Monte Carlo Trajectory Calculations of the Three-Body Recombination and Dissociation of Diatomic Molecules

Abstract

The modified phase‐space theory of reaction rates has been applied to the problem of the three‐body recombination and dissociation of diatomic molecules. The results illustrate the important influence of the weak attractive minimum in the third‐body interaction potential and the effect of barrier penetration for recombination at low temperatures. The system N₂+Ar was used as a typical illustrative example, and good agreement was obtained between the theoretical predictions and the experimental measurements of the reaction rate coefficients over the temperature range 200–12 000°K. The recrossing factor and the nonequilibrium factor were obtained from Monte Carlo trajectory calculations for states near the dissociation limit. The trajectories were sampled within the reaction zone with a weight proportional to the equilibrium reaction rate, and numerically integrated in both timewise directions to determine the complete histories of the collisions. A simple, separable function for the equilibrium transition rate R(ε_i, ε_f) from initial energy states ε_i to final energy states ε_f, which could be characterized by three parameters, was obtained to fit the numerical data and was used to solve the steady‐state master equation. Distributions of the trajectories with respect to energies and impact parameters are presented, and several typical trajectories are shown to illustrate the important features of the collisions. The contribution to the over‐all reaction rate from the ``complex mechanism'' was also obtained.