Colour of Coordination Compounds

One of the most visually obvious properties of many transition-metal complexes is their intense colour: $[\text{Ti}(\text{H}_2\text{O})_6]^{3+}$ is a striking purple, $[\text{Cu}(\text{H}_2\text{O})_4]^{2+}$ is pale blue, $[\text{Cu}(\text{NH}_3)_4]^{2+}$ is a much deeper blue, and $[\text{Ni}(\text{H}_2\text{O})_6]^{2+}$ is green. This colour has a precise physical explanation in crystal field theory (Sections 5.12-5.14): in an octahedral complex, the ligand field splits the five originally degenerate d-orbitals into a lower-energy $t_{2g}$ set and a higher-energy $e_g$ set, separated by the crystal field splitting energy $\Delta_o$. If the metal ion has partially filled d-orbitals, an electron in the lower $t_{2g}$ set can absorb a photon of visible light whose energy exactly matches $\Delta_o$ and jump up ("$d$-$d$ transition") into the higher $e_g$ set. The compound then appears coloured because the light transmitted (the light not absorbed) is deficient in the wavelengths corresponding to $\Delta_o$, and the eye perceives the complementary colour of whatever was absorbed.

For $d$-$d$ transitions to be possible at all, two conditions must both be met: the metal ion must have at least one d-electron to promote (it cannot be $d^0$), and it must also have at least one vacancy in the higher-energy orbital set for that electron to be promoted into (it cannot be $d^{10}$, where every d-orbital, both $t_{2g}$ and $e_g$, is already completely full). $\text{Sc}^{3+}$ has a $d^0$ configuration — no d-electrons at all — so no $d$-$d$ transition is possible, and $[\text{Sc}(\text{H}_2\text{O})_6]^{3+}$ is colourless. $\text{Ti}^{3+}$, immediately next to it in the periodic table, has a $d^1$ configuration: its single d-electron sits in the $t_{2g}$ set and readily absorbs a photon to jump into the empty $e_g$ set, giving $[\text{Ti}(\text{H}_2\text{O})_6]^{3+}$ its characteristic purple colour (it absorbs mainly in the yellow-green region and transmits the complementary violet/purple). …