The Cambridge Structural Database and structural dynamics.

With the availability of the computer readable information in the Cambridge Structural Database (CSD), wide ranging, largely automated comparisons of fragment, molecular, and crystal structures have become possible. They show that the distributions of interatomic distances, angles, and torsion angles for a given structural fragment occurring in different environments are highly correlated among themselves and with other observables such as spectroscopic signals, reaction and activation energies. The correlations often extend continuously over large ranges of parameter values. They are reminiscent of bond breaking and forming reactions, polyhedral rearrangements, and conformational changes. They map-qualitatively-the regions of the structural parameter space in which molecular dynamics take place, namely, the low energy regions of the respective (free) energy surfaces. The extension and continuous nature of the correlations provides an organizing principle of large groups of structural data and suggests a reconsideration of traditional definitions and descriptions of bonds, "nonbonded" and "noncovalent" interactions in terms of Lewis acids interacting with Lewis bases. These aspects are illustrated with selected examples of historic importance and with some later developments. It seems that the amount of information in the CSD (and other structural databases) and the knowledge on the nature of, and the correlations within, this body of information should allow one-in the near future-to make credible interpolations and possibly predictions of structures and their properties with machine learning methods.

Crystal structures.

A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.

Remarks on X-ray constrained/restrained wavefunction fitting.

X-ray constrained/restrained wavefunctions (XCWs/XRWs) result from a combination of theory and experiment and are therefore affected by experimental errors and model uncertainties. The present XCW/XRW procedure does not take this into account, thus limiting the meaning and significance of the obtained wavefunctions.

Mesocrystalline structure and mechanical properties of biogenic calcite from sea urchin spine.

Using X-ray scattering, we measured detailed maps of the diffuse scattering intensity distribution and a number of phonon dispersion branches for a single crystal of inorganically formed natural calcite and for high-quality mesocrystals of biogenic calcite from a Mediterranean sea urchin spine. A comparison shows that the known differences in the mechanical properties between the `strong' biogenic and `brittle' abiotic material should be attributed to the mesoscopic architecture of the crystal rather than to a modification of the calcite crystal structure. The data are rationalized by comparing them to the results of ab initio model calculations of lattice dynamics. For the mesocrystal, they are augmented by the evaluation of the faceting of the constituent nanocrystals.

Hidden diversity of vacancy networks in Prussian blue analogues.

Prussian blue analogues (PBAs) are a diverse family of microporous inorganic solids, known for their gas storage ability1, metal-ion immobilization2, proton conduction3, and stimuli-dependent magnetic4,5, electronic6 and optical7 properties. This family of materials includes the double-metal cyanide catalysts8,9 and the hexacyanoferrate/hexacyanomanganate battery materials10,11. Central to the various physical properties of PBAs is their ability to reversibly transport mass, a process enabled by structural vacancies. Conventionally presumed to be random12,13, vacancy arrangements are crucial because they control micropore-network characteristics, and hence the diffusivity and adsorption profiles14,15. The long-standing obstacle to characterizing the vacancy networks of PBAs is the inaccessibility of single crystals16. Here we report the growth of single crystals of various PBAs and the measurement and interpretation of their X-ray diffuse scattering patterns. We identify a diversity of non-random vacancy arrangements that is hidden from conventional crystallographic powder analysis. Moreover, we explain this unexpected phase complexity in terms of a simple microscopic model that is based on local rules of electroneutrality and centrosymmetry. The hidden phase boundaries that emerge demarcate vacancy-network polymorphs with very different micropore characteristics. Our results establish a foundation for correlated defect engineering in PBAs as a means of controlling storage capacity, anisotropy and transport efficiency.

Coordinative Alignment in the Pores of MOFs for the Structural Determination of N-, S-, and P-Containing Organic Compounds Including Complex Chiral Molecules.

