Parametrized version of the generalized pseudopotential theory for noble metals: Application to copper.

Abstract

A parametrized version of the generalized pseudopotential theory (GPT) of Moriarty is proposed for the special case of the noble metals. Copper is taken as an example. To define the parametrization, we consider separately the contributions which in the GPT are defined as the simple-metal limit (SML), the s-d coupling, and the overlap. The perturbation expansion is done from the basis of the atomic d states, and the d bands of the noble metal are considered to be completely filled. The SML is represented as an empty-core potential of radius ${r}_{c}$, and the s-d--coupling calculation is done exactly, but the mean energy ${E}_{d}$ of the d band relative to the conduction band is considered to be adjustable. The two parameters ${r}_{c}$ and ${E}_{d}$ are determined from particular points of the band structure. The results are found to be consistent with the large-L band-gap value and the width of the resonance of copper. The SML of the form factor, and the total form factor obtained, are in good agreement with those of the ab initio GPT. By means of the optimized random-phase approximation, we analyze the influence of the overlap on the liquid structure. We find that the expression for the overlap pair potential of Moriarty gives a good estimation of the liquid structure factor. Conversely, this quantity is used to adjust the overlap pair potential. Further concluding tests of the parametrization are done by calculating the entropy ${C}_{V}$, the compressibility, and the resistivity of the liquid. It is found that the parameters ${r}_{c}$, ${E}_{d}$, and those of the overlap are almost insensitive to volume changes with temperature in the solid and liquid under normal pressure. We conclude that the parametrized approach gives a good picture of the electron-ion and interionic interactions without losing the essence of the GPT. The method cannot replace the ab initio calculation, but could be useful in the investigation of noble-metal properties in systems which are not easily tractable in a detailed theory.