Hydrogen Activation by Carbene Systems and Proton Transfer Reactions

Hydrogen Activation by Carbene Systems and

Proton Transfer Reactions. A Reaction Electronic Flux Analysis

Fernanda Duarte Gonzalez

Department of Chemistry Pontiﬁcia Universidad Cat´olicade Chile

Date:

Approved:

Alejandro Toro-Labb´e,Supervisor

Patricio Fuentealba

Pablo Jaque

B´arbaraLoeb

Patricia Pérez Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor in Chemistry. Department of Chemistry Pontificia Universidad Catolica de Chile 2012 Abstract (Chemistry)

Hydrogen Activation by Carbene Systems and Proton Transfer Reactions. A Reaction Electronic Flux Analysis

Fernanda Duarte Gonzalez

Department of Chemistry Pontiﬁcia Universidad Catolica de Chile

Date:

Approved:

Alejandro Toro-Labb´e,Supervisor

Patricio Fuentealba

Pablo Jaque

B´arbaraLoeb

Patricia Pérez An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor in Chemistry in the Department of Chemistry in the Graduate School of Pontificia Universidad Catolica de Chile 2012 Abstract

This Thesis was performed on the theoretical analysis of reaction mechanisms in a variety of chemical processes, ranging from the study of the biologically relevant chemical reactions to more chemically-oriented reactions. All the analysis was based on the use of Density Functional Theory (DFT), as the main theoretical framework, and the use of concepts developed by our group, Reaction Force (F (ξ)) and Reaction Electronic Flux (REF) as key elements for the understanding and characterization of the reaction mechanism of chemical reactions. The Thesis includes the study of three diﬀerent chemical processes: i) Proton Trans- fer (PT) processes in small molecules and amino acids; ii) Activation of H2 by carbene systems and iii) Non enzymatic and enzymatic mechanism of cis-trans isomerization of peptide bond. The study of the PT process was analyzed in two biologically relevant systems: thioformic acid and amino acids (Ala, Phe, Try). In these systems continuum and explicit solvent eﬀect are studied in detail. Secondly, a comprehensive study of

H2 activation reaction by alkyl(amino), diamino and diamido carbene systems is presented. H2 is a non-polar, poorly reactive molecule under ambient conditions; its activation, which is relevant in several industrial and biological processes, has usually required the participation of a metal center. Motivated for recent experimental evidences showing H2 activation by nonmetallic stable alkyl amino carbene systems, the electronic properties that might be controlling the reactivity of carbene systems

iii and the mechanism by which the activation takes place have been rationalized. Finally, the cis-trans isomerization of peptide bond is analyzed. First, the chemical aspects of the non-enzymatic peptide bond isomerization are studied employing the N-acetylproline methylamide system (Ac-Pro-NHMe) as a model system, solvent eﬀect and the autocatalytic non-enzymatic mechanism and its inﬂuence on the activation barrier are also discussed. Then, the enzymatic cis-trans isomerization reaction within the Prolyl isomerase PIN1 enzyme was studied. To perform this analysis, hybrid quantum mechanical/molecular mechanical (QM/MM) methods were used within the framework provided by the Mean Reaction Force (MRF) analysis, it allows to characterizes the electronic and structural free energy contributions to the activation energy.

iv Contents

Abstract iii

List of Tables ix

List of Figures xi

List of Abbreviations and Symbols xvi

Acknowledgements xviii

1 Overview1

1.1 Potential Energy Surface (PES)...... 1

1.2 Concerted and Two-steps Mechanisms...... 2

1.3 Applications to Systems of Interest...... 3

2 Introduction6

2.1 Theoretical Background...... 6

2.1.1 Density Functional Theory...... 7

2.1.2 Chemical Reactivity Indexes in DFT...... 11

2.1.3 The Reaction Force...... 20

2.2 Hypotheses...... 25

2.3 Goals...... 26

2.3.1 General Goals...... 26

2.3.2 Speciﬁc Goals...... 26

v 3 The Catalytic Eﬀect of Water on the Proton Transfer Reaction of Thioformic Acid 28

3.1 Introduction...... 29

3.2 Computational Methods...... 30

3.3 PT reactions in gas phase: catalytic eﬀect of a water molecule..... 31

3.3.1 Reaction Force and Reaction Works...... 33

3.3.2 Natural Bond Orbital (NBO) analysis...... 35

3.3.3 Chemical Potential and Reaction Electronic Flux...... 38

3.3.4 Reactive modes...... 39

3.4 PT reactions catalyzed by a water molecule using continuum solvent model PCM...... 42

3.5 Concluding Remarks...... 45

4 Insights on the Mechanism of Proton Transfer Reactions in Amino Acids. 47

4.1 Computational details...... 49

4.2 Results and discussion...... 50

4.2.1 Energetic Parameters and Potential Barriers...... 50

4.2.2 Reaction Force Proﬁle...... 53

4.2.3 Bond Order...... 56

4.2.4 Reaction Electronic Flux...... 59

4.2.5 The Eﬀect of a Second Water Molecule...... 60

4.3 Concluding Remarks...... 66

5 The Mechanism of H2 Activation by (Amino)Carbenes 68 5.1 Introduction...... 68

5.2 Computational details...... 72

5.3 Results and discussions...... 73

5.3.1 Energy and Reaction Force Proﬁles...... 73

vi 5.3.2 Chemical Potential and Reaction Electronic Flux...... 76

5.3.3 Reaction electronic ﬂux and Potential Energy...... 79

5.3.4 Nucleophilic and Electrophilic Character of Carbenes...... 80

5.3.5 Natural Bond Analysis...... 83

5.4 Concluding Remarks...... 84

6 A more detailed understanding of H2 Activation by (Amino)Carbenes 86 6.1 Computational Methods...... 87

6.2 Results and discussion...... 88

6.2.1 Analysis of Isolated Carbenes...... 88

6.2.2 Energy and Reaction Force...... 90

6.2.3 Reaction Electronic Flux (REF)...... 93

6.2.4 Activation Hardness...... 96

6.2.5 NBO analysis...... 97

6.2.6 Dual Descriptor and Fukui Function...... 101

6.3 Concluding Remarks...... 103

7 Prolyl cis-trans Isomerization: Non-Enzymatic and Enzymatic Mech- anism 105

7.1 Non-Enzymatic peptide bond cis-trans Isomerization...... 107

7.1.1 Introduction...... 107

7.1.2 Computational Methods...... 109

7.1.3 Results and discussion...... 111

7.1.4 Conclusions...... 122

7.2 Enzymatic Catalysis by PIN1: A QM/MM Study...... 124

7.2.1 Introduction: Enzyme PIN1...... 124

7.2.2 Computational details...... 127

7.2.3 Results and discussion...... 131

vii 7.2.4 Concluding Remarks...... 148

8 General Conclusions and Perspectives 150

A Reaction Paths 154

A.1 Second-Order Implicit Trapezoid Method...... 155

A.2 Hessian Predictor-Corrector...... 157

B Molecular Dynamics 161

B.1 Newton’s Equations...... 162

B.2 Molecular Dynamics in Diﬀerent Ensembles...... 163

B.2.1 Temperature coupling...... 164

B.2.2 Pressure coupling...... 165

B.3 The potential energy function...... 166

B.4 Free Energy Calculation...... 167

B.4.1 Umbrella Sampling (US) Method...... 168

B.5 QM/MM Methods...... 171

Bibliography 174

Biography 190

viii List of Tables

◦ 6= 6= 3.1 Reaction energy (∆E ); forward (∆Ef ) and reverse (∆Er ) energy barriers and the works associated to the diﬀerent processes in the iPT, wPT and wPT(PCM) reactions (Eqns. 2.48-2.49), all values in kcal/mol...... 32

3.2 Most important interactions between Lewis and non-Lewis orbitals and second order perturbation energy values, E(2), associates to them for reactant, transition state and product structures in iPT and wPT systems...... 37

3.3 Harmonic frequencies (cm−1) for normal modes of vibration R, TS, and P for iPT reaction. ip:inplane; oop: Out-of-plane; str:stretching; bnd:bending:sym: symmetric; asym: asymmetric...... 40

4.1 Reaction energy (∆E◦) and energy barriers (∆E6=) of the PT reactions computed at the B3LYP and MP2 levels of theory with the 6-31G(d,p) basis set...... 52

4.2 Reaction energy (∆E◦); energy Barriers (∆E6=), position of the extreme points of the reaction force (ξ1, ξ2) and the reaction works of the processes computed at the B3LYP level of theory with the 6-31G(d,p) basis set. .. 55

4.3 Summary of NBO Analysis for reactant structures...... 64

◦ 6= 6= 5.1 Reaction energy (∆E ); forward (∆Ef ) and reverse (∆Er ) energy barriers together with the works associated to the diﬀerent stages of in the H2 activation process (values in Kcal/mol)...... 73

6.1 Ionization Potential (IP), Electron Aﬃnity (EA), Chemical Potential (µ), Hardness (η), Nucleophilicity (N) and Global Electrophilicity (ω) Indices for the isolated singlet carbene systems. All values in eV.... 88

− + 6.2 Local Ionization potential Imin, Fukui functions,fCarb and fCarb, local − + nucleophilicity Nf , and local electrophilicity ωfCarb indices for the − carbene center in the isolated singlet carbene systems. Imin, NfCarb, + and ω fCarb are given in eV...... 90

ix 6= 6.3 Activation Barriers ∆E , Reaction Energies ∆EP −R, and amount of work Wi(i=1-4), as deﬁned by the reaction force proﬁle in kcal/mol.. 90

6.4 NBO Analysis for structures at the minimum of the reaction force. .... 101

◦ 6= 7.1 Reaction energy (∆E ); forward (∆Ef ) energy barriers, all values are in kcal/mol...... 110

7.2 Reaction energy (∆E◦); (∆E6=) energy barriers together with the works associated to the diﬀerent stages at B3LYP 6-31G(d) level. All values are in kcal/mol except ∆S which is given in cal/(mol*Kelvin),T=298 K. ... 112

x List of Figures

1.1 Model potential energy surface showing minima, transition states, a second order saddle point, reaction paths and a valley ridge inﬂection point (from reference [2]); (b) additional investigation of the IRC path connecting the stationary points on the PES...... 2

3.1 Sketch of the intramolecular (iPT) and water assisted (wPT) proton transfer reactions...... 29

3.2 Energy (kcal/mol) and Reaction Force Proﬁle(kcal/mol*ξ) for the iPT (left) and wPT (right) processes...... 31

3.3 Transition state structure of the water assisted proton transfer reaction (bond lengths in A).˚ ...... 32

3.4 Bond distances and angles proﬁles for iPT(left) and wPT(right) reactions. 34

6= 3.5 Phenomenological contribution to W1,W2 and ∆Ef for iPT(light-grey) and wPT(dark-grey) reactions (values in Kcal/mol)...... 35

3.6 Wiberg Bond order proﬁles for iPT and wPT reactions...... 36

3.7 Chemical potential(kcal/mol) and reaction electronic ﬂux (kcal/mol*ξ) pro- ﬁles for iPT and wPT reactions...... 39

3.8 Frequency values for the normal modes of vibration or iPT reaction. See table 2.3 for description of each mode of vibration (fi, i = 1 − 9) ...... 41

3.9 Schematic representations of the displacement vector associated to the transition vector for the iPT and wPT reactions...... 41

3.10 Energy (kcal/mol) and reaction force proﬁle (kcal/mol*ξ) (top). Chemical potential(kcal/mol) and reaction electronic ﬂux (kcal/mol*ξ) (bottom) for the wPT(PCM) processes...... 43

3.11 Bond order evolution for wPT(PCM)...... 44

xi 4.1 Optimized structures for the neutral, transition state and zwitterionic form of alanine (ALA and ALA-H2O) and phenylalanine (PHE and PHE- H2O). Not shown here is reaction TRY and TRY-H2O corresponding to tryptophan which is studied in detail in reference [110]...... 51

4.2 Energy proﬁle for the intramolecular and water-mediated proton transfer reactions in Alanine ALA and ALA-H2O and Phenylalanine PHE and PHE-H2O, respectively...... 52

4.3 Reaction force proﬁle for the intramolecular and water-mediated proton transfer reactions in alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE-H2O, respectively...... 54

4.4 Bond distances (in angstroms) between donor and acceptor atoms for the water–assisted proton transfer ALA-H2O...... 55

4.5 Bond order derivatives for the bonds being formed and broken in the proton transfer reaction of alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE-H2O, respectively...... 57

4.6 Reaction electronic ﬂux proﬁles for the intramolecular and water-mediated proton transfer reactions in alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE-H2O, respectively...... 59

4.7 Isosurface at 0.01 au for the HOMO, HOMO-1 and HOMO-2 density of Phenylalanine PHE and Alanine ALA ...... 61

4.8 Molecular orbital energies for phenylalanine PHE and PHE-H2O. ... 62

4.9 Transition state structure and bond order derivatives for the systems ALA- (H2O)2-A and ALA-(H2O)2-B. Values in parenthesis show the diﬀer- ences with respect to the bond distances for ALA-H2O...... 63

4.10 Proﬁles of reaction electronic ﬂux for the water-mediated proton transfer reactions ALA-(H2O)2-A and ALA-(H2O)2-B...... 65

5.1 Desulfovibrio desulfuricans iron hydrogenase posses a Fe-binuclear center active site (PDB:1HFE) ...... 69

5.2 Nonmetallic systems able to activate H2. a) Phosphine-borane specie; b) digermanes and c) Singlet carbene systems...... 70

5.3 Sketch of the H2 activation reaction by (amino)carbenes...... 72

5.4 Energy proﬁle (in kcal/mol) for the H2 activation reactions R1–R4. ... 74

5.5 Reaction force proﬁle (in kcal/[mol ξ]) for the H2 activation reactions R1–R4. 75

xii 5.6 Proﬁle of chemical potential (in kcal/mol) and reaction electronic ﬂux for reactions R1 and R3 (in kcal/[mol ξ]) ...... 76

5.7 REF decomposition: proﬁles of polarization and electron transfer ﬂux for the H2 activation reactions R1 and R3...... 80

5.8 Dual descriptor along the reaction force proﬁle of the H2 activation reactions R1 and R3; electrophilic sites with ∆f(r) > 0 are in yellow and nucleophilic sites with ∆f(r) < 0 in red...... 81

5.9 Wiberg bond order evolution and transition state complex for the H2 activation reactions R1 and R3...... 84

6.1 Scheme 1. Alkyl amino carbene (CN-systems), diammino carbene (NN- systems) and N,N-diamidocarbenes (DAC). iPr=(CH3)2CH; Dipp = 2,6- (iPr)2-C6H3; t-But=(CH3)3C; Mes = 2,4,6-(Me)3-C6H2...... 87

6.2 Energy (in kcal/mol) and reaction force proﬁle (in kcal/[mol ξ]) for the H2 activation reactions...... 91

6.3 Distances (in A)˚ for the H2 activation reactions. Solid/ lines correspond to acyclic systems and dot lines to cyclic systems...... 92

6.4 Reaction electronic ﬂux proﬁles (in kcal/[mol ξ]) for reactions under study. 94

6.5 spx character over the carbene center and the nitrogen atom for the CN ACYC system...... 95

6.6 Correlation of the activation energy ∆E6= and activation hardness ∆η6= for the reactions under study...... 96

6.7 Proﬁle of the hardness and energy change for -IP and -EA (which are related to the HOMO and LUMO orbitals), from the reactant to the transition state, for all reactions under study (in kcal/mol)...... 98

6.8 NBO charge for nitrogen and carbene center atom and H2 molecule. ... 99

6.9 For the cyclic systems, bond order derivatives of the making/braking bonds along the reaction...... 100

6.10 Dual descriptor of both species (carbene system and hydrogen molecule) calculated independently at transition state geometry. a) CN ACYC; b) CN CYC; c)CN CYCt−Bu; d) NN ACYC: e) NN CYC; f) DAC...... 102

7.1 Schematic representation of cis/trans isomers of the prolyl peptide bond . 106

7.2 Deﬁnition of torsion angles for Ac-Pro- NHMe...... 109

xiii 7.3 Energy proﬁles for the isomerization process in gas (top) and aqueous phase (bottom) at B3LYP 6-31G(d) level of theory...... 111

7.4 Relative energy (in kcal/mol) and the optimized structure along the isomerization Path1-2 in gas phase ...... 113

7.5 Relative energy (in kcal/mol) and the optimized structure along the isomerization Path1-2 in aqueous phase ...... 114

7.6 C-N Wiberg bond order (top) and charger over the prolyl nitrogen for Path1–Path1w ...... 118

7.7 Dual descriptor at the cis, transition state and trans conﬁguration along Path1w and Path2w ...... 121

7.8 Representation of the human enzyme PIN1 (PDB:2Q5A.pdb). The N- terminal WW domain and the C-terminal peptidylprolyl cis-trans isomerase (PPIase) domain are shown in green and yellow, respectively. ... 125

7.9 Snapshot of the catalytic active site of human PIN1 with the Ace-Gly- pThr-Pro-Phe-Gln-Nme peptide and the dihedral angle ζ representing the reaction coordinate...... 126

7.10 Mean reaction force and free energy proﬁle for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in aqueous solution...... 132

7.11 C-N bond length of the rotating bond for the isomerization in solution .. 134

7.12 Model I(yellow) and Model II (green) for the protonation state of Cys113 and His157...... 136

7.13 Superposition of the cis(yellow), transition state (orange) and trans (green) structures of the substrate peptide within PIN1 for the clockwise process . 137

7.14 Ramachandran plot with respect to φ and ψ dihedral angles around Pro ligand residue from the MD simulations using CHARMM force ﬁeld, for the system in solution (left) and within the enzyme (right) ...... 138

7.15 Mean reaction force and free energy proﬁle for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in PIN1. The inset presents the mean reaction force for the clock- and anticlockwise rotation in PIN1 employing only one starting structure...... 139

xiv 7.16 Representative snapshots of the cis-isomer, transition state (ζ = 90◦) and ◦ the product (ζ = 180 , ψpThr = −50). Atoms representing the QM region are presented as spheres. The solvent accessible surface is colored according to the electrostatic potential (blue=+256.71 mV; red=-256.71 mV) calculated with the APBS software and taking only the peptide and enzyme atoms into account...... 141

7.17 Relevant peptide-enzyme distances along the reaction coordinate during the isomerization in PIN1 ...... 144

7.18 Free-energy proﬁle from NEB optimization by the QM/MM-MFEP method for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in PIN1 ...... 146

7.19 Atomic charge of the nitrogen atom in the rotating peptide bond along the reaction coordinate in the QM/MM MFEP simulations...... 147

A.1 Second-order Implicit Trapezoid Method of Gonzalez and Schlegel (GS2) (adapted from [86] ...... 156

B.1 The Leap-Frog integration method. The algorithm is called Leap-Frog because r and v are leaping like frogs over each other’s backs (adapted from [241]) ...... 163

B.2 Illustration of the free energy proﬁle of a generic chemical event, showing the reactant (R), transition state (TS), product state(P), and the contributions of some of the windows (red dashed curves) used for the umbrella sampling methods...... 168

xv List of Abbreviations and Symbols

Symbols

∆A Helmholtz free energy diﬀerence

∆E‡ Activation energy

∆E Energy diﬀerence

∆G Gibbs free energy diﬀerence

∆G‡ Activation free energy

kB Boltzmann constant

β 1/kBT

εH Eigenvalue of HOMO

εL Eigenvalue of LUMO η Hardness

µ Electronic chemical Potential

ω Electrophilicity Index

EA Electron Aﬃnity

IP Ionization Potential

T Temperature

Abbreviations

$DEL Deletion Procedure implemented in NBO analysis.

B3LYP Becke–3 (for exchange) and Lee–Yang–Parr (for correlation) functionals

xvi DFT Density Functional Theory

Cys Cysteine

Gly Glycine

His Histidine

HOMO Highest occupied molecular orbital

IRC Intrinsic Reaction Coordinate procedure

LUMO Lowest unoccupied molecular orbital

MD Molecular dynamics

MFEP Minimum free energy path

MM Molecular mechanics or molecular mechanical

MP2 Ab initio second-order Møller-Plesset

NBO Natural Bond Orbital

PES Potential energy surface

PIN1 Peptidyl-prolyl cis-trans Isomerase NIMA-interacting 1 protein

PMF Potential of mean force

REF Reaction Electronic Flux

QM Quantum mechanics or quantum mechanical

TPO Phosphothreonine

US Umbrella sampling

xvii Acknowledgements

I thank my advisor Dr. Alejandro Toro-Labbéfor his guidance during the past four and half years. I would also like to thank Dr. Esteban Vöhringer-Martinezfor his insightful discussions and collaborations. My gratitude also goes to the current members of the QTC Group: Silvia D´ıaz,Eleonora Echagaray, Santanab Giri, Soledad Gutiérrez,Daniela Guzmán,BárbaraHerrera, Ricardo Inostroza, and Karla Soto. I thank my committee members, Dr. Patricio Fuentealba, Dr. Pablo Jaque, Dr. BárbaraLoeb and Dr. Patricia Pérezfor their encouragement, insightful comments, and questions. I owe my gratitude to all those people who have helped me during the time I have been working on this research. My special thanks to Abigail Serrano, Silvia D´ıaz, Ricardo Inostroza and Esteban Vöhringer-Martinez, for keeping me aware of what really matters in life. Heartfelt thanks also to RaúlSantos, for his support and encouragement through these years. I reserve my utmost thanks to my family, specially to my parents, my brother Cris- tian, and my sister Ivonne, for their patience and help in many ways over the years. Financial support from the ComisiónNacional de InvestigaciónCient´ıfica y Tec- nológica(CONICYT), through a graduate fellowship and Beca Apoyo de Tesis grant, from the US Department of State and CONICYT through a Fulbright-CONICYT visiting scholar fellowship at Duke University, and from to L’OREAL-UNESCO through for Women in Science 2009 award is gratefully appreciated.

xviii 1

Overview

A key underlying idea of this dissertation is the concept of reaction mechanism, i.e. the detailed description of the process leading from reactants to products of a reaction, including a characterization as complete as possible of the composition, structure, energy and other properties of reactants, products, intermediates, and transition states [1]. The detailed knowledge of the reaction mechanism and how the latter can be ma- nipulated to reduce the reaction barrier, improve stereoselectivity, increase product yield, or suppress undesirable side reactions is of great interest, with application ranging from biological to industrial applications, facilitating the design of synthetic pathways, the optimization of catalytic processes, and the rational design of new compounds.

1.1 Potential Energy Surface (PES)

The potential energy surface (PES) plays a central role for the understanding of the mechanism of chemical reactions. A model surface of the energy as a function of the molecular geometry is shown in Figure 1.1 to illustrate some of the features.

1 Figure 1.1: Model potential energy surface showing minima, transition states, a second order saddle point, reaction paths and a valley ridge inﬂection point (from reference [2]); (b) additional investigation of the IRC path connecting the stationary points on the PES

The PES, which is a function of the nuclear geometry, can be understood as a hilly landscape, with valleys, mountain passes and peaks, where reactant or products correspond to the positions of the minima in the valley, while transition states corresponds to ﬁrst-order saddle point. Except in very simple cases, the potential energy surface cannot be obtained from experiment. However, the ﬁeld of computational chemistry has developed a wide array of methods for exploring potential energy surface, allowing to calculate properties of transition states and reaction intermediates not accessible to experiments and explore the reaction path connecting the transition state with reactants and products, thus providing a more detailed information into the mechanism [2,3].

1.2 Concerted and Two-steps Mechanisms

The chemical events by which the overall chemical change occurs can take place in one or in sequence of elementary steps. When the chemical process takes place in a single kinetic step the reaction mechanism can be deﬁned as concerted. In contrast, when the chemical process takes place in two-kinetically distinct steps, via a stable

2 intermediate, it can be deﬁned as a two-step reaction. Furthermore, a concerted mechanism can involve a number of chemical events, leading to a synchronous or asynchronous mechanism, where the former refers to a process where all the bond- making and bond-breaking processes take place in unison, while the latter refers to a reaction where the changes in bonding take place in a sequential way [4,5].

1.3 Applications to Systems of Interest

The studies described in this dissertation represent a series of studies of diverse chemical systems, which address topics of interest in their individual subject areas, which relevance range from biological to industrial applications, but which also illustrate the challenges facing the computational chemist, i.e to establish qualitative as well quantitative theoretical model for the understanding of reaction mechanism, as well as, to extent this models to more complex systems. Three diﬀerent chemical process will be studied:

i Proton Transfer (PT) reaction in amino acids and in small molecules.

ii Activation of H2 by non-metal-carbene systems. iii Non-Enzymatic and Enzymatic Mechanism of cis-trans Isomerization of peptide bond.

All these processes are analyzed based on the use of Density Functional Theory (DFT) as the main theoretical framework, and the use of concepts developed by our group, Reaction Force (F (ξ)) and Reaction Electronic Flux (REF) as key elements for the understanding and characterization of the reaction mechanism of chemical reactions. The ﬁrst chapter of this dissertation is an introduction to Density functional Theory (DFT). This chapter also provides a detailed rationalization of the concepts

3 of Reaction Force and Reaction Electronic Flux, which have been used along this work for the understanding and characterization of the chemical process under study. Chapter3 and Chapter4 mainly focus on the study of Proton Transfer (PT) processes in two biologically relevant systems: thioformic acid,which functional group plays an important role in the catalytic activities of enzymes such as cysteine or serine proteases, and amino acids, the building blocks of proteins. In these systems the solvent effects and the participation of a water molecule in the process are studied in detail. In Chapter3 the intramolecular ( iPT) and water-mediated (wPT) reactions in thioformic acid are studied as basic models for characterizing the catalytic effect of a single water molecule on the process. In Chapter4 the influence of the amino acid side chain on the proton transfer process and the effect of a second water molecule, which is not directly participating in the proton transfer, but acts as donor or acceptor to the reactive one is addressed. In these systems, the different effects over the activation barrier due to the participation of a single water molecule is discussed and rationalized by using the reaction force and reaction electronic flux concepts, together with electronic properties based on conceptual DFT.

In Chapters5 and6 a comprehensive study of H 2 activation reaction by alkyl(amino), diamino and diamido carbene systems is presented. H2 is a nonpolar, poorly reactive molecule under ambient conditions. Its activation, which is relevant in several industrial and biological processes, has usually required the participation of a metal center.

Motivated for recent experimental evidences showing H2 activation by nonmetallic stable alkyl amino carbene systems, in these chapters the electronic properties controlling the reactivity of carbene systems and the mechanism by which the activation takes place are elucidated. The electronic activity taking place during the reaction is described through the Reaction Electronic Flux, making possible to elucidate the chemical event leading the hydrogen activation process and to assign the energetic cost associated to them.

4 Finally, in Chapter7 the cis-trans isomerization of prolyl bonds is addressed. First, the chemical aspects of the non-enzymatic peptide bond isomerization are studied employing the N-acetylproline methylamide system (Ac-Pro-NHMe) as a model system, the solvent effect and the the autocatalytic non-enzymatic mechanism and its effect on the activation barrier are also discussed. Then, the enzymatic cis-trans isomerization reaction within the Prolyl isomerase PIN1 enzyme is studied. PIN1 specifically catalyses the isomerization of pSer-Pro or pThr-Pro peptide bonds, which is important for the regulation of a number of biological processes. In this chapter the molecular mechanism by which PIN1 catalyzes the process is studied through quantum mechanical/molecular mechanical (QM/MM) methods within the framework provided by the Mean Reaction Force (MRF) analysis that characterizes the electronic and structural free energy contributions to the activation energy. Because of the breadth of topics discussed in this document, additional background for each topic will be presented in the following chapters.

5 2

Introduction

2.1 Theoretical Background.

Molecular systems, as studied by chemists, are built up of electrons and nuclei. The basic interactions in those systems are electrostatic or Coulombic: An electron at position r is attracted to a nucleus of charge Z at R by the potential energy −Z/|r − R|, a pair of electrons at r and r0 repel one another by the potential energy 1/|r −r0|, and two nuclei at R and R0 repel one another as Z0Z/|R − R0|. The electrons must be described by quantum mechanics, while the more massive nuclei can sometimes be regarded as classical particles. The framework provided by Bohr-Oppenheimer approximation allows the simultaneous treatment of electrons and nuclei. This is more or less the general picture that rules practically every chemical system [6]. But there is still a long path from these general principles to theoretical prediction of the structures and electronic properties of atoms and molecules. Shortly after Schr¨odinger’s equation for the electronic wave function was formulated and validated for simple small systems like H and He, Dirac declared that chemistry can be explained through quantum chemistry, and that the only diﬃculty lies on the

6 mathematical treatment of these systems and the complexity of the equation to be computed [7]. In fact it is only for one-electron systems, such as the hydrogen atom, that Schr¨odinger’s equation has an exact analytical solution. Even for two-electron

molecules such as H2, numerical solutions are needed, and as the system becomes larger the computational complexity exponentially grows. As a result, approximated numerical solutions are the only practical option for the study of chemical systems, with a compromise between accuracy and computational cost. Despite somewhat discouraging Dirac’s remark, the great challenge of solving the Schr¨odingerequation for realistic situations opened a whole new area of chemistry, named Ab initio quantum chemistry. At present, a plethora of techniques are available to study molecular energetics, chemical reactions, and a whole range of chemical properties without any experimental input. A twofold classiﬁcation can be made [8], wave function based ab initio methods (such as Hartree-Fock) and density functional theory (DFT) that uses the electronic density to obtain the energy eigenvalue. In this thesis, the focus mainly lies on the density functional method, both from a conceptual as well as from a computational viewpoint.

2.1.1 Density Functional Theory

The formulation of the Hohenberg-Kohn theorems in 1964 [9] provided the starting point for the development of fundamental DFT, yielding all basic ingredients for a complete many-body theory. In a next step, Kohn and Sham [10] introduced orbitals within the formalism, which put DFT as an important computational tool within modern chemistry, representing an alternative to introduce electron correlation on a single-determinant wave-function at a very low cost (for text books, see Refs. [11,12]). In addition to these developments, density functional theory has provided an excellent framework to deﬁne a variety of well-known chemical concepts, such as the chemical potential, hardness and softness. This branch of DFT, named Concep-

7 tual density functional theory (cDFT) or chemical DFT [13, 14], has signiﬁcantly improved the understanding of chemical reactivity. The ﬁrst theorem of Hohenberg and Kohn (HK) [9] states that the external potential υ(r)(i.e. due to the nuclei) is a functional of the ground state electron density, υ(r)[ρ(r), r]. Additionally, the ground state density determines the number of electrons, N, Z ρ(r)dr = N (2.1)

It follows from the theorem that ρ(r) determines the Hamiltonian operator Hˆ and all other electronic properties of the system. Therefore, one may indeed choose the ground state electron density, rather than the N-electron wave function, as the fundamental variable for treating electronic systems. Consequently, the ground state energy of a N-electron system in an external potential υ(r), can be exactly expressed as a functional of the one electron density ρ(r).

Z E[ρ(r)] = F [ρ(r)] + υ(r)ρ(r)dr, (2.2)

Here F [ρ(r)] is called the universal HK-functional, containing the electronic kinetic

energy T [ρ(r)] and the electron-electron interaction operators Vee. Both T [ρ(r)] and

Vee[ρ(r)] are well-deﬁned but unknown functionals of the density. The second Hohenberg-Kohn theorem [9] establishes the variational principle for the ground state electron density ρ(r), i.e. the one which minimizes E. For the optimal ρ(r), subjected to the constraint that the density should at all times integrate to N = R ρ(r)dr, the energy will not change upon variation of F [ρ(r)]. Within a variational calculation this constraint is introduced via the method of Lagrange multipliers, yielding the variational condition:

Z δ E[ρ(r)] − µ ρ(r)dr − N = 0 (2.3)

8 where µ is the Lagrange multiplier. The diﬀerential Euler-Lagrange equation resulting from Eqn. 2.3,

µ = υ(r) + δF [ρ(r)]/δρ, (2.4) is the analogue of Schrödinger’stime-independent equation [14]. The physical significance of µ was later recognized by Parr and co-workers [15]. They expressed µ as the partial derivative of the systems energy with respect to the number of electrons at fixed external potential υ(r), i.e. the negative of the electronegativity, as proposed in the early 1960s by Iczkowski and Margrave [16]:

∂E µ = = −χ (2.5) ∂N υ(r)

By working with a 3-dimensional functional (the density) instead of the more complex 3N-dimensional wave functional, the HK variational theorem had the character to revolutionize electronic structure theory, unfortunately, the HK theorems did not provide any practical way to obtain the universal energy functional deﬁned in Eq. 2.2. It was the work made by Kohn and Sham in 1965 [10] which ﬁnally revolutionized and paved the way for the later success of DFT. They started from a system of N electrons noninteracting showing the same electron density of the real interacting system, for which the total energy and the Euler equation are [17] :

Z δT E[ρ(r)] = T [ρ(r)] + υ (r)ρ(r)d(r); µ = s + υ (r) (2.6) s s δρ(r) s

The exact kinetic energy of this system, Ts[ρ(r)], can be used as an approximation to the kinetic energy operator of the interacting system.

