Interface dielectric constant of water at the surface of a spherical solute

Interface dielectric constant is used to quantify polar response of water interfacing a spherical solute. This interfacial parameter, affected by the interfacial structure within about two hydration layers, is fundamentally distinct from the bulk dielectric constant (a material property). Molecular dynamics simulations are used to extract the interface dielectric constant from fluctuation relations correlating the dipole moment of the interfacial layer with the medium electrostatics. For a probe ion, one has to calculate cross-correlations between the hydration shell dipole moment and the electrostatic potential, while cross-correlations between the shell dipole moment and the electrostatic field are required for a probe dipole. All protocols produce dielectric constants of water interfacing a nonpolar solute significantly below the bulk value. We analyze corrections imposed on the fluctuation relations by protocols using periodic boundary conditions with Ewald sums to compute electrostatic interactions. These corrections are insignificant for typical simulation protocols.