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Point-group Symmetry (point-group + symmetry)
Selected AbstractsComputation on symmetry-invariant basesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2003Jian Wu Abstract There is standard methodology available to facilitate electronic structure computations on a space that is invariant under a symmetry group. Here, we focus on additional consequences that arise if the basis itself is invariant under the symmetry group (i.e., in the case that application of symmetry operations to each basis vector yields, up to proportionality, a single basis vector). In illustration of the formal development, examples are considered where the symmetries are point-group symmetries and the basis vectors are Slater determinants over singly occupied atomic orbitals, as for an open-shell valence bond (VB) model. Several other types of examples are mentioned, e.g., a basis of chemically motivated resonance structures, as for a VB model, or an orbital basis of atomic orbitals for a one-electron Hückel-type model. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 7,22, 2003 [source] X-ray atomic orbital analysis.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2008The scattering unit of X-ray crystal structure analysis is changed from atoms to the subshell electrons by X-ray atomic orbital analysis (XAO). All the atoms in the unit cell are divided into groups of subshell electrons in the XAO analysis. Each subshell is treated as an independent pseudo-atom, which enables the atomic orbitals (AO's) and the electron population of each AO expressed as a linear combination of s/p/d/f orbitals in each subshell to be determined. When the environmental condition of the sample is varied, the electron transfer among the AO's in the crystal can be traced with XAO. It is applicable mainly to analyses of the electron-density distribution in ionic solids including those with a nonstoichiometric structure. The expansion coefficients of each AO are calculated with the perturbation theory putting a point charge on each atom in the unit cell. This automatically makes the perturbation potential have the point-group symmetry of the atom in the crystal field. Then the coefficients of each AO are refined to fit to the observed structure factors keeping the orthonormal relationships among the AO's. Complex basis functions with , or , spin as well as real ones are employed for heavy atoms and the relationships among the coefficients for the AO's of an electron in the crystal fields of the 32 point-group symmetries are derived for p, d and f orbitals. The AO's thus derived can be applicable to an anti-symmetrized multi-electron system, although X-ray diffraction cannot specify the atomic terms occupied when the crystal symmetry permits the atom to have many terms. [source] Molecular crystal global phase diagrams.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 1 2010In the first part of this series [Keith et al. (2004). Cryst. Growth Des.4, 1009,1012; Mettes et al. (2004). Acta Cryst. A60, 621,636], a method was developed for constructing global phase diagrams (GPDs) for molecular crystals in which crystal structure is presented as a function of intermolecular potential parameters. In that work, a face-centered-cubic center-of-mass lattice was arbitrarily adopted as a reference state. In part two of the series, experimental crystal structures composed of tetrahedral point group molecules are classified to determine what fraction of structures are amenable to inclusion in the GPDs and the number of reference lattices necessary to span the observed structures. It is found that 60% of crystal structures composed of molecules with point-group symmetry are amenable and that eight reference lattices are sufficient to span the observed structures. Similar results are expected for other cubic point groups. [source] X-ray atomic orbital analysis.ACTA CRYSTALLOGRAPHICA SECTION A, Issue 4 2008The scattering unit of X-ray crystal structure analysis is changed from atoms to the subshell electrons by X-ray atomic orbital analysis (XAO). All the atoms in the unit cell are divided into groups of subshell electrons in the XAO analysis. Each subshell is treated as an independent pseudo-atom, which enables the atomic orbitals (AO's) and the electron population of each AO expressed as a linear combination of s/p/d/f orbitals in each subshell to be determined. When the environmental condition of the sample is varied, the electron transfer among the AO's in the crystal can be traced with XAO. It is applicable mainly to analyses of the electron-density distribution in ionic solids including those with a nonstoichiometric structure. The expansion coefficients of each AO are calculated with the perturbation theory putting a point charge on each atom in the unit cell. This automatically makes the perturbation potential have the point-group symmetry of the atom in the crystal field. Then the coefficients of each AO are refined to fit to the observed structure factors keeping the orthonormal relationships among the AO's. Complex basis functions with , or , spin as well as real ones are