ligand field theory

Crystal field theory works wonderfully for predicting splitting patterns, but it rests on a fib: it pretends ligands are just naked negative charges and that metal-ligand bonds have no electron sharing at all. That fiction cannot explain why neutral carbon monoxide splits d orbitals harder than a negative fluoride ion, and it gets the size of delta wrong in detail. Ligand field theory is the honest upgrade — it keeps the useful d-orbital splitting picture but rebuilds it using molecular orbital theory, so covalency is built in from the start.

The recipe is the molecular-orbital approach applied to a whole complex. You take the metal's valence orbitals (the five 3d, plus 4s and 4p) and the symmetry-matched combinations of the ligands' donor orbitals, and let them overlap and combine into molecular orbitals spread over the whole complex. The familiar t2g and eg labels survive, but now they are molecular orbitals with both metal and ligand character, not pure metal d orbitals. The upper eg set turns out to be antibonding (metal-ligand sigma-antibonding), and the gap delta-o is reinterpreted as the energy difference between a largely-nonbonding t2g and that antibonding eg. This is why delta depends so sensitively on the ligand: it is a bonding quantity, not just an electrostatic one.

Ligand field theory is what finally explains the spectrochemical series. Sigma-donor strength sets a baseline, but the fine ordering — why CO and CN- give huge delta while halides give small delta — comes from pi bonding, which the point-charge model cannot see at all. Pi-acceptor ligands lower t2g and widen delta; pi-donor ligands raise t2g and narrow it. In short, ligand field theory is crystal field theory with covalency restored: same diagrams, deeper and truer reasons.