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The ring-collapse mechanism which suggests reactions among the mono- to polycyclic carbon clusters has been analysed using quantum-chemical AM1 method. To have a cage structure like C28 (Td) fullerene, two different precursors are chosen and stacked with appropriate belts. All these stacking processes follow gradual and sequential paths. Various possible transition states have been located and characterized. Finally, based on deformation energies of the precursors, belts and activation barriers, the most feasible path for the formation mechanism of C28 (Td) has been proposed.

The penultimate step of the circumscribe algorithm proposed on Graph Theoretical footings is analyzed by an involved quantum–chemical AM1 method. The five C 72 isomers generated through the different base excised internal structures are subjected to a relative stability study. Finally a relationship between the C 72 isomers with their corresponding five C 78 (IPR) fullerenes has been used to establish a relative stability trend. The most unstable C 72 isomer is found to generate the most stable C 78 (IPR) isomer through the capping technique used in the circumscribing algorithm. Further, the least spherical isomer attains the most spherical geometry after capping.

The definition of topological resonance energy (TRE) has been modified and new TRE values have been calculated for closed-and open-shell configurations of heterocyclobutadienes. The quantum chemical parameters of these molecules and their dissected counterparts have been evaluated.