d-d transition and origin of colour

d–d transition: in a transition metal complex the five d orbitals are split by the ligand field into two sets of different energy. The jump of an electron from the lower set to the higher set by absorbing light is called a d–d transition.

Splitting of d orbitals (octahedral)

        ___ ___   e_g (dz², dx²−y²)
         ↑   Δo
        ___ ___ ___  t₂g (dxy, dyz, dxz)

In an isolated ion the five d orbitals have equal energy. When ligands approach, the repulsion raises the energy of e_g orbitals (which point at the ligands) more than the t₂g orbitals, giving the gap Δo.

Origin of colour

1. White light falls on the complex.
2. If Δo corresponds to a visible wavelength, an electron in t₂g absorbs that part of the light and moves to e_g.
3. The remaining wavelengths are transmitted, and the eye sees the complementary colour.

Example: [Ti(H₂O)₆]³⁺ (d¹) absorbs green-yellow (≈ 500 nm) and appears violet; [Cu(H₂O)₄]²⁺ (d⁹) absorbs red-orange and appears blue.

Ions with d⁰ (Sc³⁺, Ti⁴⁺) or d¹⁰ (Zn²⁺, Cu⁺) cannot show d–d transitions, so they are colourless. The colour depends on the metal, its oxidation state and the ligands, since these change Δo.