The Fritz Haber Research Center, Institute of Chemistry, The Hebrew University of Jerusalem , Jerusalem 91904, Israel.
J Am Chem Soc. 2017 Oct 25;139(42):15068-15073. doi: 10.1021/jacs.7b07882. Epub 2017 Oct 16.
Ionic radii play a central role in all branches of chemistry, in geochemistry, solid-state physics, and biophysics. While authoritative compilations of experimental radii are available, their theoretical basis is unclear, and no quantitative derivation exists. Here we show how a quantitative calculation of ionic radii for cations with spherically symmetric charge distribution is obtained by charge-weighted averaging of outer and inner radii. The outer radius is the atomic (covalent) radius, and the inner is that of the underlying closed-shell orbital. The first is available from recent experimental compilations, whereas the second is calculated from a "modified Slater theory", in which the screening (S) and effective principal quantum number (n*) were previously obtained by fitting experimental ionization energies in isoelectronic series. This reproduces the experimental Shannon-Prewitt "effective ionic radii" (for coordination number 6) with mean absolute deviation of 0.025 Å, approximately the accuracy of the experimental data itself. The remarkable agreement suggests that the calculation of other cationic attributes might be based on similar principles.
离子半径在化学的各个分支、地球化学、固态物理和生物物理中都起着核心作用。虽然有权威的实验半径汇编，但它们的理论基础并不清楚，也没有定量推导。在这里，我们展示了如何通过对外层和内层半径进行电荷加权平均，从具有球对称电荷分布的阳离子的定量计算中得到离子半径。外层半径是原子（共价）半径，内层是其下的封闭壳层轨道半径。外层半径可以从最近的实验汇编中获得，而内层半径可以从“修正的 Slater 理论”中计算得到，其中屏蔽（S）和有效主量子数（n*）是通过拟合等电子系列中的实验电离能获得的。这再现了实验 Shannon-Prewitt“有效离子半径”（配位数为 6），平均绝对偏差为 0.025Å，与实验数据本身的精度大致相同。惊人的一致性表明，其他阳离子属性的计算可能基于类似的原则。
