We employ a multilevel quantum mechanics and molecular mechanics method to investigate the double-inversion mechanism of the nucleophilic substitution reaction at the center: the + reaction in aqueous solution. We find that the structures of the stationary points along the reaction path are quite different from the ones in the gas phase owing to the hydrogen-bond interactions between the solute and the surrounding water molecules. The atomic-level evolutions of the structures and charge transfer along the reaction path show that this double-inversion mechanism consists of an upside-down proton inversion process and a Walden-inversion process. The computed potential of mean force at the coupled-cluster singles and doubles with perturbative triples (CCSD(T))/molecular mechanics (MM) level of theory has the two-inversion barrier heights, and reaction free energy at 11.7, 29.6, and 12.6 kcal/mol, agreeing well with the predicted ones at 12.6, 32.5, and 12.2 kcal/mol obtained on the basis of the gas-phase reaction path and the solvation free energies of the stationary points.
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