[en] Alternative expressions for vibrational and rotational spectrum constants and energies of diatomic molecular electronic states are suggested based on the perturbation theory. An algebraic method (AM) is proposed to generate converged full vibrational spectrum from limited energy data, and a potential variational method (PVM) is suggested to produce the vibrational force constants f_n's and rotational spectrum constants using the perturbation formulae and the AM vibrational constants. Applying this method to several diatomic electronic states, the calculation results show that: 1) the AM E_υmax converges to correct molecular dissociation energy; 2) the AM not only reproduce the input energies, but also generate the E_υ's of high vibrational excited states which may be difficult to be obtained experimentally or theoretically; 3) the PVM vibrational force constants f_n's may be used to measure the relative chemical bond strength of different diatomic electronic states for a molecule quantitatively