We consider the continuum limit for models of solids that arise in density functional theory and the QM-continuum approximation of such models. Two different versions of QM-
continuum approximation are proposed, depending on the level at which the Cauchy-Born rule is used, one at the level of electron density and one at the level of energy. Consistency at the interface
between the smooth and the non-smooth regions is analyzed. We show that if the Cauchy-Born rule is used at the level of electron density, then the resulting QM-continuum model is free of the so-called “ghost force” at the interface. We also present dynamic models that bridge naturally the Car-Parrinello method and the QM-continuum approximation.
Publié le : 2007-09-15
Classification:
continuum limit,
QM-continuum approximation,
density functional theory,
35Q40,
74Q05,
34E05,
74B20
@article{1188405674,
author = {E, Weinan and Lu, Jianfeng},
title = {The continuum limit and QM-continuum approximation of quantum mechanical models of solids},
journal = {Commun. Math. Sci.},
volume = {5},
number = {1},
year = {2007},
pages = { 679-696},
language = {en},
url = {http://dml.mathdoc.fr/item/1188405674}
}
E, Weinan; Lu, Jianfeng. The continuum limit and QM-continuum approximation of quantum mechanical models of solids. Commun. Math. Sci., Tome 5 (2007) no. 1, pp. 679-696. http://gdmltest.u-ga.fr/item/1188405674/