The spin gap, ∆E = E( 5 A 1g )-E( 3 E g ), predicted by our large Stochastic-GAS approach, is 6.8 kcal mol -1 , a value that is considerably larger than any result previously reported. The Stochastic-GAS spin gap is reported in Table together with the results obtained with other methods on the same model system. Computational details related to the Fe(II)-porphyrin applications can be found in the supporting information. The spin gap increases from 3.5 kcal mol -1 to 6.8 kcal mol -1 , in going from CASSCF (32, 34) to the large Stochastic-RASCI calculations. The more than doubled spin gap prediction clearly shows the importance of dynamic correction effects on top of an already large active space, that describes most of the valence correlation mechanisms. This unprecedented result should also be compared to the CASSCF(14, 16)/CASPT2 approach used earlier. While the CASPT2 also aims at recovering dynamic correlation outside the active space, the chosen active space was too small, and important high-order excitations effects (such as the correlation induced π-backdonation discussed in Reference 16,18) were missed by the second order perturbative correction. It is also important to emphasize that our approach can be further systematically improved by increasing the excitation level from RAS1 and to RAS3, a study that goes beyond the scope of the present work.