Coordinative alignment of target small molecules onto a chiral metal-organic framework (MOF-520)provides a powerful method to determine the structures of small molecules through single-crystal X-ray diffraction (SXRD). In this work, the structures of 17 molecules with eight new coordinating functionalities and varying size have been determined by this method, four of which are complex molecules being crystallized for the first time. The chirality of the MOF backbone not only enables enantioselective crystallization of chiral small molecules from a racemic mixture but also imposes diastereoselective incorporation upon achiral molecules. Crystallographic studies assisted by density functional theory (DFT) calculations indicate that the stereoselectivity of MOF-520 not exclusively comes from the steric confinement of the chiral pore environment but also from asymmetric chemical bonding of the target molecules with the framework that is able to provide sufficient energy difference between possible coordination configurations.

Comments on 'Hydrogen bonds in crystalline d-alanine: diffraction and spectroscopic evidence for differences between enantiomers'.

The recent paper by Belo, Pereira, Freire, Argyriou, Eckert & Bordallo [(2018 ▸), IUCrJ, 5, 6-12] reports observations that may lead one to think of very strong and visible consequences of the parity-violation energy difference between enantiomers of a molecule, namely alanine. If proved, this claim would have an enormous impact for research in structural chemistry. However, alternative, more realistic, explanations of their experiments have not been ruled out by the authors. Moreover, the theoretical calculations carried out to support the hypothesis are unable to differentiate between enantiomers (molecules or crystals). Therefore, the conclusions drawn by Belo et al. (2018 ▸) are deemed inappropriate as the data presented do not contain sufficient information to reach such a conclusion.

Impact of Disordered Guest-Framework Interactions on the Crystallography of Metal-Organic Frameworks.

It is a general and common practice to carry out single-crystal X-ray diffraction experiments at cryogenic temperatures in order to obtain high-resolution data. In this report, we show that this practice is not always applicable to metal-organic frameworks (MOFs), especially when these structures are highly porous. Specifically, two new MOFs are reported here, MOF-1004 and MOF-1005, for which the collection of the diffraction data at lower temperature (100 K) did not give data of sufficient quality to allow structure solution. However, collection of data at higher temperature (290 K) gave atomic-resolution data for MOF-1004 and MOF-1005, allowing for structure solution. We find that this inverse behavior, contrary to normal practice, is also true for some well-established MOFs (MOF-177 and UiO-67). Close examination of the X-ray diffraction data obtained for all four of these MOFs at various temperatures led us to conclude that disordered guest-framework interactions play a profound role in introducing disorder at low temperature, and the diminishing strength of these interactions at high temperatures reduces the disorder and gives high-resolution diffraction data. We believe our finding here is more widely applicable to other highly porous MOFs and crystals containing highly disordered molecules.

Probing the accuracy and precision of Hirshfeld atom refinement with HARt interfaced with Olex2.

Hirshfeld atom refinement (HAR) is a novel X-ray structure refinement technique that employs aspherical atomic scattering factors obtained from stockholder partitioning of a theoretically determined tailor-made static electron density. HAR overcomes many of the known limitations of independent atom modelling (IAM), such as too short element-hydrogen distances, r(X-H), or too large atomic displacement parameters (ADPs). This study probes the accuracy and precision of anisotropic hydrogen and non-hydrogen ADPs and of r(X-H) values obtained from HAR. These quantities are compared and found to agree with those obtained from (i) accurate neutron diffraction data measured at the same temperatures as the X-ray data and (ii) multipole modelling (MM), an established alternative method for interpreting X-ray diffraction data with the help of aspherical atomic scattering factors. Results are presented for three chemically different systems: the aromatic hydro-carbon rubrene (orthorhombic 5,6,11,12-tetra-phenyl-tetracene), a co-crystal of zwitterionic betaine, imidazolium cations and picrate anions (BIPa), and the salt potassium hydrogen oxalate (KHOx). The non-hydrogen HAR-ADPs are as accurate and precise as the MM-ADPs. Both show excellent agreement with the neutron-based values and are superior to IAM-ADPs. The anisotropic hydrogen HAR-ADPs show a somewhat larger deviation from neutron-based values than the hydrogen SHADE-ADPs used in MM. Element-hydrogen bond lengths from HAR are in excellent agreement with those obtained from neutron diffraction experiments, although they are somewhat less precise. The residual density contour maps after HAR show fewer features than those after MM. Calculating the static electron density with the def2-TZVP basis set instead of the simpler def2-SVP one does not improve the refinement results significantly. All HARs were performed within the recently introduced HARt option implemented in the Olex2 program. They are easily launched inside its graphical user interface following a conventional IAM.

