Crystallographic texture is a key organization feature of many technical and biological materials. In these materials, especially hierarchically structured ones, the preferential alignment of the nano constituents heavily influences the macroscopic behavior of the material. To study local crystallographic texture with both high spatial and angular resolution, we developed Texture Tomography (TexTOM). This approach allows the user to model the diffraction data of polycrystalline materials using the full reciprocal space of the crystal ensemble and describe the texture in each voxel via an orientation distribution function, hence it provides 3D reconstructions of the local texture by measuring the probabilities of all crystal orientations. The TexTOM approach addresses limitations associated with existing models: it correlates the intensities from several Bragg reflections, thus reducing ambiguities resulting from symmetry. Further, it yields quantitative probability distributions of local real space crystal orientations without further assumptions about the sample structure. Finally, its efficient mathematical formulation enables reconstructions faster than the time scale of the experiment. This manuscript presents the mathematical model, the inversion strategy and its current experimental implementation. We show characterizations of simulated data as well as experimental data obtained from a synthetic, inorganic model sample: the silica–witherite biomorph. TexTOM provides a versatile framework to reconstruct 3D quantitative texture information for polycrystalline samples; it opens the door for unprecedented insights into the nanostructural makeup of natural and technical materials.

Reaching beyond the commonly used spherical atomic electron density model allows one to greatly improve the accuracy of hydrogen atom structural param­eters derived from X-ray data. However, the effects of atomic asphericity are less explored for electron diffraction data. In this work, Hirshfeld atom refinement (HAR), a method that uses an accurate description of electron density by quantum mechanical calculation for a system of interest, was applied for the first time to the kinematical refinement of electron diffraction data. This approach was applied here to derive the structure of ordinary hexagonal ice (Ih). The effect of introducing HAR is much less noticeable than in the case of X-ray refinement and it is largely overshadowed by dynamical scattering effects. It led to only a slight change in the O—H bond lengths (shortening by 0.01 Å) compared with the independent atom model (IAM). The average absolute differences in O—H bond lengths between the kinematical refinements and the reference neutron structure were much larger: 0.044 for IAM and 0.046 Å for HAR. The refinement results changed considerably when dynamical scattering effects were modelled – with extinction correction or with dynamical refinement. The latter led to an improvement of the O—H bond length accuracy to 0.021 Å on average (with IAM refinement). Though there is a potential for deriving more accurate structures using HAR for electron diffraction, modelling of dynamical scattering effects seems to be a necessary step to achieve this. However, at present there is no software to support both HAR and dynamical refinement.

Identifying and characterizing metal-binding sites (MBS) within macromolecular structures is imperative for elucidating their biological functions. CheckMyMetal (CMM) is a web based tool that facilitates the interactive valid­ation of MBS in structures determined through X-ray crystallography and cryo-electron microscopy (cryo-EM). Recent updates to CMM have significantly enhanced its capability to efficiently handle large datasets generated from cryo-EM structural analyses. In this study, we address various challenges inherent in validating MBS within both X-ray and cryo-EM structures. Specifically, we examine the difficulties associated with accurately identifying metals and modeling their coordination environments by considering the ongoing reproducibility challenges in structural biology and the critical importance of well annotated, high-quality experimental data. CMM employs a sophisticated framework of rules rooted in the valence bond theory for MBS validation. We explore how CMM validation parameters correlate with the resolution of experimentally derived structures of macromolecules and their complexes. Additionally, we showcase the practical utility of CMM by analyzing a representative cryo-EM structure. Through a comprehensive examination of experimental data, we demonstrate the capability of CMM to advance MBS characterization and identify potential instances of metal misassignment.

The antipsychotic drug olanzapine is well known for its complex polymorphism. Although widely investigated, the crystal structure of one of its anhydrous polymorphs, form III, is still unknown. Its appearance, always in concomitance with forms II and I, and the impossibility of isolating it from that mixture, have prevented its structure determination so far. The scenario has changed with the emerging field of 3D electron diffraction (3D ED) and its great advantages in the characterization of polyphasic mixtures of nanosized crystals. In this study, we show how the application of 3D ED allows the ab initio structure determination and dynamical refinement of this elusive crystal structure that remained unknown for more than 20 years. Olanzapine form III is monoclinic and shows a similar but shifted packing with respect to form II. It is remarkably different from the lowest-energy structures predicted by the energy-minimization algorithms of crystal structure prediction.

A pressure-induced triclinic-to-monoclinic phase transition has been caught `in the act' over a wider series of high-pressure synchrotron diffraction experiments conducted on a large, photoluminescent organo-gold(I) compound. Here, we describe the mechanism of this single-crystal-to-single-crystal phase transition, the onset of which occurs at ∼0.6 GPa, and we report a high-quality structure of the new monoclinic phase, refined using aspherical atomic scattering factors. Our case illustrates how conducting a fast series of diffraction experiments, enabled by modern equipment at synchrotron facilities, can lead to overestimation of the actual pressure of a phase transition due to slow transformation kinetics.

The TIR (Toll/interleukin-1 receptor) domain represents a vital structural element shared by proteins with roles in immunity signalling pathways across phyla (from humans and plants to bacteria). Decades of research have finally led to identifying the key features of the molecular basis of signalling by these domains, including the formation of open-ended (filamentous) assemblies (responsible for the signalling by cooperative assembly formation mechanism, SCAF) and enzymatic activities involving the cleavage of nucleotides. We present a historical perspective of the research that led to this understanding, highlighting the roles that different structural methods played in this process: X-ray crystallography (including serial crystallography), microED (micro-crystal electron diffraction), NMR (nuclear magnetic resonance) spectroscopy and cryo-EM (cryogenic electron microscopy) involving helical reconstruction and single-particle analysis. This perspective emphasizes the complementarity of different structural approaches.

