Spectroscopic analysis in molecular simulations with discretized Wiener-Khinchin theorem for Fourier-Laplace transformation
Author(s)
Koyama, Akira; Nicholson, David A; Andreev, Marat; Rutledge, Gregory C; Fukao, Koji; Yamamoto, Takashi; ... Show more Show less
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© 2020 American Physical Society. The Wiener-Khinchin theorem for the Fourier-Laplace transformation (WKT-FLT) provides a robust method to obtain the single-side Fourier transforms of arbitrary time-domain relaxation functions (or autocorrelation functions). Moreover, by combining an on-The-fly algorithm with the WKT-FLT, the numerical calculations of various complex spectroscopic data in a wide frequency range become significantly more efficient. However, the discretized WKT-FLT equation, obtained simply by replacing the integrations with the discrete summations, always produces two artifacts in the frequency-domain relaxation function. In addition, the artifacts become 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 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 with the on-The-fly algorithm is illustrated by a flow chart. We also give application examples for the wave-vector-dependent dynamic susceptibility in an isotropic amorphous polyethylene and the frequency-domain response functions of the orientation vectors in an n-Alkane crystal.
Date issued
2020Department
Massachusetts Institute of Technology. Department of Chemical EngineeringJournal
Physical Review E
Publisher
American Physical Society (APS)