Statistical Computation of Reaction Probabilities

Calculations have been carried out on a high-speed electronic digital computer to determine statistically the transition probability for a simple chemical reaction. Using the London-Eyring-Polanyi form for the potential energy of the colinear system, H+H2, we have solved the classical equations of motion for the system under a great variety of conditions. Collisions of a hydrogen atom and a hydrogen molecule, with and without initial molecular vibration, were studied as a function of the total kinetic energy. By carrying out numerous calculations for a sufficiently large number of different initial conditions, we obtained an average behavior of the system, which we believe provides a satisfactory approximation to the quantum mechanical average. It was found that the reaction probability was greatest when the energy was just slightly above the activation energy. Moreover, it was observed that, if the molecule was initially vibrating, only a part of the energy of vibration was available for reducing the kinetic energy of translation required for activation. It was also found that the conversion of energy between vibration and translation was relatively improbable.