Structure Dependence ofdBands in Transition Metals

The object is to provide a simple scheme for calculating the dependence of the $d$-band structure on the position of the atoms in the crystal. The Korringa-Kohn-Rostoker method in the narrow-band approximation has been used to calculate the nonhybridizing $d$ bands for different crystal structures and for various values of volume/atom, in terms of the position and width of the $d$-scattering resonance. These bands have been fitted by near-neighbor linear combination of atomic orbitals (LCAO) parameters, as in the interpolation schemes of Hodges, Ehrenreich, and Lang, and of Mueller. It is shown that the dependence of the LCAO parameters on structure and volume can be described to a good approximation by simple structure-independent functions. The accuracy of the description for the $d$ bands of the fcc and bcc phases of Fe is about 0.01 Ry. The results are discussed in relation to recent developments in transition-metal band theory.