This study describes the framework of the quantum mechanical (QM)/Monte Carlo (MC)/free-energy perturbation (FEP) method, a FEP method based on MC simulations using quantum chemical calculations. Because a series of structures generated by interpolating internal coordinates between transition state and reactant did not produce smooth free-energy profiles, we used structures from the intrinsic reaction coordinate calculations. This method was first applied to the Diels-Alder reaction between methyl vinyl ketone and cyclopentadiene and produced ΔG( sol)‡ values of 20.1 and 21.4 kcal mol(-1) in aqueous and methanol solutions, respectively. They are very consistent with the experimentally observed values. The other two applications were the free-energy surfaces for the Cope elimination of N,N-dimethyl-3-phenylbutan-2-amine oxide in aqueous, dimethyl sulfoxide, and tetrahydrofuran solutions, and the Kemp decarboxylation of 6-hydroxybenzo-isoxazole-3-carboxylic acid in aqueous, dimethyl sulfoxide, and CH(3) CN solutions. The calculated activation free energies differed by less than 1.8 kcal mol(-1) from the experimental values for these reactions. Although we used droplet models for the QM/MC/FEP simulations, the calculated results for three reactions are very close to the experimental data. It was confirmed that most of the interactions between the solute and solvents can be described using small numbers of solvent molecules. This is because a few solvent molecules can produce large portions of the solute-solvent interaction energies at the reaction centers. When we confirmed the dependency on the droplet sizes of solvents, the QM/MC/FEP for a large droplet with 106 water molecules produced a ΔG (sol)‡ value similar to the experimental values, as well as that for a small droplet with 34 molecules.
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