Supercell Calculations in the Reduced Hartree–Fock Model for Crystals with Local Defects

David Gontier (1, 2) , Salma Lahbabi (3)

1 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique
2 MATHERIALS - MATHematics for MatERIALS
3 University Hassan II [Casablanca]

In this article, we study the speed of convergence of the supercell reduced Hartree-Fock (rHF) model towards the whole space rHF model in the case where the crystal contains a local defect. We prove that, when the defect is charged, the defect energy in a supercell model converges to the full rHF defect energy with speed L−1, where L3 is the volume of the supercell. The convergence constant is identified as the Makov-Payne correction term when the crystal is isotropic cubic. The result is extended to the non-isotropic case.

Domaines: Physique mathématique [math-ph]

David Gontier, Salma Lahbabi. Supercell Calculations in the Reduced Hartree–Fock Model for Crystals with Local Defects. Applied Mathematics Research eXpress, 2017, 2017 (1), pp.1-64. ⟨10.1093/amrx/abw010⟩. ⟨hal-01436596⟩