What is the Goundstate Structure of Intermediate-sized Carbon Clusters?

Recent study on the equilibrium structures of quantum dots of tetravalent semiconductors such as Si clusters revealed that the ground state structures of these clusters with diameters d$<$5 nm are icosahedrons comprising of tetrahedral building blocks rather than corresponding bulk-truncated clusters[1]. Among tetravalent semiconductors, carbon is the only element whose atoms could form sp, or sp$^{2}$ or sp$^{3}$ bonding configurations, leading to compact, fullerene, and bucky-diamond clusters[2]. It is then natural to raise the question as to what is the ground-state structure for the carbon cluster C$_{n}$ for a given $n \quad \ge $ 20? We have recently initiated a preliminary study on the relative stability of carbon clusters C$_{n}$ with $n $up to 700, using a molecular dynamics scheme based on a self-consistent and environment-dependent Hamiltonian developed at the U. of Louisville in the framework of the linear combination of atomic orbitals[3]. Our preliminary result indicates that in the range of $n$ studied, the carbon fullerene clusters are still the most stable clusters, in contrast to the icosahedral cluster being the ground state structure for a series of discrete $n$ values for the other tetravalent clusters. We will also discuss the other electronic properties of intermediate-sized carbon clusters. This work was supported by the U.S. DOE (DE-FG02-00ER4582). [1] Y. Zhao, \textit{et al}\textbf{\textit{.,}} Phys. Rev. Lett. \textbf{93}, 015502 (2004). [2] J. Y. Raty, \textit{et al.}\textbf{\textit{,}} Phys. Rev. Lett. \textbf{90}, 037401 (2003). [3] S.Y. Wu, \textit{et. al}., \textit{Handbook of Materials Modeling }Vo.\textbf{l,} p.2935 (2005).