We have performed a first-principles electronic-structure study of a planar structural form of a hypothetical ${\mathrm{C}}_3$${\mathrm{N}}_4$ solid and compared its energy to a fully three-dimensional form. We use a mixed basis of pseudoatomic orbitals and low-kinetic-energy plane waves to determine the single-particle Kohn-Sham wave functions. These results are tested against fully converged plane-wave-basis calculations. We find that the proposed planar form of ${\mathrm{C}}_3$${\mathrm{N}}_4$ (p-${\mathrm{C}}_3$${\mathrm{N}}_4$) is lower in energy than the hexagonal form β-${\mathrm{C}}_3$${\mathrm{N}}_4$. However, the energy difference between the two phases is small. The hexagonal β-${\mathrm{C}}_3$${\mathrm{N}}_4$ phase is insulating, with an indirect gap, while the planar form p-${\mathrm{C}}_3$${\mathrm{N}}_4$ has a semimetallic electronic structure.

• Received 12 September 1994

DOI:https://doi.org/10.1103/PhysRevB.51.2624