On stochastic reductions in molecular collision theory: Projection operator formalism; application to classical and quantum forced oscillator model

George C Schatz, Frank J. McLafferty, John Ross

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A method is developed for treating complex molecular collision processes through the application of stochastic reduction formalisms. We begin by describing a projection operator method for decomposing a complicated collision system into two (or more) subsystems, each of which is assumed to be weakly correlated (not necessarily weakly interacting) with the others. Approximations to this correlation are then introduced, and this results in a set of coupled equations for the reduced density operators (or classical phase space distributions) associated with each subsystem. We then examine the classical mechanical application of this theory to the forced oscillator model of V-T energy transfer. Arguments of multiple time scales are used to uncouple the stochastically reduced equations of motion, and thus we may evaluate the memory kernel analytically. This leads to a single diffusion equation for the time evolution of the action in the oscillator during the collision. Comparison with the corresponding exact results indicates excellent agreement of low order moments of the classical distributions of action in the limit of small energy transfer (i.e., ΔE/ℏω

Original languageEnglish
Pages (from-to)3609-3623
Number of pages15
JournalJournal of Chemical Physics
Issue number8
Publication statusPublished - 1977


ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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