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This book focuses on the main idea that highly-excited molecular vibration is a nonlinear, many-body and semiclassical system. Therefore, many ideas and techniques in nonlinear fields such as chaos, resonance, Lyapunov exponent, etc. can be incorporated into this study. Together with the Lie algebraic coset algorithm, readers are able to approach the topics in a simple arithmetic and realistic way in contrast to the traditional solving of Schroedinger equation.Covering the author's research in over two decades, these works bridge the gaps between molecular vibration and nonlinear sciences, many new characters are introduced for molecular highly-excited vibration from a fresh viewpoint of nonlinearity, especially, the chaos. Related works of the elementary ideas in this field can be found in the first three chapters for the readers to be familiar with, while the rest of the chapters offer concrete examples with flourishing ideas and results on system dynamics which are not known or neglected by the traditional wave function algorithm.
This book summarizes the highlights of our work on the bond polarizability approach to the intensity analysis. The topics covered include surface enhanced Raman scattering, Raman excited virtual states and Raman optical activity (ROA). The first chapter briefly introduces the Raman effect in a succinct but clear way. Chapter 2 deals with the normal mode analysis. This is a basic tool for our work. Chapter 3 introduces our proposed algorithm for the Raman intensity analysis. Chapter 4 heavily introduces the physical picture of Raman virtual states. Chapter 5 offers details so that the readers can have a comprehensive idea of Raman virtual states. Chapter 6 demonstrates how this bond polarizability algorithm is extended to ROA intensity analysis. Chapters 7 and 8 offer details on ROA, showing many findings on ROA mechanism that were not known or neglected before. Chapter 9 introduces our proposed classical treatment on ROA which, as combined with the results from the bond polarizability analysis, leads to a comprehensive physical picture for the Raman effect. In particular, this classical treatment unifies ROA and VCD (vibrational circular dichroism) on equal footing. In each section, Comments summarize the key ideas and their evaluation. This will help the readers to capture the core ideas of the presentations.
The book presents principles of molecular vibrational spectroscopy from the viewpoint of Raman, Raman optical activity and high excitation. The quantum mechanical basis, vibrational analysis, representation of point groups and its applications are discussed as well. With exercises, it is an essential text for graduates, lecturers, and also researchers.
Nonlinearity and Chaos in Molecular Vibrations deals systematically
with a Lie algebraic approach to the study of nonlinear properties
of molecular highly excited vibrations. The fundamental concepts of
nonlinear dynamics such as chaos, fractals, quasiperiodicity,
resonance, and the Lyapunov exponent, and their roles in the study
of molecular vibrations are presented.
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