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Title: Low rank approximation in G 0W 0 calculations

Abstract

The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in tr ansport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G 0W 0 approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green’s function (G 0) and a screened Coulomb interaction (W 0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W 0 at multiple frequencies. In this paper, we discuss how the cost of G 0W 0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank approximation on the accuracy of the G 0Wmore » 0 approximation. We also discuss how the numerical convolution of G 0 and W 0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.« less

Authors:
 [1];  [2];  [1];  [3];  [4];  [5];  [4]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
  3. Central Univ. of Finance and Economics, Beijing (China). School of Statistics and Mathematics
  4. Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Division
  5. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1379538
Grant/Contract Number:  
AC02-05CH11231; 11171232
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Science China Mathematics
Additional Journal Information:
Journal Volume: 59; Journal Issue: 8; Journal ID: ISSN 1674-7283
Publisher:
Science China Press - Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; density functional theory; G0W0 approximation; Sternheimer equation; contour deformation; low rank approximation

Citation Formats

Shao, MeiYue, Lin, Lin, Yang, Chao, Liu, Fang, Da Jornada, Felipe H., Deslippe, Jack, and Louie, Steven G. Low rank approximation in G0W0 calculations. United States: N. p., 2016. Web. doi:10.1007/s11425-016-0296-x.
Shao, MeiYue, Lin, Lin, Yang, Chao, Liu, Fang, Da Jornada, Felipe H., Deslippe, Jack, & Louie, Steven G. Low rank approximation in G0W0 calculations. United States. doi:10.1007/s11425-016-0296-x.
Shao, MeiYue, Lin, Lin, Yang, Chao, Liu, Fang, Da Jornada, Felipe H., Deslippe, Jack, and Louie, Steven G. Sat . "Low rank approximation in G0W0 calculations". United States. doi:10.1007/s11425-016-0296-x. https://www.osti.gov/servlets/purl/1379538.
@article{osti_1379538,
title = {Low rank approximation in G0W0 calculations},
author = {Shao, MeiYue and Lin, Lin and Yang, Chao and Liu, Fang and Da Jornada, Felipe H. and Deslippe, Jack and Louie, Steven G.},
abstractNote = {The single particle energies obtained in a Kohn-Sham density functional theory (DFT) calculation are generally known to be poor approximations to electron excitation energies that are measured in tr ansport, tunneling and spectroscopic experiments such as photo-emission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a many-body perturbation theory. From a computational perspective, the accuracy and efficiency of such an approach depends on how a self energy term that properly accounts for dynamic screening of electrons is approximated. The G0W0 approximation is a widely used technique in which the self energy is expressed as the convolution of a noninteracting Green’s function (G0) and a screened Coulomb interaction (W0) in the frequency domain. The computational cost associated with such a convolution is high due to the high complexity of evaluating W 0 at multiple frequencies. In this paper, we discuss how the cost of G0W0 calculation can be reduced by constructing a low rank approximation to the frequency dependent part of W 0 . In particular, we examine the effect of such a low rank approximation on the accuracy of the G0W0 approximation. We also discuss how the numerical convolution of G0 and W0 can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.},
doi = {10.1007/s11425-016-0296-x},
journal = {Science China Mathematics},
number = 8,
volume = 59,
place = {United States},
year = {Sat Jun 04 00:00:00 EDT 2016},
month = {Sat Jun 04 00:00:00 EDT 2016}
}

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Works referenced in this record:

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986