### Embedding potential method in ion-covalent crystals.

### I.V.Abarenkov

*S.Petersburg State University*

**Abstract:**

he electronic structure of ion-covalent crystals is considered.
In the embedding potential method a crystal is represented by a finite
cluster cut out from the crystal and embedded into the crystal environment.
It is assumed that in the cluster in crystal density matrix the wight of
one wave function is close to 1, so this wave function can be considered
as cluster in crystal wave function. The influence of the crystal environment
is simulated by the embedding potential. The border between cluster and crystal
environment can be drawn either between atoms or through atoms. In the first
case the inter-atomic bonds will be cut in parts, which results in big
perturbations of the system. In the second case, adopted in the present approach,
the combination of localization procedure and atomic orbitals hybridization
technique enables one to divide crystal orbitals in groups, one belonging to cluster
and the other to crystal environment, which helps to divide the system in parts
with reasonably small corresponding perturbation.
The embedding potential can be considered as consisting of several components.
One component, which can be referred to as Coulomb embedding, describes the influence
of the far environment where crystal is considered as a collection of point charges.
The general method is proposed which can be applied to any crystal and any
cluster cut out of this crystal. Another component, the near environment component,
describes the influence of those parts of cluster border atoms, which belong to the
cluster environment. Several different approximations are proposed for this component.
Finally, there is a short-range embedding potential component, which takes account
of boundary conditions change in the process of cluster localization.
All components of the embedding potential are discussed, the corresponding calculations
methods are described, and results of application to particular ion-covalent crystals
are presented.
This work was supported by the RFBR grant 15-03-07543. Research was carried out
using computational resources provided by Resource Center "Computer Center of SPbU"
(http://cc.spbu.ru).