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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.
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
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