Eliminating Symmetry Problems in Electronegativity Equalization and Correcting Self-Interaction Errors in Conceptual DFT

The chemical potential is by definition constant in molecules, and electronic charge is in principle equilibrated by bonding. Does electronegativity offer the best scale to unify these principles? According to conceptual density functional theory (c-DFT), the electronegativity equalization (ENE) and chemical potential equalization (CPE) principles seem rigorous and identical. However, the operational formulations of CPE and ENE fail to validate this claim, and frequently dramatic deviations from equalization are reported. We here eliminate the deviations to a very large extent. The problems originate from (i) c-DFT's exclusive reference to ground states and violations of the Wigner-Witmer symmetry constraints for bonding, (ii) electron self-interaction and delocalization errors. The problems are solved, and much more accurate ENE and bond polarities are obtained by replacing the ground-state electronegativity (chi(GS)) by the valence-state electronegativity (chi(VS)) and its generalization, the valence-pair-affinity (VPA, chi(VP)). The VPA is a charge dependent pair-sharing potential connected to Ruedenberg's bond theory that emphasizes the role of electron pair-density. The performances of the valence-pair equilibration (VPEq) and c-DFT's operational CPE are compared for 89 molecules with very diverse bond characters, including the "exotic" dimers Be-2, Mg-2, B-2, C-2, and Mn-2. The accuracy of VPEq is about 9 times better than that of operational CPE. Without requiring ad hoc calibrations, the VPEq bond polarities agree very well with results of state-of-the-art population analyses, and charges derived from vibrational spectra. A paradigm shift emphasizing valence states seems in order for c-DFT. Electronegativity and the chemical potential should be regarded as separate properties. (C) 2018 Wiley Periodicals, Inc.