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Anatase and brookite are robust materials with enhanced photocatalyticproperties. In this study, we used density functional theory (DFT) with ahybrid functional and the Hubbard on-site potential methods to determineelectron and hole polaron geometries for anatase and brookite and theirenergetics. Localized electron and hole polarons were predicted not to form inanatase using DFT with hybrid functionals. In contrast, brookite formed bothelectron and hole polarons. The brookite electron-polaronic solution exhibitscoexisting localized and delocalized states, with hole polarons mainlydispersed on two-coordinated oxygen ions. The Hubbard on-site potential testingover the wide range of 4 eV to 10 eV revealed that brookite polarons are formedat 6 eV, while anatase polarons are formed at 8 eV. The brookite electronpolaron was always localized on a single titanium ion under the Hubbard model,whereas the hole polaron was dispersed over four oxygen atoms, consistent withthe hybrid DFT studies. The anatase electron polarons were dispersed at loweron-site potentials but were more localized at higher potentials. Both methodspredict that brookite has a higher driving force for the formation of polaronsthan anatase.

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