where three different types of labels, differing in their spectroscopic and spin dynamics properties, have been used to extract three independent distances from a single sample by means of DEER experiments. One of these studies considered the Antennapedia homeodomain (a subset of genes which controls the formation of legs in insects), orthogonally labelled with Gd31 and Mn21 tags in complex with its cognate DNA binding site labelled with 3-(2-Iodoacetamido)-PROXYL.153 The selection and assignment of the three different distances was based on differences between the individual spectra of the three Spin Labels (also taking advantage of the spectral resolution at W-band), the different nutation frequencies for nitroxide and Gd31 and Mn21 and the longer electron spin–lattice relaxation time T1, of nitroxides compared with those of the used ions (see Fig. 20).

4 Concluding remarks This contribution provides an update on the most recent applications of Nitrones and Nitroxides though EPR spectroscopy. Despite the restricted period covered (from 2016 until the beginning of 2020), the large number of papers in diverse research areas is indicative of an excellent ‘‘state of health’’ of the applications covered here. In particular, it is worth highlighting that the use of Nitrones as Spin Traps in the field of catalysis and photocatalysis has recently attracted considerable attention, especially in the context related to the environmental aspect. This probably represents the main field of interest, in contrast with the predominance of the use of EPR Spin Trapping in biological systems previously observed. Concerning Nitroxide applications, only a slight predominance in the number of papers concerning Spin Labelling and Dynamic Nuclear Polarization has been recorded. 138 | Electron Paramag. Reson., 2021, 27, 109–145

Electron Paramag. Reson., 2021, 27, 109–145 | 139

Fig. 20 Labelling schemes. A: cartoon representation of the complex between the Antennapedia homeodomain and its cognate DNA with the measured distances among the three different tags. B: 3-(2-Iodoacetamido)-PROXYL bonded to a phosphorothioate group of the targeted oligonucleotide. C: a cysteine residue linked to EDTA-MTS for Mg21 binding. D: a p-azido-L-phenylalanine residue (AzF) linked to a Gd31 chelate (C3–Gd tag). Adapted from ref. 153 with permission American Chemical Society, Copyright 2017.

Acknowledgements ` Politecnica delle Marche (UNIVPM) is kindly acknowledged Universita for financial support. Special thanks to my co-workers S. Marano and E. Laudadio for their useful suggestions and for revising the manuscript.

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Molecules as qubits, qudits and quantum gates Eufemio Moreno-Pineda,a Daniel O. T. A. Martinsb and Floriana Tuna*b DOI: 10.1039/9781839162534-00146

Quantum coherence is a fundamental property of electron spins that could be exploited in quantum computers for the processing of information. Within quantum calculation protocols, information is encoded in two-level quantum objects (Qubits) and processed by the operations of logical quantum gates (or Qugates). Examples of qubits include electronic spins of magnetic molecules, which present the advantage that they can be easily manipulated by external electromagnetic fields, via electron paramagnetic resonance (EPR). Creation of multi-level systems (so-called Qudits, where d is the dimension of the Hilbert space) is also possible in magnetic molecules carrying both electronic and magnetic nuclear spins due to cooperative hyperfine interactions. Such qudits can simultaneously access a multitude of states reducing the number of iterations in quantumcomputation algorithms. The implementation of the Grover’s algorithm in a single molecular unit was experimentally probed in a multi-level molecular nanomagnet thanks to hyperfine transitions combined with the shielded nature of nuclear states that limits decoherence. This chapter gives an overview of the latest advances in the design and testing of molecular electron spin systems with Quantum Information Processing (QIP) attributes, while highlighting the tremendous progress made in electron spin manipulations driven by pulse EPR spectroscopy.

1

Introduction

Quantum information processing (QIP) promises to be exponentially faster and significantly more secure than anything that conventional supercomputers can possibly achieve. The central concept of QIP is that the information is encoded in a two-level quantum register, known as a quantum bit (or qubit), instead of a classical bit, with the difference that this qubit has the ability to generate and control a large number of coherent superposition states (see Fig. 1) that are other than the basis states ‘0’ and ‘1’ used in classical computation.1 The abundance of quantum states available creates the possibility for quantum parallelism and thus attainment of unmatched data processing speeds, enabling to solve certain tasks far more efficiently. If a computer cluster requires two years to factorise a 768-bit number,2 a quantum computer (QC) can factorise a 2000-bit number in only one day.3 This phenomenal power of QCs arises from the encoding of the vast Hilbert space of a general quantum state, and from using quantum mechanics to implement the calculation algorithms. Some of the most famous algorithms used in quantum computing are Shor’s algorithm4 for factorisation of integers, Grover’s algorithm5 enabling searching for single objects in a large a

Departamento de Quı´mica-Fı´sica, Escuela de Quı´mica, Facultad de Ciencias ´, Panama ´ Naturales, Exactas y Tecnologı´a, Universidad de Panama b Department of Chemistry and Photon Science Institute, University of Manchester, Oxford Road, Manchester M13 9PL, UK. E-mail: [email protected] 146 | Electron Paramag. Reson., 2021, 27, 146–187  c

The Royal Society of Chemistry 2021

Fig. 1 Schematic representation for (a) classical bit; and (b) quantum bit.

unsorted database quadratically faster than the best-known classical algorithm, and the Deutsch–Jozsa (D–J) algorithm6 able to discriminate between balanced and unbalanced functions. A number of areas could benefit from the enormous power of quantum computers. They include cryptography (safe data protection and secure communication), data management (efficient searching in large databases), material design and science (i.e. simulation of quantum systems), amongst others. Prior to these applications, many scientific problems need to be addressed. For instance, qubits are very fragile systems and could lose their quantumness in certain environments. In particular, their interaction with the surrounding spins (either electronic or nuclear) can induce strong quantum decoherence,7 and ultimately information loss. Reducing this effect is of fundamental importance. Then, the logic operation converting the initial state of qubits (input) into the final state (output) is to be performed by quantum logic gates (qugates).8 This implicitly demands a number of qubits capable to communicate through programmable inter-qubit interactions, as well as the ability to exploit quantum entanglement. These tasks are not easy to achieve. In practical terms, realisation of a quantum gate among N qubits creates the setting for coherent transitions between 2N quantum states. As the number of qubits increases, it becomes extremely difficult to control the number of interactions operating between them. Use of d-dimensional (d42) quantum systems, so-called qudits,9 instead of qubits (b ¼ 2), offers an alternative approach to tackle this problem. The advantage is that the qudits assume a higher level of freedom (i.e. dN orthogonal states), enabling quantum parallelism within a single unit with diminished error rates. Another advantage is that quantum entanglement and superposition can be achieved in qudits in large dimensions with smaller clusters of processing units compared to qubits. Several systems have been proposed as qubit candidates, including defects10 and impurities11,12 in solids, quantum dots,13 photons,14 Electron Paramag. Reson., 2021, 27, 146–187 | 147

superconducting circuits,15,16 trapped ions,17 non-magnetic18 and magnetic19–24 molecules amongst others. Each has advantages and disadvantages, making it difficult to predict which of these approaches will prove successful. The feasibility of the qubit is in proportion with its phase-memory time, T2, that is the time length that information is stored within the qubit before being lost through decoherence. Some spin qubit prototypes reach remarkable T2 values, especially in environments that are free of electron or nuclear spins. This is the case, for instance, of impurity spins in isotopically purified silicon,25 and nitrogen vacancies in diamond.26 However, realisation of universal quantum gates using spin defects as qubits is very difficult, as the rigorous conditions needed to limit decoherence (e.g. keeping qubits apart to cut off dipolar interactions) are likely to limit the coherent exchange of information between them. In this respect, a chemistry driven bottom-up approach to qubit scalability is more suitable.19,21–24,27 Molecules are highly versatile and permit tuning of their electronic structures and spin environments almost at will. Besides, they can be replicated in a large number, functionalised in the desired fashion, and even organised in a controlled manner, by chemical design tools.28–32 Indeed, an increasing number of molecular systems were found to show robust quantum coherence.33–40 Coherence times measured in some magnetic molecules are superior to other types of qubits. They can be initialised, manipulated and read-out, demonstrating great potential for realisation of quantum algorithms.9,21–23 Electron paramagnetic resonance spectroscopy (EPR) plays a crucial role in the characterisation of qubit electronic structures, and measurement of quantum coherence, entanglement, and decoherence.35,41–44 Pulse EPR methods in particular offer tremendous opportunities for qubit manipulation and read-out, and for understanding the various relaxation mechanisms involved, helping to address quantum decoherence. This Chapter summarises the most recent advances towards the implementation of quantum information processing with molecular spin systems that can function as two-level quantum objects (qubits), multilevel quantum objects (qudits) or quantum gates (qugates). Particular consideration is given to the design of such molecular spin systems, their testing and properties, and the inherent challenges that would need to be addressed for further advancement of the field.

2

Qubits

2.1 General characteristics of qubits In simple terms, a qubit is the quantum analogue of a classical bit, the fundamental unit of information of classical digital computers, commonly represented by values of 1 and 0. The two values are equivalent to the ‘spin-up’ and ‘spin-down’ orientations of the electron spin magnetic momentum, labelled, for simplicity, as TRUE/FALSE or ON/OFF states (see Fig. 1a). With the information encoded in bits, computational tasks are carried out by creation and manipulation of sequences of bits, through the operation of logic gates. 148 | Electron Paramag. Reson., 2021, 27, 146–187

By analogy, the basic unit of information in quantum computation is a quantum bit (or qubit). Qubits differ from bits in the capability of encoding, as they can exist as | 0i, | 1i and any other coherent superposition of these two states, C ¼ a|0i  b| 1i , provided |a| 2 þ |b| 2 ¼ 1. The number of coherent superposition states of a qubit is equivalent to the surface of a unitary Bloch sphere in the polar coordination system (see Fig. 1b). A generic state of the N-qubit register is then an arbitrary coherent superposition of the 2N product states, where each qubit is in either |0i or | 1i, whereas the state of a classical register is a single sequence of zeros and ones.45 Concomitant presence of a large number of classical register states is at the basis of the so-called quantum parallelism that enables a large number of operations to be conducted simultaneously at extraordinarily fast computational speeds. For instance, Shor’s integer factoring algorithm takes advantage of such quantum parallelism to perform lots of operations in a single step.4 Most superposition states require the qubits to be entangled, assuring that the states of the qubits cannot be assigned independently but only with reference to each other, irrespective of the distance between the individual qubits. Such quantum entanglement is exploited, for instance, in teleportation, ultra-dense coding, and quantum cryptography.46,47 In theory, any two-level system that can be manipulated into coherent superposition states has the attributes of a qubit. However, implementation of quantum computation requires the hardware to fulfil the five socalled DiVincenzo criteria, as follows:48 (i) The quantum computer should be a scalable physical system with well-characterised qubits; (ii) The qubit states should be initialised in a specific initial state, which suggests the time required to reset the qubit is crucial; (iii) The qubits should have long coherence times, usually longer than the gate operational time by at least a factor of 104; (iv) The quantum computer should be able to implement a universal set of quantum gates capable of influencing the total energy of the system; (v) The qubits should be individually measurable, i.e. the result of the computation can be read out. These strict criteria must be simultaneously satisfied, which makes the fabrication of feasible qubits quite difficult. There are many proposed qubit candidates, each with their particular pros and cons. Among them, use of superconducting circuits appears to be the most advanced technology, giving access to some archetype QCs, although with a limited number of operating qubits.49 However, scaling up the number of operating qubits, which would allow performing more complex algorithms and mitigating the errors induced by the limited lifetime of the qubits, remains a real challenge. Electron spins are the natural choice for a qubit, as they are by definition a two-level quantum system (ms ¼  1/2) that can be easily Electron Paramag. Reson., 2021, 27, 146–187 | 149

manipulated by electromagnetic radiation, for instance with the aid of microwave pulses. Embedding electron spins into well-defined molecular structures offers tremendous opportunity to tune their properties, such as optimizing their coherence times through controlled modification of the molecular structure or their environments. One can tune their interactions with other electronic or nuclear spins, in a control manner, to access desired level-multiplicity or superposition states, or to engineer inter-qubit molecular switches required to implement given computational schemes. Coupling these features with the tremendous progress made in the electron spin manipulation technology driven by pulsed EPR spectroscopy, significant advances can be anticipated from using molecular spin systems for QIP applications. 2.2 Evaluation of qubit performance via EPR The DiVincenzo criteria detailed above guide the design of molecular spin systems that could function as qubits, as well as the engineering of interqubit interactions. Two parameters are commonly employed to evaluate the performance of a spin qubit: the spin–spin relaxation time, T2, and the spin–lattice relaxation time, T1. The former is the quantum coherence time and dictates the superposition lifetime, i.e. the time when computations should take place. This is also known as the transverse relaxation time as it is equivalent to the time required by the magnetisation to decay within the xy-plane as a result of the spin ensemble precession around the z-axis after being tipped away from its thermal equilibrium position. Furthermore, the concepts of coherence and decoherence are mutually widely employed. They are defined as the formation of the superposition state and the decay or loss of this condition, respectively. Experimentally, T2 is determined by pulse EPR methods, by leastsquare fitting of the decay of the integrated intensity of the Hahn echo produced by a sequence of two microwave pulses (see Fig. 2a) when the inter-pulse delay, t, increases, using eqn (1):   2t Y ð2tÞ ¼ Y ð0Þexp  (1) T2 where Y(2t) is the echo integral for a pulse separation t, and Y(0) is the echo intensity extrapolated to t ¼ 0. In reality, the echo experiments measure the phase memory time constant, Tm. This is a measurable lower limit of T2, as it encompasses spin–spin and other relaxation effects from spectral and instantaneous diffusions, although often they are used interchangeably in the literature. The impact of these effects is a Hahn echo decay profile that is not adequately modelled with a simple monoexponential function, eqn (1). In this case, a stretched exponential is more suitable, as described by eqn (2), "  # 2t b Y ð2tÞ ¼ Y ð0Þexp  (2) Tm 150 | Electron Paramag. Reson., 2021, 27, 146–187

Fig. 2 EPR pulse sequences used in relaxation and coherence measurements: (a) T2 is measured with a Hahn echo sequence by varying t; (b) T1 is measured with an inversion recovery sequence by varying t; (c) Rabi oscillations are measured with a transient nutation sequence by varying tp; (d) HYSCORE measures hyperfine couplings by varying t1 and t2.

or, for strongly modulated data, eqn (3): "  # 2t b Y ð2tÞ ¼ Y ð0Þexp  ð1 þ k sinðot þ fÞÞ Tm

(3)

where b is the stretch factor, k is the modulation depth, o is the Larmor angular frequency of a nucleus I coupled to the electron spin, and f is the phase correction. A stretching parameter b between 2 and 3 would indicate that the decoherence is dominated by spin diffusion (flip-flop of nuclear spins), while a value close to 1 would suggest that it is dominated by spectral diffusion (physical motion of magnetic nuclei).33 In some circumstances, a multi-exponential function can be employed to model the relaxation behaviour, due to the occurrence of more than one relaxation processes. For instance, eqn (4) can be employed for spin dynamics that involve two relaxation regimes, one designated fast ( f ) and another slow (s), characterised by phase memory times Tm,f and Tm,s respectively.     2t 2t Y ð2tÞ ¼ Yf exp  þ Ys exp  (4) Tm;f Tm;s The spin–lattice or longitudinal relaxation time, described by the time constant T1, is essentially the time duration needed for a reverted magnetisation to return to thermal equilibrium and therefore equals the classical bit memory time. T1 is also a crucial parameter in quantum computation as it controls the initialisation time of the qubit. Experimentally, the spin–lattice relaxation time is measured with a standard three pulse magnetisation inversion recovery sequence, p–t–p/2-t–p–t-echo (see Fig. 2b), with fixed t and variable t. The time constant T1 is then obtained by fitting the echo intensity as a function of t using either a stretched (eqn (5)) or biexponential (eqn (6)) function, where b is the Electron Paramag. Reson., 2021, 27, 146–187 | 151

stretching parameter, measuring the relaxation time distribution, TSD is the spectral diffusing time constant, while Y1 and YSD are the amplitudes. TSD is commonly one order of magnitude smaller than T1. "  # t b Y ðtÞ ¼ Y ð0Þ þ Y1 exp  (5) T1 Y ðtÞ ¼ Y ð0Þ þ Y1 eðt = T1 Þ þ YSD eðt = TSD Þ

(6)

The control and understanding of T1 are crucial for the design of highperformance qubits because the phase memory time Tm, mainly determined by the spin–spin relaxation time T2 becomes limited by short spin–lattice relaxation times, T1, via the dependence T2r2T1.50,51 Controversially, it is desirable to keep T1 short in qubits to allow operational reset time. T1 varies with the temperature, and its thermal dependence can be described by different analytical functions that take into account the different spin–lattice relaxation mechanisms involved, such as the direct, Orbach and Raman processes depicted in Fig. 3. In the so-called direct process, the relaxation takes place via the emission of a single phonon that possesses the same energy hn as the energy gap to the next electronic state. Orbach and Raman processes involve absorption and reemission of higher energy phonons compared to the direct process, with the difference that the former goes through a real excited state, while the second uses a virtual excited state to relax (see Fig. 3). Equation (7) is a typical example of an analytical function describing the temperature (T) dependence of T1 under the conditions of direct and Raman spin–lattice relaxation, with the latter dominating the relaxation at a higher temperature compared to the former.38,52,53 T11 ¼ adirT þ aRamTn

(7)

Fig. 3 Representation of common spin–lattice relaxation processes. (a) Direct relaxation process. A phonon corresponding to the energy difference between states a and b is absorbed (emitted) causing a transition between these states; (b) First-order Raman process. The difference in energy of the scattered phonon causes a de-excitation from state b to a; (c) Relaxation through a second-order Raman process. The difference in energy of the scattered phonon is absorbed by the spin system. The spin system is then excited to a virtual excited state, followed by de-excitation to the ground state; and (d) Orbach process. Absorption of a phonon excites the spin system to a low-lying excited state, followed by de-excitation to state a and emission of a photon of energy corresponding to the difference in energy of the low-lying excited state and the ground state. 152 | Electron Paramag. Reson., 2021, 27, 146–187

Here, adir is the coefficient of the direct mechanism, and aRam and n are the coefficient and the exponent of the Raman mechanism respectively. To be viable, a qubit requires, in addition to a sufficiently long T2, the ability to be placed into any arbitrary superposition of the ‘up’ and ‘down’ spin states (i.e. in any arbitrary position within the surface of the Block sphere representation in Fig. 1b).54 This property enables the qubit to be coherently manipulated and is experimentally demonstrated by variablepower transient nutation experiments that involve the microwave pulse sequence depicted in Fig. 1c. In these experiments, a variable-length microwave nutation (tipping) pulse (tp) applied to the system places the spin into a particular superposition determined by the power and length of tp.34,55 Subsequent application of a Hahn-echo detection sequence allows probing the superposition by monitoring the change in intensity and phase of the resulting echo signal as the nutation pulse length increases (see Fig. 4). The resulted Rabi oscillations reflect the composition of the superposition, as the spin cycles through every possible state, and should decay in a significantly shorter time than T2 to assure this manipulation does not destabilise the qubit. Fourier analysis of the nutation data yields the frequency OR of the oscillations (Rabi frequency), which gives an indication of the time required to perform a single quantum operation at the given microwave pulse power. If the oscillations are genuinely Rabi-type, then a linear dependence of OR with the magnitude of the oscillating field B1 should be observed. The time separating a Rabi oscillation maximum from an adjacent minimum is equivalent to the spin–flip time, regarded in the context of quantum computation as the time required for a single-qubit logic operation to be completed (the NOT gate). The number of spin-flips a qubit can perform within the T2 timescale may be estimated by the figure of merit QM, defined as 2T2OR. A higher QM value assures faster calculations.

Fig. 4 Rabi oscillations generated under the application of a nutation (tipping) pulse of length tp. The orientations of the magnetisation vector following specific tp values are graphically depicted along with the employed pulse sequence. Reproduced from ref. 55 with permission from American Chemical Society, Copyright 2014. Electron Paramag. Reson., 2021, 27, 146–187 | 153

3

Molecular electron spin qubits

Interest in molecular spin systems for quantum technologies has grown rapidly in recent years and a number of recent reviews21 and perspective articles22–24,27 have highlighted the fantastic progress being made. Quantum decoherence in molecules bearing electron spins is mainly induced through electron–electron and electron–nuclei interactions, and is affected by a number of factors, such as: (i) concentration of paramagnetic species present; (ii) dynamics of the nuclear spin bath; (iii) presence of nuclear spins embedded in the ligand shells; and (iv) electronic spin structure. Understanding these effects has led to several successful strategies that enable enhancement of the coherence times of molecular qubits. These rely on the use of nuclear spin-free ligands, ligand deuteration, and magnetic dilutions, alongside other strategies that aim at working at atomic clock to cancel the effect of magnetic noise, or with rigid ligands aimed to correct for vibrational effects. One of the first polymetallic systems to be investigated for qubit implementation is a heterometallic {Cr7Ni} ring (see Fig. 5), reported by Winpenny and co-workers.41,56–59 This molecular system consists of an octagon of seven Cr31 (s ¼ 3/2) and one Ni21(s ¼ 1) ions that are antiferromagnetically coupled via carboxylate and fluoride bridges. At low temperatures, the molecule displays a well isolated S ¼ 1/2 spin ground state, regarded as a two-level system for the purpose of qubit implementation. The robustness and chemical versatility of this molecular system enabled a systematic study of the impact of electron–electron and electron–nuclei interactions on phase memory (Tm) and spin–lattice (T1) relaxation.33 For instance, variation of the template cation in [R2NH2][Cr7NiF8(Piv)16] (Piv ¼ Me3CCOO) enabled tuning of Tm at 5 K in the order: 0.38 (Me2NH21)o0.62 (nPr2NH21)o0.73 ms (Et2NH21), while varying the carboxylate bridging ligands in [nPr2NH2][Cr7NiF8(RCOO)16] enables Tm to be varied in the order 0.34 (Me2CHCOO)o0.44 (MeCOO)o0.62 ms (Me3CCOO) at 5 K.33 Moreover, substitution of the pivalate ligands by their deuterated versions improves Tm from 0.55 to 3.8 ms at 1.8 K, indicating that 1H super-hyperfine interactions contribute

Fig. 5 Molecular structures of representative molecular spin qubits. 154 | Electron Paramag. Reson., 2021, 27, 146–187

to decoherence. Further improvement in Tm is obtained with more rigid carboxylate entities, such as Ad1CO2 (see Fig. 5), as spin diffusion is less effective in this case due to smaller nuclear energy distribution for hydrogen atoms. The study also found that the more sterically hindered methyl groups are more effective in driving relaxation through spectral diffusion. To probe the effect of the nuclei of the central templating cation, the dialkylammonium cation in [R2NH2][Cr7NiF8(Piv)16] was replaced by Cs1 (100%, 133Cs, I ¼ 7/2, gH/gCs ¼ 7.6), leading to much longer Tm.33 Furthermore, by combining a Cs-templated {Cr7Ni} ring with perdeuterated pivalates (d-Piv) and deuterated solvent (d8-toluene), a significant improvement of the phase memory time to Tm ¼ 15.3 ms at 1.5 K (for Cs[Cr7NiF8(d-Piv)16]) was obtained. At low temperatures, the relaxation dynamics were found to be dominated by spin diffusion, though other decoherence sources related to molecular motion (i.e. spectral diffusion) cannot be neglected.33 One of the issues with using exchange coupled systems for computation is the need of working at very low temperatures to assure an isolated ground state for the molecule. With a large number of bridging ligands that are usually involved it becomes rather difficult suppressing unwanted electron spin–nuclear spin interactions that impact the qubit lifetime. An alternative approach is to use monometallic systems with a pure S ¼ 1/2 spin state. Warner et al. have explored such a possibility by employing a phthalocyanine (Pc) copper(II) complex, CuPc.60 The molecule was deposited as a magnetically diluted a-phase thin film using H2Pc as diamagnetic matrix to allow sufficient spatial separation between CuPc molecules in order to minimise the effects of dipolar fields that induce spin decoherence. Echo-detected field swept (EDFS) spectra were nicely resolved enabling to determine the hyperfine couplings to 63,65 Cu and phthalocyanine 14N, such as: Axx(Cu) ¼ Ayy(Cu) ¼ –83 MHz; Azz(Cu) ¼  648 MHz; Axx(N) ¼ 57 MHz and Ayy(N) ¼ Azz(N) ¼ 45 MHz. The rigidity of the molecule coupled with a high degree of dilution (0.1% doping level) enabled quantum coherence being observed over the 5–80 K range. The phase memory time Tm, measured with a two-pulse Hahn echo sequence (see Fig. 2a), increases from 1 ms at 80 K to 2.6 ms at 5 K, with T1 following a similar trend, changing from 10 ms at 80 K to 58 ms at 5 K. A subsequent study by van Slageren et al. found the spin–lattice relaxation time T1 of MPcR systems (M ¼ Cu21, VO21, Mn21 and Co21; R ¼ H, Cl, F) to increase upon decreasing spin–orbit coupling (SOC), given that the reversal of the spin to the ground state occurs via crystal field oscillations involving energy transfer to the surrounding lattice.37 Thus, VOPcR systems are expected to have a very long T1 due to vanadium having one of the smallest SOCs across transition metals. Indeed, T1 values as high as 2.4 s were recorded for deuterated acidic solutions of VOPcR. Among the series, the slowest spin–spin relaxation was obtained for CuPcCl (41  4 ms) and VOPcCl (22  5 ms) due to the abovementioned influences on the spin dynamics. At low temperatures, spin diffusion is also operative and contributes to relaxation. Sessoli et al. measured quantum coherence at room temperature (T2 ¼ 0.83 ms) in a solid-state vanadyl phthalocyanine (VOPc) complex Electron Paramag. Reson., 2021, 27, 146–187 | 155

magnetically diluted (0.1% concentration) in the titanium analogue (see Fig. 6), and reported the first-ever observation of Rabi oscillations at room temperature in a proton-rich molecular system.53 This remarkable behaviour was linked with the rigidity of the ligand, which impacts molecular vibrations, and square pyramidal geometry of the complex. Another example of a mononuclear copper(II) complex exhibiting remarkable qubit properties is (PPh4)2[Cu(mnt)2], where mnt2 ¼ maleonitriledithiolate (see Fig. 5).36 Here the environment of the metal ions was engineered so that the coupling between the electron spin and its neighbouring nuclei is minimised by using a rigid ligand that coordinates via a free nuclear-spin, sulphur atom. Its 0.001% solid-state dilution in the diamagnetic Ni(II) analogue enabled to measure a coherence time Tm ¼ 9.23 ms at 7 K which is superior to that of CuPc thin films.60 Further replacement of hydrogens in the tetraphenyl phosphonium counterion by deuterium atoms enabled to improve Tm to 68 ms at 7 K while observing quantum coherence up to room temperature (Tm ¼ 1 ms; 0.01% dilution level). Another remarkable feature is that T1 and Tm are comparable in size and independent of each other at the room temperature; on the contrary, at the lowest temperatures, T1 becomes significantly longer exceeding 87 ms at 7 K. This behaviour is explained by the relatively rigid lattice of the compound, and the squareplanar coordination geometry of the copper ion, usually expected to give longer T1 values than tetrahedral variants.61 Taking advantage of the small SOC of V41 and employing rigid, nuclear spin-free dithiolene ligands, C8S82 (see Fig. 5), Freedman et al.

