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September 2007 The continuum limit and QM-continuum approximation of quantum mechanical models of solids
Weinan E, Jianfeng Lu
Commun. Math. Sci. 5(3): 679-696 (September 2007).

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.

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Weinan E. Jianfeng Lu. "The continuum limit and QM-continuum approximation of quantum mechanical models of solids." Commun. Math. Sci. 5 (3) 679 - 696, September 2007.

Information

Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1141.35046
MathSciNet: MR2352337

Subjects:
Primary: 34E05 , 35Q40 , 74B20 , 74Q05

Keywords: continuum limit , density functional theory , QM-continuum approximation

Rights: Copyright © 2007 International Press of Boston

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Vol.5 • No. 3 • September 2007
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