tetrahedral field splitting
/ teh-truh-HEE-dral /
Sometimes only four ligands surround a metal, and they often arrange themselves not in a flat square but in a tetrahedron — picture the metal at the center of a cube with ligands on four of the eight corners, alternating. This is how [CoCl4]2- and [FeCl4]- are built. The way the d orbitals split in this four-ligand cage is tetrahedral field splitting, and the key surprise is that it is upside-down compared with the octahedron, and smaller.
Here is why it flips. In a tetrahedron, NO d orbital points straight at a ligand — the ligands sit in the gaps along the cube's body diagonals. But the orbitals that point between the axes (dxy, dxz, dyz) come closer to the ligand directions than the orbitals along the axes (dz2, dx2-y2). So now the between-axis set is pushed UP, and the along-axis set drops down. The result is the inverse of octahedral: the lower set is called e (just two orbitals) and the upper set is t2 (three orbitals), with no 'g' label because a tetrahedron has no center of inversion. The gap is delta-t, and it is small — roughly 4/9 of delta-o for the same metal and ligands, both because there are fewer ligands (four, not six) and because none of them points directly at an orbital.
The practical consequence is huge: because delta-t is so small, it almost never beats the electron-pairing energy, so tetrahedral complexes are essentially always high-spin. You will rarely if ever meet a low-spin tetrahedral complex. The small gap also tends to push absorptions toward lower energy, often giving intense colors, as in the deep blue of [CoCl4]2-.
Compare [Co(H2O)6]2+, a pale pink octahedral ion, with [CoCl4]2-, a deep blue tetrahedral ion. Same Co2+ d7 center, but the tetrahedral version has a much smaller delta-t, shifts its absorption, and is intensely colored partly because the tetrahedron's lack of a center of inversion relaxes the rules that normally make d-d bands faint.
The same metal ion can look completely different depending on whether it sits in an octahedral or tetrahedral field.
The 4/9 ratio is an idealized result for identical ligands at identical distances, not a law of nature; the real point to keep is simply that delta-t is much smaller than delta-o, which is why tetrahedral complexes are almost always high-spin.