Fully self-consistent GW and quasiparticle self-consistent GW for molecules

Two self-consistent schemes involving Hedin's GW approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent GW approximation (SCGW) and the quasiparticle self-consistent GW approximation (QSGW) within the same numerical framework. Core and valence electrons are treated on an equal footing in all the steps of the calculation. We use basis sets of localized functions to handle the space dependence of quantities and spectral functions to deal with their frequency dependence. We compare SCGW and QSGW on a qualitative level by comparing the computed densities of states (DOS). To judge their relative merit on a quantitative level, we compare their vertical ionization potentials (IPs) with those obtained from coupled-cluster calculations CCSD(T). Our results are futher compared with one-shot G(0)W(0) calculations starting from Hartree-Fock solutions (G(0)W(0)-HF). Both self-consistent GW approaches behave quite similarly. Averaging over all the studied molecules, both methods show only a small improvement (somewhat larger for SCGW) of the calculated IPs with respect to G(0)W(0)-HF results. Interestingly, SCGW and QSGW calculations tend to deviate in opposite directions with respect to CCSD(T) results. SCGW systematically underestimates the IPs, while QSGW tends to overestimate them. G(0)W(0)-HF produces results which are surprisingly close to QSGW calculations both for the DOS and for the numerical values of the IPs.