Molecular Ionization Energies from GW and Hartree-Fock Theory: Polarizability, Screening, and Self-Energy Vertex Corrections.

Accurate prediction of electron removal and addition energies is essential for reproducing neutral excitation spectra in molecules using Bethe-Salpeter equation methods. A Hartree-Fock starting point for GW/BSE calculations, combined with a random phase approximation (RPA) polarizability in the screened interaction, W, is well-known to overestimate neutral excitation energies. Using a Hartree-Fock starting point, we apply several different approximations for W to molecules in the Quest-3 database [Loos et al. J. Chem. Theory Comput. 2020, 16, 1711]. W is calculated using polarizabilities in RPA and time-dependent HF approximations. Inclusion of screened electron-hole attraction in the polarizability yields valence ionization energies in better agreement with experimental values and ADC(3) calculations than the more commonly applied RPA polarizability. Quasiparticle weights are also in better agreement with ADC(3) values when electron-hole attraction is included in W. Shake-up excitations for the 1π levels in benzene and azines are indicated only when electron-hole attraction is included. Ionization energies derived from HF eigenvalues via Koopmans theorem for molecules with nitrogen or oxygen lone pairs have the largest differences from experimental values in the molecules considered, leading to incorrect ordering of nonbonding and π bonding levels. Inclusion of electron-hole attraction in the polarizability results in correct ordering of ionization energies and marked improvement in agreement with experimental data. Vertex corrections to the self-energy further improve agreement with experimental ionization energies for these localized states.