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Structural insights into 1,4-bis­(neopent­yloxy)pillar[5]arene and the pyridine host–guest system

The crystal structure of a neo­pentyl­oxypillar[5]arene with two pyridine mol­ecules encapsulated in the macrocyclic cavity is reported.




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Ethyl (2RS,3SR,4RS)-1-ethyl-2-(furan-2-yl)-4-hy­droxy-5-oxopyrrolidine-3-carboxyl­ate

The crystal structure of a pyrrolidine analogue obtained from the stereoselective reduction of the enolic form of 4-hy­droxy-2-furyl-pyrrole­carboxyl­ate is described.




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Tracking anharmonic oscillations in the structure of β 1,3-diacetylpyrene

A recently discovered β polymorph of 1,3-diacetylpyrene has turned out to be a prominent negative thermal expansion material. Its unique properties can be linked to anharmonic oscillations in the crystal structure. The onset and development of anharmonic behavior have been successfully tracked over a wide temperature range by single-crystal X-ray diffraction experiments. Sufficient diffraction data quality combined with modern quantum crystallography tools allowed a thorough analysis of the elusive anharmonic effects for a moderate-scattering purely organic compound.




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Structural transformations and stability of benzo[a]pyrene under high pressure

This study explores the high-pressure behavior of benzo[a]pyrene, revealing two previously unknown polymorphs at 4.8 and 7.1 GPa. These findings enhance our understanding of the structural dynamics and stability of polycyclic aromatic hydro­carbons under extreme conditions.




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Exploiting fourth-generation synchrotron radiation for enzyme and photoreceptor characterization

(Time-resolved) macromolecular crystallography at the new ESRF-ID29 beamline is described.




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Crystal structure of nickel orthovanadate (Ni3V2O8) at 299 (3) K and 1323 (8) K: an X-ray diffraction study

The structure of Ni3V2O8 was studied using X-ray diffraction at temperatures of 299 and 1323 K. No phase transition at high temperature is observed. The variation in V—O bond length is small as compared with the Ni—O bond due to its high rigidity.




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A contribution to the crystal chemistry and topology of organic thiosulfates: bis(1-methylpiperazinium)·S2O3·H2O versus 1-methylpiperazinediium·S2O3·3H2O

Crystal structure and topology of two new thiosulfates formed with mono- and diprotonated species of 1-methylpiperazine is reported.




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Synthesis and structural study of the partially disordered complex hexagonal phase δ1-MnZn9.7

A detailed structural characterization of the δ1-MnZn9.7 phase is presented.




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The seventh blind test of crystal structure prediction: structure ranking methods

The results of the seventh blind test of crystal structure prediction are presented, focusing on structure ranking methods.




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Crystal structure of the incommensurate modulated high-pressure phase of the potassium guaninate monohydrate

Incommensurate phase of potassium guaninate monohydrate is the first example of a modulation in purine derivatives and of a high-pressure incommensurate crystal structure to be solved for an organic compound.




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Spin reorientation and the interplay of magnetic sublattices in Er2CuMnMn4O12

We show that the interplay of multiple magnetic sublattices in Er2CuMnMn4O12 leads to four magnetic phase transitions characterized by the onset of ferrimagnetic order, spin-reorientation, spin canting, and the polarization of Er ions. While we elucidate numerous features of this complex magnetic system, the exact nature of the low-temperature coupling between erbium and manganese, and the origin of a k = (0, 0, ½) modulation, remain intriguing topics for future studies.




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Crystal structure and compressibility of magnesium chloride heptahydrate found under high pressure

In-situ diffraction measurements reveal that magnesium chloride forms a unique high-pressure phase, a heptahydrate, above 2 GPa. The hydrogen-bonding structure appears to contain orientational disorder.




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Symmetry, magnetic transitions and multiferroic properties of B-site-ordered A2MnB'O6 perovskites (B' = [Co, Ni])

A comparative description is presented of the symmetry and the magnetic structures found in the family of double perovskites A2MnB'O6 (mainly B' = Co and some Ni compounds for comparative purposes).




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Atypical phase transition, twinning and ferroelastic domain structure in bis(ethylenediammonium) tetrabromozincate(II) bromide, [NH3(CH2)2NH3]2[ZnBr4]Br2

A unique phase transition, twinning and ferroelastic domain structure in [NH3(CH2)2NH3]2[ZnBr4]Br2 is found. The new additional domain structure is observed at the phase transition on heating, which is preserved after cooling to room temperature.