Erratum: Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction. Corrigendum.

[This corrects the article DOI: 10.1107/S1600576716001369.].

Quantum crystallography.

Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.

Definitive molecular level characterization of defects in UiO-66 crystals.

The identification and characterization of defects, on the molecular level, in metal-organic frameworks (MOFs) remain a challenge. With the extensive use of single-crystal X-ray diffraction (SXRD), the missing linker defects in the zirconium-based MOF UiO-66, Zr6 O4 (OH)4 (C8 H4 O4 )6 , have been identified as water molecules coordinated directly to the zirconium centers. Charge balancing is achieved by hydroxide anions, which are hydrogen bonded within the pores of the framework. Furthermore, the precise nature of the defects and their concentration can be manipulated by altering the starting materials, synthesis conditions, and post-synthetic modifications.

Dynamics and thermodynamics of crystalline polymorphs. 3. γ-Glycine, analysis of variable-temperature atomic displacement parameters, and comparison of polymorph stabilities.

In a series of systematic studies, we have investigated the molecular motion in crystals of the glycine polymorphs and determined their thermodynamic functions from an analysis of multitemperature atomic displacement parameters (ADPs) combined with ONIOM calculation on 15-molecule clusters. The studies are aimed at providing insight into the factors governing the relative stabilities of the α-, ß-, and γ-polymorphs. This Article, the last in the series, focuses on the most stable polymorph, γ-glycine. Multitemperature diffraction data of the γ-glycine polymorph have been collected to 0.5 Å resolution between 10 and 300 K at two synchrotron beamlines, KEK Photon Factory and ID11 of the ESRF. The ADPs of γ-glycine from these sources differ significantly, as previously observed also for the other two polymorphs. A simple model of rigid body motion explains the ADPs from KEK and their temperature dependence. It provides lattice vibration frequencies that are in line with those from Raman spectroscopy. Together with the internal vibration frequencies from an ONIOM calculation, the thermodynamic functions are estimated using the Einstein, Debye, and Nernst-Lindemann models of heat capacity. The relative stabilities of the three polymorphs of glycine are discussed on the basis of the contributions to their free energies as obtained in this work and from various experimental and theoretical studies. The comparison shows that the free-energy differences are determined primarily by differences in lattice and zero-point vibrational energies.

Glycyl-L-alanine: a multi-temperature neutron study.

Neutron diffraction data have been collected at 12, 50, 150 and 295 K for the dipeptide glycyl-L-alanine, C5H10N2O3, in order to obtain accurate positional and anisotropic displacement parameters for the H atoms. The values of these parameters serve as a benchmark for assessing the equivalent parameters obtained from a so-called Hirshfeld-atom refinement of X-ray diffraction data described elsewhere [Capelli et al. (2014). IUCrJ, 1, 361-379]. The flexibility of the glycyl-L-alanine molecule in the solid and the hydrogen-bonding interactions as a function of temperature are also considered.

Hirshfeld atom refinement.

Hirshfeld atom refinement (HAR) is a method which determines structural parameters from single-crystal X-ray diffraction data by using an aspherical atom partitioning of tailor-made ab initio quantum mechanical molecular electron densities without any further approximation. Here the original HAR method is extended by implementing an iterative procedure of successive cycles of electron density calculations, Hirshfeld atom scattering factor calculations and structural least-squares refinements, repeated until convergence. The importance of this iterative procedure is illustrated via the example of crystalline ammonia. The new HAR method is then applied to X-ray diffraction data of the dipeptide Gly-l-Ala measured at 12, 50, 100, 150, 220 and 295 K, using Hartree-Fock and BLYP density functional theory electron densities and three different basis sets. All positions and anisotropic displacement parameters (ADPs) are freely refined without constraints or restraints - even those for hydrogen atoms. The results are systematically compared with those from neutron diffraction experiments at the temperatures 12, 50, 150 and 295 K. Although non-hydrogen-atom ADPs differ by up to three combined standard uncertainties (csu's), all other structural parameters agree within less than 2 csu's. Using our best calculations (BLYP/cc-pVTZ, recommended for organic molecules), the accuracy of determining bond lengths involving hydrogen atoms from HAR is better than 0.009 Šfor temperatures of 150 K or below; for hydrogen-atom ADPs it is better than 0.006 Å(2) as judged from the mean absolute X-ray minus neutron differences. These results are among the best ever obtained. Remarkably, the precision of determining bond lengths and ADPs for the hydrogen atoms from the HAR procedure is comparable with that from the neutron measurements - an outcome which is obtained with a routinely achievable resolution of the X-ray data of 0.65 Å.

