Exact Density Functional Obtained via the Levy Constrained Search - Mori-Sanchez, Paula; Cohen, Aron J (The journal of physical chemistry letters, 2018)
A stochastic minimization method for a real-space wavefunction, Ψ(r ,r ...r ), constrained to a chosen density, ρ(r), is developed. It enables the explicit calculation of the Levy constrained search F[ρ]=min <Ψ|T+V |Ψ>, that gives the exact functional of density functional theory. This general method is illustrated in the evaluation of F[ρ] for densities in one dimension with a soft-Coulomb interaction. Additionally, procedures are given to determine the first and second functional derivatives δF/δρ(r) and δ F/δρ(r)δρ(r'). For a chosen external potential, v(r), the functional and its derivatives are used in minimizations over densities to give the exact energy, E , without needing to solve the Schrödinger equation.