Ultrahigh-resolution structures provide unprecedented details about protein dynamics, hydrogen bonding and solvent networks. The reported 0.70 Å, room-temperature crystal structure of crambin is the highest-resolution ambient-temperature structure of a protein achieved to date. Sufficient data were collected to enable unrestrained refinement of the protein and associated solvent networks using SHELXL. Dynamic solvent networks resulting from alternative side-chain conformations and shifts in water positions are revealed, demonstrating that polypeptide flexibility and formation of clathrate-type structures at hydro­phobic surfaces are the key features endowing crambin crystals with extraordinary diffraction power.

Biological materials have outstanding properties. With ease, challenging mechanical, optical or electrical properties are realised from comparatively `humble' building blocks. The key strategy to realise these properties is through extensive hierarchical structuring of the material from the millimetre to the nanometre scale in 3D. Though hierarchical structuring in biological materials has long been recognized, the 3D characterization of such structures remains a challenge. To understand the behaviour of materials, multimodal and multi-scale characterization approaches are needed. In this review, we outline current X-ray analysis approaches using the structures of bone and shells as examples. We show how recent advances have aided our understanding of hierarchical structures and their functions, and how these could be exploited for future research directions. We also discuss current roadblocks including radiation damage, data quantity and sample preparation, as well as strategies to address them.

Ultrafast, high-intensity X-ray free-electron lasers can perform diffraction imaging of single protein molecules. Various algorithms have been developed to determine the orientation of each single-particle diffraction pattern and reconstruct the 3D diffraction intensity. Most of these algorithms rely on the premise that all diffraction patterns originate from identical protein molecules. However, in actual experiments, diffraction patterns from multiple different molecules may be collected simultaneously. Here, we propose a predicted model-aided one-step classification–multireconstruction algorithm that can handle mixed diffraction patterns from various molecules. The algorithm uses predicted structures of different protein molecules as templates to classify diffraction patterns based on correlation coefficients and determines orientations using a correlation maximization method. Tests on simulated data demonstrated high accuracy and efficiency in classification and reconstruction.

3D electron diffraction (3DED) is increasingly employed to determine molec­ular and crystal structures from micro-crystals. Indomethacin is a well known, marketed, small-molecule non-steroidal anti-inflammatory drug with eight known polymorphic forms, of which four structures have been elucidated to date. Using 3DED, we determined the structure of a new ninth polymorph, σ, found within an amorphous solid dispersion, a product formulation sometimes used for active pharmaceutical ingredients with poor aqueous solubility. Subsequently, we found that σ indomethacin can be produced from direct solvent evaporation using di­chloro­methane. These results demonstrate the relevance of 3DED within drug development to directly probe product formulations.

MltG, a membrane-bound lytic transglycosyl­ase, has roles in terminating glycan polymerization in peptidoglycan and incorporating glycan chains into the cell wall, making it significant in bacterial cell-wall biosynthesis and remodeling. This study provides the first reported MltG structure from Mycobacterium abscessus (maMltG), a superbug that has high antibiotic resistance. Our structural and biochemical analyses revealed that MltG has a flexible peptidoglycan-binding domain and exists as a monomer in solution. Further, the putative active site of maMltG was disclosed using structural analysis and sequence comparison. Overall, this study contributes to our understanding of the transglycosyl­ation reaction of the MltG family, aiding the design of next-generation antibiotics targeting M. abscessus.

Three solid solutions of [CH3NH3]CoxNi1−x(HCOO)3, with x = 0.25 (1), x = 0.50 (2) and x = 0.75 (3), were synthesized and their nuclear structures and magnetic properties were characterized using single-crystal neutron diffraction and magnetization measurements. At room temperature, all three compounds crystallize in the Pnma orthorhombic space group, akin to the cobalt and nickel end series members. On cooling, each compound undergoes a distinct series of structural transitions to modulated structures. Compound 1 exhibits a phase transition to a modulated structure analogous to the pure Ni compound [Cañadillas-Delgado, L., Mazzuca, L., Fabelo, O., Rodríguez-Carvajal, J. & Petricek, V. (2020). Inorg. Chem. 59, 17896–17905], whereas compound 3 maintains the behaviour observed in the pure Co compound reported previously [Canadillas-Delgado, L., Mazzuca, L., Fabelo, O., Rodriguez-Velamazan, J. A. & Rodriguez-Carvajal, J. (2019). IUCrJ, 6, 105–115], although in both cases the temperatures at which the phase transitions occur differ slightly from the pure phases. Monochromatic neutron diffraction measurements showed that the structural evolution of 2 diverges from that of either parent compound, with competing hydrogen bond interactions that drive the modulation throughout the series, producing a unique sequence of phases. It involves two modulated phases below 96 (3) and 59 (3) K, with different q vectors, similar to the pure Co compound (with modulated phases below 128 and 96 K); however, it maintains the modulated phase below magnetic order [at 22.5 (7) K], resembling the pure Ni compound (which presents magnetic order below 34 K), resulting in an improper modulated magnetic structure. Despite these large-scale structural changes, magnetometry data reveal that the bulk magnetic properties of these solid solutions form a linear continuum between the end members. Notably, doping of the metal site in these solid solutions allows for tuning of bulk magnetic properties, including magnetic ordering temperature, transition temperatures and the nature of nuclear phase transitions, through adjustment of metal ratios.

Conformational heterogeneity of biological macromolecules is a challenge in single-particle averaging (SPA). Current standard practice is to employ classification and filtering methods that may allow a discrete number of conformational states to be reconstructed. However, the conformation space accessible to these molecules is continuous and, therefore, explored incompletely by a small number of discrete classes. Recently developed heterogeneous reconstruction algorithms (HRAs) to analyse continuous heterogeneity rely on machine-learning methods that employ low-dimensional latent space representations. The non-linear nature of many of these methods poses a challenge to their validation and interpretation and to identifying functionally relevant conformational trajectories. These methods would benefit from in-depth benchmarking using high-quality synthetic data and concomitant ground truth information. We present a framework for the simulation and subsequent analysis with respect to the ground truth of cryo-EM micrographs containing particles whose conformational heterogeneity is sourced from molecular dynamics simulations. These synthetic data can be processed as if they were experimental data, allowing aspects of standard SPA workflows as well as heterogeneous reconstruction methods to be compared with known ground truth using available utilities. The simulation and analysis of several such datasets are demonstrated and an initial investigation into HRAs is presented.

