Potential energy curves (PECs) and energy profiles of atomic O attack on pyrene as a model for graphene/graphitic surface have been computed at the density functional theory level of theory to elucidate the mechanism of O attack and chemisorption to the graphene model. The PECs were obtained by scanning the O atom distance to the nearest carbon atom on "top" and "bridge" positions in pyrene, while the energy profile was obtained from the fully relaxed geometries in triplet states. The possibility of an intersystem crossing from triplet to singlet state will be verified by the multireference wave function theory calculations. We proposed a mechanism of O attack and chemisorption reaction on graphene starting from the non-interacting O and graphene systems into the chemically bound O on graphene