On the electronegativity nonlocality paradox

The electronegativity equalization principle states that, in its ground state, the electronegativity of every component in a system is the same. A paradox then arises: molecular fragments that are very far apart must still have the same electronegativity, which seems to contradict the common assumption that spatially separated molecular species can be described independently. Density-functional theory provides the tools needed to analyze this paradox at a fundamental level, and a resolution is found from the properties of the exact Hohenberg-Kohn functional. Specifically, there is no paradox because the electronegativity is not uniquely defined for separated systems. Instead, there is an apparent electronegativity that preserves locality. This may have implications for the treatment of charge-transfer excited states. A model for the energy as a function of the number of electrons is also presented. This model gives some insight into the utility of the grand canonical ensemble formulation (at nonzero temperature) and, unlike most previous models, this model recovers the appropriate behavior in the limits of infinitely separated and/or weakly interacting subsystems.