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Variable stoichiometry and salt-cocrystal intermediate in the multicomponents of flucytosine: structural elucidation and its impact on stability

Five multicomponent solid forms of an antifungal drug flucytosine are reported with a hygroscopic stability study. A detailed CSD search on the cocrystal/salts of flucytosine is evaluated and correlated the structures based on bond angles and bond distances.




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Seed layer formation by deposition of micro-crystallites on a revolving substrate: modeling of the effective linear elastic, piezoelectric, and dielectric coefficients

The rotating substrate method of crystallite deposition is modeled, allowing computation of effective material coefficients of the layers resulting from the averaging. A worked numerical example particularized to 6mm ZnO is provided.




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Selective Acceleration and Inhibition of Crystal Growth of Glass Carbamazepine by Low-Concentration Poly(ethylene oxide):Effects of Drug Polymorph

Low-concentration poly(ethylene oxide) exhibit the polymorph-dependent effects on both the surface and bulk crystal growth of carbamazepine polymorphs. These polymorph-dependent effects of PEO were mainly attributed to the polymer enrichment at the interface and different crystal surface-polymer interactions.




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Density functional theory investigation of the phase transition, elastic and thermal characteristics for AuMTe2(M = Ga, In) chalcopyrite compounds

This study presents the first theoretical predictions of the phase transitions, elastic properties, and thermal behavior of AuMTe2 (M = Ga, In) chalcopyrite compounds. Using density functional theory and the quasi-harmonic Debye model, key mechanical and thermodynamic properties are analyzed, offering insights valuable for future experimental validation.




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Atypical phase transition, twinning and ferroelastic domain structure in bis(ethylenediammonium) tetrabromozincate(II) bromide, [NH3(CH2)2NH3]2[ZnBr4]Br2

Single-crystal growth, differential thermal analysis (DTA), derivative thermogravimetry (DTG), differential scanning calorimetry (DSC), X-ray structural studies and polarized microscopy observations of bis(ethylenediammonium) tetrabromozincate(II) bromide [NH3(CH2)2NH3]2[ZnBr4]Br2 are presented. A reversible phase transition is described. At room temperature, the complex crystallizes in the monoclinic system. In some cases, the single crystals are twinned into two or more large domains of ferroelastic type with domain walls in the (100) crystallographic plane. DTA and DTG measurements show chemical stability of the crystal up to ∼538 K. In the DSC studies, a reversible isostructural phase transition was revealed at ∼526/522 K on heating/cooling run, respectively. Optical observation on the heating run reveals that at the phase transition the plane of twinning (domain wall) does not disappear and additionally the appearance of a new domain structure of ferroelastic type with domain walls in the planes (101), (101), (100) and (001) is observed. The domain structure pattern is preserved after cooling to the room-temperature phase and the symmetry of this phase is unchanged.




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Crystal structure of nickel orthovanadate (Ni3V2O8) at 299 (3) K and 1323 (8) K: an X-ray diffraction study

Nickel orthovanadate is a promising material with potential applications in energy storage and photocatalytic devices. The crystal structure of Ni3V2O8 at 299 (3) K and 1323 (8) K was studied using X-ray powder diffraction. The sample was a single-phase orthorhombic kagome-staircase-Ni3(VO4)2-type structure (space group Cmca) at both temperatures. The phase purity and morphology was studied using energy-dispersive X-ray spectroscopy and scanning electron microscopy. The refined unit-cell parameters at 299 (3) K are a = 5.93384 (4) Å, b = 11.38318 (7) Å and c = 8.23818 (5) Å, and at 1323 (8) K are a = 6.02077 (7) Å, b = 11.48838 (7) Å and c = 8.32611 (9) Å. The obtained results indicate thermal expansion anisotropy, with a largest expansivity along a. Variations in Ni—O and V—O bonds with temperature are observed. The variation in the Ni—O bond is about one order higher in magnitude than that of the V—O bond, signifying the high rigidity of V—O bonds. The unit-cell size variations with rising effective ionic volume of the divalent A ion in the A3B2O8 family [A = Ni, Mg, Zn, Co, Mn (experimental data) and also A = Cu, Cd (theoretical data), B = V or As] are analyzed. Based on experimental and theoretical data, trends within the family are observed and the unit-cell size for reported solid solution of nickel (87%) and copper (13%) mixture in (Ni1–xCux)3V2O8 are predicted. Predictions are also provided for some hypothetical A3B2O8 ternary compound and solid solutions.




