Low rank approximation in G _{0}W _{0} calculations
The single particle energies obtained in a KohnSham 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 photoemission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a manybody 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 _{0}W _{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 _{0}W _{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 _{0}Wmore »
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division; Univ. of California, Berkeley, CA (United States). Dept. of Mathematics
 Central Univ. of Finance and Economics, Beijing (China). School of Statistics and Mathematics
 Univ. of California, Berkeley, CA (United States). Dept. of Physics; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Materials Science Division
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231; 11171232
 Type:
 Accepted Manuscript
 Journal Name:
 Science China Mathematics
 Additional Journal Information:
 Journal Volume: 59; Journal Issue: 8; Journal ID: ISSN 16747283
 Publisher:
 Science China Press  Springer
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; density functional theory; G0W0 approximation; Sternheimer equation; contour deformation; low rank approximation
 OSTI Identifier:
 1379538
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.,
Web. doi:10.1007/s114250160296x.
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/s114250160296x.
Shao, MeiYue, Lin, Lin, Yang, Chao, Liu, Fang, Da Jornada, Felipe H., Deslippe, Jack, and Louie, Steven G.. 2016.
"Low rank approximation in G0W0 calculations". United States.
doi:10.1007/s114250160296x. 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 KohnSham 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 photoemission spectroscopy. The correction to these energies can be obtained from the poles of a single particle Green’s function derived from a manybody 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/s114250160296x},
journal = {Science China Mathematics},
number = 8,
volume = 59,
place = {United States},
year = {2016},
month = {6}
}
Works referenced in this record:
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986
journal, October 1986
 Hybertsen, Mark S.; Louie, Steven G.
 Physical Review B, Vol. 34, Issue 8, p. 53905413