Wave-function-based embedding potential for ion-covalent crystals

Abstract

Many important properties of crystals are the result of the local defects. However, when one address directly the problem of a crystal with a local defect one must consider a very large system despite the fact that only a small part of it is really essential. This part is responsible for the properties one is interested in. By extracting this part from the crystal one obtains a so-called cluster. At the same time, properties of a single cluster can deviate significantly from properties of the same cluster embedded in crystal. In many cases, a single cluster can even be unstable. To bring the state of the extracted cluster to that of the cluster in the crystal one must apply a so-called embedding potential to the cluster. This article discusses a case study of embedding for ion-covalent crystals. In the case considered, the embedding potential has two qualitatively different components, a long-range (Coulomb), and a short-range. Different methods should be used to generate different components. A number of approximations are used in the method of generating an embedding potential. Most of these approximations are imposed to make the equations and their derivation simple and these approximations can be easily lifted. Besides, the one-determinant approximation for the wave function is used. This is a reasonably good approximation for ion-covalent systems with closed shells, which simplifies the problem considerably and makes it tractable. All employed approximations are explicitly stated and discussed. Every component of generation methods is described in details. The proofs of used statements are provided in a relevant appendix.