Electronic Structure of Oxygen Dangling Bond in Glassy ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$: The Role of Hyperconjugation

The electronic structure and the nature of optical transitions in oxygen dangling bond in silica glass, the nonbridging oxygen hole center (NBOHC), were calculated. The calculation reproduced well the peak positions and oscillator strengths of the well-known optical absorption bands at 2.0 and 4.8 eV, and of the recently discovered absorption band at 6.8 eV. The 2.0 eV band was attributed to transition from the $\sigma$ bond between Si and dangling oxygen to nonbonding $\pi$ orbital on the dangling oxygen. The uniquely small electron-phonon coupling associated with the 2.0 eV transition is explained by stabilization of Si-O bond in the excited state by hyperconjugation effects.

Figure 1

Orbitals related to the optical transitions in dangling oxygen bond (NBOHC) in ${\mathrm{S}\mathrm{i}\mathrm{O}}_2$ glass. Sticks show Si-O $\sigma$ bonds. For cluster calculations, three or four dangling oxygen bonds were saturated with hydrogen atoms. Lone-pair electrons on the other two oxygens are omitted for simplicity.

Figure 2

Energy level diagrams of $(\mathrm{O}\mathrm{H}{)}_4\mathrm{S}\mathrm{i}$ cluster (a) and the NBOHC cluster $(\mathrm{O}\mathrm{H}{)}_3\mathrm{S}\mathrm{i}\mathrm{\text{−}}\mathrm{O}·$ (b), showing the assignment of the observed optical absorption bands of NBOHC. Multiply degenerated levels are described as box-shape symbols for simplicity. The highest occupied MO in (b) is $n({\mathrm{O}}_{nb}{)}_y$, which is the singly occupied level.

Figure 3

Illustration of delocalization of O $2p$ lone-pair orbital due to hyperconjugation when O atom bonds to $·\mathrm{S}\mathrm{i}\mathrm{\text{−}}{\mathrm{O}}_3$ cluster. (a) Scheme of hyperconjugation in the $\mathrm{O}+\mathrm{S}\mathrm{i}\mathrm{\text{−}}(\mathrm{O}\mathrm{H}{)}_3$ cluster by transferring electronic density from oxygen $2p$ lone-pair to $e$-symmetry combination of $\mathrm{S}\mathrm{i}\mathrm{\text{−}}{\mathrm{O}}_b$ antibonding $\sigma$ orbitals. (b) calculated changes of orbital amplitudes due to hyperconjugative interaction between the filled oxygen $2p$ orbital (i) and $e$-symmetry type combination of $\mathrm{S}\mathrm{i}\mathrm{\text{−}}{\mathrm{O}}_b$ empty ${\sigma }^{*}$ antibonding orbitals (ii) which occur on bonding of O to ${\mathrm{S}\mathrm{i}\mathrm{O}}_3$ fragment to form NBOHC. The resulting bonding configuration (iii) shows transfer of electronic density from oxygen $2p$ closer to the Si atom in the center of the cluster.