Dependence of pKa on solute cavity for diprotic and triprotic acids

Abstract

A systematic study of ΔG_aq/pK_a for monoprotic, diprotic, and triprotic acids has been carried out based on DFT/aug-cc-pVTZ combined with CPCM and SMD solvation modeling. All DFT/cavity set combinations considered showed similar accuracy for ΔG_aq¹/pK_a1 (70% within ±2.5 kcal mol⁻¹ of experiment) while only the M05-2X/Pauling cavity combination gave reasonable results for ΔG_aq²/pK_a2 when both pK_a values are separated by more than three units (70% within ±5.0 kcal mol⁻¹ of experiment). The choice of experimental data is critical to the interpretation of the calculated accuracy especially for several inorganic acids. For the calculation of ΔG_aq³/pK_a3, the larger experimental uncertainty and an unrealistic orbital population of diffuse function for trianions in the gas phase hinders an evaluation of the predictive performance. We find the M05-2X functional with the Pauling cavity set is the best choice for ΔG_aq²/pK_a2 prediction in aqueous media while all DFT/cavity sets considered were competitive for ΔG_aq¹/pK_a1.