Energetics at the MP2 level of theory track the PBE0 results quite closely in both the PBE and the PBE0 opti-mizations. Both the MP2 and the DC-DFT results do inherit jumps in energy when the polaron localizes on a different site, although MP2 substantially mutes this effect as compared to HF theory. These jumps are essentially artifacts of the GGA-driven optimization and are absent when either PBE0 or HSE06 is used to optimize the geometry (Figs. 5b and S9a, respectively). Note also that in the latter two cases, the PBE functional lowers the energy even faster than the hybrid functional that is being used to optimize the geometry! This is an SIE artifact (overstabilization of fractional charges), and PBE predicts a delocalized polaron even at the PBE0-optimized geometry where PBE0 itself localizes the polaron (Fig. ). Overall, the close match between PBE0 and MP2 suggests that the former is a good level of theory for this system, although that fact is only evident in light of the MP2 results.