Fig. 6 (a) Molecular structure of VOPc; (b) EDFS and cw EPR X-band spectra; (c) Rabi oscillations at 300 K for different microwave attenuations, performed at 345 mT; (d) T1 and Tm relaxation times as a function of temperature. Reproduced from ref. 38 with permission from American Chemical Society, Copyright 2016. 156 | Electron Paramag. Reson., 2021, 27, 146–187

succeeded to achieve an impressive T2 value of 0.7 ms at 10 K for a frozen solution sample of [V(C8S8)3]2 in CS2.55 Moreover, coherent quantum Rabi oscillations were demonstrated for this compound, probing its validity as a qubit. Long coherence times (up to 152 ms at 10 K) were reported in several other vanadyl complexes where suppression of the effects of neighbouring nuclear spins has been achieved.62 Intriguingly, even in completely nuclear-spin free conditions of [V(C8S8)3]2 the coherence time rapidly decays to B1.0 ms as the temperature increases, due to rapid shortening of the T1 spin–lattice relaxation time, which limits T2. The strong effect on decoherence of both metal coordination and ligand structural rigidity was demonstrated in several other studies.39,53 For instance, comparison across families of vanadyl complexes has revealed that T1 is one order of magnitude longer in systems with a more rigid square-pyramidal environment compared to the flexible octahedral analogues.52 Optimisation of qubit performance (i.e. the expansion of its phase memory time) often focuses on magnetic dilution, with the aim of suppressing intermolecular dipolar interaction. However, this poses a fundamental paradox in the implementation of qubit protocols since quantum information processing requires an organised and controlled array of interacting qubits. A strategy to overcome this issue is to use magnetic noise resilient qubits. Such systems can be engineered by introduction of an interaction that mixes the qubit states (hyperfine interaction, for instance), creating an avoided level crossing or tunnelling gap. This situation arises when two levels cross under a magnetic field and generate the condition to observe atomic ‘‘clock transitions’’ (CT). The approach is particularly interesting for quantum computation because the spin qubit becomes insensitive to external fluctuations of magnetic fields at these particular atomic CTs, and consequently, decoherence from magnetic noise is vanished completely, enabling very long T2 times. A remarkable example of this approach is the polyoxometalate (POM) complex [Ho(W5O18)2]9 (or HoW10) in which two tungsten moieties encapsulate one Ho31 cation (see Fig. 7).35 The lanthanide ion assumes an antiprismatic coordination geometry with symmetry close to D4d. Under this local symmetry, the ground state is characterised by an mJ ¼  4 doublet, separated from the first excited states (mJ ¼  5) by ca. 20 cm1. Combination of a crystal field, hyperfine interactions and Zeeman splitting generates avoided level crossings between the mJ levels of the same mI. The tunnelling gap ofB9 GHz is comparable to the X-band microwave frequency, and thus EPR can be used to monitor these transitions. The spin qubit character of the molecule was studied using pulsed EPR in a series of single crystal dilutions of Na9[HoxY(1x)(W5O18)2].nH2O (x ranging from 0.001 to 0.25) giving long T2 coherence times up to 8.4 ms at 5 K (for x ¼ 0.001 and with a small decrease in T2 for x ¼ 0.01). For the sake of comparison, T2 measured at normal EPR transitions is two orders of magnitude shorter under the same conditions. Another approach enabling to prolong quantum coherence time in molecular spin systems is to engineer the electronic structure of the metal ion such that it behaves spectroscopically as an isotropic 2S state. Electron Paramag. Reson., 2021, 27, 146–187 | 157

158 | Electron Paramag. Reson., 2021, 27, 146–187 Fig. 7 (a) Zeeman diagram for HoW10 for mJ ¼  4 and I ¼ 7/2 ground state with the field applied parallel to the main molecular axis. The grey lines assume ideal 4

^ 4 term; (b) 3D EPR map including the B4 O ^ D4d symmetry, while the black lines include the axial B44 O 4 4 term. Dark colours correspond to stronger intensities, while red 4 arrows depict CT; (c) Variable frequency measurements at 5.0 K for diluted Na9[HoxY(1x)(W5O18)2]nH2O crystal, with y ¼ 291; and (d) Frequency versus field plot of the resonances observed in panel (c). Reproduced from ref. 35 with permission from Springer Nature, Copyright 2016.

This essentially means designing systems with quenched orbital angular momentum. Under these circumstances, the transfer of magnetisation between spin and lattice is disfavoured and T1 will not limit T2. The validity of this approach was demonstrated by Tuna et al. for a hydrogen-rich yttrium(II) complex of C3 symmetry, [Y(Cp 0 )3], where Cp 0 ¼ C5H4SiMe3 (see Fig. 8).34 The Cp 0 ligand is the opposite of what has been established so far to accomplish long coherence times in molecular qubits: it has many magnetic nuclei and the methyl substituents rotate freely and hence does not provide rigidity. However, the C3 symmetry of the complex lowers the energy of the dz2 orbital, enabling s/d orbital mixing (i.e. SOMO has a pronounced s-character). Despite a very rich nuclear spin environment, the compound shows robust quantum coherence (TmB2 ms below 30 K), including at room temperature (TmB0.4 ms) where coherent Rabi oscillations in a single crystal of 2% Y@YbCp3 0 could also be observed (see Fig. 8c). Remarkably, the study found that T1 and Tm are largely unaffected by the nature of the sample (single crystal versus THF solution) or which transition is monitored (see Fig. 8d), while g and A are essentially isotropic due to significant s-character of the SOMO orbital and quenched orbital magnetic moment. The 2S-type configuration of the compound was confirmed by Hyperfine Sublevel Correlation (HYSCORE) spectroscopy which produced similar results for various field positions. Further analysis of 13 C and 1H HYSCORE spectra (see Fig. 8e,f) confirmed that nearly 6% of electron spin density has been transferred to the Cp 0 ligands, with another portion being largely delocalised across the molecule (based on CASSCF), thus inferring that the protons on the ligands may still induce decoherence.34 As such, it is anticipated that combining this strategy with the engineering of the vibrational modes of ligands or deuteration could produce incredible results.

4 Scaling up electron spin qubits into MOFs Realisation of quantum algorithms requires the qubits to be interconnected via programmable interactions, which is not an easy task. One feasible strategy to create multi-qubit arrays is to assemble them within metal– organic frameworks (MOFs). An advantage of this strategy is that MOFs offer the possibility to organise qubits in ordered 2- or 3-D dimensions, at predefined locations that assure control over inter-qubit separations and reduced dipolar interactions. Towards this end, Freedman et al. investigated the possibility of doping Zn porphyrin MOFs with Co21 and used echospectroscopy to measure the relaxation times.63 EPR investigation of the compound formulated as [(TCPP)Co0.07Zn0.93]3[Zr6O4(OH)4(H2O)6]2 (TCPP ¼ 5,10,15,20-tetrakis(carboxy-phenyl)porphyrin) has revealed strong hyperfine interaction between Co21 S ¼ 1/2 (low-spin configuration) and I ¼ 7/2 leading to clock-type transitions and measurement of T2 and T1 values exceeding 13 and 34 ms at 5 K, respectively. Subsequently, vanadyl ions were incorporated within the [Ti(TCPP-Zn2-bpy)] MOF (bpy ¼ 4,4 0 -bipyridyl) (see Fig. 9b), at 2 and 5% VO21 dilution level.64 Detailed spin relaxation studies found T2 to be essentially temperature Electron Paramag. Reson., 2021, 27, 146–187 | 159

160 | Electron Paramag. Reson., 2021, 27, 146–187 Fig. 8 (a) Molecular structure of [Y(Cp 0 )3] anion; (b) Echo-detected spectrum at X-band on single-crystal Y@YbCp 0 3; (c) Rabi oscillations at 120 and 300 K measured at two observable positions; (d) Relaxation times measured in frozen THF solution and on single crystal; (e) 1H HYSCORE; and (d) 13C HYSCORE at B0 ¼ 347 mT, with simulations in red. Reproduced from ref. 34 with permission from Springer Nature, Copyright 2019.

independent below 60 and 100 K for 5% (0.5 ms) and 2% (1 ms) dilutions, respectively. Measurement of T1 gave 350 ms (5% doping) and 1411 ms (2% doping) at 5 K. The coherence of both doped samples was also proved via nutation experiments, leading to Rabi oscillations for both dilutions (Fig. 9c). Similar Zn2(COOR)4 paddle wheel connectors were used to assemble 2D porphyrin MOFs of formula [{CuTCPP}Zn2].32 Their magnetic characterisation has revealed only a small antiferromagnetic exchange between {CuTCPP} entities, while EPR on solutions of this compound probed coherence with T2 ranging from 2.4–5 ms, depending on the field position. Deposition of 24 layers of the 2D MOF on Mylar was achieved in this study, paving the road to hybrid device architectures based on qubits. In another study, copper(II) ions were incorporated within the zirconium porphyrinbased MOF PCN-224, yielding Cu1.0-PCN-224 (Fig. 9a).65 Contradictory to the previous reports, where magnetic dilution was employed, the multiqubit MOF in this study was studied in its neat form, maintaining weak coherence up to 80 K. This was only possible because of the large separation between the Cu21 centres bound by porphyrin linkers, with the closest Cu  Cu distance being 13.595 Å. Decreasing the copper content in the structure to 10% enabled longer qubit memory times (158 ns at 80 K; 645 ns at 10 K), indicating that inter-qubit dipolar interactions play a role in decoherence. Notably, coherent Rabi oscillations were detected for all frameworks, irrespective of spin concentration, which is a remarkable result.

5

Quantum gates

The practical implementation of molecular qubits and their integration into a real quantum computer, requires the scalability and interconnection of the qubits into arrays, ultimately leading to Quantum gates or Qugates.66 The superposition of states generated by the entangled qubits will allow the superposition of the many states as 2N (where N is the number of interconnected qubits), giving the radically improved power of quantum computers over their classical analogues. The obtained qugates would be able to perform operations that return an entangled state as the output. Examples of quantum gates are the controlled-NOT (CNOT), OiSWAP, Toffoli and Fredkin gates (see Fig. 10). Realisation of quantum gates still poses a challenge for certain qubit architectures. For instance, record coherence times have been achieved in salts doped with lanthanide ions, NV centres in diamond and phosphorus impurities in silicon, however, the intrinsic isolated nature of these systems makes their scalability rather difficult. In this context, a molecular bottom-up approach is more appropriate as it offers the possibility to construct multi-qubit spin systems by linking multiple spin qubits either through covalent or supramolecular interactions. The inter-qubit coupling can be tuned at will by using chemical linking motifs that assure the desired connectivity via noncovalent interactions, covalent bonding or supramolecular interactions, to cite only a few options. In the following sections, we will revise examples of qubit dimers that were proposed as quantum gate candidates. Electron Paramag. Reson., 2021, 27, 146–187 | 161

162 | Electron Paramag. Reson., 2021, 27, 146–187 Fig. 9 Molecular structure of (a) Cu1.0-PCN-224; and (b) [VO(TCPP-Zn2-bpy)] MOFs; and (c) Rabi oscillations obtained for [VO0.05TiO0.95(TCPP-Zn2-bpy)] at 5 K for different microwave attenuations (X-band). Reproduced from ref. 64 with permission from American Chemical Society, Copyright 2018.

Fig. 10 Representation for various quantum gates.

5.1 Qubit dimers with switchable interaction Chemistry offers immense opportunities for engineering molecular qugates. One explored strategy connects molecular qubits via paramagnetic or switchable molecular linkers. This strategy has been employed to link two {Cr7Ni} qubits, each with an S ¼ 1/2 spin state, with [Cu(NO3)2(OH2)] in order to form a weekly interacting 3-qubit system, {[NH2Pr2] [Cr7NiF8(O2CCMe3)15(O2CC5H4N)]}2[Cu(NO3)2(OH2)]).28 The compound is the first molecular system being used to probe tripartite entanglement in a qubit system utilising the Greenberger–Horne–Zeilinger (GHZ) and Werner (W) states. Linkage of {Cr7Ni} qubits via a switchable linker was achieved in [{Cr7Ni-O2C-py}-Co(SCN)2’{Cr7Ni-O2C-terpy}], due to Co21 being able to switch reversibly to Co31 (Fig. 11a).29 Interestingly, the authors used g-engineering strategies to make the g-tensor frames orthogonal to each other by using different ligands on each ring (py and terpy) and assuring cis connection to the octahedral Co21, hence building inequivalent qubits necessary for the implementation of a CNOT gate (Fig. 10). Another example is the analogue formulated as Electron Paramag. Reson., 2021, 27, 146–187 | 163

[{Cr7Ni-O2C-terpy}-Co’Cr7Ni-O2C-terpy}][ClO4] (see Fig. 11b),29 where two rings are connected by a redox-switchable centre, with the difference in this case that the two units are equivalent and similarly connected (via terpy) to the central metal; this makes the complex an example of a molecular OiSWAP gate (Fig. 10). While the CNOT gate inverts the state of the target qubit depending on the state of the control bit, the OiSWAP gate turns a two-qubit gate into a superposition of the ‘‘up’’ and ‘‘down’’ states.67 Interestingly, pulse EPR spectroscopy found Tm of Cr7Ni qubits barely affected by the presence of another Cr7Ni qubit or paramagnetic Co21. Similar behaviour has been observed in a larger {Pd12{Cr7Ni-Py2}24} aggregate.30 Likewise, simulations including the experimental T2 values resulted in high fidelities for both systems, i.e. 99.3% for the CNOT gate and 99.6% for the OiSWAP gate (see Fig. 11c, d). 5.2 Qubit dimers with non-switchable interaction Another strategy for constructing qugates is to engineer a very weak interaction between two qubit entities using an organic linker. Designing such interactions is a challenge because the communication needs to be strong enough to assure entanglement of qubits, but not too strong so that the magnetic exchange overcomes the quantum entanglement. The ratio Jh 1, where J is the coupling constant, must be greater than the decoherence rate (T21) and smaller than the Rabi frequency (OR) of single qubits, T21oJh 1oOR, which restricts J to the order of tens of MHz. This approach has been used to assemble a two-qubit CNOT gate based on a TEMPO biradical.67 In this system, two aromatic rings of the organic linker are engineered to be perpendicular to each other, forcing the g-tensors frames to be different and thus making the TEMPO moieties inequivalent. The hydrogen atoms at the radical ends were substituted by deuterium to prevent decoherence, while 15N isotopic enhancement was applied to simplify the hyperfine structure. The distance between the spin carriers was designed to be 2.0 nm, and a T2 of 1.0 ms at room temperature was observed for a 0.2% solid-state diluted system. Application of pulse EPR spectroscopy provided the dipolar parameters D ¼  9.2 MHz and E ¼ 0.02 MHz, while the inter-spin exchange coupling J ¼  0.14 MHz was determined by DEER (electron– electron resonance) spectroscopy. In this experiment the spin system is partitioned into observer spin A and pumped spin B; the coupling between them is measured with a four-pulse sequence that inverts spin B and does not excite spin A, and the effect of the pump pulses on A is detected, being essentially a CNOT operation. Hetero-qubit systems have been assembled by attaching a TEMPO radical to the molecular thread encompassed by a [2]-rotaxane Cr7Ni system (see Fig. 12a).68 The qubits are connected non-covalently, and thus, the interaction between them is purely dipolar. Such systems are interesting because the spins possess different g-values and can, therefore, be assessed independently. The weak interaction between the qubits was measured using RIDME (Relaxation Induced Dipolar Modulation) spectroscopy (see Fig. 12b). With this method, the spin-echo of the more 164 | Electron Paramag. Reson., 2021, 27, 146–187

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Fig. 11 (a) Molecular structure of [{Cr7Ni-O2C-py}-Co(SCN)2’{Cr7Ni-O2C-terpy}] and schematic representation of the CNOT gate operation (right side); (b) molecular structure of [{Cr7Ni-O2C-terpy}-Co’Cr7Ni-O2C-terpy}] and representation of the OiSWAP gate operation (right side); (c) Energy diagram of [{Cr7NiO2C-py}-Co(SCN)2’{Cr7Ni-O2C-terpy}]; (d) simulation of the pulse sequence implementing a CNOT gate. Reproduced from ref. 29 with permission from Springer Nature, Copyright 2016.

166 | Electron Paramag. Reson., 2021, 27, 146–187 Fig. 12 (a) Crystal structure of the [2]-rotaxane system; (b) schematic of the 5-pulse RIDME sequence; (c) experimental (black) and simulated (red) RIDME traces collected at 5 K at Q-band frequency; (d) Fourier transform of RIDME traces. Reproduced from ref. 68, https://doi.org/10.1002/anie.201612249, under the terms of the CC BY 4.0 license https://creativecommons.org/licenses/by/4.0/.

slowly relaxing spin is measured, and the modulation caused by the spontaneous flip-flop of the more rapidly relaxing spin allows the spin– spin dipolar interaction to be quantified. Therefore, RIDME is especially useful when two spins have different T1 relaxation times. In the case of the hetero-qubit systems, the spin of the TEMPO radical has a long T1 of 0.2 s at 10 K, while {Cr7Ni} possesses a shorter T1 of only 1 ms at 5 K. Compared to DEER, RIDME requires only the slowly relaxing spin to be measured, thus the pulse sequence was applied on the nitroxide resonant field. Besides, it benefits from being less orientation-selective and hence gives more intense signals and spectral simplicity. Analysis of the RIDME trace (see Fig. 12c,d) enables to determine both the isotropic exchange ( J¼þ 0.15 MHz) and anisotropic dipolar couplings (Dperp ¼ 9 MHz; Dpara ¼  18 MHz).68 5.3 Lanthanide-based quantum gates Lanthanide dimers represent another option of making robust and efficient quantum gates. Aromı´ and co-workers first explored this possibility with a terbium compound, [Tb2(HL)2(H2L)Cl(py)(H2O)], that displays inequivalent Tb31 pockets.69 The anisotropy of the system gives rise to an isolated ground doublet mJ ¼  6. Existence of a tilting angle between Tb31 ions, dictated by anisotropy, and the weak inter-metal interaction create the conditions for two possible quantum gates, CNOT and SWAP, depending on the resonant field used. An advantage of the SWAP gate is the fact that it can be systematically controlled via EPR pulses, avoiding the requirement of switchable interaction between the qubits. Another strategy to assemble asymmetric lanthanide qubits is to make heterometallic structures. The main challenge of this approach is the difficulty of inserting different ions at separate locations within the same molecule. Since the ionic radii across the 4f series are very similar, the electronic densities are indistinguishable under X-ray crystallography and the chemical reactivities are almost identical. However, because of the wellknown effect of lanthanide contraction, no two lanthanides are the same, therefore conferring some preference to the lanthanide ions depending on the pocket generated by the organic ligands.70 A series of lanthanide dimers of simplified formula [LnLn 0 ] were obtained using an asymmetric bridging ligand leading to the formation of pure hetero- and homometallic dinuclear lanthanide(III) complexes.71 The cerium(III)-erbium(III) dinuclear system [CeEr] is particular because both cations are Kramer’s ions and possess different magnetic configurations (see Fig. 13). Besides, all cerium stable isotopes have spin-free nuclei whilst only 22.9% of erbium stable isotopes have a nuclear spin of I ¼ 7/2, which reduces the cause of magnetic noise from hyperfine interactions. At low temperatures, both ions behave as Seff ¼ 1/2. In addition, a non-colinear arrangement of the magnetic axes is observed for the [CeEr] complex, with a tilting angle of 701, very close to that observed in the [Tb2] analogue. As a consequence, the Hilbert space, comprising four states, could in principle allow the realisation of a CNOT gate through manipulation of the states via X-band EPR photons at a field m0H ¼ 0.47 T. Furthermore, a promising coherence Electron Paramag. Reson., 2021, 27, 146–187 | 167

Fig. 13 (a) Molecular structure of the [CeEr] complex; and (b) Low energy level for [CeEr] and CNOT gate operation. Reproduced from ref. 71, https://doi.org/10.1021/ja507809w, with permission from American Chemical Society, Copyright 2014.

time of 0.4 ms was recorded at 5 K although in non-optimised conditions, thus making [CeEr] a promising candidate for a CNOT gate (Fig. 13b).

6

Multilevel qubits (qudits)

Leuenberger and Loss first proposed using the energy states of molecular magnet to perform quantum algorithms.72 This opens an opportunity of making qugates of higher complexity by employing qubits possessing more than two accessible levels, also known as qudits (where d42). Qudits have several advantages over two-level qubits, such as: (i) Qudits do not require inter-qubit coupling to make qugates;73,74 (ii) the number of elementary gates necessary to perform a computational task can be reduced;75 (iii) they can parallelise information in a smaller number of physical units;76 (iv) have diminished error rates compared to qubits;77,78 (v) more complex gates can be performed in a single physical unit;79–81 (vi) entangled qudits are less susceptible to local realistic description, making them more suitable for quantum cryptography;75 (vii) they can simplify the simulation of quantum mechanical systems with similar Hilbert space;82 (viii) entanglement and superposition could be achieved in large dimensions with smaller clusters of processing units compared to conventional qubits.78,83 Different qudit architectures were proposed, including quantum dots,84,85 defects in solids (e.g. nitrogen vacancies in Si86,87 and diamond88), vibrational and rotational states in molecules,89,90 harmonic oscillator states in superconducting circuits82 and cavities,91 hyperfine states in alkali atoms92 and electron and nuclear states in molecular magnets.21–24,93,94 As for qubits, chemistry offers all possibilities to create multilevel systems by engineering the electronic structures of molecular magnetic components involved, using chemical protocols. A selection of such molecular multilevel complexes will be discussed in the following section.

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Fig. 14 (a) Crystal structure of [Cr(C3S5)3]3; (b) Calculated energy splitting for [Cr(C3S5)3]3; and (c) Rabi oscillations for (d20-Ph4P)3[Cr0.01Ga0.99(C3S5)3]. Reproduced from ref. 95 with permission from American Chemical Society, Copyright 2016.

