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Calculations of formation energies and charge transition levels of defectsroutinely rely on density functional theory (DFT) for describing the electronicstructure. Since bulk band gaps of semiconductors and insulators are not welldescribed in semilocal approximations to DFT, band-gap correction schemes oradvanced theoretical models which properly describe band gaps need to beemployed. However, it has become apparent that different methods that reproducethe experimental band gap can yield substantially different results regardingcharge transition levels of point defects. We investigate this problem in thecase of the (+2/0) charge transition level of the O vacancy in ZnO, which hasattracted considerable attention as a benchmark case. For this purpose, wefirst perform calculations based on non-screened hybrid density functionals,and then compare our results with those of other methods. While our resultsagree very well with those obtained with screened hybrid functionals, they arestrikingly different compared to those obtained with other band-gap correctedschemes. Nevertheless, we show that all the different methods agree well witheach other and with our calculations when a suitable alignment procedure isadopted. The proposed procedure consists in aligning the electron bandstructure through an external potential, such as the vacuum level. When theelectron densities are well reproduced, this procedure is equivalent to analignment through the average electrostatic potential in a calculation subjectto periodic boundary conditions. We stress that, in order to give accuratedefect levels, a theoretical scheme is required to yield not only band gaps inagreement with experiment, but also band edges correctly positioned withrespect to such a reference potential.

Band-edge problem in the theoretical determination of defect energy levels: the O vacancy in ZnO as a benchmark case