The mechanism by which carbon condenses to form PAHs or fullerenes is a problem that has garnered considerable theoretical and experimental attention. The ring-coalescence and annealing model for the formation of C(60) involves a [2 + 2] cycloaddition reaction of a cyclopolyyne to form a tetraalkynyl cyclobuta-1,3-diene intermediate, followed by a Bergman cycloaromatization reaction of the enediyne moiety. Intramolecular trapping of the incipient p-benzyne diradical across a diyne moiety of the macrocyclic ring affords an aromatic ring that must undergo further intramolecular reactions via polyradical intermediates to produce a condensed graphitic structure or fullerene. Computational studies of a model system for the intriguing tetraalkynylcyclobuta-1,3-diene intermediate, however, reveal that the corresponding p-benzyne diradical lies in a shallow minimum with a very low barrier to ring opening to cyclooctadienediyne. This pathway has not been previously considered in the mechanism for carbon condensation.