Magic numbers of graphene multivacancies

The stabilities and atomic geometries of graphene multivacancies are studied using a first-principles calculation. We find that the atomic relaxation allows the system to have pentagons in vacancies and that this pentagon formation stabilizes the defects considerably. It is concluded that the magic numbers of the multivacancies are 2, 4, and 6. This result differs from that predicted using the conventional dangling bond counting model, which does not include any effect of lattice relaxation. An extended model, which is additionally parametrized by the number of pentagons, is constructed.