This article discusses simple but realistic models of the bonding in metallic systems. As is discussed in the introduction, such methods are valuable both to study complex systems that are intractable with more rigorous methods and to study generic properties that do not depend on the fine details of the energetics. In addition, simple models are useful for gaining a physical understanding of a system.
As discussed in the article by Vitek, a great deal of progress in the understanding of defect structures has been gained by the use of constant-volume pair potentials, that is, pair-potential models that include a volume-dependent term. In this picture, the energy is assumed to have two parts, a large density-dependent but structure-independent part and a structure-dependent part that is represented by pair interactions. This view follows from a physical picture where the metal is viewed as a uniform electron gas and the interactions between the atoms are obtained by performing perturbation theory on this reference system. This approach has a serious limitation, though, in that it is restricted to situations where the system is essentially uniform such as when the bulk or defects do not introduce significant changes in the local density. This is true for two reasons. First, there is not a clear prescription for how the structure-independent part of the energy should be treated in an inhomogeneous region. This is a serious problem since a large part of the binding energy is included in this term. Second, the pair-potential term in this picture depends on the overall density. In the vicinity of a inhomogeneity such as a surface, there is no prescription for how the pair-potential term should vary.