Coarse-graining in Interaction Space: An Analytical Approximation for the Effective Short-ranged Electrostatics

In a previous paper (Izvekov, S.; Swanson, J.M.J.; Voth, G.A.J. Phys. Chem. B 2008, 112, 4711), it was shown that the long-ranged electrostatic interactions in condensed phase can be rigorously mapped into effective short-ranged potentials using the force-matching (FM) method. This methodology is referred to as coarse-graining in interaction space. In the present paper, the asymptotic behavior of the resulting effective short-ranged interactions is investigated analytically using the theory of FM. The two major finding are: (1) under certain conditions the effective forces naturally approach zero at the FM cutoff radius, and (2) the difference between the effective FM force and the Coulomb force is an approximate linear function at shorter distances. An analytical approximation to the FM short-ranged force is then proposed based on these findings, and the result is numerically tested for liquid water systems.