An exact quantum mechanical transition state theory. 1. An overview

Abstract

Starting with the collision theory expression for the rate constant k of a thermal gas phase bimolecular reaction in terms of reaction cross sections, we derive a modified exact expression for k which has a mathematical form identical with that provided by transition state theory (TST). No approximations are introduced in this derivation and the only difference between this exact expression and the TST one is in the transmission coefficient kappa. The exact one, kappa/sup ex/, is expressed in terms of the correct reaction probabilities, whereas the TST one, kappa/sup TST/, involves transmission probabilities across appropriately defined one-mathematical-dimensional adiabatic barriers. It is shown that kappa/sup ex/ can be larger or smaller than unity, and need not approach one as the temperture of the reaction tends to infinity. Comparison of the expressions for kappa/sup ex/ and kappa/sup TST/ leads to a necessary and sufficient set of conditions for validity of TST. These involve only dynamical assumptions regarding reaction probabilities, and do not require any additional equilibrium condition among activated complexes or between them and reagents; the only equilibrium assumption made is the one among reagents, which is inherent in the definition of a thermal rate constant. A comparison of usual TSTmore » rate constants with the exact one for the H + H/sub 2/, F + H/sub 2/, and F + D/sub 2/ systems is given, the validity of the dynamical assumptions of that theory is examined, and suggestions for its improvement are presented and tested. 11 figures, 59 references.« less