Simple eigenvalue-self-consistent Δ ̄ G W 0

We show that a rigid scissors-like GW self-consistency approach, labeled here Δ̄GW0, can be trivially implemented at zero additional cost for large scale one-shot G₀W₀ calculations. The method significantly improves one-shot G₀W₀ and for large systems is very accurate. Δ̄GW0 is similar in spirit to evGW₀ 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. Δ̄GW0 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 G₀W₀ 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 Δ̄GW0 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 evGW₀ 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 evGW₀ quite well and both methods are in good agreement with the experiment.