Collision induced transitions between 2Π and 2Σ states of diatomic molecules: Quantum theory and collisional propensity rules

We develop the exact quantum description, free of any dynamical approximations, of rotationally inelastic collision induced transitions between 2Π and 2Σ electronic states of a diatomic molecule. An explicit connection is made between the matrix elements of the electrostatic coupling, described in an asymptotically exact diabatic basis, and the results of an ab initio calculation of the appropriate atom–molecule adiabatic electronic wave functions of A′ and A″ symmetry. Analysis of the quantum close-coupled equations demonstrates that the use of Franck–Condon approximations in the description of E → E energy transfer is unjustified and, furthermore, that in collisions involving homonuclear diatomic molecules the s/a permutation-inversion symmetry of the molecular wave functions will be rigorously conserved. The extension of the infinite-order sudden approximation to electronically inelastic 2Π → 2Σ processes allows us to predict two new collisional propensity rules: (a) When Δ J=0 the cross sections will become vanishingly small for transitions which conserve the e/f symmetry index of the molecular wave function. (b) In a high-J Hund’s case (b) limit transitions from either the F1 or F2 2Π-state manifolds will populate only one of the Σ-state spin-doublet levels, consistent with a physical model in which the electronic spin S is a spectator so that the relative orientation of N and S is preserved during the collision.