The molecular dissociation energies of some electronic states of hydride and N 2 molecules were studied using a parameter-free analytical formula suggested in this study and the algebraic method (AM) proposed recently. The results show that the accurate AM dissociation energies D e AM agree excellently with experimental dissociation energies D e expt , and that the dissociation energy of an electronic state such as the 2 3 Δ g state of 7 Li 2 whose experimental value is not available can be predicted using the new formula.algebraic method, diatomic molecule, vibrational energy, dissociation energy