In this chapter, we have recalled the non-BO molecular Hamiltonian and given an outline of a method for extending the very accurate non-BO calculations with ECGs to states where the diatomic molecule is excited to the first rotational state and also vibrationally excited to an arbitrary level. We have shown a vibrational frequency analysis calculation with Psi4 of the carbon dioxide molecule. We have presented the vibrational spectra for ortho-para isomerization of hydrogen molecules calculated with a non-BO method [Sharkey], with a BO method [Komasa], and their comparison with experimental data. The non-BO method is highly accurate in predicting all states, including excited states of the hydrogen molecule. The scaling of the wave functions used for both BO and non-BO methods has a factorial dependence and is considered an NP-hard problem.