Crystal field theory and colour

Crystal field theory (CFT) takes a different view: it treats the ligands as negative charges (or the negative ends of molecules) and the bond as electrostatic. As the ligands approach, their electrons repel the metal's d electrons. The five d orbitals, which were equal in energy, no longer are: they split.

In an octahedral field, two d orbitals point straight at the ligands and are pushed up: the e_g set. The other three point between the ligands and go down: the t₂g set. The gap between them is the crystal field splitting, Δ₀.

In a tetrahedral field the order is reversed: the e set is lower and the t₂ set higher. The splitting is smaller, Δt ≈ (4/9)Δ₀, so tetrahedral complexes are almost always high spin.

Some ligands split the orbitals more than others. The spectrochemical series lists them from weak to strong:

I⁻ < Br⁻ < SCN⁻ < Cl⁻ < S²⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < edta⁴⁻ < NH₃ < en < CN⁻ < CO

Where does the fourth d electron go? It can pair up in t₂g, which costs the pairing energy P, or go up into e_g, which costs Δ₀:

• Δ₀ < P (weak field ligand): electrons spread out first, giving high spin.
• Δ₀ > P (strong field ligand): electrons pair in t₂g, giving low spin.

Colour. A complex absorbs light of the right energy to lift an electron from t₂g to e_g, a d-d transition. We see the complementary colour of what is absorbed. [Ti(H₂O)₆]³⁺ (d¹) absorbs blue-green light, so it looks violet. A stronger ligand makes a bigger gap, so the complex absorbs higher-energy, shorter-wavelength light, and its colour changes. With no d electrons, or a full d¹⁰ set, no d-d transition is possible, and the complex is colourless.