Since the discovery of the fullerene C₆₀ in 1985, and its subsequent macroscopic preparation, the study of carbon clusters has revealed a rich variety of physical and chemical properties. The detailed energetics of carbon clusters is difficult to analyse experimentally because of the sensitivity of cluster formation to the prevailing conditions. Carbon clusters are very difficult to model theoretically due to the wide range of geometries and the occurrence of single, double and triple bonds.

Kent et al. calculated the energies of different clusters around the "transition to fullerene stability" (C_24-32), and identified the smallest stable geometries for each cluster size. First, candidate structures were identified for each cluster size. Low-energy structures were selected using density functional theory, and then used the diffusion quantum Monte Carlo (DMC) method to determine more accurate cluster energies.

Five C₂₄ structures were investigated: a ring, a flat graphitic sheet, a bowl-shaped structure with one pentagon, a caged structure with a mixture of square, pentagonal and hexagonal faces, and a fullerene (see picture at top of page). The graphitic sheet was found to be lowest in energy, and this structure was predicted to be the smallest stable graphitic fragment.

Three C₂₆ structures were investigated: a ring, graphitic sheet with one pentagon and a fullerene. The ring and sheet-like isomers were found to be close in energy, but the fullerene is approximately 2.5 eV lower in energy than these isomers and is therefore predicted to be the smallest stable fullerene.

For C₂₈ a fullerene was found to be the most stable structure. This prediction indicates that isolated fullerenes might be readily produced, which would facilitate investigations of C₂₈ fullerene solids, which have been discussed but not yet produced.