Convergence rates of supercell calculations in the reduced Hartree-Fock\n model

Abstract

This article is concerned with the numerical simulations of perfect crystals.\nWe study the rate of convergence of the reduced Hartree-Fock (rHF) model in a\nsupercell towards the periodic rHF model in the whole space. We prove that,\nwhenever the crystal is an insulator or a semi-conductor, the supercell energy\nper unit cell converges exponentially fast towards the periodic rHF energy per\nunit cell, with respect to the size of the supercell.\n