The resonant model potential method: a narrow d band approximation to d metal bandstructure, model Green function and density response function

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Abstract
The extension of the resonant model potential (RMP) perturbation method to the true transitional metals (with the Fermi level inside the d band) requires a new perturbative scheme. The small parameter is the ratio Sd=Wd/ epsilon s ( epsilon s is a typical s band width) which, in RMP theory, controls both the O(Sd) d band width and the O( square root Sd) hybridisation gap width. Physical properties are generally not holomorphic functions of Sd at Sd=0. This unwanted behaviour is related to the Sd resonant coupling which is large for any Sd in the so-called 'hybridisation shell' and is responsible for the Heine hybridisation gap. A method is described where this non-holomorphic contribution is separated out and approximately calculated first for the resonant bandstructure and then for the model Green functions. The method is applied to the calculation of the hybridisation contribution to the metal bandstructure energy and to the calculation of the unscreened model density response function; detailed numerical results show that the hybridisation contribution to the response function is large for the three transitional metal series.