Exploiting the Variational Principle

Abstract

Abstract This chapter begins with a discussion of the ubiquitous theorem that underlies much of the theory of interatomic forces, namely the Hellmann–Feynman theorem, and its derivation from the variational principle. Examples are given, including the description of Van der Waals forces, explaining how the theorem is completely general, but only applicable when the energy functional describing the electrons has been minimized. When this condition is satisfied, the forces on the nuclei can be calculated with classical electrostatics. First and second order perturbation theories are discussed, leading to the second-order Hohenberg–Kohn–Sham functional, and for the first time deriving the errors in it. This in turn leads to the useful functional known as the Harris–Foulkes functional, and variations on it. These functionals do not require time-consuming iteration to self-consistency in the charge density, and are the basis for some simple models.