Numerical evaluation of golden rule rates for condensed phase processes

Our recently proposed method for the numerical evaluation of golden rule rates of non-adiabatic transitions in condensed phases is generalized. As before, the method is based on propagating Gaussian wavepackets on the initial and final electronic potential surface. In the present paper these Gaussians are thermal wavefunctions obtained by thermal propagation of eigenfunctions of the position operator using either the high tenperature limit of the propagator or the local harmonic approximation to it. The high T limit is essentially equivalent to our previously proposed procedure, but is more rigorously defined. The local harmonic approximation makes it possible to extend the method to low temperature situations. The performance of the method relative to othher available procedures is examined by model calculations.