Calculating the Aqueous pK_a of Phenols: Predictions for Antioxidants and Cannabinoids

We aim to develop a theoretical methodology for the accurate aqueous pK_a prediction of structurally complex phenolic antioxidants and cannabinoids. In this study, five functionals (M06-2X, B3LYP, BHandHLYP, PBE0, and TPSS) and two solvent models (SMD and PCM) were combined with the 6-311++G(d,p) basis set to predict pK_a values for twenty structurally simple phenols. None of the direct calculations produced good results. However, the correlations between the calculated Gibbs energy difference of each acid and its conjugate base, ΔGaq(BA)°=ΔGaqA-°-ΔGaq(HA)°, and the experimental aqueous pK_a values had superior predictive accuracy, which was also tested relative to an independent set of ten molecules of which six were structurally complex phenols. New correlations were built with twenty-seven phenols (including the phenols with experimental pK_a values from the test set), which were used to make predictions. The best correlation equations used the PCM method and produced mean absolute errors of 0.26-0.27 pK_a units and R² values of 0.957-0.960. The average range of predictions for the potential antioxidants (cannabinoids) was 0.15 (0.25) pK_a units, which indicates good agreement between our methodologies. The new correlation equations could be used to make pK_a predictions for other phenols in water and potentially in other solvents where they might be more soluble.