Stochastic evaluation of fourth-order many-body perturbation energies

Doran, Alexander E.; Hirata, So

doi:10.1063/5.0047798

Title: Stochastic evaluation of fourth-order many-body perturbation energies

Journal Article · Wed Apr 07 00:00:00 EDT 2021 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0047798· OSTI ID:1774417

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Univ. of Illinois at Urbana-Champaign, IL (United States)

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green’s functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n^5.3) size-dependence of cost, which is nearly two ranks lower than the O(n⁷) dependence of the deterministic MP4 algorithm. Furthermore, it evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE_h (1.1% of the total basis-set correlation energy), 38 mE_h (2.6%), 110 mE_h (5.5%), and 280 mE_h (9.0%), respectively, after about 10⁹ MC steps.

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Research Organization:: Univ. of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Chemical Sciences, Geosciences & Biosciences Division; USDOE

Grant/Contract Number:: SC0006028; SPEC

OSTI ID:: 1774417

Alternate ID(s):: OSTI ID: 1774704

Journal Information:: Journal of Chemical Physics, Vol. 154, Issue 13; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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