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.
The 20 chapters cover the basic ideas, the concept of dynamical groups, the integrable two-mode SU(2) system, the unintegrable three-mode SU(3) system, the noncompact su(1,1) algebraic application, su(3) symmetry breaking and its application and the quantal effect of asymmetric molecular rotation. Emphasis is given to: resonance and chaos, the fractal structure of eigencoefficients, the C-H bend motion of acetylene, regular and chaotic motion of DCN, the existence of approximately conserved quantum numbers, one-electronic motion in multi-sites, the Lyapunov exponent, actions of periodic trajectories and quantization, the H function and its application in vibrational relaxation as well as the Dixon dip and its destruction and chaos in the transitional states. This approach bridges the gap between molecular vibrational spectroscopy and nonlinear dynamics.
The book presents a framework of information that readers can use to build their knowledge, and is therefore highly recommended for all those working in or studying molecular physics, molecular spectroscopy, chemical physics and theoretical physics.
* Discusses nonlinearity and chaotic phenomena in molecular vibrations
* Approaches the complicated highly excited molecular vibration
* Provides clear information for students and researchers looking to expand knowledge in this field