Selection rules

   Electronic transitions obey the following selection rules. Spin selection rule: ΔS = 0 Transitions may occur from singlet to singlet, or triplet to triplet states and so on, but a change in spin multiplicity is forbidden. Laporte selection rule: There must be a change in parity: allowed transitions: g ↔ u forbidden transitions:

g↔g       u↔ u

This leads to the selection rule: Δl = ^_1 and, thus, allowed transitions are   s →p,    p → d,    d → f ; forbidden transitions are s → s, p → p, d → d, f → f , s → d, p → f  etc.  Since these selection rules must be strictly obeyed, why do many d-block metal complexes exhibit ‘d–d’ bands in their electronic spectra?

   A spin-forbidden transition becomes ‘allowed’ if, for example, a singlet state mixes to some extent with a triplet state. This is possible by spin–orbit coupling  but for first row metals, the degree of mixing is small and so bands associated with ‘spin-forbidden’ transitions are very weak (Table 1.1).

Table 1.1 Typical Ԑ_max values for electronic absorptions; a large  Ԑ_max corresponds to an intense absorption and, if the absorption is in the visible region, a highly coloured complex.

   Spin-allowed ‘d–d’ transitions remain Laporte-forbidden and their observation is explained by a mechanism called ‘vibronic coupling’. An octahedral complex possesses a centre of symmetry, but molecular vibrations result in its temporary loss.

  At an instant when the molecule does not possess a centre of symmetry, mixing of d and p orbitals can occur. Since the lifetime of the vibration (≈10^-13 s) is longer than that of an electronic transition (≈10^-18 s), a ‘d–d’ transition involving an orbital of mixed pd character can occur although the absorption is still relatively weak (Table 1.1). In a molecule which is noncentrosymmetric (e.g. tetrahedral), p–d mixing can occur to a greater extent and so the probability of ‘d–d’ transitions is greater than in a centrosymmetric complex. This leads to tetrahedral complexes being more intensely coloured than octahedral complexes.