Simple eigenvalue-self-consistent $\overline{Δ}GW_0$

Abstract

We show that a rigid scissors-like GW self-consistency approach, labeled here $\overline{Δ}GW_0$, can be trivially implemented at zero additional cost for large scale one-shot $G_0W_0$ calculations. The method significantly improves one-shot $G_0W_0$ and for large systems is very accurate. $\overline{Δ}GW_0$ is similar in spirit to ev$GW_0$ where the self-consistency is only applied on the eigenvalues entering Green's function, while both W and the eigenvectors of Green's function are held fixed. $\overline{Δ}GW_0$ further assumes that the shift of the eigenvalues is rigid scissors-like so that all occupied states are shifted by the same amount and analogously for all the unoccupied states. We show that this results in a trivial modification of the time-dependent $G_0W_0$ self-energy, enabling an a posteriori self-consistency cycle. The method is applicable for our recent stochastic-$GW$ approach, thereby enabling self-consistent calculations for giant systems with thousands of electrons. The accuracy of $\overline{Δ}GW_0$ increases with the system size. For molecules, it is up to 0.4-0.5 eV away from coupled-cluster single double triple (CCSD(T)), but for tetracene and hexacene, it matches the ionization energies from both CCSD(T) and ev$GW_0$ to better than 0.05 eV. For solids, as exemplified here by periodic supercells of semiconductors and insulators with 6192 valence electrons, the method matches ev$GW_0$ quite well and both methods are in good agreement with the experiment.