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

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.