Crystal field theory

CFT treats the metal-ligand bond as purely ionic: anionic ligands are point charges and neutral ligands are point dipoles, and they interact with the metal only electrostatically.

In a free metal ion, or in a spherical field of charge, the five d orbitals have equal energy (degenerate). An asymmetric field from real ligands lifts this degeneracy: crystal field splitting.

Octahedral field: dx²−y² and dz² point at the ligands, feel more repulsion and rise as the eg pair; dxy, dyz and dxz point between the axes and fall as the t₂g set. The gap is Δo.

Relative to the average energy, the two eg orbitals go up by (3/5)Δo and the three t₂g orbitals go down by (2/5)Δo.

Δo grows with the field of the ligand and with the charge on the metal ion. The spectrochemical series, found by experiment from absorption spectra, orders ligands by field strength: I⁻ < Br⁻ < SCN⁻ < Cl⁻ < S²⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < edta⁴⁻ < NH₃ < en < CN⁻ < CO.

d¹ to d³ ions put their electrons singly into t₂g (Hund's rule). For d⁴ the fourth electron has a choice, set by Δo against the pairing energy P.

If Δo < P the fourth electron goes into eg, giving t₂g³ eg¹: weak field ligands, high spin complexes. If Δo > P it pairs in t₂g, giving t₂g⁴ eg⁰: strong field ligands, low spin complexes.

Calculations show that complexes of d⁴ to d⁷ ions are more stable in a strong field than in a weak one.

Tetrahedral field: the splitting is inverted and smaller, Δt = (4/9)Δo for the same metal, ligands and distances. It is rarely large enough to force pairing, so tetrahedral complexes are almost always high spin.

The g subscript (t₂g, eg) is used only for complexes with a centre of symmetry, such as octahedral and square planar ones; tetrahedral levels are written without it.