▎ 摘　　要

Complete configurations of monolayer graphene with zigzag-edged hexagonal nanohole are systematically built using three indices. The three integers lead to an atomistic precisely gap opening criteria, which steered via density functional theory based calculations. The guiding rule reveals that the semimetallic and semiconducting variation is consistent with a peculiar sequence with a period of 3 for odd and even indices differently. According to the cyclic sequence, there are one-third nanoporous graphene in our framework open a gap. The physical correspondence of Dirac point matching in reciprocal space and charge distribution in real space for the gap opening/closing is revealed. The periodic nano-perforation induced gap sizes were fitted as functions of three key indices. Furthermore, the coexistence of Dirac and flat bands is observed for some unique structures, which is sensitive to the atomic patterns. Our results indicate that the energy gap tunability of nano-perforated graphene can be used for flexible optoelectronic, photocatalytic and electrochemical applications. In particular, the atomically-thin electrically-connected geometry of nanoporous graphene suggests potential application in functional conductive coatings. The clear advantage of our system is in the combination of two properties: the possibility of applying electric voltage to the perforated sheet and rich chemically active atomic sites. (C) 2017 Elsevier Ltd. All rights reserved.