Title: Low rank approximation in G₀W₀ 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 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 numericalmore » convolution of G₀ and W₀ can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.« less

Authors:

Shao, MeiYue ^[1]; Lin, Lin ^[2]; Yang, Chao ^[1]; Liu, Fang ^[3]; Da Jornada, Felipe H. ^[4]; Deslippe, Jack ^[5]; Louie, Steven G. ^[4]

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+ Show Author Affiliations

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:

Sat Jun 04 00:00:00 EDT 2016

Research Org.:

Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:

1379538

Grant/Contract Number:  

AC02-05CH11231; 11171232

Resource Type:

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