Role of Edge Geometry and Magnetic Interaction in Opening Bandgap of Low‐Dimensional Graphene

By using a size‐dependent cohesive energy formula for two‐dimensional coordination materials, the bandgap openings of ideal graphene quantum dots (GQDs) and nanoribbons (GNRs) have been investigated systematically regarding dimension, edge geometry, and magnetic interaction. Results demonstrate that the bandgap openings in GQDs can be dominated by the change of atomic cohesive energy. Relative to zigzag GQDs, the openings in the armchair ones are more substantial, attributed to its edge instability. The change of cohesive energy can also lead to bandgap openings in zigzag and armchair GNRs. The contribution from the interedge magnetic interaction in zigzag GNRs is negligible, while the cohesive‐energy induced openings in armchair GNRs can oscillate according to the so‐called full‐wavelength effect, depending on the width. The model prediction provides physicochemical insight into the bandgap openings in graphene.