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Open Access Publications from the University of California

Low rank approximation in G 0 W 0 calculations

  • Author(s): Shao, MY;
  • Lin, L;
  • Yang, C;
  • Liu, F;
  • Da Jornada, FH;
  • Deslippe, J;
  • Louie, SG
  • et al.

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.

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