Teaching Point-Group Symmetry with Three-Dimensional Models

2011 ◽  
Vol 88 (7) ◽  
pp. 907-909 ◽  
Author(s):  
Edward B. Flint
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Teaching Point ◽  
Dimensional Models ◽  
Three Dimensional Models

scholarly journals Point-group symmetry detection in three-dimensional charge density of biomolecules

2019 ◽  
Vol 36 (7) ◽  
pp. 2237-2243
Author(s):  
Cyril F Reboul ◽  
Simon Kiesewetter ◽  
Dominika Elmlund ◽  
Hans Elmlund
Keyword(s):  
Charge Density ◽  
Single Particle ◽  
Statistical Tests ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Density Maps ◽  
Point Groups ◽  
Density Map

Abstract Motivation No rigorous statistical tests for detecting point-group symmetry in three-dimensional (3D) charge density maps obtained by electron microscopy (EM) and related techniques have been developed. Results We propose a method for determining the point-group symmetry of 3D charge density maps obtained by EM and related techniques. Our ab initio algorithm does not depend on atomic coordinates but utilizes the density map directly. We validate the approach for a range of publicly available single-particle cryo-EM datasets. In straightforward cases, our method enables fully automated single-particle 3D reconstruction without having to input an arbitrarily selected point-group symmetry. When pseudo-symmetry is present, our method provides statistics quantifying the degree to which the 3D density agrees with the different point-groups tested. Availability and implementation The software is freely available at https://github.com/hael/SIMPLE3.0.

scholarly journals Crystal structure of the coordination polymer [FeIII2{PtII(CN)4}3]

2015 ◽  
Vol 71 (1) ◽  
pp. i1-i2
Author(s):  
Maksym Seredyuk ◽  
M. Carmen Muñoz ◽  
José A. Real ◽  
Turganbay S. Iskenderov
Keyword(s):  
Crystal Structure ◽  
Coordination Polymer ◽  
Point Group ◽  
Three Dimensional ◽  
Title Complex ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Rotation Axes ◽  
Square Planar ◽  
Cyanide Ligands

The title complex, poly[dodeca-μ-cyanido-diiron(III)triplatinum(II)], [FeIII2{PtII(CN)4}3], has a three-dimensional polymeric structure. It is built-up from square-planar [PtII(CN)4]2−anions (point group symmetry 2/m) bridging cationic [FeIIIPtII(CN)4]+∞layers extending in thebcplane. The FeIIatoms of the layers are located on inversion centres and exhibit an octahedral coordination sphere defined by six N atoms of cyanide ligands, while the PtIIatoms are located on twofold rotation axes and are surrounded by four C atoms of the cyanide ligands in a square-planar coordination. The geometrical preferences of the two cations for octahedral and square-planar coordination, respectively, lead to a corrugated organisation of the layers. The distance between neighbouring [FeIIIPtII(CN)4]+∞layers corresponds to the lengtha/2 = 8.0070 (3) Å, and the separation between two neighbouring PtIIatoms of the bridging [PtII(CN)4]2−groups corresponds to the length of thecaxis [7.5720 (2) Å]. The structure is porous with accessible voids of 390 Å3per unit cell.

scholarly journals Crystal structure of langbeinite-related Rb0.743K0.845Co0.293Ti1.707(PO4)3

2015 ◽  
Vol 71 (3) ◽  
pp. 251-253 ◽  
Author(s):  
Nataliia Yu. Strutynska ◽  
Marina A. Bondarenko ◽  
Ivan V. Ogorodnyk ◽  
Vyacheslav N. Baumer ◽  
Nikolay S. Slobodyanik
Keyword(s):  
Crystal Structure ◽  
High Temperature ◽  
Point Group ◽  
Three Dimensional ◽  
Type Structure ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Point Group Symmetry ◽  
Crystallization Method ◽  
Temperature Crystallization

Potassium rubidium cobalt(II)/titanium(IV) tris(orthophosphate), Rb0.743K0.845Co0.293Ti1.707(PO4)3, has been obtained using a high-temperature crystallization method. The obtained compound has a langbeinite-type structure. The three-dimensional framework is built up from mixed-occupied (Co/TiIV)O6octahedra (point group symmetry .3.) and PO4tetrahedra. The K+and Rb+cations are statistically distributed over two distinct sites (both with site symmetry .3.) in the large cavities of the framework. They are surrounded by 12 O atoms.

scholarly journals Crystal structure of alluaudite-type NaMg3(HPO4)2(PO4)

