Truncating the expansion at the CISD level, the ground state is stabilized, but the stabilization of the excited states as due to the triple CI contribution is missing. As a result, CISD transition energies are overestimated, a spurious effect that is fixed when triple excitations are accounted for (see panels c and d). This result is fully confirmed by the comparison with RS exact diagonalization transition energies, that perfectly match with CISDT results. However, reaching triple CI in all-electron quantum chemical calculations is extremely demanding. Most often CIS(D) approaches, where double CIs are introduced perturbatively, seem to provide reasonable results as for transition energies. However, caution is needed since the wavefunctions stay at the CIS level. On the other hand, CIS(D) introduces ST gap) at the CIS level, but, as soon as correlations enter into play, from CISD up, their order is inverted, with the triplet MR state ( 3 A ′ 2 ) lying at energy higher than the relevant singlet ( 1 A ′ 2 ). However, there is another pair of states, 3 E ′ and 1 E ′ , whose energy is not too far. In particular, in the case of 2T-7N, the two triplets 3 A ′ 2 and 3 E ′ invert their energies. In this situation, while the relative energy of the two MR state would still give a negative ST gap, the presence of another non-MR triplet at low energy makes the ST inversion critical.