Convergence rates of supercell calculations in the reduced Hartree−Fock model
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 5, pp. 1403-1424.

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.

Received:
Accepted:
DOI: 10.1051/m2an/2015084
Classification: 35Q40, 65M12
Keywords: Reduced Hartree−Fock, supercell model, Riemann sums, analytic functions
Gontier, David 1; Lahbabi, Salma 2

1 UniversitéParis-Est, École des Ponts and INRIA, 77455 Marne-la-Vallée, France.
2 Université Hassan II Casablanca, ENSEM, Km 7 Route d’El Jadida, B.P. 8118 Oasis, Casablanca, Morocco.
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Gontier, David; Lahbabi, Salma. Convergence rates of supercell calculations in the reduced Hartree−Fock model. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 50 (2016) no. 5, pp. 1403-1424. doi : 10.1051/m2an/2015084. http://www.numdam.org/articles/10.1051/m2an/2015084/

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