Defining the pH* Scale in Methanol: Determination of Accurate Values for the Solvation Free Energies of CH ₃ OH ₂ ⁺ and CH ₃ O ^– in Methanol

A correction factor for the autoprotolysis constant of methanol is proposed in the present work to obtain thermodynamic data for the standard solvation free energies of CH₃OH₂⁺ and CH₃O^- ions in methanol and p<i>K</i>_a^*. Using this corrected constant, <i>K</i>_MOH^*, along with known values for the standard solvation free energy of proton Δ<i>G</i>_sol^*(H⁺) and of the methanol molecule Δ<i>G</i>_sol^*(CH₃OH), in its own liquid, in three different thermodynamic cycles, we obtain Δ<i>G</i>_sol^*(CH₃OH₂⁺) = -91.41 ± 2.76 kcal mol^-1, Δ<i>G</i>_sol^*(CH₃O^-) = -88.36 ± 2.10 kcal mol^-1, and p<i>K</i>_a^*(methanol) = 22.67 ± 2.97. To validate our approach, we applied the same thermodynamic cycles for water in its own liquid, resulting in experimental values of Δ<i>G</i>_sol^*(H₃O⁺) = -110.20 ± 1.91 kcal mol^-1, Δ<i>G</i>_sol^*(OH^-) = -104.60 ± 0.25 kcal mol^-1, and p<i>K</i>_a(water) = 15.73 ± 1.42. Employing quantum mechanics calculations combined with Monte Carlo simulation, we calculated the standard deprotonation free energy and the p<i>K</i>_a values of water and methanol in their respective liquids. These calculations were performed using an explicit model of the solvent, with Free Energy Perturbation theory in Monte Carlo simulation (FEP-MC), three different pure implicit solvation models (HF-PCM, the Conductor-like Polarizable Continuum Model (C-PCM), the solvation model based on density (SMD)), and a hybrid model (cluster-SMD). Excellent agreement with experimental data was achieved using FEP-MC, HF-PCM, and cluster-SMD. Methanol is the simplest alcohol, and its p<i>K</i>_a^* value is a critical parameter in chemical and biological systems. Hence, its understanding, along with its pH* scale, enables better control and utilization of methanol in diverse applications, ranging from pharmaceuticals to industrial processes.