The crystal structures of the elements: pseudopotential theory revisited

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Abstract
The authors reconsider the trends among the crystal structures of the elements in terms of the real-space pair interaction. Experience with the on-Fermi-sphere approximation suggests that a simple empty-core pseudopotential is sufficient to explain the trends and indeed they find it so. Calculations of the interatomic potentials have been made for different core radius Rc, atomic radius Ta and valence Z. These are presented in a form to demonstrate the trends within groups I to V and within periods of the periodic table. They show that the structural trends arise from a characteristic variation of the real-space interatomic potential with electron density and pseudopotential. This more critical and detailed discussion now justifies and supplements the qualitative ideas advanced in the 1960s. An important effect not previously discussed stems from the disappearance of the Friedel oscillations as 2kFRc approaches 1/2 pi .