Curvature-induced vitrification and polymorphism in corannulene.

Direct correlation of structure changes and thermal events in hydrated lipid established by simultaneous calorimetry and time-resolved x-ray diffraction

To examine the correlation between the atomic displacement parameters of oxygen atom and oxide-ion conductivity of rare-earth-oxide-doped ceria materials, Ce0.8R0.2O1.9 (R = La, Nd, Sm, Gd, Y, and Yb), their crystal structures have been refined by the Rietveld analyses of high-resolution (d > 0.38 Å) synchrotron powder diffraction data measured in air in situ at 29.5, 408.0, and 675.0 °C. As a reference material, pure nondoped ceria CeO2 was also investigated by the same method. Both atomic displacement parameters of cations and anions increase with temperature, which indicates the thermal vibrations and dynamic positional disorders. At a given temperature, the thermal parameters of cation in Ce0.8R0.2O1.9, UC(R), are larger than those in CeO2, UC(CeO2), which indicates that the positional disorder of cations in Ce0.8R0.2O1.9 is also larger compared with that in CeO2. Similarly, at a given temperature, the atomic displacement parameters of anions in Ce0.8R0.2O1.9, UO(R), are larger than those in CeO2, UO(CeO2), which indicates that the positional disorder of oxide ions in Ce0.8R0.2O1.9 is larger than that in CeO2. The larger positional disorders of oxide ions in Ce0.8R0.2O1.9 would be the structural origin of higher ionic conductivities of Ce0.8R0.2O1.9, compared with those of undoped CeO2. In Ce0.8R0.2O1.9, both atomic displacement parameters of cations UC(R) and of anions UO(R) decrease with increasing ionic radius of R3+ ions for the coordination number of eight r(R) from R = Yb to R = Gd, while they increase with r(R) from R = Gd to R = La. Thus, both UC(R) and UO(R) exhibit minima at R = Gd in the range from R = Yb to R = La. The mismatch between dopant rare-earth oxide and host ceria would yield the positional disorder, local distortion, and lattice strain, which leads to the larger atomic displacement parameters. The present paper discusses the correlation between the oxygen thermal parameter UO(R) and oxide-ion conductivity of Ce0.8R0.2O1.9.

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.

The new ternary phosphide La2Ni12P5 has been prepared by direct arc melting of the components as pure metals and red phosphorus. The crystal structure has been determined using X‐ray single crystal diffraction data. The compound exhibits a new type of crystal structure, P21/m with lattice parameters a = 10.911(3), b = 3.696(2), c = 13.174(4) Å, β = 108.02(2)°, V = 505,2(6) Å3, Z = 2. Atomic parameters least squares refinement of 116 independent variables (anisotropic approximation for thermal vibrations) employed 1 284 independent Io(hkl); RF = 0.0278 and RW = 0.0287. The crystal structure is characterized by trigonal prismatic arrangement of phosphorus atoms stacking variant of infinite (with phosphorus centered) columns built by metal trigonal prisms ‖ [010]. Two or three such columns are connected through common edges (lanthanum atoms). The compounds RE2Ni12P5 (where RE = Ce, Pr, Nd and Eu) display the same with La2Ni12P5 crystal structure. Lattice parameters of these compounds have been refined using powder diffraction data.

In an iterative projection algorithm proposed for ab initio phasing, the error metrics typically exhibit little improvement until a sharp decrease takes place as the iteration converges to the correct high-resolution structure. Related to that is the small convergence probability for certain structures. As a remedy, a variable weighting scheme on the diffraction data is proposed. It focuses on phasing low- and medium-resolution data first. The weighting shifts to incorporate more high-resolution reflections when the iteration proceeds. It is found that the precipitous drop in error metrics is replaced by a less dramatic drop at an earlier stage of the iteration. It seems that once a good configuration is formed at medium resolution, convergence towards the correct high-resolution structure is almost guaranteed. The original problem of phasing all diffraction data at once is reduced to a much more manageable one due to the dramatically smaller number of reflections involved. As a result, the success rate is significantly enhanced and the speed of convergence is raised. This is illustrated by applying the new algorithm to several structures, some of which are very difficult to solve without data weighting.

