The number of bound vibrational levels in a diatomic molecule

► Developed a semiempirical expression for the vibrational index at dissociation. ► Expression applies to ground states of neutral diatomic molecules having integral non-zero bond-orders. ► Expression applies to diatomic molecules having Birge-Sponer plots with negative curvature near dissociation. ► Expression does not apply to diatomic molecules that display inconsistency with Badger's rule. ► Employed the expression to make predictions for many molecules that have not been studied near the dissociation limit.