Colour of complexes

In an isolated ion the five 3d orbitals are degenerate (equal energy). When ligands approach (e.g. octahedrally), they split the d orbitals into a lower and a higher set, separated by an energy gap ΔE.

An electron in the lower set can absorb a photon of visible light whose energy exactly matches the gap and jump to the higher set — a d–d transition: $\Delta E = h\nu = \frac{hc}{\lambda}$

This requires a partially filled d sub-shell, which is why d⁰ (Sc³⁺) and d¹⁰ (Zn²⁺) complexes are colourless — no d–d transition is possible.

A complex absorbs the part of white light that matches ΔE; the light that passes through (or is reflected) is what we see. The observed colour is the complement of the absorbed colour.

Using a colour wheel: red ↔ green, blue ↔ orange, yellow ↔ violet. So a complex that absorbs red appears green; one that absorbs orange appears blue (like [Cu(H₂O)₆]²⁺).

Larger ΔE means higher-frequency, shorter-wavelength light is absorbed: $\Delta E = \frac{hc}{\lambda} \;\Rightarrow\; \text{larger } \Delta E,\ \text{shorter } \lambda$

Anything that changes ΔE changes which wavelength is absorbed, and so the colour:

• Ligand — different ligands split the d orbitals by different amounts (e.g. [Cu(H₂O)₆]²⁺ blue vs [Cu(NH₃)₄(H₂O)₂]²⁺ deep blue).
• Oxidation state — a different metal charge gives a different ΔE (e.g. Fe²⁺ vs Fe³⁺ complexes).
• Coordination number / geometry — e.g. octahedral [Cu(H₂O)₆]²⁺ (blue) vs tetrahedral [CuCl₄]²⁻ (yellow).

Colorimetry. Because a coloured solution's absorbance is proportional to its concentration, a colorimeter (set to the wavelength of maximum absorption) is used with a calibration curve of absorbance vs known concentration to find an unknown concentration.