From atoms to crystals: a mathematical journey

Abstract

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.

Hartree–Fock Theory for Pseudorelativistic Atoms

“…For a comprehensive discussion of Hartree-Fock (and other) approximations in quantum chemistry, and an extensive literature list, we refer to [10]. The aim of the present paper is to study the Hartree-Fock approximation for the pseudorelativistic operator H in (1).…”

Non-Isotropic Cusp Conditions and Regularity of the Electron Density of Molecules at the Nuclei

“…One exception is of course the archetype density functional theory, the Thomas-Fermi theory, which is mathematically and physically interesting, and very well understood, see [18] and [16]. For an interesting recent review on various mathematical problems related to the many models in computational chemistry, see [15]. For some work on the density ρ from a numerical point of view, related to regularity questions, see [2].…”

On stability and protonation of multielectron systems: The concept of proton affinity. II. Dissociative proton attachment and protonation—Deprotonation mapping

“…[27]. [24,32], the corresponding references [2][3][4][5][6] in Ref. [34], and particularly Figure 2 and Tables 2, 4, and 5 of Ref.…”