Using electronegativity and hardness to test density functionals

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 (chi) and hardness (eta) directly reflect the energy-density relationship via the chemical potential partial derivative E/partial derivative N and we thus hypothesized that they probe universality. We studied chi and eta for atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both chi and eta well. eta benefits from error cancellation, whereas chi is marred by error propagation from IP and EA; thus, almost all standard GGA and hybrid functionals display a plateau in the MAE at similar to 0.2 eV-0.3 eV for eta. In contrast, variable performance for chi 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 chi for the same systems is a hallmark of an important aspect of universality by probing partial derivative E/partial derivative 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 partial derivative E/partial derivative N and partial derivative E-2/partial derivative N-2, via chi and eta, is probably a first simple probe of universality.