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Crystal structure and compressibility of magnesium chloride heptahydrate found under high pressure

The odd hydration number has so far been missing in the water-rich magnesium chloride hydrate series (MgCl2·nH2O). In this study, magnesium chloride heptahydrate, MgCl2·7H2O (or MgCl2·7D2O), which forms at high pressures above 2 GPa and high temperatures above 300 K, has been identified. Its structure has been determined by a combination of in-situ single-crystal X-ray diffraction at 2.5 GPa and 298 K and powder neutron diffraction at 3.1 GPa and 300 K. The single-crystal specimen was grown by mixing alcohols to prevent nucleation of undesired crystalline phases. The results show orientational disorder of water molecules, which was also examined using density functional theory calculations. The disorder involves the reconnection of hydrogen bonds, which differs from those in water ice phases and known disordered salt hydrates. Shrinkage by compression occurs mainly in one direction. In the plane perpendicular to this most compressible direction, oxygen and chlorine atoms are in a hexagonal-like arrangement.




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Synthesis and structural study of the partially disordered complex hexagonal phase δ1-MnZn9.7

A detailed structural analysis of the Zn-rich δ1-MnZn9.7 phase using single-crystal X-ray diffraction is presented. The δ1 phase has been synthesized by the high-temperature synthetic route. The structure crystallizes in space group P63/mmc (Pearson symbol hP556) with unit-cell parameters: a = b = 12.9051 (2) Å and c = 57.640 (1) Å. The 556 atoms are distributed over 52 Wyckoff positions in the hexagonal unit cell: seven ordered Mn sites, 37 ordered Zn sites and eight positionally disordered Zn sites. The structure predominantly consists of Frank–Kasper polyhedra (endohedral icosahedra Zn12 and icosioctahedron Zn16) and four distinct types of glue Zn atoms. The structure comprises a 127-atom supercluster (Mn13Zn114), a 38-atom extended Pearce cluster (Mn3Zn35), a 46-atom L-tetrahedron (Mn4Zn42), a Friauf polyhedron (Zn17), a disordered icosahedral cluster (MnZn12) and four glue Zn atoms. Positionally disordered Zn sites around an Mn site can be visualized as the superimposition of three differently oriented Zn12 icosahedra.




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Crystal structure of the incommensurate modulated high-pressure phase of the potassium guaninate monohydrate

The crystal structure of the incommensurate modulated phase of potassium guaninate monohydrate has been solved on the basis of high-pressure single-crystal X-ray diffraction data. The modulated structure was described as a `mosaic' sequence of three different local configurations of two neighbouring guaninate rings. In contrast to known examples of incommensurate modulated organic compounds, the modulation functions of all atoms are discontinuous. This is the first example of the experimental detection of an incommensurate modulated crystal structure that can be modelled using the special `soliton mode' modulation function proposed by Aramburu et al. [(1995), J. Phys. Condens. Matter, 7, 6187–6196].




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Spin reorientation and the interplay of magnetic sublattices in Er2CuMnMn4O12

Through a combination of magnetic susceptibility, specific heat, and neutron powder diffraction measurements we have revealed a sequence of four magnetic phase transitions in the columnar quadruple perovskite Er2CuMnMn4O12. A key feature of the quadruple perovskite structural framework is the complex interplay of multiple magnetic sublattices via frustrated exchange topologies and competing magnetic anisotropies. It is shown that in Er2CuMnMn4O12, this phenomenology gives rise to multiple spin-reorientation transitions driven by the competition of easy-axis single ion anisotropy and the Dzyaloshinskii–Moriya interaction; both within the manganese B-site sublattice. At low temperature, one Er sublattice orders due to a finite f-d exchange field aligned parallel to its Ising axis, while the other Er sublattice remains non-magnetic until a final, symmetry-breaking phase transition into the ground state. This non-trivial low-temperature interplay of transition metal and rare-earth sublattices, as well as an observed k = (0, 0, ½) periodicity in both manganese spin canting and Er ordering, raises future challenges to develop a complete understanding of the R2CuMnMn4O12 family.




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Contrasting conformational behaviors of molecules XXXI and XXXII in the seventh blind test of crystal structure prediction

