New Directions in the Modeling of Organometallic Reactions [1st ed.] 9783030569952, 9783030569969

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Topics in Organometallic Chemistry  67

Agustí Lledós Gregori Ujaque   Editors

New Directions in the Modeling of Organometallic Reactions

67

Topics in Organometallic Chemistry Series Editors M. Beller, Rostock, Germany P. H. Dixneuf, Rennes CX, France J. Dupont, Porto Alegre, Brazil A. Fürstner, Mülheim, Germany F. Glorius, Münster, Germany L. J. Gooßen, Kaiserslautern, Germany S. P. Nolan, Ghent, Belgium J. Okuda, Aachen, Germany L. A. Oro, Zaragoza, Spain M. Willis, Oxford, UK Q.-L. Zhou, Tianjin, China

Aims and Scope The series Topics in Organometallic Chemistry presents critical overviews of research results in organometallic chemistry. As our understanding of organometallic structure, properties and mechanisms increases, new ways are opened for the design of organometallic compounds and reactions tailored to the needs of such diverse areas as organic synthesis, medical research, biology and materials science. Thus the scope of coverage includes a broad range of topics of pure and applied organometallic chemistry, where new breakthroughs are being achieved that are of significance to a larger scientific audience. The individual volumes of Topics in Organometallic Chemistry are thematic. Review articles are generally invited by the volume editors. All chapters from Topics in Organometallic Chemistry are published Online First with an individual DOI. In references, Topics in Organometallic Chemistry is abbreviated as Top Organomet Chem and cited as a journal. More information about this series at http://www.springer.com/series/3418

Agustí Lledós • Gregori Ujaque Editors

New Directions in the Modeling of Organometallic Reactions With contributions by R. Ardkhean
A. de Aguirre
O. Eisenstein
I. Fernández
V. M. Fernandez-Alvarez
S. P. Fletcher
M. Freindorf
M. Hatanaka
F. Himo
M. Jaraíz
E. Kraka
A. Lledós
S. Maeda
B. K. Mai
F. Maseras
R. S. Paton
M. Swart
G. Ujaque
T. Yoshimura

Editors Agustí Lledós Departament de Química Universitat Autònoma de Barcelona Cerdanyola del Vallès, Barcelona, Spain

Gregori Ujaque Departament de Química Universitat Autònoma de Barcelona Cerdanyola del Vallès, Barcelona, Spain

ISSN 1436-6002 ISSN 1616-8534 (electronic) Topics in Organometallic Chemistry ISBN 978-3-030-56995-2 ISBN 978-3-030-56996-9 (eBook) https://doi.org/10.1007/978-3-030-56996-9 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

The use of computational methods to analyze chemical reactivity in general, and organometallic-based catalysis in particular, has become a common practice among all the chemists working in the field. Nowadays, most PhD students have contact with theoretical calculations during their thesis, by collaborating with computational groups or commonly by performing their own calculations. Thus, theoretical calculations are a tool fully incorporated into the toolkit that a general chemist has available in the lab. This book intends to go further than routine DFT calculations of energy profiles to cover the new directions that computational chemistry is developing to advance the field of homogeneous and organometallic-based catalysis. To this aim, every chapter was commissioned to cover each of the specific aspects where modern computational chemistry is directing its efforts in the organometallic field. Chapter “What Makes a Good (Computed) Energy Profile?” is intended to give a critical overview on the general methods employed to compute energy profiles for mechanistic analysis. It includes a critical description of the main issues a “modeler” must take into consideration to obtain reliable information on reaction mechanisms. Chapter “Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions from Quantum Chemical Calculations” by Prof. Himo covers the computational analysis of reaction mechanisms to a particular process, specifically the F/ CF3/SCF3 transfer reaction, as a representative example on the use of theoretical methods to investigate reaction mechanisms. The characterization of energy profiles, however, is on the way to become a fully automated process. In addition, the automated reaction path search methods allow the exploration of the full PES without a prejudgment of the products as well as the reaction paths. Among them, one of the most successful methods is the artificial force-induced reaction (AFIR) method. Chapter “Artificial Force Induced Reaction Method for Systematic Elucidation of Mechanism and Selectivity in Organometallic Reactions,” by Profs. Miho and Maeda describes the AFIR method including examples of application to organometallic reactions. Computational studies of organometallic reactions have focused traditionally on the calculation of Gibbs energy profiles, but experiments focus on reaction rates, v

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Preface

which depend also on concentrations. Microkinetic modeling, consisting of the construction of explicit kinetic reaction networks, merges the rate constants provided by calculations to reproduce the time evolution of the reaction species; it generates data directly comparable to the experiment. The goal of the chapter “DFT-Based Microkinetic Simulations: A Bridge Between Experiment and Theory in Synthetic Chemistry,” by Prof. M. Jaraíz, is to enable the reader to carry out microkinetic modeling and simulation studies of organometallic reactions, assuming the availability of a set of DFT energy values for the reaction rates involved. To gain quantitative insight into the reactivity trends in organometallic chemistry, in the chapter “A Quantitative Approach to Understanding Reactivity in Organometallic Chemistry” Prof. I. Fernández shows that reaction energy profiles are the base for the application of activation strain model (ASM) and energy decomposition analysis (EDA) methods. In this way a deeper understanding of the physical factors controlling the reactivity can be achieved. The next three chapters show how computational chemistry can be applied to understanding new photocatalytic processes, performing ligand design in asymmetric catalysis, or studying how spin states of the complexes modulate their reactivity. Photoactivated processes play an increasingly important role in chemistry, but the accurate computational characterization of the photoexcitation of the chromophore compounds and the reactivity of the excited state are challenging. In the chapter “Computational Modeling of Selected Photoactivated Processes,” Prof. F. Maseras shows that the application of TD-DFT calculations for the photoactivation step and of conventional DFT calculations for selected regions of the potential energy surface is a powerful approach for mechanistic understanding of such processes. In the chapter “Ligand Design for Asymmetric Catalysis: Combining Mechanistic and Chemoinformatics Approaches,” Prof. R. Paton describes new methods to accelerate the experimental screening process for developing asymmetric catalysts; they show how calculations can guide experiments. Despite the success of DFT methods for reactions involving closed-shell species, DFT calculations of systems in which more than one spin state can be involved are much more challenging. Chapter “Dealing with Spin States in Computational Organometallic Catalysis,” by Prof. M. Swart, presents a detailed account of challenges posed by spin states in computational organometallic chemistry. Modifying and fine-tuning organometallic catalysts requires an in-depth understanding of the complex metal–ligand (ML) interactions playing a key role in determining the properties of organometallic compounds. In the chapter “Characterizing the Metal Ligand Bond Strength via Vibrational Spectroscopy: The Metal Ligand Electronic Parameter MLEP,” Prof. E. Kraka introduces the metal–ligand electronic parameter (MLEP), which is based on the local vibrational ML stretching force constant and that is ideally suited to set up a scale of bond strength orders. The chapters included in this volume give a general overview on how to generate and critically analyze reaction mechanisms employing and combining modern computational techniques. Moreover, some chapters also include reaction types that were not reliably affordable not too long ago. Theoretical methods are mature enough to be successfully applied to the field, though there is still room for the

Preface

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development of more accurate and size-applicable theoretical methods. Note also that the application of automated methods to analyze reaction profiles or to generate targeted ligands will become with no doubt a common approach in this field. Overall, this book is a practical guide for researchers (both theoreticians and experimentalists) interested in having an updated overview on the new directions of theoretical methods applied to organometallic reactions. Barcelona, Spain Barcelona, Spain

Agustí Lledós Gregori Ujaque

Contents

What Makes a Good (Computed) Energy Profile? . . . . . . . . . . . . . . . . . Odile Eisenstein, Gregori Ujaque, and Agustí Lledós

1

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions from Quantum Chemical Calculations . . . . . . . . . . . . . . . . . . Binh Khanh Mai and Fahmi Himo

39

Artificial Force-Induced Reaction Method for Systematic Elucidation of Mechanism and Selectivity in Organometallic Reactions . . . . . . . . . . Miho Hatanaka, Takayoshi Yoshimura, and Satoshi Maeda

57

DFT-Based Microkinetic Simulations: A Bridge Between Experiment and Theory in Synthetic Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . Martín Jaraíz

81

A Quantitative Approach to Understanding Reactivity in Organometallic Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Israel Fernández Computational Modeling of Selected Photoactivated Processes . . . . . . . . 131 Adiran de Aguirre, Victor M. Fernandez-Alvarez, and Feliu Maseras Ligand Design for Asymmetric Catalysis: Combining Mechanistic and Chemoinformatics Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 Ruchuta Ardkhean, Stephen P. Fletcher, and Robert S. Paton Dealing with Spin States in Computational Organometallic Catalysis . . . 191 Marcel Swart Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy: The Metal–Ligand Electronic Parameter (MLEP) . . . . . . 227 Elfi Kraka and Marek Freindorf

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Top Organomet Chem (2020) 67: 1–38 https://doi.org/10.1007/3418_2020_57 # Springer Nature Switzerland AG 2020 Published online: 28 July 2020

What Makes a Good (Computed) Energy Profile? Odile Eisenstein, Gregori Ujaque, and Agustí Lledós

Contents 1 2 3 4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reality and Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Chemical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 What’s Inside the Flask? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Conformational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Electronic Structure Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Spin-State Energetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 The Solvent: Chemical and Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 5 7 8 8 15 18 19 20 22 25 31 32

Abstract A good meal cannot be defined in an absolute manner since it depends strongly on where and how it is eaten and how many people participate. A picnic shared by hikers after a challenging climbing is very different from a birthday party among a family or a banquet for a large convention. All of them can be memorable and also good. The same perspective applies to computational studies. Required level of calculations for spectroscopic properties of small molecular systems and properties of medium or large organic or organometallic, polymetallic systems are different. To well-specified chemical questions and chemical systems, efficient

O. Eisenstein Department of Chemistry and Hylleraas Centre for Quantum Molecular Sciences, University of Oslo, Oslo, Norway ICGM, Université de Montpellier, CNRS, ENSCM, Montpellier, France G. Ujaque and A. Lledós (*) Departament de Química and Centro de Innovación en Química Avanzada (ORFEO-CINQA), Universitat Autònoma de Barcelona, Catalonia, Spain e-mail: [email protected]

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computational strategies can be established. In this chapter, the focus is on the energy profile representation of stoichiometric or catalytic reactions assisted by organometallic molecular entities. The multiple factors that can influence the quality of the calculations of the Gibbs energy profile and thus the mechanistic interpretation of reactions with molecular organometallic complexes are presented and illustrated by examples issued from mostly personal studies. The usual suspects to be discussed are known: representation of molecular models of increasing size, conformational and chemical complexity, methods and levels of calculations, successes and limitations of the density functional methods, thermodynamics corrections, spectator or actor role of the solvent, and static vs dynamics approaches. These well-identified points of concern are illustrated by presentation of computational studies of chemical reactions which are in direct connection with experimental data. Even if problems persist, this chapter aims at illustrating that one can reach a representation of the chemical reality that can be useful to address questions of present chemical interest. Computational chemistry is already well armed to bring meaningful energy information to numerous well-defined questions. Keywords Chemical and theoretical models · DFT calculations · Gibbs energy profile · Organometallic reactions · Reaction mechanism

Abbreviations AIMD CCSD(T) DFT DLPNO ESI-MS HF IGRRHO MD PES

Ab initio molecular dynamics Coupled-cluster method with single and double excitations and perturbative triples Density functional theory Domain-based local pair natural orbital coupled cluster method with single, double, and perturbative triple excitations Electrospray ionization mass spectrometry Hartree-Fock Ideal gas/rigid rotor/harmonic oscillator Molecular dynamics Potential energy surface

1 Introduction Computational methods based on quantum mechanical modeling are increasingly used to provide insights into mechanistic aspects of organometallic reactions [1, 2]. Usually calculations based on density functional theory (DFT) are employed to locate intermediates and transition states along a reaction pathway. The underlying conceptual framework is the potential energy surface (PES) concept that describes the total energy (electronic + nuclear) of a molecular assembly as a

What Makes a Good (Computed) Energy Profile?

3

function of the coordinates of all atoms in the molecular system. All chemically relevant structures (reactants, intermediates, transition states, and products) are stationary structures (i.e., zero-gradient) in the PES. Their associated relative Gibbs energies give the energy landscape of the reaction at given temperature and pressure, and from their sequence a reaction mechanism is inferred. A recent example from our production is shown in Fig. 1 [3], and more examples can be found in the ensuing chapters of this volume, particularly in Chap. 2 [4]. The combination of computational studies with the use of modern experimental tools has enabled great progress in the understanding of reaction mechanisms [5, 6]. The continuously increasing computing power combined with the development of efficient and user-friendly software has allowed the full incorporation of DFT calculations into the toolbox of organometallic chemists’ methods and its widespread use. However, unlike what happened with other physical methods, there is no clear awareness of the limitations of the DFT method and its main error sources. The blind acceptance of computations to interpret reaction mechanisms is behind recent fierce criticisms of computational studies, in which the authors argue that computational studies can be wrong and misleading [7, 8]. Before entering into the detailed analysis about what is behind DFT calculations of energy profiles and what they bring about, some words of caution are in order. The first issue is the proof (or disproof) of a reaction mechanism. This is a key question to all chemists interested in how their stochiometric or catalytic reactions work. For instance, “what constitutes evidence for a catalytic mechanism, as well as how mechanisms should be evaluated” was a topic of a recent Editorial of ACS Catalysis [9]. A postulated reaction mechanism is a working hypothesis, whose predictions must be compared with experiment. Such proposed mechanisms require qualitative as well as quantitative agreement with experimental observables, and those which are inconsistent with observations must be discarded. It results that a reaction mechanism cannot be proven but only disproved [6, 9]. Another point to stress is that, usually, computational methods do not discover reaction pathways, but instead evaluate reactions within the scope of existing chemical knowledge [10]. Computational studies of reaction mechanism are often focused on the productive part of the reaction, but issues like catalyst deactivation or off-cycle reactions generally are not considered [11]. This implies that only a small part of the PES surface is explored. Moreover, in general, there are multiple reaction paths connecting the given reactant and product. The automated reaction path search methods, which have attracted an increasing attention, overcome these problems and allow the exploration of the full PES without a prejudgment of the products as well as the reaction paths [10, 12, 13]. A detailed account about this topic is given in Chap. 3 [14]. It must be also pointed out that computational studies of organometallic reactions have focused traditionally on the calculation of Gibbs energy profiles, but experiments focus on reaction rates, which depend also on concentrations. Microkinetic modeling, consisting in the construction of explicit kinetic reaction networks merging the rate constants provided by calculations, allows to reproduce the evolution through time of the reaction species and, therefore, brings data directly comparable to the

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O. Eisenstein et al. Gibbs energy profile

Proposed reaction mechanism

Fig. 1 DFT computed (B3LYP-D3/BS2 in CH2Cl2) Gibbs energy profile and proposed mechanism for the asymmetric hydrogenation of N-methyl imines to amines [3]. The numbers are relative Gibbs energies in kcal mol
1

What Makes a Good (Computed) Energy Profile?

5

experiments [15]. DFT-based microkinetic simulations are described in Chap. 4 [16]. Finally, it has to be borne in mind that DFT calculations inform on the position of all nuclei at the minima and transition states but do not directly inform on the movement of the electrons which push the nuclei to change places while chemists have used the arrow-pushing description to describe and predict change of structures along a chemical transformation. In this regard, some of us [17] and other authors [18] have recently devised a simple analysis, based on the movement of localized orbitals along a reaction pathway, that allows to extract from computed energy profiles an arrow-pushing description of the electron rearrangements taken place in a reaction mechanism. This introductory chapter is not intended to be a revision on DFT calculations of reaction mechanisms. Several excellent reviews illustrate the relevance acquired by computational methods to unravel reaction mechanism involving transition metal systems [19–22]. The main goal of this chapter is to discuss factors influencing the quality of computational studies on reaction mechanisms, illustrated by selected examples. From the computational side the emphasis has been usually put on what is called the level of theory, which is the technical aspects of the quantum mechanical model (basically the choice of the functional and basis set), but as we will show along this chapter this is not the only aspect to take into account when assessing computational studies on reaction mechanisms. Recent articles have also addressed the scope and challenges [23–25] and pitfalls [26] of computational methods for studying mechanism and reactivity in homogeneous catalysis, evidencing the current practical interest of these issues.

2 Reality and Models What makes computational methods fundamentally different from the common techniques employed in the organometallic lab is that calculations always deal with models [27]. The chemical complexity inside the glass vessel where reaction occurs should be reduced and translated to something that a computer can process. In fact, as outlined in Fig. 2, any quantum mechanical calculation of a chemical reaction system implies the choice of two different models: a chemical model and a theoretical model. The chemical model is the chemical system selected to be computed, in other words, the computer representation of the real chemical world, and the theoretical model defines the level of theory to be employed and thus the computational methods to be used. As there is a whole panoply of possibilities for both, the chemical and the theoretical models, the big modelers’ dilemma is which models to choose, as illustrated in Fig. 3. When dealing with chemical models, some general considerations have to be taken into account: (1) a model is a simple representation of a system that is used to describe and simulate a more complex reality; (2) by definition, a model is always an incomplete description of the real system (Fig. 3). Regarding theoretical models, it

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Fig. 2 From the flask to the computer: chemical and theoretical models

must be stressed that although it is not feasible to solve exactly most of the quantum mechanical problems, methods have been devised to provide approximate solutions of variable degrees of accuracy, and the entire field of computational chemistry is built around approximate solutions. Proper modeling requires to know the approximations employed, or at least to be aware of how accurate the results are expected to be, according to the approximations employed. The first issue to choose the chemical model is the nature of the system to be simulated. The most usual way of performing organometallic reactions is employing molecular species in solution at temperatures often between 0 and 120 C. Simulation of this kind of reactions is the subject of this chapter. Recent thorough reviews have addressed the modeling of surface organometallic reactions [28] and heterogenous catalysis [29]. The larger and the more accurate the model, the more expensive the calculation. For this reason, the usual way of modeling an organometallic system has evolved in parallel with the increase of computing power. In the early years of DFT studies of organometallic reactions, for instance, it was common to model all the phosphine ligands as PH3 (“the theoretician phosphine”) to reduce the size of the system. Nowadays, most of the calculations are performed with the actual molecular species present in the reaction flask, with no simplification. However, this procedure is not always enough to assure a proper modeling of the system, as we will show later on.

Fig. 3 The theoreticians’ dilemma: which model to choose? A true cat (Laia, 1998–2015) and two different models of a cat

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7

3 The Challenges As commented in the previous sections, accurate modeling of an organometallic reaction relies on both a realistic description of the chemical system and a careful use of theoretical methodology. Of course, both issues are constrained by what is possible to be computed at this time. In this way the so-called “state-of-the-art” is defined as the best possible calculation at any given time. Figure 4 summarizes the key factors to take into account when studying computationally the mechanism of organometallic reactions. They are the main challenges that computational organometallic chemistry faces, regarding both the chemical model and the theoretical model, to provide reliable mechanistic information. Regarding the chemical model, the first challenge when looking for the correct mechanism is to take into account in the atomistic description of the system all the species than can affect the energy landscape of the reaction. If something is lacking in the model the correct mechanism cannot be represented on the potential energy surface of the model system. Indeed, this issue has been pointed out as a major challenge for computational mechanistic studies [30]. This implies that, in addition to consider counterions and additives when required, a careful assessment of the reagent’s speciation should be done. Furthermore, attention should be paid to compounds that can exist in many conformations, as the appropriate choice of conformer may be easily overlooked. From the theoretical side, the first issue is the accurate calculation of the electronic energy, with the goal, not yet reached, of being able to compute potential energies and enthalpies with “chemical accuracy” (error less than 1 kcal mol
1). Important advances in this direction have been made in the last years [31, 32]. However, thermodynamics and kinetics of chemical processes do not depend on electronic energies, but on Gibbs energies, which means that entropic effects should be computed and added to the enthalpy term, to obtain Gibbs energies. When modeling organometallic solution chemistry, the inclusion of the solvent in the calculations is mandatory. The way the solvent is included in the calculations is a matter of both chemical and theoretical modeling.

Fig. 4 The main challenges in computational organometallic chemistry

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The way to deal with the questions commented above is crucial to obtain reliable information on reaction mechanisms from calculations. In the next sections we illustrate the aspects outlined in Fig. 4 using examples from our work.

4 The Chemical Model The minimal model to compute an energy profile of a reaction between an organometallic and a substrate is to include the catalyst and one molecule for each reactant. However, other species, like counterions and additives, can be present in the reaction vessel. Moreover, in most of the cases the catalytically active species is not the initial organometallic complex added into the flask, and a careful speciation analysis must be performed. It is important to keep in mind that calculations cannot inform about mechanisms involving species not considered in the chemical model of the system.

4.1 4.1.1

What’s Inside the Flask? Speciation

The iridium complexes [Ir(COD)(1R)Cl] (2R) (where 1R is a P,S ligand: {CpFe[1,2-C5H3(PPh2)(CH2SR)}) hydrogenate aromatic ketones even though they do not contain active protons. To operate they require a strong base such as MeONa or tBuOK and H2 (Scheme 1). No significant activity was observed in the absence of H2 or when a weaker base such as NEt3 was used (Scheme 1) [33]. Therefore, to understand this hydrogenation reaction, the first issue is to determine the active catalytic form of 2R. This can be answered by determining the products that can be formed when the iridium complex 2R, dihydrogen, and a strong base are mixed in alcoholic solvent. To this aim, the relative stability of a number of species that can be formed after loss of COD from [Ir(COD)(1R)]+ along with solvent (iPrOH) coordination, deprotonation, and hydrogenation were investigated by means of DFT calculations [34].

Scheme 1 Asymmetric hydrogenation of alkyl aryl ketones catalyzed by complexes 2R [33]

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Fig. 5 Possible species generated from [Ir(COD)(PS)]+/H2/[MeO(MeOH)5]
, with their relative Gibbs energies in methanol solution (kcal mol
1). In blue: simple model of 1R ligand; in red: real 1R ligand. Encircled in red the most stable species [34]

Exploratory investigations used a simpler model of 1R ligand, where the ferrocene linker was replaced by a –CH¼CH– linker and the phenyl groups by H atoms. Then, the most stable systems were calculated with the real ligands. Methanol was used as a solvent, described as a continuum polarizable medium in the optimizations, but also a cluster of six solvent molecules (MeOH)6 was included in the deprotonation reactions (the base was modeled by [MeO(MeOH)5]
, see Sect. 6). The identified cationic, neutral, and anionic complexes, as well as their relative Gibbs energies in methanol are shown in Fig. 5. Starting from the cationic [Ir(COD)

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Fig. 6 Optimized structures of the dimeric copper(II) diacetate dihydrate (left) and tetrameric sodium tert-butoxide (right). The color code is: copper is orange, oxygen is red, sodium is purple, carbon is dark gray, and hydrogen is off white

(1R)]+, COD removal by hydrogenation, coupled to isopropanol coordination yields cationic [Ir(iPrOH)2(1R)]+. All complexes drawn in Fig. 5 are generated from this complex by deprotonation, hydrogenation, and/or iPrOH reductive elimination. For some complexes several isomers are possible. The conclusion from the speciation study is that the anionic tetrahydrido complex [IrH4(PS)]
(16) should be the most abundant species resulting from the addition of 2R to an alcohol solvent in the presence of H2 and a strong base. Exploration of the hydrogenation mechanisms suggests an operating cycle via a [Na+(MeOH)3Ir
H4(PS)] contact ion pair [34]. Even for simple reagents speciation can be a major issue. Copper(II) acetate is the most commonly used oxidant in oxidative coupling reactions, but full understanding of its role in catalytic cycles is still missing [35]. The representation of copper acetate in calculations is not trivial. The simplest description is Cu(OAc)2. However, in the solid state Cu(OAc)2 is a paddle-wheel dinuclear dihydrate [Cu2(μ-OAc)4(H2O)2] (Fig. 6, left) [36]. Recent electrospray ionization mass spectrometry (ESI-MS) studies of its speciation in organic solvents support extensive aggregation of Cu (OAc)2 in such media [37]. Modeling of copper(II) diacetate as monomeric or dimeric species has significant implications for calculations because it changes the spin state of the PES to explore. In the first case it is a doublet, while in the second case (two copper(II) centers) calculations must be performed for triplet or openshell-singlet states. Calculations highlight the crucial role of the dimeric copper(II) diacetate in the Cu-mediated synthesis of tetrasubstituted olefins by the addition of two nucleophiles (an acetate group and a thiolate) to an unactivated internal alkyne (Scheme 2) [38]. The dimeric copper species confers thiyl radical character to the

What Makes a Good (Computed) Energy Profile?

SH

4a

CH 3

+ H 3C

11 CH 3

+ [CuII(OAc) 2]2

2c

HFIP - HOAc

S

OAc

+ [CuI(OAc)] 2

CH 3 5ac

Scheme 2 Copper-mediated acetoxythiolation of internal alkynes [38]

Cu-coordinated thiol, which generates the active species. Moreover, the transformation, by means of a sequence of changes in the oxidation states of the two Cu (II) centers in Cu(I) centers at the end of the reaction, allows for the release of the two electrons required for the addition of two nucleophiles (SR
and AcO
1) to the alkyne [38]. The same description of copper diacetate was employed in a recent theoretical study of oxidative coupling reactions [39]. Modeling of another simple reagent, sodium tert-butoxide, has also been revisited recently [40]. NaOtBu has been widely used in the Pd-catalyzed Buchwald–Hartwig C–N cross-coupling reaction as non-nucleophilic base to assist the deprotonation event. In a recent DFT study of the Pd-catalyzed N-arylation of ammonia, Baik et al. modeled the base NaOtBu as a tetrameric cubene-type cluster (Fig. 6, right), assuming that this is the most plausible form of the base in non-polar solvent environment (1,4-dioxane, ε ¼ 2.209). The tetrameric geometry of alkali metal alkoxide is supported by previous experimental observations [41, 42] and computational results [40].

4.1.2

Counterions and Additives

When the organometallic species or any of the reagents is ionic, counterions are present in the reaction medium. They used to be considered as innocent partners and not be included in the computational model of the system. However, in the recent years an increasing amount of evidences has revealed the influence that counterions can have in organometallic transformations, particularly in those involving proton transfer steps [43, 44]. Transition metal-mediated alkyne to vinylidene isomerization is a very wellknown process that involves a proton migration step. To analyze counteranion effects in this process we combined experimental and theoretical approaches and studied the transformation of metastable π-alkyne complexes [Cp*Ru(η2-HC  CR) (iPr2PNHPy)]+ into their respective vinylidene isomers (Scheme 3) [45]. Experimental studies demonstrate that the reaction is sensitive to the counteranion present. When the counteranion is BPh4
the isomerization is very slow and requires hours to its completion. However, it takes only minutes in the presence of Cl
. The kinetic study also shows a remarkable increase in reaction rates by addition of LiCl in methanol solution. From DFT calculations a direct intramolecular 1,2-hydrogen shift in the π-alkyne complex can be discarded from its high Gibbs energy barrier. Calculations suggest that a hydrido-alkynyl intermediate is

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Scheme 3 Counteranion effect in ruthenium(II)mediated π-alkyne ! vinylidene isomerization [45]

accessible in this system, but a 1,3-hydrogen shift from the hydrido-alkynyl intermediate also exhibits rather high Gibbs energy barrier. We introduced the chloride anion in the computational model, initially as spectator species, only forming an ion pair with the ruthenium complex (Fig. 7, left). A Cl
anion placed on the ligand N-H side has no significant effect on the barrier. However, if the anion is in the vicinity of the hydrido-alkynyl moiety (Fig. 7, right) it takes an active role in the hydrogen migration. The chloride abstracts the hydrogen atom as a proton, with a significantly lower Gibbs energy barrier and transfers it to the β-carbon. The hydrido ligand should have a relatively strong acidic character to be deprotonated by a chloride. We computed a pKa value of 1.1 for this hydrogen atom, in methanol solution, giving more credit to the chloride-assisted deprotonation step. This study indicates that the role of the counteranion varies with its position. It is thus important to explore widely its influence as a function of its location. The inclusion of couteranions in the DFT study of organometallic reactions has become

Fig. 7 Role of a chloride counteranion in a ruthenium-mediated π-alkyne ! vinylidene isomerization: spectator role (left) and active role (right) [45]. In blue: Gibbs energy barrier in solution of the hydrogen migration step. Hydrogen atoms attached to carbons have been omitted for clarity

What Makes a Good (Computed) Energy Profile?

13

Scheme 4 Usual conditions for iridium-catalyzed ketone hydrogenation (above) and assumed role of the MOR base [49]

increasingly frequent, particularly with calculations of homogeneous gold-catalysis [46–48]. Introduction of countercations in the calculations is still a less common practice, although most of the strong bases employed are anions and their associated alkali metal cation. Alkoxides MOR (M ¼ alkali metal cation) are usually added in ketone hydrogenation processes as depicted in Scheme 4 [49]. The role of the base is supposed to be the deprotonation of an N-H functionality, but DFT studies revealed that the alkali cation also operates by activating the C¼O bond for the hydride transfer (Fig. 8, left). An important point for a realistic description of the process when studying the effect of cations is the solvation of cations [50]. Indeed, in the computational study of the catalytic cycle of ketone hydrogenation with an [Ìr(PS)]+ catalyst we included the Na+ cation coming from the NaOMe base solvated with three methanol solvent molecules (Fig. 8, right) [34].

Fig. 8 Transition states of the hydride transfer step in iridium-catalyzed ketone hydrogenation processes including the alkali metal cation [34, 49]. Hydrogen atoms attached to carbons have been omitted for clarity

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Scheme 5 Elementary steps analyzed for the reductive elimination process in the presence of L additives [53]

The role of an alkali cation as a Lewis acid in the formate decarboxylation catalyzed by an iron pincer complex was analyzed by DFT calculations modeling the cation as [Na(H2O)6]+ [51]. More recently, the study of the effect of Li+ cation on the formic acid dehydrogenation catalyzed by a ruthenium PNP pincer complex (RuPNP) was performed by means of density functional theory-based molecular dynamics with an explicit description of methanol solvent [52]. Since the reactions involve transfer of charged species and are performed in protic solvent mixtures (MeOH/H2O), accounting for solvent interactions and thermal fluctuations is important for a realistic and accurate description of the reaction mechanism, as we will discuss in Sect. 6. The simulations show that the cation interacts with up to four solvent methanol molecules along the reaction, highlighting the importance of considering adequate solvation of the cation. The use of additives is very common in homogeneous catalysis. However, in most cases its role is not well understood, and additives are often neglected in a computational study. Several years ago, a thorough computational study on the role of coupling additives in palladium-catalyzed reductive eliminations showcase that a detailed computational modeling of the system allows to understand their role [53]. For instance, it is known that electron-withdrawing olefins are additives that promote the reductive elimination step when they become a coordinating ligand L to the Pd metal (Scheme 5) [54, 55]. Each stage depicted in Scheme 5 was computed for all R and L combinations. The calculations suggest and the experiment shows that with bulky phosphines the addition of olefins with electron-withdrawing substituents facilitate the coupling through cis-[PdMe2(PR3)(olefin)] intermediates with much lower activation energies than the starting complex or a tricoordinated intermediate [53]. Using a synergistic approach of computations and experiments, the group of Schoenebeck gained mechanistic understanding and guided novel experiments related with the effect of additives in organometallic transformations [5]. Recently the effect of sterically bulky aluminum-based Lewis acid MAD additives (MAD: 2,6-tBu2-4-Me-C6H2O)2AlMe) in the Ni/N-heterocyclic carbene-catalyzed regioand enantioselective C-H cyclization of pyridines with alkenes were explored by DFT calculations [56], unraveling the reasons why MAD additive facilitates the reaction.

What Makes a Good (Computed) Energy Profile?

15

Despite the successful examples commented above, and others that can be found in the literature, we are still far from a regular inclusion of additives in the chemical models of organometallic systems.

4.2

Conformational Complexity

Even when there is no speciation problem and the reactive species are fully identified another important issue for the proper chemical modeling of the system is the recognition that most species have a large variety of conformations and that it is essential to consider the appropriate ones in the study. This was not a problem in the early days of computational mechanistic studies, when simple models were used such as PH3 or PMe3 for any experimentally used phosphine. But nowadays, when the actual full ligands are customarily included in the computed systems, one needs to have confidence that the relevant (lowest energy) conformer(s) are considered. Conformational diversity is often neglected in computational studies of transition metal complexes, even when relatively large systems are present. The importance of conformational search in mechanistic investigations was illustrated through the analysis of the errors that could be caused by a wrong choice of conformers in the computational study of the Suzuki–Miyaura cross-coupling between CH2 ¼ CHBr and CH2 ¼ CHB(OH)2 catalyzed by Pd(PPh3)2] or Pd(PiPr3)2 [57]. Figure 9 displays the Gibbs energy profile for the oxidative addition step to the Pd(PiPr3)2 complex, highlighting the energy differences between the least and the most stable conformer of each of the species present in the reaction pathway. In all cases the error bar is about 10 kcal mol
1, leading to wide oscillations of the computed barrier for randomly chosen conformations. A recent study has emphasized the importance and necessity of conformational analysis for appropriate choice of rotamer prior to any further mechanistic study [58]. A careful conformational search shows that the energy profile for the CO2 insertion into a nickel hydride bond of POCOP iPr nickel hydride complex can be either exergonic or endergonic depending on the rotamer choice. The POCOPiPr Ni-formato complex product of the CO2 insertion reaction has an energy difference between the lowest and highest energy rotamers as high as 16.8 kcal mol
1 [58]. Moreover, not only do conformer effects modify particular reaction barriers, but often the lowest barrier reaction pathway proceeds from a conformer that is not the lowest energy conformer, as evinced in the DFT study of C–C bond forming elementary step (reductive elimination) at Ni bisphosphine catalysts with varying phosphine side chains [59]. These studies show that errors resulting from random selection of conformers can be of the same order or magnitude, or even larger, that the ones coming from a poor choice of DFT functional or the use of a small basis set. Conformational sampling implies generating a large number of conformations whose structure needs to be optimized for allowing energy ranking. When the system becomes large the conformational space grows, and this can be a troublesome and time-consuming work. Thus, different strategies have been devised for

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Fig. 9 Gibbs energy profile for the oxidative addition of CH2 ¼ CHBr to Pd(PiPr3)2 showing the error bar associated with the energy difference between the most and least stable conformer of each species (in brackets). The lowest energy conformer of the transition state is also shown [57]

exploring the conformational space in a systematic way and avoiding, as far as possible, high level quantum mechanical calculations for all the possible rotamers. One approach, used by some of us, combines a large exploration of the conformational space using force-field based molecular dynamics (MD) simulations with high-level quantum mechanical calculations on a selected number of structures (Fig. 10) [60]. Initially classical MD simulations are performed, after incorporating the force field parameters for the metals using Seminario’s method [61] and the MCPB.py program [62]. In this way a total of 10,000 structures are generated. These structures are partitioned into k clusters in which each structure belongs to the cluster with the nearest mean serving as a prototype of the cluster (k-means clustering method). In this way these structures are clustered and the most representative structure for each of the clusters is subsequently optimized at the quantum mechanical (DFT) level. This strategy was applied to the conformational analysis of species 1_A1_H, formed by coordination of aminoalkene 2n to the β-diketiminato cobalt(II) alkyl complex

What Makes a Good (Computed) Energy Profile?

17

Fig. 10 Our strategy for exploring the conformational space [60]

1a-Co. This method leads to select conformation 8 as the lowest one in energy (Fig. 11) [60]. Similar strategies to explore wide conformational spaces, based on an initial thorough search of a whole conformational space by means of low-level methods, followed by further optimization by high-level QM methods, have been employed by other groups [63, 64].

Fig. 11 Conformational analysis of 1_A1_H, formed by coordination of the aminoalkene 2n to the β-diketiminato cobalt(II) alkyl complex 1a-Co [60]

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5 The Theoretical Model Once an appropriate model of the chemical system has been designed, the next step is the choice of the computational methodology (the theoretical model) to obtain an “accurate” energy of the computed system. It is important to remember that quantum mechanical calculations afford the internal energy of the system (electronic + nuclear at fixed nuclei positions) in vacuum and at 0 K. However, the reactions one needs to simulate take place usually in solution at temperatures between 298 and 398 K. Moreover, one needs to compute Gibbs energies because equilibrium and rate constants depend on differences in Gibbs energies, not on internal energies. The transformation of the internal energies into the Gibbs energies in solution (Gsol) adds additional approximations to those already inherent to the internal energies. The relation between the internal energy, ΔE, and the Gibbs energy, ΔG, is shown in Eq. (1): ΔG ¼ ΔE elec þ ΔH thermal
TΔS þ ΔGsolv

ð1Þ

The first term (ΔEelec) is the DFT energy and its quality depends on the reliability of the level of calculation chosen (functional + basis set) to describe the electronic state of the species and reaction under study. The second term (ΔHthermal
TΔS) introduces temperature. It gives the enthalpic and entropic contributions of the solute and requires a frequency calculation to obtain the partition functions for the solute. Therefore, these thermal and entropic corrections give the difference between Gibbs and internal energies (ΔG
ΔE.) The last term (ΔGsolv) introduces the effect of the solvent. It gives the Gibbs energy of the solute–solvent interaction. Nowadays, in many cases the electronic term is already corrected from solvent effect with a continuum description of the solvent (energy calculation with the solute inside a cavity surrounded with a dielectric medium, see Sect. 6) and the energy arising from the QM calculation is ΔEsolv, thus including ΔGsolv. In fact, the common way of proceeding nowadays is to optimize and characterize the stationary points using a medium-size basis set (BS1) and then to refine the energy by means of single-point calculations (no optimization) using an extended basis set (BS2). In this way G values are obtained from Eq. (2):  G ¼ E elec ðBS2Þ þ GðBS1Þ
E ðBS1 þ ΔG1atm!1M

ð2Þ

where Eelec (BS2) is the energy in solution computed with basis set 2, [G (BS1)
E(BS1)] are the enthalpic and entropic corrections computed with a frequency calculation of the optimized structure (basis set 1); the term ΔG1atm ! 1M is the Gibbs energy change for compression of 1 mol of an ideal gas from 1 atm to the 1 M solution phase standard state. It amounts 1.89 kcal mol
1 at 298 K for each species and only affects reactions where the number of moles change (Δn 6¼ 0) [65]. In the following sections we will address the three terms of Eq. (1) in more detail.

What Makes a Good (Computed) Energy Profile?

5.1

19

Electronic Structure Methodology

The quality of the DFT calculated energy relies on the functional employed and the basis set used. The computational efficiency, defined as the time required to complete a calculation, is very much dependent on the basis set size. For this reason, medium-size basis set are commonly employed in the optimization of large systems. A double-ζ basis set including polarization functions for all the atoms (metal and non-metal) usually gives reliable optimized structures, but accurate energies demand single-point calculations with an extended basis set. Regarding the functional, “which functional should I choose?” is usually the first question the modeler is asking him/herself before starting a computational project. It is not the goal of this chapter to describe the enormous progress that has been made in the last decades in the electronic structure methodology. An overview of the performance of DFT methods for calculations of metal complexes can be found in reference [66]. Focusing on the calculations of energy barriers in reactions with transition metal containing organometallic systems, a major problem to assess the quality of the functionals is the small number of experimentally determined Gibbs energies of activation, necessary to benchmark calculations. Another issue is that usually the reactions consist of several steps. The selected computational method should be able to adequately describe all steps, but experimental quantitative energetic information is not usually available for all steps. In the absence of experimental values, the very accurate coupled-cluster method with single and double excitations and perturbative triples, CCSD(T) with extrapolation to the complete basis set limit, is usually used for benchmarking. The CCSD(T) method is widely considered to yield results close to the full CI limit for many systems with straightforward electronic structures. Unfortunately, the size of the organometallic systems to be computed prevents its use in many cases. In the recent years local coupled-cluster methods, such as the domain-based local pair natural orbital coupled cluster method with single, double, and perturbative triple excitations (DLPNO–CCSD(T)) appear as efficient quantum chemical methods which can be used for molecules with hundreds of atoms, providing results of near-CCSD(T) quality at a fraction of the cost and with linear scaling with respect to system size [67]. With the aim of evaluating how accurate is DFT for modeling organometallic reactions, Hopmann has assessed the accuracy of a number of functional for reproducing experimental Gibbs energies of activation of 11 iridium-mediated transformations which correspond to elementary steps usually found in iridium-catalyzed chemistry [68]. Chen et al. have performed a similar study for iridium-catalyzed hydrogenation of olefins [69] and Leitner et al. for ruthenium-catalyzed hydrogenation of olefins [70]. The general conclusion of these studies is that DFT is capable of giving a meaningful description of the energy landscape of the reactions analyzed, provided that dispersion corrections are included. Today it is currently recognized that the inclusion of dispersion effects (as empirical correction, DFT-D, or by dispersion corrected functionals) is mandatory for the computational study of

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organometallic reactions. It is also known that it is preferable to include these effects at the optimization stage. Schoenebeck et al. proved the crucial role of dispersion as reactivity-controlling factor in organometallic reactivity. Using methods which included dispersion correction allowed for the first time to locate the transition states for the oxidative addition of Pd(0)L2 (L ¼ phosphine) to aromatic C
O bonds. In contrast, DFT methods without dispersion correction indicated a preferred pathway involving a phosphine dissociation for all cases considered [71]. For the benchmark studies commented above, the energy differences between functionals incorporating dispersion are usually small, around a few kcal mol
1. This could suggest a small impact of the functional. Unfortunately, this is only true because all reactions which were considered occur on the closed-shell singlet PES. However, and despite the success of DFT methods for reactions involving closedshell species, DFT calculations of systems in which more than one spin state can be involved are much more challenging. In the next subsection we will illustrate the difficulties encountered in using DFT for describing a reaction where more than one spin state could be involved and show how we tackle these problems.

5.2

Spin-State Energetics

Usually, the energy profiles obtained with functionals of similar quality only differ in a few kcal mol
1. However, major discrepancies, which can impact on the interpretation of a reaction mechanism, can appear when radical species are involved. This is a topic of current interest for first-row transition metals where one-electron steps are frequent. Non innocent redox active ligands or substrates can also favor pathways via radical species. When two (or more) spin states are close in energy the usual questions to address are the electronic nature of the ground state and the possible change of spin state along a reaction pathway. These two issues are important for chemical understanding, and Chap. 8 presents a detailed account of challenges posed by spin states in computational organometallic chemistry [72]. The relative energies of different spin states can be obtained from DFT calculations, but the values are very sensitive to the approximation used for the exchange functional, and particularly to the percentage of Hartree-Fock (HF) exchange in the functional. Usually pure functionals (0% HF exchange) stabilize low spin states and high spin states are stabilized by increasing the percentage of exact (HF) exchange [73]. Due to this effect the relative energies obtained with different functionals may differ by 10–30 kcal mol
1. The suitability of the local coupled-cluster methods, as DLPNO-CCSD(T), for describing two-spin-state reactivity is a matter of current discussion [74, 75]. A recent study concluded that even if these methods are promising the approximations used are not yet robust enough to enable applications in demanding systems [74]. The difficulties in evaluating spin-state energy gaps can be illustrated by the study of the mechanism of the cyclohydroamination of primary aliphatic alkenyl-amines catalyzed by a β-diketiminatocobalt(II) complex (Scheme 6) [60]. The question of

What Makes a Good (Computed) Energy Profile?

21

Scheme 6 Cobalt-catalyzed cyclohydroamination [60]

the lower energy spin state (doublet, D, or quartet, Q) of the pre-catalyst 1a-Co was first addressed. The energy difference between these two spin states of 1a-Co was calculated using a range of functionals with different amount of HF exchange. For comparison purposes post-Hartre-Fock methods were also used. Figure 12 displays the computed quartet-doublet energy differences. As already mentioned, higher spin states are stabilized with respect to lower spin states by increasing the amount of the exact exchange in the exchange-correlation functional [73]. This trend is also found for complex 1a-Co, with the doublet state higher in energy than the quartet state. Pure functionals give rise to an energy difference close to 10 kcal mol
1. Hybrid functionals range from 20 to 30 kcalmol
1, depending on the exact exchange introduced. Post-Hartree-Fock methods give the highest energy differences, with values of more than 50 kcalmol
1. Overall, the energy difference between doublet and quartet spin states are highly

Fig. 12 Energy difference between the quartet (Q) and doublet (D) spin states of 1a-Co computed with different methods. In all cases, the quartet state is more stable [60]

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Fig. 13 Relative energies of the quartet (green) and doublet (orange) spin states of the intermediates in the cobalt(II)-catalyzed cyclohydroamination of Scheme 6 [60]

method dependent but the quartet state remains the preferred state regardless of the computational method employed [60]. In order to check the accessibility of lower spin states during the reaction process, the energies of all the intermediates of the favored reaction mechanism in the quartet state were also computed for the doublet spin state. In all cases the energy obtained for the doublet species is always higher than for the quartet ones (between 10 and 25 kcalmol
1, M06 results) [60]. The results are gathered in Fig. 13. These results confidently indicate that the system remains at the quartet spin state during the reaction.

