A Critical Evaluation\nof the Hybrid KS DFT Functionals\nBased on the KS Exchange-Correlation Potentials

We have developed a critical methodology for the evaluation\nof\nthe quality of hybrid exchange-correlation (XC) density functional\napproximations (DFAs) based on very fundamental quantities, i.e.,\nKohn–Sham (KS) XC potentials, self-consistent electron densities,\nfirst ionization potentials (IPs), and total energies. Since the XC\npotentials, the primary objects in the current study, are not directly\naccessible for the hybrids, we calculate them by inverting the KS\nelectron densities. Utilizing this methodology, we tested 155 hybrid\nDFAs available in the LIBXC library using FCI and CCSD(T) methods\nas a reference. We have found that a group of functionals produces\nvery decent XC potentials, mainly those with a large mixture of Hartree–Fock\nexchange. Moreover, the value of IP strongly depends on the XC potential\nquality. On the other hand, we show that the XC energy is dominated\nby functional-driven error, which in some cases leads to substantial\nerrors in electronic densities. The study shows new directions for\nconstructing more accurate XC functionals within the KS-DFT framework.