Evaluation of quantum correlation functions from classical data

The general problem of evaluating quantum mechanical time correlation functions of quantities that are functions of condensed phase bath coordinates is addressed. On the basis of the relation between such a general correlation function and that for the position variable, and the analytical result for the relation of quantum and classical correlation functions of position for harmonic baths, we develop an approximate expression for the quantum correction to the general classical correlation function as an expansion in the quantum correction. The quantum corrected correlation function only requires classical correlation functions and their derivatives with respect to time and temperature. Hence, the result can be implemented directly using only computer simulated classical data. Application to analytically solved model problems involving harmonic baths demonstrates that the method is accurate both for highly nonlinear coupling and surprisingly small temperature.