O. Bokanowski, B. Grebert, N. Mauser
Local density approximations for the energy of a periodic Coulomb model
(84K, latex 2e)
ABSTRACT. We deal with local density approximations for the kinetic and exchange
energy term, $\cE_{kin}(\rho )$ and $\cE_{ex}(\rho )$,
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-Weizs\"acker 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.