▎ 摘　　要

Energy gap engineering in graphene nanostructures is one of the most important topics towards development of graphene-based electronics. In this work, based on the density functional theory, the role of the edge magnetism on the size dependence of Kohn-Sham gap and fundamental energy gap for C6nnH6n (n = 2 - 16) hexagonal graphene quantum dots (GQDs) with zigzag edges is studied. We found a transition from a nonmagnetic to an antiferromagnetic state at a certain critical diameter (similar to 3 nm), characterized by the opening of a Kohn-Sham gap as a consequence of the exchange interaction between localized edge states. Furthermore, the fundamental gap is obtained from the difference between the calculated vertical ionization and electron affinity energies. Such approximation includes relaxation in the exchange correlation potential when the electron is added to the system, which might be useful for GQDs transport properties interpretation. We found a scaling rule for the fundamental gap dependence on quantum dot size, providing a practical way to predict this property for large GQDs with zigzag edges, which currently in most demanding approaches, such as GW, is unfeasible. (C) 2019 Elsevier Ltd. All rights reserved.