6.1 Electronic spin qudits Although molecular magnetic materials often possess many electronic states, one of the main difficulties for their exploitation as multilevel qubits is the large anisotropy, which restricts the number of states for computation to the lowest ones, to be experimentally accessible using microwaves. Conversely, when the transitions lie within the experimentally accessible range, then their forbidden character precludes the manipulation of all states. Exploitation of forbidden transitions for the realisation of multilevel qubits was probed in a nuclear-spin free Cr31 system, (Ph4P)3[Cr(C3S5)3] (see Fig. 14).95 In this compound, a small zerofield splitting term (DB0.32 cm1) coupled with a relatively large rhombicity (EB0.11 cm1) creates an opportunity for ms level mixing, which is a prerequisite to access and address forbidden transitions. In order to suppress relaxation effects arising from 1H protons of Ph4P1, a fully deuterated sample was used, i.e. (d20-Ph4P)3[Cr(C3S5)3], which was subsequently diluted in the diamagnetic (d20-Ph4P)3[Ga(C3S5)3] analogue at a 1% concentration, giving (d20-Ph4P)3[Cr0.01Ga0.99(C3S5)3]. Spin–lattice relaxation times of T1 ¼ 47(5) ms and 29(3) ms were measured at 5 K for two EPR transitions occurring at 1000 and 3500 G respectively, assigned to the forbidden mS ¼  3/2 -mS ¼  3/2 and allowed mS ¼  1/2 -mS ¼  3/2 transition, respectively, with the latter carrying a small contribution from mS ¼ þ 1/2 -mS ¼ þ 3/2 (see Fig. 14b). A phasecoherence time of 1.81 ms was measured at 5 K for the high field transition, which is long enough to enable observation of Rabi oscillations that probe the ability of the system to access any arbitrary superposition state. Remarkably, such Rabi oscillations were also observed for the forbidden EPR transition (Fig. 14c), suggesting that these transitions can also be employed as qubits or a qudit with two states for computation. Jenkins et al. demonstrated the first manipulation of the electronic states embedded in a qudit, using a polyoxometalate (POM) complex, K12Gd(H2O)P5W30O110 (or GdW30).94,96 The high spin multiplicity (2S þ 1 ¼ 8), the nearly isotropic nature and the C5v local symmetry of the Gd31 ion encapsulated within the POM structure are favourable for the

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Fig. 15 (a) Crystal structure of GdW30, X-band cw EPR spectrum at room temperature on a single crystal of Y0.99Gd0.01W30. Inset of the orientation of the crystal. Below, Zeeman diagram of the GdW30 spin energy levels vs. Hz; (b) Rabi Frequencies OR,n and damping rates 1/tR,n; and (c) Rabi oscillations for transition labelled as 1 showing the coherent evolution between |000i and |001i three-qubit states. Implementation of a CCNOT gate is achieved with a resonant p pulse. Reproduced from ref. 94, https://doi.org/10.1103/ PhysRevB.95.064423, with permission from the American Physical Society, Copyright 2017.

design of qudits. Under this symmetry, a small yet sizable anisotropy occurs removing the degeneracy of the electronic states of Gd31 and thus seven mS transitions are observable in EPR (Fig. 15a). Analysis of the powder EPR data with the spin Hamiltonian in eqn (8):   1 2 ~ H ¼ D Sz  SðS þ 1Þ þ EðS2z  S2z Þ  gmB~ SH (8) 3 where D and E are the axial and rhombic zero-field splitting terms, and the other symbols have their usual meaning, gave D ¼ 1281 MHz and E ¼ 294 MHz.96 Spin-echo coherence studies on a magnetically diluted single crystal of composition Y0.99Gd0.01W30 revealed coherence times T2 ranging from 0.5 to 0.6 ms across individual transitions, and T1 of 2.3 to 2.6 ms at 6 K, which are both long enough to enable coherent manipulation of the electronic states of GdW30. Damped coherence oscillations were observed for all transitions, and were analysed with eqn (9):   tp Sy;n ðtp Þ ¼ Kn exp  (9) J0 ½OR;n ðtp  tp;0 Þ þ Sn;0 y;0 tR;n where Kn is a constant, J0 is the Bessel function of first order, O(R,n) and  1 are the frequency and the damping rate of each Rabi oscillation, tR;n respectively, t(p,0) is the evolution at short times tpttn and the last term is the nonoscillatory component. The frequencies of the spin oscillation of 170 | Electron Paramag. Reson., 2021, 27, 146–187

the states can be tuned by application of microwave power, and a linear dependence between the Rabi oscillation and h1 occurs, in agreement with OR,n ¼ gmBanh1. Likewise, the experimental Rabi oscillations showed the manipulation between a pair of electronic states (see Fig. 15b); the eight electronic states of the GdW30 complex being related to a threequbits system. To probe whether any arbitrary quantum operation could be applied to the tree-qubits system (or Qudit with d ¼ 8), the authors performed single rotation of transition 1. Taking advantage of the specific resonant frequency of transition 1, the authors were able to perform a controlled-controlled-NOT (CCNOT) or Toffoli gate, which flips the ‘‘third’’ target while the remaining two ‘‘control’’ bits do not change (see Fig. 15c). 6.2 Hybrid E–N spin qudits An alternative approach toward qudits with large Hilbert space is to exploit the electronic hyperfine-split levels or the nuclear states. This strategy was successfully demonstrated for a ytterbium single-molecule magnet, formulated as [Yb(trensal)].51,97,98 The complex has a C3v symmetry and a strong axial magnetic structure resulting in the anisotropy axis being parallel to the crystallographic 3-fold rotation axis, and stabilisation of a well-isolated doublet spin ground state (i.e. 464 cm1 energy gap to the first excited state). The existence of various Yb31 isotopes, some with non-zero nuclear spin, i.e. 171Yb (I ¼ 12; 14%) and 173 Yb (I ¼ 5/2, 17%), opens up the possibility for electron–nuclei hyperfine interactions, and thus several electronuclear transitions are observed by EPR spectroscopy (Fig. 16a). Analysis of both X-band cw and echo-detected EPR spectra measured on a single crystal of 5% Yb@Lu(trensal) enabled to determine the magnetic parameters of the complex, giving g8 ¼ 4.29 and g> ¼ 2.90, and the hyperfine coupling

Fig. 16 (a) X-band (9.7 GHz) field-swept echo-detected EPR spectra of a single crystal of [Yb(trensal)] with the field applied parallel (blue) and perpendicular (red) to the C3 axis at 5 K; Reproduced from ref. 51 with permission from American Chemical Society, Copyright 2016. (b) Nuclear Rabi oscillations for three transitions necessary to operate the errorprotected qubit. Reproduced from ref. 97 with permission from American Chemical Society, Copyright 2018. Electron Paramag. Reson., 2021, 27, 146–187 | 171

constants AI8¼ 1/2 ¼ 0.112 cm1, AI>¼ 1/2 ¼ 0.074 cm 1, AI8¼ 5/2 ¼  0.031 cm1 and AI>¼ 5/2 ¼  0.022 cm1.98 The multitude of resonances observed opens up the possibility of utilising the different nuclear spin split electronic states as quantum register, thus rendering a qubit–qudit system. Quantum coherence measurements using a standard 2-pulse Hahn echo sequence (see Fig. 2) has revealed phase memory times T2 as long as 0.5 ms below 5 K. In addition, coherent Rabi oscillations were observed for all electronuclear transitions via transient nutation experiments, suggesting that the electron can be coherently manipulated for more than 70 rotations.51 It also demonstrates that all electronuclear Yb isotope states are accessible for quantum operations. Experimental demonstration of the qubit–qudits characteristics of [Yb(trensal)] was achieved by Nuclear Magnetic Resonance (NMR) spectroscopy.97 Hussain and co-workers have probed nuclear coherence for the nuclear isotope 173Yb (I ¼ 5/2; Hilbert space d ¼ 6) present in a 2% magnetically doped crystal of a diamagnetic analogue. Transient nutation experiments demonstrated the ability to create a coherent superposition of states as demonstrated by Rabi oscillations (Fig. 16b). The results show that few hundreds of ns are adequate for device p rotations. Interestingly, the loss in coherence induced by nuclear–electron spin mixing is compensated by the improvement of the Rabi frequency (oR), which makes the gating faster. Thus, combination of a non-axial electronic ground doublet state, a long T2 and not too long T1, the enhanced oR and the well-resolved character of the transitions make the complex [173Yb(trensal)] a good qubit– qudit candidate. Thus, the multilevel structure of the 173Yb ion is useful to implement protected qubits, to eliminate the effects of amplitude or phase shift errors.

Fig. 17 (a) Representation for a hybrid electronic-nuclear spin dimer with switchable interaction; and (b) Zeeman diagram for the vanadyl complex based on EPR data, and the rf pulse needed to produce single-qubit rotation indicated by the black solid arrow resonant with the single-qubit gap, while the dashed arrows schematically represent the implementation of a CZ gate. Reproduced from ref. 99 with permission from the Royal Society of Chemistry.

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Another astonishing example of a hybrid E–N qudit is evidenced by a dimeric vanadyl complex, [PPh4]4[(VO)2(L1)2] (L1 ¼ C20H12N2O6) (see Fig. 17a),99 whose metal electronic (E) states can couple to the nuclear (N) ones (51V, I ¼7/2) via hyperfine interactions. The result of such coupling usually results in narrow EPR resonance lines in both frozen solution and solid-state magnetically diluted samples.38–40,55,100 In this compound, each hyperfine line is additionally split into two components because of a small dipolar coupling (B0.003 cm1) between the two V41 ions present in the molecule. Analysis of the cw EPR data employing the spin Hamiltonian described in eqn (10), where si ¼ 1/2, and Ii and A are the nuclear spin and hyperfine coupling tensor respectively, J is the exchange coupling parameter, and the other symbols have their usual meaning, yielded gz,x ¼ 1.982, gy ¼ 1.941, Ax,y ¼ 186 MHz, Az ¼ 498 MHz, and a very small JD  0.0016 cm1, indicative that the two metal ions are very weakly coupled. H ¼ Si¼1,2IiAsi þ mB Si¼1,2 sigB þ J(2sz1sz2  sx1sx2  sy1sy2)

(10)

To investigate the possibility of implementing a hybrid E–N qudit, the coherence times were measured under various magnetic fields and frequencies giving TmB1 ms up to 100 K, which is sufficiently long to enable coherent spin manipulations. One can anticipate that under significant magnetic fields, the energy to rotate nuclear states is normally independent of the other states, and thus single-qubit rotations can be implemented by means of MW pulses. In contrast, because of the E–N hyperfine interaction, the rotation of the electron-spin that is coupled to nuclear spins is contingent upon the state of the nuclei. Thus, the effect of the MW pulse is contingent on the nuclear states, and this can be implemented in conditional two-qubit gates, where an indirect interaction between the electronic spins coupled to the nuclear states, acting as a switch. For applied fields employed in X- and Q-band experiments, the leading term is the Zeeman interaction. Three groups of states can be distinguished according to the total MS component along the applied field. The logical states of the qubits, i.e. |1i and |0i are encoded in both ms ¼  1/2 states of the electron spin of the MS ¼  1 level, of the 4 states of the (2I þ 1)2 nuclear spin manifold (see Fig. 17b). These states correspond to the mI ¼ 7/2 and mI ¼ 5/2 states of each V nucleus. Note that while the system is kept at the MS ¼  1 state, the energy to rotate the nuclear spins is independent of other nuclei. Thus, single qubits rotations can be performed between the mI ¼ 7/2 and mI ¼ 5/2 states. In contrast, a controlled-shift (Cj) two-qubit gate can generate entanglement between the qubits, thus, adding a phase to the |00i states while leaving the remaining three states unaffected. This type of gate is able to generate a highly entangled state from a factorised wavefunction. For [PPh4]4[(VO)2(L1)2], this gate can be implemented by employing the EPR resonance transition corresponding to the MS ¼  1 and MS ¼ 0 states (see Fig. 17b). Under the operation of hyperfine interactions, the excitations are nuclear spin-dependent allowing the implementation of the CZ gate (when j¼p), while the rest of potential transitions will be Electron Paramag. Reson., 2021, 27, 146–187 | 173

unaffected because of the different resonance frequencies needed to excite those particular states. Notably, the numerical simulation of the 2-qubit gate resulted in high fidelities (97%) even after the inclusion of decoherence. Moreover, the system was employed as a quantum simulator of the time evolution of the magnetisation of S ¼ 1 experiencing magnetisation quantum tunnelling yielding excellent results. 6.3 Operating nuclear spin qudits via QTM As described in the previous section, an alternative for the realisation of qudits is to utilise the electronic hyperfine-split levels or the nuclear states. In the [Yb(trensal)] example, the ground doublet electronic state of the single-ion magnet can be considered as a qubit, while the nuclear spin states give access to the qudit characteristics. While the electronic doublet of the qubit can be accessed via EPR transitions, the nuclear states can be manipulated via EPR and NMR pulses. The advantage of exploiting nuclear spins as quantum bits lies in their inherent shielding from the environment, affording extremely long coherence times and very low error rates.101 Unfortunately, the intrinsic shielding of the nuclear spins makes their interaction with other nuclear spins very weak. For this reason, the close nature of nuclear spins, along with their small magnetic moment make their integration into circuits, read-out and manipulation a difficult task. Despite the challenging characteristics of nuclear spins, the read-out and manipulation of nuclear spins can be achieved and has in fact been demonstrated in NV centres,102,103 silicon11,12,104 and molecular nanomagnets.105,106 Furthermore, the nuclear spins in the Single-Molecule Magnets (SMM) offer a larger number of states for manipulation, depending on the nuclear spin of the metal ion. This is the case of the nuclear spins of Tb31 ion in the phthalocyanine sandwich complex [TbPc2] (see Fig. 18a). The square-antiprismatic (D4d) coordination geometry of the metal ion gives an axial anisotropy which favours single-molecule magnetism.9 Similar to other SMMs, it shows slow relaxation of the magnetisation, as well as several quantum effects, not observable in conventional systems, such as the quantum tunnelling of the magnetisation (QTM), spin oscillations and quantum phase interference. The [TbPc2] system can be considered as comprising three magnetic components: (i) an S ¼ 1/2 organic p-radical, delocalised over the two aromatic Pc ligands; (ii) an electronic spin J ¼ 6 of the Tb31 ion, generated by the two phthalocyanine (Pc) ligands, leading to a well-isolated electron spin ground state doublet of |J ¼ þ 6mi and |J ¼  6ki with a uniaxial anisotropy axis perpendicular to the Pc plane; (iii) the nuclear spin of the lanthanide (I ¼ 3/2), which splits the electronic doublet spin ground state into four different quantum states. i.e. states | 6, 3/2i, | 6, 1/2i, | 6, þ1/2i, and |  6, þ3/2i (see Fig. 18). The magnetic behaviour of [TbPc2] can be described by a Hamiltonian, eqn (11):   1 2 (11) H ¼ Hlf þ gJ m0 mB J  H þ Ahf I  J þ P IZ  ðI þ 1Þ I ; 3

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Fig. 18 (a) Representation of the [TbPc2] SMM embedded in a spin-transistor geometry; (b) Schematic representation of the read-out cascade occurring in the [TbPc2]-transistor; and (c) conductance jumps (top) and their histograms (bottom) obtained from conductance measurements during magnetic field sweeps; each jump is assigned to a nuclear spin state of terbium. Reproduced from ref. 9 with permission from the Royal Society of Chemistry.

with hlf is the ligand field Hamiltonian (hlf ¼ aB02O02 þ b(B04O04 þ B44O44) þ g(B06O06 þ B46O46)) with Bkq representing the ligand field parameters, whilst a, b and g are the Stevens tabulated constants. The second term is the Zeeman energy and the third and the fourth term are the hyperfine interactions and the quadrupole term, respectively. Under strict D4d symmetry quantum tunnelling of the magnetisation is not possible. However, m-SQUID measurements on diluted single crystals of TbPc2 have shown several QTM events, which are ascribed to the lowering of the symmetry to C4, allowing the presence of transverse anisotropy terms (B44O44 þ B46O46) in the ligand field Hamiltonian.110 These terms induce mixing of the |Jz ¼  6i states causing an avoided level crossing at zero field, which is further split into four components due to strong hyperfine interaction between the |Jz ¼  6i and I ¼ 3/2 of Tb31 causing four avoided level crossings, i.e. mI ¼  3/2 and 1/2, with a tunnel splitting of around 20 MHz.106,109 More importantly, the quadrupole term causes an uneven separation between the mI states. At zero external magnetic field a non-equal separation of the mI states is experimentally obtained, i.e. n01E2.45 GHz, n12E3.13 GHz and n23E3.81 GHz separates the mI states.107 This is an aspect of utmost importance for the initialisation and manipulation of Electron Paramag. Reson., 2021, 27, 146–187 | 175

the nuclear states of the system since it allows the independent manipulation of the different nuclear states in the TbPc2. Furthermore, the ferromagnetic coupling between the p-radical and the Tb31 ion has proven important for the read-out of the qudit.107,109 Electronic transport under variable magnetic fields revealed the hysteretic behaviour for [TbPc2] molecules, similar to the stepped magnetic hysteresis observed in bulk m-SQUID studies108–110 (see Fig. 18b, c). The read-out procedure is based on the highly efficient detection of the quantum tunnelling of magnetisation of the electronic magnetic moment at particular values of the magnetic field corresponding to the four avoided energy-level crossings.105,106 By recording the conductance as a function of time, it was possible to monitor the dynamics of the four different nuclear spin states, allowing the determination of the relaxation times (T1) exceeding several tens of seconds. Furthermore, the electrical read-out of time-trajectories yields fidelities of 95%, while Ramsey fringes allow extracting a dephasing time of T*2E64 ms for the nuclear spin qudit93,105,106,111 (see Fig. 19). The true advantage of this qudit system with d ¼ 4 (where d ¼ 2I þ 1) was demonstrated by the realization of the quantum Grover’s algorithm in a single molecular unit of [TbPc2] (see Fig. 20).94 The implementation of a molecular system possessing multiple states was first proposed by

Fig. 19 Schematic representation of Ramsey Fringes sequence: (a) Initialisationmanipulation-probe. The above example involves the | þ 3/2i2| þ 1/2i subspace and can be applied to any other |  mIi set: (i) a pulse of n 01 frequency and duration t ¼ p/2 is applied to a given nuclear spin | þ 1/2i projecting the spin into the equatorial plane; (ii) Precession of the spin into the x-plane during a t time; (iii) a second p/2 pulse projects the y component of the spin state into the z-plane. The final state is finally determined via sweeping the field. (b–d) Experimental Ramsey fringes decay reveal coherence time values T2* of 0.28, 0.3 and 0.32 ms for the 1st, 2nd and 3rd, respectively. Reproduced from ref. 9 with permission from the Royal Society of Chemistry. 176 | Electron Paramag. Reson., 2021, 27, 146–187

Fig. 20 (a) The Grover algorithm is implemented using four different steps: initialisation, Hadamard gate, Grover gate and final read-out. (b) is the evolution of the population as a function of the Hadamard gate pulse length. Starting from the green state, after a pulse of duration of 130 ns, the population of all the states are equal. (c) is the evolution of the population as a function of the Grover gate pulse length. Starting from a superposed state (obtain by a Hadamard pulse sequence) the system oscillated between this superposed state and a desired state (here the black one). This population oscillation is the fingerprint of the Grover algorithm implementation. Reproduced from ref. 9 with permission from the Royal Society of Chemistry.

Loss and Leuenberger, with the main advantage being the lack of intermolecular coupling between qubits.73 The Grover’s algorithm was performed with the [TbPc2] embedded in a transistor-like configuration. To achieve the algorithm, a succession of two gates is required: (i) a Hadamard gate, which starts from an initialised state to create a superposition of all qudits states, and (ii) the Grover gate, which amplifies the amplitude of the sought state, initially labelled via its phase or energy. Finally, by making use of the quantum amplitudes to determine the probabilities of an event, it is possible to find the sought state. Note that the Hadamard gate allows the superposition of states; that is, if a number of qubits n is prepared at a given initial state followed by a Hadamard gate applied to each qubit, a total of n-qubits superposition is achieved. These states represent all possible combinations of the n qubits X2n 1 ffi from 0 to 2n  1, i.e. H j 0i H j 0i    H j 0i ¼ p1ffiffiffi j ji. The 2n j¼0 resulting superposition of states comprises all possible solutions of a given problem, acting as shortcuts accelerating the computation process. The Hadamard gate is very important in quantum computing due to the facility to create exponentially many states, employing solely polynomial operations. The operation of a highly superposed state allows the Grover’s algorithm to succeed in a quadratic speed up, compared to classical algorithms.5 This algorithm can be applied from search in unsorted databases to pattern matching. Electron Paramag. Reson., 2021, 27, 146–187 | 177

For the realisation of the Grover algorithm, the simultaneous manipulation of the mI states is required to create a superposition of the four nuclear spin states creating a qudit (with d ¼ 4 for I ¼ 3/2). This is achieved by a multifrequency pulse containing the resonance frequencies for each transition. Following the superposition, pulse parameters (frequencies and amplitudes) are tuned to reach a resonance condition in between the superposed states and the sought state. As a result, the qudit populations start to oscillate and the population of the labelled state briefly increase. This experiment demonstrated for the first time the experimental Grover’s algorithm on an SMM.94 The successful realisation of the Grover’s algorithm in a single molecule of [TbPc2] was possible because of the multilevel properties of the system, i.e. d ¼ 4, where the four nuclear spin states act as quantum bits. This experiment undoubtedly demonstrates the advantage of the multilevel qudits (d42) over their two-level qubits (b ¼ 2) counterparts, allowing the realisation of algorithms and gates without the requirement of inter-qubit coupling, an unavoidable requirement in electronic qubits. Additionally, entanglement and superposition of states can be carried out in qudits with smaller clusters of processing units compared to conventional qubits. The larger qudit state dimension may offer greater flexibility for different applications. Following the positive initialisation, manipulation, read-out and realisation of a quantum algorithm employing the nuclear-spins embedded in [TbPc2] as qudit (d ¼ 4), systems possessing larger accessible multiplicity of states, to act as quantum registers, are desirable; a larger number of states for quantum computation would permit the realisation of more complex and advanced algorithms. In this sense, a simple approach is based on isotopological chemistry.112–114 Taking advantage of isotopic enrichment, SMMs with larger Hilbert space can be synthesised. This is the case of negatively charged double-decker dysprosium complex Et4N[DyPc2]115 (see Fig. 21a). The natural composition of Dy31 includes seven isotopes, with two different nuclear spin states, I ¼ 0 and 5/2. However, with a judicious selection of the right isotope for the synthesis of the complex, it is possible to prepare isotopically enriched complexes with an enlarged Hilbert space. This is the case of Et4N[163DyPc2] with I ¼ 5/2, which displays stepped hysteresis curves in m-SQUID studies, characteristic of the reversal of electronic spins via the hyperfine driven QTM (see Fig. 21b–d).115 The steps can be nicely reproduced with the Hamiltonian eqn (11), when taking into account the hyperfine coupling and quadrupolar terms Ahf ¼ 0.0051 cm1 and P ¼ 0.014 cm1, respectively. As the nuclear spin isotope embedded in the complex is 163Dy31, a total of six accessible states are available for computation, leading to a qudit with d ¼ 8. Note that due to the existence of the quadrupolar term, an uneven separation between the nuclear states is present, which is an important requirement for the independent manipulation of the nuclear states. Naturally, a limiting factor for the synthesis of molecules possessing larger Hilbert states by isotopic enrichment is the nuclear state contained in a given lanthanide, i.e. the nuclear state is limited to the ions. For 178 | Electron Paramag. Reson., 2021, 27, 146–187

Electron Paramag. Reson., 2021, 27, 146–187 | 179

Fig. 21 (a) Crystal structure of Et4N[163DyPc2] with I ¼ 5/2; (b–d) m-SQUID data for Et4N[163DyPc2] (I ¼ 5/2) revealing the hyperfine-driven quantum tunnelling events associated to the nuclear spins embedded in the dysprosium ion. Reproduced from ref. 115 with permission from John Wiley & Sons, Copyright r 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

example, the largest nuclear spin state for lanthanide is I ¼ 7/2 (d ¼ 8), while for the entire periodic table it is I ¼ 9/2 (d ¼ 10). As inferred, this would limit the size of the qudits. An approach to extend the Hilbert space beyond the natural limit would be by inter-qudit coupling. Unfortunately, nuclear spins are well shielded from the environment, thus, making their interaction with other qudits very difficult to implement. Some of us have shown that the interaction between qudits is possible by the indirect coupling of the nuclear spin states via electronic exchange.116 The cooperative behaviour of both, electron– electron interactions and nuclear spin multiplicity in a dinuclear complex, namely [Tb2Pc2Hx8Pc] (where Pc ¼ phthalocyaninato and Hx8 Pc ¼ 2,3,9,10,16,17,23,24-octahexylphthalocyaninato), was revealed via m-SQUID measurements (see Fig. 22). The compound features a tripledecker complex, with two Tb31 ions intercalated between Pc moieties. The natural isotopic occurrence of Tb31 ions (100% I ¼ 3/2) and the proximity between the Tb31 ions in the molecule permit the communication between the Tb31 ions. Static magnetic studies, i.e. wMT(T), showed an upsurge at low temperature due to magnetic interactions between the Tb31 ions (see Fig. 22b), whilst dynamic magnetic studies revealed the desired SMM character. m-SQUID investigations on a diluted sample (1% [Tb2Pc2Hx8Pc] at 99% [Y2Pc2Hx8Pc]) validate the SMM character and the quantum nature of the complex. To account for the coupling between Tb31 ions, an additional term is included in the Hamiltonian describing this system (eqn (12)): h ¼  2J1  hdip  J2 þ h1Tb þ h2Tb

(12)

where the first term describes the interaction between the electronic states of the Tb31 ions, while the second and third terms contain the information in eqn (11) for each Tb31 ion. In contrast to the [TbPc2] complex, where solely four hyperfine driven QTM (hf-QTM) events are observed, the m-SQUID hysteretic loops of [Tb2Pc2Hx8Pc] show a multitude of QTM events, corresponding to the reversal of the electronic spin. This is attributed to the hf-QTM induced by the exchange between the electronic states of Tb31. Simulation of the Zeeman diagram yields a P parameter similar to that found for [TbPc2], and a slightly larger Ahf value of þ0.0215 cm1. This approach is useful in view of increasing the multiplicity of accessible nuclear states associated with the ground electronic doublet. For instance, going up one increment in the multiplicity of the states of the molecule pushes the qudit order to d ¼ 16, where d ¼ (2I þ 1)n and n ¼ 2. Notably, the separation between hyperfine states is uneven due to the quadrupole interactions of the nuclear states (see Fig. 22c–e). This difference in the energy gap separating the different states permits their independent manipulation, which together with the possibility of extending the Hilbert space, opens an opportunity to create advanced quantum logic gates and algorithms. 180 | Electron Paramag. Reson., 2021, 27, 146–187

Fig. 22 (a) Crystals structure of [Tb2Pc2Hx8Pc]; (b) static magnetic studies showing a ferromagnetic interaction between the Tb31; (c) m-SQUID hysteresis loops; (d) first derivative of the hysteresis loops showing the quantum tunnelling events arising from co-tunnelling at the different nuclear spin states; and (e) Zeeman diagram accounting for the hyperfine interactions and exchange interactions [Tb2Pc2Hx8Pc] operating in the complex. Reproduced from ref. 116 with permission from American Chemical Society, Copyright 2018.

