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Title: Stochastic resolution of identity second-order Matsubara Green’s function theory

Abstract

We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [5];  [6];  [7]
  1. Mercedes-Benz Research and Development North America, Sunnyvale, CA (United States); Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
  3. Molecular Sciences Software Inst., Blacksburg, VA (United States)
  4. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  5. Hebrew Univ. of Jerusalem (Israel)
  6. Univ. of California, Los Angeles, CA (United States)
  7. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ., Ramat Aviv (Israel)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; USDOE
OSTI Identifier:
1577602
Alternate Identifier(s):
OSTI ID: 1568913
Grant/Contract Number:  
AC02-05CH11231; DEAC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 151; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Stochastic resolution of identity second-order Matsubara Green’s function theory. United States: N. p., 2019. Web. doi:10.1063/1.5108840.
Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, & Rabani, Eran. Stochastic resolution of identity second-order Matsubara Green’s function theory. United States. https://doi.org/10.1063/1.5108840
Takeshita, Tyler Y., Dou, Wenjie, Smith, Daniel G. A., de Jong, Wibe A., Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Tue . "Stochastic resolution of identity second-order Matsubara Green’s function theory". United States. https://doi.org/10.1063/1.5108840. https://www.osti.gov/servlets/purl/1577602.
@article{osti_1577602,
title = {Stochastic resolution of identity second-order Matsubara Green’s function theory},
author = {Takeshita, Tyler Y. and Dou, Wenjie and Smith, Daniel G. A. and de Jong, Wibe A. and Baer, Roi and Neuhauser, Daniel and Rabani, Eran},
abstractNote = {We create a stochastic resolution of identity representation to the second-order Matsubara Green’s function (sRI-GF2) theory. Using a stochastic resolution of the Coulomb integrals, the second order Born self-energy in GF2 is decoupled and reduced to matrix products/ contractions, which reduces the computational cost from O(N5) to O(N3) (with N being the number of atomic orbitals). Currently, the method can be viewed as an extension to our previous work on stochastic resolution of identity second order Møller-Plesset perturbation theory [T. Y. Takeshita et al., J. Chem. Theory Comput. 13, 4605 (2017)] and offers an alternative to previous stochastic GF2 formulations [D. Neuhauser et al., J. Chem. Theory Comput. 13, 5396 (2017)]. We show that sRI-GF2 recovers the deterministic GF2 results for small systems, is computationally faster than deterministic GF2 for N > 80, and is a practical approach to describe weak correlations in systems with 103 electrons and more.},
doi = {10.1063/1.5108840},
journal = {Journal of Chemical Physics},
number = 4,
volume = 151,
place = {United States},
year = {2019},
month = {7}
}

Journal Article:
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Figures / Tables:

FIG. 1 FIG. 1: (a) Correlation energy as a function of the number of H atoms (N = 10, 80, 200, 500). We have averaged over 10 independent sRF-GF2 runs. sRI-GF2 results agree well with deterministic GF2 well. For a weakly correlated system such as H dimer chain, the correlation energy growsmore » almost linearly with the number of H atoms. (b) Correlation energy per electron as a function of the number of H atoms. The stochastic error is estimated using 10 independent sRI-GF2 runs,$\frac{σ}{\sqrt{10}}$ . Here, σ is the standard deviation of 10 independent sRI-GF2 runs with different sampling seeds. The difference in correlation energy per electron between deterministic and stochastic GF2 are within the statistical error. In both cases, we have used Ns = 800 stochastic orbitals in our sRI-GF2 calculations.« less

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Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.