Quantum Mechanical Tunneling in Chemical Physics

Content: 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
Abstract: ''This text explores methodologies that can be usefully applied to various realistic problems in molecular spectroscopy and chemical dynamics. It covers the direct evaluation of reaction rate constants for both electronically adiabatic chemical reactions on a single adiabatic potential energy surface and non-adiabatic chemical reactions in which two or more adiabatic potential energy surfaces are involved. It also discusses the non-adiabatic tunneling phenomenon that represents one class of non-adiabatic transitions on which the authors have made an extensive research so far''