Ab initio Hartree-Fock study of structural and electronic properties of β-${\mathrm{Si}}_3$${\mathrm{N}}_4$ and β-${\mathrm{C}}_3$${\mathrm{N}}_4$ compounds

Structural and electronic properties of β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$ and β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$ compounds are studied using the ab initio Hartree-Fock method. The crystalline orbital program c r y s t a l-92 has been used to evaluate the equilibrium binding energy, lattice parameters bulk modulus, band structure, density of states, and charge-density data of these materials. The calculated structural properties show good agreement with previous density functional calculations and with available experimental information. As expected, the Hartree-Fock cohesive energy is underestimated with respect to the values obtained with other methods that include electron correlation. On the other hand, the band energy gaps are overestimated. The calculated value of the bulk modulus for β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$ of 4.50 Mbar is slightly smaller than the value of 4.66 Mbar obtained for diamond with the same method. The charge-density analysis shows a small amount of charge transference between carbon and nitrogen indicating the prevalence of a covalent bond in β-${\mathrm{C}}_3$ ${\mathrm{N}}_4$. A mixture of ionic and covalent behavior was found from the charge distribution of β-${\mathrm{Si}}_3$ ${\mathrm{N}}_4$. The charge-density maps and a Mulliken population analysis emphasize the existence of two nitrogen sites with different bonding properties, for the two compounds studied.