Regolith draws intensive research attention because of its importance as the basis for fabricating materials for future human space exploration. Martian regolith is predicted to consist of defect-rich crystal structures due to long-term space weathering. The present report focuses on the structural differences between defect-rich and defect-poor forsterite (Mg2SiO4) – one of the major phases in Martian regolith. In this work, forsterites were synthesized using reverse strike co-precipitation and high-energy ball milling (BM). Subsequent post-processing was also carried out using BM to enhance the defects. The crystal structures of the samples were characterized by X-ray powder diffraction and total scattering using Cu and synchrotron radiation followed by Rietveld refinement and pair distribution function (PDF) analysis, respectively. The structural models were deduced by density functional theory assisted PDF refinements, describing both long-range and short-range order caused by defects. The Raman spectral features of the synthetic forsterites complement the ab initio simulation for an in-depth understanding of the associated structural defects.

OaPAC is a recently discovered blue-light-using flavin adenosine dinucleotide (BLUF) photoactivated adenylate cyclase from the cyanobacterium Oscillatoria acuminata that uses adenosine triphosphate and translates the light signal into the production of cyclic adenosine monophosphate. Here, we report crystal structures of the enzyme in the absence of its natural substrate determined from room-temperature serial crystallography data collected at both an X-ray free-electron laser and a synchrotron, and we compare these structures with cryo-macromolecular crystallography structures obtained at a synchrotron by us and others. These results reveal slight differences in the structure of the enzyme due to data collection at different temperatures and X-ray sources. We further investigate the effect of the Y6W mutation in the BLUF domain, a mutation which results in a rearrangement of the hydrogen-bond network around the flavin and a notable rotation of the side chain of the critical Gln48 residue. These studies pave the way for picosecond–millisecond time-resolved serial crystallography experiments at X-ray free-electron lasers and synchrotrons in order to determine the early structural intermediates and correlate them with the well studied pico­second–millisecond spectroscopic intermediates.

Density functional theory methods are applied to crystal structures and stabilities of phases from the aleksite homologous series, PbnBi4Te4Sn+2 (n = homologue number). The seven phases investigated correspond to n = 0 (tetradymite), 2 (aleksite-21R and -42R), 4 (saddlebackite-9H and -18H), 6 (unnamed Pb6Bi4Te4S8), 8 (unnamed Pb8Bi4Te4S10), 10 (hitachiite) and 12 (unnamed Pb12Bi4Te4S14). These seven phases correspond to nine single- or double-module structures, each comprising an odd number of atom layers, 5, 7, (5.9), 9, (7.11), 11, 13, 15 and 17, expressed by the formula: S(MpXp+1)·L(Mp+1Xp+2), where M = Pb, Bi and X = Te, S, p ≥ 2, and S and L = number of short and long modules, respectively. Relaxed structures show a and c values within 1.5% of experimental data; a and the interlayer distance dsub decrease with increasing PbS content. Variable Pb—S bond lengths contrast with constant Pb—S bond lengths in galena. All phases are n-fold superstructures of a rhombohedral subcell with c/3 = dsub*. Electron diffraction patterns show two brightest reflections at the centre of dsub*, described by the modulation vector qF = (i/N) · dsub*, i = S + L. A second modulation vector, q = γ · csub*, shows a decrease in γ, from 1.8 to 1.588, across the n = 0 to n = 12 interval. The linear relationship between γ and dsub allows the prediction of any theoretical phases beyond the studied compositional range. The upper PbS-rich limit of the series is postulated as n = 398 (Pb398Bi4Te4S400), a phase with dsub (1.726 Å) identical to that of trigonal PbS within experimental error. The aleksite series is a prime example of mixed layer compounds built with accretional homology principles.

K3FeTe2O8(OH)2(H2O)2 was synthesized under hydrothermal conditions from Te(OH)6, FeSO4·7H2O and 85 wt% KOH in a 1:2:6 molar ratio. The crystal structure is built of a triperiodic network. One disordered water molecule per formula unit is located in a channel and can be partially removed by heating. Systematic one-dimensional diffuse scattering indicates a polytypic character, which is best described by application of the order–disorder theory. The major polytype is monoclinic with pseudo-orthorhombic metrics. It is interrupted by fragments of an orthorhombic polytype. The diffraction intensities are analyzed using structure factor calculations.

Single-crystal X-ray diffraction analysis of small molecule active pharmaceutical ingredients is a key technique in the confirmation of molecular connectivity, including absolute stereochemistry, as well as the solid-state form. However, accessing single crystals suitable for X-ray diffraction analysis of an active pharmaceutical ingredient can be experimentally laborious, especially considering the potential for multiple solid-state forms (solvates, hydrates and polymorphs). In recent years, methods for the exploration of experimental crystallization space of small molecules have undergone a `step-change', resulting in new high-throughput techniques becoming available. Here, the application of high-throughput encapsulated nanodroplet crystallization to a series of six di­hydro­pyridines, calcium channel blockers used in the treatment of hypertension related diseases, is described. This approach allowed 288 individual crystallization experiments to be performed in parallel on each molecule, resulting in rapid access to crystals and subsequent crystal structures for all six di­hydro­pyridines, as well as revealing a new solvate polymorph of nifedipine (1,4-dioxane solvate) and the first known solvate of nimodipine (DMSO solvate). This work further demonstrates the power of modern high-throughput crystallization methods in the exploration of the solid-state landscape of active pharmaceutical ingredients to facilitate crystal form discovery and structural analysis by single-crystal X-ray diffraction.

The interaction of intense synchrotron radiation with molecular crystals frequently modifies the crystal structure by breaking bonds, producing fragments and, hence, inducing disorder. Here, a second-rank tensor of radiation-induced lattice strain is proposed to characterize the structural susceptibility to radiation. Quantitative estimates are derived using a linear response approximation from experimental data collected on three materials Hg(NO3)2(PPh3)2, Hg(CN)2(PPh3)2 and BiPh3 [PPh3 = triphenylphosphine, P(C6H5)3; Ph = phenyl, C6H5], and are compared with the corresponding thermal expansivities. The associated eigenvalues and eigenvectors show that the two tensors are not the same and therefore probe truly different structural responses. The tensor of radiative expansion serves as a measure of the susceptibility of crystal structures to radiation damage.

