Structure Solution Method Research Articles

Structure and System Nonprobabilistic Reliability Solution Method Based on Enhanced Optimal Latin Hypercube Sampling

Using the convex model approach, the bounds of uncertain variables are only required rather than the precise probability distributions, based on which it can be made possible to conduct the reliability analysis for many complex engineering problems with limited information. This paper aims to develop a novel nonprobabilistic reliability solution method for structures with interval uncertainty variables. In order to explore the entire domain represented by interval variables, an enhanced optimal Latin hypercube sampling (EOLHS) is used to reduce the computational effort considerably. Through the proposed method, the safety degree of a structure with convex modal uncertainty can be quantitatively evaluated. More importantly, this method can be used to deal with any general problems with nonlinear and black-box performance functions. By introducing the suggested reliability method, a convex-model-based system reliability method is also formulated. Three numerical examples are investigated to demonstrate the efficiency and accuracy of the method.

Not quite the beginning: early days in 1970s Oxford

In the early 1970s there were only a handful of protein crystallography groups in the world, and less than a dozen structures had been solved. Although we were missing many of the methods and facilities that we now take for granted, we did solve structures, albeit rather slowly, and we did get some things right. We worried about errors. We worried about how to collect the best intensity data, and how to reduce radiation damage, at that time by cooling to near 00. We appreciated the value of anomalous scattering in phasing, and tried to make the best use of it in the refinement of heavy atom parameters, allowing for the estimated errors. Simon French introduced us to the ideas of Bayesian statistics in dealing with noisy data. We saw the beginnings of molecular replacement as a method for structure solution. And we learnt how to collaborate on software development, which led to the start of the CCP4 project at the end of the decade.

Why was the structure of the niobium silicate AM-11 so difficult to solve?

The synthesis of the polycrystalline niobium silicate catalyst AM-11 was first reported in 1998 [1], but its structure proved to be elusive. In 2007 we received two samples from the Aveiro group. At the time, we were looking for a material suitable for the application of the texture method of structure solution, and AM-11 seemed to be ideal for this purpose. One of the samples had needle and the other platelet morphology, and textured samples could be prepared in both cases. The conventional powder diffraction pattern could be indexed on a hexagonal, an orthorhombic or a monoclinic unit cell, so this was the first issue to be resolved. The texture measurements quickly revealed that the crystal system was orthorhombic, but the structure resisted solution. We then tried applying the precession electron diffraction technique in combination with high-resolution powder diffraction data, but beyond confirming the orthorhombic symmetry, these data did not help us to solve the structure. Another attempt was made with a new sample and an improved texture setup, but to no avail. Rotation electron diffraction data and high-resolution transmission electron microscopy images showed that some disorder was present and helped to define the space group, but the structure remained a mystery. The powder charge-flipping routine in Superflip [2], yielded tantalizingly clear electron density maps, but they could not be interpreted sensibly. The unit cell parameters were seen to be related to those of the titanium silicate zorite [3] (one axis doubled in AM-11), so the problem was taken up once again last year. By starting with a simplified zorite framework structure with Nb in place of Ti, and performing what amounts to manual Fourier recycling, the surprisingly simple structure (1Nb, 3 Si, 9 O), which is significantly different from zorite, finally revealed itself. There is some stacking disorder, but the structure is otherwise innocuous. What made it so difficult to solve?

Structures and Properties of Diastereomeric Multi-component Crystals

Multi-component crystals composed of two different chiral molecules have the potential to form diastereomers. In the present study a selection of chiral amides and acids was employed to form multi-component crystals. Since growing these multi-component crystals from solution failed, solvent assisted grinding was used. The resulting diastereomeric pairs, which are present as polycrystalline powders showed distinctly different powder diffraction patterns. In order to elucidate the crystal structures direct space global optimization structure solution methods were successfully used in several cases. A potential application of these diastereomeric multi-component crystals is the determination of the absolute configuration of one of the two components based on the known absolute configuration of the other.[1] In addition, Raman spectroscopy and DSC were employed to determine thermodynamic properties. In subsequent grinding experiments racemic conglomerates and racemates formed the starting material. These experiments demonstrated in several cases a relationship between melting point differences and preferential formation of only one diastereomer.

