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arXiv · 2004.09792

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

Akira Koyama·David A. Nicholson·Marat Andreev·Gregory C. Rutledge·Koji Fukao·Takashi Yamamoto
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Abstract

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.

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Akira Koyama, David A. Nicholson, Marat Andreev, Gregory C. Rutledge, Koji Fukao, Takashi Yamamoto. 2020-04-21. Discretized Wiener-Khinchin theorem for Fourier-Laplace transformation: application to molecular simulations. https://arxiv.org/abs/2004.09792

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