Low rank approximation in G 0 W 0 calculations

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 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) W (0) approximation. We also discuss how the numerical convolution of G (0) and W (0) can be evaluated efficiently and accurately by using a contour deformation technique with an appropriate choice of the contour.