Motions of two distinct ions can get correlated because the polarization induced by the ions can propagate through intervening water and can interfere with each other. This important aspect, which is not included in the continuum model based theories, has not been studied adequately. We calculate the effective force between two oppositely charged and similarly charged ions fixed in water as a function of separation distance R. At short separations, R less than 1.5 nm, the effective force vastly differs from the 1/epsilon R-s(2) dependence advocated by the screened Coulomb's force law (SCFL), where epsilon(s) is the static dielectric constant of the medium. This breakdown of the SCFL is shown to be due to the persistent interference between the polarizations created by the two charges in a manner similar to the vortex-antivortex pair formation in the XY model Hamiltonian. The distance dependence of dielectric constants, epsilon(s)(R), extracted from our simulation exhibits interesting features and can be used in future modeling. In addition, we show that the force-force time autocorrelation between two neighboring ions decays differently at short separation and analyze the friction on the ion pair at different separation distances.
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