Clarification of the electronic asymmetry in Π-state Λ doublets with some implications for molecular collisions

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Abstract
The asymmetry of the orbital part of the electronic wave functions and electronic charge distributions in 1Π, 2Π, and 3Π Λ doublets is carefully examined, to clear up considerable past confusion on this subject. The results are: (1) For 1Π and 3ΠΩ=1 states the electronic wave function in the e Λ‐doublet levels is symmetric with respect to reflection in the plane of rotation of the molecule and, in the f levels, antisymmetric. (2) For 2Π and 3Π0,2 states, in the Hund’s case (a) limit the electronic distributions in both Λ‐doublet levels are cylindrically symmetric. (3) As the case (b) limit is approached, the F1 e and F2 f wave functions of a 2Π state acquire an increasing degree of symmetric character with respect to reflection in the plane of rotation, while the F1 f and F2 e levels acquire antisymmetric character. In a 2Σ+–2Π radiative transition, the main branch P and R lines probe 2Π levels which are symmetric with respect to reflection in the plane of rotation while the main branch Q lines probe levels which are antisymmetric. The reflection symmetry of Π‐state electronic wave functions is shown to be independent of the number of π electrons, while the cylindrical asymmetry of the electronic charge distribution does depend on the electron occupancy. This formal analysis is used to draw implications for product Λ‐doublet populations in photodissociation and reactive processes leading to Π‐state molecules, and for collisions of Π‐state molecules with surfaces.