Reactivity for the Diels-Alder reaction of cumulenes: a distortion-interaction analysis along the reaction pathway.

Cumulenes, including allene, ketenimine, and ketene, can be employed as dienophiles in Diels-Alder type reactions. The activation energies of a Diels-Alder reaction between cyclopentadiene and either the C ═ C bond or the other C ═ X (X = C, N, or O) bond in cumulenes have been calculated by G3B3, CBS-QB3, M06-2X, and B3LYP methods. The reactivity trend for the C ═ C bond in cumulenes is allene > ketenimine > ketene and that of the C ═ X bond in cumulenes is ketene > allene > ketenimine. Application of distortion-interaction analysis only at transition states does not give a satisfactory explanation for these reactivities. By employing distortion-interaction analysis along reaction pathways, we found that the reactivity of the C ═ C and C ═ X bond in cumulenes is controlled by both of its distortion and interaction energies. The lowest distortion energy of allene leads to its highest reactivity; the higher interaction energy results in higher activation energy of ketene than that of ketenimine. Compared with the reactivity of the C ═ X bond in cumulenes, the C ═ O bond in ketene has the lowest activation energy to react with cyclopentadiene, due to its lowest interaction energy, whereas the lower distortion energy of ketenimine than that of allene leads to a higher reactivity. The distortion energy of the reactants can be attributed to folding ability and molecule strain. The corresponding interaction energy of the reactants is controlled by orbital interaction, closed-shell repulsion, and static repulsion.