Electron states inα-quartz: A self-consistent pseudopotential calculation

Self-consistent pseudopotentials are used to investigate the electronic structure of $\alpha$-quartz. We present calculations for the band structure, electronic density of states, optical response functions, pseudocharge densities, and x-ray emission spectra. We find excellent agreement between theory and experiment with respect to photoemission and uv absorption data. The chemical bonding present in $\alpha$-quartz as determined from pseudocharge density contour maps is consistent with other theoretical calculations. The theoretical x-ray emission spectra, as obtained from an orthogonalized-plane-wave scheme, are compared with experimental data. The calculated silicon and oxygen $K$ spectra agree very well with experiment; however, the $\mathrm{Si} L_{2,3}$ spectrum exhibits substantial disagreement with the data. An explanation is proposed based upon the formation of amorphous elemental Si in Si${\mathrm{O}}_2$ during electron irradiation.