Influence of water content on the [2σ+2σ+2π] cycloaddition of dimethyl azodicarboxylate with quadricyclane in mixed methanol–water solvents from QM/MM Monte Carlo simulations

Mixed quantum mechanics/molecular mechanics Monte Carlo (QM/MM/MC) simulations combined with the free energy perturbation (FEP) theory have been performed to investigate the mechanism and solvent effect of the [2σ+2σ+2π] cycloaddition reaction between dimethyl azodicarboxylate and quadricyclanes in the binary mixture solvents of methanol and water by varying the water content from 0 to 100 vol%. The two-dimensional potentials of mean force (2D PMF) calculations demonstrated that the mechanism of the reaction is a collaborative asynchronous procedure. The transition structures do not show large variation among different solvents. The calculated free energies of activation indicated that the QM/MM/MC method reproduced well the tendency of rate enhancement from pure methanol to methanol–water mixtures to “on water” with the water content increasing obtained in the experimental observation. The analyses of the energy pair distribution and radial distribution functions illustrated that hydrogen bonding plays an indispensable role in the stabilization of the transition structures. According to the results in methanol–water mixtures at different volume ratios, it is clear that the site-specific hydrogen bond effects are the central reason which leads to fast rate increases in progressing from a methanol–water volume ratio of 3 : 1 to 1 : 1. This work provides a new insight into the solvent effect for the [2σ+2σ+2π] cycloaddition reaction.