It is worth noting that the ‘glue’ type potentials cannot be expanded in a sum of two-body, three — body, four-body, etc. terms. Three-body terms enter into the free electron picture through nonlinear response of the electron gas, and into the tight — binding picture in the fourth moment description and beyond.

At constant second moment, increasing the fourth and higher even moments of the DOS tends to lead to a bimodal distribution. Bimodal distributions will be favored by materials with half-filled bands. Thus, three-body terms are likely to be important in struc­tures with few small-membered rings of atoms, and hence, small low moments. The bcc structure is a borderline example of this, but the classic is the dia­mond structure. Diamond has no rings of less than six atoms, resulting in a strongly bimodal DOS. This bimodal structure in the tight-binding representation is also interpreted as bonding and antibonding states in a covalent picture.

Interatomic potentials for carbon and silicon fall into this category. However, once a band gap is opened, the Fermi energy and perfect screening are lost, and the rigid band approximation is less appropriate.