Precursors toC60fullerene formation

It is shown that the free energy of ${\mathrm{C}}_{20}$ clusters favors a transformation from a closed cage (fullerene) structure at low temperatures to a more open corrannulene structure and then to a ring structure as the temperature is increased. The corrannulene structure can be thought of as a fragment of ${\mathrm{C}}_{60}$ and is an efficient precursor to its formation. These results are applicable to other carbon clusters of similar sizes and are consistent with the experimental findings that high temperatures are necessary for the formation of substantial quantities of ${\mathrm{C}}_{60}$.