Density functionals for coulomb systems

TLDR

Several less obvious problems remain in the theory of density functionals. The paper aims to discuss mathematical connections between N‑particle wave functions and single‑particle densities, establish the mathematical foundations of universal density functional theory for ground‑state energy, and review explicit functionals that provide rigorous energy bounds. The authors review explicit functionals that yield rigorous bounds on the ground‑state energy. They show that the HK functional is not defined for all densities and present several ways to overcome this limitation.

Abstract

Abstract This paper has three aims: (i) To discuss some of the mathematical connections between N ‐particle wave functions ψ and their single‐particle densities ρ ( x ). (ii) To establish some of the mathematical underpinnings of “universal density functional” theory for the ground state energy as begun by Hohenberg and Kohn. We show that the HK functional is not defined for all ρ and we present several ways around this difficulty. Several less obvious problems remain, however. (iii) Since the functional mentioned above is not computable, we review examples of explicit functionals that have the virtue of yielding rigorous bounds to the energy.