F [ρ(r)] = Ts[ρ(r)] + J[ρ(r)] + Exc[ρ(r)] (2.7) 9 where J[ρ(r)] is the classical electron-electron repulsion term and Exc[ρ(r)] is the exchange-correlation functional, which contains the diﬀerence in both kinetic and potential energy between.

Exc[ρ(r)] = F [ρ(r)] − Ts[ρ(r)] − J[ρ(r)] (2.8)

Hence, Exc[ρ(r)] is the component of F [ρ(r)] which takes care of the non-classical part of the potential and kinetic energy related to electron interactions.The exchange and correlation energies are defined together despite the fact that the exact mathematical representation of the exchange energy is well known in terms of a Fock-like expression. This is because there is a cancellation of errors in approximations to the exchange- correlation term by defining the two together. The exchange-correlation potential is defined as the functional derivative of the exchange correlation energy with respect to the density: δE [ρ] υ [r, ρ(r)] = xc (2.9) xc δρ(r)

In this way the Euler equation is expressed as follows,

δT µ = υ (r) + s (2.10) eff δρ(r)

and the eﬀective potential is given by:

δJ[ρ] δE [ρ] υ (r) = υ(r) + + xc (2.11) eff δρ(r) δρ(r) where the only unknown term is the exchange-correlation potential. Therefore, the

solution for the real system with external potential υeff (r) can be found by solving the set of equations, named the Kohn-Sham equations,

1 [− ∇2 + υ (r)]φ (r) = φ (r) (2.12) 2 eff i i i

10 where υeff (r) is an external eﬀective potential in which the particles are moving,

φi are the (orthonormal) spin-orbitals (KS orbitals). The electronic density, ρ(r), is

obtained by summing over the occupied Kohn- Sham orbitals, φi:

X 2 ρ(r) = |φi(r)| (2.13) i

and is, in principle, the exact density of the interacting system. The total energy of the interacting electronic system is expressed as a sum of functionals of the density

Z E[ρ(r)] = Ts[ρ(r)] + J[ρ(r)] + Exc[ρ(r)] + υ(r)ρ(r)dr (2.14)

To solve a problem, one need only approximate the exchange-correlation energy and

solve eqns. 2.12-2.13 self consistently. A ladder of approximations to construct Exc as a function of local ingredients at r has been proposed [18]. Breakthroughs over the past two decades [19–22] have led to the development of functionals capable of remarkable accuracy and breadth of applicability across the periodic table, although it is important to note that there remain limitations as well [23].

2.1.2 Chemical Reactivity Indexes in DFT

The fundamental precept of the density functional theory of chemical reactivity is that quantities measuring the response of the energy with respect to various per- turbations (as a change in the number of electrons in the molecule or a change in external electric ﬁelds) may be regarded as reactivity indices [24]. The variation of the electronic energy respect to N and υ(r), which constitute the canonical ensemble, may be expressed up to second order as [25]:

Z 2 ∂E δE 1 ∂ E 2 dE = dN + dυ(r)dr + 2 (dN) (2.15) ∂N υ(r) δυ(r) N 2 ∂N υ(r) | {z } | {z } | {z }

µ ρ(r) η

11 Z 2 ZZ 2 δ E 1 δ E 0 0 + dυ(r)drdN + 0 dυ(r)dr dυ(r )dr δυ(r)∂N 2 δυ(r)δυ(r ) N | {z } | {z }

f(r) β(r, r0) where r is the position vector, µ the electronic chemical potential, ρ(r) the electron density, η the hardness, f(r) the Fukui function, and β(r, r0) the linear response function. The chemical potential, hardness and Fukui function are well established chemical DFT descriptor that have resulted fundamental for the characterization of the chemical process under study (Chapter3-Chapter7). The next paragraphs will provide a brief descriptions of these indices and their relationship with chemical concepts. In this Thesis emphasis has been payed on the theoretical analysis of the reaction electronic ﬂux concept, derived from the chemical potential, which is also introduced in the next section.

Electronic Chemical Potential and Electronegativity

Electronegativity is an old idea originally introduced by Pauling in 1932 that describes the capability of an atom in a molecule to attract electrons [13, 26]. Pauling quantified this concept through thermodynamical arguments relating bond energies. A few years later, Mulliken proposed a simple definition of electronegativity, namely the arithmetic average of ionization potential (IP) and electron affinity (IP) [27],

1 χ ≈ (IP + EA) (2.16) 2

In this way the chemical potential can be numerically obtained as follows:

1 µ ≈ − (IP + EA) (2.17) 2

The idea of electronegativity as a chemical potential was later proposed by Iczkowski and Margrave [16], who pointed out that the Mulliken deﬁnition is just the ﬁnite

12 difference approximation to a partial derivative of the energy, E, versus the number of electrons. In this context, µ, the Lagrange multiplier in Eqn.2.4, naturally acquires its chemical significance within the cDFT framework. Kohn, Becke and Parr [28] have emphasized the chemical significance of µ as characterizing the escaping tendency of electrons from the equilibrium system.

Further approximation using the Koopmans theorem [29](I = −εh and A = −εL) allows to write µ in terms of the energy of the frontier HOMO and LUMO molecular orbital energies,

1 µ ' (ε + ε ) (2.18) 2 L H

Eq. 2.17/2.18 provide a way to determine numerical values of µ all along the reaction coordinate, thus leading to µ(ξ).

Hardness and Softness

The hardness and softness terms were originated from Pearson’s Hard and Soft Acids and Bases (HSAB) principle [30], who concluded that hard acids preferably interact with hard bases and soft acids with soft bases. A formal deﬁnition of hardness was then given by Parr and Pearson [31], as the second partial derivative of the energy with respect to the number of electrons. The global softness, S, is simply equal to its inverse [32].

1 1 η ≈ (IP − EA) ≈ ( − ) (2.19) 2 2 LUMO HOMO

1 S = (2.20) η

The hardness can be thought of as a resistance to charge transfer, while the softness as a measurement of the ease of transfer. In this context, the principle of maximum

13 hardness (PMH), which states that molecules arrange themselves to be as hard as possible [33] has been also formulated. From this principle, it is expected that along the reaction path the hardness of a chemical species should go through a minimum at the transition state and through maxima for reactants and products [34]. However the PMH does not hold well in many cases. Its formal proof, given by Parr and Chattaraj [33], requires that the electronic chemical potential and the external potential must remain constant, which is impossible to satisfy during the course of a chemical reaction. Chandra and Uchimaru [35], based on a finite difference approximation, have showed that the hardness profile passes through an extremum at the point where the first energy derivatives of N − 1 and N + 1 electron systems cancel that of the N electron:

dE dE dE N+1 + N−1 = 2 N (2.21) dξ dξ dξ

dEN Since dξ |TS = 0 dE dE N+1 | = − N−1 | (2.22) dξ TS dξ TS even though the chemical potential does not remain constant along the process.

Reaction Electronic Flux

The variation of µ along the reaction pathway, µ(ξ), leads to the concept of reaction electronic ﬂux (REF), deﬁned as the negative derivative of the chemical potential [36]:

dµ J(ξ) = − (2.23) dξ

The J(ξ) proﬁle has proved to be useful in the characterization of electronic activity that is actually taking place along the reaction coordinate [36–38]. In this way, the descriptor has been used along Chapter3-Chapter7 not only to characterize the

14 electron activity taken place along the process but also to assign the energetic cost associated to every chemical events, A more detailed analysis of this concept has been carried out in Chapter5 and Chapter6, where the electronic activity taking place during a chemical reaction has been characterized through a phenomenological decomposition of J(ξ) in terms of electronic polarization and transfer contributions Jp and Jt, respectively [37–39]:

J(ξ) = Jp(ξ) + Jt(ξ) (2.24)

The polarization ﬂux can be determined by partitioning the reactive complex in molecular fragments and taking advantage of the counterpoise method, which treats the fragments separately along the reaction coordinate [40–42]. As a result, chemical potential of each fragments are determined along the reaction coordinate, this leads

i i to define individual fluxes, Jp(ξ),associated to fragment i. Jp(ξ) is interpreted as the electronic activity of the fragment i due to the remaining fragments that form the supermolecular system. In this context, the polarization flux is defined as the sum of the n fragments fluxes [38]:

n X (i) Jp(ξ) = Jp (ξ) (2.25) i=1

N dµ J (i)(ξ) = − i i (2.26) p N dξ

where Ni is the number of electrons associated to fragment i and N is the total number of electrons of the system. For example, for a two–fragment supermolecule:

N dµ N dµ J (ξ) = J (A)(ξ) + J (B)(ξ) = − A A − B B (2.27) p p p N dξ N dξ

whit NA + NB = N and µA(ξ) and µB(ξ) the chemical potentials of the fragments A and B, respectively. In this context, the polarization ﬂux of fragment i accounts for

15 the deformation of its electronic density formed by Ni electrons, in response to the external ﬁeld created by the other fragment(s). Then, the ﬂux associated to electronic transfer is then given by,

n dµ X Ni dµi J (ξ) = J(ξ) − J (ξ) = − + (2.28) t p dξ N dξ i=1

This partition has been utilized in the analysis of the reaction mechanism of the

H2 activation by carbene systems in Chapter5. Interpretation of J(ξ) came out making the analogy to thermodynamic concepts [39, 43], so that J(ξ) > 0 can be associated to spontaneous electron activity, driven by bond strengthening and/or formation. J(ξ) < 0 is associated to non-spontaneous electron activity and is mainly related with bond weakening and/or breaking processes. Finally J(ξ) = 0 has been related to the absence of electron activity, other than the basal activity observed at equilibrium. It is worth to mention that a more deep analysis of J(ξ) can be made from inspection of the numerical deﬁnition of µ(ξ) in terms of ionization potential and electron aﬃnity

in Eqn. 2.16, µ ≈ 1/2[EN+1 − EN−1], such that J(ξ) can be expressed in terms of two components: 1 dE 1 dE J(ξ) = − N+1 + N−1 (2.29) 2 dξ 2 dξ

dE Introducing the reaction force concept [44], F (ξ) = − dξ , REF can be expressed as:

1 J(ξ) = (F − F ) (2.30) 2 N+1 N−1 where FN+1 and FN−1 are respectively, the reaction forces for the (N +1) and (N −1) electron systems along the reaction coordinate ξ. The REF will be equal to zero when the reaction forces satisfy:

FN+1 = FN−1 (2.31) 16 Additionally, the condition for REF to have an extremum along the reaction coordinate is dJ(ξ) dF dF = 0 ⇒ N+1 = N−1 (2.32) dξ dξ dξ

Moreover, J(ξ) will be positive if FN+1 > FN−1 and negative otherwise. So spontaneous rearrangements of the electron density occurs when the reaction force of the anionic system is larger that of the cationic one. The REF proﬁle can have an extrema at any point along the reaction coordinate if Eqn. 2.32 is satisﬁed, which may not necessarily happen at the transition state. An

special case will be symmetrical reaction profiles, where FN+1 = FN−1 = 0 at the transition state. In these cases, a zero value of J(ξ) will be always obtained at the transition state. Asymmetry processes will differ from this behavior. Similarly, one can make the whole analysis of the REF profile based on the opera- tional definition of µ using the HOMO and LUMO orbital energies (Eq. 2.16). In this case the components of the REF will be given by:

1 d 1 d J(ξ) = − HOMO − LUMO (2.33) 2 dξ 2 dξ

Where the variation of J(ξ) along the reaction coordinate will depend on the change of the HOMO/LUMO orbital energies. J(ξ) will be zero if both slopes are equal and of diﬀerent sign, and it will show an extremum if the second derivative of the orbital energies are equal and of diﬀerent sign. In this framework, the decrease(increase) of the LUMO derivative will contribute to positive(negative) values of J(ξ), while increase(decrease) of the HOMO derivative will contribute to negative(positive) values.

In analogy to FN+1 and FN−1, the derivative of the HOMO and LUMO energy will provide information about how the system is aﬀected under addition or subtrac- tion of the electrons, respectively. Viewed as a chemical process it corresponds to

17 nucleophilic and electrophilic attack, respectively, or from the point of view of the substrate to changes in the electrophilic and nucleophilic character, respectively.

Fukui function

Local descriptors reflect the properties of the different sites within the molecule and therefore may vary from point to point in space. They are directly related to the electron density distribution and to the change of it under the influence of an approaching reagent. Fukui first recognized the importance of frontier orbitals as principal factors gover- ning the ease of chemical reactions and the stereoselective path [45]. Later, Parr and Yang [46] demonstrated that frontier theory can be rationalized from DFT. They defined the Fukui function of a molecule as the variation in the electronic density ρ(r) upon changing the number of electrons N in the system:

∂ρ(r) f(r) = (2.34) ∂N υ(r) f(r) reﬂects the ability of a molecule to accept (donate) electrons from (to) another system. Due to the discontinuity of the electron density with respect to the number of electrons, two Fukui functions, f +(r) and f −(r), the right and left-hand side derivatives of Eqn. 2.34, have been deﬁned, the former measures the electrophilic character at point r in a molecule and the later the nucleophilic character at point r. The Fukui index on an atom k is obtained through integration within the atomic basin of atom k [47],

+ fk = pk(N + 1) − pk(N) (2.35) with pk(N + 1) and pk(N) the electronic populations on atom k in the (N + 1) and N electron systems, respectively. Natural population analysis (NPA) will be used to estimate the Fukui indexes. Furthermore, the electrophilic and nucleophilic character

18 can be written in terms of its local contributions [48–50], respectively:

+ + − − ωk = fk ω ; Nk = fk N (2.36) where ω = µ2/2η is the global electrophilicity of the system and N(x) = −[IP (x) − IP (TCNE)] corresponds to the nucleophilicity index. In 2005, Morell et al. [51] proposed a new descriptor for chemical reactivity, termed the dual descriptor:

∆f(r) ' f +(r) − f −(r) ' ρLUMO(r) − ρHOMO(r) (2.37) which allows the electrophilic and nucleophilic regions within a molecule be detected simultaneously; it will be positive in electrophilic regions and negative in nucleophilic regions. This descriptor will be used in the Chapter5 and Chapter6, in order to characterize to nature of the carbene systems under study, as well as in Chapter7 with the aim to characterize electronic aspects of the cis-trans isomerization process. Two other local descriptor related with the Fukui function are the local softness and local hardness. In 1985, local softness was deﬁned by Yang and Parr [32]:

∂ρ(r) s(r) = (2.38) ∂µ υ(r) s(r) has a direct connection with the Fukui function. Applying the chain rule of diﬀerentiation, one obtains:

∂ρ(r) ∂N s(r) = = f(r)S (2.39) ∂N υ(r) ∂µ υ(r)

As easily seen s(r) integrates to S as f is normalized to unity. In contrast, defining a corresponding local quantity for the hardness has been difficult [52]. The first definition for it was proposed by Berkowitz [53]:

δµ η(r) = (2.40) δρ(r) υ(r) 19 However, in contrast to the local softness, it does not integrate to the global hardness. An attempt to fix this drawback has been recently proposed by Gál et al. [54]. Based in the fact that the chemical potential in DFT emerges as an additive constant term in the number conserving functional derivative of the energy, they defined a local chemical potential, which once is differentiated respect to the number of electrons leads to local hardness that integrate to the global hardness.

∂µ(r) η(r) = (2.41) ∂N υ(r)

where µ(r) is the local chemical potential

ρ(r) µ(r) = µ = f(r)µ (2.42) N

Eq 2.41 gives the following expression for the local hardness:

∂f(r) η(r) = µ + f(r)η (2.43) ∂N

It interesting to note that the local chemical potential deﬁned in Eqn. 2.42 would provide a starting point for the analysis of the reaction electronic ﬂux concept in terms of the constituent atoms of a systems. Even though the present work does not include direct application of this partition, it is suggested in order to be considered in future works.

2.1.3 The Reaction Force.

Derivatives of the potential energy of a molecular system are of fundamental importance in any aspect of theoretical chemistry. The Hellmann Feynman theorem [55] gives a viewpoint in the origin of these forces; according to it, the force acting on a

20 nucleus α is the sum of contributions of the other nuclei and of all the electrons:

Fα = −∇hΨ|H|Ψi = −hΨ|∇H|Ψi (2.44) Z n−n = − ρ(r)i(r)dr + Fi (2.45)

∂Vαi where H is the electronic Hamiltonian, ρ(r) is the electron density at r, and i = ∂ri is the electric ﬁeld at any point r due to the nucleus α. In the context of chemical process, the reaction force concept has been introduced by Toro-Labb´eas the variation of the potential energy E(ξ) of the system with respect to the reaction coordinate ξ [44]:

dE F (ξ) = − (2.46) dξ which has been shown to be a scalar quantity [56]. From the expression in Eqn. 2.46 the force can be expressed as follows,

N d X 1 d Z d F (ξ) = − hψ | − ∇2|ψ i − υ (r)ρ(r)dr − V (2.47) dξ i 2 i dξ eff dξ nn i

where υeff (r) is an eﬀective potential in which the particles are moving. This implies that the force acting along the chemical process is just the classical electrostatic attraction exerted on the nucleus in question by the other nuclei and by the electron charge density distribution for all electrons. The electronic term of the

force is given by the electronic density ρ(r) and the eﬀective potential υeff (r), while

d the structural term − dξ Vnn gives the total force acting on the ith nucleus from all other nuclei. For an one-step reaction, the reaction force profile has a minimum and a maximum at the inflection points of E(ξ), located at ξ1 and ξ2. This pattern allows three regions to be defined, namely, reactant, transition state, and product, with well-established tendencies as evidenced in refs. [57–60].

21 The reactant region (ξR ≤ ξ ≤ ξ1), involves preparation of reactants to chemical transformation and is dominated by structural rearrangements. This step of the

reaction requires an amount of work W1,

Z ξ1 W1 = − F (ξ)dξ (2.48) ξR

The transition state region (ξ1 < ξ < ξ2) is governed by the transition from activated

reactants at ξ1 to activated products at ξ2, and involves bond breaking/forming processes accompanied by strong ﬂuctuations in some electronic properties. The

work that is necessary to reach the TS from ξ1 is W2,

Z ξTS W2 = − F (ξ)dξ (2.49) ξ1

Finally the product region (ξ2 ≤ ξ ≤ ξP ), is mainly dominated by the relaxation process toward the equilibrium geometry of the product. These evidences can be understood from the predominance of either the structural and/or electronic term in Eqn. 2.46. Within this scheme the energy barrier, ∆E6=, can be written as the sum of two contributions

6= ∆E = [E(ξTS) − E(ξR)] = W1 + W2 (2.50)

W1 is primarily the energy needed to overcome the resistance to the structural

changes in the first region of the process, while W2 supports the first stage of the transition to products. One important consequence of decomposing ∆E6= into its two components is that it reveals how an external agent, such as a solvent or a catalyst, affects the process. Is its influence mainly upon the structural changes that occur

upon W1, or is it upon electronic factors, that is, W2?[38,59,61–63].

R ξ2 For the forthcoming analysis, it is also deﬁned: W3 = − F (ξ)dξ and W4 = ξTS

22 − R ξP F (ξ)dξ such that the reverse process can be analyzed within the same frame- ξ2 work and its activation energy expressed as:

6= ∆Er = [E(ξTS) − E(ξP )] = −W3 − W4 (2.51)

Finally, the reaction energy can be recovered as follows:

◦ ∆E = [E(ξP ) − E(ξR)] = W1 + W2 + W3 + W4 (2.52)

The components of the Energy and the Reaction Force

As part of this work, it has been shown [62] that the energy change along the reaction coordinate can be expressed in terms of the diﬀerent contributions to the total energy, namely the electronic kinetic energy Ek(ξ) and the potential energy components, the external potential Ene(ξ) and the repulsive terms Enn(ξ) and Eee(ξ):

E(ξ) = Ek(ξ) + Eee(ξ) + Ene(ξ) + Enn(ξ) (2.53) such that, the reaction force becomes:

F (ξ) = Fk(ξ) + Fee(ξ) + Fne(ξ) + Fnn(ξ) (2.54)

The reaction works are then written as:

Wi = Wi(k) + Wi(ee) + Wi(ne) + Wi(nn) (i = 1, 4) (2.55) such that, further partition of the activation energy emerges:

6= ∆E = W1 + W2

= [(W1 + W2)k + (W1 + W2)ee (2.56)

+(W1 + W2)ne + +(W1 + W2)nn]

A similar expression can be obtained for the reaction energy. Thus, the reaction force provides a rational way for a detailed partition of the activation energy. This partition will be used in the forthcoming analysis in Chapter3.

23 Mean Reaction Force

In analogy to the reaction force as defined in Eqn. 2.46, the concept of Mean Reaction Force has been recently defined [64]. It is defined as the negative derivative of the free energy along the reaction path,

dA hF (ξ)i = − (2.57) dξ

and has proven to unveil valuable mechanistic insights in catalysis at interfaces [64]. Due to its derivation from the free energy along a reaction path, it includes – within a correct description – the inﬂuence of the environment on reaction mechanisms, which is crucial in enzyme catalysis. It also provides a direct access to the characterization of diﬀerent processes taking place along the path and a rational partitioning of the activation energy ∆G6= in terms of its contributions.

6= ∆G = [G(ξTS) − G(ξR)] = W1 + W2 (2.58)

These terms can be mainly associated to structural or electronic free energy contributions to the activation free energy [59, 65]. Additionally, the reaction energy is expressed as follows

◦ ∆G = W1 + W2 + W3 + W4 (2.59)

In analogy to the expresion given in Eqn. 2.50-2.52. These contributions are crucial to uncover the origin of enzyme catalysis in general and it will be use in the study presented in Chapter 7.2.

24 2.2 Hypotheses

• The complementary use of reaction force, reaction electronic ﬂux and other DFT-based descriptors allows to characterize the reaction mechanism of processes under study: i) Proton Transfer (PT) reaction in amino acids and in

small molecules, ii) Activation of H2 by non-metal-carbene systems and iii) Non-Enzymatic and Enzymatic Mechanism of cis-trans Isomerization of peptide bond.

• The Reaction Electronic ﬂux allows to determine and quantify the electronic activity taking place along the chemical processes.

• The joint use of local and global reactivity descriptors provides insights about the reaction mechanism, allowing to characterize key aspects about the reactivity of a chemical system.

• The electrophilic/ nucleophilic nature of carbene systems are a fundamental

criteria for understanding its reactivity over H2. In this regard, the dual descriptor (Eq. 2.37) will help to identify the nature of these systems, as well as the favorable/unfavorable orbital interactions and its inﬂuence on the activation process.

• The catalytic eﬀect arising either from intramolecular interaction or enzymatic catalysis in the cis-trans isomerization of peptide bond reactions can be understood within the framework provided by the reaction force concept. In particular, enzymatic catalysis can be adequately addressed by use of QM/MM methods combined with the mean reaction force concept.

25 2.3 Goals

2.3.1 General Goals

The objective of the present work is to provide a detailed description of the mechanism behind important chemical reactions, which relevance range from biological to industrial applications, by means of computational and theoretical tools. Three different chemical process will be studied: i) Proton Transfer processes in amino acids and in small molecules, where the catalytic effect of water is addressed; ii) Ac- tivation of H2 by non-metal-carbene systems and iii) Non-Enzymatic and Enzymatic Mechanism of cis-trans Isomerization of peptide bond. On the other hand, from a methodological point of view, the objective is to provide a general framework to study chemical processes, based in the concepts of Reaction Force and Reaction electronic flux.

2.3.2 Speciﬁc Goals Proton Transfer Processes

• Analyze the role played by the solvent in PT reactions, in particular the catalytic eﬀect of a single water molecule on the activation barrier. To this aim, the intramolecular (iPT) and water-mediated (wPT) reactions in thio-carboxylic acid are studied as basic models.

• Quantify the eﬀect of a water on PT reactions in amino acids, characterize the physical nature of the energy barriers, and address the inﬂuence of the amino acid side chain on the process.

• Analyze the eﬀect of a second, not intervening water molecule, that could changes the proton acceptor and donor properties of the reactive water molecule modulating the reaction mechanism.

26 Activation of H2 by non-metal-carbene systems

• Elucidate the reaction mechanism of H2 activation by amino-carbene model systems, rationalizing these results in terms of the available experimental results for these systems.

• Assign the energetic cost and the physical nature associated to the chemical events that drive the process along the reaction coordinate through the use of the reaction electronic ﬂux proﬁle.

• Evaluate theoretical descriptors that could be used as a criteria for the cha-

racterization and prediction of the reactivity of carbene systems upon H2

Non-Enzymatic and Enzymatic Mechanism of cis-trans Isomerization

• Provide a detailed understanding of the autocatalytic non-enzymatic mechanism and its inﬂuence on the activation barrier of the cis-trans isomerization of prolyl-peptide bonds.

• Elucidate the catalytic eﬀect of Prolyl-Peptide Isomerase enzyme PIN1 on the cis-trans isomerization of peptides. Also, to provide a detailed picture of this process through the used of the mean reaction force concept.

27 3

The Catalytic Eﬀect of Water on the Proton Transfer Reaction of Thioformic Acid

Proton transfer (PT) reactions play an important role in many chemical and biological processes. A large number of theoretical and experimental studies [66, 67] have been carried out to enrich the information regarding the mechanisms of PTs in tautomeric equilibria and other processes. The role of water as catalyst in chemical reactions has attracted considerable attention in recent years [68–71]. Water can mediate the transfer of a proton through membrane protein proton channels [67,72], in the photosensor green ﬂuorescent protein [73], in the catalysis by carbonic anhydrase [74] and in a number of other process. However many molecular details remain elusive, and the speciﬁc role of a single water molecule as a catalyst still remains unclear. In this context, two mechanism for the PT reaction have been proposed: a direct mechanism where both, donor and acceptor atoms, are concerted to achieve the processes without intervention of solvent molecules, and a water-mediated process, where

Part of this chapter has been previously published as: Fernanda Duarte and Alejandro Toro- Labb´e.Water catalysis of the keto-enol Tautomerization Reaction of Thioformic Acid. Mol. Phys., 2010, 108, 1375.

28 the proton(s) are transferred through water molecules either in a concerted motion or in a stepwise fashion [75]. The water-mediated tautomerization is an example of the water-mediated multiple proton transfer reactions frequently encountered in biochemical processes. In this chapter the reaction mechanism of the intramolecular (iPT) and water- mediated (wPT) proton transfer reaction in thioformic acid (Figure 3.1) are studied by means of the analysis of energy, reaction force and reaction electronic flux- in order to elucidate the catalytic effect of water. In addition, solvent effects including Polarizable Continuum Model (PCM) are also analyzed. Finally, a new partition of the energy barrier is also proposed (Eqns. 2.54-2.56), which in the framework of the reaction force concept can be a useful to study chemical processes.

3.1 Introduction.

Thiol-thione tautomerism of thioformic acid and their derivatives has been previously studied focused on the important role that this functional group plays in chemistry, biology and pharmacy [57, 58, 76–79]. Those studies have shown discrepancies con- cerning the solvent eﬀect in the stabilization of tautomeric forms: whereas Kato et

Figure 3.1: Sketch of the intramolecular (iPT) and water assisted (wPT) proton transfer reactions.

29 al [77] reported that the thione acid exists predominantly in polar solvents at very low temperatures, Jemmis and co-workers [80] found from ab initio calculations, including continuum treatments of the solvent, that the thione forms HC(S)OH is less predominant irrespective of the solvent polarity. Attempts to solve this discrepancy were made by Delaere et al. [78], who found that intermolecular interaction with the solvent play a crucial role in the thiol-thione equilibrium, stabilizing the thione isomers. Additionally Toro-Labb´e et al. [81] found that, by including continuum treatments of the solvent, the activation barrier is only slightly aﬀected.

3.2 Computational Methods.

For geometrical optimizations the B3LYP [82–85] hybrid functional with the 6- 311++G** basis set was used. Calculations in solution were performed with the polarizable continuum model (PCM) [86] as implemented in the Gaussian 03 package, where the liquid is assimilated to a continuum characterized by a dielectric constant of 78.39 for water. Moreover, the default cavity was modiﬁed by adding individual spheres to hydrogen atoms involved directly in the proton transfer, using the keyword SPHEREONH. The minimum energy path in going from reactants to products were calculated through the intrinsic reaction coordinate procedure (IRC) [87, 88]. Using the geometries obtained from the IRC procedure, molecular properties were determined through single point calculations. Natural bond orbital (NBO) [89] analysis was performed to identify the atoms or fragment involved in the electronic ﬂux taking place during the reaction. All calculation were carried out using the Gaussian 03 program [90].

30 3.3 PT reactions in gas phase: catalytic eﬀect of a water molecule.

The energy and reaction force profiles for both, iPT and wPT, processes in gas phase are presented in Figure 3.2 and the energetic parameters are displayed in Table 3.1. The vertical lines, displayed in Figure 3.2 and in the forthcoming figures, indicate the limits of the reaction regions that have been determined from the critical points of the reaction force profiles. The iPT reaction presents an energy barrier about three times higher than in wPT. In addition iPT was found to be thermodynamically unfavorable with ∆E◦= 2.2 kcal/mol, while in wPT the reaction was found to be exergonic by 1.2 kcal/mol. As evidenced previously by Daelere et al. [78] hydrogen-bonded interactions in O-H···O complexes are stronger than in S-H···O complexes, and thus play a crucial role in

35 35 iPT wPT 30 30 25 25 20 20 15 15 10 10

Energy [kcal/mol] 5 Energy [kcal/mol] 5 0 0 -5 -5 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

30 30 iPT wPT 20 20 ] ] ξ ξ 10 10

0 0

-10 -10 Force [kcal/mol* Force [kcal/mol* -20 -20

-30 -30 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ] Figure 3.2: Energy (kcal/mol) and Reaction Force Proﬁle(kcal/mol*ξ) for the iPT (left) and wPT (right) processes.

31 ◦ 6= 6= Table 3.1: Reaction energy (∆E ); forward (∆Ef ) and reverse (∆Er ) energy barriers and the works associated to the diﬀerent processes in the iPT, wPT and wPT(PCM) reactions (Eqns. 2.48-2.49), all values in kcal/mol.

◦ 6= 6= Reaction ∆E ∆Ef ∆Er W1 W2 W3 W4 iPT 2.2 33.3 31.2 23.0 10.3 -10.5 -20.7 wPT -1.2 12.1 13.2 9.6 2.5 -4.6 -8.7 wPT(PCM) -2.0 8.3 10.4 6.6 1.7 -4.6 5.7

stabilizing the thione isomers. The reason the substantial reduction of the energy in wPT is the formation of a six-member cyclic complex (Figure 3.3), stabilized by two hydrogen bonds: O1-H7-O6 and S4-H5-O6. These speciﬁc interactions are absent in iPT, due to a relatively large distance betweens oxygen atom and the H5-S4 bond (2.6 A).˚ Considering only the energies of the bonds involved in the reaction that leads to forming and breaking processes (87.5 kcal/mol for S-H and 110.2 kcal/mol for O-H)

6= 6= it would be expected that ∆Ef <∆Er [57, 76]. However, the reaction involves not

Figure 3.3: Transition state structure of the water assisted proton transfer reaction (bond lengths in A).˚

32 only the S-H cleavage and the O-H bond formation, but also the electronic reordering that brings the CO double bond into a single bond and the CS single bond into a double bond character; in this case, the transfer occurs not only through bond breaking/forming processes, determined by the relative hydrogen donor-acceptor power of sulfur and oxygen atoms [57, 58], but also by electron delocalization in the SCO group, occurring simultaneously with structural rearrangement. It is in these processes where the water molecule can play an important role as a catalyst.