Difficulties encountered in modelling the scattering of fluorine in organic compounds have been investigated through refinements of accurate X-ray and neutron diffraction data measured on tetrafluoroterephthalonitrile, TFT, at 122.4 K. Multipole refinements led to a highly contracted octopole on fluorine. The subsequent analysis revealed that fluorine does not possess a valence octopole but exhibits anharmonic thermal motion that can be modelled by the octopole multipole parameters. The scattering contribution from the octopole shows the same cubic dependence in the scattering vector as the Gram-Charlier expansion of the nuclear displacements to third order. The analysis also showed that refinement of third-order Gram-Charlier coefficients on fluorine requires data to at least 0.93 A(-1) resolution in sinthetas/lambda. The X-ray data extending to 1.27 A(-1) were of sufficient resolution to include third-order Gram-Charlier coefficients for N, F and the cyano C atoms in the refinement, whereas the neutron data only enabled refinement of the third-order Gram-Charlier coefficients for nitrogen. The refinements of the neutron and X-ray diffraction data yielded identical atomic displacement parameters for all the atoms. Though inclusion of anharmonic motion for N and F atoms provides the best model, it does not affect the crystal electron density, and all intramolecular bond critical points have identical features. Application of the anharmonic model, however, leads to small differences in the intermolecular interactions, which is illustrated by the electrostatic potential adjacent to the N atom. The characteristics of the C-F bond were elucidated by the topological analysis of the crystal electron density, which also supported the proposed quinonoid structure of the benzene ring.

Crystal structure of NaCl-type transition metal monocarbides MC (M = V, Ti, Nb, Ta, Hf, Zr), a neutron powder diffraction study

Powder X-ray diffraction has some inherent advantages over traditional single-crystal X-ray diffraction in accurately determining electron densities and structural parameters due to the lower requirements for sample crystallinity, simpler corrections and measurement simultaneity. For some simple inorganic materials, it has been shown that these advantages can compensate for disadvantages such as peak overlap and error-prone background subtraction. Although it is challenging to extend powder X-ray diffraction-based electron-density studies to organic materials with significant peak overlap, previous results using a dedicated vacuum diffractometer with a large image-plate camera (AVID) demonstrated that it can be done. However, the vacuum setup with the off-line detector system was found to prohibit a widespread use. Fast microstrip detectors, which have been employed at a number of powder diffraction beamlines, have the potential to facilitate electron-density studies. Nevertheless, no electron-density studies even for materials with slight peak overlap have been performed with microstrip detectors. One of the most critical problems has been a difference in sensitivity between microstrip channels, which substantially defines the dynamic range of a detector. Recently, a robust approach to this problem has been developed and applied to a total scattering measurement system (OHGI) with 15 MYTHEN microstrip modules. In the present study, synchrotron powder X-ray diffraction data obtained with OHGI are evaulated in terms of multipole electron densities and structural parameters (atomic positions and displacement parameters). These results show that, even without a dedicated setup and perfect samples, electron-density modelling can be carried out on high-quality powder X-ray diffraction data. However, it was also found that the required prior information about the sample prohibits widespread use of the method. With the presently obtainable data quality, electron densities of molecular crystals in general are not reliably obtained from powder data, but it is an excellent, possibly superior, alternative to single-crystal measurements for small-unit-cell inorganic solids. If aspherical atomic scattering factors can be obtained from other means (multipole databases, theoretical calculations), then atomic positions (including for hydrogen) and anisotropic atomic displacement parameters (non-hydrogen atoms) of excellent accuracy can be refined from synchrotron powder X-ray diffraction data on organic crystals.

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.

Correlation coefficients (CCs) between the mean atomic displacement parameters (B values) of the main-chain and the side-chain atoms in selected high-resolution protein structures are distributed over a broad range (0.5-1.0). The distribution of CCs is found to be related to the mean difference in B values of Calpha and Cbeta atoms. High CCs are also associated with the frequent occurrence of consecutive Calphaatoms with relatively high B values. The distribution of CCs and its relation to the mean difference between the B values of Calpha and Cbeta atoms shows dependence on the package used for refinement (X-PLOR, PROLSQ or TNT). These observations reflect the differences in the way B-value constraints are handled in these packages. Further differences are discernible in the distributions for proteins refined using the same package. It is likely that these differences are related to the different refinement protocols or weighting schemes followed by investigators. The resolution of these issues is important for evolving correct strategies for the refinement of the atomic displacement parameters in X-ray diffraction studies of proteins. Furthermore, it may be possible to develop refinement-validation tools by observing the features that are invariant in the distribution of atomic displacement parameters.

