First-Principles Calculation of pK a Values for Organic Acids in Nonaqueous Solution

Electronic structure theory, mainly the density functional theory (DFT), is applied to calculate the pK a values for a variety of organic acids in several nonaqueous solvents: namely DMSO, MeCN, and THF. Following the supermolecule approach the solute molecule, together with a few solvent molecules in close proximity, is treated explicitly by the electronic structure theory, and the remaining solvent environment is approximated by using a standard dielectric continuum model. It is found that in most cases including only one explicit solvent molecule gives satisfactory results for pK a estimations. Next, the equilibrium position free energy difference is calculated between a reference acid−base pair whose pK a is known experimentally and the acid−base pair whose pK a is to be determined theoretically. This bypasses the step of treating the solvated proton that most of the current theories have difficulty with and, to a large extent, induces favorable error cancelations in the final theoretical results. Accurate theoretical predictions of pK a values are thus obtained at a moderate level of theory (MP2 single point on B3LYP/6-31+G(d) optimized geometry) for a series of organic acids spanning a wide range of acidities in DMSO, MeCN, and THF. Furthermore, the correlation between the pK a values of these acids in different solutions is investigated theoretically, and excellent agreement is found with the experimental results.