Transition state theory and grand canonical partition functions

Abstract

A partial differential equation for the number density of a D-dimensional grand canonical ensemble is used to derive a simple expression for the reaction rate of transition state theory as a function of temperature and chemical potential. The reaction rate equation is valid for both Bose–Einstein and Fermi–Dirac statistics. In the limiting case where the chemical potential goes to minus infinity, it is shown that this reaction rate equation reduces to the well-known Eyring reaction rate equation of transition state theory. By expanding the reaction rate equation in a Taylor series about the equilibrium activity, it is shown how rate equations can be derived giving the approach to equilibrium.