  The standard Maxwell formulation of the problem of polarized dielectrics
suffers from a number of difficulties, both conceptual and practical. These
difficulties are particularly significant in the case of liquid interfaces,
where the ability of the interfacial multipoles to change their orientations to
minimize their free energies leads to interfacial polarization localized within
a thin microscopic layer. A formalism to capture this physical reality of
localized interfacial polarization is proposed and is based on the surface
charge as the source of microscopic electric fields in dielectrics. The surface
charge density incorporates the local structure of the interface into
electrostatic calculations. The corresponding surface susceptibility and
interface dielectric constant provide local closures to the electrostatic
boundary value problem. A robust approach to calculate the surface
susceptibility from numerical simulations is proposed. The susceptibility can
alternatively be extracted from a number of solution experiments, in particular
those sensitive to the overall dipole moment of a closed dielectric surface.
The theory is applied to the solvent-induced spectral shift and high-frequency
dielectric response of solutions.
