Double Group Research Articles

Congruence subgroups and crystallographic quotients of small Coxeter groups

Abstract Small Coxeter groups are precisely the ones for which the Tits representation is integral, which makes the study of their congruence subgroups relevant. The symmetric group S n {S_{n}} has three natural extensions, namely the braid group B n {B_{n}} , the twin group T n {T_{n}} and the triplet group L n {L_{n}} . The latter two groups are small Coxeter groups, and play the role of braid groups under the Alexander–Markov correspondence for appropriate knot theories, with their pure subgroups admitting suitable hyperplane arrangements as Eilenberg-MacLane spaces. In this paper, we prove that the congruence subgroup property fails for infinite small Coxeter groups which are not virtually abelian. As an application, we deduce that the congruence subgroup property fails for both T n {T_{n}} and L n {L_{n}} when n ≥ 4 {n\geq 4} . We also determine subquotients of principal congruence subgroups of T n {T_{n}} , and identify the pure twin group P ⁢ T n {PT_{n}} and the pure triplet group P ⁢ L n {PL_{n}} with suitable principal congruence subgroups. Further, we investigate crystallographic quotients of these two families of small Coxeter groups, and prove that T n / P ⁢ T n ′ {T_{n}/PT_{n}^{\prime}} , T n / T n ′′ {T_{n}/T_{n}^{\prime\prime}} and L n / P ⁢ L n ′ {L_{n}/PL_{n}^{\prime}} are crystallographic groups. We also determine crystallographic dimensions of these groups and identify the holonomy representation of T n / T n ′′ {T_{n}/T_{n}^{\prime\prime}} .

Synthesis, characterization and biological activity of a novel N1, N5-bis[2-hydroxyphenyl]-2-methyl-1,5-diaminopentane Schiff base: Effect of methylene spacers on biological activities

A novel ONNO donor tetradentate Schiff base ligand N,N'-bis[2- hydroxyphenyl]-2-methyl-1,5-diaminopentane (1) is synthesized and characterized by using 1H, 13C NMR spectroscopy and mass spectrometry. Biological studies on newly synthesized ligand are carried out and results are compared with the biological activities of known Schiff base ligands: N,N'-bis[{2- hydroxyphenyl }]-1,4-diaminobutane (2) and N,N'-bis[{2- hydroxyphenyl }]-1,3-diaminopropane (3). This comparative study highlights the effect of increasing methylene linkage on the biological activity of these ligands. The anti-microbial activities of all three ligands have been screened against two distinct gram-positive and gram-negative bacteria. In-vitro results of this comparative analysis are also supported by comprehensive molecular docking studies with DNA gyrase subunit B protein of gram-positive bacterium S. aureus and FabH–CoA complex of gram-negative bacterium E. coli. Experimental studies reveal that the spacer group plays a vital role in controlling the biological activities of the ligand. These findings are in good agreement with the theoretical findings. The study demonstrates that the biological activity of ligands is enhanced with increments in the number of spacers. Thus, the newly synthesized ligand (1) with the most extended spacer among the three showed the highest biological activity compared to other two ligands, similar to the popular drug Ciprofloxacin.

The Eisenlohr-Farris algorithm for fully transitive polyhedra

The purpose of this note is to present a method for classifying three-dimensional polyhedra in terms of their symmetry groups. This method is constructive, and it is described in terms of the conjugation classes of crystallographic groups in \(\mathbb{E}^3\). For each class of groups \(\Gamma\) the method can generate without duplication all polyhedra in three-dimensional space on which \(\Gamma\) acts fully-transitively. It was proposed by J. M. Eisenlohr and S. L. Farris for generating every fully transitive polyhedron in \(\mathbb{E}^d\). We also illustrate how the method can be applied in the Euclidean space \(\mathbb{E}^3\).

