The ring-collapse mechanism that suggests the reactions among the mono- to polycyclic carbon clusters has been analyzed using semiempirical AM1 and HF/6-31G* methods. The two cage structures D-2 (chiral) and T-d (achiral) for the C-28 clusters are considered. Basing on the ring-stacking/circumscribing model and the ring-collapse mechanism various precursors are selected along with some appropriate carbon belts. Reactions between the precursors and the belts are found to be endoergic and lead to stable intermediates. All these stacking processes follow gradual and sequential paths. Various possible transition states structures (TSs) have been located and the barrier heights are found to be well within the earlier prescribed limits. Further, stacking the stable intermediates by suitable carbon belts generate the desired cage structures. The second step of the stacking resembles the annealing mechanism for the formation of the cage structures that is essentially an exoergic process. In this annealing process cascade-type bond formation is visualized. Finally, basing on the deformation energies of the precursors and the barrier heights, it is observed that monocyclic precursors are more suitable for the fullerene growth mechanism. (C) 2000 American Institute of Physics. [S0021-9606(00)30414-7].