DC-DFT geometry optimizations afford a properly localized hole in these doped silica clusters precisely because the energy and gradient avoid the use of a DFT density. To emphasize this point, Table reports Mulliken "spin charges" (from ρ α -ρ β ) for the oxygen atoms around the Al defect, obtained either from the HF density or else the BLYP density at the optimized geometry of the cluster. (Despite the limitations of the Mulliken procedure, these charges have proven to be an effective way to characterize localization or delocalization of a radical center. ) For the DC-DFT cases in Table , this means that we perform the geometry optimization using ρ HF but then evaluate ρ BLYP at the optimized geometry, for demonstrative purposes. Results based on ρ HF represent the proper DC-DFT procedure.