Structural homeomorphism between the electron density and the virial field

Keith, Todd A.; Bader, R. F. W.; Aray, Yosslen

doi:10.1002/(sici)1097-461x(1996)57:2<183::aid-qua4>3.0.co;2-u

Cited by 191 publications

(136 citation statements)

References 31 publications

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“…In other words, there is a single line of maximally negative potential energy density linking the same attractors which share a bond path [15]. This line of ''maximum stability'' in real space is termed a ''virial path''.…”

Section: The Bond and Virial Paths And The Molecular And Virial Graphsmentioning

confidence: 99%

An Introduction to the Quantum Theory of Atoms in Molecules

Matta

Boyd

2007

The Quantum Theory of Atoms in Molecules

484

599

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Section: The Bond and Virial Paths And The Molecular And Virial Graphsmentioning

confidence: 99%

An Introduction to the Quantum Theory of Atoms in Molecules

Matta

Boyd

2007

The Quantum Theory of Atoms in Molecules

484

599

View full text Add to dashboard Cite

“…How can the properties of a lone pair be described? Popelier proposed that these type of studies form a unified theoretical framework, named Quantum Chemical Topology (QCT) inspired in the seminal work of Bader, [48,49,51,[69][70][71] for general topological analysis of scalar functions, such as the source function, [72] the momentum density, [73] the electron pair density, [74] the nuclear potential energy field, [75] the virial field, [76] as well as the Laplacian of charge density. [48,53,77,78] In fact, topological analysis of various scalar fields, different to electron density, is now used in computational chemistry, such as the scalar field derived from the molecular electrostatic potential [79] ; even the mathematical framework of topological analysis has been applied by Mezey on the study of potential energy hypersurfaces.…”

Section: Electron Density Q(r)mentioning

confidence: 99%

Unraveling reaction mechanisms by means of Quantum Chemical Topology Analysis

Andrés

González-Navarrete

Safont

2014

Int J of Quantum Chemistry

100

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A chemical reaction can be understood in terms of geometrical changes of the molecular structures and reordering of the electronic densities involved in the process; therefore, identifying structural and electronic density changes taking place along the reaction coordinate renders valuable information on reaction mechanism. Understanding the atomic rearrangements that occur during chemical reactions is of great importance, and this perspective aims to highlight the major developments in quantum chemical topology analysis, based on the combination of electron localization function and catastrophe theory as useful tools in elucidating the bonding and reactivity patterns of molecules. It reveals all the expected, but still ambiguous, elements of electronic structure extensively used by chemists. The chemical bonds determine chemical reactivity, and this technique offers the possibility of their visualization, allowing chemists to understand how atoms bond, how and where bonds are broken/ formed along a given reaction pathway at a most fundamental level, and so, better following and understanding the changes in the bond pattern. Their results clearly herald a new era, in which the atomic imaging of chemical bonds will constitute a new method for examining chemical structures and reaction mechanisms. The important feature of this procedure is that in practice the scope of its values is systemindependent. In addition, from a practical point of view, it is cheap to calculate and implement because wave functions are the required input, which are easily available from standard calculations. To capture these results two reaction mechanisms: isomerization of C(BH) 2 carbene and the thermal cycloheptatriene-norcaradiene isomerizations have been selected, indicating both the generality and utility of this type of analysis.

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“…In addition, other topological analysis of scalar functions have been also developed such as the source function [98], the momentum density [99], the electron pair density [100], the nuclear potential energy field [101], the virial field [102], the Laplacian of charge density [66,[103][104][105], and the electron localizability indicator [106]. Da Silva and…”

Section: Topological Analysismentioning

confidence: 99%

Chemical structure and reactivity by means of quantum chemical topology analysis

Andrés

González-Navarrete

Safont

2015

Computational and Theoretical Chemistry

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Chemical structure and bonding are key features and concepts in chemical systems which are used in deriving structure-property relationships, and hence in predicting physical and chemical properties of compounds. Even though the contemporary high standards in determination, using both theoretical methods and experimental techniques, questions of chemical bonds as well as their evolution along a reaction pathway are still highly controversial. This paper presents a working methodology to determine the structure and chemical reactivity based on the quantum chemical topology analysis.QTAIM and ELF frameworks, based on the topological analysis of the electron density and the electron localization function, respectively, have been used. We have selected two examples studied by the present approach, to show its potential: (i) QTAIM study on the α -Ag 2 WO 4 , for the simulation of Ag nucleation and formation on α -Ag 2 WO 4 provoked in this crystal by the electron-beam irradiation. (ii) An ELF and Thom´s catastrophe theory study for the reaction pathway associated with the decomposition of stable planar hypercoordinate carbon species, CN 3 Mg 3 + .3Chemistry is the science of substances: their structure, their properties, and the reactions that change them into other substances, as Linus These procedures are hugely successful and they can be considered as an energeticsdriven approach to computational theoretical and chemistry. Then, this research field constitutes a central application of quantum chemistry to the study of stationary points of PESs [53] and the pathways connecting them. The shape of an adiabatic PES is conventionally regarded as a function of the nuclear skeleton, ignoring the wealth of information that can be provided by the total electronic charge density distribution ρ(r).The driving force for the nuclear motion is the potential, which arises from In this context, the electronic structure of a molecule is described in real space terms using topological analysis. Beyond the well-known approach of the QTAIM, which relies on the properties of the electron density ρ(r) when atoms interact, topological analysis of different scalar functions can be employed, such as the electron localization function (ELF) method [90][91][92][93]. Originally, ELF can be developed based on the conditional pair density [90] or can be derived from the kinetic energy density [94].In the latter context, ELF is seen as the scaled difference between the positive kinetic energy density and the von Weizsäcker term [95], whereby the scaling function is the 8 kinetic energy density of the homogeneous electron gas (Thomas-Fermi term) [96,97]. The pictures of a molecule as drawn by the QTAIM and ELF analysis are complementary. Thus, the QTAIM analysis is based on the topology of the electron density ρ(r), whereas the ELF analysis is based on the topology of the electron localization function using the conditional probability for the same spin pairs which is closely related to the local excess of kinetic energy due to the Paul...

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Structural homeomorphism between the electron density and the virial field

Cited by 191 publications

References 31 publications

An Introduction to the Quantum Theory of Atoms in Molecules

An Introduction to the Quantum Theory of Atoms in Molecules

Unraveling reaction mechanisms by means of Quantum Chemical Topology Analysis

Chemical structure and reactivity by means of quantum chemical topology analysis

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