The postulated identity of the operational chemical potential, μ, with the negative of the ground-state electronegativity, μ = –X
GS, is a cornerstone of conceptual DFT (cDFT). However, a trend has developed to overestimate the applicability and accuracy of the corresponding
equalization principles. The operational molecular μ
mol in general does not result from equalizing atomic μ
at values. Frequent violations of the strict Wigner-Witmer symmetry rules by cDFT cause μ
mol ≠ μ
in homonuclear diatoms. Consequently the previous general proofs of the chemical potential equalization (CPE) principle and its equivalence to the electronegativity equalization (ENE) principle seem inadequate. Such fundamental limitations of cDFT need to be addressed, and solutions proposed
also in connection with violations of the variational principle due to electron-self-interaction errors. Mulliken's valence-state definition of electronegativity, χVS, intrinsically fulfils the Wigner-Witmer rules, and ENE by χVS is surprisingly accurate for homonuclear
diatoms. For polar bonds a charge dependent generalization of Mulliken's χVS is introduced as “Valence-Pair-Affinity,” VPA. It is consistently derived from Ruedenberg's theory of the chemical bond and does neither violate the variational principle nor the Wigner-Witmer
rules. VPA is locally equilibrated in 2-center electron-pair bonds, but not in the whole molecule. The partial atomic charges obtained by VPA equilibration are consistent and agree well with those obtained by Natural Bond Orbital population analysis and the ones found in Klopman's “equipotential
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