Model for the $E_2^{\prime }$ Center in Alpha Quartz

A model for the paramagnetic $E_2^{\prime }$ center in alpha quartz is tested by means of semiempirical molecular-orbital calculations. The $E_2^{\prime }$ center is proposed to be a variant of the $E_4^{\prime }$ center (a hydrogen atom substituted for an oxygen atom) with one silicon neighbor relaxed outward, into a "bonded interstitial" position. This silicon is responsible for most of the unpaired spin. The calculations indicate that $E_2^{\prime }$ is slightly more stable than $E_4^{\prime }$, and that there is a large barrier between the two configurations (0.6 eV). Further implications of this model are discussed.