Chemical Bonding Effects in the OxygenKαX-Ray Emission Bands of Silica

Abstract

Self-consistent-field (SCF) atomic and molecular orbitals and energy levels for O, SiO, and collinear ${\mathrm{Si}}_2$O are used to interpret the oxygen $K\alpha$ soft-x-ray emission spectrum of silica. The O and ${\mathrm{Si}}_2$O orbitals are calculated in both the frozen-orbital (FO) and relaxed-orbital (RO) approximations. The results are used to calculate the emission-line energies and oscillator strengths for the oxygen $K\alpha$ spectrum of each species. The calculated separation between the $\pi$ and $\sigma$ emission lines of collinear ${\mathrm{Si}}_2$O in both the RO approximation (6.9 eV) and the FO approximation (6 eV) are somewhat larger than the observed separation between the principal emission peak and low-energy satellite in silica (5 eV), but it is shown that the bending of the Si-O-Si bond in silica will reduce the separation. The calculated position of the principal line for ${\mathrm{Si}}_2$O (525.7 eV in the RO approximation) is in good agreement with the principal peak observed in silica (526 eV). The $3p$ and $3s$ atomic orbitals of silicon are found to be strongly modified from their free-atom shape in both SiO and ${\mathrm{Si}}_2$O; enough to make an order-of-magnitude difference between oscillator strengths calculated in the SCF and linear-combination-of-atomic-orbitals approximations. The modifications of the oxygen valence orbitals are relatively small. The oxygen $sp$ hybridization is quite small. The atomic population of the $5\sigma \left(\mathrm{SiO}\right)$ level is 88% $2s\left(\mathrm{O}\right)$, 2% $2p\left(\mathrm{O}\right)$, 4% $3p\left(\mathrm{Si}\right)$ and 5% $3s\left(\mathrm{Si}\right)$. The $d$ hybridization is also small: a maximum of 5% $3d\left(\mathrm{Si}\right)$ in the $2{\pi }_u\left({\mathrm{Si}}_2\mathrm{O}\right)$ level and 1% $3d\left(\mathrm{O}\right)$ in the $2{\pi }_g\left({\mathrm{Si}}_2\mathrm{O}\right)$ level. Crossover transitions in a literal sense are negligible. The $2s\left(\mathrm{O}\right)$ line in the silicon $K\beta$ spectrum of SiO, for example, [the $5\sigma \left(\mathrm{SiO}\right)\to 1\sigma \left(\mathrm{SiO}\right)$ transition], is almost entirely a vertical transition which comes from the small $3p\left(\mathrm{Si}\right)$ admixture. An atomic population analysis gives ionicities of ${\mathrm{Si}}^{+0.78\mathrm{}}$ ${\mathrm{O}}^{-0.78\mathrm{}}$ and

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