Ab initio calculations on CO4 centers in silicon dioxide

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)₄]^qt, with charge number q_t = 0 and + 1. The positions of the C and O atoms were varied to achieve minimum total energies, while the fixed protons served to simulate the rigid crystal surroundings. In the optimized configuration of the neutral cluster, the C? O bond lengths are appreciably longer than typical C? O bonds, indicating relatively weak bonds for a carbon impurity at a silicon site. For comparison, the relative positions of all nine atoms in the [C(OH)₄]⁰ model were allowed to vary. This unconstrained model yielded more normal bond lengths and was lower in energy than the fixed-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 α-quartz. In the fixed-H models, the twofold local symmetry was found to be retained when q_t is 0 but not when q_t 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 6-31G) 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(OSiH₃)₄]⁰.