Derivation of a Master Equation for Intramolecular Relaxation Using Projection Operator Techniques in Liouville Space

A generalized master equation is derived to describe intramolecular rearrangement processes. It is an inhomogeneous equation, including memory effects. The derivation is based on the Liouville space formalism. Because chemically relevant information is contained in the off-diagonal elements of the density matrix, a non-diagonal coarse-graining projector is used. All necessary assumptions are stated explicitly. By making further approximations, the master equation can be reduced to an inhomogeneous von Neumann equation with an effective Liouville operator the imaginary part of which is responsible for relaxation-like coarse-grained solutions. All neglected terms are given in closed form. The character of the solutions of the master equation is discussed in “coordinate-free” manner, i.e. without referring to the underlying Hübert space.