What is the ground-state structure of intermediate-sized carbon   clusters?
  A comprehensive study on the relative structural stability of various nanostructures of carbon clusters (including fullerenes, cages, onions, icosahedral clusters, bucky-diamond clusters, spherically bulk terminated clusters, and clusters with faceted termination) in the range of d < 5 nm has been carried out using a semi-empirical method based on a self-consistent and environment-dependent/linear combination of atomic orbital (SCED-LCAO) Hamiltonian. It was found that among these nanostructures with the same diameter, fullerenes are still the most stable structure, in contrast to the icosahedral cluster being the ground state structure for a series of discrete n values for other tetravalent clusters. The transformations from a bucky-diamond structure to an onion structure, or to a cage structure, or from an onion structure to a cage structure have been observed using a finite temperature molecular dynamics scheme based on the SCED-LCAO Hamiltonian. It was also found that the size-dependence of the HOMO-LUMO gap of fullerene shows an oscillation as a function of its diameter (d). Such oscillation is associated with the symmetry of the fullerene, and the magnitude of oscillation appears to decrease as its size increases. 
Ming Yu, Indira Chaudhuri, C. Leahy, C. S. Jayanthi, and S. Y. Wu