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 (phi_d?v?phi_{d 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 (phi_d?v?phi_{d minutes} ) in terms of the position and width of the resonance of v and the tail of the localized d state phi_d(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 phi_d(r), the general expressions can also reproduce the corresponding results obtained by pettifor via the kkr band structure equations.