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 plc calculations using only the Gibbs energy difference between an acid and its conjugated base in aqueous solution (Delta G(s(BA))). The parameters were obtained by least-squares fits of Delta G(s(BA)) vs experimental pK(a) 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 pK(a) units. Moreover, mean unsigned errors lower than 0.35 pK(a) 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 pK(a) 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.