The Minimum Kinetic Energy Orbital and the Band Structure of Sodium

Citation

Surratt, Grover Timothy (1971) The Minimum Kinetic Energy Orbital and the Band Structure of Sodium. Master's thesis, California Institute of Technology. doi:10.7907/2665-JE74. https://resolver.caltech.edu/CaltechTHESIS:04292010-111816149

Abstract

For calculations on molecules and solids it has proven useful to replace the various core electrons with a pseudo-potential. The most common method for doing this, that of Phillips andKleinman, suffers from the disadvantage that the pseudopotential obtained is not unique. It has previously been shown, however, th t the non-uniqueness problem can be resolved by the use of ab-initio GI orbitals as the basis for the potential. Such potentials have proven quite satisfactory in replacing the core electrons in molecular and solid-state calculations. Unfortunately, systems of ten or more electrons are not accessible to GI, so that the approach cannot be used for sodium, for example. We have examined the GI orbitals and effective potentials for Li, Be+, B++ and compared these orbitals and potentials with those obtained from the usual Hartree-Fock formalism, but employing an extra condition on the orbitals to ensure uniqueness. It was found that a condition suggested (but apparently never tried) by Cohen and Heine, that the Hartree-Fock core orbitals be allowed to mix with the valence orbital in such a way as to minimize the kinetic energy, produced orbitals and potentials nearly identical to those from the GI method. We then employed this method to obtain local potentials for the ^2S, ^2P and ^2D states of sodium.. These potentials were found to reproduce the spectrum of sodium quite well. These potentials were then used to study the energy levels of sodium metal at the high symmetry points in the Brillouin zone, employing the GI band structure formalism.

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