CLASSICAL AND QUANTUM DYNAMICS OF HIGHLY EXCITED LOCAL MODES

A classical and semiclassical discussion is presented of the stretching dynamics of ABA triatomics for which a local mode picture provides a good zeroth order description. A model for H(,2)O is used for illustration. The time dependent classical solutions are expressed to an excellent approximation in terms of the solutions of a two-fold hindered rotor. The transformation to this representation leads to a simple picture of the transition from "local" to "normal" mode behavior. Quadratic coupling between the bonds is shown to lead to nonlinear resonant energy transfer. Quantum calculations in this representation are carried out for the spectral splittings. A WKB analysis is used to relate the spectral splittings to classical energy transfer rates and quantum dynamical tunneling and reflection probabilities. Isotope effects are discussed for the H(,2)O-D(,2)O pair.; Fermi resonance interactions are examined in a curvilinear coordinate perspective. The coupling which gauges the Fermi interaction in CO(,2) between the symmetric stretch fundamental and the bend overtone is shown to be primarily kinetic. It arises from the functional dependence of the effective masses on the internal coordinates. These ideas are further developed to model the vibrational dynamics of highly excited CH and CD overtones of benzene and perdeuterobenzene. The origin, path, and time scale for the overtone decay are described. Key coupling terms, which lead to Fermi resonance interactions between the CH stretch and in-plane ring modes, are identified and are shown to lead to quantum dynamics and spectral features consistent with the experimental overtone spectra of Reddy, Heller, and Berry {lcub}J. Chem. Phys. 76, 2814 (1982){rcub}. The same coupling terms lead to analogous classical decay of overtones through a succession of nonlinear resonance interactions between the CH stretch and in-plane ring modes.