Quantum Statistical Mechanical Theory of the Rate of Exchange Chemical Reactions in the Gas Phase

A theory of the reaction rate of simple exchange reactions in the gas phase is developed on the basis of the quantum-statistical mechanical theory of linear irreversible processes due to Kubo et al. A formal expression for the rate coefficient is found near the equilibrium point. A number of relations are derived concerning the scattering amplitudes for the collisions involved in the above reactions. By making use of these relations, the rate constant is expressed in terms of the reaction cross sections in a way which coincides with that known from a more intuitive collisional approach. Since no ad hoc assumptions are made, the present theory can be said to provide a statistical mechanical foundation for the collision theory in the particular case discussed.