Separable Unimolecular Reaction Rate Theory - A General Formulation

Abstract

The separable unimolecular reaction rate theory recently obtained on the basis of classical internal dynamics of the reactant molecule is here derived from more general arguments which allow the theory to be extended to quantum dynamics. The derivation is based on the Liouville equation, in its classical or quantum mechanical form, and projection operator techniques familiar from nonequilibirum statistical mechanics. The quantum dynamical theory is formulated in three representations: (i) the Wigner-Moyal Γ-space representation; (ii) the density matrix representation; (iii) the master equation representation. The formulation of the new rate theory is now essentially complete. It can be used, e.g., to derive simplified theories in a more rigorous manner or to study time-dependent reaction rates on the very short time scales available with recently developed experimental techniques.