Dependence of the virial exciton model on basis set and exact-exchange fraction

The exchange-only (uncorrelated) singlet-triplet energy difference in one-electron excited configurations is 2K_if, where K_if is the Coulomb self-energy of the product of the transition orbitals. A nonempirical, virial-theorem argument was presented by Becke [J. Chem. Phys. 148, 044112 (2018)] that the correlated singlet-triplet energy difference should be half of this, namely, K_if. This incredibly simple result gave HOMO-LUMO singlet excitation energies in small-molecule benchmark sets as good as the popular TD-B3LYP time-dependent approach to excited states. In a subsequent application to long-chain polyenes approaching the polyacetylene limit [A. D. Becke, J. Chem. Phys. 149, 081102 (2018)], we found a dramatic dependence of the optical gap on the amount of exact exchange in the density functionals used to generate the orbitals. Here, we assess the effect of the exact-exchange fraction in standard small-molecule tests. Also, we assess two basis-set extremes: the highly practical cc-pVDZ basis set and the higher-quality aug-cc-pVTZ.