BONDED AND PROMOLECULE RADII FOR MOLECULES AND CRYSTALS

Within the context of the total electron density distribution, a well-defined set of radii known as bonded radii can be derived by measuring, along the bond path, the distance between the center of an atom and the point of minimum electron density. As the properties of a crystal, including its total energy, are determined by its electron density distribution, such radii provide an objective measure of atomic size and a basis for understanding and correlating physical and chemical properties.

Bonded radii observed for chloride and oxide anions are not constant for a given coordination number, as assumed in derivations of lists of ionic and crystal radii, but increase in a regular way with bond length. On the other hand, bonded radii observed for cations show a much smaller increase with coordination number than that reported in studies of ionic and crystal radii. An examination of the electron density distributions observed for the alkali halides, fluorides, oxides, and silicates indicates that the distributions in such crystals can be regarded as largely atomic in nature, despite bond type. Promolecule radii calculated for spherically averaged electron density distributions for corresponding coordinated polyhedra with bond lengths and angles fixed at values observed in crystals reproduce to within approximately 0.05 angstrom the Tosi-Fumi radii derived for the alkali halides with the rock salt structure and bonded radii observed for the silica polymorphs, BeO, MgO, CuCl, CaF2, and CuBr. The close correspondence of promolecule and bonded radii indicates that the electron density distribution of individual atoms in these crystals decreases rapidly with distance. Reliable estimates of bonded radii of atoms in crystals are obtained from a calculated charge density distribution for the corresponding coordinated polyhedra making up such crystals, using Roothaan-Hartree-Fock wave functions.