Structure Solution Method Research Articles

Solid-state supramolecular organization, established directly from powder diffraction data, and photoluminescence efficiency of rigid-core oligothiophene-S,S-dioxides.

The "rigid-core" material 3,5-dimethyl-2,3'-bis(3-methylthiophene)-dithieno[3,2-b:',3'-d]thiophene-4,4-dioxide (DTTOMe4) has the highest photoluminescence ever reported for thiophene-based molecules in the solid state. We report the structure of this material, determined directly from powder X-ray diffraction data using the Genetic Algorithm method for structure solution, followed by Rietveld refinement, and the structural properties are discussed in relation to the structures of the corresponding subsystems DTTO and DTTOMe. While the crystal structures of the latter compounds contain cofacial dimers, the crystal structure of DTTOMe4 comprises layers of molecules aligned in an antiparallel fashion. Intermediate neglect of differential overlap with single configuration interaction (INDO/SCI) calculations on the intermolecular interactions in the three crystal structures show that the different solid-state photoluminescence efficiencies of DTTOMe4, DTTOMe, and DTTO cannot be correlated with the different types of dipole-dipole alignment in the solid state. Instead, photoluminescence efficiencies correlate well with the rate of formation of nonradiatively decaying charge-transfer pairs upon photoexcitation. Because of larger intermolecular distances in DTTOMe4, the photoluminescence is less effectively quenched by charge-transfer processes than in DTTOMe and DTTO.

Electron crystallography of aluminum alloy phases

Abstract A series of structure analyses during 1994-2001 by electron crystallographic techniques applied to phases in aluminum alloys are reviewed. Methods for structure solution employ electron diffraction intensity data collected by the precession technique, by selected area micro-diffraction and by the convergent-beam technique. High-resolution electron microscope images (HRTEM) are treated by different kind of processing, including exit wave reconstruction. Crystallographic calculations are performed either by direct method or Patterson and Fourier procedures, assuming kinematical scattering, or by refinement from models derived from HRTEM images. Dynamical scattering calculations can be introduced in the refinement stage or as a correction procedure applied to part of the intensity data. The phases studied include primary Al-Fe-(Si) particles, Al-Mn-Si dispersoids, Al-Co quasicrystals and two types of precipitate phases in age-hardening Al-Mg-Si and Al-Zn-Mg alloys.

An Overview of Some Developments in Crystallographic Computing Methods Worldwide

The field of computational methods for X-ray crystallographic structure solution is currently in a state of rapid flux, arising both from internal development of the methods employed, and from external pressures of new applications of the technology. These pressures have formed a basis for a number of new, large scale collaborative projects involving a range of disciplines and geographical groupings. The paper will examine some of the motivations for change, and then some of the new projects which are arising from them will be discussed in more detail.

Structures of three substituted arenesulfonamides from X-ray powder diffraction data using the differential evolution technique

The structures of three substituted arenesulfonamides have been solved from laboratory X-ray powder diffraction data, using a new direct-space structure solution method based on a differential evolution algorithm, and refined by the Rietveld method. In 2-toluenesulfonamide, C(7)H(9)NO(2)S (I) (tetragonal I4(1)/a, Z = 16), the molecules are linked by N-H...O=S hydrogen bonds into a three-dimensional framework. In 3-nitrobenzenesulfonamide, C(6)H(6)N(2)O(4)S (II) (monoclinic P2(1), Z = 2), N-H...O=S hydrogen bonds produce molecular ladders, which are linked into sheets by C-H...O=S hydrogen bonds: the nitro group does not participate in the hydrogen bonding. Molecules of 4-nitrobenzenesulfonamide, C(6)H(6)N(2)O(4)S (III) (monoclinic P2(1)/n, Z = 4), are linked into sheets by four types of hydrogen bond, N-H...O=S, N-H...O(nitro), C-H...O=S and C-H...O(nitro), and the sheets are weakly linked by aromatic pi...pi stacking interactions.

Differential evolution as a method of structure solution from powder diffraction data

Differential evolution as a method of structure solution from powder diffraction data

New opportunities in biological and chemical crystallography

Banerjee [Proc. R. Soc. (1933), 141, 188-193] offered a new way of approaching the crystallographic phase problem which not only broke new ground beyond the 'trial and error' structure solution method of that time but also heralded the extremely powerful direct methods of crystallography of the modern era from the 1970s onwards in chemical crystallography. Some 200000 crystal structures are known today. More complex crystal structures such as proteins required new experimental and theoretical methods to solve the phase problem. These are still evolving, and new methods and results involving synchrotron radiation at softer X-ray wavelengths (2 A) are reported. In addition, an overview is given of the new opportunities that are possible for biological and chemical crystallography, especially via harnessing synchrotron radiation and neutron beams.

