Microscopic theory of condensed phase chemical reactions. I. Pair phase space kinetic equation

Abstract

A repeated ring kinetic theory describing the reversible chemical reaction A+B?C+D is obtained. We derive a kinetic equation for the equilibrium time correlation function of the solute pair phase space density. The solute–solvent and solvent–solvent interactions are described by a hard sphere potential. The solute–solute interactions consists of both hard and soft potential terms. This choice permits the use of a pseudo-Liouville operator formalism to obtain the kinetic theory. This greatly simplifies the derivation by comparison with a Liouville operator formalism for continuous potentials. The solute is dilute such that the kinetic theory describes isolated solute pairs interacting with the solvent. The static memory function of the kinetic equation is treated exactly. It describes solute propagation induced by direct interaction, Enskog collisions with the solvent and by the potential of mean force operating between the solute pair. The dynamic memory function is obtained at the repeated ring level of approximation. It describes solute propagation by dynamically correlated collisions (collective effects). Specialization of the reactive theory to exclusively hard sphere interactions is given. Also, nonreactive kinetic equations with elastic hard and/or soft solute–solute interactions are presented. In a companion paper we begin an analysis of the configuration space projection of these phase space kinetic equations and the associated transport coefficients of diffusion and reaction.