Practical evaluation of condensed phase quantum correlation functions: A Feynman–Kleinert variational linearized path integral method

We report a new method for calculating the Wigner transform of the Boltzmann operator in the canonical ensemble. The transform is accomplished by writing the Boltzmann operator in a semiharmonic form, utilizing the variational centroid effective frequencies introduced by Feynman and Kleinert (FK). The approximate many-body Wigner transformed Boltzmann operator is then utilized with a linearized path integral (LPI) representation for correlation functions. It is shown that this new FK-LPI method is capable of calculating quite accurately the short time behavior of linear and highly nonlinear correlation functions for low temperature Lennard-Jones model systems and that it is vastly superior to classical dynamics. The feasibility of the FK-LPI method for large systems is illustrated by considering a model liquid composed of 32 oxygen molecules with periodic boundary conditions. Initial conditions for molecular dynamics are obtained from its Boltzmann Wigner transform and the FK-LPI method is shown to describe correctly the zero-point motion of the liquid. The effective frequency representation of the Wigner transformed thermal density operator provides an efficient way of sampling nonclassical initial conditions for molecular-dynamics simulations more generally. Applications to vibrational energy relaxation and rate constant calculations in complex molecular systems are discussed.