The O/β-quartz interaction is described by combining our time-dependent semiclassical approach to atom-molecule/surface scattering with first-principles electronic structure calculations at the DFT (PBE0) level of accuracy. In particular, the O, O(2) interaction potentials with an on-top Si atom and its nearest O atom both localized over three different silica clusters have been calculated as a function of the oxygen-silica approaching distance. The calculated DFT potential energy surface has been used in semiclassical trajectory calculations to investigate the sticking and inelastic reflection of oxygen atoms from a model β-quartz surface. The collisional mechanism, including the role played by the phonon dynamics, is brought to light and accurate sticking probabilities are calculated at five impact energies in the range [0.05-0.8] eV and T(S) = 1000 K. The different catalytic response of β-quartz and β-cristobobalite to the atomic oxygen flux is also discussed and highlighted.