Accurate modeling of conformational energies is key to the crystal structure prediction of conformational polymorphs. Focusing on molecules XXXI and XXXII from the seventh blind test of crystal structure prediction, this study employs various electronic structure methods up to the level of domain-local pair natural orbital coupled cluster singles and doubles with perturbative triples [DLPNO-CCSD(T1)] to benchmark the conformational energies and to assess their impact on the crystal energy landscapes. Molecule XXXI proves to be a relatively straightforward case, with the conformational energies from generalized gradient approximation (GGA) functional B86bPBE-XDM changing only modestly when using more advanced density functionals such as PBE0-D4, ωB97M-V, and revDSD-PBEP86-D4, dispersion-corrected second-order Møller–Plesset perturbation theory (SCS-MP2D), or DLPNO-CCSD(T1). In contrast, the conformational energies of molecule XXXII prove difficult to determine reliably, and variations in the computed conformational energies appreciably impact the crystal energy landscape. Even high-level methods such as revDSD-PBEP86-D4 and SCS-MP2D exhibit significant disagreements with the DLPNO-CCSD(T1) benchmarks for molecule XXXII, highlighting the difficulty of predicting conformational energies for complex, drug-like molecules. The best-converged predicted crystal energy landscape obtained here for molecule XXXII disagrees significantly with what has been inferred about the solid-form landscape experimentally. The identified limitations of the calculations are probably insufficient to account for the discrepancies between theory and experiment on molecule XXXII, and further investigation of the experimental solid-form landscape would be valuable. Finally, assessment of several semi-empirical methods finds r2SCAN-3c to be the most promising, with conformational energy accuracy intermediate between the GGA and hybrid functionals and a low computational cost.




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Assessment of the exchange-hole dipole moment dispersion correction for the energy ranking stage of the seventh crystal structure prediction blind test

The seventh blind test of crystal structure prediction (CSP) methods substantially increased the level of complexity of the target compounds relative to the previous tests organized by the Cambridge Crystallographic Data Centre. In this work, the performance of density-functional methods is assessed using numerical atomic orbitals and the exchange-hole dipole moment dispersion correction (XDM) for the energy-ranking phase of the seventh blind test. Overall, excellent performance was seen for the two rigid molecules (XXVII, XXVIII) and for the organic salt (XXXIII). However, for the agrochemical (XXXI) and pharmaceutical (XXXII) targets, the experimental polymorphs were ranked fairly high in energy amongst the provided candidate structures and inclusion of thermal free-energy corrections from the lattice vibrations was found to be essential for compound XXXI. Based on these results, it is proposed that the importance of vibrational free-energy corrections increases with the number of rotatable bonds.




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Polymorph sampling with coupling to extended variables: enhanced sampling of polymorph energy landscapes and free energy perturbation of polymorph ensembles

A novel approach to computationally enhance the sampling of molecular crystal structures is proposed and tested. This method is based on the use of extended variables coupled to a Monte Carlo based crystal polymorph generator. Inspired by the established technique of quasi-random sampling of polymorphs using the rigid molecule constraint, this approach represents molecular clusters as extended variables within a thermal reservoir. Polymorph unit-cell variables are generated using pseudo-random sampling. Within this framework, a harmonic coupling between the extended variables and polymorph configurations is established. The extended variables remain fixed during the inner loop dedicated to polymorph sampling, enforcing a stepwise propagation of the extended variables to maintain system exploration. The final processing step results in a polymorph energy landscape, where the raw structures sampled to create the extended variable trajectory are re-optimized without the thermal coupling term. The foundational principles of this approach are described and its effectiveness using both a Metropolis Monte Carlo type algorithm and modifications that incorporate replica exchange is demonstrated. A comparison is provided with pseudo-random sampling of polymorphs for the molecule coumarin. The choice to test a design of this algorithm as relevant for enhanced sampling of crystal structures was due to the obvious relation between molecular structure variables and corresponding crystal polymorphs as representative of the inherent vapor to crystal transitions that exist in nature. Additionally, it is shown that the trajectories of extended variables can be harnessed to extract fluctuation properties that can lead to valuable insights. A novel thermodynamic variable is introduced: the free energy difference between ensembles of Z' = 1 and Z' = 2 crystal polymorphs.




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The seventh blind test of crystal structure prediction: structure ranking methods

A seventh blind test of crystal structure prediction has been organized by the Cambridge Crystallographic Data Centre. The results are presented in two parts, with this second part focusing on methods for ranking crystal structures in order of stability. The exercise involved standardized sets of structures seeded from a range of structure generation methods. Participants from 22 groups applied several periodic DFT-D methods, machine learned potentials, force fields derived from empirical data or quantum chemical calculations, and various combinations of the above. In addition, one non-energy-based scoring function was used. Results showed that periodic DFT-D methods overall agreed with experimental data within expected error margins, while one machine learned model, applying system-specific AIMnet potentials, agreed with experiment in many cases demonstrating promise as an efficient alternative to DFT-based methods. For target XXXII, a consensus was reached across periodic DFT methods, with consistently high predicted energies of experimental forms relative to the global minimum (above 4 kJ mol−1 at both low and ambient temperatures) suggesting a more stable polymorph is likely not yet observed. The calculation of free energies at ambient temperatures offered improvement of predictions only in some cases (for targets XXVII and XXXI). Several avenues for future research have been suggested, highlighting the need for greater efficiency considering the vast amounts of resources utilized in many cases.