5.3

Entropy

Computational mechanistic studies of chemical reactions rely on Gibbs energy profiles. As commented above, this requires the calculation of entropic contributions (Eqs. (1) and (2)). This is an important factor, notably when there is a change of molecularity (dissociation or association). In this case, the TΔS term at room temperature of the corresponding elementary step amounts about 10 kcal mol
1 [76]. The total entropy of a molecule is the sum of translational, rotational, and vibrational contributions. To derive the partition functions of these contributions, the usual approach is the ideal gas/rigid rotor/harmonic oscillator approach (IGRRHO) calculated in gas phase. However, organometallic reactions usually take place in solution, and the entropic terms must be evaluated in solution. The proper method to

What Makes a Good (Computed) Energy Profile?

23

Fig. 14 Gibbs energy profiles (B3LYP) for the formation of cyclic carbonate from CO2 and 1,2-epoxyhexane catalyzed al Al(III) complex in 1-hexanol solvent. Black line: no entropic corrections to the IGRRHO values; orange line: translational entropy neglected; green line: Martin correction, adding a pressure term that makes the ideal gas to have the density of solvent; blue: Wertz correction based on a ratio related to the molar entropy lost by the solvent. Reproduced from reference [78], with permission from the Royal Society of Chemistry

calculate this term has been a matter of numerous discussions in the past decades. The calculation of the translational entropy in solution has been the most controversial and a summary of this controversy can be found in reference [25]. In the ideal gas approach, it is introduced via particle in a box model by the Sackur-Tetrode equation, and the validity of this equation in solution-phase situations has been questioned [77]. A number of corrections to IGRRHO have been proposed, including the complete neglect of the translational terms of the entropy, considering only one-half or two-thirds of it, modifying the Sackur-Tetrode equation or adding a pressure effect. The importance to evaluate properly the entropic contribution for the calculations of Gibbs energy profiles is illustrated in the study of the Al(III) catalyzed formation of cyclic carbonates from CO2 and epoxides, depicted in Fig. 14 [78]. It is thus interesting to know if the IGRRHO can still be used as an approximation to the entropic contribution. To analyze how the way the entropic term is computed affects the reaction Gibbs energy, the ligand exchanges in the Pd(Ph3)2 complex drawn in Scheme 7 were studied [79]. All processes involve ligand association/ dissociation and therefore are prone to exhibit strong entropic effects. The free energies obtained with different approaches related with the IGRRHO approximation were compared with those obtained from Ab Initio Molecular Dynamics simulations (AIMD). In these simulations 1,000 solvent (toluene) molecules were included. The AIMD method gives the free energy from a completely different approach, unrelated to those of the IGRRHO treatment [80]. The relative free energies of species A, B, C, and D (Scheme 7) obtained with the different models are collected in Table 1. Enthalpic and entropic contributions on the IGRRHO

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Scheme 7 Ligand association-dissociation in Pd(0) complexes [79]

approximation have been obtained with DFT calculations with the PBE-D3 functional, which includes dispersion effects and by means of optimizations in solvent (toluene, SMD model). Results collected in Table 1 shows that the best agreement with the AIMD values is obtained with the direct IGRRHO approach (Table 1, entry 1), with no further corrections. Harvey and Fey found very good quantitative agreement between Gibbs energies in solution for the oxidative addition of PhX to Pd(0)L2 complexes computed in solution using DFT-D functionals and the standard IGRRHO approach and experimental kinetic data [86]. The same conclusion arises from the revisitation by Harvey and Sunoj of the Morita-Baylis reaction mechanism [24]. Overall, these results suggest that part of the errors historically associated with the calculation of translational and rotational entropies in the framework of the Table 1 Relative free energies (kcal mol
1) for species A, B, C, and D (Scheme 7) computed by several IGRRHO-based approximations and AIMD [79]

Standard IGRRHO AIMD St ¼ 0a (1/2)Sb (2/3)Sc Modifiedd Sackur-Tetrode equation Pressuree factor Wertz Correctionf Standard IGRRHO + low-frequency Correctiong a

A Pd (PPh3)2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

B (tol)Pd (PPh3)2 1.6 1.8
13.2
7.2
4.3
2.5
1.6
1.9
1.3

C (tol)Pd (PPh3) 16.7 19.1 19.0 17.6 18.1 16.7

D (tol)2Pd (PPh3)2 21.9 19.8 8.3 15.2 17.5 17.8

Mean absolute difference vs AIMD 1.6 0.0 7.5 5.0 3.1 2.9

16.7 16.8 15.7

18.7 18.5 20.6

2.3 2.4 2.5

Setting the translational term to 0 Setting the translational term to ½ (Sgas-phase) c Setting the translational term to 2/3 (Sgas-phase) d Reference [81] e Gas-phase entropy corrected with a pressure solvent dependent parameter [82] f Reference [83] g Raising of low-lying vibrational frequencies to 100 cm
1 [84, 85] b

What Makes a Good (Computed) Energy Profile?

25

IGRRHO approach came from the lack of dispersion forces in the calculations [79]. It appears that the best currently available way to handle entropic effects for species in solution is through the usual IGRRHO expressions, combined with a continuum solvent treatment of solvation (see next section) and using a dispersioncorrected functional. It is also recommended to compute the partition functions using the calculations obtained with the continuum solvent model, rather than in vacuum. This means that the stationary points have to be located and optimized “in solvent” and the frequencies calculated in the same conditions. When gas-phase and solutionphase geometries and frequencies are similar, the use of gas-phase geometries and frequencies can be a useful approximation. However, for cases where liquid and gas-phase solute structures differ appreciably or when stationary points present in liquid solution do not exist in the gas phase, using partition functions computed for molecules optimized in solution becomes necessary [84].

6 The Solvent: Chemical and Theoretical Model Most of organometallic chemistry is carried out in solvent even though if important developments have been achieved for organometallic on solid supports [87–89]. In parallel, gas phase organometallic reactions has been a topic of interest [90–94]. Several studies were devoted to a better understanding of the difference between gas-phase and solution chemistry (an interesting contrast to reaction in condensed phases) [95–99]. In this chapter, we focus on the reactions occurring in solution. As it should be apparent from what was described before, a good description of solvent effects is essential to a good description of the reaction. Implementing the solvent impacts on both the chemical and computational parts of the computations. Indeed, there are three main approaches for including solvation effects: implicit solvent model, hybrid cluster-continuum model, and explicit solvation (Fig. 15). They differ in accuracy and computational cost. The implicit solvent model, which describes the solvent as a continuum polarizable medium characterized by its dielectric constant ε [100], is the most common way and the computationally less time-consuming approach to treat solvation

Fig. 15 Three different models to include solvent into quantum mechanical calculations

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effects. The solute is placed inside a solvent cavity and the interaction between the solute and the solvent is calculated at the cavity boundaries (Fig. 15, left). The current models have been carefully parameterized to reproduce known experimental solvation Gibbs energies. Continuum models have proved their usefulness to model organometallic reactions and nowadays its use has become mandatory in the organometallic field even for solvents with low dielectric constant [101]. Despite their success, one should not forget that implicit solvent models describe poorly specific interactions between solute and solvent. Moreover, these models fail if solvent molecules take active part in the reaction. For these reasons, in the recent years the studies using hybrid cluster-continuum models in which several solvent molecules are incorporated to the quantum mechanical description of the system, which in turn is placed inside a continuum model, have become increasingly frequent (Fig. 15, middle) [102]. This approach has been successful in many cases, but has an important limitation, related with the limited and fixed number of solvent molecules which can be included. In addition, in the case of a relatively large number of molecules, the geometrical optimization with a high number of positional and conformational isomers can make the study intractable. These limitations vanish using explicit solvent models (Fig. 15, right) in which the solute is placed in a box containing a sufficiently large number of molecules, and molecular dynamics are performed for the whole system either at the quantum, hybrid QM/MM, or full MM levels. However, these calculations may be computationally demanding, and their uses for the study of organometallic reactions are just starting as described in a recent review [80] and the examples shown in the next paragraphs. A recent study has compared explicit and implicit solvent modeling on non-catalyzed and Ag-catalyzed intramolecular C-O coupling between terminal alkyne and β-ketoester moieties to yield a furan ring [103]. The reaction takes place in dimethylformamide (DMF), a highly polar (ε ¼ 36.7) but non-H bond forming solvent. QM/MM molecular dynamics simulations were performed with the explicit solvent model. Analysis of the trajectories obtained from QM/MM calculations indicated neither direct solvent participation in the reaction nor any site-specific reactant–solvent interaction. In this system both solvent approaches give similar energies, pointing out that when a sufficiently mobile, fluctuating solvent shell is present it can be efficiently substituted by implicit solvent models with a huge reduction of the computational costs. A similar approach was employed to compare explicit and implicit solvation models in modeling the free energy profile of the reductive elimination step in Suzuki-Miyaura coupling. The reductive elimination of 2 Ph ligands from Pd(PPh3)2 was modeled in a diverse set of solvents (benzene, toluene, DMF, ethanol, and water) using both QM/MM molecular dynamics simulations and a continuum model (SMD) [104]. Whereas a reasonable correlation between both solvent representations was found in aprotic solvents, the correlation was poor for ethanol and water. The paper stresses the need for considering explicit solvation for modeling Pd-catalyzed reactions in protic solvents [104]. Indeed, this can be a rather general conclusion. Ab initio molecular dynamics simulations of the ruthenium-catalyzed transfer hydrogenation reaction converting formaldehyde into methanol in an explicit methanol solution showed that methanol solvent molecules

What Makes a Good (Computed) Energy Profile?

27

Fig. 16 Relative Gibbs energy (kcal mol
1), in methanol solvent, of the ion pair ([Ir(pic)2(cod)]+, [OCH3]
) with respect to the neutral complex [Ir(pic)2(MeOC8H12)] (2a), with a continuum solvent model and with a cluster-continuum solvent model which incorporates five solvent molecules [106]. Hydrogen atoms attached to carbons have been omitted for clarity

play an active role in the reaction. The reaction in solution may follow a different mechanism than that in the gas phase [105]. In such a case the common computational approach of complementing a quantum-chemical description of the reacting species with a continuum model of the solvent will fail to capture important effects. A proper understanding of reactions in hydrogen-bonded solvents requires taking into account the nearest solvating molecules on an atomistic level. As discussed in the preceding paragraph, specific interactions with the solvent are important in protic solvents such as methanol, particularly on proton transfer reactions. The importance of the proper description of the methanol solvent can be appreciated comparing the relative Gibbs energies in methanol solvent of the ion pair ([Ir(pic)2(cod)]+,[OCH3]
) with respect to the neutral complex [Ir (pic)2(MeOC8H12)] (2a) (Fig. 16). With a pure continuum model the ion pair lies 28.4 kcal mol
1 above 2a, but when a cluster of five molecules of methanol was incorporated to stabilize methoxide anion it was found to be only 11.0 kcal mol
1 above 2a, in much better agreement with the experimental evidences [106]. Another point to be considered when choosing the solvent model is the possibility of solvent coordination to the metal. Divalent ZnMe2 is an important reagent in Negishi couplings, often performed in the low polar tetrahydrofuran solvent (ε ¼ 7.6). We analyzed, by experimental and computational methods, the speciation of ZnMe2, ZnMeCl, and ZnCl2 in THF solution, concluding that the species in THF solution are ZnL2(THF)2 [107]. As a consequence, a cluster-continuum model for the solvent is recommended to obtain a more-correct representation. The presence or absence of THF produces a marked effect on the thermodynamics of the Negishi catalysis and a lesser effect on the kinetics of the transmetallation step, as can be inferred from Fig. 17. A sensitive issue in the hybrid cluster-continuum modeling of the solvent for a reaction is the number of solvent molecules to be included in the cluster, that is, in

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Fig. 17 Gibbs energy profile of the Negishi transmetallation step (kcal mol
1): (top) without explicit THF and (bottom) with two coordinating THF molecules (M06 optimizations in THF described by the SMD continuum model, from reference [107])

the quantum mechanical description of the system. A careful analysis of the influence of the number of solvent molecules should be carried out. This point is illustrated with three examples: the transmetallation step in Suzuki-Miyaura couplings [108], the reductive elimination from Au(III) complexes [109], and the copper-catalyzed hydration of alkenes [110]. The Gibbs energy profiles for three different processes depicted in Fig. 18 evidence how sensitive are the relative energies of the species involved in the reaction, and particularly the reaction barriers, to the number of water molecules incorporated into the cluster-continuum solvation model. For the bromide-by-hydroxide replacement in the palladium-hydroxo mechanism for the Suzuki-Miyaura transmetallation step, similar barriers of 24.2 and 22.9 kcal mol
1 were obtained for the entering OH
solvated by 3 and 4 water

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Fig. 18 Influence of the number of solvent molecules in hybrid cluster-continuum models on the computed Gibbs energy profile: (a) bromide-by-hydroxide replacement leading to a palladium hydroxo complex in the palladium-hydroxo mechanism for the Suzuki-Miyura transmetallation step [108]; (b) reductive elimination from Au(III) complex to form a C–C bond [109]; (c) nucleophilic attack step of the copper-catalyzed hydration of alkenes [110]. On the right, optimized structure of the transition step with the converged number of water molecules for (a) and (c). (a) SuzukiMiyaura transmetallation step, (b) reductive elimination from Au(III) complex, (c) nucleophilic attack of Cu-catalyzed hydration of alkene

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molecules, respectively [108]. Therefore, the series was considered to be converged at n ¼ 3 (green line in Fig. 18a) because the change in the Gibbs energy profile is not significantly modified (by approximately 1 kcal mol
1) with respect to n ¼ 4 (purple line in Fig. 18a). The reductive elimination from Au(III) complex to form a C–C bond was also found to be sensitive to the surrounding number of MeOH solvent molecules. Thus, the reductive elimination barrier was modified from 18.5 kcal/mol from pure continuum model, to 24.2 kcal/mol when including 12 MeOH molecules. Last model approaches the experimental value and corresponds to the complete solvation sphere observed on a MD simulation (green line in Fig. 18b). This effect turned to be crucial to understand the difference between the reaction in solution and inside the cavity of a metallocage [109]. The copper-mediated hydration of α,β-unsaturated 2-acylpyridines in water is a more challenging case because the solvent is also the reagent. First, via QM calculations, the barrier associated with the nucleophilic attack (TSN1) was computed using chains of (H2O)n water molecules, with n equal to 4, 5, 6, and 7 (Fig. 18c). The results show that the barrier is essentially converged at n ¼ 6 [110]. The distribution of water molecules around the copper complex was then assessed in an explicitly solvated system, by means of classical MD simulations. The radial distribution function of water molecules around the double bond shows a minimum around 5.25 Å. Within this distance, about 12 water molecules surround the double bond, six on each side, thus validating the cluster-continuum model [110]. An organometallic reaction that challenges computational methods to describe the solvent is the Grignard reaction. For this reason, and despite it has been employed for more than 100 years, its mechanism has remained elusive until recently. Difficulties in elucidating the Grignard’s mechanism have been mainly related to speciation problems (a solution of Grignard reagents contains a variety of chemical species), the existence of competing mechanisms (polar mechanism, entailing nucleophilic addition or radical mechanism arising from the homolytic Mg-C bond breaking), and the crucial, but not well-understood role of the solvent (an ethereal solvent often THF) in both the Schlenk equilibrium and the C–C bond formation mechanism. Recent ab initio molecular dynamics simulations with an explicit model of the THF solvent, built up by placing the Grignard reagent in a box with a large number of THF molecules (Fig. 19), have shed light to this longstanding controversy [111, 112]. The Schlenk equilibrium implies the transformation of CH3MgCl into MgCl2 and Mg(CH3)2. The AIMD study shown the way that the solvent (THF) plays a crucial role in assisting Cl/Me exchange. The exchange is promoted by making the 2 Mg atoms electronically different, and these differences are created by different solvation of the 2 Mg centers. Thus, it is the change in the solvation number what is inducing the interchange of the methyl and chloride groups between two magnesium centers [111]. Regarding the reaction of an organomagnesium species RMgX where its organic residue R is added to an electrophilic substrate (Grignard reaction), AIMD simulations revealed that the solvent needs to be considered as a reactant for both the nucleophilic and the radical reactions. Solvent dynamics is essential for representing the energy profile. [112] Only an explicit solvent model able to include

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Fig. 19 Simulation box used in the study of the Grignard equilibria. The (MgCH3Cl)2 species were simulated in an orthorhombic periodic box of dimensions 25.2  15.0 Å  15.0 Å3, containing 42 THF molecules. Reproduced from [111]

in the QM system a large number of solvent molecules and to take into account its dynamics have been able to unravel the complexity inherent to this apparently simple and synthetically relevant reaction.

7 Conclusions In the abstract, we suggested a parallel between a good meal and a good computation. Let us return to this comparison. A good meal is strongly dependent on the circumstances during which the meal is eaten. Likewise, the quality of a calculation is defined by its aims: question to be answered, size of the chemical system to be treated, nature of the media, and physical conditions in which the chemical systems is set. The link between the calculations and the question to be asked is an essential question. This is well illustrated in the recent study and retraction of an experimental and computational study of a cryptand-encapsulated Co–O–Co unit [113]. This chapter was retracted because of a reassignment of the nature of the complex which was no longer an oxo but a hydroxy complex. However, as stated “The authors note that the magnetism study, X-ray absorption data, and the theoretical/ computational studies stand on their own merit.” In particular, the calculations were not aimed at probing the existence of the complex but at indicating electronic properties associated with a proposed formula. Thus, at no point could the calculations indicate that the oxo form was not present. In contrast, quantum calculations were useful for structural reassignment when specifically set for this purpose as illustrated by two selected examples [114, 115]. The overall global success in the calculations to reproduce structural features has resulted in the use of theory to determine structures not easily amenable to experimental methods [116, 117].

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As mentioned earlier, this chapter had no intention to be comprehensive. Other examples from the recent literature could have been chosen. It is aimed at illustrating that theoretical treatments of experimental questions which could not be treated few years ago can be done. As computational chemistry became more powerful, new horizons opened and new difficulties appear but they can be overcome provided that an appropriate protocol, which acts as quality control, is applied. We described in detail the many facets of this protocol. They are associated with the chemical complexity of the solute (what is in the flask and how to treat the vast number of structural possibilities), the complexity created by the media (the numerous facets of the effects of the solvent), and the diverse challenges associated with the calculations of the electronic energies and the entropy. It is quite probable that this protocol needs to be updated as new difficulties appear. However, in its present state it should help the practitioner to navigate safely avoiding the many pitfalls that arise during the study. The pleasure to reproduce in silico the experiment through a “good” computational study and thus to propose a mechanistic pathway based on a solid procedure will be fulfilling. Acknowledgments Financial support (GU and AL) was provided by the Spanish Ministerio de Economía y Competitividad (MINECO) (Grant CTQ2017-87889-P). OE was in part supported by Research Council of Norway (RCN) through the COE Hylleraas Center for Quantum Molecular Sciences (Grant number 262695).

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Top Organomet Chem (2020) 67: 39–56 https://doi.org/10.1007/3418_2020_45 # Springer Nature Switzerland AG 2020 Published online: 2 June 2020

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions from Quantum Chemical Calculations Binh Khanh Mai and Fahmi Himo

Contents 1 2 3 4

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zinc-Catalyzed Aminofluorination of Alkenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhodium-Catalyzed Oxyfluorination and Trifluoromethylation of Diazocarbonyl Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Reactions with N–F and N–SCF3 Reagents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

40 41 42 46 49 53 54

Abstract Electrophilic F/CF3/SCF3 transfer reactions have recently emerged as a promising strategy to introduce fluorine substituents to organic compounds at mild conditions with high reactivity and selectivity. Several safe and stable electrophilic reagents have been introduced and have found interesting applications in synthetic chemistry. To control the reactivity and selectivity of these reactions, metal catalysts are typically used in combination with the reagents. Herein, we describe our recent efforts to elucidate the detailed mechanisms and origins of selectivity for a number of metal-catalyzed electrophilic F/CF3/SCF3 transfer reactions using density functional theory calculations. Focus is on reactions employing hypervalent fluoroiodine and nitrogen-based reagents, with zinc or rhodium as the metal catalysts. The roles of the metal ions are discussed, and some novel mechanistic ideas have emerged from these calculations that can have bearing on other reactions for introducing fluorinecontaining groups.

B. K. Mai and F. Himo (*) Department of Organic Chemistry, Arrhenius Laboratory, Stockholm University, Stockholm, Sweden e-mail: [email protected]

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Keywords Density functional theory (DFT) · Fluorination · Hypervalent iodine · Metal catalyst · Reaction mechanism

1 Introduction Introduction of fluorine substituents can dramatically change the physical and chemical properties of organic compounds, such as their metabolic stability, lipophilicity, and membrane permeability [1, 2]. Accordingly, organofluorine compounds have found numerous applications in, e.g., the pharmaceutical and agrochemical industries [3–7]. In addition, 18F-labelled organic compounds are increasingly applied in medical diagnostics as radiotracers in positron-emission tomography, due to the special radionuclear properties of this isotope [8–10]. The increasing demand for synthetic fluorine-containing organic compounds has led to the emergence of new strategies to introduce fluorine to diverse substrates [11– 17]. Depending on the form of fluorine atom transferred, the introduction of fluorine substituents to organic compounds can be classified as being either nucleophilic, electrophilic, or radical [17–19]. While all three strategies have some advantages and disadvantages in terms of reactivity and selectivity, the use of electrophilic fluorination reagents in combination with metal catalysts constitutes an important trend in fluorination chemistry in recent years and has led to significant breakthroughs [15, 17–27]. A number of stable, safe, and easy-to-handle electrophilic reagents have been developed, such as the ones shown in Scheme 1: (X)–I–F/CF3-based hypervalent iodines [11, 13, 20], N-fluorobenzenesulfonimide (NFSI) [28, 29], and trifluoromethylthio-dibenzenesulfonimide (N(SCF3)SI) [30]. In particular, the airand thermostable versions of hypervalent iodine reagents, which contain a benziodoxole(on) carrier for the F/CF3 groups, have been extensively employed and found many interesting applications, allowing for the synthesis of a large diversity of organofluorine compounds [11, 21–27, 31, 32]. Szabó and co-workers have recently reported several elegant methods for the introduction fluorine or fluorine-containing substituents into diverse alkenes and diazocarbonyl compounds in one-pot syntheses by using various electrophilic

F

I

O

F3C

I

O O

1

2

PhO2S

N F 3

SO2Ph

PhO2S

SO2Ph N SCF3 4

Scheme 1 Electrophilic reagents considered in the current study: fluoro-benziodoxole 1, trifluoromethyl-benziodoxolone (Togni reagent, 2), N-fluorobenzenesulfonimide (NFSI, 3), and trifluoromethylthio-dibenzenesulfonimide (N(SCF3)SI, 4)

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . .

41

fluorine reagents, including hypervalent iodines and nitrogen-based reagents, in combination with silver, zinc, and dirhodium catalysts [21, 23–27]. The developed reactions are very interesting because they are typically fast and take place at mild conditions with high regioselectivities and good yields, providing thus excellent latestage strategies to introduce fluorine-containing substituents to bioactive molecules. Mechanistic details of reactions using electrophilic reagents have been studied using both experimental [33–38] and computational [39–53] methodologies. A number of computational studies have also been reported on the activation mechanisms of the fluoro-benziodoxole 1 [54–57] and Togni reagent 2 [58–64], which has certainly provided deeper insights into the characteristics of these compounds. However, the level of understanding of the reactions involving electrophilic reagents, in particular in combination with metal catalysts, is still rather poor, which is an obstacle to the further development of these reactions and to finding new protocols to control and enhance the regio- and stereoselectivities. To this end, quantum chemical calculations can be used to fill this knowledge gap. Quantum chemistry, most importantly density function theory (DFT), is today an essential tool for mechanistic studies of organic and organometallic reactions. The steady improvements of the computational methodologies and the computing resources have made it possible to treat ever-larger systems with ever-increasing accuracy [65–71]. We have in recent years embarked the study of mechanisms of fluorination reactions using computational methodology. In this contribution, we will summarize our experiences by discussing a number of examples. We expect that the detailed understanding of the mechanisms and the origin of selectivity gained from the calculations will facilitate the development of new and improved catalytic systems in this interesting field of chemistry.

2 Technical Details All results discussed were obtained using that B3LYP functional [72, 73], a method that has been used extensively to explore a vast number of organic and organometallic reactions. The free energies represent Gibbs energies, where the rigid-rotor harmonic oscillator (RRHO) approximation has been employed based on analytical frequency calculations. Solvation effects were evaluated by single-point calculations on the optimized structures using implicit solvent models, such as the conductor-like polarizable continuum model (CPCM) [74, 75] and the solvation model based on density (SMD) method [76]. In addition, dispersion effects were included by the D3 or D3(BJ) versions of Grimme’s dispersion method [77, 78]. An important issue that must be noted here is that when the size of the model increases, a thorough conformational search is very important, because each structure can have a number of possible conformers. One has therefore to be careful and perform many calculations in order to identify the lowest-energy conformation for each individual intermediate and transition state. In the examples discussed below, typically 10–20 geometries were optimized for each reported structure by explicitly

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considering various possible rotamers of the molecules and also different relative binding modes of the reactants. In addition, before any mechanistic investigation, a so-called computational speciation study should be carefully carried out in order to identify the most stable complex that could be formed in the mixture of all starting materials, including metal catalysts, reactants, additive reagents, and solvents [79–81]. The most stable complex obtained from this study is used as a starting structure for further mechanistic investigation. Failure to identify the lowest-energy starting complex can lead to large errors in the following energy barriers and might thus result in wrong conclusions about the chemistry. In the case of the zinc-catalyzed aminofluorination reaction discussed below, for example, a careful computational speciation investigation showed that the most stable zinc the complex was a dicationic octahedral structure, in which all six ligands positions were occupied by reagent 1, coordinated by its fluorine atom (see React below). This surprising finding gave a hint as to how the zinc can catalyze the reaction by activating the reagent.

3 Zinc-Catalyzed Aminofluorination of Alkenes The first example of computational mechanistic studies discussed here concerns the aminofluorination reaction reported by Szabó and co-workers using fluorobenziodoxole reagent 1 in combination with zinc catalyst 5 (Scheme 2) [23]. This is an elegant and efficient method to synthesize a wide range of heterocycles with tertiary fluorine substituents with high regioselectivity at mild conditions. The catalytic cycle originally proposed for this reaction involved an iodocyclopropylium cation intermediate formed by the coordination of π-electron of the C¼C double bond to the low-lying empty orbital of the hypervalent iodine [23]. This kind iodonium cation intermediate has been proposed to play an important role in a number of other fluorination reactions [21, 22, 27]. However, this intermediate could not be located in the calculations. As shown in Fig. 1, constrained optimizations by forcing the C¼C double bond to be close to the iodine atom demonstrated that such an intermediate would be associated with very high energies, and the proposal could thus be dismissed [79]. An alternative novel mechanism could instead be put forward on the basis of the calculations. A very interesting initial result of the calculations was that the fluorobenziodoxole reagent was found to coordinate to the zinc ion by its fluorine atom, rather than its oxygen (see React in Fig. 2), in contrast to previous proposals. The F NHTs 6

I

O

[Zn(BF4)2•xH2O] (5)

F

(1 mol%)

+ 1

CH2Cl2, RT, 4h

Scheme 2 Zn-catalyzed aminofluorination of alkenes [23]

NTs 7

(1)

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . .

43

Fig. 1 Energy as a result of constrained optimizations forcing the C¼C double bond of the substrate to be close to the iodine

calculations showed next that an isomerization of the fluoro-benziodoxole is a necessary first step to activate the reagent by making the fluorine substituent trans to the phenyl group instead of the oxygen (Scheme 3). Subsequently, an unexpected reaction was found to occur between the substrate 6 and the activated fluorobenziodoxole reagent. Namely, the C¼C double of the substrate inserts into the activated I–F bond (TS2), whereby the I–F bond is broken and two new C1–I and C2–F bonds are formed, resulting in Int2 (Fig. 2). No coordination of 6 to the catalyst was observed prior to TS2. This reaction step was termed “metathesis” due to the similarity of TS2 with the four-membered transition state of the metalcatalyzed olefin metathesis reaction. From Int2, a change of coordination to give Int3 takes place in which the oxygen atom instead of the fluorine coordinates to zinc ion, upon which a nucleophilic substitution via TS3 can occur, providing hetero-ring Int4. To close the catalytic cycle and regenerate the zinc catalyst, a proton transfer from the nitrogen to the oxygen was found to take place, releasing final product 7 and the iodoarene side product. The rate-determining step of the catalytic cycle was identified to be the nucleophilic substitution (TS3), with an overall barrier of 23.1 kcal/mol relative to Int3 (Scheme 3), in good agreement with the experimental conditions. It was further found that the zinc catalyst plays an important role in all steps of the catalytic cycle, i.e., facilitating the isomerization, metathesis, and substitution steps. Without coordination to the metal ion, the activation barriers for all steps become much higher [79]. A similar role of other Lewis acids had previously been observed for the isomerization of phenyliodine diacetate [82, 83]. Importantly, the proposed

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B. K. Mai and F. Himo

Fig. 2 Optimized geometries selected relevant structures involved in the Zn-catalyzed aminofluorination. Bond distances are given in Å and relative energies are in kcal/mol. The ligands of zinc catalyst are omitted for clarity [79]

mechanism of Scheme 3 could also account for the observed regioselectivity. The reverse metathesis transition state (TS2’), where the C1–F and C2–I are formed instead of C1–I and C2–F, was calculated to be 16.4 kcal/mol higher in energy than TS2. Interestingly, Cheng, Xue, and co-workers have reported theoretical investigations of reactions of various alkenes with hypervalent iodine reagent 1. They also found that the mechanisms for these reactions take place via initial isomerization and metathesis steps [54, 56].

Scheme 3 Catalytic cycle of Zn-catalyzed aminofluorination proposed on the basis of DFT calculations. Red numbers are calculated Gibbs energies (kcal/mol) for each intermediate and transition state relative to React [79]

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . . 45

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B. K. Mai and F. Himo

4 Rhodium-Catalyzed Oxyfluorination and Trifluoromethylation of Diazocarbonyl Compounds The next examples discussed here are concerned with the oxyfluorination and oxytrifluoromethylation reactions of diazocarbonyl compounds with hypervalent iodine reagents 1 and 2, respectively, employing dirhodium catalyst 8 (Scheme 4) [24]. These multi-component reactions run rapidly and efficiently at mild conditions, and very interestingly, the same type of products could be obtained under similar conditions, which is somewhat unusual because the reactivities of reagents 1 and 2 are, in most cases, quite different [21, 84]. The catalytic cycle for the oxyfluorination reaction using reagent 1 proposed on the basis of our calculations is shown in Scheme 5 [81]. In accordance with the originally proposed mechanism [85, 86], the reaction was found to start with nitrogen dissociation to give a Rh-carbene intermediate, followed by an O–H insertion to the carbene species producing an onium ylide intermediate Int8. Both experimental [87, 88] and theoretical [89–92] support existed for these initial steps. From Int8, it was, very interestingly, found that the proton of the hydroxyl moiety can transfer to the carbonyl group with a very low barrier, providing a stable enol intermediate Int9 (Scheme 5), in which the C¼C double bond coordinates to the Rh ion in an η2 fashion. The enol intermediate provides thus the requisite C¼C double bond for the following iodine-assisted fluoro transfer [81]. To proceed, fluoroiodine reagent 1 enters the catalytic cycle, and a concerted proton transfer-electrophilic addition step (TS9, Fig. 3) is calculated to take place, giving thus a new hypervalent iodine intermediate, Int10. At TS9, a C–I bond is formed, and a proton is transferred from hydroxyl moiety of the enol to the oxygen center of the fluoroiodine, resulting in the breaking of the C–O bond of 1. From Int10, the coordination of the Rh ion changes from the oxygen to the fluorine atom, providing a slightly more stable intermediate Int11, which can undergo a cis-trans isomerization via TS10 to yield Int12. At this intermediate, the fluorine is trans to phenyl group, and a ligand coupling can take place via TS11 to form the C–F bond. To close the catalytic cycle, a ligand exchange occurs, releasing final product 11 (Scheme 5). The optimized structures of TS9, TS10, and TS11 are shown in Fig. 3. F

O N2

I

OH

O +

+

[Rh2(OAc)4] (8) (1 mol%)

O O F

CH2Cl2, RT, 15 min 9

1

O N2

F3C

I

10 [Rh2(OAc)4] (8) (1 mol%)

O +

+

11 OH

O

CH2Cl2, RT, 15 min 9

2

10

(2)

O O CF3

(3)

12

Scheme 4 Rh-catalyzed oxyfluorination (2) and oxytrifluoromethylation (3) of diazo carbonyl compounds with hypervalent fluoroiodine reagents [24]

F

Ph

O

F Ph

I

Ph

I O F

O OH

[Rh]

O Ph

O

I Ph Int11 -32.2

O

O OH F

F Ph

Ligand exchange

11 Ph

N2

1

9

Int5 0.0

F

N2

Ph

N2

O

[Rh] TS6 22.6

O

O OH

Ph

I

F

O

1

O Ph Int9 -31.0

OH

Ph

O H [Rh]

Ph

TS7 8.1

Ph

F

TS8 -5.0

[Rh]

Ph O H O

O Ph TS9 -10.7

I

Ph

HO [Rh] O

Ph [Rh]

O

Ph

O

H Int8 [Rh] -7.1

10

Proton transfer via TS8

Ph

O-H insertion via TS7

Proton transfer / Electrophilic addition via TS9

Ph O Int10 -29.0

[Rh]

O

[Rh]

O

I

Carbene Ph [Rh] formation [Rh] Int6 Int7 via TS6 4.1 5.6

Coordination change

[Rh]

Isomerization via TS10

[Rh]

Ph

O

F

9

Ph

O

Ligand coupling via TS11

Int13 Ph -70.2

[Rh]

I OH

O

O

O

O

Int12 -42.9 Ph

[Rh]

I

O

Rh

TS10 -26.4

O OH

TS11 -33.1

Ph

O

I

F

O

OO

Rh

Scheme 5 Catalytic cycle of Rh-catalyzed oxyfluorination using hypervalent fluoroiodine reagent proposed on the basis of DFT calculations. Red numbers are calculated Gibbs energies (kcal/mol) for each intermediate and transition state relative to Int5 [81]

Ph

O

OH

[Rh] =

O

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . . 47

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B. K. Mai and F. Himo

Fig. 3 Optimized structures for selected transition states along the catalytic cycle of Rh-catalyzed oxyfluorination and oxytrifluoromethylation. Bond distances are given in Å. The second reagent that binds to Rh atom and most of hydrogen atoms are omitted for clarity [81]

Based on the calculated energies, the rate-determining step was found to be the carbene formation (TS6), with a barrier of 22.6 kcal/mol relative to Int5 (Scheme 5). However, the barrier for the concerted proton transfer-electrophilic addition transition state TS9 is calculated to be 20.3 kcal/mol, which is quite close to carbene formation TS. Therefore, the rate-determining step could not be singled out confidently on the basis of the DFT calculations alone. The calculated barrier for the overall catalytic cycles is in good agreement with the temperature and reaction time of the experiments [24]. The dirhodium catalyst was found to play important roles in several steps of the reaction mechanism. First, the activation barrier for the carbene formation without dirhodium catalyst was calculated to be 10.7 kcal/mol higher than TS6 [81], which is consistent with the fact that diazocarbonyl compound 2 is a stable reagent at room temperature. Moreover, the dirhodium catalyst serves also as a Lewis acid, similarly to the zinc ion discussed above, to facilitate the cis-trans isomerization of the hypervalent iodine intermediate Int11. Turning to the oxytrifluoromethylation reaction with Togni reagent 2 (Scheme 4), it was found that this reaction proceeds with essentially the same mechanism as the

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . .

49

oxyfluorination. The initial steps up to Int10 are identical, i.e., the carbene formation, O–H insertion, and proton transfer, giving the stable Rh-enol intermediate and the concerted proton transfer-electrophilic addition. The next step has to differ, however, because the trifluoromethyl group of 2 cannot coordinate to the rhodium ion as the fluorine atom of 1 does. Therefore, the following isomerization step cannot be catalyzed by the metal ion and takes place with a much higher barrier, making this step rate-determining for the entire reaction, with an overall barrier of 24.8 kcal/mol. The optimized structures of the TS9CF3, TS10CF3, and TS11CF3 are also given in Fig. 3.

5 Reactions with N–F and N–SCF3 Reagents The final examples discussed here are the oxyaminofluorination and oxyaminotrifluoromethylthiolation reactions of diazocarbonyl compounds catalyzed by the same dirhodium catalyst 8 as in the previous case, but using NFSI 3 or N (SCF3)SI 4 as reagents (Scheme 6) [25, 26]. The calculations show that the two reactions follow exactly the same mechanism, but the energies differ considerably [93]. The initial steps for these reactions involve the formation of carbene intermediate Int16 and a nucleophilic attack of tetrahydrofuran (THF) 13 to yield the onium ylide intermediate Int17, as shown in Scheme 7. These steps are well-established [25, 26] and were calculated to be similar to those in the Rh-catalyzed fluorination discussed in the previous section (Scheme 5). Next, the calculations show that the coordination of the Rh ion changes from the carbon to the oxygen center of onium ylide, giving a slightly less stable Rh-enolate intermediate Int18 (see energy profile in Fig. 4). This coordination change provides thus an alkene intermediate, which is prone to attack by the electrophilic reagent. The steps up to Int18 do not involve reagents 3 and 4, and their energies are therefore identical for both reactions [93]. From Int18, NFSI reagent 3 enters the cycle and the subsequent fluorination is calculated to take place via TS17F forming the C–F bond and an ion-pair intermediate, Int19F. The activation barrier for this step is calculated to be 11.6 kcal/mol O N2

+

PhO2S

9

N F

SO2Ph

+

3

[Rh2(OAc)4] (8) (1 mol%) O

9

PhO2S

SO2Ph N + SCF3 4

F

(1 mol%) O 13

SO2Ph N SO2Ph

(4)

SO2Ph N SO2Ph

(5)

14 [Rh2(OAc)4] (8)

+

O

CH2Cl2, RT, 2-3h

13

O N2

O

CH2Cl2, RT, 2-3h

O O SCF3 15

Scheme 6 Rh-catalyzed oxyaminofluorination and oxyaminotrifluoromethylthiolation of diazocarbonyl compounds using N–F and N–SCF3 reagents [25, 26]

O

F TS18 F

F

O

O

N

9

14

N SO2Ph

PhO2S N F 3

SO2Ph

SO2Ph N SO2Ph Electrophilic fluorination via TS17

[Rh]

N2

13

Ph

Coordination change

O

Ph

[Rh]

O

Int17 (onium ylide)

Ph

O

13 Ph

[Rh]

O

TS16

O

Int16 (Rh-carbene) [Rh]

Nucleophilic attack via TS16

N2

O

N2

[Rh] TS15

O

Carbene formation via TS15

Int18 (Rh-enolate)

Ph

O

Int15

O

[Rh] Int14 9

[Rh]

Ph

SO2Ph

Ligand exchange SO2Ph N SO2Ph

Nucleophilic attack via TS18

Int20 F

O

F

O

SO2Ph

TS17 F

PhO2S

F

O

F Int19 F

O

O

Ph

[Rh]

Ph

[Rh]

SO2Ph N C SO2Ph O H H

Ph

[Rh]

Ph

O

O

Scheme 7 Catalytic cycle of Rh-catalyzed oxyamino-fluorination proposed on the basis of DFT calculations [93]

Ph

[Rh]

[Rh] =

O O Rh O O O O Rh O O O

50 B. K. Mai and F. Himo

Fig. 4 Calculated free energy profiles (kcal/mol) for Rh-catalyzed oxyaminofluorination (red line) and oxyaminotrifluoromethylthiolation (blue line) [93]

Mechanisms of Metal-Catalyzed Electrophilic F/CF3/SCF3 Transfer Reactions. . . 51

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B. K. Mai and F. Himo

Fig. 5 (a) Optimized structures for the fluorination and trifluoromethylthiolation transition states. Energies relative to Int17 are indicated (kcal/mol). The second THF molecule that binds to Rh atom and most of hydrogen atoms are omitted for clarity. (b) The σ orbitals of NFSI and N(SCF3)SI along with their calculated orbital energies (eV)

relative to Int17 (Fig. 4). The onium ylide intermediate Int17 can also undergo an electrophilic attack by NFSI reagent 3 to form the C–F bond without the coordination change. However, the transition state for this scenario was calculated to be 4.1 kcal/mol higher than TS17F, which shows that the formation of C¼C double is very important to promote the electrophilic attack by nitrogen-based reagents [93]. The final step of the reaction is an SN2 attack by the nitrogen species (PhSO2)2N, opening the tetrahydrofuran ring and yielding thus the final product. The barrier for this TS18F is very low, only 3 kcal/mol. Similarly, when the N(SCF3)SI reagent 4 is used instead of NFSI, Rh-enolate Int18 is attacked by the electrophilic SCF3 moiety via TS17SCF to form a C–SCF3

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bond, which is followed by nucleophilic attack and ligand exchange steps, leading to the formation of final product 15. The activation barrier for TS17SCF is calculated to be 8.8 kcal/mol relative to Int17 (Fig. 4). The optimized structures of fluorination/ trifluoromethylthiolation transition states TS17F/TS17SCF are given in Fig. 5. According to the calculated energy profiles shown in Fig. 4, the rate-determining step for both reactions is thus the initial carbene formation. It is finally interesting to compare the activation barriers of TS17F and TS17SCF, which are calculated to be 11.6 and 8.8 kcal/mol, respectively, relative to Int17. The energies of the σN-F orbital of NFSI and the σN-SCF3 orbital of N(SCF3)SI are calculated to be 0.78 eV and 1.14 eV, respectively (Fig. 5). This shows that the σN-SCF3 orbital is easier to be attacked by the HOMO of the C¼C double bond than the σN-F orbital, which explains the lower barrier of TS17SCF compared to TS17F.

6 Conclusions To summarize, we have in this review discussed a number of representative DFT studies from our laboratory on metal-catalyzed F/CF3/SCF3 transfer reactions using different electrophilic reagents. Detailed reaction mechanisms were elucidated and compared with experimental findings, and origins of catalysis and selectivity were highlighted. A number of novel mechanistic features have emerged from these investigations. The calculations reveal that the availability of alkene substrates and/or the formation of requisite intermediates containing C¼C double bond is critical and facilitates the electrophilic F/CF3/SCF3 transfer reactions. The introduction of fluorine substituents using hypervalent iodine reagents can take place via metathesis or concerted proton transfer-electrophilic attack transition state, whereas for the N–F based reagents, the +F/+SCF3 electrophiles transfer directly from reagents to alkenes to form C–F/C–SCF3 bonds. The differences in the activation mechanisms for hypervalent iodine and nitrogen-based reagents can thus generate different types of products under similar reaction conditions [32]. We believe thus that the insights gained by the calculations can be extended to other electrophilic F/CF3/SCF3 transfer reactions and will certainly be very valuable in order to develop new and improved experimental protocols. Finally, the presented work is a testament to the power of modern quantum chemical methods in the field of homogenous catalysis, a development that will undoubtedly continue with even more momentum in the future. Acknowledgment We thank co-workers and collaborators who contributed to this work, in particular Dr. Jiji Zhang and Prof. Kálmán J. Szabó. BKM thanks the Carl-Trygger Foundation for a postdoctoral fellowship. We thank the Knut and Alice Wallenberg Foundation (Dnr: 2018.0066) for financial support.

