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

Alexander E. Doran, So Hirata

Research output: Contribution to journalArticlepeer-review


The use of many control variates is proposed as a method to accelerate the second-A nd 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.

Original languageEnglish (US)
Article number0020584
JournalJournal of Chemical Physics
Issue number9
StatePublished - Sep 7 2020

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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