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.
Accepté le :
DOI : 10.1051/m2an/2015084
Mots-clés : Reduced Hartree−Fock, supercell model, Riemann sums, analytic functions
@article{M2AN_2016__50_5_1403_0,
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},
volume = {50},
number = {5},
year = {2016},
doi = {10.1051/m2an/2015084},
zbl = {1356.35195},
mrnumber = {3554547},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015084/}
}
TY - JOUR AU - Gontier, David AU - Lahbabi, Salma TI - Convergence rates of supercell calculations in the reduced Hartree−Fock model JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2016 SP - 1403 EP - 1424 VL - 50 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015084/ DO - 10.1051/m2an/2015084 LA - en ID - M2AN_2016__50_5_1403_0 ER -
%0 Journal Article %A Gontier, David %A Lahbabi, Salma %T Convergence rates of supercell calculations in the reduced Hartree−Fock model %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1403-1424 %V 50 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015084/ %R 10.1051/m2an/2015084 %G en %F M2AN_2016__50_5_1403_0
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. http://www.numdam.org/articles/10.1051/m2an/2015084/
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