All-Electron Gaussian-Based G₀W₀ for Valence and Core Excitation Energies of Periodic Systems

Abstract

We describe an all-electron G₀W₀ implementation for periodic systems with k-point sampling implemented in a crystalline Gaussian basis. Our full-frequency G₀W₀ 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 → 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 G₀W₀ 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-ζ quality, we find the mean absolute relative error of the extrapolated G₀W₀@PBE band gaps to be only 5.2% when compared to experimental values. For core excitation binding energies (CEBEs), we find that G₀W₀ predictions improve significantly over those from DFT if the G₀W₀ calculations are started from hybrid functionals with a high percentage of exact exchange.

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