Accurate Prediction of Acidity Constants in Aqueous Solution via Density Functional Theory and Self-Consistent Reaction Field Methods

Abstract

We have developed a protocol for computing the acidity constant (pKa) of organic compounds via ab initio quantum chemistry and continuum solvation methods. Density functional (DFT) calculations employing large basis sets are used to determine the gas-phase deprotonation energies. Solvation effects are treated via a self-consistent reaction field (SCRF) formalism involving accurate numerical solution of the Poisson−Boltzmann equation. Dielectric radii are parametrized for each functional group of interest to optimize solvation free energy calculations for neutral and charged species. While the intrinsic accuracy of these approaches is quite impressive (errors on the order of a few kcal/mol), it is not quite good enough to achieve the target accuracy that we have set for pKa prediction of 0.5 pKa units. Consequently, two further empirical parameters, scaling and additive factors, are determined for every functional group of interest by linear fitting directly to pKa data for a training set. With this additional parametrization, an average accuracy on the order of 0.5 pKa units is achieved. A wide range of coverage of ionizable groups is presented with special focus on chemistry of importance in pharmaceutically active compounds. In addition to obtaining data for large and diverse training sets, we have also selected a subset of known drugs for which pKa’s have been measured and made predictions for these compounds without further adjustment of parameters. The results are similar in quality to that of the training set despite the considerable size and complexity of many of these molecules, demonstrating the ability of the method to accurately handle substituent effects without explicit parametrization thereof. The method has been optimized from a computational viewpoint so that it is tractable even for relatively large pharmaceutical compounds in the 50−100 atom range.