8.10 Conclusions

In conclusion, the prediction of the relative energies of carbon clusters is a severe test of calculational accuracy because of the widely different geometries and the presence of single, double, and triple bonds. Current density functionals give very similar structures but widely differing relative energies. DMC calculations show that for $\mathrm {C}_{24}$ the fullerene is not the lowest energy isomer. The lowest energy $\mathrm {C}_{24}$ structure is a sheet structure, which is expected to be the smallest stable graphitic fragment. The smallest energetically stable fullerenes are predicted to be the highly strained $\mathrm {C}_{26}$ cluster of $\mathrm{C}_{2v}$ symmetry and the spin polarized $^5A_2$ state of the $\mathrm {C}_{28}$ cluster of $\mathrm{T}_{d}$ symmetry.

This prediction lends support to proposals that a $\mathrm {C}_{28}$ solid could be synthesised by surface deposition of $\mathrm {C}_{28}$ fullerenes. [162,163] Depending on its abundance, this route may be either hampered or facilitated by the chemical reactivity of the $\mathrm {C}_{28}$ fullerene.