Density Functional Theory

Abstract

The Hartree–Fock (HF) method provides a straightforward approach to construct mean fields in many-fermion systems. We have exemplified its capabilities in a few examples (Chap. 5). The HF approach, however, suffers from some limitations, on the formal side due to the average treatment of interactions and on the practical side due to the involved exchange term. To go beyond HF strictly speaking implies including correlations, which will be discussed in Chap. 9. Still, there is an alternative “effective” path which consists in building a simple HF approximation (or even Hartree approximation , namely without including exchange), on top of effective interactions . The construction of such effective interactions of course requires some elaborate calculations but it allows to include correlation effects in the interaction itself, which allows a mean-field description of the given system, mostly at the technically simple Hartree level. Such effective approaches usually constitute a large step forward to more self-consistent modeling. The formally sound way to formulate such effective theories proceeds through energy-density functionals as a starting point.