**8.2. Spin selection rule**

The selection Rule for Spin Angular Momentum is

Δ S = 0

Thus transitions such as 2S→ 2P and 3D→ 3P are allowed, but transition such as 1S→ 3P is forbidden. The same rule is also stated in the form of a statement,

*Electronic Transitions between the different states of spin multiplicity are forbidden.* 

The selection Rule for total angular momentum, J, is

$$\Delta \text{ J = 0 } \text{or } \pm 1$$

The transitions such as 2P1/2 → 2D3/2 and 2P3/2 → 2D3/2 are allowed, but transition such as 2P1/2 → 2D5/2 is forbidden since Δ J= 2.

There is no selection rule governing the change in the value of n, the principal quantum number. Thus in hydrogen, transitions such as 1s → 2p, 1s → 3p, 1s → 4p are allowed.

Usually, electronic absorption is indicated by reverse arrow, ← , and emission is indicated by the forward arrow, → , though this rule is not strictly obeyed.

## **8.3. Mechanism of breakdown of selection rules**

#### *8.3.1. Spin-orbit coupling*

For electronic transition to take place, Δ S = 0 and Δ L= ± 1 in the absence of spin-orbit coupling. However, spin and orbital motions are coupled. Even, if they are coupled very weakly, a little of each spin state mixes with the other in the ground and excited states by an amount dependent

upon the energy difference in the orbital states and magnitude of spin –orbit coupling constant. Therefore electronic transitions occur between different states of spin multiplicity and also between states in which Δ L is not equal to ± 1. For example, if the ground state were 99% singlet and 1% triplet (due to spin– orbit coupling) and the excited state were 1% singlet and 99 % triplet, then the intensity would derive from the triplet –triplet and singlet-singlet interactions. Spin-orbit coupling provides small energy differences between degenerate state.

This coupling is of two types. The single electron spin orbit coupling parameter ζ, gives the strength of the interaction between the spin and orbital angular momenta of a single electron for a particular configuration. The other parameter, λ, is the property of the term. For high spin complexes,

$$\mathcal{A} = \pm \bigvee\_{S} \Big\langle \begin{array}{c} \\ \mathbf{2S} \end{array} \Big| $$

Here positive sign holds for shells less than half field and negative sign holds for more than half filled shells. S is the same as the one given for the free ion. The λ values in crystals are close to their free ion values. Λ decreases in crystal with decreasing Racah parameters B and C. For high spin d5 configuration, there is no spin orbit coupling because 6S state is unaffected by the ligand fields. The λ and ζ values for 3d series are given in Table-5.


**Table 5.** λ and ζ values for 3d series

#### *8.3.2. La Porte selection rule*

Physically 3d (even) and 4p (odd) wave functions may be mixed, if centre of inversion (i) is removed. There are two processes by which i is removed.

