Transition State Theory and Beyond — A Constrained Phase Space Approach

Abstract

AbstractThe information‐theoretic, maximum entropy formalism for the computation of reaction rates is reviewed, with several applications and computational examples. Attention is focused on the essential ideas and, for simplicity, the analytical development is carried out only for collinear collisions at a given total energy. Particular attention is given to the theories which are of maximal entropy subject to a constraint on the mean number of times n that a critical surface enroute from reagents to products is crossed by the system. Transition state theory is derived as the special case when the mean number of crossings is taken to be unity. The approximation n = 1 is often exact in the threshold region, but as the energy increases it rapidly deteriorates. When n > 1, it is found not to be a dominant constraint. Rather, the nonuniform distribution of trajectories in phase space is the major restriction on the reaction rate. It proves possible to treat this case analytically, and explicit results, illustrated by the H + H2 and F + H2 reactions, are provided.