The relative stabilities of closed fullerene, cumulene, and polyacetylene carbon structures, as well as the cohesive energies for clusters of size n = 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 50, and 60 have been examined using ab initio self-consistent-field and second-order Moller-Plesset perturbation theory and analytical derivative geometry optimization methods. These geometries and relative stabilities constitute the primary findings of this work. All calculations were carried out using the DISCO program with atomic basis sets derived from van Duijneveldt's carbon (6s,3p) primitive orbital basis set, contracted to [3s2p]. For n greater-than-or-equal-to 32, the fullereness are predicted to be the most stable, and their cohesive energies are predicted to increase monotonically as n varies from 24 to 60. The optimized geometries obtained here are very near those obtained earlier by others for the few species where such data exist. Based on earlier work employing larger atomic orbital bases, the relative energies of the fullerene structures are expected to be lowered even further as larger basis sets are employed. Hence, it is likely that the smallest cluster for which the fullerene structure is the most stable has n < 32. Comparing our computed electron binding energy for C24- to the experimental vertical detachment energy of this species supports the claim that n = 24 may be the smallest energetically favored fullerene.
