The search for the ground state structures through geometry optimizations and total energies calculations was performed using the plane-wave Vienna Ab initio Simulation Package (VASP) code based on DFT. The projector augmented wave (PAW) method was used for the atomic potentials with all valence states, especially in regard of such light element as carbon. DFT exchange-correlation (XC) effects were considered using the generalized gradient approximation (GGA) . For the relaxation of the atoms onto ground state geometry, a conjugate-gradient algorithm was applied. Improved tetrahedron method with corrections according to Methfessel-Paxton scheme was applied for geometry optimization and energy calculations. A special k-point sampling was applied for approximating the reciprocal space Brillouin-zone (BZ) integrals. For better reliability, the optimization of the structural parameters was carried out along with successive self-consistent cycles with increasing mesh until the forces on atoms were less than 0.02 eV/Å and the stress components below 0.003 eV/Å 3 .