Monte Carlo explicitly correlated many-body Green's function theory

Cole M. Johnson, Alexander E. Doran, Seiichiro L. Ten-No, So Hirata

Research output: Contribution to journalArticle

Abstract

A highly scalable stochastic algorithm is proposed and implemented for computing the basis-set-incompleteness correction to the diagonal, frequency-independent self-energy of the second-order many-body Green's function (GF2) theory within the explicitly correlated (F12) formalism. The 6-, 9-, 12-, and 15-dimensional integrals comprising the F12 correction are directly evaluated by the Monte Carlo method using appropriate weight functions for importance sampling. The method is naturally and easily parallelized, involves minimal memory space and no disk I/O, and can use virtually any mathematical form of a correlation factor. Its computational cost to correct all ionization energies (IEs) is observed to increase as the fourth power of system size, as opposed to the fifth power in the case of the deterministic counterparts. The GF2 calculations and their F12 corrections for the first IEs of C60 and C70 were executed on 128 graphical processing units (GF2) and 896 central processing units (F12), respectively, to reach the results with statistical errors of 0.04 eV or less. They showed that the basis-set-incompleteness (from aug-cc-pVDZ) accounts for only 50%-60% of the deviations from experiments, suggesting the significance of higher-order perturbation corrections.

Original languageEnglish (US)
Article number174112
JournalJournal of Chemical Physics
Volume149
Issue number17
DOIs
StatePublished - Nov 7 2018

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Ionization potential
Green's function
Green's functions
Importance sampling
Program processors
Monte Carlo methods
Data storage equipment
ionization
Processing
Monte Carlo method
central processing units
energy
Costs
Experiments
sampling
formalism
costs
deviation
perturbation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

Cite this

Monte Carlo explicitly correlated many-body Green's function theory. / Johnson, Cole M.; Doran, Alexander E.; Ten-No, Seiichiro L.; Hirata, So.

In: Journal of Chemical Physics, Vol. 149, No. 17, 174112, 07.11.2018.

Research output: Contribution to journalArticle

Johnson, Cole M. ; Doran, Alexander E. ; Ten-No, Seiichiro L. ; Hirata, So. / Monte Carlo explicitly correlated many-body Green's function theory. In: Journal of Chemical Physics. 2018 ; Vol. 149, No. 17.
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