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1.  Diffuse scattering study of aspirin forms (I) and (II) 
Full three-dimensional diffuse scattering data have been recorded for both polymorphic forms [(I) and (II)] of aspirin and these data have been analysed using Monte Carlo computer modelling. The observed scattering in form (I) is well reproduced by a simple harmonic model of thermally induced displacements. The data for form (II) show, in addition to thermal diffuse scattering (TDS) similar to that in form (I), diffuse streaks originating from stacking fault-like defects as well as other effects that can be attributed to strain induced by these defects.
Full three-dimensional diffuse scattering data have been recorded for both polymorphic forms [(I) and (II)] of aspirin and these data have been analysed using Monte Carlo computer modelling. The observed scattering in form (I) is well reproduced by a simple harmonic model of thermally induced displacements. The data for form (II) show, in addition to thermal diffuse scattering (TDS) similar to that in form (I), diffuse streaks originating from stacking fault-like defects as well as other effects that can be attributed to strain induced by these defects. The present study has provided strong evidence that the aspirin form (II) structure is a true polymorph with a structure quite distinct from that of form (I). The diffuse scattering evidence presented shows that crystals of form (II) are essentially composed of large single domains of the form (II) lattice with a relatively small volume fraction of intrinsic planar defects or faults comprising misoriented bilayers of molecular dimers. There is evidence of some local aggregation of these defect bilayers to form small included regions of the form (I) structure. Evidence is also presented that shows that the strain effects arise from the mismatch of molecular packing between the defect region and the surrounding form (II) lattice. This occurs at the edges of the planar defects in the direction only.
PMCID: PMC2992034  PMID: 21099031
diffuse scattering; polymorphism; aspirin; harmonic model
2.  Stacking faults and superstructures in a layered brownmillerite 
Stacking faults in Ca4Fe2Mn0.5Ti0.5O9 have been examined using X-ray diffraction and high-resolution transmission electron microscopy. Electron diffraction revealed two superstructures with ordered stacking sequences.
Single crystals of Ca4Fe2Mn0.5Ti0.5O9 have been synthesized using a flux method. The structural characterization using single-crystal X-ray diffraction revealed the space group Amma and unit-cell dimensions of a = 5.3510 (6), b = 26.669 (3), c = 5.4914 (6) Å. The structure is isotypic with Sr3NdFe3O9 [Barrier et al. (2005 ▶). Chem. Mater. 17, 6619–6623] and exhibits separated brownmillerite-type layers. One-dimensional diffuse scattering shows that the unit cell is doubled along c by alternating the intra-layer order of tetrahedral chains, causing stacking faults along the b direction. A computer simulation was performed, proving that the observed intensity variations along the diffuse scattering rods originates from two different local structures depending on the configuration of the tetrahedral chains. Selected-area electron diffraction experiments exhibit well ordered regions characterized by satellite reflections corresponding to two different superstructures. Both superstructures can be described using the superspace group A21/m(0βγ)0s, with γ = 0.5 and β ≃ 0.27 or β = 0.
PMCID: PMC3222140  PMID: 22101537
layered brownmillerite; diffuse scattering; stacking faults; modulated structure
3.  Determining the structure of a benzene7.2-silicalite-1 zeolite using a single-crystal X-ray method 
An orthorhombic benzene-silicalite-1 single crystal was obtained from a monoclinic twin crystal, and the structure was determined by a single-crystal method for the first time.
A simple method for preparing orthorhombic single crystals of benzene-silicalite-1 was developed. A silicalite-1 crystal was pressed with a weight of 2 g along the +c and −c crystallographic axes while the temperature was increased to 473 K. The temperature was then slowly reduced to 313 K, and these heating and cooling steps were repeated three times. After the orthorhombic single crystals adsorbed benzene, the crystal structure of the resulting benzene-silicalite-1 was determined. There were two kinds of benzene molecules in the asymmetric unit. One was located at the intersection of the straight channels and the sinusoidal channels with the benzene ring parallel to the ac plane. The other benzene was located in the middle of the straight channel.
