Towards a first principles prediction of pKa: COSMO-RS and the cluster-continuum approach

The COSMO-RS method, a post-quantum chemistry extension of the quantum chemical dielectric continuum solvation model COSMO with a statistical thermodynamics treatment for realistic solvation simulation, has been applied to the prediction of the aqueous pK(a) of acids and bases. The combination of the COSMO-RS approach to pK(a) prediction with the cluster-continuum approach (explicit solvation of the solute compound with one or more solvent molecules) was used on three data sets consisting of 94 acids and 75 bases. Correlation of the calculated free energies of dissociation in water with the experimental aqueous pK(a) of the solute acids and bases in their bare state and explicitly solvated by one or two solvent molecules showed an increase of the regression slope with the number of explicit solvent molecules, thus showing a regression slope that is closer to the theoretical value than the slope found for bare solutes. It was found that the cluster-continuum approach is limited to a pK(a) range of strong to moderately weak acids and bases, because the optimisations of the solvent-solute complexes of the ionic species of very weak acids (such as the anion of tert-butanol) did not lead to the desired complexes, but yielded dissociation products.