Quantum Chemical AM1 Treatment of the Circumscribing Algorithm: Fullerene Growth Mechanism

A graph theoretically formulated circumscribing algorithm for the fullerene growth mechanism has been analyzed using the quantum chemical AM1 method. Following different routes, two small fullerenes C₂₈ (T_d and D₂ and C₂₆ (D_3h) have been constructed from monocyclic/polycyclic precursors and circumscribed with appropriate carbon belts. The deformation energies (DE) and the average bond lengths 〈R〉 of the precursors have been computed. The DE values suggest that there is a chance of bond cleavage of the polycyclic precursors as the growth process proceeds toward the cage formation. On the other hand, the monocyclic precursors are found to have significantly lower deformation energies than the polycyclic precursors. Further, with analysis of 〈R〉 values of the polycyclic and monocyclic cases at different stages, it is observed that the 〈R〉 values of the polycyclic cases decrease gradually, depicting a shrinkage in the precursors which may be detrimental to the growth process, whereas monocyclic precursors tend to swell, corroborating the tendency of the system to grow which may be conducive for the growth process.