Collision Dynamics and the Statistical Theories of Chemical Reactions. I. Average Cross Section from Transition-State Theory

Abstract

By recasting the transition‐state‐theory formula for the reaction rate of a general bimolecular reaction and making use of Laplace transform techniques, an expression for the average reaction cross section as a function of the total system energy is derived; the result for three‐dimensional collisions have been given previously by Marcus. For the collinear model, a reaction probability replaces the cross section. Cross sections and probabilities for a number of special cases are given. It is shown that under certain conditions, improper high‐energy limits result. The relation of the present conclusions to unimolecular rate theory is indicated.