Importance of kink energy in calculating the formation energy of a graphene edge

The formation energy of an arbitrary graphene edge or that of other 2D materials has been estimated as a summation of the armchair (AC) and zigzag (ZZ) edge sites. Such an estimation assumes that each site is independent from its neighboring sites, which is unlikely due to the overlap of electron densities. Here, we show that to accurately calculate the formation energy of graphene edges with various functional groups the energy of the junction between AC and ZZ sites, the ``kink energy,'' is essential. It is significant that the kink energies of graphene edges with different functional groups are all negative, namely, kink formation stabilizes the chiral graphene edges.