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A comparative first-principles investigation on the defect chemistry of TiO$_2$ anatase

Understanding native point defects is fundamental in order to comprehend the properties of TiO$_2$ anatase in technological applications. Several first-principles studies have been performed in order to investigate the defect chemistry of this material. The reported values are, however, scattered over a wide range. In this manuscript we perform a comparative study employing different approaches based on semilocal, DFT+$U$ and screened hybrid functionals in order to investigate the dependence of defect properties, such as formation energies and charge transition levels, on the employed computational method. While the defects in anatase, like in most transition-metal oxides, generally induce the localization of electrons or holes on atomic sites, we notice that, provided an alignment of the valence bands has been performed, the calculated defect formation energies and transition levels using semi-local functionals are in a fair agreement with those obtained using hybrid functionals. A similar conclusion can be reached for the thermochemistry of the Ti-O system and the limit values of the elemental chemical potentials. We interpret this as a cancellation of error between the self-interaction error and the overbinding of the O$_2$ molecule in semi-local functionals. Inclusion of a $U$ term in the electron Hamiltonian offers a convenient way for obtaining more precise geometric and electronic configurations of the defective systems.