An additional advantage of the proposed step-wise orbitals optimization, the PFRS, is the decrease of computational cost, that comes with the reduction of the number of occupied-activevirtual rotations when performing orbital optimization. This leaded to a reduction of around three times in the calculation time, when our approach is compared to the simultaneous optimization of all orbitals in an usual SA-CASSCF for this system. The actual reduction in time will depend on the number of ligand orbitals and basis set size, but for the present calculations, with our computational resource, the average real time for the usual CASSCF was of 40 hour, while our proposed two-step procedure took 12 hour in average.