Empirically Fitted Parameters for Calculating pKa Values with Small Deviations from Experiments Using a Simple Computational Strategy.

Two empirically fitted parameters have been derived for 74 levels of theory. They allow fast and reliable pKa calculations using only the Gibbs energy difference between an acid and its conjugated base in aqueous solution (ΔGs(BA)). The parameters were obtained by least-squares fits of ΔGs(BA) vs experimental pKa values for phenols, carboxylic acids, and amines using training sets of 20 molecules for each chemical family. Test sets of 10 molecules per family-completely independent from the training set-were used to verify the reliability of the fitting parameters method. It was found that, except for MP2, deviations from experiments are lower than 0.5 pKa units. Moreover, mean unsigned errors lower than 0.35 pKa units were found for the 98.6%, 98.6%, and 94.6% of the tested levels of theory for phenols, carboxylic acids and amines, respectively. The parameters estimated here are expected to facilitate computationally based estimations of pKa values of species for which this magnitude is still unknown, with uncertainties similar to the experimental ones. However, the present study deals only with molecules of modest complexity, thus the reliability of the FP method for more complex systems remains to be tested.

Searching for Computational Strategies to Accurately Predict pKas of Large Phenolic Derivatives.

Twenty-two reaction schemes have been tested, within the cluster-continuum model including up to seven explicit water molecules. They have been used in conjunction with nine different methods, within the density functional theory and with second-order Møller-Plesset. The quality of the pKa predictions was found to be strongly dependent on the chosen scheme, while only moderately influenced by the method of calculation. We recommend the E1 reaction scheme [HA + OH(-) (3H2O) ↔ A(-) (H2O) + 3H2O], since it yields mean unsigned errors (MUE) lower than 1 unit of pKa for most of the tested functionals. The best pKa values obtained from this reaction scheme are those involving calculations with PBE0 (MUE = 0.77), TPSS (MUE = 0.82), BHandHLYP (MUE = 0.82), and B3LYP (MUE = 0.86) functionals. This scheme has the additional advantage, compared to the proton exchange method, which also gives very small values of MUE, of being experiment independent. It should be kept in mind, however, that these recommendations are valid within the cluster-continuum model, using the polarizable continuum model in conjunction with the united atom Hartree-Fock cavity and the strategy based on thermodynamic cycles. Changes in any of these aspects of the used methodology may lead to different outcomes.