Topological analysis of the experimental electron density

Tsirelson, Vladimir G.

doi:10.1139/v96-131

Cited by 31 publications

(62 citation statements)

References 37 publications

(23 reference statements)

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“…This is most pronounced for the covalent interactions, which are worst described by the rigid-atom model usually used for X-ray diffraction refinement. However, comparative topological studies of the theoretical and experimental charge densities of the compounds displaying shared interactions (Abramov & Okamura, 1996;Tsirelson, 1996) revealed that atomic thermal-motion effects are not crucial for the possibility of quantitative and semiquantitative evaluation of the respective charge density and its Laplacian at the bond critical point from a highly accurate X-ray diffraction experiment. Such accuracy does not seem to be limiting for the semiquantitative evaluation of the local kinetic energy at the bond critical point of the accurate experimental charge density by the suggested method.…”

Section: Some Experimental Results and Discussionmentioning

confidence: 99%

“…The latter field of application is now rapidly developing (e.g. Kapphann, Tsirelson & Ozerov, 1988;Craven & Stewart, 1990;Destro, Bianchi, Gatti & Merati, 1991;Gatti, Bianchi, Destro & Merati, 1992;Destro & Merati, 1995;Iversen, Larsen, Souhassou & Takata, 1995;Tsirelson, 1996;Tsirelson & Ozerov, 1996) owing to the possibility of analytical representation of the experimental electron density by various multipole models (Hirshfeld, 1971;Stewart, 1976;Hansen & Coppens, 1978), which allow analytical or numerical evaluation of the total electrondensity Laplacian and gradient vector field. In the present work, an attempt to develop an approach for the evaluation of electronic kinetic energy density at the bond critical-point region from the experimental electron density is described.…”

Section: Introductionmentioning

confidence: 99%

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On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

Abramov¹

1997

Acta Crystallogr A Found Crystallogr

554

424

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A simple new approach for the evaluation of the electronic kinetic energy density, G(r), from the experimental (multipole-fitted) electron density is proposed. It allows a quantitative and semi-quantitative description of the G(r) behavior at the bond critical points of compounds with closed-shell and shared interactions, respectively. This can provide information on the values of the kinetic electron energy densities at the bond critical points, which appears to be useful for quantumtopological studies of chemical interactions using experimental electron densities.

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Section: Some Experimental Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

Abramov¹

1997

Acta Crystallogr A Found Crystallogr

554

424

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“…In this situation, the only way to evaluate indirectly to what extent quantitative values of topological characteristics depend on the atomic thermal motion effects may be a comparative topological analysis of theoretical and experimental charge densities simultaneously. Previously, such studies of L-alanine (Gatti, Bianchi, Destro & Merati, 1992) and urea (Tsirelson, 1996, and references therein) crystals have revealed quantitative, within 5%, and semiquantitative, within 10-20% (or even qualitative, within 60%), agreement between theoretically and experimentally evaluated values of p and V2p, respectively, at the bond critical points (saddle points of p between bonded atoms) between nonhydrogen atoms. The worst agreement was found between experimental and theoretical values of these properties for C--N and N--O interactions in lithium bis(tetramethylammonium) hexanitrocobaltate(III) (Bianchi, Gatti, Adovasio & Nardelli, 1996).…”

Section: Introductionmentioning

confidence: 88%

“…The field of its application to experimental (X-ray diffraction) charge densities is rapidly developing now (e.g. Kapphahn, Tsirelson & Ozerov, 1988;Craven & Stewart, 1990;Gatti, Bianchi, Destro & Merati, 1992;Destro & Merati, 1995;Iversen, Larsen, Souhassou & Takata, 1995;Tsirelson & Ozerov, 1996) owing to the possibility of analytically representing experimental p by various multipole techniques (Hirshfeld, 1971;Stewart, 1976;Hansen & Coppens, 1978), allowing analytical evaluation of the Laplacian, V2p, and gradient vector field of p. Although it seems that there is no fundamental restriction on the applicability of topological analysis to experimental p (Tsirelson, 1996), the numerical results in this case are affected by the thermal atomic motions in crystals (Tsirelson, 1996;Gatti, Bianchi, Destro & Merati, 1992) and in fact refer to the mean thermal nuclear distribution. In this situation, the only way to evaluate indirectly to what extent quantitative values of topological characteristics depend on the atomic thermal motion effects may be a comparative topological analysis of theoretical and experimental charge densities simultaneously.…”

