Rigorous derivation of the "X alpha" exchange potential: a deformation approach

We deal with the "Slater-Gasper-Kohn-Sham" local density approximation for the exchange potential of Hartree-Fock models. Our mathematical rigorous me thod to derive the famous "third root term" as well as higher order correct ions is based on deformations (local scaling transformations) of plane wave s and the "high density limit" of infinite number of particles. On the leve l of the exchange energy, this gives a rigorous justification of the Dirac term. For the kinetic energy, this method gives also a rigorous derivation of the Thomas-Fermi-von-Weizsacker model. (C) 2000 Elsevier Science B.V. Al l rights reserved.