Quantum Chemical Calculation of p<i>K</i>_as of Environmentally Relevant Functional Groups: Carboxylic Acids, Amines, and Thiols in Aqueous Solution

Developing accurate quantum chemical approaches for calculating p<i>K</i>_as is of broad interest. Useful accuracy can be obtained by using density functional theory (DFT) in combination with a polarizable continuum solvent model. However, some classes of molecules present problems for this approach, yielding errors greater than 5 p<i>K</i> units. Various methods have been developed to improve the accuracy of the combined strategy. These methods perform well but either do not generalize or introduce additional degrees of freedom, increasing the computational cost. The Solvation Model based on Density (SMD) has emerged as one of the most commonly used continuum solvent models. Nevertheless, for some classes of organic compounds, e.g., thiols, the p<i>K</i>_as calculated with the original SMD model show errors of 6–10 p<i>K</i> units, and we traced these errors to inaccuracies in the solvation free energies of the anions. To improve the accuracy of p<i>K</i>_as calculated with DFT and the SMD model, we developed a scaled solvent-accessible surface approach for constructing the solute–solvent boundary. By using a “direct” approach, in which all quantities are computed in the presence of the continuum solvent, the use of thermodynamic cycles is avoided. Furthermore, no explicit water molecules are required. Three benchmark data sets of experimentally measured p<i>K</i>_a values, including 28 carboxylic acids, 10 aliphatic amines, and 45 thiols, were used to assess the optimized SMD model, which we call SMD with a scaled solvent-accessible surface (SMD_sSAS). Of the methods tested, the M06-2X density functional approximation, 6-31+G­(d,p) basis set, and SMD_sSAS solvent model provided the most accurate p<i>K</i>_as for each set, yielding mean unsigned errors of 0.9, 0.4, and 0.5 p<i>K</i> units, respectively, for carboxylic acids, aliphatic amines, and thiols. This approach is therefore useful for efficiently calculating the p<i>K</i>_as of environmentally relevant functional groups