Bonded Radii and the Contraction of the Electron Density of the Oxygen Atom by Bonded Interactions

The bonded radii for more than 700 bonded pairs of atoms, comprising more than 50 oxide crystals, extracted from experimental and theoretical electron density distributions, are averaged and compared with the ionic radii for first, second, and third row atoms. At odds with the assumption of a "fixed" ionic radius of 1.40 Å for the oxide anion, the bonded radius for the anion, r(b)(O), decreases systematically from 1.40 to 0.65 Å as the electron density distribution of the atom is progressively polarized and contracted by its bonded interactions. The radii for the more electropositive metal atoms agree with the ionic radii when the electron density distribution of the anion is largely unpolarized by its bonded interactions. However, those for the more electronegative metal atoms are progressively larger than the ionic radii as the electron density distribution of the anion is progressively polarized and contracted along the bond vectors with decreasing bond length. The progressive decrease of r(b)(O) indicates that the compilation of sets of ionic radii, based on a fixed radius for the oxide anion, is problematic and impacts the accuracy of the ionic radii for the metal atoms. The assumption of a "fixed" radius for the anion, made in the derivation of sets of radii, not only results in unrealistic negative ionic radii for the more electronegative atoms but also in ionic radii that are as much as 0.5 Å smaller than the bonded radii, particularly for the more electronegative M atoms. The lack of agreement between the ionic and the bonded radii for the more shared bonded interactions is ascribed to the progressive increase in the polarization and contraction of the electron density of the oxide anion by the bonded interactions with a concomitant decrease in the radius of the anion, a factor that was largely neglected in the compilation of the ionic radii for fluoride, oxide, sulfide, and nitride crystals. The close agreement of the bonded radii and procrystal bonded radii is consistent with the argument that the chemical forces that govern the electron density distributions and bonded radii are largely atomic in nature, resulting in comparable electron density distributions.