Strongly localized molecular orbitals for  -quartz

Danyliv, O.D.; Kantorovich, Lev

doi:10.1088/0953-8984/16/41/006

Cited by 5 publications

(9 citation statements)

References 37 publications

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“…For example, the Adams-Gilbert equations (11) were used for the self-consistent calculations of several overlapping electron groups. [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.…”

Section: Short-range Embeddingmentioning

confidence: 99%

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%

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

Abarenkov

Boyko

2015

Int J of Quantum Chemistry

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“…Note that there could be several localized orbitals associated with every such region forming an EG. 20,21 Thus, each region has an EG associated with it, and each EG may contain several doubly occupied localized orbitals. For instance, in the case of the Si crystal, one needs four localized regions associated with four bonds; each bond is represented by an EG containing a single doubly occupied localized orbital, 20 eight valence electrons in total in the primitive cell.…”

Section: B Self-consistent Procedures For Calculating Localized Mosmentioning

confidence: 99%

“…To find the MOs localized in each of the regions, we define localizing functionals ⍀ A ͓͕ i , i A͖͔, ⍀ B ͓͕ i , i B͖͔, etc., for each of them. 20,21 Various examples of the localization functionals were given in Refs. 20 and 21 ͑see also references therein͒.…”

Section: B Self-consistent Procedures For Calculating Localized Mosmentioning

confidence: 99%

“…Depending on the specific type of chemical bonding in the system, the groups outside the cluster could be atoms ͑ions͒, bonds, or molecules. 16,17,20,21 Note that this family of methods rely on wave functions of every group to be "strongly" orthogonal 18,19 to each other which results in their less localized character to accommodate this specific requirement, and thus leads to less computationally efficient schemes.…”

Section: Introductionmentioning

confidence: 99%

“…We concentrate here on threedimensional periodic systems as the localized MOs of the perfect bulk crystal are required anyway to represent the environment region in the embedding scheme based on group functions. We have shown previously 20,21,25 that by lifting the orthogonality condition, highly localized molecular orbitals ͑LMOs͒ may be obtained that can span the whole occupied Fock space, and thus are capable of representing correctly the system total electron density. 25 Our method, which is similar in spirit to some existing one-electron methods, [26][27][28] is based on the partitioning of the entire periodic system into overlapping electronic groups ͑EGs͒ corresponding to atoms, ions, bonds, or molecules comprising the entire system.…”

Section: Introductionmentioning

confidence: 99%

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Treating periodic systems using embedding: Adams-Gilbert approach

2007

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A direct-space electronic structure method for electronic structure calculations of periodic systems, based on highly localized ͑noncanonical͒ molecular orbitals ͑MOs͒ and the quantum cluster embedding, is suggested. The method utilizes a modified Adams-Gilbert approach that allows one to find self-consistently ͑for the given geometry͒ the system energy and the corresponding localized MOs which give the correct total electron density. The approach suggested here can also be considered as an exact derivation of embedded quantum cluster models. We illustrate this method on a Hartree-Fock calculation of a model periodic He system and the MgO crystal, and the results are compared with a conventional approach based on canonical Bloch-like orbitals as implemented in the CRYSTAL code. Our method, which scales linearly with the system size, can also be used to solve the Kohn-Sham equations of density-functional theory.

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Modeling and LCAO Calculations of Point Defects in Crystals

Ėvarestov

2012

Springer Series in Solid-State Sciences

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Strongly localized molecular orbitals for -quartz

Cited by 5 publications

References 37 publications

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

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

Treating periodic systems using embedding: Adams-Gilbert approach

Modeling and LCAO Calculations of Point Defects in Crystals

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