Density Functional Theory of Atoms and Molecules

Abstract

The Schrödinger equation is a (linear) partial differential equation that can be solved exactly only in very few special cases such as the Coulomb potential or the harmonic oscillator potential. For more general potentials or for problems with more than two particles the quantum mechanical problem is no easier to solve than the corresponding classical one. In these situations variational methods are one of the most powerful tools for deriving approximate eigenvalues E and eigenfunctions ψ. These approximations are done in terms of a theory of density functionals as proposed by Thomas, Fermi, Hohenberg and Kohn. This chapter explains briefly the basic facts of this theory.