The languages that physicists and chemists use in regarding the HOMO-LUMO gaps, HOCO-LUCO gaps, band gaps, fundamental gaps, and optical excitation thresholds can be quite different, and the difference in language has the very serious consequence that it changes the way that different communities interpret their calculations. We studied the relations between these kinds of quantities for a large number of exchange-correlation functionals. Surprisingly, despite large differences in functional forms, a consistent relation with the percentage of Hartree-Fock exchange was discovered. Furthermore, we concluded that with presently available functionals the orbital energies should be treated as intermediate mathematical variables in the calculation of excitation energies rather than as the energies of independent-particle reference states for quasiparticle theory.
“Relationships between Orbital Energies, Optical AND fundamental Gaps, Exciton Shifts in Approximate Density Functional Theory and Quasiparticle Theory” Y. Shu, and D. G. Truhlar, Journal of Chemical Theory and Computation 16, 7 (2020). doi,org/10.1021/acs.jctc.0c00320
