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.

Keywords:

• Fullerenes
• dodecahedral clusters C₂₀
• Si₂₀
• Ge₂₀
• DFT
• PBE96/FLAPW
• crystal [X₂₈]_n
• energy gap

Acknowledgments

This work was financially supported by Grant of the Chemistry and Materials Science Branch of Russian Academy of Science.