Quantum chemical AM1 study of growth mechanisms of fullerenes: A facile C₂ insertion technique

Insertion of a C₂ molecule (fragment) into the cavity of a hexagonal belt containing 10 hexagons generates a honeycomb lattice (C₄₂H₁₆) and two hydrocarbons containing one and two pairs of {7,5} ring pairs. The vibrational frequency analysis reveals that the hydrocarbon having only one {7,5} ring pair behaves as a transition-state-like structure. The generation of the hydrocarbon containing two {7,5} ring pairs appears to be an innate process compared with the honeycomb lattice when the C₂ fragment is inserted into the vacant space of the hexagonal belt. A very small amount of excitation energy (0.0108 kcal/mol) is required for the annihilation of a {7,5} ring pair to a {6,5} ring pair. Considering two common frames, the motion of the {7,5} and {6,5} ring pairs are studied. The motion of these ring pairs are found to be so natural that there is an insignificant change in the property-like second-order hyperpolarizability ((γ)).