Theoretical description of hole localization in a quartz Al center: The importance of exact electron exchange

The “classical” model of the ${[\mathrm{AlO}}_4{]}^0$ defect center in irradiated quartz, an Al impurity having replaced a four-coordinated Si atom, is that a hole forms in a nonbonding orbital of an oxygen atom, with consequent asymmetric relaxation along that particular Al-O direction. This model has been proposed years ago, based on the analysis of the electron-paramagnetic-resonance spectra of Al-containing crystalline ${\mathrm{SiO}}_2$ and analysis of Hartree-Fock cluster model calculations. Three recent theoretical studies based on first-principle density-functional theory (DFT) and band-structure plane-wave calculations proposed an alternative model where the hole is completely delocalized over four oxygen neighbors to the Al impurity, at 0 K. Using cluster models containing as many as 104 Si and O atoms and various theoretical approaches, we show that the delocalized picture is an artifact of the DFT approach and that a fully localized hole is obtained when an exact treatment of the exchange term is used. The validity of this conclusion is based on the direct comparison of computed and measured quantities such as the ${}^{17}\mathrm{O}$ hyperfine and ${}^{27}\mathrm{Al},$ ${}^{29}\mathrm{Si}$ superhyperfine coupling parameters, the ${}^{27}\mathrm{Al}$ nuclear quadrupole effect, and the derivable local distortion around the defect. This work shows that great care is needed when DFT is used to describe localized holes in insulators.