How to Predict the pKa of Any Compound in Any Solvent

Acid-base properties of molecules in nonaqueous solvents are of critical importance for almost all areas of chemistry. Despite this very high relevance, our knowledge is still mostly limited to the pK(a) of rather few compounds in the most common solvents, and a simple yet truly general computational procedure to predict pK(a)'s of any compound in any solvent is still missing. In this contribution, we describe such a procedure. Our method requires only the experimental pK(a) of a reference compound in water and a few standard quantum-chemical calculations. This method is tested through computing the proton solvation energy in 39 solvents and by comparing the pK(a) of 142 simple compounds in 12 solvents. Our computations indicate that the method to compute the proton solvation energy is robust with respect to the detailed computational setup and the construction of the solvation model. The unscaled pK(a)'s computed using an implicit solvation model on the other hand differ significantly from the experimental data. These differences are partly associated with the poor quality of the experimental data and the well-known shortcomings of implicit solvation models. General linear scaling relationships to correct this error are suggested for protic and aprotic media. Using these relationships, the deviations between experiment and computations drop to a level comparable to that observed in water, which highlights the efficiency of our method.