Do Small Hole Polarons Form in Bulk Rutile TiO?

Hole transport and localization through small polarons are essential to the performance of TiO in photocatalysis applications. The existence of small hole polarons in bulk rutile TiO 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 TiO.