Ab initio calculations on CO₄ centers in silicon dioxide

Abstract

Ab initio SCF-MO Hartree-Fock calculations were performed using the STO-3G, 6-31G, and 6-31G* basis sets to model hypothetical substitutional carbon impurities in silicon dioxide. We utilized nine-atom clusters, [C(OH),]qt, with charge number qt = 0 and + 1. The positions of the C and 0 atoms were varied to achieve minimum total energies, while the fured protons served to simulate the rigid crystal surroundings. In the optimized configuration of the neutral cluster, the C-0 bond lengths are appreciably longer than typical C-0 bonds, indicating relatively weak bonds for a carbon impurity at a sipcon site. For comparison, the relative positions of all nine atoms in the [C(OH),]O model were allowed to vary. This unconstrained model yielded more normal bond lengths and was lower in energy than the fured-proton model by 6.80 eV with the 6-31G* basis set. The free-H model compared favorably with the x-ray diffraction data for an analogous orthocarbonate. Our results are in concert with the lack of reports of any substitutional carbon impurity in a-quartz. In the fured-H models, the twofold local symmetry was found to be retained when qt is 0 but not when qt is + 1. For the latter ion, the unrestricted H-F calculations indicate that this paramagnetic center has its spin population almost entirely on one oxygen ion and is high in energy (5.31 eV with 631G) compared to the diamagnetic neutral one. Conclusions reached with the nine-atom clusters were confirmed by a series of calculations on the extended model [C(0SiH3)Jo.