Continuous symmetry measures
01 Sep 1992-Journal of the American Chemical Society (American Chemical Society)-Vol. 114, Iss: 20, pp 7843-7851
TL;DR: In this article, the authors proposed a continuous symmetry measure to quantify the distance of a given (distorted molecular) shape from any chosen element of symmetry, allowing one to compare the symmetry distance of several objects relative to a single symmetry element.
Abstract: We advance the notion that for many realistic issues involving symmetry in chemistry, it is more natural to analyze symmetry properties in terms of a continuous scale rather than in terms of "yes or no". Justification of that approach is dealt with in some detail using examples such as: symmetry distortions due to vibrations; changes in the "allowedness" of electronic transitions due to deviations from an ideal symmetry; continuous changes in environmental symmetry with reference to crystal and ligand field effects; non-ideal symmetry in concerted reactions; symmetry issues of polymers and large random objects. A versatile, simple tool is developed as a continuous symmetry measure. Its main property is the ability to quantify the distance of a given (distorted molecular) shape from any chosen element of symmetry. The generality of this symmetry measure allows one to compare the symmetry distance of several objects relative to a single symmetry element and to compare the symmetry distance of a single object relative to various symmetry elements. The continuous symmetry approach is presented in detail for the case of cyclic molecules, first in a practical way and then with a rigorous mathematical analysis. The versatility of the approah is then further demonstrated with alkane conformations, with a vibrating ABA water-like molecule, and with a three-dimensional analysis of the symmetry of a (2 3 21 reaction in which the double bonds are not ideally aligned.
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TL;DR: In this article, the concept of the continuous shape measures is summarized and the derived tools, the shape maps and the path deviation functions are described, the main stereochemical trends that have been deduced from the application of such tools to more than 23,000 crystallographically independent fragments of coordination numbers between four and eight are also summarized.
827 citations
TL;DR: Reference polyhedra, shape maps, and minimal-distortion interconversion paths are presented for eight-vertex polyhedral and polygonal structures within the CShM framework, and structural classification is shown to be greatly facilitated by these tools.
Abstract: A stereochemical study of polyhedral eight-vertex structures is presented, based on continuous shape measures (CShM). Reference polyhedra, shape maps, and minimal-distortion interconversion paths are presented for eight-vertex polyhedral and polygonal structures within the CShM framework. The application of these stereochemical tools is analyzed for several families of experimental structures: 1) coordination polyhedra of molecular transition-metal coordination compounds, classified by electron configuration and ligands; 2) edge-bonded polyhedra, including cubane structures, realgar, and metal clusters; 3) octanuclear transition-metal supramolecular architectures; and 4) coordination polyhedra in extended structures in inorganic solids. Structural classification is shown to be greatly facilitated by these tools, and the detection of less common structures, such as the gyrobifastigium, is straightforward.
659 citations
TL;DR: This work developed a general methodology and a general computational tool, which identifies the minimal distance of a given structure to a desired general shape with the same number of vertexes, and employs this tool to evaluate quantitatively the degree of polyhedricity within distorted polyhedra.
Abstract: The continuous symmetry measures approach, designed to assess quantitatively the degree of any symmetry within any structure, is extended to the important class of the polyhedra. For this purpose, we developed a general methodology and a general computational tool, which identify the minimal distance of a given structure to a desired general shape with the same number of vertexes. Specifically, we employ this tool to evaluate quantitatively the degree of polyhedricity within distorted polyhedra, taking as examples the most central and abundant polyhedral structures in chemistry in general and in coordination chemistry in particular, namely the tetrahedron, the bipyramid, the octahedron, the cube, the icosahedron, and the dodecahedron. After describing the properties of the symmetry measurement tool, we show its application and versatility in a number of cases where the deviation from exact symmetry has been an issue, including z-axis Jahn−Teller type polyhedral distortions, tantalum hydride complexes, pen...
602 citations
584 citations
TL;DR: A procedure for analyzing and classifying publicly available crystal structures has been developed and has been used to identify high-resolution protein-ligand complexes that can be assessed by reconstructing the electron density for the ligand using the deposited structure factors.
Abstract: A procedure for analyzing and classifying publicly available crystal structures has been developed. It has been used to identify high-resolution protein-ligand complexes that can be assessed by reconstructing the electron density for the ligand using the deposited structure factors. The complexes have been clustered according to the protein sequences, and clusters have been discarded if they do not represent proteins thought to be of direct interest to the pharmaceutical or agrochemical industry. Rules have been used to exclude complexes containing non-drug-like ligands. One complex from each cluster has been selected where a structure of sufficient quality was available. The final Astex diverse set contains 85 diverse, relevant protein-ligand complexes, which have been prepared in a format suitable for docking and are to be made freely available to the entire research community (http://www.ccdc.cam.ac.uk). The performance of the docking program GOLD against the new set is assessed using a variety of protocols. Relatively unbiased protocols give success rates of approximately 80% for redocking into native structures, but it is possible to get success rates of over 90% with some protocols.
541 citations
References
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01 Jan 1977
TL;DR: Molecular Orbitals and Frontier Orbitals.
Abstract: Molecular Orbitals and Frontier Orbitals. Ionic Reactions. Thermal Pericyclic Reactions. Radical Reactions. Photochemical Reactions. Exceptions.
2,548 citations
01 Jan 1989
TL;DR: In this article, a qualitative valence bond model for organic reactions is proposed for the Diels Alder reaction, which is based on the potential energy surface topology of potential energy surfaces.
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215 citations
Book•
01 Jan 1986TL;DR: In this article, simple and combined symmetries are used to combine symmetry in molecular shapes and geometrical properties of atoms and molecules, and space-group symmetry is used to fuse them.
Abstract: Simple and Combined Symmetries.- Molecular Shape and Geometry.- Helpful Mathematical Tools.- Molecular Vibrations.- Electronic Structure of Atoms and Molecules.- Chemical Reactions.- Space-Group Symmetries.- Crystals.
174 citations