Nonequilibrium Effects in Unimolecular Reaction Theory

Abstract

The rate constant for a unimolecular reaction is just the lowest eigenvalue of a relaxation matrix which describes all microscopic processes which may occur in the system undergoing reaction. A general solution to this eigenvalue problem has been given in a previous paper, including explicit corrections for non‐steady‐state behavior, but with one restriction, that the reactant energy distribution of states with insufficient energy to react (below the critical energy for reaction) is the equilibrium distribution. This is the so‐called equilibrium assumption for reactant states. States above this critical energy barrier will always have less than their equilibrium population, approaching their equilibrium value in the high‐pressure limit. In this paper the eigenvalue problem is solved without this restriction, i.e., for the case that any or all reactant levels have nonequilibrium effects due to depletion of levels by reaction. This then completes a direct connection between the master equation and the theoretical unimolecular rate constant. The input for the problem is a table of microscopic transition probabilities for the master equation. The method suggested here produces a theoretically and computationally useful expression for the rate constant as a direct consequence of this input. The solution explicitly includes such effects as (a) inelastic scattering in the reactive gas, including many‐shot effects, (b) nonequilibrium effects, and (c) non‐steady‐state effects. The expected relative importance of these effects is discussed. As a guide in writing a master equation a generalized Lindemann mechanism was assumed operative since it affords some comparisons with RRKM theory. However, other mechanisms with strong time ordering between heat bath relaxation and reaction can be employed in this formulation. (When this ordering breaks down one can, in general, no longer discern first‐order kinetics, and a different observable must be defined.)