The number of bound vibrational levels in a diatomic molecule

A simple semiempirical expression has been developed for estimating the effective non-integer vibrational index at dissociation, υ_D, in diatomic systems. The expression is given by,^υD=1. 78349×^Deωe-58,where the dissociation energy and the fundamental vibrational frequency must be expressed in the same units. This expression gives reliable results for a wide variety of ground electronic states of neutral systems, but underestimates the vibrational index for diatomic cations, most excited states and zero bond-order molecules. The expression is successful for electronic states that have a Birge-Sponer plot displaying a downward curvature as the dissociation limit is approached.