2015 ◽  
Vol 71 (7) ◽  
pp. 813-815 ◽  
Author(s):  
Ahmed Ould Saleck ◽  
Abderrazzak Assani ◽  
Mohamed Saadi ◽  
Cyrille Mercier ◽  
Claudine Follet ◽  
...  
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
The Other ◽  
Group Symmetry ◽  
Strong Hydrogen Bond ◽  
Site Symmetry ◽  
Point Group Symmetry ◽  
Hydrogen Phosphate ◽  
Hydrothermal Conditions ◽  
Different Types

The title compound, sodium trimagnesium bis(hydrogen phosphate) phosphate, was obtained under hydrothermal conditions. In the crystal, two types of [MgO6] octahedra, one with point group symmetry 2, share edges to build chains extending parallel to [10-1]. These chains are linked together by two kinds of phosphate tetrahedra, HPO4and PO4, the latter with point group symmetry 2. The three-dimensional framework delimits two different types of channels extending along [001]. One channel hosts the Na+cations (site symmetry 2) surrounded by eight O atoms, with Na—O bond lengths varying between 2.2974 (13) and 2.922 (2) Å. The OH group of the HPO4tetrahedron points into the other type of channel and exhibits a strong hydrogen bond to an O atom of the PO4tetrahedron on the opposite side.

scholarly journals Crystal structures of Sr(ClO4)2·3H2O, Sr(ClO4)2·4H2O and Sr(ClO4)2·9H2O

2014 ◽  
Vol 70 (12) ◽  
pp. 510-514 ◽  
Author(s):  
Erik Hennings ◽  
Horst Schmidt ◽  
Wolfgang Voigt
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Water Molecules ◽  
Point Group Symmetry ◽  
Rotation Axes ◽  
Dimensional Network ◽  
Tricapped Trigonal Prism ◽  
Trigonal Prismatic Coordination ◽  
Solid Liquid

The title compounds, strontium perchlorate trihydrate {di-μ-aqua-aquadi-μ-perchlorato-strontium, [Sr(ClO4)2(H2O)3]n}, strontium perchlorate tetrahydrate {di-μ-aqua-bis(triaquadiperchloratostrontium), [Sr2(ClO4)4(H2O)8]} and strontium perchlorate nonahydrate {heptaaquadiperchloratostrontium dihydrate, [Sr(ClO4)2(H2O)7]·2H2O}, were crystallized at low temperatures according to the solid–liquid phase diagram. The structures of the tri- and tetrahydrate consist of Sr2+cations coordinated by five water molecules and four O atoms of four perchlorate tetrahedra in a distorted tricapped trigonal–prismatic coordination mode. The asymmetric unit of the trihydrate contains two formula units. Two [SrO9] polyhedra in the trihydrate are connected by sharing water molecules and thus forming chains parallel to [100]. In the tetrahydrate, dimers of two [SrO9] polyhedra connected by two sharing water molecules are formed. The structure of the nonahydrate contains one Sr2+cation coordinated by seven water molecules and by two O atoms of two perchlorate tetrahedra (point group symmetry ..m), forming a tricapped trigonal prism (point group symmetrym2m). The structure contains additional non-coordinating water molecules, which are located on twofold rotation axes. O—H...O hydrogen bonds between the water molecules as donor and ClO4tetrahedra and water molecules as acceptor groups lead to the formation of a three-dimensional network in each of the three structures.

Refinement of the crystal structure of zirconyl chloride octahydrate

1968 ◽  
Vol 46 (22) ◽  
pp. 3491-3497 ◽  
Author(s):  
Thomas C. W. Mak
Keyword(s):  
Crystal Structure ◽  
Axial Symmetry ◽  
Experimental Error ◽  
Least Squares Method ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Zirconium Atom ◽  
Zirconyl Chloride

The crystal structure of zirconyl chloride octahydrate, ZrOCl2•8H2O, has been refined by the least-squares method with new three-dimensional data. Existence of the [Zr4(OH)8(H2O)16]8+ tetranuclear complex has been confirmed. However, the coordination polyhedron about each zirconium atom differs considerably from the D4d antiprismatic geometry reported previously. It is, in fact, more closely related to the D2d dodecahedron, and has twofold axial symmetry within the limits of experimental error. Mean bond lengths in the [Zr4(OH)8(H2O)16]8+ complex, which approximates closely to D2d point-group symmetry, are: Zr—OH (bridging) = 2.142 ± 0.019 Å and Zr—OH2 (terminal) = 2.272 ± 0.032 Å.

scholarly journals Dimanganese(II) hydroxide vanadate, Mn2(OH)[VO4]

