# Low rank approximation in G _{0}W _{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 _{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:

- 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:

- 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}

}

*Citation information provided by*

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Web of Science

Works referenced in this record:

##
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies

journal, October 1986

- Hybertsen, Mark S.; Louie, Steven G.
- Physical Review B, Vol. 34, Issue 8, p. 5390-5413