Numerical integration for ab initio many-electron self energy calculations within the GW approximation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:286

Article

Liu, Fang¹  Lin, Lin^2,3  Vigil-Fowler, Derek^4,8  Lischner, Johannes^4,8  Kemper, Alexander F.³  Sharifzadeh, Sahar^5,6  da Jornadad, Felipe H.^4,8  Deslippe, Jack⁷  Yang, Chao³  Neaton, Jeffrey B.^4,8,9  Louie, Steven G.^4,8 

[1] Cent Univ Finance & Econ, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

[3] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA

[4] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA

[5] Boston Univ, Dept Elect & Comp Engn, Boston, MA 02215 USA

[6] Boston Univ, Div Engn & Mat Sci, Boston, MA 02215 USA

[7] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, NERSC, Berkeley, CA 94720 USA

[8] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Div Mat Sci, Berkeley, CA 94720 USA

[9] Univ Calif Berkeley, Lawrence Berkeley Natl Lab, Mol Foundry, Berkeley, CA 94720 USA

关键词: GW;    Self energy;    Convolution;    Numerical integration;    Trapezoidal rule;    Principal value integration;    COHSEX;    XCOR;    Dyson's equation;   

DOI  :  10.1016/j.jcp.2015.01.023

来源: Elsevier

【 摘 要 】

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free