employed for heavy atoms and the relationships among the coefficients for the AO's of an electron in the crystal fields of the 32 point-group symmetries are derived for p, d and f orbitals. The AO's thus derived can be applicable to an anti-symmetrized multi-electron system, although X-ray diffraction cannot specify the atomic terms occupied when the crystal symmetry permits the atom to have many terms. [source] Zones and sublattices of integral latticesACTA CRYSTALLOGRAPHICA SECTION A, Issue 6 2004A. Janner Methods are presented for an analysis of zones and sublattices of integral lattices, whose relevance is revealed by sharp peaks in the frequency distribution of hexagonal and tetragonal lattices, as a function of the axial ratio . Starting from a few examples, zone symmetries, lattice,sublattice relations and integral scaling transformations are derived for hexagonal lattices with axial ratios , , and 1 (the isometric case) and for the related and tetragonal lattices. Sublattices and zones connected by linear rational transformations lead to rational equivalence classes of integral lattices. For properties like the axial ratio and the point-group symmetry (lattice holohedry), rational equivalence can be extended so that also metric tensors differing by an integral factor become equivalent. These two types of equivalence classes are determined for the lattices mentioned above. [source] Alkaline metal oxoantimonates(III), A3[SbO3] (A = K or Cs)ACTA CRYSTALLOGRAPHICA SECTION C, Issue 10 2001Franziska Emmerling The two title trialkaline trioxoantimonates(III), tripotassium trioxoantimonate(III), K3[SbO3], (I), and tricaesium trioxoantimonate(III), Cs3[SbO3], (II), crystallize in the cubic Na3[AsS3] structure type in space group P213. The structures show discrete ,-tetrahedral [SbO3]3, anions with C3v point-group symmetry. The Sb,O distances are 1.923,(4),Å in (I) and 1.928,(2),Å in (II), and the O,Sb,O bond angles are 99.5,(2)° in (I) and 100.4,(1)° in (II). [source] `Broken symmetries' in macromolecular crystallography: phasing from unmerged dataACTA CRYSTALLOGRAPHICA SECTION D, Issue 4 2010Marc Schiltz The space-group symmetry of a crystal structure imposes a point-group symmetry on its diffraction pattern, giving rise to so-called symmetry-equivalent reflections. Instances in macromolecular crystallography are discussed in which the symmetry in reciprocal space is broken, i.e. where symmetry-related reflections are no longer equivalent. Such a situation occurs when the sample suffers from site-specific radiation damage during the X-ray measurements. Another example of broken symmetry arises from the polarization anisotropy of anomalous scattering. In these cases, the genuine intensity differences between symmetry-related reflections can be exploited to yield phase information in the structure-solution process. In this approach, the usual separation of the data merging and phasing steps is abandoned. The data are kept unmerged down to the Harker construction, where the symmetry-breaking effects are explicitly modelled and refined and become a source of supplementary phase information. [source] Structure of the heterodimeric neurotoxic complex viperotoxin F (RV-4/RV-7) from the venom of Vipera russelli formosensis at 1.9,Å resolutionACTA CRYSTALLOGRAPHICA SECTION D, Issue 10 2003Markus Perbandt The presynaptic viperotoxin F is the major lethal component of the venom of Vipera russelli formosensis (Taiwan viper). It is a heterodimer of two highly homologous (65% identity) but oppositely charged subunits: a basic and neurotoxic PLA2 (RV-4) and an acidic non-toxic component with a very low enzymatic activity (RV-7). The crystal structure of the complex has been determined by molecular replacement and refined to 1.9,Å resolution and an R factor of 22.3% with four RV-4/RV-7 complexes in the asymmetric unit, which do not exhibit any local point-group symmetry. The complex formation decreases the accessible surface area of the two subunits by ,1425,Å2. Both PLA2s are predicted to have very low, if any, anticoagulant activity. The structure of viperotoxin F is compared with that of the heterodimeric neurotoxin vipoxin from the venom of another viper, V. ammodytes meridionalis. The structural basis for the differences between the pharmacological activities of the two toxins is discussed. The neutralization of the negative charge of the major ligand for Ca2+, Asp49, by intersubunit salt bridges is probably a common mechanism of self-stabilization of heterodimeric Viperinae snake-venom neurotoxins in the absence of bound calcium. [source] Structure of pteridine reductase (PTR1) from Leishmania tarentolaeACTA CRYSTALLOGRAPHICA SECTION D, Issue 9 2003Haiyan Zhao The protozoan parasites Leishmania utilize a pteridine-reducing enzyme, pteridine reductase (PTR1), to bypass antifolate inhibition. The crystal structure of PTR1 from L. tarentolae has been solved as a binary complex with NADPH at 2.8,Å resolution. The structure was solved by molecular-replacement techniques using the recently reported L. major PTR1 structure as a search model. Comparisons of the present structure with the L. major PTR1 