A significant part of the present and future of optoelectronic devices lies on thin multilayer heterostructures. Their optical properties depend strongly on strain, being essential to the knowledge of the stress level to optimize the growth process. Here the structural and microstructural characteristics of sub-micron a-ZnO epilayers (12 to 770 nm) grown on r-sapphire by metal–organic chemical vapour deposition are studied. Morphological and structural studies have been made using scanning electron microscopy and high-resolution X-ray diffraction. Plastic unit-cell distortion and corresponding strain have been determined as a function of film thickness. A critical thickness has been observed as separating the non-elastic/elastic states with an experimental value of 150–200 nm. This behaviour has been confirmed from ultraviolet photoelectron spectroscopy, X-ray photoelectron spectroscopy and high-resolution transmission electron microscopy measurements. An equation that gives the balance of strains is proposed as an interesting method to experimentally determine this critical thickness. It is concluded that in the thinnest films an elongation of the Zn—O bond takes place and that the plastic strained ZnO films relax through nucleation of misfit dislocations, which is a consequence of three-dimensional surface morphology.

The compression behavior of [Rb(18-crown-6)][SbCl6] crystal under pressure up to 2.16 (3) GPa was investigated in a diamond anvil cell (DAC) using a mixture of pentane–iso­pentane (1:4) as the pressure-transmitting fluid. The compound crystallizes in trigonal space group R3 and no phase transition was observed in the indicated pressure range. The low value of pressure bulk modulus [9.1 (5) GPa] found in this crystal is a characteristic of soft materials with predominant dispersive and electrostatic interaction forces. The nonlinear relationship between unit-cell parameters under high pressure is attributed to the influence of reduced intermolecular H⋯Cl contacts under pressure over 0.73 GPa. It also explains the high compression efficiency of [Rb(18-crown-6)][SbCl6] crystals at relatively low pressures, resulting in a significant shift of the Rb atom to the center of the crown ether cavity. At pressures above 0.9 GPa, steric repulsion forces begin to play a remarkable role, since an increasing number of interatomic H⋯Cl and H⋯H contacts become shorter than the sum of their van der Waals (vdW) radii. Below 0.9 GPa, both unit-cell parameter dependences (P–a and P–c) exhibit hysteresis upon pressure release, demonstrating their influence on the disordered model of Rb atoms. The void reduction under pressure also demonstrates two linear sections with the inflection point at 0.9 GPa. Compression of the crystal is accompanied by a significant decrease in the volume of the voids, leading to the rapid approach of Rb atoms to the center of the crown ether cavity. For the Rb atom to penetrate into the center of the crown ether cavity in [Rb(18-crown-6)][SbCl6], it is necessary to apply a pressure of about 2.5 GPa to disrupt the balance of atomic forces in the crystal. This sample serves as a compression model demonstrating the influence of both attractive and repulsive forces on the change in unit-cell parameters under pressure.

The NaZr2P3O12 family of materials have shown low and tailorable thermal expansion properties. In this study, SrZr4P6O24 (SrO·4ZrO2·3P2O5), CaZr4P6O24 (CaO·4ZrO2·3P2O5), MgZr4P6O24 (MgO·4ZrO2·3P2O5), NaTi2P3O12 [½(Na2O·4TiO2·3P2O5)], NaZr2P3O12 [½(Na2O·4ZrO2·3P2O5)], and related solid solutions were synthesized using the organic–inorganic steric entrapment method. The samples were characterized by in-situ high-temperature X-ray diffraction from 25 to 1500°C at the Advanced Photon Source and National Synchrotron Light Source II. The average linear thermal expansion of SrZr4P6O24 and CaZr4P6O24 was between −1 × 10−6 per °C and 6 × 10−6 per °C from 25 to 1500°C. The crystal structures of the high-temperature polymorphs of CaZr4P6O24 and SrZr4P6O24 with R3c symmetry were solved by Fourier difference mapping and Rietveld refinement. This polymorph is present above ∼1250°C. This work measured thermal expansion coefficients to 1500°C for all samples and investigated the differences in thermal expansion mechanisms between polymorphs and between compositions.

The molecule of anti-epileptic drug lamotrigine [LAM; 3,5-diamino-6-(2,3-dichlorophenyl)-1,2,4-triazine] is capable of the formation of multicomponent solids. Such an enhanced tendency is related to the diverse functionalities of the LAM chemical groups able to form hydrogen bonds. Two robust synthons are recognized in the supramolecular structure of LAM itself formed via N—H⋯N hydrogen bond: homosynthon, so-called aminopyridine dimer or synthon 1 [R22(8)] and larger homosynthon 2 [R32(8)]. The synthetic procedures for a new hydrate and 11 solvates of LAM (in the series: with acetone, ethanol: two polymorphs: form I and form II, 2-propanol, n-butanol, tert-butanol, n-pentanol, benzonitrile, acetonitrile, DMSO and dioxane) were performed. The comparative solid state structural analysis of a new hydrate and 11 solvates of LAM has been undertaken in order to establish robustness of the supramolecular synthons 1 and 2 found in the crystal structure of LAM itself as well as LAM susceptibility to build methodical solid state supramolecular architecture in the given competitive surrounding of potential hydrogen bonds. The aminopyridine dimer homosynthon 1 [R22(8)] has been switched from para-para (P-P) topology to ortho-ortho (O-O) topology in all crystal structures, except in LAM:n-pentanol:water solvate where it remains P-P. Homosynthon 2 [R32(8)] of the LAM crystal structure imitates in the LAM solvates as a heterosynthon by replacing the triazine nitrogen proton acceptor atoms of LAM with the proton acceptors of solvates molecules.