3.3.1 Reaction Force and Reaction Works.

The amount of work associated to each region, obtained using Eqns. 2.48-2.49,

is quoted in Table 3.1. Note that W1 and W2 in iPT are much higher than in wPT; thus, showing that the eﬀect of the water molecule is felt in both preparative and transition regions, being the later mainly aﬀected. W1 in wPT is 41% of the one in iPT, while W2 is just 25% of the value found in iPT. These results show

6= that the effect of a water molecule on ∆Ef is not only facilitating the structural rearrangement needed for the proton transfer to occurs, which is evidenced in the analysis of structural parameters in Figure 3.4. It also affects the electronic activity taking place at the transition state region. Analysis of the evolution of the SCO angle in iPT shows a drastic decrease of this angle at the reactant region, thus suggesting it is a reactive mode in the process, allowing the donor and acceptor atoms to get closer to each other, after it the proton transfer process is the chemical event that drives the reaction. A completely different behavior is found in wPT, in this case the water molecule act as a bridge in the proton transfer leading to a less restrained complex where donor and acceptor groups requires much less structural rearrangements in order to be activated (see Figure 3.4, right).

6= To get a more detailed picture on the energetic barriers, ∆Ef and its contributions

33 W1 and W2 in terms of the nature of the reaction works invested in each region were analyzed. Figure 3.5 displays the percentage distribution of the phenomenological

6= components of W1,W2 and ∆E . It can be noticed that both iPT and wPT

6= reactions present similar distribution for W1 and ∆Ef , they are mainly due to the works associated with the external potential Wne and repulsion terms, which are about 50% of the respective overall value, while the contribution of Wk is practically negligible. For W2, it can be observed that the contribution of Wk is signiﬁcantly large, about 14% for both reactions, thus conﬁrming that the electronic factors play a major role in the transition state region. In addition, it can be observed that the percentage of the external potential contributions to W2 is higher in iPT than in wPT, 52% and 37% respectively. The above analysis suggests that the higher W2 value for iPT, due to the external potential component Wne, is most probably due to coupling between the structural rearrangement and electronic reordering needed to activate the transfer, which is reduced in wPT where the water molecule facilitate this structural rearrangement, thus, causing the reduction of the overall reaction barrier.

iPT wPT 2.8 130 2.8 130 2.6 2.6 2.4 2.4 125 125 2.2 2.2 2 2 1.8 120 1.8 120 1.6 1.6

Distance [A] 1.4 Distance [A] 1.4 115 Angle SCO[…] 115 Angle SCO[…] 1.2 1.2 1 O-H 1 Ow-H H-S H-S 0.8 110 0.8 110 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ] Figure 3.4: Bond distances and angles proﬁles for iPT(left) and wPT(right) reactions.

34 6= Figure 3.5: Phenomenological contribution to W1,W2 and ∆Ef for iPT(light-grey) and wPT(dark-grey) reactions (values in Kcal/mol).

3.3.2 Natural Bond Orbital (NBO) analysis

To characterize the change of the electronic density along the reaction coordinate, the evolution of the Wiberg bond order∗ along the reaction coordinate have been analyzed; their proﬁles are shown in Figure 3.6. In iPT the CO and CS bond order

∗ It refers to the NAO-Wiberg Bond Index, which correspond to the sums of squares of oﬀ-diagonal density matrix elements between pairs of atoms in the NAO basis, and are the NAO counterpart of the Wiberg bond index [91]

35 iPT wPT

O1-C3 O6-H7 2 H-S4 2 O1-C3 H-O1 O1-H7 C3S4 H5-S4 1.5 1.5 H5-O6 C3-S4

1 1

Wiberg Bond Order 0.5 Wiberg Bond Order 0.5

0 0 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ] Figure 3.6: Wiberg Bond order profiles for iPT and wPT reactions. cross each other at the TS, indicating that a maximum electronic delocalization is reached at this point. Delocalization is principally due to hyperconjugation effect† on the O1-C2-S4 fragment, which is increased at the transition state region as evidenced through the NBO analysis, described in the next paragraph. Note that the bond order between the hydrogen atom and donor/acceptor atoms cross each other after the TS, indicating that the electronic reordering in O1-C2-S4 moiety induces the process of electronic transfer, weakening the S4-H5 bond. On the other hand, in wPT, CO and CS bond orders cross each other simultaneously to S4-H5 and H5-O6, at the TS point, while the crossing of O6-H7 and O1-H7 bond orders occurs later. This evidences that the second proton transfer on the O6-H7-O1 fragment is induced by the first transfer on the S4-H5-O6 fragment. This result is also in agreement with the nature of the acceptor/donor atom, the sulfur atom is better donor than oxygen, being the second one much better acceptor than donor. The most important interactions in these systems were analyzed within the framework of the NBO procedure, using second-order perturbation theory [93, 94] (Table 3.2). It can be seen that in iPT and wPT the main stabilization arises from the lone pair of the oxygen(sulphur) atom to the antibonding C-S(C-O), evidencing the

† The hyperconjugation is a quantum effect defined as the stabilizing interaction arising from the overlap off an occupied orbital (sigma or a lone pair) with an empty or partially filled orbital to result in an extended molecular orbital that enhances the stability of the system [92].

36 Table 3.2: Most important interactions between Lewis and non-Lewis orbitals and second order perturbation energy values, E(2), associates to them for reactant, transition state and product structures in iPT and wPT systems.

Reaction Donor (LP) Acceptor BD∗ E(2) iPT (R) S O–C 28.7 O C–S 32.3 wPT (R) S O–C 32.3 O C–S 27.7 Ow H–S 7.1 O1 H–O 3.7 wPT(PCM) (R) S O–C 33.1 O C–S 26.6 Ow H–S 5.9 O1 H–O 3.7 iPT (P) S O–C 17.2 O C–S 52.2 wPT (P) S O–C 14.1 O C–S 60.4 Ow H–O1 22.5 S H–O6 5.0 wPT PCM(P) S O–C 14.5 O C–S 66.1 Ow H–O1 33.4 S H–O6 0.1 hyperconjugative eﬀect in this fragment. Inclusion of water only slightly aﬀects these interactions; it leads to an increase of the S-(CO) interaction and a lowering of the O-C-S one. In addition, in wPT, contribution to the molecular stabilization is further given by the water molecule through the overlap of its oxygen lone pair and the S-H bond and in a lesser extent between the oxygen lone pair of the carbonyl group with O-H bond of the water. At the product state this stabilization, which now arises from the sulphur lone pair to the O-H bond is smaller (5 kcal/mol). However a larger stabilization also arises from the oxygen lone pair toward the O-H bond, which leads to a net stabilization of the thione system.

37 3.3.3 Chemical Potential and Reaction Electronic Flux.

Figure 3.7 shows the chemical potential µ(ξ) and the reaction electronic flux J(ξ) for both reactions, which have been calculated using Eqs.(2.18) and (2.23) respectively. It can be noticed that the most important changes exhibited by these electronic properties occur at the TS region. Additionally, the profiles exhibit different trends confirming that the water participation induces a different mechanism for the PT reactions. In iPT, µ changes strongly along the reaction coordinate, reaching a minimum at the TS, then it increases dramatically to reach its final value at the product. Contrary to this, in wPT, µ is fairly constant in the reactants region, then it increases sharply until reaching a maximum at the TS and then it decreases, passes through a minimum to converge monotonically to the product value. In iPT the electronic activity at the reactants region must probably be due to polarization effect induced by OCS bending mode (Figure 3.4), then it becomes spontaneous (J(ξ) > 0) due to the hypercojugation effect and incipient weakening of the S-H bond and strengthening of C=S bond. Entering the TS region the electronic activity in the iPT reaction is driven by the O-H bond formation process, but then the breaking process of the S-H and C=O double bond takes over and the REF becomes negative. The relaxation process is associated with non spontaneous electronic reordering (J(ξ) < 0), structural changes are necessary for the relaxation process and cleavage of the S-H bond, which is the chemical event that drives the reaction after the transition state. A different behavior is observed for wPT, here the electronic activity out of the equilibria is largely concentrated at the transition state region with two narrow asymmetric peaks in the REF profile, the first one, more intensive than the second one, which emphasize the non-spontaneous nature of the electronic reordering. The electronic activity observed in the limit between the reactant and TS region seems to be driven

38 -100 -100 iPT wPT -102 -102

-104 -104

-106 -106

-108 -108 [kcal/mol] [kcal/mol] µ -110 µ -110

-112 -112

-114 -114

-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

15 15 iPT wPT 10 10 ] ] ξ 5 ξ 5

0 0

-5 -5 REF [kcal/mol* REF [kcal/mol*

-10 -10

-15 -15 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ] Figure 3.7: Chemical potential(kcal/mol) and reaction electronic ﬂux (kcal/mol*ξ) pro- ﬁles for iPT and wPT reactions. by the S-H breaking bond process. Then the electronic reordering becomes highly spontaneous and driven by the formation processes. In summary, the above analysis indicates a more localized electronic activity at the TS region in wPT whereas in iPT some electronic activity is also observed in the reactants and products regions, indicating that in these regions the preparative and relaxation stages of the reaction involve some degree of coupling between electronic reordering and structural changes.

3.3.4 Reactive modes

Chemical reactions can be described as the consequence of molecular collision at an angle that enables energy transfer, and vibrational excitation that leads to bond loosening and cleavage. Therefore insight into the mechanism can be obtained by

39 vibrational analysis, where the reactive modes that activate and drive the process along the pathway can be identiﬁed and followed along the process. Table 3.3 shows the harmonic frequencies and normal modes of vibration for the iPT reaction obtained from frequency calculations at the same level of theory. It is important to note that most of the vibrational modes do not remains the same throughout the iPT reaction, in such case a vibrational correlation diagram, which correlates the vibrational frequencies of the reactant with those of the product through those of the transition state can be establish along the reaction coordinate with help of the symmetry criteria [95]. As can be seen in Figure 3.8, all frequencies are positive at the reactant and product regions. However, once the system enters the transition state region, an imaginary frequency(f2) that corresponds to the transition vector appears (i.e., the one and only normal mode with a negative eigenvalue that characterizes the transition state). This mode is shown in Figure 3.9 and corresponds to the hydrogen motion between the donor and acceptor atoms. It is important to notice that this mode is negative not only at the TS structure but throughout the entire TS region (ξ=0.41-0.6), in accordance with the concept of Zewail and Polanyi who deﬁne a transition region as continuum of transient, unstable states [96,97].

Table 3.3: Harmonic frequencies (cm−1) for normal modes of vibration R, TS, and P for iPT reaction. ip:inplane; oop: Out-of-plane; str:stretching; bnd:bending:sym: symmetric; asym: asymmetric.

Reactant TS Product Mode Frequency Mode Frequency Mode Frequency oop H2(f1) 427 Reaction coordinate (f2) 1751i OCS ip bnd.(f2) 465 (H2 motion) OCS ip bnd H2-O str (f2) 432 OCS ip bnd(f5) 651 oop H2 (f1) 678 C-S str+H2 ip (f3) 667 CS str+H2 (f3) 875 CS str+H2 (f5) 953 oop H5 (f4) 942 oop H2/5 asym (f1) 926 oop H2/5 asym (f4) 956 ip H5 (f5) 945 oop H2/5 sym (f4) 1013 H2/5 ip+CO str.(f3) 1231 ip H2 (f6) 1380 ip H5(f6) 1269 H2 ip+CO str (f6) 1282 C-O str (f7) 1774 C-O str 1526 C-S str+ip H2/5 asym (f7) 1454 +ip H2/5 asym.(f7) S-H2 str (f8) 2670 C-H2 str (f8) 1771 C-H5 str (f9) 3140 C-H5 str (f9) 2960 C-H5 str (f9) 3128 O-H2 str (f8) 3697

40 Frequency iPT

f1 f2 3000 f3 f4 f5 2000 f6 f7 f8 1000 f9

0 Frequency [cm-1]

-1000

0 0.2 0.4 0.6 0.8 1 1.2 1/2 ξ [a0amu ]

Figure 3.8: Frequency values for the normal modes of vibration or iPT reaction. See table 2.3 for description of each mode of vibration (fi, i = 1 − 9)

Since the geometry of the transition state is a four-centered one, the stretching modes and the bending modes are strongly coupled. The correlation diagram shows that in the early stage of reaction, the mode that then become the transition vector is mainly

−1 composed of that OCS bending (432 cm , f2). Therefore, this mode is considered to give the most preferable initial direction to promote the H motion between both

−1 donor and acceptor. Additionally, the S-H2 stretching (2670 cm , f8), only found

Figure 3.9: Schematic representations of the displacement vector associated to the transition vector for the iPT and wPT reactions.

41 in the reactant region, also plays an important role. At the product it becomes the O-H2 stretching mode, which shows a higher frequency value (3697 cm−1), in agreement with the fact that this bond is stronger than the S-H bond. Therefore, it can be concluded that in order to activate the proton transfer it is necessary ﬁrst to activate the OCS bending mode, leading to the large change in this angles observed previously in Figure 3.4. Comparison with the active modes in wPT reaction shows that it is the bending mode between the two fragment H2O+HSCHO (S4-H2-O6 angle), instead of the OCS bending in iPT, the reactive mode at the reactant region. Then it leads to the mode associated to the motions of both hydrogen atoms being transferred, the reaction coordinate (Figure 3.9 and Table 3.3). In this case, no activation of the OCS bending mode is needed to activate the process. On the other hand, stretching mode of S4-H2 and O6-H7 bonds are also activate at the reactant region. At the TS they corresponds to two stretching modes in the H2 -H5 pseudo-bond. The previous analysis indicate that the participation of a water molecule in the process leads to a new reaction mechanism where diﬀerent normal modes must be activated in order to drive the process.

3.4 PT reactions catalyzed by a water molecule using continuum solvent model PCM

In this section, the effect of the solvent as a continuum is studied for the water- catalyzed proton transfer process. For the iPT it has been previously found that, inclusion of continuum solvent effect only produces a small reduction of the activation barrier [81]. Inclusion of solvent as a continuum model (wPT(PCM), Table 3.1) leads to a decrease of the activation barrier by 3.7 kcal/mol, but a similar reaction energy, thus confirming that stability of the HOCHS isomer is mainly due to specific interactions

42 12 wPT(PCM) wPT(PCM) 10 10 ] 8 ξ 5 6 0 4 Energy [kcal/mol] 2 Force [kcal/mol* -5

0 -10 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

-92 15 wPT(PCM) wPT(PCM) -94 10 ]

-96 ξ 5 -98 0 -100 [kcal/mol] µ -5

-102 REF [kcal/mol*

-104 -10

-106 -15 -3 -2 -1 0 1 2 3 -3 -2 -1 0 1 2 3 1/2 1/2 ξ [a°amu ] ξ [a°amu ] Figure 3.10: Energy (kcal/mol) and reaction force proﬁle (kcal/mol*ξ) (top). Chemical potential(kcal/mol) and reaction electronic ﬂux (kcal/mol*ξ) (bottom) for the wPT(PCM) processes.

with the water molecule. Even though the kinetics of the process is very similar, the main difference between wPT and wPT(PCM) is observed in the shape of the potential energy profile. As can be seen from Figure 3.2 the energy profile for wPT has the classical form of an elementary step, whereas the energy profile for wPT(PCM) evidences a shoulder after the energy maximum (Figure 3.10). Even though the latter process seems to be a stepwise processes, only one transition state that connects reactants and products was found, thus corresponding to an asynchronous concerted process. These results indicate that each elementary step is associated with one proton transfer, the first occurring at the S4–H2–O6 moiety and the second at O6–H7–O1 moiety. As can be observed in Figure 3.11, the TS associated to wPT(PCM) shows that the

43 O1-C3 2 O1-H7 O6-H7 H5-S4 H5-O6 1.5 C3-S4

Wiberg Bond Order 0.5

0 -3 -2 -1 0 1 2 3 1/2 ξ [a°amu ]

Figure 3.11: Bond order evolution for wPT(PCM). proton transfer occurring between the S donor atom and the oxygen atom of water precedes the proton transfer from the oxygen of water to oxygen acceptor atom. NBO analysis also agrees with this larger asynchronicity of the process. In this system the stabilizing interaction from the oxygen to the S-H antibonding orbital at the transition state is larger than in wPT, while the interaction from the oxygen lone pair to the O-H antibonding orbital is much smaller. The asynchronicity of this process leads to a reaction force profiles that vanishes at the transition state region; it is expected that at this stage relaxation of the first proton transfer and activation of the second one takes place simultaneously. It is the superposition of these processes which can lead to a unique transition state. Analysis of the reaction works shows a lowering by 30% throughout W1 and W2. In this case the electronic reordering in the O1–C3–S4 moiety and the proton transfer in the O6-H7–O1 fragment mainly take place once the transition state have been reached. Finally the solvent influence in W4 is again evident, it decreases by about 35%, which is due to the continuum model favors a shorter and consequently stronger hydrogen bond between the O6 and O7 atoms. The asynchronicity of this process is also evidenced trough the analysis of the REF

44 and the bond order profiles. The larger change in the bond order are in accordance with the position of the two larger peaks in the REF profile, thus indicating that these correspond principally to electron transfer process. In terms of the REF the initially transference flux is driven by the S4-H2/H2-O6 breaking/forming bond process. Afterward, the O6–H7/H7–O1 bond orders cross each other at the end of the transition state region.

3.5 Concluding Remarks.

• A water molecule acts as a catalyst in the PT in thioformic acid. It lowers the activation energy roughly by a factor of three compared with the non- catalyzed process. A closer analysis indicates that the water acting as a proton donor/acceptor reduces the work associated not only to the structural reorganization required to activate the reaction, but also it facilitates changes in the electron conﬁguration.

• It was found that the electronic activity in iPT reaction is initiated at the reactants region; this activity can be mainly associated to polarization eﬀects on the OCS fragment. At the transition state region the electron activity increases: at this stage the proton transfer process taking place is coupled to electronic reordering at the OCS fragment. In wPT the electron activity is mainly localized at the transition state region, where both proton transfer process takes place in an slightly asynchronous manner.

• Analysis of vibrational modes indicates that participation of a water molecule leads to a new reaction mechanism, where diﬀerent normal modes must be activated in order to activate the process. It involves the activation of a bending mode between the two fragments, rather than the OCS bending mode found in iPT.

45 • Although inclusion of solvent as a continuum model only leads to small decrease of the activation barriers, it induces a much more asynchronous proton transfer process, where a transition state evidencing an early proton transfer within the S-H· can be stabilized. This asynchronicity can be clearly identiﬁed through the analysis of the reaction force and REF proﬁles.

46 4

Insights on the Mechanism of Proton Transfer Reactions in Amino Acids.

Amino acids are the basic building blocks of proteins. It is well known that in the gas phase they are predominantly in the canonical (N) form, while in solid state or aqueous solution the zwitterionic (Z) is the most stable form, which results from favorable solute-solvent electrostatic interactions due to its large dipole moment [98, 99]. Basic understanding of the proton transfer (PT) reactions associated with the isomerization process from the neutral amino acid to the corresponding zwitterionic form is essential for many biochemical processes. In this chapter, the potential energy, the reaction electronic flux profiles and the reaction force will be used as a general framework to gain insights on the stability of tautomeric species, the mechanism of the proton transfer and the effect of water in the proton transfer path of alanine (Ala), phenylalanine (Phe), and tryptophan (Try). This information together with the analysis of the evolution of key structural and electronic properties along the reaction coordinate will allow to elucidate the mechanism of the reaction as well as

Part of this chapter has been previously published as: Fernanda Duarte, Esteban Vohringer- Martinez and Alejandro Toro-Labb´e. Insights on the Mechanism of Proton Transfer Reactions in Amino Acids. Phys. Chem. Chem. Phys., 2011, 13, 7773–7782.

47 the effect of the side-chain over the process. For the PT reaction in glycine (Gly) with a discrete water molecule in vacuum the energy barrier of the N→Z tautomerization has been calculated to be 9.1 kcal/mol [100]. Addition of a solvent continuum model reduces the energy barrier to 4 kcal/mol [100], and replacement of the discrete water molecule with a continuum results in a barrier of 2.4 kcal/mol at the MP2/6-31+G(d,p) level of theory [101]. Rodziewicz et al. studied micro-hydration of phenylalanine in vacuum using ab initio molecular dynamic simulations and reported the energetically most favorable interconversion path between the neutral and zwitterionic forms to be through a H2O bridge (no zwitterionic free-energy minimum is found for naked Phe), with a free energy barrier of 8.3 kcal/mol for Phe(H2O) and 3.4 kcal/mol for Phe(H2O)3 (where 1 water molecule is oriented toward the aromatic ring) [102]. Yamabe et al. [103] studied the proton-transfer pathways of glycine mediated by n (n =0-4) water molecules employing a solvent continuum model. They found an energy barrier of 9.93 kcal/mol for the intramolecular PT and a higher energy barrier for the n-water catalyzed reactions (11.54 kcal/mol(n=1); 14.08 kcal/mol(n=2); 10.98 kcal/mol(n=3); 12.8 kcal/mol(n=4)). This is different than the proton transfer process studied in the previous chapter, and also different to other reactions, where water-mediated processes have shown lower barriers than the direct one. Such catalytic effect have been postulated in the action of enzymes (e.g., carbonic acid anhydrase [104]) as well as in other proton transfer reactions [62,99,105–110]. From the above studies it can concluded that the addition of more water molecules does not necessarily lead to a smaller activation barrier. Their specific position seems much more important and may in some situations catalyze the reaction or change its mechanism. Previous works have studied the effect of water molecules either participating in the proton transfer, most of them focussed on the amino acid Glycine, or in coordination with the functional groups of the amino acid. In

48 this study, however, the focus was on the effect of a second water molecule, which is not directly participating in the proton transfer, but acts as donor or acceptor to the the reactive one and may affect the reaction mechanism. The alanine and phenylalanine amino acids have been chosen in order to analyze the effect of the side-chain on the reaction mechanism. These results will be compared with the one obtained for tryptophan, which during the development of this work was studied for other integrant of the group [111]. Thereby, in this chapter the influence of the amino acid side chain and the participation of water(s) molecule(s) on the proton transfer process will be addressed, with the aim of analyzing the role played by the solvent in the PT reaction and characterize the physical nature of energy barriers. The latter goal will be achieved by making use of the partition of the activation energy provided by the reaction force analysis (Eqn. 2.46).

4.1 Computational details

All the structures have been optimized using the B3LYP functional [82–84] with standard 6-31G(d,p) basis set. The minimum energy path in going from reactants to products were calculated through the intrinsic reaction coordinate procedure (IRC=ξ)[87,88] using a step size of 0.01 amu 1/2bohr (a more detailed description of this methodology can be found in Appendix A). Frequency calculations on reactants, transition states, and products were performed to conﬁrm the nature of the corresponding stationary point along the reaction path. Using the geometries obtained from the IRC procedure, molecular properties were determined through single point calculations. Calculations in solution were performed with the polarizable continuum model (PCM) [86] as implemented in the Gaussian 03 package [90], where the liquid is represented with a continuum characterized by a dielectric constant of 78.39 for water. The default cavity was modiﬁed by adding individual spheres to hydrogen

49 atoms involved directly in the proton transfer (using the keyword SPHEREONH). The extra spheres were necessary to match the isosurface of the electron density in reactants and products and to keep the hydrogen atoms inside the cavity in the transition states. The natural bond orbital [89] analysis was also carried out to obtain Wiberg bond index along the reaction coordinate and to evaluate the direction and magnitude of the donor-acceptor interactions. Reactants, transition state, and products were also optimized at the MP2/6-31G(d,p) level for comparison. All

calculations were carried out using Gaussian 03 program [90].

4.2 Results and discussion

4.2.1 Energetic Parameters and Potential Barriers

Figure 4.1 shows the reactions under study: reaction ALA and PHE are the intramolecular proton transfer process and reaction ALA-H2O and Figure PHE-H2O are the water-mediated process in alanine and phenylalanine respectively. The potential energy profiles along the intrinsic reaction coordinate for these reactions are displayed in Figure 4.2. The IRC calculation did not always converge to the reference structure. In order to establish the connection of the reported energy minima of reactant and product to the IRC path, an optimization of the last structure from the IRC calculation was performed. This optimization always converged to the reference structure shown in Figure 4.1. The profiles have the classical form of an elementary step, indicating that for the water-mediated proton transfer the mechanism of these processes is a concerted double proton transfer via the binding water molecule. The reaction energies (∆E◦), energy barriers (∆E6=) and reaction works for these reactions are summarized in Table 4.1. These results are also compared with the recent study on tryptophan (TRY and TRY-H2O, respectively) [111]. Calculations on minimum and transition state geometries for all systems were performed with the B3LYP and MP2 methods in order to compare different levels of theory. Energy

50 Figure 4.1: Optimized structures for the neutral, transition state and zwitterionic form of alanine (ALA and ALA-H2O) and phenylalanine (PHE and PHE-H2O). Not shown here is reaction TRY and TRY-H2O corresponding to tryptophan which is studied in detail in reference [110]. barriers diﬀer by about 1 kcal/mol from the MP2 energies, in agreement with previous studies [102, 112]. Therefore, it can be concluded that the B3LYP/6-31G(d,p) level is suitable to study the title reactions with a good compromise between accuracy and computational cost. Intramolecular PT reactions are all endoenergetic with similar ∆E◦ values. It is remarkable that the reaction energies associated with these reactions are about two

51 7 7 ALA PHE 6 6

5 5

4 4

3 3

Energy [kcal/mol] 2 Energy [kcal/mol] 2

1 1

0 0 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

7 7 ALA-H2O PHE-H2O 6 6

5 5

4 4

3 3

Energy [kcal/mol] 2 Energy [kcal/mol] 2

1 1

0 0 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 4.2: Energy profile for the intramolecular and water-mediated proton transfer reactions in Alanine ALA and ALA-H2O and Phenylalanine PHE and PHE-H2O, respectively. times those of water-mediated processes. Thus indicating the key role of the water molecule stabilizing the zwitterionic structure through specific interactions, which cannot be described only with the continuum model. Also the energetic barrier of the PT process is affected when a discrete water molecule is introduced; ∆E6= values

Table 4.1: Reaction energy (∆E◦) and energy barriers (∆E6=) of the PT reactions computed at the B3LYP and MP2 levels of theory with the 6-31G(d,p) basis set.

Reaction ∆E◦ ∆E6= DFT MP2 DFT MP2 ALA 1.5 0.6 3.6 3.6 TRY 1.5 -0.7 3.8 3.7 ALA-H2O -0.6 -2,0 5.9 6.9 a TRY-H2O -0.8 -2.6 5.7 6.7

a Ref. [111]

52 in these systems are about two times those of the intramolecular process. Comparison with glycine systems shows the same trend [100, 113], but lower values than for the water-assisted processes here studied.

4.2.2 Reaction Force Proﬁle

Reaction force proﬁles are comparatively presented in Figure 4.3. The critical points

at ξ1 and ξ2 (red dash vertical lines in the reaction force profiles) define the reaction regions, allowing the energetic barrier decomposition in terms of the work invested in each region (Table 4.2). An initial slope analysis of the reaction force profile shows the evolution of the forces opposing the preparation step. The shape of the reaction force profile for the intramolecular and the water-mediated proton transfers do not depend on the nature of the amino acid. In the water-mediated processes F(ξ) decreases relatively

slow and almost linearly until ξ ≈ −0.6, then a rapid decrease sets in until ξ1, the minimum of F(ξ), denoting a change in the nature of these forces. First, they are mostly related to structural changes, in which the main feature is the approximation of the water molecule to the functional groups of the amino acid. It was observed that the donor-acceptor distances between amino acid and water only change in the reactant and product region (see Figure 4.4). Then, once reached ξ ≈ −0.6, the breaking/forming bond processes become activated and the proton transfers process is the driving force. This is different to the intramolecular processes, where the first linear decrease in the reaction force is assigned to the approximation between the donor and acceptor functional groups. In the previous chapter it was shown that the effect of a water molecule upon activation processes is on both W1 and

W2, diminishing the structural rearrangement needed to activate the process, but also facilitating electronic changes [59, 60, 62]. In the present situation however, the water molecule actually increases the energy barrier. It is observed that both

53 8 8 ALA PHE 6 6

] 4 ] 4 ξ ξ 2 2 0 0 -2 -2

Force [kcal/mol* -4 Force [kcal/mol* -4 -6 -6 -8 -8 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

8 8 ALA-H2O PHE-H2O 6 6

] 4 ] 4 ξ ξ 2 2 0 0 -2 -2

Force [kcal/mol* -4 Force [kcal/mol* -4 -6 -6 -8 -8 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 4.3: Reaction force proﬁle for the intramolecular and water-mediated proton transfer reactions in alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE- H2O, respectively.

W1 and W2 values for the water-mediated process are higher than those for the intramolecular one. In the intramolecular process, ALA for example, the ﬁrst step of the reaction to reach the minimum of the force requires 2.6 kcal/mol (W1); the work that is needed to approximate the donor and acceptor to each other. W1 is larger than the work W2 (1.0 kcal/mol), required for the transfer of the hydrogen, thus, indicating that 72% of the activation barrier principally, but not exclusively, involves structural rearrangement. In the water-mediated process (ALA-H2O) both

W1 and W2 increase equally by a factor of 1.6, indicating that additional energy is necessary, ﬁrst to bring the amino acid and the water molecule closer to each other, but also to promote the proton transfer through the reordering of the electron density. Previous studies in other intramolecular proton transfer processes, such as the study

54 Table 4.2: Reaction energy (∆E◦); energy Barriers (∆E6=), position of the extreme points of the reaction force (ξ1, ξ2) and the reaction works of the processes computed at the B3LYP level of theory with the 6-31G(d,p) basis set.

◦ 6= Reaction ∆E ∆E ξ1 ξ2 W1 W2 W3 W4 ALA 1.5 3.6 -0.3 0.2 2.6 1.0 -0.6 -1.5 PHE 1.8 3.7 -0.3 0.2 2.7 1.0 -0.5 -1.4 TRYa 1.5 3.8 -0.3 0.2 2.7 1.1 -0.6 -1.7 ALA-H2O -0.6 5.9 -0.3 0.3 4.3 1.6 -1.3 -5.2 PHE-H2O 0.9 6.4 -0.4 0.3 4.8 1.6 -1.2 -4.3 a TRY-H2O -0.8 5.7 -0.3 0.3 4.3 1.4 -1.3 -5.2 ALA-(H2O)2-A -0.7 5.4 -0.3 0.3 4.0 1.4 -1.3 -4.8 ALA-(H2O)2-B -0.6 5.2 -0.5 0.4 3.3 1.9 -1.2 -4.6

a Ref. [111]

in thioformic acid system discussed previously [62] and nucleic acid bases [110] for example, have shown that addition of a water molecule reduces the energy barrier. In those system a strained four-member ring conformation is reached in order to activate the intramolecular PT; in such case participation of a water molecule led to a less strained six-member ring at the transition state and to a reduction of the activation energy. In this case, however, ALA-PHE-TRY systems have already

2.7 N-Ow O -O 2.65 w

2.6

2.55

2.5 Distance[A] 2.45

2.4

2.35 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 ξ [a°amu ]

Figure 4.4: Bond distances (in angstroms) between donor and acceptor atoms for the water–assisted proton transfer ALA-H2O.

55 a less strained ﬁve-member ring geometry (see Figure 4.1), where the amount of deformation needed to reach the activated reactant structure at ξ1 is comparatively smaller than the referenced proton transfer processes. Additionally, the participation of a water molecule implies an initial reorientation of it to act as a bridge in the proton transfer, thus involving an additional structural work which is absent in the intramolecular processes.

Once the TS is reached, the energy required from the TS to ξ2,W3, also increases by a factor about 2 in the water-mediated processes respect to the intramolecular one. The total transition state energy W2 + |W3| increases by a factor about two suggesting an increase of the electronic activity in the transition state region. Finally,

W4 increases by a factor of three, which is mainly due to the stabilization conferred to the zwitterion structure by the presence of a water molecule. The nature of the amino acid side chain (methyl, Toulol, 2-methylindol) has practically no eﬀects on the energy barrier. The detailed reaction force analysis shows that the component of the energy barrier, W1 and W2, are comparable, suggesting that the energetic issue is practically localized within the reactive part of the system and involves the atoms situated at the vicinity of the transferred proton.

