Calculation of a resonant model potential for copper, silver, and gold

Abstract The ionic resonant model potential (RMP) v 0 ( E ) = w 0 ( E ) + v res ( E ) for d‐band metals considered previously is slightly generalized in order to take into account the energy dependence and nonlocality of the s and p scattering which were previously neglected. The RMP v 0 is written as w 0 ( E ) + + v res ( E ) where w 0 is a general Heine‐Abarenkov‐like potential and v res is a finite‐rank operator which acts on d states and is strongly energy‐dependent. The RMP parameters appropriate for the metallic state are calculated from first principles by requiring that the screened metal RMP \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{ions} {\rm}v_0 (E){\rm +}V_e $\end{document} is equivalent to the true HFS self‐consistent potential. The calculation is done using a Wigner‐Seitz spherical approximation, consistently for the true potential and the model potential. The method is applied to the three noble metals. The results are: (i) the enrgy dependence of the s and p potentials is significant; (ii) the s–p non‐locality is large; (iii) the d potential v res has indeed the resonant form U /( E − ℰ( E )) with ℰ( E ) only slightly energy‐dependent. A simpler model potential is then derived (ℰ( E ) is replaced by its Fermi level value; the energy dependence of w 0 ( E ) is only approximately taken into account through an effective mass approximation) and applied to the calculation of a few illustrative physical quantities. The results are satisfactory, at least for copper and silver, but some physical quantities (such as the elastic constants calculated up to second order according to the long‐wave method) are found to be sensitive to the value of the somewhat arbitrary model radius R m (the best results are obtained for the largest R m satisfying the non‐overlap condition).