Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 153, Issue 9, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/5.0020584
Keywords
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Funding
- Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC) - U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational
- U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences [DE-SC0006028]
- National Science Foundation [OCI-0725070, ACI-1238993]
- State of Illinois
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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 and 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 vertices of certain configurations by zero-valued overlap-integral vertices in their Goldstone diagrams. The variances and covariances 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.
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