The dissociation energy of twelve diatomic molecules has been determined by fitting four-parameter potential functionU(r)=D_e[[1−exp{−b(r−r_e)}]/ [1−Cexp{−b(r−r_e)}]]² to the true Rydberg-Klein-Rees (RKR) curves for their fifteen electronic states using the mean square deviation as the criterion for the selection of the best fit. Average deviation ofD_e has been found to be 2.7% as compared to 20.5% obtained with Lippincott’s potential function for these molecules. In addition the anharmonocity constantω_ex_e has also been calculated for the same electronic states yielding average mean deviation 8.9%.

A universal relation between the Sutherland parameter, Δ (= k_er_e^/2/2D_e) and the dimensionless parameter G (= 8ω_ex_e/B_e), has been established using 40 electronic states, which include ground as well as excited states of polar and non-polar molecules. This relation is used to predict the dissociation energy of four lowest electronic states of S₂ molecule. The respective values for the states X³Σ_g^/−, a¹Δ_g, b¹Σ_g^/+ and B³Σ_u^/− turn out to be 36557, 31431, 28247 and 13429 cm⁻¹, and are in good agreement with the experimental values. Furthermore, metastable states a¹Δ_g and b¹Σ_g^/+ of S₂ are shown to dissociate into ³P₁ + ³P₁ as against the dissociation of X³Σ_g^/− into ³P₂ + ³P₁. In addition, a relation between Sutherland parameter Δ and internuclear distance r_e, viz., Δ=2.2r_e has been obtained for the ground state of alkali diatomic molecules.