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, upsilon(D), in diatomic systems. The expression is given by, upsilon(D) = 1.78349 x D-e/omega(e) 5/8, 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. (C) 2013 Elsevier Inc. All rights reserved.