Acidity constants from vertical energy gaps: density functional theory based molecular dynamics implementation

The question of how to compute acidity constants (pK(a)) treating solvent and solute at the same level of theory remains of some interest, for example in the case of high or low pH conditions. We have developed a density functional theory based molecular dynamics implementation of such a method. The method is based on a half reaction scheme computing free energies of dissociation from the vertical energy gaps for insertion or removal of protons. Finite system size effects are important, but largely cancel when half reactions are combined to full reactions. We verified the method by investigating a series of organic and inorganic acids and bases spanning a wide range of pK(a) values (20 units). We find that the response of the aqueous solvent to vertical protonation/deprotonation is almost always asymmetric and correlated with the strength of the hydrogen bonding of the deprotonated base. We interpret these observations in analogy with the picture of solvent response to electronic ionization.