7

Conclusions and perspectives

Although the field of molecular quantum bits is still in its dawn, it has conquered remarkable achievements in a short period of a few years. Looking ahead, there are still many obstacles, such as achieving longer coherence times, being able to implement quantum operations and discovering effective ways for scaling-up a large number of qubits. The simultaneous addressability of every DiVincenzo criteria is the major issue. More specifically, the challenge of connecting two (or more) qubits that can transfer information over is still unresolved. Nevertheless, the understanding of fundamental mechanisms of quantum coherence, the way it relates to the chemical design and how it can be optimised has been a major objective for researchers and can already be considered quite advanced, thus the path to the future is already paved. EPR techniques will walk hand on hand with molecular qubits since it has been shown as a powerful technique not just for the characterisation of molecular spin qubits and qudits, but also for the manipulation, and implementation of complex quantum gates. Molecular nanomagnets have been proposed as quantum bits for quantum computing, due to their bewildering properties and the possibility of chemical design, allowing researchers to tune their electronic and nuclear properties at will by chemical tools. As already shown, some of these systems have already achieved impressive coherence times, Electron Paramag. Reson., 2021, 27, 146–187 | 181

competing with other qubits platforms. Additionally, chemistry offers the possibility of engineering the inter-qubit coupling, which is a common problem with other platforms such as NV centres, impurities in Si, and superconducting Qubits. Undoubtedly, molecular platforms show superior characteristics in this respect, and inter-qubit couplings by chemical means were already demonstrated, leading to molecular qugates. Likewise, the multilevel characteristics of magnetic molecules can represent new means for the realisation of advanced quantum gates and algorithms. Their advantageous characteristics have led to their integration into hybrid architectures, such as their incorporation in superconducting circuits,117–119 where the manipulation of the states is conducted via EPR pulses. Furthermore, the chemical control that chemists have over the molecular properties of molecular qubits have propitiated the investigation of luminescence methodologies to readout120–123 the magnetic properties of the systems. Further progress in quantum information technologies requires the development of novel experiments that can reliably measure the qubit quantum behaviour and entanglement. As the vast majority of molecular systems proposed as qubits or qudits drive their properties from electronic and nuclear states, development of novel experiments that can simultaneously probe and manipulate all these degrees of freedom will be necessary, though important steps were made in this direction. The experiments will ideally combine optical and pulse magnetic resonance techniques (EPR and NMR), which offers vast opportunities for precise spin manipulation, qubit preparation and read-out.

Acknowledgements The authors wish to thank The Royal Society (UK) for the award of an International Exchanges COST Share Grant, the Engineering and Physical Sciences Research Council (UK) for funding of the National EPR Facility at The University of Manchester, The Leverhulme Trust (UK) for a Research Fellowship to F.T., and the University of Manchester for a President’s Doctoral Scholar Award to D.M.

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Continuous-wave rapid scan EPR Mark Tseytlin DOI: 10.1039/9781839162534-00188

Rapid scan (RS) is a novel and, at the same time, an ‘aged’ EPR method. The spin system evolution under the rapid-passage conditions was well-understood at the dawn of magnetic resonance. The recent progress has been made mostly along the practical dimension. Algorithms and instrumentation have been developed with the goal to measure undistorted EPR spectra with enhanced sensitivity. Both frequency and magnetic field scan methods were developed. The latter, continuous-wave RS EPR, is the topic of this book chapter.

1

Introduction

Quoting the Bruker webpage, rapid-scan (RS) EPR is a ‘revolutionary technique that can improve the signal to noise ratio and significantly decreases the acquisition time (down to milliseconds)’. The EPR community is well-aware of this new technique but mostly from attending conferences and reading research papers. Only a few laboratories are currently using RS EPR in their research. Most of them have home-build systems.1–5 With the commercialization of this method, RS upgrades and new systems will become available to EPR users across the globe. RS has the potential to become a mainstream method for EPR spectroscopy and imaging. The traditional first-derivative continuous-wave (CW) technique may become obsolete in 10–15 years. We are not quite there yet. RS EPR of today has limitations that are both algorithmic and instrumental. Despite these limitations, this method has proven to significantly enhance EPR sensitivity for a range of experimental conditions. RS EPR has been particularly beneficial for imaging applications. This book chapter pursues two major objectives. First is to show that RS EPR is not a standalone technique but rather a logical step in the evolution of continuous-wave (CW) spectroscopy and imaging (non-CW frequency-sweep RS is described in a separate chapter). This evolutionary perspective will help the reader see a bigger picture and mentally connect the concepts described in this chapter to the ‘common-knowledge’ EPR. The second objective is to provide the users and method-developers with an in-depth description of the current state-of-the-art of RS EPR methodology. Toward this goal, the key underlying principles and concepts are described in detail. The advantages and limitations of RS EPR are analyzed. Future directions and the ways to overcome the current constraints are discussed that give the reader a big-picture perspective on the evolution of CW RS EPR. The term ‘rapid-scan’ has been used to describe different types of experiments in both EPR and NMR. For example, some of the Bruker EPR Biochemistry Department, West Virginia University, Morgantown, WV 26506, USA. E-mail: [email protected] 188 | Electron Paramag. Reson., 2021, 27, 188–213  c

The Royal Society of Chemistry 2021

spectrometers are equipped with a set of coils that permit fast linear sweeps of the magnetic field within a limited magnetic field range. In this ‘rapid scan’ mode, the conventional first-derivative EPR spectra can be measured but in shorter time intervals compared to the conventional ‘slow scan’ mode. The term ‘rapid scan’ was recently re-defined. The current version describes a different type of experiment. In this experiment, the transient response of the spin system that resembles free induction decay signals (FID) is measured. Numerical transformation of these transient signals to absorption EPR spectra has been developed that enabled the novel RS EPR technology.6–8 To avoid confusion between the former and current rapid scan methods, the first-derivative ‘rapid’ mode is now called ‘fast scan EPR’.9 Another potential reason for the confusion may be the comparisons between RS and CW experiments often made in the recent literature.10,11 However, it is important to keep in mind that field-scan RS EPR belongs to the class of CW methods (frequency-scan techniques are not considered in this chapter). RS EPR uses wide magnetic field scans that cover the entire EPR spectrum. Both the amplitude and frequency of the alternating excitation field are constant. This is the definition of the continuous-wave condition. RS EPR is one of the CW methods. There are others. One of the examples is a rapid magnetic field scan version called NARS, which is stands for the nonadiabatic rapid sweep.12–15 NARS is also a CW method that uses linear scans and direct signal detection. A multi-harmonic method that uses multi-channel digital phase-sensitive detection to reconstruct the first derivative spectrum is another example of CW spectroscopy.16,17 Simultaneous measurement of up to five modulation harmonics is now enabled in modern Bruker spectrometers. The concept of rapid passage can be described in different ways. In this chapter, we pursue a practical approach to this definition, the approach that permits the development of algorithms that deliver sensitivity enhanced undistorted EPR spectra. From this algorithmic standpoint, it is convenient to distinguish the slow-scan and rapid-scan regimes. In the slow-scan regime the magnetic field Bz(t) passes through the resonance slow enough so that the spin system response R(t) in a given time moment depends only on the resonance conditions in this exact moment of time: R(t)pEPR(Bz(t))

(1)

Data processing in this case is quite straightforward. The time-domain signal directly maps into the magnetic field domain spectrum. In practice, the EPR spectrometer substitutes the time axis with the magnetic field axis in the real-time using a pre-defined calibration table. It is important to realize that eqn (1) can be violated in the conventional CW(1) experiment. EPR spectra may be distorted, for example, if the modulation frequency and/or amplitude are large compared to the EPR linewidth. In this case, one may be dealing with the rapid-passage effect. When the magnetic field rapidly passes through the resonance during the time that is short compared to T2*, the spin system experiences an excitation pulse. The response of the spin system resembles that of traditional free Electron Paramag. Reson., 2021, 27, 188–213 | 189

induction decay (FID) signal observed in pulsed EPR methods. R(t) in a given moment of time becomes a sum of the spins system responses that have happened before the time t. As a result, eqn (1) does not apply to this experimental situation that will be referred to as the rapid-scan regime. A general solution that relates EPR spectrum to RS signal was recently found.6 This solution permits using arbitrary magnetic field scan waveforms. To distinguish several types of CW methods that will be discussed in this chapter, the following annotations will be used:  CW(1) will denote the first-harmonic experiment that uses magnetic field modulation and phase-sensitive detection to measure the first derivative of the EPR spectrum  CW(N) will denote the experiment that simultaneously measures spectra corresponding to N harmonics of the modulation frequency,18–20 and the first derivative spectrum is reconstructed numerically.16,17  RS is the method that scans through the entire EPR spectrum and the spin system response is directly digitized and post-processed to obtain the absorption line. NARS belongs to the class of RS methods. It is important to note that these definitions relate to the corresponding experimental designs and data processing methods, not the properties of the sample and scan regimes. The RS EPR method is designed to work equally well in both slow-scan eqn (1) and rapid-scan regimes provided that the scan encompasses the entire spectrum. CW(1) and CW(N) methods work only in the slow-scan regime. It is important to identify the driving force behind the most recent EPR developments, including the RS technique. This force is the digital revolution. For example, RS EPR was enabled by the availability of fast digitizers equipped with a field-programmable gate array (FPGA) chip that permits real-time averaging. Arbitrary waveform generators and digital frequency sources are also examples of enabling technologies. Digital revolution will continue, and the current state of the art is likely to become a transient point in the evolution of CW spectroscopy and imaging. RS EPR technology is likely to merge with pulsed EPR along its evolutionary trajectory.21,22 This chapter is divided into several sections, the first of which examines several underlying concepts that are essential for the understanding of RS EPR. This block is followed by the Instrumentation section which describes the special aspects of the RS EPR hardware designs with the focus on the magnetic field scan EPR. Summary and Future directions is in the last section of this book chapter.

2

Underlying concepts

2.1 Linear time-invariant system Linear system approximation is used to model a wide variety of systems in mathematics, physics, engineering, and other branches of science and technology. Let us consider an example that is close to the field of 190 | Electron Paramag. Reson., 2021, 27, 188–213

magnetic resonance, a low noise amplifier (LNA). The purpose of the amplifier is to increase the output voltage y(t) of the input signal x(t) by a factor of Gain, y(t) ¼ Gain * x(t). Ideally, the amplifier works in the regime where Gain does not depend on x(t). Signals of arbitrary shapes are equally amplified with the same gain. It is also expected from an LNA that if the input signal is delayed by the time t, the amplifier would produce the output that is also delayed by t, y(t þ t) ¼ Gain * x(t þ t). Such an amplifier behaves as a linear time-invariant system (LTI). Any LTI system is uniquely characterized by its impulse response function h(t). To experimentally find this function, x(t) in the form of the shortest possible pulse has to be applied to the system. The system output then becomes an experimental approximation of the impulse response function, y(t)Dh(t). The shorter the pulse, the more accurate h(t) measurement becomes. In reality, the LTI approximation is not always valid. For example, LNA deviates from the linear behavior when the input signal exceeds a certain power level. The result is amplifier saturation and distortion of the output signal. The linear system approximation approach can be applied to EPR. The electron spin system can be described as LTI under the condition of low excitation power. In this case, the free induction decay (FID) signal observed after a short pulse becomes h(t). For relatively small magnetization turning angles, doubling the pulse amplitude would double the FID intensity without changing its temporal shape. Similar to the amplifier example, the spin system can be saturated by the use of excessive power. In this case, such a system cannot be modeled as an LTI anymore. Let’s consider a single line 1/2 spin system. A short low-power excitation pulse is applied to the system at resonance conditions. Let’s also assume that the resonator quality factor, Q, is relatively low so that the entire EPR spectrum is excited by the pulse. In this case, the spin system response becomes the impulse response function of the spin system h(t) ¼ FID(t). Fourier transformation of FID(t) gives the EPR spectrum in the frequency domain: EPR(o) ¼ FT{FID(t)}

(2)

It follows from the LTI theory that output y(t) is the convolution of the input x(t) and the impulse response function FID(t). y(t) ¼ x(t) # FID(t).

(3)

In eqn (3) x(t) is an arbitrary time-dependent function, which is commonly denoted as B1(t) in EPR textbooks. Using the property of Fourier transformation with the respect to convolution of two functions, y(t) in eqn (3) can be transformed into the frequency domain Y(o) ¼ X(o)EPR(o)

(4)

It follows from eqn (4) that in the linear response regime, the EPR spectrum can be obtained using deconvolution: EPR(o) ¼ Y(o)/X(o)

(5)

Electron Paramag. Reson., 2021, 27, 188–213 | 191

In eqn (4), Y(o) is the Fourier transform of the experimentally measured signal y(t), which is the spin system response to x(t) excitation. X(o) is the frequency domain representation of the alternating magnetic field B1(t). In practice, eqn (5) can be used to compute EPR spectra provided that: LTI model is valid

(5.1)

The external magnetic field is not changing, Bz(t) ¼ B0 ¼ const (5.2) Denominator |X(o)| ¼ |FT {B1(t)}|40 does not have zeros. (5.3) The first two conditions are rather straightforward. The third requirement imposes restrictions on B1(t). One-directional frequency sweep,23,24 and polyphase sequences, such as the Frank sequence25 are examples of the excitation functions that do not cause the division by zero problems. The field-scan continuous-wave RS EPR experiment does not satisfy the second and third conditions. The external magnetic field Bz(t) is not constant. The third condition is violated as well. RS EPR is a CW method. In the frame of reference associated with the excitation frequency, B1(t) is a constant. Fourier transformation of a constant is dfunction. Division by d-function in eqn (5) would not produce any meaningful results. Yet, the LTI model can be used to reconstruct EPR spectra from RS signals using eqn (5). The enabling deconvolution strategy is the numeric transformation into a new reference frame. Experimentally, the signal is measured in the frame associated with the excitation source, so that B1(t) ¼ const, and the magnetic field is changing Bz(t)aconst. Transformation of the signal into a frame associated with the scan field Bz(t) solves both the second and third conditions for eqn (5) simultaneously. The result of the transformation is B1(t)aconst and Bz(t) ¼ const. This signal modification is equivalent to a change from the magnetic scan experiment to the frequency scan experiment. The reference frame transformation permits the use of the deconvolution procedure in eqn (5) since all three conditions are satisfied. A detailed analysis of this transformation will be provided in the following section. 2.2 Signal–Spectrum transformation A paper titled ‘General Solution for Rapid Scan EPR Deconvolution Problem’ was recently accepted to the Journal of Magnetic Resonance6 that describes a general approach to the problem of RS EPR deconvolution. This paper also mathematically justifies the reference frame transformation introduced in the preceding section. Starting from the Bloch equations, the following expression was derived that can be used to deconvolve EPR spectra from RS signals: FT{rs(t)F*(t)} ¼ –o1EPR(o)FT{F*(t)mz(t)} 192 | Electron Paramag. Reson., 2021, 27, 188–213

(6)

that mathematically relates a power-normalized slow-scan EPR(o) lineshape and the quadrature rapid scan EPR signal: rs(t) ¼ mx(t) þ i my (t),

(7)

where mx(t) and my(t) are the transverse components of spin magnetization, and mz(t) is the longitudinal magnetization component. CW excitation with o1 ¼ |ge | B1 was assumed for the derivation of eqn (6). This equation is valid for an arbitrary magnetic field scan Bz(t) included in the complex conjugate of the phase transformation function F(t):6 Ð F*(t) ¼ exp{ ij(t)}, j(t) ¼ |ge | t0Bz(t)dt. (8) It follows from eqn (6) that the LTI spin system approximation can be used when mz(t) does not significantly vary over time and can be substituted by a constant. It is convenient to define this constant as: Ð mz(t) Domz(t) 4¼ 1/P P0mz(t)dt, (9) whereomz(t)4is the average of longitudinal magnetization over the time of measurement. As a result, eqn (6) can be simplified to a form FT{rs(t)F*(t)} ¼  o1EPR(o)omz(t)4FT{F*(t)}

(10)

that permits reconstruction of the EPR spectrum from the RS signal rs(t) in two steps. The first step is the transformation of the experimentally measured signal: e ¼ rsðtÞF*ðtÞ rsðtÞ

(11)

into a frame of reference associated with the Larmor frequency of the spins. This transformation is equivalent to changing the magnetic field scan experiment to that where the frequency is scanned. If we do not take into account the engineering aspects, the scanning field through resonance using CW excitation and scanning frequency through resonance at constant B0 are analogous experiments. These two types of measurements are equivalent from the standpoint of the acquired information. These two measurements are analogous in the same way as a perfect FID signal is equivalent to a corresponding slow-scan EPR spectrum. One is transformed into another by the means of Fourier transformation. The shape is different, but the information is the same. The use of eqn (11) leads to a transformation of the magnetic field e waveform Bz(t) into B1(t). Also, rsðtÞ becomes the signal that would have been measured in the frequency scan experiment. The second and the final step in the signal processing is deconvolution: e EPRðoÞ / FTfrsðtÞg=FTfF*ðtÞg

(12)

The proportionally sign in eqn (12) is used to indicate that in practice it is quite difficult to accurately take into account the multitude of factors that affect the signal intensity. These factors include but are not limited to resonator type and Q-factor, sample, all gain and loss stages along the signal path to the digitizer. The transformation of RS signals into EPR Electron Paramag. Reson., 2021, 27, 188–213 | 193

spectra using eqn (11) and (12) has been demonstrated with a wide range of nitroxides, trityls, and other radicals that have both resolved and unresolved hyperfine structures. The EPR spectrum intensity is proportional to the amplitude of the excitation field B1 ¼ o1/g. The users of the standard first-harmonic CW EPR spectrometers know this fact well. The derivative line intensity improves linearly with B1 until the spin system becomes power saturated. The EPR lines broaden and its intensity tends to decrease. In the standard CW(1) experiment, the excitation energy delivered to the spin system is evenly distributed throughout the spectrum as the magnetic field slowly sweeps across the EPR line at a constant rate. This is not always the case for RS EPR. Except for the linear scan, the scan rate varies with time. For example, the sinusoidal waveform has its highest rate in the middle point of the scan. The scan rate is zero at the waveform extrema. In the general case of an arbitrary magnetic field waveform, different spin packets experience different scan rates. Faster transition through the resonance conditions means less time for the spins to interact with the excitation field. The result is a smaller turning angle of the magnetization vector, and a weaker EPR signal. The reverse is also true. Relatively slower scan (in rapid-scan regime) should produce a stronger spin system response, provided the system is not power saturated. However, regardless of the location within the scan, eqn (11–12) accurately reconstruct EPR line intensities in the reconstructed spectra. The mathematics in the equation works in a way that effectively normalizes intensities to the instantaneous scan rates. The flip side of such normalization is that the noise levels in the reconstructed spectra become scan dependent. Two separate lines of equal intensity may have different signal-to-noise ratios, SNR, as a result. 2.3 Steady-state solution for RS EPR The use of periodic magnetic field scans is essential for RS EPR. It permits maximizing SNR of EPR spectra by the means of signal averaging. The period of the scan can be optimized with respect to the spin relaxation times to achieve the highest possible repetition rate. RS signal must be averaged, preferably with no or little overhead time. Modern FPGA-based digitizers can perform this task at very high, up to several giga-samples per second, sampling rates. The goal of this section is to concisely summarize the theory of periodic signals and to show how this theory applies to RS EPR. Any periodic perturbation to a physical system causes a periodic response. For an LTI spin system this general statement can be expressed as follows: y(t þ P) ¼ x(t þ P) # FID(t),

(13)

where P is the period. Any periodic signal is known to have a discrete spectrum: P ikost x(t) ¼ N , (14) k ¼ NXke y(t) ¼

PN

k ¼ NYke

194 | Electron Paramag. Reson., 2021, 27, 188–213

ikost

,

(15)

os ¼ 2p/P.

(16)

In eqn (14–15), Xk and Yk are discrete Fourier coefficients. The RS signal driven by a magnetic field scan Bz(t) ¼ Bz(t þP) becomes periodic, and the EPR spectrum deconvolved from this signal is discrete: EPR(ok) ¼ Yk/Xk, ok ¼ kos,

(17)

Yk ¼ FT{rs(t)F*(t)},

(18)

Xk ¼ FT{F*(t)}.

(19)

RS signal ‘resets’ every period, rs(t) ¼ rs(t þP). As a result, it is impossible to measure the impulse response of the spin system, FID(t), that is longer than P. FID(t) must completely decay to zero within one scan period: P ¼ 2p = os 4 5T2* ;

(20)

where T2* the effective transverse relaxation time. If this condition does not hold, the FID signal gets truncated, and the EPR spectrum becomes distorted. Related to the eqn (20) constrain is the fact that the EPR signal is sampled in the frequency domain with the increment equal to os (see eqn (16)). It is not possible to increase the number of points per EPR spectrum experimentally unless a different scan frequency is used to inter-sample the spectrum. After the periodic magnetic field scan is turned on, the spin system comes to a dynamic steady-state equilibrium within the characteristic relaxation times independent of the initial condition. For spin 1/2 system, numerical integration of the Bloch equations can be used to demonstrate this phenomenon. Fig. 1 shows how the transverse mx(t) and

Fig. 1 Numerical solution of the Bloch equations that converges to a dynamic equilibrium. (a) RS signal mx(t) and my(t) normalized to the equilibrium magnetization M0. (b) magnetization component mz(t) normalized to M0. Computational parameters for the spin system were T1 ¼ 100 ms and T2 ¼ 10 ms. Magnetic field scan waveform Bz(t) ¼ 1/2 Bpp cos (2pfst), where fs ¼ 30 kHz and Bpp ¼ 1G. The CW excitation field amplitude was B1 ¼ 15 mG. Electron Paramag. Reson., 2021, 27, 188–213 | 195

my(t) components of the magnetization vector come to the equilibrium with T2 ¼ 10 ms, while the longitudinal mz component reaches steadystate with the characteristic spin–lattice relaxation time T1 ¼ 100 ms. The steady-state solution of the Bloch equations can be found directly26 without solving the differential equations. Using the periodicity condition, the Bloch equations can be transformed into a system of linear equations, that can be numerically solved in a computationally efficient way. A MATLAB function is available in EasySpin (http://www.easyspin.org) that finds the steady-state solution using the user’s input parameters. The LTI approximation simplifies the system of Bloch equations by assuming a small variation of mz(t) during the field scan. In this case, an analytical steady-state solution can be derived for an arbitrary-periodic magnetic field scan function. Eqn (11) and (12) can be used to transform RS signals into EPR spectra. 2.4 Signal to noise enhancement Averaging periodic signals helps to reduce or eliminate the overhead time during which the RS signal is not measured. Signal intensity grows proportionally to the number of averages Naver, and noise levels increase as the square root of Naver. As a result, SNR /

pffiffiffiffiffiffiffiffiffiffi Naver :

It is tempting to suggest that RS EPR sensitivity can be improved by increasing the scan frequency (decreasing period P) so that a larger number of signals can be averaged per unit time. Unfortunately, Nature prohibits such a simple solution for increasing SNR. Users of CW(1) instruments may have observed that decreasing sweep time in combination with averaging does not improve the final result if the total experimental time is constant. EPR spectra acquired in a shorter time are nosier than those measured using a longer sweep. The summation of noisier spectra gives the same net SNR gain. In the case of the rapid-scan regime, the situation is not as straightforward, but the time-defines-SNR concept is still true. Faster passage through resonance reduces the time during which the spin system interacts with B1. In the reference frame associated with the scanning field (see the Signal – spectrum transformation section), the spins experience a short-pulsed excitation, which is often called a chirp pulse in the magnetic resonance literature.27 A faster scan means a shorter pulse and a smaller turning angle for the magnetization vector. The result is a weaker EPR signal. As in the case of CW(1), the increased number of averages compensates for the loss in the signal intensity, so that the net SNR gain remains the same. It is important to note that this logic applies only if the noise is white, which is often the case for CW(1). The white noise assumption does not apply to RS EPR that uses broadband detection. The role of the noise spectrum will be discussed in the following sections. Yet, SNR can be enhanced by maximizing the scan frequency, but for a reason different from signal averaging. At higher scan rates, rapid 196 | Electron Paramag. Reson., 2021, 27, 188–213

passage rescues the spin system from saturation. LTI model remains valid at higher excitation field strength. In the linear response regime, the signal intensity is proportional to B1. Enhanced signal directly translates into an SNR gain, provided that the noise is powerindependent. In reality, the frequency source may contribute to the noise level and somewhat diminish the RS EPR sensitivity improvement. Fig. 2 illustrates the signal enhancement effect using the results of numerical computations. Common for RS EPR, the sinusoidal magnetic field waveform was used to compute the steady-state magnetization vector components (see Section 2.3 for details). Three sets of RS simulations are compared, in which only two parameters were varied: the scan frequency fs ¼ 1/P and excitation field B1. The green traces in the figure correspond to the linear response condition for the spin system, B1 ¼ 6 mG, and fs ¼ 2 kHz. Blue-colored signals and spectra correspond to the power-saturation conditions. B1 was increased by a factor of 10 (from 6 mG to 60 mG). The result was a larger turning angle for the magnetization vector (mz(t) in Fig. 2a), linewidth broadening, and reduction in intensity. Note that in Fig. 2b the spectra are normalized to B1, and in Fig. 2c they normalized to the peak intensities. Increasing the scan frequency by a factor of 10 (from 2 kHz to 20 kHz), returns the spin system into the linear response regime. As a result, an accurate spectral shape of the EPR spectrum is reconstructed. In full accordance with eqn (10), the spectral intensity becomes proportional to the averaged over period longitudinal magnetization, which is approximately equal to 0.75 in the units of M0 (see Fig. 2a, red trace). The total signal gain between the red and green spectra is approximately seven.