4.2.3 Bond Order

The Wiberg bond orders along the reaction coordinate reveal no dependence on the amino acid side chain. The major changes in the bond orders occur for all reactions within the TS region. To gain more insight into the change of the electronic density along the reaction coordinate, the derivative of bond orders with respect to the reaction coordinate was calculated for the transferred hydrogen and the donor or acceptor atoms (Figure 4.5). A negative sign in the derivative indicates bond weakening or dissociation, while a positive sign accounts for bond formation or strengthening. In the intramolecular processes, the charge transfer taking place during the di-

56 ALA PHE

N-H N-H 0.4 C-OH 0.4 C=O C=O C-OH 0.2 COO-H 0.2 COO-H

0 0

-0.2 -0.2

-0.4 -0.4 Wiberg Bond Order Derivative Wiberg Bond Order Derivative -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

ALA-H2O PHE-H2O

N-H N-H 0.4 0.4 NH-Ow NH-Ow COO-H COOH-Ow COOH-O 0.2 w 0.2 COO-H C-OH C-OH C=O C=O 0 0

-0.2 -0.2

-0.4 -0.4 Wiberg Bond Order Derivative Wiberg Bond Order Derivative -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 4.5: Bond order derivatives for the bonds being formed and broken in the proton transfer reaction of alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE- H2O, respectively. ssociating bond H–O and the forming bond H–N occurs simultaneously: Notice that while those bonds are dissociated and formed respectively, electronic reordering also takes place in the O=C–O moiety. Both C–O bond reorganize their electronic density in order to compensate the additional charge due to the migration of the proton. In the water-mediated process, the proton transfers occur in a concerted but asynchronous way: at the reaction force minimum the ﬁrst proton transfer takes place between the oxygen of the carboxyl group and the water molecule in combination with the electronic reordering at the O=C–O moiety. Once these derivatives reach their maximum change, the second proton transfer is activated, reaching its maximum at the reaction force maximum. In the water-mediated process, the asynchronicity of the proton transfers lead to a

57 transition state where the water molecule has three coordinated hydrogen atoms,

+ representing a H3O hydronio-cation like structure. This is reﬂected in the shorter

hydrogen bond distance of Ow ··· H bonds (1.19 A)˚ in comparison to the N··· H and COO··· H bonds (1.32 A˚ and 1.26 A˚ respectively), as well as in the partial increased positive charge of +0.5—e— for this complex entering the transition state region. The stability of this species at the transition state and its influence over the mechanism will be analyzed in the last section. In the previous analysis, it was seen that the participation of a water molecule strongly influence over the energy and mechanism in the PT reaction, whereas for different side chains almost no influence was observed. In order to explore more in detail this aspect the electronic flux J(ξ) profiles (calculated from Eqns. 2.16 and 2.23) for each of these reactions were analyzed. They are shown in Figure 4.6. As general feature it can be observed that a negative flux, which is characteristic of a non-spontaneous electronic reordering process, dominates the picture along the reaction coordinate. Although the shape of each one is quite different. Comparison of the intramolecular and water-mediated process in alanine, reactions ALA and ALA-

H2O, show that for the former the REF minimum is centered at the transition state, while in ALA-H2O it is shifted to the minimum of the force, with almost zero ﬂux regimen during the ﬁrst part of the reactant region (from reactant to ξ=-0.7). The

energy required at this point in ALA-H2O, which matched the end of the linear decrease of the reaction force, is 1.8 kcal/mol while in ALA it is only 0.8 kcal/mol (from reactant to ξ=-0.8). These results conﬁrm the fact that a lower structural work is needed in ALA to bring the donor and acceptor close to each other to begin

the PT process. In contrast, for ALA-H2O the structural rearrangements, identiﬁed as the approximation of the water molecule to the functional groups of the amino

acid, leads to higher W1 values. The previous result shows how the REF concept can provide a useful partition to analyze and quantify structural and electronic reordering

58 2 1 ALA PHE 0 0.5 -2

] ] 0 ξ -4 ξ -0.5 -6 -1 -8 -1.5 -10 REF [kcal/mol* REF [kcal/mol* -12 -2 -14 -2.5 -16 -3 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

2 1 ALA-H2O PHE-H2O 0 0.5 -2

] ] 0 ξ -4 ξ -0.5 -6 -1 -8 -1.5 -10 REF [kcal/mol* REF [kcal/mol* -12 -2 -14 -2.5 -16 -3 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 4.6: Reaction electronic ﬂux proﬁles for the intramolecular and water-mediated proton transfer reactions in alanine, ALA and ALA-H2O, and phenylalanine, PHE and PHE-H2O, respectively.

along the process.

4.2.4 Reaction Electronic Flux

Comparison with the bond order derivative profiles suggests that the maximum change in the REF is associated with reordering in the O=C–O moiety. In R1 the maximum flux is observed at the transition state region, where the reordering in the O=C–O moiety takes place at the same time than the proton transfer process occurs. In R4 this reordering occurs earlier, at the reaction force minimum, coupled to the first proton transfer between the oxygen atoms, which correlate with the maximum flux. Comparing aromatic side chains, as present in phenylalanine, with alanine it can be

59 noted that they reveal smaller electronic ﬂuxes (Figure 4.6). The frontier orbitals in

+ − alanine are localized on the reactive center (NH3 and COO ), thus given directly insight of the electronic activity taking place due to the proton transfer. The situation is different in phenylalanine, where the higher occupied molecular orbital (HOMO) is localized on the aromatic substituent. Close inspection of the orbitals in phenylalanine shows that during the reaction not only the HOMO orbital is affected but also the HOMO-2 orbital, which is in fact located into the reactive center, see Figure 4.7-4.8. It can be noted that along the process the HOMO orbital is shifted from the aromatic ring to the reactive center, where it is similar to the alanina’s HOMO. In this case the REF profile in phenylalanine describe indirectly the electronic changes take place in the reactive center along the process, thus explaining the different magnitude observed between these systems.

4.2.5 The Eﬀect of a Second Water Molecule

As it has been mentioned before, the participation of one water molecule in the proton transfer process leads to a transition state where the water molecule has three coordinated hydrogen atoms. This coordination is similar to the one present in

+ + + H3O -ion. This cation beside the (H5O2) and (H9O4) ions, which are the so-called Zundel [114] and Eigen [115] forms of the cations respectively, has been the topic of extensive research, since they play a crucial role in the proton transfer mechanism in neat liquid water [116, 117]. It has been proposed that the addition of a second

+ water molecule to the H3O -ion stabilizes the ion forming the Zundel ion [118,119]. To analyze the possible stabilization of the obtained transition states, a second water molecule was added as a hydrogen donor and as a hydrogen acceptor to ALA-H2O.

The respective structures are shown in Figure 4.9. In structure ALA-(H2O)2-A the second H2O molecule is positioned over the water oxygen atom acting as a proton donor while in ALA-(H2O)2-B it is located right below the other water molecule

60 Figure 4.7: Isosurface at 0.01 au for the HOMO, HOMO-1 and HOMO-2 density of Phenylalanine PHE and Alanine ALA

acting as proton acceptor, representing a Zundel-cation like structure.

In ALA-(H2O)2-A the energy barrier is reduced by 0.5 kcal/mol and match about the same reaction energy of ALA-H2O (see Table 4.2). The reaction works W1

and W4, which are more related to structural rearrangements, are little aﬀected

compared to ALA-H2O, while W2 and W3 corresponding to electronic changes

remain unaffected. The main difference to ALA-H2O is reflected in the reaction mechanism. The second water molecule induces first the transfer of the proton on the water molecule to the amino-group, which represents the reverse order observed

in ALA-H2O, while the proton of the carboxyl group is passed at the maximum of the reaction force after reaching the transition state (see Figure 4.9). The added

61 PHE PHE -0.22 0.01

-0.23 0

-0.24 -0.01

-0.25 -0.02 Energy LUMOs [hartree] Energy HOMOs [hartree] -0.26 -0.03 Homo-2 Homo-1 Lumo Homo Lumo+1 -0.27 -0.04 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 1/2 1/2 ξ [a0amu ] ξ [a0amu ]

PHE-H2O PHE-H2O -0.22 0.01

-0.23 0

-0.24 -0.01

-0.25 -0.02 Energy LUMOs [hartree] Energy HOMOs [hartree] -0.26 -0.03 Homo-2 Homo-1 Lumo Homo Lumo+1 -0.27 -0.04 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a0amu ] ξ [a0amu ]

Figure 4.8: Molecular orbital energies for phenylalanine PHE and PHE-H2O. water molecule acting as donor reduces the electron density through the H–bond on the reactive water molecule involved in the proton transfer. This reduction is accompanied by a decreased electronegativity of its oxygen atom, transforming it in a better proton donor with respect to the nitrogen atom and a worse proton acceptor with respect to the oxygen atom of the carboxyl group. This change in the nature of the water oxygen atom is also observed in the reduced distances with respect to the transition state structure of ALA-H2O between the nitrogen atom and the proton from the water molecule (1.22 A)˚ as well as in the COO–H distance (see Figure 4.9).

+ In ALA-(H2O)2-B, where the H3O -ion is expected to be more stabilized by forming the Zundel-cation, the energy barrier decreases by 0.7 kcal/mol. Here, the reaction works present the same changes as in ALA-(H2O)2-A, although more pro- nounced. The order of the transferred hydrogens is preserved with respect to ALA-

H2O, whereas the absolute value of minimum and the maximum of the reaction force

62 ALA-(H2O)2-A

N-H 0.4 NH-Ow COO-H COOH-O 0.2 w C-OH C=O 0

-0.2

-0.4 Wiberg Bond Order Derivative -1.5 -1 -0.5 0 0.5 1 1.5 1/2 ξ [a°amu ]

ALA-(H2O)2-B

N-H 0.4 NH-Ow COO-H COOH-O 0.2 w C-OH C=O 0

-0.2

-0.4 Wiberg Bond Order Derivative -1.5 -1 -0.5 0 0.5 1 1.5 1/2 ξ [a°amu ]

Figure 4.9: Transition state structure and bond order derivatives for the systems ALA- (H2O)2-A and ALA-(H2O)2-B. Values in parenthesis show the diﬀerences with respect to the bond distances for ALA-H2O. increases leading to a larger transition state region, and therefore an earlier proton transfer of the carboxyl group and a later transfer to the amino group along the reaction coordinate. This is also shown in the bond derivatives, where the respective extrema are more separated. The added water molecule, therefore, transforms the oxygen water molecule in a better acceptor, which is reﬂected in shorter distances towards the two transferred protons. This change in the nature of the water oxygen atom over the mechanism was also analyzed with the NBO analysis. NBO theory describes the formation of a AH··· B hydrogen bond as the charge transfer from the lone pair nB of the proton acceptor to

∗ ∗ the vacant antibonding orbital σAH of the proton donor. The nB → σAH delocaliza-

63 Table 4.3: Summary of NBO Analysis for reactant structures.

∗ (2) Reaction Donor (nB) Acceptor (σ ) E ∗ (kcal/mol) AH nB →σAH ∗ ALA-H2O LP(1) N BD Ow–H 30.38 ∗ LP(2) Ow BD COO–H 39.57 ∗ ALA-(H2O)2-A LP(1) N BD Ow1–H 36.94 ∗ LP(2) Ow1 BD COO–H 31.40 ∗ LP(2) Ow1 BD Ow2–H 13.27 ∗ ALA-(H2O)2-B LP(1) N BD Ow1–H 27.26 ∗ LP(2) Ow1 BD COO–H 45.05 ∗ LP(2) Ow2 BD Ow1–H 22.57

tion leads to energy lowering that can be quantiﬁed by the second order perturbation

(2) theory, where the second order perturbation E ∗ values can be used to estimate nB →σAH the relative strength of hydrogen bonds.

In ALA-H2O two strong intermolecular interactions are found between nOw and

∗ ∗ σ COO–H orbitals and between nN and σ Ow–H. These interactions cause elongation of the respective X–H bond by increasing the population of its antibonding orbital

(2) and, thus, promote the proton transfer process. From the E ∗ values (see Table nB →σAH 4.3) it can be concluded that the proton involved in the strengthened hydrogen bond is the one which is transferred ﬁrst in the direction from the carboxyl group to the

(2) water molecule( E ∗ = 39.57 kcal/mol), in agreement with the order obtained nB →σAH from the Bond Order derivatives proﬁles in ALA-H2O.

When a second water molecule is added, acting as a proton donor (ALA-(H2O)2-

A), the strength of COOH··· Ow hydrogen bond decreases respect to the OwH··· N hydrogen bond. In this case, due to the intermolecular interactions created between

Ow and the O–H of the second water molecule, the electron donor (proton acceptor)

(2) ability of the oxygen Ow is reduced in the COOH··· Ow hydrogen bond (Ei→j∗ = 31.40 kcal/mol), leading to a stronger interaction between the nitrogen lone pair and the

∗ (2) σ Ow–H orbital (Ei→j∗ = 36.94 kcal/mol). Thus, during the reaction it is this proton transfer process which is activated ﬁrst. In ALA-(H2O)2-B, where the second water

64 ALA-(H2O)2-A ALA-(H2O)2-B 5 5 REF REF

0 0 ] ] ξ ξ

-5 -5

-10 -10 REF [kcal/mol* REF [kcal/mol* -15 -15

-20 -20 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 4.10: Proﬁles of reaction electronic ﬂux for the water-mediated proton transfer reactions ALA-(H2O)2-A and ALA-(H2O)2-B.

molecule acts as a proton acceptor, a stronger interaction is found in COOH··· Ow, (2) thus favoring an earlier proton transfer process (E ∗ = 45.05 kcal/mol). nB →σAH

It can also be noted that in ALA-(H2O)2-B the amount of work W1 is reduced by 1 kcal/mol compared to ALA-H2O. This lower value for W1, which is mainly associated to structural rearrangement needed to start the process, this is in line with

(2) the higher E ∗ value of the COOH··· OW hydrogen bond in this system. The nB →σAH stronger hydrogen bond in ALA-(H2O)2-B at the reactant structure implies that a lower structural reorganization will be necessary to bring the donor and acceptor atoms close to each other to begin the PT process, thus making the PT process more favorable. In terms of the REF, the addition of a second water molecule leads to a diﬀerent pattern depending of the character of the second water (see Figure 4.10). In ALA-

(H2O)2-A, when it acts as a proton donor, the REF minimum is shifted from the reaction force minimum to the maximum. Thus, conﬁrming that the REF is mostly associated with reordering in the O=C–O moiety due to the proton transfer from the COOH group to water.

65 4.3 Concluding Remarks.

• The results show that the bridging water molecule stabilizes the zwitterionic form and increases the reaction barriers by a factor of two in all studied systems with a marginal inﬂuence of the amino acid side chain (methyl, Toulol, 2-methylindol). About 70% of the activation barrier involves structural rearrangement.

• The water-mediated processes correspond to a concerted, though asynchronous motion of the two protons toward the respective acceptor atom: the hydrogen atom of the carboxyl group leads the transfer while the hydrogen atom of the bridging water to the ammonium group is transferred later. The NBO analysis have provided a detailed description of the order of the transferred protons and the asynchronicity of the processes.

• Comparison of these results with the REF profiles suggest that the maximum flux is associated with an electronic reordering in the O=C–O moiety, while the amplitude depends on the nature of the side chain. Aromatic side chains, where the frontier orbitals are not located on the reactive atoms, present smaller fluxes than alanine.

• A second water molecule acting as donor or acceptor with respect to the bridging reactive one reduces in both cases the energy barrier. This not intervening water molecule varies the donor and acceptor character of the reactive one which changes the order of the transferred protons or moves the transition state region towards the reactants or products. The diﬀerences in the reaction mechanism can be understood from the hydrogen bond strength obtained from second order perturbation theory within the NBO analysis. This approach provide a very simple, transparent, and complete picture on how a water molecule

66 can modulate the mechanism of a chemical reaction.

67 5

The Mechanism of H2 Activation by (Amino)Carbenes

5.1 Introduction

Hydrogen H2 is not only considered to be the fuel of the future, but it is also vital in several industrial processes, organic synthesis and in biological functions [120, 121].

Because the covalent bond in the H2 molecule is strong (103 kcal/mol) [122], this molecule is not very reactive under ambient conditions. In microorganisms, both the production and the uptake of molecular hydrogen is catalyzed by metalloenzymes named hydrogenases [123]. These enzymes contain nickel and/or iron-sulfur clusters (in which case the activation of the hydrogen molecule takes place at the redox-active) or an iron-containing cofactor (Figure 5.1), which are critical for the enzymatic activity [124,125]. In industrial processes, catalytic hydrogenation is usually carried out using heterogeneous or homogeneous transition metal catalysts, typically, platinum group metal derivatives, iron and group 6 metal complexes [120]. In these systems

Part of this chapter has been previously published as Fernanda Duarte and Alejandro Toro- Labb´e. H2 activation reaction by (amino)carbene systems. Analysis from the perspective of the Reaction Force and Reaction Electronic Flux. J. Phys. Chem. A, 2011, 115, 3050–3059.

68 Figure 5.1: Desulfovibrio desulfuricans iron hydrogenase posses a Fe-binuclear center active site (PDB:1HFE)

the bond activation is facilitated by interaction of the σ-bonding orbital of H2 with a vacant d orbital on the metal and through a back donation from an occupied metal

d orbital to the empty σ* orbital of H2 [120]. Despite bond activation by transition- metal complexes has enormous utility, there are nonetheless certain disadvantages, for example many precious metals, such as platinum, can be environmentally un- friendly or economically prohibitive. In recent years, however, it has been shown that also stable nonmetallic systems are capable to activate molecular hydrogen (see e.g. [126] and references therein). These systems include fullerene [127], digermanes [128], phosphine-borane species [129], and stable singlet carbene systems [130] (Figure 5.2). In the last years, particular interest has been payed in the last group, where stable (alkyl)(amino)carbenes (AACs) [131] have represented a remarkable breakthrough, being able to activate not only molecular hydrogen, but also a variety

of small molecules, including CO [132], NH3 [130] and P4 [133], as well as strong bonds, such as Si-H, B-H and P-H σ-bonds [134]. Carbenes are neutral compounds featuring a divalent carbon atom. In its singlet state carbene systems possess a low-lying unoccupied p orbital and a sp2-type lone pair at

69 Figure 5.2: Nonmetallic systems able to activate H2. a) Phosphine-borane specie; b) digermanes and c) Singlet carbene systems. the same atom, and therefore it might be expected that they are suitable for donation and back-donation that activate H2, thus mimicking the behavior of metals (see figure 5.2). The effect of substituents, through hyperconjugation, mesomeric or inductive effects (see e.g. [135] and references cited therein), and other affecting the single- triplet separation energy have been extensively studied in the literature [135–139]. These studies have shown that while π electron donor substituent stabilize singlet states, σ electron donor groups stabilize triplet states. The π -donor/σ-acceptor substituents have been associated to stabilization of the singlet and destabilization the triplet. However, more recently, it was shown that π -donor/σ-acceptor amino substituents stabilize not only the singlet but also the triplet states, with stabilization of the triplet states much less than the singlet states [140]. π -donor/σ-acceptor amino substituents have a great influence over the stability and electronic properties of stable carbene systems. For instance, AAC systems have shown excellent properties for the activation of several small molecules, while their diamino analogous do not display similar reactivities. This different reactivity pattern have been mainly associated to a lack of electrophilic character in diamino

70 carbene systems [130]. Very recently, Bielawski et al. [141] reported the synthesis of a carbene system where the two diamino substituent were replaced by diamido structures in a six-member ring, with the aim to increase the electrophilic character of the system. The chemistry displayed by this system has been surprising, in contrast to diamino carbene systems, they have been able to activate CO and NH3 [141, 142]. However no reaction has been observed between this system and H2. Concerted as well as stepwise mechanisms for activation reactions with singlet carbenes are conceivable, where the favored route strongly depends on both the polarity of the bond being activated and the philicity of the carbene. The stepwise reaction pathway is expected for nucleophilic or electrophilic carbenes, while for biphilic carbenes the activation process can become concerted [137,143]. Computational in- vestigations, have suggested a concerted, asynchronous process for the activation of C–H, H–H, and N–H bonds. Additionally it has been shown that molecular hardness (η)[11] may be used as a guide to predict the reactivity of carbenes towards the X–H bond [144,145].

In this and next chapter the H2 activation reaction is studied. In order to rationalize the experimental results, the chemical events that drive the H2 activation reaction and the influence of the substituent are analyzed in detail through a combined use of conceptual DFT based reactivity descriptors [11,14,51] within the framework defined by the Reaction Force analysis [44]. The first part of this study will be focused into the analysis of model alkyl amino (R1-R2) and diamino carbenos ( R3-R4), these systems are displayed in Figure 5.3. The aim in this study will be to obtain a detailed picture of the reaction mechanism by means of the reaction electronic flux, using the partition proposed in Section 2.1.2 (Eqns. 2.24-2.28).

71 Figure 5.3: Sketch of the H2 activation reaction by (amino)carbenes.

5.2 Computational details

All the structures have been fully optimized using the B3LYP [82–85] functional with standard 6-311G** basis set. The minimum energy path in going from reactants to products were calculated through the intrinsic reaction coordinate procedure (IRC=ξ)[87,88]. Frequency calculations on reactants, transition states, and products were performed to conﬁrm the nature of the corresponding stationary point along the reaction path. Using the geometries obtained from the IRC procedure, molecular properties were determined through single point calculations at the same level of theory. The counterpoise method using the H2 + carbene fragmentation, keeping the geometry they have at each point along the reaction coordinate, was used to determine the polarization ﬂux. Natural Bond analysis (NBO) [89] were carried out to obtain Wiberg bond index and the natural charges along the reaction coordinate.

All calculation were carried out using the Gaussian 03 program [90].

72 5.3 Results and discussions.

5.3.1 Energy and Reaction Force Proﬁles.

The energy and reaction force proﬁles are displayed in Figures 5.4 and 5.5; Table 5.1 contains the energetic information of the reactions. All reactions are thermodynamically controlled, being strongly exothermic. Reactions R1 and R2 exhibit ∆E◦ values that are about twice those of R3 and R4. On the other hand, the energy barrier are considerably higher in R3 and R4 with respect to the values of R1 and R2. These results indicate that the presence of a second amino group is unfavorable both kinetically and thermodynamically, since it decreases the exothermicity of the reaction by a factor of 1.8 and increases the energy barrier by a factor of 1.6. Al- though they do not give insights about the nature of the energy barrier or the aspects that might be inhibiting the reactions, these results are consistent with the fact that di(amino)carbene systems are experimentally inert toward the H2 activation [130]. The amount of work involved at each step along ξ was obtained by integration of the reaction force. It can be observed that in all reactions the energy barrier is determined by W1, that represents about 70% of the energy barrier. This amount of work principally, but not exclusively, involves the approach of the H2 molecule to the carbene center, leading to changes in the C–(H–H) and N–C–X (X=N,C) angles.

The work that follows in the TS region, from ξ1 to the transition state, is given by

◦ 6= 6= Table 5.1: Reaction energy (∆E ); forward (∆Ef ) and reverse (∆Er ) energy barriers together with the works associated to the diﬀerent stages of in the H2 activation process (values in Kcal/mol).

◦ 6= 6= Reaction ∆E ∆Ef ∆Er W1 W2 W3 W4 R1 -58.3 21.3 79.6 15.9 5.4 -46.3 -33.3 R2 -54.2 23.7 77.9 17.3 6.4 -45.5 -32.4 R3 -32.4 34.3 66.7 24.4 9.9 -45.2 -21.5 R4 -30.2 35.0 65.2 25.6 9.4 -43.8 -21.4

73 40 40 R1 R2

20 20

0 0

-20 -20 Energy [kcal/mol] Energy [kcal/mol] -40 -40

-60 -60 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a amu ] ξ [a°amu ] °

40 40 R3 R4

20 20

0 0

-20 -20 Energy [kcal/mol] Energy [kcal/mol] -40 -40

-60 -60 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 5.4: Energy proﬁle (in kcal/mol) for the H2 activation reactions R1–R4.

6= W2. The contributions of W2 to ∆E is smaller than W1 and almost the same for all reactions (about 30%). However, it is important to note that when going from

R1 to R3,W2 increases in a larger percentage compared to W1. The situation is opposite for the reverse reaction where the activation energy increases and the components W3 and W4 present a diﬀerent pattern of change: while W3 remains quite constant, W4 experiments considerable changes due to the presence of the second amino group, that decreases by a factor about 1.5. In this context the irreversibility of the reactions seem to be ensured by a large value of W3. The chemical events that deﬁne the forward reactions are basically the breaking of the H–H bond and the forming of two C–H bonds; the reverse reaction involves the opposite events, namely two C–H bonds breaking and the H–H bond forming. Taking into account the bond energies involved in this reaction, forming processes will lead

74 50 50 R1 R2 40 40 ] ξ ]

ξ 30 30

20 20

10 10

0 0 Force [kcal/mol* -10 Force [kcal/mol* -10

-20 -20

-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a amu ] ξ [a°amu ] °

50 50 R3 R4 40 40 ] ]

ξ 30 ξ 30

20 20

10 10

0 0 Force [kcal/mol* Force [kcal/mol* -10 -10

-20 -20

-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 5.5: Reaction force proﬁle (in kcal/[mol ξ]) for the H2 activation reactions R1– R4. to exothermic reactions whereas breaking ones lead to endothermic reactions. In this context, reversibility of reactions R1–R4 is not possible because the reverse reactions are overall net breaking process. In principle one can argue that the addition of external species, as a metallic center, could add bond forming processes thus lowering

W3 to facilitate the formation of the hydrogen molecule [146]. In Catalytic dehy- drogenation of Ammonia–borane for example [147], a nickel N-heterocyclic carbene (NHC) catalyst releases free NHC into the reaction media, which after dehydro- genates Ammonia-borane, is regenerated by Ni catalysts and releasing H2. Although

NHC does not activate H2 molecule, a similar approach could by interesting to in- vestigate with alkyl(amino) carbenes.

75 15 R1 R1 -50 10 ] ξ 5 -55 0 [kcal/mol]

µ -60 -5 REF [kcal/mol*

-65 -10

-15 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

15 R3 R3 -50 10 )] ξ 5 -55 0 [kcal/mol]

µ -60 -5 REF[kcal/(mol*

-65 -10

-15 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 5.6: Proﬁle of chemical potential (in kcal/mol) and reaction electronic ﬂux for reactions R1 and R3 (in kcal/[mol ξ])

5.3.2 Chemical Potential and Reaction Electronic Flux.

Taking into account that the cyclic systems have shown a similar behavior to its acyclic analogues and the observed changes in reaction and activation energies are mostly due to substitution of a methyl group by amino group, hereafter only acyclic systems, reactions R1 and R3, will be discussed in detail. For these systems the profiles of µ(ξ) and J(ξ), which have been calculated using the HOMO and LUMO energies, are shown in Figure 5.6. It can be noticed that in both reactions the chemical potential is relatively constant in the reactant region. Afterwards a broad peak in the transition state region sets in, and remains until the product region. During the first part of the reactant region, the REF presents a similar trend in both reactions, practically following a zero flux regime thus providing clear evidence

76 that at this stage the structural changes associated to the approaching of the two

fragments are predominant and determine the first part of the activation energy W1. Afterwards, entering the TS region of R1 and R3, a positive REF begins to emerge, this electronic reordering process (J(ξ)>0) activates the bond breaking and bond forming processes. A closer view shows that in R3 a maximum in the flux profile is reached at the reaction force minimum, while in R1 it is observed later, just before the transition state. After the maximum, at the TS region, both reactions begin to display some differences in the REF profiles. In R1 J(ξ) is positive until the TS

configuration where it is zero (J(ξTS)≈0). Then a broad negative peak shows up at the TS region becoming positive at the product region. In R3 J(ξ) becomes negative before the TS configuration where it is a minimum, then it shows a narrow positive peak at the product region. It seems that in order to reach the TS configuration, a spontaneous process that can be associated with polarization of the carbene moiety is necessary. In R3 this effect comes together with the H–H bond breaking and the weakening of the C···N bond, indicating that an electron transfer process is also necessary. These processes mostly take place before the TS configuration. For both reactions, a negative flux regime dominates the transition state region in a non spontaneous electronic reordering. To confirm the above finding and to elucidate the origin of the REF at different points along the reaction coordinate, fragmentation of the supermolecule was made

setting H2 and the carbene units as the molecular fragments all along the reaction coordinate. The results for polarization and transfer ﬂux, obtained through (Eqns. 2.24–2.27), are displayed in Figure 5.7. It shows for each reaction the contributions

Jp(ξ) and Jt(ξ) to J(ξ) (left panel) and the fragment contributions to Jp(ξ) (right panel). It can be noticed that polarization and charge transfer processes occur quite simultaneously along the reaction coordinate, with polarization effects being spontaneous Jp(ξ)>0 and most electronic transfer effects being non–spontaneous along the 77 reaction coordinate. At the first stage, the positive REF (J(ξ) >0) observed in R1 mainly comes from the polarization of carbene center due to the interaction with the hydrogen molecule; at this point electronic transfer activity is almost absent. It only becomes dominant at the transition state region, with a global minimum in the second part of the TS region. A different behavior of the REF is observed for R3 where the main contribution to the

initial REF peak comes from electronic transfer Jt(ξ), showing a local maximum value at the minimum of the reaction force, with a smaller contribution from polarization.

Then, during the first part of the TS region, Jt(ξ) decreases constantly reaching its minimum at the TS geometry. Thus, it shows that the major charge transfer between the two fragments and bond breaking/forming process was completed in the first part of the TS region. It can be noted that in both reactions, polarization of the carbene molecule increases along the reaction coordinate, which is not only due to the polarized carbon center but also due to the electronic reordering over the C–N bond(s). At the product region both systems show a positive peak which is again originated by the polarization of the carbene fragment. In this case, the rotation and pyramidalization of the NH2 group from the planar structure, results in a spontaneous electronic reordering (J(ξ) >0) that leads to the product state. In summary, after the zero flux regime observed for both systems at the reactant region, the activation process of R1 and R3 occurs in a different way. In R1 a spontaneous polarization flux (Jp(ξ) >0), which starts at the end of the reactant region, activates the reaction and the subsequent non–spontaneous electronic transfer flux

(Jt(ξ) <0) at the TS region. Here, the electron transfer activity is mainly located in the second part of the TS region. On the other hand, in R3 the activation process is mainly due to a spontaneous electron transfer processes, with a smaller contribution from polarization. For this system, a non–spontaneous(Jt(ξ) <0) electronic transfer ﬂux drives the process in order to reach the TS structure. Finally, at the prod-

78 uct region the polarization process begins to dominate in both systems and comes together with the structural relaxations to reach the corresponding product of the reactions. In the next sections the observed electronic activity will be related to local properties, adding some valuable information in order to support the electronic ﬂux analysis.

5.3.3 Reaction electronic ﬂux and Potential Energy.

The zero flux regime observed in the reactant region of both reactions confirms that W1 is mainly due to the structural preparation of the reactants to produce the chemical change. In particular, the energy required in R1 from reactant to ξ=-1.1, which match the end of a zero flux regimen and it can thus be directly associated to structural rearrangements, is about 12.9 kcal/mol. After this point, electronic activity starts to take place, being mainly localized at the transition state region, this electronic activity is mainly associated to polarization process on carbene with some electronic transfer (see Figure 5.7). The energy required for this stage is 8.4 kcal/mol. In short, the activation energy of R1 is about 60% associated to structural rearrangement and the remaining 40% is mainly due to polarization effects. In R3 the electron transfer peak emerges within the reactant region, thus indicating that W1 contains some electronic activity, in fact only 16.5 kcal/mol in W1 are due to structural rearrangement. The remaining energy needed to reach the transition state is mainly due to electron transfer with a smaller contribution from polarization activity. In summary, the previous analysis confirms that the reactant region involves predominantly structural effects, whereas in the TS region the electronic effects are predominant. R3 features an early electron transfer activity that shows up before leaving the reactant region. The nature of the activation energy in R1 and R3 is quite similar in terms of the contribution of structural rearrangements. However, the

79 R1 R1 20 20 J H2 15 Jt Carbene Jp 15 Jp ] ] ξ 10 ξ 5 10

0 5 -5 REF [kcal/mol* REF [kcal/mol* 0 -10 -15 -5 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

R3 R3 20 20 J H2 15 Jt Carbene Jp 15 Jp ] )] ξ ξ 10 5 10

0 5 -5 REF [kcal/mol* REF[kcal/(mol* 0 -10 -15 -5 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 5.7: REF decomposition: profiles of polarization and electron transfer flux for the H2 activation reactions R1 and R3. electronic processes that after that take place are different. R1 is activated mainly through electron polarization, while R3 is mostly activated due to electronic transfer effects.

