Molecular dynamics simulations of carbon cluster nucleation was conducted using a modified form of the Chelikowsky interatomic potential. The simulations were performed for systems containing 40 to 80 carbon atoms using annealing procedures which are more physically realistic than those used in the past. The results show that at temperatures above melting, long linear chains form early in the nucleation process and subsequently close to form monocyclic rings. Once the temperature is decreased below the melting point the network of rings closes forming hollow spheroidal structures characteristic of the fullernes. The pattern of growth results confirm predicted growth processes, indicating the advantages of Hamiltonian dynamics over previously used Langevin dynamics.