Energy gaps of graphene clusters: the first-principles calculations based on high-throughput screening

With the enumeration of the triangular lattice fragments, we have systematically investigated the graphene clusters (CnHm,n=14-24) with various sizes and shapes, whose structural stabilities and electronic properties are studied by the Huckel molecular orbital (HMO) method and the first-principles calculation. According to the formation energies, we show the structural stabilities of the clusters are closely related to the shape and size, as well as the chemical potential of hydrogen. The energy gaps obtained from the HMO method are in the same trend with the ones calculated by the first-principles calculations, indicating the effective screening of the gap minimum and maximum in a fast speed. There is a general decreasing of the energy gaps with the size increment due to the quantum confinement, meanwhile, the gaps are also highly dependent on the shape of the clusters for those with the same number of carbon atom.