Electrostatic potentials and covalent radii

We begin with a brief overview of the electrostatic potential V(r) as a fundamental determinant of the properties of systems of electrons and nuclei. The minimum of V(r) along the internuclear axis between two bonded atoms is a natural and physically meaningful boundary point, at which the electrostatic forces of the two nuclei upon an element of charge exactly cancel. We propose that the distances from nuclei to V(r) bond minima provide the basis for a well-defined set of covalent radii. Density functional calculations at the B3PW91/6-311+G** level were carried out for 59 molecules to locate the V(r) minima in 95 bonds and use these as the basis for determining single- and multiple-bond covalent radii for eight first- and second-row atoms plus hydrogen. It was found to be unrealistic to assign a single covalent radius to each atom; different values are needed for bonds to first- and second-row atoms, as well as to hydrogen. Using these results, we are able to predict the bond lengths of 33 single and multiple bonds with average errors of less than 0.04 A relative to experimental data.