Abstract An accurate relation, connecting dissociation energy D0, force constant for infinitesimal amplitude ke and internuclear equilibrium distance re has been deduced from Varshni and Shukla's potential function. It is of the form D0=ke {A + B re 2 + C re 4), where A, B and C are constants and are the same for groups of similar diatomic molecules. The values of D0 estimated by this relation are in better agreement with the observed ones than those estimated by Somayajulu, and Tandon et al.