Carbon Condensation via [4 + 2] Cycloaddition of Highly Unsaturated Carbon Chains

We present computational studies of reaction pathways for alkyne/polyyne dimerization that represent plausible early steps in mechanisms for carbon condensation. A previous computational study of the ring coalescence and annealing model of C₆₀ formation revealed that a 1,4-didehydrobenzocyclobutadiene intermediate (p-benzyne derivative) has little to no barrier to undergoing an unproductive retro-Bergman cyclization, which brings into question the relevance of that reaction pathway. The current study investigates an alternative model, which proceeds through an initial [4 + 2] cycloaddition instead of a [2 + 2] cycloaddition. In this pathway, the problematic intermediate is avoided, with the reaction proceeding via a (potentially) more kinetically stable tetradehydronaphthalene derivative. The computational studies of the [2 + 2] and [4 + 2] model systems, with increasing alkyne substitutions, reveal that the para-benzyne diradical of the [4 + 2] pathway has a significantly greater barrier to ring opening than the analogous intermediates of the [2 + 2] pathway and that alkyne substitution has little effect on this important barrier. These studies employ spin-flip, time-dependent density functional theory (SF-TDDFT) to provide suitable treatment of open-shell diradical intermediates.