Crystal chemistry and first principles devising of C4 as the simplest dense carbon allotrope

From crystal chemistry rationale and geometry optimization onto ground state structures with DFT-based computations, a novel ultra-hard body centered tetragonal C4 (tet-C4) is proposed as the simplest dense carbon allotrope. tet-C4 is identified as cohesive as diamond, and likewise built of corner sharing C4 tetrahedra in all directions. Qualified as mechanically stable from the elastic constants combinations, tet-C4 has Vickers hardness identical to that of both cubic and hexagonal (lonsdaleite) diamond. Dynamical stability of tet-C4 derived from all positive phonon bands also allows obtaining heat capacity close to the experimental data of diamond. The electronic band structure shows insulating tet-C4 with a large indirect band gap of 5 eV.