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Diffusion Monte Carlo (DMC) calculations were performed for an accuratedescription of the nature of the O$_2$ adsorption on a single layer graphene.We investigated the stable orientation of O$_2$ at a specific adsorption siteas well as its equilibrium adsorption energy. At equilibrium adsorptiondistances, an O$_2$ molecule was found to prefer a horizontal orientation,where the O-O bond is parallel to the graphene surface, to the verticalorientation. However, the vertical orientation is favored at the O$_2$-graphenedistances shorter than the equilibrium distance, which could be understood bythe steric repulsion between O and C atoms. Contrary to previous DFTcalculations, our DMC calculations show that the midpoint of a C-C bond (abridge site) is energetically preferred for the O$_2$ adsorption to a center ofa hexagonal ring (a hollow site). The lowest DMC adsorption energy was found atan intermediate point between a hollow and a bridge site, where the O$_2$adsorption energy was estimated to be -0.142(4) eV that was in very goodagreement with the recently-reported experimental value. Finally, we have foundthat O$_2$ is very diffusive on the surface of graphene with the diffusionbarrier along a bridge-hollow-bridge path being as small as ~ 11 meV.

Diffusion Monte Carlo Study of the O$_2$ Adsorption on a Single Layer Graphene