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X-ray crystallographic structure of a novel enantiopure chiral isothiourea with potential applications in enantioselective synthesis

The synthesis of a chiral isothiourea, namely, (4aR,8aR)-3-phenyl-4a,5,6,7,8,8a-hexahydrobenzo[4,5]imidazo[2,1-b]thiazol-9-ium bromide, C15H17N2S+·Br−, with potential organocatalytic and anti-inflammatory activity is reported. The preparation of the heterocycle of interest was carried out in two high-yielding steps. The hydrobromide salt of the isothiourea of interest provided suitable crystals for X-ray diffraction analysis, the results of which are reported. Salient observations from this analysis are the near perpendicular arrangement of the phenyl ring and the mean plane of the heterocycle. This conformational characteristic may be relevant with regard the stereoselectivity induced by the chiral isothiourea in asymmetric reactions. Furthermore, evidence was found for the existence of an S...Br− halogen bond.




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Synthesis and crystal structure of Ba2Y0.87(1)Mn1.71(1)Te5

We report the structural characterization of a new quaternary telluride, Ba2Y0.87(1)Mn1.71(1)Te5, which was synthesized by the direct reaction of the elements inside a vacuum-sealed fused-silica tube. The quaternary phase is the first member of the Ba–M–Mn–Te system (M = Sc and Y). The composition and structure of the phase were elucidated using SEM–EDX (scanning electron microscopy–energy dispersive X-ray spectrometry) and single-crystal X-ray diffraction (SCXRD) studies. The title phase is nonstoichiometric and crystallizes in the monoclinic system (space group C2/m) having the refined unit-cell parameters a = 15.1466 (8), b = 4.5782 (3), c = 10.6060 (7) Å and β = 116.956 (2)°, with two formula units (Z = 2). The pseudo-two-dimensional crystal structure of Ba2Y0.87(1)Mn1.71(1)Te5 consists of distorted YTe6 octahedra and MnTe4 tetrahedra as the building blocks of the structure. The YTe6 octahedra are arranged to form infinite one-dimensional chains by sharing edges along the [010] direction. These chains are further connected to the MnTe4 tetrahedra along the c axis to create layered two-dimensional polyanionic [Y0.87(1)Mn1.71(1)Te5]4− units. The stuffing of Ba2+ cations in between the layers of [Y0.87(1)Mn1.71(1)Te5]4− anions brings the charge neutrality of the structure. Each Ba atom in the structure sits at the centre of a distorted monocapped trigonal prism-like polyhedron of seven Te atoms.




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Crystal structures of three uranyl–acetate–bipyridine complexes crystallized from hydraulic fracking fluid

Hydraulic fracking exposes shale plays to acidic hydraulic fracking fluid (HFF), releasing toxic uranium (U) along with the desired oil and gas. With no existing methods to ensure U remains sequestered in the shale, this study sought to add organic ligands to HFF to explore potential U retention in shale plays. To test this possibility, incubations were set up in which uranyl acetate and one organic bipyridine ligand (either 2,2'-, 2,3'-, 2,4'-, or 4,4'-bipyridine) were added to pristine HFF as the crystallization medium. After several months and complete evaporation of all volatiles, bulk yellow crystalline material was obtained from the incubations, three of which yielded crystals suitable for single-crystal analysis, resulting in two novel structures and a high-quality structure of a previously described compound. The UO2VI acetate complexes bis(acetato-κ2O,O')(2,2'-bipyridine-κ2N,N')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,2'-bipyridine]UVIO2(CH3CO2)2, (I), and bis(acetato-κ2O,O')(2,4'-bipyridine-κN1')dioxidouranium(VI), [U(C2H3O2)2O2(C10H8N2)2] or [2,4'-bipyridine]2UVIO2(CH3CO2)2, (III), contain eight-coordinate UVI in a pseudo-hexagonal bipyramidal coordination geometry and are molecular, packing via weak C—H...O/N interactions, whereas catena-poly[bis(2,3'-bipyridinium) [di-μ-acetato-μ3-hydroxido-μ-hydroxido-di-μ3-oxido-hexaoxidotriuranium(VI)]–2,3'-bipyridine–water (1/1/1)], (C10H9N2)2[U3(C2H3O2)2O8(OH)2]·C10H8N2·H2O or {[2,3'-bipyridinium]2[2,3'-bipyridine][(UVIO2)3(O)2(OH)2(CH3CO2)2·H2O]}n, (II), forms an ionic one-dimensional polymer with seven-coordinate pentagonal bipyramidal UVI centers and hydrogen-bonding interactions within each chain. The formation of these crystals could indicate the potential for bipyridine to bind with U in shale during fracking, which will be explored in a future study via ICP-MS (inductively coupled plasma mass spectrometry) analyses of U concentration in HFF/bipyridine/shale incubations. The variation seen here between the molecular structures may indicate variance in the ability of bipyridine isomers to form complexes with U, which could impact their ability to retain U within shale in the context of fracking.




