Having obtained a localized polaron at the HF level, we next investigate whether that localization persists with DFT. Starting from the HF-optimized structure of [Ti 21 O 70 H 56 ] -, we re-optimized the geometry using either PBE or PBE0 and monitored s(Ti * ) as a proxy for polaron localization. Results are plotted in Fig. . Bond-length analysis along the PBE0 optimization pathway (Fig. ) suggests a localized polaron, and a plot of s(Ti * ) along the same pathway (Fig. ) demonstrates that the extra electron indeed remains localized on Ti * . In contrast, if s(Ti * ) is computed instead using the PBE functional (along the same PBE0 optimization trajectory), the polaron seems stable but a significant fraction of the spin density is transferred onto other atoms, resulting in s(Ti * ) < 0.6.