Formulation of atomic positions and carbon–carbon bond length in armchair graphene nanoribbons: an ab initio study

In this paper, we investigate the atomic positions of single layer armchair graphene nanoribbon for two cases, with and without hydrogen-passivate edges, accurately and propose a formula which either removes the need of structural relaxation generally or decreases its time extremely (up to seven times). We also propose a general pattern (hyperbolic) for these positions. On the other hand, we show that edge effect influences several atoms near the edge not just one. These results can be used in software, which compute atomic positions and can increase their efficiency. In addition, we prove that the C–C bond distance depends on dimer number and differs in length and width directions, especially for narrow AGNRs. The maximum value of these differences is about 0.017 A ° .