A parameter-free formula is suggested to evaluate the molecular dissociation energy of a stable diatomic electronic system. The full vibrational spectra {EυAM} and theoretical dissociation energies DeAM are studied using the algebraic method (AM) and the suggested analytical formula for some electronic states of Li2, K2, Na2, and Sr2 molecules which have regular (Morse-like) potentials. Both the {EυAM} and the calculated DeAM agree excellently with known experimental values for each electronic state.