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.

Hydrogen atoms in bridging positions from quantum crystallographic refinements: influence of hydrogen atom displacement parameters on geometry and electron density

Hydrogen atom positions can be obtained accurately from X-ray diffraction data of hydrogen maleate salts via Hirshfeld atom refinement.

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.

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.

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 [Capelliet 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 Å for 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.

Modelling diffuse scattering of the disordered crystal structure of Na2SiF6

Many crystalline materials are not perfectly ordered, but are disordered to a smaller or larger extent. The properties of such materials are often related to the nature of the disorder. In diffraction experiments, disorder is observable as diffuse scattering. In routine X-ray structure determinations, only Bragg reflections are considered, leading to average crystal structure models. Methods to derive the average structure from the Bragg reflections are very well established, whereas diffuse scattering is rarely accounted for and mostly ignored. Our attempts at modelling the disordered structure of crystalline sodium fluorosilicate will be presented. Although the average crystal structure is known [1], there is some uncertainty about the true space group [2]. Na2SiF6assumes a crystalline morphology that resembles that of ice and is therefore known as an ice–analog material [3]. In the average crystal structure (in space group P321), the asymmetric unit contains two ordered sodium cations (both sitting on a two-fold axis) and two disordered SiF62-anions (one sitting on a 3-fold axis and the other on a 32 site). Each anion can occupy two alternative sites in the unit cell, related by a non-crystallographic mirror plane at z = ¼. The occupation is mutually exclusive for both anions. Diffuse scattering can be observed as planes perpendicular to l in the hnl and nkl precession images where these diffuse planes can be found at integer l. For l odd, the diffuse scattering is more intense. Also there are diffuse clouds of intensity around certain Bragg peaks. In the hkn planes, diffuse streaks are visible parallel to a*, b*, and a* - b*, while some Bragg peaks have diffuse clouds of intensity around them. The pattern of streaks and clouds evolves when going to higher order planes. In the figure below, the hk1 precession image is illustrated. The observed diffuse scattering features will be interpreted in terms of structural models obtained by Monte Carlo simulations.

Studying structure disorder in DL-Norvaline by single crystal diffuse scattering

Diffraction methods are the most important methods to study the three-dimensional arrangement of matter at the atomic level. Real materials are often not perfectly ordered and the resulting diffraction pattern may contain a weak continuous or structured background known as diffuse scattering, in addition to sharp Bragg peaks. Our motivation is to analyse diffuse scattering in order to learn about the Short Range Order (SRO) of disordered crystals and improve the tools to model disorder phenomena. We are now investigating the SRO in DL-Norvaline which crystallizes in three known temperature-dependent phases. At least two of them (beta-phase space group C2/c above -700C, alpha-phase P21/c around -900C) show disordered average structures in which the alkyl side chain adopts several conformations [1]. The scattering data were collected using synchrotron radiation and a noise-free Pilatus pixel detector at the ESRF BM01A station. The diffraction pattern of the β-phase shows diffuse streaks parallel to a reciprocal lattice axis and diffuse clouds around low angle reflections [2] (Fig. 1). These features result from static and dynamic disorder. The diffuse streaks indicate disorder amongst stacks of layers of molecules, while the diffuse clouds arise from thermal motion. The modelling of the disorder involves the use of the Monte Carlo and differential evolution algorithms embedded in ZODS [3]. Our progress with model development will be presented.

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

The molecular dynamics in the crystal and the thermodynamic functions of the β-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 β-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 β-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 β-phase with higher H and G is found to be less stable than the α-phase in the temperature range of the experiment.

