Science China Mathematics

, Volume 59, Issue 8, pp 1593–1612 | Cite as

Low rank approximation in G0W0 calculations

  • MeiYue Shao
  • Lin Lin
  • Chao Yang
  • Fang Liu
  • Felipe H. Da Jornada
  • Jack Deslippe
  • Steven G. Louie
Articles

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 transport, 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 W0 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 W0. 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.

Keywords

density functional theory G0W0 approximation Sternheimer equation contour deformation low rank approximation 

MSC(2010)

65F15 65Z05 

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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • MeiYue Shao
    • 1
  • Lin Lin
    • 1
    • 2
  • Chao Yang
    • 1
  • Fang Liu
    • 3
  • Felipe H. Da Jornada
    • 4
    • 5
  • Jack Deslippe
    • 6
  • Steven G. Louie
    • 4
    • 5
  1. 1.Computational Research DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  2. 2.Department of MathematicsUniversity of California at BerkeleyBerkeleyUSA
  3. 3.School of Statistics and MathematicsCentral University of Finance and EconomicsBeijingChina
  4. 4.Department of PhysicsUniversity of California at BerkeleyBerkeleyUSA
  5. 5.Materials Science DivisionLawrence Berkeley National LaboratoryBerkeleyUSA
  6. 6.NERSCLawrence Berkeley National LaboratoryBerkeleyUSA

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