A stable local density functional approach to ion-ion correlations

We propose a new approach for incorporating counterion correlations into Poisson-Boltzmann-like theories, which is based on a local density functional for the system of counterions. Our derivation is inspired by the Debye-Huckel approach to the one-component plasma (OCP). An artificial instability due to the OCP's homogeneous background charge which is absent in the original counterion system- is overcome by excluding the background from the vicinity of a central ion. The resulting free energy density is convex and thus applicable within a local density approximation. For the simple example of a strongly charged stiff rod surrounded by its counterions we demonstrate that the Poisson-Boltzmann free energy functional augmented by our new correction accounts for the correlations present in this system when compared to molecular dynamics simulations.