The Si surface oxidation by O₂ molecules was studied by the first principles calculations. It was revealed that an O₂ molecule is adiabatically chemisorbed from a spin-triplet to spin-singlet state conversion through a spin-orbit interaction when the O₂ molecule arrives at the Si surface with a low incident energy. The sticking probability of the O₂ molecule is strongly dependent on its incident energy at the early stage of oxidation. The energy barrier for O₂ dissociative chemisorption was found to increase according to the depth from the Si surface. The layer-by-layer oxidation was predicted for the topmost several layers because of this energy barrier increase with the subsurface layers, but it is not well understood for deeper subsurface oxidation by this mechanism. The mechanism for the deeper layer-by-layer oxidation is proposed.