Localized directed orbitals representing chemical bonds in ion‐covalent crystals

Abarenkov, I. V.; Boyko, Maksim A.; Sushko, Peter V.

doi:10.1002/qua.24367

Cited by 3 publications

(8 citation statements)

References 11 publications

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Section: Short-range Embeddingmentioning

confidence: 99%

“…There are many ways to achieve orbitals localization. [54,55] One of the simplest ways is to consider the orbital uðrÞ as localized the in cluster that brings maximum to the integral…”

Section: Ion-covalent Crystalmentioning

confidence: 99%

“…Orbitals in crystal localization methods are discussed in details in [54,55] . Application of the Adams-Gilbert method to an MgO crystal is given in [58] .…”

Section: Ion-covalent Crystalmentioning

confidence: 99%

“…[54,58,71] The particular form of potential depends on the localization functional employed. Two particular functionals, [58] one of which maximizes the Mullikens [72] net atomic population in the selected region [54,55,73,74] and the other [53,54] use a Fock operator for the localizing operatorÂ, produce similar results.In the AIMP approach, [19] the approximate one-electron orbitals are used for the cluster environment, and the embedding potential is derived using the corresponding coulombexchange operators. In [75] , a number of simple trial potentials with parameters are selected and parameters are defined with the trial and error method to reproduce a number of specifically chosen properties of the cluster in a crystal.…”

mentioning

confidence: 99%

“…There are many ways to achieve orbitals localization. [54,55] One of the simplest ways is to consider the orbital uðrÞ as localized the in cluster that brings maximum to the integralwhere wðrÞ is some positive function equal to zero outside the cluster. Different equations for the functional W can be used for different criteria of localization.…”

mentioning

confidence: 99%

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

Abarenkov

Boyko

2015

Int J of Quantum Chemistry

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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...

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Section: Short-range Embeddingmentioning

confidence: 99%

“…There are many ways to achieve orbitals localization. [54,55] One of the simplest ways is to consider the orbital uðrÞ as localized the in cluster that brings maximum to the integral…”

Section: Ion-covalent Crystalmentioning

confidence: 99%

“…Orbitals in crystal localization methods are discussed in details in [54,55] . Application of the Adams-Gilbert method to an MgO crystal is given in [58] .…”

Section: Ion-covalent Crystalmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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

Abarenkov

Boyko

2015

Int J of Quantum Chemistry

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Local Orbitals in Quantum Chemistry

Amor

Evangelisti

Leininger

et al. 2021

Lecture Notes in Chemistry

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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Application of the embedding potential method in calculations of the electronic structure and X-ray emission spectra of crystal MgO clusters

2015

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K and L X-ray emission spectra of Mg atoms in a MgO crystal are calculated. The wave functions and energies of the crystal needed for calculating the intensities of these spectra are obtained in calculations of crystalline clusters by the embedding potential method. In this method, a finite cluster is considered instead of an infinite crystal and the effect of the crystalline environment on the cluster is simulated by a potential that is usually called the "embedding potential." The electronic structure of clusters of different sizes and geometries in the embedding potential field is calculated by the Hartree-Fock and density functional methods. Qualitative agreement between calculated spectra and experimental data testifies that the embedding potential correctly describes the effect of the crystalline environment on the cluster.

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Localized directed orbitals representing chemical bonds in ion‐covalent crystals

Cited by 3 publications

References 11 publications

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

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

Local Orbitals in Quantum Chemistry

Application of the embedding potential method in calculations of the electronic structure and X-ray emission spectra of crystal MgO clusters

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