Spin charges computed at the PBE0 level along the HF optimization trajectory (Fig. ) also correspond to a localized defect. In contrast, the PBE functional partially delocalizes the polaron even when HF structures are used, with s(Ti * ) < 0.6 at the HF-optimized geometry as compared to HF and PBE0 values s(Ti * ) ≈ 1. This is the same behavior that was observed for Al-doped silica. In the HF-optimized structure of [Ti 21 O 70 H 56 ] -, all of the Ti * -O bonds are longer than their values in the neutral structure but two of them exhibit significantly greater elongation, corresponding to an electron-polaron that localizes on two Ti-O bonds (Fig. ).