Geodesic
Convergence rates of supercell calculations in the reduced Hartree−Fock model
Gontier, David 1 idref     ; Lahbabi, Salma 2 idref  
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 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

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.

Reçu le :
Accepté le :
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. 
@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},
     year = {2016},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {5},
     doi = {10.1051/m2an/2015084},
     zbl = {1356.35195},
     mrnumber = {3554547},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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://geodesic.mathdoc.fr/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

Cité par Sources :