The electronic structure and stability of germanium tubes Ge₃₀H₁₂ and Ge₃₃H₁₂

The geometries of non-tetrahedral and ultrastable silicon and germanium nanocrystals X18H12 and X19H12 (X = Si, Ge) have recently been predicted for the development of cluster-based nanomaterials for energy and microengineering purposes. To further explore the possibility of larger Ge clusters, we investigated in this work the molecular and electronic structure of the germanium tube Ge30H12, composed of six parallel, planar hexagons using DFT calculations. Insertion of Ge atoms at the center of three inner hexagons of Ge30H12 leads to a Ge33H12 tube, which is also an energy minimum structure. The electronic structure and molecular orbital shapes of these tubes can be predicted by the wavefunctions of a particle on a hollow cylinder model and a cylinder model. Different aromaticity indices including PDI, Iring, ING, MCI, and INB, as well as the electron localization function (ELF) were calculated to evaluate the electron delocalization and the aromaticity of the Ge tubes considered.