In this book we mainly discuss the following three tunneling phenomena based on our recent theoretical developments: (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. The corresponding physical processes can be naively understood in terms of a reaction path in which (1) two endpoints are fixed, (2) one endpoint is fixed and one is free, and (3) both ends are free. Quantum mechanical tunneling manifests itself in a very wide range of natural phenomena and the subjects we deal with here constitute only a small portion of the whole area.
In spite of the long history of studies of quantum mechanical tunneling phenomena, however, the theory of multidimensional tunneling has not yet been satisfactorily developed. Recently, we have successfully developed practical and useful methods applicable to real multidimensional systems for the above-mentioned problems. Basic theories, practical methodologies, and actual numerical applications to real molecular systems are presented so that the reader can hopefully comprehend the basic concepts and dynamics of multidimensional tunneling phenomena and use the methods directly in various problems of molecular spectroscopy and chemical dynamics, if necessary.
Insufficiency of the low-dimensional treatments that are often employed for practical problems and intriguing effects of multidimensionality are demonstrated and clarified conceptually as well as numerically. Furthermore, attention is called to the nonadiabatic tunneling phenomenon, which is quite ubiquitous in molecular systems and yet manifests unique and intriguing phenomenon in comparison with ordinary tunneling. In this book, quite a bit of mathematics is used for the development and explanation of basic theories; thus a background knowledge of mathematics is required at the level of graduate students.
This book is intended as a standard reference for comprehending the phenomena and solving practical problems in the fields of chemical physics. H. N. mainly wrote the whole contents and thus is responsible for all chapters. G. M. shares responsibility for Chapters 6, 7, and 8 and Section 9.1. We would like to thank all the collaborators for their contributions in the development of the methods and various applications to real molecular systems that clearly demonstrate the usefulness of our methods. H. N. would like to express his sincere thanks to National Chiao Tung University in Hsinchu, Taiwan, and people at the Institute of Molecular Science, Department of Applied Chemistry, Faculty of Science of the university for providing this nice opportunity to work on this book.
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