Photodissociation Wigner-Witmer Rules

The non-crossing rule requires that adiabatic potential energy curves which belong to electronic states of the same symmetry species (same A, S for nonrelar tivistic curves, same Cl for relativistic curves) do not cross. The Wigner-Witmer 

When atom-1 approaches atom-2, the axial electric field created by atom-1 lifts the 2L + 1 Ml-degeneracy of atom-2 and vice-versa. Here Ml is the projection of L into the internuclear axis and is related to the molecular A quantum number as 

The spin is not affected by the axial electric field, thus the atomic spins, Si and S2, couple to form the molecular spin quantum number as 

An example of this weak spin-orbit limit nonrelativistic adiabatic correlation is given by the HBr+ system. The lowest energy dissociation asymptote is Br+(3P) +H(2S), thus Si = 1, S2 = 1/2 and S can be 3/2 (quartet state) or 1/2 

A good way to check that the adiabatic correlation has been done correctly is to check whether the total degeneracy of the molecular states is equal to that of the atomic states. In the case of HBr+ — H(2S) + Br+(3P), the molecular degeneracy is4 + 8 + 4 + 2 = 18 and the atomic degeneracy is2x3x3 = 18. 

---