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Title: Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates

Abstract

Herein, the use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals as well as their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertexes of certain configurations by zero-valued overlap-integral vertexes in their Goldstone diagrams. The variances and co- variances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.

Authors:
ORCiD logo [1]; ORCiD logo [1]
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  1. Univ. of Illinois at Urbana-Champaign, IL (United States)
Publication Date:
Research Org.:
Univ. of Illinois at Urbana-Champaign, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; National Science Foundation (NSF); State of Illinois
OSTI Identifier:
1657519
Alternate Identifier(s):
OSTI ID: 1657626
Grant/Contract Number:  
SC0006028; OCI-0725070; ACI-1238993
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 153; Journal Issue: 9; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; Correlation energy; Monte Carlo methods; Supercomputer; Many body perturbation calculations; Stochastic processes; Perturbation theory; Integral transforms; High performance computing; Frontiers of stochastic electronic structure calculations

Citation Formats

Doran, Alexander E., and Hirata, So. Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates. United States: N. p., 2020. Web. doi:10.1063/5.0020584.
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Doran, Alexander E., & Hirata, So. Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates. United States. https://doi.org/10.1063/5.0020584
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Doran, Alexander E., and Hirata, So. Thu . "Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates". United States. https://doi.org/10.1063/5.0020584. https://www.osti.gov/servlets/purl/1657519.
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@article{osti_1657519,
title = {Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates},
author = {Doran, Alexander E. and Hirata, So},
abstractNote = {Herein, the use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals as well as their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertexes of certain configurations by zero-valued overlap-integral vertexes in their Goldstone diagrams. The variances and co- variances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.},
doi = {10.1063/5.0020584},
journal = {Journal of Chemical Physics},
number = 9,
volume = 153,
place = {United States},
year = {Thu Sep 03 00:00:00 EDT 2020},
month = {Thu Sep 03 00:00:00 EDT 2020}
}
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https://doi.org/10.1063/5.0020584
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