For the Al[OSi(OH) 3 ] 4 complex, Al-O distances are not reported in Table for for the hybrid functionals because in these cases the hole migrates to the surface of the cluster as the geometry is relaxed, ultimately delocalizing over the surface oxygen atoms around the Si centers (Fig. ). Therefore even the hybrid functionals PBE0 and B3LYP qualitatively fail in their description of the hole-polaron in this system, consistent with previous results. In contrast, upon relaxing the structure of each doped silica cluster using DC-DFT, starting from the localized MP2 structure, the localization is preserved in all cases, i.e., for corrected versions of BLYP (Fig. ), B3LYP (Fig. ), PBE, and PBE0. Note that the DC-DFT spin densities in Fig. are the HF densities at the DC-DFToptimized geometry, because plotting DFT spin densities would be inconsistent with the strategy of DC-DFT, which is to avoid introducing SIE by avoiding the DFT density altogether. Consistent with the localized spin densities, bond lengths in Table show that all four DC-DFT methods afford a single elongated Al-O bond, with bond lengths that are within ≤ 0.03 Å of MP2 results, for both the shorter and longer Al-O bonds.