On the basis of the density functional theory, we studied the geometries and energetics of O atoms adsorbed on graphene edges for simulating the initial stage of the edge oxidization of graphene. Our calculations showed that oxygen atoms are preferentially adsorbed onto the graphene edges with the zigzag portion, resulting in a large adsorption energy of about 5 eV. On the other hand, the edges with armchair shape are rarely oxidized, or the oxidization causes substantial structural reconstructions, because of the stable covalent bond at the armchair edge with the triple bond nature. Furthermore, the energetics sensitively depends on the edge angles owing to the inhomogeneity of the charge density at the edge atomic sites.

Using the density functional theory, we study the energetics and electronic structures of graphene nanoribbons of which edges are substituted by N atoms. Our calculations showed that the edge N atoms with pyridinic structure mimic the π environment of C atoms, participating the π electron network of C atoms.In contrast, N atoms act as impurities for the π electron network of the nanoribbons when their edges are terminated by H atoms, leading to versatile edge localized state those are hardly synthesized using C and H atoms. The total energy of N-doped nanoribbons is the same as that of the pristine graphene nanoribbons, irrespective to the edge hydrogenation, and gradually decreases with increasing the nanoribbon width.We also found that the edge hydrogenation decrease and increase the stability of the N-doped graphene nanoribbons with armchair and zigzag edges, respectively.