Semiclassical Optical Model for Molecular Collisions

Abstract

The construction of a semiclassical optical model for molecular collisions to consider explicitly the dynamics of more than a single nuclear degree of freedom is investigated. A sample model is developed for nonreactive systems as the direct multidegree analog of the semiclassical optical model for a single nuclear degree of freedom. In this model all nuclear degrees of freedom, moving in a complex potential, are treated explicitly through the integration of Hamilton's equations of motion in complex time and complex phase space. Calculations are performed for probabilities of elastic collinear collisions of an atom with a diatomic oscillator in its ground vibrational state with excited vibrational states energetically accessible. Agreement is obtained with exact quantum-mechanical results for just the real part of the potential, through variation of an adjustable parameter in the imaginary part of the potential. Extensions and variations of this model toward the simplification of more-complicated calculations on reactive and three-dimensional systems are discussed.