Tunnelling in Molecules: Nuclear Quantum Effects from Bio to Physical Chemistry (ISSN)

Description

The field of quantum tunnelling has been rapidly developing in the 21st century, yet there are no updated books on its applications in chemistry. Including theoretical and experimental chapters, from the physical and organic to the biochemistry fields, this new book provides a broad and conceptual perspective of the reactivity of molecules lead by quantum mechanical tunnelling. Cover Preface Contents Chapter 1 Direct Observation of Tunnelling Reactions by Matrix Isolation Spectroscopy 1.1 Introduction 1.2 Description of Simple Mathematic Models for Tunnelling Computations 1.3 The Matrix Isolation Method: Creating the Conditions for Direct Observation of Tunnelling-driven Chemistry 1.4 Interpretation of Kinetic Decays Observed in Cryogenic Matrices 1.5 NIR and IR-induced Chemistry 1.6 Conformational Isomerizations by Tunnelling 1.7 Bond-breaking/Bond-forming H-atom Tunnelling (H-shifts) 1.8 Heavy-atom Tunnelling Author Contributions Acknowledgements References Chapter 2 Tunnelling Instability in Molecular Systems. An Exercise in Computational Chemistry Prediction Power 2.1 Introduction and Motivation 2.1.1 Stability in the Eye of the Beholder? 2.2 A Primer: Computational Design of an Impossible Molecule 2.3 Theoretical and Computational Digression 2.3.1 Quantum Tunnelling: Theoretical and Practical Considerations 2.3.2 Electronic Structure Methods and Methodological Challenges 2.4 Quantum Tunnelling Instability: Past and Future 2.4.1 Some Published Examples 2.4.1.1 Ozone 2.4.1.2 CMe5+ 2.4.1.3 Pericyclic Reactions 2.4.2 Some Unpublished Examples: Pericyclic Deazatation 2.5 Final Words Abbreviations References Chapter 3 Proton Tunnelling and Proton-coupled Electron Transfer in Biological Systems: Theory and Experimental Analysis 3.1 Introduction 3.2 Basic Rate Expressions and Time Scale Separations 3.2.1 Time Scale Separations 3.2.2 Rate Expression for Electronically Adiabatic and Vibrationally Non-adiabatic Proton Transfer with a Fixed Donor-Acceptor Distance 3.2.3 Rate Expression for Electronically Non-adiabatic PCET with Fixed Donor-Acceptor Distance 3.2.4 Basic Properties of the D-A Sub-system 3.2.4.1 Coordinate Space and Duschinsky Mixing 3.2.4.2 Einstein Approximation for the D-A Mode Frequency 3.2.4.3 Linear Approximation for D-A Coupling to the Tunnelling Rate 3.2.5 The Observed Rate and the Role of Protein Conformational Interconversions 3.3 Electronically Non-adiabatic Proton-coupled Electron Transfer in Biomolecules 3.3.1 Theoretical Treatment of D-A Motion in the Quantum and Classical Limits 3.3.1.1 Two-dimensional Quantum Treatment of the D-A and H/D Coordinates 3.3.1.2 Classical Treatment of the D-A Coordinate 3.3.2 KIE Analysis in the Classical Harmonic Limit 3.3.3 Effect of Anharmonic D-A Interactions and Local Electric Fields 3.3.3.1 Background 3.3.3.2 A Simple Anharmonic Donor-Acceptor Model 3.3.4 Application to Soybean Lipoxygenase 3.4 Electronically Adiabatic and Vibrationally Non-adiabatic Proton Tunnelling in Biomolecules 3.4.1 Proton Tunnelling Rate Expression Using a Quantized D-A Oscillator 3.4.2 Kinetic Isotope Effect in the Electronically Adiabatic Limit 3.4.3 Application of the Electronically Adiabatic 2D Quantum Model to the Ground State Proton Transfer in GFP 3.5 Conclusion Appendix: Table of Parameters Acknowledgements References Chapter 4 From Tunnelling Control to Controlling Tunnelling 4.1 Introduction 4.2 Tunnelling Control in Chemical Reactions 4.3 Promoting and Inhibiting Tunnelling via Nuclear Motion in 14NH3 4.4 Tunnelling Switching 4.5 Coherent Control of Tunnelling with Laser Fields 4.6 Summary and Conclusions Acknowledgements References Chapter 5 From Nuclear Fluxes During Tunnelling to Electronic Fluxes During Charge Migration 5.1 Introduction 5.2 Quantum Theory 5.3 Application to the Stereomutation of CHFBr by Nuclear Tunnelling 5.4 Application to Electronic Charge Migration in HCCBr+ 5.5 Comparison of the Results for Stereomutation of CHFBr by Nuclear Tunnelling and for Axial Electronic Charge Migration in HCCBr+ 5.6 Conclusions Acknowledgements References Chapter 6 Tunnelling and Parity Violation in Chiral and Achiral Molecules: Theory and High-resolution Spectroscopy 6.1 Introduction 6.2 Parity Violation in Chiral Molecules in the Framework of the SMPP 6.2.1 Introductory Remarks 6.2.2 Basic Theory 6.2.3 Parity-violating Potential Hypersurfaces and Vibrational Effects 6.3 The Interplay of Tunnelling and Parity Violation in Chiral Molecules 6.4 The Quantum Wavepacket