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Title: Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum

Abstract

Here, we develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. Finally, this is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3]; ORCiD logo [4];  [5]; ORCiD logo [6]
+ Show Author Affiliations
  1. Univ. of California, Berkeley, CA (United States)
  2. Mercedes-Benz Research and Development North America, Sunnyvale, CA (United States)
  3. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  4. Hebrew Univ. of Jerusalem (Israel)
  5. Univ. of California, Los Angeles, CA (United States)
  6. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Tel Aviv Univ. (Israel)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division; Israel Science Foundation
OSTI Identifier:
1603547
Grant/Contract Number:  
AC02-05CH11231; 800/19
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 15; Journal Issue: 12; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; hydrogen; approximation; molecules; electrical energy; electron correlation

Citation Formats

Dou, Wenjie, Takeshita, Tyler Y., Chen, Ming, Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. United States: N. p., 2019. Web. doi:10.1021/acs.jctc.9b00918.
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Dou, Wenjie, Takeshita, Tyler Y., Chen, Ming, Baer, Roi, Neuhauser, Daniel, & Rabani, Eran. Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum. United States. https://doi.org/10.1021/acs.jctc.9b00918
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Dou, Wenjie, Takeshita, Tyler Y., Chen, Ming, Baer, Roi, Neuhauser, Daniel, and Rabani, Eran. Fri . "Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum". United States. https://doi.org/10.1021/acs.jctc.9b00918. https://www.osti.gov/servlets/purl/1603547.
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@article{osti_1603547,
title = {Stochastic Resolution of Identity for Real-Time Second-Order Green’s Function: Ionization Potential and Quasi-Particle Spectrum},
author = {Dou, Wenjie and Takeshita, Tyler Y. and Chen, Ming and Baer, Roi and Neuhauser, Daniel and Rabani, Eran},
abstractNote = {Here, we develop a stochastic resolution of identity approach to the real-time second-order Green's function (real-time sRI-GF2) theory, extending our recent work for imaginary-time Matsubara Green's function [ Takeshita et al. J. Chem. Phys. 2019 , 151 , 044114 ]. The approach provides a framework to obtain the quasi-particle spectra across a wide range of frequencies and predicts ionization potentials and electron affinities. To assess the accuracy of the real-time sRI-GF2, we study a series of molecules and compare our results to experiments as well as to a many-body perturbation approach based on the GW approximation, where we find that the real-time sRI-GF2 is as accurate as self-consistent GW. The stochastic formulation reduces the formal computatinal scaling from O(Ne5) down to O(Ne3) where Ne is the number of electrons. Finally, this is illustrated for a chain of hydrogen dimers, where we observe a slightly lower than cubic scaling for systems containing up to Ne ≈ 1000 electrons.},
doi = {10.1021/acs.jctc.9b00918},
journal = {Journal of Chemical Theory and Computation},
number = 12,
volume = 15,
place = {United States},
year = {2019},
month = {10}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1021/acs.jctc.9b00918
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Cited by: 17 works
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Figures / Tables:

Figure 1 Figure 1: second-order Born self energy for molecules: direct (upper) and exchange (lower) correlations. See also Eq. (6). Note that the exchange correlations (lower) are not included in GW approximation.
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    Works referencing / citing this record:

    Stochastic many-body perturbation theory for electron correlation energies
    journal, December 2019

    • Li, Zhendong
    • The Journal of Chemical Physics, Vol. 151, Issue 24
    • DOI: 10.1063/1.5128719
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