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Analytical models representing X-ray form factors of ions

Parameters in analytical models for X-ray form factors of ions f0(s), based on the inverse Mott–Bethe formula involving a variable number of Gaussians, are determined for a wide range of published data sets {s, f0(s)}. The models reproduce the calculated form-factor values close to what is expected from a uniform statistical distribution with limits determined by their precision. For different ions associated with the same atom, the number of Gaussians in the models decreases with increasing net positive charge.




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Automated selection of nanoparticle models for small-angle X-ray scattering data analysis using machine learning

Small-angle X-ray scattering (SAXS) is widely used to analyze the shape and size of nanoparticles in solution. A multitude of models, describing the SAXS intensity resulting from nanoparticles of various shapes, have been developed by the scientific community and are used for data analysis. Choosing the optimal model is a crucial step in data analysis, which can be difficult and time-consuming, especially for non-expert users. An algorithm is proposed, based on machine learning, representation learning and SAXS-specific preprocessing methods, which instantly selects the nanoparticle model best suited to describe SAXS data. The different algorithms compared are trained and evaluated on a simulated database. This database includes 75 000 scattering spectra from nine nanoparticle models, and realistically simulates two distinct device configurations. It will be made freely available to serve as a basis of comparison for future work. Deploying a universal solution for automatic nanoparticle model selection is a challenge made more difficult by the diversity of SAXS instruments and their flexible settings. The poor transferability of classification rules learned on one device configuration to another is highlighted. It is shown that training on several device configurations enables the algorithm to be generalized, without degrading performance compared with configuration-specific training. Finally, the classification algorithm is evaluated on a real data set obtained by performing SAXS experiments on nanoparticles for each of the instrumental configurations, which have been characterized by transmission electron microscopy. This data set, although very limited, allows estimation of the transferability of the classification rules learned on simulated data to real data.




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Bond topology of chain, ribbon and tube silicates. Part II. Geometrical analysis of infinite 1D arrangements of (TO4)n− tetrahedra

In Part I of this series, all topologically possible 1-periodic infinite graphs (chain graphs) representing chains of tetrahedra with up to 6–8 vertices (tetrahedra) per repeat unit were generated. This paper examines possible restraints on embedding these chain graphs into Euclidean space such that they are compatible with the metrics of chains of tetrahedra in observed crystal structures. Chain-silicate minerals with T = Si4+ (plus P5+, V5+, As5+, Al3+, Fe3+, B3+, Be2+, Zn2+ and Mg2+) have a grand nearest-neighbour 〈T–T〉 distance of 3.06±0.15 Å and a minimum T⋯T separation of 3.71 Å between non-nearest-neighbour tetrahedra, and in order for embedded chain graphs (called unit-distance graphs) to be possible atomic arrangements in crystals, they must conform to these metrics, a process termed equalization. It is shown that equalization of all acyclic chain graphs is possible in 2D and 3D, and that equalization of most cyclic chain graphs is possible in 3D but not necessarily in 2D. All unique ways in which non-isomorphic vertices may be moved are designated modes of geometric modification. If a mode (m) is applied to an equalized unit-distance graph such that a new geometrically distinct unit-distance graph is produced without changing the lengths of any edges, the mode is designated as valid (mv); if a new geometrically distinct unit-distance graph cannot be produced, the mode is invalid (mi). The parameters mv and mi are used to define ranges of rigidity of the unit-distance graphs, and are related to the edge-to-vertex ratio, e/n, of the parent chain graph. The program GraphT–T was developed to embed any chain graph into Euclidean space subject to the metric restraints on T–T and T⋯T. Embedding a selection of chain graphs with differing e/n ratios shows that the principal reason why many topologically possible chains cannot occur in crystal structures is due to violation of the requirement that T⋯T > 3.71 Å. Such a restraint becomes increasingly restrictive as e/n increases and indicates why chains with stoichiometry TO<2.5 do not occur in crystal structures.




