An Ab Initio Study on Silicon and Germanium Nanotubes

First principles calculations using hybrid density functional theory have been performed to examine the electronic and geometric structure properties of single-walled silicon (SWSiNT) and germanium (SWGeNT) nanotubes. Finite clusters $X_m H_n$(X = Si or Ge) are used to model the nanotubes ($e.g.$ the smallest SWSiNT is modeled as Si$_{60}$H$_{12}$). Hydrogen termination is done to simulate the effect of longer tubes as well as to take care of end effects. A pseudopotential basis set has been used for the silicon atoms$^{1}$ and complete geometry optimizations of the structures has been carried out using the Gaussian 03 suite of programs.$^{2}$ Computer simulations predict that the existence and stability of the nanotubes are highly dependent on the ratio of the \textit{sp}$^{2}$ to \textit{sp}$^{3}$ hybridization. Results will be presented on cohesive energies, HOMO- LUMO gaps, and other electronic structure properties and their dependence on the tube diameter. We will discuss the density of states (DOS) to explain the possible metallic or semi-conducting character of the tubes. Detailed comparisons with published data in the literature will also be presented. * Work supported, in part, by the Welch Foundation, Houston, Texas (Grant No. Y-1525). $^{1 }$P. J. Hay and W. R. Wadt, J. Chem. Phys. \textbf{82}, 270 (1985). $^{2 }$\textit{Gaussian03}, Revision A.1, M. J. Frisch \textit{et al}.$,$ Gaussian Inc., Pittsburgh, PA , 2003.