Boundary Conditions for Quantum Clusters Embedded in Classical Ionic Crystals

  • John M. Vail


In order to understand the boundary condition problem, consider a single electron trapped at a negative ion vacancy in a crystal: it is called an F center. It is bound in a potential well due to the net positive charge near the vacancy. Treating the ions as point charges produces one picture. Taking account of the electronic structure of the ion produces a physically more correct picture, in which each ion adds its core repulsion to the original effective potential. In this picture, the quantum-mechanical analysis is based on a complete set of one-electron basis functions, which may be delocalized. It is possible to transform, by unitary transformation, to a new set of basis functions which are localized on individual sites. The unitary transformation leaves the physics of the system unchanged, but in the equation that determines the one-electron functions, the repulsive potentials of surronding ions are reduced. The contribution to the effective potential, from the transformation, which produces this reduction is called a Kunz-Klein localizing potential (KKLP).1


Shell Model Unitary Transformation Orbital Radius Perfect Lattice Quantum Cluster 
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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • John M. Vail
    • 1
  1. 1.Department of PhysicsUniversity of ManitobaWinnipegCanada

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