Precise estimation of transfer free energies for ionic species between similar media

Transfer properties and partition coefficients for individual ions are relevant in a variety of scientific and engineering contexts, such as predicting the effects of different electrolytes on biomacromolecules in a preferential interaction sense or predicting the distribution of heavy metal ions in soils, rivers, etc. Computer simulations allow free energies of transfer to be estimated by considering single ions explicitly. When the two media under consideration are similar to each other regarding ion solvation, the resultant free energies are small in absolute magnitude. In these cases, it is advisable to simulate the transfer process directly. Here, we demonstrate how this can be achieved using two-dimensional umbrella sampling in conjunction with canonical ensemble molecular dynamics simulations where two liquid media are in direct contact. By calculating full two-dimensional potentials of mean force, these simulations allow the estimation of single-ion transfer free energies by integrating this surface accordingly. We report statistical accuracies to highlight that very high precision is achieved and needed to make even just qualitative statements about the transfer process. We close by discussing implications of our results for the specific case considered: the transfer of polypeptide side chain analogs from water to aqueous denaturant solutions.