Geodesic
Convergence rates of supercell calculations in the reduced Hartree−Fock model
Gontier, David1  ; Lahbabi, Salma2 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1403-1424

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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.

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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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     author = {Gontier, David and Lahbabi, Salma},
     title = {Convergence rates of supercell calculations in the reduced {Hartree\ensuremath{-}Fock} model},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1403--1424},
     publisher = {EDP-Sciences},
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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 , Tome 50 (2016) no. 5, pp. 1403-1424. doi: 10.1051/m2an/2015084

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