Computational Insights into Endo/Exo Selectivity of the Diels-Alder Reaction in Explicit Solvent at Ab Initio Quantum Mechanical/Molecular Mechanical Level

The microscopic insight into the endo/exo stereoselectivity of the Diels-Alder (DA) reaction between cyclopentadiene and methyl vinyl ketone (MVK) has posed a challenge to the computational chemists, which requires an accurate free-energy (FE) landscape. Although ab initio (ai) quantum mechanical/molecular mechanical (QM/MM) calculations are capable of providing accurate conformation energies, they are far too expensive for free-energy calculations, in which large-scale sampling in the phase space is always indispensable. Recently, on the basis of the idea of reference-potential methods, a new approach termed MBAR+wTP method was proposed by us (Li; et al. J. Chem. Theory Comput. 2018, 14, 5583) for the calculations of ai QM/MM FE profiles with a much less computational expense. In this work, we applied this method to investigate the endo/exo stereoselectivity of the Diels-Alder (DA) reaction at B3LYP/MM level and the results indicate that this method can yield more accurate activation free energies than the semiempirical Hamiltonian PM6 and the "sampling-free" quantum mechanical methods at B3LYP and MP2 levels using a polarizable continuous solvent model (PCM). The stereoselectivity mainly comes from the solvation effect. At the transition state, the first peak of the solvent distribution near the oxygen atom in MVK is slightly closer for the endo pathway than that for the exo pathway, whereas the difference at PM6 level is negligible. Nonetheless, in terms of the stereoselectivity, we obtained an endo/exo ratio of 2 with this method, which is still 1 order of magnitude smaller than the experimental measurement. Although the endo/exo ratio from the MP2/PCM calculation agrees well with the experiment, the absolute reaction barriers deviate by about 5 kcal mol^-1. This work issues a warning to the use of the computational methods that are routinely employed for the study of organic reactions in the condensed phase, and it also brings a new method that is affordable and more reliable.