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.

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.

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.

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.

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.

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.

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.

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 P31c 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.

Molecular dynamics simulations of structure and dynamics of organic molecular crystals.

A set of model compounds covering a range of polarity and flexibility have been simulated using GAFF, CHARMM22, OPLS and MM3 force fields to examine how well classical molecular dynamics simulations can reproduce structural and dynamic aspects of organic molecular crystals. Molecular structure, crystal structure and thermal motion, including molecular reorientations and internal rotations, found from the simulations have been compared between force fields and with experimental data. The MM3 force field does not perform well in condensed phase simulations, while GAFF, CHARMM and OPLS perform very similarly. Generally molecular and crystal structure are reproduced well, with a few exceptions. The atomic displacement parameters (ADPs) are mostly underestimated in the simulations with a relative error of up to 70%. Examples of molecular reorientation and internal rotation, observed in the simulations, include in-plane reorientations of benzene, methyl rotations in alanine, decane, isopropylcyclohexane, pyramidal inversion of nitrogen in amino group and rotation of the whole group around the C-N bond. Frequencies of such dynamic processes were calculated, as well as thermodynamic properties for reorientations in benzene and alanine. We conclude that MD simulations can be used for qualitative analysis, while quantitative results should be taken with caution. It is important to compare the outcomes from simulations with as many experimental quantities as available before using them to study or quantify crystal properties not available from experiment.

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.

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.

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.].

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.