Hagit Zabrodsky

Bio: Hagit Zabrodsky is an academic researcher from Bar-Ilan University. The author has contributed to research in topics: Continuous symmetry & Symmetry number. The author has an hindex of 7, co-authored 8 publications receiving 1017 citations.

Continuous symmetry measures

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.

Continuous Symmetry Measures. 2. Symmetry Groups and the Tetrahedron

Abstract: We treat symmetry as a continuous property rather than a discrete "yes or no" one. Here we generalize the approach developed for symmetry elements (Part 1: J. Am. Chem. SOC. 1992,114,7843-7851) to any symmetry group in two and three dimensions. Using the Continuous Symmetry Measure (CSM) method, it is possible to evaluate quantitatively how much of any symmetry exists in a nonsymmetric configuration; what is the nearest symmetry group of any given configuration; and how the symmetrized shapes, with respect to any symmetry group, look. The CSM approach is first presented in a practical easy-to-implement set of rules, which are later proven in a rigorous mathematical layout. Most of our examples concentrate on tetrahedral structures because of their key importance in chemistry. Thus, we show how to evaluate the amount of tetrahedricity (Td) existing in nonsymmetric tetrahedra; the amount of other symmetries they contain; and the continuous symmetry changes in fluctuating, vibrating, and rotating tetrahedra. The tool we developed bears on any physical or chemical process and property which is either governed by symmetry considerations or which is describable in terms of changes in symmetry.

The Rich Stereochemistry of Eight‐Vertex Polyhedra: A Continuous Shape Measures Study

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.

Continuous Symmetry Measures. 5. The Classical 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...

Diverse, High-Quality Test Set for the Validation of Protein−Ligand Docking Performance

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.