Fig. 2 Computational results for the steady-state solution of the Bloch equations. Magnetic field scan was used with the peak-to-peak amplitude, Bpp ¼ 5G. Transverse and longitudinal relaxation times were T1 ¼ 10 ms and T2 ¼ 1 ms, respectively. The inhomogeneous envelope had Gaussian shape with the full width at the half magnitude, GLFWHM ¼ 0.2 G. Two parameters were varied in the computations: scan frequency fs and B1. Three combinations of these parameters were used: {B1 ¼ 6 mG, fs ¼ 2 kHz}, {B1 ¼ 60 mG fs ¼ 2 kHz}, and {B1 ¼ 60 mG, fs ¼ 20 kHz} for the green, blue and red traces, respectively. (a) mz components; (b) Deconvolved EPR spectra normalized to B1; (c) Deconvolved EPR spectra normalized to their peak intensity. Electron Paramag. Reson., 2021, 27, 188–213 | 197

Fig. 3 Comparison of CW(1) and RS EPR signal responses to magnetic field modulation.

Besides the rapid passage enhancement effect, there is an additional signal gain factor that is attributed to the direct detection of the EPR signal. CW(1) detection requires that the field modulation amplitude is small compared to the linewidth. Fig. 3 demonstrates how this requirement results in an attenuated CW(1) signal in comparison with the fullscan full-amplitude response measured in the RS EPR signal. Theoretical limits for RS EPR sensitivity enhancement for a specific sample can be evaluated using EasySpin simulation and the equations provided in this and the previous sections. In practice, several hardwarerelated factors need to be taken into account, such as the resonator type and quality factor, source frequency and noise specifications, background signal, sample heating, etc. These factors will be examined in the next sections. 2.5 Noise spectrum and averaging of periodic signals Signal periodicity does not only have implications for the RS signal but also for noise. Averaging of a periodic signal in the time-domain is equivalent to applying a comb filter in the frequency domain, f ¼ o/2p:28 Hðf Þ ¼

sinðp Naver f =fs Þ ; fs ¼ 1=P Naver sinðpf =fs Þ

(22)

It is important to note that eqn (22) is valid only for continuous uninterrupted signal averaging. To demonstrate the connection between signal averaging and the comb shape of H(f) (see Fig. 4), let’s consider a sinusoidal signal of frequency fs. The amplitude and phase of this signal need to be measured in the presence of white noise. This is a very common engineering problem that is often solved by using phasesensitive detections at fs. The noise spectrum spreads over all frequencies, including fs and its harmonics. The measuring instrument cannot distinguish the signal from the noise at Kfs, where K is an integer. As a result of averaging, the frequencies close at Kfs will be attenuated less compared to those further from Kfs. Fig. 4a and b shows H(f) function (blue traces) for Naver ¼ 50 and Naver ¼ 200, respectively. As the number of averages increases, the combs in the filter become sharper. The noise components that deviate in the frequency domain from fs and its harmonics are suppressed stronger. If the signal is not truly periodic and/or there is a time interruption between the averaging events, the logic of frequency-selective noise 198 | Electron Paramag. Reson., 2021, 27, 188–213

Electron Paramag. Reson., 2021, 27, 188–213 | 199

Fig. 4 Phase noise spectrum (red traces) produced by a standard frequency source (ROS-1015-119 þ , Minicircuits, NY USA) compared with H(f) in eqn (22) and Fourier transform of the RS signal. The scan frequency was fs ¼ 100 kHz for all graphs. (a) H(f) was computed using eqn (22) with Naver ¼ 50. (b) H(f) was computed using eqn (22) with Naver ¼ 200. (c) RS signal was computed using the following parameters: Transverse and longitudinal relaxation times were T1 ¼ 1 ms and T2 ¼ 1 ms, respectfully. The inhomogeneous envelope had Gaussian shape with the full width at the half magnitude, GLFWHM ¼ 50 mG. The amplitude of the CW excitation field was B1 ¼ 1mG. Magnetic field scan was sinusoidal with the peak-to-peak amplitude, Bpp ¼ 4G. The time-domain RS signal was Fourier-transformed, and the absolute value of the result (blue square-shaped symbols) plotted in (c).

suppression does not apply. Averaging of CW(1) EPR spectra in commercial EPR instruments is a good example. In this case, noise is equally reduced with respect to signal across the relevant signal bandwidth. If the noise is white, synchronous versus interrupted averaging does not affect the final SNR as far as the total averaging time is the same. In many experimental situations, including RS EPR, the noise is not white. In this case, understanding the concept of periodic averaging and its implications for RS EPR becomes important for SNR maximization. Fig. 4 (red traces, right-side y-axis) shows the phase noise spectrum of a standard voltage-controlled oscillator (ROS-1015-119 þ , Minicircuits, NY USA). The noise spectrum is compared with the RS signal in the frequency domain. Fig. 4c shows RS EPR signal (blue dots) spread much wider compared to the frequency range of the noise. Most of the signal energy is in the area where there is very little source noise. This situation is very favorable for the RS EPR in terms of phase noise suppression. Fig. 4 also illustrates the reason for using magnetic field modulation in CW(1). There is substantially less noise power at 100 kHz (f/fs ¼ 1) compared to that at the carrier frequency (f / fs ¼ 0). 2.6 Periodic background The users, and especially developers, of EPR, are familiar with the ‘hand-waving’ effect. This term describes a situation when the movement of an object in the vicinity of a resonator affects its impedance, and therefore coupling to the transmission line. The weak interaction between the radiofrequency (RF) and a distant object may be strong in comparison with the impedance changes induced by the spin system. Not every movement will be problematic for RS EPR. As we discussed in the previous section, any non-EPR signal that is not synchronous with the scan frequency is very efficiently suppressed by signal averaging. The major source of the background signal observed in RS EPR is the scan itself. Scan coils placed in the magnet play an unintended role of speakers. A working RS system often produces an annoying sound that can be heard by the human ear if the scan frequency is within the acoustic range. This sound causes vibration of the resonator, the sample, and the environment. As a result, the resonator tuning and coupling get modulated,29,30 and a periodic signal is observed in the signal channel. This phenomenon, which is observed in electronic devices, is called the microphonic effect. The users of CW(1) EPR may observe this phenomenon by doing a very wide magnetic field sweep starting from zero. As the magnetic field strength increases, so does the interaction of the field with the modulation coils. The microphonic signal, which becomes stronger with the increased field strength, contributes to the DC offset in the spectrum. As a result, a rising baseline slope can be observed. There are two standard approaches to the microphonic problem: hardware and software. First, as an engineer you do your best to suppress it in the design, for example by using an RF (MW) shield and/or avoiding 200 | Electron Paramag. Reson., 2021, 27, 188–213

mechanical resonances at the frequencies of interest. However, as RS EPR pushes sensitivity boundaries, there will always be a periodic background signal that is comparable to the spin system response signal in intensity. Unfortunately, the periodic microphonic signal cannot be removed by signal averaging because it has the same fs fundamental frequency. Several strategies have been developed to remove the residual background signal.30–32 They are based on five assumptions: 1. The microphonic effect is magnetic field dependent. For this reason, off-resonance subtraction that requires a substantial change in the external magnetic field may not work. Also, this approach lengthens the acquisition time by measuring EPR-free signals. 2. Small changes in the magnetic field (field step) do not significantly affect the background. There is no additional data acquisition overhead. Two RS signals are measured that are offset one with respect to the other, and the background signal remains unchanged. 3. The reversal of the direction of the external magnetic field (absolute value does not change) changes the sign of the Larmor frequency precession but does not affect the background signal. 4. Periodic background can be limited to a limited number of fs harmonics. High order harmonics are substantially weaker and can be neglected. This is especially true if the sinusoidal waveform is used. 5. Up-scan and down-scan EPR signals can be separated in the frequency domain. Resonance conditions occur twice during the scan period: when the magnetic field is increasing, dBz(t)/dt40, and when it is decreasing, dBz(t)/dto0. In the increasing case, the Larmor frequency increases after passing the resonance conditions. In dBz(t)/dto0 case, it is decreasing. As a result, the two corresponding RS EPR signals can be separated in the frequency domain by the means of Fourier transformation. 2.7 Rapid scan waveform selection Two approaches, hardware, and software were discussed in the previous section in the context of the background problem. These two sides of any novel experimental design have to be taken into consideration. The selection of the optimum magnetic field scan function is not an exception. 2.7.1 Hardware considerations. To date, two types of magnetic scan waveforms have been used: linear (triangular) and sinusoidal. Our recent paper6 makes it possible to use an arbitrary scan function, Bz(t), in RS EPR experiments. However, it does not mean that any function will be practical from the engineering and data-processing standpoints. Two major hardware-related challenges can be distinguished. First is the engineering problem of generating wide and fast magnetic field scans. If an efficient high inductance coil is used, it would resist any change in the current flowing through this coil. The scan coil inductance, L, can be compensated with a capacitor, C, to zero the reactive Electron Paramag. Reson., 2021, 27, 188–213 | 201

impedance of the LC assembly. The coil resonated at a specified frequency fs (eqn (23)) can now generate wide and fast magnetic scans.33 fs ¼

1 pffiffiffiffiffiffi ; 2p LC

(23)

However, this approach limits the choice of Bz(t) function to a single frequency waveform: Bz(t) ¼ 0.5 Bpp sin (2pfst)

(24)

This sinusoidal waveform may not always be optimum from the SNR optimization standpoint. The scan width Bpp is analogous to the sweep width in CW(1) and is selected to cover the entire EPR line. Increasing Bpp beyond the needed range for the purpose of increasing the scan rate does not improve SNR. Increasing the scan frequency does improve EPR sensitivity (see Section 2.4). However, the maximum scan rate becomes a function of fs, and therefore constrained by the requirement in eqn (25): ratemax ¼ pfs Bpp o

pBpp ; 5T2*

(25)

To achieve higher rates, a non-sinusoidal waveform has to be used. A trapezoid would be a good example of a function that decouples the scan frequency and the scan rate. However, the practical implementation of such a waveform would require the use of a low inductance coil. It is possible to partially compensate for the lack of coil efficiency with the use of a high-current power supply, such as one of the FAST-PS-1K5 series manufactured by CAEN ELS (Italy). Currents up to 100 A can be generated. 2.7.2 Algorithmic considerations. Eqn (11–12) permit the use of an arbitrary magnetic field scan, Bz(t), provided that the absolute value of the denominator Xk does not approach zero (see eqn (5.3)): |Xk |4e ~ Xaver ¼ o|Xk |4, 8k.

(26)

In eqn (26), e is a positive threshold parameter that is comparable to the average of |Xk |. If it is small relative to Xaver, the deconvolution problem may become ill-posed. Fig. 5 illustrates the origin of illposedness in RS EPR deconvolution. A truncated triangular waveform Bz(t) was chosen for the demonstration purposes. This function is represented by the frequency units in Fig. 5a: f ðtÞ ¼

g Bz ðtÞ: 2p

(27)

Function f(t) ramps up from 0 to 6 MHz and then ramps down from 6 to 3 MHz. The corresponding phase transformation function F(t) is shown in Fig. 5b. In this plot, the frequency of oscillations in any given moment of time t is equal to f(t). Two frequency regions can be examined:  R1: 0 MHzo f(t) o 3 MHz  R2: 3 MHzo f(t) o 6 MHz 202 | Electron Paramag. Reson., 2021, 27, 188–213

Fig. 5 Computational demonstration of ill- and well-posedness in RS EPR deconvolution. (a) Magnetic field waveform expressed in the linear frequency units. (b) Imaginary part of the phase transformation function; (c) The absolute value of X(f).

In the R1 region, f(t) is monotonic. There is only one instance t that corresponds to a given f(t) value. It can be seen in Fig. 5c that |X(f)| is overall flat in this region. This is because this function is inversely proportional to the rate of frequency change dfs(t)/dt, which is constant in R1. The longer the waveform dwells at t, the larger the f(t) contribution into X(f). In the R2 region, f(t) is not monotonic. It passes through the same frequency twice. |X(f)| in this region shows an oscillatory behavior. This pattern is the result of interference between two frequency contributions that occur at different time instances t1 and t2. Fourier transformation adds these two contributions together causing the oscillatory behavior. The relative phase of F(t) between t1 and t2 moments is equal to: ð t2 dj ¼ ðt1 ; t2 Þ ¼ g

Bz ðtÞdt; f ðt1 Þ ¼ f ðt2 Þ: t1

When dj approaches 0, a constructive interface takes place. When dj is close to p, the two contributions corresponding to t1 and t2 instances cancel each other out. In this case, |X(f)| approaches zero (see f ¼ 5.43 MHz) as an example. The deconvolution problem is well-posed in R1, and the EPR spectrum can be reliably reconstructed from the corresponding RS signal. Recovery of the EPR spectrum from RS signal in R2 is a challenging task for two reasons. The first reason is noise amplification due to the division by small value. For example, the EPR spectrum in the vicinity of f ¼5.43 MHz may be strongly corrupted by noise. The second reason is that the RS EPR signal itself may demonstrate the oscillatory behavior. Division of two oscillating functions, one of which is experimental and the other is theoretical may be problematic. A small inaccuracy in the scan amplitude Electron Paramag. Reson., 2021, 27, 188–213 | 203

calibration will affect phase in eqn (8) and cause the EPR spectrum distortion. It can be concluded therefore that the deconvolution problem is ill-posed in the region R2. Any periodic function f(t) must pass through the same ordinate value at least twice per period. It follows from this statement that the RS deconvolution procedure must be ill-posed for any magnetic field waveform. As a result, the transformation of RS signals into EPR spectra becomes basically impossible. And yet, RS EPR methodology has been successfully used and passed numerous verification tests. The algorithms have been developed that very reliably reconstruct EPR spectra. The mathematical trick used in these algorithms is a substitution of the experimental waveform with a monotonic function that only coincides with the experimental one in the region of interest. For example, a triangular function can be mathematically replaced by two perfect saw-tooth functions for up- and down-scan, respectively. This substitution will be valid only if the RS signal measured during the up-field scan can be clearly separated from the RS signal measured during the down-field scan. Each of these signals is deconvoluted using the corresponding ramp-up and ramp-down saw-tooth functions. The R2 region problem becomes two independent R1-like problems, each of which is well-posed. The immediate restriction imposed by such a mathematical trick is the requirement that each up- and down-scan RS signal must completely decay within each half-scan. First RS EPR experiments were done using periodic triangular magnetic field waveforms because the deconvolution problem was initially solved for a linear scan.32,34–36 The deconvolution problem was later found for the non-linear sinusoidal waveform.1,8,30 In this case (see discussion above), the scan coil can be resonated at the frequency of interest using capacitors. The new algorithmic approach to non-linear magnetic field scans permitted a substantial increase in the scan rate. As was discussed above, the rate increase can be translated into an SNR enhancement (see Section 2.4). Scan frequency up to 1 MHz has been used37 in RS EPR experiments with the scan rate of 60 MG s1. Similar to the triangular scan case, up- and down-scan signals are separated in the sinusoidal deconvolution algorithm. This algorithm requires that each half-scan RS signal decays before it reaches the turning point where the magnetic field changes its direction. This requirement was relaxed later when a full-scan algorithm was developed.7 It was demonstrated that the ill-posedness of the deconvolution procedure can be avoided if the fullscan model is used for the signal and the half-scan model for the excitation term B1(t) after reference frame transformation using eqn (11). Waveforms intermediate between the ‘perfect’ linear and sinusoidal may be of practical use. For example, a smoothed trapezoid function will permit decoupling between the scan rate and scan frequency.

3

Instrumentation

The goal of this section is to give a big-picture introduction to the current instrumental designs and the experimental problems they address. 204 | Electron Paramag. Reson., 2021, 27, 188–213

A detailed description of specific hardware solutions can be found in the cited references.

3.1 Radiofrequency systems Continuous-wave excitation is narrowband by definition. The CW(1) method measures the signal (sometimes complex) centered around fs in the frame of reference associated with the source frequency. The bandwidth of this signal, which is defined by the sweep rate and filter parameters, is quite narrow (see combs at f/fs ¼ 1 in Fig. 4). As a result, both the excitation and detection in CW(1) are narrowband. In pulsed EPR, the broadband excitation is combined with broadband detection. Quadrature signal containing mx(t) and my(t) components is measured. RS EPR occupies a niche somewhat in-between the CW(1) and pulsed methods. It combines narrowband excitation (like in CW(1)) and broadband quadrature detection (as in pulsed EPR). There is no dead-time. However, the power saturation of the detector may become a problem. It was discussed in the preceding parts of this chapter that RS signal intensity can be maximized by the concurrent use of: (i) the fastest possible scan frequency and (ii) the highest spin excitation power within the LTI constraint. In reality, the theoretical sensitivity limit may not always be reached. The use of high excitation powers worsens the problem inherent in any CW method: detection of weak spin signals in the presence of strong excitation. Two approaches to EPR resonator designs have been used to solve the problem of detection/excitation isolation. The first is a single-mode reflection resonator. In this approach, the separation is achieved by critical coupling, CC, of the resonated circuit to 50 Ohms transmission line. At CC conditions, little incident power is reflected from the resonator. EPR upsets the impedance balance causing reflection that is detected as the spin system response. The higher the incident power, the more challenging it becomes to protect the detector from power saturation. The second approach is the bi-modal resonator,5,38–42 in which both modes are tuned to the same frequency. In this design, the excitation and detection are physically decoupled as two orthogonal resonance circuits. Neither reflection nor bi-modal approaches are perfect. Even for a very carefully tuned system, small changes in the sample-loaded resonator and/or environment may upset the balance and cause detector saturation and/or increase in the noise level. The problem of detection/excitation isolation is exacerbated in RS EPR in comparison with the standard CW(1) method that uses low excitation powers. Both the reflected and transmitted powers are proportional to the incident power. The latter has to be higher in RS EPR to enhance SNR. Ideally, real-time feedback controls have to be used for the resonator tuning, matching, and isolation (for a bimodal system). Some progress has been made in this direction. For example, field-programmable gate array (FPGA) technology was recently used for continuous resonator tuning and coupling.2 An alternative timediscrete method for automatic frequency correction was proposed as well.1 Both approaches permit the detections of both quadrature signal components, which is essential for RS EPR data processing (see Section 2). Electron Paramag. Reson., 2021, 27, 188–213 | 205

Several dedicated continuous-wave RS EPR systems have been designed and built in Denver, West Virginia, and Osaka universities. Analog, semi-digital, and fully digital approaches to generate the source frequency and to detect RS signals have been explored. Digital control over the excitation frequency provides a higher degree of flexibility and accuracy compared to the analog-controlled sources. Importantly, it also enables new RS experimental designs, such as the near-baseband quadrature detection method.43 Several commercial digital frequency sources are now available that have low phase noise, permit small frequency increments, and fast switching time. The excitation signal can also be generated by the frequency mixing of a low-noise fixed source with an arbitrary waveform generator.1 This approach gives more flexibility, for example, due to fast switching between the tuning and operational modes. It could also be a less expensive option compared to the fully digital system.43 RS signal can be downconverted to the baseband frequency and measured using two separate I and Q quadrature channels. Imperfections in phase shifters and/or gain introduce a nonorthogonality between the channels that may negatively affect RS data processing if not software-corrected.30 Direct detection at the carrier frequency solves this problem.43 Separation of I and Q components, in this case, is done numerically. However, this method requires perfect suppression of the reflected or transmitted excitation power that may overwhelm the video amplifier and/or digitizer. The baseband detection eliminates this CW contribution very effectively. A near-baseband detection method was proposed43 to produce a perfect quadrature signal and, at the same time, eliminate the unwanted RF ‘leakage’ signal. 3.2 Comparison of reflection and bi-modal resonators Reflection types of resonators are more common because they are relatively simple from the standpoint of design and control. The adjustment of a single matching parameter is sufficient for achieving critical coupling (CC) of the resonator to the 50 Ohms transmission line. At CC frequency, which is often called the resonance frequency, the reflection is minimum. Depending on the excitation power and LNA gain, the reflection levels measured as the scattering parameter, S11, in the range from 50 dB to 30 dB are usually acceptable. If a tunable frequency source is used, it can be easily tuned to the frequency of CC. In the case of a fixed-frequency source, a tuning control (often a trimmer capacitor) can be added to the resonator design. At CC conditions, EPR signals can be amplified (20–40 dB gain) and measured without saturating the first stage low-noise amplifier (LNA). Using a critically coupled resonator in the reflection mode solves the signal saturation problem. There is also a noise part that needs to be examined. The critical coupling can be achieved only of a single frequency, deviation from which causes reflection. The intensity of reflection depends on the resonator quality factor Q. The larger the offset, the stronger the reflection levels are. Even if the fundamental frequency of the source is perfectly adjusted to eliminate reflection, spurious and 206 | Electron Paramag. Reson., 2021, 27, 188–213

noise components are always generated by a non-ideal oscillator. No source is perfect; however, some are better than the others. Fig. 4 demonstrates the phase noise spectrum of a Minicircuits ROS-1015-119 þ source. The noise power drops with the frequency offset but the levels are still significant within the MHz range. In this frequency range, there is no CC. As a result, the noise gets reflected. Larger off-resonance offsets and higher Q values result in stronger refection. For this reason, it becomes important to use low phase noise frequency sources for RS EPR detection in the reflection mode. Fig. 6 illustrates the noise reflection concept. The source frequency, f0, is denoted as a red arrow is surrounded by small blue arrows indicating noise. The arrow lengths do not reflect any actual noise spectrum values. The reflected noise pattern depends on the resonator bandwidth, BW: BW ¼ f0/Q.

