  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.
