A parameter-free formula is suggested to evaluate the molecular dissociation energy of a stable diatomic electronic system. The full vibrational spectra (E(upsilon)(AM)) and theoretical dissociation energies D(e)(AM) are studied using the algebraic method (AM) and the suggested analytical formula for some electronic states of Li(2), K(2), Na(2), and Sr(2) molecules which have regular (Morse-like) potentials. Both the (E(upsilon)(AM)) and the calculated D(e)(AM) agree excellently with known experimental values for each electronic state.