From atoms to crystals: A mathematical journey

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. © 2005 American Mathematical Society.