HOMO-LUMO Intervals from Modern Density Functionals as Fundamental Gap Estimators

Abstract

Use of the Kohn-Sham eigenvalue gap (highest occupied molecular orbital to lowest unoccupied, HOMO-LUMO) as a fundamental gap (I-A, I= ionization potential, A= electron affinity) estimator is a long-standing challenge for relatively simple exchange-correlation functionals, e.g. meta-GGAs. The LAK meta-GGA [T. Lebeda et al. Phys. Rev. Lett. 133, 136402 (2024)] was developed to emphasize certain constraints in ways intended to make the LAK KS gaps close to the HSE06 hybrid functional [A.V. Krudau et al. J.Chem. Phys. 125, 224106 (2006)] gaps. The LAK functional was tested against a small atomization data set and a very small bond length set, with no molecular HOMO-LUMO gap testing. Here we test LAK against widely used, large reference data sets for molecular heats of formation, bond lengths, harmonic frequencies, I, and A and compare with r2SCAN [J.W. Furness et al., J. Phys. Chem. Lett. 11, 8208 (2020)] as well as HSE06 and PBE0, a quite different hybrid. On these tests LAK does not give meaningfully better geometries, heats of formation, HOMO-LUMO gaps, or DFT IP theorem satisfaction than r2SCAN. Compared against experimental I and A values the same holds; LAK results resemble r2SCAN results, not HSE06. Moreover, the HOMO and LUMO shifts generated by the NCAPR GGA [J. Carmona-Espindola et al., J. Chem. Phys. 157, 114109 (2022)] as derivative discontinuity estimates, correct the bare NCAPR HOMO and LUMO eigenvalues to substantially better agreement with experiment for both fundamental gap and IP theorem than do the meta-GGAs (LAK, r2SCAN) or hybrids (HSE, PBE0). We discuss possible reasons why LAK behaves differently for molecules and solids.