A unified framework for quantum activated rate processes. II. The nonadiabatic limit

A recently proposed unified theoretical framework for quantum activated rate constants is further developed and explored. The case of electronically nonadiabatic rate processes is considered, and the weak coupling limit explicitly investigated by an expansion of the rate constant expression. By virtue of this approach, a semiclassical Golden Rule expression is derived after a series of steepest descent approximations. The semiclassical analysis in turn reveals a closed form path integral expression for the quantum activated rate constant in the nonadiabatic (Golden Rule) limit which is free of harmonic and/or classical approximations for the many-dimensional nuclear (vibronic) modes. The latter expression is amenable to direct calculation in realistic systems through computer simulation.