Relationships between atomic chemical potentials, electrostatic potentials, and covalent radii

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Abstract
The chemical potential μ of a many-electron system equals its total electrostatic potential V(r) at any point r at which δT/δρ =−δ(εX+εC)/δρ, where ρ is the electronic density and T, εX, and εC are, respectively, the kinetic, exchange, and correlation energy functionals. The Thomas–Fermi–Dirac theory predicts that this relationship is satisfied at all points at which ρ=0.008 72. This prediction has been tested for 25 ground-state atoms and has been found to give unsatisfactory results; the values of V(r) at the points in question are not in good agreement with μ, as approximated by −0.5(I+A), I and A being the atomic ionization potentials and electron affinities. However, an investigation of the radial distances rμ at which V(r) does equal μ shows that these are very close to the standard covalent radii of the atoms. (This supports an early electronegativity formulation by Gordy.) It is also shown that there is a very good correlation between μ and VQ, the electrostatic potential created at rμ by the nuclear and electronic charge within this radial distance from the nucleus. VQ is therefore a direct measure of the electronic rearranging power of the atom in the formation of chemical bonds. This further demonstrates the special significance of rμ with regard to the bonding properties of the atom.