Electronic Selection Rules :- Electronic transitions in atoms

Electronic Selection Rules 

Electronic transitions in atoms

Atoms are described by the primary quantum number n, angular momentum quantum 

number L, spin quantum number S, and total angular momentum quantum number J. 

Based on Russell-Saunders approximation of electron coupling, the atomic term 

symbol can be represented as (2S+1) LJ

.

1. The total spin cannot change, ΔS=0;

2. The change in total orbital angular momentum can be ΔL=0, ±1, but 

L=0 ↔ L=0 transition is not allowed;

3. The change in the total angular momentum can be ΔJ=0, ±1, but J=0 ↔ J=0 

transition is not allowed;

4. The initial and final wave functions must change in parity. Parity is related to the 

orbital angular momentum summation over all elections Σ li, which can be even 

or odd; only even ↔ odd transitions are allowed.

1.6.2 Electronic transitions in molecules:

The electronic-state configurations for molecules can be described by the primary 

quantum number n, the angular momentum quantum number Λ, the spin quantum 

number S, which remains a good quantum number, the quantum number Σ (S, S-1, ..., 

-S), and the projection of the total angular momentum quantum number onto the 

molecular symmetry axis Ω, which can be derived as Ω=Λ+Σ. The term symbol for 

the electronic states can be represented as

Group theory makes great contributions to the prediction of the electronic selection 

rules for many molecules. An example is used to illustrate the possibility of electronic 

transitions via group theory.

1. The total spin cannot change, ΔS=0; the rule ΣΔ=0holds for multiplets;

If the spin-orbit coupling is not large, the electronic spin wavefunction can be 

separated from the electronic wavefunctions. Since the electron spin is a magnetic

effect, electronic dipole transitions will not alter the electron spin. As a result, the spin 

multiplicity should not change during the electronic dipole transition.

2. The total orbital angular momentum change should be ΔΛ=0, ±1;

3. Parity conditions are related to the symmetry of the molecular wavefunction 

reflecting against its symmetry axis. For homonuclear molecules, the g ↔ u transition 

is allowed.