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Top Organomet Chem (2020) 67: 57–80 https://doi.org/10.1007/3418_2020_51 # Springer Nature Switzerland AG 2020 Published online: 5 July 2020

Artificial Force-Induced Reaction Method for Systematic Elucidation of Mechanism and Selectivity in Organometallic Reactions Miho Hatanaka, Takayoshi Yoshimura, and Satoshi Maeda

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Concept of the Artificial Force-Induced Reaction (AFIR) Method . . . . . . . . . . . . . . . . . . . 2.2 Three Calculation Schemes for the AFIR Method: MC-AFIR, SC-AFIR, and DS-AFIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Reactivity and Selectivity Based on Chemical Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Understanding the Entire Reaction Path Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Applications of the AFIR Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Transition State Sampling Using the MC-AFIR Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

M. Hatanaka (*) Institute for Research Initiatives, Division for Research Strategy, Nara Institute of Science and Technology (NAIST), Ikoma, Nara, Japan Graduate School of Science and Technology and Data Science Center, NAIST, Ikoma, Nara, Japan Department of Chemistry, Faculty of Science and Technology, Keio University, Kohoku-ku, Yokohama, Japan e-mail: [email protected] T. Yoshimura Institute for Research Initiatives, Division for Research Strategy, Nara Institute of Science and Technology (NAIST), Ikoma, Nara, Japan Department of Chemistry, Faculty of Science and Technology, Keio University, Kohoku-ku, Yokohama, Japan S. Maeda Institute for Chemical Reaction Design and Discovery (WPI-ICReDD), Hokkaido University, Sapporo, Japan Department of Chemistry, Faculty of Science, Hokkaido University, Sapporo, Japan Research and Services Division of Materials Data and Integrated System (MaDIS), National Institute for Materials Science, Tsukuba, Japan e-mail: [email protected]

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3.2 Exhaustive Reaction Path Search Using the SC-AFIR Method . . . . . . . . . . . . . . . . . . . . . . . 70 4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

Abstract The computational methods to find the transition states (TSs) are powerful to understand the mechanisms of organometallic reactions. Recently, automatic and systematic search methods of reaction pathways have attracted attention. Among them, one of the most successful methods is the artificial force-induced reaction (AFIR) method. The advantage of the AFIR method is that the reaction pathways can be explored without the prejudgment of the products as well as the reaction coordinates. In this chapter, the concept and algorithms of the AFIR method are described. We also introduce the recent AFIR studies about organometallic reactions and show how the exhaustively gathered TSs contribute to a better understanding of the reaction mechanism and the origin of the selectivity. Keywords Artificial force-induced reaction (AFIR) method · Asymmetric catalytic reaction · Global reaction route mapping (GRRM) · Transition state sampling

1 Introduction Computational chemistry has contributed to the elucidation of the reaction mechanism of organometallic reactions [1–4]. One of the great advantages of computational chemistry is the ability to calculate the stability and geometry of transition state (TS). Many quantum chemical calculation softwares are capable of performing geometry optimization calculations [5], which enable us to obtain the TS along the path of presumed reaction mechanisms. To provide a reasonable initial structure for a geometry optimization calculation, however, enough experience is needed. Thus, computational methodologies to easily obtain TSs for presumed reaction mechanisms have been actively developed. One of the conventional methods is the relaxedscan method (or the coordinate driving method) [6], which repeats energy minimization, while changing the designated coordinate, in the coordinate space orthogonal to that, and gives the energy maximum point along the obtained potential curve as an approximate TS structure. Besides this method, various methods have been developed, including double-end methods, which use the structure of product to guide deciding the search direction [7–14]. Some readers may think that double-end methods could always provide the best reaction path connecting the start and final points of the reaction. In many organometallic reactions, however, it is not true. In general, there are multiple reaction paths connecting the given reactant and product. Among the paths, the most kinetically favorable one is the best reaction path. If there are multiple reaction paths with

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similar activation barriers, they all contribute to the actual reaction mechanism. Therefore, the comprehensive search for kinetically preferable paths is required. Such an extensive search of reaction paths toward multiple types of products makes it possible to semiquantitatively estimate their formation ratio (regio- and/or stereoselectivity); thus, methods to extensively search for paths to designated products have also been actively pursued [15–22]. Besides the difficulty due to the existence of multiple paths, we often meet the difficulty due to the lack of information on products, byproducts, and intermediates. It depends on one’s experience and the degree of complexity of the system to be analyzed whether one can presume an appropriate reaction mechanism. If it is difficult to presume the reaction mechanism, it is necessary to use an automated (unbiased) reaction path search method that systematically searches for reaction paths leading to various (both known and unknown) intermediates and products. Therefore, various methods have been developed for this purpose [23–46]. Although some of these methods can also be applied to organometallic reactions, one that has been used most successfully would be our artificial force-induced reaction (AFIR) method [30]. It was in 2012 when this method was applied to the full catalytic cycle for the first time [47]. Since then, its practical applications have been made to various organometallic systems [19, 25, 48–60]. The AFIR method is available in the GRRM17 program [44]. This chapter, therefore, focuses on the introduction of the theory and applications of the AFIR method.

2 Theory 2.1

Concept of the Artificial Force-Induced Reaction (AFIR) Method

The concept of the AFIR method is that a reaction is induced by pushing reactive parts to each other. Figure 1 shows the conceptual diagram of the AFIR method. The black line represents a potential energy profile of a reaction in which A and B react to form a chemical bond between them. There is a barrier along this profile that prevents A + B to form a chemical bond giving the product A-B. It is possible, Fig. 1 A schematic illustration of the idea of the AFIR method

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however, to remove the barrier by adding a penalty function that is proportional to the distance between A and B (rAB). We call this penalty function as a force term because it applies a constant force between the two atoms. The blue line shows the energy curve of F(rAB) that is obtained by the sum of the potential energy E(rAB) and the force term αrAB. We call the newly defined function F(rAB) “AFIR function.” On the F(rAB) curve, energy minimization allows reaching A-B. After following the F (rAB) curve, the potential energy curve E(rAB) can be reproduced, from which the positions of local minimum and local maximum can also be identified. The reproduced potential energy profile is called “AFIR path.” The obtained AFIR path is useful to find the actual local minimum and TS. One possible way is that the local minima and maxima along the AFIR path are used as the input structures for the optimization of intermediates and TSs, respectively. A more robust way is applying a path optimization method such as locally updated plane (LUP) method [8, 9] to the AFIR path to obtain better input structures for the optimization of intermediates and TSs. To practically apply to polyatomic systems, the AFIR function F(Q) is defined as follows: P P i2A j2B ωij r ij F ðQ Þ ¼ E ðQ Þ þ α P P i2A j2B ωij

ð1Þ

where E(Q) is the potential energy at the coordinate Q and rij is the distance between the atoms i and j. The force term αrij was summed with a weight function ωij for all the pairs of atoms included in the fragments A and B. Note that the fragments are arbitrarily defined by researchers or automatically given by the GRRM program as explained below. The weight function ωij is expressed as follows:  ωij ¼

Ri þ R j r ij

p ð2Þ

where Ri and Rj represent the covalent bond radii of the atoms i and j. p is an arbitrary real number, which is set to 6.0 by default. The calculation results do not largely change regardless of the value of p; similar results are obtained in the range of about 4.0 to 8.0. The parameter α in Eq. 1 that determines the strength of the force is given by the following equation: α¼h 2

16

γ  pffiffiffiffiffiffiffiffiffiffiγ16 i  1þ 1þε R0

ð3Þ

Here, γ is called the model collision energy parameter and gives an approximate upper limit of the barrier that the system can surmount by the artificial force. R0 and ε are the constants, set to 3.8164 Å and 1.0061 kJ mol1, respectively, whose values are from the Lennard-Jones (LJ) parameters for the Ar-Ar pair. The value of

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parameter α corresponds to the mean force that acts on the two Ar atoms in their direct collision on the LJ potential with collision energy γ, in the area from the minimum to the turning point. It was shown with some examples that paths followed by the minimization of the AFIR function were close to the actual reaction paths. In other words, the form of the AFIR function was carefully designed so that paths obtained by the minimization of the AFIR function resemble actual reaction paths as closely as possible. This made it possible to obtain reaction paths just by repeating a simple task that is a minimization of a single, continuous function. To sum up, the approximate reaction path, called the AFIR path, can be obtained by the minimization of the AFIR function in Eq. 1, which can be calculated only from the following three input data: (1) compounds (starting structures) included in the system; (2) definition of the fragmentation (A and B in Eq. 1), which usually includes the reactive atoms in each compound; and (3) value of γ. From the AFIR path, the real TSs as well as the local minima can be computed easily. It should be noteworthy that the value of γ can be decided depending on the purpose. The small γ value could be appropriate to the limited search of the AFIR paths with low activation barriers. The search area could be extended by using the larger γ.

2.2

Three Calculation Schemes for the AFIR Method: MC-AFIR, SC-AFIR, and DS-AFIR

There are three types of algorithms used in the AFIR method. The first is the multicomponent-AFIR (MC-AFIR) algorithm, which is applicable to the systems including two or more compounds. This algorithm takes the various initial structures, in which the mutual position and orientation of each compound are generated randomly. Then, the AFIR function is minimized starting from these initial structures. If the system includes three compounds A, B, and C, force terms between A and C and between B and C are added to Eq. (1). The number of force terms thus increases depending on the number of compounds included in the system. The second is the single-component AFIR (SC-AFIR) algorithm that automatically defines various fragments in a given system composed of either a single molecule or a complex of multiple compounds and applies the artificial force between all pairs of the defined fragments to induce various geometrical deformations. We note that such operations induce not only chemical bond reorganizations but also conformational changes. For instance, an attractive force applied between two methylene groups at different sites in a hydrocarbon first induces a structural change to a conformer in which the two methylene groups are close to each other and finally causes bond reorganizations between the two methylene groups. Fragments are automatically defined for all the atoms included in a system; hence, their combination becomes enormous in a large system. Therefore, an option is available, where the users can specify a small number of atoms (called target atoms) from

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which fragments are defined. When the reaction mechanism is known to a certain extent, the computational effort can be dramatically reduced by specifying the only atoms involved in the mechanism as target atoms. The SC-AFIR algorithm finds many local minimum structures along AFIR paths starting from the initial structure. By default, the SC-AFIR algorithm is applied to all local minimum structures obtained, resulting in a global reaction route map. Even in a small system, a huge number of local minimum structures are obtained, which makes it difficult to apply the AFIR method to all local minimum structures. Therefore, the limited search options are available, which apply the AFIR method only to (1) the input structure, (2) the local minimum structures having the same covalent bond patterns as the input structure, (3) the relatively stable local minimum structures, or (4) the local minimum structures that are kinetically accessible from the input structure. The third is the double-sphere AFIR (DS-AFIR) algorithm that searches for only one path connecting two given structures. This method is named because the path obtained by this method at the zero-force limit is similar to the path obtained by the sphere optimization method [61] and that by the saddle method [62], respectively, in low- and high-energy regions, where the former method traces energy minima on the hypersphere while expanding the sphere radius while the latter method traces them with contracting the sphere radius. The DS-AFIR algorithm tends to obtain the shortest distance path, like other double-end methods when multiple paths exist between two given structures. In general, the shortest distance path tends to be the kinetically most favorable path in one-step processes. It should be noted, however, that in multistep processes, the shortest distance path is not necessarily the kinetically most favorable one.

2.3

Reactivity and Selectivity Based on Chemical Kinetics

The calculated energy levels of local minima and TSs are useful to discuss the reactivity and selectivity. According to the transition state theory, the rate constant can be evaluated by the Gibbs energies of local minima and TSs. When an intrinsic reaction coordinate (IRC) path [63] connects two local minima i and j via one TS, the rate constant kij of the elementary step of thermal reaction from i to j can be estimated by the following equations: k B T ðΔG{ij ΔGi Þ=RT e h  2 1 hν{ Γ ¼1þ 24 k B T

k ij ¼ Γ

ð4Þ ð5Þ

Here, ΔGi and ΔG{ij are the relative Gibbs energies of the local minimum i and the TS between i and j, respectively, kB is the Boltzmann constant, T is the temperature, h is the Planck constant, R is the gas constant, and ν{ is the magnitude

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of the imaginary frequency at the TS. The transmission coefficient Γ in the expression of Eq. (5) is used to take account of a part of the tunneling effect (see ref. [64] for more advanced tunneling theories). Eq. 4 is the expression for unimolecular reactions, and the factor (RT/p0)n1 is multiplied in the nth-order reactions, where p0 corresponds to the standard atmosphere, i.e., 1 atm. In many cases, the reactivity is discussed based on the rate constant at the ratedetermining elementary step. If the most stable structure in the reactant region (the most stable local minimum prior to the TS of rate-determining step) is known, the reactivity is discussed based on the rate constant calculated by the Gibbs energy difference between the TS of the rate-determining step and the most stable local minimum prior to the TS. If thermal equilibrium in the reactant region is assumed, the generalized pre-equilibrium approximation model (or Shaffer’s model) can be applied [65, 66]. In this model, the overall reaction profile is divided into the reactant region R and the others. Then, the overall rate constant from R to the product region is estimated by the following equation: k0ij ¼ P

{ eΔGi =RT k T Γ B eðΔGij ΔGi Þ=RT ΔG =RT p h p2R e

ð6Þ

where ΔG{ij is the relative Gibbs energy of the TS of rate-determining step, ΔGi is the relative Gibbs energy of the local minimum i that is directly linked to the TS through the IRC path toward the R side, and ΔGp is the relative Gibbs energy of a local minimum p belonging to R. The k’ij is obtained by multiplying the Boltzmann distribution of the local minimum i in R to the kij, assuming immediate equilibration in R. The formation ratio among multiple products can be estimated by taking the Boltzmann distribution of the TSs of the rate-determining step from the reactant region R to them. This approach is simple; however, the comprehensive search of the TSs that give each product is needed to evaluate the ratio quantitatively. This approach can be interpreted as the generalized pre-equilibrium approximation model assuming no return from the product sides to R. According to Eq. (6), the overall rate constant from R to one of the product (labeled with n) regions Pn is calculated as follows: kR!Pn ¼

X i2R

"

X j2Pn

{ eΔGi =RT k T P Γ B eðΔGij ΔGi Þ=RT ΔG =RT p h p2R e

# ð7Þ

where the sets R and Pn represent all local minima in the reactant and n-th product regions, respectively. If two local minima i and j are not connected via a TS, the value of ΔG{ij is set to infinity. Meanwhile, if there is no return from the product, the population of the n-th product region Pn at time t is calculated by the following equation:

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Z PPn ðt Þ ¼ k R!Pn

t

PR ðt Þdt

ð8Þ

0

Here, PR(t) and PPn ðt Þ correspond to the population at t of the reactant region R and the n-th product region Pn, respectively. Then, the ratio of PPn ðt Þ relative to the total population of all products is calculated by the following equation: P P ΔG{ij =RT PPn ðt Þ k R!Pn i2R j2Pn e P ¼P P P ¼P { m PPm ðt Þ m k R!Pm eΔGij =RT m

i2R

ð9Þ

j2Pm

Equation (9) represents the Boltzmann distribution of all TSs at the boundary between R and Pn. That is, the selectivity of the reaction can be evaluated based on the Boltzmann distribution of the TS, assuming the generalized pre-equilibrium approximation model and no return from the product region.

2.4

Understanding the Entire Reaction Path Network

To understand complex reaction path networks, network coarse-graining is effective. The rate constant matrix contraction (RCMC) method can realize this systematically based on the chemical kinetics [67]. This method generates a set of states called superstates by combining states (local minima) that transit back and forth on a timescale shorter than a specified value tMAX. This procedure, which combines states into a superstate, is called a contraction. The RCMC method reduces an N  N rate constant matrix for N local minimum structures (MIN) into an n  n rate constant matrix by M times of contraction procedures (n + M ¼ N). Each superstate is a weighted sum of N MINs. When the contribution of MINi to superstate j is ωji, the sum of ωji for all superstates is 1, expressed as follows: Xn j¼1

ωji ¼ 1

ð10Þ

The off-diagonal elements of the resultant n  n rate constant matrix correspond to the overall rate constant from one superstate to another. Since all the rate constants in the reduced n  n rate constant matrix are smaller than specified 1/tMAX, no numerical problem occurs while simulating time evolution. Moreover, it is very useful in elucidating the reaction mechanism, which can be coarse-grained as a transition between a few superstates. It is also possible to predict the selectivity of the reaction by comparing the overall rate constants to the superstate corresponding to different products. The actual contraction procedure is algebraic treatment on the rate constant matrix, but the only conceptual description is given here (see a recent review article [68] for more details of the RCMC method).

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The RCMC method can also estimate the propagation of a given initial distribution up to tMAX. To do this, the traffic volume index Λi has been introduced as an index to estimate the transition volume of population for MINi, where Λi is the sum of the population inflow to and outflow from MINi during M times of contraction procedures [69]. This Λi makes it possible to distinguish MINs with population inflow/outflow from those without that at given initial conditions (population, temperature, and reaction time). Specifically, a reference to Λi during the automated reaction path search allows automatic determination of kinetically important ones among the obtained MINs. Then, the search continues only from kinetically important MINs, eliminating kinetically meaningless regions. This treatment improves the search efficiency dramatically. It should be pointed out, however, that because the Λi value changes every time when the search expands the reaction path network, it is necessary to re-evaluate the Λi value using the RCMC method whenever a new TS is found. The automated reaction path search based on this treatment can also be regarded as on-the-fly kinetic simulation.

3 Applications of the AFIR Method 3.1

Transition State Sampling Using the MC-AFIR Method

One of the advantages of the AFIR method is the TS sampling. To elucidate the mechanism of catalytic reactions, especially the origin of the selectivities, such as chemo-selectivity and stereoselectivity, the TSs affording the major and minor products need to be computed. As mentioned above, the ratio of each product is proportional to the Boltzmann distribution of the corresponding TS. Thus, some pre-selected TSs are not enough to predict the ratio of the products. All the TSs having low activation barriers must be gathered exhaustively. In the case of geometrically rigid systems, the geometry of TSs could be prejudged based on the experience of researchers. In the case of flexible systems, however, it is difficult to prejudge the TS geometries because there could be a number of TSs whose geometries are slightly different. One of the flexible systems is the lanthanide complex in solution. Lanthanide tri-cations (Ln3+) have characteristic electron configurations: open-shell 4f electrons are shielded by closed-shell 5s and 5p electrons from outside. Thus, Ln3+ does not have a rigid coordination sphere, which allows the flexible coordination numbers and structures. In fact, the coordination number of water molecules around Ln3+ in solution is still a topic for open discussion because the value depends on the experimental measurements [70–72]. The Ln3+ complexes are also gathering attention as water-tolerant Lewis acid catalysts. Though the first Ln3+-catalyzed reaction in water solution, called the Kobayashi modification of the Mukaiyama aldol reaction (Scheme 1) [73, 74], was reported in 1994 and a number of experimental measurements were performed to understand the mechanism, there were unsolved questions concerning the role of water. One question is why the product yield of the

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Scheme 1 Kobayashi modification of the Mukaiyama aldol reaction [71]

Fig. 2 Fragments to define the artificial force functions

Mukaiyama aldol reaction catalyzed by Ln(OTf)3 in organic solvent dramatically increased upon addition of water. Another is why the diastereoselectivity of this aqueous reaction shows opposite diastereoselectivity to the same reaction with anhydrous condition. Both two questions were answered based on the information obtained by the MC-AFIR method [48]. To apply the MC-AFIR method, the reactive fragments need to be defined by the users. In this case, all the atoms except for the phenyl group of 1 and the alkyl moiety of 2 were involved in the fragments (Fragm.1–4; see Fig. 2), and several MC-AFIR schemes were carried out. To find step-by-step reaction pathways, every pair of fragments was focused on and the artificial forces were applied to the pair. To explore concerted reaction pathways, artificial forces are simultaneously applied to selected three fragments. In order to cover all the possible approaches, initial relative orientations of the molecules were determined randomly, and at the same time, the initial approach directions of the molecules were selected randomly. Starting from the initial structure, the minimization of the AFIR function was performed. The local minima and local maxima on the AFIR path were focused on as approximate intermediates and approximate TSs, respectively, from which the real intermediates and TSs could be obtained by the geometry optimization without any artificial forces. Second, among the optimized intermediates, the most stable structure (or some of the most stable structures) was picked up, and new fragmentation was defined for the following AFIR calculations. This calculation scheme was repeated until reach to the product 3. Figure 3 shows the most favorable reaction pathway, which answered the first question why the product yield of this catalytic reaction in organic solvent dramatically increased upon addition of water. With water molecules, the equilibrium should shift to the forward direction because the product 8 is enough stabilized by

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Fig. 3 Gibbs energy profile of aqueous Mukaiyama aldol reaction catalyzed by Eu(H2O)8. There reference of the Gibbs energy (ΔG ¼ 0.0) is Eu(OH2)8 + 1 + 2

trimethylsilyl dissociation. Without water molecules, however, the proton transfer and trimethylsilyl dissociation could not take place. Therefore, the backward reaction from 5 to 4 should proceed easily, slowing down the overall reaction. Once the most favorable reaction pathway was clarified, the origin of the stereoselectivity could be discussed based on the TSs of the rate-determining step. As shown in Fig. 3, the TS of the proton transfer had the highest energy level. However, it could be stabilized more as the number of explicit water molecules increases. Thus, it can be said that the rate-determining step of this reaction is the carbon-carbon bond formation step. To estimate the diastereo ratio of the product, as mentioned in Sect. 2.3, the TSs of the carbon-carbon bond formation step need to be gathered exhaustively. In this case study, the MC-AFIR method was applied to gather the TSs. The initial position of the reactant 2 was randomly determined around the complex Eu(H2O)8(1), and the artificial force was applied between the two reactive carbon atoms. We call this procedure “TS sampling.” As a result, 164 transition states were obtained, among which 91 and 73 afforded syn- and anti-products. The Boltzmann distribution of all the obtained TSs reproduced the experimental diastereo ratio (syn: anti), and the reason of the diastereoselectivity dependence on the amount of water was explained by the different hydrogen bond network patterns in the most stable syn- and anti-TSs [19]. The TS sampling using the MC-AFIR method was also applied to discuss the stereoselectivity in asymmetric catalytic reactions [49]. Scheme 2 shows the aqueous Mukaiyama aldol reaction catalyzed by the chiral Ln(III) complex [75]. In this case, the Ln3+ catalyst itself had a flexible structure, i.e., a number of conformers. To find all the possible conformations, another automated reaction path search method, called the anharmonic downward distortion following (ADDF) method [24, 29], was applied. (Note that the computational cost of the ADDF method is pretty high. At that time, the ADDF method was applied on the potential energy surface calculated by the semiempirical PM6 method [76], and then obtained local minima were reoptimized at the B3LYP-D3 level of theory. Nowadays, the similar

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Scheme 2 Aqueous Mukaiyama aldol reaction catalyzed by the chiral Ln(III) complex [73]

Fig. 4 Three stable conformers (conf. A, B, and C) of the chiral catalyst (a), the definition of the dihedral angle ϕ (b), and the distribution of the relative Gibbs energies (ΔΔG in kcal mol1) and the dihedral angles ϕ for the TSs of the C-C bond formation step involving each conformer (c)

conformation search can be done by the SC-AFIR method with a low computational cost.) The TSs of the stereo-determining step were gathered by the MC-AFIR method with the artificial force between the reactive carbon atoms starting from various initial structures including several stable conformers of the catalyst. Figure 4 shows the distribution of the obtained TSs along with the dihedral angle around the reactive carbon atoms. Surprisingly, the structure of the catalyst moiety in the most stable TS was not the most stable conformer (called conf. A) but the second lowest conformer (called conf. B). The most stable TS affording the opposite enantiomeric product also did not involve the structure of conf. A but the third lowest conformer (conf. C). Based on this information, the strategy to improve the enantioselectivity could be built. The simplest strategy was to destabilize the TS affording the opposite enantiomeric product. As mentioned above, the most stable TSs for the major enantiomer and minor enantiomer came from the different conformers of the catalyst, conf. B and conf. C, respectively. Thus, the enantioselectivity could be

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Scheme 3 Four examples (a–d) of the fragments and the artificial forces for the reaction system including 2 and H2O. The L atoms in the same fragment are surrounded in red line. The arrows shown with the plus symbols (in purple) represent the artificial forces to push the fragments. The arrows shown with the minus symbols (in green) represent the repulsive artificial forces to pull the fragments away

improved by reducing the existing probability of conf. C itself. One way to change the existing probability of each conformer is changing the Ln3+ center. This idea was consistent with the experimental results. As shown above, the exhaustive sampling of the TSs of the stereo-determining step made it possible to reproduce the experimental product ratio quantitatively and to establish the strategy for improving the selectivity. It is worth noting that the definition of fragments and artificial forces for the MC-AFIR method is flexible and left to the users. For instance, four definitions of the fragmentations and artificial forces for the MC-AFIR method could be considered to find the reaction pathways between silyl enol ether 2 and a water molecule. In Scheme 3a, all the atoms except for sp3 carbon atoms and adjacent hydrogen atoms are selected as reactive atoms, and the artificial forces were set for every pair between reactive atoms of 2 and those of H2O. In Scheme 3b, one more artificial force, repulsive force between O and H atoms in H2O (shown as the green arrow with the minus symbol), was added to those defined in Scheme 3a. The repulsive force could be helpful to accelerate the dissociation of fragments. When we can prejudge which atoms (or moieties) interact with each other, the artificial force between specific atom pairs (or moiety pairs) shown in Scheme 3c could be possible. Although specific artificial force could accelerate the calculation very effectively, too specific artificial force could cause the missing important pathways. For instance, the artificial force shown in Scheme 3d could accelerate finding the pathway toward the enol; however, it should miss the pathway toward the ketone and other minor product (see Scheme 4). In most cases, we can prejudge the reactive atoms or moieties based on the chemical knowledge, and the MC-AFIR method could be the powerful tool to gather the TSs whose orientations and approach directions are different. However, it is still possible to miss the important reaction pathways due to the bad user’s definition of

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Scheme 4 Possible products from 2 and H2O obtained by the MC-AFIR with the definition shown in Scheme 3a

the fragmentation and artificial forces. One of the methods to overcome this problem is the SC-AFIR method.

3.2

Exhaustive Reaction Path Search Using the SC-AFIR Method

Next, we present a reaction path network constructed by the SC-AFIR algorithm. In the SC-AFIR algorithm, many fragments are automatically assigned in a given system to induce various geometrical deformations by pushing them together or pulling them apart. In default setting, such fragments are defined around all atoms in a system, and the artificial force is applied to all fragment pairs. Therefore, the total cost increases in proportion with N2 depending on the number of atoms N in the system. Moreover, the procedure is applied to all obtained local minimum structures. An SC-AFIR search with this default setting provides a global reaction path network including all local minima and TSs accessible by the artificial force of a given γ. However, the application of such an exhaustive search is limited to relatively simple systems. In order to expand the applicability of SC-AFIR, various options are available. An option which limits atoms to which fragments are assigned (target atoms) and those which limit local minima to which the search procedure is applied are frequently used for this purpose. Below, case studies on Co-catalyzed hydroformylation and Rh-catalyzed asymmetric hydrogen shift reaction are presented. Hydroformylation The Co-catalyzed hydroformylation would be the most thoroughly studied organometallic system [77–82]. Several reports showing application results of automated reaction path search methods have also been made [26, 36, 47, 83, 84]. We have presented a result of applications such as a preliminary version of the SC-AFIR algorithm in which ligands are recognized as fragments and a semiautomatic search that applies the SC-AFIR method sequentially by limiting the target structure with a bonding pattern. This time, we report the result of applying the kinetic navigation, which determines the target structure based on the traffic volume Λi obtained by the RCMC method. In this search, the temperature T and reaction time tMAX when applying the RCMC method were set to T ¼ 300, 400, 500 K and tMAX ¼ 3,600 s. The reaction system was assumed to include HCo(CO)3, CO, H2, and C2H4, and random structures, in which their mutual

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Scheme 5 The entire reaction mechanism extracted using the RCMC method from the reaction path network of Fig. 5 obtained by the SC-AFIR search

positions and orientations were randomly generated, were used as initial structures. The target atoms were H and Co of HCo(CO)3, C of CO, two H of H2, and two C of C2H4, and γ was set to 300 kJ/mol. The AFIR path obtained in the search was refined by the LUP method. The contraction at T ¼ 300, 400, 500 K and tMAX ¼ 103 s by the RCMC method was performed on the reaction path network consisting of approximate paths by the LUP method, and TS and IRC were calculated for the paths that acted as a bottleneck in the transition between the obtained superstates. Therefore, this reaction path network is a hybrid network consisting of the approximate paths obtained by the LUP method and the IRC paths. Kinetic analysis using this network gives approximate solutions for events that proceed in a shorter timescale than 103 s. As for events of a longer timescale than 103 s, on the other hand, it has been shown that the error of using the approximate paths is small enough to be negligible numerically [85]. Electronic structure calculations were performed by Gaussian16, with ωB97X-D functional, SDD basis function and effective core potential for Co, and D95v(d) basis function for other atoms. In Gibbs energy calculations, the normal mode frequencies below 50 cm1 were set to 50 cm1 [86]. Scheme 5 shows the reaction mechanism extracted systematically by the RCMC method from the reaction path network obtained by the search under the above conditions. The label under each structure indicates the number of the local minimum structure on the reaction path network, but the number itself has no significant meaning. 720 and 745 are conformers yet have a structure in which the main product propionaldehyde is coordinated to the active species HCo(CO)3; therefore, their generation was predicted. Moreover, the mechanism to reach 720 or 745 is also in line with the one previously reported. Now, we would like to emphasize that the entire processes from the search to the final extraction of the reaction mechanisms were carried out without any human intervention, except for specifying the atomic

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Fig. 5 The reaction path network for the HCo(CO)3 + CO + H2 + C2H4 system obtained by the SC-AFIR search. Each dot represents local minimum structure, and lines connecting them correspond to reaction paths. Representative structures of the superstates obtained by the contraction applying the RCMC method at T ¼ 400 K and tMAX ¼ 1010 s are shown together with their structure number and relative Gibbs energy against 22

composition, reaction conditions, and target atoms. How this reaction mechanism was extracted from the reaction path network is described as follows. Figure 5 shows the obtained reaction path network. This reaction path network contains 2,601 local minimum structures (nodes). It also shows representative structures along the main reaction path among the superstates obtained by the contraction applying the RCMC method at T ¼ 400 K and tMAX ¼ 1010 s. The representative structures here correspond to local minimum structures contributing most (in terms of the product of the coefficient of the superstate and the Boltzmann distribution) to the corresponding superstate. The label of each representative structure includes the relative Gibbs energy value against 22, which is the representative structure of the reactant superstate. Figure 6 shows the TSs that are acting as the bottlenecks among these ten superstates and local minimum structures obtained as IRC path endpoints from the TSs. In each local minimum structure label, the number of the representative structure of the superstate to which each belongs is indicated in parentheses. These are metastable structures belonging to each superstate and relax to a representative structure in each superstate within 1010 s. These ten structures can be extracted systematically from the reaction path network of Fig. 5. First, contraction using the RCMC method was performed with

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Fig. 6 TSs that are acting as the bottlenecks between superstates obtained by the RCMC method and local minimum structures obtained as IRC path endpoints from the TSs. In each local minimum structure label, the number of the representative structure of the superstate (see Fig. 5) to which each belongs is indicated in parentheses

tMAX ¼ 10n s (n ¼ 10 ~ 3). In the contraction at tMAX ¼ 103 s, the reactant 22 was contracted to the superstate whose representative structure was 1425, which means within 103 s, 22 transformed to 1425. The results were similar at tMAX ¼ 102 s and 101 s. At tMAX ¼ 100 s, however, 22 was contracted to the superstate where 22 itself was the representative structure. Also, the TS of the bottleneck between the superstates whose representative structures were 22 and 1425 turned to be TS262/796. The bottleneck TS corresponds to the most energetically favorable one among the TSs connecting local minimum structures belonging to different superstates. We note that there are multiple TSs connecting local minimum structures belonging to different superstates. In this example, among eight TSs whose forward and backward IRCs reached local minimum structures belonging to the superstate of 22 and 1425, respectively, TS262/796 was most energetically favorable. TS262/796 is a ligand substitution reaction of HCo(CO)4 and affirms the previous studies that this step is the rate-determining step of the hydroformylation reaction.

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At tMAX ¼ 102 s, 262 was contracted to the superstate whose representative structure was 22, while 796 was contracted to the one with 745 being a representative structure. Moreover, TS1270/1167 was obtained as the TS of the bottleneck between the superstates whose representative structures were 745 and 1425. When down to tMAX ¼ 105 s, 796 was contracted to the superstate whose representative structure was 116, resulting in TS511/541 as the TS of the bottleneck between the superstates whose representative structures are 116 and 745. At tMAX ¼ 106 s, 1167 was contracted to the superstate whose representative structure was 1167 itself, and TS1282/1165 was obtained as the TS of the bottleneck between the superstates whose representative structures were 1167 and 1425. At tMAX ¼ 108 s, 1270 was contracted to the superstate whose representative structure was 226, and TS80/350 was obtained as the TS of the bottleneck between the superstates whose representative structures were 745 and 226. At tMAX ¼ 109 s, it was found that 745 was a resting state because both 541 and 80 were contracted to the superstate whose representative structure was 720. Further, TS81/166 was obtained as the TS of the bottleneck between the superstates whose representative structures were 720 and 226. At tMAX ¼ 1010 s, 796 was contracted to the superstate whose representative structure was 23, and 1270 was contracted to the superstate whose representative structure was 1270 itself. Also, TS203/279 and TS475/1270 were obtained as the TS of the bottleneck between the superstates whose representative structures were 23 and 116 and the ones with 226 and 1270 being representative structures, respectively. Additionally, because Fig. 5 shows a hybrid network consisting of approximate paths by the LUP method and IRC paths, the TS of the bottleneck obtained by the contraction at tMAX < 103 s was gained by reoptimizing the approximate paths of the resultant bottlenecks. The reaction mechanism extracted from the reaction path network by the RCMC method is consistent with the reaction mechanism of the hydroformylation reported so far. This study extracted the steps that took a longer timescale than 1010 s as kinetically important steps. We could go on further; the CO coordination step to CH3CH2-Co(CO)3, the H2 coordination step to CH3CH2CO- Co(CO)3, and the H-H bond dissociation step on Co, which proceed on a shorter timescale than 1010 s (through barriers not exceeding ~22 kJ/mol), can be extracted by performing contraction at tMAX < 1010 s. The above result shows that it was possible to execute from the construction of the reaction path network by the SC-AFIR method to the extraction of the reaction mechanism by the RCMC method without any human intervention. In addition to the main product propionaldehyde, the network in Fig. 5 suggests the generation of other products, such as propan-1-ol by adding H2 to 226 and propyl formate by adding H2 to 1425. Previous theoretical studies suggested the generation of ethane [47, 83, 84]. Although paths giving ethane were obtained in the search, little ethane was generated at 400 K on this reaction path network; rather, it was found that ethane became the main product at 500 K. Besides this, many minor byproduct candidates are predicted on this reaction path network. In an actual reaction system, however, it can be imagined that 226 and 1425 are hardly generated because of the rapid replacement of propionaldehyde in 720 and 745 with

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Scheme 6 Asymmetric isomerization reaction using Rh-BINAP complex [88]

Scheme 7 Reaction system used and settings in ONIOM and SC-AFIR

surrounding CO. The chemical composition used in this calculation cannot describe the coordination of CO after propionaldehyde is generated. Similarly, the addition of H2 to 226 and 1425 cannot be described by this calculation, either. There is a previous calculation suggesting that the addition of C2H4 and H2 to 351 will produce ketone [47], which this composition again cannot describe. To take all these into consideration, a calculation must be done after adding at least one extra molecule of each CO, H2, and C2H4, respectively. In addition, Co carbonyl complex is dimerized at the beginning, and one more catalyst molecule is necessary for calculation including its effect. Calculation considering two molecules each would be a future subject. Asymmetric Hydrogen Shift Lastly, we introduce an example of SC-AFIR study [55] on asymmetric hydrogen shift reaction [87]. The reaction scheme is shown in Scheme 6 [88]. This reaction had been studied theoretically using a model system [89], while we considered the entire system using the actual BINAP ligand. It may seem to be difficult to apply the SC-AFIR algorithm because this system consists of more than 100 atoms. However, the application of the SC-AFIR algorithm has been achieved by using appropriate search options and the ONIOM method [90, 91]. Scheme 7 illustrates the model (black) and real (red and black) systems adopted in the ONIOM calculation, where the B3LYP-D3 method was adopted as the high-

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Fig. 7 (a) Reaction mechanism and (b) a simplified reaction path network (the minimum spanning tree) obtained by the SC-AFIR search, for asymmetric isomerization in Scheme 6. In (b), each dot represents local minimum structure, and lines connecting them correspond to reaction paths

level method and the UFF was used as the low-level method. In Scheme 7, the target atoms in SC-AFIR are indicated with an asterisk (*). The SC-AFIR algorithm can be applied even to a system of this size by using the ONIOM method and by designating a few target atoms. The search was applied only to the local minimum structures having the chemical bonding pattern identical to the input structure. In this system, the chemical bonding pattern changes twice when the hydride transfers from the position 1 in the substrate to Rh and when the hydride transfers back from Rh to the position 3 in the substrate to generate the product. Therefore, we prepared three inputs: one is for the reactant complex, the second one is for the intermediate state including Rh-hydride species, and the third one is for the product complex. In these three SC-AFIR searches, γ was set to 300 kJ/mol. By applying the SC-AFIR algorithm to the system modeled using the ONIOM method, we obtained a reaction path network consisting of hundreds of local minimum structures. Figure 7a illustrates the reaction mechanism obtained, of which the SC-AFIR algorithm was used to examine the reaction steps from after the substrate binding to before the product release. The substrate binding step was also examined by the MC-AFIR algorithm, but the results are omitted here. Figure 7 illustrates the dissociative mechanism in which one of the ligands is decoordinated before the substrate binding. The associative mechanism, which we don’t discuss here, was also studied in the original study [55], which has been revealed to be energetically disadvantageous. Since the reaction path network obtained by the SC-AFIR algorithm was very complicated, Prim’s method, a graph theoretical algorithm, was applied to obtain the network corresponding to the minimum spanning tree (Fig. 7b). In this network, nodes representing the reactant-catalyst complex

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Fig. 8 The energy profile of the kinetically most favorable path for each of the major (black) and minor (blue) products

are shown in green, those for the Rh-hydride species are in yellow, and those for the product-catalyst complex are in pink. Figure 8 illustrates the energy profile obtained by selecting the kinetically most favorable path for each of the major and minor products from this network. The selectivity can be explained by comparing the highest energy points of each energy profile. It should be noted that selectivity is determined not at the TS of the hydride transfer step but the TS of a coordination bond rearrangement step. The most stable structure in the reactant region is that in which the substrate is coordinated to Rh in a chelate form by the amine nitrogen and the C¼C double bond. To change from this structure to the TS of C-H activation, the amine nitrogen must dissociate from Rh. Figure 8 verifies that the selectivity was determined in the process of the amine nitrogen being dissociated from Rh. In other words, the selectivity was elucidated by taking account of the entire reaction path network rather than focusing only on the TS of chemical bonds reorganization step. Although such cases might be rare, this application could prove the importance of exploring the reaction path network in mechanistic studies on organometallic reactions.

4 Conclusion The information of the transition states (TSs) is indispensable to better understanding of the mechanism of organometallic reactions. Though a number of the computational methods have been developed, finding TSs was still not easy because of the

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difficulty in prejudgment of the reaction coordinate. To overcome this problem, automated reaction path search methods, such as the artificial force-induced reaction (AFIR) method, have been developed. The concept of the AFIR method is that the reactive parts are pushed together (or pulled apart) by the artificial force to surmount the activation barrier. The AFIR method does not require the information on the products as well as the reaction coordinates. The TSs having different conformations as well as those affording major and minor products can be gathered exhaustively. The obtained numerous TSs are useful to estimate the product ratio (selectivity), which is done by the conventional Boltzmann distribution analysis or using an advanced kinetic method like the rate constant matrix contraction (RCMC) method. The AFIR method has three algorithms called MC-AFIR, SC-AFIR, and DS-AFIR. MC-AFIR is powerful to find the TSs for the specific reaction step. In the case studies of the lanthanide-catalyzed Mukaiyama aldol reactions, the MC-AFIR was used to gather the TSs of the rate-determining steps exhaustively. The experimental stereo ratios were reproduced by considering the Boltzmann distribution of all obtained TSs. A comparison of the two lowest TSs was not enough to get a deep insight into the origin of the stereoselectivity. We also introduced two case studies of the SC-AFIR. For hydroformylation of ethylene catalyzed by HCo (CO)3, a reaction path network consisting of both the major channel and the channels to various byproducts was generated automatically. Furthermore, the systematic extraction of reaction mechanisms from the complex reaction path network was demonstrated using the RCMC method. In the application to asymmetric isomerization catalyzed by Rh-BINAP, it was demonstrated that using the ONIOM method and adopting appropriate options of the SC-AFIR allowed us to generate a reaction path network for the system consisting of more than 100 atoms. These examples illustrated the practical applicability of automated reaction path search using the AFIR method to studies on the mechanisms of organometallic reactions.

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Top Organomet Chem (2020) 67: 81–106 https://doi.org/10.1007/3418_2020_44 # Springer Nature Switzerland AG 2020 Published online: 11 July 2020

DFT-Based Microkinetic Simulations: A Bridge Between Experiment and Theory in Synthetic Chemistry Martín Jaraíz

Contents 1 2 3 4 5

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Identification of Mechanisms: Experimental Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Calculation of DFT Energies: Theoretical Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Running Kinetic Simulations: A Brief Tutorial . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Case Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.1 Example 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2 Example 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Abstract The goal of this chapter is to enable the reader to carry out microkinetic modeling and simulation studies of synthetic chemistry problems, assuming the availability of a set of DFT energy values for the reaction rates involved. To this end, after a brief introduction, we describe the tools that we use and the modeling methodology that we follow and then provide a short tutorial and input files for the microkinetic simulator that we normally use (available free of charge). Finally, we analyze two case examples to show the remarkable level of insight and prediction power attainable with this DFT-based microkinetic modeling methodology. Keywords DFT · Mechanism · Microkinetic · Modeling · Reaction rate · Simulation

Electronic supplementary material The online version of this chapter (https://doi.org/10.1007/ 3418_2020_44) contains supplementary material, which is available to authorized users. M. Jaraíz (*) Department of Electronics, University of Valladolid, Valladolid, Spain e-mail: [email protected]

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Abbreviations CAD DFT QM QM/MM RPKA TST

Computer-aided design Density functional theory Quantum mechanics Quantum mechanics/molecular mechanics Reaction progress kinetic analysis Transition-state theory

1 Introduction Computer-aided design (CAD) is today an essential tool in fields such as electronics, architecture, or mechanical and civil engineering. Complex electronic circuits, highperformance aircrafts, high-rise buildings, or sophisticated bridges can be designed from start to finish, and costly fabrication can be undertaken with the confidence that the result will meet the features and behaviors predicted by CAD programs. Synthetic chemistry is a more complex and elusive field. Although electronic circuits are also assembled with devices (transistors) based on quantum mechanics (QM) effects, those effects remain internal to each device (that can be seen as a building brick) and the interaction of devices can be treated with simple and classical circuit laws. By contrast, in synthetic chemistry, where building blocks are atoms and molecules, not only the internal behavior but also the interactions between the different blocks need to be described by their quantum properties. This results in two special traits: prediction of the results can become a very complex problem, but it pays off by the richness of features that can be obtained that is incomparably more varied than those of, for example, a set of electronic devices of similar complexity. Synthetic chemistry can be regarded as the purposeful execution of a system of chemical reactions to obtain a product. For a reaction mechanism (Fig. 1 (a) and (b)), the energy profile (c) determines the kinetic concentration over time (d) that the reactants will follow, normally through the formation of intermediates, to yield the desired products and possibly some undesired by-products. Figure 1a, b shows two equivalent representations of the reaction mechanisms. Computers can be used in synthetic chemistry for two different roles: 1. Automatization: Control of the instruments to perform the desired processing tasks 2. Computation: Design and optimization of new synthetic routes Both roles can be played within two different environments: industry and research. However, the use of computation is seen from a different perspective in each environment. For industrial applications, the goal is the precise and targeted modeling of a specific reaction, and this is often easier to achieve by constructing

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Fig. 1 A reaction mechanism (a) visualized as a scheme in (b). The energy profile (c) determines the concentration over time (d) that the reactants R1, R2 will follow, through the formation of intermediates I1, I2, to yield the desired product P, and possibly undesired by-products BP

reaction kinetics models based on empirical laws. On the contrary, in research it is worth to go deeper into the details of elementary reactions (microkinetic modeling) to be able to envisage and design new, groundbreaking synthetic routes that, in the long term, will pay off for the additional time and cost. For further reading on microkinetic modeling, see a recent review [1] and references thereof as well as Refs. [2–10]. Instead of assembling yet another review, the goal of this chapter is to enable the reader to carry out microkinetic modeling and simulation studies of synthetic chemistry problems, assuming the availability of a set of DFT energy values for

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the reaction rates involved. To this end, after a brief introduction, we describe the tools that we use and the modeling methodology that we follow and provide a short tutorial and input files for the microkinetic simulator that we normally use (available free of charge). Finally, we analyze two case examples to show the level of insight and prediction power attainable with this DFT-based microkinetic modeling methodology. In an elementary reaction, the reactants form products in a single step (without intermediates) with a single transition state (or with no barrier). Unlike empirical laws, which encapsulate several unknown reaction steps, elementary reactions have the advantage that they can be calculated directly by QM methods. One simply has to minimize the reactants and products and find the transition state, using algorithms implemented in QM software. Semiempirical and QM/MM can also be, for some systems, good methods to achieve computational rates. Indeed, it would always be desirable to describe our reaction by means of elementary reactions. The trade-off is twofold: 1. The difficulty to figure out a plausible mechanism 2. The computation time and effort to find the transition states There are some theoretical and experimental tools that can help our chemical intuition and expertise in the forefront task of finding a plausible mechanism. Regarding theoretical tools, an update on automated reaction profile search methods can be found in chapter “Artificial Force-Induced Reaction Method for Systematic Elucidation of Mechanism and Selectivity in Organometallic Reactions” of this book. Those methods can provide candidate mechanisms as well as the involved transition-state structures. Ideally, this would be the preferred approach. However, while they are being used routinely for the second task, the computational cost of automated search of reaction profiles can be prohibitive for the size of molecules involved in most cases of practical interest. In those cases, it is necessary to rely on chemical knowledge and intuition and previous modeling expertise. Fortunately, there are some experimental tools that can provide guidance even in the cases that are not amenable to be treated by theoretical search methods. In this regard, we briefly present the reaction progress kinetic analysis (RPKA) methodology [2], as an experimental tool for identifying the mechanisms, and then the theoretical tools that we routinely employ to obtain the computationally derived rate constants.

