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 C 28 (T d and D 2 ) and C 26 (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.Low-mass fullerenes possessing high curvature and increased strain owing to the presence of adjacent pentagonal rings could lead to solids with unusual intermolecular bonding and electronic properties.1 The recent synthesis 1 of macroscopic quantities of solid fullerene C 36 might be viewed as another milestone in the study of fullerene chemistry. The C 36 fullerene synthesis begs the question of a possible synthesis of even smaller fullerenes than C 36 . After the epoch making discovery of C 60 (Buckminsterfullerene 2 ) in 1985, fullerene chemistry had to wait reluctantly for 6 more years until C 60 was synthesized in bulk quantity for the full experimental characterization. 3 At that juncture the progress in the characterization of the lower fullerenes is considered to be only of theoretical interest. But, now with the synthesis of C 36 by Piskoti et al., 1 a new area in the lower fullerene domain has emerged. Though fullerene is now wellrecognized as an attractive new material and numerous reports regarding its applications have been proposed, the mechanism of how such a symmetric hollow cage structure can be self-assembled has remained as an intriguing problem.In recent years, several attempts have been made both theoretically and experimentally in order to unveil the mystery of fullerene growth mechanism. Experiments on resistive evaporation of two carbon rods with different degrees of enrichment in 13 C have revealed that the carbon vapor consists of smaller clusters before the process of fullerene formation starts. 4 Further, experimental gas ion chromatography studies of the structure of the carbon clusters lead to the formation of the possible paths of fullerene formation through the coagulation of monocycles and gradual transformations of polycyclic structures into fullerene cages.
5-7These elementary carbon clusters such as monocyclic rings or polycyclic rings are termed as precursors 5,...