The results shown in figure 8.7 confirm that the treatment of correlation has a profound effect on the relative energies. All of the density functionals give different orderings of the energies, and none gives the same ordering as DMC. The graphitic sheet is placed lowest in energy by DMC, in agreement with each of the density functionals except BLYP, which places the ring lowest in energy. The low energy of the graphitic sheet is expected because the structure accommodates a large number (7) of hexagonal rings without significant strain. This structure is expected to be the smallest stable graphitic fragment, as for smaller clusters ring structures should be lower in energy. Neither DMC or the density functionals find the fullerene to be energetically stable.
The multi-determinant wavefunction gives a slightly lower DMC energy than the single determinant wavefunction, confirming that CI wavefunctions have better nodal surfaces than HF wavefunctions. However, the ring and sheet-like isomers remain very close in energy, approximately eV above the fullerene.
Spin-polarized DFT calculations show the ground state of the symmetry fullerene to be a spin-polarized state. DMC predicts that this spin-polarized fullerene is the lowest energy isomer of , and this is supported by each of the density functionals except BLYP.
The spin-polarized fullerene has four unpaired electrons and is therefore reactive. This property has been exploited in atom trapping experiments in which fullerenes containing a single atom have been prepared by laser vaporization of a graphite-MO (M = Ti, Zr, Hf or U) composite rod.  The prediction that the fullerene is the most stable isomer of indicates that isolated fullerenes might be produced, thereby facilitating the investigation of possible fullerene solids, which have been discussed but not yet produced. [162,163] (A fullerene solid has recently been reported. )
The DMC data strongly indicates that, of those considered, the fullerene is the most stable isomer. The fullerene has the lowest DMC energy in both spin-polarized and non spin-polarized states, and is substantially more stable than the sheet and ring. DMC calculations finds the spin-polarized state to be 2.08(20) eV more stable than the unpolarized state, which is 1.10(26)eV more stable than the sheet. Small changes in the geometries are therefore unlikely to change the energetic ordering.