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Recent mathematical results on the quantum modeling of crystals

Catto, Isabelle; Lions, Pierre-Louis; Le Bris, Claude (2000), Recent mathematical results on the quantum modeling of crystals, in Mireille Defranceschi, Claude Le Bris, Mathematical models and methods for ab initio quantum chemistry, Springer : Berlin Heidelberg, p. 95-120. 10.1007/978-3-642-57237-1_5

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Type
Chapitre d'ouvrage
Date
2000
Book title
Mathematical models and methods for ab initio quantum chemistry
Book author
Mireille Defranceschi, Claude Le Bris
Publisher
Springer
Published in
Berlin Heidelberg
ISBN
978-3-540-67631-7
Pages
95-120
Publication identifier
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Author(s)
Catto, Isabelle cc
Lions, Pierre-Louis
Le Bris, Claude
Abstract (EN)
We describe in this paper a strategy, the so-called thermodynamic limit process, to build in a rigorous mathematical manner the quantum-mechanical models for the ground-state energy of solid crystals. These models are the analogues for the solid state of well-known models issued from Quantum Chemistry, namely Thomas-Fermi, Hartree and Hartree-Fock type models. We shall present a broad overview on recent mathematical studies on this topic.
Subjects / Keywords
Density functional theory; Hartree model; Hartree-Fock models