Carbon nitride compounds with 1:1 stoichiometry

We have examined various structures of carbon nitride with 1:1 stoichiometry and determined that for this stoichiometry ${\mathrm{sp}}^2$ bonding of nitrogen is energetically preferable to ${\mathrm{sp}}^3$. We found the zinc-blende and rocksalt phases to be mechanically unstable. They relax to a rhombohedral phase composed of buckled carbon nitride sheets with interplanar covalent bonds. The rhombohedral phase has a bulk modulus of 253 GPa. Two other structures made essentially of ${\mathrm{sp}}^2$ bonds were studied, the H-6 and bct-4 and they have bulk moduli of 345 and 375 GPa, respectively. We also calculate the structure based of the high-pressure phase of GeP and find it to be unfavorable due to its low binding energy. Using the general valence rule, we can state the requirements of a semiconducting or an insulating structure for this compound. Inspired by existing structures, we calculated the phases based on the Β-InS and GaSe compounds. Both these structures contain C-C bonds. We find that the Β-InS phase has a bulk modulus of 78 GPA. The GaSe structure is made of layers where the C-C bond is perpendicular to the plane of the layers. It is the most energetically favorable of all phases considered and it has a bulk modulus of 199 GPa.