When the optimization is performed instead with PBE, then not only is the PBE polaron significantly delocalized, with s(Ti * ) < 0.2, but also the spin charge com- puted using PBE0 indicates that PBE-driven changes in both lengths cause delocalization at the PBE0 level. The values of s(Ti * ) starts at ≈ 1 when computed with PBE0 but falls to < 0.5 along the PBE optimization pathway, with significant fluctuations in between (Fig. ). When the HF density is evaluated along this PBE optimization trajectory, the Mulliken charges indicate hopping of the polaron between Ti atoms. This behavior likely arises from a combination of HF theory's strong tendency to localize combined with a GGA optimization that is driving elongation of multiple Ti-O bonds. At any given step along the pathway, the HF calculation localizes the polaron on the longest Ti-O bond, but which bond is longest switches several times over the course of the optimization (Fig. ). These observations are significant in view of a standard operating procedure in computational materials science, which is to perform geometry optimizations using GGA functionals (in order to avoid the high cost of hybrid DFT under periodic boundary conditions) but then to use hybrid functionals for single-point calculations at GGAoptimized geometries. Our results demonstrate that PBE optimization drives the system into structures that are severely affected by SIE, with elongated bonds (consistent with a fully delocalized spin defect) from which a PBE0 single-point calculation cannot recover. A PBE0 calculation at the PBE-optimized geometry thus affords a delocalized polaron, and this is a qualitatively different result as compared to what is obtained when PBE0 is used for the optimization. We next evaluate the performance of DC-DFT along the PBE and PBE0 optimization pathways. The PBE pathway is more interesting insofar as a major change in polaron localization is observed in this case, as evident from the spin charges in Fig. . We seek to assess the extent to which this density-driven error is mitigated by DC-DFT. This assessment requires a benchmark that is SIE-free, for which we choose MP2/def2-SVP, as the treatment of dynamical correlation may help to assuage a tendency towards over-localization that is exhibited by the HF method, which is evident from its behavior for fractional-electron systems. 80 MP2 is not always be a good choice for transition metal systems but the closedshell nature of the Ti 4+ ions makes it acceptable here, and MP2 has been used in other (unrelated) work to provide benchmarks for TiO 2 clusters. Figure reports the results of single-point energy calculations along the PBE and PBE0 optimization trajectories. The starting point is a HF-optimized structure, hence the HF energy immediately rises as either a PBE-or PBE0-driven optimization moves the system away from the minimum-energy HF geometry. Notable discontinuities in the HF energy along the PBE pathway (Fig. ) arise when the localized HF polaron jumps between Ti centers, as a result of HF theory's tendency to over-localize unpaired spins, combined with simultaneous structural distortion of numerous Ti-O bonds due to PBE delocalization error. In Fig. , one can observe that the HF polaron is localized on a different Ti atom in the starting and ending structures of the PBE optimization trajectory.