Calculation of the free energy of polarization: Quantifying the effect of explicitly treating electronic polarization on the transferability of force-field parameters

The lack of an explicit description of electronic polarization in nonpolarizable force fields usually results in an incomplete transferability of force-field parameter sets when applied in simulations of the system of interest in either a polar or an apolar environment. For example, the use of nonpolarizable parameter sets optimized to reproduce experimental data on properties of pure liquids of polar compounds commonly yields too low solubilities in water for the corresponding compounds. The reason is that the fixed charge distributions calibrated for the pure liquid might correspond to too low molecular dipole moments in case of hydration. In the current study, we quantitatively show that explicit inclusion of electronic polarization can improve the transferability of biomolecular force-field parameter sets. With this aim, free energies of polarization, Delta G(pola), have been calculated, with Delta G(pola) corresponding to the free energy difference between identical systems described by a polarizable and a nonpolarizable model. Using a nonpolarizable model and a polarizable one (based on the charge-on-spring approach) for dimethyl ether (DME), which were both parametrized to reproduce experimental values for pure liquid properties, small values were found for Delta G(pola) for the pure liquid or when a DME solute was solvated in the apolar solvent cyclohexane. For the solute hydrated in water, however, Delta G(pola) was found to be of the same order of magnitude as the discrepancy between the free energy of hydration from simulation using a nonpolarizable solute model and the experimental value. Thus, introducing polarizabilities clearly improves the transferability of the parameter set. Additionally, in calculations of an anion solvated in DME, Delta G(pola) for the solvent adopted relatively large values. From an estimation of the errors in the calculated free energy differences, it was furthermore shown that the calculation of Delta G(pola) offers an effective and accurate method to obtain differences in solvation (or excess) free energies between systems described by polarizable and nonpolarizable models when compared to a direct calculation of solvation (or excess) free energies.