Semicontinuum (Cluster-Continuum) Modeling of Acid-Catalyzed Aqueous Reactions: Alkene Hydration

An effort is made to reduce the errors of continuum solvation models (CSMs) with semicontinuum modeling to achieve 3 kcal mol^-1 agreement with experiment for acid-catalysis activation Gibbs energies. First, two underappreciated CSM issues are reviewed: errors in the CSM solvation Gibbs energies grow beyond 5 kcal mol^-1 (i) as ions are made smaller and (ii) as water clusters grow larger. Second, the computational reproduction of the known Gibbs energies (Δ_rG and Δ^‡G) of the paradigmatic reaction ethene + H₂O + H₃O⁺ → TS⁺ → ethanol + H₃O⁺ is attempted. It is argued that, despite the >5 kcal mol^-1 solvation errors for ions, it is possible to employ error cancellation strategies to reduce the errors in the reaction and activation Gibbs energies to 3 kcal mol^-1 accuracy. A new 3 kcal mol^-1 effect due to solvent-molecule "placement" (confinement from 1 M bulk concentration) was isolated and proved useful. Third, computational reproduction of the known entropies (Δ_rS and Δ^‡S) of the paradigmatic reaction is attempted using Trouton's constant and neglect of solvent structure reorganization effects (which must cancel well for this reaction); this worked well for Δ_rS but needs empirical correction of ∼11 cal mol^-1 K^-1 for Δ^‡S due to solvent disorientation when H₃O⁺ is consumed. These entropy estimates allow for enthalpy (Δ_rH and Δ^‡H) estimation from the Gibbs energy values. Fourth, two recommended options, including A + H₃O⁺·2W → [AHOH₂⁺·2W]^‡, are shown to also work well for the activations of propene and isobutene.