Department of Geosciences, Virginia Tech, Blacksburg, Virginia 24061, USA.
J Phys Chem A. 2013 Feb 21;117(7):1632-40. doi: 10.1021/jp310462g. Epub 2013 Jan 31.
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.
从实验和理论电子密度分布中提取的超过 700 对键合原子（包括 50 多种氧化物晶体）的键合半径进行了平均，并与第一、二、三列原子的离子半径进行了比较。与氧化物阴离子“固定”离子半径为 1.40 Å 的假设不一致，阴离子的键合半径 r(b)(O) 从 1.40 Å 系统地减小到 0.65 Å，因为原子的电子密度分布通过其键合相互作用逐渐极化和收缩。当阴离子的电子密度分布通过其键合相互作用基本没有极化时，对于更正电性的金属原子，其半径与离子半径一致。然而，对于更电负性的金属原子，随着阴离子的电子密度分布沿着键矢量逐渐极化和收缩，键长减小，半径逐渐大于离子半径。r(b)(O) 的逐渐减小表明，基于氧化物阴离子的固定半径来编制离子半径集是有问题的，并且会影响金属原子的离子半径的准确性。在推导半径集时假设阴离子的“固定”半径不仅导致更电负性原子的不切实际的负离子半径，而且还导致离子半径比键合半径小 0.5 Å，尤其是对于更电负性的 M 原子。对于更共享的键合相互作用，离子半径与键合半径之间缺乏一致性，这归因于氧化物阴离子的电子密度通过键合相互作用逐渐极化和收缩，同时阴离子半径减小，这一因素在氟化物、氧化物、硫化物和氮化物晶体的离子半径编制中基本上被忽略。键合半径与预晶键合半径的紧密一致表明，控制电子密度分布和键合半径的化学力在很大程度上是原子性质的，导致可比较的电子密度分布。