(29)

The noise frequencies that are comparable to or larger than BW are affected the most. For this reason, the use of reflection resonators in CW(1) EPR is well justified. Usually, EPR signals are modulated at the frequency 100 kHz (or less), which is often small compared to the resonator BW. For example, consider an X-band spectrometer with a high Q ¼ 5000 cavity. Using eqn (29), BWD2 MHzc100 kHz. Interestingly, this mismatch between the signal and resonator bandwidths points to a largely under-optimized use of the detection system in CW(1). Pulsed and RS EPR are better-optimized experiments in this sense. The detection system bandwidth usually matches that of the measured RS signal. However, RS EPR as a CW method can be negatively affected by the reflected phase noise. There are two noise-related trends that counteract each other. On one hand, the source noise intensity is decreasing with the frequency offset (see Fig. 4). On the other hand, the reflection is intensified with the same offset. Given the limited phase noise range specified for modern high-end frequency synthesizers, RS signal bandwidth, BWRS, of 10 MHz or more may be sufficient to solve the noise reflection problem. BWRS can be estimated experimentally or by using

Fig. 6 (a) Illustration of reflected and transmitted noise concept in the case of a resonator critically coupled at f0. (b) Experimentally measured reflected noise. Electron Paramag. Reson., 2021, 27, 188–213 | 207

numerical simulations. The upper bandwidth limit for an arbitrary waveform can be calculated as: maxfBWRS g ¼ Df ¼

g Bpp ; Bpp ¼ maxfBz ðtÞg  minfBz ðtÞg: 2p

(30)

Df in eqn (30) is the full swing range of the Larmor frequency from the lowest to the highest value (or vice versa). Bi-modal design, two decoupled orthogonal resonators, solves the problem of phase noise very efficiently for two reasons. The first reason is that the purpose of the excitation mode is to deliver power to the sample not to detect EPR. The phase noise which is reflected to its source (see Fig. 6), does not add up to the measured signal. In fact, the excitation resonator works as a bandpass filter that cleans the source from noise. The higher the Q, the better is the filter. The second reason is the intermode decoupling. The transmitted noise is attenuated by the isolation factor that can be as good as 60 dB.41 An over-simplified concept of a bimodal design is illustrated in Fig. 7. This figure shows two orthogonal coils that represent two resonators. In the perfect theoretical world, these two coils are completely decoupled according to the Faraday’s induction law. If the radiofrequency (RF) power is applied to the red coil, the net magnetic field flux created by this coil through the detection (green) coil is zero. In this case, the S21 parameter (measures the inter-coil energy transmission) would be lower than the detection limit. If a paramagnetic sample is now placed in the middle of both coils, and the spin system is excited at f0, a transverse spin magnetization will be generated. If the detection loop is tuned to the same frequency f0, it will detect a noise-free

Fig. 7 Illustration of the bi-modal resonator concept. The excitation resonator (red loop, red bar) gives mode #1. The detection resonator (green loop, green bar) operates in mode #2. Both modes are resonated at the same frequency. The green and red loops are orthogonal, and therefore de-coupled. There is no direct energy transmission from #1 to #2. However, at the EPR conditions, the spin generated magnetization induces a detectable signal in the detection resonator. 208 | Electron Paramag. Reson., 2021, 27, 188–213

EPR signal. Neither RF carrier nor noise is transmitted from the red loop to the green loop in this case. In the not-so-perfect real world, some amount of the carrier and noise will be picked up by the detection coil. This amount, defined as isolation, is measured as the S21 parameter. The isolation is often adjusted by delicate mechanical positioning of the excitation and detection resonators to achieve mutual decoupling of the two. The result is a very efficient suppression of the phase noise. In comparison with the narrow-banded critically coupled reflection mode, the inter-mode isolation is broadband. Two modes of the bimodal resonator are decoupled within the bandwidth of interest. As a result of the decoupling, the transmitted noise power is additionally attenuated by the S21 value. Inter-mode isolation of 30 to 60 dB can be achieved, depending of the design and electric properties of the sample. An example of the resonator tuning patterns is shown in Fig. 8. This figure demonstrates a screenshot taken from the network analyzer that was used to fine-tune a bi-modal resonator, which was developed at West Virginia University for pre-clinical EPR imaging. In this figure, both the excitation (port 1) and detection (port 2) resonators are critically coupled at about 800 MHz. Isolation between the ports, S21, is approximately 50 dB at the resonance frequency but varies within the resonator bandwidth. In RS experiments, the noise is reduced twice: (i) bandpass filtering that depends on the Q-factor of the excitation mode; (ii) approximately 40 dB to 60 dB attenuation depending on the frequency. In comparison with the single-mode reflection design, bi-modal resonators are more complex both in terms of their construction and operation. Minimum of three independent controls are required: (i) frequency of either of the modes; (ii) coupling of the detection resonator; (iii) isolation adjustment. Ideally, the fourth coupling control for the excitation resonator has to be added to maximize the power delivered to the spins and filter noise. The major challenge in operating the bi-modal system is that in practice all of these parameters may be and often are

Fig. 8 Scattering parameters measured for the bi-modal RS EPR resonator at 800 MHz. (a) S11 (yellow), S22 (green), S21 (blue) logarithmic scale. (b) S11 (yellow), S22 (green) on a Smith Chart display. Isolation (S21) at the resonance frequency is approximately 50 dB. Both resonators (modes) are nearly critically coupled. Electron Paramag. Reson., 2021, 27, 188–213 | 209

interdependent to a degree. If the two modes are weakly coupled, tuning of one of the modes produces a change in the tuning pattern of the other mode. Several iterations may be required to achieve the desired tuning, coupling, and isolation. 3.3 Scan coils and driver The scan coils are an essential part of the RS spectrometer. Their purpose is to generate the magnetic field Bz(t). The selection of the coil design would depend on two factors: (i) the specific waveform (e.g., saw-tooth, triangular, sinusoidal), and (ii) the spectral width which defines the scan amplitude. These two factors may be inter-dependent. For example, a sinusoidal scan permits achieving the fastest and widest scan by the resonating a high-efficiency high-inductance coil with a capacitor or bank of capacitors.1,44 A perfect triangular waveform is impossible to generate since it has infinite bandwidth. However, a good practical approximation can be realized using a dedicated coil driver.45 The amplitude of the magnetic field scan is limited in this case due to the uncompensated inductive impedance. The general solution of the deconvolution problem6 permits the use of an intermediate smoothed triangular waveform that can be limited to the 3rd and 5th harmonics of the scan frequency. In this case, partial impedance compensation is possible to achieve a larger scan amplitude. The coil drivers for both linear and sinusoidal waveforms have been designed, manufactured, and successfully used in the University of Denver laboratory.17,44,45 These drivers tightly control the current flowing through the scan coils. An alternative approach was implemented at West Virginia University. A simple and inexpensive setup was used that consisted of a computer-controlled function generator and a standard 1.8 kW audio amplifier.1 In this approach, the input voltage generated by the function generator is controlled to achieve the desired current. A MATLAB routine continuously measures the current amplitude and phase and makes corrections to the input. In addition to low cost, this approach has an advantage for EPR imaging. During the data acquisition, the scan amplitude changes several times to adjust for the increasing spectral width. To reduce wasted experimental time, no corrections are made after switching the input to the audio amplifier. The actual values of the scan amplitude and phase are measured and used for data processing. These values may be slightly off the initial target due to amplifier nonlinearity. However, it is not important as far as the correct values are known and used in post-processing. Commercial CW(1) instruments may not be easily modified or upgraded to do RS EPR measurements. They do not usually permit quadrature detection. In addition, the detection bandwidth is very limited. However, an existing pulsed EPR system can be RS-upgraded relatively easily.10,46 The bridge can be used as-is. In principle, the existed system for field modulation can be utilized for very small samples and narrow EPR spectra. Homogeneity of the scan field across the sample becomes important for RS EPR. As a result, dedicated scan coils and coil driver are 210 | Electron Paramag. Reson., 2021, 27, 188–213

the essential upgrades. The coils & driver system can be relatively easily built using inexpensive commercial parts.1 If a real-time FPGA digitizer, such as Bruker’s SpecJet, is not available, it can be independently purchased. Several off-the-shelf options exist that can be integrated into the existed spectrometers. Software provided by the vendors can be used in this case to measure RS signals. Writing your own code or using thirdparty software, such as SpecMan4EPR by Femi Instruments, is also an option.

4 Summary and future directions Continuous-wave RS EPR as of today is a transient step in the evolution of CW spectroscopy. The standard CW(1) method may be considered as a first step. In this method, the problem of noisy sources was solved by using field-modulation and phase-sensitive detection. However, CW(1) operates in a sub-optimum regime both in terms of used power and the detector bandwidth. The development of multi-harmonic detection of overmodulated EPR spectra CW(N)16,17slightly improved sensitivity. CW(N) can be considered as a more general approach, for which CW(1) is a special single-harmonic case. This method has an advantage of measuring EPR spectra in the magnetic field range limited only by the magnet. The disadvantage of the algorithm used to reconstruct spectra from the multiple harmonics is that it is limited to the slow-scan regime (see eqn (1)). RS EPR algorithm works both in slow-scan and rapid-scan regimes but requires that the scan covers the entire EPR spectrum. This requirement limits RS EPR applications. A more inclusive approach needs to be developed, for which CW(N) and RS methods will be special cases. CW(N) algorithm needs to include the rapid passage conditions, or equally RS EPR should include a slow magnetic field sweep.

References 1

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High-frequency EPR: current state and perspectives ˇedivy´, Oleksii Laguta, Andriy Marko, Antonı´n Sojka, Matu ´ ˇs S Vinicius T. Santana and Petr Neugebauer* DOI: 10.1039/9781839162534-00214

Starting from its discovery, electron paramagnetic resonance (EPR) is a constantly developing technique following technological advances in generation and detection of microwaves, creation of strong magnetic fields, and fast digitalization, among others. In this chapter, we discuss developments in the field of high-frequency EPR (HFEPR) with a special focus on experiments in the frequency domain compared to the traditional field domain EPR. We present significant progress in the experimental determination of Zeeman diagrams (frequency vs. field EPR maps) and discuss the advantages of HFEPR for investigating high-spin systems, particularly single-molecular magnets (SMMs). Besides, we dedicate a section to discuss the advances in the studies of the cyclotron resonance in thin-films and modern solid-state materials like graphene (graphite). Furthermore, the importance of HFEPR for dynamic nuclear polarisation (DNP) is discussed. At last, we demonstrate the possibility to access very short relaxation times (B1 ns) by implementing frequency rapid scans, emphasizing the power of frequency domain EPR. This technique allowed to perform, for the first time, multi-frequency relaxation studies in a single spectrometer at frequencies above 100 GHz.

1

Introduction

Since 1944 when Ye. K. Zavoisky performed the first electron paramagnetic resonance (EPR) experiments in Kazan (USSR), there was vast development in the field of magnetic resonance.1 Probably one of the most significant advances in EPR was achieved by increasing the operating microwave (mw) frequency and corresponding spectrometer’s static magnetic field, which enables accurate studies of paramagnetic species that would not be accessible at low fields (see, e.g. Fig. 1). In 1957, G. Feher foresaw such importance of increasing the irradiation frequency to enhance both sensitivity and resolution of EPR spectrometers.2 However, it took a few decades until this prediction could be experimentally realized. The first to overcome the initial problems was the group of Ya. S. Lebedev from Moscow in the 1970s with the implementation of the first 148 GHz (D-band)/5.3 T EPR spectrometer.3 Several groups followed the work of Lebedev across the world in the 1980s. The group of W. R. Potter (Roswell Park Memorial Institute, Buffalo, New York, USA) used 70 GHz (V-band)/2.5 T spectrometer to investigate trapped electrons in irradiated single crystals of polyhydroxy compounds.4 The group of ¨bius (Freie Universita ¨t Berlin, Germany) reported in 1984 an EPR K. Mo spectrometer operating at 94 GHz (W-band)/3.4 T.5 In 1988, the group of J. H. Freed (Cornell University, Ithaca, New York, USA) pushed the limit to CEITEC – Central European Institute of Technology, ˇova 123, 612 00 Brno, Czech Republic. Brno University of Technology, Purkyn E-mail: [email protected] 214 | Electron Paramag. Reson., 2021, 27, 214–252  c

The Royal Society of Chemistry 2021

Fig. 1 Illustrative demonstration of the enhanced resolution achieved at higher frequencies and magnetic fields. First-derivative continuous-wave EPR spectra of (a) a nitroxide radical (14N-TEMPOL) in frozen water solution with well-resolved hyperfine structure Azz (Section 3) as frequency increases (Reproduced from ref. 7 with permission from the Royal Society of Chemistry) and (b) powder of SrTiO3 perovskite (inset) doped with Mn at different microwave frequency/B0 settings. Green spheres – Sr21 (or the substituting Mn21) atoms, blue sphere – Ti41 (or the substituting Mn41) atom, red spheres – O atoms. More information about EPR on perovskites can be found in ref. 8.

250 GHz/8.9 T by applying quasi-optics (QO) made of Teflon lenses in EPR for the first time.6 The first pulsed high-frequency EPR spectrometer operating at 95 GHz was reported in 1989 by the group of J. Schmidt (Huygens Laboratory, Leiden, Netherlands).9 Simultaneously, L.-C. Brunel developed a multifrequency high-frequency EPR (HFEPR) spectrometer (Grenoble High Magnetic Field Laboratory, GHMFL, France) going to fields as high as 20 T using resistive magnets.10,11 In 1992, the group of R. G. Griffin (Francis Bitter National Magnet Laboratory, Massachusetts Institute of Technology, USA) reported a pulsed spectrometer operating at 140 GHz.12 At the same time in the Griffin group, the first pioneering work on high-frequency dynamic nuclear polarisation (DNP) was conducted.13,14 A few years later, in 1995, a pulsed HFEPR spectrometer operating even at 604 GHz using a pulsed far-infrared laser was reported in the group of P. Wyder (GHMFL).15 This renaissance was further boosted by reports, in 1998, of an EPR spectrometer relying on QO techniques based on reflection (mirrors) and corrugated waveguides in the group of P. C. Riedi (St. Andrews University, Scotland, UK); indeed, that approach established the way how the low-loss broadband HFEPR spectrometers are used nowadays in most HFEPR laboratories. EPR has traditionally been performed at a fixed mw frequency (GHz range) while sweeping the external magnetic field (field domain). This approach overcame limited sweep ability of available mw sources at that time. Besides, working at a fixed frequency allows using a cavity or other type of resonator to enhance the sensitivity of the EPR technique.16 In the 1960 and 70s, several frequency-domain magnetic resonance (FDMR) studies had appeared mainly by Sievers and Richards.17,18 This work was mostly discontinued after 1980 due to low sensitivity and lacking technology. From the late 1990s, the FDMR technique was revived by A. Mukhin, M. Dressel and J. van Slageren using backward wave oscillators (BWOs) operating from 30 GHz to 1400 GHz and magnetic fields up Electron Paramag. Reson., 2021, 27, 214–252 | 215

to 8 T.19–22 And later, by A. Schnegg using coherent synchroton radiation from 150 GHz–1200 GHz (1500 GHz) up to 10 T.23,24 Further advances were hindered because of a limited availability of microwave sources operating in a broad frequency range. Nowadays, high-speed electronics is getting more accessible on the market, which is also affecting the terahertz range (300 GHz–30 THz)25 where broadband sources became available. In 2018, P. Neugebauer and J. van Slageren et al. demonstrated the first ultra-broadband EPR spectrometer operating in field and frequency domains.26 They have shown the advantages of performing experiments at a fixed static magnetic field by sweeping mw frequency. Some of these experiments are described later in this chapter. In many samples, the energy splittings of interest are caused by fieldindependent interactions, such as zero-field splitting (ZFS) or crystal-field splitting (discussed in Sections 3 and 4.1). In an FDMR spectrum recorded even at zero field, the energy spectrum of the material under study is then directly read off while in the field domain these properties must be achieved by extrapolation. The precise determination of magnetic parameters by EPR very often requires a multifrequency study,27 usually presented in the form of frequency-field plots such as those in ref. 28–31. Accordingly, in the field domain, the HFEPR spectrum must be recorded at many different frequencies, and this approach is extremely time-consuming since the ramp speed of superconducting magnets is limited by the cooling capacity of the cryogenic system. It may take around one hour for a field sweep of 15 T in closed-cycle (‘‘cryogen-free’’) systems. On the other hand, in FDMR, the full sweep within a frequency band, which could be over 100 GHz widey, can be performed in a matter of seconds or even faster in the so-called rapid-scan regime. Thus, it is logical to record FDMR spectra continuously during the magnetic field ramp. As a result, instead of recording several conventional field-swept EPR spectra, one obtains a detailed and continuous two-dimensional frequency-field map (a Zeeman diagram) such as one presented in Fig. 2. Thus, FDMR is inherently faster than HFEPR. Another advantage of FDMR concerns samples with an energy spectrum that spans over a very broad energy range up to several THz. In that case, magnetic fields required for field domain HFEPR cannot be achieved with direct current (DC) magnets any longer. Besides, FDMR spectra can be recorded while the superconducting magnet is in the persistent mode, thus saving on the non-renewable resource of liquid helium. Finally, applying a sizable magnetic field can change the properties of the sample itself, and can also lead to higher-order field dependent interactions becoming nonnegligible (discussed in Section 3). Despite the technical improvements of the solid-state mw sources, their output power is still not high enough to make the pulse HFEPR relaxation studies as versatile and widespread as in X-band (10 GHz)

y

For a free electron (ge ¼ 2.0023), the frequency range of 100 GHz corresponds to a magnetic field span of 3.6 T.

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Fig. 2 (a) A two-dimensional frequency-field EPR map of 14N-TEMPOL (S ¼ 12, I14N ¼ 1) dissolved in polystyrene, resulting in a 2.5 mg film withB1016 spins. The map with a resolution of 10 0001000 points in frequency and field direction, respectively, was acquired by the collection of single frequency scans while sweeping the magnetic field. (b) The extracted field and frequency domain spectra from the map in (a). Instrumental artefacts are discussed in the text. (c) Illustration of EPR and FDMR experiments at EPR fixed frequency (energy) and FDMR fixed magnetic field (B0,FDMR), respectively.

Fig. 3 First multifrequency rapid-scan HFEPR of LiPc powder recorded using frequency sweeps at a rate b/2p ¼ 105 THz s1. The three spectra recorded at different magnetic fields (corresponding to 190, 202 and 224 GHz) display oscillations (wiggles) as the sweep rate is faster than the relaxation time of the LiPc. Solid curves – experiments, dashed – fit with the modified Bloch equations corresponding to T2 indicated in the picture. Reproduced from ref. 32 with permission from Elsevier, Copyright 2018.

or Q-band (35 GHz). As an improvement in this direction, Hyde et al. showed in 2010 the power of frequency rapid-scan at W-band.33 The idea of the method is to sweep the frequency of microwaves at rates that are comparable or faster than the spin relaxation processes, a unique way how to access spin dynamics. In 2018, O. Laguta and P. Neugebauer et al. extended the application of this method to a frequency range close to 200 GHz and showed the first multifrequency relaxation studies using frequency rapid-scan in HFEPR. (Fig. 3). Using this approach, they were able to detect fast relaxation of Lithium Phthalocyanine (LiPc) powder at 200 GHz frequency range.32 All these reasons mentioned above such as the fast acquisition of Zeeman diagrams and access to very short spin relaxation times favour performing experiments in the frequency domain.

2

Instrumentation

A typical continuous-wave (CW) HFEPR spectrometer consists of the following main parts: a mw bridge, a probe with a sample holder, a superconducting magnet with a variable temperature insert (VTI), a phase-sensitive detection system (lock-in amplifier) and an operator computer with software (Fig. 4). Some of the key instrumentation features relevant to our studies will be briefly discussed in the following text. The mw bridge is the heart of any EPR spectrometer. It generates mw for the excitation of a sample, and it detects the reflected power that corresponds to the EPR signal coming back from the sample. In the case of HFEPR, the high-frequency mw source is usually a modular system, consisting of a low frequency (10 GHz range) phase-locked synthesizer and a chain of active or passive frequency multipliers. This approach can deliver a quasi-gapless operation range of 90–1100 GHz. Such sources have already proven to be the best choice for CW EPR.26 Their only 218 | Electron Paramag. Reson., 2021, 27, 214–252

Electron Paramag. Reson., 2021, 27, 214–252 | 219

Fig. 4 (a) A basic scheme of a typical CW EPR spectrometer showing the main components. Pictures (b) and (c) show commonly used principles of mw detection used in HFEPR spectrometers, direct and superheterodyne, respectively.

problem is limited output power, especially at the frequencies beyond 300 GHz where it rapidly drops below one milliwatt. Information on other high-frequency sources, such as klystrons, Gunn diodes, far infrared lasers, backward wave oscillators and others, can be found in ref. 40. A truly broadband gapless source of microwaves can be obtained using a photoconductive antenna (PCA) based mw emitters, which can work in CW34 and pulse regime.35 Despite the current limited output power of these devices (below one milliwatt), the technology looks promising and potentially can help in minimizing of the spectrometer’s size and cost. The propagation in the high frequency mw bridge is provided by low loss free space propagation between QO components (lenses, mirrors, polarizers, splitters, etc.).36 We call it QO, as the size of the components is in only a few orders of magnitude larger (cm) than the size of the mw wavelength (mm) (see Table 1). The QO ensures the low loss coupling of the beam to the probe as well as back from the probe to the detection system. The probe directs the mw power to a sample in the centre of magnetic field in a cryostat. It could be 1 m to 2 m long in the case of closed cycle (cryogen-free) or wet magnets, respectively. Due to limited space (few centimetres) in cryostats, the mw propagates inside of an oversized corrugated waveguide.37 Depending on the spectrometer’s type, the probe can have a resonant38 or a non-resonant26,39 cavity at the end of the waveguide. In the first case, the spectrometer usually operates in the reflection mode, and in the latter in the induction mode (Fig. 5). To generate a uniform magnetic field B0 of several Tesla at the sample space, superconducting magnets are used. In case of necessity to use a very high magnetic field (above 20 T), one can use one of the large-scale facilities dedicated to high magnetic fields, for example National High Magnetic Fields Laboratories in Tallahassee or Grenoble, where HFEPR experiments at these extreme conditions can be performed. Additionally, for some applications such as study of solid-state materials, the possibility to continuously ramp the magnetic field from positive to negative Table 1 Field and energy relationship for EPR and NMR relevant frequencies. The highlighted frequencies refer to some of the commercially available EPR and NMR spectrometers from Bruker.

EPR Frequency

EPR wavelength

Resonant field (for g ¼ 2.0023)

EPR Energy

(GHz)

(mm)

(T)

(meV)

(cm1)

(MHz)

(m)

9.4 (X-band) 35 (Q-band) 95 (W-band) 263 (J-band) 329 395 461 527 593 661 1000

31.89 8.56 3.15 1.14 0.91 0.76 0.65 0.57 0.51 0.45 0.30

0.335 1.249 3.390 9.385 11.740 14.095 16.444 18.805 21.160 23.490 35.683

0.038 0.144 0.392 1.088 1.361 1.634 1.907 2.180 2.453 2.734 4.136

0.31 1.17 3.16 8.77 10.97 13.17 15.38 17.58 19.78 22.05 33.36

15 53 145 400 500 600 700 800 900 1000 1518

19.99 5.66 2.07 0.75 0.60 0.50 0.43 0.38 0.33 0.29 0.20

220 | Electron Paramag. Reson., 2021, 27, 214–252

1H-NMR frequency

1H-NMR wavelength

Electron Paramag. Reson., 2021, 27, 214–252 | 221

Fig. 5 Quasi-optical (QO) mw bridge designs with the direct mw detection: (a) reflection mode, (b) induction mode. The indicated polarisation (circular arrows) in the picture refers to the case of fulfilled resonance condition. Note: for simplicity, we omit refocusing elements (lenses or mirrors), which are otherwise necessary for the actual systems.

values is highly desirable (see Section 4.2 and Fig. 13a).40–42 To control the sample’s temperature, it is necessary that the magnet is equipped with a VTI cryostat that is typically operating in the temperature range of 2 K to 300 K. To increase substantially the spectrometer’s sensitivity, a phasesensitive detection system (magnetic field modulation) is implemented as in X- or Q-band spectrometers. In addition to the strong static B0 field, a weak Bm field oscillating at fmod frequency (kHz range) is applied with the help of a small modulation coil located close to the sample. That results in the amplitude modulation of the EPR signal at the same fmod frequency. A lock-in amplifier is used to demodulate the signal and obtain the first derivative of the absorption spectrum (Fig. 1). Finally, all HFEPR spectrometer’s instruments are connected to, and controlled by a computer with a dedicated software, typically homewritten. This computer is also used for initial data processing and analysis. 2.1 Detection schemes and propagation of high-frequency mw Modern HFEPR spectrometers utilize two approaches to detect mw. The most straightforward scheme, shown in Fig. 4b, can be called a direct detection. A circulator redirects weak reflected microwaves to the detector, a zero-biased Schottky diode (ZBD) or a liquid He cooled InSb bolometer.28,43 The latter has several times higher sensitivity and by one order of magnitude lower noise. Moreover, bolometers have much broader operating frequencies range so that one unit covers the whole spectrometer’s range. However, they have a long response time (few microseconds), and they are more expensive in the maintenance due to the cooling by the liquid He or implementing a closed-cycle system. On the other hand, ZBDs are compact and can easily have a response rate of several GHz. Such a fast response is essential for pulsed and rapid-scan EPR experiments. However, the operating range of a ZBD is limited by its waveguide size.44 As a result, one would need several detectors to cover 90–500 GHz range. A more complicated scheme involving two mw sources is called a superheterodyne detection, Fig. 4c. In this approach, incident mw power is transformed into a signal at an intermediate frequency (IF) instead of a DC signal, as typically occurs in the direct detection. That is done by mixing (multiplying) the mw signal (RF) reflected from the sample with a signal from a local oscillator (LO) using a mixer (a Schottky diode)z. The result of RF and LO multiplication is two signals at frequencies f(LO1RF) and f(LORF): Acosð2pfLO tÞ  Bcosð2pfRF tÞ ¼ z

AB ½cosð2pðfLO  fRF ÞtÞ þ cosð2pð fLO þ fRF ÞtÞ 2

(1)

Abbreviations RF and LO came from the classic radio technology. RF, radio frequency, is the signal containing the message and which is picked up by the antenna. LO, local oscillator, is a very stable signal generated by an oscillator inside of the radio.

