Empirical Conversion of pKa Values between Different Solvents and Interpretation of the Parameters: Application to Water, Acetonitrile, Dimethyl Sulfoxide, and Methanol

An empirical conversion method (ECM) that transforms pK(a) values of arbitrary organic compounds from one solvent to the other is introduced. We demonstrate the method's usefulness and performance on pK(a) conversions involving water and organic solvents acetonitrile (MeCN), dimethyl sulfoxide (Me2SO), and methanol (MeOH). We focus on the pK(a) conversion from the known reference value in water to the other three organic solvents, although such a conversion can also be performed between any pair of the considered solvents. The ECM works with an additive parameter that is specific to a solvent and a molecular family (essentially characterized by a functional group that is titrated). We formally show that the method can be formulated with a single additive parameter, and that the extra multiplicative parameter used in other works is not required. The values of the additive parameter are determined from known pK(a) data, and their interpretation is provided on the basis of physicochemical concepts. The data set of known pK(a) values is augmented with pK(a) values computed with the recently introduced electrostatic transform method, whose validity is demonstrated. For a validation of our method, we consider pK(a) conversions for two data sets of titratable compounds. The first data set involves 81 relatively small molecules belonging to 19 different molecular families, with the pK(a) data available in all four considered solvents. The second data set involves 76 titratable molecules from 5 additional molecular families. These molecules are typically larger, and their experimental pK(a) values are available only in Me2SO and water. The validation tests show that the agreement between the experimental pK(a) data and the ECM predictions is generally good, with absolute errors often on the order of 0.5 pH units. The presence of a few outliers is rationalized, and observed trends with respect to molecular families are discussed.