First-principles investigations of tricarbon: From the isolated C3 molecule to a novel ultra-hard anisotropic solid

Based on crystal chemistry considerations and quantum density functional theory ground state calculations, rhombohedral rh-C3 hexagonal h-C6 carbon allotropes are proposed energetically calculated as new stable ultra-hard phases likewise lonsdaleite. Along the two kinds of in linear C2-C1-C2 lattice, distorted tetrahedra C2(sp3) with an angle 106.17{\deg} (smaller than ideal 109.4{\deg}) C1(sp)-like hybridizations inferred from charge projections. The elastic constants point to a strong anisotropy mechanical properties exceptionally large C33 values (1636 GPa 1610 GPa, respectively), exceeding that lonsdaleite (1380 GPa), due presence aligned tricarbon units along c-axis. Both characterized by bulk moduli high hardness slightly less those diamond. Weak metallic behavior both is identified electronic band structure calculations.