Analytic Treatment of the Pair Density in Kohn-Sham Density Functional Theory

We have developed a new treatment of the LDA functional in Kohn-Sham density functional theory which is expressed in terms of the pair density of a non-interacting system of particles, thus avoiding from the outset self-interaction effects. The pair density is expressed explicitly in terms of the density using a orthonormal and complete basis expressed as a functional of the density. This allows its functional differentiation with respect to the density by analytic means. The method is illustrated with numerical results for the potential in the case of one and three dimensional systems and is compared to the potentials obtained from the Hartree term.