Carbon clusters near the crossover to fullerene stability

The energetic stability of structural isomers of ${\mathrm{C}}_{24},$ ${\mathrm{C}}_{26},$ ${\mathrm{C}}_{28},$ and ${\mathrm{C}}_{32}$ clusters, including fullerenes, is studied using diffusion quantum Monte Carlo methods. We predict that a ${\mathrm{C}}_{24}$ isomer is the smallest stable graphitic fragment and that the smallest stable fullerenes are the ${\mathrm{C}}_{26}$ and ${\mathrm{C}}_{28}$ clusters with $C_{2v}$ and $T_d$ symmetry, respectively. Given suitable experimental conditions these small fullerenes should therefore be producible in abundance, facilitating production of fullerene-based solids.