The N 4 cluster is anti-ferromagnetically ordered for CAS and connected GAS spaces, hence we conclude from the previous discussion that we can target spin pure states with selected m s values and s = |m s |. The results in Figure confirm precisely this aspect. CAS and connected GAS energies, obtained using the SD representation, are undistinguishable from the corresponding energies obtained in a spin-adapted basis. Also, the calculated spin quantum number from the expectation value of the Ŝ2 operator (Figure ) confirms that for this system all states are pure spin eigensolutions, despite the fact that an SD basis has been utilized.