Dynamics and thermodynamics of crystalline polymorphs: α-glycine, analysis of variable-temperature atomic displacement parameters

Multitemperature synchrotron diffraction data to 0.5 Å resolution in the temperature range 10-298 K and neutron data at 18 K of the α-glycine polymorph have been collected at the KEK photon factory (PF), SPring-8 and the Institut Laue Langevin (ILL) for the study of molecular motion in the crystal and of the associated thermodynamic functions. Atomic displacement parameters (ADPs) of non-H atoms are obtained from refinements based on nonspherical atomic scattering factors (invariom model) to minimize correlation between parameters describing thermal motion and valence electron density. The ADPs in the temperature range 50-298 K from SPring-8 connect smoothly with those from neutron diffraction at 18 K and 288-323 K. The combined ADPs from both sources covering the temperature range 18-323 K are used for a normal-mode analysis in the molecular mean field approximation. The lattice vibration frequencies from the ADP analysis and the internal vibration frequencies from an ONIOM (B3LYP/6-311+G(2d,p):PM3) calculation together with the Einstein, Debye, and Nernst-Lindemann models of heat capacity are used to calculate Cp, Hvib, and Svib values that are in good agreement with those from calorimetry.

Low-energy contamination of Mo microsource X-ray radiation: analysis and solution of the problem

In recent years, microsource sealed tubes in combination with multilayer optics have been adopted in many crystallography laboratories for very low power X-ray generation, monochromatization and high-brilliance microfocusing. All these factors allow high-performance experiments on a laboratory scale. However, a fundamental defect of this technology has been discovered, namely a significant contamination of the characteristic radiation by low-energy photons. Some simple experiments are reported, showing that the contamination can significantly reduce the accuracy of the measured intensities, especially when Mo Kα radiation is used. A simple and economic solution to the problem is proposed: an aluminium filter approximately 100 µm thick, which efficiently removes the low-energy contaminant photons.

Temperature-dependent analysis of thermal motion, disorder and structures of tris(ethylenediamine)zinc(II) sulfate and tris(ethylenediamine)copper(II) sulfate

The crystal structures of the title compounds have been determined in the temperature range 140–290 K for the zinc complex, and 190–270 K for the copper complex. The two structures are isostructural in the trigonal space group P{\bar{3}1c} with the sulfate anion severely disordered on a site with 32 (D 3) symmetry. This sulfate disorder leads to a disordered three-dimensional hydrogen-bond network, with the N—H atoms acting as donors and the sulfate O atoms as acceptors. The displacement parameters of the N and C atoms in both compounds contain disorder contributions in the out-of-ligand plane direction owing to ring puckering and/or disorder in hydrogen bonding. In the Zn compound the vibrational amplitudes in the bond directions are closely similar. Their differences show no significant deviations from rigid-bond behaviour. In the Cu compound, a (presumably) dynamic Jahn–Teller effect is identified from a temperature-independent contribution to the displacement ellipsoids of the N atom along the N—Cu bond. These conclusions derive from analyses of the atomic displacement parameters with the Hirshfeld test, with rigid-body models at different temperatures, and with a normal coordinate analysis. This analysis considers the atomic displacement parameters (ADPs) from all different temperatures simultaneously and provides a detailed description of both the thermal motion and the disorder in the cation. The Jahn–Teller radii of the Cu compound derived on the basis of the ADP analysis and from the bond distances in the statically distorted low-temperature phase [Lutz (2010). Acta Cryst. C66, m330–m335] are found to be the same.

Stacking disorder: the hexagonal polymorph of tris(bicyclo[2.1.1]hexeno)benzene and related examples

X-ray diffractograms of tris(bicyclo[2.1.1]hexeno)benzene, crystallized at the interface between a benzene solution and a layer of acetonitrile, show hexagonal symmetry and streaks of diffuse scattering along c*. The heavily faulted layer stacking is analyzed qualitatively and quantitatively in terms of a systematic protocol. This protocol requires partitioning the crystal structure into layers in such a way that pairs of adjacent layers may be stacked in different, but geometrically equivalent ways, which are dictated by the layer group symmetry. This approach is shown to provide a consistent alternative for analysis of a number of related cases provided the layers are defined on the basis of geometrical criteria rather than chemical intuition.

Specific heat of molecular crystals from atomic mean square displacements with the Einstein, Debye, and Nernst-Lindemann models

Analysis of atomic displacement parameters (ADPs) from multitemperature diffraction data provides mean-field molecular translation and libration frequencies. These quantities have been combined with molecular deformation frequencies calculated ab initio, e.g. by DFT methods, to calculate the specific heat Cv of molecular crystals of naphthalene, anthracene, and hexamethylenetetramine. If the difference Cp - Cv is represented by the Nernst-Lindemann relation, Cp curves from diffraction experiments and ab initio calculations agree well with those based on calorimetry. Agreement is better if the Debye rather than the Einstein model is chosen to represent the contribution of the translational vibrations. Compressibilities estimated from the differences Cp - Cv are 2-5 times higher than those obtained from compressibility measurements at 298 K and Grüneisen constants derived from the temperature dependence of ADPs.

