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A first-principles study was applied to research the oxygen reduction reaction(ORR)and oxygen evolution reaction(OER)activities of nanocarbon materials with different nitrogen-doping and topological defects.Pyridine nitrogen,pyrrolic nitrogen,quaternary nitrogen on the edge or in the bulk phase,pentagon and heptagon carbon rings defects were considerated systematically.A nitrogen-free configuration with adjacent pentagon and heptagon carbon rings is revealed to exhibit the lowest overpotential for both ORR and OER,which indicating topological defects of nanocarbon materials as the active site for ORR/OER for the first time.Three kinds of bifunctional graphene catalysts with controllable nitrogen doping and topological defects were achieved experimentally and the actual ORR/OER activities agreed with theoretical results pretty well.The novel insights on the activity originate and versatile synthetic strategy facilitate the development of advanced metal-free carbocatalysts for a wide range of electrocatalytic applications.