Correcting DFT errors through v-representable density partitioning

The recently introduced Self-Attractive Hartree (SAH) decomposition is a method to partition electron density into smooth localized fragments. The fragment densities are obtained through a regularized maximization of self-repulsion. The resulting set of eigenvalue equations resembles Kohn-Sham equations for electrons experiencing self-attractive Hartree potential and external potential common for all fragments. Ground-state solutions of these equations are by construction v-representable and effectively visualize bonding patterns in molecular systems.
We show how these smooth density fragments can be used to correct errors of approximate density functionals like self-interaction or missing van der Waals interactions. To this end we introduce the many-pair expansion (MPE), which is a systematically improvable correction scheme converging to the exact energy. Possible applications in density embedding approaches and orbital-free DFT are also discussed.