Examination of How Well Long-Range-Corrected Density Functionals Satisfy the Ionization Energy Theorem

Siriluk Kanchanakungwankul, Donald G. Truhlar

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16 Scopus citations


We calculated the vertical ionization energies (VIE) of 99 species in two ways to examine the accuracy of several long-range-corrected (LC) hybrid meta functionals in comparison with a gradient approximation (GA), global hybrids, and doubly hybrids. In the category of LC functionals, we examined both those with meta ingredients (i.e., that depend on the kinetic energy density) and those without them. The LC-hybrid meta functionals examined are M11, revM11, M11plus, and ωB97M-V. The reference data used to assess accuracy consist of 95 molecules and 4 atoms in the GW100 set. The two methods studied are the ΔSCF method (involving the difference of neutral and cation self-consistent field (SCF) energies) and the ionization energy theorem (involving the orbital energy of the highest occupied molecular orbital, HOMO). We calculated linear correlation coefficients ( r 2) and mean absolute deviations (MADs) between each approach and the reference VIE value from the CCSD(T)/def2-TZVPP level of theory. We compared the new LC-hybrid meta calculations to calculations with the 10 functionals in a previous VIE study by Brémond et al. and to the calculations with LC-BLYP (LC-Becke, Lee-Yang-Parr), CAM-B3LYP (Coulomb-attenuating-method Becke-3-parameter Lee-Yang-Parr), LC-ωHPBE, and ωB97X-D. The results show that Minnesota LC-hybrid meta functionals have the smallest mean absolute deviation of ionization energy theorem VIEs with the reference data; the LC-ωHPBE functional also does quite well in this test. This is very encouraging and indicates that LC-hybrid meta functionals would be the best starting points for the tuning strategy that has been shown to be a very good procedure for improving time-dependent density functional calculations, and it also helps explain the good success of LC-hybrid meta functionals for molecular excitation energies.

Original languageEnglish (US)
Pages (from-to)4823-4830
Number of pages8
JournalJournal of Chemical Theory and Computation
Issue number8
StatePublished - Aug 10 2021

Bibliographical note

Funding Information:
This research was supported as part of the Nanoporous Materials Genome Center by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under award DE-FG02-17ER16362 as part of the Computational Chemical Sciences Program.

Publisher Copyright:
© 2021 American Chemical Society.

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  • Journal Article


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