# Allowed/Forbidden Transition Dipole Moments

1. Apr 30, 2015

### sams

Hello Everyone,

Kindly, may anyone please tell me what are the allowed and forbidden transition dipole moments between different molecular electronic states in diatomic molecules?

Thank you so much in advance...

2. May 1, 2015

### Quantum Defect

The basic rule is: |<f|dipole operator|i>|2 < > 0

Where <f| is the final state, |i> is the initial state, and the dipole operator is sandwiched in between.

Starting from this rule, you can use symmetry properties of the different kinds of rovibronic wavefunctions to come up with selection rules. Things like you can only change between certain kinds of electronic states. I.e. you can go from a Sigma state to another Sigma state (the first electronic transition in H2 is like this), but you can't change from a Sigma state to a Delta state. For homonuclear diatomic molecules, you can only have transitions between gerade and ungerade states. Again, the first electronic transition in H2 shows this, as well.

"Allowed" transitions also occur between states of the same spin family. Singlet --> singlet, and triplet --> triplet, but not singlet --> triplet.

The problem with all of these rules is that they assume molecules know about all of our nomenclature for the different states, and obey themselves. The reality is that there are all sorts of perturbations, and the actual states in many molecules are admixtures of different states for which we have a name. I.e. you can see singlet --> triplet transitions in things were the actual states are mixtures of singlet-like and triplet-like basis states. The very strong transition in Hg at 253.7 nm is an example of one of these (1^S --> 3^P).

If you are interested in diatomics, Herzberg's Diatomics is the standard text. A more readable text is the one by Jeff Steinfeld ("Molecules and Radiation").

3. May 1, 2015

### DrDu

Note also that there are no allowed or forbidden dipole moments but allowed or forbidden dipole transitions. A dipole transition is forbidden iff the transition dipole moment vanishes.

4. May 2, 2015

### sams

Actually, I am interested in heteronuclear diatomic molecules. What about the selection rules of heteronuclear diatomic molecules? Is there allowed transitions between doublet Sigma+ and doublet Delta electronic states? In my recent calculations I have obtained such transitions, but no transitions is obtained between doublet Sigma+ and doublet Sigma-!

5. May 2, 2015

### DrDu

Heteronuclear diatomic molecules belong to the symmetry group $C_{\infty v}$. The dipole moment operators transform like x,y and z and you can look up the corresponding representations and characters in a character table for this group.
Given the irreps of the inital and final state, you can check whether the matrix elements transform like the totally symmetric representation.

6. May 3, 2015

### sams

Thank you so much DrDu and Quantum Defect for your help and for your kind support....