SnGe4N4O4 was synthesized at high pressure (16 and 20 GPa) and high temperature (1200 and 1500°C) in a large-volume press. Powder X-ray diffraction experiments using synchrotron radiation indicate that the derived samples are mixtures of known and unknown phases. However, the powder X-ray diffraction patterns are not sufficient for structural characterization. Transmission electron microscopy studies reveal crystals of several hundreds of nanometres in size with different chemical composition. Among them, crystals of a previously unknown phase with stoichiometry SnGe4N4O4 were detected and investigated using automated diffraction tomography (ADT), a three-dimensional electron diffraction method. Via ADT, the crystal structure could be determined from single nanocrystals in space group P63mc, exhibiting a nolanite-type structure. This was confirmed by density functional theory calculations and atomic resolution scanning transmission electron microscopy images. In one of the syntheses runs a rhombohedral 6R polytype of SnGe4N4O4 could be found together with the nolanite-type SnGe4N4O4. The structure of this polymorph was solved as well using ADT.

Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.

The structures of three multicomponent crystals formed with imidazole-based drugs, namely metronidazole, ketoconazole and miconazole, in conjunction with tri­thio­cyanuric acid are characterized. Each of the obtained adducts represents a different category of crystalline molecular forms: a cocrystal, a salt and a cocrystal of salt. The structural analysis revealed that in all cases, the N—H⋯N hydrogen bond is responsible for the formation of acid–base pairs, regardless of whether proton transfer occurs or not, and these molecular pairs are combined to form unique supramolecular motifs by centrosymmetric N—H⋯S interactions between acid molecules. The complex intermolecular forces acting in characteristic patterns are discussed from the geometric and energetic perspectives, involving Hirshfeld surface analysis, pairwise energy estimation, and natural bond orbital calculations.

Ion radii are derived here from the characteristic (grand mean) bond lengths for (i) 135 ions bonded to oxygen in 459 configurations (on the basis of coordination number) using 177 143 bond lengths extracted from 30 805 ordered coordination polyhedra from 9210 crystal structures; and (ii) 76 ions bonded to nitro­gen in 137 configurations using 4048 bond lengths extracted from 875 ordered coordination polyhedra from 434 crystal structures. There are two broad categories of use for ion radii: (1) those methods which use the relative sizes of cation and anion radii to predict local atomic arrangements; (2) those methods which compare the radii of different cations (or the radii of different anions) to predict local atomic arrangements. There is much uncertainty with regard to the relative sizes of cations and anions, giving rise to the common failure of type (1) methods, e.g. Pauling's first rule which purports to relate the coordination adopted by cations to the radius ratio of the constituent cation and anion. Conversely, type (2) methods, which involve comparing the sizes of different cations with each other (or different anions with each other), can give very accurate predictions of site occupancies, physical properties etc. Methods belonging to type (2) can equally well use the characteristic bond lengths themselves (from which the radii are derived) in place of radii to develop correlations and predict crystal properties. Extensive quantum-mechanical calculations of electron density in crystals in the literature indicate that the radii of both cations and anions are quite variable with local arrangement, suggesting significant problems with any use of ion radii. However, the dichotomy between the experimentally derived ion radii and the quantum-mechanical calculations of electron density in crystals is removed by the recognition that ion radii are pr­oxy variables for characteristic bond lengths in type (2) relations.

In the course of an investigation of the supramolecular behaviour of copper(II) complexes with the 5-phenyl­imidazole/perchlorate ligand system (`blend') remarkable solvatomorphism has been observed. By employing a variety of crystallization solvents (polar protic, polar/non-polar aprotic), a series of 12 crystalline solvatomorphs with the general formula [Cu(ClO4)2(LH)4]·x(solvent) have been obtained [LH = 5-phenyl­imidazole, x(solvent) = 3.3(H2O) (1), 2(methanol) (2), 2(ethanol) (3), 2(1-propanol) (4), 2(2-propanol) (5), 2(2-butanol) (6), 2(di­methyl­formamide) (7), 2(acetone) (8), 2(tetra­hydro­furane) (9), 2(1,4-dioxane) (10), 2(ethyl acetate) (11) and 1(di­ethyl ether) (12)]. The structures have been solved using single-crystal X-ray diffraction and the complexes were characterized by thermal analysis and infrared spectroscopy. The solvatomorphs are isostructural (triclinic, P1), with the exception of compound 9 (monoclinic, P21/n). The supramolecular structures and the role of the various solvents is discussed. All potential hydrogen-bond functionalities, both of the [Cu(ClO4)2(LH)4] units and of the solvents, are utilized in the course of the crystallization process. The supramolecular assembly in all structures is directed by strong recurring Nimidazole–H⋯Operchlorate motifs leading to robust scaffolds composed of the [Cu(ClO4)2(LH)4] host complexes. The solvents are located in channels and, with the exception of the disordered waters in 1 and the di­ethyl ether in 12, participate in hydrogen-bonding formation with the [Cu(ClO4)2(LH)4] complexes, serving as both hydrogen-bond acceptors and donors (for the polar protic solvents in 2–6), or solely as hydrogen-bond acceptors (for the polar/non-polar aprotic solvents in 7–11), linking the complexes and contributing to the stability of the crystalline compounds.

Magnetic materials featuring triangular arrangements of spins are frequently investigated as platforms hosting magnetic frustration. Hexagonal perovskites with ordered vacancies serve as excellent candidates for two-dimensional triangular magnetism due to the considerable separation of the magnetic planes. In this work, the effects of chemical pressure on the ferromagnetic ground state of Ba2La2NiW2O12 by substitution of Ba2+ with Sr2+ to produce Sr2La2NiW2O12 are investigated. The two materials are characterized using synchrotron-based XRD, XANES and EXAFS in addition to magnetometry in order to correlate their crystal structures and magnetic properties. Both materials form in space group R3, yet as a result of the enhanced bending of key bond angles due to the effects of chemical pressure, the TC value of the magnetic Ni2+ sublattice is reduced from ∼6 K in Ba2La2NiW2O12 to 4 K in Sr2La2NiW2O12.

