Dielectric response of the water hydration layer around spherical solutes

We calculate the local dielectric function $\varepsilon \left(r\right)$ inside the hydration layer around a spherical solute (i) from molecular dynamics simulations including explicit solutes and (ii) theoretically using the nonlocal dielectric function of bulk water which includes the radial electric field, but not the explicit solute. The observed agreement between the two concepts shows that while $\varepsilon \left(r\right)$ is strongly different from bulk, this difference is not due to restructuring of the hydrogen bond network but is mostly a consequence of the field geometry. The dielectric response differs for anions and cations, yielding a natural explanation for the well-known charge asymmetry of ionic solvation in agreement with experimental data.

Figure 1

Cut through the simulated system: the sphere in the center of the droplet is the solute; the black spheres are the wall particles.

Figure 2

(a) The radial density profiles around three different solutes ranging from purely repulsive (hydrophobic) to very attractive (hydrophilic). (b) The inverse radial component of the local dielectric permittivity shows strongly oscillatory behavior but with a shorter wavelength than the density oscillations. Interestingly, the oscillating permittivity is almost independent of the water-ion interaction parameters. (c) Changing the Lennard-Jones interaction distance (ion size) ${\sigma }_{iO}$ leads to a shift but not to qualitative changes in the dielectric profiles.

Figure 3

The nonlocal dielectric response of bulk water calculated from our MD simulations (gray dots) and the corresponding empirical fit function (solid line). Due to the singularity for $k=0$ we add the bulk value [66] for SPC/E, ${\varepsilon }_{nl}(k=0)=71$, manually [56].

Figure 4

Comparison of the local dielectric constant calculated from MD simulation including explicit ions from Fig. 2 (solid lines) to the same quantity obtained solely from bulk water properties using the nonlocal model of [51] with ${\varepsilon }_{nl}\left(k\right)$ from our bulk MD simulations (dashed lines). The good agreement demonstrates that the response around a spherical solute is mostly determined by bulk water properties and not so much caused by a restructuring of water in the hydration layer.

Figure 5

(a) Radial dielectric profile around a charged solute. The dielectric profiles around the positive charges show almost no phase shift but a slightly larger amplitude compared to $q=0$. The profiles around the negative charges are shifted towards a smaller radius. (b) The solvation energy for different partially charged solutes (dots) calculated solely from dielectric profiles as those shown in (a). The results show an asymmetry of the solvation energy of 108 kJ/mol in good agreement with full free-energy calculations [71].