Some problems related to electronegativity equalization

The principle of electronegativity equalization, as originally proposed by Sanderson, indicates that when chemical reagents come into contact, they undergo electron transfer until each reagent has the same chemical potential. This powerful principle not only explains why electrons are transferred from less electronegative to more electronegative atoms in molecules, but also is important for explaining solvent effects on chemical reactions. (In reactions in solution, the electronegativity of the reagents are effectively "pinned" to the chemical potential of the solvent.) There is a paradox related to the electronegativity equalization principle, however: two atoms that are very far apart should have the same electronegativity, but this seems counterintuitive: how can the presence of a Cesium atom in Paris effect the chemical potential of a Fluorine atom in Loutraki? Berkowitz has called this "spooky action at a distance" the "EPR paradox of conceptual density-functional theory." By analyzing the structure of the exact density functional, however, one can resolve the paradox: in the limit of infinite separation, molecules have no well-defined chemical potential because the density functional variational principle is stationary not only for the ground state (Cs in Paris and F in Loutraki), but also for some excited states (e.g., Cs+ in Paris and F- in Loutraki; Cs- in Paris and F+ in Loutraki). Practical electronegativity equalization calculations that need to be able to reproduce not only the "dense" limit, but also the asymptotic interactions will need to address this matter. To this end, a practical method based on the finite-temperature grand-canonical ensemble (with a geometry-dependent temperature) is proposed.