Synthesis experiments were conducted in the quaternary system K2O–Na2O–CaO–SiO2, resulting in the formation of a previously unknown compound with the composition K0.72Na1.71Ca5.79Si6O19. Single crystals of sufficient size and quality were recovered from a starting mixture with a K2O:Na2O:CaO:SiO2 molar ratio of 1.5:0.5:2:3. The mixture was confined in a closed platinum tube and slowly cooled from 1150°C at a rate of 0.1°C min−1 to 700°C before being finally quenched in air. The structure has tetragonal symmetry and belongs to space group P4122 (No. 91), with a = 7.3659 (2), c = 32.2318 (18) Å, V = 1748.78 (12) Å3, and Z = 4. The silicate anion consists of highly puckered, unbranched six-membered oligomers with the composition [Si6O19] and point group symmetry 2 (C2). Although several thousands of natural and synthetic oxosilicates have been structurally characterized, this compound is the first representative of a catena-hexasilicate anion, to the best of our knowledge. Structural investigations were completed using Raman spectroscopy. The spectroscopic data was interpreted and the bands were assigned to certain vibrational species with the support of density functional theory at the HSEsol level of theory. To determine the stability properties of the novel oligosilicate compared to those of the chemically and structurally similar cyclo­silicate combeite, we calculated the electronegativity of the respective structures using the electronegativity equalization method. The results showed that the molecular electronegativity of the cyclo­silicate was significantly higher than that of the oligostructure due to the different connectivities of the oxygen atoms within the molecular units.

In recent decades, sustained theoretical and software developments have clearly established that representation analysis and magnetic symmetry groups are complementary concepts that should be used together in the investigation and description of magnetic structures. Historically, they were considered alternative approaches, but currently, magnetic space groups and magnetic superspace groups can be routinely used together with representation analysis, aided by state-of-the-art software tools. After exploring the historical antagonism between these two approaches, we emphasize the significant advancements made in understanding and formally describing magnetic structures by embracing their combined use.

Organic–inorganic hybrid crystals have diverse functionalities, for example in energy storage and luminescence, due to their versatile structures. The synthesis and structural characterization of a new cobalt–vanadium-containing compound, 2[Co(en)3]3+(V4O13)6−·4H2O (1) is presented. The crystal structure of 1, consisting of [Co(en)3]3+ complexes and chains of corner-sharing (VO4) tetrahedra, was solved by single-crystal X-ray diffraction in the centrosymmetric space group P1. Phase purity of the bulk material was confirmed by infrared spectroscopy, scanning electron microscopy, elemental analysis and powder X-ray diffraction. The volume expansion of 1 was found to be close to 1% in the reported temperature range from 100 to 300 K, with a volume thermal expansion coefficient of 56 (2) × 10−6 K−1. The electronic band gap of 1 is 2.30 (1) eV, and magnetic susceptibility measurements showed that the compound exhibits a weak paramagnetic response down to 1.8 K, probably due to minor CoII impurities (<1%) on the CoIII site.

The magnetic and crystal structures of manganese and nickel monoxides have been studied using high-resolution neutron diffraction. The known 1k-structures based on the single propagation vector [½ ½ ½] for the parent paramagnetic space group Fm3m are forced to have monoclinic magnetic symmetry and are not possible in rhombohedral symmetry. However, the monoclinic distortions from the rhombohedral crystal metric allowed by symmetry are very small, and the explicit monoclinic splittings of the diffraction peaks have not been experimentally observed. We analyse the magnetic crystallographic models metrically compatible with our experimental data in full detail by using isotropy subgroup representation approach, including rhombohedral solutions based on the propagation vector star {[½ ½ ½], [−½ ½ ½], [½−½ ½], [½ ½ −½]}. Although the full star rhombohedral RI3c structure can equally well fit our diffraction data for NiO, we conclude that the best solution for the crystal and magnetic structures for NiO and MnO is the 1k monoclinic model with the magnetic space group Cc2/c (Belov–Neronova–Smirnova No. 15.90, UNI symbol C2/c.1'c[C2/m]).

JANA2020 is a program developed for the solution and refinement of regular, twinned, modulated, and composite crystal structures. In addition, JANA2020 also includes a magnetic option for solving magnetic structures from powder and single-crystal neutron diffraction data. This tool uses magnetic space and superspace symmetry to describe commensurate and incommensurate magnetic structures. The basics of the underlying formulation of magnetic structure factors and the use of magnetic symmetry for handling modulated and non-modulated magnetic structures are presented here, together with the general features of the magnetic tool. Examples of structures solved in the magnetic option of JANA2020 are given to illustrate the operation and capabilities of the program.

An exhaustive search for missing symmetry was performed for 223 076 entries in the ICSD (2023-2 release). Approximately 0.65% of them can be described with higher symmetry than reported. Out of the identified noncentrosymmetric entries, ∼74% can be described by centrosymmetric space groups; this has implications for compatible physical properties. It is proposed that the information on the correct space group is included in the ICSD.

The embedded call to a special version of the web-based Bilbao Crystallographic Server tool k-SUBGROUPSMAG from within GSAS-II to form a list of all possible commensurate magnetic subgroups of a parent magnetic grey group is described. It facilitates the selection and refinement of the best commensurate magnetic structure model by having all the analysis tools including Rietveld refinement in one place as part of GSAS-II. It also provides the chosen magnetic space group as one of the 1421 possible standard Belov–Neronova–Smirnova forms or equivalent non-standard versions.

Onchocerca volvulus causes blindness, onchocerciasis, skin infections and devastating neurological diseases such as nodding syndrome. New treatments are needed because the currently used drug, ivermectin, is contraindicated in pregnant women and those co-infected with Loa loa. The Seattle Structural Genomics Center for Infectious Disease (SSGCID) produced, crystallized and determined the apo structure of N-terminally hexahistidine-tagged O. volvulus macrophage migration inhibitory factor-1 (His-OvMIF-1). OvMIF-1 is a possible drug target. His-OvMIF-1 has a unique jellyfish-like structure with a prototypical macrophage migration inhibitory factor (MIF) trimer as the `head' and a unique C-terminal `tail'. Deleting the N-terminal tag reveals an OvMIF-1 structure with a larger cavity than that observed in human MIF that can be targeted for drug repurposing and discovery. Removal of the tag will be necessary to determine the actual biological oligomer of OvMIF-1 because size-exclusion chomatographic analysis of His-OvMIF-1 suggests a monomer, while PISA analysis suggests a hexamer stabilized by the unique C-terminal tails.

