Graphene based quantum dots and antidots are two nanostructures of primary importance for their fundamental physics and technological applications, particularly in the emerging field of graphene-based nanoelectronics and nanospintronics. Herein, based on first principles density functional theory calculations, we report a comparative study on the electronic structure of these two structurally complementary entities, where the bandgap opening, edge magnetism and the role of hydrogenation are investigated. Our results show the diversity of electronic structures of various dots and antidots, whose properties are sensitive to the edge detailed geometry (including size and shape and edge type). Hydrogen passivation plays an essential roal in affecting the related properties, in particular, it leads to larger bandgap values and suppress the edge magnetism. The frontier orbital analysis is employed to rationalize and compare the complicated nature of dots and antidots. Based on the specific geometrical consideration and the total energy competition of the ground antiferromagnetic and the ferromagnetic states, some magnetic structures (the unpassivated 42-atom-antidot and 54-atom-dot) are proposed to be useful as magnetic switches.
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