All-electron Gaussian-based $G_0W_0$ for Valence and Core Excitation Energies of Periodic Systems

TL;DR

This paper presents an all-electron Gaussian-based $G_0W_0$ implementation for periodic systems, enabling accurate quasiparticle energy calculations and band gap predictions without virtual state truncation, applicable to a wide range of materials.

Contribution

The authors develop a full-frequency $G_0W_0$ method using Gaussian bases that eliminates virtual state truncation and includes finite size corrections, improving accuracy for periodic systems.

Findings

Rapid convergence of band gaps with basis size.

Mean absolute relative error of 5.2% for band gaps.

Significant improvement in core excitation energies from hybrid functional starting points.

Abstract

We describe an all-electron $G_0W_0$ implementation for periodic systems with $k$-point sampling implemented in a crystalline Gaussian basis. Our full-frequency $G_0W_0$ method relies on efficient Gaussian density fitting integrals and includes both analytic continuation and contour deformation schemes. Due to the compactness of Gaussian bases, no virtual state truncation is required as is seen in many plane-wave formulations. Finite size corrections are included by taking the $q \to 0$ limit of the Coulomb divergence. Using our implementation, we study quasiparticle energies and band structures across a range of systems including molecules, semiconductors, rare gas solids, and metals. We find that the $G_0W_0$ band gaps of traditional semiconductors converge rapidly with respect to the basis size, even for the conventionally challenging case of ZnO. Using correlation-consistent bases of polarized triple-zeta quality, we find the mean absolute relative error of the extrapolated $G_0W_0$@PBE band gaps to be only 5.2% when compared to experimental values. For core excitation binding energies (CEBEs), we find that $G_0W_0$ predictions improve significantly over those from DFT if the $G_0W_0$ calculations are started from hybrid functionals with a high percentage of exact exchange.