Clarification of the electronic asymmetry of Λ doublets in 3Π electronic states of diatomic molecules

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Abstract
The reflection symmetry of the spatial part of the electronic wave function for 3Π diatomic molecular states is examined carefully for the individual Λ doublet levels by means of an approach presented earlier [M. H. Alexander and P. J. Dagdigian, J. Chem. Phys. 8 0, 4325 (1984)]. The results are: For a 3Π molecule in Hund’s case (a) the electronic wave function in the Ω=1 (F2) e levels will be antisymmetric and, in the the f levels, symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation of the molecule. The electronic wave functions in the F1 and F3 levels will not have a defined plane of symmetry. By contrast, in the Hund’s case (b) high J limit, the electronic wave function in the F1e, F2 f, and F3e levels will be antisymmetric and, in the F1 f, F2e, and F3 f levels, symmetric with respect to reflection. Thus, the symmetry of the wave functions in the F2Λ‐doublet levels reverses with the passage from case (a) to case (b). In the case (b) limit, the main branch P and R lines of a 3Π–3Σ− transition will probe antisymmetric levels, irrespective of the Fi level of the 3Π state, while the main branch Q lines will probe symmetric levels. This will be reversed for a 3Π–3Σ+ transition. At low J, in the case (a) limit, in a 3Π–3Σ− transition the P2i and R2i lines with i odd and the Q2i lines with i even will probe antisymmetric levels, while the P2i and R2i lines with i even and the Q2i lines with i odd will probe symmetric levels; the other 18 rotational branches probe levels with no well‐defined reflection symmetry.