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We investigate the long-standing problem of the hole localization at the Alimpurity in quartz SiO$_2$, using a relatively recent DFT hybrid-functionalmethod in which the exchange fraction is obtained \emph{ab initio}, based on ananalogy with the static many-body COHSEX approximation to the electronself-energy. As the amount of the admixed exact exchange in hybrid functionalshas been shown to be determinant for properly capturing the hole localization,this problem constitutes a prototypical benchmark for the accuracy of themethod, allowing one to assess to what extent self-interaction effects areavoided. We obtain good results in terms of description of the chargelocalization and structural distortion around the Al center, improving withrespect to the more popular B3LYP hybrid-functional approach. We also discussthe accuracy of computed hyperfine parameters, by comparison with previouscalculations based on other self-interaction-free methods, as well asexperimental values. We discuss and rationalize the limitations of our approachin computing defect-related excitation energies in low-dielectric-constantinsulators.

Communication: Hole localization in Al-doped quartz SiO2 within ab initio hybrid-functional DFT