Atomistic Simulation of Materials pp 239-244 | Cite as

# Boundary Conditions for Quantum Clusters Embedded in Classical Ionic Crystals

## Abstract

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}

## Keywords

Shell Model Unitary Transformation Orbital Radius Perfect Lattice Quantum Cluster## Preview

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## References

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