Monte Carlo explicitly correlated secondorder manybody perturbation theory
A stochastic algorithm is proposed and implemented that computes a basissetincompleteness (F12) correction to an ab initio secondorder manybody perturbation energy as a short sum of 6 to 15dimensional integrals of Gaussiantype orbitals, an explicit function of the electronelectron distance (geminal), and its associated excitation amplitudes held fixed at the values suggested by Tenno. The integrals are directly evaluated (without a resolutionoftheidentity approximation or an auxiliary basis set) by the Metropolis Monte Carlo method. Applications of this method to 17 molecular correlation energies and 12 gasphase reaction energies reveal that both the nonvariational and variational formulas for the correction give reliable correlation energies (98% or higher) and reaction energies (within 2 kJ mol ^{1} with a smaller statistical uncertainty) near the completebasisset limits by using just the augccpVDZ basis set. The nonvariational formula is found to be 2–10 times less expensive to evaluate than the variational one, though the latter yields energies that are bounded from below and is, therefore, slightly but systematically more accurate for energy differences. Being capable of using virtually any geminal form, the method confirms the best overall performance of the Slatertype geminal among 6 forms satisfying the same cusp conditions. Lastly, not having to precomputemore »
 Authors:

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 Univ. of Illinois, UrbanaChampaign, IL (United States). Dept. of Chemistry
 Virginia Polytechnic Inst. and State Univ. (Virginia Tech), Blacksburg, VA (United States). Dept. of Chemistry
 Publication Date:
 Grant/Contract Number:
 FG0212ER46875; SC0008692; FG0211ER16211
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 145; Journal Issue: 15; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Univ. of Illinois, UrbanaChampaign, IL (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
 OSTI Identifier:
 1473885
 Alternate Identifier(s):
 OSTI ID: 1329495
Johnson, Cole M., Doran, Alexander E., Zhang, Jinmei, Valeev, Edward F., and Hirata, So. Monte Carlo explicitly correlated secondorder manybody perturbation theory. United States: N. p.,
Web. doi:10.1063/1.4964854.
Johnson, Cole M., Doran, Alexander E., Zhang, Jinmei, Valeev, Edward F., & Hirata, So. Monte Carlo explicitly correlated secondorder manybody perturbation theory. United States. doi:10.1063/1.4964854.
Johnson, Cole M., Doran, Alexander E., Zhang, Jinmei, Valeev, Edward F., and Hirata, So. 2016.
"Monte Carlo explicitly correlated secondorder manybody perturbation theory". United States.
doi:10.1063/1.4964854. https://www.osti.gov/servlets/purl/1473885.
@article{osti_1473885,
title = {Monte Carlo explicitly correlated secondorder manybody perturbation theory},
author = {Johnson, Cole M. and Doran, Alexander E. and Zhang, Jinmei and Valeev, Edward F. and Hirata, So},
abstractNote = {A stochastic algorithm is proposed and implemented that computes a basissetincompleteness (F12) correction to an ab initio secondorder manybody perturbation energy as a short sum of 6 to 15dimensional integrals of Gaussiantype orbitals, an explicit function of the electronelectron distance (geminal), and its associated excitation amplitudes held fixed at the values suggested by Tenno. The integrals are directly evaluated (without a resolutionoftheidentity approximation or an auxiliary basis set) by the Metropolis Monte Carlo method. Applications of this method to 17 molecular correlation energies and 12 gasphase reaction energies reveal that both the nonvariational and variational formulas for the correction give reliable correlation energies (98% or higher) and reaction energies (within 2 kJ mol1 with a smaller statistical uncertainty) near the completebasisset limits by using just the augccpVDZ basis set. The nonvariational formula is found to be 2–10 times less expensive to evaluate than the variational one, though the latter yields energies that are bounded from below and is, therefore, slightly but systematically more accurate for energy differences. Being capable of using virtually any geminal form, the method confirms the best overall performance of the Slatertype geminal among 6 forms satisfying the same cusp conditions. Lastly, not having to precompute lowerdimensional integrals analytically, to store them on disk, or to transform them in a nonscalable densematrixmultiplication algorithm, the method scales favorably with both system size and computer size; the cost increases only as O(n4) with the number of orbitals (n), and its parallel efficiency reaches 99.9% of the ideal case on going from 16 to 4096 computer processors.},
doi = {10.1063/1.4964854},
journal = {Journal of Chemical Physics},
number = 15,
volume = 145,
place = {United States},
year = {2016},
month = {10}
}
Works referenced in this record:
NWChem: A comprehensive and scalable opensource solution for large scale molecular simulations
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 Valiev, M.; Bylaska, E. J.; Govind, N.
 Computer Physics Communications, Vol. 181, Issue 9, p. 14771489