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From atoms to crystals: a mathematical journey


Authors: Claude Le Bris and Pierre-Louis Lions
Journal: Bull. Amer. Math. Soc. 42 (2005), 291-363
MSC (2000): Primary 35Bxx, 35Jxx, 35Pxx, 49Kxx, 81Q05, 81Q10, 82Bxx
Published electronically: April 18, 2005
MathSciNet review: 2149087
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Abstract: We present an overview of some works on the models of computational quantum chemistry. We examine issues such as the existence of ground states (both for the electronic structure and the configuration of nuclei), the foundations of the models of the crystalline phase, and the macroscopic limits. We emphasize the connections between the physical modelling, the numerical concerns and the mathematical analysis of the problems.


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Additional Information

Claude Le Bris
Affiliation: CERMICS, École Nationale des Ponts et Chaussées, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée, France
Email: lebris@cermics.enpc.fr

Pierre-Louis Lions
Affiliation: Collège de France, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
Email: lions@dmi.ens.fr

DOI: http://dx.doi.org/10.1090/S0273-0979-05-01059-1
Received by editor(s): November 20, 2004
Published electronically: April 18, 2005
Additional Notes: This article is an extended version by the two authors of notes based upon a series of lectures given by PLL at Collège de France during the fall semester of the academic year 2003/04.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.