5.3.4 Nucleophilic and Electrophilic Character of Carbenes.

Since the philicity of the carbene has been suggested to be one of the factors that determines the reaction mechanism, in this section the evolution of the dual descriptor ∆f(r) along the reaction coordinate is discussed (Eqn. 2.37). ∆f(r) functions have been calculated at the five key points along the reaction coordinate: reactants, force minimum, transition state, force maximum and products. In Figure 5.8 the dual descriptor is displayed along the reaction force profiles for R1 and R3; three-dimensional maps of the nucleophilic/electrophilic behavior of the different

80 Figure 5.8: Dual descriptor along the reaction force proﬁle of the H2 activation reactions R1 and R3; electrophilic sites with ∆f(r) > 0 are in yellow and nucleophilic sites with ∆f(r) < 0 in red.

sites within the composite systems are shown; areas in yellow are electrophilic sites with ∆f(r) > 0 whereas red areas display nucleophilic sites with ∆f(r) < 0. First, at the reactants, it is possible to note that in R1 the carbene center is biphilic because it features both electrophilic (yellow) and nucleophilic (red) character, the nucleophilic character is due to the lone pair on the carbene atom while the electrophilic character has its origin in the electron deﬁcient carbon atom, formally the

2pz atomic orbital. Additionally, it can be noted that the nitrogen atom has an important electrophilic character. In R3 the carbene center is markedly nucleophilic

81 and the nitrogen atoms show a very small electrophilic character. The feasibility

of the H2 activation reaction is closely related to the electrophilic capability of the carbene center. This is observed in R1 from the very beginning of the reaction whereas in R3 it is acquired through the structural rearrangements that initiate the reaction. Eventually, a very small electrophilic character emerges at the carbene center in R3 by the force minimum and increases within the transition state region. It is interesting to point out that at the reaction force minimum the nucleophilic power of the carbene in R3 is partially transferred to the hydrogen molecule, thus indicating an “early” electron transfer from carbene center to one hydrogen atom, in agreement with the previous observations in its REF profiles. In contrast, the nucleophilic behavior of the hydrogen in R1 emerges only at the TS configuration, where the electron transfer process starts to dominate. The biphilic behavior of the carbene center of R1 indicates that it may mimic a metallic center thus facilitating the activation of H–H bond. In contrast to this, in R3 the dual behavior is observed well entered the transition state region, making R3 much less feasible for H2 activation than R1, thus explaining the much low energy barrier in R1 in comparison to that of R3 (see the energetic data in Table 5.1). The transition state configuration of R1 still presents a carbene center featuring both nucleophilic and electrophilic behavior whereas in R3 the electrophilic character largely predominates over the nucleophilic power. Finally once reached the reaction force maximum systems evolve similarly, in both reactions the products show that the nucleophilic character is exclusively localized on the nitrogen atoms, while the central carbon atom exhibit a neutral behavior. It is this neutrality over the carbon center which causes the irreversibility of the process, as indicated by the high W3 values. In principle, reversibility can be forced by inducing an electrophilic behavior in that center through the action of external agents such as external fields or catalysts.

82 5.3.5 Natural Bond Analysis.

Figure 5.9 displays the evolution of the Wiberg bond order along the reaction coordinate for the critical bonds deﬁning the main chemical events that take place during the reaction. It can be seen that the H4–H5 and C1–Hn (n=4,5) bonds begin to change before reaching the transition state region; these changes, together with the

constant polarized charges observed in H2, reveal that at the beginning of the transition state an electron transfer (earlier in R3) and polarization takes place which is characterized by a positive ﬂux. Note in R1 that along the reaction coordinate the C1–C2 bond remains fairly constant, thus indicating that the methyl substituent acts only as spectator of the electronic processes that are taking place. On the other hand, the C–N bond order remains practically constant within the reactant region

at a value that suggests a double bond character with a planar NH2 group. This

bond evolves toward a single C–N bond at the product region where the NH2 group becomes pyramidal; as expected, the main changes of the C–N bonds are observed at the TS region and they are in part responsible of the increase in the polarization ﬂux. In the transition state region, the charge transfer and bond breaking/forming processes take place. In R1 the H4–H5 bond breaks and the C1–Hn bonds are formed in a quite synchronous way, with the electron transfer processes mostly centered in the second part of the TS region. This synchronicity is in agreement with the previously discussed biphilic nature of the carbene. In R3 the C1–Hn bonds forming processes are asynchronous, in this case the C1–H4 bond has been almost completely formed at the TS point, while the C1–H5 bond achieves formation later. At the transition state only a 40% of the C1–H5 bond formation has been achieved, compared with the 80% formation of the C1–H4 bond. This asynchronous process is featured in the REF proﬁle where an early electron transfer process takes place at the beginning of

83 R1 R3 1.6 1.6 C1-C2 C1-N2 1.4 C1-N3 1.4 C1-N3 C1-H4 C1-H4 1.2 C1-H5 1.2 H4-H5 1 H4-H5 1 C1-H5 0.8 0.8 0.6 0.6 0.4 0.4

Wiberg Bond Order 0.2 Wiberg Bond Order 0.2 0 0 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 1/2 1/2 ξ [a°amu ] ξ [a°amu ]

Figure 5.9: Wiberg bond order evolution and transition state complex for the H2 activation reactions R1 and R3. the TS region, indicating the ﬁrst bond forming process. Then, at the end of the transition state a shoulder due to charge transfer processes is again observed.

5.4 Concluding Remarks.

• In the present work a comprehensive study of the H2 activation reaction by (amino)carbene systems has been performed. It was demonstrated that the reaction electronic ﬂux partition results in a useful tool for the reaction mechanism analysis. Local descriptors, such as the dual descriptor, have also validated the results provided by the REF analysis.

• It was found that the electronic activity in alkyl(amino)carbene reactions is initiated by spontaneous polarization, followed by a non spontaneous electronic

84 transfer. Bi(amino) carbene systems feature an early electron transfer activity that shows up before leaving the reactant region.

• It has been found that in all cases the activation energy is mostly due to struc-

tural rearrangements, given by W1 values. However, the electronic processes that take place after are diﬀerent of nature. R1 is activated mainly through electron polarization at the carbene center, while R3 is mostly activated due to electronic transfer eﬀects.

• Biphilic behavior of the carbene center of alkyl(amino)carbenes indicates that these systems may mimic a metallic center thus facilitating the activation of H–H bond. This biphilic character allows an optimal polarization and helps to the synchronicity in the bond formation processes. Contrary, nucleophilic carbene centers lead to an early electronic transfer and an asynchronous bond formation processes.

• The irreversibility for this process arises from the high W3 values associated with the breaking process of the C–H bonds. It is proposed that external agents

could help to lower the reverse activation energy to produce H2.

85 6

A more detailed understanding of H2 Activation by (Amino)Carbenes

One of the keys for the isolation and enhanced reactivity of the carbenes capable to mimic the behavior of metal systems lay in the recognition that they require very large substituents to prevent secondary reactions such as dimerization [126]. In order to understand the inﬂuence that the substituents have over the whole activation process, as well as the cyclization eﬀect, in this chapter the study of hydrogen activation has been carried out using the crystal structure of the compounds used by experimentalist [130,141]. Additionally, the recently synthesized diamido carbene (DAC) system [141], where the two diamino substituents of the carbene center are replaced by diamido structures in a six-membered structure, has been also been studied (Figure 6.1). The chemistry displayed by this system has been surprising, in contrast to diamino carbene systems, as it is able to activate CO and NH3 [141,142], a reaction also observed in (alkyl)amino carbenes. However no reaction has been observed between this system and H2, even though (alkyl)amino carbenes can activate H2 [130] and that

86 Figure 6.1: Scheme 1. Alkyl amino carbene (CN-systems), diammino carbene (NN- systems) and N,N-diamidocarbenes (DAC). iPr=(CH3)2CH; Dipp = 2,6-(iPr)2-C6H3; t- But=(CH3)3C; Mes = 2,4,6-(Me)3-C6H2.

−1 the bond-dissociation energies of NH3 and H2 are similar (107 and 103 kcal mol , respectively) [122, 148]. Tolman electronic parameter (TEP 2055 cm−1) for such diamidocarbenes showed a considerable loss of nucleophilicity and σ-donicity [149], which could be related with its unreactivity∗.

6.1 Computational Methods

The geometry optimizations of all key stationary points were carried out using the B3LYP functional [82–85] with the Pople‘s basis set 6-311G(d,p). Transition states were fully optimized and characterized by harmonic vibrational frequency analysis. The minimum energy path in going from reactants to products was calculated

∗ The Tolman electronic parameter (TEP) is a measure of the electron donating or withdrawing ability of a ligand. It is determined by measuring the frequency of the A1 C-O vibrational mode of a complex LNi(CO)3 by infrared spectroscopy, where L is the ligand being studied.

87 through the intrinsic reaction coordinate procedure (IRC=ξ)[150, 151]. Using the geometries obtained from the IRC procedure, molecular properties were determined through single point calculations at the same level of theory. Natural bond orbital (NBO) analysis [89] was carried out to determine atomic charges from natural population analysis (NPA), using the NBO program version 3.1 available in Gaussian 09 program [152].

6.2 Results and discussion

6.2.1 Analysis of Isolated Carbenes.

In a ﬁrst part of this chapter, a brief analysis of the electronic properties of the isolated carbene systems is presented. Along this chapter the following nomenclature is used CN, NN and DAC refers to (alkyl)amino, diamino and diamido carbenes systems, respectively, while ACYC(CYC) refers to acyclic(cyclic) systems. Note that for DAC only the cyclic structure is considered (Figure 6.1). In order to analyze the eﬀect of aromatic substituents over t-bu substituent the t-bu analogous of CN CYC and DAC systems have been also studied, which have not been reported in literature; they are denominated CN CYCt−Bu and DACt−Bu, respectively. Table 6.1 lists global reactivity properties for these systems. It can be observed that

Table 6.1: Ionization Potential (IP), Electron Aﬃnity (EA), Chemical Potential (µ), Hardness (η), Nucleophilicity (N) and Global Electrophilicity (ω) Indices for the isolated singlet carbene systems. All values in eV.

IP EA N µ η ω CN ACYC 6.58 -1.66 4.79 -2.46 4.12 0.73 CN CYC 6.90 -1.00 4.47 -2.95 3.95 1.10 CN CYCt−Bu 6.79 -1.70 4.58 -2.54 4.25 0.76 NN ACYC 6.35 -1.99 5.01 -2.18 4.17 0.57 NN CYC 7.42 -2.15 3.95 -2.64 4.78 0.73 DAC 7.51 0.33 3.86 -3.92 3.59 2.14 DACt−Bu 7.64 0.09 3.72 -3.87 3.78 1.98

88 DAC is by far a better electrophile. It has been hypothesized that this high electrophilicity renders its reactivity toward isocyanides, carbon monoxide, and other nu- cleophiles [149]. It is followed by CN CYC, where the high electrophilicity shown by this system is mainly due to the presence of the aromatic ring substituent. Substitu- tion of it by a ter-butyl substituent leads to a similar electrophilic/nucleophilic power than that of CN ACYC. On the other hand, DAC and NN CYC are the less nucleophilic among the group, while the NN ACYC system shows the higher nucleophilicity. In general, acyclic systems show a higher(lower) nucleophilicity(electrophilicity) than their cyclic analogous, because rings tend to delocalize the electronic charge.

It has been argued that the reactivity of these systems over H2 and NH3 strongly depend on how carbenes may mimic the behavior of transition metals, i.e to show a nucleophilic and electrophilic behavior on the same atom center [130]. In order to gain more insight about the carbene center, the Fukui function (Eq. 2.35) and local electrophilicity and nucleophilicity on the carbene center have been calculated, as well as the local ionization potential. Table 6.2 confirms that the carbene center in CN systems are more nucleophilic and electrophilic than NN systems. It is interesting to notice that the electrophilic power is much more affected upon substitution of the α carbon atom by a nitrogen than the nucleophilic power, where the former decreases considerably. Also note that DAC is the more electrophilic and the less nucleophilic of the group. The values of the local ionization potential, indicative of the least tightly bound electrons, are quite consistent with the Fukui function. For all the systems the smaller values are found near the carbene center. In summary, these results provide evidence of the different nature of the carbene systems under study. CN systems exhibit a dual behavior with quite important electrophilic and nucleophilic power. In contrast to this, NN compounds are mostly nucleophilic with a weak electrophilic tendency. DAC shows the largest electrophilic

89 power at the carbene center but a very low local nucleophilicity, thus suggesting that these systems might be less favorable for the activation process.

6.2.2 Energy and Reaction Force.

In the second part of this chapter the H2 activation reaction is studied in detail. To this aim the potential energy, reaction force, and DFT-based reactivity descriptors are analyzed for the reactions CARBENE+H2 (Figure 6.1). For comparison the energetics parameters for CN CYCt−Bu asnd DACt−Bu systems are also included in Table 6.3 The minimum-energy paths and reaction force along the intrinsic reaction coordinate for the activation of molecular hydrogen are displayed in Figure 6.2. It

− + Table 6.2: Local Ionization potential Imin, Fukui functions,fCarb and fCarb, local − + nucleophilicity Nf , and local electrophilicity ωfCarb indices for the carbene center − + in the isolated singlet carbene systems. Imin, NfCarb, and ω fCarb are given in eV.

− + − + Reaction Imin fCarb fCarb NfCarb ω fCarb CN ACYC 5.29 0.56 0.45 2.67 0.33 CN CYCt−Bu – 0.56 0.42 2.50 0.32 CN CYC 5.55 0.53 0.25 2.36 0.28 NN ACYC 7.79 0.45 0.02 2.26 0.01 NN CYC 6.15 0.53 0.02 2.08 0.01 DAC CYC 6.39 0.28 0.30 1.06 0.64 DACt−Bu 0.51 0.26 0.52 1.91

6= Table 6.3: Activation Barriers ∆E , Reaction Energies ∆EP −R, and amount of work Wi(i=1-4), as deﬁned by the reaction force proﬁle in kcal/mol.

6= ◦ 6= ∆E ∆E W1 % ∆E W2 W3 W4 CN ACYC 18.9 -59.7 14.6 77% 4.3 -48.1 -30.5 CN CYC 22.7 -50.7 17.7 78% 5.0 -47.5 -25.9 CN CYCt−Bu 23.4 -48.9 17.8 76% 5.6 -47.1 -25.2 NN ACYC 27.4 -43.4 22.1 81% 5.3 -41.1 -29.7 NN CYC 30.5 -27.1 21.6 71% 8.9 -38.8 -18.8 DAC 24.5 -51.2 18.5 76% 5.9 -48.5 -27.1 DACt−Bu 25.2 -47.3 18.9 75% 6.3 -45.8 -26.7

90 was first noted that energy converges slowly to the reactants, so that the last structure obtained from the IRC calculation was converged to obtain the actual reactant system. The energy profiles of the diamino systems are different from the ones shown by the CN systems, they are broader at the transition state region and show a higher activation energy. It can be observed that the presence of a second amino group leads to products that are thermodynamically less favorable than the ones produced by alkyl amino carbene systems. On the other hand, the DAC system shows an energy profile closer to the ones of the CN-systems but with a higher energy barrier.

The reaction works (W1-W4) involved at each step along ξ were obtained by integration of the reaction force proﬁle within the speciﬁc reaction region; these values

Energy (CN) Force (CN) 50 30 Acyc Acyc Cyc Cyc 20 DAC 40 Dac 10 ] 30 ξ 0 20 -10 -20 10

Energy [kcal/mol] -30 Force [kcal/mol* 0 -40 -10 -50 -60 -20 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 ξ ξ

Energy (NN) Force (NN) 50 30 Acyc Acyc Cyc Cyc 20 40 10 ] 30 ξ 0 20 -10 -20 10

Energy [kcal/mol] -30 Force [kcal/mol* 0 -40 -10 -50 -60 -20 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 ξ ξ

Figure 6.2: Energy (in kcal/mol) and reaction force proﬁle (in kcal/[mol ξ]) for the H2 activation reactions.

91 are also quoted in Table 6.3. It has been shown that the ﬁrst step of an elementary process is mainly, but not exclusively, associated with structural reorganization of

the reactants to reach the activated reactant conﬁguration at ξ1, the minimum of the

reaction force. In the present situation, W1 is basically due to the approach of the H2 molecule to the carbene and variation of the X-C-N angle (X=N,C). The H-H bond distance remain almost constant until the minimum of the force, thus evidencing that at this point the bond breaking process starts to take place (Figure 6.3). Table 6.3 show that in all cases the main contribution to the energy barrier comes

from W1, being more than 70% of it. The CN systems show a W1 representing about 77% of the energy barrier. In the NN compounds the dispersion of the contribution

6= of W1 to ∆E goes from 71% (NN CYC) to 81% (NN ACYC) whereas W1 in DAC corresponds to 76% of the activation energy. The above results indicate that the

energy barrier in the H2 activation reaction by carbene systems are mostly of structural nature. A more detailed analysis of the physical nature of the energy barrier will be provided in the next section through the analysis of the reaction electronic ﬂux. In summary, from a kinetic point of view, these results suggest that the most favorable systems to activate H2 are alkyl amino carbene systems, in particular the

Distances (CN) Distance (NN) 5 5 C-H1 C-H1 4.5 C-H2 4.5 C-H2 H1-H2 H1-H2 4 4 C-H1(DAC) C-H2(DAC) H -H (DAC) 3.5 3.5 1 2

3 3

2.5 2.5

Distance [A] 2 Distance [A] 2

1.5 1.5

1 1

0.5 0.5 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 ξ ξ

Figure 6.3: Distances (in A)˚ for the H2 activation reactions. Solid/ lines correspond to acyclic systems and dot lines to cyclic systems.

92 acyclic system which shows the lower activation energy. Diamino carbene systems show larger activation barrier, and a larger contribution from electronic activity in NN CYC, in agreement with the results previously found in model systems.

6.2.3 Reaction Electronic Flux (REF)

During a chemical reaction bonds are broken and others are formed. As mentioned in Chapter2, the electronic activity taking place during a chemical reaction is identified and characterized through the reaction electronic flux; the REF profiles were obtained from finite differences approximation (Eqns. 2.17 and 2.23); which provide better results than the use of frontier orbital energies, even though both are qualitatively similar, specially in DAC systems where there is a crossing between the LUMO and LUMO+1 orbitals and between the HOMO-1 and HOMO orbitals. These profiles are displayed in Figure 6.4. It can be observed that all reactions are initiated with a zero flux regime until approaching the transition state region. In all cases the electronic activity starts to show up at the end of the reactant region, thus indicating that W1 also include some electronic effects. Grey vertical lines are displayed in the REF profiles to indicate the starting point of the electronic activity, where the REF shows variations larger than 1.0 kcal/mol. The energy required to go from reactant to

ξa, which match the end of a zero flux regime, for acyclic systems is 10.2 and 16.5 kcal/mol for CN and NN, respectively. These quantities correspond to a 70% and 74% of W1, respectively, thus, confirming that almost 30% of W1 includes simultaneously both, structural and electronics effects. Compared to model systems the structural contribution to the activation barrier is slightly smaller for CN ACYC (53% of ∆E6=) and larger for NN CYC (60% of ∆E6=). After the vertical grey lines displayed in the REF profiles (Figure 6.4), the electronic activity is evident, especially in the NN carbene systems. Therefore, the first part of the H2 activation process are mainly of structural nature, then the electron activity

93 REF (CN acyc) REF (CN cyc) 10 10

] 5 ] 5 ξ ξ

0 0

REF [kcal/mol* -5 REF [kcal/mol* -5

-10 -10 -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 ξ ξ

IA REF (NN acyc) REF (NN cyc) 10 10

] 5 ] 5 ξ ξ

0 0

-5 REF [kcal/mol* -5 REF [kcal/mol*

-10 -10 -8 -6 -4 -2 0 2 4 6 8 -6 -4 -2 0 2 4 6 ξ ξ

REF (DACH2) 10

] 5 ξ

REF [kcal/mol* -5

-10 -6 -4 -2 0 2 4 6 ξ

Figure 6.4: Reaction electronic flux profiles (in kcal/[mol ξ]) for reactions under study. starts to take place, thus indicating that structural reordering is readily coupled with electron activity. It is important to note that the electron activity has a different nature in cyclic and acyclic systems. In ACYC systems J(ξ) starts to increase indicating the formation of the first bond at the transition state region; the earlier electron activity in NN ACYC is mainly due to an earlier electron transfer, from the carbene center to the hydrogen molecule, which leads to the formation of one C-H bond and the formation of an hydride-like ion. In the cyclic systems the REF shows negative values at the beginning of the electron

94 spx(CN acyc) 3 N C

2.5

x 2 sp

1.5

1 -6 -4 -2 0 2 4 6 ξ

Figure 6.5: spx character over the carbene center and the nitrogen atom for the CN ACYC system. activity. It suggests that in these systems bond weakening and breaking processes are driving the reaction when leaving the reactant region. Within the transition state region the electronic activity of the five reactions follow the same pattern, in all cases bond breaking processes are driving the mechanism. Negative J(ξ) are followed by positive values of the REF assessing the formation processes taking place leaving the transition state region and entering the product region. It is clear from the REF profiles that the larger electronic activity is observed within the transition state region, where it exhibits one or two critical points. The nucleophilic attack of the carbene center to form the first C-H bond and, in a lesser extent, the second C-H bond are the event that drives the reactions. At the end of the transition state region, the later formation of the second C-H bond is observed in most cases. At the product region electronic activity is also found, which in all cases is mainly due to the pyramidalization of the carbene center as well as the nitrogen atom which finally achieves an sp3 like character (see Figure 6.5).

From these results it is evident that the nature of W1 is not only structural, but it also exhibits an electronic component. In acyclic systems about 30% of W1 evidences electronic contribution, while in cyclic systems this contribution is larger, specially in NN CYC where about of 80% of W1 involves some degree of electronic activity

95 ∆ η≠/∆E≠ 30 NNcyc 25 y=2.0554x-35.68 NNacyc 20

[kcal/mol] CNcyc(t-Bu) ≠

∆ η 10 CNcyc DAC CNacyc 5

0 15 20 25 30 35 ∆E≠ [kcal/mol]

Figure 6.6: Correlation of the activation energy ∆E6= and activation hardness ∆η6= for the reactions under study. coupled to structural rearrangement.

6.2.4 Activation Hardness

Analysis of the evolution of hardness along the process shows that it reaches a minimum at or near the transition state (data not shown), in agreement with the principle of maximum hardness [33]. In addition, its change from reactant to the transition state is larger for the systems with larger energy barrier. Zhou and Parr [153] deﬁned the activation hardness as the diﬀerence between the hardnesses of the transition

6= state and the reactants ∆η = (ηTS − ηR) finding that smaller activation hardness is associated with faster reaction for electrophilic aromatic substitution reactions. For the reactions under study a good correlation between ∆E6= and ∆η6= was obtained, with a proportionality parameter equal to 2 (Figure 6.6). Only DAC systems differ from the general tendency. As will be later analyzed it is mainly due to the different nature of its substituent. A deeper analysis of the activation hardness index (Eqn. 2.19) can be made in terms of it components. The hardness is defined from the ionization potential and

96 electron aﬃnity, and related to the HOMO-LUMO gap, therefore the change of each of these values when going from reactant to transition state allows to understand the origin of the change in ∆η6=. The NN-systems show that both -IP and -EA values change in a quite large extent, which is related to a decrease in the HOMO-LUMO gap. In contrast, the other systems show an smaller change, specially CN ACYC for which the -IP remains quite constant, The fact that DAC does not follows the trend can be understand from the change of its -IP and -EA values. Even though this system shows an smaller ∆η6=, comparable to CN CYC, the presence of the amide substituent leads to a very low -IP and -EA value. In this case, the π∗ orbital of the C=O double bond is involved in an unusually low LUMO orbital thus leading to a low -EA. It also leads to a decrease of the -IP value (HOMO orbital), in this case the lone pair on N does not contribute in the same extent to the HOMO orbital centered on the carbene atom. From the previous analysis it can be concluded that the activation hardness appears to be an excellent index for predicting the more favorable occurrence or not of the

H2 activation by carbenes systems. NN ACYC/CYC, are less favorable to react, in agreement with experimental results. It also indicates that not only the magnitude of the change, but also the origin of the hardness is fundamental to rationalize experimental results. Even thought DAC possess a ∆η6= comparable to CN ACYC/CYC, it shows a very low HOMO orbital, which is only slightly aﬀected in going from the reactant to the transition state.

6.2.5 NBO analysis

Figure 6.8 presents the evolution of the electronic population on the carbene center and the total charge of the H2 molecule. It can be seen that at the reactant structure the carbene center shows a more positive charge going from CN to DAC systems. As the process takes place it is clear that NN systems shows an intense electron

97 Figure 6.7: Proﬁle of the hardness and energy change for -IP and -EA (which are related to the HOMO and LUMO orbitals), from the reactant to the transition state, for all reactions under study (in kcal/mol).

activity. For these systems it can be seen that at the reactant region the H2 molecule starts to have a large negative charge while the carbene center shows an increase of its positive charge, thus indicating a net electron transfer from this center to the hydrogen molecule

On the other hand, CN systems shows a polarization of the H2 molecule, one H becomes negatively and the other positively charged, while the net charge of the H2 systems remains near to zero until the transition state region, as can be conﬁrmed from Figure 6.8. Therefore in this case the electron activity observed at the end of the reactant region and at the beginning of the transition state region can be mainly associated to polarization of the H2 molecule by the carbene center. Again, DAC system shows a behavior similar to the CN systems. However, it shows a much more positive charge on the carbene center, in agreement with the low nucleophilic power of this system. This due to the presence of amido substituent which acts as stronger σ electron acceptor compared to the amino group. Figure 6.9 shows the Wiberg bond order derivative for the cyclic systems, which provides a more detailed description of the electronic activity observed through the

98 Charge NBO Ccarb atom NBO Charge H1+H2 0.4 0.4 CNacyc CNCyc 0.3 0.3 NNAcyc 2 NNCyc 0.2

DAC +H 0.2 Cyc 1 0.1 carb 0.1 0 -0.1 0 Charge C CNacyc -0.2 CNCyc NBO Charge H -0.1 NNAcyc -0.3 NNCyc DAC -0.2 -0.4 Cyc -6 -4 -2 0 2 4 6 -6 -4 -2 0 2 4 6 ξ ξ

Figure 6.8: NBO charge for nitrogen and carbene center atom and H2 molecule.

REF. It can be seen that in all systems, the H-H and one of the C-H bond order derivative start to change at the reactant region, in agreement with the REF. Once

ξ1 is reached, a 23% of the C-H1 and a 32% and C-H2 bond has been formed in CN ACYC, while in NN ACYC a 40% and 26% of the respective bonds has been formed. These results evidence an early electronic activity and the asynchronicity in the process. For the cyclic systems show in Figure 6.9 it is also evidenced. NN CYC

shows a more asynchronous process, at the transition state 86% of the C-H1 and only

a 34% of C-H2 has been formed, while in CN CYC and DAC the asynchronicity is lesser, a 73/52% of C-H bonds in CN ACYC have been formed (in DAC 74% and 50%). Finally, an analysis of the charge transfer process was carried out through the second order perturbation analysis provided by the NBO procedure. Table 6.4 shows the most important donor-acceptor interactions and their energies for the system’s geometry at the minimum of the force between the carbene center lone pair and the antibonding σ∗ H-H bond. Additionally, in CN-systems a backbone donation of the same magnitude occur from the H-H bond orbital toward the antibonding π∗ orbital of the carbene system. In NN-systems, it was found that the donation from the lone pair to the antibonding σ∗ H-H bond is much larger than in CN-systems, thus

99 NBO bond order derivative (CN cyc) 0.8 dN-Ccarb 0.6 dC7-Ccarb dH1-Ccarb 0.4 dH2-Ccarb dH -H 0.2 1 2 0 -0.2 -0.4 -0.6 derivative Wiberg Bond Order -0.8 -6 -4 -2 0 2 4 6 ξ

NBO bond order derivative (NN cyc) 0.8 dN1-Ccarb 0.6 dN2-Ccarb dH1-Ccarb 0.4 dH2Ccarb dH1H2 0.2 0 -0.2 -0.4 -0.6 derivative Wiberg Bond Order -0.8 -6 -4 -2 0 2 4 6 ξ

Derivative NBO bond orders(DAC) 0.8 dN1-Ccarb 0.6 dH25-Ccarb dH58-Ccarb 0.4 dH25-H58 0.2 0 -0.2 -0.4 -0.6 derivative Wiberg Bond Order -0.8 -6 -4 -2 0 2 4 6 ξ

Figure 6.9: For the cyclic systems, bond order derivatives of the making/braking bonds along the reaction.

100 confirming an earlier charge transfer in these systems. However this interaction is not offset by the back donation from the H-H bond. It is negligible or unfavorable, as observed in NN ACYC where it occurs directly on the filled lone pair orbital of the carbene center. On the other hand, DAC shows a much smaller interaction energy from the lone pair

to the antibonding σ∗ H-H bond, conﬁrming its low nucleophilic power toward H2, which can be invoked to understand the diﬃculty of this system to activate molecular hydrogen. DAC system shows a backbone interaction towards the antibonding lone pair on the carbene center, but again it is smaller compared with the interaction observed in alkyl amino carbenes.

6.2.6 Dual Descriptor and Fukui Function

∆f(r) has been shown to be a useful descriptor for describing stereo-electronic eﬀects. It will be positive in electron accepting regions and negative in electron donating regions. It is then stated that favorable chemical events occur when good electron ac- ceptors regions (∆f(r) >0) are aligned with good electron donors regions(∆f(r) <0) [154].

Table 6.4: NBO Analysis for structures at the minimum of the reaction force.

∗ (2) Reaction Donor (nB) LP(1) Acceptor (σ ) E ∗ (kcal/mol) AH nB →σAH ∗ CN acyc Ccb BD H1 –H2 61.25 ∗ BD H1 –H2 BD N1 –Ccarb 42.46 ∗ CN cyc Ccb BD H1 –H2 88.13 ∗ BD H1 –H2 BD N1 –Ccarb 49.17 ∗ NN acyc Ccb BD H1 –H2 142.75 BD H1 –H2 LP Ccarb 69.26 ∗ NN cyc Ccb BD H1 –H2 167.35 ∗ BD H1 –H2 BD N1 –Ccarb 6.77 ∗ DAC Ccb BD H1 –H2 18.59 BD H1 –H2 LP* Ccarb 11.05

101 The dual descriptor was calculated at the transition state geometry of the species, carbene and hydrogen molecule (see Figure 6.10). Diﬀerences in the magnitude of the lobule as well as in the overlap between the negative and positive lobules are found along the group. CN ACYC presents the most favorable systems for the interaction

... carbene H2, it shows the larger overlap between the electrophilic carbene center with the nucleophilic lobule centered in H-H bond as well as between the nucleophilic lobule on the carbene former with the electrophilic lobule on H-H, which at this point correspond to the already formed C-H bond. On the other side, NN CYC presents the less favorable scenario, the electrophilic region on the carbene center is negligible, which is in line with the previous conclusion from the NBO analysis, suggesting that the absence of a good matching between electrophilic and nucleophilic zones does not allow a ”backbone” interaction from the more populated antibonding σ∗ H-H bond to the carbene system.

a) b) c)

d) e) f)

Figure 6.10: Dual descriptor of both species (carbene system and hydrogen molecule) calculated independently at transition state geometry. a) CN ACYC; b) CN CYC; c)CN CYCt−Bu; d) NN ACYC: e) NN CYC; f) DAC.

102 In CN CYC the magnitude of the lobules is smaller than in CN ACYC, however a good overlap is found. Replacement of the aromatic ring by ter-butyl substituent (6.10 c)) leads to an overlap similar to the one observed in CN ACYC. Finally, NN ACYC and DAC although indicate electrophilic region on the carbene center, show an unfavorable orientation that does not allow a good overlap between the nucleophilic and electrophilic regions.

6.3 Concluding Remarks.

• Analysis of the intrinsic reactivity on carbene systems evidences that local DFT-based index results are adequate to characterize the intrinsic reactivity of the carbene center studied in this chapter, whereas their global analogues fail to provide a clear trend. Overall, the electrophilic power is much more aﬀected upon substitution of the α carbon atom by a nitrogen than the nucleophilic power, the former decreases considerably in diamino carbene systems.

