First-principles calculation of pKa 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.