Embedding and atomic orbitals hybridization

摘要

In calculation, the electronic structure of crystals, especially those containing point defects, the embedding approach is proved to be useful and convenient. In this approach, a finite part of the crystal, referred to as cluster, is considered instead of infinite crystal and the influence of the rest of the crystal is simulated by the embedding potential. The key problems of this approach are the cluster selection and the embedding potential generation. To select a cluster, the Wigner-Seitz unit cell is used in the present approach and every border atom, situated at the unit cell face, edge, or vertex is symmetrically "divided" among adjacent unit cells sharing this atom. The atomic hybrid orbitals are used for the border atoms partition between neighboring clusters. It is shown that contrary to the conventional hybridization scheme, the nonorthogonal and even linearly dependent atomic hybrid orbitals can be used to construct the border atom density matrix. This density matrix can be made to satisfy the proper point symmetry and to match the number of equivalent hybrid orbitals and the number of nearest neighbors. Two different types (one-center and multicenters) of the embedding potential corresponding to the border atom are considered in the article. As a particular example of the border atom the oxygen ion in ZrO_2, MgO, and TiO _2 rutile crystals is considered.