Effects of self-consistency and plasmon-pole models onGWcalculations for closed-shell molecules

We present theoretical calculations of quasiparticle energies in closed-shell molecules using the $GW$ method. We compare three different approaches: a full-frequency ${G}_{0}{W}_{0}$ ($\mathrm{FF}\text{\ensuremath{-}}{G}_{0}{W}_{0}$) method with density functional theory (DFT-PBE) used as a starting mean field; a full-frequency $G{W}_{0}$ ($\mathrm{FF}\text{\ensuremath{-}}G{W}_{0}$) method where the interacting Green's function is approximated by replacing the DFT energies with self-consistent quasiparticle energies or Hartree-Fock energies; and a ${G}_{0}{W}_{0}$ method with a Hybertsen-Louie generalized plasmon-pole model (HL $\mathrm{GPP}\text{\ensuremath{-}}{G}_{0}{W}_{0}$). While the latter two methods lead to good agreement with experimental ionization potentials and electron affinities for methane, ozone, and beryllium oxide molecules, $\mathrm{FF}\text{\ensuremath{-}}{G}_{0}{W}_{0}$ results can differ by more than one electron volt from experiment. We trace this failure of the $\mathrm{FF}\text{\ensuremath{-}}{G}_{0}{W}_{0}$ method to the occurrence of incorrect self-energy poles describing shake-up processes in the vicinity of the quasiparticle energies.