**8. Selection rules**

8 Advanced Aspects of Spectroscopy

are given in Table-3.

d1 d9 d2 d8 d3 d7 d4 d6 d5 d10

**Table 3.** Microstates of different dn configuration

**7. Multiple term symbols of excited states** 

Configuration Ion Term symbol

Ti2+,V3+,Cr4+

Cr3+,V2+,Mn4+ Ni3+,Co2+ Cr2+,Mn3+ Fe2+,Co3+ Mn2+, Fe3+ Zn2+

**Table 4.** Terms arising from dn configuration for 3d ions (n=1 to10)

Ti3+,V4+ Cu2+

Ni2+

Similarly for a d2 configuration, the number of microstates is given by 10! / 2! (10 – 2)!

 10 9 8 7 6 5 4 3 2 1 <sup>45</sup> 2 18 7 6 5 4 3 2 1 

Thus a d2 configuration will have 45 microstates. Microstates of different dn configuration

dn configuration d1,d9 d2,d8 d3,d7 d4,d6 d5 d10

No.of microstates 10 45 120 210 252 1

The terms arising from dn configuration for 3d metal ions are given Table-4.

2D

6S

3F, 3P, 1G, 1D, 1S

4F, 4P, 2( H, G, F, D, D, P)

5D , 3( H, G, F, F, , D, P, P ), 1(I, ,G, G, F, D, D, S,S)

6S, 4(G, F, D, P), 2(I, H, G, G, F, F), 2(D, D, D, P, S)

## **8.1. La Porte selection rule**

This rule says that transitions between the orbitals of the same sub shell are forbidden. In other words, the for total orbital angular momentum is Δ L = ± 1. This is La Porte allowed transitions. Thus transition such as 1S→ 1P and 2D→ 2P are allowed but transition such as 3D→ 3S is forbidden since Δ L = -2 .That is, transition should involve a change of one unit of angular momentum. Hence transitions from *gerade* to *ungerade* (*g* to *u*) or vice versa are allowed, i.e., *u* → *g* or *g* → *u* but not *u* → *u* or *g* → *g*. In the case of p sub shell, both ground and excited states are odd and in the case of d sub shell both ground and excited states are even. As a rule transition should be from even to odd or vice versa.

The same rule is also stated in the form of a statement instead of an equation:

*Electronic transitions within the same p or d sub-shell are forbidden, if the molecule has centre of symmetry.* 
