Energetics, relative stabilities, and size-dependent properties of nanosized carbon clusters of different families: fullerenes, bucky-diamond, icosahedral, and bulk-truncated structures.

Structures and relative stabilities of carbon clusters belonging to different families have been investigated for diameters d < or = 5 nm based on an efficient semiempirical molecular dynamics (MD) scheme as well as a density functional theory based simulation. Carbon clusters studied include fullerenes and fullerene-derived structures (e.g., cages and onions), icosahedral structures, bucky-diamond structures, and clusters cut from the bulk diamond with spherical and facetted truncations. The reason for using a semiempirical MD is partly due to the large number of different cases (or carbon allotropes) investigated and partly due to the size of the clusters investigated in this work. The particular flavor of the semiempirical MD scheme is based on a self-consistent and environment-dependent Hamiltonian developed in the framework of linear combination of atomic orbitals. We find that (i) among the families of carbon clusters investigated, fullerene structures have the lowest energy with the relative energy ordering being E(fullerene) < E(onion) < E(icosahedral) < E(bucky-diamond) < E(bulk-truncated), (ii) a crossover between bucky-diamond and icosahedral structures is likely at d approximately 8 nm, (iii) the highest occupied molecular orbital-lowest unoccupied molecular orbital gap as a function of the diameter for the case of fullerenes shows an oscillatory behavior with the gap ranging from 2 eV to 6 meV, and the gap approaching that of gapless graphite for d > 3.5 nm, and (iv) there can be three types of phase transformations depending on the manner of heating and cooling in our simulated annealing studies: (a) a bucky-diamond structure --> an onionlike structure, (b) an onionlike --> a cage structure, and (c) a bucky-diamond --> a cage structure.