On the Accuracy of the Direct Method to Calculate pK(a) from Electronic Structure Calculations

[Image: see text] The direct method (HA((soln)) ⇌ A((soln))(–) + H((soln))(+)) for calculating pK(a) of monoprotic acids is as efficient as thermodynamic cycles. A selective adjustment of proton free energy in solution was used with experimental pK(a) data. The procedure was analyzed at different levels of theory. The solvent was described by the solvation model density (SMD) model, including or not explicit water molecules, and three training sets were tested. The best performance under any condition was obtained by the G4CEP method with a mean absolute error close to 0.5 units of pK(a) and an uncertainty around ±1 unit of pK(a) for any training set including or excluding explicit solvent molecules. PM6 and AM1 performed very well with average absolute errors below 0.75 units of pK(a) but with uncertainties up to ±2 units of pK(a), using only the SMD solvent model. Density functional theory (DFT) results were highly dependent on the basis functions and explicit water molecules. The best performance was observed for the local spin density approximation (LSDA) functional in almost all calculations and under certain conditions, as high as those obtained by G4CEP. Basis set complexity and explicit solvent molecules were important factors to control DFT calculations. The training set molecules should consider the diversity of compounds.