• Aromatics substituents in the amino group have almost no eﬀect in the electronic properties on the carbene center nor in the reaction mechanism. Even though they increase the global electrophilicity of the system, they do not alter the electronic nature of the carbene center.

• The global activation hardness index have shown to be a good descriptor for diﬀerentiating the kinetic aspects that aﬀects the reactivity of (alkyl)amino

and diamino systems over H2. Nevertheless, it remains challenging to obtain a more general global descriptor that can include the diﬀerences found in DAC system.

• It would be expected that from a kinetic point of view, DAC system should shows a similar behavior to the one found for the (alkyl)amino carbene systems.

103 However, a detailed analysis of its intrinsic reactivity as well as analysis on the reaction mechanism have evidenced that a system described by a poor nucleophilic carbene center leads to a less favorable orbital interactions along the activation process.

• Acyclic alkyl amino carbene systems are most suitable to carry out the activa-

tion of H2, they present the smaller activation barrier, and the more nucleophilic and electrophilic carbene center.

• Comparison with results obtained using model systems evidences that, in general, the use of model systems provide comparatively adequate results. How- ever due to the larger coupling between structural and electronic eﬀects they do not provide an adequate picture of the chemical events that drive the relaxation process.

• At this point it is also worthwhile to mention that along this study a more detailed rationalization of the reaction electronic ﬂux concept has been provided as well as new elements that could be useful for establishing a formal connection between this descriptor and chemical concepts. This work is in progress.

104 7

Prolyl cis-trans Isomerization: Non-Enzymatic and Enzymatic Mechanism

In proteins the peptide bond between the amide nitrogen and the carbonyl carbon atom are typically found in the trans conﬁguration. A special case is the peptide bond preceding a proline residue, where the cis conformation becomes feasible due to a

steric interaction between the Cδ- atom of the proline side chain and backbone atoms destabilizing the trans conformer [155,156] (Figure 7.1). The cis-trans isomerization of this peptide bond is a rather slow process at room temperature owing to the large energy barrier, but it has been shown to play an important role in protein folding [157, 158]. This is likely since native proteins bear the cis isomer which is not naturally synthesized in the ribosome. Additionally, the isomerization reaction is also used as a molecular timer in a number of biological processes, including cell signaling [159], ion channel gating [160] and gene expression [161,162] and its deregulation is related to pathological conditions, such as cancer [163, 164] and Alzheimer’s disease [165, 166]. In this context, Prolyl peptide cis-trans isomerases (PPIases), [167–169] as well as

Part of this chapter is included in: Fernanda Duarte, Esteban Vohringer-Martinez, and Ale- jandro Toro-Labb´e.Enzyme catalysis of cis-trans peptide bond isomerization by PIN1: What the mean reaction force and QM/MM simulations can tell us. Phys. Chem. Chem. Phys. (submitted)

105 Figure 7.1: Schematic representation of cis/trans isomers of the prolyl peptide bond catalytic and autocatalytic [170–172] mechanisms for prolyl amide isomerization have been recognized as accelerators of protein folding that may have important roles in various biological systems. In the present chapter the cis-trans isomerization process will be studied in detail. In the first section, the chemical aspects of peptide bond isomerization are studied employing the N-acetylproline methylamide system (Ac-Pro-NHMe) as a model for the study of the cis-trans isomerization of prolyl bond. The reaction mechanism of this process is described using DFT-based reactivity descriptors within the framework of the reaction force concept. The objective is to provide a detailed understanding on the non-enzymatic mechanism, characterizing the autocatalytic and the solvent effect over the mechanism and the activation barrier. The second part of this chapter will focus on the enzymatic isomerization by the Pro- lyl isomerase PIN1 enzyme [168,169]. PIN1 have been recognized to be fundamental in the regulation of a number of biological processes, specifically when phosphorylated Threonine/Serine-Proline sequence is present. With the aim to elucidate the molecular mechanism by which the prolyl isomerase PIN1 can regulate the cis-trans isomerization process and accelerate it, the enzyme-catalyzed process is studied employing extensive QM/MM molecular dynamics simulations in combination with the mean reaction force framework (Eqn. 2.57). As a reference the isomerization process of the five-residue peptide used in this study is analyzed in solution, using explicit solvent models.

106 7.1 Non-Enzymatic peptide bond cis-trans Isomerization

7.1.1 Introduction

Non-enzymatic peptide cis-trans isomerization has been extensively studied experimentally [170–176] and theoretically [173, 177–181]. In most of these studies N- Methylacetamide (Ac-NHMe) [173, 174, 177, 180, 182] and N-acetylproline methylamide (Ac-Pro-NHMe) [176,179,183,184] have been used as a minimal and standard model for the study of the cis-trans isomerization of proline-containing residues. Ro- tational barriers of 18.9 kcal/mol (cis-trans) and 21 kcal/mol (trans-cis) have been measured for Ac-NHMe by H1 NMR at 60◦C in water [174]. For Ac-Pro-NHMe Beausoleil et al. reported an activation barrier of 19.8 kcal/mol (cis-trans) and 20.4 kcal/mol (trans-cis), and an energy diﬀerence of 0.6 kcal/mol, being the trans state

◦ more stable, by using NMR experiments at 25 C in H2O[176]. Solvent eﬀects are known to play a key role in the barrier of C–N rotation. For instance, in Ac-NHMe ∆G6= can be increased by up to 3 kcal/mol (>100-fold rate decrease) simply by changing the environment from a nonpolar, non-hydrogen-bonding solvent to water [173, 174, 177]. This eﬀect has been explained by selective stabilization of the more polar ground state in water, versus the transition state of the isomerization. The reverse process, transfer of an amide from water to a hydrophobic environment, termed desolvation, has been proposed to be biologically important as a mechanism for the catalysis of amide isomerization [185, 186]. Higashijima et al. showed that NMR spectra of Ace-Pro-NHMe greatly depended on the polarity of the solvent used. Theoretical studies by Kang et al., at HF level using a conductor-like polarizable continuum (CPCM) model, showed that the cis populations and barriers for the rotation of the prolyl peptide bond for Ac-Pro-NHMe are increased with the increase of solvent polarity [183]. They also studied the preferred conformations of these systems and its derivatives in gas, water and chloroform using self-consistent

107 reaction field (SCRF) theory at different levels of theory [183,187,188]. In addition to the desolvation mechanism, other possible mechanisms for the catalytic acceleration of peptide bond isomerization have been proposed. Among them, acid- catalyzed isomerization by the rare N-protonation can be easily obtained at very low pH, but this type of catalysis is of course not significant under biological conditions. Other mechanisms such as a nucleophilic one has not yet been observed in non-enzymatic systems. Catalysis via formation of a carbonium ion intermediate appears to be improbable energetically [189]. Thus under cellular conditions, intermolecular non-enzymatic catalysis is difficult to obtain. By contrast, intramolecular non-enzymatic catalysis, through an intramolecular N-H...N hydrogen bond interaction, has been proposed [172,179]. The pathway connecting the cis-trans minimum in gas phase has been analyzed by Fischer et al. using empirical energy functions and ab-initio calculations. They found that the ζ dihedral angle (Figure 7.2) is more suitable for describing the progress of the reaction than the canonical ω angle. A trans-cis activation barrier of 17.9 and 20.7 kcal/mol for the anticlockwise and clockwise pathway, respectively, was reported by these authors. Yonezawa et al. reported the cis-trans isomerization of Ace-Pro-NHMe using explicit solvent model with QM/MM simulations [179], finding a cis-trans activation barrier of 20.9 and 21.2 kcal/mol for the anticlockwise and clockwise direction respectively, and a reaction energy of 4 kcal/mol. Most of the theoretical studies carried out in this system have mainly focused on the preferred conformations in different environments, and the relative energies of minimum and transition state conformations; however, no detailed reaction pathways have been reported. The aim of this study is to provide a detailed analysis of the non-enzymatic mechanism, characterizing the solvent effect and the autocatalytic effect (i.e intramolecular interactions proposed to assist prolyl isomerisation) on the mechanism and the ac-

108 Figure 7.2: Deﬁnition of torsion angles for Ac-Pro- NHMe. tivation barrier. This goal will be achieved by making use of the partition of the activation energy provided by the reaction force analysis and by the analysis of electronic properties using NBO analysis and the DFT-based dual descriptor.

7.1.2 Computational Methods

The geometry optimizations of all key stationary points were carried out using the B3LYP functional [82–85] with the Pople’s basis set 6-31G(d). Transition states were fully optimized and characterized by harmonic vibrational frequency analysis. Calculations on minimum and transition state geometries for all systems were also performed with extended basis set and at the MP2 level. Calculations in solution were performed with the polarizable continuum model (PCM) as implemented in the Gaussian 09 package [190], where the liquid is represented with a continuum characterized by a dielectric constant of 78.4 for water. As previously reported by Kang, who evaluated the effect of basis set and level of calculation on the structures and energetics of the rotation for Ac-NHMe, the energies obtained with B3LYP are in good agreement with the MP2 results, the reaction energy and energy barrier differ by less than 1 kcal/mol. The effect of the basis set was also very small and the 6-31G(d) basis set was found to be suitable to study the title reactions with a good compromise between accuracy and computational cost (Table 7.1).

109 ◦ 6= Table 7.1: Reaction energy (∆E ); forward (∆Ef ) energy barriers, all values are in kcal/mol.

∆E6= ∆E6= ∆E◦ ∆E6= ∆E6= ∆E◦ ∆E◦ anti clock anti clock

ts−cptH ts−cptH tn−oc−cptH ts−cnptH ts−cnptH tnhoc−cnptH tnptH −cnptH GAS HF 6-31g(d) 16.6 14.9 -3.0 17.3 15.6 -5.6 X B3lyp 6-31g(d) 17.6 16.2 -4.3 18.9 16.9 -7.1 X MP2 6-31g(d) 17.5 15.3 -3.5 16.9 15.8 -6.8 X PCM HF 6-31g(d) 17.9 16.2 -0.45 20.0 18.3 -1.2 -1.3 B3lyp 6-31g(d) 18.7 17.3 -2.3 21.4 20.0 -3.2 -0.9 MP2 6-31g(d) 18.7 16.7 -1.5 20.0 19.3 -2.7 -0.8 B3lyp 6-31g(d,p) 18.7 17.3 -2.2 21.4 20.0 -3.3 -0.9 B3lyp 6-311g(d,p) 18.5 17.2 -1.8 21.4 19.9 -2.7 -0.9

The minimum energy path from reactants to products were calculated through the

SCAN procedure. The dihedral angle ζ, deﬁned by the atoms Cα-OCO-Cδ(Pro)-

Cα(Pro) (see ﬁgure 7.2), was used as reaction coordinate as proposed by Karplus et al. [184, 191]. Diﬀerent starting structures were used for the SCAN procedure in order to explore the energy surface; the angle was changed 2◦ at each step. ∗ The rotation of the carbonyl moiety can be clockwise or counterclockwise, this determines whether carbon R1 in Figure 7.2 is on the same side or the opposite site of the proline ring relative to carbon C=O of proline during the isomerization, the two directions are referred to as clockwise and anticlockwise, respectively. Using the geometries obtained from the SCAN procedure, molecular properties were determined through single point calculations at the same level of theory. Natural bond orbital (NBO) analysis [89, 94] was carried out to determine atomic charges from natural population analysis (NPA) and to obtain stabilizing interaction energies

∗ This angle was used, instead of the canonical ω used in other works [192], so as to uncouple the 0 change of the isomerization from that of the pyramidalization. The ω angle (OCO-CCO-N-Cδ(Pro)) used for Yonezawa et al. in a QM/MM study [179] was also tested. However the use of this angle as the reaction coordinate also involved a considerable coupling between the isomerization and pyramidalization process.

110 by deletion procedure using the NBO program version 3.1 available in Gaussian 09 package [152]. Thermochemical values were obtained using unscaled vibrational frequencies.

7.1.3 Results and discussion 6.1.3.1 Energy Proﬁles

The energy proﬁles for the isomerization of Ac-Pro-NHMe in gas and aqueous phase are shown in Figure 7.3, and the energetic data are displayed in Table 7.2. Two mutually exclusive accessible reaction pathways were found, which diﬀer each other in the structure of their conformers as well as in their energetics (see Figure 7.4- 7.5). Path1g/Path2g refers to the lower/higher energy pathways in gas phase and

Pathsgas

Path1g Path2 20 g

5 Energy [kcal/mol] 0

-5 Clockwise Anticlockwise

-150 -100 -50 0 50 100 150 ξ

Pathspcm

Path1w Path2 20 w

5 Energy [kcal/mol] 0

-5 Clockwise Anticlockwise

-150 -100 -50 0 50 100 150 ζ

Figure 7.3: Energy proﬁles for the isomerization process in gas (top) and aqueous phase (bottom) at B3LYP 6-31G(d) level of theory.

111 Table 7.2: Reaction energy (∆E◦); (∆E6=) energy barriers together with the works associated to the diﬀerent stages at B3LYP 6-31G(d) level. All values are in kcal/mol except ∆S which is given in cal/(mol*Kelvin),T=298 K.

6= 6= ◦ 6= 6= ◦ ◦ GAS ∆E ∆Edel ∆E W1 W2 W3 W4 ∆G ∆S ∆G ∆S Path1gAnticlock 16.2 20.0 -4.3 9.2 7.0 -5.7 -14.8 16.1 -3.6 -3.7 -1.5 Path1gClock 17.6 18.9 -4.3 11.3 6.3 -10.4 -11.5 16.8 -1.5 -3.7 -1.5 Path2gAnticlock 16.9 -7.1 8.3 8.6 9.8 -14.2 17.1 -4.5 -5.2 -5.5 Path2gClock 18.9 -7.1 12.0 6.9 -13.0 -13.0 19.8 -6.6 -5.2 -5.5 6= 6= ◦ 6= 6= ◦ ◦ WATER ∆E ∆Edel ∆E W1 W2 W3 W4 ∆G ∆S ∆G ∆S Path1wAnticlock 17.3 21.3 -0.5 9.6 7.7 -6.7 -11.1 17.4 -4.1 -1.1 2.2 Path1wClock 18.7 21.6 -2.3 11.9 6.8 -9.1 -11.4 18.2 -2.3 -2.1 -0.8 Path2wAnticlock 20.0 -3.2 10.5 9.5 -9.0 -14.2 20.0 -4.0 -1.8 -4.3 Path2wClock 21.4 -0.9 12.7 8.7 -8.4 -13.9 21.5 -4.3 -0.1 -2.4 exp(25◦)[176] 19.8 -0.6

Path1w /Path2w to their analogous pathways when including solvent effects. The differences between both pathways lie in the presence or not of some intramolecular interaction, as will be discussed later. The energetic data show that the isomerization process is in all cases dominated by entalphic, and not entropic contributions. The free energy for the isomerization process in solution, for which experimental data are available, is -1.1 kcal/mol along the lower-energy pathway; in all cases the trans is the most stable conformer. Such difference agrees with the experimental value of -0.6 kcal/mol [176]. The free energy barrier along this pathway is 17.4 kcal/mol (Anticlockwise) and 18.2 kcal/mol (Clockwise) from the cis to the trans conformation. NMR experiment in water as solvent provides a value of 19.8 kcal/mol. Inclusion of specific water-peptide interactions as well as solvent reorganization energy has not been taken into account in this study and could affect the agreement of these results with the available experimental data. The two pathways under study evidence a minimum at ζ ≈ 0, corresponding to the cis isomer, and two nonequivalent transition states, for the anticlockwise (ζ ≈ 85) and clockwise (ζ ≈ −85) direction. Along Path1 the ψ angle (see Figure 7.2) is

112 Path1 9

15 ...... o E ...... 10 (ij (.) ~ >- e> Q) 5 e w o

-5 -150 -100 -50 o 50 100 150 ~ Path2gas 20

...... o 10 ...... E (ij (.) ~ >- 5 ....Cl Q) e w o

-5 Anticlopkwise

-150 -100 -50 o 50 100 150 ~

Figure 7.4: Relative energy (in kcal/mol) and the optimized structure along the isomerization Path1-2 in gas phase

113 15 o~ E ca...... 10 M. >- ....C'l Q) 5 e w o

-5 -150 -100 -50 o 50 100 150 ~

Path4w

~ 15 o E ca...... (..) 10 ~ >. ....Cl Q) 5 we o

-5 -150 -100 -50 o 50 100 150 ~

Figure 7.5: Relative energy (in kcal/mol) and the optimized structure along the isomerization Path1-2 in aqueous phase

114 close to zero, thus allowing an intramolecular NH···N between the NH group of methylamide and the nitrogen atom of proline. Along Path2, however, ψ is larger than 90◦ and no intramolecular interaction between both groups exist neither at the cis nor at the transition state conformation. These results evidence the important role that this interaction could play on the process by decreasing the activation barrier. However they do not give insight about the nature of its effect on the energy barrier. To get a more detailed vision of this catalytic effect on the activation barrier, in both gas and aqueous phase, the reaction force analysis is of great utility. Taking into account the entalphic nature of the activation barrier, this analysis will be based on the potential energy profiles, in which case the mean reaction force, including entropic effects, is expected to be close to the reaction force as defined in Eqn. 2.46. In the next section the solvent effect and the autocatalytic effect will be analyzed in detail.

6.1.3.2 Eﬀect of Solvent on the isomerization process

The eﬀect of the solvent is found not only on the activation barrier but also in the number of the conformers found. In gas phase the cis and transition state conformation diﬀer each other along Path1 and Path2, however they converge to the only trans conformer found in this phase, which corresponds to the one having the interaction between the NH group of methylamide and the carbonyl group preceding proline (Figure ??, top). In aqueous phase, however, in addition to this trans con-

former, which is common to Path1wclock and Path2wanticlock pathways, two other less stable trans conformers exist. One of these two additional trans conformers possesses the NH···N hydrogen bonding interaction found at the cis conformation

(Path1wanticlock), while the other one does not posses any of the previously described intramolecular interaction (Path2wclock).

115 These results are in agreement with experimental data [193, 194] which have shown that the trans conformer having the intramolecular NH···OC interaction is predominant in nonpolar solvents and that it becomes less favourablee as solvent polarity increases. These results also have important implications, evidencing that while cis to trans autocatalysis can take place in both polar and non polar environments, the reverse autocatalysis, from the trans to the cis isomer, can only take place in polar environments, where the carbonyl group preceding the proline residue can be stabilized and the NH···N interaction achieved. Therefore it would be important for the design of the prolyl isomerases (PPI) active-site to provide such stabilization. The PIN1 enzyme, for example, possesses an hydrophobic pocket at its active-site that is important for the binding of the prolyl ring; however it also possesses a Glutamine and Serine amino acids that have been found to be close to the prolyl bond under isomerization and that could be therefore able to provide such stabilization through hydrogen bonding interactions. Going from gas to aqueous phase there is also an increases on the activation barrier for both pathways, being larger along Path2, where the NH···N interaction does

6= not exist. ∆Ecis−trans increases only 1.1 kcal/mol in Path1w, however in Path2w it increases by 3 kcal/mol. This increase on the barrier, arises since the cis conformers are more stabilized than the transition states. The larger effect along Path2, where the NH···N interaction is absent can be understood by analyzing the dipole moment along each of these pathways: Path2 possesses a cis conformer having a much larger dipole moment (6.3 D) than the one along Path1 (1.3 D), therefore it is expected that the former will be more stabilized in aqueous phase. At the transition state, even though dipole moment differ among the different conformation (ranging from 3 to 5 D) the stabilization achieved in aqueous phase is quite similar. As a result the increase on the activation barrier in aqueous phase is mainly due to the larger stabilization of the cis isomer.

116 It has been suggested that the nonpolar environment of peptidyl-prolyl isomerases plays a key role in the catalysis. However, since the change on the activation barrier is only about 1-3 kcal/mol it is suggested that other specific interactions must exist at the active site of these enzymes that lead to a larger catalytic effect. These aspects will be discussed in detail in the second part of this Chapter. The solvent effects on the isomerization in water can also be rationalized by exam- ining the (O)C–N bond along the process (Figure 7.6). The Wiberg bond order at the cis conformation shows a double-bond character which becomes weaker as the system moves to the transition state. At the cis conformation, this bond is stronger in aqueous phase compared to gas phase, while at the transition state, the effect of the solvent is negligible and all systems show similar bond order values. This confirms that the larger effects going from the gas to aqueous phase are found in the cis conformer rather than at the transition state.

6.1.3.3 Intramolecular Catalysis

The pathways having the lower activation barrier (Path1g and Path1w in gas and aqueous phase, respectively), possess a cis isomer with the NH···N hydrogen bonding interaction. It has been suggested that this interaction stabilizes the transition state, thus decreasing the rotational barrier [184]. Experimental estimation of this interaction have been carried out by Cox et al. [172], who showed it may reduce the cis-trans activation barrier by 2.6 kcal/mol. Comparison between Path1 and Path2 suggests that the presence of this hydrogen bonding interaction has effects along both clockwise and anticlockwise direction, in gas and aqueous phase. However the larger difference is found in aqueous phase and along the anticlockwise direction. In gas phase, both cis and transition state configurations are almost equally stabilized going from Path2g to Path1g, thus leading to a smaller effect over the activation barrier. In aqueous phase however, the stabilization of the transition state configuration in

117 C-N Wiberg bond order C-N Wiberg bond order 1.3 1.3 N-C Path1g C-N Path1w N-C Path2 N Path2 1.25 g 1.25 w

1.2 1.2

1.15 1.15

1.1 1.1

1.05 1.05

1 1 C-N Wiberg bond order C-N Wiberg bond order

0.95 0.95

0.9 0.9 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 ζ ζ

Nitrogen Charge Nitrogen Charge -0.4 -0.4 Npro Path1g Npro Path1w Npro Path2g N Path2w -0.45 -0.45

-0.5 -0.5

-0.55 -0.55

-0.6 -0.6 Nitrogen Charge Nitrogen Charge

-0.65 -0.65

-0.7 -0.7 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 ζ ζ

Figure 7.6: C-N Wiberg bond order (top) and charger over the prolyl nitrogen for Path1–Path1w

Path1w compared to Path2w is three times larger than the one obtained for the cis , thus leading to a larger energy difference between both pathways. In Path1w the transition states are stabilized by about 3.5 kcal/mol while the cis isomer is only 0.9 kcal/mol more stable than the one found along Path2w, thus leading to the larger net decrease of the activation barrier. Taking into account that the general mechanism for which the cis-trans isomerization process takes place is the same either in gas or in aqueous phase, hereafter only the pathways in aqueous phase, Path1w and Path2w, will be discussed in detail. The reaction mechanism, and the catalytic effect provided by this hydrogen bonding interaction, can be better understood in terms of the reaction regions that are defined from the critical points of the reaction force profile (red dot lines in Figure ??). These regions are characterized by the specific amount of work necessary to achieve each

118 stage of the reaction. Table 7.2 shows that in most cases the larger contribution

to the activation barrier come from W1, specially in the clockwise direction. Along

Path1w, for example, the contribution of W1 to the activation barrier is 55% and 64% in the anticlockwise and clockwise direction, respectively. Therefore in order

to activate the isomerization process, going from the cis conformer to ξ1 a larger energetic cost is required along the clockwise direction. It is expected that this energetic cost will be due to both structural and electronic reordering, which due to the nature of the chemical process under study are strongly coupled. To get more insights on the catalytic effect afforded by the intramolecular interaction between the NH group and the lone pair of prolyl nitrogen, the stabilizing effect of this interaction have been estimated by using deletion analysis as implemented in NBO 3.1 ($DEL keyword). Briefly, this This analysis is performed by (1) deleting specific elements (or blocks of elements) from the Kohn-Sham matrix, (2) re-diagonalizing this new Kohn-Sham matrix to obtain a new density matrix, and (3) passing this density matrix to the SCF routines for a single pass through the SCF energy evaluator. The difference between this deletion energy and the original SCF energy provides a useful measure of the energy contribution of the deleted terms. The energetic barriers obtained from this analysis are compared with the one originally obtained (Table 7.2 third column). As expected, deletion of this interaction leads to an increase of the activation barrier. In the clockwise direction, this effect matches the increase on ∆E6= obtained for Path2w, thus allowing to directly associate this energy difference to the stabilizing effect due to the intramolecular NH···N interaction. For the anticlockwise direction, however, deletion of the NH···N interaction leads to an activation energy even larger than one obtained in Path2w, it seems that along this direction other effects, such as relaxation of the nuclei, can compensate in part the absence of this interaction. Analysis of this stabilizing interaction in terms of the reaction works provides in-

119 teresting results. In Path1wAnticlock, the NH···N interaction leads to a stabilizing effect in both W1 and W2, while in the clockwise direction the stabilizing effect is only found in W2. In this case deletion of the interaction leads to a W1 value 1.1 kcal/mol lower and a W2 value 4.0 kcal/mol larger than one obtained when the interaction is taken into account. From these results it is clear that the origin of this autocatalytic effect due to the NH···N interaction, has a different effect depending on the direction of the rotation of the prolyl bond. The autocatalysis is larger and more favorable in the anticlockwise direction, where both W1 and W2 values are smaller when the interaction is present. By contrast, in the clockwise direction this interaction is unfavorable at the beginning of the process, and only shows an stabilizing effect at the transition state region. It can be concluded that the anticlockwise process result more favorable due favorable interactions along this pathway.

6.1.3.4 Dual descriptor

The dual descriptor ∆f(r)[51] allows to simultaneously identify nucleophilic and electrophilic regions within a molecule as well as favorable inter/intramolecular interactions, which result when the nucleophilic regions of one molecule (∆f(r) <0 ; red regions in plots) align with the electrophilic regions of another molecule (∆f(r) >0); yellow regions in plots), and vice versa. In order to analyze these interactions, and the electronic changes taking place along the process, the dual descriptor have been studied at the cis , transition state and trans conformer. Here, as mentioned before, only the pathways studied in aqueous phase will be analyzed, ﬁnding similar results in gas phase. The dual descriptor at the cis conformation shows a quite diﬀerent pattern for each of the pathways. In Path1w the cis, conformer posses a LUMO orbital mainly localized at the acetyl moiety, which leads to a favorable interaction between the positive and negative lobules centered in the carbonyl carbon and nitrogen atom, respectively.

120 Figure 7.7: Dual descriptor at the cis, transition state and trans conﬁguration along Path1w and Path2w

In Path2w, however, the absence of the intramolecular NH···N interaction leads to a LUMO orbital localized at the carbonyl group of proline. For this system the LUMO+1 orbital, instead of the LUMO one, is centered in the carbonyl moiety next to the nitrogen atom, thus been less favorable. This results also conﬁrm the stabilizing eﬀect of the intramolecular interaction on the cis isomer. Rotation around the (O)C–N bond can take place along a transition where the nitrogen lone pair is at the same side(syn) or opposite side(anti) relative to the C–O bond. The dual descriptor shows clearly this feature. In Path1w both transition states, in the anticlockwise/clockwise direction, have a syn conformation, where the nitrogen lone pair, associated to the larger red lobule centered at the nitrogen atom,

121 is found above the plain. This conformation leads to a more favorable interaction between this center and the NH group above it, as also evidenced from the second order perturbation theory within the NBO analysis. In Path2w, the transition states shows a nitrogen lone pair above/below the plane for the anticlockwise/clockwise direction, which tend to minimize the interaction with the carbonyl group. In both cases no hydrogen donor group interacts with this localized lone pair. Finally at the trans state a competition between electrostatic and orbital interactions leads to a more stable trans state having an intramolecular hydrogen bond between the NH and the carbonyl group.

7.1.4 Conclusions

• Two mutually exclusive accessible reaction pathways were found in gas and aqueous phase for the non-enzymatic cis-trans isomerization. They diﬀer each other in the structure of their conformers as well as in their energetics.

• The eﬀect of the solvent is found not only on the activation barrier but also in the number of the conformers found in this phase. It favors the stabilization of three instead of just one trans conformer, as found in the gas phase. The stabilization of a trans conformer having the NH···N interaction also favors the autocatalysis to take place in both reverse and forward direction. In particular nonpolar environments stabilization of the carbonyl group preceding proline is required in order to maintaing the intramolecular NH···N interaction.

• The increase of the activation barrier in aqueous phase is mainly due to the larger stabilization of the cis isomer rather than at the transition state. The larger eﬀect along Path2 is associated to the polarity of its cis conformer, which is largely stabilize in aqueous phase.

• The catalytic eﬀect of the intramolecular interaction has been analyzed in detail

122 through NBO analysis and within the reaction force framework. It can be concluded that this eﬀect is larger along the anticlockwise direction, resulting

in a decreases of both W1 and W2 values. By contrast, the catalytic eﬀect

along the clockwise direction is only evidenced in W2, showing an unfavorable eﬀect in the ﬁrst part of the process.

• The dual descriptor resulted to be a good one for describing the pyramidalization taking place along the process. It evidences that the intramolecular interaction favor a syn transition state, while the absence of it leads to a transition state where the nucleophilic lobule tend to minimize the interaction with the carbonyl group.

• Analysis of the reaction electronic ﬂux in this systems is currently under study, in order to provide additional elements for the analysis of the possible diﬀerent pathways found for this process.

123 7.2 Enzymatic Catalysis by PIN1: A QM/MM Study

Having analyzed in detail key aspects of the non-enzymatic cis-trans isomerization of prolyl bond in a model system, in this section the analysis will be extended to the enzymatic process. The aim is to elucidate the catalytic eﬀect of the Peptidyl Prolyl cis-trans Isomerase (PPIase) PIN1 on the cis-trans isomerization. A combined approach based on Molecular Dynamics (MD) simulation, using the umbrella sampling method, and quantum mechanics calculations has been used for this study. A detailed description of the theoretical methods used in this study is given in Appendix B.

7.2.1 Introduction: Enzyme PIN1.

PIN1 distinguishes itself from all other known PPIases through its unique substrate specificity for the pSer-Pro or pThr-Pro amide bonds. It has been found that side chain phosphorylation at threonine or serine residues decelerates both cis to trans and trans to cis isomerization rates [195, 196] and that an strict control of the cis/trans populations of these pThr/pSer-Pro motifs is fundamental to ensure proper regulation of cellular signaling [197]. In this context, PIN1 has emerged as a critical regulator [198]. PIN1 specifically catalyses the cis-trans isomerization of the pThr/pSer-Pro imide linkages with a selectivity over non-phosphorylated motifs of more than 1300-fold [199]. PIN1 is a two domain-enzyme with a WW domain which binds pThr/pSer-Pro moiety with high affinity and a catalytic active peptidyl-prolyl isomerase domain, named PPIase domain. Studies have shown that the catalytic PPIase domain possesses full isomerase activity even without the other domain and the flexible linker connecting the two [200]. At the entrance to the active site of the PPIase domain a positively charged cluster formed by a triad of basic residues, Lys-63, Arg-68 and Arg-69 sta-

124 Figure 7.8: Representation of the human enzyme PIN1 (PDB:2Q5A.pdb). The N- terminal WW domain and the C-terminal peptidylprolyl cis-trans isomerase (PPIase) domain are shown in green and yellow, respectively. bilizes the negative charged phosphate group of the pThr-Pro (see representative structure of equilibrated peptide Ace-Gly-pThr-Pro-Phe-Gln-Nme in PIN1 in Figure 7.9). The aliphatic proline side chain is cradled in a hydrophobic pocket formed by the residues Phe-134, Met-130 and Leu-122. A hydrogen bond between the proline carbonyl oxygen atom and the backbone amide group of Gln-131 also contributes to maintain this residue essentially fixed. Following the peptide sequence a second hydrogen bond between the amide group of the glutamine residue and the carbonyl oxygen atom of the Gln-129 residue of the PPIase domain fixes this part of the peptide inhibiting its rotation during the isomerization process. Although several experimental studies on the PIN1 activity have been reported, the exact mechanism by which PIN1 catalyzes the cis-trans isomerization process remains elusive and is still a subject of controversy. Both covalent [169, 192] and noncovalent [201] mechanisms have been invoked. According to the covalent mechanism, based on the original paper describing the crystal structure of PIN1, catalysis takes place first through a proton transfer process from the thiol group of Cys-113 to His-59, followed by a nucleophilic attack of the sulphur atom of Cys-113 to the car-

125 Cys-113

Lys-63

Ser-154

Arg-68 Arg-69 Figure 7.9: Snapshot of the catalytic active site of human PIN1 with the Ace-Gly-pThr- Pro-Phe-Gln-Nme peptide and the dihedral angle ζ representing the reaction coordinate. bonyl group. However, the fact that Cys113D and His59L mutants remain functional called this mechanism into question [201,202]. The noncovalent catalysis mechanism, on the other hand, suggests that Cys-113 plays a key role maintaining an overall elec- tronegative environment, which might destabilize the double bond character of the prolyl bond [201]. Experimental determination of the pKa value of this residue, however, has not been possible. To elucidate the mechanistic features that give rise to the catalytic power of PIN1 a complete characterization of the reaction mechanism during the isomerization process is needed. However, studying the isomerization in the enzyme alone is not enough to understand its catalytic power: the characterization of the isomerization in aqueous solution is required to compare the results obtained in the enzyme. Therefore, extensive molecular dynamic simulations with standard force fields in combination with the QM/MM methodology have been carried out for the reaction in the two different environments. In addition, to include also correlation effects of the electrons – known to be crucial for activation barriers – the QM/MM-minimum free energy

126 path (MFEP) method has been applied on the enzyme reaction [203].

