Electronic structure ofE1′centers in SiO2

A linear combination of localized orbitals-molecular orbital (LCLO-MO) cluster method is applied to calculate the electronic structure of ${E_1}^{\prime }$ centers in the $\alpha$-quartz structure of Si${\mathrm{O}}_2$. An ${\mathrm{O}}^{-}$ vacancy model, implying a net charge of $\mathrm{}\left|e\right|\mathrm{}$, is used. This corresponds to the $F^{+}$ center in simpler oxides. Calculations on the intrinsic ${E_1}^{\prime }$ center predict a highly asymmetric relaxation of the two silicons adjacent to the ${\mathrm{O}}^{-}$ vacancy. Detailed calculations of hyperfine parameters are carried out, and reasonable agreement with experiment is obtained. The asymmetric relaxation of the two silicons is an example of a pseudo-Jahn-Teller effect; parameters associated with this description are obtained and appear to be reasonable. Calculations on the extrinsic ${E_1}^{\prime }$ (Ge) center in Si${\mathrm{O}}_2$ also give satisfactory results.