Quantum-chemical calculations, at the self-consistent-charge density-functional-based non-orthogonal tight binding (SCC-DFTB) level, are used to provide the input for unimolecular reaction rate theory calculations to predict the temperatures at which rapid, i.e., microsecond timescale, equilibration between mono-cyclic and bi-cyclic carbon clusters can occur. The computational results are discussed in the form of a set of trends for their variation with the size of the cluster, the length of the carbon-carbon bond broken or formed, the vibrational frequencies, the energy differences and the rate constants. The temperatures used experimentally to prepare fullerenes and nanotubes are compatible with the rapid equilibration of rings and bi-cyclic rings, a factor that explains the lack of defects in these higher forms of carbon clusters and the general trend towards the formation of the most stable fullerene for a given nuclearity. (C) 2002 Published by Elsevier Science B.V.