Chemistry: Why are the ionic radii of high spin metal ions greater than that of low spin metal ions?

Faraz Arastu, some graduate-level physics

Answered Nov 14, 2015

Ionic radius is a funny concept because it implies that the electron cloud is spherical. This is not 100% accurate. Electron orbitals are described by probability density functions called wavefunctions, and the d-orbitals can be visualized as follows:

These are clearly not spheres. So why do measurements indicate ionic 'radii' of high-spin compounds are larger than their low-spin counterparts? Picture a d5$d^5$ octahedral high-spin compound. All d-orbitals would be occupied by 1$1$ electron (imagine all the above orbitals on 1$1$ set of axes).

The corresponding low-spin compound would only have 3$3$ out of 5$5$ orbitals occupied, so (depending on your frame of reference) the dz2$d_{z^2}$ and dx2−y2$d_{x^2-y^2}$ would be unoccupied. This implies the low-spin electrons are confined to a somewhat smaller space, giving a smaller measured radius. Again, please remember this is an oversimplification and better left to the quantum physicists to explain.

Sources: Periodic Trends in Ionic Radii, Spin states (d electrons)