Prediction of acid pK_a values in the solvent acetone based on COSMO-RS

In this contribution we extent the use of the conductor-like screening model for realistic solvation (COSMO-RS) to the prediction of pK_a values in acetone, a commonly used dipolar aprotic solvent. For this, we calculated the Gibbs free energy of dissociation of 120 organic acids (nine acrylic acids, 87 benzoic acids, nine phenols, and 15 benzenesulfonamides) using COSMO-RS at the two levels BP-TZVP and BP-TZVPD-FINE and determined the parameters for a linear free energy relation for the $p{K}_a$ prediction by performing linear fits to experimental values. Our results suggest that the data set dissects into two groups, with the phenols being different from the other three subsets. The acrylic and benzoic acids and the sulfonamides can be treated together and yield an excellent linear correlation ( $r^2>0.95$ ) with an RMSD of only ~0.3. The slope is found to be significantly smaller than the theoretical value ( $1/\mathrm{RT}\ln 10$ ), only 45% of it, which is in accordance with findings in the literature. The phenols, however, while similarly well correlated in their own subset with an RMSD of 1.7-1.9, exhibit a slope larger than one. We discuss both a higher uncertainty in the reference values as well as physical origins as possible reasons.