Embedded cluster ab initio study of the neutral oxygen vacancy in quartz and cristobalite

The oxygen vacancy in silica is characterized theoretically using an ab initio unrestricted Hartree-Fock, embedded-cluster approach. Two models are adopted for the host crystal, alpha-quartz and beta-cristobalite. The defect formation energy, the transition energies from the ground to the first excited singlet and triplet states and the corresponding luminescence are considered. The electronic structure of the defect in the different states is analysed, and it is shown that the excitation corresponds to a transition between a bonding and an anti-bonding combination of the dangling orbitals of the two silicon atoms adjacent to the vacancy. The influence of the size of the cluster and of the basis set adopted are discussed; the latter proves to be more important. Difficulties in the convergence procedure were encountered, especially in the case of the vacancy in quartz, which prevented us from obtaining a complete set of results. However, from a comparison of the two crystal systems and an analysis of the data obtained, it is concluded that the excitation and luminescence energies (approximate to 5.5 and approximate to 3.5 eV to the triplet, and approximate to 8.5 and approximate to 7 eV to the singlet excited states) are compatible with the hypothesis that the oxygen vacancy is a model of the oxygen-deficient centre SiODC(I) in silica. The formation energy of the vacancy is estimated at about 7 eV.