PMCID: PMC3222141  PMID: 22101540
ZSM-5; MFI; silicalite-1; benzene-silicalite-1
4.  Deducing chemical structure from crystallographically determined atomic coordinates 
An improved algorithm has been written for assigning chemical structures to incoming entries to the Cambridge Structural Database.
An improved algorithm has been developed for assigning chemical structures to incoming entries to the Cambridge Structural Database, using only the information available in the deposited CIF. Steps in the algorithm include detection of bonds, selection of polymer unit, resolution of disorder, and assignment of bond types and formal charges. The chief difficulty is posed by the large number of metallo-organic crystal structures that must be processed, given our aspiration that assigned chemical structures should accurately reflect properties such as the oxidation states of metals and redox-active ligands, metal coordination numbers and hapticities, and the aromaticity or otherwise of metal ligands. Other complications arise from disorder, especially when it is symmetry imposed or modelled with the SQUEEZE algorithm. Each assigned structure is accompanied by an estimate of reliability and, where necessary, diagnostic information indicating probable points of error. Although the algorithm was written to aid building of the Cambridge Structural Database, it has the potential to develop into a general-purpose tool for adding chemical information to newly determined crystal structures.
PMCID: PMC3143025  PMID: 21775812
Cambridge Structural Database; structure assignment; catena structure; disorder resolution; Bayesian statistics
5.  Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4  
The superspace maximum entropy method (MEM) density in combination with structure refinements has been used to uncover the modulation in incommensurate Rb2ZnCl4 close to the lock-in transition. Modulated atomic displacement parameters (ADPs) and modulated anharmonic ADPs are found to form an intrinsic part of the modulation. Refined values for the displacement modulation function depend on the presence or absence of modulated ADPs in the model.
A combination of structure refinements, analysis of the superspace MEM density and interpretation of difference-Fourier maps has been used to characterize the incommensurate modulation of rubidium tetrachlorozincate, Rb2ZnCl4, at a temperature of T = 196 K, close to the lock-in transition at T lock-in = 192 K. The modulation is found to consist of a combination of displacement modulation functions, modulated atomic displacement parameters (ADPs) and modulated third-order anharmonic ADPs. Up to fifth-order Fourier coefficients could be refined against diffraction data containing up to fifth-order satellite reflections. The center-of-charge of the atomic basins of the MEM density and the displacive modulation functions of the structure model provide equivalent descriptions of the displacive modulation. Modulations of the ADPs and anharmonic ADPs are visible in the MEM density, but extracting quantitative information about these modulations appears to be difficult. In the structure refinements the modulation parameters of the ADPs form a dependent set, and ad hoc restrictions had to be introduced in the refinements. It is suggested that modulated harmonic ADPs and modulated third-order anharmonic ADPs form an intrinsic part, however small, of incommensurately modulated structures in general. Refinements of alternate models with and without parameters for modulated ADPs lead to significant differences between the parameters of the displacement modulation in these two types of models, thus showing the modulation of ADPs to be important for a correct description of the displacive modulation. The resulting functions do not provide evidence for an interpretation of the modulation by a soliton model.
PMCID: PMC3098556  PMID: 21586828
aperiodic crystals; incommensurate modulated structures; MEM density; ADPs
6.  Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations 
The accuracy of a dispersion-corrected density functional theory method is validated against 241 experimental organic crystal structures from Acta Cryst. Section E.
This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data. 241 experimental organic crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the experimental and the minimized crystal structures were subjected to statistical analysis. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 experimental crystal structures are reproduced very well: the average r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095 Å (0.084 Å for the 225 ordered structures). R.m.s. Cartesian displacements above 0.25 Å either indicate incorrect experimental crystal structures or reveal interesting structural features such as exceptionally large temperature effects, incorrectly modelled disorder or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect.
PMCID: PMC2940256  PMID: 20841921
dispersion-corrected density functional theory; organic structures
7.  Towards a generalized vision of oxides: disclosing the role of cations and anions in determining unit-cell dimensions 
Theoretical calculations of the electron-localization function show that, at the volumes of the two CaO phases (rocksalt and CsCl type), the parent Ca structures (fcc: face-centred cubic; sc: simple cubic) exhibit charge-concentration zones which coincide with the positions occupied by the O atoms in their oxides. For the first time, the structure type, dimension and topology of CaO and BaSnO3 are explained in univocal physical terms.
