Understanding Rate Accelerations for Diels−Alder Reactions in Solution Using Enhanced QM/MM Methodology

The Diels−Alder reactions of cyclopentadiene with 1,4-naphthoquinone, methyl vinyl ketone, and acrylonitrile have been investigated using QM/MM calculations in water, methanol, acetonitrile, and hexane. This extends an earlier AM1-based QM/MM study (J. Phys. Chem. B 2002, 106, 8078) that only investigated the reactions in water and utilized gas-phase optimized structures as starting points for computations of one-dimensional potentials of mean force (PMFs). Presently, the stationary points were located automatically in multiple solvents by computing two-dimensional PMFs, and the QM method is now PDDG/PM3. The resultant geometries are improved, and relative free energies of activation are well reproduced, e.g., ΔG^‡ for the reaction with naphthoquinone is computed to increase upon transfer from water to methanol, acetonitrile, and hexane by 3.2, 4.1, and 5.1 kcal/mol, while the experimental values are 3.4, 4.0, and 5.0 kcal/mol. Ab initio MP2/6-311+G(2d,p) calculations using the CPCM continuum solvent model on gas-phase CBS-QB3 geometries were also found to yield accurate ΔG^‡ values in water. However, only the QM/MM methodology reproduced the large rate increases in proceeding from aprotic solvents to water. The dominant factors for the rate variations are enhanced hydrogen bonding for the polarized transition states and reduction in hydrophobic surface area.