Ab-initio study on structural, magnetic, electronic and optical properties of SrCo1−xAxO3 (A = Fe or Cr, x = 0.125 and 0.25)

Herein, a first-principles study on the structural, electronic, optical and magnetic properties of SrCo[Formula: see text]AxO3 ([Formula: see text] or Cr, [Formula: see text] and 0.25) was conducted. For all calculations, ultrasoft pseudo-potentials plane wave (USPPW) and the generalized gradient approximation (GGA) with the default exchange-correlation parameterization of Perdew–Burke–Ernzerhof (PBE) were employed and with Hubbard correction. The crystal structures of SrCo[Formula: see text]A[Formula: see text]O3 and SrCo[Formula: see text]A[Formula: see text]O3 ([Formula: see text] or Cr) are determined as a supercell of [Formula: see text] cell cubic perovskite structure (Pm-3m) with symmetry space group No. 221. No energy gap was observed at the Fermi level for both SrCo[Formula: see text]Cr[Formula: see text]O3 and SrCo[Formula: see text]Cr[Formula: see text]O3 compounds, indicating their metallic properties. The magnetic moment calculations showed that the doping of Fe into SrCoO3 resulted in a higher net magnetic moment and all materials studied here was ferromagnetic ground states. Dielectric functions indicate the metallic conductivity for all materials studied here. The different values of the real part for materials present that this material has a Drude-like dielectric function behavior.

Accurate computational design of three-dimensional protein crystals.

Protein crystallization plays a central role in structural biology. Despite this, the process of crystallization remains poorly understood and highly empirical, with crystal contacts, lattice packing arrangements and space group preferences being largely unpredictable. Programming protein crystallization through precisely engineered side-chain-side-chain interactions across protein-protein interfaces is an outstanding challenge. Here we develop a general computational approach for designing three-dimensional protein crystals with prespecified lattice architectures at atomic accuracy that hierarchically constrains the overall number of degrees of freedom of the system. We design three pairs of oligomers that can be individually purified, and upon mixing, spontaneously self-assemble into >100 µm three-dimensional crystals. The structures of these crystals are nearly identical to the computational design models, closely corresponding in both overall architecture and the specific protein-protein interactions. The dimensions of the crystal unit cell can be systematically redesigned while retaining the space group symmetry and overall architecture, and the crystals are extremely porous and highly stable. Our approach enables the computational design of protein crystals with high accuracy, and the designed protein crystals, which have both structural and assembly information encoded in their primary sequences, provide a powerful platform for biological materials engineering.

Structural, physicochemical characterization and antimicrobial activities of a new tris(8-quinolinolato-κ2N,O)cobalt(III) ethanol solvate [Co(C9H6NO)3].(C2H6O)

We report herein the synthesis and physicochemical characterization of a new 8-hydroxyquinoline cobalt(III) complex ethanol solvate with formula [Co(C9H6NO)3].(C2H6O). This compound was been prepared by slow evaporation at room temperature and characterized by single crystal X-ray diffraction. It crystallizes in the monoclinic system, spaces group P21/n. The central cobalt ion has a slightly distorted square bipyramidal environment, coordinated by three chelating 8-hydroxyquinoline molecules. Structural cohesion is primarily established by π-π interactions between the neighboring rings of quinoline groups and intermolecular hydrogen bonds O-H…O connecting the cobalt complex entities and uncoordinated ethanol molecules.The title compound has been characterized by the infrared (IR) and the UV–Visible (UV–Vis) spectra. Intermolecular interactions in the crystal structure were quantified by Hirshfeld surface analysis. The band gap of the complex was calculated using solid-state reflectance spectra, and the results show that the complex acts as a semiconductor. Moreover, the new compound exhibits high antibacterial and antifungal activities, as detected by the well agar diffusion against various bacterial and fungal clinical strains. The superior inhibitory effect was observed against Klebsiella pneumoniae, Candida albicans and Candida glabrata with zones inhibition of about 17.5, 17.5 and 17 mm, respectively.

Incommensurate magnetic structure of CrAs at low temperatures and high pressures.

