Classical S Matrix for Rotational Excitation; Quenching of Quantum Effects in Molecular Collisions

Abstract

A previously developed theory in which exact solutions of the classical equations of motion for a complex collision system (i.e., numerically computed trajectories) can be used to generate the classical limit of the quantum mechanical $S$ matrix (the “classical $S$ matrix”) for the scattering process is applied to rigid rotor–atom collisions (rotational excitation). Comparison with essentially exact quantum results shows that transition probabilities (the square modulus of an S‐matrix element) between individual quantum states are given reasonably accurately by classical dynamics provided the interference terms are properly accounted for; a strictly classical approach (neglect of interference) gives poor agreement with the quantum values. For averaged collision properties, however, it is found that interference and tunneling effects are rapidly quenched. The linear atom–diatom system (vibrational excitation) and the rigid rotor–atom system are both investigated with regard to this question, namely, how much averaging is necessary to quench these quantum effects. Results indicate that even summation over a few quantum states is often sufficient to make a completely classical treatment appropriate.