Overview

This text provides a theoretical description of highly-excited long-living vibrational/rotational excitations in anharmonic molecules. It comprises the classical and quantum theory of local modes, their effect upon the infrared (IR) aspects of molecules and upon the kinetics of intramolecular relaxation, and presents a semi-empirical theory that relates the geometrical parameters of the molecule to the IR spectra.

Full Product Details

Author:   Alexander A. Ovchinnikov ,  Nikolai S. Erikhman ,  Kirill A. Pronin
Publisher:   Springer Science+Business Media
Imprint:   Kluwer Academic/Plenum Publishers
Edition:   2001 ed.
Dimensions:   Width: 15.50cm , Height: 2.20cm , Length: 23.50cm
Weight:   1.540kg
ISBN:  

9780306466113

ISBN 10:   0306466112
Pages:   355
Publication Date:   30 November 2001
Audience:   College/higher education ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1 Introduction.- 2 Classical theory of nonlinear vibrational systems; local modes.- 2.1 Survey of classical mechanics; introduction to local modes.- 2.2 Method of averaging.- 2.3 Two weakly coupled Morse oscillators: dynamics and local - mode formation.- 2.4 Analysis of phase trajectories with the help of Poincare sections, numerical results.- 3 Coupled nonlinear oscillators: formation and decay of local modes.- 3.1 Two weakly coupled nonlinear oscillators: decay of normal modes.- 3.2 Multi-oscillator systems: local modes’ and normal modes’ representations.- 3.3 Morse oscillators: calculation of resonance linewidths and criteria for the appearance of local modes.- 3.4 Coupled nonlinear oscillators: localized vibrational excitations and their asymptotic stability.- 3.5 Canonical transformation to local - mode representation.- 4 Discrete breathers.- 4.1 Breathers in Hamiltonian lattices.- 4.2 Discrete breathers in one-dimensional chains.- 4.3 Arguments for the existence of discrete breathers: some mathematics.- 4.4 Discrete breathers: numerical experiments.- 4.5 Discrete breathers in lattices with a homogeneous potential.- 4.6 An exactly solvable Hamiltonian lattice.- 5 Quantum theory of vibrational - rotational spectra in XY2 - type molecules.- 5.1 Quantum theory of two Morse oscillators: stretching — vibration spectra in XY2 molecules.- 5.2 Stretching — vibration spectra: nonresonant modes’ effect upon clusterization of levels.- 5.3 Spectrum of stretching vibrations in XY2 molecules: numerical studies.- 6 Quantum Hamiltonians of vibrational — rotational excitations in polyatomic molecules; method of contact transformations.- 6.1 Quantum Hamiltonian of polyatomic molecules.- 6.2 Molecular Hamiltonian in the inner basis representation ’coordinates -angles’.- 6.3 Contact transformation.- 6.4 Vibrational-rotational Hamiltonian for XY2 molecule in the inner basis representation ’coordinates - angles’.- 7 Semiclassical rotational spectra of rigid and semi-rigid molecules; clusterization of levels and internal symmetry.- 7.1 Spectrum of polyatomic molecules: clusterization of rotational levels.- 7.2 Rotational spectrum of rigid and semi-rigid molecules: semi-classical approach.- 7.3 Symmetry - based analysis of rotational clusters.- 7.4 Tunnelling matrix.- 7.5 Violation of permutation symmetry and the super-hyperfine structure.- 8 Interaction of vibrations and rotations; polyads and their spectra.- 8.1 Interaction of local vibration modes and rotation in hydrides.- 8.2 Rotational - vibrational spectrum in the vicinity of bifurcation points.- 8.3 Spectral properties of systems with Fermi resonances.- 9 Intramolecular relaxation of vibrations in the presence of local modes.- 9.1 Localized long - living vibrational states in molecular crystals.- 9.2 Population inversion of localized long - living vibrational states in a cold lattice.- 9.3 Interaction of isolated levels with the continuous spectrum.- 10 IR spectra and intramolecular relaxation.- 10.1 Redistribution of intramolecular energy: influence of multi-mode resonance.- 10.2 Relation between the absorption linewidths, intramolecular vibrations evolution, and unimolecular decay rates.- 10.3 Effect of anharmonicity on IR spectra of polyatomic molecules.- 10.4 Correlation between structure and IR spectra in polyatomic molecules.- 11 Conclusion.

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