Equivalence of resonance and tight binding descriptions of the d band in transition metals

Abstract

In the tight binding theory of transition metals, the d band arises out of the interatomic matrix elements (phid?v?phid minutes ). In the resonance theory of transition metals, on the other hand, the d band is described in terms of the intra-atomic resonance parameters of the potential v. The equivalence of these two seemingly different points of view is demonstrated by deriving general analytic expressions for (phid?v?phid minutes ) in terms of the position and width of the resonance of v and the tail of the localized d state phid(r). The derivation is accomplished by expanding the d state centred on one site in terms of spherical harmonics centred on the second site and then approximating the surviving l=2 expansion coefficient. The accuracy of this procedure is verified in detail for the metals copper and iron. For special forms of the tail of phid(r), the general expressions can also reproduce the corresponding results obtained by pettifor via the kkr band structure equations.