The magnetic structure of chromium arsenide CrAs is studied with neutron powder diffraction at ambient pressure in the temperature range 1.5-300 K as well as with neutron single-crystal diffraction at 2 K and 0.12 GPa. The material undergoes an anti-isostructural phase transition at TN = 267 K and atmospheric conditions, in which both orthorhombic phases have the same space-group symmetry (Pnma, Z = 4) but different distortions of the parent hexagonal structure of the NiAs type (P63/mmc, Z = 2). The magnetic structure below TN is incommensurate with the propagation vector k = (0, 0, kc). At ambient pressure, the component kc decreases from kc = 0.3807 (7) at 260 K to kc = 0.3531 (6) at 50 K. Below this temperature, it is basically constant. With increasing pressure at 2 K, kc is also constant within standard uncertainties [kc = 0.353 (2)]. For the analysis of the magnetic structure, a group-theoretical approach based on the space group of the nuclear structure and its subgroups is used. To avoid falling into false minima in the refinements, a random search for magnetic moments in the models is implemented. In the literature, the magnetic structure has been determined on the basis of powder diffraction data as a double helix propagating along the c axis. Although this double-helical model leads to satisfactory agreement factors for our powder data, it does not reproduce the intensities of the magnetic satellite reflections measured on single-crystal data in a satisfactory way and can therefore be discarded. Instead, several other models are found that lead to better agreement. Each of them is spiral-like with directional components in all three directions and with no spin-density wave character that would cause a non-constant magnetic moment. In all these models, the ordering of the spins is neither a pure helix nor a pure cycloid. Instead, the unit vectors of the spin rotation planes make an angle α, 0° < α < 90°, with respect to the c* direction. The model in superspace group P21.1'(α0γ)0s yields the best agreement factors in the refinements of the neutron single-crystal and powder diffraction data. This model is unique as it is the only one in which all the magnetic moments rotate with the same chirality.

Simultaneous existence of magnetic and ferroelectric orders in bi-phase composites for multiferroic applications

Multiferroic materials has brought evolutionary impact in multifunctional devices that are exclusively based on magnetoelectric coupling. In this work, a bi-phasic composite series of the form; (1–x)[Bi0.8La0.2FeO3] + x[Zn0.5Co0.5Fe2O4] was prepared using sol–gel auto–combustion. The X-ray diffraction analysis confirmed the rhombohedrally distorted cubic structure of BiFeO3 and normal spinel cubic structure of Zn0.5Co0.5Fe2O4 having R3c and Fd-3 m space group symmetry, respectively. A reduction in average crystallite size was observed by gradually enhancing the substituent spinel contents (x). Energy dispersive X-ray confirmed the presence of all the constituent elements in accordance with stoichiometrically calculated values. Mostly the particles having spherical shapes were observed via micro-graphical analysis. At x = 0.2, the composite sample showed the highest value of recoverable energy density as 7.2 × 10-2 mJ/cm3 with the highest value of % efficiency ∼ 88.83 %. A clear enhancement in saturation magnetization was observed from 0.16 to 19.87 emu/g. The remanent magnetization also increased from 0.018 to 6.363 emu/g by enhancing the spinel phase contents. Furthermore, coercivity also increased significantly from 672.98 Oe to 841.89 Oe in the composite samples. The highest squareness ratio Mr:Ms was observed at x = 0.3. These distinctive properties of the nanocomposites lead toward potential applications in multiferroic and spintronic devices.

Crystal structure, electronic structure, and optical properties of Cu4ZnGe2S7 and Cu4CdGe2S7: Polar diamond-like semiconductors exhibiting second harmonic generation

The novel I4-II-IV2-VI7 quaternary diamond-like semiconductors (DLSs), Cu4ZnGe2S7 and Cu4CdGe2S7, were prepared from the constituent elemental powders at elevated temperatures. Cu4ZnGe2S7 crystallizes in the polar, chiral space group C2 and adopts the Cu4NiSi2S7 structure-type, which can be considered a derivative of the cubic diamond structure. The cadmium analog takes on the Cu5Si2S7 structure-type, which is related to the hexagonal diamond structure, and displays polar, Cc space group symmetry. Both compounds contain [Ge2S7]6- anions created by corner-sharing GeS4 tetrahedra. The crystal structures were carefully evaluated using: 1) extended connectivity tables, 2) minimum bounding ellipsoid analysis, and 3) bond valence sum (BVS) and global instability index (G) calculations. Both compounds are thermally stable up to temperatures exceeding 950 °C and melt incongruently. As assessed using diffuse reflectance spectroscopy, Cu4ZnGe2S7 and Cu4CdGe2S7 possess optical bandgaps of 1.65 eV and 1.90 eV, respectively, which are narrower than the analogous I2-II-IV-VI4 DLSs. Electronic structure calculations show that both compounds are direct-bandgap semiconductors with significant contributions of Cu-d and S-p orbitals to the states at the top of the valence band. While Cu4CdGe2S7 displays a weak second harmonic generation (SHG) response, the second-order nonlinear optical susceptibility, χ(2), of Cu4ZnGe2S7 is 14.8 ± 1.5 pm V-1, assessed using the Kurtz-Perry powder method and an optical-grade AgGaSe2 (AGSe) reference. Both compounds exhibit laser-induced damage threshold values similar to AGSe, ∼0.1 GW cm-2, for λ = 1.064 µm using picosecond laser pulses. Most importantly, Cu4ZnGe2S7 exhibits a phase-matching behavior at λ = 3.1 µm. These results suggest that Cu4ZnGe2S7 holds potential for use in low-powered laser applications involving efficient wave mixing in the mid-IR region.