The nitro­gen–sulfur Schiff base proligand S-n-octyl 3-(1-phenyl­ethyl­idene)di­thio­carbazate, C17H26N2S2 (HL), was prepared by reaction of S-octyl di­thio­carbamate with aceto­phenone. Treatment of HL with nickel acetate yielded the complex bis­[S-n-octyl 3-(1-phenyl­ethyl­idene)di­thio­carbazato]nickel(II), [Ni(C17H25N2S2)2] (NiL2), which was shown to adopt a tetra­hedrally distorted cis-square-planar coordination geometry, with the NiSN planes of the two ligands forming a dihedral angle of 21.66 (6)°. Changes in the geometry of the L ligand upon chelation of Ni2+ are described, involving a ca 180° rotation around the N(azomethine)—C(thiol­ate) bond.

The compounds bis­(morpholine-κN)gold(I) chloride, [Au(C4H9NO)2]Cl, 1, and bis­(morpholine-κN)gold(I) bromide, [Au(C4H9NO)2]Br, 2, crystallize isotypically in space group C2/c with Z = 4. The gold atoms, which are axially positioned at the morpholine rings, lie on inversion centres (so that the N—Au—N coordination is exactly linear) and the halide anions on twofold axes. The residues are connected by a classical hydrogen bond N—H⋯halide and by a short gold⋯halide contact to form a layer structure parallel to the bc plane. The morpholine oxygen atom is not involved in classical hydrogen bonding.

The title compound, C5H5NO2, is a hy­droxy­lated pyridine ring that has been studied for its involvement in microbial degradation of nicotinic acid. Here we describe its synthesis as a formic acid salt, rather than the standard hydro­chloride salt that is commercially available, and its spectroscopic and crystallographic characterization.

The reaction of cadmium bromide tetra­hydrate with 3-amino­pyrazole (3-apz) in ethano­lic solution leads to tautomerization of the ligand and the formation of crystals of the title compound, catena-poly[[di­bromido­cadmium(II)]-bis­(μ-3-amino-1H-pyrazole)-κ2N3:N2;κ2N2:N3], [CdBr2(C3H5N3)2]n or [CdBr2(3-apz)2]n. Its asymmetric unit consists of a half of a Cd2+ cation, a bromide anion and a 3-apz mol­ecule. The Cd2+ cations are coordinated by two bromide anions and two 3-apz ligands, generating trans-CdN4Br2 octa­hedra, which are linked into chains by pairs of the bridging ligands. In the crystal, the ligand mol­ecules and bromide anions of neighboring chains are linked through inter­chain hydrogen bonds into a two-dimensional network. The inter­molecular contacts were qu­anti­fied using Hirshfeld surface analysis and two-dimensional fingerprint plots, revealing the relative qu­anti­tative contributions of the weak inter­molecular contacts.

Single crystals of tricadmium orthophosphate, Cd3(PO4)2, have been synthesized successfully by the hydro­thermal route, while its powder form was obtained by a solid-solid process. The corresponding crystal structure was determined using X-ray diffraction data in the monoclinic space group P21/n. The crystal structure consists of Cd2O8 or Cd2O10 dimers linked together by PO4 tetra­hedra through sharing vertices or edges. Scanning electron microscopy (SEM) was used to investigate the morphology and to confirm the chemical composition of the synthesized powder. Infrared analysis corroborates the presence of isolated phosphate tetra­hedrons in the structure. UV–Visible studies showed an absorbance peak at 289 nm and a band gap energy of 3.85 eV, as determined by the Kubelka–Munk model.

In the title compound, C15H14N2O2·H2O, the 1H-pyrrole ring makes a dihedral angle of 59.95 (13)° with the phenyl ring. In the crystal, the mol­ecules are connected by C—H⋯O hydrogen bonds into layers parallel to the (020) plane, while two mol­ecules are connected to the water mol­ecule by two N—H⋯O hydrogen bonds and one mol­ecule by an O—H⋯O hydrogen bond. C—H⋯π and π–π inter­actions further link the mol­ecules into chains extending in the [overline{1}01] direction and stabilize the mol­ecular packing. According to a Hirshfeld surface study, H⋯H (49.4%), C⋯H/H⋯C (23.2%) and O⋯H/H⋯O (20.0%) inter­actions are the most significant contributors to the crystal packing.

We report the synthesis and structures of two transition-metal complexes involving 2-(2-hy­droxy­phen­yl)benzimidazole (2hpbi – a ligand of inter­est for its photoluminescent applications), with cobalt, namely, bis­[μ-2-(1H-1,3-benzo­diazol-2-yl)phenolato]bis­[ethanol(thio­cyanato)­cobalt(II)], [Co2(C13H9N2O)2(NCS)2(C2H6O)2], (1), and manganese, namely, bis­[μ-2-(1H-1,3-benzo­diazol-2-yl)phenolato]bis­{[2-(1H-1,3-benzo­diazol-2-yl)phenolato](thio­cyanato)­mang­an­ese(III)} dihydrate, [Mn2(C13H9N2O)4(NCS)2]·2H2O, (2). These structures are two recent examples of a fruitful collaboration between researchers at the Laboratoire de Chimie de Coordination Organique/Organic Coordination Chemistry Laboratory (LCCO), University of Dakar, Senegal and the National Crystallography Service (NCS), School of Chemistry, University Southampton, UK. This productive partnership was forged through meeting at Pan-African Conferences on Crystallography and quickly grew as the plans for the AfCA (African Crystallographic Association) developed. This article therefore also showcases this productive partnership, in celebration of the IUCr's 75 year anniversary and the recent inclusion of AfCA as a Regional Associate of the IUCr.