2 Identification of Mechanisms: Experimental Tools As a notable experimental tool, the reaction progress kinetic analysis (RPKA) [11, 12] methodology “employs in situ measurements and simple manipulations to construct a series of graphical rate equations that enable analysis of the reaction to be accomplished from a minimal number of experiments. Such an analysis helps to describe the driving forces of a reaction and may be used to help distinguish between different proposed mechanistic models” [11]. Instead of using only single yields and conversion values, “monitoring the time evolution of the reaction can yield

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Table 1 Examples of RPKA signatures and corresponding catalytic cycles

Adapted with permission from [12]. Copyright (2015) American Chemical Society

significant further clues about issues that can be problematic in classical experimental approaches, such as catalyst activation and deactivation, as well as substrate and product inhibition or acceleration.” RPKA “gives the same information provided by

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classical kinetic approaches with only a fraction of the number of separate experiments” [11]. Like what Table 1 shows, the RPKA methodology provides a sort of a catalog of several types of catalytic cycles that represent the overall reaction mechanisms and the corresponding RPKA signature or fingerprint (left column, two representations of the same data set) that should be observed by carrying out a few experiments and some graphical manipulation of concentration over time data [12]. For example, by using the RPKA methodology, the different kinetic profiles displayed in entry (a) prompt us which is the catalyst resting state in each case for the catalytic A + B ¼ C reaction shown. The plots of entry (b) suggest that there are off-cycle equilibria, the plots of entry (c) that there is a product acceleration effect, and so other cases not shown here. Note that in all cases the reaction mechanism corresponds to the same overall chemical reaction A + B ¼ C. Thus, valuable hints toward identifying the underlying mechanisms can be obtained by carrying out an RPKA study at the outset of a reaction modeling task. As shown with a variety of examples in Ref. [11], a simple protocol encompassing just four experiments provides a comprehensive, if in some cases preliminary, kinetic analysis of any new reaction.

3 Calculation of DFT Energies: Theoretical Tools In a DFT-based microkinetic model (Fig. 1), all reaction steps are elementary reactions. For a single transition-state reaction like k1

AþB Ð C k 1

the rate of change of [A] is 

d½A ¼ k 1 ½A½B  k1 ½C dt

where k1, k1 are the forward and reverse rate constants, respectively. Following the transition-state theory (TST) [13], each rate constant is given by the Eyring equation k¼

k B T ΔGo,{ =RT kB T ΔH o,{ =RT ΔSo,{ =R e e ¼ e h h

dH0, dS0 are the enthalpy and entropy differences between the transition state and the reactants (k1) or products (k1) of this elementary reaction step. The G0 values, calculated with a QM software at standard conditions of 1.0 atm, are transformed to use concentrations in units of mol/L instead of pressure in atm according to

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G0 ½mol=L ¼ G0 ½atm  RT  ln ð24:5Þ In summary, the parameters that we need to run kinetic simulations are the forward and reverse Gibbs energy barriers ΔG0{ for each reaction step, and, consequently, we need to find the minimum of reactants and products and the transition states. Generally, the optimization of a structure to a minimum does not pose special difficulties and should be preceded by a conformational study. Finding the transition states is usually the hard task, in both difficulty and computation time. Chapter “Artificial Force-Induced Reaction Method for Systematic Elucidation of Mechanism and Selectivity in Organometallic Reactions” of this book covers this and related issues and tools in depth. After obtaining all the minima and TSs, we can calculate the forward and reverse Gibbs energy barriers, which are the parameters needed to perform DFT-based kinetic simulations. Since Gaussian and other QM programs yield the separate contributions of enthalpy and entropy, it is preferable to use them separately instead of the Gibbs energy for a better account of temperature effects on the rate constants (Eyring equation). Here we discuss and show examples of a methodology for synthetic chemistry consisting in the accurate analysis of real-time experimental data through DFT-based reaction kinetics simulations. The calculated DFT barrier values have a range of uncertainty for a given functional, and different functionals can yield somewhat different values. Besides, due to the exponential dependence of reaction rates with the barrier heights, none of those sets of values can, in fact, reproduce the real-time experimental data of a given experiment. As an example, Fig. 2 shows the simulated results using the as-calculated DFT barrier values (top) compared to those obtained with the refined values that closely reproduce the experimental data (bottom). Basically, the method consists in performing microkinetic simulations to find, within the DFT uncertainty ranges, a valid set of barrier values (here referred to as “tuned” or “refined”) that reproduce the real-time experimental data. Once this set is found, this physically based (DFT) simulator becomes a powerful, predictive, and accurate tool for testing different experimental conditions, planning new experiments, and improving the design of the reaction mechanism. Those fine-tuned DFT values should be taken with care. Not any tuning can be acceptable, and it is necessary to make a work of observation and elimination of other error sorts like other mechanisms, other resting state species, or effects of solvent.

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As-Calculated 0.06

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Fig. 2 Simulated reactant (blue) and product (red) vs time for four experiments. Top: using the as-calculated DFT barrier values. Bottom: using the fine-tuned DFT barrier values. Adapted with permission from [14]. Copyright (2017) American Chemical Society

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Fig. 3 The COPASI kinetic simulator. Snapshots from input file ParamEstim.cps. (a) Reactions can be written directly in its input panel, (b) Values or expressions for the rate constants and other parameters can be defined in the Global Quantities, (c) Rate constants are assigned to reactions, and (d) COPASI can generate the reaction diagram

4 Running Kinetic Simulations: A Brief Tutorial Once we have a candidate model for the reaction mechanisms and the DFT energy values (Gibbs energy barriers), the next task is to simulate the experiments. If the simulation agrees with the experimental data, then the proposed scheme is a plausible mechanism, although this agreement by itself does not rule out other possible mechanisms. The reaction kinetics simulations presented here have been carried out with the biochemical system simulator COPASI [15] that generates and solves numerically the set of differential equations corresponding to the kinetic reactions to obtain the concentration over time data of each species A(t), B(t). . . starting from the initial concentrations. The temperature can be different for each experiment (run) and can also be defined as a function of time. Like other similar programs, COPASI has a user-friendly graphical interface, online Support Manual and is available free of

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charge. Some groups have also written their own code, where they can introduce correcting factors and optimize them at will. Here we provide a brief tutorial of its use for DFT-based microkinetic modeling. We have implemented the input files for several examples discussed below, and they are included in the Supplementary Information (SI). Reactions can be written directly, as shown in Fig. 3a. The reader can also follow these comments with COPASI loading the ParamEstim.cps input file included in the SI. Species are created automatically from them or may have been defined previously, but we have to specify the initial concentration of each one. We can define the necessary rate constants (rb01k, rb01kr. . .) in the Global Quantities entry (Fig. 3b) and then assign each rate constant to its reaction (Fig. 3c). The corresponding differential equations are automatically generated and can be seen in the Mathematical entry of the object tree, on the left panel. In COPASI, apart from giving energies and equations, one can introduce directly the computational reaction rates. COPASI can also generate graphical Diagrams or schemes that can be manually modified (Fig. 3d). Once all the Reactions, Species, and necessary Global Quantities have been defined and initialized, COPASI is ready for Time Course simulations, under the Tasks entry on the left panel. To carry out a Time Course simulation and visualize the results for the current parameter values and initial concentrations, we simply have to choose or define an output graph with the Output Assistant button (located at the bottom right of the Time Course main panel, Fig. 4), set the time Duration and number of Intervals or Interval Size, and click Run. The Plots can be modified and deactivated in the Output Specifications entry of the left panel. A handy feature of COPASI is the use of Sliders (Fig. 4) to easily modify parameters (temperature, initial concentrations, barrier heights, etc.) and rerun the simulation instantly. To visualize the Slider’s panel of the active Task (Time Course), go to the Tools menu or click on its icon located below the menu. Another useful task, called Parameter Estimation, allows the optimization of parameters to obtain the best fit to a set of experimental data. The parameters to be optimized from a Start Value (e.g., the as-calculated DFT values) within specified Upper and Lower Bounds (the computation estimated error) are included in the Parameters list (Fig. 5a) by first clicking on the green “+” button. This adds a new line to the Parameters list window. And then the Object can be selected by clicking the COPASI logo button located left to the “+” button. The Hooke and Jeeves can be chosen as a good Method for these optimizations. An experimental data file (ParamEstim-Experiments.txt, included in the SI), like the one shown in Fig. 5c, can be prepared with Excel. It should have a header row, with a column named Time. Experiments are separated by an empty line. Click on the Experimental Data button of the Parameter Estimation panel, add the data file (Fig. 5b), specify the Separator (use “tab” for easy copy/paste to Excel), and select Time Course as Experiment Type. The header names should appear listed in the Column Name as shown. Assign the appropriate Type and Model Object to each header. To propagate the definitions

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Fig. 4 Time Course task Panel, example of Plot window and Sliders

from one experiment to the next, click on the corresponding Copy Settings checkbox. Weights are also assigned by COPASI to the dependent parameters, to renormalize the curves so that, for example, in Fig. 6, the green and blue curves are amplified to the same maximum height as the red one. Set the weights to 0 if you wish to ignore an experiment during optimization. Clear the 0’s to have COPASI reassign weights. You may need to first uncheck the Copy Settings to avoid propagation. As an interesting use of this feature, we can, for example, duplicate Exp1 in the data file experiment as Exp1a with only the data points of the regions that we want to fit (e.g., the initial 1,000 s) and then use Exp1a for optimization and Exp1 for visualization of the fit to the full data set.

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Fig. 5 Parameter Estimation task. (a) Definition of search range for each parameter, (b) Correspondence between internal parameters and the names used in input data file, (c) example of input data format, and (d) Example of Progress of Fit plot

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Fig. 6 Parameter Estimation “per Experiment” plots for two experiments

COPASI performs the Parameter Estimation task through calls to a simplified, faster version of the Time Course for the duration of each experiment, regardless of the Duration and Interval size values of the Time Course panel. Before running the task, we can use the Output Assistant to select a Progress of Fit plot as well as the set

Fig. 7 The Parameter Estimation Result panel displays, for each optimized parameter, the Lower and Upper Bounds, and the Start and optimized Value

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of plots “per Experiment” to get a plot window for each experiment (Fig. 6), where we can see the experimental data (symbols) and the simulation with the optimized parameter values (solid lines). These optimized values can be seen by clicking Result (below Parameter Estimation) on the left panel (Fig. 7). Click on the Update Model button to set the optimized values as the current parameter values (and as Initial values for further Parameter Estimation runs). As commented below, it is better to start adjusting initially the minimum possible number of equations and add later second-order effect equations. The Optimization task optimizes an Expression to, for example, minimize the cost for a 95% conversion time of 3,600 s (Fig. 8). We have not needed to use this task, instead we always used Parameter Estimation. Figure 9, from the Scan-Events-2DColorContours.cps input file (our COPASI implementation of the reaction studied in [16]), shows an example of the use of Events in COPASI to find the time at which conversion is 95% during a Time Course. Normally it is necessary to introduce a Delay only if one of the trigger variables is likely to change at that time. Events are also useful, for example, to add a reactant or additive after a time required for the activation of a precatalyst or to simulate several experiments consecutively (to generate Fig. 2, load the EventsSequence.cps input file; execute the Time Course task). In Fig. 9 the Target variable (_P%sec, its current value, not its InitialValue) is assigned the value of the Expression (current Time, it can also be a formula) when the Trigger Expression is true (use ¼¼ for comparison, ¼ for assignment): concentration of Prod equals the initial value of the Global Quantity _P%. The Parameter Scan task (Fig. 10, use the same input file) can be used to plot, for example, the time for 95% conversion versus temperature and catalyst concentration as a 2D contour color map.

Fig. 8 Example of Optimization of an Expression. In this case, the parameters specified are optimized within the specified ranges to “minimize” the Expression

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Fig. 9 Example of definition of an Event to record the Time (current value of the P%sec global Quantity) at which a given condition (the Trigger Expression) is met

Fig. 10 Example of 2D contour color map (compare with Fig. 4 of [16]), resulting from the 2D Parameter Scan shown to the right

Finally, an example of using different Parameter Sets can be seen in the ParameterSets.cps input file (reaction scheme of Fig. 13). A Set includes the initial

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values of concentrations and Global Quantities and the Kinetic Parameters. Thus, we can store and retrieve different candidate solutions to our problem.

5 Case Examples Now we discuss some case examples to show how DFT-based microkinetic simulations can be used to get a deep understanding of a reaction mechanism that, in turn, may help improve reaction conditions or the reaction mechanism itself (better reaction steps, catalysts, or additives).

5.1

Example 1

Catalyst deactivation [17] is one of the key mechanisms that determine whether a catalytic process is suitable for large-scale manufacturing. Finding deactivation mechanisms is therefore one of the most relevant tasks in the kinetic modeling of catalytic processes for industrial applications because, once the mechanism is known, it is possible to devise methods to avoid or mitigate it. Deactivation mechanisms are usually sought by trying to figure out possible chemical reactions that temporarily trap or permanently degrade the catalyst. The case presented here is an example of a particular deactivation mechanism (Fig. 11) in which, according to our proposed model [14], a solvent THF molecule temporarily locks a substrate-catalyst intermediate (A) into an inactive state (LTHF) by hindering the return from a reversible reaction (r8). It is experimentally known that addition of collidine hydrochloride (collHCl) inhibits the deactivation mechanism. In our proposed model, based on DFT calculations, collHCl forms a complex (LcollHCl) that prevents the formation of the L THF complex. We calculated the DFT energies at B3LYP-D3/6-31 + G(d, p) level of theory. As shown in Fig. 2 above, the results simulated with the as-calculated DFT values are useless, especially for experiments 2, 3, and 4. Figure 11 shows experiments at two different concentrations without (Exp1, Exp2) and with (Exp3, Exp4) collHCl. Exp1 exhibits strong catalyst deactivation effects (slow conversion) after about 5 min. We used only three (plus the initial one) experimental data points (large cross symbols in Fig. 11a) to fine-tune the raw DFT values within the calculation error bars. The simulator (input file EventsSequence.cps from SI) closely reproduces all the experimental data, having “seen” only three data points, used for fine-tuning the DFT values. The DFT-based simulator, which has not seen any experiments with collHCl, predicts the drastic suppression of catalyst deactivation, as shown by comparing the Exp1, Exp3 curves. It also predicts other four experiments for different concentrations of epoxide, catalyst, and additive. Considering that the only guidance to optimize this 32-barrier simulator has been three experimental

Fig. 11 An example of microkinetic catalytic cycle, experimental data, and simulated results. Adapted with permission from [14]. Copyright (2017) American Chemical Society

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data points, it can be concluded that the DFT foundation of the model must be playing a key role in the predictive character of this simulator. Exp1 is the only curve that does not reach its final asymptotic value within the reported time span. Inspection of the simulated results for an extended period of time (Fig. 12) reveals that the epoxide supply (E curve) is almost exhausted by then, and a much slower rise of the product signal is predicted to begin at that time, corresponding to the release of L from the LTHF trapping state toward the lowest energy state, the product P. This was confirmed by using only the first half of the Exp1 data points; essentially the same prediction was obtained. This is an example of how kinetic simulations can suggest experiments to further verify a proposed model. This example has shown the predictive character of a DFT-based simulator. As discussed in [14], it seems that such prediction capability stems from the DFT-derived reaction scheme that is likely to be the same regardless of the DFT functional employed. For example, for another complex reaction network also with more than 30 barriers (Fig. 13), already the as-calculated DFT barrier values predict almost the correct shape and yields for the concentration over time data of several reagents and products, although on a time scale about 360 times faster than the experiment. As also shown (input file ParameterSets.cps), an excellent agreement with experiment can be easily obtained by simply adjusting one of the four measured time curves.

5.2

Example 2

Figure 13 is an example of a complex kinetic scheme that might predict, by using suitably chosen barrier values, a wealth of different results. The allowed ranges (error bars) of the DFT values impose constraints that reduce that variability, but do

Fig. 12 Simulation of Exp1 for an extended time span predicting a third, slower transient (beyond the experimental data range. Adapted with permission from [14]. Copyright (2017) American Chemical Society

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Fig. 13 Experimental data (symbols, from Ref. [18]), simulation with the as-calculated barriers (dashed lines, time scale multiplied by 360 and shifted) and with the refined barriers (solid lines). Only the experimental data of “Yield of 2” were used to refine the complex 36-barrier DFT-RK simulator shown to the right. Adapted with permission from [14]. Copyright (2017) American Chemical Society

not always provide guidance enough to prevent the model to reproduce an experimental data set with two different sets of fine-tuned DFT values, DFT1 and DFT2, that activate different pathways of the complex reaction network. Consequently, different conclusions and predictions can be reached depending on the DFT set chosen. As an example, we use the comprehensive catalytic mechanism proposed by Yu et al. [19] to explain the effects of residual water on the reactivity and regioselectivity of tris(pentafluorophenyl)borane catalyst in the ring-opening reaction of 1,2-epoxyoctane by 2-propanol. The model proposed includes competitive binding reactions, traditional Lewis-acid catalysis, and nonconventional water-mediated and alcohol-mediated catalysis. Like other groups, they have followed the common procedural approach of starting, right from the beginning, with all the mechanisms and equations that are suspected to play some role and adjust only a reduced set of the many independent parameters involved. Their microkinetic model consists of 130 reactions with a total of 149 independent parameters. They used 9 adjustable parameters to influence the rate constants of 29 reactions to achieve optimal agreement between the model output and experimental kinetic data in the training set (7 out of 21 experiments). The model was verified with the remaining 14 experiments, yielding moderate to good predictions, with some outliers. Because the system of equations is heavily under-constrained (many parameters, few experimental constraints), such a loose modeling approach can lead, as shown in [20] for the present case, to several pitfalls. To avoid those pitfalls, we propose as an alternative modeling approach the inverse strategy, that is, starting with the minimum number of reactions that can describe the expected dominant mechanisms and adjusting all the DFT values. Out of their 130 reactions, we selected 8 reactions (Fig. 14) as the dominant mechanisms [20]. The rationale for the selection of the 8 steps included in Fig. 14 is as follows. (a) We start with only the traditional Lewis acid catalytic cycles that

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Fig. 14 Dominant mechanisms from a complex system. Adapted with permission from [20]. Copyright (2019) American Chemical Society

generate the experimentally observed products P1 and P2 (reactions R1, R2, R3), plus the competitive binding reactions of FAB with the alcohol and water (reactions R4, R5), and compare the simulation results with the experimental data. (b) To improve the agreement between simulation and experiment, we add reactions R6 and R7 because P1 and P2 can react with the epoxide to give second-generation ringopened products PP1 and PP2. At this point we already get a fairly good agreement. (c) To improve it further, we added the second-shell binding of the epoxide (reaction R8). Next, we implemented that reduced model in COPASI (ParamEstim.cps input file) and optimized all the 14 independent parameters, starting from the as-calculated DFT values and ranges proposed by Yu et al. (using 2 kcal/mol for unspecified ranges). We used a set of only 5 experiments for training and obtained an accuracy similar to that of the 130 reactions model. Figure 15 is an example of experimental regioselectivity and mass-balance data versus model output that can be obtained with this model. It also displays good experiment-simulation agreement for the dependence, on the initial water level, of the initial rate constant and regioselectivity. Our model, with only Lewis-acid-catalyzed and no water-mediated pathways, reproduces accurately the same experimental observations that are explained by the model of Yu et al. by means of their additional water-mediated pathways. As a

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bonus, the reduced number of equations translates into a reduced number of DFT values that need to be calculated and, therefore, in a considerable reduction of time and effort (by a factor of 10 in this case). It is interesting to note that, for example, under the conditions of some of their experiments, a fast process, not included in the current mechanisms of Fig. 14, shows up after about 1,000 s (Fig. 16, solid lines, simulation; dash-dot, experiment). This may correspond to the time needed to build up a steady state concentration of an intermediate, like FABH2O, that feeds a water-mediated catalytic cycle with rates and regioselectivities different from those of the Lewis acid catalytic cycle, as pointed out by Yu et al. In such cases, one can develop and calibrate a starting model to reproduce the initial stages of the reaction and then add other mechanisms. In fact, for the training experiments 1, 2, and 11 of this example, we used only the data points up to 1,000 s. Afterward, the water-mediated and alcohol-mediated catalytic cycles could be added, as a refinement of the mechanisms already implemented and calibrated to a first approximation.

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Fig. 16 Measured data of experiment 17 reveals that a faster process begins after an induction period of about 1,000 s. Adapted with permission from [20]. Copyright (2019) American Chemical Society

6 Summary In summary, the overall steps followed to develop and exploit a DFT-based microkinetic simulator are: 1. Identify the reaction mechanisms and propose a reaction scheme. 2. Calculate the DFT energies (Gibbs energies of minima and transition states). 3. Use a kinetic simulator to: (a) Fine-tune the DFT values with a set of experimental data and verify the implemented model with another data set (b) Use the implemented DFT-based microkinetic simulator to: • Get a deeper insight on the contribution of each mechanism and suggest a test for experimental verification of the proposed model • Optimize the reaction conditions within specified ranges To recapitulate, Fig. 17 shows an example of the modeling stages followed to develop a reliable and predictive catalytic microkinetic model applying this incremental tight modeling protocol (see Ref. [14] for a detailed derivation of the DFT model). Figure 17a represents the mechanisms that we expect to be dominant or essential: the main catalytic cycle. Figure 17b, c includes secondary mechanisms that contribute to explain further details of experimental observations. Thus, in the last modeling stage (Fig. 17c), we can safely use only three points (large symbols shown in Exp1) to refine the many parameters involved because the system, by starting from the dominant mechanisms, has already been settled within the correct local

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Fig. 17 Example of model development following the incremental tight modeling protocol. Adapted with permission from [20]. Copyright (2019) American Chemical Society

minima in the previous modeling steps. Indeed, this accurate and complex model cannot be obtained by directly trying to adjust Fig. 17c to fit the three data points starting from the as-calculated DFT values. Finally, it is worth reflecting on the fact that, although only three experimental data points were needed to supplement the theoretical calculations, they were at the same time indispensable to make the predictive power of DFT calculations a reality.

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This remark has a bearing on current efforts to develop theoretical-only methods that can yield predictions with the accuracy required for direct use in synthetic chemistry: even if the kinetic parameters of Fig. 11 were calculated with, let us say, 0.1 kcal/mol accuracy, it would still be necessary to figure out and calculate also all the possible interaction mechanisms down to that interaction energy level. Since those accurate and complex calculations are not yet available, more accessible alternatives are being sought in the meantime, like the combined DFT-microkinetic methodology that we have discussed here.

References 1. Besora M, Maseras F (2018) WIREs Comput Mol Sci 8:e1372 2. Mhadeshwar AB, Vlachos DG (2005) J Catal 234:48 3. Prieto C, González Delgado JA, Arteaga JF, Jaraíz M, López-Pérez JL, Barrero AF (2015) Org Biomol Chem 13:3462 4. Gokhale AA, Dumesic JA, Mavrikakis M (2008) J Am Chem Soc 130:1402 5. Rush LA, Pringle PG, Harvey JN (2014) Angew Chem Int Ed 53:8672 6. Szlapa EN, Harvey JN (2018) Chem A Eur J 24:17096 7. Pérez-Soto R, Besora M, Maseras F (2020) Org Lett. https://doi.org/10.1021/acs.orglett. 0c00367 8. Darù A, Hu X, Harvey JN (2020) ACS Omega 5:1586 9. Brezny AC, Landis CR (2019) ACS Catal 9:2501 10. Robertson C, Habershon S (2019) Catal Sci Tech 9:6357 11. Blackmond DG (2005) Angew Chem Int Ed 44:4302 12. Blackmond DG (2015) J Am Chem Soc 137:10852 13. Cramer CJ (2004) Essentials of computational chemistry. Wiley, Chichester 14. Jaraíz M, Enríquez L, Pinacho R, Rubio JE, Lesarri A, López-Perez JL (2017) J Org Chem 82:3760 15. COPASI v 4.24 available free of charge from http://copasi.org 16. Weires NA, Caspi DD, Garg NK (2017) ACS Catal 7:4381 17. Crabtree RH (2015) Chem Rev 115:127 18. Zhang L, Yang H, Jiao L (2016) J Am Chem Soc 138:7151 19. Yu Y, Zhu Y, Bhagat MN, Raghuraman A, Hirsekorn KF, Notestein JM, Nguyen ST, Broadbelt LJ (2018) ACS Catal 8:11119 20. Jaraíz M, Rubio JE, Enríquez L, Pinacho R, López-Perez JL, Lesarri A (2019) ACS Catal 9:4804

Top Organomet Chem (2020) 67: 107–130 https://doi.org/10.1007/3418_2020_43 # Springer Nature Switzerland AG 2020 Published online: 15 May 2020

A Quantitative Approach to Understanding Reactivity in Organometallic Chemistry Israel Fernández

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Activation Strain Model of Reactivity and Energy Decomposition Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Representative Applications of the ASM and EDA-NOCV Methods . . . . . . . . . . . . . . . . . . . . . 3.1 Diels–Alder Cycloaddition Reaction Involving Metallaanthracenes . . . . . . . . . . . . . . . . 3.2 Oxidative Addition Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Gold Complexes in π-Acid Catalysis: Hydroamination and Hydroarylation . . . . . . . . 3.4 Intramolecular Reactions: β-Cl vs β-H Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract This chapter presents the combination of the activation strain model (ASM) of reactivity and the energy decomposition analysis (EDA) methods as an alternative approach to gain quantitative insight into the reactivity trends in organometallic chemistry. Besides a brief presentation of the basics of these quantum chemical methods, representative recent applications of this approach to fundamental transition metal (TM)-mediated reactions are discussed. The selected transformations span from typical oxidative addition or β-elimination processes to more intricate gold (I)-mediated hydroarylation or hydroamination reactions, therefore covering a good number of different processes in organometallic chemistry. The contents of this chapter show not only the good performance of this computational methodology to understand the physical factors controlling the reactivity in organometallic chemistry but also its usefulness toward the rational design of more efficient transformations.

I. Fernández (*) Departamento de Química Orgánica I and Centro de Innovación en Química Avanzada (ORFEO-CINQA), Facultad de Ciencias Químicas, Universidad Complutense de Madrid, Madrid, Spain e-mail: [email protected]

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Keywords Activation strain model · DFT calculations · Energy decomposition analysis · Reactivity

Abbreviations ASM DFT EDA NOCV

Activation strain model Density functional theory Energy decomposition analysis Natural orbitals for chemical valence

1 Introduction Organometallic compounds are ubiquitous in practically all fields of chemistry, from transition metal-mediated organic synthesis to materials science or medicinal chemistry. For this reason, understanding the ultimate factors which govern their reactivity is crucial in order to rationally design new organometallic compounds with potential applications as catalysts, new materials, or drugs. In this sense, computational organometallic chemistry has emerged as a really powerful and valuable tool, particularly in the last decades, as clearly shown in the different chapters of the present book. This is mainly due to tremendous development of computer science together with the progress made on new theoretical methods (mainly based on the density functional theory) and computational chemistry software. As a result, it is nowadays relatively easy to compute large systems having transition metals and/or bulky ligands in their structures. In this particular book chapter, we shall focus on a relatively recent computational methodology which is based on the combination of the so-called activation strain model (ASM) of reactivity and energy decomposition analysis (EDA) methods. This approach has enormously contributed to our current understanding of fundamental transformations not only in organic chemistry but also in transition metal-mediated processes. Herein, we will present the good performance of this combined method to provide a deeper and quantitative understanding of the reactivity of organometallic species. To this end, selected representative applications of this approach (mainly coming from our laboratories) to transition metal-mediated reactions will be discussed.

2 The Activation Strain Model of Reactivity and Energy Decomposition Analysis Methods As the theoretical background and applications of ASM have been reviewed recently [1–4], herein we shall only briefly describe the basics of this approach.

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Fig. 1 Illustration of the activation strain model for the oxidative addition of a phenyl halide (PhX) to a generic transition metal complex ([M])

By means of the ASM of reactivity, the height of reaction barriers can be described and rationalized in terms of the original reactants. This approach is a systematic development of the so-called energy decomposition analysis (EDA; see below) [5–8] used initially to understand the nature of the chemical bonding in stable molecules. Within this method, which is also known as the distortion/interaction model [3], the potential energy surface ΔE(ζ) is partitioned into two contributions along the reaction coordinate ζ, namely, the strain ΔEstrain(ζ) associated with the deformation (or distortion) experienced by the reactants during the transformation plus the interaction ΔEint(ζ) between these increasingly deformed reactants (Eq. 1): ΔEðζÞ ¼ ΔE strain ðζÞ þ ΔE int ðζÞ

ð1Þ

Whereas the strain ΔEstrain(ζ) depends on both the rigidity of the reactants and the reaction pathway under consideration, the interaction ΔEint(ζ) between the reactants depends on their electronic structure and on their mutual orientation as they approach each other. It is the interplay between ΔEstrain(ζ) and ΔEint(ζ) which determines where the barrier arises, namely, at the point satisfying dΔEstrain(ζ)/ dζ ¼ dΔEint(ζ)/dζ. According to this model, the activation energy of a reaction ΔE6¼ ¼ ΔE(ζTS) consists of the activation strain ΔE6¼strain ¼ ΔEstrain(ζTS) plus the transition state (TS) interaction ΔE6¼int ¼ ΔEint(ζTS) (Eq. 2; see also Fig. 1 for an oxidative addition of aryl halides to a generic transition metal complex):

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ΔE 6¼ ¼ ΔE6¼ strain þ ΔE6¼ int

ð2Þ

The energy decomposition analysis (EDA) method [5–8] can be used to further decompose the interaction energy between the deformed reactants. Within this approach, the ΔEint(ζ) term is further partitioned into the following chemically meaningful terms (Eq. 3): ΔEint ðζÞ ¼ ΔV elstat ðζÞ þ ΔE Pauli ðζÞ þ ΔE orb ðζÞ þ ΔEdisp ðζÞ

ð3Þ

The ΔVelstat term, which is usually attractive, corresponds to the classical electrostatic interaction between the unperturbed charge distributions of the deformed reactants. The Pauli repulsion ΔEPauli derives from the destabilizing interactions between occupied orbitals and is, therefore, responsible for any steric repulsion. The stabilizing orbital interaction term, ΔEorb, is calculated in the final step of the energy partitioning analysis when the molecular orbitals relax to their optimal form. The ΔEorb term is always attractive as the total wavefunction is optimized during its calculation. This term accounts for charge transfer (interaction between occupied orbitals on one fragment with unoccupied orbitals on the other, including HOMO– LUMO interactions), polarization (empty-occupied orbital mixing on one fragment due to the presence of another fragment) and electron-pair bonding. Finally, the dispersion ΔEdisp term considers the interactions resulting from dispersion forces. Moreover, the NOCV (natural orbitals for chemical valence) [9, 10] extension of the EDA method can be also used to further partitioning the ΔEorb term. The focus of the NOCV method is the deformation density Δρ(r), which corresponds to the difference between the densities of the fragments/reactants before and after bond formation. Δρ(r) is expressed as a sum of pairs of complementary orbitals (ψ –k, ψ k) corresponding to eigenvalues (ν–k, νk) with the same absolute value but opposite in sign (Eq. 4): Δρorb ðr Þ ¼

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N=2   X υk ψ 2k ðr Þ þ ψ 2k ðr Þ ¼ Δρk ðr Þ

ð4Þ

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The complementary pairs of NOCV define the channels for electron charge transfer between the molecular fragments. Therefore, Eq. (4) makes it possible to express the total charge deformation Δρ(r) associated with the bond formation in terms of pairwise charge contributions Δρk(r) coming from particular pairs of NOCV orbitals. The EDA-NOCV approach therefore considers pairwise energy contributions for each pair of interacting orbitals to the total bond energy. Thus, the EDA-NOCV method provides not only qualitative but also quantitative information about the individual strength of orbital interactions in chemical bonds, even in molecules/ systems without symmetry (Ci symmetry).

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3 Representative Applications of the ASM and EDA-NOCV Methods 3.1

Diels–Alder Cycloaddition Reaction Involving Metallaanthracenes

Metallabenzenes are organometallic compounds characterized by the formal replacement of a CH unit in benzene by an isolobal transition metal fragment [11–14]. Since the isolation and full characterization in 1982 of the first metallabenzene [15], an osmabenzene complex, a good number of different metallabenzenes and related compounds have been synthesized. However, fused-ring metallabenzenes are rare, and for this reason, their chemistry has been comparatively much more underdeveloped. Despite that, recent years have witnessed significant progress in this particular field [16–19]. For instance, Frogley and Wright successfully prepared the first metallaanthracene complex, the iridaanthracene 1 shown in Scheme 1 [20]. This species is able to undergo a Diels–Alder cycloaddition reaction with maleic anhydride to produce, after spontaneous loss of a proton, the corresponding neutral fusedring iridabenzofuran cycloadduct 2 (Scheme 1). This finding indicates that iridaanthracene 1 behaves similarly to its all-carbon counterpart, anthracene, which produces a similar cycloadduct in the presence of maleic anhydride [21]. Despite this

Scheme 1 Diels–Alder cycloaddition reaction involving iridaanthracene 1 described by Frogley and Wright (see reference [20])

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Fig. 2 Computed reaction profiles for the Diels–Alder reaction (endo approach) between maleic anhydride and anthracene (blue) or iridaanthracene 1 (black). Relative energies and bond distances are given in kcal/mol and ångstroms, respectively. All data have been computed at the BP86-D3/ def2-TZVPP//RI-BP86-D3/def2-SVP level (see reference [22] for computational details)

evident similarity, the actual influence of the transition metal fragment in the Diels– Alder reactivity was completely unknown until our recent study based on the application of the ASM-EDA (NOCV) approach [22]. According to the computed reaction profiles for the Diels–Alder processes involving anthracene and iridaanthracene 1 (Fig. 2), the former cycloaddition is clearly favored from both kinetic (ΔΔE6¼ ¼ 3.4 kcal/mol) and thermodynamic (ΔΔER ¼ 2.3 kcal/mol) points of view. Therefore, it becomes evident that the presence of the transition metal fragment in the structure of anthracene leads to a significant decrease of the Diels–Alder reactivity of the central six-membered ring. Figure 3 shows the computed activation strain diagrams (ASDs) for the cycloaddition reactions involving maleic anhydride and anthracene (solid lines) and iridaanthracene (dashed lines) from the respective initial reactant complexes up to the corresponding transition states. Although both processes exhibit rather similar ASDs, it becomes clear that the interaction between the deformed reactants is much stronger for the cycloaddition involving anthracene than for the analogous process involving its organometallic counterpart along the entire reaction coordinate. This stronger interaction is able to offset the slightly less destabilizing strain energy computed for the reaction involving the metallaanthracene and is therefore responsible for the lower barrier computed for the anthracene system.

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Fig. 3 Comparative activation strain diagrams of the [4 + 2]-cycloaddition reaction between maleic anhydride and anthracene (solid lines) and iridaanthracene (dashed lines) along the reaction coordinate projected onto the forming CC bond distance. All data have been computed at the ZORA-BP86-D3/TZ2P//RI-BP86-D3/def2-SVP level (see reference [22] for computational details)

According to the EDA method, which further decomposes the ΔEint term into chemically meaningful contributions, the stronger interaction computed for the process involving anthracene results mainly from stronger electrostatic and orbital attractions between the strained reactants along the entire reaction coordinate. As graphically shown in Fig. 4, the ΔVelstat and ΔEorb terms are clearly more stabilizing for the anthracene system, despite its organometallic counterpart benefits from a less destabilizing Pauli repulsion. As a consequence, a higher (i.e., stronger, more stabilizing) interaction between the reactants is computed which ultimately results into the lower barrier computed for the reaction involving the parent anthracene. Moreover, the NOCV method can be also used to further explore the different orbital contributions to the total ΔEorb term. This method identifies two main molecular orbital interactions in these cycloaddition reactions, namely, the π(metalla/anthracene) ! π(maleic anhydride) and the reverse π(maleic anhydride) ! π(metalla/anthracene) interactions (Fig. 5). As expected for a normal electronic demand Diels–Alder reaction, the former interaction is higher than the latter. Interestingly, both orbital interactions are significantly more stabilizing for the transformation involving anthracene (see Fig. 5 for the interactions occurring at the same consistent CC bond forming distance of 2.3 Å). As a result, the total orbital interactions between the reactants in the metallaanthracene + maleic anhydride cycloaddition are comparatively weaker, which, together with the less stabilizing electrostatic attractions, lead to the reduced Diels–Alder reactivity of this

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Fig. 4 Decomposition of the interaction energy for the [4 + 2]-cycloaddition reactions between maleic anhydride and anthracene (solid lines) and iridaanthracene (dashed lines) along the reaction coordinate projected onto the forming CC bond distance. All data have been computed at the ZORA-BP86-D3/TZ2P//RI-BP86-D3/def2-SVP level (see reference [22] for computational details)

Fig. 5 Plot of the deformation densities Δρ (computed at the ZORA-BP86-D3/TZ2P//RI-BP86D3/def2-SVP level) of the pairwise orbital interactions between maleic anhydride iridaanthracene and associated stabilization energies for the process involving iridaanthracene (in black) and anthracene (blue). The color code of the charge flow is red ! blue

iridaanthracene. Similarly, higher activation barrier than that computed for the cycloaddition involving anthracene was systematically computed for other metallaanthracenes regardless of the transition metal fragment present in the system. The above example clearly illustrates the applicability of the ASM-EDA(NOCV) approach to rationalize the reactivity of organometallic compounds. In the following

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subchapters, we will focus on completely different processes where the transition metal fragment can be tuned to efficiently modify the reactivity.

3.2

Oxidative Addition Reactions

Oxidative addition typically constitutes the first and also the rate-limiting step in the catalytic cycle of a good number of cross-coupling reactions [23]. This process involves the cleaving of a C–X bond and forming of two new coordination bonds at the transition metal (TM), which results in an increase of its oxidation state by 2 units. In principle, two main mechanisms can be envisaged for this fundamental reaction: (a) the concerted pathway, which involves the simultaneous formation of the TM–C and TM–X bonds in the corresponding transition state, and (b) an SN2-type mechanism, where the central carbon atom is attacked by the transition metal fragment forming a cationic [TM–R]+ species and an X leaving group [23– 25]. The competition between both mechanisms has been thoroughly studied by Bickelhaupt and co-workers with the help of the ASM method on reactions involving Pd(0)-complexes and different alkyl and aryl halides [26, 27]. In addition, the activation of other bonds, such as C–H and C–C bonds, has been also quantitatively analyzed in detail [28]. Very recently, this research group has also explored similar oxidative addition reactions mediated by iron complexes, finding that whereas palladium complexes favor C–Cl activations, 1Fe(CO)4 shows a strong preference for activating C–H bonds [29]. Herein, we have selected the oxidative addition of aryl C–X (X ¼ halide) bonds mediated by gold(I) complexes [30]. Compared to Pd(0)-mediated processes, the analogous transformation involving Au(I) ! Au(III) is considered to be kinetically very sluggish despite being thermodynamically feasible [31]. However, the reasons behind the reluctance of gold(I) to activate C–X bonds were not fully understood. For this reason, we decided to apply the ASM method to understand in detail the factors governing the oxidative addition of aryl halides to Au(I) [32]. To this end, we selected the parent reaction involving phenyl iodide and (Me3P)AuCl, a representative species widely used in gold(I)-mediated transformations. As readily seen in Fig. 6, which shows the corresponding ASD from the initial stages of the transformation up to the respective concerted transition state, although the interaction energy between the deformed reactants is clearly stabilizing from the beginning of the process, it cannot compensate for the strong destabilizing effect of the strain energy. Therefore, it becomes clear that the high energy required to deform the reactants from their equilibrium geometries to the geometries they adopt at the transition state is the main reason behind the high barriers computed for the gold(I)mediated oxidative additions. The partitioning of the strain energy into contributions coming from each reactant clearly suggests that the major contributor to the total ΔEstrain term is the distortion

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Fig. 6 Activation strain diagram of the oxidative addition reaction of and PhI to (Me3P)AuCl projected onto the forming AuC distance. All data have been computed at the M06/def2-TZVPP// B3LYP/def2-SVP level (see reference [32] for computational details)

associated with the gold(I) complex. Indeed, the total strain energy ΔEstrain(ζ) curve is nearly identical to the ΔEstrain(ζ) ([Au]) curve along the entire reaction coordinate and only in the proximities of the transition state region, the distortion of phenyl iodide becomes significant (Fig. 7). This can be of course ascribed to the energy associated with the angle change or bending of the initially linear L–Au(I)–X complex, which constitutes therefore the main factor controlling the entire transformation. The strain associated with the bond breaking in the aryl substrate is comparatively much less significant. Further support to the above conclusion, i.e., control of the process by the deformation required by the initial gold(I) complex, was provided experimentally by Bourissou and co-workers [33]. These authors described the relatively facile oxidative addition of aryl iodides to Au(I) by using the cationic, highly bent carborane diphosphine (DPCb) gold(I) complex depicted in Scheme 2. Indeed, with this type of bent complexes, the oxidative addition of the CAr–I bond proceeds quantitatively even at low temperature (10 to 10 C). This sharply contrasts to the analogous process involving cationic linear diphosphine Au(I) complexes, where no oxidative addition takes place. According to the ASM, it is found that the bent complex requires a deformation energy only ca. 6 kcal/mol, which confirms that the pre-organization present in this bent complex is key to achieve a facile oxidative addition reaction.

