Density Functional Theory Prediction of the Relative Energies and Isotope Effects for the Concerted and Stepwise Mechanisms of the Diels−Alder Reaction of Butadiene and Ethylene

Density-functional theory has been applied to the study of the mechanism of the Diels−Alder reaction of butadiene and ethylene. Both synchronous concerted and two-step diradical mechanisms were studied at the Becke3LYP/6-31G* level. The lowest energy stepwise pathway has a free energy of activation 7.7 kcal/mol above that of the concerted path. Spin correction of the spin-contaminated diradical transition structure energy reduces this energy difference to 2.3 kcal/mol. A study of the H2 potential energy surface suggests that the spin-projection procedure overcorrects the energies of diradical species; the diradical energies likely fall between the corrected and uncorrected values. Thus, the free energy of concert for the Diels−Alder reaction is predicted to be between 2.3 and 7.7 kcal/mol, in excellent agreement with thermochemical estimates. Energies of reaction and geometries of the reactants and product are in good agreement with available experimental results. Calculated secondary kinetic isotope effe...