Computational Study of Tunneling in the Electrocyclic Reactions of Helical Systems

Chemical reactions can proceed by passing over the reaction barrier and/or by tunneling through the barrier––the latter being a quantum mechanical effect. From biochemistry to astrochemistry, tunneling dominates the rates of many reactions, provided the reaction barrier is narrow enough. Tunneling by heavy atoms (e.g. carbon) is known to contribute to some pericyclic reactions. Helical systems give rise to electrocyclic reactions that are exceptions to the Woodward-Hoffmann rules. Solomek et al. observed that the electrocyclic ring closure of a cethrene derivative occurs via a forbidden pathway, and they reported a measured activation energy (14.1 kcal/mol) much lower than the calculated energy barrier, suggesting a significant contribution from tunneling. We report computational results on the potential energy surfaces and tunneling contributions for the electrocyclic ring closures of two model systems, C14H12 and C16H12, to further understand the contribution of heavy-atom tunneling in the electrocyclic reactions of helical systems. Barrier heights, distances moved by the reacting carbons, barrier widths, and tunneling transmission coefficients computed with Bell’s formula are presented and compared with the parent electrocyclization of 1,3,5-hexatriene.