CFSE and geometry preference
/ CFSE geometry /
Why does one metal ion prefer to be octahedral, another tetrahedral, and a third square planar? Several forces vote — the size of the ions, how many ligands can physically fit, electrostatic repulsion between ligands — but for d-block metals there is an extra voter that often tips the result: the crystal field stabilization energy. Different geometries give different CFSE for the same number of d electrons, so a metal can prefer the geometry that earns it the most CFSE. This is the CFSE contribution to geometry preference.
Work the comparison for one case. An octahedral field gives a larger delta and lets electrons sink deep into a t2g set worth -2/5 delta-o each; a tetrahedral field gives a delta only about 4/9 as big and a smaller, oppositely-ordered stabilization. So for d-counts where the lower octahedral set can be filled preferentially — especially d3, d8, and low-spin d6 — the octahedral CFSE is much larger than the tetrahedral CFSE, and the difference (the octahedral site preference energy) strongly favors the octahedron. For d0, high-spin d5, and d10 the CFSE is zero in every geometry, so CFSE casts no vote and other factors (size, electrostatics) decide freely.
This shows up vividly in real solids and solutions. In spinel oxides of formula AB2O4, which ions choose the octahedral holes versus the tetrahedral holes is governed largely by octahedral site preference energies — Cr3+ (d3) and Ni2+ (d8) cling to octahedral sites, while ions with zero CFSE distribute more freely. The same logic biases which complexes form in solution and helps rationalize why certain geometries dominate for certain d-electron counts. CFSE never acts alone, but it is a real and sometimes decisive thumb on the scale.
In the spinel oxides, Cr3+ (d3) has a very large octahedral site preference energy and is found almost exclusively in octahedral holes, which is one reason chromium spinels adopt a normal spinel structure. By contrast Mn2+ (high-spin d5, zero CFSE everywhere) has no such preference and sits wherever size and charge balance dictate.
d3 and d8 ions hoard octahedral sites; zero-CFSE ions like high-spin d5 do not care.
CFSE is only one term among several and rarely the largest: ionic size, ligand-ligand repulsion, and lattice or solvation energies usually dominate, so CFSE decides the geometry only when those other factors are nearly balanced — it tips close calls, it does not overrule everything.