Systematic energetics study of graphene nanoflakes: From armchair and zigzag to rough edges with pronounced protrusions and overcrowded bays

Using the PM3 molecular orbit method, we have determined the cohesive energies of 214 fully relaxed hexagonal graphene nanoflakes with different edge structures. The energies of flakes with deep and ultra-deep bays, and protrusions with trio-carbons (C3H3) and quadro-carbons (C4H4) were determined. The pristine hexagonal zigzag flakes (C24H12, C54H18, C96H24, C150H30, C216H36, C294H42, and C384H48) are found to become more energetically stable with size. Yet, the addition of bays or protrusions reduces their relative stability. Inclusion of shallow armchair bays keeps the planar structure of the flakes intact and leads to small changes in energy. HH fjord overcrowding in deep and ultra-deep bays leads to twisting and bending of the flakes and very strong destabilization. For selected flakes, we also calculated the energies of structural isomers where the relative positions of bays or protrusions are systematically varied. We develop structure–energy relationships (SERs) by comparing tendencies for the energetic variability of the structural isomers.