A simple model for the treatment of imaginary frequencies in chemical reaction rates and molecular liquids

A simple model is presented for treating local imaginary frequencies that are important in the study of quantum effects in chemical reactions and various dynamical processes in molecular liquids. It significantly extends the range of accuracy of conventional local harmonic approximations (LHAs) used in the linearized semiclassical initial value representation/classical Wigner approximation for real time correlation functions. The key idea is realizing that a local Gaussian approximation (LGA) for the momentum distribution (from the Wigner function involving the Boltzmann operator) can be a good approximation even when a LHA for the potential energy surface fails. The model is applied here to two examples where imaginary frequencies play a significant role: the chemical reaction rate for a linear model of the H+H(2) reaction and an analogous asymmetric barrier-a case where the imaginary frequency of the barrier dominates the process-and for momentum autocorrelation functions in liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). We also generalize the LGA model to the Feynman-Kleinert approximation.