Growth of Sr6Rh5O15 single crystals from high-temperature solutions: structure determination using the traditional 3-D and the 4-D superspace group methods and magnetic measurements on oriented single crystals.

Single crystals of Sr6Rh5O15 were grown from a molten potassium carbonate flux. The structure was solved by both the traditional 3-D crystallographic approach and the 4-D superspace group approach using JANA2000. Both methods produced an equivalent structure determination, thereby confirming the 4-D superspace group approach as an effective structure solution method for 3-D commensurate composite structures. Sr6Rh5O15 corresponds to the n = 1, m = 1 member of the A3n+3mA'nB3m+nO9m+6n family of 2H hexagonal perovskite-related oxides. This compound is characterized by pseudo-one-dimensional polyhedral chains of four face-sharing RhO6 octahedra followed by one RhO6 trigonal prism. These chains in turn are separated by [Sr](infinity) chains. Magnetic measurements were carried out on oriented single crystals, and a very large magnetic anisotropy in the magnetic susceptibility was observed.

Solving Complex Zeolite Structures from Powder Diffraction Data

To understand the technologically important properties of zeolites and their analogs, structure analysis is essential. However, most new zeolites are prepared in polycrystalline form, so powder diffraction methods of structure solution must be applied, and these have their limitations. In an effort to extend the range of structural complexity that can be addressed when only powder diffraction data are available, a number of new approaches have been explored in recent years. Three that were developed in our research group are described. The first involves the active use of chemical information in an automated structure solution process (focus); the second, the generation of structure envelopes to facilitate structure solution in direct (model-building) space; and the third, the exploitation of preferred orientation (texture) to obtain better estimates of the relative intensities of overlapping reflections. The focus approach is specific to zeolites, but the other two are generally applicable. All three methods have been applied to real problems, and examples are given. The determination of the structure of the high-silica zeolite UTD-1F, with 117 atoms in the asymmetric unit, using the texture approach demonstrates the power of powder diffraction techniques in structure analysis.

Practical experience with the use of halides for phasing macromolecular structures: a powerful tool for structural genomics.

The crystal structure of pepstatin-insensitive carboxyl proteinase (PCP) from Pseudomonas sp. 101, an enzyme with no overall sequence similarity to any other proteinases of known structure, was solved using crystals soaked in sodium bromide solution and then cryocooled. A data set collected at the bromine peak absorption wavelength was sufficient for calculation of an excellent map and the entire process of phasing and tracing the maps required almost no direct human intervention. The process of structure solution using single-wavelength data was compared with three-wavelength multiwavelength anomalous diffraction (MAD); although the latter resulted in slightly better maps, the use of this much more labor-intensive approach did not significantly improve the ability to solve the structure. The successful phasing approaches are compared with several less successful attempts utilizing other crystal forms of the enzyme and the practical aspects of the use of bromine as a heavy-atom derivative are discussed. In conclusion, the use of halides with single-wavelength diffraction data fulfills the requirements of being a first-choice method of high-throughput structure solution for the emerging field of structural genomics.

Solving Crystal Structures from Powder Diffraction Data using Genetic Algorithms

Many solids can be prepared only as microcrystalline powders and are not suitable for investigation by single crystal diffraction methods. To establish the structural properties of such materials, it is necessary to solve the crystal structure directly from powder diffraction data. Here we highlight fundamentals and applications of a method for structure solution from powder diffraction data in which a hypersurface based on the profile R-factor is searched using Genetic Algorithm techniques.

Towards the real structure of quasicrystals and approximants by analysing diffuse scattering and deconvolving the Patterson

Methods based on X-ray area detectors are presented for acquiring and analysing single-crystal X-ray diffraction data from quasicrystals and approximants. These methods are complementary to high-resolution diffractometry and fully exploit the possibilities of modern two-dimensional X-ray detector systems (imaging plates and charge coupled devices) such as the on-line read-out capability and the possibility to collect large volumes of reciprocal space in a quantitative and rapid way. In contrast to a classical point detector, area detectors allow the measurement of a very large number of Bragg reflections in a reasonable time scale, as is shown with a large unit-cell periodic approximant in the Al-Co-Ni alloy system. For large approximants exhibiting strong pseudosymmetry, direct methods for structure solution usually fail. Recently implemented Patterson deconvolution techniques are shown to succeed. The extension of techniques for area detectors – beyond the standard application of collecting integrated Bragg intensities – to the quantitative acquisition of continuous and diffuse scattering data is presented with particular emphasis on quasicrystals. One of the key techniques is the quantitative reconstruction of undistorted layers and volumes in reciprocal space. This is crucial for developing and comparing possible models for structural disorder in quasicrystals. Examples for decagonal Al-Co-Ni and icosahedral Al-Mn-Pd are given in respect to possibilities and limitations of X-ray area detectors.

