Quantum Mechanical Tunneling in Chemical Physics

Quantum Mechanical Tunneling in Chemical Physics

by Hiroki Nakamura, Gennady Mil'nikov

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Product Details

ISBN-13: 9781466507326
Publisher: CRC Press
Publication date: 04/19/2016
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 226
File size: 3 MB

About the Author

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.

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

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