Discretized Wiener-Khinchin theorem for Fourier-Laplace transformation: application to molecular simulations

The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to calculate numerically single-side Fourier transforms of arbitrary autocorrelation functions from molecular simulations. However, the existing WKT-FLT equation produces two artifacts in the output of the frequency-domain relaxation function. In addition, these artifacts are more apparent in the frequency-domain response function converted from the relaxation function. We find the sources of these artifacts that are associated with the discretization of the WKT-FLT equation. Taking these sources into account, we derive the new discretized WKT-FLT equations designated for both the frequency-domain relaxation and response functions with the artifacts removed. The use of the discretized WKT-FLT equations is illustrated by a flow chart of an on-the-fly algorithm. We also give application examples of the discretized WKT-FLT equations for computing dynamic structure factor and wave-vector-dependent dynamic susceptibility from molecular simulations.