222 | Electron Paramag. Reson., 2021, 27, 214–252

and the component with the higher frequency is inherently filtered out. This process is known as down-conversion.45 By selecting a large enough difference between fLO and fRF the intermediate frequency fIF ¼ fLO  fRF can be sufficiently high (several GHz) for the effective suppression of 1/f noise. Moreover, the usage of relatively cheap, low noise highperformance amplifiers for this frequency range further improves the spectrometer’s sensitivity. The IF signal can be then digitized for the digital signal processing or further down-converted to a DC signal. Another advantage of this detection scheme is that it is possible to measure both absorption and dispersion EPR signals simultaneously.46 The technological advances in QO systems resolve the problem of mw propagation losses in metallic waveguides at frequencies above 95 GHz.6,37 In QO systems, the microwaves propagate in free space as a Gaussian beam, and the essential elements of the bridge, such as circulators and isolators, can be made with polarizing grids and Faraday rotators.36,47 An example of a simple reflection system utilizing a QO bridge is shown in Fig. 5a. The beam propagating from the source has the polarisation parallel to the wires of the grid and, therefore, it is reflected towards the Faraday rotator. The Faraday rotator changes the beam polarisation by 451 and by another 451 after it is reflected from the resonator since the rotator rotates the polarisation always in the same direction. As a result, the reflected beam becomes perpendicularly polarized relatively to the grid and can freely pass through it. The reflection mode requires high quality-factor (Q factor) cavities to ensure a weak reflection to avoid damaging the very sensitive mw detector. This approach complicates the performance of multifrequency HFEPR because each frequency requires a separate cavity (or tuning conditions), and the frequency domain HFEPR cannot be implemented altogether. A good way to overcome this difficulty is to use non-resonant cavities along with the induction mode bridge, which is schematically presented in Fig. 5b. The first allows for working in the frequency domain, and the second delivers high sensitivity and isolation between the excitation and detection arms of the mw bridge. In the induction mode, one measures the change of polarisation of the reflected beam. Transitions between spin levels can occur only under a circularly polarized excitation with the polarisation direction defined by the sign of the effective g-factor.48–50 The linearly polarized excitation beam can be interpreted as a sum of right- and left-hand circularly polarized beams of equal intensity. If the EPR condition is not matched, the sample does not alter the beam’s polarisation, and after reflection, it freely passes through the polarizer indicated as ‘  451’ in Fig. 5b, which is placed between the probe and the circulator. At the resonance condition, the sample absorbs one of the circular components of the beam, changing its polarisation from linear to slightly elliptical. The ‘  451’ polarizer reflects towards the detector the very weak, orthogonally polarized component of the beam (also known as a cross-polarized component) which contains the EPR signal. The rest of mw power (more than 99%) goes back through the polarizer, and the circulator directs it to the absorber. The main drawback of the induction mode is the presence of standing waves, Electron Paramag. Reson., 2021, 27, 214–252 | 223

which appear because of the reflection of mw mostly between the source and a sample, and between the detector and a sample. A good way to suppress them is to introduce an isolator at the front of the detector as it is shown in Fig. 5b. An example of the overall effect obtained on the spectrometer at the Institute of Physical Chemistry in the University of Stuttgart (AG van Slageren) is given in ref. 26. The relative amplitude of standing waves was reduced by a factor of 3 (Fig. 6). Arel ¼

standing waves amplitude MW power

(2)

When performing HFEPR in the frequency domain (sweeping frequency at a constant magnetic field), the phase of the EPR signal should change, in the ideal case, linearly with the mw frequency as f  fstart jð f Þ ¼ 360  . For example, if at fstart ¼ 300 GHz the EPR line has fstart a pure absorption shape, then at f ¼ 375 GHz it will change to the dispersion signal. This effect can be taken into account either during the spectrum post-processing adding a linear term into the phase correction or by tuning the LO phase in superheterodyne systems. Unfortunately, in real systems, standing waves cause phase distortions so that the phase is not a linear function of the mw frequency anymore, and without a detailed characterisation of the standing waves the phase correction is impossible. Moreover, even slight changes in the QO system alter the standing waves completely. To address this problem, we, together with

Fig. 6 Reduction of standing waves by introducing the QO isolator at the front of the detector. Reproduced from ref. 26 with permission from the Royal Society of Chemistry. 224 | Electron Paramag. Reson., 2021, 27, 214–252

Thomas Keating Ltd and Virginia Diodes Inc., developed a special QO bridge with a superheterodyne detection (Fig. 7). Two phase-locked synthesizers generate microwaves in 9–14 GHz range with the frequency shift of d/N GHz. The source ‘‘S1’’ is used for the sample excitation, and the source ‘‘S2’’ is used as LO generator to drive the mixers ‘‘M1’’ and ‘‘M2’’. The QO bridge is designed in such a way that the distances between the sources and the mixers are equal. The result is that the phase difference Dj between the cross- and co-polarized microwaves is the same at the inputs of both mixers no matter what distortions standing waves can cause. Moreover, during a frequency sweep, Dj is also constant. The output of the mixer ‘‘M1’’ is a periodic signal at the intermediate frequency fIF ¼ d containing two components of the magnetisation: Mx cos(2p fIFt þ Dj) þ My sin(2p fIFt þ Dj). The down-converted copolarized component ACPcos(2p fIFt þ Dj) is then used as LO to drive the low-frequency IQ mixer ‘‘M3’’. After the final mixing, we obtain absorption and dispersion signals separately. In dynamic nuclear polarisation experiments (see Section 4.3), it is very important to saturate the EPR transition to obtain the maximum nuclear magnetic resonance (NMR) enhancement. Due to the very limited available mw power, particularly at 329 GHz and higher, the excitation with circularly polarized mw is very desirable. The easiest way to manipulate the polarisation is the so-called Martin–Puplett interferometer schematically depicted in Fig. 8. The input linearly polarized beam (solid black arrow) is split in two by a polarizing grid rotated by 451 relatively to the beam’s polarisation. Then these two beams (orthogonally polarized to each other) are reflected by the roof mirrors with the polarisation being rotated by 901. One of the mirrors is mounted on a translation stage and works as a delay line introducing controllable phase difference between two arms of the interferometer. The resulting mw can be expressed as I45cos(ot) þ I45cos(ot þ Dj), where Dj is the phase difference. To obtain a circularly polarized wave the phase difference has to be p/4, e.g. the length on one of the arms has to be a quarter-wave longer or shorter than the other one. The selectiveness of the beam’s polarisation also allows for the experimental determination of the sign of the effective g-factor. A more detailed review of HFEPR related instrumentation can be found elsewhere.36,43,46,51

Fig. 7 The superheterodyne detection system in Brno FRaScan spectrometer (Fig. 18b). S and M correspond to synthesizer and mixer, respectively. Electron Paramag. Reson., 2021, 27, 214–252 | 225

Fig. 8 A scheme of Martin–Puplett interferometer. The black arrow indicates an input beam with a vertical (01) polarisation, which is split equally into þ451 (reflected) and 451 (transmitted) polarized beams by the þ451 polarizer. The roof mirrors flip the polarisation by 901 and one of them is movable allowing to change the path length (phase) with respect to the other path. They are recombined on the output of the Martin–Puplett interferometer into a desired polarisation (linear, circular or elliptical).

3

Theoretical basics

Quantitatively, the positive role of a large static magnetic field magnitude, B0, and of the corresponding mw frequency, f, in a spectrometer can ˆ, be estimated by analysing the spin interactions. The Hamiltonian, H which describes a paramagnetic system in an EPR experiment is a sum of terms describing specific spin interactions, which play important roles in ˆ contains the term H ˆ eZ corresperformed measurements. Usually, H ponding to the Zeeman interaction of an unpaired electron with the static ˆ eZ magnetic field B0. For a system with only one unpaired electron spin, H is given by g ^ ^ Ze ¼  H h e B0 g S ge

(3)

ˆ ¼ (S ˆx, S ˆy, S ˆz) is the spin wherein  h is the reduced Planck constant, S vector operator, ge and ge are the gyromagnetic ratio and g-factor of free electron, respectively. The anisotropy of the electron Zeeman interaction caused by the spin–orbit coupling is described by the g-tensor g in the expression (3). For more complicated paramagnetic systems including many high spin systems (e.g., transition metals), the expression (3) is generalized correspondingly.52 ˆ MW(t), which describes the electron spin The Hamiltonian term H interaction with the mw field B1(t) oriented perpendicularly to B0, has a form similar to (3), i.e., g ^ ^ MW ðtÞ ¼  H h e B1 ðtÞg S ge 226 | Electron Paramag. Reson., 2021, 27, 214–252

(4)

Usually, EPR experiments are performed on samples containing a macroscopic number of paramagnetic centres. In such systems, there exist magnetic dipolar and Heisenberg exchange interactions among electron spins. Under certain conditions, these interactions can play a significant role and can be detected in EPR measurements. For instance, electron spin dipolar interaction is successfully observed in Pulsed Electron–Electron Double Resonance (PELDOR) experiments on systems of spin pairs.53 For a spin pair, the Hamiltonian of spin dipolar interaction is given by ˆ1DdipS ˆ2 ˆ dip ¼  H hS ˆ2 wherein Ddip is the magnetic dipolar interaction tensor and ˆ S1 and S denote the vector spin operators of the first and the second spin, respectively. In case, when the wave function of the two spins overlap, the Heisenberg exchange interaction,54 which is described by the term ˆ J ¼ hˆ H S1 J ˆ S2 with J denoting the tensor of exchange interaction, becomes important. If a paramagnetic system contains nuclear spins, then there exists ˆN also the nuclear Zeeman interaction H Z , which can be included in the N ˆ full Hamiltonian. However, HZ is usually small at frequencies and fields used in EPR and does not change spectra significantly. In contrast, the hyperfine interaction of nuclear spins with unpaired elecˆ HF, is much more pronounced (see Fig. 1a). For one electron trons, H ˆ HF is written as and one nuclear spin system, H ˆ ˆ HF ¼  H hˆIAS

(5)

wherein ˆI ¼ (Iˆx, ˆIy, ˆIz) is the nuclear spin vector operator and A is the hyperfine interaction tensor. Some paramagnetic molecules can have high electron spin state (S41/2) due to the interaction of several electrons. Such systems exhibit splitting of the energy spin states even at zero magnetic fields, as are for example single-molecule magnets (SMMs) discussed later. To the second order of approximation,55 this splitting is described by the Hamiltonian term wherein DZFS is the traceless tensor of ZFS interaction. In its principal axes frame the tensor DZFS can be comfortably expressed via two parameters D and E, representing the axial and rhombic anisotropy of the system, i.e.,  hDZFS ¼ diag(D/3 þ E,  D/3  E, 2D/3). D and E are related by 1/3rE/Dr þ 1/3. When the ratio E/D ¼ 1/3 the system is rhombic, whereas in the case of E ¼ 0 the system is axially symmetric. D can be either negative or positive, corresponding to an easy-axis or an easy-plane anisotropy, respectively.56 ˆDZFSˆ ˆ ZFS ¼ hS H S

(6)

ˆ , is obtained by adding Based on the foregoing, the full Hamiltonian, H all the important interaction terms, which should be written using appropriately defined spin operators for the investigated spin system. For Electron Paramag. Reson., 2021, 27, 214–252 | 227

example, to interpret the EPR spectra of SMMs, the Hamiltonian is written as   X q q g ^2x  S ^ ^2Z  1 SðS þ 1Þ þ E½S ^2y þ ^ ^ CF ¼  ^ ¼H ^ Ze þ H h e B0 g SþD S Bk O H k 3 ge k;q

(7)

^ Ze is the electron Zeeman interaction and the crystal field term where H ˆ HCF is the sum of the second-order ZFS term (6) written in the principal axes frame and of the Hamiltonian term Sk,qBqkO^qk describing higher-order corrections associated with a large spin values S. Herein, Oqk are Stevens operators and the Bqk terms are the corresponding parameters, which are defined by the symmetry of the complex.54 With the introduced spin interaction Hamiltonians, many advantages of high magnetic fields can be explained. For instance, in a paramagnetic system with dominating electron Zeeman interaction, a higher magnetic field B0 leads to a higher energy gap (see expression (3)) and, hence, to a larger population difference of spin states according to statistical mechanics. This increases equilibrium spin magnetisation and, consequently, signals detected in EPR experiments. Increasing of the static magnetic field and corresponding mw frequency also improve the resolution of g-tensor anisotropy. Fig. 1a shows clearly resolved g-tensor principal values at high field in comparison to low field with smeared edges by the inhomogeneous line broadening for 14 N-TEMPOL (I14N ¼ 1). Fig. 1b shows another illustrative example where high magnetic fields help to completely separate spectra of Mn21 (g ¼ 2.0032) and Mn41 (g ¼ 1.9920) in SrTiO3:Mn powder, I55Mn ¼ 5/2. For high-spin systems, the ZFS interaction can be comparable or even stronger than the electron spin Zeeman interaction. An increase of the static magnetic field magnitude B0 can significantly shift the balance of these interactions in favour of the Zeeman interaction, allowing us to treat ZFS as a small perturbation in the full spin Hamiltonian. According to this approach, the line width of the central transition of paramagnetic systems with a half integer spin, which are determined in the second order of the perturbation theory, is inversely proportional to B0. Hence a high magnetic field can provide for well resolved EPR spectra with sharp peaks for paramagnetic systems with ZFS interaction. The Hamiltonian terms introduced above are generally enough for the representation of an investigated paramagnetic system in equilibrium. When the system is excited, for example, by irradiating mw in EPR experiments, then its spin dynamics can be described by the density ^(t), which is found from the Liouville/von Neumann equation, matrix, r ih

@^ rðtÞ ^ ^ðtÞ ¼ ½HðtÞ; r @t

(8)

^(t), the electron spin magnetization vector M(t), which is observed With r in experiments, is calculated as, ˆr ^(t)}. M(t)ptrace{S 228 | Electron Paramag. Reson., 2021, 27, 214–252

(9)

Once spin magnetization is tilted from its equilibrium value M0 along the external magnetic field B0 by a resonant mw irradiation, the relaxation processes, which return spin magnetization to the equilibrium, start to take place. In many cases, the relaxation of the longitudinal and transversal components of M(t) with respect to B0 can be well approximated by exponential functions, Mz ðtÞ ¼ M0  ½Mz ð0Þ  M0 expðt=T1 Þ; Mx;y ðtÞ ¼ Mx;y ð0Þexpðt=T2 Þ;

(10)

with the characteristic relaxation times T1 and T2, respectively. Determination of T1 and T2 times is important in many magnetic resonance studies.

4 Applications Practical applications using EPR have been reported in excellent textbooks, research papers and review articles.27,30,57–72 The many benefits of extending the frequency range to hundreds of GHz have been described in the previous section, including improved resolution for the study of organic radicals (Fig. 1a) and access to high ZFS in high spin systems. Indeed, HFEPR is well-established as the technique of choice to the study of electronic and magnetic properties of transition metal compounds with high ZFS.27 We present how it has contributed to the precise determination of the intrinsic magnetic parameters of SMMs.26 Nevertheless, the advantages of this technique go beyond molecular paramagnetic and magnetic compounds. Here, we also present HFEPR as a tool to investigate the electronic properties of solid-state materials such as graphene. Literature reports also include the approach of high field magneto-optical principles to investigate Weyl semi-metals.73–75 4.1 Single-molecule magnets By the end of the 1980s, molecular magnetism had seen the emergence of a new research area: the study of high nuclearity spin clusters, which are complex molecules containing a large number of spins most often carried by transition metal ions.76 Among these molecules, the ones possessing a large spin ground state associated with an Ising type anisotropy (Fig. 9a) have been under particular focus.77 The large macroscopic spin of these molecular systems (Fig. 9b) together with a negative ZFS results in the presence of a barrier for the reversal of their magnetisation at low temperatures. The main consequence is a slow relaxation of magnetisation that, below a blocking temperature, leads to a behaviour quite similar to that of superparamagnets.78 Due to these properties, they have been named SMMs. At low temperatures, they exhibit hysteresis in their magnetisation curve with a step-like shape (Fig. 9c), a signature of the presence of Quantum Tunneling of the Magnetisation (QTM).79,80 HFEPR proved to be one of the most powerful methods to precisely determine the magnetic anisotropy of SMMs.81–104 Electron Paramag. Reson., 2021, 27, 214–252 | 229

Fig. 9 (a) Schematic description of energy levels in SMMs using double well potential (Ising type anisotropy) at zero magnetic field, finite temperature and integer spin S. The height of the barrier D between the two ground MS states is proportional to the size of D (axial ZFS parameter) and S2. Thanks to the energy barrier D the system can be blocked in one of the MS state. The system relaxes into equilibrium either by overcoming the energy barrier or via QTM. (b) Fe4 complex is an example of SMM which is composed by four antiferromagnetically coupled FeIII ions with spin of 5/2 leading to a total giant spin of molecule 5. (c) A hysteresis loop recorded for the Fe4 complex at 40 mK. Typical steps in magnetisation are observed due to QTM presented in SMMs between the opposite MS states on the other side of an energy barrier, with below indicated corresponding Zeeman diagram. Reproduced with permission from W. Wernsdorfer.

SMMs possess a large spin ground state S, resulting from exchange interactions between their magnetic centres. Often, it is possible to stabilise a large spin ground state even when only antiferromagnetic interactions are present, due to the competition between all the magnetic exchange pathways resulting from the structure of the molecule. SMMs have an easy-axis magnetisation that results from a spin ground state S with a negative axial ZFS term, D. Thus, inside the ground multiplet, the levels MS ¼  S are the lowest in energy and the level MS ¼ 0 is the highest, with an energy difference DEDS2 for integer S and DED(S2  1/4) for noninteger S, where D is an energy barrier for the reversal of the magnetisation (Fig. 9a). At temperatures where only the ground spin state is thermally populated, the relaxation time of the magnetisation increases due to the reversal barrier of spin energy D and it is dependent on types of active relaxation processes. At high temperatures, these processes originate in the exchange of energy with the phonon bath, through lattice vibrations. The relaxation processes consist into three basic types: Orbach process (two-phonon relaxation process allows spin to reorient by climbing over D, fundamental for the occurrence of SMMs), direct process (a singlephonon process involving phonons with the same energy as the magnetic resonance quantum hf, spin relaxation without a need to overcome D), Raman process (two-phonon process with strong temperature but no magnetic field dependence).106 230 | Electron Paramag. Reson., 2021, 27, 214–252

At lower temperatures, relaxation takes place through quantum tunnelling among the lowest MS states, and it is temperature independent. The steps in the magnetisation curve (Fig. 9c) appear when tunnelling is made possible by energy levels degeneracy. If D is sufficiently high (and relaxation processes other than Orbach are suppressed), the magnetisation can be preserved for a long time. Therefore, it is in principle possible to store information in such a molecule. The first complex identified to behave as an SMM was the Mn12Ac complex with D ¼ 43 cm1.77,107 Despite being the first SMM discovered, and despite the enormous synthetic effort to increase D, the Mn12Ac complex lost the record of the highest temperature for which magnetic hysteresis was observed two decades after its discovery and a new record was set by unique Mn6 complex D ¼ 60 cm1.108,109 However, due to difficulties of obtaining SMMs with large energy barrier using polynuclear transition metal complexes110,111 the interest moved to mononuclear SMMs so-called Single-Ion Magnets (SIMs) based on lanthanides and actinides.112 The great interest is due to their large angular momenta and their huge anisotropies.113 The origin of the huge magnetic anisotropy is a consequence of the crystal field (CF) splitting of the ground multiplet of the lanthanide ion.114 These properties lead to slow relaxation of the magnetic moment to SMM behaviour, making them potentially suitable for use in novel ultrahigh-density magnetic data storage devices in future. The strategy proved to be successful, and recently, SIMs with high blocking temperature and even magnetic hysteresis up to 80 K were reported for organometallic Dy(III) compounds.115,116 Besides the interest in the increase of D, another significant trend in SMM research nowadays is examining SMM behaviour of the complexes organised on solid surfaces or anchored to them.117–121 For applications such as information storage, quantum computing122–124 or molecular spintronics,125,126 it is necessary to find a way how to deposit molecules on suitable substrates and to maintain their properties upon this deposition. The preparation of bulk SMM compounds with high blocking temperatures followed by the characterisation of their intrinsic magnetic parameters with HFEPR and magnetic FIR spectroscopies are the first steps in the search of suitable materials for applications in future electronic devices. The next step is based on the study of their behaviour when deposited on the surface of substrates, such as silicon, gold, hexagonal boron nitride (hBN), graphene and others. This step has to overcome important challenges ranging from the intactness of the molecules during the deposition procedure to the detection of thin layers beyond the sensitivity of HFEPR spectrometers. To solve the detection problem, in situ spectroscopy has a vital role and a promising approach relies in the use of nanostructured graphene as radiation detectors (bolometers).127 4.1.1 Examples. In this section, we highlight some of the most important features of HFEPR for the study of SMMs on a particular case of Fe4 molecule. Due to the large anisotropy of SMMs, these Electron Paramag. Reson., 2021, 27, 214–252 | 231

complexes are inaccessible to classical EPR spectrometers operating at low frequencies (X-band, 0.3 cm1), either being EPR silent or giving rise to incomplete spectra. Going to higher frequencies to overcome the energy gaps of the ground spin multiplet is necessary, also because SMMs have integer spin values. To give an (extreme) example, the splitting between the lowest occupied states MS ¼  10 and MS ¼  9 in the Mn12Ac is about 10 cm1 (300 GHz); hence EPR spectrometers operating at low frequencies cannot probe these transitions. 4.1.2 Powdered samples. The ZFS parameters, introduced with the spin Hamiltonian in Section 3 of this chapter, can be obtained from HFEPR either on polycrystalline (powdered) or single crystal samples. The powdered samples are pressed into pellets to avoid orientation effects caused by strong magnetic field, typically 10–25 mg of a sample is needed for a 1 mm thick and 5 mm diameter pellet. Powder HFEPR spectra are often sufficient, because large amount of information on magnetic anisotropy can be extracted from its analysis. Experimental powder spectra obtained for a Fe4 sample (complex 2 in ref. 81) at 230 GHz, 5 K and 20 K are shown in Fig. 10a. The spectrum can be divided into two parts, perpendicular and parallel around the central g-value (8.2 T). From the field range extension of these two regions, we can determine the sign of D parameter of ZFS. In this case, the sign is negative. The parallel region corresponds to signal coming from molecules with easy-axis of anisotropy aligned with the applied field. Conversely, the signal in the high field part of the spectrum corresponds to the magnetic field in the molecules’ hard-plane of anisotropy (for details about magnetic anisotropy see Section 3). The negative sign of the D-parameter is further confirmed by the measurements at different temperature, where we see rise and decrease of the peak amplitudes in the parallel region, note the peak at the low field part of the spectra at 5 K and 20 K. Furthermore, MS2(MS  1) transitions can be easily assigned and the spacing between the consecutive peaks is proportional to 2D, D ¼  0.449 cm1. The careful inspection of the spacing of the parallel transitions (Fig. 10c) reveals that the line-to-line separation slightly increases when moving to high magnetic field, thus pointing to presence of higher order terms of the giant spin Hamiltonian, which are better distinguished from single crystal measurements as discussed below. 4.1.3 Single-crystal samples. Single crystal studies are performed to obtain a better knowledge of the magnetic anisotropies, especially to determine magnitude of the higher order terms in the spin Hamiltonian description (eqn (7)). Fig. 11a shows a single crystal HFEPR spectrum of the same complex as in Fig. 9b recorded at 230 GHz and 10 K with the orientation of the easy-axis along applied magnetic field B0. The line at B0 ¼ 4 T corresponds to the extreme of the powder spectrum in the low field part. From complete single crystal studies (Fig. 11b), recording of spectra along the easy-axis and the complete rotation in 232 | Electron Paramag. Reson., 2021, 27, 214–252

Fig. 10 (a) HFEPR spectra of compressed powder of Fe4 complex 2 in ref. 81 recorded at 230 GHz, 5 and 20 K. (b) Zeeman diagram simulated using EasySpin105 with red arrows indicating transitions at 230 GHz. For Do0, the ground state corresponds to Ms ¼ 5, which has a higher population at lower temperatures and explains the higher intensity of the low-lying transition 5 -  4 as temperature decreases. (c) Detailed view on MS2MS  1 transitions in parallel region indicating presence of higher order terms by increasing spacing between the consecutive transitions.

