Introduction

Abstract

Density functional theory provides a powerful tool for computations of the quantum state of atoms, molecules and solids, and of ab-initio molecular dynamics. It was conceived in its initial naïve and approximative version by Thomas and Fermi immediately after the foundation of quantum mechanics, in 1927. Just thirty years ago, in the middle of the sixties, Hohenberg, Kohn and Sham on the one hand established a logically rigorous density functional theory of the quantum groundstate on the basis of quantum mechanics, and on the other hand, guided by this construction, introduced an approximative explicit theory called the local-density approximation, which for computations of the quantum groundstate of many-particle systems proved to be superior to both Thomas-Fermi and Hartree-Fock theories. From that time on, density functional theory has grown vastly in popularity, and a flood of computational work in molecular and solid state physics has been the result. Motivated by its success, there has been always a tendency to widen the fields of application of density functional theory, and in these developments, some points which were left somewhat obscure in the basic theory, were brought into focus from time to time. This led in the early eighties to a deepening of the logical basis, essentially by Levy and Lieb, and finally Lieb gave the basic theory a form of final mathematical rigour. Since that treatment, however, is based on the tools of modern convex functional analysis, its implications only gradually became known to the many people who apply density functional theory. A thorough treatment of the dependence on particle number on the basis of Lieb’s theory is given for the first time in the present text.