Do Small Hole Polarons Form in Bulk Rutile TiO₂?

Hole transport and localization through small polarons are essential to the performance of TiO₂ in photocatalysis applications. The existence of small hole polarons in bulk rutile TiO₂ has been, however, controversial with contradicting evidence from theory and experiments. Here, we use first-principles computations and more specifically a Koopmans' compliant hybrid functional and charge correction to study small hole polarons in bulk rutile. We find that a fraction of exchange exists, satisfying Koopmans' compliance for the polaron state and reproducing the band gap provided that charge correction is used. We clearly show that first-principles computations indicate that the small hole polaron is only slightly stable, with a formation energy tens of millielectronvolts below that of the delocalized state in bulk for rutile and more stable for anatase TiO₂.