Reaction of FeCl2·4H2O with KSCN and 3-cyano­pyridine (pyridine-3-carbo­nitrile) in ethanol accidentally leads to the formation of single crystals of Fe(NCS)(Cl)(3-cyano­pyridine)4 or [FeCl(NCS)(C6H4N2)4]. The asymmetric unit of this compound consists of one FeII cation, one chloride and one thio­cyanate anion that are located on a fourfold rotation axis as well as of one 3-cyano­pyridine coligand in a general position. The FeII cations are sixfold coordinated by one chloride anion and one terminally N-bonding thio­cyanate anion in trans-positions and four 3-cyano­pyridine coligands that coordinate via the pyridine N atom to the FeII cations. The complexes are arranged in columns with the chloride anions, with the thio­cyanate anions always oriented in the same direction, which shows the non-centrosymmetry of this structure. No pronounced inter­molecular inter­actions are observed between the complexes. Initially, FeCl2 and KSCN were reacted in a 1:2 ratio, which lead to a sample that contains the title compound as the major phase together with a small amount of an unknown crystalline phase, as proven by powder X-ray diffraction (PXRD). If FeCl2 and KSCN is reacted in a 1:1 ratio, the title compound is obtained as a nearly pure phase. IR investigations reveal that the CN stretching vibration for the thio­cyanate anion is observed at 2074 cm−1, and that of the cyano group at 2238 cm−1, which also proves that the anionic ligands are only terminally bonded and that the cyano group is not involved in the metal coordination. Measurements with thermogravimetry and differential thermoanalysis reveal that the title compound decomposes at 169°C when heated at a rate of 4°C min−1 and that the 3-cyano­pyridine ligands are emitted in two separate poorly resolved steps. After the first step, an inter­mediate compound with the composition Fe(NCS)(Cl)(3-cyano­pyridine)2 of unknown structure is formed, for which the CN stretching vibration of the thio­cyanate anion is observed at 2025 cm−1, whereas the CN stretching vibration of the cyano group remain constant. This strongly indicates that the FeII cations are linked by μ-1,3-bridg­ing thio­cyanate anions into chains or layers.

The title mol­ecule, C29H44N8O, adopts a conformation resembling a two-bladed fan with the octyl chains largely in fully extended conformations. In the crystal, C—H⋯O hydrogen bonds form chains of mol­ecules extending along the b-axis direction, which are linked by weak C—H⋯N hydrogen bonds and C—H⋯π inter­actions to generate a three-dimensional network. A Hirshfeld surface analysis of the crystal structure indicates that the most important contributions for the crystal packing are from H⋯H (68.3%), H⋯N/N⋯H (15.7%) and H⋯C/C⋯H (10.4%) inter­actions.

The reaction between the (R,S)-fixolide 4-methyl­thio­semicarbazone and PdII chloride yielded the title compound, [Pd(C20H30N3S)2]·C2H6O {common name: trans-bis­[(R,S)-fixolide 4-methyl­thio­semicarbazonato-κ2N2S]palladium(II) ethanol monosolvate}. The asymmetric unit of the title compound consists of one bis-thio­semicarbazonato PdII complex and one ethanol solvent mol­ecule. The thio­semicarbazononato ligands act as metal chelators with a trans configuration in a distorted square-planar geometry. A C—H⋯S intra­molecular inter­action, with graph-set motif S(6), is observed and the coordination sphere resembles a hydrogen-bonded macrocyclic environment. Additionally, one C—H⋯Pd anagostic inter­action can be suggested. Each ligand is disordered over the aliphatic ring, which adopts a half-chair conformation, and two methyl groups [s.o.f. = 0.624 (2):0.376 (2)]. The disorder includes the chiral carbon atoms and, remarkably, one ligand has the (R)-isomer with the highest s.o.f. value atoms, while the other one shows the opposite, the atoms with the highest s.o.f. value are associated with the (S)-isomer. The N—N—C(=S)—N fragments of the ligands are approximately planar, with the maximum deviations from the mean plane through the selected atoms being 0.0567 (1) and −0.0307 (8) Å (r.m.s.d. = 0.0403 and 0.0269 Å) and the dihedral angle with the respective aromatic rings amount to 46.68 (5) and 50.66 (4)°. In the crystal, the complexes are linked via pairs of N—H⋯S inter­actions, with graph-set motif R22(8), into centrosymmetric dimers. The dimers are further connected by centrosymmetric pairs of ethanol mol­ecules, building mono-periodic hydrogen-bonded ribbons along [011]. The Hirshfeld surface analysis indicates that the major contributions for the crystal cohesion are [atoms with highest/lowest s.o.f.s considered separately]: H⋯H (81.6/82.0%), H⋯C/C⋯H (6.5/6.4%), H⋯N/N⋯H (5.2/5.0%) and H⋯S/S⋯H (5.0/4.9%).

In the title mol­ecule, C7H7N3O, the pyrimidine ring is essentially planar, with the propynyl group rotated out of this plane by 15.31 (4)°. In the crystal, a tri-periodic network is formed by N—H⋯O, N—H⋯N and C—H⋯O hydrogen-bonding and slipped π–π stacking inter­actions, leading to narrow channels extending parallel to the c axis. Hirshfeld surface analysis of the crystal structure reveals that the most important contributions for the crystal packing are from H⋯H (36.2%), H⋯C/C⋯H (20.9%), H⋯O/O⋯H (17.8%) and H⋯N/N⋯H (12.2%) inter­actions, showing that hydrogen-bonding and van der Waals inter­actions are the dominant inter­actions in the crystal packing. Evaluation of the electrostatic, dispersion and total energy frameworks indicates that the stabilization is dominated by the electrostatic energy contributions. The mol­ecular structure optimized by density functional theory (DFT) calculations at the B3LYP/6–311 G(d,p) level is compared with the experimentally determined structure in the solid state. The HOMO–LUMO behaviour was also elucidated to determine the energy gap.