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GraphT–T (V1.0Beta), a program for embedding and visualizing periodic graphs in 3D Euclidean space

Following the work of Day & Hawthorne [Acta Cryst. (2022), A78, 212–233] and Day et al. [Acta Cryst. (2024), A80, 258–281], the program GraphT–T has been developed to embed graphical representations of observed and hypothetical chains of (SiO4)4− tetrahedra into 2D and 3D Euclidean space. During embedding, the distance between linked vertices (T–T distances) and the distance between unlinked vertices (T⋯T separations) in the resultant unit-distance graph are restrained to the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is restrained to be equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. The notional interactions between vertices are described by a 3D spring-force algorithm in which the attractive forces between linked vertices behave according to Hooke's law and the repulsive forces between unlinked vertices behave according to Coulomb's law. Embedding parameters (i.e. spring coefficient, k, and Coulomb's constant, K) are iteratively refined during embedding to determine if it is possible to embed a given graph to produce a unit-distance graph with T–T distances and T⋯T separations that are compatible with the observed T–T distances and T⋯T separations in crystal structures. The resultant unit-distance graphs are denoted as compatible and may form crystal structures if and only if all distances between linked vertices (T–T distances) agree with the average observed distance between linked Si tetrahedra (3.06±0.15 Å) and the minimum separation between unlinked vertices is equal to or greater than the minimum distance between unlinked Si tetrahedra (3.713 Å) in silicate minerals. If the unit-distance graph does not satisfy these conditions, it is considered incompatible and the corresponding chain of tetrahedra is unlikely to form crystal structures. Using GraphT–T, Day et al. [Acta Cryst. (2024), A80, 258–281] have shown that several topological properties of chain graphs influence the flexibility (and rigidity) of the corresponding chains of Si tetrahedra and may explain why particular compatible chain arrangements (and the minerals in which they occur) are more common than others and/or why incompatible chain arrangements do not occur in crystals despite being topologically possible.




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Instrumental broadening and the radial pair distribution function with 2D detectors

The atomic pair distribution function (PDF) is a real-space representation of the structure of a material. Experimental PDFs are obtained using a Fourier transform from total scattering data which may or may not have Bragg diffraction peaks. The determination of Bragg peak resolution in scattering data from the fundamental physical parameters of the diffractometer used is well established, but after the Fourier transform from reciprocal to direct space, these contributions are harder to identify. Starting from an existing definition of the resolution function of large-area detectors for X-ray diffraction, this approach is expanded into direct space. The effect of instrumental parameters on PDF peak resolution is developed mathematically, then studied with modelling and comparison with experimental PDFs of LaB6 from measurements made in different-sized capillaries.




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Structure of the outer membrane porin OmpW from the pervasive pathogen Klebsiella pneumoniae

Conjugation is the process by which plasmids, including those that carry antibiotic-resistance genes, are mobilized from one bacterium (the donor) to another (the recipient). The conjugation efficiency of IncF-like plasmids relies on the formation of mating-pair stabilization via intimate interactions between outer membrane proteins on the donor (a plasmid-encoded TraN isoform) and recipient bacteria. Conjugation of the R100-1 plasmid into Escherichia coli and Klebsiella pneumoniae (KP) recipients relies on pairing between the plasmid-encoded TraNα in the donor and OmpW in the recipient. Here, the crystal structure of K. pneumoniae OmpW (OmpWKP) is reported at 3.2 Å resolution. OmpWKP forms an eight-stranded β-barrel flanked by extracellular loops. The structures of E. coli OmpW (OmpWEC) and OmpWKP show high conservation despite sequence variability in the extracellular loops.




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Crystal structure of the RNA-recognition motif of Drosophila melanogaster tRNA (uracil-5-)-methyltransferase homolog A

Human tRNA (uracil-5-)-methyltransferase 2 homolog A (TRMT2A) is the dedicated enzyme for the methylation of uridine 54 in transfer RNA (tRNA). Human TRMT2A has also been described as a modifier of polyglutamine (polyQ)-derived neuronal toxicity. The corresponding human polyQ pathologies include Huntington's disease and constitute a family of devastating neuro­degenerative diseases. A polyQ tract in the corresponding disease-linked protein causes neuronal death and symptoms such as impaired motor function, as well as cognitive impairment. In polyQ disease models, silencing of TRMT2A reduced polyQ-associated cell death and polyQ protein aggregation, suggesting this protein as a valid drug target against this class of disorders. In this paper, the 1.6 Å resolution crystal structure of the RNA-recognition motif (RRM) from Drosophila melanogaster, which is a homolog of human TRMT2A, is described and analysed.




