Modern valence-bond description of chemical reaction mechanisms:: Diels-Alder reaction

The electronic mechanism for the gas-phase Diels-Alder cycloaddition reaction is studied through a combination of modern valence-bond (VB) theory in its spin-coupled (SC) form and intrinsic reaction coordinate calculations utilizing a complete-active-space self-consistent field (CASSCF) wave function. Throughout the reaction, the nonorthogonal SC orbitals resemble well-localized sp(x) hybrids, each of which remains permanently attached to a single carbon atom. The changes in the shapes of these SC orbitals, together with the variations of the overlaps between neighboring orbitals, produce a lucid picture of the parallel breaking of the butadiene and ethene pi bonds and of the formation of the two new sigma bonds, closing the ring, and of the cyclohexene pi bond. The analogue of classical VB resonance, namely, the active-space spin-coupling pattern within the SC wave function, shows no resonance well before and well after the transition structure (TS). At and around the TS, this pattern is dominated by two Kekule Rumer spin functions of comparable weight. This and other resemblances to the well-known SC description of benzene (similar orbital shapes, equalization of the overlaps between neighboring orbitals) indicate clearly that the Diels-Alder reaction passes through a geometry, very close to the TS, at which it is aromatic. The visual changes in the SC wave function as the system follows the reaction path strongly suggest that the best schematic representation of the Diels-Alder reaction is through a "homolytic" mechanism, in which six half-arrows indicate the simultaneous breaking of the three pi bonds on the reactants and formation of the three new bonds, two sigma and one pi, in the product.