Quantum Mechanical Tunneling in Chemical Physics

Quantum Mechanical Tunneling in Chemical Physics

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Features

  • Offers a solid introduction of basic low-dimensional theories
  • Explains concepts and theories and gives numerical demonstrations of multidimensional effects
  • Provides accurate new methods developed by the authors to treat real chemical problems in multi-dimensional systems
  • Presents practical numerical applications for real polyatomic molecules such as hydroperoxy radicals, vinyl radicals, malonaldehyde, and formic acid dimers
  • Includes explanations of some peculiar phenomena that cannot be explained by one-dimensional theories
  • Describes a method to detect caustics in multi-dimensional space
  • Contains appendices with proofs and derivations of equations, and Fortran code to find tunneling paths in multi-dimensional space

Summary

Quantum mechanical tunneling plays important roles in a wide range of natural sciences, from nuclear and solid-state physics to proton transfer and chemical reactions in chemistry and biology. Responding to the need for further understanding of multidimensional tunneling, the authors have recently developed practical methods that can be applied to multidimensional systems. Quantum Mechanical Tunneling in Chemical Physics presents basic theories, as well as original ones developed by the authors. It also provides methodologies and numerical applications to real molecular systems.

The book offers information so readers can understand the basic concepts and dynamics of multidimensional tunneling phenomena and use the described methods for various molecular spectroscopy and chemical dynamics problems. The text focuses on three tunneling phenomena: (1) energy splitting, or tunneling splitting, in symmetric double well potential, (2) decay of metastable state through tunneling, and (3) tunneling effects in chemical reactions. Incorporating mathematics to explain basic theories, the text requires readers to have graduate-level math to grasp the concepts presented.

The book reviews low-dimensional theories and clarifies their insufficiency conceptually and numerically. It also examines the phenomenon of nonadiabatic tunneling, which is common in molecular systems. The book describes applications to real polyatomic molecules, such as vinyl radicals and malonaldehyde, demonstrating the high efficiency and accuracy of the method. It discusses tunneling in chemical reactions, including theories for direct evaluation of reaction rate constants for both electronically adiabatic and nonadiabatic chemical reactions. In the final chapter, the authors touch on future perspectives.

Table of Contents

Introduction

One-Dimensional Theory
Exactly Solvable Cases
WKB Approximation and Connection Formula
Comparison Equation Method
Diagrammatic Technique
Instanton Theory and Modified WKB Method
Energy Levels in a Double Well Potential
Decay of Metastable State

Two-Dimensional Theory
WKB Theory
Instanton Theory

Multidimensional Effects: Peculiar Phenomena
Effects of Vibrational Excitation on Tunneling Splitting
Insufficiency of Two-Dimensional Model
Proton Tunneling in Tropolone

Nonadiabatic Tunneling
Definition and Qualitative Explanation
One-Dimensional Theory

Multidimensional Theory of Tunneling Splitting
General Formulation
How to Find Instanton Trajectory
How to Use the Theory
Case of Low Vibrationally Excited States

Numerical Applications to Polyatomic Molecules
N-Dimensional Separable Potential Model
Hydroperoxy Radical HO2
Vinyl Radical C2H3
Malonaldehyde C3O2H4
Formic Acid Dimer (DCOOH)2

Decay of Metastable States
General Formulation
Numerical Application

Tunneling in Chemical Reactions
Determination of Caustics and Propagation inTunneling Region
Direct Evaluation of Reaction Rate Constant

Concluding Remarks and Future Perspectives

Appendix A
Proofs of Equation (2.95) and Equation (2.110)
Appendix B Derivation of Equation (6.80)
Appendix C Herring Formula in Curved Space
Appendix D Derivation of Equation (6.97)
Appendix E Computer Code to Calculate Instanton Trajectory
Appendix F Derivation of Some Equations in Section

Bibliography

Index

Author Bio(s)

Hiroki Nakamura, is a professor at the Institute of Molecular Science, Faculty of Science, National Chiao Tung University in Taiwan and Professor Emeritus at the Institute for Molecular Science, National Institutes of Natural Sciences in Japan.