By employing first-principles calculations within the framework of density functional theory, we investigated the structural, electronic, and magnetic properties of graphene and various two-dimensional carbon-nitride (2DNC) nanosheets. The different 2DCN gives rise to diverse electronic properties such as metals (C3N2), semimetals (C4N and C9N4), half-metals (C4N3), ferromagnetic-metals (C9N7), semiconductors (C2N, C3N, C3N4, C6N6, and C6N8), spin-glass semiconductors (C10N9 and C14N12), and insulators (C2N2). Furthermore, the effects of adsorption and substitution of hydrogen atoms as well as N-vacancy defects on the electronic and magnetic properties are systematically studied. The introduction of point defects, including N vacancies, interstitial H impurity into graphene and different 2DCN crystals, results in very different band structures. Defect engineering leads to the discovery of potentially exotic properties that make 2DCN interesting for future investigations and emerging technological applications with precisely tailored properties. These properties can be useful for applications in various fields such as catalysis, energy storage, nanoelectronic devices, spintronics, optoelectronics, and nanosensors.

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