TOTAL ENERGY OF D-BAND METALS . ALKALINE-EARTH AND NOBLE METALS

We consider the sum of the one-electron energies of the occupied bands for a metal which has d bands interacting with nearly-free-electron bands. Using Hubbard's hybrid form of the Korringa-Kohn-Rostoker band-structure method, we consistently retain terms in the energy to first order in the width of the d scattering resonance. For the alkaline-earth and noble metals (the metals at each extreme of the transition series), it is shown that the lowest-order effect of the interaction between the d bands and the free-electron bands, and, in the case of a noble metal, also the effect of the finite width of the full d bands, results in a simple net contribution to the total energy given by Ud=(10Γπ)ln(|ε0-εF|ε0), where ε0 and Γ are the energy and width of the d scattering resonance, and εF is the Fermi energy for the unperturbed free-electron band. It is shown that this term is to be added to the usual pseudopotential contribution to the total energy, where, if the pseudopotential is expressed in Ziman's phase-shift formulation, the d phase shift is to be replaced by the residual phase shift which remains after the resonance part is extracted. It is also shown that the term Ud gives a negligibly small contribution to the cohesive energy and to the compressibility of Cu, indicating that the d-band contributions to these properties are to be found either in the volume dependence of the energy of the d resonance, or in contributions to the total energy of the metal other than that of the total band-structure energy. © 1969 The American Physical Society.