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The energy gap of graphene nanoflakes is important for their potential application in nano-devices; however, it is still a challenge to perform a systemic search of systems with large gaps due to the presence of numerous candidates. Herein, we showed an ideal feasible approach that involved structural recognition, simplified effective evaluation, and successive optimization strategy. Considering the local bonding environment of carbon atoms, we first proposed a tight-binding model with the parameters fitted from the first-principles calculations of possible GNFs; this model provided an ideal avenue to screen the candidates with high accuracy and efficiency. Via combining the Monte Carlo tree search method and the congruence check, we determined the correlation between structures and the gap distributions according to the carbon numbers, and the results were confirmed via the first-principles calculations. The structural stabilities of the candidates with different numbers of hydrogen atoms might be modulated by the chemical potential of hydrogen, whereas the candidates with larger gaps might be more stable for the isomers with the same number of C and H atoms. Note that the gap variation is dominated by the structural features despite the quantum confinement effect since the gap maximum fluctuates rather than gradually decreasing with the increase in size. Our finding shows the gap variety of GNFs due to the configuration diversity, which may help explore the potential application of GNFs in nano-devices and fluorescence labeling in biomedicine.

Gap maximum of graphene nanoflakes: a first-principles study combined with the Monte Carlo tree search method