Definition of a `guiding function' in global optimization: a hybrid approach combining energy and R-factor in structure solution from powder diffraction data

Two global optimization problems of current interest in solid state sciences are crystal structure prediction (optimization of structure with respect to computed energy) and direct-space techniques for crystal structure solution from powder diffraction data (optimization of structure with respect to R-factor). As the energy and R-factor hypersurfaces are based on the same parameter space but have differing characteristics, there is a direct opportunity to blend these approaches together in the definition of a hybrid hypersurface. A strategy for combining R-factor and energy within a direct-space method for structure solution from powder diffraction data is proposed. Normalized energy and normalized R-factor functions are defined, and are combined using a sliding weighting function to give a hybrid figure-of-merit G, which behaves as energy when energy is high (thus using energy to guide the calculation towards energetically plausible structures) and gives increasing importance to R-factor as lower energies are approached. This concept of a `guiding function' may be widely applicable in other global optimization problems.

Crystal Structure Solution from Neutron Powder Diffraction Data by a new Monte Carlo Approach Incorporating Restrained Relaxation of the Molecular Geometry

We report the development of a new aspect of the Monte Carlo method for crystal structure solution from powder diffraction data and demonstrate the advantages of this new approach by applying it to solve the low-temperature crystal structure (phase II) of perdeuterated pyrene from neutron powder diffraction data. In previous applications of our Monte Carlo technique, the structural fragment was constrained to have a standard geometry throughout the calculation, whereas in the new approach, restrained relaxation of the structural fragment from standard geometry is considered for each structure sampled during the calculation. The new approach gives rise to a substantially improved discrimination (in terms of the weighted profile R factor Rwp) between the correct structure solution and incorrect structures sampled during the Monte Carlo calculation [for the calculation with standard geometry of the structural fragment, Rwp ranged from circa 27.5–30% for `wrong' structures to 21.2% for the best structure solution (i.e. discrimination ~6.3%); for the calculation with relaxation of the geometry of the structural fragment, Rwp ranged from circa 24–26% for `wrong' structures to 11.6% for the best structure solution (i.e. discrimination ~12.4%)]. The work reported here represents the first application of the Monte Carlo method for structure solution using neutron powder diffraction data; the new methodology (applicable to both neutron and X-ray powder diffraction data) represents a substantial enhancement of the scope and potential of the method, particularly for cases in which the discrimination in Rwp between the correct structure solution and incorrect structure solutions is expected to be inherently small.

RNA crystallography.

The current state of three-dimensional structure analysis of RNA by x-ray crystallography is summarized. The methods of sample preparation, crystallization, data collection, and structure solution are discussed, followed by a review of the RNA structures that have been determined and of common structural features, and finally, an appraisal of future prospects for x-ray crystal structure analysis of RNA.

Protein Crystallography in the Soft X-ray Region: Crystal Lifetime and Diffraction Efficiency

Multiwavelength anomalous diffraction on the sulfur (5.01 A) and phosphorus (5.77 A) absorption K-edges seems to offer a solution to one of the most appealing problems of protein crystallography - the determination of the phases of structure amplitudes. However, a strong increase in absorption of X-rays in this region may impede the development of this method of structure solution. Analytical expressions for diffraction efficiency and normalized diffraction efficiency have been derived in the present paper. It is shown that the crystal lifetime in the soft X-ray region will be significantly shorter than the lifetime of a macromolecular crystal exposed to 1-1.5 A X-rays during diffraction data collection. An optimum crystal size has been estimated.

The development of Monte Carlo methods for crystal structure solution from powder diffraction data: simultaneous translation and rotation of a structural fragment within the unit cell

This paper reports the successful application of a Monte Carlo technique to the solution of the crystal structure of p-methoxybenzoic acid from X-ray powder diffraction data collected on a conventional laboratory diffractometer. The `structural fragment' used in the Monte Carlo structure solution calculation comprised the C and O atoms of the benzoate group (i.e. C6CO2) plus the O atom of the methoxy group in the para position. The structural fragment was translated and rotated through the unit cell under a Monte Carlo algorithm, with trial structures accepted or rejected on the basis of Metropolis importance sampling. The best position of this structural fragment was discriminated readily (using the profile R-factor Rwp to assess the agreement between experimental and calculated X-ray powder diffractograms) from `wrong' positions sampled during the Monte Carlo calculation, and the best position was then used as the initial structural model in Rietveld refinement and difference-Fourier calculations. This represents the first successful report of the use of simultaneous translation and rotation of the structural fragment in crystal structure solution from experimental powder diffraction data using the Monte Carlo method.

