All-electron Gaussian-based $G_0{W}_0$ for Valence and Core Excitation Energies of Periodic Systems

Abstract

We describe an all-electron $G_0{W}_0$ implementation for periodic systems with $k$-point sampling implemented in a crystalline Gaussian basis. Our full-frequency $G_0{W}_0$ 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 $G_0{W}_0$ 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 $G_0{W}_0$@PBE band gaps to be only 5.2% when compared to experimental values. For core excitation binding energies (CEBEs), we find that $G_0{W}_0$ predictions improve significantly over those from DFT if the $G_0{W}_0$ calculations are started from hybrid functionals with a high percentage of exact exchange.

14 pages, 5 figures, 6 tables

References in corpus (17)

• Recent developments in the PySCF program package
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Efficient implementation of the GW approximation within the all-electron FLAPW method
• Band convergence and linearization error correction of all-electron GW calculations: The extreme case of zinc oxide
• Linear density response function in the projector-augmented wave method: Applications to solids, surfaces, and interfaces
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Towards GW Calculations on Thousands of Atoms
• Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining sub eV Error from a Restricted Open-Shell Kohn-Sham Approach
• Gaussian and plane-wave mixed density fitting for periodic systems
• Automation methodologies and large-scale validation for $GW$, towards high-throughput $GW$ calculations
• Ab Initio Full Cell GW+DMFT for Correlated Materials
• Core level binding energies in solids from first-principles
• Dielectric anisotropy in the GW space-time method
• Efficient dielectric matrix calculations using the Lanczos algorithm for fast many-body $G_0{W}_0$ implementations
• Robust analytic continuation approach to many-body GW calculations
• Fermi level pinning by defects can explain the large reported carbon 1s binding energy variations in diamond

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