Molecular-dynamics simulations using a recently proposed two-body potential were employed to study the structure of amorphous ${\mathrm{SiO}}_{2}$ at ambient pressure and the densification that occurs at high pressure. The structures obtained at ambient conditions are in good agreement with experiment. The oxygen coordination number about silicon atoms in the network increases from 4 to about 5 in the material taken to 15 GPa and reaches 6 at high pressures. A densification with a volume reduction of about 20% was calculated for samples subjected to pressures of 15 GPa and higher and then recovered at 1 bar. The transformation is primarily driven by the increased stability of the higher Si-O coordination at high pressures. The oxygen coordination number of amorphous ${\mathrm{SiO}}_{2}$ is calculated to be about 4.2--4.4 for samples recovered from 15--20 GPa. The calculations suggest that a new crystalline phase is formed at about 100 GPa.