Benchmarking the computed proton solvation energy and absolute potential in non-aqueous solvents

Proton solvation energies and absolute potentials are of critical importance in all areas of chemistry. But despite their relevance they are only known in water with a sufficient degree of accuracy while we still lack fundamental understanding in non-aqueous solvents. Here, we report an extensive benchmark for different DFT or ab-initio methods, the solvation models, and the choice of reference compounds for computing proton solvation energies and absolute potentials. Our computations indicate, that cationic acids (ammonium and iminium ions) allow for the most accurate prediction of these parameters in water while neutral acids (e.g. alcohols, carboxylic acids) display an unphysical correlation between their pKa and the proton solvation energy. The CCSD(T)/SMD computations are the most accurate method for predicting the proton solvation energy. For non-aqueous solvents, excellent error cancelation has been observed for all considered parameters. Furthermore, we report a fundamental flaw in solvation models for non-aqueous solvents, causing an unphysical correlation between the pKa and the proton solvation energy in DMSO. This work thoroughly evaluates the most critical parameters affecting the computed proton solvation energies using DMSO as a test case.