pK_a prediction in non-aqueous solvents

Acid dissociation constants ( $p{K}_a$ ) are widely measured and studied, most typically in water. Comparatively few datasets and models for non-aqueous $p{K}_a$ values exist. In this work, we demonstrate how the $p{K}_a$ in one solvent can be accurately determined using reference data in another solvent, corrected by solvation energy calculations from the COSMO-RS method. We benchmark this approach in 10 different solvents, and find that $p{K}_a$ values calculated in six solvents deviate from experimental data on average by less than 1 $p{K}_a$ unit. We observe comparable performance on a more diverse test set including amino acids and drug molecules, with higher error for large molecules. The model performance in four other solvents is worse, with one MAE exceeding 3 $p{K}_a$ units; we discuss how such errors arise due to both model error and inconsistency in obtaining experimental data. Finally, we demonstrate how this technique can be used to estimate the proton transfer energy between different solvents, and use this to report a value of the proton's solvation energy in formamide, a quantity that does not have a consensus value in literature.