Molecular Vibrations

An Algebraic and Nonlinear Approach

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 Schrödinger 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.

Sample Chapter(s)
1. Pendulum Dynamics

Contents:

• Preface
• Pendulum Dynamics
• Algebraic Approach to Vibrational Dynamics
• Chaos
• C–H Bending Motion of Acetylene
• Assignments and Classification of Vibrational Manifolds
• Dixon Dip
• Quantization by Lyapunov Exponent and Periodic Trajectories
• Dynamics of DCO/HCO and Dynamical Barrier Due to Extremely Irrational Couplings
• Dynamical Potential Analysis for HCP, DCP, N2O, HOCl and HOBr
• Chaos in the Transition State Induced by the Bending Motion

Readership: Postgrads and researchers in nonlinear science and analysis.
Key Features:

• It broadens the prospects of molecular vibration to high excitation
• It broadens the treatment of molecular vibration to algebraic and nonlinear methods