1st Edition

Quantum Mechanical Tunneling in Chemical Physics

By Hiroki Nakamura, Gennady Mil'nikov Copyright 2013
    226 Pages 67 B/W Illustrations
    by CRC Press

    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.

    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

    Biography

    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.