Effect of dimensionality of a crystal lattice on the properties of a localized impurity

The changes of electron density due to the presence of a localized impurity in a crystal lattice are examined in dependence on the lattice dimensionality. The Koster–Slater impurity model developed for the case of a three‐dimensional simple cubic lattice has been taken as the basis of examinations. Ordinary bound states, virtual bound states, and delocalized electron states are considered in each lattice case. For the delocalized states extended in a one‐dimensional lattice the amplitude of the oscillatory changes of the electron density due to the impurity perturbation does not decrease with the distance from the impurity position, whereas for a two‐dimensional lattice this amplitude decreases roughly proportionally to the reciprocal value of the square root of the distance from the impurity. Let us note that a well‐known amplitude characterizing the decrease of the oscillatory change of the electron density in a three‐dimensional system is proportional to the reciprocal value of the third power of the distance from the impurity position. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 80: 61–78, 2000