Toward the accurate calculation of pKa values in water and acetonitrile

We present a simple approach for the calculation of accurate pKa values in water and acetonitrile based on the straightforward calculation of the gas-phase absolute free energies of the acid and conjugate base with use of only a continuum solvation model to obtain the corresponding solution-phase free energies. Most of the error in such an approach arises from inaccurate differential solvation free energies of the acid and conjugate base which is removed in our approach using a correction based on the realization that the gas-phase acidities have only a small systematic error relative to the dominant systematic error in the differential solvation. The methodology is outlined in the context of the calculation of a set of neutral acids with water as the solvent for a reasonably accurate electronic structure level of theory (DFT), basis set, and implicit solvation model. It is then applied to the comparison of results for three different hybrid density functionals to illustrate the insensitivity to the functional. Finally, the approach is applied to the comparison of results for sets of neutral acids and protonated amine cationic acids in both aqueous (water) and nonaqueous (acetonitrile) solvents. The methodology is shown to generally predict the pKa values for all the cases investigated to within 1 pH unit so long as the differential solvation error is larger than the systematic error in the gas-phase acidity calculations. Such an approach is rather general and does not have additional complications that would arise in a cluster-continuum method, thus giving it strength as a simple high-throughput means to calculate absolute pKa values. This article is part of a Special Issue entitled: Metals in Bioenergetics and Biomimetics Systems.