RIEMANN ZEROS AND THE INVERSE PHASE PROBLEM

Finding a universal method of crystal structure solution and proving the Riemann hypothesis are two outstanding challenges in apparently unrelated fields. For centrosymmetric crystals however, a connection arises as the result of a statistical approach to the inverse phase problem. It is shown that parameters of the phase distribution are related to the non-trivial Riemann zeros by a Mellin transform.

A combined method for automatic structure solution of proteins of unknown fold

A combined method for automatic structure solution of proteins of unknown fold

Generation and applications of structure envelopes for porous metal–organic frameworks

The synthesis of polycrystalline, as opposed to single-crystalline, porous materials, such as zeolites and metal–organic frameworks (MOFs), is usually beneficial because the former have shorter synthesis times and higher yields. However, the structural determination of these materials using powder X-ray diffraction (PXRD) data is usually complicated. Recently, several methods for the structural investigation of zeolite polycrystalline materials have been developed, taking advantage of the structural characteristics of zeolites. Nevertheless, these techniques have rarely been applied in the structure determination of a MOF even though, with the electron-density contrast between the metal-containing units and pore regions, the construction of a structure envelope, the surface between high- and low-electron-density regions, should be straightforward for a MOF. Herein an example of such structure solution of MOFs based on PXRD data is presented. To start, a Patterson map was generated from powder diffraction intensities. From this map, structure factor phases for several of the strongest reflections were extracted and a structure envelope (SE) of a MOF was subsequently constructed. This envelope, together with all extracted reflection intensities, was used as input to theSUPERFLIPsoftware and a charge-flipping (CF) structure solution was performed. This structure solution method has been tested on the PXRD data of both activated (solvent removed from the pores;dmin= 0.78 Å) and as-synthesized (dmin= 1.20 Å) samples of HKUST-1. In both cases, our method has led to structure solutions. In fact, charge-flipping calculations using SE provided correct solutions in minutes (6 min for activated and 3 min for as-synthesized samples), while regular charge flipping or charge flipping with histogram matching calculation provided meaningful solutions only after several hours. To confirm the applicability of structure envelopes to low-symmetry MOFs, the structure of monoclinic PCN-200 has been solvedviaCF+SE calculations.

Structure refinement from precession electron diffraction data

Electron diffraction is a unique tool for analysing the crystal structures of very small crystals. In particular, precession electron diffraction has been shown to be a useful method for ab initio structure solution. In this work it is demonstrated that precession electron diffraction data can also be successfully used for structure refinement, if the dynamical theory of diffraction is used for the calculation of diffracted intensities. The method is demonstrated on data from three materials - silicon, orthopyroxene (Mg,Fe)(2)Si(2)O(6) and gallium-indium tin oxide (Ga,In)(4)Sn(2)O(10). In particular, it is shown that atomic occupancies of mixed crystallographic sites can be refined to an accuracy approaching X-ray or neutron diffraction methods. In comparison with conventional electron diffraction data, the refinement against precession diffraction data yields significantly lower figures of merit, higher accuracy of refined parameters, much broader radii of convergence, especially for the thickness and orientation of the sample, and significantly reduced correlations between the structure parameters. The full dynamical refinement is compared with refinement using kinematical and two-beam approximations, and is shown to be superior to the latter two.

