Simple eigenvalue-self-consistent $\bar{\Delta }G{W}_0$

Abstract

We derive a general form of eigenvalue self-consistency for $G{W}_0$ in the time domain and use it to obtain a simplified postprocessing eigenvalue self-consistency, which we label $\bar{\Delta }G{W}_0$. The method costs the same as a one-shot $G_0{W}_0$ when the latter gives the full frequency-domain (or time-domain) matrix element of the self-energy. The accuracy of $\bar{\Delta }G{W}_0$ increases with system size, as demonstrated here by comparison to other $GW$ self-consistency results and to CCSD(T) predictions. When combined with the large-scale stochastic $G_0{W}_0$ formulation $\bar{\Delta }G{W}_0$ is applicable to very large systems, as exemplified by periodic supercells of semiconductors and insulators with 2048 valence electrons. For molecules the error of our eventual partially self-consistent approach starts at about 0.2eV for small molecules and decreases to 0.05eV for large ones, while for the periodic solids studied here the mean-absolute-error is only 0.03eV.

7 pages, 3 figures, 2 tables

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• Dopant levels in large nanocrystals using stochastic optimally tuned range-separated hybrid density functional theory
• GW with hybrid functionals for large molecular systems
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Nonmonotonic band gap evolution in bent phosphorene nanosheets