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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 these systems is difficult to analyse because of
the extreme sensitivity of cluster formation to experimental
conditions and the great challenges posed to theoretical methods. We
have performed very accurate calculations of the relative energies of
clusters around the `transition to fullerene stability'
(C24-32), and have identified the smallest stable
geometries for each cluster size. We have found that common
theoretical methods can give very different results, even for the
larger clusters.
Our investigations were focused on identifying the smallest stable
cluster geometry at each cluster size. The number of
candidate structures, even for quite small clusters, is very large. We
adopted the strategy of selecting low-energy structures using density
functional theory and the results of past investigations, and then
using the more accurate and expensive Quantum Monte Carlo (QMC) method
to determine the cluster energies. QMC methods have previously been used in our group to study the properties of the group-IV materials carbon, silicon and germanium, obtaining cohesive (binding) energies in very good agreement with experiment. Carbon clusters are very difficult to model accurately due to the wide range of geometries and the occurrence of single, double and triple bonds. Our results show that current density functional methods are of very variable accuracy in these carbon systems and that greater accuracy is required to determine the energetically stable structures. We investigated five C24 structures: 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).
Three C26 structures were investigated: a ring, graphitic sheet with one pentagon and a fullerene.
The geometries of these structures were obtained using density functional theory. We carefully tested the dependence of the geometries, and found only a small dependence on the method used to obtain the geometries.
Our results confirm that an accurate treatment of electron correlation is critical for accurate results. The treatment of electron correlation has a profound effect on the relative energies of the different structures. We find the lowest energy structure of C24 to be a graphitic sheet, and this structure is predicted to be the smallest stable graphitic fragment.
For C26, we find the ring and sheet-like isomers to be close in energy, but the fullerene is approximately 2.5 eV below these isomers and is therefore predicted to be the smallest stable fullerene. Small changes in the geometries are highly unlikely to change this conclusion. Our results for C28 show that a fullerene is again the most stable structure. This prediction indicates that isolated fullerenes might be readily produced. This would facilitate investigations of C28 fullerene solids, which have been discussed but not yet produced. |
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