X-ray diffraction and the development of the mineral crystal chemistry

After the epochal experience of Friedrich and Knipping suggested and interpreted by Laue, the scene rapidly moved to England where the young Bragg correctly explained the results of the Munich discovery and showed how to use X-rays to determine the arrangement of atoms in crystals and, in few years, actually derived the structures of several inorganic compounds. Their comparison permitted Bragg to assert that crystals are composed of “inelastic spheres in contact” and that “it is possible to assign to the sphere representing an atom… a constant diameter.” The development of these concepts by various authors (Wasastjerna, Goldschmidt, …) led to the well-known Table of ionic radii by Pauling, who—at the same time—proposed the rules for the stability of ionic compounds, based on the concept of coordination polyhedra as building elementary modules of inorganic compounds. The stability rules of Pauling, as well as the conception, formulated by Bragg, of the structures of complex oxides as characterized by ‘close packing’ of oxygen anions, were the main guiding lines in the ‘trial and error’ procedures to determine the atomic arrangements in minerals and in inorganic compounds in general. The increasing number of known structures raised the need for proper classification schemes, largely based on elementary structural units (as the silicon tetrahedra in silicates) and the various ways of their connection. At the same time the wide basis of structural data and the increased precision and accuracy of those data stimulated the revision of the old compilations of ionic radii as well as a re-formulation of the Pauling’s rule of valence-bond balance. Examples are presented of the application of the crystal chemical concepts to some important mineralogical, geochemical and geophysical problems. An explosive growth of structural knowledge in the last decades of the twentieth century was stimulated by the new techniques of data collection, the high speed of computing and the advent of direct methods of structure solution, which resulted not only in an enormous increase in the number of known structures, but also in unraveling very complex arrangements. This increasing structural knowledge accompanied and stimulated the development of a new way to look at the arrangements of inorganic compounds, based on their modular aspects. The concept of assembling different, geometrically compatible modules, mainly structural layers, to build up complex structures has been very productive; in fact it not only consented a deep knowledge of the structural relationships inside wide families of natural and synthetic compounds, but also favored the solution of complex structural problems and permitted careful previsions of new possible structural arrangements. Few lines of future developments of the crystal chemical study of minerals are briefly presented and discussed: ‘synergy’ between mineralogists and material chemists; computational simulations of structural arrangements; new experimental approach through automated electron diffraction tomography.

The two-dimensional XPD charge-flipping method for structure solution from powder diffraction data

The two-dimensional XPD charge-flipping method for structure solution from powder diffraction data

(Z)-3-Methyl-N-(7-nitroacridin-3-yl)-2,3-dihydro-1,3-benzothiazol-2-imine from laboratory powder diffraction data

The title compound, C(21)H(14)N(4)O(2)S, belongs to a family of molecules possessing nonlinear optical properties in solution. Its structure has been solved from laboratory X-ray powder diffraction data using a new direct-space structure solution method, where the atomic coordinates are directly used as parameters and the molecular geometry is described by restraints. The molecular packing is controlled by two systems of π-π interactions and one weak edge-to-face interaction.

Detour into two dimensions: a new method for powder structure solution

Detour into two dimensions: a new method for powder structure solution

Patterson function direct methods for structure solution from powder data

Patterson function direct methods for structure solution from powder data

Crystal Structure Determination from Laboratory X-ray Powder Diffraction Data

Structure determination from laboratory powder diffraction data can be considered routine today as emphasized by the significant increase in the number of published structures, both organic and/or inorganic compounds solved in this way. In the past about 10 years, many significant developments in instrumentation, such as computer technology and powder diffraction methodology, allow determination of crystal structures, the size and complexity of which are only limited by data quality and computing power. New detector technologies (mostly strip detectors), faster PCs and powerful methods of structure solution (especially the direct space and the charge flipping methods) contributed most to an ever increasing success rate. Also monochromater for incident beam (like CuKα1 or MoKα1) is not always required for structure determination.

Reconstruction strategies for structure solution using precession electron diffraction data from hybrid inorganic-organic framework materials

Precession electron diffraction has received significant recent attention, and has the potential to complement x-ray structure solution methods in situations where the latter are difficult to apply. Certain materials systems may nevertheless present challenges for solution by electron diffraction, and this is particularly true when the unit cell includes light element components. Drawing specifically on our work with hybrid inorganic-organic framework materials, we describe recent approaches to reconstructing their crystal potentials, which have led to significant improvements in the accuracy and quality of the derived potential maps for this type of structure.

A new type of cubic-stacked layer structure in anthoinite, AlWO3(OH)3

Anthoinite, AlWO3(OH)3, from the Mt. Misobo Mine, Democratic Republic of the Congo, has triclinic symmetry with cell parameters a = 8.196(1) A, b = 9.187(1) A, c = 11.316(1) A, α = 92.82(1)°, β = 94.08(1)°, γ = 90.23(1)°, space group I 1, Z = 8. The structure was solved by applying ab initio structure solution methods (Reverse Monte Carlo/Simulated Annealing) to both X-ray and neutron powder diffraction data and was refined using the Rietveld method. The structure is built up of two types of M4(O,OH)16 planar tetrameric clusters of edge-sharing octahedra, one containing predominantly Al and the other predominantly W. The Al-rich and W-rich clusters interconnect via corner sharing to form stepped layers parallel to (001). The layers are held together by strong hydrogen bonding. The structure can be described as a rocksalt derivative structure, with the close-packed anion layers parallel to (012), and with Al and W atoms ordered into one third of the octahedral sites within the cubic close-packed anion lattice. The structure is complicated by partial disorder between Al and W in the tetrameric clusters and associated disorder in the H atom sites. Infrared and 27Al MAS NMR results are also presented for anthoinite.

