Effects of self-consistency and plasmon-pole models on GW calculations 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 $G_0W_0$ (FF-$G_0W_0$) method with density functional theory (DFT-PBE) used as a starting mean field; a full-frequency $GW_0$ (FF-$GW_0$) 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 $G_0W_0$ method with a Hybertsen-Louie generalized plasmon-pole model (HL GPP-$G_0W_0$). While the latter two methods lead to good agreement with experimental ionization potentials and electron affinities for methane, ozone, and beryllium oxide molecules, FF-$G_0W_0$ results can differ by more than one electron volt from experiment. We trace this failure of the FF-$G_0W_0$ method to the occurrence of incorrect self-energy poles describing shake-up processes in the vicinity of the quasiparticle energies.