Kinematic Model for Atom–Diatom Reactions

Abstract

A simple model for atom–diatom reactions is completely analyzed. The model represents the molecule by two hard spheres nearly in contact and the atom by a third hard sphere. Energy and momentum transfers among the three particles are calculated for all values of molecular orientation and collision parameters. On the basis of the kinematic analysis and in terms of an activation parameter, probabilities are assigned to the various reactions which may occur. Using as parameters the bond length of H₂ and the activation energy for H+H₂, the model predicts (a) the energy dependence of the H+H₂ cross section, in agreement with the complete classical analysis of Karplus et al.; (b) rate constants for hydrogen isotopic exchange reactions which agree with experiment when threshold effects do not dominate; and (c) the hot‐atom behavior of the T+H₂ and T+D₂ systems in substantial agreement with both experiment and the complete classical analysis. Methods for extending the model are discussed.