Periodicity - Colored complexes (HL only)

Transition metals form colored compounds due to the partially filled $d$-orbitals. In an isolated gaseous ion, the five $d$-orbitals are degenerate (equal in energy).

When ligands approach the central metal ion to form a complex, the repulsion between the lone pairs on the ligands and the electrons in the $d$-orbitals causes the orbitals to split into two sets of different energy levels. In octahedral complexes, these are the $t_{2g}$ (lower energy: $d_{xy}$, $d_{yz}$, $d_{xz}$) and $e_g$ (higher energy: $d_{z^2}$, $d_{x^2-y^2}$) levels.

The energy difference between these levels is denoted as $\Delta E$. When light shines on the complex, an electron can be promoted from a lower energy $d$-orbital to a higher energy $d$-orbital (a $d-d$ transition) by absorbing a photon of energy equal to $\Delta E$.

The color observed is the complementary color to the wavelength of light absorbed. For example, if a complex absorbs blue light, it will appear orange.

The magnitude of $\Delta E$, and thus the color, depends on four factors: 1. The identity of the metal ion (nuclear charge), 2. The oxidation state of the metal (higher oxidation state usually leads to larger $\Delta E$), 3. The nature of the ligand (Spectrochemical series), and 4. The geometry of the complex (e.g., octahedral vs. tetrahedral).

The Spectrochemical Series ranks ligands by their ability to split $d$-orbitals: $I^- < Br^- < S^{2-} < Cl^- < F^- < OH^- < H_2O < SCN^- < NH_3 < en < NO_2^- < CN^- < CO$.