Vibrational dynamics of defect modes in vitreous silica

Abstract

Ab initio molecular orbital calculations on clusters of atoms consisting of various types of silica rings (3-, 4-, 5-, and/or 6-membered rings) that can be found in vitreous silica are performed at the Hartree-Fock (HF) level. We optimized the geometries of the clusters at the HF/6--31 G $(d)$ level; the average Si-O, O-O, and Si-Si bond distances and Si-O-Si and O-Si-O bond angles calculated for the clusters are in good agreement with the observed ones. The optimized geometries of the 3- and 4-membered rings are rather, although not perfectly, symmetric, whereas those of the 5- and 6-membered rings are considerably distorted. The clusters yield the well-localized breathing modes of the 4- and 3-membered rings, which are found to be quite consistent with the observed frequencies and isotopic shifts of the ${D}_{1}$ and ${D}_{2}$ defect lines, seen at 495 and $606{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1},$ respectively, in the Raman spectra of vitreous silica.