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Density functional theory (DFT) is widely used to study defects in monolayergraphene with a view to applications ranging from water filtration toelectronics to investigation of radiation damage in graphite moderators. Toassess the accuracy of DFT in such applications, we report diffusion quantumMonte Carlo (DMC) calculations of the formation energies of some common andimportant point defects in monolayer graphene: monovacancies, Stone-Walesdefects, and silicon substitutions. We find that standard DFT methodsunderestimate monovacancy formation energies by around 1 eV. The disagreementbetween DFT and DMC is somewhat smaller for Stone-Wales defects and siliconsubstitutions. We examine vibrational contributions to the free energies offormation for these defects, finding that vibrational effects arenon-negligible. Finally, we compare the DMC atomization energies of monolayergraphene, monolayer silicene, and bulk silicon, finding that bulk silicon issignificantly more stable than monolayer silicene by 0.7522(5) eV per atom.

Point defect formation energies in graphene from diffusion quantum Monte Carlo and density functional theory