Investigating Polaron Formation in Anatase and Brookite TiO₂ by Density Functional Theory with Hybrid-Functional and DFT + U Methods

Abstract

Anatase and brookite are robust materials with enhanced photocatalytic properties. In this study, we used density functional theory (DFT) with a hybrid functional and the Hubbard on-site potential methods to determine electron- and hole-polaron geometries for anatase and brookite and their energetics. Localized electron and hole polarons were predicted not to form in anatase using DFT with hybrid functionals. In contrast, brookite formed both electron and hole polarons. The brookite electron-polaronic solution exhibits coexisting localized and delocalized states, with hole polarons mainly dispersed on two-coordinated oxygen ions. Hubbard on-site potential testing over the wide 4.0-10 eV range revealed that brookite polarons are formed at U = 6 eV, while anatase polarons are formed at U = 8 eV. The brookite electron polaron was always localized on a single titanium ion under the Hubbard model, whereas the hole polaron was dispersed over four oxygen atoms, consistent with the hybrid DFT studies. The anatase electron polarons were dispersed at lower on-site potentials but were more localized at higher potentials. Both methods predict that brookite has a higher driving force for the formation of polarons than anatase.