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Expression, purification and crystallization of the photosensory module of phytochrome B (phyB) from Sorghum bicolor

Sorghum, a short-day tropical plant, has been adapted for temperate grain production, in particular through the selection of variants at the MATURITY loci (Ma1–Ma6) that reduce photoperiod sensitivity. Ma3 encodes phytochrome B (phyB), a red/far-red photochromic biliprotein photoreceptor. The multi-domain gene product, comprising 1178 amino acids, autocatalytically binds the phytochromobilin chromophore to form the photoactive holophytochrome (Sb.phyB). This study describes the development of an efficient heterologous overproduction system which allows the production of large quantities of various holoprotein constructs, along with purification and crystallization procedures. Crystals of the Pr (red-light-absorbing) forms of NPGP, PGP and PG (residues 1–655, 114–655 and 114–458, respectively), each C-terminally tagged with His6, were successfully produced. While NPGP crystals did not diffract, those of PGP and PG diffracted to 6 and 2.1 Å resolution, respectively. Moving the tag to the N-terminus and replacing phytochromobilin with phycocyanobilin as the ligand produced PG crystals that diffracted to 1.8 Å resolution. These results demonstrate that the diffraction quality of challenging protein crystals can be improved by removing flexible regions, shifting fusion tags and altering small-molecule ligands.




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Structural and biochemical characterization of the M405S variant of Desulfovibrio vulgaris formate dehydrogenase

Molybdenum- or tungsten-dependent formate dehydrogenases have emerged as significant catalysts for the chemical reduction of CO2 to formate, with biotechnological applications envisaged in climate-change mitigation. The role of Met405 in the active site of Desulfovibrio vulgaris formate dehydrogenase AB (DvFdhAB) has remained elusive. However, its proximity to the metal site and the conformational change that it undergoes between the resting and active forms suggests a functional role. In this work, the M405S variant was engineered, which allowed the active-site geometry in the absence of methionine Sδ interactions with the metal site to be revealed and the role of Met405 in catalysis to be probed. This variant displayed reduced activity in both formate oxidation and CO2 reduction, together with an increased sensitivity to oxygen inactivation.




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X-ray crystal structure of a designed rigidified imaging scaffold in the ligand-free conformation

Imaging scaffolds composed of designed protein cages fused to designed ankyrin repeat proteins (DARPins) have enabled the structure determination of small proteins by cryogenic electron microscopy (cryo-EM). One particularly well characterized scaffold type is a symmetric tetrahedral assembly composed of 24 subunits, 12 A and 12 B, which has three cargo-binding DARPins positioned on each vertex. Here, the X-ray crystal structure of a representative tetrahedral scaffold in the apo state is reported at 3.8 Å resolution. The X-ray crystal structure complements recent cryo-EM findings on a closely related scaffold, while also suggesting potential utility for crystallographic investigations. As observed in this crystal structure, one of the three DARPins, which serve as modular adaptors for binding diverse `cargo' proteins, present on each of the vertices is oriented towards a large solvent channel. The crystal lattice is unusually porous, suggesting that it may be possible to soak crystals of the scaffold with small (≤30 kDa) protein cargo ligands and subsequently determine cage–cargo structures via X-ray crystallography. The results suggest the possibility that cryo-EM scaffolds may be repurposed for structure determination by X-ray crystallography, thus extending the utility of electron-microscopy scaffold designs for alternative structural biology applications.




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Preliminary X-ray diffraction and ligand-binding analyses of the N-terminal domain of hypothetical protein Rv1421 from Mycobacterium tuberculosis H37Rv

Mycobacterium tuberculosis can reside and persist in deep tissues; latent tuberculosis can evade immune detection and has a unique mechanism to convert it into active disease through reactivation. M. tuberculosis Rv1421 (MtRv1421) is a hypothetical protein that has been proposed to be involved in nucleotide binding-related metabolism in cell-growth and cell-division processes. However, due to a lack of structural information, the detailed function of MtRv1421 remains unclear. In this study, a truncated N-terminal domain (NTD) of MtRv1421, which contains a Walker A/B-like motif, was purified and crystallized using PEG 400 as a precipitant. The crystal of MtRv1421-NTD diffracted to a resolution of 1.7 Å and was considered to belong to either the C-centered monoclinic space group C2 or the I-centered orthorhombic space group I222, with unit-cell parameters a = 124.01, b = 58.55, c = 84.87 Å, β = 133.12° or a = 58.53, b = 84.86, c = 90.52 Å, respectively. The asymmetric units of the C2 or I222 crystals contained two or one monomers, respectively. In terms of the binding ability of MtRv1421-NTD to various ligands, uridine diphosphate (UDP) and UDP-N-acetylglucosamine significantly increased the melting temperature of MtRv1421-NTD, which indicates structural stabilization through the binding of these ligands. Altogether, the results reveal that a UDP moiety may be required for the interaction of MtRv1421-NTD as a nucleotide-binding protein with its ligand.