A reliable and efficient first principles-based method for predicting pK(a) values. III. Adding explicit water...

A popular method for predicting pK(a) values for organic molecules in aqueous solution is to establish empirical linear least-squares fits between calculated deprotonation energies and known experimental pK(a) values. In virtually all such calculations, the empirically observed slope of the pK(a) vs. ΔE fit is significantly less than the theoretical value, 1/(2.303RT) (which is 0.73 mol/kcal at room temperature). In our own continuum solvation calculations (Zhang et al., J Phys Chem A 2010, 114, 432), the empirical slope for carboxylic acids was only 0.23 mol/kcal, despite the excellent fit to the experimental pK(a) values. There has been much speculation about the reason for this phenomenon. Although the ΔE - pK(a) relation neglects entropic effects, these are expected to largely cancel. The most likely cause for the strange behavior of the fitted slope is explicit solute-solvent (water) interactions, especially involving the ions, which cannot be described accurately by continuum solvation models. We used our previously developed pK(a) protocol (OLYP/6-311+G(d,p)//3-21G(d) with the COSMO solvation model) to investigate the effect of adding one or two explicit water molecules to the system. The slopes for organic acids (especially carboxylic acids) are much closer to the theoretical value when explicit water molecules are added to both the neutral molecule and the anion. However, explicit water molecules have almost no effect on the slopes for organic bases. Adding explicit water molecules to the ions only produces intermediate results. Unfortunately, linear fits involving explicit water molecules have much larger errors than with continuum solvation models alone and are also much more expensive. Consequently, they are not suitable for large-scale pK(a) calculations. The results compared with literature values showed that our predicted pK(a) s are more accurate.