Perturbed Morse-Oscillator Approximation in Reactive Collisions. I. An Attractive Potential

Abstract

Reactive collisions in three‐center reactions of the type A + BC → AB + C are considered quantum mechanically in terms of a model based upon a perturbed Morse oscillator and a linear‐collision complex. The developed formalism is then applied to the reaction H+Br₂→HBr+Br using the diatomics‐in‐molecules method to obtain a potential‐energy surface for the reaction. This potential is attractive, that is, releasing the heat of reaction upon the approach of the hydrogen atom. Computed cross sections are larger both for the higher allowed vibrational quantum numbers of the product molecule as well as for the higher rotational states possible for each given vibrational state. These results are in agreement with the trend of semiclassical calculations using a similarly attractive potential. To establish a clear dependence of the cross sections on the vibrational state of HBr, it was necessary to treat the relative translation between HBr and Br as a potential scattering problem rather than assuming free relative motion. The calculated total cross sections were essentially independent of the initial conditions of the collision due to the neglect of activation energy in the Morse basis functions of the perturbed stationary‐state expansion.