7.2.2 Computational details Construction of the Initial Structure.

Molecular dynamics simulations were performed with the Gromacs 4.5.3 software package [204]. A time step of 2 fs in combination with the velocity rescaling temperature coupling algorithm of Bussi et al. [205](τ = 0.1 ps) and the Berendsen pressure coupling algorithm [206] were used. The electrostatic interactions were calculated with the Particle-Mesh-Ewald method, a cut-off radius of 1.0 nm, pme-order of 4 and a spacing of 0.1 nm. The van der Waals interactions were described by a shifting function, which switches the forces to zero between 0.8 and 0.9 nm. The neighbor list was updated every 5 steps and its cut-off was set to 1.0 nm. All hydrogen bonds were constraint with the LINCS algorithm of order 4 [207]. The QM/MM molecular dynamics simulation were performed in combination with the Gaussian 03 package [90] in an electrostatic embedding as incorporated in the Gromacs 4.5.3 package. Electrostatic interactions in the MM region were treated with the reaction field method (cut-off radius = 1.0 nm, switching radius = 0.9 nm

r = 78) and the time step was reduced to 1fs. The neighbor list was updated at every step.

System Setup

The crystal structure of an inhibitor bound complex of PIN1 with PDB ID 2Q5A (1.5 A˚ resolution) [208] was used as a starting structure for this study. The inhibitor was modiﬁed to match the sequence of the substrate, Ace-Gly-pThr-Pro-Phe-Gln- Nme. Since the inhibitor already provided the substrate backbone, only redundant atoms were deleted and the capping residues were added at the end positions. The CHARMM27 force ﬁeld with the CMAP (a 2D dihedral energy grid correction map)

127 correction [209] and the AMBER99sb [210] force field were utilized in combination with the charges provided by Craft et al. [211] for the threonine phosphate group (for the CHARMM27 force field the charges provided by Lee et al. were used instead [212]). Residues 39-50 were not resolved in the crystal structure, which originates from their high flexibility as shown in various NMR studies [213,214]. To solve this issue a terminal group was added to the end residues Ser-38 and Glu-51. Additionally, a harmonic restrain (k = 400 kJ mol−1 nm−2, distance = 1.48 nm) was applied in all reported simulations on their Cα atoms to maintain their interaction imposed by the missing residues. In a second step this imposed restraint on the protein dynamics was validated modeling the missing residues with the Amber10 package and the Xleap program: comparison of the two output structures with the unrestrained and restraint systems after an equilibration of 50 ns yielded no differences in the secondary structure nor in the catalytic cavity. The obtained enzyme structure with the peptide substrate was solvated in a cubic box with a side length of 8 nm employing the SPC model for the water molecules [215]. Counter ions were added to obtain a physiological salt concentration (0.154 mol/L) of the neutral system. The whole simulation system was first minimized, simulated with position restraint on all Cα atoms for 500 ps and equilibrated for 50 ns. The equilibrated structure, which contained the peptide bond in cis configuration, served as starting structure for the isomerization to the trans isomer. The dihedral angle ζ, defined by the atoms Cα(pThr)-OCO(pThr)-Cδ(Pro)-Cα(Pro) (Figure 7.9), was used as reaction coordinate as proposed by Karplus et al. [184, 191]. The dihedral angle was restraint with a force constant of 500 kJ mol−1rad−2 starting at 0◦ for 5 ns. The obtained output structure served as input for the subsequent 5 ns simulation where the dihedral angle was increased (anticlockwise) or decreased (clockwise) by 10◦, according to the nomenclature used previously in the model system. This

128 procedure was performed until 180◦, which corresponds to the trans conﬁguration. The subsequent use of output structures and the 5 ns equilibration ensures a proper equilibration of the peptide and the enzyme during the rotation. A second reaction coordinate, described by the ψ angle of the threonine phosphate residue, had to be introduced once reached 140◦. The second reaction coordinate was needed to avoid unfavorable interactions with the enzyme. The simulation procedure was the same and the chosen ζ and ψpThr values were: 140/90, 150/70, 160/50, 160/30, 160/10, 160/-10,160/-30,170/-30,180/-30 and 180/-50. The cis-trans isomerization was also performed in aqueous solution to identify the origin of the catalysis. For the aqueous solution simulations the equilibrated peptide from the enzyme in the cis conﬁguration was isolated and solvated in a cubic box with 5 nm box length and physiological NaCl concentration and equilibrated for 5 ns. The isomerization was performed in the same consecutive manner as described above.

QM/MM Molecular Dynamics

Starting structures for the QM/MM simulations were obtained from the last 4 ns of the MM simulations along the reaction path. The step size in the reaction coordinate was increased to 20◦, since it did not change significantly the mean reaction force and free energy profile of the MM simulations and reduced considerably the computational cost of the QM/MM simulations. The restrain force constant was doubled for simulations around the minimum and maximum of the mean reaction force to minimize the deviation from the restraint value of the reaction coordinate. The QM atoms were treated with the HF/3-21G method and the link atom method was used for the covalent QM-MM interactions. For the reaction in solution three simulations with different starting structures were considered per value of the reaction coordinate. In the enzyme the number of starting structures, where only ζ was restraint, was increased to five to account for the

129 heterogeneous nature of the environment provided by the enzyme.

The Mean Reaction Force

The deviation of the dihedral angle from its restraint value for each simulation and its standard deviation were used to calculate the mean reaction force [64] employing the Umbrella Integration method from K¨astner et al. [216–218] (for more details of this methods see AppendixB). The free energy proﬁle along the reaction coordinate was obtained by numerical integration applying the Simpson rule. For the reaction in the enzyme where two reaction coordinates were needed the mean reaction force was obtained within the linear approximation for each coordinate and the free energy by integration over one and then the other coordinate.

QM/MM MFEP simulations

To improve the description of the QM system and to include electron correlation, avoiding the high computational cost of direct QM/MM molecular dynamics, simulations of the enzyme-catalyzed isomerization were performed using the QM/MM Minimum Free Energy Path approach of Yang et al. [203], which has been success- fully applied to study the reaction mechanisms of several enzymes [139,219,220]. A detailed description of the method can be found in previous works. [203,220,221]. In this method, the QM subsystem is optimized in the MM environment. The general procedure is based on two steps; ﬁrst, a ﬁnite ensemble generated via molecular dynamics simulations is used to calculate the potential of mean force surface; then, the QM conformations are optimized on this calculated potential of mean force surface. Both steps, QM optimization and the MM sampling are sequentially performed until convergence. The reaction path on the Potential of mean force surface is optimized using the nudged-elastic-band (NEB) method [222]. Within this approach the full QM degrees

130 of freedom are used to construct a discrete reaction path from the reactant state to the product state, each NEB optimization step consisted of one QM calculation followed by 160 ps of MD simulation for the computation of the free energies and free-energy gradients. The parameters of the CHARMM force field were used to describe the classical MM interactions. In all simulations, a dual cut-off of 9 and 12 A˚ was used to separate the short- and medium-range interactions. The integration time steps were 1 fs for short- range forces, 4 fs for medium-range forces, and 8 fs of long-range electrostatic forces. The medium-range QM/MM electrostatic interactions were modeled as pure classical interactions between the ESP point charges on the QM atoms and the point charges on the MM atoms; only the short-range neighboring MM atoms were included in the quantum mechanical calculation for the energy, gradient, and ESP charges. The Merz-Singh-Kollmam [223] scheme was used for ESP charge fitting. The temperature of the system was kept at 300 K by a Berendsen thermostat [206]. The MD simulations and minimizations were carried out with the program Sigma which was interfaced with Gaussian 03 to perform the QM calculations. For the QM calculations, the B3LYP/6-31G* method was used, while the QM/MM hybrid bonds were modeled with the pseudobond method [224].

7.2.3 Results and discussion Isomerization in aqueous solution

To understand the origin of the catalytic effect and to compare to the reaction mechanism in the enzyme, the cis-trans isomerization was first studied in aqueous solution. The free energy profile, based on the data collected from MD simulation and processed using the Umbrella Integration method, for both CHARMM and AMBER force field showed qualitatively similar results. In solution both isomers are close in energy, in agreement with experimental results [176]. However the energy barrier was underestimated. Previous theoretical studies [178] in a model system have shown that

131 120 2 100 1 80

0 60 G [kJ /mol] F [kJ /mol/°] -1 40

-2 20 0 -20 0 20 40 60 80 100 120 140 160 180 -20 0 20 40 60 80 100 120 140 160 180 cis Dihedralζ [°] trans cis Dihedralζ [°] trans Figure 7.10: Mean reaction force and free energy profile for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in aqueous solution. for the AMBER force field the dihedral parameter associated to the rotation has to be modified in order to reproduce the experimental activation energy. Because force fields by their own are known to be unable to describe chemical reactions, QM/MM simulations at HF/3-21G level were carried out to study the cis-trans isomerization process.

The QM region involved all atoms in the amino acid sequence starting at the Cα atom of threonine phosphate until the N-H group of phenylalanine (20 atoms in total). Due to the high computational cost, windows only every 20◦ were considered and only 15 ps per window could be simulated. Extending the simulation time to 25 ps for one starting structure did not alter the results considerably and even longer simulations were not feasible considering the number of windows. The average value of ζ and its standard deviation were calculated for each window as the average value over the three performed QM/MM simulations. These values served to calculate the mean reaction force employing the umbrella integration method of Kästner et al. [216–218] and its integration along the reaction coordinate yielded the free energy profile. The mean reaction force and the free energy profile along the reaction coordinate ζ are shown in Figure 7.10. The cis configuration presents a minimum at a ζ-value ≤ 0◦ where the mean reaction force is zero. The mean reaction force crosses zero again

132 at the transition state (ζ = 80◦) and reaches the product represented by the trans isomer at 180◦. The minimum of the mean reaction force, which describes the point of overtaking electronic rearrangements along the reaction coordinate, is reached at ' 50◦ and the maximum describing the almost completed electronic reorganization and the onset of structural relaxation at 120◦. The free energy proﬁle exhibits an activation barrier to reach the transition state from the cis-isomer of 119 kJ/mol (28 kcal/mol). This value compares well with the value of 105 kJ/mol (24.9 kcal/mol) of Yonezawa et al. who studied the cis-trans isomerization of Ace-Pro-Nme in explicit water with QM/MM simulations [179], although it is larger than the experimental value of 84.1 kJ/mol (20.1 kcal/mol)

−2 for the Ala-Ala-Thr(PO3 )-Pro-Phe-NH-Np of Schutkowski et al. [195]. The cis- trans free energy diﬀerence of 26 kJ/mol (6.2 kcal/mol), however, does not match the experimental observation of a more stable trans isomer. Since the aim of this study is to elucidate the reaction mechanism and the catalytic power of the enzyme rather than to provide the cis-trans ratio in solution further simulations were not considered. As shown in a previous study [64] the separation of the reaction mechanism in different processes provided by the mean reaction force allows also to study the nature of the free energy barrier and to assign its structural and electronic contributions (Eqns. 2.58). The activation of the cis isomer is dominated by the structural contribution W1= 95 kJ/mol (22.6 kcal/mol) and a small electronic part of W2= 24 kJ/mol (5.7 kcal/mol). Once reached the transition state the system relaxes with an electronic contribution of W3=-56 kJ/mol (-13.3 kcal/mol) and a structural component of W4=-37 kJ/mol (-8.8 kcal/mol). Compared with the model system previously studied, the contribution due to W1 is larger, which can be associated to larger structural reordering needed to activate the process. To validate the separation of the reaction mechanism in electronic and structural

133 changes by the mean reaction force, another descriptor of electronic activity was considered: Along the reaction coordinate the nitrogen atom of the peptide bond turns from a sp2- to a sp3-hybridization at the transition state, where the free electron pair is located on the nitrogen atom. This is accompanied with a change in bond character of the peptide bond from pseudo double to single bond at the transition state and should be reﬂected in an increase of the peptide bond length. Indeed, as shown in Figure 7.11 the largest changes in the bond length are observed between ζ = 50◦ and ζ = 120◦ conﬁrming the separation in structural and electronic contributions provided by the minimum and the maximum of the mean reaction force.

0.142

0.141

0.14

0.139

0.138

0.137

0.136 C-N bond [nm] 0.135

0.134

0.133

0.132 -20 0 20 40 60 80 100 120 140 160 180 Dihedral ζ [°] Figure 7.11: C-N bond length of the rotating bond for the isomerization in solution

Yonezawa et al. reported that the isomerization in aqueous solution is catalyzed by an intramolecular hydrogen bond between the amino hydrogen atom of the residue following proline and the nitrogen atom in the peptide bond. In this work this hydrogen bond, which was present in the starting structure, was preserved during the whole rotation until ζ = 100◦ in agreement to their results. After the transition state, however, the peptide adopted an extended conﬁguration and the average distance between these two atoms increased. This would indicate the loss of the intramole-

134 cular catalysis after the transition state. Indeed, the electronic contribution, which is the most affected by the hydrogen bond, is larger for the reverse reaction starting from the trans isomer. Therefore, the mean reaction force correctly identifies the catalytic effect of the intramolecular hydrogen bond decreasing the electronic contribution by ' 20 kJ/mol. This catalytic active intramolecular hydrogen bond in the isomerization reaction in solution was also proposed in an experimental study by Cox et al. [172] and in the enzymatic catalysis of FK506 binding protein by Fischer et al. [191].

Protonation state of Active site Residues in PIN1

A still unresolved issue is the protonation state of the nucleophilic Cys residue [169, 201, 213]. This residue has been considered important for both to the nucleophilic (deprotonated state) and the noncovalent mechanism (normal state) and no experimental determination of pKa has been possible. It is well established that the cysteine thiol is a poor nucleophile. However, based in the original paper describing the crystal structure of PIN1, it was hypothesized that the catalysis takes place first through a proton transfer process from the thiol group of Cys-113 to His-59, followed by a nucleophilic attack of the sulphur atom of Cys-113 to the carbonyl group. To test the hypothesis of a negatively charged sulphur atom at this position contributing to the catalysis, simulation were carried out with two different sets of protonation states, which differ in protonation state of Cys113 and His157. Model I corresponding to the protonation states of Cys and His in its neutral form and Model II corresponding to a system where the proton of Cys-113 is transferred through His-59 to His-157 (Figure 7.12). For each model a 50 ns MD simulation was carried out. During the course of the simulation, however, it was found that the peptide starts moving out of the cavity in Model II, while the distance between substrate and the basic pocket, as well as the bond distance O(TPO)-S(Cys), increased. This observation together

135 Figure 7.12: Model I(yellow) and Model II (green) for the protonation state of Cys113 and His157

with the mutation studies showing no functional dependence of the enzyme on His- 59 and His-157 [201, 202] favors a neutral protonation state of Cys-113 during the isomerization reaction.

Active site

Structural analyses of the cis, transition state, and trans states provide valuable insights into the mechanism of isomerization. Inspection of the active site indicates that during the course of the reaction most of the changes are localized toward the N-terminal of the peptide (Figure 7.13), where the Proline ring remains essentially ﬁxed in the hydrophobic pocket. The larger changes are found in the C-terminal, where the P-loop is highly perturbed during the rotation of the carbonyl group of TPO, in agreement with experimental studies, based in crystal structures and NMR analysis [208]. This behavior have also been reported in another family of isomerases, named CypA, through simulations methods [225]. Within the enzyme the proline ring remains essentially ﬁxed due to favorable nonpo-

136 Figure 7.13: Superposition of the cis(yellow), transition state (orange) and trans (green) structures of the substrate peptide within PIN1 for the clockwise process

lar interaction between the proline residue with the hydrophobic pocket but also to a tight hydrogen bonding interactions between the carbonyl Pro(O) with the backbone amide of Gln131 and between the NH group of Gln5 with the carbonyl of Gln129, which distances are almost constant along the process for both the clockwise and counterclockwise process. Figure 7.14 shows the distribution of conformers over conformational space of φ vs ψ for the Pro ligand residue during the isomerization process, when the peptide is either solvated in water or in complex with PIN1. Within the enzyme there is a higher tendency to preserve a type VIa turns conformation along the process, which is characterized by a ψ values close to 0◦, which favors an intramolecular hydrogen bond between the lone pair of the imide nitrogen and the following amide N-H group. In solution however the type VIb turn, which is characterized by a ψ values close to 180◦, is also populated. As said before, after the transition state the peptide in solution achieves an extended conformation. Within the enzyme the intramolecular hydrogen bond is more favorable along the anticlockwise direction. For the clockwise path this hydrogen bonding interaction is weaker, in this case another weak interaction is also found between the NH backbone

137 -rama PRO149 anticlock continuous rama PRO149 anti 2iti

150 150

100 100

50 50 ψ ψ 0 -10 0 a10

Psi -20 Psi a20 -40 a40 -50 -60 -50 a60 -80 a80 -100 a100 -100 -120 -100 a120 -140 a140 -150 -160 -150 a160 -180 a180 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Phi φ Phi φ

rama PRO149 clock sol continuous rama PRO149 clock 2iti

150 150

100 100

50 50 ψ ψ 0 10 0 10

Psi 20 Psi 20 40 40 -50 60 -50 60 80 80 100 100 -100 120 -100 120 140 140 -150 160 -150 160 180 180 -150 -100 -50 0 50 100 150 -150 -100 -50 0 50 100 150 Phi φ Phi φ

Figure 7.14: Ramachandran plot with respect to φ and ψ dihedral angles around Pro ligand residue from the MD simulations using CHARMM force ﬁeld, for the system in solution (left) and within the enzyme (right) of Phe and the carbonyl oxygen atom of TPO. These results show that the enzyme environment favor an autocatalysis in the peptide, similar to the features found in the FK506 binding protein (FKBP) [184].

Free Energy in PIN1

The output structure of each window in the anti- and clockwise rotation served as input for a QM/MM molecular dynamics simulation of 15 ps. The same procedure as for the isomerization in solution was followed: step size of the windows was increased to 20◦ due to the expensive computational cost; the same atoms were taken into the QM region and the average value of ζ and its standard deviation were used to

138 2 120 2 1 0

F [kJ /mol/°] -1 100 1 -2 -180 -135 -90 -45 0 45 90 135 180 trans cis trans 80 Dihedralζ [°] 0 60 G [kJ /mol] F [kJ /mol/°] -1 40 20 -2 0 0 45 90 135 180 225 270 315 360 0 45 90 135 180 225 270 315 360 cis ∆ angle [°] trans cis ∆ angle [°] trans Figure 7.15: Mean reaction force and free energy profile for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in PIN1. The inset presents the mean reaction force for the clock- and anticlockwise rotation in PIN1 employing only one starting structure. calculate the mean reaction force. In the inset of Figure 7.15 the mean reaction force as function of the dihedral angle ζ in the two directions of rotation is shown. The mean reaction force presents some discontinuities, which could be ascribed to the use of only one starting structure. The rotation in anticlockwise direction (towards positive values) displays smaller values than the other direction. Along this direction of rotation, which is also noted with the arrow in Figure 7.9, the carbonyl oxygen atom is able to interact with the enzyme residues (Cys-113 and Ser-154). In the opposite direction the carbonyl group has to rotate through the inside of the IVa-turn formed by the peptide, disrupting the intramolecular hydrogen bond, found to catalyze the reaction in solution. The observations described above lead us to focus only on the anticlockwise rotation which seems more favorable. To eliminate the discontinuities in the mean reaction force profile coming from poor sampling of possible peptide and enzyme conformations, five starting structures from the last 4 ns of the MM simulations were used as input for QM/MM simulations for each window yielding a total simulation time of more than 600 ps (for the simulations restraining only ζ). The average value of ζ and the standard deviation for each

139 window were obtained as the average of the five simulations and used to calculate the mean reaction force shown in Figure 7.15. The obtained mean reaction force until the transition state can now be compared to the reaction in solution to elucidate possible changes in the reaction mechanism: The enzyme shifts the minimum of the cis-isomer to ζ values larger than zero and towards the transition state leaving the value of the mean reaction force minimum unaffected at 50◦. The transition state is also shifted to 90◦ in respect to the value in solution of 80◦. The free energy barrier to reach the transition state from the cis-isomer equals to 114 kJ/mol (27.1 kcal/mol), which is smaller than the value in aqueous solution but in the error range. In analogy to the isomerization in solution contributions to the activation barrier due to electronic reorganizations or structural rearrangements have been identified through the mean reaction force. In the enzyme the value for W1 which represents the structural contribution is 43 kJ/mol (10.2 kcal/mol) and the electronic part W2 amounts to 71 kJ/mol (16.9 kcal/mol). The smaller value of W1 with respect to the solution reaction indicates that the enzyme reduces the energy needed to fulfill the structural rearrangements to reach the transition state, which is in line with the shift of the minimum of the cis isomer. This destabilization of the reactant in the enzyme with respect to the reactant in solution was already observed by Fischer et al. for the rotamase catalysis of the FK506 binding protein [191]. This reduction in the contribution of the structural rearrangements, however, is counterbalanced by the energy required for the electronic reorganization in the enzyme. To discern possible effects of the environment on the electron reorganization the electrostatic potential, arising from the enzyme and the peptide, was calculated for representative structures of the cis isomer and the transition state (ζ = 90◦) with the APBS software [226] and mapped into the solvent accessible surface of the enzyme as shown in Figure 7.16. Throughout the isomerization reaction the carbonyl group

140 R

Figure 7.16: Representative snapshots of the cis-isomer, transition state (ζ = 90◦) and ◦ the product (ζ = 180 , ψpThr = −50). Atoms representing the QM region are presented as spheres. The solvent accessible surface is colored according to the electrostatic potential (blue=+256.71 mV; red=-256.71 mV) calculated with the APBS software and taking only the peptide and enzyme atoms into account.

141 of the threonine residue, which is part of the rotating peptide bond, is surrounded by a negative charged environment. A negative environment, in principle, should favor the rotation due to a reduction of the double bond character of the peptide bond [189, 201]. To track the residues responsible for the negative charge, the electrostatic potential was recalculated leaving out the peptide and the phosphate group of the threonine residue resulting in a neutral to positive environment (from the basic residue triad Lys-63, Arg-68 and Arg-69). Therefore, the negative environment originates from the peptide itself and not the enzyme and should in principle also be present for the isomerization in solution, although possibly slightly diminished due to the larger dielectric constant of the surrounding water molecules. Since global electrostatic inﬂuences seems not to be responsible for the increased energy of the electronic reorganization direct atom-atom interactions to the carbonyl group of the rotating peptide bond were analyzed. As above mentioned in the introduction and shown in Figure 7.9 the residues Cys-113 and Ser-154 might be involved in direct interactions to the peptide during the isomerization. In fact, for angles smaller than 50◦ the carbonyl oxygen atom is hydrogen bonded to the Cys-113 through a weak hydrogen bond due to the rather small atomic charges of the sulphur and hydrogen atom. After the minimum of the mean reaction force, however, the carbonyl oxygen atom interacts with the Ser-154 residue through a strong hydrogen bond, since the hydroxyl group possesses larger atomic charges. This strong hydrogen bond, in contrast to the negative electrostatic potential, would stabilize a negatively charged carbonyl oxygen atom and increase the double bond character of the peptide bond either than the single one necessary to reach the transition state. The increased double bond character of the rotating bond through stabilization by hydrogen bonds between the enzyme and the peptide throughout the second region of the mean reaction force explains the larger energy necessary for the electronic reorganization of the system, which counterbalance the intramolecular catalysis on

142 the nitrogen atom identified in solution. Rotating the peptide bond further from the transition state results in unfavorable interactions between its rotating part (left part of the peptide in Figure 7.9) and the enzyme. These unfavorable interactions are also reflected in the mean reaction force shown in the inset of Figure 7.15, which gets negative at 140◦ and would lead to a steeply increasing free energy after this point. To avoid this interaction starting at ζ = 140◦ a second reaction coordinate represented by the ψ angle of threonine phosphate residue was considered. A relaxation of this coordinate to reach the trans isomer after the transition state, was already proposed in the work of Velazquez et al. [227], who applied accelerated molecular dynamics to obtain a free energy map of this angle together with ω angle of the peptide bond. Values of ζ and ψ were chosen to match the minimum energy path of their proposed free energy map (see Methods section) and therefore, allow a proper relaxation of the peptide. The reaction coordinate shown in Figure 7.15, therefore, represents in the first part only the dihedral angle ζ and after 140◦ a combination of the change in this dihedral angle and the mentioned ψ backbone angle (resulting in values larger than 180◦). As can be seen from the mean reaction force the addition of the second reaction coordinate leads to values around zero force at 140◦ and therefore, avoids the interaction with the enzyme. The product is reached at ζ = 180◦ and ψ = −50◦, which corresponds to the trans isomer with the ψ angle in the αR region of the Ramachandran plot (see Figure 7.16 bottom) and matches the minimum obtained by Velazquez et al. [227] Therefore, in comparison to the reaction in solution the largest effect of the enzyme is observed in the free energy profile after the transition state. If the trans isomer

◦ would posses a ψpThr angle above 100 , which corresponds to the β-region in the Ramachandran plot, the free energy proﬁle derived from the mean reaction force shown in the inset of Figure 7.15 would predict a steeply decreasing free energy until

143 1.6 OTPO -- HOSER OTPO -- SHCYS 1.4 NPRO -- HNPHE OTPO -- NE2GLN SHCYS -- HOSER 1.2

0.8

itne[nm] Distance 0.6

0.4

0.2

0 0 50 100 150 200 250 300 350 ∆ angle [°] Figure 7.17: Relevant peptide-enzyme distances along the reaction coordinate during the isomerization in PIN1

140◦, a shallow minimum, before reaching the barrier of less than 10 kJ/mol to pass the transition state to the cis isomer. However, the aﬃnity of PIN1 to this conformer can be assumed to be very small due to the unfavorable interaction discussed above. It seems much more likely that PIN1 binds the trans conformer in the relaxed form

◦ with a ψpThr angle ' −50 , corresponding to the αR-region of the Ramachandran plot. Indeed, this region was already identified by Velazquez et al. [227] to be more favorable than the β region for the trans isomer in PIN1. From this conformer first the ψ angle has to be rotated to reach positive values crossing the first transition state with an activation energy of ' 20 kJ/mol. This transition state is governed by the steric interaction of the peptide backbone atoms with the proline ring. Together with the rotation of the ψ angle towards positive values the ζ angle decreases and a shallow minimum is reached for ζ = 140◦ and ψ = 90◦. From this point only ζ decreases towards the transition state at ζ = 90◦ with an activation barrier of less than 10 kJ/mol. The small activation barrier can be attributed to the absence of the hydrogen bond to the Ser-104 residue (see Figure 7.17).

144 The presence of two minima for the trans isomer was also reported by Fischer et al. [191], who studied the catalytic effect of FKBP on the cis-trans isomerization of the same peptide bond. They could identify two trans minima which differ in the ψ angle preceding the proline residue and were separated by a barrier of 23.4 kJ/mol, which is in agreement with the above results. The obtained results for the whole isomerization in the enzyme and solution has to be compared to a recent work of Greenwood et al. , who measured NMR spectra of the PPIase domain in combination with part of the APP peptide [228]. Applying line- shape analysis and fitting the signals of 5 proline protons to a four state model with seven parameters they were able to deduce the activation barrier for the isomerization reaction. They reported a value of 54.5 kJ/mol for the barrier from the cis isomer in the enzyme and a trans isomer with a slightly larger binding constant. The reduction of the barrier with respect to the isomerization in solution (84.4 kJ/mol) was 65%.

QM/MM-MFEP Reaction path

To exclude the small basis set and the neglect of electron correlation as the source of the discrepancy, the QM/MM-MFEP method combined with the NEB method was employed to optimize the reaction path. This method includes electron correlation in the description of the QM system and has been applied to study enzyme catalysis of several reactions [139, 219, 220]. The rotation for both clock- and anticlockwise direction along ζ were studied conﬁrming the previous results of a lower energy barrier

‡ for the anticlockwise rotation than for the one in clockwise direction (∆Eclock = 119 kJ/mol). The obtained free energy proﬁle in anticlockwise rotation along ζ is shown in Fi- gure 7.18. In agreement with the results above the minimum of the cis conformer is displaced to larger ζ values (ζ = 9.8◦) compared to the reaction in solution. The transition state is found at 68◦, where the imide nitrogen becomes pyramidal with

145 80

20 G[kJ/mol] 0

-20

0 20 40 60 80 100 120 140 160 180 Dihedral c [ °] Figure 7.18: Free-energy proﬁle from NEB optimization by the QM/MM-MFEP method for the cis-trans isomerization of Ace-Gly-pThr-Pro-Phe-Gln-Nme peptide in anticlockwise direction in PIN1

localized lone pair electrons, as evidenced by analysis of the ESP charges (see Figure 7.19). The obtained activation barrier for the isomerization reaction from the cis- isomer is 60 ± 10 kJ/mol (14±2), the error displays the standard deviation of the last optimized n cycles, where the NEB method is known to present convergence problems in complex systems [220]. This value is considerably smaller than the one reported above and closer to the results obtained for the model system using the PCM model, confirming the results discussed above that the enzyme does not alter the activation barrier of the isomerization reaction from the cis conformer. Following the isomerization after the transition state in Figure 4.6 a 20-25 kJ/mol (5-6 kcal/mol) more stable trans isomer compared to the cis form is observed. The difference to the results reported above could be attributed to the fact that unfavorable interactions in the MM region (rotating arm with the enzyme) are not directly taken into account in QM/MM MFEP methodology where the optimization of reaction paths only includes degrees of freedom of the QM region. From this analysis it can be concludes that the enzyme does not affect the total activation barrier of the cis isomer. If the energetics derived from the NMR mea-

146 0.4

0.2

-0.2

-0.4

-0.6 Nitrogen ESP Charge -0.8

-1 0 20 40 60 80 100 120 140 160 180 Dihedral c [°] Figure 7.19: Atomic charge of the nitrogen atom in the rotating peptide bond along the reaction coordinate in the QM/MM MFEP simulations.

surements are correct the enzymatic catalysis must be related to another eﬀect, which is not accounted for within this methodology. One possible explanation is that the origin of the catalysis is due to conformational changes in the enzyme which drive the reaction. These conformational changes, however, occur on a time scale of the NMR experiment and are not accessible with molecular dynamics simulations. Indeed, one of the conclusions of the authors in the experimental study was that overall exchange time of the isomers match the time scale observed of conformational changes. The results for the isomerization of the trans isomer show that the enzyme catalyses the reaction by imposing a consecutive rotation of two angles to reach the transition state from the minimum. Conformational changes of the enzyme may be also involved contributing to the conversion between the two minima. The observed large decrease in the activation barrier from the trans isomer would also explain why no crystal structure of this isomer could be obtained so far. To conceive the impact of the results on the biological processes in which PIN1 is involved, however, the binding aﬃnity of this isomer in respect to the other has to be acquired.

147 7.2.4 Concluding Remarks.

• The mean reaction force was able to identify structural and electronic contributions to the activation barriers and reaction energies for the isomerization reaction in solution and in the enzyme. In solution an intramolecular hydrogen bond to the nitrogen atom of the proline ring reduced the energy required for the electronic rearrangements from the cis isomer. The obtained activation barrier was in agreement with a recent computational study and experiment.

• In the enzyme, it was found that a direct nucleophilic attack from a deprotonated cysteine to the carbon of carbonyl is unlikely. The catalysis is shown to occur through a noncovalent mechanism, where the rotation takes place along the N-terminal.

