Calculations are carried out for silica glass under pressure, using the modified neglect of differential overlap semiempirical electronic structure method. The pressure-volume equation of state exhibits discontinuous changes that coincide with the lowest normal-mode frequency decreasing to zero; these results indicate that mechanical instabilities occur due to the disappearance of local minima on the potential-energy surface. These electronic structure results corroborate previous force field results, and thus strengthen the conclusion that localized mechanical instabilities occur in silica glass under high pressure. The mechanical instabilities lead to localized structural transformations that increase the ion coordination and shift the ring size distribution to smaller ring sizes. The structural transformations proceed by highly cooperative rigid unit modes, in which ${\mathrm{SiO}}_{4}$ tetrahedra rotate and translate with little internal distortion.