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

The asymmetry of the orbital part of the electronic wave functions and electronic charge distributions in 1Pi, 2Pi, and 3Pi Λ doublets is carefully examined, to clear up considerable past confusion on this subject. The results are: (1) For 1Pi and 3Pi= 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 2Pi and 3Pi/sub 0,2/ 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 2Pi 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+--2Pi radiative transition, the main branch P and R lines probe 2Pi 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 Pi-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 3+-doublet populations in photodissociation and reactive processes leading to Pi-state molecules, and for collisions of Pi-state molecules with surfaces