From this point onward a myriad of population analysis may be used, but a comparison among them goes beyond the scope of this study. Therefore, we will discuss how the multi-d -occupancy character can be identified in the Mulliken population analysis. Despite of the many limitations and caveats associated to this measurement, its cheapness, simplicity and wide implementation among quantum chemistry codes make any possible application, even if semi-quantitative, valuable for large systems. Figure shows how the Mulliken d population varies with the w and m weights for the S 2+ and S + ground states, at the CASCI level of theory using the PFRS approach. Starting with the latter, as previously discussed, the wave function has a pure d 10 -occupancy character independently of the orbitals. However, the Mulliken population values falls-down to 9.65, that way, the value per se is not quantitatively reliable. On the other hand, we can trace a qualitative dependence between these values and the weights: the increase of the weight w leads to a reduction of the d pop , as shown by any of the full lines; and when the weight m increases, d pop also increases, as shown by the any vertical set of points. As a consequence, when these opposite effects are applied at the same time, as for m = w (filled points), the d pop variation is relatively small and between 10.0 and 9.9, in line with the previous discussion for this state.