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 (<i>S</i>) and effective principal
quantum number (<i>n</i>*) 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
