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Low rank approximation in G0W0 calculations

Science China Mathematics 2016年第8期59卷 1593-1612页

作者： SHAO MeiYue LIN Lin YANG Chao LIU Fang DA JORNADA Felipe H. DESLIPPE Jack LOUIE Steven G. Computational Research Division Lawrence Berkeley National LaboratoryBerkeleyCA 94720USA Department of Mathematics University of California at BerkeleyBerkeleyCA 94720USA School of Statistics and Mathematics Central University of Finance and EconomicsBeijing 100081China Department of Physics University of California at BerkeleyBerkeleyCA 94720USA Materials Science Division Lawrence Berkeley National LaboratoryBerkeleyCA 94720USA NERSC.Lawrence Berkeley National Laboratory Berkeley.CA 94720.USA

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_0W_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_0W_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_0W_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.

关键词： density functional theory GoW0 approximation sternheimer equation contour deformation lowrank approximation

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