# Defining the pH* Scale in Methanol: Determination of Accurate Values for the Solvation Free Energies of CH3OH2 + and CH3O– in Methanol

## TL;DR

This paper determines accurate solvation free energies of ions in methanol and defines a pH* scale, important for chemical and biological applications.

## Contribution

The paper introduces a correction factor for methanol's autoprotolysis constant to derive precise thermodynamic values.

## Key findings

- ΔG_sol*(CH3OH2+) = −91.41 ± 2.76 kcal mol–1 in methanol.
- pK_a*(methanol) = 22.67 ± 2.97, validated using thermodynamic cycles.
- FEP-MC and HF-PCM models show excellent agreement with experimental data.

## Abstract

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 pK
a
*. Using this corrected constant, K
MOH
*, along with known values for the standard solvation free energy
of proton ΔG
sol
*(H+) and of the methanol molecule
ΔG
sol
*(CH3OH), in its own liquid, in three
different thermodynamic cycles, we obtain ΔG
sol
*(CH3OH2
+) = −91.41 ± 2.76 kcal mol–1, ΔG
sol
*(CH3O–) = −88.36 ± 2.10
kcal mol–1, and pK
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 ΔG
sol
*(H3O+) = −110.20
± 1.91 kcal mol–1, ΔG
sol
*(OH–) = −104.60 ± 0.25 kcal mol–1, and pK
a(water) = 15.73 ± 1.42.
Employing quantum mechanics calculations combined with Monte Carlo
simulation, we calculated the standard deprotonation free energy and
the pK
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 pK
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.