Crystal Structure Solution from Powder X-ray Diffraction Data: The Development of Monte Carlo Methods To Solve the Crystal Structure of the γ-Phase of 3-Chloro-trans-cinnamic Acid

Many important crystalline materials do not form single crystals of sufficient size and/or quality for single-crystal diffraction studies, and in such cases it is essential that the crystal structure can be solved from powder diffraction data; however, there are many difficulties associated with solving crystal structures, ab initio, from powder diffraction data. In this paper, we report the successful application of a Monte Carlo technique to solve the (previously unknown) crystal structure of the γ-phase of 3-chloro-trans-cinnamic acid from powder X-ray diffraction data. The “structural fragment” used in the Monte Carlo calculation comprised a rigid trans-cinnamic acid molecule (with the chlorine and hydrogen atoms omitted) with its oxygen atoms at a fixed distance from the crystallographic center of symmetry, and with the center of symmetry lying in the molecular plane. The structural fragment was rotated by a random angular displacement around a random axis constrained to pass through the center of symmetry. The “correct” position of this structural fragment was discriminated readily (on the basis of the agreement between experimental and calculated powder X-ray diffractograms) from “wrong” positions sampled during the Monte Carlo calculation, and the “correct” position was then used as the initial structural model in Rietveld refinement and difference Fourier calculations. The paper concludes with a discussion of general considerations relating to the application of the Monte Carlo method for crystal structure solution from powder diffraction data.

Structure determination of racemic trichogin A IV using centrosymmetric crystals.

Direct methods of crystal structure solution are greatly facilitated in centrosymmetric space groups where the complexity of the phase-problem is reduced. For most peptides and proteins, crystallization in a centrosymmetric arrangement is precluded by an intrinsic dissymmetry due to the constituent chiral amino acid residues. The synthetic accessibility of peptide sequences containing amino acids of either chirality offers the possibility for co-crystallization of racemic crystals. We report here the first use of such an approach for the de novo structure determination of a medium-sized molecule, trichogin A IV, which is a constituent of a fungal lipopeptaibol mixture possessing membrane-modifying properties of biological interest.

Crystal structure determination by neutron powder diffraction using structural and packing constraints

In the past, crystal structure determination of solids consisting of molecules (or atom groups) whose geometry and size are known approximately has often been attempted using neutron powder diffraction profile refinement techniques, but without inclusion of this information. A method of structure solution has therefore been developed to include it. The proposed method does not require a set of structure factors and thus avoids the problems encountered in separating peaks in a powder diffraction scan. A successful test was conducted with a previously determined (yet treated as unknown) crystal structure, where direct methods had failed to solve the structure due to incorrect peak separation. Two computer programs, MODEL and PARAM, that implement the method are described.

Structure of 1,1,3(RS),6,6,8(RS)-hexamethyl-cis-10b(SR),10c(SR)-perhydro-1H,6H-3a(SR), 5a(SR) 8a(SR), 10a(SR)-tetraazapyrene determined by X-ray diffraction methods. A semiempirical method of structure solution

The crystal and molecular structure of the title compound hexamethyl-perhy-drotetraazapyrene (I) has been determined by X-ray diffraction methods. The compound crystallizes in the triclinic system, space groupP¯1, with cell dimensionsa=7.715(1),b=10.580(2),c=11.926(2) A, andα=94.37(1)°,β=104.87(1)°, and γ=107.27(1)°. Since the usual direct methods failed, the structure was solved by a semiempirical optimization of packing a model ofI in the unit cell, in terms of the van der Waals' intermolecular energy. The atomic parameters at the most energetically favored position were then refined by least squares against 2396 observed unique reflections, giving a finalR of 0.067. The semiempirical solution used here seems to be limited to particular cases. The molecule ofI consists of two fused piperazine and two fused hexahydropyrimidine rings, having slightly distorted chair conformations. The rings form a foldedcis-10b,10c system of almost exactC2 point group symmetry. The lone methyl groups in positions 3 and 8 (at the folding) are found to be axially attached. The geminal methyl groups in positions 1 and 6 are situated away from the folding.