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Fig. 7 Contributions to the total strain energy along the reaction coordinate up to the transition state for the reaction between PhI and (Me3P)AuCl. All data have been computed at the M06/def2TZVPP//B3LYP/def2-SVP level (see reference [32] for computational details)

Scheme 2 Oxidative addition of PhI to carborane diphosphine gold(I) complex reported by Bourissou and co-workers (see reference [33])

3.3

Gold Complexes in π-Acid Catalysis: Hydroamination and Hydroarylation

3.3.1

α-Cationic Phosphines in Gold(I)-Catalyzed Hydroarylation of Alkynes

Recently, Alcarazo and co-workers developed a series of monocationic phosphines containing cyclopropenium, pyridium, imidazolium, or amidinium substituents (Fig. 8) (for recent reviews, see: [34, 35]). These species, when used as ligands,

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Fig. 8 Computed reaction profile for the selected gold(I) hydroarylation reactions. Relative free energies are given in kcal/mol. All data have been computed at the B3LYP/def2-SVP level (see reference [38] for computational details)

were found to induce a remarkable acceleration of gold(I)- or Pt(II)-catalyzed hydroarylation reactions when compared to their neutral counterparts (i.e., PPh3 or P(OPh)3) [36, 37]. To understand this reactivity enhancement induced by α-cationic phosphine, we compared the gold(I)-catalyzed hydroarylation reactions of phenylacetylene with mesitylene in the presence of neutral PPh3 or cationic 2-methylpyridiniophosphine [38]. It was found that the initial nucleophilic addition to the corresponding π-complex constitutes the rate-determining step of the entire transformation. Interestingly, our calculations (see Fig. 8) indicate that the process involving the cationic ligands proceeds with a much lower activation barrier than that involving the parent neutral triphenylphosphine (ΔΔE6¼ ~ 10 kcal/mol), which is fully consistent with the acceleration observed experimentally. According to the ASM method, it becomes evident that the lower barrier computed for the cationic system finds its origin mainly in the stronger interaction between the deformed reactants along the entire transformation (see Fig. 9). This higher interaction derives, according to the EDA method, exclusively from the much more stabilizing orbital interactions between the reactants, as graphically shown in Fig. 10. Indeed, the rest of the energy contributions are nearly identical for both hydroarylation reactions. Therefore, it can be concluded that the cationic ligand, as

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Fig. 9 Comparative activation strain diagrams for the gold(I) hydroarylation reactions involving PPh3 (L1, solid lines) and cationic 2-methylpyridiniophosphine (L2, dashed lines) along the reaction coordinate projected onto the forming CC bond distance. All data have been computed at the PCM(dichloroethane)-B3LYP-D3/def2-TZVP//B3LYP/def2-SVP level (see reference [38] for computational details)

compared to the parent process involving PPh3 as a ligand, induces a stronger orbital attraction between the nucleophile and the π-complex from the initial stages of the transformation. This enhanced interaction is then translated into the computed lower barrier for the process involving the cationic phosphine ligand. The above findings strongly suggest that the α-cationic ligand significantly increases the π-acceptor ability of the initial acetylene-Au(I) complex. To quantitatively support this hypothesis, we applied the NOCV method to not only identify but also quantify the main orbital contributions present in these initial π-complexes. Two main molecular orbital interactions are identified by the NOCV method, namely, the donation from the π-molecular orbital of the acetylene fragment to the vacant AuP antibonding orbital of the [AuL]+ moiety and the backdonation from a doubly occupied atomic orbital located at the transition metal to the π(C  C) molecular orbital (see Fig. 11 for L ¼ PPh3). Not surprisingly, the former interaction is higher than the latter regardless of the ligand attached to the transition metal. Interestingly, this main orbital interaction is significantly stronger for the cationic ligand, which nicely confirms the higher acceptor ability of the corresponding π-complex, which ultimately leads to a remarkable enhancement of its reactivity. Similar strong π(C¼C) ! σ(Au–P) donations were computed for related cationic phosphines having cyclopropenium or imidazolium substituents [38], which confirms the activating role of these ligands in these gold(I)-catalyzed transformations.

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Fig. 10 Decomposition of the interaction energy for the gold(I) hydroarylation reactions involving PPh3 (L1, solid lines) and cationic 2-methylpyridiniophosphine (L2, dashed lines) along the reaction coordinate projected onto the forming CC bond distance. All data have been computed at the ZORA-BP86-D3/TZ2P//B3LYP/def2-SVP level (see reference [38] for computational details)

Fig. 11 Plot of the deformation densities Δρ of the pairwise orbital interactions present in the [(Ph3P)Au+]–phenylacetylene π-complex and associated stabilization energies (in black). Values in blue refer to the analogous complex involving the cationic 2-methylpyridiniophosphine (L2). The color code of the charge flow is red ! blue. Data computed at the ZORA-BP86-D3/TZ2P//B3LYP/ def2-SVP level (see reference [38] for computational details)

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Gold(I)-Catalyzed Anti-Markovnikov Hydroamination of Alkenes

The hydroamination of alkenes constitutes one of the most versatile and powerful tools for the construction of new C–N bonds [39, 40]. This process is usually mediated by different transition metal compounds with gold complexes playing a prominent role, especially in the last decade [41–45]. Despite that, selective methods leading to the corresponding anti-Markovnikov reaction products are rather limited, which still constitutes the major shortcoming of the method. In this sense, Widenhoefer and co-workers recently described the first gold(I)catalyzed anti-Markovnikov hydroamination reaction of alkenes [46], where the stereochemical outcome of the process strongly depends on the nature of the initial substrate. Thus, the reactions involving alkylidenecyclopropanes and 1-methylimidazolidin-2-one as nucleophile lead preferentially to the corresponding antiMarkovnikov reaction product (M/aM ratio up to 1:25; see Fig. 12a). In sharp contrast, the analogous gold(I)-catalyzed hydroaminations of different 1-alkenes (such as isobutene or styrene) or the related methylenecyclobutane are completely Markovnikov-selective (Fig. 12b) [47]. Extensive calculations on the corresponding reaction profile firmly suggest that, similar to the above-described hydroarylation reactions, the nucleophilic addition to the initial gold(I) π-complex, formed upon coordination of the substrate C¼C double

Fig. 12 Gold(I)-catalyzed hydroamination reactions described by Widenhoefer and co-workers (see references [46, 47])

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Fig. 13 Comparative activation strain diagrams for the gold(I)-catalyzed hydroamination reaction of isobutene along the reaction coordinate projected onto the forming CN bond distance. All data were computed at the M06/6-31G(d,p)&SDD(f) level (see reference [48] for computational details)

bond to the cationic gold(I) catalyst, constitutes the rate-determining step of the entire transformation. In addition, this particular reaction step also determines the selectivity outcome of the entire process [48]. We then applied the ASM method to this key reaction step to understand the influence of the nature of the initial substrate on the reaction. To this end, we compared both the Markovnikov and anti-Markovnikov approaches for the processes involving isobutene and alkylidenecyclopropane (ACP) from the initial π-complexes up to the corresponding transition states (Figs. 13 and 14). For the isobutene system, it becomes evident that the Markovnikov pathway benefits from a much stronger interaction energy between the deformed reactants along the entire reaction coordinate. As the strain term is nearly identical for both approaches, the Markovnikov addition is then preferred, as experimentally observed. The scenario is markedly different for the analogous reaction involving ACP. In this case, once again the interaction energy favors the Markovnikov addition; however, the antiMarkovnikov pathway benefits from a much less destabilizing strain energy along the entire reaction coordinate which is able to offset the stabilizing effect of the ΔEint

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Fig. 14 Comparative activation strain diagrams for the gold(I)-catalyzed hydroamination reaction of 1-benzyl-2-methylenecyclopropane along the reaction coordinate projected onto the forming CN bond distance. All data were computed at the M06/6-31G(d,p)&SDD(f) level (see reference [48] for computational details)

term. As a result, the anti-Markovnikov addition is favored for the process involving the ACP, which is fully consistent with the experimental findings. The results above suggest that the distortion induced by the coordination of the gold(I) catalyst to the alkene provokes significant changes in the electronic structure of the resulting initial π-complex, which are then translated into the computed barriers for the nucleophilic addition step. Indeed, the NOCV method indicates that the π-backdonation from the transition metal fragment to the π(C¼C) molecular orbital in the initial π-complex nicely correlates with the computed antiMarkovnikov barrier heights for a series of differently substituted alkenes (Fig. 15). Therefore, the stabilization energies associated with the π-backdonation deformation density given by the EDA-NOCV method can be used as a quantitative and reliable measure of the anti-Markovnikov addition barrier.

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Fig. 15 Plot of the computed Gibbs activation barriers for the gold(I)-catalyzed anti-Markovnikov hydroamination step of different alkenes vs the NOCV π-backdonation in the initial π-complex

3.4

Intramolecular Reactions: β-Cl vs β-H Elimination

Although the ASM method was originally conceived to be applied to intermolecular (i.e., bimolecular) reactions, it can be successfully applied to intramolecular (i.e., unimolecular) transformations as well [49, 50]. To illustrate this issue, we have selected the β-elimination reaction, a fundamental process in organometallic chemistry [51]. The β-hydride elimination, which typically occurs in metal–alkyl complexes and involves the formation of a π bond and a metal-bound hydride, is perhaps one of the most popular and widely studied β-elimination reactions. Despite that, β-chloroalkyl ligands may also engage in β-chloride eliminations [52–54]. For instance, Figueroa and co-workers reported that the nickel(II) complex depicted in Scheme 3 readily decomposes into NiCl2L2 and the corresponding olefin upon heating at 75 C [55]. Kinetic studies for this transformation suggest a first-order process with a negative activation entropy, which is fully compatible with an intramolecular β-Cl elimination reaction. This result prompted us to computationally explore the factors

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Scheme 3 β-elimination process described by Figueroa and co-workers (see reference [55])

controlling this β-Cl elimination reaction as well as the differences with the analogous β-H elimination [56]. Our calculations clearly indicate that both the β-Cl and β-H elimination reactions occur concertedly through a four-membered transition state which is associated with the simultaneous M–X and C¼C bond formation and C–X bond breaking (Fig. 16). Fig. 16 Computed reaction profile for the studied β-Cl (blue) and β-H (black) elimination reactions. Relative free energies (ΔG, at 298.15 K) are given in kcal/mol. All data have been computed at the PCM (pentane)-M06L/def2TZVP//M06L/def2-SVP level (see reference [56] for computational details)

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Fig. 17 Comparative activation strain diagrams for the β-Cl (solid lines) and β-H (dashed lines) elimination along the reaction coordinate projected onto the forming C–X bond stretch. All data have been computed at the M06L/def2-TZVP//M06L/def2-SVP level (see reference [56] for computational details)

According to the data gathered in Fig. 16, it becomes evident that whereas the β-Cl elimination reaction proceeds with a feasible activation barrier (ΔG6¼ ¼ 24.0 kcal/ mol), the barrier for the analogous β-H elimination is prohibitive (ΔG6¼ > 50 kcal/ mol). To understand such a remarkable difference, the ASM was applied next. Due to the intramolecular nature of the transformation, we decided to use the closed-shell singlets [Cl2C–CCl3] and [M]+ as fragments. Therefore, the initial complex can be viewed as a “very strongly bound reactant complex” in which the barrier for the elimination reaction arises from the change in the strain (ΔΔEstrain) and the change in interaction (ΔΔEint) between these fragments in going from the initial reactant to the corresponding transition state. Using this fragmentation scheme, we computed the corresponding ASDs for both β-elimination reactions. As graphically shown in Fig. 17, it becomes clear that the change in the interaction energy favors the β-H elimination reaction as compared to the analogous β-Cl elimination. However, it cannot compensate for the highly destabilizing effect of the change in the deformation energy, which is clearly much higher for the process involving the hydride elimination. This highly destabilizing strain energy constitutes then the major factor leading to the unfeasible high barrier computed for the β-H elimination reaction in these Ni(II) species. At variance, the change in the strain

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energy for the analogous β-Cl elimination is only slightly destabilizing which results in the much lower activation barrier computed for this transformation.

4 Summary and Outlook By means of selected representative examples, we have presented in this chapter an overview of the good performance of the combination of the ASM and EDA (NOCV) methods in aiding a detailed and quantitative understanding of the reactivity in transition metal-mediated transformations. The selected representative recent applications span from fundamental oxidative addition or β-elimination reactions to more intricate gold(I)-catalyzed hydroarylation or hydroamination reactions, therefore covering a good number of different processes in organometallic chemistry. This alternative method, which is rooted on accurate quantum chemical calculations and is fully applicable to any chemical transformation (including intramolecular processes), allows us to get a deeper, quantitative insight into the physical factors governing the barrier heights and associated reactivity trends in chemistry. Despite its relatively recent introduction, the ASM-EDA (NOCV) is nowadays a consolidated methodology which has greatly contributed to our current understanding of fundamental processes in chemistry. In addition, the insight gained by this methodology can be used for the so much desired rational design of more efficient or entirely novel transformations, particularly in organometallic chemistry. Acknowledgments Financial support was provided by the Spanish Ministerio de Economía y Competitividad (MINECO) and FEDER (Grants CTQ2016-78205-P and CTQ2016-81797REDC).

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Top Organomet Chem (2020) 67: 131–152 https://doi.org/10.1007/3418_2020_50 # Springer Nature Switzerland AG 2020 Published online: 22 July 2020

Computational Modeling of Selected Photoactivated Processes Adiran de Aguirre, Victor M. Fernandez-Alvarez, and Feliu Maseras

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Photoredox-Catalyzed Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Dual Ni–Photoredox Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Light-Driven Catalytic Trichloromethylation of Acylpyridines . . . . . . . . . . . . . . . . . . . . . 3 Photoactivated Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Photoinduced Oxidative Decarboxylation of a Nonheme Iron(III) Complex . . . . . . . 3.2 Light-Driven Insertion of Dioxygen into Pt(II)–C Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract Photoactivated processes play an increasingly important role in chemistry. Their widespread use is still relatively recent, and the application of computational methods to the treatment of the large systems usually involved in experimentally relevant systems is even more recent. The application of TD-DFT calculations for the photoactivation step and of conventional DFT calculations for selected regions of the potential energy surface has been demonstrated as a powerful tool for mechanistic understanding. This contribution presents four representative examples of this application, highlighting the successes and the struggles of this type of treatments. Keywords Density functional theory · Iridium · Iron · Nickel · Photocatalysis · Photosensitizers · Platinum · Time-dependent density functional theory

A. de Aguirre, V. M. Fernandez-Alvarez, and F. Maseras (*) Institute of Chemical Research of Catalonia (ICIQ), Tarragona, Catalonia, Spain e-mail: [email protected]; [email protected]

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Abbreviations CASPT2 CASSCF DFT LMCT MECP MLCT MM OIRE ONIOM OSS PET QM SET SMD TD-DFT UFF

Complete active space second-order perturbation theory Complete active space self-consistent field Density functional theory Ligand-to-metal charge transfer Minimum energy crossing point Metal-to-ligand charge transfer Molecular mechanics Oxidatively induced reductive elimination Own N-layered integrated molecular orbital and molecular mechanics Open-shell singlet Photoinduced electron transfer Quantum mechanics Single electron transfer Solvation model based on density Time-dependent density functional theory Universal force field

1 Introduction The increasing chemical use of light is one of the most exciting developments of modern chemistry. Sunlight is an inexhaustible source of energy, [1] and photoactivated reactions allow the generation of kinetically and thermodynamically disfavored products which are not accessible through thermal activation [2]. Moreover, photochemistry can be considered as a green and sustainable methodology in the sense that using the activation force of sunlight avoids the necessity of hightemperature or high-pressure conditions. Photoactivation can also facilitate process tuning, as the photoactivity of the absorbent molecule can be turned off by shutting down the light source, either totally or in a specific wavelength. Despite their potential advantages, light-driven transformations have been an underdeveloped field for many decades. The excited state of many organic molecules can only be accessed upon irradiation in the ultraviolet (UV) region, and this high-energy light can cause undesired side processes, such as decomposition. For instance, the absorbed energy may be in the order of the bond dissociation energy of some C–C bonds [3]. Another problem is the possible role of deactivation pathways such as fluorescence, phosphorescence, or nonradiative relaxation, which can restore the original ground state of the molecule and hence shut down the photoactivated reaction [4]. The development of transition metal-based photosensitizers has allowed to tackle some of these problems and lead to the efficient transformation of solar energy into chemical potential [5, 6]. Photosensitizers have some characteristic features: they

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have strong absorption in the visible light spectra, they have long excited state lifetimes, and, importantly, they are stable under photolytic conditions. Photosensitizers based on Ru(II) and Ir(III) complexes with polypyridyl ligands have been among the most extensively used in light-driven reactions [7, 8]. Photosensitizers based on other transition metals such as Cu [9], Au [10], or Fe, [11] have also been developed. Different organic chromophores have been also found to absorb light and photocatalyze target reactions [12, 13]. The first reports on the use of a Ru-based complex as a photocatalyst appear in 1978 [14]. However, the renaissance of the photoredox catalysis applied on synthetic organic chemistry starts in 2008 with two simultaneous publications. Both of these works took advantage of the ability of [Ru(bpy)3]Cl2 (bpy ¼ 2,2’bipyridine) complex to absorb visible light photons. MacMillan’s group reported the combination of a photocatalyst with an organocatalyst for the asymmetric alkylation of aldehydes triggered by sunlight [15]. Yoon and coworkers reported a [2+2] enone cycloaddition activated by visible light [16]. It is noteworthy that despite the similarities between these two studies, an important conceptual difference exists between them. The system reported by Yoon needs a sacrificial reagent to complete the photocatalytic cycle; in the system reported by MacMillan, an intermediate of the organocatalytic cycle regenerates the ground state of the photocatalyst. Dual systems like that reported by MacMillan have attracted huge interest in recent years [17]. Their defining characteristic is that a photocatalyst is combined with another system which is not able to absorb light by itself. The two systems react in a symbiotic manner merging the features of the two individual processes, which results in a novel reactivity that cannot be accomplished by either of the two systems acting independently [18]. Modern photochemistry usually relies on the ability of the photosensitizers to react to carry out single electron transfer (SET) steps upon irradiation to the triplet excited state. Single electron transfer from or to a substrate opens the door to novel reactivity which is complementary to the more classical two-electron chemistry [19, 20]. This approach involving photoinduced electron transfer (PET) is usually called photoredox catalysis in the chemical literature. The excited state of a chromophore organic molecule or metal-based complex is both a stronger oxidant and reductant species. Thus, upon irradiation, two photocatalytic cycles can exist, as outlined in Fig. 1. If the initial electron transfer reduces the substrate, this pathway is termed oxidative quenching because the photocatalyst evolves to an oxidized intermediate. Alternatively, if the first electron transfer is from the substrate to the excited form of the photosensitizer, the pathway is called reductive quenching. In reductive quenching, the substrate is oxidized while the photoredox catalyst is reduced. In both cases, the photocatalyst is ultimately regenerated to its initial form by accepting or donating an electron [21]. An alternative to photoinduced electron transfer is direct energy transfer. The most common mechanism for this type of processes is the Dexter energy transfer [22]. In Dexter energy transfer, the photosensitizer does not transfer any electron but the excitation, as shown in Fig. 2. The key in this event is a nonradiative relaxation of the photocatalyst synchronized with the generation of the excited state of the

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Fig. 1 Different pathways in photoredox catalysis. PS represents the photosensitizer. A, D, and S stand for acceptor, donor, and substrate, respectively

Fig. 2 Schematic diagram for Dexter energy transfer

substrate. Several rules must be fulfilled for this mechanism to take place. The energy transfer must be a thermodynamically favorable step, and a wave function overlap must exist between the photosensitizer and the substrate. Computational methods are nowadays an established tool for the understanding and elucidation of reaction mechanisms in many fields of chemistry [23–26]. Excited states present, however, an intrinsically complex challenge. Different electronic states with close energies are often involved, and intersystem crossings between them are common. The accurate computational characterization of the photoexcitation of the chromophore compounds and the reactivity of the excited state would require in most cases computationally demanding ab initio multiconfiguration methods like CASSCF/CASPT2 [27, 28]. There is a rich body of studies on excited states with these approaches [29, 30], but these methods are often too expensive for the type of systems involved in most photoredox catalysis of practical interest. Recent years have witnessed the appearance of an alternative approach based on the exclusive use of density functional theory (DFT) [31] to the computational

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Fig. 3 Schematic representation of the application of Marcus theory to an exergonic outer-sphere SET. ΔG is the Gibbs energy of the reaction, λ is the reorganization energy parameter, and ΔG{ is the energy barrier for the SET step

treatment of photoactivated processes [32–34]. Even without an accurate description of state crossings in the excited state, useful information can be obtained on the photocatalytic process. The nature of the photoexcitation, namely, the identity of the orbitals involved, can be investigated via time-dependent DFT (TD-DFT) [35], which allows the calculation of absorption spectra. Once the excited system relaxes to a fluorescent or phosphorescent state, its subsequent evolution can be analyzed with standard DFT techniques. The main nuance to the application of DFT to these processes is the need to describe single electron transfer (SET) between the two redox partners, which is critical when the photosensitizers acts as a photoredox catalyst. These SET steps have been found crucial for the course of many processes, such as dual Ni– photoredox-catalyzed reactions [36–38]. A systematic procedure to compute and estimate the barrier for these SET steps in outer-sphere processes is the application of the Marcus theory [39, 40]. This theory states that the activation barrier for an outersphere electron transfer process can be estimated as the intersection point of the product and reactant energy wells. To calculate this barrier, only the Gibbs energy of the reaction together with a rearrangement parameter is necessary (see Fig. 3). The rearrangement parameter can be split into two individual terms: the nuclei and the solvent parameter. The nuclear parameter can be calculated as the energy difference between products and reactants in gas phase. The solvent parameter is the energy difference associated with the change from the reactant to the product solvent cage. A full explanation of the applicability and features of the Marcus theory can be found on a recent publication by our group on the electron transfer steps in a well-defined homogeneous catalyst for water oxidation [39, 41]. It is worth noting that Marcus theory is not always required to treat SET steps. In inner-sphere electron transfer steps, a connection exists, even if temporary, between the two redox centers. From a computational perspective, these inner-sphere steps can be calculated with conventional transition state theory [36, 37, 42]. In this contribution, we will review four recent computational studies on the reactivity of photoactivated systems, which we consider representative of the current

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state-of-the-art in the field. These systems have been successfully investigated with computational DFT-based methods. The results are organized in two blocks. The first block corresponds to photoredox catalysis. First, a formally typical photoredox process will be discussed where the synthesis of indolines from alkenes and iodoacetanilide is accomplished by a combination of a Ni(0) catalyst and a Ru-based photosensitizer. Next, the light-driven catalytic trichloromethylation of acylpyridines catalyzed by an Ir complex will be discussed. The peculiarity of this system is that the same metal complex absorbs the light and catalyzes the reaction, without an external photosensitizer. The second block contains two examples that cannot be strictly defined as photocatalysis, but rather as photoactivation. They are the photoinduced oxidative carboxylation of a nonheme Fe(III) complex and the light-induced insertion of dioxygen into a Pt(II)-methyl bond.

2 Photoredox-Catalyzed Reactions 2.1

Dual Ni–Photoredox Catalysis

Nickel catalysis has been extensively used in the recent years for the development of novel transformations [43]. Nickel is more abundant and less toxic than other second- and third-row transition metals. On top of that, Ni exhibits an inherent ability to change its oxidation state by one unit at a time [44]. This behavior is complementary to the more traditional two-electron chemistry found in other metals such as Pd [45, 46]. Thus, the combination of nickel-based catalysts with photoredox active complexes such as [Ru(bpy)3]2+ can take advantage of the ability of these systems for the SET processes [47, 48]. This gives access to intermediates not reachable by other means, promoting a different reactivity [49]. Here, we will discuss the computational characterization of the full catalytic cycle for the synthesis of indoline products catalyzed by a symbiotic photoredox Ni system carried out in our group [50]. This system is remarkable because of the diversity of nickel oxidation states present in the catalytic cycle. Calculations were carried out using a B3LYP-D3 functional with a continuum acetone solvent introduced with the SMD methodology. The SET steps between the photosensitizer and the Ni catalyst were studied using the Marcus theory. The whole computed mechanism will be discussed here, with special attention to the steps with participation of the photosensitizer. The reaction starts with the oxidative addition of the iodoacetanilide reactant to the Ni(0) complex; the Gibbs energy profile is shown in Fig. 4. The transition state TSox.add for the concerted oxidative addition has a barrier of 19.8 kcal/mol. This is, however, not the favored path for this step. Ni complexes have been previously shown to react via halide abstraction to activate aryl halide substrates, and this is the case also here. Halide abstraction proceeds through the open-shell singlet (OSS) surface via an inner-sphere single electron transfer event. The activation barrier found for this mechanism TS1–2 is 6.1 kcal/mol, 13.7 kcal/mol lower than the

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Fig. 4 Gibbs energy profile for the competitive pathways of the C–I activation. Energies in kcal/ mol

formally simpler concerted oxidative addition. After the transition state TS1–2, a Ni (I) complex is obtained, and the aryl radical moiety is released to the media. After, the Ni(I) intermediate can release the initial alkene ligand and trap the aryl radical forming the Ni(II) intermediate. After a rearrangement, the final intermediate 3 of this step is found to be 44.0 kcal/mol below the initial reactants. The second step of the mechanism is the regioselective migratory insertion of the alkene into the Ni(II)-Caryl bond, shown in Fig. 5. The reported experimental selectivity was reproduced by calculation. The activation barrier for the desired transition state TS3–4 was 22.1 kcal/mol, while the transition states to produce the other possible regioisomers were found between 4 and 6 kcal/mol above this transition state. This step does not produce any modification in the oxidation state of the Ni center. New Ni–C and C–C bonds are formed, while the Ni–Caryl is broken. The reaction continues with the rearrangement and deprotonation steps shown in Fig. 6. The ligand rearranges in the metal coordination sphere to bring the N atom close the Ni center. Then, NEt3, the base present in stoichiometric amount, deprotonates the complex. We computed alternative pathways for this step, for example, changing the order between rearrangement and deprotonation. They were all higher in energy. Evolution from intermediate 6 is shown in the Gibbs energy profile in Fig. 7. The Ni(II) intermediate 6 contains the two atoms that must bind through reductive

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Fig. 5 Gibbs energy profile for the alkene insertion step into the Ni–C bond. Energies in kcal/mol n-hex

H I 4 -40.9 H

IPr NiII

N

Ac

5 -38.4

IPr

NEt3 I-[HNEt3]+

NiII n-hex O N H I

6 -53.3 IPr

n-hex N

NiII O

Fig. 6 Rearrangement and deprotonation steps

elimination already attached to the metal center. But direct reduction elimination from this intermediate is totally prohibitive. The transition state associated with this step TS6-Ni(II) has a barrier of 66.0 kcal/mol. Here is where the photosensitizer plays a crucial role. Without the aid of the photocatalyst, the reaction would reach only this step. If the photosensitizer reaches its excited state, its high oxidation potential can oxidize the Ni(II) complex 6 to the Ni(III) intermediate 7 in a thermodynamically favorable step. Thus, we examined with Marcus theory the barrier for the outersphere electron transfer event. The two redox partners involved in this step are the Ni

Computational Modeling of Selected Photoactivated Processes

n-hex

IPr N

NiII O

TS6-Ni(II)

n-hex

12.7

IPr N

-47.2 *[Ru]

n-hex

N

O

O

[Ru]

-45.5

+

n-hex

2+

IPr NiII

NiIII

TS7-8

SET6-7 6 -53.3

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n-hex 7 -65.0

n-hex

N Ac

IPr N

NiIII O

IPr NiI

8 -85.8 n-hex

[Ru]

SET8-1

[Ru]

-73.5

2+

1

+

-84.5 IPr Ni0 n-hex

Fig. 7 Gibbs energy profile for the indoline formation from the intermediate 6. Energies in kcal/ mol

(II) complex 6 reported above and the excited form of the [Ru(bpy3)]2+ photoredox catalysts. A single electron transfer must take place from the nickel system to the ruthenium system, resulting in a Ni(III) intermediate and a reduced Ru (I) photocatalysts. The nuclear and the solvent reorganization energies were calculated following the procedure reported before by our group [51]. The outer-sphere SET6–7 has a low barrier of 6.1 kcal/mol for the generation of the Ni(III) intermediate 7. From this intermediate 7, the reductive elimination proceeds smoothly with a barrier of 19.5 kcal/mol, TS7–8. This tremendous change in the reaction barrier after the oxidation of the metal center has also been observed in an iridium system, and the whole process has been labeled as oxidatively induced reductive elimination (OIRE) [52]. Finally, the initial species 1 is regenerated by the reduced form of the photocatalysts closing both photocatalyzed and catalyzed cycles. Again, we applied the Marcus theory to estimate the outer-sphere SET barrier. We found it at 12.3 kcal/ mol from intermediate 8. Although this step is slightly endergonic, the low barrier found for the halide abstraction mechanism will push the reaction toward a new catalytic cycle, as the electron rebound alternative has a higher barrier. The proposed mechanism is compatible with nonproductive pathways that may occur during the reaction due to the high reactivity of the excited state of the photocatalyst. For instance, ruthenium photocatalysts could accept or donate an

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electron with other species in solution. Most of these nonproductive pathways would return to the main catalytic cycle. They may reduce the reaction rate, but not modify the final outcome. In summary, the full mechanism for the indoline synthesis from 20 -iodoacetanilide and alkene catalyzed by a combination of Ni/Ru dual system could be fully characterized. The barriers for the outer-sphere SET were successfully calculated applying the Marcus theory.

2.2

Light-Driven Catalytic Trichloromethylation of Acylpyridines

A number of natural products bear trichloromethyl groups. They are interesting because of their pharmacological properties [53, 54]. Many efforts have been done to develop strategies for the insertion of this group into organic molecules. These methodologies can be stoichiometric [55, 56] or catalytic (mainly with Ru [57, 58] and Ti [59, 60] catalysts). However, methodologies for an effective enantioselective addition of trichloromethyl groups have been limited. Most of the strategies to achieve this goal involve redox-mediated radical addition, presenting thus a perfect opportunity for the treatment of this reaction with a photocatalytic approach. Trichloromethylation has been achieved in selected case without need of an external photosensitizer. Meggers and coworkers [61] developed an iridium system which is capable to photoinduced single electron transfer to catalyze the enantioselective trichloromethylation of 2-acylpyridines and 2-acyl imidazoles. The unique features of this chiral Λ-iridium complex are that it acts as both the asymmetric catalysts and the photosensitizer [62]. The bidentate ligands in this octahedral complex are responsible for the chirality of the system. They are arranged in a left-handed propeller-type coordination [63]. In this section, we will present our computational study of the reaction reported by Meggers and coworkers. Although the original publication analyzed the origin of enantioselectivity, here we will only focus on the steps where light plays a direct role. Calculations were carried out with an ONIOM method, ωB97X-D for the QM region and UFF for the MM region. The MM region consisted of the methyl substituents in the tert-butyl groups of the catalyst.

2.2.1

Overall Catalytic Cycle

As is the usual case in photoredox catalysis, the whole reaction mechanism consists of two linked cycles that we can label as “light” and “dark.” They are shown in Fig. 8. The two cycles cross in two points. The first of them is the transfer of the CCl3 radical generated by the interaction of the photogenerated excited state iridium complex A with the BrCCl3 substrate. The second connection is in the electron

Computational Modeling of Selected Photoactivated Processes

A

*

N Ir3+*

O

BrCCl3

SETA-B 63.2

H

N

141

A 58.1

N

CCl3

TSB-4 26.2

hν

"DARK" CYCLE 1

13.2

Ir3+

N

3 2 -8.9

H 2

Ir3+ N

N

H

CCl3

N

N

H

N

SET4-5 -0.6

B

N

N O

H

O

N

3 2.3

Ir3+

N

O

+ Ir

"DARK" CYCLE

N Ir4+

1 0.0

O

B

+ BaseH

Base

N

B 17.3

"LIGHT" CYCLE TSPA

N

TSB-4

N

O N

H 4

Ir3+

3

4 -8.1

N O N

CCl3

N 5

5

N Ir3+

O N

-30.3 CCl3

N

Fig. 8 Gibbs energy pathway for the trichloromethylation mechanism. Energies in kcal/mol

transfer SET4–6, which regenerates the initial form of the iridium complex 3. The particularity of this system is that the photosensitizer in the “light” cycle is the intermediate species in the “dark” cycle. Thus, two units of intermediate 3 need to be generated. For the sake of clarity, the origin of relative energies is the initial catalyst 1 in a tetracoordinate form, after decoordination of the two acetonitrile ligands. The computed mechanism starts with the coordination of the substrate to the initial catalyst 1, which results in a 8.9 kcal/mol stabilization in intermediate 2. Then, the lutidine base abstracts a proton from 2 resulting in complex 3. This step is endergonic by 11.2 kcal/mol. The barrier associated with the proton abstraction process is 22.1 kcal/mol, affordable in the experimental conditions. From intermediate 3, the system absorbs a photon to promote an electron to the excited state. The feasibility of this excitation was confirmed by TD-DFT calculations, where we found a strong metal-to-ligand charge transfer (MLCT) associated with a band at 387 nm with an oscillator strength of 0.1482. Then, the excited states can relax to its triplet complex A which is found at 58.1 kcal/mol above the initial reactants. From this point, we applied the Marcus theory, and we found a low barrier of 5.1 kcal/mol for the outersphere single electron transfer step SETA-B from complex A to the BrCCl3 substrate. This SET step generates three fragments: the cationic complex B, where the Ir(III) complex has been oxidized to Ir(IV), the bromide anion, and the CCl3 radical.

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Finally, a new complex 3 can trap the CCl3 radical in the “dark” cycle to make a new C–C bond, in a kinetically affordable and highly exergonic step, through TSB-4. Complex 4 can transfer back one electron to the cationic intermediate B in the “light” cycle. The barrier for this SET step was found to be 7.5 kcal/mol, as estimated by the Marcus theory. The resulting complex 5 after the SET4–5 step in the “dark” cycle can release the product to start a new turnover.

2.2.2

Propagation vs Termination

In the experimental paper, Meggers and coworkers proposed that the electron transfer event could take place from 4 to the BrCCl3 substrate following a propagation pathway. So, we carried out calculations on this alternative mechanism which would run on the above mentioned “dark” cycle. The results are summarized in Fig. 9. As explained in the previous section, intermediate 4 can transfer an electron to the transient intermediate B via SET4–5 following a termination pathway. The alternative mechanism follows a propagation pathway in which intermediate 4 can transfer one electron to the BrCCl3 reactant, trough SETprop, liberating the CCl3 radical which at the same time could react with a new molecule of intermediate 3. In the later mechanism, no extra photons are needed. The activation barrier for SETprop is 10.0 kcal/mol (estimated with Marcus theory), which is higher than SET4–5 (7.5 kcal/mol from intermediate 4). This would suggest that the termination pathway is favored by 2.5 kcal/mol. However, the concentration of the species involved in each pathway would play a crucial role in this step. Complex B is a transient intermediate of the catalytic cycle formed after the photoexcitation and electron transfer event of complex 3. On the other hand, BrCCl3 is one of the main substrates of the reaction, thus in much higher concentration than intermediate B. Consequently, propagation is the most competitive pathway in the first stages of the reaction. Later, as the concentration of the BrCCl3 reagent decreases, the termination pathway will be favored. This is in full consonance with the quantum yield of Fig. 9 Gibbs energy profiles for the propagationtermination competition. Energies in kcal/mol

PROPAGATION

TERMINATION

SETPROP 1.9 CCl3

BrCCl3 4

5 5

Ir3+

-15.3 N Ir3+ N

O N

N

CCl3

SET4-5

B

-0.6

4 -8.1 O N

3

CCl3

N 5

5

N Ir3+ N

O N

-30.3 CCl3

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5 obtained experimentally. For each photon absorbed by the system, five molecules of the final product are generated.

2.2.3

Potential Alternatives for Photon Absorption

In the cycle reported above, the photon is absorbed by complex A. This intermediate is formed upon the coordination of the substrate followed by deprotonation with the lutidine base. There are, however, other species involved in the catalytic cycle that could absorb light. We studied thus species I, 1, and 2 to determine their photoactivation properties. To do so, we ran TD-DFT calculations on these three complexes and applied Marcus theory to check if the activation of the BrCCl3 substrate was possible from the corresponding excited states. The results are summarized in Fig. 10. Catalyst precursor I shows a strong absorption band at 347 nm which is associated with a metal-to-ligand charge transfer (MLCT) with an oscillator strength (ƒ) of 0.2912. The computed absorption wavelength is compatible with the experimental observation. However, precursor I has to be discarded as a possible photosensitizer, because the decoordination of the two acetonitrile ligands is a barrierless process which leads to the formation of the more stable complex 1. Thus, the equilibrium between both complexes would be totally displaced to complex 1. I

It

N Ir

NCMe

hν

NCMe

λmax 444 nm

N

N

7.0

82.2 1t

N

N

hν

Ir N

2t O N

H

hν

O N

BrCCl3

H

ΔG = 41.6 kcal/mol

CCl3

N 45.6 A

N

N

N Ir

λmax 373 nm

N

2.3

CCl3

N

-8.9

Ir

ΔG = 40.1 kcal/mol

45.2

N Ir

BrCCl3

Ir

λmax 347 nm

0.0

3

NCMe

N

1

2

NCMe

Ir

O N

H

hν λmax 387 nm

B

N Ir N 58.1

O N

H

BrCCl3

ΔG = 5.1 kcal/mol

N Ir

O N

H

N 17.3

Fig. 10 Wavelength maximum absorption and outer-sphere SET for selected intermediates. Energies in kcal/mol

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Complex 1 is a photoactive species with a MLCT band at 444 nm (ƒ ¼ 0.0596). After the photoactivation process, the excited form of the complex would evolve to a triplet state with an energy of 45.2 kcal/mol. This complex would fade back to the ground state as it would not be able to activate BrCCl3 because the estimated barrier for the SET process is prohibitively high (40.1 kcal/mol). We found a similar behavior for the coordinatively saturated complex 2. The complex can absorb light promoting an MLCT with an associated band at 373 nm (ƒ ¼ 0.1704), but the barrier for SET is too high. Finally, complex 3 has an MLCT band at 387 nm with an oscillator force of 0.1482. Most importantly, its excited triplet form A can perform the outer-sphere SET event with a low barrier of 5.1 kcal/mol for the activation of the BrCCl3 substrate, confirming that this is the active photosensitizer species [64]. In summary, the full mechanism for the trichloromethylation of 2-acylpyridines was calculated with DFT tools. We were able to reproduce all the experimental observations using standard DFT, TD-DFT, and Marcus theory calculations.

3 Photoactivated Reactions 3.1

Photoinduced Oxidative Decarboxylation of a Nonheme Iron(III) Complex

Photoactive iron(III) complexes bearing carboxylato ligands are well characterized in coordination and bioinorganic chemistry [65, 66]. Iron(III) complexes of simple organic acids like malonate or citrate can be activated by UV and blue light [67, 68]. The process results ultimately in CO2 extrusion and reduction of the metal center to iron(II) [69, 70]. This process is used by plants and microorganisms for iron processing in cases of scarcity of the element, but its mechanism is poorly understood. In this section, we describe our computational study on the light-driven irreversible oxidation of the ligand of an iron(III) complex, [Fe(tpena)]2+ (tpena ¼ N,N, N0 -tris(2-pyridylmethyl)ethylenediamine-N0 -acetate). This work was carried out with the experimental group of McKenzie [71]. The reaction sequence starts with the photoactivation of the complex followed by CO2 extrusion. Then, the system can trap a triplet dioxygen molecule to produce a putative alkylperoxide complex. The latter can easily evolve to a Fe(IV)-oxo species. This species undergoes a proton transfer from methylene to oxo, which results in the release of a formaldehyde molecule. Finally, the iron(III) hydroxide complex is reduced. The presentation here will focus on the computational work on the steps involving light. All the energies reported in this section are Gibbs energies obtained with B3LYP-D3 functional, including zero-point energies, entropic corrections, solvation, and dispersion.

Computational Modeling of Selected Photoactivated Processes

3.1.1

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Photoactivation Step

Experimental data indicate two potential starting points for the photoactivation step: the high-spin sextet state mer-[Fe(tpena)]2+ and the low-spin doublet fac-[Fe (tpena)]2+. The calculations showed that both complexes have similar energies which agree with the similarities for the FeIII/FeII redox potentials found [72]. We next ran TD-DFT calculations to evaluate the vertical absorptions of both fac and mer complexes. The fac complex in its low-spin state did not show any active band in the near UV or visible range. On the other hand, the mer isomer in the sextet spin state show a ligand-to-metal charge transfer (LMCT) band with maximum absorption at 377 nm. Consequently, we concluded that the reaction advances through this isomer. The orbitals associated with the photoactivation step are shown in Fig. 11. The transition is related to the transfer of a β electron of the lone pair of the nitrogen on the glycyl arm of the ligand to a d orbital of the iron center. So, the iron center is reduced to Fe(II). The spin density on the sextet resulting from the excitation is mostly localized on the iron center with four electrons. The remaining unpaired electron is delocalized between the carboxylate group and the nitrogen. At this point, we would have liked to compute the evolution of the excited system through the intersystem crossing (ISC), but this was not feasible with a reasonable computational cost. Instead, we tried relaxation of the excited sextet state inside the TD-DFT approach. This showed in the first steps a remarkably lengthening of the Fe–N distance of the glycyl arm and a more discrete elongation of the Fe–O distance. Predictably, the TD-DFT optimization crashed before the system was fully optimized, likely because of the intrusion of other states. However, we think that these calculations are sufficient to strongly suggest that the carboxylic moiety loses its anionic characters, becoming less coordinating, and the attached nitrogen group becomes a planar sp2 center. This would naturally lead to the release of the former carboxylate in the form of a CO2 molecule. These calculations cannot predict the final spin state of the intermediate resulting from the relaxation and CO2 extrusion, which could be doublet, quartet, or sextet spin. The complex cannot be isolated experimentally, as it is very reactive, but Mössbauer data are available. Comparison between experimental Mössbauer parameters and those calculated with DFT indicate this intermediate is in the doublet spin state. The unpaired electron in this intermediate 1 is found on the N-CH2 arm. Fig. 11 Molecular orbitals involved in the key excitation of initial complex mer-[Fe(tpena)]2+

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3.1.2

Reaction Mechanism

The computed Gibbs energy profile is shown in Fig. 12. After the formation of the transient complex 1, it can react with dioxygen to form the alkylperoxo species 2. The system then evolves through TS2–3 with a low barrier (8.9 kcal/mol) to form an Fe(IV)-oxo intermediate 3 containing a terminal CH2O group with radical character on the oxygen atom. The terminal group can be released as formaldehyde through TS3–4 with a barrier of 15.2 kcal/mol, transferring the radical character to the nitrogen atom of the former glycyl moiety, 4. The oxo group now can abstract a proton of the vicinal methylene group to reach intermediate 5 in a downhill manner. The doublet state complex 25 will likely evolve to the most stable sextet spin state 65. The sextet spin state of this intermediate was experimentally characterized, and we could confirm its nature with the calculated Mössbauer parameters. Finally, complex 6 5 reacts with the solvent (MeCN) releasing a water molecule and forming the product of the reaction [Fe(SBPy3)(MeCN)]2+, 6. It is worth mentioning that during the mechanism, there may be some crossing points between the different spin state surfaces. Nevertheless, these crossing points will only affect to the relative energies of the intermediates but would not add chemical insight.

N N N

FeIII

N

N CH2

CO2

N N

1

N

22.7

N

O2

N

Fe N H2C

N

N O

FeIV O N TS3-4

O

N

C O H2

13.8 CH2O

TS2-3 6.3

N

mer 0.0

N N N

FeIII N

N O O

3

-2.6

-2.4

N

N

N

N N

N

2

FeIII

N O

N C H2

O

N N

FeIV

FeIV O

N

N

N N

4

N

-12.4

O

FeII

N

N

N NCMe

N C O H2

25

N N N

FeIII N

-55.9 N

6 -49.2

65

-64.3 OH

Fig. 12 Gibbs energy profile of the reaction starting from mer-[Fe(tpena)]2+. All the energies correspond to the doublet spin state complexes. Energies in kcal/mol

Computational Modeling of Selected Photoactivated Processes

147

The stepwise mechanism for the O2-dependent oxidative deglycination of the nonheme [Fe(tpena)]2+ complex was thus fully elucidated. The presence of a carboxylato group in the ligand allows an electron transfer from this group to the metal center (LMCT) upon irradiation. The nature of this band was identified with TD-DFT techniques. In addition, transient intermediates were characterized with experimental and computational techniques.

