Adequacy of Approximations in GW Theory

TL;DR

This paper critically examines the accuracy of GW approximation calculations in electronic structure theory, focusing on sources of error, basis set dependence, and the validity of common approximations across different materials.

Contribution

It provides a comprehensive analysis of errors in GW calculations using an all-electron approach and evaluates the validity of the ext{G}_0 ext{W}_0 ext{ approximation} for various materials.

Findings

GW calculations underestimate bandgaps in simple semiconductors

Better agreement with experiments occurs when the self-energy is not renormalized

Pseudopotential-based GW calculations have limitations for certain materials

Abstract

We use an all-electron implementation of the GW approximation to analyze several possible sources of error in the theory and its implementation. Among these are convergence in the polarization and Green's functions, the dependence of QP levels on choice of basis sets, and differing approximations for dealing with core levels. In all GW calculations presented here, G and W are generated from the local-density approximation (LDA), which we denote as the \GLDA\WLDA approximation. To test its range of validity, the \GLDA\WLDA approximation is applied to a variety of materials systems. We show that for simple sp semiconductors, \GLDA\WLDA always underestimates bandgaps; however, better agreement with experiment is obtained when the self-energy is not renormalized, and we propose a justification for it. Some calculations for Si are compared to pseudopotential-based \GLDA\WLDA calculations, and some aspects of the suitability of pseudopotentials for GW calculations are discussed.