Molecular States, Symmetry and Allowed Transitions

[tomothy]

I have a question about allowed transitions and molecular states. For an electric dipole transition between two states (say molecular or atomic) to have a non-zero probability of occurring, the transition dipole moment $\langle \psi_{f}|\textbf{μ}\left|\psi_{i} \right \rangle$ must be non-zero. This can be determined by considering the irreducible symmetry representations to which each state/operator belongs i.e. $\Gamma ( \psi_{f} ) \otimes \Gamma \left(x,y,z \right) \otimes \Gamma \left(\psi_{i}\right)$ must contain the totally symmetric irreducible representation at least once.

My question is, are the initial states and final states to be considered the overall molecular states or the individual single electron states? e.g. in diatomic hydrogen, for a $\sigma_{g} \rightarrow \sigma_{u}$ transition, are the initial and final states the electron states of the electron being excited or the overall initial and final molecular states (i.e. of both electrons)?

 

[DrClaude]

It is the many-electron state that must be considered.