Multi-Level Monte Carlo Path Integral Molecular Dynamics for Thermal Average Calculation in the Nonadiabatic Regime
Year: 2021
Author: Xiaoyu Lei, Zhennan Zhou
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 321–354
Abstract
With the path integral approach, the thermal average in multi-electronic-state quantum systems can be approximated by the ring polymer representation on an extended configuration space, where the additional degrees of freedom are associated with the surface index of each bead. The primary goal of this work is to propose a more efficient sampling algorithm for the calculation of such thermal averages. We reformulate the extended ring polymer approximation according to the configurations of the surface indexes, and by introducing a proper reference measure, the reformulation is recast as a ratio of two expectations of function expansions. By quantitatively estimating the sub-estimators, and minimizing the total variance of the sampled average, we propose a multi-level Monte Carlo path integral molecular dynamics method (MLMC-PIMD) to achieve an optimal balance of computational cost and accuracy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2020-0137
Numerical Mathematics: Theory, Methods and Applications, Vol. 14 (2021), Iss. 2 : pp. 321–354
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Multi-level Monte Carlo method Langevin sampling path integral molecular dynamics thermal average.