Charge Decomposition Analysis of the Electron Localizability Indicator: A Bridge between the Orbital and Direct Space Representation of the Chemical Bond

Wagner, Frank R.; Bezugly, Viktor; Kohout, Miroslav; Grin, Yuri

doi:10.1002/chem.200700013

Cited by 266 publications

(266 citation statements)

References 27 publications

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“…Consequently, the ELI-D is strictly justified within wave function-based theories, e.g., Hartree-Fock (HF) and post-HF methods such as the complete active space (CAS) and configuration interaction (CI) methods [84][85][86]. However, at least formally, the functional can be derived from the Kohn-Sham orbitals within the framework of DFT yielding reliable results [87]. A detailed description of the formulation is available in references [82,[87][88][89].…”

Section: Topological Analysis Of the Electron Densitymentioning

confidence: 99%

“…However, at least formally, the functional can be derived from the Kohn-Sham orbitals within the framework of DFT yielding reliable results [87]. A detailed description of the formulation is available in references [82,[87][88][89]. In brief, Υ D (r) can be expressed as the product of the electron density with the pair-volume function (8):…”

Section: Topological Analysis Of the Electron Densitymentioning

confidence: 99%

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Electronic structure theory to decipher the chemical bonding in actinide systems

Dognon

2017

Coordination Chemistry Reviews

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International audienceThe chemical bonding in actinide compounds is usually analysed by inspecting the shape and the occupation of the orbitals or by calculating bond orders which are based on orbital overlap and occupation numbers. However, this may not give a definite answer because the choice of the partitioning method may strongly influence the result possibly leading to qualitatively different answers. In this review, we summarized the state-of-the-art of methods dedicated to the theoretical characterisation of bonding including charge, orbital, quantum chemical topology and energy decomposition analyses. This review is not exhaustive but aims to highlight some of the ways opened up by recent methodological developments. Various examples have been chosen to illustrate this progress

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Section: Topological Analysis Of the Electron Densitymentioning

confidence: 99%

Section: Topological Analysis Of the Electron Densitymentioning

confidence: 99%

Electronic structure theory to decipher the chemical bonding in actinide systems

Dognon

2017

Coordination Chemistry Reviews

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“…33 The topological analysis of ELI provides information regarding the nature of bonds (twoor multi-centered, number of electrons participating in the bond), lone-pair-like features and core shells. 34,35 The basin intersection technique allows identification of individual atom contributions to the electron populations of the bond basins. 36 The ED and ELI were calculated using a module implemented in the FPLO package.…”

Section: Electronic Structure Calculationsmentioning

confidence: 99%

Thermoelectric properties of the Zintl phases Yb₅M₂Sb₆(M = Al, Ga, In)

et al. 2015

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a Zintl compounds with chemical formula Yb 5 M 2 Sb 6 (M = Al, Ga, and In) form one of two known A 5 M 2 Pn 6 structure types characterized by double chains of corner-linked MPn 4 tetrahedra bridged by Pn 2 dumbbells. High temperature electronic and thermal transport measurements were used to characterize the thermoelectric properties of Yb 5 M 2 Sb 6 compounds. All samples were found to exhibit similar high p-type carrier concentrations, low resistivity and low Seebeck coefficients in agreement with the band structure calculations. These results, combined with previous studies, suggest that Yb 5 M 2 Sb 6 compounds are semimetals (i.e., they lack an energy gap between the valence and conduction bands), in contrast to the semiconducting alkaline earth (Ca, Sr, Ba) and Eu based A 5 M 2 Sb 6 compounds. Yb 5 M 2 Sb 6 compounds have very low lattice thermal conductivity, comparable to other closely related A 5 M 2 Sb 6 and A 3 MSb 3 phases. However, due to the semimetallic behaviour, the figure of merit of investigated samples remains low (zT < 0.15).

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“…A very good measure for atomic interactions which can be compared by PNS is given by the electron localizability approach [57][58][59][60][61]108]. By topological analysis of the Electron Localizability Indicator (or Electron Localization Function) different atomic interactions can be indentified and ascribed to the distinct space parts within a crystal structure.…”

Section: Geometry Topology and Bondingmentioning

confidence: 99%

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

Nesper¹,

Grin

2011

Zeitschrift Für Kristallographie

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Abstract. We are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives, i.e. minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science. History and developmentMinimal surfaces are a middle aged problem in mathematics mostly addressed since the 19 th century, but constitute an eternal fascination for humans probably since the earliest days of conscious thought. The intriguing fascination of soap bubbles is related to a deep feeling of harmony and beauty, the priming of which we simply do not know [1]. It may be due to a comprehensive intuitive understanding of the world without concrete knowing just like the feeling of harmony which is created by the golden ratio and five-fold symmetry. Why does the most irrational number 1 induce such a state of comfort in human minds? We do not know, just as nobody knows why the fine structure constant approaches more and more the value 1/137, the denominator being 33 rd prime number. To solve this question was the last great goal of Wolfgang Pauli who was not only a great physicist and mathematician but also stressed the importance of intuitive solutions to physical problems, amongst others by dreaming [2].A mathematical treatment of minimal surfaces goes back to Lagrange's work in the 18 th century which resulted in the Euler-Lagrange equation [3]. In the 19 th century the experiments of J. Plateau contributed much to mathematical research on such objects and led to the formulations of Plateau's problem which turned out to be unsolvable in general analytical form. The quest for deriving minimal surfaces and periodic minimal surfaces as well as for their analytical formulation increased by the end of the 19 th century especially by H. A. Schwarz [4] and in the beginning of the 20 th century by D. Hilbert [5]. Hilbert was not only one of the greatest mathematicians of modern age but also a mathematical puri...

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Charge Decomposition Analysis of the Electron Localizability Indicator: A Bridge between the Orbital and Direct Space Representation of the Chemical Bond

Cited by 266 publications

References 27 publications

Electronic structure theory to decipher the chemical bonding in actinide systems

Electronic structure theory to decipher the chemical bonding in actinide systems

Thermoelectric properties of the Zintl phases Yb₅M₂Sb₆(M = Al, Ga, In)

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

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Charge Decomposition Analysis of the Electron Localizability Indicator: A Bridge between the Orbital and Direct Space Representation of the Chemical Bond

Cited by 266 publications

References 27 publications

Electronic structure theory to decipher the chemical bonding in actinide systems

Electronic structure theory to decipher the chemical bonding in actinide systems

Thermoelectric properties of the Zintl phases Yb5M2Sb6(M = Al, Ga, In)

Periodic Space Partitioners (PSP) and their relations to Crystal Chemistry

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Product

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Thermoelectric properties of the Zintl phases Yb₅M₂Sb₆(M = Al, Ga, In)