Migration of hole polarons in anatase and rutile TiO2 through piecewise-linear functionals

We investigate the migration properties of hole polarons in rutile and anatase TiO2 using Hubbard U semilocal and hybrid functionals with parameters set to enforce the piecewise linearity condition. The polarons in anatase and in rutile are found to be stable with both functionals, leading to similar atomic structures, charge densities, and formation energies. To address migration properties, we determine the minimum energy paths for all nonequivalent hopping transitions through a cost-effective scheme of hybrid-functional accuracy, which combines nudged elastic band optimization at the Hubbard U semilocal level with hybrid-functional single-point calculations. For anatase, the migration occurs through hopping transitions preserving the localized nature of the polaron charge density. A kinetic Monte Carlo simulation yields a mobility of 0.04 cm2V-1s-1 at room temperature and indicates that the effective activation energy closely corresponds to the lowest transition barrier. At variance, in rutile, we find that the minimum energy path involves a delocalized intermediate state for all transitions. The low excitation energies calculated in this process suggest that experimental observations for rutile concerning the activated behavior of positive charge carriers should not be associated with polaron states.