Many studies have been reported about the catalytic recombination of oxygen and nitrogen on silicon dioxide surface, which is quite important for the reentry of a space vehicle. But, the reaction mechanism is not fully understood. Hence, in this study, we are constructing a catalytic reaction model using the ab initio calculations and the Monte Carlo calculations in order to reveal the reaction mechanism. Here, the adsorption and desorption of O and N atoms were investigated on the α-quartz (0001) surface ended with Si atoms using density functional theory and standard transition state theory. The adsorption energy of 7.55eV for O and 5.29eV for N were obtained, and large impact of the surface coverage ratio on the adsorption process was confirmed.