XVI. Representations of the Electron Density and its Topographical Features

Smith, Vedene H.; Price, P. F.; Absar, Ilyas

doi:10.1002/ijch.197700032

Cited by 52 publications

(17 citation statements)

References 48 publications

(6 reference statements)

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“…This is clearly observed in electron density distributions generated by quantum-mechanics methods [18,19]. It is also put in practice in crystal structure determination processes, where a model of the crystalline structure is built from the high-density regions found in experimental electron density maps (EDMs).…”

Section: Topological Analysis Approachmentioning

confidence: 92%

Similarity and complementarity of molecular shapes: Applicability of a topological analysis approach

Leherte

Latour

Vercauteren

1996

J Computer-Aided Mol Des

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Developments based on a topological analysis approach of electron density maps are presented and applied to two different fields: the interpretation of electron density maps of proteins and the description of shape complementarity between a cyclodextrin host and a guest molecule. A global representation of the electron density distribution, through the location, identification and linkage of its critical points (points where the gradient of the density vanishes, i.e., peaks and passes), is generated using the program ORCRIT. On one hand, the interpretation of protein electron density maps is based on similarity evaluations between graphs of critical points and known structures. So far, the method has been applied to 3 A resolution maps for the recognition of secondary structure motifs using a procedure relevant to expert systems in artificial intelligence. Satisfying matches between critical point graphs and their corresponding protein structure depict the ability of the topological analysis to catch the essential secondary structural features in electron density maps. On the other hand, mapping the accessible volume of a host molecule is achieved by representing the peaks as ellipsoids with axes related to local curvature of the electron density function. Related energies of the interacting species can also be estimated. A qualitative comparison is made between the results generated by the topological analysis and energy values obtained by conventional molecular mechanics calculations. A positive comparison and a close complementarity between cyclodextrin and ligands shows that the topological analysis method gives a good representation of the electron density function.

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Section: Topological Analysis Approachmentioning

confidence: 92%

Similarity and complementarity of molecular shapes: Applicability of a topological analysis approach

Leherte

Latour

Vercauteren

1996

J Computer-Aided Mol Des

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“…QTAIM provides a powerful method for the study of all bonding types, particularly in strained and unusual bonding environments, in the ground state, metastable states, and for excited states, can define the real space metallicity and has explained the “ cis ‐effect.” QTAIM has had many successes in prediction and correlation with experimental data . Early work by Bader and co‐workers drew on the mathematical work of Collard and Hall, Johnson and Smith to capture the essential nature of a molecule into a suitably simple form in real space: the molecular graph, which is defined as the set of critical points and the associated bond‐paths. The molecular graph provides a topological overview of the characterizing chemical features derived from a many‐body space, replacing the concept of geometrical degrees of freedom.…”

Section: Theory and Methodsmentioning

confidence: 99%

Quantum topological resolution of catalyst proficiency

Jenkins

Xiao

et al. 2015

Int J of Quantum Chemistry

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The purpose of this exploratory investigation is to characterize, contrast, and explain the differences between efficient Ni(π‐allyl)2 and inefficient Pd(π‐allyl)2 systems in the catalyzed cross‐coupling of alkanes. Within the framework of the quantum theory of atoms in molecules, we have created quantum topology phase diagrams (QTPDs) for nonisomeric species by the creation of aggregate‐isomers; simple sum rules are introduced to ensure that the Poincaré‐Hopf relation is obeyed. We show that the catalyzed reaction cycles can be represented as a directed QTPD where each species of the main reaction cycle forms a closed loop. The topological position of the unwanted side products relative to the main reaction cycle for each catalyst is also considered. We find the more efficient Ni(π‐allyl)2 catalyst produces a reaction cycle on the QTPD that contains no “missing” topologies, preferentially proceeding to desired product at 94% yield, while avoiding wasteful side‐product pathways, disconnected from the major pathway by “missing” topologies. The converse is true for the less efficient Pd(π‐allyl)2 catalyst, whose reaction pathway markedly bifurcates to final yields of 56% and 44% for product and side‐product, respectively. We subsequently used our nearest neighbor ring‐critical point approach to show that the species of the main reaction cycle of the efficient Ni(π‐allyl)2 catalyst facilitates the desired chemical transformation whilst more effectively barring the formation of unwanted side product, with respect to the inefficient Pd(π‐allyl)2 catalyst. The findings from the QTPD analysis are in agreement with traditional energetic‐barrier interpretations of reaction pathway preference. © 2015 Wiley Periodicals, Inc.

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“…HKT guarantees that all the molecular information is encoded in the electron density, however to obtain a physical description of chemical systems, additional postulates area mandatory for extracting observable information in terms of atomic contributions [68]. In this context, the seminal works of Collard and Hall [69], Johnson [70], and Smith [71] to form a topological theory of molecular structure need to be cited. For a distribution of electronic charge associated with a nuclear configuration X the topological properties can be condensed into the number of different types of critical points of q(r, X), that is, where the associated gradient vector Δ q(r, X) vanishes.…”

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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XVI. Representations of the Electron Density and its Topographical Features

Cited by 52 publications

References 48 publications

Similarity and complementarity of molecular shapes: Applicability of a topological analysis approach

Similarity and complementarity of molecular shapes: Applicability of a topological analysis approach

Quantum topological resolution of catalyst proficiency

Chemical structure and reactivity by means of quantum chemical topology analysis

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