Supplemental Material

Theoretical best estimate (TBE) and computed excited state energies for all molecules considered in this work in eV. TBE were obtained from Loos et al., J. Chem. The- ory Comput. (2020) 16, 1711 and Christiansen et al., J. Chem. Phys. (1996), 105, 6921. The column heading CIS refers to a conventional CIS calculation. Column head- ings TDA@RPA, FULL@RPA, TDA@scTDHF and TDA@TDHF refer to the type of Bethe-Salpeter equation and polarizability calculation used to calculate the self-energy. FULL/TDA imply that the B matrix in Eq. 1 in the main text is included/omitted. RPA, scTDHF and TDHF refer to the screening employed in the polarizability and screened interaction calculations.