Electronic structure and stability of fullerene polymers

[2+2]

cycloaddition reaction between \chem{C_{60}} molecules is studied theoretically using the semi-empirical quantum chemical AM1 method. The studies are aimed at understanding of photo- and pressure polymerization of pristine \chem{C_{60}} and polymerization of the alkali metal (\chem{\chemvar{A}})/\chem{C_{60}} complex, \chem{\chemvar{A}_{1}C_{60}}. Full geometry optimizations of the [2+2] cycloaddition reaction, have been performed for neutral as well as anionic \chem{C_{60}} dimers. Based on these geometries, th e reaction barriers were calculated. Vanishing barriers were found for the anionic dimer and in the first singlet (\state{}{S}{1}) and triplet (\state{}{T}{1}) excited states of the neutral dimer, results that indicate spontaneous polymerisation for these systems in full agreement with experimental observations. The occurrence of the [2+2] cycloaddition reaction is fully understood from a detailed analysis of the molecular orbitals and how these correlate with the change in the interfullerene distance. We have located a critical intermolecular distance, R_{\text{C}}=\valunit{2.12}{\Angstrom}, for which the [2+2] cycloaddition occurs as a result of an interchange in the position in the energy spectrum between the highest occupied and lowest unoccupied molecular orbitals.