Quantum Mechanical Tunneling in Chemical Physics: 1st Edition (Hardback) book cover

Quantum Mechanical Tunneling in Chemical Physics

1st Edition

By Hiroki Nakamura, Gennady Mil'nikov

CRC Press

226 pages | 67 B/W Illus.

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pub: 2013-04-12
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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


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



About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Physical & Theoretical
SCIENCE / Spectroscopy & Spectrum Analysis