The [C₆H₁₀]^•+ Hypersurface:  the Parent Radical Cation Diels−Alder Reaction

Various possible reaction pathways between ethene, 1, and butadiene radical cation (cis-, 2, trans-, 11) have been investigated at different levels of theory up to UCCSD(T)/DZP//UMP2(fc)/DZP and with density functional theory at B3LYP/DZP. A stepwise addition involving open chain intermediates and leading to the Diels−Alder product, the cyclohexene radical cation, 6, (path A) was found to have a total activation barrier ΔG^298≠ = 6.3 kcal mol^-1 and a change in free Gibbs energy, ΔG²⁹⁸, of −33.5 kcal mol^-1. On the E° potential energy surface, all transition states are lower in energy than separated 1 + 2, the exothermicity ΔE = −45.6 kcal mol^-1. A more direct path B could be characterized as stepwise with one intermediate only at the SCF level but not at electron-correlated levels and hence might actually be a concerted strongly asynchronous addition with a very small or no activation barrier (UCCSD(T)/DZP//UHF/6-31G* gives a ΔG^298≠ of 0.8 kcal mol^-1). The critical step for another alternative, the cyclobutanation−vinylcyclobutane/cyclohexene rearrangement, is a 1,3-alkyl shift which involves a barrier (ΔG^298≠) only 1.7 kcal mol^-1 higher than that of path A for both cis-, 2, (path C) and trans-butadiene radical cation, 11 (path D). However, from the 1 + 11 reactions, ring expansion of the vinylcyclobutane radical cation intermediate, 14, to a methylene cyclopentane radical cation, 16, (path E) requires an activation only 1.3 kcal mol^-1 larger than for path D. While cis/trans isomerization of free butadiene radical cation requires a high activation (24.9 kcal mol^-1), a reaction sequence involving addition of ethene (to stepwise give an open chain intermediate 13 and vinyl cyclobutane radical cation, 10) has a barrier of only 3.5 kcal mol^-1 (ΔG^298≠). This sequence also makes ethene and butadiene radical cations to exchange terminal methylene groups.