How to Predict the p<i>K</i>_a 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 pKa of rather few compounds in the
most common solvents, and a simple yet truly general computational
procedure to predict pKa’s of any
compound in any solvent is still missing. In this contribution, we
describe such a procedure. Our method requires only the experimental
pKa 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 pKa 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 pKa’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.