3.2

Light-Driven Insertion of Dioxygen into Pt(II)–C Bonds

Metal-carbon complexes are major intermediates in many catalytic processes. However, the direct functionalization of alkyl ligands into useful products remains still a challenge. Many efforts have been done in recent years for the use of readily accessible reactants that can be inserted into the M–C bond and release functionalized products [73, 74]. In the field of alkene oxidation, Pt(II) and Pd (II) organometallic complexes have been used for this quest. Several oxidation agents have been used in combination with the aforementioned catalysts, such as Cl2, [75] PhICl2, [76] PhI(OAc)2 [76], and RSSR, [77] among others. In any case, the ideal scenario would be the use of environmental benign oxidant such as H2O2 or O2, especially the latter. Dioxygen is, however, a difficult reactant, it is in low concentration in solution, and it often presents high barriers. In a collaboration with the group of Britovsek, we carried out a computational DFT study on the reaction of the 6,60 -diaminoterpyridines Pt(II)-methyl complex with the O2 molecule upon irradiation of the system [78]. Modifications on the 6,60 positions of the terpyridine ligands change the behavior of the system, and the rationalization of these effects is a challenge.

3.2.1

Photoactivation Step

The photoinduced excitation of square planar Pt(II) and Pd(II) complexes bearing pyridinic ligands has been previously studied by computational and experimental methods. These complexes show a long lifetime in the triplet state upon irradiation. The maximum absorption band is associated with a metal-to-ligand charge transfer (MLCT). For this reason and to avoid the usage of high expensive multireference methods, such as CASSCF, we did not study the intersystem crossing (ISC) from the excited singlet state to the triplet state. The TD-DFT calculations, at M06 level of theory, showed two strong bands at 404 nm (ƒ ¼ 0.1343) and 364 nm (ƒ ¼ 0.2789). Both bands correspond to a metalto-ligand charge transfer (MLCT) events. These results agree with the experimental spectrum for the complex [79]. The nature of these bands is associated with the transfer from a d orbital of the metal to a π* orbital of the terpyridine ligand. Figure 13 show the key absorption orbitals associated with the photoactivation step.

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Fig. 13 Molecular orbitals involved in the key absorption band for complex A

Fig. 14 Optimized geometries for the intermediates participating in the photoexcitation step, singlet ground state on the left (A) and triplet excited state on the right (3A). Selected distances in Å and angles in degrees

The phosphorescent state resulting from excitation will be in the triplet state, so we proceeded next to its calculation. The geometry changes from the singlet ground state complex to the triplet state are remarkable (see Fig. 14). The steric repulsion between the methyl group and the amine groups of the terpyridine ligand forces the methyl ligand to move partly out of the plane even in the ground state complex (N-Pt-Me angle, 167.2 ). This distortion is more notable in the triplet state (N-Pt-Me angle, 117.7 ), which also increases the distance between the Pt center and the methyl from 2.08 to 2.12 Å. This rearrangement is driven by the photoexcitation and opens a vacant in the metal center for the incoming dioxygen.

3.2.2

O2 Insertion into the M–C Bond

The overall mechanism for this reaction is depicted in Fig. 15 but will not be discussed in detail here. Only the reaction between the photoexcited complex and triplet O2 will be addressed. The photoexcited complex 3A can react with a molecule of dioxygen through two main pathways, shown in Fig. 16. In both mechanisms, the spin state of the overall system is zero, as the preferred approach between the triplet dioxygen and the

Computational Modeling of Selected Photoactivated Processes

N N

N

NH2

Pt

Me O NH2

N

N

NH2

Pt

N

3O

31.8

3A

Me NH2

O

23.2 N N

N Pt

N

Pt

NH2

N

B 23.9

NH2 O O

O

N

C 0.0

N

-19.7

-26.6 N

23.3

N

N

3C

13.0 - 3O2

5.7

N

O

NH2 O

TS F-G F

N

N Pt

Me NH2

O

NH2 O

Pt

NH2 TS 3C-A

N Pt

NH2 Me

NH2 A

N NH2 O Pt O

Me NH2

23.8

N N NH2 Pt O N O Me NH2

-17.6

N

31.3

TS C-F

MECP C-3C

Me

N

TS C-G

NH2

hν

N

Pt

Me NH2

Me O NH2

N

N

N

TS 3A-B

2

149

G

O Me

NH2 O

-48.0

N N

N Pt

NH2

NH2

O O

Me

Fig. 15 Gibbs energy profile for the full scenario of the O2 insertion into the Pt(II)–Me bond upon irradiation. Energies are Gibbs energies in solution, in kcal/mol. MECP stands for minimum energy crossing point

N N

N Pt

Me NH2

3O

2

NH2 O

O

TS 3A-D 36.1 TS 3A-B 31.8

N

3A

N

Me NH2

23.2 N N

N Pt

N Pt

Me NH2

NH2 N N

N Pt

NH2

NH2 + O O

B 6.3 D 1.5

O

NH2 O N NH2 Pt O N O Me NH2 N

C 0.0

Me

Fig. 16 Gibbs energy profile for the alternative pathways for the reaction between 3A and 3O2. Energies relative to intermediate C in kcal/mol

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excited triplet state 3A complex would generate a neat spin of 0, i.e., the dioxygen approximates in an antiferromagnetic manner to the complex. The lower reaction path starts with the coupling of one unpaired electron on the dioxygen with one unpaired electron of the metal center, forming intermediate B on the open-shell singlet (OSS) surface. In B, one electron is localized in the terminal oxygen, and the other one is arranged antiparallel in the σ*Pt—Me orbital. This intermediate is found at 23.9 kcal/mol above the initial reactants (A + 3O2). This step is barrierless on the Gibbs energy surface, but we can estimate an entropic barrier of ca. 8 kcal/mol. Finally, the system evolves to intermediate C on the closed shell singlet as a result of the quenching between the two antiparallel electrons. The side-on peroxide-kind coordination of the dioxygen molecule moves the methyl group of the complex to the apical position. Intermediate C has an energy of 17.6 kcal/mol above the reactants. Free singlet oxygen has an energy of 22.7 kcal/mol; therefore, this pathway is more favorable than the generation of singlet oxygen. An alternative mechanism involves a single electron transfer step (SET) from the metal to the dioxygen molecule, which implies the homolytic dissociation of the Pt– Me bond. We were able to find this transition state TS 3A-D with an activation barrier of 12.9 kcal/mol, from intermedia 3A. As a result of this event, two fragments are generated: a tricoordinate Pt(II) complex with a vacant site on the fourth coordination position and a methylperoxo radical. Nevertheless, this alternative pathway is not competitive for the parent system because the direct coupling between the dioxygen and the complex is favored by ca. 5 kcal/mol. To sum up, we have presented the mechanism for the insertion of dioxygen into the Pt(II)–methyl bond of the [Pt(terpyridine)Me]+ complex, upon irradiation of the complex to its excited triplet state. To determine the nature of the photoexcitation, TD-DFT methods have shown a good agreement between the computed and the experimental absorption bands. In the early steps of the mechanism, the 3O2 molecule is trapped by the excited complex on the open-shell singlet (OSS) surface with a low barrier. The Pt(IV)-peroxo intermediate generated after the coupling between the excited complex and the dioxygen is lower in energy than the free singlet oxygen, confirming that there is not an energy transfer event to form free singlet dioxygen.

4 Conclusions Photoactivated processes are gaining importance because of their versatility and the access they provide to new products. They pose a challenge for computational chemistry because of their intrinsic electronic complexity and the size of the systems involved. But recent years have witnessed the increased application of DFT calculations to the field through a combination of TD-DFT treatments for photoexcitation, conventional DFT calculations for selected regions of the Gibbs energy profile, and reasonable assumptions for the parts (intersystem crossing between same spin spates) that cannot be properly computed with this treatment. In this chapter, we

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have presented four successful applications of this type of calculations covering a variety of representative cases. Both photocatalytic processes and photoactivated reactions can be computed, and calculations can provide new mechanistic insight into the processes. The short -term future should be an increased number of the contributions of computational chemistry to photoactivated processes.

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Top Organomet Chem (2020) 67: 153–190 https://doi.org/10.1007/3418_2020_47 # Springer Nature Switzerland AG 2020 Published online: 30 June 2020

Ligand Design for Asymmetric Catalysis: Combining Mechanistic and Chemoinformatics Approaches Ruchuta Ardkhean, Stephen P. Fletcher, and Robert S. Paton

Contents 1 2 3 4

Introduction: Chirality in Life and Medicine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Access to Enantioenriched Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Privileged Ligands: Phosphoramidites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Approaches for Ligand Design in Asymmetric Catalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Serendipitous Discovery and High-Throughput Screening (HTS) . . . . . . . . . . . . . . . . . . . 4.2 Mechanistically Driven Ligand Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Quantitative Structure-Selectivity Relationships (QSSRs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 QSAR Best Practices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Collecting Molecular Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Predicting Enantioselectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 QSSR-Driven Ligand Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Predicting Yield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Predicting Product Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

155 156 159 161 162 164 170 171 173 174 179 181 184 185 186 186

Abstract A core element to the successful development of asymmetric catalytic reactions is finding a suitable chiral catalyst or ligand. The discovery and optimization of chiral catalysts can be enormously challenging. Traditionally, chemists have

R. Ardkhean Faculty of Medicine and Public Health, HRH Princess Chulabhorn College of Medical Science, Chulabhorn Royal Academy, Bangkok, Thailand S. P. Fletcher Chemistry Research Laboratory, University of Oxford, Oxford, UK R. S. Paton (*) Chemistry Research Laboratory, University of Oxford, Oxford, UK Department of Chemistry, Colorado State University, Fort Collins, CO, USA e-mail: [email protected]

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approached this endeavour by screening existing ligands. The most promising structures are then modified based on mechanistic knowledge, chemical intuition and the results of screening experiments, with the aim of optimizing selectivity and yield. However, this empirical approach has begun to change: new methods to accelerate the experimental screening process have emerged together with computational and physical-organic approaches that provide a systematic, and hopefully faster, route to new catalysts. Practical and theoretical understanding of highthroughput screening and multi-parameter optimization are now requirements at the cutting edge of the field, in addition to synthetic and mechanistic expertise. In this chapter, we summarize the recent examples of combinatorial approaches taken to discover and develop asymmetric catalytic transformations. In particular, we highlight the use of quantitative models to predict reaction outcomes. A series of guidelines are presented to aid chemists in adopting these approaches, followed by illustrated examples of recent work in this area. Keywords Asymmetric catalysis · Chiral ligand design · Computational modelling · Enantiomeric excess · Quantitative structure-selectivity relationships (QSSR)

Abbreviations AARON AD AIC ANOVA ASO BINOL BINAP CAPT cat. CIP COD dba DCM DFT (DHQD)2PHAL DNA dr ee EPR er etc. FF GC-MS HPLC

An automated reaction optimizer for new (catalysts) Applicability domain Akaike information criterion Analysis of variance Average steric occupancy 1,10 -Bi-2-naphthol 2,20 -Bis(diphenylphosphino)-1,10 -binaphthyl Chiral anion phase transfer Catalytic Cahn-Ingold-Prelog 1,5-Cyclooctadiene Dibenzylideneacetone Dichloromethane Density functional theory Hydroquinidine 1,4-phthalazinediyl diether Deoxyribonucleic acid Diastereomeric ratio Enantiomeric excess Electron paramagnetic resonance Enantiomeric ratio et cetera Force field Gas chromatography-mass spectrometry High-performance liquid chromatography

Ligand Design for Asymmetric Catalysis: Combining Mechanistic and. . .

hr HRMS HTS IR kcal kJ LMOCV LOOCV M

Min MLR MM mol NBO NBS NMR OECD OLS PA PCA PLS Q2MM QM QSAR QSSR RMSE rt SD TADDOL TMS TS UTS UV-vis vs XPS

155

Hour(s) High-resolution mass spectrometry High-throughput screening Infrared Kilocalories Kilojoules Leave-many-out cross-validation Leave-one-out cross-validation Molarity Minute(s) Multivariate linear regression Molecular mechanics Mole Natural bond order N-Bromosuccinimide Nuclear magnetic resonance Organization for Economic Co-operation and Development Ordinary least squares regression Phosphate anion Principal component analysis Partial least squares regression Quantum guided molecular mechanic Quantum mechanic Quantitative structure-activity relationship Quantitative structure-selectivity relationship Root-mean-square error Room temperature Standard deviation α,α,α0 ,α0 -Tetraaryl-2,2-disubstituted 1,3-dioxolane-4,5dimethanol Trimethyl silyl Transition states Universal training set Ultraviolet-visible spectroscopy Versus X-ray photoelectron spectroscopy

1 Introduction: Chirality in Life and Medicine The word ‘chiral’ originates from the Greek χείρ (cheir), meaning hand. It first appeared in the scientific literature between 1884 and 1904, nearly 50 years after Pasteur’s discovery of molecular stereochemistry was presented in 1848. Terms such as chiral and chirality were coined by Sir William Thompson, who was ennobled in

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1892, becoming Baron Kelvin, the first British scientist to be elevated to the House of Lords [1]. Kelvin’s definition of chirality was later refined by Eliel and Wilen to mean ‘Not superposable with its mirror image, as applied to molecules, conformations, as well as macroscopic objects such as crystals’ [2]. The left- and right‘handed’ forms of a molecule are called enantiomers (from ἐναντίoς (enantios), meaning opposite). The composition of a mixture of enantiomers can be quantified in terms of the enantiomeric excess (ee), the percentage difference between one enantiomer and the other equated with optical purity, or the enantiomeric ratio (er). Both terms are commonly encountered in current literature as expressions of enantioselectivity and the relative merits debated [3]. The sense of chirality can be assigned based on different rules, of which the Cahn-Ingold-Prelog (CIP) system, i.e. R or S is most universally used. The enantiomeric excess of an R/S mixture is given in Eq. 1. ee ¼

jR  Sj  100 ¼ j%R  %Sj RþS

ð1Þ

where R and S denote the amount of R and S enantiomer, respectively. The study of chirality not only serves the fundamental curiosity regarding the chemical origins of homochirality but also plays a vital enabling role in the discovery of innovative medicines, agrochemicals and materials. More than half of the molecules used as drugs are chiral molecules, and newly approved drugs are now dominated by single-enantiomer compounds ahead of racemates [4]. New regulatory guidelines emerged as the differential actions and toxicities of enantiomers became apparent and, along with other economic forces, have led to fewer approvals of racemates than achiral or single-enantiomer medicines worldwide. The controlled production of enantiopure molecules via enantioselective chemical synthesis is now more important than ever. The requirement for new asymmetric methods to prepare enantioenriched compounds is as pressing as ever, and the design of new chiral catalysts and ligands lies at the heart of this endeavour.

2 Access to Enantioenriched Materials Prior to the discovery of catalytic asymmetric methods, several synthetic approaches were developed by chemists to gain access to enantioenriched materials: by using natural enantiomerically pure starting materials (the chiral pool [5]), separating enantiomers by resolution [6] and using a chiral auxiliary [7]. Representative examples for each of these approaches are shown in Fig. 1. These approaches have proven successful, although they are limited by the requirement of a stoichiometric chiral starting material or reagent or, in the case of a separation, by the loss of half of the material produced. Furthermore, the preparation and screening of several structural analogues of, e.g. chiral auxiliaries is challenging, especially when compared with modern catalytic methods, and so the

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Fig. 1 Examples of accessing the chiral pool, chiral resolution and chiral auxiliaries in asymmetric synthesis: (a) chiral pool, (b) chiral resolution, (c) chiral auxiliary

prospect of systematically optimizing these methods (especially with the aid of computation) is relatively low. In contrast, a more efficient approach is asymmetric catalysis. This enables the selective synthesis of enantioenriched materials using only a catalytic (i.e. sub-stoichiometric) amount of a chiral species. In theory, one chiral molecule has the potential to catalyse the formation of a large quantity of an optically active substance. Compared to the other approaches, asymmetric synthesis is desirable because there is no need to rely on the availability of the natural enantiomer (chiral pool) or wasting materials (50% of mass in kinetic resolutions is unwanted, and use of chiral auxiliaries requires additional steps to introduce the auxiliary and liberate the desired molecule). In addition, the development of a catalytic system uses sub-stoichiometric chiral species to accelerate the reaction. These considerations add to the overall efficiency and atom economy of an asymmetric reaction [8]. The ability of homogeneous transition metal complexes to catalyse a wide variety of chemical transformations has inspired chemists to design and prepare chiral

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a) Hydrogenation O

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N squalene K2OsO2(OH)4, (DHQD)2PHAL K3Fe(CN)6 AD-mix-β K2CO3 HO

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OH

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Fig. 2 Examples of asymmetric catalytic reactions: (a) asymmetric hydrogenation by Noyori and (b) asymmetric dihydroxylation by Sharpless

ligands that make these complexes function as chiral catalysts for asymmetric synthesis. The quest for novel, efficient chiral transition metal catalysts has been an ongoing endeavour for the past 40 years. The impact of asymmetric catalysis in chemistry was recognized by the 2001 Nobel Prize, awarded to Knowles, Noyori and Sharpless for their work on catalytic asymmetric hydrogenation and oxidation using complexes of transition metals with chiral ligands (Fig. 2). An example of Noyori’s asymmetric enamide hydrogenation is shown in Fig. 2a. Using catalytic amount of the chiral Ru-BINAP (2,20 -bis(diphenylphosphino)-1,10 -binaphthyl) complex, this transformation yields the reduced product in high enantio- and diastereoselectivity, a precursor for the carbapenem class of ‘last resort’ antibiotics [9]. Figure 2b shows an example of a Sharpless asymmetric dihydroxylation of squalene catalysed by an Os-(DHQD)2PHAL (a hydroquinidine 1,4-phthalazinediyl diether) complex, in which the six internal alkenes are enantioselectively functionalized in a single synthetic step [10]. The relevance of these reactions to the development of computational approaches to study asymmetric catalysis is also high. While Ru-BINAP-catalysed hydrogenations prompted some of the earliest DFT studies of asymmetric catalytic reactions [11], mixed quantum mechanics/ molecular mechanics (QM/MM) and quantum-guided molecular mechanics (Q2MM) methods have been applied to uncover the origins of enantioselectivity in these processes. In landmark studies, Ujaque, Maseras and Lledós [12] showed that the inclusion of hundreds of conformations was necessary to accurately describe the levels of enantioselectivity in Sharpless dihydroxylation with QM/MM calculations, while Norrby [13] developed accurate transition state force fields that enabled a rapid conformational analysis to be performed to uncover general models for

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enantioselectivity for this reaction. The growth of asymmetric catalytic reactions is intertwined with the development of modern electronic structure and parametric methods [14].

3 Privileged Ligands: Phosphoramidites Metal-ligand complexes promote many transformations, and in enantiopure, chiral form, they can be used to effect asymmetric catalysis. While a given transition metal may catalyse several reaction types with broad substrate scope and efficiency, no single chiral ligand results in uniformly high levels of enantioselectivity. However, among the plethora of chiral ligands, a few stand out because of their versatility. A common feature of these so-called privileged ligands that function across a wide variety of chemical transformations is the presence of C2 symmetry elements [15]. These ligands are able to induce good to excellent levels of enantioselectivity in various reactions, even though the ligated metal and the associated reaction mechanisms may differ drastically. Members of this privileged ligand class include BINOL (1,10 -bi-2-naphthol) [6] and BINAP (2,20 -bis(diphenylphosphino)-1,10 -binaphthyl) [16], used in Diels-Alder reactions, hydrogenation, Heck reactions, aldol reactions, etc.; Brintzinger’s ligand [17] used in alkene and imine reduction, Ziegler-Natta polymerization, etc.; TADDOL [18] used in Diels-Alder reactions, aldehyde alkylation, iodolactonization, etc.; and bisoxazolines [19] used in DielsAlder reactions, Mukaiyama aldol, conjugate addition, cyclopropanation, etc. (Fig. 3). Salen, tartrate and cinchona alkaloids are also included in this original group. This array of ligands emphasizes that the source of chirality may come from stereogenic centres or from axial chirality due to restricted rotation about a biaryl bond. DuPhos phospholanes [20], Solvias Josiphos families [21], the Reetz [22] and Trost ligands [23] and ChiralQuest phosphines [24] (Fig. 3) have all been successfully applied in industrially useful reactions such as hydrogenations, aldol reactions and asymmetric allylic alkylations. These chiral ligands are notable for their synthetic accessibility and modular structures. Library development of structurally related ligands is made possible, gaining the attention of computational and synthetic chemists focussed on ligand design. As we shall also discuss, the modularity of these ligands is also instrumental when exploring statistical relationships between catalyst/ ligand structure and enantioselectivity. A fixed ‘scaffold’ ensures that structural variations can be described by their features alone, rather than those of the entire catalyst structure. Furthermore, the simplifying assumption that mechanistic steps remain consistent across different catalyst structures can be made more safely when only minor perturbations are explored in experiment. This is particularly important for expensive QM studies. Privileged structures such as BINOL also feature as a core structural element in many ligands, for example, the Reetz and ChiralQuest ligands. In addition, the BINOL subunit is a common chiral backbone in phosphoramidite ligands used

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Fig. 3 Examples of privileged chiral ligands used in asymmetric catalysis

with a transition metal. These ligands show versatility towards a wide range of transformations such as conjugate addition, 1,2-addition, allylic substitutions, crosscouplings, cycloaddition and hydroborylation/hydrosilylations [25]. Many of these transformations show a large substrate scope with very good to excellent ee, for instance, an asymmetric hydrogenation where known substrate scope includes αand β-amino acids, dicarboxylic acids, esters, cinnamic acids, amines and heterocycles [26]. Many of these types of ligands are commercially available, such as DSM MonoPhos and Feringa’s ligand (Fig. 4). Structural features common to many privileged ligands include relatively rigid structures, C2-symmetry elements and heteroatoms able to bind strongly with the transition metals. However, such criteria are neither necessary nor sufficient to create a selective chiral catalyst. It is possible to synthesize chiral ligands with all of these features which do not perform well and vice versa. The search for a chiral ligand that performs well for a given transformation of interest remains extremely challenging and remains heavily reliant on trial-and-error experimentation. In our own search for new ligands [27–29], phosphoramidite scaffolds have proven especially attractive

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Coordinate to metals: Cu, Rh, Ir, Au, Reactions: Hydrogenation, Cycloadditions, Allylic substitutions, etc.

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Ph O P O

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Fig. 4 Phosphoramidite ligands: general structure and commercially available chiral phosphoramidites

due to their modular structure. This ensures that structures, and therefore reactivity and selectivity, are tunable parameters. In addition, the BINOL backbone is commercially available in both R and S forms, so that the choice of enantiomers is not limited like in ligands derived from some chiral pool structures such as ligands derived from carbohydrates [30].

4 Approaches for Ligand Design in Asymmetric Catalysis At the time of writing, no general all-purpose catalyst exists: furthermore, the development of a chiral catalyst or ligand capable of catalysing all chemical transformations in high selectivity is implausible. As new target molecules constantly emerge, the need to discover new methods and to develop new chiral ligands naturally follows. However, the selection or design of the most appropriate chiral ligand and catalyst remains a challenge without a straightforward solution. When a new asymmetric transformation is being developed, the most widely practised approach to date has been to identify a group of selected ligands and catalysts and screen them for desirable catalytic properties for the reaction. This traditional Edisonian approach to ligand development is inherently characterized by trial-and-error discovery more so than systematic design. More modern approaches to catalyst or ligand discovery attempt to minimize the reliance on randomness by more effective use of knowledge: this may come from mechanistic studies and/or from the emerging interrelationships between catalyst structure and selectivity. Experimental and computational methods are employed in both aspects. We will avoid describing these modern approaches to catalyst discovery as rational, since, by implication, previous studies were not. To do so overlooks the expertise and chemical logic of scientists involved in chiral catalyst discovery to date. Instead, we point to the possibility of efficiency gains from minimizing reliance on randomness in terms of time, effort and material resources. In this chapter, we now discuss the evolution of ligand design from serendipitous discovery and high-throughput screening towards mechanistically driven ligand discovery and quantitative model-led ligand discovery.

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Serendipitous Discovery and High-Throughput Screening (HTS)

Enabled by modern technology, such as automated robotic systems, it is possible to accelerate the process of trial-and-error experimentation to generate results rapidly. For example, Macmillan has used high-throughput screening and GC-MS as a means to analyse product formation, leading to a discovery of a novel Ir-catalysed α-amino C-H photoredox arylation, terming the procedure ‘accelerated serendipity’ (Fig. 5) [31]. While this transformation was racemic, the growing availability of high-throughput screening (HTS) platforms has meant that this paradigm has begun to impact asymmetric catalysis. Examples of rapid screening platforms in asymmetric catalysis have been applied by de Vries and Lefort to transition metal-catalysed asymmetric hydrogenations. Here, the in situ synthesis of 32 BINOL-derived phosphoramidite ligands and 64 hydrogenation reactions were carried out by Premex 96-multireactor within 2 days (Fig. 6a) [32]. Feringa, de Vries and Minnaard also applied this approach to rhodium-catalysed asymmetric addition of arylboronic acids by synthesizing 20 chiral phosphoramidite ligands in situ and used them in the subsequent reaction giving up to 87% ee of the desired product (Fig. 6b) [33]. The modular nature of phosphoramidite ligands makes such an approach feasible, since a library of candidate ligands can be synthesized with relative ease. The ability to screen multiple reactions at a time is a promising approach; however, the reliable analysis of reaction progress, product formation and selectivity is equally as important. The traditional approach of experimentally quantifying enantioselectivity using chiral high-performance liquid chromatography (HPLC) becomes the bottleneck. Recent advances in ee determination have aimed to make HTS of chiral catalysts more attractive. With supercritical fluid chromatography, Regalado and Welsh (at Merck) have shown that the ee of 50 different scalemic mixtures can be analysed in less than a minute each on customized short chiral columns (1–2 cm) [34]. Others have developed, to a certain extent, more specialized (in a sense, less widely used) systems. Anslyn and co-workers have developed a circular dichroism-based host-guest system to determine the ee of vicinal diols, α-hydroxyacids, vicinal diamines, cyclohexanones, amines, α-chiral aldehydes, carboxylates, amino acids and secondary alcohols within 7% or lower average error (Fig. 7a) [35]. For chiral amines and amino acids, a few other methods have been developed to analyse their ee values [36] such as the use of nuclear magnetic resonance (NMR) and fluorescence detection of chiral boronate and amine assembly by Anzenbacher (Fig. 7b) [37], 19F NMR probing of a chiral palladium pincer complex with chiral amines developed by Zhao and Swager [38] (Fig. 7c) while a DNA biosensor to detect the chiral amino acid derivative tyrosinamide developed by Heemstra (Fig. 7d) [39]. Despite the early promise of HTS approaches for chiral catalyst discovery, some drawbacks remain. Firstly, specialized tools or chemical systems are often required for screening and analysis. Secondly, there is no guarantee that screening will yield

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a) Rh(COD)2BF4, H2 (6 bar), DCM

O Ph

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R = H, alkyls, acyls, aryls, heteroaryls, etc.

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Rh(acac)(C2H4)2 20 chiral ligands

+ Acetone reflux, overnight in 96 well plates

Cl upto 87% ee

Fig. 6 Asymmetric reaction optimization by parallel screening of chiral ligand libraries: (a) de Vries’s rhodium-catalyzed asymmetric hydrogenation, (b) Minnaard’s rhodium-catalyzed asymmetric addition

any promising results – it is impossible to find the needle if we are looking in the wrong haystack! Also, in the absence of a statistical or mechanistically informed approach, these approaches do not offer a systematic way forwards in the context of reaction development. HTS will, however, generate lots of data – both positive and negative (i.e. successful and unsuccessful reactions). In conjunction with approaches to interpret this data, this can be highly valuable (Sect. 5).

4.2

Mechanistically Driven Ligand Discovery

Mechanistic information provides a ‘bottom-up’ approach to chiral ligand design. This approach is based on drawing logical assumptions from previous and ongoing mechanistic study (which may be experiment, computational or both), particularly how enantioselectivity is induced by the catalyst. For small-molecule catalysts, modern computational tools are firmly embedded in the first line of attack in catalyst design [40]. However, this is not (yet) a panacea. Computational studies of asymmetric catalysis face similar challenges as other areas of study, relating to finding the plausible reaction pathway(s) from multiple possibilities, accurately describing the effects of non-covalent interactions (e.g. dispersion, hydrogen bonding, etc.) and solvation, sampling the conformations of flexible species, describing the vibrational and entropic contributions to the Gibbs energies/chemical potentials of reacting species, the effects of numerical approximations in standard computational chemistry programs and the breakdown of statistical rate theories [41]. As discussed later, these challenges are perhaps more acute given the relatively small energetic differences of a few kcal/mol underlying much of asymmetric catalysis. In conformationally flexible catalysts, the energy changes due to the change in conformation alone could overwhelm the actual energy difference underlying the

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L-DNA Scalemic Tyrosinamide

A = Fluorescein B = Hexachlorofluorescein

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Fig. 7 Examples of ee detection techniques: (a) Anslyn’s circular dichroism-based host-guest system, (b) Anzenbacher’s fluorescence detection system, (c) Zhao and Swager’s 19F NMR probe of Pd pincer complexes, (d) Heemstra’s DNA biosensor

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stereoselectivity [42]. This emphasizes the necessity in thorough and comprehensive conformational sampling of the transition structures. Nonetheless, collaborative computational and experimental approaches have shown promise. A plethora of successful mechanistic studies prior to 2014 have been highlighted by Wu, showing examples where experimental findings were explained by modelling, models substantiated or eliminated by experimental results, and cases which led to the development of more powerful solutions to reactivity or selectivity problems [43].

4.2.1

QM-Based Methods

Quantum mechanical calculations have proven to be very useful in the elucidation of reaction mechanisms and rationalizing experimental findings. Qualitative models often provide satisfying rationalizations of experimental results but lack the ability to make quantitative predictions. Modelling (and hopefully predicting) enantioselectivity requires quantitative evaluation of the stabilities of competing diastereomeric transition states. Enantiomeric enrichment arises from the difference in the rate of irreversible stereodetermining steps of competing pathways involving diastereomeric transition state structures (ΔΔG{) in both the regime from a common reactant and cases where reactants rapidly interchange in accordance with the CurtinHammett principle (Fig. 8). By definition, asymmetric catalysis requires kinetic control, since enantiomeric products are equally stable. Experimentally reported measurements of enantioselectivity; % ee and % er can be expressed in terms of ΔΔG{ as follows:

ΔΔG‡

ΔΔG‡ ΔGA‡ ΔGA‡

ΔGB‡

ΔGB‡

ΔG0AB

RA

RB

R

P(A)

P(A)

k1

R

k2

P(B)

a) Kinetic control

P(A)

P(B)

P(A)

k1

RA

RB

k2

P(B)

b) Curtin-Hammett principle

P(B)

Fig. 8 Schematic energy profile (LHS) from a common prochiral reactant and (RHS) illustrating a Curtin-Hammett regime with rapidly converting diastereomeric intermediates prior to the stereodetermining step. In each case, labels A and B are indicative of diastereomeric complexes formed between a chiral catalyst and either enantiomer of reactants and products

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Table 1 Percentage and ratio of enantiomers, % ee and its equivalence ΔΔG{ at 298 K R (%) 0.05 0.5 5 10 25 50 75 90 95 99.5 99.95

S (%) 99.95 99.5 95 90 75 50 25 10 5 0.5 0.05

er (of R) 0.0005 0.005 0.05 0.11 0.33 1.00 3.00 9.00 19.0 199 1999

ee (of R) (%) 99.9 99.0 90.0 80.0 50.0 0.0 50.0 80.0 90.0 99.0 99.9

|ΔΔG{| (kJ/mol) 18.83 13.11 7.30 5.44 2.72 0.00 2.72 5.44 7.30 13.11 18.83

|ΔΔG{| (kcal/mol) 4.50 3.13 1.74 1.30 0.65 0.00 0.65 1.30 1.74 3.13 4.50

|ΔΔG{| ¼ absolute value of ΔΔG{

ΔΔG{ðR=SÞ ¼ RT ln ðR=SÞ ¼ RT ln

ð100 þ %eeR Þ ð100  %eeR Þ

ð2Þ

Using these equations, % ee and its equivalence in % er and ΔΔG{ at 298 K are tabulated in Table 1. Due to the logarithmic relationship between enantioselectivity and ΔΔG{, prediction errors in competing energies are more strongly emphasized at low selectivity. For example, allowing for a computational error within 1 kcal/mol, an unselective (i.e. racemic) reaction at 273 K is predicted to proceed within a range  73% ee, while for an inherently more selective reaction giving 99% ee, the same error bounds are with 94–99.8% ee (Fig. 9). While singular predictions of enantioselectivity values are challenging, the successful ranking of a series of structures and the enrichment of an initial dataset of catalyst have been accomplished using Q2MM calculations [44]. The statistical performance of QM methods for enantioselectivity predictions has not been widely studied, in part due to the significant computational demands required. DFT accuracy in organocatalytic epoxidations has been shown to yield modest correlation coefficients (R2 ¼ 0.65) across a set of nearly 50 reactions, with a mean unsigned error of 0.65 kcal/mol at the B3LYP/6-31G(d) level of theory, which performed better than M062X or the use of a larger basis set [45]. Further study is required in this area. Despite these challenges, computational mechanistic studies of asymmetric catalytic reactions have resulted in experimentally validated improvement of enantioselectivity. In the context of rhodium-catalysed transformations with chiral phosphoramidites, Paton, Anderson and co-workers used DFT calculations (wB97XD) to explore the mechanism and selectivity of enantio- and diastereoselective cycloisomerization [46]. Three iterations of the starting ligand were informed by computational analysis, showing the relevance of a Rh-arene interaction for chiral recognition in the transition states, and an unexpected pathway

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Fig. 9 Enantiomeric excess at 298 K: error bounds in ee prediction allowing for different levels of accuracy in the estimation of ΔΔG{ (kcal/mol). (Enantiomeric excess error of ee  0 kcal/mol in white, ee  0.25 kcal/mol in blue, ee  0.5 kcal/mol in green and ee  1.0 kcal/mol in red)

in which oxidative cyclization occurs prior to activation of a vinylcyclopropane. The improved ligand gives 99.9% ee (Fig. 10a). Liu and Brummond optimized enantioselectivity in a dynamic kinetic asymmetric Pauson-Khand reaction of allenyl acetates based on computations of competing transition states. This analysis (M06// B3LYP) revealed an unexpected ‘alkene unbound’ pathway for the predicted best phosphoramidite ligand, which gave an er of 86:14 in experiment after only four experimental variants (Fig. 10b) [47]. More recent efforts have focussed on automation of the computational workflow to obtain competing transition structures. Wheeler reported an automated reaction optimizer for new catalysts (AARON) based on DFT screening which was applied to enantioselective rhodium-catalysed asymmetric hydrogenation of enamines (Fig. 10c) [48]. This tool was developed to enable the automated construction, calculation and analysis of transition structures without the need for manual manipulation.

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Fig. 10 Theory-led chiral ligand optimization in rhodium catalysis: (a) asymmetric ynamide cycloisomerization and (b) dynamic kinetic asymmetric Pauson-Khand reaction of allenyl acetates; (c) automated prediction of chiral ligand effects in hydrogenation

4.2.2

Molecular Mechanics Approaches

The computational demands imposed by large and flexible systems may be too excessive to apply QM calculations. As mentioned above, combined QM/MM approaches have played a significant role in the development of computational models for asymmetric catalysis [49]. Even so, cheaper methods may be required, particularly in the context of screening several catalysts. While one typically expects to suffer a loss in accuracy when using less costly approaches such as molecular mechanics, some of the best predictive results to date have been obtained at this level of theory. This is, in part, attributable to the fact that prior to the advent of dispersioncorrected DFT methods, force fields already described these interactions through parametrized interatomic potentials. Additionally, the ability to parametrize a reaction-specific force field allows one to fit to a high-level reference PES. The transition state-specific force field approach developed by Norrby and Wiest has been applied and tested for enantioselectivity prediction. Force field parameterization uses QM data, thus the term quantum-guided molecular mechanics (Q2MM) [44]. The method has been successfully applied to various transition metal-catalysed transformations such as rhodium-catalysed enamide hydrogenations to predict the enantioselectivity of new chiral ligands and reactants (Fig. 11) [50]. In this, and other examples, a strong correlation is obtained between predicted and experimental levels of enantioselectivity for different substrate and ligand structures. The computational cost of Low Mode/Monte Carlo conformational sampling of the transition structures

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Chiral ligands: R PPh2 PPh2 R

R’

R’’ P

P

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OR3 O

Chiral ligands

R2

O

Rh catalyst, H2 R1

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Fig. 11 Quantum-guided molecular mechanics (Q2MM) calculation of ee in rhodium-catalysed hydrogenation using a transition state force field

is much reduced compared to QM level of theory. Furthermore, inversion of the imaginary normal mode before reconstructing the full Hessian means that each TS is represented as a minimum on the PES, making structure optimization less challenging than a conventional saddle point optimization. More recent developments of this methodology have seen the workflow being automated such that reaction queries can be submitted as 2D structures via a web interface, known as the CatVS program [51].

5 Quantitative Structure-Selectivity Relationships (QSSRs) Quantitative structure-activity relationships (QSARs) have been used by biologists and medicinal chemists for more than six decades [52]. During ligand screening, more often than not, only a portion of the data collected offers insightful information,

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while the rest is not obvious to interpret. QSAR, however, exploits all data collected (both positive and negative results) with the aim of predicting the behaviour of compounds of interest. Perhaps the simplest and most easily interpretable form is the linear free energy relationship, which has been used by organic chemists since the 1930s following the pioneering work from Hammett [53]. In the context of asymmetric catalysis and enantioselectivity, the quantitative structure-selectivity relationship (QSSR) asserts that there is a fundamental relationship between selectivity and a quantitative description of the reactants, catalyst and other reaction conditions. Although the physical basis underlying such a relationship typically results from common mechanistic features shared across the different reactions, model creation in itself does not require a mechanistic hypothesis to be formulated. QSSR and QSAR share a common approach, with the exception that the endpoints differ (i.e. activity and selectivity).

5.1

QSAR Best Practices

The experimental design of a QSAR study requires careful consideration at each stage: data collection, parameter selection, model construction, validation and interpretation. A substantial body of literature exists to steer chemists clear of common pitfalls in this process. Tropsha has summarized a rigorous protocol for QSAR practices. Dearden, Cronin and Kaiser published a critical review on QSAR model construction and helpfully include a checklist of errors to be aware of supported by case studies [54]. Sigman has recently published a review on multivariate linear regression (MLR) for reaction development [55]. Denmark and co-workers have recently published a comprehensive review featuring multiple types of QSSR models used in enantioselective catalysis, particularly the molecular interaction field 3D-QSSR [56]. Detailed terminologies, definitions and practices regarding QSAR models and case studies can be found in Organization for Economic Co-operation and Development (OECD) guidelines, underlining the importance of the approach far outside of chemistry [57]. Distilled from the literature, we now summarize the most widely accepted QSAR practice, as applied to the development of catalytic reactions, in a flow chart displayed below (Fig. 12). This process can be divided into four stages starting with data collection and processing, model building, model validation (which is intertwined with model building in a feedback loop) and application. In each step on the flow chart below, requirements and generally accepted criteria are summarized in a form of checklist boxes. For example, in the first step of data processing, it is crucial that all the data are homogeneous, i.e. with identical units and collected in identical manner to avoid any random artefacts incurred during data collection. In addition, repeats are important to show that the data is reproducible and to minimize random error. Moving forwards to model construction, data (dependent parameter, yi) is split into training set (used in model construction) and testing set (to validate the model). Chemical descriptors for the training data are collected, and most relevant are selected during

Fig. 12 Flow chart and checklist for QSSR model construction and application

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model construction. The models are then validated prior to application. If they fail validation, new descriptors need to be collected and/or new forms of models need to be generated. Only models that pass external validation can be used to predict or have any physical meaning attached to them. Details for each step are discussed below. Another type of QSSR that has a distinct methodology in generating the descriptors is the molecular interaction field (MIF)-based 3D-QSSR pioneered by Lipkowitz [58] and Kozlowski [59]. MIF describes the whole 3D structure of the molecules and therefore is termed a global descriptor. It consists of interaction energies between a selected chemical probe placed on each point on a threedimensional grid over the 3D structures of the molecules, creating a large amount of data at a practical computational cost. These data can be strongly correlated so PLS is a preferred method to generate a 3D-QSSR model. This technique circumvents one of the difficult questions in QSSR model generation about which local descriptors to collect, since the whole of the information on the 3D structures are recorded within the MIF. However, the conformations and the alignments of the molecular structures will strongly affect the values of the MIF so they need to be handled with careful considerations. A commonly known type of MIF-based QSSR is the comparative molecular field analysis method or CoMFA. MIF-based QSSRs have been adopted by many in both academic groups [60–62] and industry [63, 64]

5.2

Collecting Molecular Descriptors

A crucial part of QSSR model building is collecting or generating the physiochemical descriptors (independent parameters, xi, which describe the chiral ligands/catalyst/substrates/additive structures). These parameters can take the form of empirical (i.e. macroscopic) parameters from experiment, such as Hammett constants, or computed (i.e. atomistic) parameters. Data curation is required for treatment of empirical data in similar manner to the dependent parameters (Yi). Numerous sources of physiochemical descriptors are available in the literature such as empirical and computed steric parameters: A parameters [65], B parameters [66], Charton parameters [67], Taft parameters [68], Verloop’s Sterimol parameters [69], their variants for substituted cyclopentadienyl rings [70] and conformationally flexible chains [71], Bo’s three-dimensional descriptors [72], electronic parameters, Hammett parameters, charges, orbital energies, and other parameters such as spectroscopic parameters (IR frequencies, NMR shielding tensors, etc.). There are also descriptors developed especially for certain types of compounds, e.g. for P-donor ligands such as Tolman angles [73–75] and continuous chirality descriptors developed by Denmark for chiral compounds [76]. Further treatment of these data by standardization is sometimes practised (Eq. 3). This transforms the raw data to dimensionless data with mean ¼ 0 and standard deviation (SD) ¼ 1.

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x¼ where x ¼ 1n

n P

xi  x s

ð3Þ

xi (sample mean), n ¼ number of data points,

i¼1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n 1 X s¼ ðx  xÞ2 ðsample standard deviation of xÞ: n  1 i¼1 i It is recommended that any co-linearity among parameters should be avoided or used with caution in multivariate linear regression (MLR). There is no rigid criterion on correlation limits, but r2 > 0.8 is highly discouraged [54].

5.3

Model Construction

Two of the principal questions in model construction relate to what type of regression to use and which descriptors to include in the final model. Some studies suggest that choices of chemical descriptors affect the prediction performance of QSAR models to greater extent than choices of model optimization techniques [52]. Both of the questions will be discussed in detail below.

5.3.1

Types of Regression

Regression is a study of relationships. There are many types of regression used in QSAR studies. In here we focus on types of regressions which have been applied to asymmetric catalysis. Merits and drawbacks associated with each method are listed below. 1. Ordinary least squares regression (OLS) ✓most transparent ✓ easily reproducible ✗not recommended for confounded parameters (highly correlated parameters) This type of regression has been most commonly used in asymmetric catalysis. The idea behind least squares regression is the minimization of the quantity that relates to the differences between the observed data ðyi Þ and the predicted data ð byi Þ such as the sum of squares of vertical deviations Σni¼1 ½yi  byi 2 ).

Models with only one independent parameter are termed univariate linear (or non-linear) regressions. A model that contains multiple independent parameters is called a multiple least squares regression. The linear form is termed multivariate linear regression (MLR).

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2. Partial least squares regression (PLS) ✓deals with larger data with many variables ✗ can be hard to interpret model and identify outliers PLS finds the multidimensional direction in the space of the parameters (i.e. similar to principal component analysis, PCA, it uses linear combinations of these parameters) that has the maximum covariance with the observations. PLS regression is particularly suited when the number of descriptors outnumbers the observations and when there is collinearity between these descriptors. This is a common scenario encountered in a catalyst optimization project, due to the difficulty of synthesizing many different structures, as compared to the ease with which parameters can be generated! 3. Other types of model construction methods Machine learning algorithms such as neural networks, k-nearest neighbours, random forest, etc. can be used to generate QSSR models, typically when larger datasets are available. The availability of datasets containing at least several hundred reactions has generally been limited in the development of asymmetric catalytic reactions. As datasets begin to emerge on this scale, more advanced statistical algorithms will find use in this area.

