Near-edge x-ray-absorption fine structure of crystalline silicon dioxides

We present the results of first-principles molecular-orbital calculations of three forms of silicon dioxides, i.e., α-quartz, α-cristobalite, and β-cristobalite. The discrete variational (DV)-Xα method is employed on model clusters of (${\mathrm{Si}}_5$ ${\mathrm{O}}_{16}$ ${)}^{12\mathrm{-}}$ using minimal basis set. The Si-K, ${\mathit{L}}_{23}$, and O-K x-ray emission spectra (XES) and near-edge x-ray-absorption fine structures (NEXAFS) are compared with the calculated partial density of states (PDOS) following the electric dipole selection rule. We find that our PDOS at the ground state agrees well with fine structures of the experimental NEXAFS in the range of ≤30 eV as well as the XES. It means that the emission effects associated with the electronic transitions do not change the spectral shapes remarkably from those of the PDOS in these compounds. Assignments of all subband features are, therefore, successfuly made without taking these effects into account explicitly. Conduction band ≤30 eV from the edge can be decomposed into 12 subbands that are generated by bonding, antibonding, and nonbonding interactions of ${\mathit{a}}_1$, e, and two kinds of ${\mathit{t}}_2$ molecular orbitals in the individual (${\mathrm{SiO}}_4$ ${)}^{4\mathrm{-}}$ tetrahedron under ${\mathit{T}}_{\mathit{d}}$ symmetry. The difference in the manner of (${\mathrm{SiO}}_4$ ${)}^{4\mathrm{-}}$ tetrahedral linkage among ${\mathrm{SiO}}_2$ polymorphs is shown most clearly in the Si-${\mathit{L}}_{23}$ NEXAFS.