• In the enzyme the activation barrier from the cis isomer resembles the one in solution, but through the separation by the mean reaction force a reduced structural contributions represented as a destabilization of the reactant could be identiﬁed. This reduction, however, was counterbalanced by the larger electronic part which originates from peptide-enzyme hydrogen bonds which increase the double bond character of the rotating peptide bond.

• The largest inﬂuence of the enzyme was observed for the activation of the trans isomer to the transition state. The enzyme induces through unfavorable interactions to the rotating peptide a rotation in the ψ-angle of the preceding threonine phosphate residue. Consideration of this second reaction coordinate produces to stable isomers which can be converted through a small barrier of ' 20 kJ/mol. From the less stable one the energy required to reach the transition state amounts to 10 kJ/mol, indicating that the isomerization reaction of the trans conformer should be achievable at room temperature in presence of the

148 enzyme.

149 8

General Conclusions and Perspectives

In this thesis, the joint use of the potential energy, the reaction electronic (REF) flux, DFT-based reactivity descriptors, and NBO analysis, within the framework of the reaction force analysis, has allowed to gain insight into the mechanism of a variety of chemical process occurring in diverse domains of chemistry. This theoretical framework have proven to be of great use in the characterization of the reaction mechanisms as well as in the interpretation of a variety of both experimental and theoretical results. In the specific case of proton transfer processes, the effect of an active water molecule was addressed. It was found that the catalytic effect of water cannot be generalized, because it depends on the nature of the systems. In this sense, in thioformic acid the bridging water molecule decreases the reaction barrier, while in amino acids it is increased by a factor of two, with a marginal influence of the amino acid side chain. The later results have been interpreted in terms of the energy required to bring the amino acid and the water molecule closer to each other and to promote the proton transfer through the reordering of the electron density.

150 In overall, the water-mediated process advances by a concerted though asynchronous mechanism. The aforementioned methods allow to identify the order of the transferred protons. Furthermore, a second, not intervening water molecule, acting as donor or acceptor with respect to the bridging reactive one, can change the proton acceptor and donor properties of the reactive water molecule modulating the reaction mechanism. In this regard, the diﬀerences in the reaction mechanism can be understood from the hydrogen bond strength between donor-acceptor atoms and totally characterized by means of the theoretical approach used in this thesis, which evolves as promising tools to not only characterize but also externally manipulate reaction mechanisms.

A second group of reactions studied correspond to the H2 activation process by carbene systems. It can be concluded that the REF descriptor, and its phenomenological partition, is capable to put forward details of the reaction mechanism that otherwise were not evidenced. The REF analysis have also provided a general framework to assign the energetic cost associated to every chemical event that drives the process, thus giving crucial information to rationalize the reported experimental results. The irreversibility for this process stems from the high values of W3, associated with the breaking process of the C–H bonds. It is proposed that external agents could help to lower the reverse activation energy to produce H2. Analysis of the intrinsic reactivity on carbene systems evidences that local DFT- based index results adequate to characterize the reactive nature of the carbene, whereas their global counterpart fails to provide a clear trend and they are therefore not recommended. Nevertheless, it remains challenging to make predictions about the success or failure for the DAC carbene system over the chemical reaction. Overall, biphilic behavior of the carbene center has been shown to be fundamental. This study shows that acyclic alkyl amino carbene systems are the most suitable for this type of reactions.

151 A final application concerns the cis-trans isomerization of prolyl bond. In the non- enzymatic mechanism, the intramolecular catalysis was fully characterized along the reaction by using the reaction force framework and Natural Bond orbital analysis. The detailed analysis of this mechanism and the characterization of key intramolecular interactions involved in the process allows to suggest strategies for manipulation of the active site in Prolyl Isomerase enzymes. The study in this model systems was extended to more complex systems where the enzymatic process was fully analyzed within the enzyme PIN1. Different reaction pathways, based in experimental results, where analyzed; it was suggested that PIN1 catalyzes the process through a noncovalent mechanism, where the rotation takes place along de N-terminal site. The larger catalytic effect of PIN1 in the process was observed for the activation of the trans isomer to the transition state, where the enzyme catalyses the reaction by imposing a consecutive rotation of two angles to reach the transition state from the minimum. Conformational changes of the enzyme may be also involved contributing to the conversion between the two minima. The observed large decrease in the activation barrier from the trans isomer would also explain why no crystal structure of this isomer has been obtained so far. However, to conceive the impact of the results on the biological processes in which PIN1 is involved, the binding affinity of this isomer in respect to the other has to be acquired. From a theoretical point of view, it was found that the QM/MM approach is needed in order to study the enzymatic process, where inclusion of the dynamic nature of the systems must be taken into account. Additionally, in order to reach a better understanding of the catalysis, the reaction mechanism in solution and within the enzyme has been analyzed using the Mean Reaction Force framework that allows a detailed characterization of the different processes taking place as the reaction advances. Electronic and structural free energy contributions to the activation were determined thus providing explanation of the physical nature of the free energy

152 barriers involved in the reactions.

153 Appendix A

Reaction Paths

Equilibrium geometries, transition states, and reaction paths are central in the study of chemical reactions. The reaction path is coordinate dependent, and at zero temperature is defined on a potential energy surface (PES) as the steepest descent path (SDP) from a first order saddle point, the transition state. At finite temperature the reaction does not take a single path and the various dynamic paths may differ considerably from the SDP. In a mass-weighted cartesian coordinate system the SDP is known as the intrinsic reaction coordinate (IRC) [229]. Defining s as the reaction coordinate, or arc length along the path, the simplest method of following a reaction path is to solve the differential equation for the intrinsic reaction path [87,229]:

dx g(x) = − (A.1) ds |g(x)|

where x is the vector of coordinates and g is the energy gradient at x in mass weighted Cartesian coordinates. Several methods for integration of ordinary diﬀerential equation (ODE) have been proposed, however due to the stiﬀness of the ODE in Eqn. A.1

154 many of them become unstable. These methods may be classified as either explicit or implicit. Explicit methods take each step using derivative information only at the starting point; while implicit methods take each step using derivative information at both the starting and the unknown next point. As a result, implicit must be solved iteratively starting with an initial guess, which results more difficult to implement and computationally more expensive than explicit methods, however, they tend to be numerically more stable than the former and therefore more accurate for solving stiff ODE [230].

A.1 Second-Order Implicit Trapezoid Method

A widely used method has been the second-order implicit trapezoid method of Gon- zalez and Schlegel (GS2). [87, 88], currently implemented in the Gaussian package (version G94-G03). Because this method has result fundamental for the study of the reaction mechanisms described in Chapter3-5, the aim of this appendix has been to provide a brief but clear description of the methodology utilized.

Lets consider a point xk on the reaction path (Figure A.1). In order to obtain the next point xk+1 along the pathway, a step of length s/2 is taken along gk yielding

∗ an intermediate point xk+1, where no energy or gradient calculation is made:

1 g(x) x∗ = x − s (A.2) k+1 k 2 |g(x)|

The approximation to the next point on the path xk+1 is found by minimizing the en-

∗ ergy with the distance |xk+1 −xk+1| constrained to be s/2. Because of the constraint, xk and xk+1 lie on an arc of a circle tangent to gk and gk+1 The constrained optimization is carried out making use of the Taylor series expansion of the PES about x0:

155 Figure A.1: Second-order Implicit Trapezoid Method of Gonzalez and Schlegel (GS2) (adapted from [86]

1 E = E + gt ∆x + ∆xtH ∆x + ... (A.3) 0 0 2 0

where ∆x, g0, and H0 are the displacement vector of the current position from x0

, the gradient, and Hessian at x0, respectively. Since the radius of the sphere must be ﬁxed at s/2, a Lagrange function is constructed using the constraint:

1 2 ptp = s ; p = x − x∗ (A.4) 2 k+1 k+1

and truncating the Taylor’s expansion in Eqn. A.3 at the quadratic term:

" # 1 1 1 2 L(λ) = E0 + gt∆x + ∆xtH∆x − λ ptp − s (A.5) 2 2 2

where λ is the undetermined multiplier. Since ∂L(λ)/∂∆x and ∂L(λ)/∂(λ) must be zero at the minimum (stationary conditions), the following expression for ∆x is obtained:

∆x = −(H − λI)−1(g − λp0) (A.6)

156 where I is the unit matrix. The value of λ must be chosen so that p = p0+∆x satisﬁes Eqn. A.4. With a suitable initial guess, the equation to obtain λ is then iteratively solved. To ensure that the reaction path is followed in the descent direction, λ must be less than the lowest eigenvalue of H. If the predicted displacement, ∆x in Eqn. (A.6), is larger than the desired cutoﬀ, the process is repeated [Eqns. (A.3)-(A.6)]. The Hessian H in A.5-A.6 is calculated analytically only at the transition state. At all other points, it is updated by using the BFGS formula [88]

∆g0∆g0t (H00∆x0)(∆x0T H00) ∆H0 = H00 + − (A.7) ∆g0t∆x0 ∆x0T H00∆x0

with ∆g0 = g0 − g”,and ∆x0 = x0 − x”. The primes and double primes refer to the current and previous points, respectively.

A.2 Hessian Predictor-Corrector

A new integrator for the steepest descent pathway has been introduced in the last version of Gaussian package (G09) [152]. This integrator is a Hessian based predictor- corrector (HPC) algorithm that affords pathways comparable to higher-order schemes but with a lower computational cost [150,151]. A predictor-corrector scheme is made up of three processes: i) a predictor step (P) moves from the current point to a guess for the next point, ii) the function and any necessary derivatives are evaluated (E), iii) the current point is refined by a corrector step (C) [230]. The HPC methods follows a P-E-C scheme where each integration step on the reaction path includes a single Local quadratic approximation (LQA) integration (P step), a single PES evaluation (E step), and the modified Bulirsch- Stoer (mBS) integration [230, 231] on a fitted distance weighted interpolant (DWI) surface (C step). Because the C step is carried out on the fitted surface only one

157 PES evaluation is required per IRC point. This contrasts with the previously used GS2 method where three to ﬁve optimization cycles, each of which requires a PES evaluation are typically needed to complete the integration of each point on the reaction path. The LQA integrator is based upon a second order Taylor series of the PES truncated at the quadratic term (Eqn. A.3)[232, 233]. Taking the ﬁrst derivative of Eqn. A.3 with respect to ∆x gives the gradient as:

g(x) = g0 + H0∆x (A.8)

Substituting Eqn. A.8 into Eqn. A.1 gives

dx g + H ∆x = − 0 0 (A.9) ds |g0 + H0∆x|

In the LQA method of Page and McIver, Eq. A.9 is integrated by introducing an independent parameter, t, such that

ds dx = |g + H ∆x| = −[g + H ∆x] (A.10) dt 0 0 dt 0 0

The solution of the later is:

t x(t) = x0 + A(t)g0 A(t) = Uα(t)U (A.11) where U is the matrix of column eigenvectors of the Hessian and α(t) is a diagonal matrix. In order to integrate Eqn. A.9, a value of t must be obtained such that the step size (s − s0) is taken. To accomplish this, iterations over successive Euler

ds integrations of dt in Eqn. A.10 are used. The initial value for the Euler step size, δt, is estimated by

1 s − s δt = 0 (A.12) NEuler |g0|

158 The numerical integration of Eqn. A.10 can be carried out readily in the Hessian eigenvector space,

ds X 2 = −[ g0 exp−2λit]1/2 (A.13) dt 0i i where

0 t g0 = U g0 (A.14)

At the start of the integration, when x corresponds to the TS, the gradient is zero and hence the transition vector must be used in place of g0 . For the corrector step, the modified Bulirsch-Stoer algorithm is used. Briefly, this algorithm integrates over a given interval with some step size h. Then, using a smaller step size reintegrates over the same interval. The results of these two integrations are then fit as a function(s) of h and extrapolated to h=0 (corresponding to the case where an infinite number of steps are taken), this step is made using Euler integrator. If the truncation error of this extrapolation is less than 1x10−6amu1/2bohr the extrapolated result is taken as the final integration solution, the integration is considered complete, and the next predictor step is taken using the corrected position and gradient. If the error is larger, the process is repeated using more steps in the Euler integration. Over the course of a complete reaction path integration, the mBS integration will require a large number of function evaluations. For this reason, the corrector integration is carried out on a local surface which is fitted to the data from the predictor step instead of on the actual PES. The present method employs DWI surfaces, where the energy on the DWI surface, EDWI , at position x is written as a linear combination of Taylor series expanded about the Ndata data points,

N Xdata EDWI = wiTi (A.15) i=1 159 where wi and Ti are the weight and Taylor series values about data point i. Each Taylor series is expanded to second order such in Eqn. A.3

160 Appendix B

Molecular Dynamics

Because of the complexity of system treated in Chapter7, which involves explicit treatment of the solvent and a large number of degrees of freedom, full quantum mechanical calculations are not feasible. In this case classical dynamic calculations can be suitable to describe the motion of the nuclei in the systems. However, they do not include electrons, which are fundamental for describing chemical reactions and other electronic processes, such as charge transfer or electronic excitation. In order to combine the advantages of both techniques, QM/MM approaches have been developed during the last decades [234–236]. They have resulted a valuable tool for the modeling of reactive biomolecular systems at a reasonable computational eﬀort while providing the necessary accuracy. In Chapter7 this approach have been used for the study of the enzymatic catalysis of the cis-trans isomerization process by the enzyme PIN1, where a combined approach based on MD simulations, using umbrella sampling (US) method, and quantum mechanical (QM) method has been used. This Appendix presents an overview of these methods, with emphasis on the com-

161 putational techniques used in Chapter7

B.1 Newton’s Equations.

The principle of MD consists in generating trajectories for a ﬁnite ensemble of particles by integrating numerically the classical equations of motion, which, for each particle i, write [237,238]:

d2x (t) F (t) = m i (B.1) i i dt2 ∂V (x) Fi(t) = − ∂xi(t) where xi is the position, t the time and V (x) is the potential energy function of the N-particle system. Even though the equations are simplistic in its form, there is no analytical solution to the equation of motion for systems of more than two particles, so it must be solved numerically. Numerous algorithms have been developed for solving these equations, and most of them are derived from the widely used Verlet algorithm [239]. As other algorithms, it assumes that the positions and dynamic properties can be approximated as Taylor series expansions. The algorithm used for the MD simulations in this Thesis is the leap-frog [240] version of the Verlet algorithm [239], implemented in the simulation package GROMACS [204]. This method uses the following relationships:

∆t ∆t ∆t v(t + ) = v(t − ) + F(t) (B.2) 2 2 m with new positions at next time step ∆t given by:

∆t r(t + ∆t) = r(t) + ∆tv(t + ) (B.3) 2

∆t In this algorithm, the velocities v(t + 2 ) are ﬁrst calculated from the velocities at ∆t time v(t − 2 ) and the accelerations at time t (Eqn. B.2). The positions r(t + ∆t) 162 Figure B.1: The Leap-Frog integration method. The algorithm is called Leap-Frog because r and v are leaping like frogs over each other’s backs (adapted from [241]) are then deduced from the velocities just calculated together with the positions at time r(t) (Eqn. B.3). The velocities at time t can be calculated by the relationship:

1 ∆t ∆t v(t) = v(t + ) + v(t − ) (B.4) 2 2 2

∆t The velocities thus leap-frog over the positions to give their values at t + 2 . The positions then leap over the velocities to give their new values at t + ∆t, and so on. Hence the name leap-frog (Figure B.1).

B.2 Molecular Dynamics in Diﬀerent Ensembles

The simplest MD simulation of a system under periodic boundary conditions is evolved under constant energy and constant volume conditions (NVE). Although thermodynamic results can be transformed between ensembles, this is strictly only possible in the limit of inﬁnite system size, also known as the thermodynamic limit. This makes desirable to perform the simulation in a diﬀerent ensemble that could be more directly related to experimental data, for example where either the temperature and/or the pressure are considered as independent, rather than derived quantitate.

163 B.2.1 Temperature coupling

There are diﬀerent approaches to conducting molecular dynamics at constant temperature, rather than constant energy, by introducing a thermostat. In this work the Velocity Rescaling was used for most of the calculations except for the MFEP calculations, where the Berendsen thermostat [206] was used instead. The Berendsen thermostat [206] mimics weak coupling to an external heat bath with

a given temperature T0. The eﬀect of this algorithm is that a deviation of the system

temperature from T0 is slowly corrected according to

dT (T − T ) = 0 (B.5) dt τ

It means that a temperature deviation decays exponentially with a time constant τ, which determines how tightly the bath and the systems are coupled together. The heat ﬂow into or out of the system is eﬀected by scaling the velocities of each particle every step with a time-dependent factor λ, given by:

∆t T 1/2 λ = 1 + 0 − 1 (B.6) τB T (t − ∆t/2)

with ∆t < τB < ∞. In the limit τB → ∞ the Berendsen thermostat is inactive and the simulation runs in a microcanonical ensemble. A correct statistical mechanical ensemble for this thermostat is unknown, however it is clear that the statistical ensemble associated with this thermostat is neither the canonical nor the microcanonical ensemble [241,242]. The error associated to it scales with 1/N, so for very large systems most ensemble averages will not be aﬀected signiﬁcantly. A similar thermostat which does produce a correct ensemble is the velocity rescaling thermostat [205]. Basically, it is a Berendsen thermostat to which a properly constructed random force is added, so as to enforce the correct distribution for the

164 kinetic energy [205].

s dt KK0 dW dK = (K0 − K) + 2 (B.7) τT Nf τT

where K is the kinetic energy, Nf the number of degrees of freedom and dW a Wiener process. There are no additional parameters, except for a random seed. This thermostat produces a correct canonical ensemble and still has the advantage of the Berendsen thermostat: ﬁrst order decay of temperature deviations and no oscillations.

B.2.2 Pressure coupling

With similar reasoning to that behind the need for temperature coupling, a system can also be coupled to a pressure bath to give the correct representation of a molecular system. In order to maintain internal pressure, the Berendsen pressure coupling algorithm was used in this work. For the MFEP calculations the Canonical ensemble was used instead. Because in the condensed phase the systems are hardly compress- ible it is expected that the Helmholtz free energy ∆A obtained from this ensemble will be numerically very similar to the Gibbs free energy ∆G resulting from an NPT ensemble [218]. The Berendsen pressure coupling algorithm rescales the coordinates and box vector at every step with a matrix µ, which has the eﬀect of a ﬁrst-order kinetic relaxation of the pressure towards a given reference pressure P0 [238,243]:

dP (P − P) = 0 (B.8) dt τp

The scaling matrix µ is given by

∆t µij = δij − βij[P(0)ij − Pij(t)] (B.9) 3τp 165 The β value in the equation represents the isothermal compressibility of the system, where for water at 1 atm and 300 K, β = 4.6x10−5bar−1.

B.3 The potential energy function

The potential energy function constitutes the corner stone of all molecular mechanics calculations, as it should reproduce the intra- and intermolecular interactions of the system as faithfully as possible [237]. In principle, this functional should write as an N-term sum:

X X X X X X V (x) = υ1(xi) + υ2(xi, xj) + υ3(xi, xj, xk) + ... (B.10) i i j>i i j>i k>j

where υ1(xi), υ2(xixj), ...represent the intramolecular potential, the pair interaction potential, and so on. It can be argued that υ2(xi, xj) constitute the prevailing term of the intermolecular contribution [244]. This point of view is at the origin of the so-called pairwise approximation, in which higher order eﬀects are partially included in an eﬀective potential:

X X X eff V (x) = υ1(xi) + υ2 (xij) (B.11) i i j>i

As an example the potential energy functions provided by the amber force ﬁeld is the following [245]:

166 X 2 X 2 V (x) = kr(r − r0) + kθ(θ − θ0) (B.12) bonds angles

X X Vn + (1 + cos(nφ − γ)) 2 torsions n

" 12 6# 1 X Rij Rij 1 X qiqj + 1−4 εij − 2 + kvdW rij rij kcoulomb 4π01rij i

" 12 6# X Rij Rij 1 X qiqj + εij − 2 + rij rij kcoulomb 4π01rij i1−4 i1−4

in which kr and r0 denote, respectively, the force constant of the chemical bond and its equilibrium length, kθ and θ0, the force constant of the valence angle and its equilibrium value, and Vn/2, n and γ, the torsional barrier, its periodicity and phase.

0 and 1 are, respectively, the vacuum and the relative dielectric permittivities. qi is the partial charge borne by atom i. Rij and ij correspond to the van der Waals parameters for the pair of atoms ij. The last two line evidences the distinction between interactions of atoms separated by exactly three chemical bonds (i.e. the so-called 1-4 terms), and all others.

B.4 Free Energy Calculation

MD simulations allows not only to obtain valuable information on the structural properties and the dynamics of a given system, but also it allows to explore the free energy landscape in the neighborhood of local minima. If a system posses an ergodic behavior it will visit all region of the conﬁgurational space that have an energy within a range of the order of kBT , however it will be extremely diﬃcult to properly sample other regions of the conformational space. In order to cope with this problem it is necessary to apply methodologies that are capable of accelerating rare events, such

167 Figure B.2: Illustration of the free energy proﬁle of a generic chemical event, showing the reactant (R), transition state (TS), product state(P), and the contributions of some of the windows (red dashed curves) used for the umbrella sampling methods. as those involving the crossing of large free energy barriers (Figure B.2). In the last decades, several methodologies have been developed for the study of rare event. In general, three approach have been developed: (1) methods that sample the system in equilibrium, (2) non-equilibrium sampling techniques, and (3) methods that introduce additional degrees of freedom, along which the free energy is calculated [246]. The former includes thermodynamic integration [238, 247, 248], slow growth [249], umbrella sampling [250] and Steered MD (SMD) [251]. The second group include methods based in Jarzynski equality [252]. Finally the third group include methadynamics and λ-dynamics. In the next paragraph the umbrella sampling methods, and in particular the umbrella integration method, will be presented in detail.

B.4.1 Umbrella Sampling (US) Method

The free energy surface along a chosen coordinate is known as the potential of mean force (PMF) [253]. The PMF can be formally obtained as follows:

A(ξ) = −kBT ln Q(ξ) (B.13)

168 where Q(ξ) is the partition function of the system, which can be obtained by integrating out all degrees of freedom but ξ [218]:

R dN r)δ[ξ(r) − ξ] exp(−βV ) Q(ξ) = (B.14) R dN r) exp(−βV )

Q(ξ)dξ can be interpreted as the probability of ﬁnding the system in a small interval dξ around ξ. If the pressure, rather than the volume, is kept constant, the Gibbs free energy (usually denoted as G) is obtained. Apart from the change in the ensemble, the following formalisms and derivations are equivalent for A and G. In computer simulations, the direct phase-space integrals used in Eqn. B.14 is impossible to calculate. However, if the system is ergodic, i.e., if every point in phase space is visited during the simulation, then Q(ξ) is equal to:

1 Z t P (ξ) = lim ρ[ξ(t0)]dt0 (B.15) t→∞ t 0 that is, the ensemble average Q(ξ) becomes equal to the time average P (ξ) for inﬁnite sampling in an ergodic system. In Eqn. B.15 t denotes the time and ρ counts the occurrence of ξ in a given interval. So, in principle, A(ξ) can be directly obtained from MD simulations by monitoring P (ξ) along the reaction coordinate ξ. In practice, however, regions in conﬁguration close to the minimum will be sampled well, whereas regions of higher energy will be rarely sampled. The US method, pioneered by Torrie and Valleau [250], attempts to overcome this sampling problem by adding a restraining potential w to the potential V (r), so that

c the reaction coordinate is restrained near to a speciﬁed value ξi (Figure B.2). This potential could, for example, be harmonic in shape [238,253].

b u Vi = Vi (ξ) + wi(ξ) (B.16) 1 w (ξ) = K(ξ − ξc)2 (B.17) i 2 169 The superscript b denotes biased quantities, whereas the superscript u denotes unbiased quantities. The equilibrium value of this potential is chosen to be a set of intermediate points ξ(1), ..., ξ(n − 1) between ξ(0) and ξ(n), so that the reaction coordinate is driven between the two endpoint values. Each molecular dynamics

b simulation will then yield a biased probability distribution P (ξ)i about each point ξ(i),

R dN rδ[ξ0 − ξ] exp(−β[V (r) + w (ξ0(r))]) P b(ξ) = i (B.18) i R N 0 d r exp(−β[V (r) + wi(ξ (r))])

On the other hand, the unbiased distribution is:

R dN rδ[ξ0 − ξ] exp(−βV (r)) P u(ξ) = (B.19) i R dN r exp(−βV (r))

Because the bias depends only on ξ and the integration in the numerator is performed over all degrees of freedom but ξ, Eqn. B.18 can be expressed as:

R dN rδ[ξ0 − ξ] exp(−βV (r) P b(ξ) = exp(−βw (ξ))x (B.20) i i R N 0 d r exp(−β[V (r) + wi(ξ (r))])

Using Eqn. B.19 results in:

R dN rδ[ξ0 − ξ] exp(−β[V (r) + w (ξ(r))]) P u(ξ) = P b(ξ)x exp(βw (ξ))x i (B.21) i i i R dN r exp(−βV (r)

b = Pi (ξ)x exp(βwi(ξ))xhexp(−βwi(ξ))i (B.22)

b From Eqn. B.21, Ai(ξ) can be readily evaluated. Pi (ξ) is obtained from an MD simu- 1 lation of the biased system, wi(ξ) is given analytically, and Fi = −( β ) lnhexp(−βwi(ξ))i is independent of ξ :

1 A(ξ) = − ln[P b(ξ)] − w (ξ) + F (B.23) i β i i i

170 Fi cannot directly be obtained from sampling. One of the more common methods to combine the results from diﬀerent windows and obtain A(ξ) is the weighted his- togram analysis method (WHAM) [254, 255], where F (ξ) is iteratively calculated. An alternative to WHAM is umbrella integration(UI) method [216–218], where, the problem of calculating Fi is avoided by averaging the mean force rather than the distribution P :

∂Au(ξ) 1 ∂ ln[P b(ξ)] dw (ξ) i = − i − i (B.24) ∂ξ β ∂ξ dξ

b The distribution P (ξ)i can be approximated by a normal distribution, which only

b b 2 depends on the mean value ξi and the variance (σi ) of ξ in each window. These two quantities can be easily sampled during the simulation,

∂Au(ξ) 1 ξ − ξb i = i − K(ξ − ξref ) (B.25) b 2 i ∂ξ β (σi )

The curves of the mean forces of the diﬀerent windows can directly be averaged to result in a global mean force [216]:

windows ∂Au(ξ) X ∂Au(ξ) = p (ξ) i (B.26) ∂ξ i ∂ξ i

The resulting global mean force can be numerically integrated. In this work the free energy proﬁle along the reaction coordinate was obtained by numerical integration applying the Simpson rule.

B.5 QM/MM Methods

Force ﬁelds used in MD simulation do not considerer explicitly the inﬂuence of electrons, which are indirectly expressed by empirical parameters that are assigned on the basis of experimental data or on the basis of results from high-level ab-initio

171 calculations. Even though they have probe to be valid for the study of a larger number of processes and molecular systems, they can result inadequate for the study of chemical reactions. Combination of quantum mechanics (QM) and molecular mechanics (MM) have become the method of choice for modeling reactions in biomolecular systems, in that case the reacting part of the system is treated quantum mechanically, while the re- mainder is modeled using the force ﬁeld. In the study presented in chapter7, the electronic embedding approach was used to describe the interactions between the electrons of the QM and the MM atoms and between the QM nuclei and the MM atoms:

n M 2 N M 2 X X e Qj X X e ZAQJ HQM/MM = HQM − + (B.27) 4π0riJ eπ0RAJ i J A J where n and N are the number of electrons and nuclei in the QM region, respectively, and M is the number of charged MM atoms. The first term on the right hand side is the original electronic Hamiltonian of an isolated QM system. The first of the double sums is the total electrostatic interaction between the QM electrons and the MM atoms. The total electrostatic interaction of the QM nuclei with the MM atoms is given by the second double sum. When the division between QM and MM regions occurs across covalent chemical bonds, the QM/MM boundary must be treated independently, in order to satisfy the valency of the QM system. The most popular prescription of treating this boundary problem is the link atom approach, where an atom, generally a hydrogen atom, is added to the MM side of the broken covalent bond to satisfy the valence of the QM region. The link atoms are treated as normal atoms in the QM calculations, where the force on this atom is distributed over the two atoms of the bond, while the broken bond is still treated by the MM force field. For the QM/MM-MFEP calculation the pseudobond model instead of the link atom

172 approach has been used to treat the QM-MM crossing bond [224, 256]. A pseudobond Yps–X consist in an atom with a one-free-valence boundary (Yps) connected to another atom. The Yps atom is modeled to make the Yps–X pseudobond mimic the original Y–X bond with similar bond length, ESP ﬁtted charges, deprotonation energy and bond dissociation energy [224]. It is made by parametrizing the basis set, in this case a STO–2G (STO–Slater-type orbital) basis set, and the eﬀective core potential:

ψs = gs(α1,R) + d1gs(α2,R)

ψp = gp(α1,R) + d2gp(α2,R)

where gs and gp are normalized s- and p-type Gaussians, α1 and α2 are the exponents, and d1 and d2 are the coeﬃcients. For the eﬀective core potential of the seven-valence- electron boundary atom, an angular momentum independent formula is used.

V eff (r) = a exp(−br2)/r

The parameters used in this work are the following:

sp3 sp2,carbonyl sp3 sp3 Cps( ) –C( ) Cps( ) –N( ) a 23.1 18.4 b 10.8 9.5 α1 1.18 0.78 α2 0.29 0.17 d1 4.99685 0.78895 d2 0.79341 0.31400

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189 Biography

Fellowships

1. Visiting Scholar Fulbright-Conicyt Scholarship October 2010-June 2011

2. Scholarship for Ph.D Studies, CONICYT March 2008-February 2012

3. For Women in Science award, L0Or´eal-UNESCO,September, 2009.

4. Distinction Best PhD of the year 2008/2009 in Chemistry, PUC, December, 2009.

5. Fellowship to Attend X Interuniversity course of Theoretical Chemistry and Compu- tational Modeling (TCCM), CONICYT, September 2009

Publications

1. Fernanda Duarte and Alejandro Toro-Labb´e. Water catalysis of the keto-enol Tautomerization Reaction of Thioformic Acid. Mol. Phys., 2010, 108, 1375.

2. Fernanda Duarte and Alejandro Toro-Labb´e.H2 activation reaction by (amino)carbene systems. Analysis from the perspective of the Reaction Force and Reaction Electronic Flux. J. Phys. Chem. A 2011, 115, 3050–3059.

3. Fernanda Duarte, Esteban Vohringer-Martinez and Alejandro Toro-Labb´e. In- sights on the Mechanism of Proton Transfer Reactions in Amino Acids. Phys. Chem. Chem. Phys., 2011, 13, 7773–7782.

Manuscript in Preparation

1. Fernanda Duarte, Esteban Vohringer-Martinez, and Alejandro Toro-Labb´e. Enzyme catalysis of cis-trans peptide bond isomerization by Pin1: What the mean reaction force and QM/MM simulations can tell us.

190 Presentations

1.( Poster) Fernanda Duarte; Esteban Vohringer-Martinez; Alejandro Toro-Labb´e. Elucidating the Catalytic Mechanism of the Enzyme PIN1 in the cis-trans Peptide Isomerization by QM/MM Simulations (Best Poster Award). Workshop in Molecular Simulation & Drug Design. Center for Bioinformatics and Molecular Simulations (CBSM). Universidad de Talca, Chile. December 4. 2011.

2.( Poster) Fernanda Duarte; Alejandro Toro-Labb´e. Mechanism of H2 activation by

(amino)carbenes. 62nd Southeastern/66th Soutwest Regional Meeting, New Orleans, United States, November 30- December 4. 2010.

3.( Oral Presentation) Fernanda Duarte. H2 activation reaction by(amino)carbene systems singlet. Analysis from the perspective of the Reaction Force and Reaction Electronic Flux. XXVIII Chilean Conference on Chemistry, Chillan, Chile, November 3-6, 2009

4.( Poster) Fernanda Duarte; Alejandro Toro-Labb´e. Theoretical Study of Intramolec-

ular and Assisted by Water Proton Transfer Reactions. 6th Congress of the Interna- tional Society for Theoretical Chemical Physics. Vancouver, Canada, July 19-24, 2008.

191