Dodecahedral clusters and novel cubic allotropic forms of carbon, silicon, and germanium: Computer simulation

A method is described for building up novel three-dimensional periodical structures consisting of atoms C, Si or Ge. Polyhedral dodecahedral shape clusters X-20 are basis of such lattices. Three-dimensional nets with simple cubic lattices can be produced on the base of X-20 clusters. Each cluster X-20 has six neighboring clusters X-20. Two neighboring clusters are bound by two covalent bonds. It is found that large size cavities are contained in such structures. Cubic clusters X-8 can be disposed in these cavities. Each cluster X-8 has eight neighboring clusters X-20 and is covalently linked with one of these clusters. As a result, periodical crystalline structures [X-8@(X-20)(8)](n) (or [X-28](n)) with simple cubic lattice can be produced. The lattice parameters of these crystals were found using DFT-PBE optimized calculations of clusters X-8@(X-20)(8) and X-8@(X20H13)(8). Structure of the [C-28](n) crystal was obtained more accurate by the PBE96/FLAPW method. Calculations of density of states show that the crystal is dielectric with an energy gap of 3.3 eV.