Off-Diagonal Self-Energy Terms and Partially Self-Consistency in GW Calculations for Single Molecules: Efficient Implementation and Quantitative Effects on Ionization Potentials

The GW method in its most widespread variant takes, as an input, Kohn-Sham (KS) single particle energies and single particle states and yields results for the single-particle excitation energies that are significantly improved over the bare KS estimates. Fundamental shortcomings of density functional theory (DFT) when applied to excitation energies as well as artifacts introduced by approximate exchange-correlation (XC) functionals are thus reduced. At its heart lies the quasi-particle (qp) equation, whose solution yields the corrected excitation energies and qp-wave functions. We propose an efficient approximation scheme to treat this equation based on second-order perturbation theory and self-consisent iteration schemes. We thus avoid solving (large) eigenvalue problems at the expense of a residual error that is comparable to the intrinsic uncertainty of the GW truncation scheme and is, in this sense, insignificant.