Synthesis and structural characterization of Ti(III) and Mo(III) complexes supported by PNP pincer ligands

New Ti(III) and Mo(III) complexes of formulae [(PNP-Ph)TiCl3], 1, and [(PNP-iPr)MoCl3], 2, where PNP-Ph = N,N’-bis(diphenylphosphino)-2,6-diaminopyridine and PNP-iPr = N,N’-bis(diisopropylphosphino)-2,6-diaminopyridine were synthesised, in moderate yields, by reaction of MCl3·(THF)3 (M = Ti and Mo) with the suitable ligand precursor. The solid-state molecular structures of complexes 1 and 2 were obtained by single-crystal X-ray diffraction. Crystal data for C37H41Cl3N3O2P2Ti (1·(C4H8O)2): triclinic, space group P-1 (no. 2), a = 10.0945(4) Å, b = 10.3002(4) Å, c = 18.6233(7) Å, α = 92.412(2)°, β = 91.108(2)°, γ = 101.705(3)°, V = 1893.65(13) Å3, Z = 2, µ(MoKα) = 0.559 mm-1, Dcalc = 1.361 g.cm-3, 20760 reflections measured (2.021 ≤ Θ ≤ 27.130), 8327 unique (Rint = 0.0399, Rsigma = 0.0414) which were used in all calculations. The final R1 was 0.0316 (I &gt; σ(I)) and wR2 was 0.0850 (all data). Crystal data for C17H33Cl3MoN3P2 (2): tetragonal, space group I41/a (no. 88), a = b = 19.468(4) Å, c = 31.711(6) Å, α = β = γ = 90°, V = 12019(5) Å3, Z = 16, µ(MoKα) = 0.816 mm-1, Dcalc = 1.202 g.cm-3, 42367 reflections measured (2.569 ≤ Θ ≤ 25.347), 5498 unique (Rint = 0.1408, Rsigma = 0.1293) which were used in all calculations. The final R1 was 0.1005 (I &gt; σ(I)) and wR2 was 0.3194 (all data). The coordination geometry around the titanium and molybdenum centers is best described as octahedral, with three donor atoms of the PNP ligand and one chlorine atom occupying the equatorial plane. The axial positions of the octahedron are occupied by the other two chlorido ligands in both complexes. The NH spacer groups in the PNP ligands have an important role in the establishment of hydrogen bonds between the complexes and molecules of the solvent or neighbouring species.

A Scalar Product for Computing Fundamental Quantities in Matter

We introduce a systematic way to obtain expressions for computing the amount of fundamental quantities such as helicity and angular momentum contained in static matter, given its charge and magnetization densities. The method is based on a scalar product that we put forward which is invariant under the ten-parameter conformal group in three-dimensional Euclidean space. This group is obtained as the static restriction (frequency ω=0) of the symmetry group of Maxwell equations: The fifteen-parameter conformal group in 3+1 Minkowski spacetime. In an exemplary application, we compute the helicity and angular momentum squared stored in a magnetic Hopfion.

