▎ 摘　　要

Vacancies in graphene have been proposed to give rise to pi-like magnetism in carbon materials, a conjecture which has been supported by recent experimental evidence. A key element in this "vacancy magnetism" is the formation of magnetic moments in vacancy-induced electronic states. In this work we compute the charging energy U of a single-vacancy-generated localized state for bulk graphene and graphene ribbons. We use a tight-binding model to calculate the dependency of the charging energy U on the amplitudes of the localized wave function on the graphene lattice sites. We show that for bulk graphene U scales with the system size L as (ln L)(-2), confirming the predictions in the literature, based on heuristic arguments. In contrast, we find that for realistic system sizes U is of the order of eV, a value that is orders of magnitude higher than the previously reported estimates. Finally, when edges are considered, we show that U is very sensitive to the vacancy position with respect to the graphene flake boundaries. In the case of armchair nanoribbons, we find a strong enhancement of U in certain vacancy positions as compared to the value for vacancies in bulk graphene.