Dodecahedral Clusters and Novel Cubic Allotropic Forms of Carbon, Silicon, and Germanium: Computer Simulation

Abstract

A method is described for building up novel three‐dimensional periodical structures consisting of atoms C, Si or Ge. Polyhedral dodecahedral shape clusters X20 are basis of such lattices. Three‐dimensional nets with simple cubic lattices can be produced on the base of X20 clusters. Each cluster X20 has six neighboring clusters X20. Two neighboring clusters are bound by two covalent bonds. It is found that large size cavities are contained in such structures. Cubic clusters X8 can be disposed in these cavities. Each cluster X8 has eight neighboring clusters X20 and is covalently linked with one of these clusters. As a result, periodical crystalline structures [X8@(X20)8]n (or [X28]n) with simple cubic lattice can be produced. The lattice parameters of these crystals were found using DFT‐PBE optimized calculations of clusters X8 @ (X20)8 and X8 @ (X20H13)8. Structure of the [C28]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.