Local density approximations for the energy of a periodic Coulomb model

We deal with local density approximations for the kinetic and exchange energy terms of a periodic Coulomb model. For the kinetic energy, we give a rigorous derivation of the usual combination of the von-Weizsacker term and the Thomas-Fermi term in the “high density” limit. Furthermore, we justify the inclusion of the Dirac term for the exchange energy and the Slater term for the local exchange potential. Our method is based on deformations (local scaling transformat ions) of plane waves in a periodic box.

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