Section: Introductionmentioning

confidence: 99%

A Topological Analysis of Charge Densities in Diamond, Silicon and Germanium Crystals

Abramov¹,

Okamura²

1997

Acta Cryst Sect A

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The Hansen-Coppens multipole model of charge density has been fitted to highly accurate published experimental and theoretical structure factors for diamond, silicon and germanium crystals. Analysis of both model experimental and theoretical charge densities using the resulting model parameters was performed in terms of Bader's topological theory. The general topology of the charge density appeared to be identical for all crystals, containing the four possible types of critical points of rank three, and no non-nuclear attractors between neighboring atoms were found within achieved accuracy. Theoretical and experimental values of charge density and its Laplacian show quantitative and semiquantitative agreement, respectively, at the critical points of model charge densities. For Ge crystals, such agreement is worse at the ring critical point. These results suggest the possibility of semiquantitative (within 10-30%) study of the topological characteristics of highly accurate X-ray charge densities of crystals displaying shared interatomic interactions. Comparative topological analysis of the chemical bond in this series of crystals is discussed in terms of the quantum topological theory.

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“…20 This association was confirmed by further theoretical calculations of the density and, most importantly, by the topological analysis of experimentally measured electron densities. [21][22][23][24] Such calculations 25 and experiments [26][27][28][29] have now provided thousands of examples, demonstrating that every classical structure is but a mapping of the "bonds" onto the network of bond paths. EVery classical structure is mirrored by a molecular graph: the network of bond paths linking neighboring, that is, bonded, nuclei.…”

Section: Relating Structure To the Measurable Electron Densitymentioning

confidence: 99%

Definition of Molecular Structure: By Choice or by Appeal to Observation?

2010

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There are two schools of thought in chemistry: one derived from the valence bond and molecular orbital models of bonding, the other appealing directly to the measurable electron density and the quantum mechanical theorems that determine its behavior, an approach embodied in the quantum theory of atoms in molecules, QTAIM. No one questions the validity of the former approach, and indeed molecular orbital models and QTAIM play complementary roles, the models finding expression in the principles of physics. However, some orbital proponents step beyond the models to impose their personal stamp on their use in interpretive chemistry, by denying the possible existence of a physical basis for the concepts of chemistry. This places them at odds with QTAIM, whose very existence stems from the discovery in the observable topology of the electron density, the definitions of atoms, of the bonding between atoms and hence of molecular structure. Relating these concepts to the electron density provides the necessary link for their ultimate quantum definition. This paper explores in depth the possible causes of the difficulties some have in accepting the quantum basis of structure beginning with the arguments associated with the acceptance of a "bond path" as a criterion for bonding. This identification is based on the finding that all classical structures may be mapped onto molecular graphs consisting of bond paths linking neighboring atoms, a mapping that has no known exceptions and one that is further bolstered by the finding that there are no examples of "missing bond paths". Difficulties arise when the quantum concept is applied to systems that are not amenable to the classical models of bonding. Thus one is faced with the recurring dilemma of science, of having to escape the constraints of a model that requires a change in the existing paradigm, a process that has been in operation since the discovery of new and novel structures necessitated the extension of the Lewis model and the octet rule. The paper reviews all facets of bonding beginning with the work of Pauling and Slater in their accounting for crystal structures, taking note of Pauling's advocating possible bonding between large anions. Many examples of nonbonded or van der Waals interactions are considered from both points of view. The final section deals with the consequences of the realization that bonded quantum atoms that share an interatomic surface do not "overlap". The time has come for entering students of chemistry to be taught that the electron density can be seen, touched, and measured and that the chemical structures they learn are in fact the tracings of "bonds" onto lines of maximum density that link bonded nuclei. Matter, as we perceive it, is bound by the electrostatic force of attraction between the nuclei and the electron density.

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Topological analysis of the experimental electron density

Abstract: Abstract:Methods of topological analysis of the experimental electron density reconstructed from X-ray diffraction data are described. Their advantages and drawbacks are discussed and the results for organic and inorganic crystalline solids are presented.

Cited by 31 publications

References 37 publications

On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

On the Possibility of Kinetic Energy Density Evaluation from the Experimental Electron-Density Distribution

A Topological Analysis of Charge Densities in Diamond, Silicon and Germanium Crystals

Definition of Molecular Structure: By Choice or by Appeal to Observation?

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