Why are d-d electronic transitions forbidden and weakly absorbing? Why do they occur at all?

I am unable to understand why d-d electronic transitions are forbidden? Why are they weakly absorbing and apart from that, why do they occur at all?

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In order for an electronic transition to be allowed (occur with strong intensity), certain "selection rules" must be obeyed. You may already be familiar with the rule that the electron spin quantum number cannot change during a transition. It is this rule that forbids singlet-to-triplet absorption or emission (emission follows the same rules as absorption) and consequently makes phosphorescent emission so much weaker than fluorescent emission.

• $\ce{\Delta S = 0}$ the Spin rule

Another rule, often referred to as the "LaPorte" rule or the "Orbital" rule, states that in molecules with a center of symmetry (centrosymmetric molecules), transitions within a subshell are forbidden when $\ce{\Delta l =0}$.

• $\ce{\Delta l = \pm 1}$ the LaPorte rule

The orbital angular momentum quantum number "l" describes the type of orbital (s, p, d, f) within the subshell. In centrosymmetric molecules, the various s, p, d, f orbitals cannot mix within a subshell. For example, the 4d orbital cannot mix with the 4p orbital in a centrosymmetric molecule, such mixing being symmetry forbidden. Octahedral complexes can be centrosymmetric. In such a case 3p->3p, 3d->3d transitions would be forbidden by LaPorte's rule. Tetrahedral molecules do not have a center of symmetry and p-d orbital mixing is allowed, so in the case of tetrahedral molecules 3p->3p and 4d->4d transitions may appear stronger because a small amount of another orbital may be mixed into the p or d orbital thereby removing the violation of LaPorte's rule.

If we can do something to remove the centrosymmetric nature of an octahedral complex, then we "relax" LaPortes rule and weak transitions can be observed. For example, if a molecular vibration removes the molecular center of symmetry, then a d->d transition can occur if light is absorbed at that instant. Things such as spin-orbit coupling, vibronic coupling, or ligands that can mix with the metal's d orbitals would all allow relaxation of LaPorte's rule and thereby permit weak transitions to be observed.

• An important point is that only spin-orbit coupling allows singlet and triplet states to mix and so overcomes the 'forbiddenness' of the $\Delta S$=0 selection rule. This coupling is enhanced by paramagnetic species and heavy atoms in a molecule or solvent. Also note that phosphorescence always has a longer lifetime than fluorescence whatever its quantum yield. – porphyrin Jul 12 '16 at 20:53