Synthesis and characterization of Pt/CuBi2O4. Application to photocatalytic H2 evolution under visible light

The platinized spinel Pt/CuBi2O4 (Pt/CBO) is successfully employed as catalyst for the H2 formation under visible irradiation for the first time. CBO is synthetized by sol gel route from nitrates precursors and calcined at 800 °C. The X-Ray Diffractometry (XRD), X-Ray photoelectron spectroscopy (XPS), UV–Visible diffuse reflectance, Raman spectroscopy and Scanning Electron Microscopy (SEM/EDX) were used for the physical characterization. CBO crystallizes in a tetragonal symmetry (Space Group: P4/ncc). The spinel is p-type semiconductor with a narrow optical gap (1.51 eV) with a transition directly permitted. The reduction of adsorbed H2O molecules to gaseous H2 at ∼ -0.5 VAg/Agcl is evidenced by cyclic voltammetry. The latter is determined from the capacitance measurement in KOH (0.1 M) solution where the spinel exhibits a chemical stability with an exchange current of 50 µA cm−2. The conduction band deriving from the Bi3+: 6p, (3.59 eV/Vacuum / −1.15 VAg/Agcl) is energetically localized above the H2O level (∼-0.7 VAg/Agcl), leading to the feasibility of CBO for the H2 release. The photo-electrochemical activity shows an optimal H2 formation of 270 µmol with a release rate of 8.1 µmol h−1 (mg catalyst)−1 under visible illumination (LED lamp: 3 × 13 W, 1.65 × 1019 photons s−1) in KOH electrolyte (0.1 M) using I− as reducing agent. Pt-islands deposited under UV light improves significantly the photocatalysis (61 %) due to its low overvoltage (∼70 mV) with a quantum yield of 0.91 %, compared to CBO alone.

Urban Youth of the European Sector of the Russian Arctic Zone: Behavior in the Information Space, Values and Political Orientations in 2021–2022 (case of Pomorie)

The article summarizes the data of sociological surveys of young people, mainly aged 18– 24 years, held in the European sector of the Arctic zone of Russia (main cities of the Arkhangelsk region) in 2021 and 2022. Survey was aimed to identifi cation of indicators of the behavior and preferences of the target group in the information space, trust in various sources of information, as well as its personal values and political orientations in the context of Special Military Operation in Ukraine. It has been revealed that the main source of information is the Internet, while information of a political nature is not the main object of interest for urban youth. A constant decline in the youth audience of TV as a channel for obtaining information, as well as a consistently low level of trust in the official media, were noted. In terms of personal values, the basic traditional institutions such as labor, family, love, friendship still retain relevance for the urban youth of the Russian Arctic (in the case of Arkhangelsk and Severodvinsk). The amount of income is significant, but not the only main motive that determines the choice of a job. In the special political and international conditions after February 2022, young citizens of the Russian Federation in Pomorie, for the most part, remain optimistic about the future development of Russia and trust in state institutions, prospects for relations with Western countries. In general, the data obtained do not create grounds for assessing the urban youth of the European sector of the Russian Arctic (in the case of Pomorye) as a source of negative social potential that threatens political stability in the macroregion.

Accessibility of Lithium Cations in VSH‐2 Zeotype: Structural Effects and Formation of Protonated Water Clusters

AbstractThe accessibility of lithium cations in microporous vanadosilicate VSH‐2Cs of composition Cs2(VO)(Si6O14) ⋅ 3H2O was investigated by Single Crystal X‐ray Diffraction, Attenuated Total Reflection Fourier Transformed Infrared Spectroscopy and Density Functional Theory calculations. The topological symmetry of VSH‐2Cs is described in space group Cmca. After Li‐ion exchange, the structure of VSH‐2Li adopted monoclinic symmetry (space group C2/c) with a=17.011(2) Å, b=8.8533(11) Å, c=12.4934(16) Å, β=91.677(4)°, V=1880.7(4) Å3. The strong interactions between Li ions and oxygen‐framework atoms drive the main deformation mechanism, which is based on cooperative rotation of SiO4 and VO5 units around their oxygen atoms that behave as hinges. Exchange of Cs+ by Li+ is incomplete and accompanied by the formation of protonated species to counterbalance the electrostatic charge. The incorporation of protons is mediated by the presence of water dimers in the structural channels. H2O molecules in VSH‐2Li account not only as “space‐fillers” after the removal of large Cs ions but also mediate proton transfer to compensate the negative charge of the host vanadosilicate framework.

Benchmark Crystal Structure of Defect-Free Spinel ZnFe2O4.

