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We use the first principle calculation to investigate the intrinsic magnetism of graphitic carbon nitrides (GCNs). By preserving three-fold symmetry, the GCN building blocks have been built out of different combinations between 6 components which are C atom, N atom, s-triazine, heptazine, heptazine with C atom at the center, and benzimidazole-like component. That results in 20 phases where 11 phases have been previously reported, and 9 phases are newly derived. The partial density of states and charge density have been analyzed through 20 phases to understand the origin of the presence and absence of intrinsic magnetism in GCNs. The intrinsic magnetism will be present not only because the GCNs comprising of radical components but also the    $$\pi$$  π -conjugated states are not the valence maximum to break the delocalization of unpaired electrons. The building blocks are also employed to study alloys between g-   $$\hbox {C}_3\hbox {N}_4$$  C 3 N 4 and g-   $$\hbox {C}_4\hbox {N}_3$$  C 4 N 3 . The magnetization of the alloys has been found to be linearly dependent on a number of C atoms in the unit cell and some magnetic alloys are energetically favorable. Moreover, the intrinsic magnetism in GCNs can be promoted or demoted by passivating with a H atom depending on the passivated positions.

Presence and absence of intrinsic magnetism in graphitic carbon nitrides designed through C–N–H building blocks