Theoretical calculations of the electron-localization function show that, at the volumes of the two CaO phases (rocksalt and CsCl type), the parent Ca structures (fcc: face-centred cubic and sc: simple cubic, respectively) exhibit charge concentration zones which coincide with the positions occupied by the O atoms in their oxides. Similar features, also observed for the pairs Ca/CaF2 and BaSn/BaSnO3, are supported by recent high-pressure experiments as well as electron-localization function (ELF) calculations, carried out on elemental K. At very high pressures, the elemental K adopts the hP4 structure, topologically identical to that of the K atoms in high-pressure K2S and high-temperature α-K2SO4. Moreover, the ELF for the hP4 structure shows charge concentration (∼ 2 electrons) at the sites occupied by the S atoms in the high-pressure K2S phase. All these features confirm the oxidation/high-pressure equivalence as well as the prediction of how cation arrays should be metastable phases of the parent metals. For the first time to our knowledge, the structure type, dimension and topology of several oxides and fluorides (CaO, CaF2 and BaSnO3) are explained in univocal physical terms.
PMCID: PMC2873863  PMID: 20484804
electron localization; high-pressure experiments
8.  A complicated quasicrystal approximant ∊16 predicted by the strong-reflections approach 
The structure of the quasicrystal approximant ∊16 was predicted by the strong-reflections approach based on the known approximant ∊6.
The structure of a complicated quasicrystal approximant ∊16 was predicted from a known and related quasicrystal approximant ∊6 by the strong-reflections approach. Electron-diffraction studies show that in reciprocal space, the positions of the strongest reflections and their intensity distributions are similar for both approximants. By applying the strong-reflections approach, the structure factors of ∊16 were deduced from those of the known ∊6 structure. Owing to the different space groups of the two structures, a shift of the phase origin had to be applied in order to obtain the phases of ∊16. An electron-density map of ∊16 was calculated by inverse Fourier transformation of the structure factors of the 256 strongest reflections. Similar to that of ∊6, the predicted structure of ∊16 contains eight layers in each unit cell, stacked along the b axis. Along the b axis, ∊16 is built by banana-shaped tiles and pentagonal tiles; this structure is confirmed by high-resolution transmission electron microscopy (HRTEM). The simulated precession electron-diffraction (PED) patterns from the structure model are in good agreement with the experimental ones. ∊16 with 153 unique atoms in the unit cell is the most complicated approximant structure ever solved or predicted.
PMCID: PMC2811402  PMID: 20101079
quasicrystal approximant; strong-reflections approach; electron diffraction; inverse Fourier transformation
9.  Topological properties of hydrogen bonds and covalent bonds from charge densities obtained by the maximum entropy method (MEM) 
The maximum-entropy charge densities of six amino acids and peptides reveal systematic dependencies of the properties at bond critical points on bond lengths. MEM densities demonstrate that low-order multipoles (l max = 1) and isotropic atomic displacement parameters for H atoms in the multipole model are insufficient for capturing all the features of charge densities in hydrogen bonds.
Charge densities have been determined by the Maximum Entropy Method (MEM) from the high-resolution, low-temperature (T ≃ 20 K) X-ray diffraction data of six different crystals of amino acids and peptides. A comparison of dynamic deformation densities of the MEM with static and dynamic deformation densities of multipole models shows that the MEM may lead to a better description of the electron density in hydrogen bonds in cases where the multipole model has been restricted to isotropic displacement parameters and low-order multipoles (l max = 1) for the H atoms. Topological properties at bond critical points (BCPs) are found to depend systematically on the bond length, but with different functions for covalent C—C, C—N and C—O bonds, and for hydrogen bonds together with covalent C—H and N—H bonds. Similar dependencies are known for AIM properties derived from static multipole densities. The ratio of potential and kinetic energy densities |V(BCP)|/G(BCP) is successfully used for a classification of hydrogen bonds according to their distance d(H⋯O) between the H atom and the acceptor atom. The classification based on MEM densities coincides with the usual classification of hydrogen bonds as strong, intermediate and weak [Jeffrey (1997) ▶. An Introduction to Hydrogen Bonding. Oxford University Press]. MEM and procrystal densities lead to similar values of the densities at the BCPs of hydrogen bonds, but differences are shown to prevail, such that it is found that only the true charge density, represented by MEM densities, the multipole model or some other method can lead to the correct characterization of chemical bonding. Our results do not confirm suggestions in the literature that the promolecule density might be sufficient for a characterization of hydrogen bonds.
