Theory and computer simulation of perfect and defective solids

Bredow, Thomas; Dronskowski, Richard; Ebert, H.; Jug, Karl

doi:10.1016/j.progsolidstchem.2009.11.006

Cited by 4 publications

(3 citation statements)

References 186 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although the development of periodic methods based on the supercell model (SCM) has made substantial advances in the recent years, it would be highly desirable to have a periodic approach that is closely related to the molecular case and does not require significant modifications in the molecular formalism and, therefore, in the program code.…”

Section: Introductionmentioning

confidence: 99%

“…However, due to boundary effects and the neglect of long-range interactions, these models never reproduce the real electronic structure of such extended systems. [1] Although the development of periodic methods based on the supercell model (SCM) has made substantial advances in the recent years, [2][3][4] it would be highly desirable to have a periodic approach that is closely related to the molecular case and does not require significant modifications in the molecular formalism and, therefore, in the program code. The cyclic cluster model (CCM) [5] is such an approach.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The cyclic cluster model at hartree–fock level

Peintinger

Bredow

2014

J Comput Chem

Self Cite

View full text Add to dashboard Cite

We present the implementation of the cyclic cluster model (CCM) formalism at the Hartree-Fock (HF) level. In contrast to other periodic models, the CCM is a Γ-point approach. Integration is carried out in real space within a finite interaction area determined by the size and the shape of the cluster that corresponds to a supercell of the solid, surface, or polymer. Particular care has to be taken for the proper treatment of three- and four-center integrals that involve basis functions located at the boundaries of the Wigner-Seitz supercell, which defines the interaction region. The similarity between the CCM formalism and molecular approaches allows in principle the application of sophisticated post HF methods to solid-state problems with only moderate modification of the molecular code. We show for selected model systems, that with our approach, the electronic structure and energetics obtained by the conventional supercell model is fully reproduced.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The cyclic cluster model at hartree–fock level

Peintinger

Bredow

2014

J Comput Chem

Self Cite

View full text Add to dashboard Cite

show abstract

“…[43][44][45][46] A comprehensive review of different models applicability for description of the real crystals bulk and surface properties can be found in. [47][48][49] In this article, the wave function-based embedding for ioncovalent crystals is considered.This article outline is the following. First, the embedding is demonstrated in the simple case of one electron in the periodic potential with a single local impurity potential.…”

mentioning

confidence: 99%

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

Abarenkov

Boyko

2015

Int J of Quantum Chemistry

View full text Add to dashboard Cite

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. V C 2015 Wiley Periodicals, Inc. DOI: 10.1002/qua.25041Introduction An immediate solution of the Schroedinger equation for a real crystal is impossible due to an enormous number of particles in the system and a complicated system structure. However, a real crystal consists of similar, almost identical, repeating parts. Therefore, one can substitute a real crystal with its model as an infinite system with translational symmetry. This model is usually referred to as a perfect crystal. The first methods which were applied to a perfect crystal problem are: the WignerSeitz cell method, [1,2] the tight-binding method, [3,4] the orthogonalized plane wave method, [5] the augmented plane wave method, [6] the Korringa-Kohn-Rostoker method [7,8] and their modifications. There are, at present, a wide variety of methods that can be used to calculate the perfect crystals properties. However, many technologically important crystal properties are the result of crystal defects and impurities. These defects and impurities break down the perfect crystal translational symmetry. Many of these defects are local and their properties are determined by a comparatively small region of the crystal. Although the actual region is small, it is still part of the large system. There are two general approaches to this problem. One of them uses the well-developed methods of band structure calculations. The system is accord...

show abstract

Point Defects

and

Knowles

2012

Crystallography and Crystal Defects

View full text Add to dashboard Cite

Theory and computer simulation of perfect and defective solids

Cited by 4 publications

References 186 publications

The cyclic cluster model at hartree–fock level

The cyclic cluster model at hartree–fock level

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

Point Defects

Contact Info

Product

Resources

About