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Understanding native point defects is fundamental in order to comprehend theproperties of TiO$_2$ anatase in technological applications. Severalfirst-principles studies have been performed in order to investigate the defectchemistry of this material. The reported values are, however, scattered over awide range. In this manuscript we perform a comparative study employingdifferent approaches based on semilocal, DFT+$U$ and screened hybridfunctionals in order to investigate the dependence of defect properties, suchas formation energies and charge transition levels, on the employedcomputational method. While the defects in anatase, like in mosttransition-metal oxides, generally induce the localization of electrons orholes on atomic sites, we notice that, provided an alignment of the valencebands has been performed, the calculated defect formation energies andtransition levels using semi-local functionals are in a fair agreement withthose obtained using hybrid functionals. A similar conclusion can be reachedfor the thermochemistry of the Ti-O system and the limit values of theelemental chemical potentials. We interpret this as a cancellation of errorbetween the self-interaction error and the overbinding of the O$_2$ molecule insemi-local functionals. Inclusion of a $U$ term in the electron Hamiltonianoffers a convenient way for obtaining more precise geometric and electronicconfigurations of the defective systems.

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