Dynamics in Chiral Molecules Where Either Tunnelling or Parity Violation Dominates 6.4.1 Exact and Approximate Studies of Tunnelling in Prototypical Molecules with Transient Chirality: Hydrogen Peroxide and Ammonia Isotopomers 6.4.2 Tunnelling in Chiral Molecules Where Parity Violation Dominates Over Tunnelling 6.4.3 Tunnelling Switching in Chiral and Achiral Molecules 6.4.4 Tunnelling Stereomutation and Racemization Kinetics in Chiral Molecules 6.5 Spectroscopic Approaches Towards Tunnelling and Parity Violation in Chiral Molecules 6.6 Concluding Remarks Acknowledgements References Chapter 7 Instanton Theory to Calculate Tunnelling Rates and Tunnelling Splittings 7.1 Introduction 7.2 Theory 7.2.1 Imaginary Free-energy Approach 7.2.2 Partition Functions 7.2.3 Instanton Paths 7.2.4 Rate Constants 7.2.5 Unimolecular and Bimolecular Cases 7.2.6 Tunnelling Splittings 7.3 Implementation and Practical Use 7.4 Conclusions Acknowledgements References Chapter 8 Semiclassical Multidimensional Tunnelling Calculations 8.1 Introduction 8.2 Theory 8.3 Validation 8.4 Extensions 8.5 Concluding Remarks Abbreviations Acknowledgments References Chapter 9 The Calculation of Tunnelling Splittings Illustrated on Malonaldehyde 9.1 Introduction 9.2 Semiclassical Methods 9.2.1 The WKB Approximation 9.2.2 Semiclassical Instanton 9.3 Malonaldehyde 9.4 Early Calculations 9.4.1 Eckart Potential 9.4.2 The Reaction Surface Hamiltonian 9.4.3 Instantons 9.4.4 The Approximate Instanton Method 9.4.5 Least-action Tunnelling Path 9.4.6 ‘‘Semiclassical" Trajectory Simulations 9.5 Recent Calculations 9.5.1 Global and Semi-global Potential Energy Surfaces 9.5.2 Multidimensional Instanton and Path Integrals 9.5.3 Quantum Dynamics 9.5.4 The Revival of Approximate Methods 9.6 State-selected Tunnelling Splittings 9.7 Conclusion Funding Abbreviations Acknowledgements References Chapter 10 Quantum-dynamical Calculation of Rate Constants in Polyatomic Reactions Employing the Quantum Transition State Concept 10.1 Introduction 10.2 Theory of Thermal Rate Constant Calculations 10.2.1 Scattering Theory 10.2.2 Flux Correlation Functions 10.2.3 Connection to Transition State Theory 10.3 Quantum Transition State Concept 10.3.1 Thermal Flux Operator 10.3.2 Working Equations 10.3.3 Overall Rotational Motion 10.3.4 Natural Reaction Channels 10.3.5 Beyond Rate Constants 10.4 Numerical Quantum Dynamics: Standard Wave Packets 10.4.1 Wavefunction Representations 10.4.1.1 Discrete Variable Representation 10.4.1.2 Fast Fourier Transformation Representation 10.4.2 Time Propagation 10.4.2.1 Split Operator Propagator 10.4.2.2 Short Iterative Lanczos Propagator 10.4.3 Obtaining Eigenstates 10.5 Numerical Quantum Dynamics: Multiconfigurational Time-dependent Hartree 10.5.1 Time-dependent Basis and Equations of Motion 10.5.1.1 Time Propagation 10.5.2 Useful Extensions of MCTDH 10.5.2.1 State-averaging 10.5.2.2 Mode Combination 10.5.2.3 Multi-layer MCTDH 10.5.3 Correlation DVR 10.5.4 Eigenstate Calculations within MCTDH 10.5.5 Statistical Approaches for Calculating Rotational Motion and Partition Functions 10.6 Examples 10.6.1 Cl+H2→HCl+H 10.6.1.1 Treatment of Spin-Orbit Coupling 10.6.2 H2+OH→H2O+H 10.6.2.1 The J-shifting Approximation 10.6.3 H+CH4→H2+CH3 10.6.3.1 Multilayer MCTDH Considerations 10.6.3.2 Comparing Different PES 10.6.3.3 Natural Reaction Channels Acknowledgements References Chapter 11 Eigenstate Approaches for High Resolution Spectroscopy of Tunnelling in Small Molecular Systems 11.1 Introduction 11.1.1 Symmetric Double Minimum 11.1.2 General Asymmetric Case 11.2 Computational Methods 11.2.1 Direct-product Discrete Variable Representation Grids and Iterative Eigensolvers 11.2.2 Rovibrational Perturbation Theory Based on Curvilinear Vibrational Mean-field Theory 11.2.3 Kinetic Energy Operators 11.2.4 Coordinate Systems and Body-fixed Frame Embedding 11.2.5 Potential Energy Surfaces 11.3 Examples 11.3.1 H2O2 11.3.2 CH3- 11.3.3 gauche-Butadiene 11.3.4 S1 Acetylene 11.3.4.1 cis-trans Tunnelling and Tunnelling Staggerings 11.4 Outlook Acknowledgements References Chapter 12 The Tunnelling Flight Time 12.1 Introduction 12.2 The Tunnelling Flight Time 12.2.1 Preliminaries 12.2.2 Definitions 12.2.3 The Tunnelling Flight Time 12.2.4 Numerical Examples - Symmetric Barriers 12.2.5 Numerical Examples - Asymmetric Barriers 12.2.6 Classical Wigner Dynamics 12.3 Time and Above-barrier Quantum Reflection 12.3.1 Preliminaries 12.3.2 Phase Times 12.4 Larmor Time vs. Flight Time 12.4.1 Complex Time 12.4.2 The Larmor Clock 12.5 Discussion Acknowledgements References Subject Index