2014 ◽  
Vol 70 (7) ◽  
pp. i33-i33 ◽  
Author(s):  
Kewen Sun ◽  
Angela Möller
Keyword(s):  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Site Symmetry ◽  
Point Group Symmetry ◽  
Distorted Octahedral Coordination ◽  
Trigonal Bipyramidal ◽  
Distorted Octahedral ◽  
Coordination Spheres ◽  
Distorted Trigonal Bipyramidal

Dimanganese(II) hydroxide vanadate was obtained from hydrothermal reactions. The crystal structure of the title compound is isotypic with that of Zn2(OH)[VO4]. Three crystallographically independent Mn2+ions are present, one (site symmetry .m.) with a distorted trigonal-bipyramidal and two (site symmetries .m. and 1) with distorted octahedral coordination spheres. These polyhedra are linked through common edges, forming a corrugated layer-type of structure extending parallel to (100). A three-dimensional framework resultsviaadditional Mn—O—V—O—Mn connectivities involving the two different tetrahedral [VO4] units (each with point-group symmetry .m.). O—H...O hydrogen bonds (one bifurcated) between the OH functions (both with point-group symmetry .m.) and the [VO4] units complete this arrangement.

scholarly journals Crystal structure of high-spin tetraaquabis(2-chloropyrazine-κN4)iron(II) bis(4-methylbenzenesulfonate)

2015 ◽  
Vol 71 (7) ◽  
pp. 776-778
Author(s):  
Bohdan O. Golub ◽  
Sergii I. Shylin ◽  
Sebastian Dechert ◽  
Maria L. Malysheva ◽  
Il`ya A. Gural`skiy
Keyword(s):  
Crystal Structure ◽  
Hydrogen Bonds ◽  
High Spin ◽  
Supramolecular Structure ◽  
Complex Cation ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Point Group Symmetry ◽  
Π Interactions

The title salt, [FeII(C4H3ClN2)2(H2O)4](C7H7O3S)2, contains a complex cation with point group symmetry 2/m. The high-spin FeIIcation is hexacoordinated by four symmetry-related water and twoN-bound 2-chloropyrazine molecules in atransarrangement, forming a distorted FeN2O4octahedron. The three-dimensional supramolecular structure is supported by intermolecular O—H...O hydrogen bonds between the complex cations and tosylate anions, and additional π–π interactions between benzene and pyrazine rings. The methyl H atoms of the tosylate anion are equally disordered over two positions.

scholarly journals Structure cristalline de type alluaudite KNa5Mn3(MoO4)6

2015 ◽  
Vol 71 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Chahira Bouzidi ◽  
Wafa Frigui ◽  
Mohamed Faouzi Zid
Keyword(s):  
Solid State ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Dimensional Structure ◽  
Site Symmetry ◽  
Structural Description ◽  
Point Group Symmetry ◽  
The Third ◽  
New Phase

The new phase potassium pentasodium trimanganese hexakis(molybdate), KNa5Mn3Mo6O24, has been synthesized using solid-state methods. The structure is composed ofM2O10(M= Mn, Na) dimers and MoO4tetrahedra (point group symmetry 2) sharing corners and forming layers parallel to (100), which are linkedviacommon corners of another type ofMO4tetrahedra, forming a three-dimensional structure with two types of large channels along [001] in which two types of Na+cations (one with site symmetry 2, one with -1) and K+cations (site symmetry 2, half-occupation) are located. Mn2+and the third type of Na+cations are located at the same siteMwith occupancies of 0.75 and 0.25, respectively. A comparative structural description is provided between the structure of the title compound and those of the related phases Cu1.35Fe3(PO4)3and NaAgFeMn2(PO4)3.

scholarly journals Crystal structure of tris(ethylenediammonium) hexasulfatopraseodymium(III) hexahydrate

2014 ◽  
Vol 70 (10) ◽  
pp. 235-237 ◽  
Author(s):  
Peter Held
Keyword(s):  
Crystal Structure ◽  
Water Molecule ◽  
Point Group ◽  
Three Dimensional ◽  
Group Symmetry ◽  
Water Molecules ◽  
Point Group Symmetry ◽  
Framework Structure ◽  
Crystal Water ◽  
Medium Strength

In the title salt, (C2H10N2)3[Pr2(SO4)6]·6H2O, the PrIIIcation is surrounded ninefold by five sulfate groups (two monodentate and three chelating) and by one water molecule [range of Pr—O bond lengths 2.383 (3) to 2.582 (3) Å]. The [Pr(SO4)5(H2O)] groups are arranged in sheets parallel to (010). Two crystal water molecules and two ethylenediammonium cations (one with point group symmetry -1) connect the sheetsviaO—H...O and N—H...O hydrogen bonds from weak up to medium strength into a three-dimensional framework structure.

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