TY - JOUR
T1 - Stochastic evaluation of fourth-order many-body perturbation energies
AU - Doran, Alexander E.
AU - Hirata, So
N1 - Funding Information:
This work was supported by the Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational Chemical Sciences Program and also by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0006028. It is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Award Nos. OCI-0725070 and ACI-1238993) and The State of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.
Publisher Copyright:
© 2021 Author(s).
PY - 2021/4/7
Y1 - 2021/4/7
N2 - 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(n5.3) size-dependence of cost, which is nearly two ranks lower than the O(n7) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mEh (1.1% of the total basis-set correlation energy), 38 mEh (2.6%), 110 mEh (5.5%), and 280 mEh (9.0%), respectively, after about 109 MC steps.
AB - 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(n5.3) size-dependence of cost, which is nearly two ranks lower than the O(n7) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mEh (1.1% of the total basis-set correlation energy), 38 mEh (2.6%), 110 mEh (5.5%), and 280 mEh (9.0%), respectively, after about 109 MC steps.
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U2 - 10.1063/5.0047798
DO - 10.1063/5.0047798
M3 - Article
C2 - 33832241
AN - SCOPUS:85103828686
VL - 154
JO - Journal of Chemical Physics
JF - Journal of Chemical Physics
SN - 0021-9606
IS - 13
M1 - 134114
ER -