5.3.2

Selecting Parameters

There are many selection methods used in QSAR such as genetic algorithms, stepwise regressions, simulated annealing, etc. [77–79]. In the context of QSSR applied to asymmetric catalysis, PCA and PLS are most often used in molecular interaction field-based 3D-QSSR [56]. In MLR, automated parameter selection algorithms can be applied to retain only those that contribute with statistical significance, including via open access software such as R [80]. One such approach is forward selection, which starts with an empty initial model. Parameters are included one at a time to improve the model based on set criteria to determine model quality such as the adjusted coefficient of determination (R2adj), the Akaike information criterion (AIC) or significance ( p-value) until the model cannot be improved further. In contrast, backward elimination starts from a full model with all parameters included and eliminates one parameter at a time. The objective in both approaches is to remove extraneous parameters that do not contribute significantly to the predictive power of a final model.

5.3.3

Evaluation of Fit for MLR

MLR has been most often used in asymmetric catalysis. The following guidelines and criteria are collected from the literature regarding MLR [54, 57, 81, 82]. Notably, universal consensus has yet to be agreed. Nevertheless, standard practices and criteria do emerge from recent literature.

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The most common statistical treatment to measure goodness of fit of a MLR is the correlation coefficient, R2 (Eq. 4). If R2 > 0.5, the variance in the experimental data explained by the model is greater than unexplained variance. An acceptable value is at the discretion of the user. A value of R2 ¼ 1 indicates that the regression has a perfect fit, while the threshold of acceptable values varies from 0.7 to 0.9 [54, 57]. n P

R2 ¼ 1:0 

i¼1 n P

ðyi  byi Þ2 ð yi  yÞ 2

ð4Þ

i¼1

where yi , byi , y¼measured, predicted and averaged dependent variable and n ¼ number of data points. Over-fitting is a phenomenon where too many parameters are used, leading to models with better fit but reduced predictive ability. This arises because the model accounts for random errors specific to the training set [83]. The adjusted correlation coefficient R2adj (Eq. 5) penalizes the use of additional parameters. n P

R2adj

¼ 1:0 

ðyi  byi Þ2 =ðn  k  1Þ

i¼1

n P

2

ð y i  y Þ =ð n  1Þ

ð5Þ

i¼1

where yi , byi , y ¼ measured, predicted and averaged dependent variable, n ¼ number of data points, and k ¼ number of independent variables in the model. Another ‘rule of thumb’ is that the amount of data points, n, must be several times larger than the number of parameters, k: for example, n > 4k or n > 3k have been suggested [81, 84].

5.3.4

Model Validation

Evaluation of significance is needed in any statistic model in order to estimate how certain one can be between the true correlation and random occurrences. Analysis of variance (ANOVA), particularly the T-test and the F-test, is also commonly used. The null hypothesis is that the slope (coefficients) of each of the parameters within the model is equal to zero. So if the statistic is larger than the set criterion, i.e. for a T-test at threshold (α) of 0.05 at specified degree of freedom, we can reject the null hypothesis and therefore say that the parameters or the model shows statistically significant correlation with the confidence level of 95% [85].

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5.3.5

177

Internal Validation

The next step is to validate the models. This can be divided into internal and external validation. Internal validation is considered necessary, but not sufficient, for the demonstration of a suitable model [82]. External validation must also be carried out prior to application of the model. A variety of internal validation methods are available [81]. Leave-one-out (LOOCV) or leave-many-out cross-validation (LMOCV) are among the most used in asymmetric catalysis QSSR. In LMOCV or LOOCV, a number (M) or one (O) data point is left out as a test set and the rest of the data is used as a training set. The measure of fit of the resultant models, the predictive squared correlation coefficient, q2, is calculated (Eq. 6). Because there are many possible ways to split the data when M > 1, fixed iterations of LMOCV are commonly used within an affordable computational time. As a consequence, not all possible combinations of data splitting are evaluated. This means the q2 from non-exhaustive LMOCV may not be the same for different observers depending on how the data is split. This is not a problem for LOOCV. Tropsha’s recommended value for LOOCV q2 is >0.6 [81]. There are many other methods for QSSR validation such as bootstrapping [86] and y-randomization [87]. n P

q ¼ 1:0  2

i¼1 n P

ðyi  byi Þ2 ðyi  ytr Þ2

ð6Þ

i¼1

where yi , byi , ytr ¼ measured, predicted and averaged dependent variable and n ¼ number of data points in the training set.

5.3.6

External Validation

A set of data that has not been used to train the model is called an external testing set. It is highly recommended that the external testing set must be representative of the whole range of both dependent and independent parameters. The definition of q2ext is similar to Eq. 6. The term y from the testing data or, alternatively, the training set has been used; however, the latter has been shown to give too optimistic values in some case studies [88]. Tropsha published multiple recommended criteria for predictive power of a model based on external testing data such as R2ext > 0:6 and q2ext > 0.5 [81].

5.3.7

Outliers

Outliers may reflect experimental error or model failure. In the latter scenario, this may indicate the involvement of a different process, such as competing side reactions or a change in mechanism. This is why it is crucial to make sure data is

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reproducible. Ways to quantify boundaries to identify outliers by statisticians are discussed elsewhere [89]. In QSSR studies, Lipnick recommended that outliers lie 3 or more standard deviations away from the mean of residual [90]. Sigman has calculated the degree of deviation to quantify the error of extrapolation data. A tolerance of 10–20% error was accepted for inliers [91].

5.3.8

Applicability Domain (AD)

Like all models, regressions capture parts of reality. Therefore, all models are inherently incorrect but are likely to be useful within a certain limit. Models are highly dependent upon the inputs. They will break down if we try to predict unseen data that drastically differ from the input data. This is a common problem around extrapolation (prediction that falls outside the domain covered by the training data). ‘Domain of applicability’ or ‘applicability domain’ (AD) is a non-rigid limit between extrapolation and interpolation (prediction that falls within the domain covered by the training data). In practice, the line between performance of chemicals within AD and outside is not a sharp one. The change in predictability of a model is a gradual rather than a sudden drop across AD. AD therefore acts as a guide which needs to be substantiated by expert judgement. AD helps define a quantitation limit (where predictions are not quantitative anymore) or define the domain of linearity of the model (outside this, it is not necessarily linear anymore). Defining an AD with QSSR should help the end user of the model balance the validity of a predicted value. Some argue that defining an AD is in fact inappropriate because the utilization of the model outside the AD isn’t outright invalid, only less reliable. Furthermore, predictions of compounds within a model AD should still be treated with caution in certain cases [92]. AD therefore helps the end user to be aware of the approximate limits of a model, between extrapolation and interpolation, and to make choices accordingly. One definition of AD is ‘The applicability domain of a (Q)SAR model is the response and chemical structure space in which the model makes predictions with a given reliability’ [57]. One way to define an AD is to give it a descriptive definition based on the structures and the physiochemical properties of the training dataset and the observed properties (dependent variables). This serves the purpose above without being too rigid about the exact mathematical formula of the domain. More quantitative assessments of AD are described elsewhere [57].

5.3.9

When a Model Disappoints. . .

Even when compounds appear to be within the AD, there is no guarantee that the prediction of such compounds will be reliable. In QSAR, an activity landscape might contain ‘cliffs’ where a sudden change in activity is observed with subtle structural changes. In the presence of these activity cliffs, even interpolation can fail. An equivalence of the notorious activity cliffs seen in QSAR and QSSR is perhaps the

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change in mechanistic pathways which can be informative and potentially provide insight to alternative reaction pathways.

5.3.10

Model Utilization

Utilization of regression is categorized into two types: prediction and physical interpretation [93]. Often in QSAR, one trades a meaningful model for a highly predictive one. However, in QSSR for asymmetric catalysis, in some cases, applications of regression can lie in the sweet spot where the models have been illustrated to be both predictive and not too complicated which allows for meaningful interpretations [94]. Chemists have used QSSR to model, predict and optimize levels of enantioselectivity since the turn of the twenty-first century [58, 59, 62, 85, 95, 96]. Attention to this approach continues to grow [97–101]. We select recent examples at the frontier of QS(A/S)R applied to asymmetric catalysis to discuss here. Examples of work on MIF-based 3D-QSSR have been comprehensively discussed in a recent review by Denmark and co-workers and are not included here [56].

5.4

Predicting Enantioselectivity

Sigman has pioneered modern applications of QSSR to asymmetric transformations, publishing numerous examples of the use of regression-assisted reaction optimization and mechanistic elucidation [102–104]. Recently, in collaboration with Miller, the Sigman laboratory has carried out multivariate modelling for the atroposelective bromination of arylquinazolinones involving a tetrapeptide catalyst [105]. Predicted product enantioselectivity was expressed in terms of calculated parameters: NBO charges, IR stretches, a multidimensional steric Sterimol (L ) parameter and a crystallographically derived parameter; main chain angles (Fig. 13). The QSSR models derived from different conformations of peptides suggest that the multiple conformers of the peptide β-turn contribute to the stereodetermining transition structures. The utility of this approach is evident since the conformational complexity of the catalyst structure precludes the calculation of competing transition structures for all of the structural variants studied. Denmark used a machine learning algorithm – a deep feedforward neural network – to construct quantitative models to predict enantioselectivity of thiol additions catalysed by chiral phosphoric acids (Fig. 14) [106]. His work is an exemplar of a complete chiral ligand design workflow, consisting of (1) defining a synthetically accessible virtual library of the chiral ligands, (2) defining a universal training set (UTS) as a recommended starting point to synthesize and test the ligands, (3) generating descriptors and models and (4) validating the models using internal and external validations.

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NBS, Peptide 3, N

N

OH

PhMe/CHCl3, rt, 1 hr then TMSCHN2, MeOH

O

N

Br

Br

N

O Br

R1R N Me2N O

2

HN O HN

O

NH O O

R3 R4

Peptide 3

type II’ β-hairpin

type I’ pre-helical β-turn

Fig. 13 QSSR model for atroposelective bromination of arylquinazolinones using tetrapeptide catalyst. Reprinted with permission from Crawford JM, Stone EA, Metrano AJ, et al. (2018) J Am Chem Soc 140:868–871. Copyright 2018 American Chemical Society

In this work, they collected and used the chemical structures of the chiral ligands and the substrates, along with the products; hence, the combination of these data allow for the application of machine learning to the problem with moderate number of 24 chiral ligands. This work showed that, even when the training data with lower selectivities are used (capped at substrate-ligand combination that gave 30 orbitals in stochastic CASSCF, including all Goutermann orbitals [135, 136]. Especially for the d-shell, it was essential to include a double shell of orbitals [137].

3.2.2

Coupled Cluster

The coupled cluster approach is an alternative and efficient method to reach full CI, and unlike truncated CI, it is size consistent. Often it is assumed that CCSD(T) is the golden standard, although it is in many cases not yet fully accurate. This is in particular true for paramagnetic transition-metal complexes, where many choices have to be made regarding the choice of orbitals and how to solve the CC equations (vide infra). Approximations can be made, such as Neese’s domain-based local pair natural orbitals (DLPNO) [138, 139] or local CC, which will be described in more detail in Sect. 3.4, or Kats/Manby’s distinguishable cluster approximation [140] which with a computational cost similar to CCSD often provides results of CCSD(T) quality, and hence can be a very attractive method for the future.

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3.2.3

203

Combined Efforts

Even though the double shell was needed for getting consistent results, in a number of systems, it was found that 3s3p correlation was not satisfactorily described by CASPT2 [141]. In order to remedy this, Pierloot and Harvey [133] therefore followed the QM/QM Quild [142] approach whereby specific energies are subtracted and added; in their case, they used CCSD(T) calculations for only the 3s3p correlation in order to correct the CASPT2 results. A separate approach was performed by the Stuttgart team, where first the orbitals were prepared as best as possible with stochastic CASSCF, which can then be followed by coupled cluster using these orbitals [134].

3.3

Combining Wavefunctions and Density Functionals: MC-PDFT and DMRG-PDFT

A recent new development is the combination of multiconfigurational methods with pair-density functional theory (MC-PDFT), as done by Truhlar and Gagliardi and co-workers [143]. The idea behind MC-PDFT is to use a multiconfigurational selfconsistent field (MC-SCF) wavefunction with correct spin and space symmetry to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. For the remaining part of the total energy, this is combined with a functional which has the on-top pair density as ingredient, in contrast to regular Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. This was followed very recently by including DMRG (DMRG-PDFT) [144].

3.4

Methods Put to the Test: Recent Benchmark Studies

Over the years, many studies [31, 65, 67, 68, 70, 85, 111, 112, 145–159] have been reported on spin-state splittings for a wide variety of transition metals, in different oxidation states, using a variety of DFAs and wavefunction methods. One of the motivations for the ECOSTBio COST Action CM1305 [160] was indeed to gather experts from different areas of chemical research and move forward in the search for consensus on transition-metal chemistry and which computational and experimental methods could be used for getting accurate descriptions of the geometry, electronic structure, and spectroscopy of transition-metal complexes. In the past year, a number of benchmark studies have appeared which focus mainly on the computational aspect, which will be discussed below. Additionally, a recent review by Que and co-workers focuses on the formation of FeV(O), or sometimes FeIV(O), complexes

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[161], which are too reactive to be characterized by X-ray crystallography, but can be characterized by (UV-Vis, EPR, (r)Raman, X-ray absorption) spectroscopy, and sets challenges to be solved by a combination of theory and experiment. Being able to know which theoretical method gives reliable results for which property is therefore of the utmost importance. Radon investigated recently [162] a number of iron complexes, with different coordinating ligands: [Fe(H2O)6]3+, [Fe(en)3]3+, [Fe(tacn)2]2+, [Fe(acac2trien)]+ (en ¼ ethylenediamine, tacn ¼ 1,4,7-triazacyclononane, H2acac2trien ¼ Schiff base obtained from the 1:2 condensation of triethylenetetramine with acetylacetone); he used different QC methods, CCSD(T), CASPT2, NEVPT2, MRCISD+Q, and a number of DFAs, to compare with experimental data (spin-forbidden transition energies, spin-crossover enthalpies) that were corrected for environment effects for a fair comparison. The main conclusions were [162] (1) the confirmation of the validity of canonical CCSD(T), in particular when used with Kohn-Sham orbitals; (2) systematic overstabilization of high-spin states by CASPT2, which can be corrected partially by Pierloot/Harvey’s CASPT2/CC approach [133]; (3) NEVPT2 is performing worse than CASPT2; (4) the MRCISD+Q results depend strongly on the size-consistency correction; and (5) few DFAs were able to give a balanced description of all spin-state energetics (among which OPBE). In fact, among the top performing DFAs are three developed in my group (OPBE, S12g, SSB-D) and (surprisingly) B2PLYP-D3 which was not reliable in other benchmark studies; Kaupp’s local hybrid LH14t-calPBE [163] was also found among the best. DFAs that performed well for the litmus test for spin states ([FeII(amp)2(Cl)2]0 and [FeII(dpa)2]2+) [74] such as LC-wPBE or B97-D3 (used by Radon with the D2 form for dispersion) are also present at the top. Surprisingly, neither the widely used TPSSh [66, 152] nor Truhlar newest family [164] (MN15, MN15L) were found to perform well. Moreover, strangely enough, while Perdew’s MVS functional [165] performed excellently [85] for the litmus test, here it apparently gave disappointing results (results that are similar to those of the S12h hybrid functional, which was known [74] to fail as expected for spin states because of the inclusion of 25% HF exchange). Finally, Radon also commented on the finding by Song and co-workers who claimed that DFAs and CCSD(T) failed dramatically for spin-state splittings for a number of Fe(II) complexes, for which they used Diffusion Monte Carlo (DMC) data as reference (no experimental data were available to compare with). One of the complexes, [FeII(NCH)6]2+, had been used by others, who found, e.g., with CCSD(T) within the complete basis set (CBS) limit that the high-spin (S ¼ 2) was favored over the low-spin (S ¼ 0) state (i.e., ΔEHL ¼ ΔEHS – ΔELS ¼
2 kcal mol
1) [126]. However, the DMC data favored clearly the high-spin (
27.1 kcal mol
1), close to the value of
28.9 kcal mol
1 observed with BHandH (50% HF exchange!); based on these results, the authors claimed that the DFAs and CCSD(T) were wrong and DMC right. Radon argued that most likely the DMC data should not be trusted, based among others on the results for the [Fe(tacn)2]2+ complex with a similar FeIIN6 octahedral coordination. This is a spin-crossover compound, favoring the low spin experimentally at low temperatures (+3.8 kcal mol
1), which was very well reproduced by KS-UCCSD(T) data (+0.6 kcal mol
1), and through an estimate for

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basis set incompleteness (F12) the experimental value of +3.8 kcal mol
1 was confirmed. One should therefore be careful when using DMC data for spin states as reference data, since they may have an intrinsic bias toward high-spin states; it would be interesting to see the effect of the choice of orbitals (Kohn-Shamvs. Hartree-Fock) in DMC calculations. The failure of DMC was corroborated in a recent study with the DLPNO and canonical variants of CCSD(T) by Neese and co-workers [139] that confirmed the much smaller ΔEHL value for [FeII(NCH)6]2+. Early 2019, a second benchmark study was published [166], now focusing mainly (but not exclusively) on coupled cluster (CC) approaches. This largely confirmed what Mikael Johansson had reported at WATOC2017 when he discussed results for the DLPNO variant of CC for a simple Fe(II) complex with bipyridine ligands and argued for using SSB-D [73] as the reference because it gave automatically (and fast) the correct answer. Feldt and Harvey made a systematic study of the effect of all kinds of choices to be made when dealing with spin states and coupled cluster: (1) which orbitals to use, HF or Kohn-Sham; (2) restricted or unrestricted orbitals to be used; (3) solving CC equations in restricted or unrestricted fashion; (4) which level of CC is needed (CCSD, CCSD(T), CCSDT, CCSDT(Q)); and (5) how good are approximated CC such as local CC or DLPNO CC for spin states. They focused on model systems for high-valent metal-oxo species, [FeIV(O) (NH3)5]2+ and [FeIV(O)(He)5]2+ with methane as substrate, to study the oxidation reaction energy profile; they used the helium “ligand” (with shortened Fe-He distance to make sure the spin density remains similar to that observed with the ammonia ligands) for enabling the CCSDT and CCSDT(Q) calculations. From all the different flavors of CC, the UKS-UCCSD(T) was found to perform best when comparing with the CCSDT/CCSDT(Q) data for the helium systems and with DMRG/CASPT2 for the ammonia systems. Not surprisingly, using restricted open-shell Kohn-Sham orbitals and solving the CC equations in spin-restricted fashion (ROKS-RCCSD(T)) was the worst of the four options. Both the local CC and DLPNO-CCSD(T) approaches, although promising new approaches, are not yet robust enough to serve as benchmark references [166]. The barriers for the oxidation reaction in either the triplet state (24.6 kcal mol
1) or the quintet state (13.7 kcal mol
1) confirm the previous study by Shaik and co-workers [167] that showed the smaller barrier when following the quintet state, but also that a spin-switch must be made when starting from the complex in the triplet ground state. Note that Feldt, Harvey, and co-workers argued [166] that the barrier for the 3TS was slightly too low. Interestingly, this slight upshift brings it very close to the barriers as predicted by OPBE (already the best performing DFA in the Shaik study [167]), which showed values [166] of 27.3 and 12.9 kcal mol
1 (arguably, both within 1 kcal mol
1 from the most accurate CC results, and hence a confirmation of its excellent behavior for first-row transition metals). In a follow-up study [168], Feldt and co-workers showed that the local CC and DLPNO-CCSD(T) methods seemed to have systematic biases, DLPNO overstabilizing high-spin states and local CC overestimating triplet states. In a series of papers, Cao and Ryde focused on the mechanism of nitrogenase, carrying out systematic approaches with, e.g., a large number of broken-symmetry

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states [169], the resting state and adding 1–4 electrons (E0-E4) with at least 50 possible positions for the proton for each case [170], and a combination of molecular dynamics, quantum mechanical (QM) cluster, combined QM and molecular mechanics (QM/MM), QM/MM with Poisson-Boltzmann and surface area solvation, QM/MM thermodynamic cycle perturbations, and quantum refinement methods to settle the most probable protonation state of the homocitrate ligand in nitrogenase [171]. They needed this diversified approach because the DFAs used typically in the study on nitrogenase show no consensus on where the protons should go in the E0–E4 states; the primary reason for this is that the DFAs give relative energies that differ by close to 140 kcal mol
1(!!) [172], which is 4–30 times larger than what is observed for other systems. It is caused mainly because the hydrogens can bind as protons to carbides or sulfides or as hydrides to metals. The preference for one or the other seemed to correlate with the amount of HF exchange present in the DFA, but without a clear conclusion which DFA gives the best results for nitrogenase. Some gave better results for the structures, while others gave better results for the H2 dissociation energies. Most importantly, no DFA was able to predict the stability of an E4 structure with two bridging hydride ions as lowest in energy, as spectroscopic experiments indicated [172].

4 Multi-state Reactivity Most reactions in chemistry follow a single potential energy surface, because in general these spin-allowed reactions are much faster than spin-forbidden alternatives [173]. However, sometimes the spin-forbidden reactions are favored with spinswitching accelerating the reactions or allowing them thermodynamically; this is in particular true when the reactions are carried out in the gas phase or when (transition) metals are involved. For instance, for the energy profiles shown in Fig. 6, the favored spin state of the reactant shows a larger barrier for the reaction than the other spin state. Therefore, during the reaction, it may be favorable to switch spin states through, e.g., a MECP or spin-orbit coupling (see Sects. 2.1.1 and 2.1.2), which has a much smaller energetic cost than the reaction barrier; after the barrier has been passed, the reaction can proceed following the same spin state, or with a second spin-state switching, the original spin state can be retrieved. Much depends on the kinetic energy with which the complex goes down after the barrier, the exothermicity of the reaction on both spin states, and the temperature at which the reaction takes place. The reactions of, e.g., MH+ with methane (M ¼ Fe, Co, Ni) in the gas phase are good examples [173, 174] of these spin-forbidden reactions; with FeH+ and CoH+, the barrier of the starting spin state (Fig. 6, in red, quintet for FeH+, quartet for CoH+) shows a large barrier, where in the gas phase there is not enough energy available to surmount it. Switching spin state also does not help because also the lower-spin state (Fig. 6, in blue, triplet for FeH+, doublet for CoH+) still has to cross a barrier that is higher in energy than is available (Fig. 6, left). For NiH+ on the other hand, the spin-state switching from the triplet (red) to singlet (blue) state leads to a

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Fig. 6 Schematic relative energy profiles for different spin states with unproductive (left) and productive (right) reactions in the gas phase reactions of MH+ + CH4 (M ¼ Fe, Co, Ni)

small barrier (Fig. 6, right), for which sufficient energy is available. Through two MECPs the reaction proceeds, and the final product of NiCH3+ + H2 is obtained. This switching between different spin states was called two-state reactivity [2] and shown to be valid for many reactions involving transition metals [175], both in the gas phase, and was also shown to hold for transition-metal enzymes [176].

4.1

Exchange-Enhanced Reactivity

In 2011, Shaik introduced the exchange-enhanced reactivity (EER) principle, a generalization of the two-state or multi-state reactivity, which could explain the spin-state selectivity of oxidation reactions involving high-valent metal-oxo complexes, and could be considered as Hund’s rule of chemical reactivity [177]. Vital for its understanding is the exchange interaction (see Fig. 1); the more exchange there is, the more favored is the electronic state. The oxidation reactions involving metal-oxo species typically occur in two steps: a hydrogen-atom transfer (HAT) takes place in the first step, leaving a substrate radical and a metal-hydroxo (radicaloid) species, which then (re)combine in the rebound step (see Fig. 7). As can be seen in the figure, during the oxidation reaction, in both steps the metal center is enriched with an additional electron, which could bring about more exchange interactions; these could help in lowering the barrier. This is indeed what was observed by Shaik and co-workers [177]. A typical example was reported in 2012 [178], for explaining the axial ligand effect for Mn(V)-complexes; three spin states were observed for the latter (singlet, S ¼ 0, and two triplets, SA ¼ 1 and SB ¼ 1, depending on which orbitals were occupied; see Fig. 8). Of course, the DFA affects the spin-state ordering of the reactants already, but more important is that the

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Fig. 7 Reaction mechanism and typical energy profile for oxidation reaction involving high-valent metal-oxo species

Fig. 8 Exchange-enhanced reactivity explained for MnV(O)-complex [178]

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barrier was lowest for the second triplet (SB ¼ 1). This lowering of the barrier resulted directly from the electron pushing that is taking place in the reaction: for the singlet state and triplet SA, the number of exchange interactions at the metal increases only slightly; however, for triplet SB, the reaction along the triplet state in fact involves a quadruplet at the metal which is coupled anti-ferromagnetically with the substrate radical. This quartet state at the metal has more exchange interactions at the metal and hence is much favored for the TS structure. At the same time, following this spin state also leads to a more favored product, which according to the Bell-Evans-Polanyi principle will lead to a lowering of the barrier [179]. And of course, the possibility of reaching the quartet state at the TS needs that the acceptor orbital is sufficiently low in energy for this to occur; hence, the ligand field plays an important role as well [180]. These effects of spin state and exchange, ligand field, and the reaction energy driving force are therefore not mutually exclusive but probably different interpretations of the same manifestation which shows that spin-state switching can and does occur.

5 Catalysis The balance between reactivity and stability is a subtle one, one cannot have both at the same time. Maximizing reactivity means loss of characterizability, and in contrast enhanced stability reduces reactivity. In order to improve catalysts, or even understand how they work, it is therefore necessary to strike the right balance. This is not always easy, and in particular with highly reactive species, the possibilities to fully characterize them, or even what the actual active species looks like, are sometimes remote. Often, only a precursor is fully characterized, with indirect evidence through, e.g., isotope effects on Raman spectra giving insights on what the active species might look like. Useful evidence is more and more being provided by computational chemistry, which allows to study the different possibilities of what the active species might look like, explore their stability and spectroscopy, and compare these with experimental data. This is not an easy task and often needs a long-term investment in mutual understanding between experimentalists and theoreticians. Doing a blind test, whereby the experimentalist provides ideas of what the complexes might look like, but does not provide spectroscopic characterization, has been shown to provide mutual trust if the theoretician is able to reliably predict what the spectroscopy would look like. Independent validation of the computational methods used on known properties helps in understanding catalysis, where only the unknowns are known.

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C-H Activation

Activation of C–H bonds in substrates efficiently and selectively is one of the main challenges in inorganic chemistry [181]. High-valent metal-oxygen species have been used extensively, following the examples posed by Nature, which often use first-row transition metals such as iron, copper, or manganese [4–9]; understanding their reactivity to understand how the transition-metal enzymes function is one of the goals of biomimetic chemistry. There are two main routes toward this understanding (spectroscopy and theory), which in recent years have gone more and more in parallel and are now often used simultaneously within one project [182–184]. However, the characterization of highly reactive complexes remains sometimes preliminary [185, 186] or open for interpretation [26, 187, 188]; experimental evidence for the existence of (labile) species often comes from isotope labeling, which should/ could lead to shifts in mass spectrometry [185] or Raman spectroscopy [25]. The strength of C–H bonds in substrates [189] determines the potency of different biomimetic complexes, with strong bonds such as those in methane or benzene as the more stronger ones (ca. 105–110 kcal mol
1). For these latter bonds, more reactive complexes are needed; however, at the same time, the more reactive the complex is, the less likely is that it can be fully characterized by X-ray crystallography or spectroscopy. Indeed, the first structurally characterized Fe(IV)-oxo complex [190] is unable to oxidize cyclohexane’s C–H bond (ca. 99 kcal mol
1). Sometimes, the experimentally observed bond dissociation energies (BDEs) need adapting, as shown recently by Klein and co-workers [191].

5.1.1

(c)PCET vs. HAT

In the typical oxidation mechanism (see Fig. 7), it is assumed that the electron and proton move simultaneously (e.g., as a hydrogen in HAT reactions); however, this is not necessarily always the case and/or not for all spin states. An alternative pathway could be proton-coupled electron transfer (PCET), which comes in many guises [192–194], where the proton and electron could be transferred simultaneously or consecutively and to the same place or to different places. HAT is one example of the many possibilities, where they are transferred at the same time and to the same place; concerted PCET is one of the other possibilities, where the transfer is taking place at the same moment, but to different places; distinguishing between the two options is not easy and open to interpretation. A major step forward was reported early 2018, when Klein and Knizia used [195] the intrinsic bond orbital (IBO) [196, 197] view to investigate two prototypical model systems that cleave C–H bonds. By comparing the IBOs along the intrinsic reaction coordinate (IRC) profiles, they showed that for the taurine dioxygenase (TauD-J), an Fe(IV)-oxo active species, a HAT profile was observed; in the process of cleaving the C–H bond, one electron (here, an α electron) moves together with the proton and forms a new bond together with a second electron from the Fe ¼ O moiety (here, a β electron). By plotting the changes in the IBOs as a function of the reaction coordinate, they were able to show nicely that

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the electron flow associated with HAT is continuous and smooth [195]. Instead, for the cPCET pathway of lipoxygenase, with an Fe(III)-hydroxo as active species, a different picture was observed; the α electron of the C–H bond remains on the substrate, while the β electron is transferred to the iron center and ends up in a non-bonding d-orbital. Hence, the IBO view allows a nice visual representation of the electron flow in these reactions, which helps both in our understanding of the reactions that are taking place, and, as in this case, is able to distinguish between different mechanisms such as HAT and cPCET.

5.1.2

Ligand Modification

As mentioned above, the [FeIV(O)(TMC)]2+ complex [190] (TMC ¼ 1,4,8,11tetramethyl-1,4,8,11-tetraazacyclotetradecane) is fairly stable and unable to oxidize cyclohexane. Recently, together with the groups of Ray and Nam, we reported a modification of the TMC ligand that was observed to be six orders of magnitude faster [198]. One of the NMe groups of the TMC ring was replaced by oxygen (TMCO), which changes the ligand field and lowers the σ* acceptor orbital; simultaneously, the spin state changed from a triplet state (S ¼ 1) for [FeIV(O)(TMC)]2+ to quintet for [FeIV(O)(TMCO)]2+ (with the S12g DFA). The change in spin state makes that a spin-switch is no longer needed to reach the spin state with the lowest barrier along the oxidation pathway; however, most importantly, the barrier reduced dramatically (ca. 12 kcal mol
1) [199]. This change in barrier resulted as the combination of two effects, an electronic one based on the energy of the σ* orbital and a steric one based on the possibility of the substrate to reach the iron-oxo moiety [199]. In a separate study, the TMC ligand was modified to change the shape of the transition-metal complex by removing the N-Me methyl groups which were replaced by hydrogens (TMCH); as a result, the complex went from flat to V-shaped (see Fig. 9, middle) [200]. The competition between hydrogen (HAT; Fig. 9, left) and oxygen (OAT; Fig. 9, right) atom transfer was studied, with all possible combinations for the structure of the active species [201].

Fig. 9 Three-dimensional structures for FeIV(O) with TMCH ligand (middle) and the corresponding HAT (left) and OAT (right) transition structure

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For both the TMCO and TMCH ligands, the S12g/TZ2P computed Mössbauer parameters for the isomer shift (δ) and quadrupole splitting (ΔEq) were in excellent agreement with experiment.

5.2

Intradiol vs. Extradiol Selectivity

The activation of dioxygen for incorporating the oxygen atoms into a catechol can be achieved using transition-metal enzymes, leading to either intradiol or extradiol incorporation (see Fig. 10). The enzymes use either an FeII (extradiol) or FeIII (intradiol) in the active site, with different coordination environments (see Scheme 1). Surprisingly, Banse and co-workers reported in 2001 [202] that an Fe(III) biomimetic complex was able to perform either pathway, depending on the presence or absence of methyls on the ligating nitrogens of the 2,11-diaza[3,3](2,6) pyridinophane ligand. Intrigued by these findings, we explored [203] the full catalytic cycle by computational chemistry and observed a variety of spin states along the reaction. After binding of the dioxygen (2), nucleophilic attack on the catechol takes place (3), and the O–O bond is broken (4) which leads to the branching point where either intradiol (5i) or extradiol (5e) path is taken (see Fig. 10). Surprisingly enough, our study [203] seemed to indicate an almost constant switching of spin states, with the mechanism starting with R ¼ H in low spin (S ¼ 1/2), then switching over to high spin (S ¼ 5/2), and then to intermediate spin (S ¼ 3/2) at the branching point (4); from there a switch to HS leads to the smallest barriers, but in subsequent steps, the IS and HS states continue to switch as ground state. For R ¼ Me, the spin-state splittings are larger, in particular around the branching point, and only at the final product does it switch from IS to HS. For a large part, this comes from the impossibility to form H-bonds with the carbonyl group at the branching point 4, which increases the spin-state splitting. Also the competition between extradiol and intradiol activity is drastically affected; with R ¼ H both pathways show comparable barriers and hence both products can be formed; for R ¼ Me however, only the intradiol pathway is now viable. The preference for either extradiol/intradiol (R ¼ H) or intradiol (R ¼ Me) was indeed observed experimentally.

Fig. 10 Branching point in selectivity between extradiol and intradiol reactivity

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Scheme 1 Reaction mechanisms taking place in active sites of extradiol (a) and intradiol (b) enzymes

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Fig. 11 Competing pathways in catalase reactivity of a MnII complex [50]

5.3

Catalase

Protecting our body from harmful substances like superoxide (O2• –) or hydrogen peroxide (H2O2) is achieved by a variety of enzymes: superoxide dismutases to transform superoxide into hydrogen peroxide, which is coupled to a catalase enzyme that transforms the peroxide into water oxygen. A number of biomimetic complexes have been reported for the latter process [204], most of which are based on manganese. Despite their obvious societal interest, these complexes have not gained much attention, which is why we focused on their activity in two families of Mn complexes [50, 205]. The first family (MnIII) was inspired by Doctrow and co-workers [206, 207], while the latter (MnII) resulted from a recent study by Britovsek and co-workers [208]. The oxidation state of Mn (II vs. III) showed to be vital in understanding some differences in the mechanism, although both followed the proposed ping-pong mechanism [209] where the transformation of peroxide into water/dioxygen takes place in two phases. In the first phase, O–O bond breaking leads to a Mn(O) species and water; the Mn-oxo then performs HAT on an additional peroxide molecule in the second phase, twice, to build the second water molecule and leaves the deprotonated peroxide behind as (triplet) dioxygen. Nevertheless, with the MnII complex [50], a competing reaction pathway was discovered, based on a dihydroxo intermediate (see Fig. 11). Interestingly enough, the ping-pong mechanism was most favored on the sextet state, while the dihydroxo mechanism followed the quartet state. The reaction mechanism is controlled by a spin-state switching triggered by Mn coordination going from octahedral (in the ping-pong

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route) to trigonal prismatic (in the dihydroxo path). It should be added that the overall rate-determining step is however the O–O bond breaking in the first phase.

6 Conclusions and Perspectives Spin states are shown to play a vital role in many organometallic and bioinorganic chemistry reactions and need a combined effort of spectroscopy, theory, synthesis, and catalysis in order to understand in great detail how the transition-metal complexes are able to perform their catalytic activity. This is in particular true for highly reactive complexes (e.g., putative FeV(O) species), for which unambiguous proof of their existence and character may be difficult to obtain. Computational chemistry should (and does) provide useful insights since it allows for direct comparison with experiment through, e.g., spectroscopy, but has not yet matured to the level where a foolproof methodology has been provided that withstands scrutiny by experimentalists and theorists alike. Especially in cases where experimental proof is scarce, and computational chemistry provides puzzling answers (such as an O–O distance of 2.1 Å, which may hold one electron in it [186, 187] or otherwise be understood as a transition-state structure), there is no straightforward path leading toward clear understanding, only toward continued validation, confirmation, prediction, crossvalidation, and agony. Although clear advances have been made in theory, with spin-state consistent DFAs (OPBE, SSB-D, S12g), DMRG-PT2, CASPT2/CC, stochastic CASSCF, local and DLPNO coupled cluster, benchmarks on a variety of systems of interest to the organometallic and bioinorganic communities have shown that there is not yet a practical tool that is able to provide results consistent with full CI and/or experiment for the transition-metal complexes. Moreover, because of the system sizes and the unfavorable scaling of wavefunction theory, such advances are not foreseen in the immediate future (coming years); however, with the advent of quantum computing and deep learning, a decade from now, the picture may have changed completely. This chapter focused on the chemistry taking place in the catalysis, with a molecular point of view where a 2D drawing should be able to explain the chemistry. However, naturally, molecules and transition-metal complexes are not static at all, and (explicit) solvent effects and molecular dynamics simulations should be taken into account as well (as described in other chapters). Nevertheless, adding these effects would make the complex view on transition-metal catalysis even more complicated and therefore was ignored here. The analysis of the chemical aspect of calculations, and validation of these with experiments, is playing an ever larger role in transition-metal chemistry research nowadays. Within Europe this was no doubt stimulated by the very successful COST Actions on transition-metal chemistry in recent years (CM1003, CM1205, CM1305).

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Acknowledgments MINECO (CTQ2014-59212-P, CTQ2017-87392-P), FEDER (UNGI10-4E801), and the COST Association (CM1305, ECOSTBio) are gratefully thanked for financial support, and CSUC is thanked for extensive computer time.

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Top Organomet Chem (2020) 67: 227–270 https://doi.org/10.1007/3418_2020_48 # Springer Nature Switzerland AG 2020 Published online: 25 July 2020

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy: The Metal–Ligand Electronic Parameter (MLEP) Elfi Kraka and Marek Freindorf

Contents 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 The Tolman Electronic Parameter (TEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Local Vibrational Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Theory of Local Vibrational Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Application of the Local Vibrational Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Assessment of the TEP with the Local Mode Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 TEP and Mode–Mode Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Correlation Between CO and ML Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 The Metal–Ligand Electronic Parameter (MLEP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Relative Bond Strength Order (BSO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Intrinsic Strength of Nickel–Phosphine Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Special Role of Carbene Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Ionic Ligands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Generalization of the MLEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract The field of organometallic chemistry has tremendously grown over the past decades and become an integral part of many areas of chemistry and beyond. Organometallic compounds find a wide use in synthesis, where organometallic compounds are utilized as homogeneous/heterogeneous catalysts or as stoichiometric reagents. In particular, modifying and fine-tuning organometallic catalysts has been at the focus. This requires an in-depth understanding of the complex metal– In memoriam of Dieter Cremer. E. Kraka (*) and M. Freindorf Computational and Theoretical Chemistry Group (CATCO), Department of Chemistry, Southern Methodist University, Dallas, TX, USA e-mail: [email protected]

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ligand (ML) interactions which are playing a key role in determining the diverse properties and rich chemistry of organometallic compounds. We introduce in this article the metal–ligand electronic parameter (MLEP), which is based on the local vibrational ML stretching force constant, fully reflecting the intrinsic strength of this bond. We discuss how local vibrational stretching force constants and other local vibrational properties can be derived from the normal vibrational modes, which are generally delocalized because of mode–mode coupling, via a conversion into local vibrational modes, first introduced by Konkoli and Cremer. The MLEP is ideally suited to set up a scale of bond strength orders, which identifies ML bonds with promising catalytic or other activities. The MLEP fully replaces the Tolman electronic parameter (TEP), an indirect measure, which is based on the normal vibrational CO stretching frequencies of [RnM(CO)mL] complexes and which has been used so far in hundreds of investigations. We show that the TEP is at best a qualitative parameter that may fail. Of course, when it was introduced by Tolman in the 1960s, one could not measure the low-frequency ML vibration directly, and our local mode concept did not exist. However, with these two problems solved, a new area of directly characterizing the ML bond has begun, which will open new avenues for enriching organometallic chemistry and beyond. Keywords Local vibrational mode · Tolman electronic parameter · Transition metals · Vibrational spectroscopy

Abbreviations ACS BDE BSO CEP DFT LEP LTEP MC MD ML MLEP NHC [NiFe] PES QALE TEP ZPE

Adiabatic connection scheme Bond dissociation energy Bond strength order Computational electronic parameter Density functional theory Lever electronic parameter Local Tolman electronic parameter Metal carbon Molecular dynamics Metal ligand Metal–ligand electronic parameter N-heterocyclic carbene Nickel iron hydrogenase Potential energy surface Quantitative analysis of ligand effects Tolman electronic parameter Zero-point energy

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1 Introduction Since French chemist Louis Claude Cadet de Gassicourt synthesized the first organometallic compound tetramethyldiarsine in 1706 [1], organometallic chemistry has tremendously grown and become an integral part of many areas of chemistry and beyond [2–12]. A number of researchers have been awarded the Nobel Prize in Chemistry for their work in the area of organometallic chemistry: 1912 – Victor Grignard, discovery of the Grignard Reagent, and Paul Sabatier, hydrogenation of organic species in the presence of metals 1963 – Karl Ziegler and Giulio Natta, Ziegler–Natta catalyst 1973 – Geoffrey Wilkinson and Ernst Otto Fischer, sandwich compounds 2001 – William Standish Knowles, Ryoji Noyori, and Karl Barry Sharpless, asymmetric hydrogenation 2005 – Yves Chauvin, Robert Grubbs, and Richard Schrock, metal-catalyzed alkene metathesis 2010 – Richard F. Heck, Ei-ichi Negishi, and Akira Suzuki, palladium-catalyzed cross-coupling reactions [13] Organometallics are strictly defined as chemical compounds, which contain at least one bonding interaction between a metal and a carbon atom belonging to an organic molecule. However, aside from bonds to organyl fragments or molecules, bonds to “inorganic” carbon, like carbon monoxide (metal carbonyls), cyanide, or carbide, are generally considered as organometallic compounds as well. Likewise, in addition to the traditional main group metals [4–16] and transition metals [2], lanthanides and actinides [17, 18], as well as semimetals, i.e., elements such as boron, silicon, arsenic, and selenium [19, 20], are also considered to form organometallic compounds, e.g., organoboranes [21], broadening the range of organometallic compounds substantially. One of the major advantages of organometallic compounds is their high reactivity, which finds wide use in synthesis, where organometallic compounds are utilized as homogeneous/heterogeneous catalysts or as stoichiometric reagents [22– 28]. Major industrial processes using organometallic catalysts include hydrogenation, hydrosilylation, hydrocyanation, olefin metathesis, alkene polymerization, alkene oligomerization, hydrocarboxylation, methanol carbonylation, and hydroformylation, to name just a few [9, 29–31]. Organometallic complexes are also frequently used in cross-coupling reactions [32, 33], and they have attracted a lot of attention in the field of organometallic-mediated radical polymerization [34– 38]. The production of fine chemicals relies on soluble organometallic complexes or involves organometallic intermediates, which often guarantee stereospecific products [7]. A recently evolving field is organometallic electrochemistry, which is devoted to finding solutions for the production of reliable, affordable, and environmentally friendly energy, fuels, and chemicals such as methanol or ammonia [39, 40]. Organometallic compounds have recently been discussed as an excellent alternative to the organic active layers used for solar cells or other light-emitting devices, due to their better properties such as thermal and chemical stability [41], and

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it has been suggested that organometallic benzene derivatives may even serve as potential superconducting materials [42]. Organometallic catalysis has allowed the development of an impressive number of chemical transformations that could not be achieved using classical methodologies. Most of these reactions have been accomplished in organic solvents, and in many cases in the absence of water, and under air-free conditions. The increasing pressure to develop more sustainable transformations has stimulated the discovery of metal-catalyzed reactions that can take place in water. A particularly attractive extension of this chemistry consists of the use of biologically relevant aqueous solvents, as this might set the basis to transform catalytic metal complexes into biological settings [8, 11, 43–45]. These trends go in line with the recently invoked interest of pharmaceutical research and development for organometallics [46], in particular their use as potential anticancer drugs [47–49]. There is a continuous scientific endeavor being aimed at optimizing currently applied organometallic compounds and/or finding new ones with advanced properties and a broader scope of applications. In particular, modifying and fine-tuning homogeneous organometallic catalysts has been at the focus. However, there is a huge number of possible combinations between one of the 28 transition metals of the first, second, and third transition metal period (excluding Tc) or one of the 12 metals of periods 2–6 and an even larger amount of possible ligands (L). Attempts to find suitable organometallic complexes for catalysis reach from trial-and-error procedures to educated guesses and model-based strategies [50–58], which is nowadays strongly supported and guided by quantum chemical catalyst design exploring the catalytic reaction mechanism [59] or the physical properties of the catalyst [60]. Physical property-based approaches, which recently started to involve data science and machine learning techniques, provide the ability to examine large swaths of chemical space [61, 62], but the translation of this information into practical catalyst design may not be straightforward, in particular if the proposed properties do not directly relate to measurable quantities. In this connection, one has searched since decades for measurable parameters that can be used as suitable descriptors to assess the catalytic activity of a metal complex, mainly focusing on identifying possible metal–ligand (ML) bond descriptors. The ML interaction, often highly covalent in nature in the case of organometallics, plays a key role in determining their diverse properties and rich chemistry, combining aspects of traditional inorganic and organic chemistry. Therefore, the detailed understanding of the ML bond is a necessary prerequisite for the fine-tuning of existing and the design of the next generation of organometallic catalysts. Two popular strategies to describe the catalytic activity of a transition metal complex in homogeneous catalysis as a function of the ML bond are based (1) on the ML bond dissociation energies (BDEs) [63–68] and (2) on molecular geometries to predict via BDE values and/or bond lengths the ease replacement of a given ligand or the possibility of enlarging the coordination sphere of a transition metal during catalysis. While these attempts have certainly contributed to the chemical understanding of metal and transition metal complexes, one has to realize that BDE values or bond lengths provide little insight into the intrinsic strength of the ML bond. The BDE is a reaction parameter that includes all changes, which take place during the dissociation

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process. Accordingly, it includes any (de)stabilization effects of the products to be formed. The magnitude of the BDE reflects the energy needed for bond breaking but also contains energy contributions due to geometry relaxation and electron density reorganization in the dissociation fragments. Therefore, the BDE is not a suitable measure of the intrinsic strength of a chemical bond as it is strongly affected in non-predictable ways by the changes of the dissociation fragments. Accordingly, its use has led in many cases to a misjudgment of bond strength [69–74]. Also the ML bond length is not a qualified bond strength descriptor. Numerous cases have been reported illustrating that a shorter bond is not always a stronger bond [75–79]. Other computational approaches utilized to determine the strength of the ML bond include molecular orbital approaches [80, 81] or energy decomposition methods [82– 84]. However, also these approaches provide more qualitative rather than quantitative results [69, 85]. On the other hand, detailed information on the electronic structure of a molecule and its chemical bonds is encoded in the molecular normal vibrational modes [86]. Therefore, vibrational spectroscopy should provide a better basis for a quantitative bond strength descriptor, which will be discussed in the next section.