Accurate structural models are of paramount importance for elucidating structure-property relationships in functional materials. Spinels (AB2O4) form a highly important family of materials with complex crystal structures, and subtle structural details have a critical bearing on understanding their physical properties. In some spinels, the space group symmetry is debated, and in general, point defects such as cation inversion and interstitials add complexity. Most studies of spinels concern powder materials, and this challenges deep structural characterization. In fact, most published spinel structures have dubious atomic displacement parameters (ADPs), which is a typical sign of problematic structural description in the refinement of diffraction data. Here, we use various X-ray and neutron diffraction techniques to establish a benchmark crystal structure for the essentially defect-free spinel ferrite ZnFe2O4, which is a widely studied frustrated magnet. It is shown that the appearance of Fd3̅m forbidden reflections in the ZnFe2O4 single-crystal neutron diffraction data is an artifact of multiple scattering rather than the loss of inversion symmetry. We then provide benchmark ADPs and demonstrate how strongly these parameters affect the refined cation inversion. The ADPs reported here may be used as reference data to test the soundness of refined structural models, possibly to constrain those based on suboptimal data quality, and thereby provide a more accurate fundamental understanding of the structure-property relationship in spinel-type materials.

The structure effect on the physicochemical properties of Gemini surfactants used as viscosity reducer for heavy oil

The structure of surfactants is a key factor affecting their physicochemical properties. Our earlier work synthesized Gemini surfactants CEA-n with different structures. In this paper, the effects of polyether chain length, spacer groups number and the hydrophobic alkyl chain length of surfactants CEA-n on the interfacial properties, wettability, rheological properties and emulsion stability were fully studied in detail, and the effects of surfactant structure on their temperature tolerance and salt resistance properties were explored. The results showed that the variation of polyether chain length of surfactant molecules had the greatest impact on the interfacial tension (IFT), and the surfactants with longer alkyl chains had better interfacial film strength. The wettability of various surfactant systems was investigated by the sessile drop method, and the contact angle decreased remarkably from 92.6° to 17.9° in a short time (300 s) after adding surfactant CEA-6. Judging from the fluid type, each heavy oil emulsion system exhibited pseudoplastic fluid characteristics, and dilute shear phenomenon was observed in the range of 0–50 s−1 with an increasing shear ratio. The particle size, dispersibility and coalescence of the heavy oil O/W emulsion droplets of each system were observed through the microscopic images of the emulsions, and the factors affecting the stability of the emulsions were systematically studied by bottle test. It was found that the increase of oil-water ratio, surfactant concentration and mixing speed would improve the stability of O/W emulsions, while high temperature would accelerate the demulsification process. All these results established the structure-property relationship of surfactant molecules.

Influence of oxygen stoichiometry on [formula omitted] spin state transitions and magnetic properties in [formula omitted] cobaltites

The layered EuBaCo2O5+δ (δ= 0.47) (EBCO) cobaltite shows various magnetic phases at high temperature and magnetic glassy state at low temperature. Further, the various magnetic phases of the EBCO are coupled with the spin state transition of Co3+ octahedra. In the present study, we report the structural and magnetization properties of the EBCO by changing the oxygen stoichiometry. The various oxygen compositions were obtained after post annealing the as-prepared EBCO cobaltite under argon and oxygen atmospheres and the final stoichiometry was detected from the iodometric titrations. The δ= 0.13 and 0.67 samples show the tetragonal symmetry (space group, P4/mmm), whereas the δ= 0.41, 0.47 and 0.58 samples show the orthorhombic symmetry (space group, Pmmm). The magnetization measurements on the δ= 0.13 sample shows the paramagnetic to antiferromagnetic ordering at TN= 288 K and the electrical resistivity analysis shows the Co2+ and Co3+ charge ordering at TCO= 180 K. Further, the δ= 0.13 sample show the absence of the ferromagnetic phase and Co3+ spin state transitions. The δ= 0.58 and 0.67 samples show the coexistence of ferromagnetic and antiferromagnetic phases, however, the features of Co3+ intermediate spin (IS) to low spin (LS) state transition is suppressed, which is observed in δ= 0.47 sample at 151 K. Our results indicate a tuning of the crystal structure along with the magnetic properties and also the Co3+ spin state transitions by oxygen stoichiometry variation in EuBaCo2O5+δ cobaltites.