Adsorption of Harmful Organic Vapors by Flexible Hydrophobic Bis-pyrazolate Based MOFs

Highly porous homoleptic Ni(bpb) and Zn(bpb) materials have been obtained by reaction of nickel(II) and zinc(II) salts with the deprotonated form of the 1,4-(4-bispyrazolyl)benzene ligand (H2bpb). Ab-initio structure solution methods and thermodiffractometry have allowed the determination of their crystal structures, framework flexibility, and thermal stability. The different stereochemical requirements of the Ni(II) and Zn(II) ions induce, in Ni(bpb) and Zn(bpb), rhombic and square channels, respectively, accounting for 57 and 65% of the total cell volume. The two materials feature high adsorption capacities toward small gaseous molecules (N2 and Ar at 77 K, CO2 and CH4 at 273 K), peaking at 22 mmol g−1 of N2 in the case of the zinc(II) derivative, which is reflected by a very large surface area (above 2000 m2 g−1). The flexibility, size, and hydrophobic nature of their channels are adequate also for the incorporation of organic vapors. In this regard, the adsorption of benzene and cyclohexane has been studied under static conditions at 303 K, while that of thiophene has been investigated in dynamic conditions, by measurement, at 298 K, of the breakthrough curves of a flow of CH4/CO2 containing 30 ppm of thiophene. Ni(bpb) and Zn(bpb) are outperforming adsorbents, uptaking up to 0.34 g of thiophene per gram of material. The presence of humidity (60%), which is a major drawback for practical applications of MOFs, does not significantly affect the performance of Ni(bpb) in the removal of thiophene, at variance with Zn(bpb) and HKUST-1, Cu3(btc)2 (btc = benzene-1,3,5-tricarboxylate), which become ineffective in the presence of moisture. Additional XRPD studies have been performed on benzene-loaded Ni(bpb) samples in order to shed some light on the affinity of this material for aromatic guests.

Molecular structure from X-ray diffraction

The main crystallographic databases have increased in size substantially in the last few years and been joined by a free to use alternative. Results from the most recent crystal structure prediction exercise show that there has been a significant advance in the methods used. The principal improvements in structure solution methods include the extension of techniques originally developed for protein structure determination to powder crystallography, and the application of low resolution phasing information from solution scattering to solid-state structure analysis. Methods for validating structures have highlighted some examples of problems arising from careless work and obvious fraud.

Comparison of different approaches for automatic structure solution

High-throughput crystallography needs robust algorithms capable to deal with a large variety of different cases, should be largely insensitive to experimental and structural criteria, and needs to have a seamless transition between the different steps that can be identifed in the complete structure determination process. These steps have remained largely unchanged since decades, i.e. space group determination using the systematic extinction conditions followed by the structure solution step by (usually) direct methods using the symmetry determined in the preceding step, and fnalized by structural refnement. The newly developed structure solution method charge fipping has made it very advantageous to postpone the symmetry determination step to after the structure solution step using a robust analysis of the symmetry of the determined phases in P1. This makes it possible to determine in one step structures where the symmetry analysis based on systematic extinctions is doubtful or even incorrect [1]. We present here a comparison between the traditional approach based on symmetry determination by analysis of systematic absences and structure solution by direct methods on the one hand and structure solution by charge fipping and symmetry determination by analysis of phased refections on the other hand. The comparison is done on more than 500 structures of variable size and composition and diffraction data of intermediate to excellent quality using default parameters for all data sets, i.e. without any intermediate human intervention, with the aim to determine success rates in automatic structure solution using widely available and free crystallographic software.

Prodigious pores

A chiral zeolite with very large pores has been made, and has been characterized by a new structure-solution method