Are thermodynamic cycles necessary for continuum solvent calculation of pKas and reduction potentials?

Continuum solvent calculations of pK(a)s and reduction potentials usually entail the use of a thermodynamic cycle to express the reaction free energy in terms of gas phase energies and free energies of solvation. In this work, we present a systematic study comparing the solution phase free energy changes obtained in this manner with those directly computed within the SMD solvation model against a large test set of 117 pK(a)s and 42 reduction potentials in water and DMSO. The inclusion of vibrational contributions in the free energy of solvation has a negligible impact on the accuracy of thermodynamic cycle predictions of pK(a)s and reduction potentials. Additionally, when gas phase energies in the thermodynamic cycle are computed at more accurate levels of theory, very similar results (mean unsigned difference of 0.5 kcal mol(-1)) can be achieved when the high-level computations (MP2/GTMP2Large and G3(MP2)-RAD(+)) are directly carried out within the continuum model. Increasing the accuracy of the electronic structure theory may or may not improve the agreement with experiment suggesting that the error is largely in the solvation model. For amino acids where their gas and solution phase species exist as different tautomers, the direct approach provided a significant improvement in calculated pK(a)s. These results demonstrate that direct calculation of solution phase pK(a)s and reduction potentials within the SMD model provides a general and reliable approximation to corresponding thermodynamic cycle based protocols, and is recommended for systems where solvation induced changes in geometry are significant. Further studies are necessary to ascertain whether the results are generalisable to other continuum solvation models.