Direct Computation of Influence Functional Coefficients from Numerical Correlation Functions

Influence functional methods provide a powerful approach for simulating the dynamics of a system embedded in a harmonic bath, which may be parametrized to reflect a variety of environments and chemical processes. In this work, we develop a procedure for calculating the coefficients of the discretized influence functional using the classical approximation to the time correlation function, which is usually available through molecular dynamics simulations. This procedure circumvents the calculation of a spectral density via Fourier inversion of the correlation function. When the correlation function is available with high precision, we find that the direct procedure yields results just as accurate as those obtained using the spectral density expressions. However, when statistical noise is present, the direct procedure produces more accurate results. The direct procedure is efficient and easy to implement.