The continuum limit and QM-continuum approximation of quantum mechanical models of solids

Weinan E, Jianfeng Lu

Research output: Contribution to journalArticle

3 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)679-696
Number of pages18
JournalCommunications in Mathematical Sciences
Volume5
Issue number3
DOIs
StatePublished - Jan 1 2007

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Continuum limit
  • Density functional theory
  • QM-continuum approximation

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