Laporte selection rule

Why are so many transition-metal solutions only faintly colored, even though they clearly absorb visible light? Part of the answer is a rule of thumb about which electronic jumps light is allowed to drive. The Laporte selection rule says that in a molecule with a center of symmetry, an electron can only be promoted between orbitals of opposite parity — and a d-to-d jump breaks that rule.

Parity is about how an orbital behaves under inversion, the operation of pushing every point through the center to the opposite side. An orbital that comes back unchanged is called gerade (g, German for even); one that flips its sign is ungerade (u, odd). The s and d orbitals are g; the p and f orbitals are u. Light's electric field can flip parity, so it readily drives g-to-u or u-to-g transitions, but a d-d transition is g-to-g — no parity change — so it is Laporte-forbidden. The same logic forbids the d-d band in a perfect octahedron (which has a center of inversion), making it intrinsically weak.

Why does it matter? It explains the gentle pastel colors of most octahedral complexes: their d-d bands are forbidden, so the molar absorptivity is small (often only 1 to 100 in the usual units) and little light is taken up. But the rule is relaxed, not absolute, in two important ways. A complex with no center of symmetry — most notably a tetrahedral one — escapes the rule entirely, which is why tetrahedral complexes like [CoCl4]2- are far more deeply colored than octahedral ones. And even centrosymmetric complexes break the rule slightly through vibronic coupling, the brief loss of symmetry as the molecule vibrates, which lets a little intensity leak through.