Home About us Contact
|
Home About us Contact | ||
|
|
||
Different Symmetries (different + symmetry)
Selected AbstractsUnderstanding chemical shielding tensors using group theory, MO analysis, and modern density-functional theoryCONCEPTS IN MAGNETIC RESONANCE, Issue 2 2009Cory M. Widdifield Abstract In this article, the relationships between molecular symmetry, molecular electronic structure, and chemical shielding (CS) tensors are discussed. First, a brief background on the CS interaction and CS tensors is given. Then, the visualization of the three-dimensional nature of CS is described. A simple method for examining the relationship between molecular orbitals (MOs) and CS tensors, using point groups and direct products of irreducible representations of MOs and rotational operators, is outlined. A number of specific examples are discussed, involving CS tensors of different nuclei in molecules of different symmetries, including ethene (D2h), hydrogen fluoride (C,v), trifluorophosphine (C3v), and water (C2v). Finally, we review the application of this method to CS tensors in several interesting cases previously discussed in the literature, including acetylene (D,h), the PtX42, series of compounds (D4h) and the decamethylaluminocenium cation (D5d). © 2009 Wiley Periodicals, Inc. Concepts Magn Reson Part A 34A: 91,123, 2009. [source] Eigensolution of symmetric frames using graph factorizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2004A. Kaveh Abstract In this paper, decomposition of matrices of special patterns to submatrices of smaller dimensions is briefly described. The graph models of frame structures with different symmetries are decomposed and appropriate processes are designed for their healing in order to form the corresponding factors. The eigenvalues and eigenvectors of the entire structure are then obtained by evaluating those of its factors. The methods developed in this article, simplifies the calculation of the natural frequencies and natural modes of the planar frames with different types of symmetry. Copyright © 2004 John Wiley & Sons, Ltd. [source] Structures and stability of lithium monosilicide clusters SiLin (n = 4,16): What is the maximum number, magic number, and core number for lithium coordination to silicon?JOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 11 2008Ning He Abstract In the coordination, hypervalent and cluster chemistry, three important characteristic properties are the maximum coordination number, magic number, and core coordination number. Yet, few studies have considered these three numbers at the same time for an MLn cluster with n larger than 8. In this article, we systematically studied the three properties of SiLin (n = 4,16) clusters at the B3LYP/6-31G(d), B3LYP/6-311++G(2d), and CCSD(T)/6-311++G(3df)//B3LYP/6-311++G(2d) (for energy only) levels. Various isomeric forms with different symmetries were calculated. For each SiLin (n = 4,9), silicon cohesive energy (cE) from SiLin , Si + Lin reaction, vertical ionization potential (vIP), and vertical electron affinity (vEA) were obtained for the lowest-energy isomer. We found that the maximum Li-coordination number of Si is 9, which is the largest number among the known MLin clusters. All cE, vIP, and vEA values predicted that 6 is the magic Li-coordination number of Si. For small SiLin (n , 6) clusters, Li atoms favor direct coordination to Si, whereas for larger SiLin (n , 7) clusters, there is a core cluster that is surrounded by excessive Li atoms. The core Li-coordination number is 6 for SiLin (n = 7,8), 7 for SiLin (n = 9,10), 8 for SiLin (n = 11,15) and 9 for SiLin (n , 16). Through the calculations, we verified the relationship between the structure and stability of SiLin with the maximum coordination number, magic number, and core coordination number. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008 [source] Two-dimensionally modulated structure of the rare-earth polysulfide GdS2,x (x = 0.18 , 13/72)ACTA CRYSTALLOGRAPHICA SECTION B, Issue 6 2003Rafael Tamazyan The crystal structure of GdS2,x is determined by single-crystal X-ray diffraction as a 144-fold superstructure of the ZrSSi structure type. The superstructure is described as a two-dimensional, commensurately modulated structure with the superspace group P4/n(,,½)(00)(ss) and with , = 1/4 and , = 1/3. Structure refinements within the classical approach, employing the 144-fold supercell, fail because most of the superlattice reflections have zero intensities within the experimental resolution. Within the superspace approach the absent superlattice reflections are systematically classified as higher-order satellite reflections. Accordingly, the superspace approach has been used to refine the structure model comprising the basic structure positions and the amplitudes of