Convergence rates of supercell calculations in the reduced Hartree−Fock model
1 UniversitéParis-Est, École des Ponts and INRIA, 77455
2 Université Hassan II Casablanca, ENSEM, Km 7 Route d’El Jadida, B.P. 8118 Oasis, Casablanca, Morocco.
Revised: 27 October 2015
Accepted: 28 October 2015
This article is concerned with the numerical simulations of perfect crystals. We study the rate of convergence of the reduced Hartree−Fock (rHF) model in a supercell towards the periodic rHF model in the whole space. We prove that, whenever the crystal is an insulator or a semi-conductor, the supercell energy per unit cell converges exponentially fast towards the periodic rHF energy per unit cell, with respect to the size of the supercell.
Mathematics Subject Classification: 35Q40 / 65M12
Key words: Reduced Hartree−Fock / supercell model / Riemann sums / analytic functions
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