allowed us to identify regions of flexibility in the molecule. PTR1 is a member of the growing family of short-chain dehydrogenases (SDR) which share the characteristic Tyr(Xaa)3Lys motif in the vicinity of the active site. The functional enzyme is a tetramer and the crystallographic asymmetric unit contains a tetramer with 222 point-group symmetry. [source] Crystallization and preliminary X-ray diffraction analysis of Pseudomonas aeruginosa phosphorylcholine phosphataseACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 8 2010Lisandro H. Otero Pseudomonas aeruginosa phosphorylcholine phosphatase (PchP) catalyzes the hydrolysis of phosphorylcholine to produce choline and inorganic phosphate. Phosphorylcholine is released by the action of haemolytic phospholipase C (PlcH) on phosphatidylcholine or sphingomyelin. PchP belongs to the HAD superfamily and its activity is dependent on Mg2+, Zn2+ or Cu2+. The possible importance of PchP in the pathogenesis of P. aeruginosa, the lack of information about its structure and its low identity to other members of this family led us to attempt its crystallization in order to solve its three-dimensional structure. Crystals of the protein have been grown and diffraction data have been obtained to 2.7,Å resolution. The crystals belonged to the monoclinic space group C2, with unit-cell parameters a = 137.16, b = 159.15, c = 73.31,Å, , = 117.89°. Statistical analysis of the unit-cell contents and the self-rotation function suggest a tetrameric state of the molecule with 222 point-group symmetry. [source] Cloning, purification and preliminary X-ray analysis of the C-terminal domain of Helicobacter pylori MotBACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 4 2008Anna Roujeinikova The C-terminal domain of MotB (MotB-C) contains a putative peptidoglycan-binding motif and is believed to anchor the MotA/MotB stator unit of the bacterial flagellar motor to the cell wall. Crystals of Helicobacter pylori MotB-C (138 amino-acid residues) were obtained by the hanging-drop vapour-diffusion method using polyethylene glycol as a precipitant. These crystals belong to space group P21, with unit-cell parameters a = 50.8, b = 89.5, c = 66.3,Å, , = 112.5°. The crystals diffract X-rays to at least 1.6,Å resolution using a synchrotron-radiation source. Self-rotation function and Matthews coefficient calculations suggest that the asymmetric unit contains one tetramer with 222 point-group symmetry. The anomalous difference Patterson maps calculated for an ytterbium-derivative crystal using diffraction data at a wavelength of 1.38,Å showed significant peaks on the v = 1/2 Harker section, suggesting that ab initio phase information could be derived from the MAD data. [source] The quaternary structure of the amidase from Geobacillus pallidus RAPc8 is revealed by its crystal packingACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 12 2006Vinod B. Agarkar The amidase from Geobacillus pallidus RAPc8, a moderate thermophile, is a member of the nitrilase enzyme superfamily. It converts amides to the corresponding acids and ammonia and has application as an industrial catalyst. RAPc8 amidase has been cloned and functionally expressed in Escherichia coli and has been purified by heat treatment and a number of chromatographic steps. The enzyme was crystallized using the hanging-drop vapour-diffusion method. Crystals produced in the presence of 1.2,M sodium citrate, 400,mM NaCl, 100,mM sodium acetate pH 5.6 were selected for X-ray diffraction studies. A data set having acceptable statistics to 1.96,Å resolution was collected under cryoconditions using an in-house X-ray source. The space group was determined to be primitive cubic P4232, with unit-cell parameter a = 130.49 (±0.05) Å. The structure was solved by molecular replacement using the backbone of the hypothetical protein PH0642 from Pyrococcus horikoshii (PDB code 1j31) with all non-identical side chains substituted with alanine as a probe. There is one subunit per asymmetric unit. The subunits are packed as trimers of dimers with D3 point-group symmetry around the threefold axis in such a way that the dimer interface seen in the homologues is preserved. [source] Preliminary investigation of the three-dimensional structure of Salmonella typhimurium uridine phosphorylase in the crystalline stateACTA CRYSTALLOGRAPHICA SECTION F (ELECTRONIC), Issue 4 2005Olga K. Molchan Uridine phosphorylase (UPh) catalyzes the phosphorolytic cleavage of the C,N glycosidic bond of uridine to ribose 1-phosphate and uracil in the pyrimidine-salvage pathway. The crystal structure of the Salmonella typhimurium uridine phosphorylase (StUPh) has been determined at 2.5,Å resolution and refined to an R factor of 22.1% and an Rfree of 27.9%. The hexameric StUPh displays 32 point-group symmetry and utilizes both twofold and threefold non-crystallographic axes. A phosphate is bound at the active site and forms hydrogen bonds to Arg91, Arg30, Thr94 and Gly26 of one monomer and Arg48 of an adjacent monomer. The hexameric StUPh model reveals a close structural relationship to Escherichia coli uridine phosphorylase (EcUPh). [source] | ||||||||||