Approximate sum rule for diatomic vibronic states as a tool for the evaluation of molecular properties

Abstract

The approximate sum rule < v 1| fΔ U n g| v 1 > ≈ Σ v 2 < v 1| f| v 2 > < v 2| g| v 1> ( E v1 - E v2 ) n , where f, g are operators which couple the vibrational levels v 1, v 2 of two interacting electronic states and Δ U= U 1— U 2 is the difference of the corresponding internuclear potentials, is numerically tested for radiative lifetimes, electronic polarizabilities, fine-structure constants and Landé factors for the vibronic states of the NaK molecule. The approximation is demonstrated to have high accuracy and efficiency for non-diagonal systems, especially for those with significant continuum contributions. Simple ways of estimating the sum rule accuracy are given.