  We present a simple, unified theory for the self-energy of an ion near a
dielectric interface. Our theory accounts for both the short-range (solvation)
and long-range (image force) electrostatic forces, charge polarization induced
by these forces, and the cavity energy. In contrast to previous models, our
self energy is continuous across the interface and thus applicable to both the
water and air (oil) sides of the interface. With no fitting parameters, we
predict the specific ion effect on the interfacial affinity of halogen anions
at the water/air interface, and the strong adsorption of hydrophobic ions at
the water/oil interface, in agreement with experiments and atomistic
simulations.
