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1 CERMICS - Centre d-Enseignement et de Recherche en Mathématiques et Calcul Scientifique 2 MICMAC - Methods and engineering of multiscale computing from atom to continuum Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech 3 AGM - Laboratoire d-Analyse, Géométrie et Modélisation

Abstract : In this article, we set up a functional setting for mean-field electronic structure models of Hartree-Fock or Kohn-Sham types for disordered crystals. The electrons are quantum particles and the nuclei are classical point-like articles whose positions and charges are random. We prove the existence of a minimizer of the energy per unit volume and the uniqueness of the ground state density of such disordered crystals, for the reduced Hartree-Fock model rHF. We consider both short-range Yukawa and long-range Coulomb interactions. In the former case, we prove in addition that the rHF ground state density matrix satisfies a self-consistent equation, and that our model for disordered crystals is the thermodynamic limit of the supercell model.

Keywords : random Schrödinger operators disordered crystals electronic structure Hartree-Fock theory mean-field models density functional theory thermodynamic limit

Author: Eric Cancès - Salma Lahbabi - Mathieu Lewin -



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