Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy

Soohaeng Yoo Willow; Jinmei Zhang; Edward F. Valeev; So Hirata

doi:10.1063/1.4862255

Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy

Soohaeng Yoo Willow, Jinmei Zhang, Edward F. Valeev, So Hirata

Research output: Contribution to journal › Article › peer-review

Abstract

A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H₂O, CH₄, and C₆H₆ within a few mE_h after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.

Original language	English (US)
Article number	031101
Journal	Journal of Chemical Physics
Volume	140
Issue number	3
DOIs	https://doi.org/10.1063/1.4862255
State	Published - Jan 21 2014

ASJC Scopus subject areas

Physics and Astronomy(all)
Physical and Theoretical Chemistry

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abstract = "A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H2O, CH4, and C6H6 within a few mEh after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.",

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AB - A stochastic algorithm is proposed that can compute the basis-set-incompleteness correction to the second-order many-body perturbation (MP2) energy of a polyatomic molecule. It evaluates the sum of two-, three-, and four-electron integrals over an explicit function of electron-electron distances by a Monte Carlo (MC) integration at an operation cost per MC step increasing only quadratically with size. The method can reproduce the corrections to the MP2/cc-pVTZ energies of H2O, CH4, and C6H6 within a few mEh after several million MC steps. It circumvents the resolution-of-the-identity approximation to the nonfactorable three-electron integrals usually necessary in the conventional explicitly correlated (R12 or F12) methods.

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Communication: Stochastic evaluation of explicitly correlated second-order many-body perturbation energy

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