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Difference in Coulomb electrostatic energy for localized versus delocalized electrons and electron pairs
  • Hanno Essén,
  • Johan Stén
Hanno Essén
Royal Institute of Technology

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Johan Stén
University of Helsinki
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Abstract

The free electron Fermi gas with completely delocalized electrons represents the simplest model for conduction electrons in a metal. In more detailed models of solid state physics electrons in the conduction band are also normally assumed to be delocalized over the entire crystal (in LCAO orbitals). According to the uncertainty principle delocalization minimizes the kinetic energy. The Coulomb repulsion energy on the other hand is clearly smaller for states in which the electrons localize apart from one-another. As a consequence Wigner showed that a sufficiently thin electron gas will condense to a crystal of localized electrons. Here we will show, using a model that gives exact results, that the Coulomb repulsion energy of localized charge distributions is lower than that of delocalized distributions. Our new exact result should lead to better estimates of the effect in real metals. We point out that localization of electron pairs is energetically favorable.