Fig. 11 (a) Single crystal HFEPR spectrum of the same Fe4 complex as in Fig. 9b recorded at 230 GHz and 10 K in orientation of magnetic field applied along easy axis of the Fe4 complex.39,128 (b) Map of evolution of resonance lines of Fe4-complex in the rotation around easy axis, with applied field in hard plane, together with corresponding simulation. The simulation was performed with the software SIM from H. Weihe. Reproduced from ref. 129 with permission from P. Neugebauer.

the hard plane (rotation around C3 axis, easy axis of Fe4 complex) allows precise determination of the higher order terms.85 Research in the field of molecular materials also points towards the potential of HFEPR for the studies of the crossings of Ms states (Fig. 9c), tuned with the direction and magnitude of magnetic field with interesting consequences such as long coherence times in quantum bits130,131 or detection of intermolecular exchange coupling and quantum phase transitions.132–135 Furthermore, thanks to the anisotropy of molecular systems, one could distinguish the preferential orientation of molecules on a surface with HFEPR.136 Electron Paramag. Reson., 2021, 27, 214–252 | 233

4.2 Solid-state materials – HFEPR on graphene and graphite Graphene is a relatively young material, observed for the first time in 2004 by K. S. Novoselov and A. K. Geim.137 Since its discovery, graphene has fascinated thousands of scientists as well as engineers around the world. To the end of 2019, there were more than 200 000 publications dealing with graphene according to Web of Science. The structure of graphene, which is the basic unit for the construction of bulk graphite,138 consists of a one-atom thick twodimensional (2D) lattice of carbon atoms with a honeycomb shape and has extraordinary electronic properties. The electronic properties are the consequence of its linear band structure (dispersion) in the vicinity of the K and K 0 points, often called Dirac points. At the Dirac points, the conduction and valence bands are touching each other, which makes graphene a zero-gap semiconductor (or a zero-overlap semimetal). The linearity of the dispersion makes graphene unique with respect to conventional materials with a classical parabolic dispersion, leading to charge carriers (electrons and holes) acting as massless particles, Dirac fermions, with a Fermi velocity n F of about 106 m s1, which approaches the speed of light. These unique properties of graphene do not only exist at very low temperatures and extreme conditions, as might be expected, but they are preserved up to room temperature, as we and others have shown.139 Combined, this makes graphene an excellent playground for probing quantum electrodynamic properties like the Klein paradox and Zitterbewegung and makes graphene a promising material for future technological applications.140–144 Recently, there has been a great deal of progress in preparation of manmade graphene by methods including chemical vapor deposition (CVD) and epitaxial growth. However, the quality (in terms of electron mobility) of these manmade graphene samples does not yet reach those of graphene decoupled from bulk graphite, evidenced by our observation of mobilities of 107 cm2 V1 s1 in graphene on graphite via HFEPR spectroscopy.40,41,146 This extremely high mobility enables the Landau level quantization to appear at magnetic fields as low as 1 mT.41 The ability to produce graphene of exceedingly high quality on a large scale is an essential prerequisite for the development of graphene-based devices. High-quality graphene displays ballistic electron transport at large distances which, if this material is successfully incorporated into devices, will lead to a breakthrough in electronics. It can be foreseen that in near future, graphene’s superior material characteristics, ranging from its crystal structure over mechanical strength to the electronic properties will be elaborated in novel devices which are nowadays impossible due to limited quality of currently used materials. The electronic properties of graphene samples are typically investigated by transport measurements. However, these measurements only probe the Fermi level.147 Furthermore, the transport measurement itself may cause defect formation in graphene, obscuring the properties intrinsic to the sample.146 Spectroscopic measurements, on the other hand, allow noninvasive measurement of the electronic structure, not only in the vicinity of the Fermi level, but throughout the entire band 234 | Electron Paramag. Reson., 2021, 27, 214–252

structure. A review on the applications of low-frequency EPR in graphene can be found in ref. 148. For the investigation of low-energy excitations, magneto-optical methods such as HFEPR and far infrared (FIR) magnetospectroscopy are relevant in particular, benefiting from their high sensitivities, as shown by a number of previous studies, including our own works.41,42,139,149 Among these methods, HFEPR probes the lowest energy range between 100–1000 GHz (0.4–4 meV, 3.3–33 cm1), while FIR typically probes the energy range from 1 to 10 THz (4–40 meV, 33–334 cm1). In magnetic field, the electronic states in graphene become quantized into Landau levels (LLs) En: En ¼  v F

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2e hB j n j;

n ¼    ; 2; 1; 0; 1; 2;   

(11)

where n is the LL index,  refers to electron (þ) and hole () states and e is the electron charge. Due to graphene’s unique pffiffiffi linear band structure, the LLs are not equally spaced and evolve with B (Fig. 12a). This implies rather high sensitivity of electronic states (LLs) in graphene to the applied magnetic field. Conversely, the investigation of the LLs in a magnetic field allows detailed understanding of the low-energy electronic structure of graphene. Fig. 13a displays how powerful HFEPR is today with respect to previously used instruments. Experiments performed on single flakes of natural graphite of size 1 mm2 mm and thickness 25 mm at 210 GHz and 5 K are shown in Fig. 13a. The spectrum is very rich. In the low field region signal originating from graphene is visible.41 At fields of 0.05–0.80 T, about 20 cyclotron resonance harmonics are observed originating from conduction electrons in bulk graphite, where the fundamental cyclotron resonance can be observed at about 0.8 T. Signals at fields above 0.8 T are not fully understood and are currently under investigation. To compare the superior quality expressed by many spectral features of the present HFEPR data, the averaged magnetoabsorption spectrum of high quality graphite of diameter 1 cm and

Fig. 12 (a) Left: Schematic evolution of LLs Ln in graphene with applied magnetic field B0. Right: Optically allowed transitions in p-doped graphene for a given magnetic field B0. n and m denote indexes of LLs. (b) Spectrum with peaks corresponding to the transitions depicted in (a). The spectra indicate extraordinary quality of graphene on top of bulk graphite. For more details see ref. 41. Electron Paramag. Reson., 2021, 27, 214–252 | 235

Fig. 13 (a) A single shot magneto-absorption (HFEPR) spectrum of natural graphite of approximate size of 1 mm2 mm and thickness 25 mm at 210 GHz and 5 K. The spectrum is very rich, where in the low field region signal originating from graphene is visible, at fields above 0.8 T not fully understood spectral features are observed. In the inset: picture of the graphite sample. For data comparison: (b) An averaged magneto-absorption spectrum of high-quality graphite of diameter 1 cm and thickness 25 mm recorded by Galt et al. at 24 GHz and 1.1 K. Adapted from ref. 144 with permission from the American Physical Society, Copyright 1956. (c) An averaged magneto-absorption spectrum of pyrolytic graphite of size 1 cm0.7 cm and thickness about 1 mm recorded by Doezema et al. at 890 GHz and 4.2 K. Adapted from ref. 145 with permission from the American Physical Society, Copyright 1979.

thickness 25 mm recorded by Galt et al. at 24 GHz and 1.1 K is shown in Fig. 13b.144 In Fig. 13c, the averaged magneto-absorption spectrum of pyrolytic graphite of size 1 cm0.7 cm and thickness about 1 mm recorded by Doezema et al. at 890 GHz and 4.2 K is presented.145 Furthermore, the HFEPR is very sensitive to impurities of investigated samples. This is very valuable information to the industry dealing with the large-scale production of graphene for future applications. 4.3 Dynamic nuclear polarisation Nuclear magnetic resonance (NMR) is an intrinsically insensitive technique because of a very low equilibrium spin polarisation (B105) even in magnetic fields above 9.4 T (400 MHz, 1H-NMR). On the other hand, electrons have typically three orders of magnitude higher polarisation. Accordingly, it would be great to transfer the electron spin polarisation to the nuclei. This process is known as the dynamic nuclear polarisation (DNP), and it can result in the NMR signal enhancement, E, by thousands of times.150 This enhancement in NMR can lead to the decrease of the signal acquisition time by six orders of magnitude. Note that the acquisition time is proportional to the square of the signal-to-noise enhancement factor (an enhancement of E saves the time by a factor of E2). Historically, even small progresses in magnetic resonance spectroscopy have dramatically changed the landscape of what is possible in NMR, including magnetic resonance imaging (MRI) diagnostics. 236 | Electron Paramag. Reson., 2021, 27, 214–252

In DNP experiments, the electron spin polarisation is transferred from native paramagnetic centres or added special polarising agents151,152 to NMR active nuclei by mw irradiation of EPR transitions.13,14,153–155 The first demonstration of DNP at NMR relevant magnetic field magnitudes (high field for EPR) was done by R. Griffin’s group.13,14 In general, there are three main DNP mechanisms: solid effect, cross effect and Overhauser effect.155,156 The solid effect is dominant in the case of simplest S ¼ 1/2 polarizing agents, such as BDPA, trityl radical. The EPR line is homogeneously broadened and its width is much smaller than the nuclear Larmor frequency o. In contrast, in the cross effect the EPR linewidth is much larger than o. This is the case for polarizing agents with more than one unpaired electron, strong hyperfine interaction and high g-factor anisotropy – TEMPO, AMUPol, etc.151,152 Consequently, this effect is observed at high magnetic fields. There is a strong belief that the liquid DNP via Overhauser effect can enormously increase the sensitivity of NMR and MRI in hospital applications (see Fig. 14a).157 For liquid solutions the DNP enhancement can be written as E¼

hIz i  I0 g ¼ e fsx I0 gn

(12)

Where ge and gn are the gyromagnetic ratios of the electron and the nucleus, respectively, i.e. ge/gnE660 for protons, f ¼ 1  T1R/T1W is the leakage factor, which is determined from the nuclear T1 in the presence (T1R) and in the absence of radicals in the solution (T1W), and reflects

Fig. 14 (a) Comparison between 400 MHz 1H-NMR (no DNP, mw OFF) and liquid-state 400 MHz/263 GHz 1H-DNP of water using 14N-TEMPOL as a polarising agent. An integrated enhancement of E ¼  83 can be observed in the water proton signal. The inset shows the reference spectrum (no DNP) enlarged by a factor of 100 for comparison. Note that a factor of e2 corresponds to a measurement 7000 faster, bringing extremely beneficial consequences to MRI diagnostics (monitoring real-time processes in the human body). (b) NMR line shifts of the peak of a pure water sample (triangles) and a 1 M 14NTEMPOL in water sample (star), plotted against the incident mw power. Through the microwave heating calibration each irradiation power can be assigned a sample temperature (temperature scale on top). By subtracting the temperature shift from the total NMR shift the pure paramagnetic shift is obtained, which can be scaled to yield the saturation factor (squares, scale on the right). Reproduced from ref. 153 with permission from the Royal Society of Chemistry. Electron Paramag. Reson., 2021, 27, 214–252 | 237

the influence of radicals on the nuclear relaxation rate of the used solvent. x is the coupling factor reflecting the nature of the polarisation transfer between the electron and nuclear spins. The factor s denotes the saturation factor, which describes how well the electron transition is saturated by the mw irradiation. It ranges from 0 for no saturation, i.e. thermal population, to 1 for a fully saturated electron spin transition with equalised populations. To understand and optimise DNP at high magnetic fields the contribution from all factors needs to be accessed experimentally. Fig. 14 shows determination of the saturation factor s in a combination of EPR and NMR experiments, which were performed in our previous work.153 In these experiments, the shift of the water proton NMR line position was observed as a function of mw power, which also causes the electron spin level saturation. By subtracting the effect of water warming by the mw irradiation, an elegant approach to determine the saturation factor was demonstrated at a high magnetic field of 9.2 T. Generally, DNP is determined by the transition rates and relaxation processes between energy levels of electron nuclear spin system. Hence it is very important to study T1 and T2 times at the DNP relevant magnetic fields – 8 T and higher which corresponds to EPR at frequencies above 200 GHz (see Table 1). Unfortunately, due to the technical difficulties the common approach of pulse methods is limited at these frequencies. For more details on DNP please refer to ref. 155.

5

Frequency rapid scan EPR at high magnetic fields

5.1 Principles of rapid scan In most CW-EPR experiments, a sample is irradiated by mw with a fixed frequency. At the same time, the energy gap between spin states is gradually changed by varying an external magnetic field B0, which changes the strengths of electron and nuclear Zeeman interactions. During this process, the energy difference among spin states (Ms) can match with the energy of the mw quanta. If the transitions between these states are allowed, then absorption of mw energy and deviation of the electron spin magnetisation from the equilibrium is observed resulting in measurement of an EPR spectrum (Fig. 1). However, there is a less common approach to this conventional method, which is currently more accessible due to the recent development of mw technics. In this approach, the mw frequency is not fixed but can be swept over a large range (see Fig. 2). Notice that the spectral features recorded by sweeping mw frequency are reversed with respect to a conventional EPR (sweep of B0). This is due to the fact that by changing frequency, one changes the excitation energy, while in the conventional EPR the energy is kept constant and the resonance condition is met by the varying magnetic field (see Fig. 2c). However, it is not always possible to exactly obtain frequency scan spectra from conventional EPR spectra recorded by changing magnetic field by a simple reversing and rescaling of the B0 axis. This might be caused by the fact that large variation of B0 during conventional EPR experiment can drastically change field dependent electron Zeeman 238 | Electron Paramag. Reson., 2021, 27, 214–252

interaction and the balance of this interaction with field independent spin interactions such as ZFS or hyperfine interaction. This can lead to a nonlinear dependence of the Hamiltonian eigenvalues on B0. Additionally, spin relaxation rates can also depend on magnetic field, that makes frequency scan experiments performed with constant relaxation rates, whereas for the interpretation of field scan experiments the variation of relaxation rates during the measurements has to be accounted. Hence, frequency scan EPR experiments can provide complementary information about paramagnetic systems especially with broad EPR spectra with widths over tens of gigahertz. Advantageously, the frequency sweep can be performed much faster in comparison to the variation of the B0 field. This enables a faster record of EPR spectra, reduction of measurement time and improving of signal-tonoise ratio. Additionally, when the frequency sweep is made on the time 2 scales shorter than the relaxation times T1 and T2, i.e., when df/dtZT 1,2 , then the shape of EPR spectra becomes more complicated featuring wiggles of spectral lines as seen in Fig. 3 and Fig. 15. Such approach to record EPR spectra with rapidly varied irradiating frequency was originally proposed for NMR and is called rapid scan.158,159 It was observed for the first time by N. Bloemberger et al.160 The emergence of rapid scan spectral wiggles can be already derived from the Bloch equations, 0



1 T2

B dM B B ¼ B Do B dt @ 0

Do 1 T2 o1

1

0 C B C B C o1 CM þ B B C @ 1 A  T1 0

0

1

C 0 C C; C M0 A

(13)

T1

which describe ensemble spin magnetisation M(t) under classical assumptions.161 In the last equation, Do ¼ o  o0 is the difference between o ¼ 2pf and the spin magnetic moment precession angular velocity o0. o1 ¼ gB1 is determined by the magnitude of the microwave magnitude B1. M0 is the value of the sample equilibrium magnetisation. In linear approximation for small B1, the system of eqn (13) can be solved analytically for a time dependent irradiating frequency o(t), with a

Fig. 15 (a) an illustration of influence of the sweep rate in the rapid scan EPR, (b) an example of frequency swept rapid scan HFEPR spectrum of LiPc recorded at 8 T (B224 GHz resonance frequency), its deconvolution, and simulation with T2 ¼ 2.2 ns. Electron Paramag. Reson., 2021, 27, 214–252 | 239

constant sweep rate b, i.e., do/dt ¼ b ¼ const. For the complex transversal magnetisation M1 ¼ Mx þ iMv, the solution of the eqn (13) is ð1 Mþ ðoÞ ¼ io1 M 0

 2  bt t   iðo  o0 Þt dt exp i T2 2

(14)

Fig. 15a shows frequency rapid scan EPR signals, which were computed for the three fixed values of sweep rate b using the last expression. It demonstrates the appearance of signal wiggles by changing the sweep rate from a value much smaller than T 22 to a value much larger than T 22. In more complicated cases, when, for example, the sweep rate is not constant, the Bloch eq. (13) can be solved numerically. In order to describe frequency rapid scan EPR experiments taking into account the quantum nature of high and/or many interacting spin systems with complex relaxation processes, computations of spin density matrix and magnetisation need to be performed based on the Liouville/von Neumann eqn (8), that is a topic of our current research. In this situation, experimental data can be analysed by direct simulations of observed rapid scan EPR signals employing an appropriate computational strategy. From the eqn (14), it follows that rapid scan spectra can be converted into corresponding slow scan spectra. To perform this conversion, an experimentally obtained M1(o) is transferred to the time domain signal S(t) by a Fourier transform. Further S(t) is divided by the driving function exp(ibt2/2) and transferred back to the frequency domain by the inverse Fourier transformation. The slow scan spectra obtained in this way can benefit from the well-developed interpretation and analysis tools of EPR spectroscopy. However, the conversion of rapid into slow scan spectra can be complicated by artefacts. New methods to diminish these artefacts are being developed.162,163 Additional information related to the treatment of rapid scan data can be found in another chapter of this book written by M. Tseitlin. 5.2 Experimental tools for rapid scan EPR The first rapid-scan EPR experiments were performed by Gareth and Sandra Eaton’s group from Denver University in 2005.159 Since then, they have published a number of works dealing with rapid scan EPR at X-band and lower frequencies164–166 and its processing.167–169 In collaboration with Bruker corporation, they have developed and released an accessory for Bruker X-band spectrometers for field domain rapid scan EPR in 2019.170 The main driving force was to improve the signal-to-noise ratio which works particularly well for systems with long relaxation times.171,172 The reason for increased signal-to-noise ratio is that the saturation effects appear at much higher mw power compared to the conventional CW EPR. As the low frequency spectrometers use a singlemode cavity to increase the mw field in the sample, the only possible way of performing rapid scan EPR is to sweep the magnetic field. This approach requires developing of special modulation coils to reach large 240 | Electron Paramag. Reson., 2021, 27, 214–252

sweeps (at least several mT) and, at the same time, high modulation frequency (preferably hundreds of kHz). There were also attempts to use the ENDOR rf coils for generating fast sweeps.173 In the case of broad EPR lines when the scan amplitude cannot cover the whole spectrum, the field stepping can be of help. Several rapid-scan signals are recorded at different values of B0 and then they are all merged into one spectrum.174 HFEPR can benefit from the rapid-scan regime mostly in terms of extracting spin relaxation time as it was shown in the previous section. In HFEPR, it is much more convenient to use the frequency scans instead of sweeping the magnetic field. Firstly, to produce magnetic field sweeps covering entire spectra (anisotropic samples), high-current capable largesized coils with cooling systems are required, and that is very difficult to achieve in the limited space of cryostats. Secondly, the frequency can be swept much faster and cover a wider spectral range. The first rapid scan HFEPR experiment was performed at 94 GHz in 2010 by Hyde et al.33 As a mw source they used a frequency-tuneable yttrium iron garnet (YIG) oscillator with a series of frequency up-conversion mixers. As a result, the highest sweep rate was 180 THz s1 over a 44 MHz range. These parameters are only limited by the YIG oscillator tuning speed, which is usually below 1 GHz ms1. The oscillator’s frequency is controlled by the current flowing through the tuning coil surrounding the YIG sphere. Consequently, the generation of fast and broad sweeps is impossible. A good alternative is to utilise a voltage-controlled oscillator (VCO) where the output mw frequency is controlled by voltage. The tuning speed is tremendously higher and can reach tens of GHz ms1 with the sweep range of 10 GHz. The only drawback is that at such broad sweeps, the linearity of the frequency sweeps is not perfect. With a VCO operating in 8–15 GHz and subsequent multiplication by a factor of 18, we achieved sweeps as fast as 3105 THz s1 and up to 20 GHz broad in the 200 GHz range.32 With such scans it is possible to measure spin relaxation times down to 1 ns which would be never possible for pulsed HFEPR because of the cavity ringing (see Fig. 3). While studying fast relaxation, a special care should be taken with the detection system, e.g. the detector’s bandwidth (or response rate) should not be less than the frequency of wiggles (oscillations in the rapid-scan signal). Otherwise, the high-frequency part of the signal will be attenuated which effectively will decrease the extracted T2. With increasing of the sweep rate, the wiggles appear at higher frequencies. An illustrative example is presented in Fig. 16. For a spin 12 system with T2 ¼ 100 ns a relatively slow detector with 100 MHz bandwidth is enough to record a rapid-scan signal. However, for T2 ¼ 10 ns the detection bandwidth has to be increased to 1 GHz, and in the extreme case of T2 ¼ 1 ns — at least 10 GHz is needed. The essential complication in rapid scan (HF)EPR is the background signal which can be several orders of magnitude stronger than the desired EPR spectrum.32,33,171 This signal appears in field and frequency domain experiments. In the first case, the possible source of the background can be manifold, including temperature drifts, ground loops, vibrations produced by the modulation coil and others.175 Several Electron Paramag. Reson., 2021, 27, 214–252 | 241

Fig. 16 To illustrate the frequency bandwidth of rapid-scan signals simulated for different T2 times. The sweep rate was adjusted for each spectrum to keep the condition df/dt ¼ 10/(2pT22) ¼ 1.6106, 6.4104, 1.6104, 6.4102 and 1.6102 THz s1 for T2 ¼ 1, 5, 10, 50 and 100 ns, respectively. The inset shows an example of the rapid-scan signal.

Fig. 17 Off-resonance removal of background signal in frequency rapid scan HFEPR. (a) Magnified part of the signal. (b) Result of the subtraction. Reproduced from ref. 32 with permission from Elsevier, Copyright 2018.

methods for the background removal have been developed employing Fourier transformation filtering, fitting of the background with subsequent subtraction and instrumentational approaches.162,163,175 In the case of the frequency domain rapid scan HFEPR, the background comes from the standing waves between the mw components (Fig. 17), and perhaps the best way of dealing with it is the off-resonance subtraction.32,33 In this method, one records two data sets - the on-resonance 242 | Electron Paramag. Reson., 2021, 27, 214–252

signal, when the EPR line lies within the sweep range, and the off-resonance signal, when the EPR line is shifted outside the sweep range by changing B0. Then the off-resonance data is subtracted from the onresonance one.

6

Conclusion

In this chapter, we have introduced the HFEPR technique as a dynamically developing method for modern applications in many research areas ranging from material science to medical diagnostics. At the beginning we presented an historical overview of the technic evolution, which is laconically illustrated in Fig. 18 for the time since the first EPR observation until recent days. Further we introduced the hardware of a HFEPR spectrometer and described the theoretical basics for quantitative analysis of experimental data. We then moved to the applications of HFEPR starting with single-molecule magnets, where HFEPR proved to be one of the most powerful methods to precisely determine the magnetic anisotropy of these systems. The power of the technique was explained on an example of a Fe4-complex. This was followed by applications in solid state physics, demonstrating a high sensitivity of recent instruments on graphene and graphite. The last brief example in HFEPR spectroscopy was its application in signal enhancement of NMR spectroscopy via DNP. Although we provided an overview of current HFEPR applications in molecular magnetism and solid-state materials, there is a multitude of research fields taking advantage of this powerful technique. Principles of the conventional CW EPR (field domain) with respect to FDMR (frequency domain) were discussed extensively, including the advances in frequency rapid scan HFEPR. Nowadays, over 90% of CW HFEPR spectrometers are still developed to operate in the field domain because it is technically easier, the mw phase can be adjusted with a QO delay line, or at the down-conversion mixer or digitally during the post-processing. However, the acquisition time for a spectrum is rather

Fig. 18 Photographs documenting more than 75 years progress in development of EPR spectrometers. Left) A copy of original Zavoisky spectrometer operating around 12 MHz, build in 1944. Image credit: Dr S. Zvyagin at the Ye. Zavoisky Memorial Laboratory at Kazan State University, Russia. Right) Under development (ERC Starting Grant AN714850) broadband HFEPR spectrometer operating up to 1 THz at the Central European Institute of Technology (CEITEC), Brno University of Technology, Czech Republic, used for the measurements shown in Fig. 1b, Fig. 2, Fig. 13a, and Fig. 19b. Electron Paramag. Reson., 2021, 27, 214–252 | 243

long and is limited by the sweeping rate of a superconducting magnet. Particularly, for becoming more and more popular cryogen-free (closedcycle) magnets the full sweep can take easily over one hour. On the other hand, the mw frequency scan can be performed much faster, usually in several seconds if the phase-sensitive detection with the magnetic field modulation is used. The main challenge is still the suppression of standing waves (Fig. 17) since they do not only reduce the mw power reaching the sample but also decrease the isolation of the detection arm. From the instrumentation point of view, it can be achieved by implementing additional isolators (Fig. 6). In some cases, digital filtering of recorded spectra can be also useful. As an illustration of FDMR advantages, which have a high potential to extend HFEPR applications, we presented continuous 2D frequency-field maps (Zeeman diagrams) for 14N-TEMPO and molecular magnet Mn12Ac in Fig. 2 and Fig. 19b, respectively. Especially the last demonstrates enormous time saving in multifrequency measurements in comparison to conventional CW-EPR, which requires large sweeps of magnetic field. As a matter of fact, within a band, a full sweep up to 16 T taking about 1.5 hours covers a range of tens of gigahertz. An additional frequency swept map can be seen in Fig. 19a, and the time necessary to acquire it is only limited by the sweep rate of the magnet. Much is still unknown about spin interactions on surfaces and spin dynamics at frequencies above 95 GHz. In the present form, pulsed HFEPR methods are not suitable to study many crucial samples including thin films and bulk materials. Currently, the highest frequency commercially available pulsed HFEPR spectrometer operates at 263 GHz. This spectrometer is restricted to that fixed frequency and due to the use of cavities with mm dimensions, only to either powdered or liquid samples.

Fig. 19 (a) High-resolution 20 00010 000 points HFEPR frequency vs. field map (Zeeman diagram) of a single-chain magnet104 (Mn2saltmen complex) at 30 K overlaid by a simulation in grey dotted lines using parameters from ref. 26. The map was recorded in 8 hours. On the right, the extracted EPR in comparison with conventional CW EPR spectrum. Reproduced from ref. 26 with permission from the Royal Society of Chemistry. (b) Mn12Ac78 HFEPR map (30 000786 points) overlaid by a simulation in green dotted lines using parameters from ref. 176. Both simulations in (a) and (b) were performed with EasySpin.105 244 | Electron Paramag. Reson., 2021, 27, 214–252

The pulsed 263 GHz EPR spectrometer uses very tiny single mode cavity of size 0.5 mm (l/2) and the sample is placed into 100 mm capillary which is a limitation. It means that almost nothing is known about electron spin relaxation at higher frequencies, especially of thin films and bulk materials. This is particularly a problem in quantum computation at THz frequencies and the rapidly growing hyperpolarisation methods (DNP) in NMR, where in both cases optimisation of the spin relaxation of the system is essential. Furthermore, the combination of high mw power and the single mode cavity requires a delay (deadtime) between the end of the last excitation mw pulse and the start of data acquisition to allow the cavity response to ring down and to protect sensitive detectors from burn out. Moreover, the high-power sources are very expensive (4 100 kh) and thus not widely accessible to the scientific community. This means that the pulsed EPR spectroscopy concept is inherently limited to relaxation times longer than several hundreds of nanoseconds. A promising alternative is shown in this chapter (Section 5), where the frequency rapid scan HFEPR is introduced. We show that the spin coherence time can be extracted if the frequency sweep rate is fast compared to the relaxation times.32 For sweep rates faster than the coherence time, the directly detected spectrum will show oscillations in the signal response (transient effects, wiggles) (Fig. 3), which allow the determination of the coherence time.159 Rapid scan EPR, which was pioneered by the Denver group, is performed by few groups mainly at low frequencies (below 10 GHz) by fast magnetic sweeps at a constant microwave frequency using resonant cavities.33,177 Nowadays, it is possible by current technology to build THz-Frequency-Rapid-Scan-EPR (FRaScan) spectrometer shown in Fig. 18 (ERC Starting Grant AN714850), capable of capturing spin dynamics of various systems at the user selected frequency in broad frequency range. The widely used software for EPR simulations EasySpin has already implemented a module for the simulation of spectra in the frequency domain.105,178

Acknowledgements The authors would like to acknowledge all the people from the CEITEC MOTES group for the preparation of this chapter. We also wish to acknowledge the groups (in alphabetical order) of Dr Anne-Laure Barra, Prof. Andrea Cornia, Prof. Sandra S. and Gareth R. Eaton, Prof. Edgard ¨bius, Groenen, Dr Jeffrey Hesler, Dr Valentin Laguta, Prof. Klaus Mo Dr Milan Orlita, Prof. Thomas F. Prisner, Prof. Joris van Slageren, Prof. Graham Smith, Prof. Mark Tseitlin, Prof. Shimon Vega, Prof. Høgni Weihe, Prof. Wolfgang Wernsdorfer, Dr Richard Wylde, Dr Sergey Zvyagin and many others who were involved in the work presented in this chapter.

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