Local Model Potentials for Metals: Limitations and Applications

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Abstract
The suitability and usefulness of local model potentials as approximate replacements for more accurate nonlocal potentials are discussed. The properties of a general local potential, which includes as subcases the empty-core potential, the optimized model potential (OMP), and the point-ion potential, are reviewed. Scattering properties of "linearly screened" and "minimum-perturbation" local model potentials are calculated and the usefulness of phase-shift matching as a selection criterion for potentials is discussed. Properties of the local OMP are studied in detail and particular emphasis is given to the relation between ion-core cancellation in real space and the validity of perturbation theory. A nonlinear Fermi-Thomas model is used to calculate an optimum core radius for each metal. This core radius is found to correlate well with the Pauling ionic radius. The calculated core radii are used to extend the local OMP to the entire Periodic Table and thence to study trends in elemental properties. A striking correlation is observed between superconducting transition temperature and a parameter characterizing the electron-phonon interaction in terms of the local OMP.