PMCID: PMC2749645  PMID: 19767685
topological properties; hydrogen bonding; maximum entropy method; charge densities; peptides; amino acids
10.  Compounds with a ‘stuffed’ anti-bixbyite-type structure, analysed in terms of the Zintl–Klemm and coordination-defect concepts 
Compounds with a ‘stuffed anti-bixbyite’ structure, such as Li3AlN2, were analysed in terms of both the extended Zintl–Klemm concept and the coordination-defect concept. For the first time, inorganic crystal structures are seen as a set of ‘multiple resonance structures’ (Klemm pseudo-structures) which co-exist as the result of unexpected electron transfers between any species pair comprising either like or unlike atoms, cations or anions. If this is the driving force controlling crystal structures, the conventional oxidation states assigned to cations and anions lose some of their usefulness.
The bixbyite structure (Mn2O3) () is often described as a distorted face-centered cubic (f.c.c.) array of Mn atoms, with O atoms occupying 3/4 of the tetrahedral holes. The empty M 4 tetrahedra are centred at 16c. In anti-bixbyite structures (Mg3N2), cation vacancies are centred in empty N4 tetrahedra. If 16 hypothetical atoms were located at this site they would form the structure of γ-Si. This means that anti-bixbyite structures are ideally prepared to accommodate Si(Ge) atoms at these holes. Several compounds (Li3AlN2 and Li3ScN2) fully satisfy this expectation. They are really anti-bixbyites ‘stuffed’ with Al(Sc). The presence of these atoms in 16c is illuminated in the light of the extended Zintl–Klemm concept (EZKC) [Vegas & García-Baonza (2007 ▶). Acta Cryst. B63, 339–345], from which a compound would be the result of ‘multiple resonance’ pseudo-structures, emerging from electron transfers between any species pair (like or unlike atoms, cations or anions). The coordination-defect (CD) concept [Bevan & Martin (2008) ▶. J. Solid State Chem. 181, 2250–2259] is also consistent with the EZKC description of the pseudo-structures. A more profound insight into crystal structures is gained if one is not restricted to the contemplation of classical anions and cations in their conventional oxidation states.
PMCID: PMC2628973  PMID: 19155554
Zintl–Klemm concept; coordination-defect concept; multiple resonance structure; electron transfer
11.  Orientational disorder and phase transitions in crystals of (NH4)2NbOF5  
Structural phase transitions in a crystal of (NH4)2NbOF5 are the consequence of dynamic changes in its structural units as the temperature decreases. Using X-ray diffraction, it is possible to identify O and F atoms in the disordered structure of (NH4)2NbOF5 as a result of its dynamic nature.
Ammonium oxopentafluoroniobate, (NH4)2NbOF5, was synthesized in a single-crystal form and the structures of its different phases were determined by X-ray diffraction at three temperatures: phase (I) at 297 K, phase (II) at 233 K and phase (III) at 198 K. The distorted [NbOF5]2− octahedra are of similar geometry in all three structures, with the central atom shifted towards the O atom. The structure of (I) is disordered, with three spatial orientations of the [NbOF5]2− octahedron related by a jump rotation around the pseudo-threefold local axis such that the disorder observed is of a dynamic nature. As the temperature decreases, the compound undergoes two phase transitions. The first is accompanied by full anionic ordering and partial ordering of the ammonium groups (phase II). The structure of (III) is completely ordered. The F and O atoms in the structures investigated were identified via the Nb—X (X = O and F) distances. The crystals of all three phases are twinned.
PMCID: PMC2553555  PMID: 18799840
ammonium oxopentafluoroniobate; distorted octahedra; dynamic orientational disorder; phase transitions; twinning; vibrational spectra

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