Three-Dimensional Analytic Model of Vibrational Energy Transfer in Molecule-Molecule Collisions

Abstract

Athree-dimensionalsemiclassicalanalyticmodelofvibrationalenergytransferincollisionsbetweentworotating diatomic molecules has been extended for molecule ‐molecule collision. The model is based on analysis of classical trajectories of free-rotating (FR) molecules acted upon by a superposition of repulsive exponential atom-to-atom potentials. The energy transfer probabilities have been evaluated using the nonperturbative Forced Harmonic Oscillator (FHO) model. The model predicts the probabilities for vibrational energy transfer as functions of the total collision energy, orientation of molecules during a collision, their rotational energies, and impact parameter. The model predictions have been compared with the results of three-dimensional close-coupled semiclassical trajectorycalculationsusingthesamepotentialenergysurface.Thecomparisondemonstratesnotonlyremarkably good agreement between the analytic and numerical probabilities across a wide range of collision energies, but also shows that the analytic FHO-FR model correctly reproduces the probability dependence on other collision parameters such as rotation angles, angular momentum angles, rotational energies, and impact parameter. The model equally well predicts the cross sections of single-quantum and multiquantum transitions and is applicable up to very high collision energies and quantum numbers. Most importantly, the resultant analytic expressions for the probabilities do not contain any arbitrary adjustable parameters commonly referred to as steric factors . The present work essentially completes development of the analytic rate database for vibrational energy transfer among air species, increasing the range of applicability of the FHO-FR model.