A revolution in resolution is occurring now in electron microscopy arising from the development of methods for imaging single particles at cryogenic temperatures and obtaining electron diffraction data from nanocrystals of small organic molecules or macromolecules. Near-atomic or even atomic resolution of molecular structures can be achieved. The basis of these methods is the scattering of an electron beam due to the electrostatic potential of the sample. To analyse these high-quality experimental data, it is necessary to use appropriate atomic scattering factors. The independent atom model (IAM) is commonly used although various more advanced models, already known from X-ray diffraction, can also be applied to enhance the analysis. In this study a comparison is presented of IAM and TAAM (transferable aspherical atom model), the latter with the parameters of the Hansen-Coppens multipole model transferred from the University at Buffalo Databank (UBDB). By this method, TAAM takes into account the fact that atoms in molecules are partially charged and are not spherical. Structure refinements were performed on a carbamazepine crystal using electron structure-factor amplitudes determined experimentally [Jones et al. (2018). ACS Cent. Sci. 4, 1587-1592] or modelled with theoretical quantum-mechanical methods. The results show the possibilities and limitations of the TAAM method when applied to electron diffraction. Among others, the method clearly improves model fitting statistics, when compared with IAM, and allows for reliable refinement of atomic thermal parameters. The improvements are more pronounced with poorer-resolution diffraction data.

Electronic, vibrational, and anharmonic studies on some binary clathrate AxSi136 (A = Na, K, Rb, Cs; 0 < x ≤ 24) are theoretically presented. The Fermi energy lies in the range of 1.1 eV to 1.4 eV for NaxSi136 and increases as stoichiometry (x) is tuned from 8 to 12 to 16. The determined isotropic “Mexican-hat” shape of the guest-host potential describing Na motion in the Si28 cage indicates the “off-center” position when the temperature is elevated beyond zero. Accordingly, the calculated Na “off-center” displacements correlate well with the X-Ray Diffraction (XRD) data (0.4 Å–0.5 Å) for a similar composition range (0 < x < 24). The lack of first-principles analysis on quartic anharmonicity motivates us to initiate a self-consistent model to examine the temperature-dependent rattling frequency Ω(T) of the guest (Na, Rb). The predicted values of Ω(T) for Na24Si136 at 300 K are significantly higher (approximately six times larger) than the value at absolute zero, which contrasts with the case of Rb8Si136. Moreover, underestimation of the isotropic atomic displacement parameter Uiso is caused by the temperature-dependent quartic anharmonicity of Na, and this discrepancy might be offset by the square of the “off-center” displacement.

C 2 H 8 ASN06, monoclinic, Pl2i/cl (No. 14), a= 7.919(2) , b= 4.744(1) , c =17.59(1) , = 91.71(4), V= 660.5 3 , = 4, R st (F) = 0.021, wR(F 2 ) = 0.050, T= 293 K.

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.

Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with limited sample preparation. Thus, potential systematic errors such as extinction and twinning commonly encountered in single-crystal studies of small-unit-cell inorganic structures can be overcome with synchrotron powder diffraction. It is shown that the standard Hansen-Coppens multipole model is not flexible enough to fit the static theoretical structure factors, whereas fitting of thermally smeared structure factors has much lower residuals. If thermally smeared structure factors (experimental or theoretical) are fitted with a slightly wrong radial model (s(2)p(2) instead of sp(3)) the radial scaling parameters (kappa' parameters) are found to be inadequate and the ;error' is absorbed into the atomic displacement parameter. This directly exposes a correlation between electron density and thermal parameters even for a light atom such as carbon, and it also underlines that in organic systems proper deconvolution of thermal motion is important for obtaining correct static electron densities.