Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

Cruz, J. César; Garza, Jorge; Yanai, Takeshi; Hirata, So

doi:10.1063/5.0091973

Title: Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

Journal Article · Thu May 19 00:00:00 EDT 2022 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0091973· OSTI ID:1870088

^[1]; Garza, Jorge ^[1];

^[2];

^[3]

Universidad Autónoma Metropolitana-Iztapalapa, Mexico CIty (Mexico)
Nagoya Univ. (Japan)
Univ. of Illinois at Urbana-Champaign, IL (United States)

A second-order many-body perturbation correction to the relativistic Dirac–Hartree–Fock energy is evaluated stochastically by integrating 13-dimensional products of four-component spinors and Coulomb potentials. The integration in the real space of electron coordinates is carried out by the Monte Carlo (MC) method with the Metropolis sampling, whereas the MC integration in the imaginary-time domain is performed by the inverse-cumulative distribution function method. The computational cost to reach a given relative statistical error for spatially compact but heavy molecules is observed to be no worse than cubic and possibly quadratic with the number of electrons or basis functions. This is a vast improvement over the quintic scaling of the conventional, deterministic second-order many-body perturbation method. The algorithm is also easily and efficiently parallelized with 92% strong scalability going from 64 to 4096 processors.

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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; Japan Society for the Promotion of Science (JSPS); USDOE

Grant/Contract Number:: SC0006028; AC02-05CH11231; 620190; 21H01881; 21K18931; SPEC

OSTI ID:: 1870088

Alternate ID(s):: OSTI ID: 1871505; OSTI ID: 1871618

Journal Information:: Journal of Chemical Physics, Vol. 156, Issue 22; ISSN 0021-9606

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

Country of Publication:: United States

Language:: English

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Title: Stochastic evaluation of four-component relativistic second-order many-body perturbation energies: A potentially quadratic-scaling correlation method

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