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Bound-state plus continuum electron densities, and Slater sum, in a bare Coulomb field

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Abstract

After reporting numerical studies based solely on s-states of total (s + p + d etc.) bound-state densities, which allow the range of validity of the simplest density functional theory of Thomas and Fermi to be critically assessed, two areas in which analytical progress proves possible are focused on. The first of these is the local density of states in the continuum, for which an exact formula is derived. The second concerns the Slater sum, for which an explicit differential equation is established. Prior to this, only the Bloch equation satisfied by the off-diagonal generalization of the Slater sum, namely the canonical density matrix, was available.

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Authors and Affiliations

  1. GSI, Planckstrasse 1, 6100, Darmstadt 11, Germany

    S. Pfalzner

  2. University of Oxford, Theoretical Chemistry Department, 5 South Parks Road, OX13 UB, Oxford, UK

    H. Lehmann & N. H. March

Authors
  1. S. Pfalzner
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  2. H. Lehmann
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  3. N. H. March
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Pfalzner, S., Lehmann, H. & March, N.H. Bound-state plus continuum electron densities, and Slater sum, in a bare Coulomb field. J Math Chem 16, 9–18 (1994). https://doi.org/10.1007/BF01169191

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  • DOI: https://doi.org/10.1007/BF01169191

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