First principles calculations of aqueous pKa values for organic and inorganic acids using COSMO-RS reveal an inconsistency in the slope of the pKa scale

The COSMO-RS method, a combination of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for more realistic solvation (RS) simulations, has been used for the direct prediction of pK(a), constants of a large variety of 64 organic and inorganic acids. A highly significant correlation of r(2) = 0.984 with a standard deviation of only 0.49 between the calculated values of the free energies of dissociation and the experimental pK(a) values was found, without any special adjustment of the method. Thus, we have a theoretical a priori prediction method for pK(a), which has the regression constant and the slope as only adjusted parameters. Such a method can be of great value in many areas of physical chemistry, especially in pharmaceutical and agrochemical industry. To our surprise, the slope of pKa vs DeltaG(diss) is only 58% of the theoretically expected value of 1/RTln(10). A careful analysis with respect to different contributions as well as a comparison with the work of other authors excludes the possibility that the discrepancy is due to weaknesses of the calculation method. Hence, we must conclude that the experimental pK(a) scale depends differently on the free energy of dissociation than generally assumed.