Using electronegativity and hardness to test density functionals

Klaus August Moltved, Kasper Planeta Kepp*

*Corresponding author for this work

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Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT’s predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (χ) and hardness (η) directly reflect the energy–density relationship via the chemical potential ∂E/∂N and we thus hypothesized that they probe universality. We studied χ and η for atoms Z = 1–36 using 50 diverse functionals covering all major classes. Very few functionals describe both χ and η well. η benefits from error cancellation, whereas χ is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at ∼0.2 eV–0.3 eV for η. In contrast, variable performance for χ indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional, we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes “non-universality” and large dependency on exact exchange. Thus, we argue that performance for χ for the same systems is a hallmark of an important aspect of universality by probing ∂E/∂N. With this metric, B98, B97-1, PW6B95D3, MN-15, rev-TPSS, HSE06, and APFD are the most “universal” among the tested functionals. B98 and B97-1 are accurate for very diverse metal–ligand bonds, supporting that a balanced description of ∂E/∂N and ∂E2/∂N2, via χ and η, is probably a first simple probe of universality.
Original languageEnglish
Article number244113
JournalJournal of Chemical Physics
Issue number24
Publication statusPublished - 2020

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