We have examined the potential energy hypersurfaces for the carbon-rich phases of carbon nitride, CN and ${\text{C}}_3\text{N}$, and discovered low-energy structures different from those reported previously. Trends in the preferred local bonding environments have been analyzed as a function of nitrogen content. For each composition, several structures with similar energies were found, but they have very different equilibrium volumes; the structure produced during synthesis will strongly depend on the preparation conditions. When low densities are favored, conjugated planar-ring structures with $s{p}^2$ hybridized carbon are most likely to be formed. These structures are similar to those suggested as potential photocatalytic materials. At high pressures, the preferred structures contain three-coordinate nitrogen and $s{p}^3$ hybridized carbon, including the $\beta \text{-InS}$ structure, which we predict to be the thermodynamically preferred structure for CN under positive hydrostatic pressures. This structure has a moderately high bulk modulus with a lower formation energy than $\beta {\text{-C}}_3{\text{N}}_4$ and so should be more easily synthesized.

• Received 28 July 2009

DOI:https://doi.org/10.1103/PhysRevB.80.174111