the modulation functions of the three crystallographically independent atoms. The quality of fit to the diffraction data and the values of the refined parameters are independent of the assumption on the true symmetry (incommensurate or a 12,×,12,×,2, I -centred superlattice with different symmetries). Arguments of structural plausibility then suggest that the true structure is a superstructure with space group I, corresponding to sections of superspace given by (t1, t2) equal to [(4n, 1)/48, (4m, 3)/48] or [(4n, 3)/48, (4m, 1)/48] (n and m are integers). Analysis of the structure, employing both superspace techniques (t plots) and the supercell structure model all show that the superstructure corresponds to an ordering of vacancies and an orientational ordering of S dimers within the square layers of the S2 atoms. [source] Phosphate tungsten bronze series: crystallographic and structural properties of low-dimensional conductorsACTA CRYSTALLOGRAPHICA SECTION B, Issue 5 2001P. Roussel Phosphate tungsten bronzes have been shown to be conductors of low dimensionality. A review of the crystallographic and structural properties of this huge series of compounds is given here, corresponding to the present knowledge of the different X-ray studies and electron microscopy investigations. Three main families are described, monophosphate tungsten bronzes, Ax(PO2)4(WO3)2m, either with pentagonal tunnels (MPTBp) or with hexagonal tunnels (MPTBh), and diphosphate tungsten bronzes, Ax(P2O4)2(WO3)2m, mainly with hexagonal tunnels (DPTBh). The general aspect of these crystal structures may be described as a building of polyhedra sharing oxygen corners made of regular stacking of WO3 -type slabs with a thickness function of m, joined by slices of tetrahedral PO4 phosphate or P2O7 diphosphate groups. The relations of the different slabs with respect to the basic perovskite structure are mentioned. The structural description is focused on the tilt phenomenon of the WO6 octahedra inside a slab of WO3 -type. In this respect, a comparison with the different phases of the WO3 crystal structures is established. The various modes of tilting and the different possible connections between two adjacent WO3 -type slabs involve a great variety of structures with different symmetries, as well as the existence of numerous twins in MPTBp's. Several phase transitions, with the appearance of diffuse scattering and modulation phenomena, were analysed by X-ray scattering measurements and through the temperature dependence of various physical properties for the MPTBp's. The role of the W displacements within the WO3 -type slabs, in two modulated structures (m = 4 and m = 10), already solved, is discussed. Finally, the complexity of the structural aspects of DPTBh's is explained on the basis of the average structures which are the only ones solved. [source] UROX 2.0: an interactive tool for fitting atomic models into electron-microscopy reconstructionsACTA CRYSTALLOGRAPHICA SECTION D, Issue 7 2009Xavier Siebert Electron microscopy of a macromolecular structure can lead to three-dimensional reconstructions with resolutions that are typically in the 30,10,Å range and sometimes even beyond 10,Å. Fitting atomic models of the individual components of the macromolecular structure (e.g. those obtained by X-ray crystallography or nuclear magnetic resonance) into an electron-microscopy map allows the interpretation of the latter at near-atomic resolution, providing insight into the interactions between the components. Graphical software is presented that was designed for the interactive fitting and refinement of atomic models into electron-microscopy reconstructions. Several characteristics enable it to be applied over a wide range of cases and resolutions. Firstly, calculations are performed in reciprocal space, which results in fast algorithms. This allows the entire reconstruction (or at least a sizeable portion of it) to be used by taking into account the symmetry of the reconstruction both in the calculations and in the graphical display. Secondly, atomic models can be placed graphically in the map while the correlation between the model-based electron density and the electron-microscopy reconstruction is computed and displayed in real time. The positions and orientations of the models are refined by a least-squares minimization. Thirdly, normal-mode calculations can be used to simulate conformational changes between the atomic model of an individual component and its corresponding density within a macromolecular complex determined by electron microscopy. These features are illustrated using three practical cases with different symmetries and resolutions. The software, together with examples and user instructions, is available free of charge at http://mem.ibs.fr/UROX/. [source] | ||||||||||