Semiclassical S-matrix theory of vibrationally inelastic collisions between two diatomic molecules

Abstract

We derive a semiclassical S matrix for vibrationally inelastic collisions between two diatomic molecules, assuming a collinear geometry. Our theory incorporates a quantum mechanical superposition principle with classical dynamics and, as such, is an extension of the atom‐diatomic molecule theory of Miller. The several approximations to the S matrix differ in the complexity with which the interference between various classical trajectories is treated. We report numerical calculations for H₂–D₂ and D₂–D₂ collisions based on two different interaction potentials. The cruder approximations yield transition probabilities which agree with exact quantum mechanical results to within a factor of 2. More sophisticated approximations to the S matrix yield excellent quantitative agreement with the quantum calculations. We also examine in detail the classical dynamics of the collision process and show that the molecules pass through a number of intermediate states during the encounter.