We deal with local density approximations for the kinetic and exchange energy term, ℰ kin (ρ) and ℰ ex (ρ), of a periodic Coulomb model. We study asymptotic approximations of the energy when the number of particles goes to infinity and for densities close to the constant averaged density. For the kinetic energy, we recover the usual combination of the von-Weizsäcker term and the Thomas–Fermi term. Furthermore, we justify the inclusion of the Dirac term for the exchange energy and the Slater term for the local exchange potential.
Local density approximations from finite systems