Energies of strained silica rings

The energies of strained two-member and three-member rings of SiO₄ tetrahedra are calculated using models based on continuous SiO₂ networks. These rings are considered to form highly reactive ``defect'' centers in vitreous SiO₂ and at its surface. The calculations are based on a generalized gradient approximation to density-functional theory, and give strain energies of 1. 23 and 0. 25 eV for two- and three-member rings, considerably smaller than those previously estimated from Hartree-Fock calculations applied to small hydrogen-terminated molecular models. Structural results are compared with experiment for solids and molecules containing such rings. Changes in bond charge densities due to ring strain are illustrated, and modifications of the electronic states of relaxed SiO₂ networks caused by strained ring defects are discussed.