Average structures of the disordered ß-phase of Pigment Red 170: a single-crystal X-ray diffraction study.

The ß-phase of the industrially important Pigment Red 170 (ß-P.R. 170) has a structure with severe layer stacking disorder. The single-crystal X-ray diffraction pattern consists of a difficult-to-disentangle mix of Bragg diffraction superimposed on rods of diffuse scattering which impede the estimation of accurate Bragg intensities. Two average monoclinic structure models with the same unit-cell dimensions, but different extents of disorder in the layers and different space groups seem plausible, one with the non-conventional space group setting B2(1)/g (No. 14, Z' = 2) and one in P2(1)/a (No. 14, Z' = 4). Disordered molecules related by a translation of 0.158b are present in all layers of the B2(1)/g model and in every second layer of the P2(1)/a model. Layer-to-layer contacts are practically the same in both models. According to order-disorder theory, both models are valid superposition structures. Structure-factor calculations show that the pattern of strong and weak Bragg reflections is very similar for the two models. R factors indicate that the B2(1)/g model is the most economic representation of the average structure. However, given the limitations in data processing, the P2(1)/a model should not be discarded and further insight sought from a detailed analysis of the experimental diffuse scattering. The difficulties encountered in this analysis raise the question of whether or not the concept of an average structure is applicable in practice to ß-P.R. 170.

TiGePt--a study of Friedel differences.

The X-ray single-crystal diffraction intensities of the intermetallic compound TiGePt were analysed. These showed beyond doubt that the crystal structure is non-centrosymmetric. The analysis revolves around the resonant-scattering contribution to differences in intensity between Friedel opposites hkl and \bar h\bar k\bar l. The following techniques were used: R(merge) factors on the average (A) and difference (D) of Friedel opposites; statistical estimates of the resonant-scattering contribution to Friedel opposites; plots of 2A(obs) against 2A(model) and of D(obs) against D(model); the antisymmetric D-Patterson function. Moreover it was possible to show that a non-standard atomic model was unnecessary to describe TiGePt. Two data sets are compared. That measured with Ag Kα radiation at 295 K to a resolution of 1.25 Å(-1) is less conclusive than the one measured with Mo Kα radiation at 100 K to the lower resolution of 0.93 Å(-1). This result is probably due to the fact that the resonant scattering of Pt is larger for Mo Kα than for AgKα radiation.

Dynamics and thermodynamics of crystalline polymorphs. 2. ß-Glycine, analysis of variable-temperature atomic displacement parameters.

The molecular dynamics in the crystal and the thermodynamic functions of the ß-polymorph of glycine have been determined from a combination of molecular translation-libration frequencies reflecting the temperature dependence of atomic displacement parameters (ADPs), with frequencies derived from ONIOM(DFT:PM3) calculations on a 15-molecule ß-glycine cluster. ADPs have been obtained from variable-temperature diffraction data to 0.5 Å resolution collected with X-ray synchrotron (10-300 K) and sealed tube radiation (50-298 K). At the higher temperatures, the ADPs of ß-glycine from synchrotron are larger than those from sealed tube probably due to different experimental conditions. The lattice vibration frequencies from normal-mode analysis of ADPs and the internal vibration frequencies from ONIOM(B3LYP/6-311+G(2d,p):PM3) calculations agree with those from spectroscopy. Estimation of thermodynamic functions using the vibrational frequencies, the Einstein and Debye models of heat capacity, and the room-temperature compressibility provides C(p), H(vib), and S(vib) that agree with those from calorimetry. The ß-phase with higher H and G is found to be less stable than the α-phase in the temperature range of the experiment.