Decomposition of isolated molecules: A transition state treatment

It is argued that, contrary to the assumption of RRKM theory, reactant states near the critical surface frequently may not be at statistical equilibrium with the bulk of reactant states. The main objective of this work is to examine conditions under which the RRKM specific unimolecular rate constant expression nevertheless remains valid. The analysis proceeds by casting the general, time-dependent, decomposition rate of isolated molecules into time-independent form and applying a transition state approximation similar to that introduced by Miller for bimolecular reactions. In the process of carrying out this program, the following is achieved: (a) A potentially useful unimolecular rate expression, analogous to Miller's transition state theory rate formula for bimolecular reactions, is obtained; (b) a criterion for choosing critical configurations similar to the Bunker-Pattengill recipe is derived when classical mechanics is obeyed; (c) features of a recent calculation of unimolecular reaction dynamics are explained.