Interplay of Spin Conversion and Structural Phase Transformations: Re-Entrant Phase Transitions in the 2-Propanol Solvate of Tris(2-picolylamine)iron(II) Dichloride

Crystal structures, magnetic and thermodynamic properties of the spin-crossover compound tris(2-picolylamine)iron(II) dichloride (with 2-propanol solvent molecules) have been measured in the temperature range from 15 to 293 K. X-ray diffraction, SQUID, and calorimetric experiments all showed two first-order phase transitions with hysteresis loops, a narrow one at T(1) approximately 196 K and a broad, triangular one covering the range 153<T(2)<166 K. Crystal structures were analysed at fourteen temperatures in a cooling cycle and at seven temperatures in a heating cycle. They reveal a complex, temperature-dependent ordering behaviour of both the complex cations and the alcohol molecules. A phenomenological model accounting for spin conversion, solvent ordering and coupling between the two processes describes the observed phase transitions and ordering phenomena reasonably well. Similarities and differences in the behaviour of the corresponding ethanol solvate with the same crystal architecture are discussed. It is concluded that spin-crossover behaviour depends as much on molecular properties as it does on intermolecular interactions, both of the spin active and the spin inactive components.

Crystalline, Mixed-Valence Manganese Analogue of Prussian Blue: Magnetic, Spectroscopic, X-ray and Neutron Diffraction Studies

The compound of stoichiometry Mn(II)3[Mn(III)(CN)6]2.zH2O (z = 12-16) (1) forms air-stable, transparent red crystals. Low-temperature single crystal optical spectroscopy and single crystal X-ray diffraction provide compelling evidence for N-bonded high-spin manganese(II), and C-bonded low-spin manganese(III) ions arranged in a disordered, face-centered cubic lattice analogous to that of Prussian Blue. X-ray and neutron diffraction show structured diffuse scattering indicative of partially correlated (rather than random) substitutions of [Mn(III)(CN)6] ions by (H2O)6 clusters. Magnetic susceptibility measurements and elastic neutron scattering experiments indicate a ferrimagnetic structure below the critical temperature Tc = 35.5 K.

Phosphoenolpyruvate- and ATP-dependent dihydroxyacetone kinases: covalent substrate-binding and kinetic mechanism

Dihydroxyacetone (Dha) kinases are a sequence-conserved family of enzymes, which utilize two different phosphoryldonors, ATP in animals, plants, and some bacteria, and a multiphosphoprotein of the phosphoenolpyruvate carbohydrate phosphotransferase system (PTS) in most bacteria. Here, we compare the PTS-dependent kinase of Escherichia coli and the ATP-dependent kinase of Citrobacter freundii. They display 30% sequence identity. The binding constants of the E. coli kinase for eleven short-chain carbonyl compounds were determined by acetone precipitation of the enzyme-substrate complexes. They are 3.4 microM for Dha, 780 microM for Dha-phosphate (DhaP), 50 microM for D,L-glyceraldehyde (GA), and 90 microM for D,L-glyceraldehyde-3-phosphate. The k(cat) for Dha of the PTS-dependent kinase is 290 min(-1), and that of the ATP-dependent kinase is 1050 min(-1). The Km for Dha of both kinases is <6 microM. The X-ray structures of the enzyme-GA and the enzyme-DhaP complex show that substrates as well as products are bound in hemiaminal linkage to an active-site histidine. Quantum-mechanical calculations offer no indication for activation of the reacting hydroxyl group by the formation of the hemiaminal. However, the formation of the hemiaminal bond allows selection for short-chain carbonyl compounds and discrimination against structurally similar polyols. The Dha kinase remains fully active in the presence of 2 M glycerol, and phosphorylates trace impurities of carbonyl compounds present in glycerol.