A theoretical treatment of thea 3Σ1+ →X1Σ++ spin-forbidden dipole-allowed radiative transition in NO+

The radiative lifetime of the spin-forbidden dipole-allowed transition a 3Σ1+ →X1Σ0++is determined using ab initio electronic structure techniques. This transition acquires intensity as a result of the spin–orbit induced perturbations, a 3Σ+1∼1Π1 and X1Σ0++∼3Π0+ where the notation is meant to imply that the a 3Σ+1 and X1Σ0++ states are perturbed by all the states of the indicated symmetry in a given configuration state function (CSF) space. A near degeneracy of the A 1Π and a 3Σ+ potential energy curves necessitates the use of quasidegenerate perturbation theory when treating the a 3Σ+1∼1Π1 interaction. The nonrelativistic (zeroth order CI), and relativistic (first order perturbed), wave functions are expanded in CSF spaces of dimension 0.5–1.4×106. To our knowledge, this represents the first treatment of the spin–orbit interaction within the full microscopic Breit–Pauli approximation in a CSF space of greater than 1 million CSFs. The radiative lifetimes (τv) of the transitions (a 3Σ+,v)→X 1Σ+ were found to be τv=455, 467, 478, 488, 495 ms for v=0, 1, 2, 3, 4, respectively. These results are in good agreement with the experimental determination of Kuo et al. [J. Chem. Phys. 92, 4849 (1990)] who found τ=530(+300,−100) ms. The results of this treatment are compared with those of a single perturber model in which the a 3Σ+→X 1Σ+ transition is attributed exclusively to the a 3Σ+∼A 1Π perturbation. This model is shown to be only qualitatively correct.