Vibrational-Rotational Excitations in Nonlinear Molecular Systems

by Alexander A. Ovchinnikov, Nikolai S. Erikhman, Kirill A. Pronin

Overview

"If there would be no God ~ then what a staff-captain am I?" ~ said one of the characters in a novel by Dostoevskii. In a similar way we can exclaim: "If there would be no nonlinearity ~ than what physics would that be'?". Really, the most interesting and exciting effects are described by non­ linear equations, and vanish in the linear approximation. For example, the general theory of relativity by A.Einstein comes to mind first - one of the most beautiful physical theories, which is in fact essentially nonlinear. Next, the phase transitions crystal ~ liquid and liquid ~ gas are due to the anhar­ monicity of inter-particle interactions, to dissociation and infinite motion. Similarly, transitions into the superconducting state or the superftuid would be impossible with purely harmonic interaction potentials. Another bril­ liant achievement in nonlinear physics was the construction of a laser and the subsequent development of nonlinear optics. The latter describes the in­ teraction of the matter with light of super-high intensity, when multi-quanta intra-molecular transitions become essential. Last, we should note here the very beautiful mathematical theory ~ the theory of catastrophes. Its subject is the study of invariant general properties of multi-dimensional surfaces in the vicinity of bifurcation points with respect to continuous transformations.

Product Details

ISBN-13:	9781461354949
Publisher:	Springer US
Publication date:	09/25/2012
Edition description:	Softcover reprint of the original 1st ed. 2001
Pages:	355
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

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.