2 The Tolman Electronic Parameter (TEP) Experimentalists have used vibrational properties to describe chemical bonding including metal and transition metal catalysts for a long time [87–113] despite the fact that the rationalization of this use was never derived on a physically or chemically sound basis. Vibrational force constants seemed to be the best choice for describing the strength of chemical bonds, because they are independent of the atomic masses. However, it turned out that force constants derived from normal vibrational modes are dependent on the coordinates used to describe the molecule [114–118]. Therefore, the use of normal vibrational frequencies, which are directly available from experiment, was suggested. Because of the relatively large mass of M, ML vibrational frequencies appear in the far-infrared region, which was experimentally not accessible in the early 1960s. Therefore, the idea of a spectator ligand came up, which should have a high stretching frequency, i.e., easy to measure, and which was well-separated from all other frequencies in the spectrum. The metal spectator stretching frequency had to be sensitive to the strength of the ML bond and any electronic changes at M resulting from modifications of L, and it had to be common to most transition metal complexes. This idea was realized in several investigations on transition metal complexes, whereas suitable spectator and sensor ligands such as nitriles, isonitriles, and nitrosyl and carbonyl groups were tested, assuming that the CN, NC, NO+, or CO stretching frequencies are sensitive with regard to the electronic configuration of M in the transition metal complex and a given ML bond, so that a spectroscopical (indirect) description of the latter seemed to be possible. Strohmeier’s work on chromium, vanadium, manganese, tungsten, and other complexes [119, 120] made the lead in the field of metal–ligand

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investigations with contributions from Fischer [121], Horrocks [122, 123], and Cotton [124–127]. Strohmeier ordered transition metals according to their π-donor ability: Cr > W > Mo > Mn > Fe. The overall proof of concept which emerged from these more or less scattered studies was that L acts as a σ-donor and/or a πacceptor according to which the electron density at M is changed. This change can be monitored by the metal spectator ligand stretching frequency, which provides indirect evidence on the nature of L and the ML bond. However, it was the pioneering work of Tolman who combined and systemized these findings, culminating in the Tolman electronic parameter (TEP) as ML bond strength measure [128–130]. Originally, Tolman focused on tertiary phosphines (L ¼ PR3) interacting with a nickel–tricarbonyl rest, where the three CO ligands take the role of a spectator group measuring the interaction of L with Ni. Tolman defined the TEP as the A1symmetrical CO stretching frequency of the nickel–tricarbonyl–phosphine complex according to the following relationship: TEP ¼ ωðNi; CO, A1 Þ ¼ 2, 056 þ pL

ð1Þ

with P(t-Bu)3 as a suitable reference with pL ¼ 0 and ω(CO, A1) ¼ 2,056 cm1. Tolman considered P(t-Bu)3 as the most basic phosphine because of its strong σdonor and absent π-acceptor ability. This leads to an increase of the electron density at Ni, which is transferred via the d-orbitals into the antibonding π ⋆(CO) orbitals as sketched in Fig. 1a, b. The CO bond length is increased, and the A1-symmetrical CO stretching mode is redshifted to the value of 2,056 cm1 compared to the CO stretching frequency in carbon monoxide of 2,071 cm1 [132]. Any other, less basic phosphine leads to a lower electron density at Ni and thereby to a higher CO stretching frequency ω(L) and the ligand-specific increment pL ¼ ω(L)  2,056. In this way, the basicity of phosphine ligands can be estimated by simply measuring the vibrational spectra (infrared or Raman) of the corresponding nickel–tricarbonyl–phosphine complex. Tolman used phosphine ligands because they cover a wide range of distinct electronic and steric properties, seldom participate directly in the reactions of a transition metal complex, and can they be used to modulate the electronic properties of the adjacent metal center. In addition, he relied on the following important assumptions: 1. ω(CO, A1) is well separated from other frequencies, so it can be easily measured and identified in the IR spectrum. 2. The ω(CO, A1) stretching mode does not couple with other vibrational modes, i.e., can be considered as local mode. 3. There is a general correlation between ω(CO, A1) and ω(ML). In literally hundreds of studies on transition metal–carbonyl complexes, the original Tolman concept has been applied, and in some studies, its general applicability has been tested. For example, Otto and Roodt [133] fitted the CO frequencies measured by Strohmeier for trans-[Rh(CO)ClL2] (Rh-Vaska) complexes with the CO frequencies of Tolman’s nickel–tricarbonyl–phosphines and obtained a quadratic relationship, which suggests that besides the σ-donor activity of the trialkyl

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+z R

R

R

R

R

R P

P

or

3dx2 - y 2

C

3dz 2

(lp)

+x

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3dz 2

C O

C

C C

C

(CO)

O

-y

O

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a

-donation

C

-donation

b p

3dxz

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3dyz

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O C O

-back donation

O

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F

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3dxz

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C

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Ni

c

X

X

Pseudo(EX3)

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O O

Ni C C

O

C

O

-donation

O

f

C C

O O

-back donation

Fig. 1 Schematic overview over possible orbital interactions between ligand L and the [Ni(CO)3] group in [Ni(CO)3 L] complexes. Reproduced from Ref. [131] with permission of the Royal Society of Chemistry

phosphines, for other ligands, a second ML bonding mechanism in a form of a strong π-acceptor ability becomes dominant. A series of 14 linear relationships between the TEP and the CO stretching frequencies of V, Cr, Mo, W, Mn, Fe, and Rh complexes has been published by Kühl [134]: TEP ¼ AωðM; CO, A1 Þ þ B

ð2Þ

where each new type of a given transition metal complex (with the same transition metal (M)) required a different relationship with correlation coefficients R2 ranging from 0.799 to 0.996. A significant data scattering suggested that for a given transition metal (M), complexes of the type [RnM(CO)mL] may be subject to different ML bonding mechanisms depending on the ligands R and L and the coordination numbers m and n. ML bonding might also be affected by the environment (solvent, crystal state, etc.). As indicated in Fig. 1c–d, there may be also [RnM (CO)mL] interactions which are not reflected by ω(CO, A1). In addition, Tolman’s choice of the t-Bu reference has been challenged by Arduengo’s N-heterocyclic carbenes (NHCs) [135–137], which are stronger σ-donors than the t-Bu reference, so that a TEP < 2,056 cm1 and a negative pL value results. Parallel to the experimental efforts obtaining TEP values, computational chemists started to determine CO stretching frequencies of carbonyl–metal complexes in the

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The TEP Periodic Table Mg Ti Zr

V

Cr Mn Fe Co Ni Mo

Zn

Ru Rh Pd

W Re Os Ir Pt Au Fig. 2 Use of the TEP throughout the periodic table. Experimentally derived TEPs have been discussed for Ni (blue) [128–130, 138, 151–160] which were correlated with the TEPs of transition metals given in green by Kühl [134]. Reproduced from Ref. [131] with permission of the Royal Society of Chemistry. For specific references, see Pd [161–168], Pt [164, 169], Co [170, 171], Rh [153, 166, 172–175], Ir [153, 163, 175–180], Fe [172, 181], Ru [182–188], Os [189, 190], Re [191– 193], Mn [119, 120, 194], Cr [122, 195–198], Mo [155, 173, 195], W [170, 199], V [120], Ti [200, 201], Zr [202], Mg [120], Cu [203, 204], Au [168, 205–208], and Zn [162]

harmonic approximation for molecules in the gas phase and to use them as a computational electronic parameter (CEP) for the description of ML bonding [138]. Most of the computational investigations suggested that CEPs obtained for Ni, Ir, or Ru complexes correlate well with the experimental TEPs [139–144], provided model chemistries are applied, which are suitable for the description of metal complexes [139, 141, 145]. CEP values based on semiempirical calculations were published for LMo(CO)5, LW(CO)5, and CpRh(CO)L complexes [146] or rhodium Vaska-type complexes [147]. However, the results depend on the parametrization of the used semiempirical method. In addition to gas phase TEPs, CEPs were also calculated for CO adsorbed by Ni–Au clusters [148]. Several review articles have summarized the experimental and theoretical work in this field [134, 149, 150]. Figure 2 gives on overview of the use of the TEP in a form of a TEP periodic table, where the manifold of transition metal complexes for a given M can be retrieved from the literature given in the figure caption. As a consequence of the widespread use of the TEP, attempts to relate or complement it by other measured or calculated properties of the transition metal complex emerged over time. Tolman himself realized that the bulkiness of a ligand can outweigh the electronic factors, which was the reason why he introduced the cone angle θ as a measure for the steric requirements of the ligand [128, 130]. The Lever electronic parameter (LEP) was introduced, which is based on the ratio of the redox potentials of closely related complexes such as those of Ru(III) and Ru(II), which can be electrochemically determined [209, 210], and which can be set into a relationship to the TEP [138]. It has been disputed whether the molecular electrostatic potential can be used to derive the CO stretching frequencies of transition metal–carbonyl complexes [211, 212]. Alyea and co-workers [213] suggested ways of differentiating between σ and π effects influencing the CO stretching frequencies by referring to thermochemical data such as pKa values. Giering combined electronic and steric effects to what he coined the quantitative analysis of ligand effects (QALE) model [212]. Coll and co-workers introduced an average local ionization energy I(r)

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .

235

that, if integrated over the van der Waals surface of ligand L, can be related to the TEP and Tolman’s cone angle, as was demonstrated for phosphines and phosphites. However, this approach turned out to be only reliable for ligands (L) with high polarizability [214]. Although the TEP is still today one of the most popular measures used by the experimental and computational chemistry community for quantifying the catalytic activity of transition metal complexes based on vibrational spectroscopy, criticism on the TEP has been raised by several authors in the recent literature [139, 177, 192, 205, 206, 215–221], in particular with regard to the validity of Tolman’s original assumption of uncoupled CO stretching modes. The normal vibrational modes in a molecule always couple [86]. There are only a few examples for uncoupled, non-delocalized, i.e., local, vibrational modes. The bending vibration of the water molecule is such an example of a local vibration, where the frequency is not contaminated by coupling contributions. In general, mode–mode coupling depends on the orientation of the mode vectors: vibrational modes with orthogonal mode vectors do not couple. Also, difference in the atomic masses can suppress coupling. For example, for the light–heavy–light arrangement of an acyclic three-atom molecule, the central atom can function as a “wall,” thus largely suppressing mode–mode coupling [222]. The TEP is based on measured or calculated normal mode CO stretching frequencies, which may be effected by mode–mode coupling between the CO stretchings or even between the CO and the MC stretching modes. There are two different coupling mechanisms between vibrational modes as a consequence of the fact that there is a kinetic and a potential contribution to the energy of a vibrational mode [86]. The electronic coupling between modes is reflected by the off-diagonal elements of the force constant matrix. By diagonalizing the force constant matrix Fq expressed in terms of internal coordinates qn, i.e., a transformation to normal coordinates and related normal modes, the electronic mode–mode coupling is eliminated. However, the resulting normal mode force constants are still contaminated by kinematic mode–mode coupling, and as described above, they depend on the internal coordinates chosen to describe the molecular geometry. Already in the 1960s, Decius [117] attempted to solve the force constant problem by using the inverse force constant matrix Γ ¼ ðFq Þ1 and introducing the so-called compliance constants Γnn as bond strength descriptors. However, the relationship of the compliance constants to normal or other vibrational modes was unclear. Hence, the compliance constants remained force constants without a mode and a frequency. Also a given Γnn is related to off-diagonal elements Γmn (m 6¼ n), the physical meaning of which is unclear. This led to criticism and questions about the usefulness of compliance constants [223]. For example, why should one only use the diagonal Γnn terms without considering the role of the off-diagonal Γmn terms when chemical bonds were described. There were also questions about the physical meaning of compliance constants related to redundant internal coordinates. Therefore, needed for an advanced TEP model are local vibrational modes, which fulfill the following requirements:

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1. They must be uniquely related to both experimentally derived and calculated normal modes. 2. Each local mode must be independent of the isotope composition of the rest of the molecule. 3. Each local mode must possess a corresponding local mode force constant, frequency, mass, and intensity. 4. The local mode force constant must be independent of the internal coordinates used for the description of the molecular geometry.

3 Local Vibrational Mode Analysis As will be shown in this section, the Konkoli–Cremer local vibrational modes fulfill all of these requirements. In 1998, Konkoli and Cremer [78, 224, 225] derived for the first time local vibrational modes directly from normal vibrational modes by solving the mass-decoupled Euler–Lagrange equations, i.e., by solving the local equivalent of the Wilson equation for vibrational spectroscopy [86]. They developed the leading parameter principle [224], which states that for any internal, symmetry, curvilinear, etc. coordinate, a local mode can be defined. This mode is independent of all other internal coordinates used to describe the geometry of a molecule, which means that it is also independent of using redundant or nonredundant coordinate sets. The number of local vibrational modes can be larger than Nvib (N: number of atoms, Nvib ¼ 3N  6 for a nonlinear and 3N  5 for a linear molecule), and therefore, it is important to determine these local modes, which are essential for the reproduction of the normal modes. This can be accomplished via an adiabatic connection scheme (ACS), which relates local vibrational frequencies to normal vibrational frequencies by increasing a scaling factor λ from zero (local frequencies) to 1(normal frequencies). For a set of redundant internal coordinates and their associated local modes, all those local mode frequencies converge to zero for λ ! 1, which do not contribute to the normal modes, so that a set of meaningful Nvib local modes remains [85, 226]. In this way, a 1:1 relationship between local (adiabatically relaxed) vibrational modes and normal vibrational modes has been established [85]. Cremer and co-workers developed a method for calculating from a complete set of Nvib measured fundamental frequencies, the corresponding local mode frequencies [76]. In this way, one can distinguish between calculated harmonic local mode frequencies (force constants) and experimentally based local mode frequencies (force constants), which differ by anharmonicity effects [227, 228]. Zou and co-workers [85] proved that the reciprocal of the compliance constant of Decius is identical with the local force constant of Konkoli and Cremer, so that for the first time the physical meaning of the compliance constants could be established. They could also show that the local vibrational modes of Konkoli and Cremer are the only modes, which uniquely relate to the normal vibrational modes [85]. A local stretching force constant associated with the bond length qn is related to the second derivative of the molecular energy with regard to qn, i.e., to the curvature of the

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237

Born–Oppenheimer potential energy surface (PES) in the direction of the internal coordinate qn. For an increasing bond length described by qn, this coordinate becomes the coordinate of bond dissociation. Zou and Cremer [229] demonstrated that by approximating the PES in this direction by a Morse potential and freezing the electron density during the dissociation process, the local stretching force constant is directly related to the intrinsic strength of a bond, which qualifies the local stretching force as unique quantitative bond strength measure. Before proceeding with the derivation of the local vibrational modes, it is useful to point out that the term local mode has been used by different authors in different ways: 1. The Konkoli–Cremer local vibrational modes are the unique and only equivalents of the normal modes, which are obtained by utilizing the Wilson equation of vibrational spectroscopy [86]. The Konkoli–Cremer local modes are related to the isolated modes of McKean obtained by isotope substitution [230], which represent a good approximation for the Konkoli–Cremer local vibrational modes. 2. Henry and co-workers [231–235] use the term local modes in connection with local mode (an)harmonic oscillator models to describe the overtones of XH stretching modes. Therefore, microwave spectroscopists and other experimentalists refer to local modes often in connection with overtone spectroscopy. 3. Reiher and co-workers [236–238] calculate unitarily transformed normal modes of a polymer being associated with a given band in the vibrational spectrum, where the criteria for the transformation are inspired by those applied for the localization of molecular orbitals. The authors speak in this case of local vibrational modes, because the modes are localized in just a few units of a polymer. However, these so-called localized modes are still delocalized within the polymer units. 4. In solid-state physics, the vibrational mode(s) of an impurity in a solid material is (are) called local modes [239, 240].

3.1

Theory of Local Vibrational Modes

In Eq. (3), the Wilson equation of vibrational spectroscopy is given [86, 231, 241, 242]: e ¼ MLΛ e Fx L

ð3Þ

where Fx is the force constant matrix expressed in Cartesian coordinates xi (i ¼ 1,    e collecting the vibrational eigenvectors lμ in its 3N ); M is the mass matrix, matrix L columns; and Λ is a diagonal matrix with the eigenvalues λμ, which leads to the (harmonic) vibrational frequencies ωμ according to λμ ¼ 4π 2 c2 ω2μ . The number of vibrational modes is given by Nvib, i.e., translational and rotational motions of the molecule are already eliminated. The tilde above a vector or matrix symbol indicates

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e¼ e Fx L mass weighting. By diagonalizing the force constant matrix according to L Λ, the normal mode eigenvectors and eigenvalues are obtained. Usually, the normal mode vectors elμ are renormalized according to L ¼  R 1=2 e M , where the elements of the mass matrix MR are given by mRμ ¼ L  { 1 el elμ and represent the reduced mass of mode μ. Equation 3 can be written in μ different ways. For example, without mass weighting as shown in Eq. (4): Fx L ¼ MLΛ

ð4Þ

One obtains L{FxL ¼ K and L{ML ¼ MR, which define the diagonal normal force constant matrix K and the reduced mass matrix MR, respectively. One can express the molecular geometry in terms of internal coordinates qn rather than Cartesian coordinates xn, and by this, the Wilson equation adopts a new form: [86] e ¼ G1 DΛ e Fq D

ð5Þ

e collects the normal mode vectors e where D dμ (μ ¼ 1, . . ., Nvib) column-wise, and matrix G ¼ BM1B{ (Wilson G-matrix) gives the kinetic energy in terms of internal e has the property to diagonalize Fq and to coordinates [86]. The eigenvector matrix D { q e ¼ Λ. If one does not mass weight the matrix D and works with e FD give D 1 q F D ¼ G DΛ, diagonalization leads to D{FqD ¼ K. Properties of a Local Mode The local mode vector an associated with the internal coordinate qn, which leads the nth local mode, is given by [224]:

an ¼

K1 d{n dn K1 d{n

ð6Þ

where the local mode is expressed in terms of normal coordinates Qμ. K is the diagonal normal mode force constant matrix (see above) and dn is a row vector of the matrix D. The local mode force constant k an of mode n (superscript a denotes an adiabatically relaxed, i.e., local mode) is obtained via Eq. (7):  1 k an ¼ a{n Kan ¼ dn K1 d{n

ð7Þ

Local mode force constants, contrary to normal mode force constants, have the advantage of being independent of the choice of the coordinates used to describe the molecule in question [76, 224]. In recent work, Zou and co-workers proved that the compliance constants Γnn of Decius [117] are simply the reciprocal of the local mode force constants: kan ¼ 1=Γnn [85, 226, 243].

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239

The reduced mass of the local mode an is given by the diagonal element Gnn of the G-matrix [224]. Local mode force constant and mass are needed to determine the local mode frequency ωan 

ωan

2

¼ 14π 2 c2 k an Gnn

ð8Þ

Apart from these properties, it is straightforward to determine the local mode infrared intensity or the Raman intensity [244]. Adiabatic Connection Scheme (ACS) Relating Local to Normal Mode Frequencies With the help of the compliance matrix Γq ¼ ðFq Þ1 , the vibrational eigenvalue (Eq. (5)) can be expressed as [85]: e ¼ G1 D eΛ ðΓq Þ1 D

ð9Þ

eΛ e ¼ Γq R GR

ð10Þ

e is given by: where a new eigenvector matrix R  1 { e ¼ ðΓq Þ1 D e ¼ Fq D e¼ D e R K

ð11Þ

Zou and co-workers partitioned the matrices Γq and G into diagonal (Γqd and Gd) and off-diagonal parts (Γqod and God) [85]:   e λ Λλ e λ ¼ Γq þ λ Γq R ðGd þ λ God Þ R d od

ð12Þ

The off-diagonal parts can be successively switched on by increasing a scaling factor λ from zero to one so that the local modes given by the diagonal parts (λ ¼ 0) are adiabatically converted into normal modes defined by λ ¼ 1. Each λ defines e λ and Λλ , respectively. specific set of eigenvectors and eigenvalues collected in R Equation (12) is the basis for the ACS.

3.2

Application of the Local Vibrational Mode Analysis

The local mode analysis has been successfully applied to characterize covalent bonds [73, 75, 229, 245–248] and weak chemical interactions such as halogen [72, 249–252], chalcogen [253–255], pnicogen [256–258], and tetrel interactions [74] as well as H-bonding [227, 228, 259–263] and BH  π interactions [264, 265]. Recently, the local mode analysis was for the first time successfully applied to periodic systems [266, 267]. Some highlights include:

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• The intrinsic bond strength of C2 in its 1 Σþ g ground state could be determined by its local stretching force constant. In comparison with the local CC stretching force constants obtained for ethane, ethene, and acetylene, an intrinsic bond strength half way between that of a double bond and that of a triple bond was derived. These results, based on both measured and calculated frequency data, refute the verbose discussion of a CC quadruple bond [229]. • The modeling of liquid water with 50 mers and 1,000 mers using both quantum chemistry and molecular dynamics (MD) simulations at different temperatures led to a set of interesting results [260]. The local mode analysis revealed that there are 36 hydrogen bonds in water clusters of different strength. In warm water, the weaker H-bonds with predominantly electrostatic contributions are broken, and smaller water clusters with strong H-bonding arrangements remain that accelerate the nucleation process leading to the hexagonal lattice of solid ice. Therefore, warm water freezes faster than cold water in which the transformation from randomly arranged water clusters costs time and energy. This effect known in the literature as the Mpemba effect, according to its discovery by Mpemba in 1969 [268], could now for the first time be explained at the atomistic level. • For the first time, nonclassical H-bonding involving a BH. . .π interaction was described utilizing both quantum chemical predictions and experimental realization. According to the Cremer–Kraka criterion for covalent bonding [269, 270], this interaction is electrostatic in nature and the local BH. . .π stretching force constant is as large as the H-bond stretching force constant in the water dimer [264, 265]. • A method for the quantitative assessment of aromaticity and antiaromaticity based on vibrational spectroscopy was developed [271], which led to a new understanding of the structure and stability of polycyclic gold clusters based on a new Clar’s Aromaticity Rule equivalent [272, 273].

4 Assessment of the TEP with the Local Mode Analysis The local mode analysis will be used in the following section to test Tolman’s basic assumptions: (1) that the ω(CO, A1) normal mode does not couple with other vibrational modes, and (2) that there is a general correlation between ω(CO, A1) and ω(ML).

4.1

TEP and Mode–Mode Coupling

A potential contamination of the CO stretching frequencies due to mode–mode coupling was already considered by Crabtree and co-workers [138] who tried to correct computationally the CO stretching frequencies of 66 nickel–tricarbonyl

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .

241

complexes [Ni(CO)3L]. However, their attempt to eliminate mode–mode coupling by manipulating the Hessian of calculated second energy derivatives failed to remove the kinematic coupling between the CO stretching vibrations and other vibrations, as was pointed out by Kalescky and co-workers in their local mode study of Crabtree’s 66 nickel–tricarbonyl complexes. This work led for the first time to decoupled, local CO stretching modes [145]. Setiawan and co-workers extended the original set of 66 nickel–tricarbonyl complexes to a more comprehensive set of 181 nickel–tricarbonyl complexes [Ni(CO)3L], shown in Figs. 3 and 4, including besides phosphine ligands also nitrogen and cyano, amines, arsines, stilbines, bismuthines, boron compounds, carbonyl, thiocarbonyl, carbenes, water and ethers, thioethers, haptic ligands, and anions [274]. In Fig. 5a, the normal mode frequencies ω(CO, A1) are correlated with the corresponding local mode frequencies ωa(CO) for both experimental and calculated frequencies. If the TEP would be without any coupling errors, i.e., the normal mode ω(CO, A1) stretching frequencies would be completely local as assumed by Tolman, all data points should be found along the dashed line, which defines modedecoupled, i.e., local TEP values. Instead data points (experimental, brown color; calculated, green color, Fig. 5a) suggest more positive TEP values in particular with decreasing local CO stretching frequency. In other words, a lower CO stretching frequency does not necessarily indicate a stronger Ni–CO π-back bonding but a larger mode–mode coupling. It also seems that the ω(CO, A1) stretching mode, chosen by Tolman, does not necessarily reflect the total red shift of the CO stretching as indicated in Fig. 1e–f. These findings hold for both measured and calculated TEP values (CEPs) excluding that the harmonic approximation used for the CEPs causes the deviation between normal and local mode frequencies. The mode–mode coupling can also directly be assessed by the coupling frequencies ωcoup(CO) shown in Fig. 5b as function of ωa(CO). They are defined as the difference between the local mode frequency and the corresponding normal mode frequency being connected via an ACS, i.e., ωcoup ¼ ω(λ ¼ 1)  ω(λ ¼ 0), which reflects the changes in the local mode frequency ωa ¼ (λ ¼ 0) caused by mode–mode coupling. Large coupling frequencies are obtained when the starting local mode frequencies are close or identical (degeneracy caused by symmetry) and the mass ratio of the vibrating atoms is comparable. The sum of local mode and coupling frequency is always identical to the corresponding normal mode frequency. When adding the sum of coupling frequencies to the sum of local mode frequencies, the zero-point energy (ZPE) is recovered [85]. Fig. 5b suggests qualitatively an inverse relationship between coupling frequencies and the local CO stretching frequencies, i.e., a smaller CO stretching frequency ωa(CO) implies a larger mode–mode coupling. Anionic ligands with strong σ- and/or π-donor capacity lead to the largest errors as Ni–CO π-back bonding is connected with a change in the Ni–C bond and an increased Ni–C and CO coupling. This means that for neutral and anionic ligands, TEP errors of 40–100 cm1 can be expected making the use of the uncorrected TEP highly questionable. Overall more electronegative ligands lead to higher TEP errors, whereas cationic ligands such as NO+ or HC+ give more reliable TEP values. Detailed insight into mode–mode coupling can be obtained by two special features of the local mode analysis, which allow the comprehensive analysis of a

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H

H H

N H

F

Me N

H H

H H

P H

Me P

H H

H As H

H N F F

H

N

H

Me Me

N

Me Me

N

H

Me

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H P F F

Me Me

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Me Me

P

F F

F

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Cl

N

Cl

Me Me

N

Et Et

N

Ph Ph

N

Et

Ph

F

Cl P Cl Cl

Br P Br Br

F F

Me Me

P

CF3

Et P

Et Et

Ph Ph

P

H

Me

F As H H

H As F F

F As F F

Cl As Cl Cl

Br As Br Br

Me Me

Ph

At I

At

Cl N H H

C6F5 N C F 6 5 C6F5

NH2 N NH 2 NH2

NMe2 N NMe 2 NMe2

I

N

Br Br

CF3

P

I

Br

Cl

N

I

At I

P I

C6F5 C6F5

P

C6F5

I As I I

Me As H H

As H

Me Me As Me

Me Me As CF3

Et As Et Et

Ph Ph As Ph

H Sb H H

F Sb H H

H Sb F F

F Sb F F

Cl Sb Cl Cl

Br Sb Br Br

I Sb I I

Me Sb H H

Sb H

Me Me

Me Me Sb Me

Me Me Sb CF3

Et Sb Et Et

Ph Ph Sb Ph

C6F5 Sb C6F5 C6F5

H Bi H H

F Bi H H

H Bi F F

F Bi F F

Cl Bi Cl Cl

Br Bi Br Br

Me Bi H H

Me Me

Bi H

Me Me Bi Me

Me Me Bi CF3

Et Bi Et Et

Ph Ph Bi Ph

At

N

C6F5 As C6F5 C6F5

I Bi I I

C6F5 Bi C6F5 C6F5

P

OMe OMe

N

OMe

H

Cl

At

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At

NH2 P NH 2 NH2

H N Cl Cl

P

H H

NMe2 P

NMe2 NMe2

Cl Cl

OMe OMe

P

OMe

At As At At

Cl As H H

H As Cl Cl

NH2 As NH 2 NH2

NMe2 As NMe2 NMe2

OMe OMe As OMe

At Sb At At

Cl Sb H H

H Sb Cl Cl

NH2 Sb NH 2 NH2

NMe2 Sb NMe2 NMe2

OMe OMe Sb OMe

At Bi At At

Cl Bi H H

H Bi Cl Cl

NH2 Bi NH 2 NH2

NMe2 Bi NMe 2 NMe2

OMe OMe Bi OMe

Fig. 3 Schematic representation of the 181 ligands of [Ni(CO)3L] complexes investigated by Setiawan and co-workers [274]: part 1. Reproduced from Ref. [274] with permission of the American Chemical Society

vibrational spectrum, (1) the adiabatic connection scheme (ACS) and (2) the decomposition of each normal mode into local mode contributions, which will be discussed in the following section for [Ni(CO)3F], the complex with the largest coupling error of 100 cm1. Figure 6a shows how the three equivalent local vibrational CO modes ωa(5,6,7) of [Ni(CO)3F] are transformed into the A1 normal mode ω18, i.e., the TEP

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .

C H H

H

CH2

CH

H

CH2

CH

C F F

Me

OMe

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C Cl Cl

Me

Me

NMe2

C

F C C

C

F

NH2

NMe2

N N

N C H

N C Me

Et O Et

H S H

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243

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H

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Cl O Cl

Cl O H

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Cl

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OH

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OH

F

H C C H

H

H C N

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P H H O

H

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Me

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At

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C C O

Y R

Fig. 4 Schematic representation of the 181 ligands of [Ni(CO)3L] complexes investigated by Setiawan and co-workers [274]: part 2. The four conformational possibilities of a complex are given in the bottom row. Reproduced from Ref. [274] with permission of the American Chemical Society

and into the two degenerate E normal modes ω16 and ω17 by switching on the masses via the perturbation parameter λ. The three equivalent local mode frequencies ωa(5,6,7) (λ ¼ 0) have a value of 2,019 cm1 revealing a redshift of 225 cm1 compared to the stretching frequency of carbon monoxide calculated at the same level of theory. Fully switching on the masses (endpoint: λ ¼ 1) leads to a mass

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(a) Tolman Electronic Parameter TEP [cm-1]

2300 2250

Anionic Ligands (L)

Neutral Ligands (L)

Cationic Ligands (L)

Calculated TEP Measured TEP

2200 2150

A1-symmetrial CO stretching frequency

2100 Ideal TEP without coupling

2050 Coupling error

2000

Ni L

1950 OO

1900 1900

2000 2100 Local Stretching Frequency

a

C

2200 -1 (CO) [cm ]

2300

(b) F-

100

OMe-

Ni

Cl-

Coup(CO)

[cm-1]

NO-

80 H-

40

NC-

SH-

L

NCMe C Br- OH2 OO OMe2 SMe2 I NF3 SH CO 2 SMeNH3, NMe3 (H2) CH-3 PH2Me PHF2 PH3 N2 PMe3 CF2 C=CH2 P(OMe)3 NCH CNPF3 (C2H4) PCl3 CH2 CS PH2F SiH-3

CCH-

60

OH-

20

NO+

CH+

2000

2100 a (CO) [cm-1]

2200

2300

Fig. 5 Mode–mode coupling of the normal mode stretching frequencies ω(CO, A1) corresponding to the TEP [131]. Calculated with the M06 functional [275] using Dunning’s aug–cc–pVTZ basis set [276]. (a) Correlation between local mode stretching frequencies ωa(CO) and normal mode stretching frequencies ω(CO, A1) corresponding to the TEP for experimental and calculated harmonic vibrational frequencies. Reproduced from Ref. [131] with permission of the Royal Society of Chemistry. (b) Coupling frequencies ωcoup(CO) compared with the corresponding local mode stretching frequencies ωa(CO). The TEP is stronger contaminated by ωcoup(CO) for weaker Ni–L bonds. Reproduced from Ref. [131] with permission of the Royal Society of Chemistry

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .

245

splitting of 81 cm1 resulting in the ω18(A1) frequency of 2,118 cm1 and the two degenerate ω16, 17(E) frequencies of 2,037 cm1. So the TEP is only redshifted by 116 cm1 compared to carbon monoxide, in line with the finding that TEP values are generally higher in value than their local mode counterparts. The lowering of the local CO stretching frequency is the result of σ-donation and π-back donation involving both eg and t2g symmetrical 3d(Ni) orbitals (see Fig. 1). By using the normal A1-symmetrical CO stretching frequency as a bond strength descriptor, the full amount of CO weakening cannot be correctly described, because of the massdependent splitting of A1 and E-symmetrical modes. Figure 6a suggests that for [Ni (CO)3F] , the degenerate ω16,17(E) frequencies would have been a better choice as bond strength descriptors. The ACS analysis can be complemented by a decomposition of the 18 normal modes of [Ni(CO)3F] into local mode contributions, as shown in Fig. 6b and Table 1. All CO stretching modes including the TEP couple to some extend with the NiC stretching modes, leading to a non-negligible admixture of about 4%. In summary, the local mode analysis is an essential tool for the quantification of mode– mode coupling, which depends on the nature of the ML bond, the symmetry of the complex, and its geometry. If for a given complex all Nvib normal vibrational frequencies are known (measured or computed), one can easily determine the local CO stretching frequencies and use these local, mode–mode coupling free frequencies, which we have coined LTEPs [274] instead of the TEPs as ML bond strength descriptors.

4.2

Correlation Between CO and ML Bonding

However, even if mode–mode coupling free LTEPs would be used, there is still an important open question, i.e., does the CO stretching frequency reflect ML bonding as assumed by Tolman? This question can be answered by comparing the local mode CO force constants ka(CO) with the corresponding local NiL force constants ka(NiL) (as shown in Fig. 7) for the set of 181 [NiCO3L] complexes [274]. Since (1) the local constants are independent of the choice of the coordinates used to describe the molecule under consideration and (2) they are directly linked to the intrinsic bond strength, we will use local mode force constants instead of local mode frequencies throughout the remainder of this work. Clearly, there is no general relationship between ka(CO) and ka(NiL) for this large set of [NiCO3L] complexes calling Tolman’s assumption into question. Subsets of data points belonging to a well-defined type of ligand show rather qualitative relationships, indicated by the different dashed blue lines in Fig. 7. This can be seen as an extension of Kühl’s findings that for each transition metal complex with a different metal, i.e., V, Cr, Mo, W, Mn, Fe, or Rh, a different relationship has to be used [134]. The results presented in Fig. 7 show that even within the Ni–phosphine complexes, there is no unique relationship. One has to distinguish between normal trialkyl phosphines (purple filled dots in Fig. 7), phosphines with electronegative

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(a)

a

F8

2120

Ni

2100

O5C2

18(A1)

C4O7

2100

C3O6

2118 cm-1

2080

mass dependent splitting

2060 a

2040

2037 cm-1

Free CO stretching: 2234 cm-1

2000 0

0.1

1

2

0.2

3

4

0.3

5

6

0.4 0.5 0.6 Scaling factor

7

8

9

0.7

0.8

2060 2040 2020

16-17(E)

2019 cm-1

2080

[cm-1]

(5,6,7)

2020

(b)

2120

= TEP

µ

Local mode frequencies

2140 Normal mode frequencies

[cm-1]

2140

2000 1.0

0.9

10 11 12 13 14 15 16 17 18

100.0

Local Mode Character [%]

7.3

90.0

7.9

80.0

7.9

70.0

7.3

9.2

14.6 33.0 29.0

9.2

18.2

17.5

40.0

17.5

18.2

36.0

30.0 15.2

6.6

8.5

6.6

8.5 9.0

5.3 26.8

33.9

6.7

22.6

64.0

F8 48.0

55.9

Ni 32.0

38.7

O5C2

C4O7 C3O6

33.9

9.5 22.6

18.3

A2

9.5

11.8

E

E

16.7

A1

A1

E

E

A1

E

E

E

E

A1

18 21 37 20 37 20 0 49 0 49 9 47 3 44 3 44 8 41 9 37 0 34 0 34 0 26

E

71

47

E

54

47

A1

71

E

26.5

26.1

5.3

8.2

E

32.0 8.5

8.7

18.3

28.4

5.7 5.7

Ni1-F8 Ni1-C2 Ni1-C3 Ni1-C4 C2-O5 C3-O6 C4-O7 F8-Ni1-C2 F8-Ni1-C3 F8-Ni1-C4 C2-Ni1-C3 C2-Ni1-C4 Ni1-C2-O5 (x) Ni1-C3-O6 (x) Ni1-C4-O7 (x) Ni1-C2-O5 (y) Ni1-C3-O6 (y) Ni1-C4-O7 (y)

9.0

8.5

15.2

26.5

38.7

91.0

8.4

0.0

26.2

33.2

8.2

10.0

20.0

14.0

29.0

11.6

7.3

32.0 16.0 48.0 25.2

7.3

20.0

26.6

15.6

11.6

16.0

26.2

8.2 8.2

50.0

8.6

19.9

14.0

13.6

60.0

6.9

6.8

14.5

14.8

8.8

6.9

8.5 18.5

TEP

Normal Mode µ

Fig. 6 Analysis of normal vibrational frequencies of [Ni(CO)3F] in terms of local vibrational frequencies, calculated with M06/aug–cc–pVTZ [274]. (a) Adiabatic connection scheme (ACS) for [Ni(CO)3F] showing how the three equivalent local vibrational CO modes ωa(5,6,7) are transformed into the A1 normal mode ω18 and the two degenerate E normal modes ω16 and ω17 by switching on the masses via the perturbation parameter λ. (b) Decomposition of the 18 normal vibrational modes of [Ni(CO)3F] into 18 local vibrational modes. Each of the 18 normal mode vectors dμ is represented by a bar (mode numbers are given at the top of each bar, symmetry, and calculated frequencies at the bottom of each bar). Each dμ vector is decomposed in terms of 18 local mode vectors an. The local mode parameters are presented in a form of a color code (right side of diagram; for numbering of atoms, see diagram in the lower right corner). Contributions larger than 5% are given within the partial bars representing a local mode

Characterizing the Metal–Ligand Bond Strength via Vibrational Spectroscopy:. . .

247

Table 1 Characterization of the 18 normal modes μ of [Ni(CO)3F] in terms of local mode contributions, calculated at the M06/aug–cc–pVTZ level of theory Mode 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

Local mode contributions in percentage 63.9% (C3-O6, C4-O7), 32.0% 4.1% Ni-C 48.0% C3-O6, 48.0% C4-O7 64.0% C2-O5, 16.0% C4-O7, 16.0% C3-O6 33.9% Ni1-C2, 20.0% Ni1-C3-O6 (y), 19.9% Ni1-C4-O7 (y), 8.5% Ni1-C4, 8.5% Ni1-C3 25.2% Ni1-C2-O5 (x), 22.6% Ni1-C3, 22.6% Ni1-C4, 11.5% (C2-Ni1-C3, C2-Ni1-C4), 6.9% Ni1-C3-O6 (y), 6.9% Ni1-C4-O7 (y) 53.0% (Ni1-C3-O6 (x), Ni1-C4-O7 (x)), 26.6% Ni1-C2-O5 (y) 55.9% Ni1-C2, 14.0% Ni1-C3, 14.0% Ni1-C4 38.7% Ni1-C4, 38.7% Ni1-C3, 6.8% Ni1-C2-O5 (x) 52.3% (Ni1-C3, Ni1-C4), 26.1% Ni1-C2, 16.7% Ni1-F8 91.0% Ni1-F8 36.0% Ni1-C2-O5 (y), 18.0% (Ni1-C3-O6 (x), Ni1-C4-O7 (x)), 11.8% Ni1-C2, 8.6% Ni1-C3-O6 (y), 8.5% Ni1-C4-O7 (y), 6.7% F8-Ni1-C2 29.0% Ni1-C3-O6 (x), 29.0% Ni1-C4-O7 (x), 19.1% (Ni1-C3, Ni1-C4), 10.7% (F8-Ni1-C3, F8-Ni1-C4), 8.7% Ni1-C2-O5 (x) 33.9% Ni1-C2-O5 (x), 33.2% Ni1-C3-O6 (y), 33.0% Ni1-C4-O7 (y) 26.8% F8-Ni1-C2, 14.6% Ni1-C4-O7 (y), 14.5% Ni1-C3-O6 (y), 13.6% Ni1-C2-O5 (y), 13.3% (F8-Ni1-C3, F8-Ni1-C4) 36.6% (F8-Ni1-C3, F8-Ni1-C4), 23.2% (C2-Ni1-C3, C2-Ni1-C4), 18.5% (Ni1-C3-O6 (x), Ni1-C4-O7 (x)), 15.6% Ni1-C2-O5 (x) 36.4% (Ni1-C3-O6 (x), Ni1-C4-O7 (x)), 18.5% Ni1-C2-O5 (y), 17.1% (C2-Ni1-C3, C2-Ni1-C4), 16.4% (F8-Ni1-C3, F8-Ni1-C4), 8.4% F8-Ni1-C2 28.4% F8-Ni1-C2, 14.8% Ni1-C2-O5 (y), 14.5% (F8-Ni1-C3, F8-Ni1-C4), 8.2% C2-Ni1-C4, 8.2% C2-Ni1-C3, 7.3% Ni1-C4-O7 (y), 7.3% Ni1-C3-O6 (y) 35.1% (C2-Ni1-C3, C2-Ni1-C4), 30.3% (F8-Ni1-C3, F8-Ni1-C4), 15.9% (Ni1-C3-O6 (x), Ni1-C4-O7 (x)), 8.8% Ni1-C2-O5 (x)

The numbering of atoms is given in Fig. 6

substituents, and those with bulky substituents (sterically hindered phosphines, open black circles). It also has to be noted that while some of the relationships shown in Fig. 7 show the right trend, i.e., a stronger NiL bond, leads to a weaker CO bond, others predict an increase of the CO bond strength with increasing NiL bond strength. This contradicts Tolman’s assumption that an increase of the electron density at the metal atom leads to increased CO π-back donation leading to an increased population of the CO anti-bonding π-orbital and a weakening of the CO bond that can be identified by a lower CO stretching frequency. Overall, the scattering of data point is too large to derive any reliable mode of prediction. The obvious success of TEP studies reported in the literature is more a result of restricting the studies to a smaller set of chemically similar complexes (often