Dynamics, transition states, and timing of bond formation in Diels-Alder reactions

Abstract

The time-resolved mechanisms for eight Diels-Alder reactions have been studied by quasiclassical trajectories at 298 K, with energies and derivatives computed by UB3LYP/6-31G(d). Three of these reactions were also simulated at high temperature to compare with experimental results. The reaction trajectories require 50-150 fs on average to transverse the region near the saddle point where bonding changes occur. Even with symmetrical reactants, the trajectories invariably involve unequal bond formation in the transition state. Nevertheless, the time gap between formation of the two new bonds is shorter than a C ─ C vibrational period. At 298 K, most Diels-Alder reactions are concerted and stereospecific, but at high temperatures (approximately 1,000 K) a small fraction of trajectories lead to diradicals. The simulations illustrate and affirm the bottleneck property of the transition state and the close connection between dynamics and the conventional analysis based on saddle point structure.

Scheme 1.

(A) Diels–Alder reactions R1-R8 investigated by trajectory calculations. B3LYP/6-31G(d) and M06-2X/6-31G(d) (in parentheses) activation barriers and distortion energies of reactants at the saddle point geometries are given in kcal/mol. See SI Appendix, Scheme S1, for activation enthalpies and free energies for these reactions. (B) Saddle point for reaction R1 optimized by B3LYP/6-31G(d). Bond distances are given in angstrom. Carbon: cyan; hydrogen: white. See SI Appendix for TS geometries for other reactions.

Fig. 1.

Superposition of sampled TS geometries in the reactions of (A) butadiene and ethylene at 298 K (R1, Scheme 1); (B) butadiene and ethylene at 1,180 K; (C) 2-hydroxybutadiene and cyanoacetylene at 298 K (R8, Scheme 1). The distribution of forming C─C bond lengths in TS geometries are shown. The forming C─C bond length at the saddle point is marked with a red line in each of the distribution plots. See SI Appendix for similar figures for other reactions.

Fig. 2.

(A–C) Distances of the two forming C─C bonds in reactions R1 at 298 K, R1 at 1,180 K, and R8 at 298 K, respectively. Contour plots are calculated with UB3LYP/6-31G(d). Energies are in kcal/mol relative to separate reactants. (D) forming C─C bond lengths vs. time in R1 at 298 K. (E and F) Shorter bond (d1) and longer bond (d2) lengths vs. time in R8 at 298 K. Time zero is the time at which the trajectory crosses the TS—i.e., the starting point of each trajectory. Trajectories are stopped when the C─C bond is < 1.6 Å. Transition zone is highlighted in green. See SI Appendix for plots for other reactions.

Fig. 3.

(A) Velocity of C─C bond formation (relative velocity along the bond axis) vs. bond length in R1. (B and C) Velocity of C─C bond formation vs. bond length for the shorter bond (B) and longer bond (C) in R8. In each plot the thin lines represent velocities for individual trajectories, while the median velocity is shown in bold blue. (D) Potential energy relative to the electronic energy of separated reactants vs. forming C─C bond length in R1. Median kinetic energy (red) and potential energy (blue) are shown in bold. (E and F) Potential energy vs. forming C─C bond length for the shorter bond (E) and longer bond (F) in R8. Transition zone is highlighted in green. See SI Appendix for plots of other reactions.