Electromagnatic radiation :- Vibrational Selection rules

 Vibrational Selection rules

1 Transitions with Δv=±1, ±2, ... are all allowed for anharmonic potential, but the 

intensity of the peaks become weaker as Δv increases.

2 v=0 to v=1 transition is normally called the fundamental vibration, while those 

with larger Δv are calledovertones.

3 Δv=0 transition is allowed between the lower and upper electronic states with 

energy E1 and E2 are involved, i.e. (E1, v''=n) → (E2, v'=n), where the double 

prime and single prime indicate the lower and upper quantum state.

4 The geometry of vibrational wavefunctions plays an important role in vibrational 

selection rules. For diatomic molecules, the vibrational wavefunction is symmetric 

with respect to all the electronic states. Therefore, the Franck-Condon integral is 

always totally symmetric for diatomic molecules. The vibrational selection rule 

does not exist for diatomic molecules.

For polyatomic molecules, the nonlinear molecules possess 3N-6 normal vibrational 

modes, while linear molecules possess 3N-5 vibrational modes.

Let's consider a single photon transition process for a diatomic molecule. The 

rotational selection rule requires that transitions with ΔJ=±1 are allowed. Transitions 

with ΔJ=1 are defined as R branch transitions, while those with ΔJ=-1 are defined as 

P branch transitions. Rotational transitions are conventional labeled as P or R with the 

rotational quantum number J of the lower electronic state in the parentheses. For 

example, R(2) specifies the rotational transition from J=2 in the lower electronic state 

to J=3 in the upper electronic state.

2. ΔJ=0 transitions are allowed when two different electronic or vibrational states are 

involved.