GW self-screening error and its correction using a local density functional

Abstract

The self-screening error in electronic structure theory is the part of the self-interaction error that would remain within the GW approximation if the exact dynamically screened Coulomb interaction, W , were used, causing each electron to artificially screen its own presence. This introduces error into the electron density and ionization potential. We propose a simple, computationally efficient correction to GW calculations in the form of a local density functional, obtained using a series of finite training systems; in tests, this eliminates the self-screening errors in the electron density and ionization potential.The GW approximation [1, 2] within many-body perturbation theory is widely used to compute the selfenergy in many-electron systems [3][4][5][6][7][8][9], but has limitations. Higher-order terms beyond GW (known as vertex corrections) include a "self-screening" correction [10] related to the self-interaction familiar in density-functional theory (DFT) [11,12]. Attempts to correct the entirety of the self-interaction error via explicit vertex corrections have proved challenging [13,14]. We adopt a physically more direct approach to the self-screening correction.A GW calculation normally takes a DFT calculation as its starting point. The goal is to improve the quantities calculated from DFT, such as the ionization potential (IP) [9]. However, the self-screening error is known to have an adverse effect on the IP. Furthermore, the effect of the GW procedure on the electron density is not widely understood. We focus on the computation of the electron density from the Green's function [15] and IP. We use the space-time method to solve Hedin's equations [16]. Thus the GW method can be used in several flavors: one-shot (G 0 W 0 ), semi self-consistency (GW 0 ) and full self-consistency (GW ) [8]. We identify the self-screening error inherent in all GW calculations via the use of an effective potential. We then propose a simple and computationally inexpensive correction term that is a local potential added to the self energy and applicable to any GW calculation. Finally we test our self-screening correction (ssc) by comparing the GW +ssc electron density and IP to the exact quantities from systems of few electrons in 1D where the many-electron Schrödinger equation (SE) can be solved exactly. For these model systems we find that the spurious effects of the self-screening error on the density and the IP are removed.Within GW the screened interaction W amounts to dynamically adjusting the strength of the bare Coulomb interaction between electrons. One merit of the exchange operator of Hartree-Fock theory is that it exactly corrects the self-interaction error introduced by the Hartree potential. If the Coulomb interaction in the Hartree-Fock exchange operator were screened using the exact irreducible polarizability P , Hartree-Fock's self-interaction correction would be improperly reduced, so that part of the self-interaction error -the self-screening error -remains uncorrected. It may be thought of as each electro...

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