Communications in Mathematical Sciences
- Commun. Math. Sci.
- Volume 5, Issue 3 (2007), 679-696.
The continuum limit and QM-continuum approximation of quantum mechanical models of solids
Weinan E and Jianfeng Lu
Abstract
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.
Article information
Source
Commun. Math. Sci. Volume 5, Issue 3 (2007), 679-696.
Dates
First available in Project Euclid: 29 August 2007
Permanent link to this document
https://projecteuclid.org/euclid.cms/1188405674
Mathematical Reviews number (MathSciNet)
MR2352337
Zentralblatt MATH identifier
1141.35046
Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics 74Q05: Homogenization in equilibrium problems 34E05: Asymptotic expansions 74B20: Nonlinear elasticity
Keywords
continuum limit QM-continuum approximation density functional theory
Citation
E, Weinan; Lu, Jianfeng. The continuum limit and QM-continuum approximation of quantum mechanical models of solids. Commun. Math. Sci. 5 (2007), no. 3, 679--696. https://projecteuclid.org/euclid.cms/1188405674.
