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The surface and edge chemistry are vital points to assess a specific application of graphene and other carbon nanomaterials. Based on first-principles density functional theory, we investigate twenty-four chemical functional groups containing oxygen and nitrogen atoms anchored to the edges of armchair graphene nanoribbons (AGNRs). Results for the band structures, formation energy, band gaps, electronic charge deficit, oxidation energy, reduction energy, and global hydrophilicity index are analyzed. Among the oxygen functional groups, c