The quantitative search for the ground state energies, the ground state structures, and the related mechanical and dynamical properties requires accurate calculations, which have been performed within VASP (Vienna Ab initio Simulation Package (VASP) based on the DFT . The atomic potentials with all valence states (especially, with respect to such light elements as boron and carbon) were considered using the projector augmented wave (PAW) method . DFT exchange-correlation effects were considered within a generalized gradient functional (GGA) according to Perdew, Burke and Ernzerhof . The relaxation of the atoms to the ground state structures was performed with conjugate-gradient algorithm according to Press et al. . The Blöchl tetrahedron method with corrections according to the Methfessel and Paxton scheme was used for geometry optimization and energy calculations, respectively. Brillouin-zone (BZ) integrals were approximated using a special k-point sampling according to Monkhorst and Pack . The structural parameters were optimized until the forces on the atoms were below 0.02 eV/Å, and all stress components were below 0.003 eV/Å 3 . The calculations were converged at an energy cut-off of 400 eV for the plane-wave basis set regarding the k-point integration in the reciprocal space from k x (6)×k y (6)×k z (6) up to k x ×k y ×k z for the final convergence and relaxation to zero strains. In the post-treatment process of the ground state electronic structures, the charge density projections were operated onto the carbon atomic sites. The elastic constants C ij and the phonon band structures were calculated to evaluate the mechanical and dynamic stabilities. The electronic band structures were obtained using the all-electrons DFT-based ASW method and the exchange correlation GGA functional .