Excited states from GW/BSE and Hartree–Fock theory: Effects of polarizability and transition type on accuracy of excited state energies

GW and Bethe–Salpeter equation (BSE) methods are used to calculate energies of excited states of organic molecules in the Quest-3 database [Loos et al., J. Chem. Theory Comput. 16, 1711 (2020)]. The self-energy in the GW approximation is conventionally calculated using the RPA polarizability. Inclusion of a screened electron–hole interaction in the polarizability was recently shown to improve predictions of experimental ionization energies in organic molecules [C. H. Patterson, J. Chem. Theory Comput. 20, 7479 (2024)]. Self-energies from RPA or screened time-dependent Hartree–Fock (TDHF) polarizabilities in the GW/BSE method are used to calculate 141 singlet excited states in Quest-3. Theoretical best estimate excited state energies from the CC3 coupled cluster method and aug-cc-pVTZ basis sets are used to benchmark GW/BSE and CIS calculations using the same molecular geometries and basis sets. Differences between GW/BSE or CIS excited state energies and best estimate values show that there are systematic variations in the accuracies of excited state energies classified as ππ*, nπ*, πR (Rydberg), or nR character. The origin of these variations is the accuracy of self-energies of states of nonbonding vs π bonding character. In particular, N or O lone pair states require large self-energy corrections owing to strong orbital relaxation in the localized hole state, while π states have smaller corrections. Self-energies from a screened TDHF vs RPA polarizability are typically over(under)estimated for nonbonding states, leading to under(over)estimation of energies of excited states of nπ* or nR character.