Averaging material tensors of any rank in textured polycrystalline materials: Extending the scope beyond crystallographic proper point groups

In many modern micromechanical applications, there is usually a need to perform the orientational averaging of certain material tensors weighted by an orientation distribution function (ODF). The computation of these averages is seen to be very simplified by means of the so-called generalized spherical harmonic method (GSHM), which is based on the classical assumption that the ODFs are defined in the rotation group SO(3). A priori, this makes the averaging strictly applicable only to polycrystals with crystallite symmetry defined by one of the 11 proper point groups. Despite the interest in the study of materials belonging to any of the other 21 point groups, few studies have properly considered such cases. This is crucial for physical properties represented by odd-order tensors such as the third-order linear piezoelectric tensor. The goal of this work is to extend the applicability of the GSHM to crystallites with symmetry that belongs to the orthogonal group O(3). Thus, a simple formula is provided for the averaging of material tensors of any rank in textured polycrystals containing crystallites with symmetry defined by any of the 32 crystallographic point groups. Our work presents a simple yet rigorous method for indirect averaging on the orthogonal group, using averaging on SO(3). We demonstrate the full equivalence between our proposed method and averaging properly on O(3) through a detailed proof provided in this paper. This proof represents a significant contribution to the field, providing a practical and reliable approach for researchers working with crystalline materials. The results reported here confirm the validity of closed-form expressions previously derived by the authors for piezoelectric materials.

NMR chemical shift prediction and structural elucidation of linker-containing oligo- and polysaccharides using the computer program CASPER

Carbohydrate structures containing alkyl groups as aglycones are useful for investigating enzyme activity and glycan-protein interactions. Moreover, linker-containing oligosaccharides with a spacer group are commonly used to print glycan microarrays or to prepare protein-conjugates as vaccine candidates. The structural accuracy of these synthesized glycans are essential for interpretation of results from biological experiments in which the compounds have been used and NMR spectroscopy can unravel and confirm their structures. An approach for efficient 1H and 13C NMR chemical shift assignments employed a parallel NOAH-10 measurement followed by NMR spin-simulation to refine the 1H NMR chemical shifts, as exemplified for a disaccharide with an azidoethyl group as an aglycone, the NMR chemical shifts of which have been used to enhance the quality of CASPER (http://www.casper.organ.su.se/casper/). The CASPER program has been further developed to aid characterization of linker-containing oligo- and polysaccharides, either by chemical shift prediction for comparison to experimental NMR data or as structural investigation of synthesized glycans based on acquired unassigned NMR data. The ability of CASPER to elucidate structures of linker-containing oligosaccharides is demonstrated and comparisons to assigned or unassigned NMR data show the utility of CASPER in supporting a proposed oligosaccharide structure. Prediction of NMR chemical shifts of an oligosaccharide, corresponding to the repeating unit of an O-antigen polysaccharide, having a linker as an aglycone and a non-natural substituent derivative thereof are presented to exemplify the diversity of structures handled. Furthermore, NMR chemical shift predictions of synthesized polysaccharides, corresponding to bacterial polysaccharides, containing a linker are described showing that in addition to oligosaccharide structures also polysaccharide structures having an aglycone spacer group can be analyzed by CASPER.

Crystal structure of Methionyl-tRNA Synthetase from Rickettsia typhi in complex with its cognate amino acid

Rickettsia typhi is the causative agent of murine typhus (endemic typhus), a febrile illness that can be self-contained, though in some cases it can progress to death. The three dimensional structure of Methionyl-tRNA Synthetase from R. typhi (RtMetRS) in complex with its substrate l-methionine was solved by molecular replacement and refined at 2.30 Å resolution in space group P1 from one X-ray diffraction dataset. Processing and refinement trials were decisive to establish the lower symmetry space group and indicated the presence of twinning with four domains. RtMetRS belongs to the MetRS1 family and was crystallized with the CP domain in an open conformation, what is distinctive from other MetRS1 enzymes whose structures were solved with a bound L-methionine (therefore, in a closed conformation). This conformation resembles the ones observed in the MetRS2 family.