Lukas Palatinus

SUPERFLIP – a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions

SUPERFLIP is a computer program that can solve crystal structures from diffraction data using the recently developed charge-flipping algorithm. It can solve periodic structures, incommensurately modulated structures and quasicrystals from X-ray and neutron diffraction data. Structure solution from powder diffraction data is supported by combining the charge-flipping algorithm with a histogram-matching procedure. SUPERFLIP is written in Fortran90 and is distributed as a source code and as precompiled binaries. It has been successfully compiled and tested on a variety of operating systems.

Crystallographic Computing System JANA2006: General features

Abstract JANA2006 is a freely available program for structure determination of standard, modulated and magnetic samples based on X-ray or neutron single crystal/ powder diffraction or on electron diffraction. The system has been developed for 30 years from specialized tool for refinement of modulated structures to a universal program covering standard as well as advanced crystallography. The aim of this article is to describe the basic features of JANA2006 and explain its scope and philosophy. It will also serve as a basis for future publications detailing tools and methods of JANA.

EDMA : a computer program for topological analysis of discrete electron densities

EDMA is a computer program for topological analysis of discrete electron densities according to Baders theory of atoms in molecules. It locates critical points of the electron density and calculates their principal curvatures. Furthermore, it partitions the electron density into atomic basins and integrates the volume and charge of these atomic basins. EDMA can also assign the type of the chemical element to atomic basins based on their integrated charges. The latter feature can be used for interpretation of ab initio electron densities obtained in the process of structure solution. A particular feature of EDMA is that it can handle superspace electron densities of aperiodic crystals in arbitrary dimensions. EDMA first generates real-space sections at a selected set of phases of the modulation wave, and subsequently analyzes each section as an ordinary three-dimensional electron density. Applications of EDMA to model electron densities have shown that the relative accuracy of the positions of the critical points, the electron densities at the critical points and the Laplacian is of the order of 10−4 or better.

Symmetry determination following structure solution in P1

A new method for space-group determination is described. It is based on a symmetry analysis of the structure-factor phases resulting from a structure solution in space group P1. The output of the symmetry analysis is a list of all symmetry operations compatible with the lattice. Each symmetry operation is assigned a symmetry agreement factor that is used to select the symmetry operations that are the elements of the space group of the structure. On the basis of the list of the selected operations the complete space group of the structure is constructed. The method is independent of the number of dimensions, and can also be used in solution of aperiodic structures. A number of cases are described where this method is particularly advantageous compared with the traditional symmetry analysis.

Charge flipping combined with histogram matching to solve complex crystal structures from powder diffraction data

The charge-flipping structure-solution algorithm introduced by Oszlányi and Süto in 2004 has been adapted to accommodate powder diffraction data. In particular, a routine for repartitioning the intensities of overlapping reflections has been implemented within the iterative procedure. This is done by modifiying the electron density map with a histogram-matching algorithm, and then using the Fourier coefficients obtained from this map to repartition the structure factor amplitudes within each overlap group. The effectiveness of the algorithm has been demonstrated with five test examples covering different classes of materials of varying complexity (ZSM-5 ([Si96O192]), cimetidine (C10H16N6S), a polysalicylide ((C7O2H)6), the low-temperature modification of 4-methylpyridine-N-oxide (C6H7NO) with 8 molecules in the asymmetric unit, and a zirconium phosphate phase (|(C5H6N)4 (H2O)2| [Zr12P16O60(OH)4F8])). It was also used to solve the structure of a layer silicate (|(CH3)4N)8 (H2O)20| [Si24 O56]), whose space group was unclear. These structures, with 17–64 non-H atoms in the asymmetric unit (68–288 in the unit cell), could all be solved in a straightforward manner. Histogram matching proved to be an essential component of the algorithm for the more complex structures. The clear advantages of the charge-flipping algorithm are that (1) all calculations are performed in P1, so space group ambiguities, which are common with powder diffraction data, are irrelevant, (2) no chemical information such as bond distances, bond angles, or connectivity are required, so there is no danger of making incorrect assumptions about the structure, (3) it is equally effective for both organic and inorganic structures, and (4) it is fast, requiring only seconds to minutes per run.

The maximum-entropy method in superspace

One of the applications of the maximum-entropy method (MEM) in crystallography is the reconstruction of the electron density from phased structure factors. Here the application of the MEM to incommensurately modulated crystals and incommensurate composite crystals is considered. The MEM is computed directly in superspace, where the electron density in the (3+d)-dimensional unit cell (d > 0) is determined from the scattering data of aperiodic crystals. Periodic crystals (d = 0) are treated as a special case of the general formalism. The use of symmetry in the MEM is discussed and an efficient algorithm is proposed for handling crystal symmetry. The method has been implemented into a computer program BayMEM and applications are presented to the electron density of the periodic crystal NaV(2)O(5) and the electron density of the incommensurate composite crystal (LaS)(1.14)NbS(2). The MEM in superspace is shown to provide a model-independent estimate of the shapes of the modulation functions of incommensurate crystals. The discrete character of the electron density is found to be the major source of error, limiting the accuracy of the reconstructed modulation functions to approximately 10% of the sizes of the pixels. MaxEnt optimization using the Cambridge and Sakata-Sato algorithms are compared. The Cambridge algorithm is found to perform better than the Sakata-Sato algorithm, being faster, always reaching convergence, and leading to more reliable density maps. Nevertheless, the Sakata-Sato algorithm leads to similar density maps, even in cases where it does not reach complete convergence.

Ab initio determination of incommensurately modulated structures by charge flipping in superspace.

The charge flipping algorithm proposed by Oszlányi & Suto [Acta Cryst. (2004), A60, 134-141] for ab initio reconstruction of crystal structures is generalized towards superspace. Its efficiency is demonstrated by successful reconstruction of eight known incommensurately modulated structures from experimental data. The output of the charge flipping algorithm is an electron density with symmetry P1. The symmetry of the structure is recovered by locating the positions of symmetry operators and averaging the density over the symmetry-related pixels. The reconstruction of a modulated structure by the charge flipping algorithm and the accuracy of the result is demonstrated in detail on the modulated structure of tetraphenylphosphonium hexabromotellurate(IV) bis[dibromoselenate(I)].

Unraveling the Perplexing Structure of the Zeolite SSZ-57

X-ray analysis reveals a zeolite structure in which 10-sided channels are periodically disrupted by 12-sided channels. Previous high-resolution x-ray powder diffraction and transmission electron microscopy studies of the zeolite SSZ-57 could not fully elucidate the structural basis for its puzzling adsorption behavior, which appears to be intermediate between that of a medium- (10-ring) and a large-pore (12-ring) zeolite. Now by applying advanced crystallographic techniques (structure solution in four-dimensional space and interpretation of three-dimensional diffuse scattering by Monte Carlo simulation) and crystal chemistry considerations to high-quality single-crystal x-ray diffraction data collected on a microcrystal (about 2 micrometers by 2 micrometers by 8 micrometers), we have been able to derive a comprehensive description of its silicate framework structure. The framework is related to that of ZSM-11 but is commensurately modulated along the c axis (P4¯m2, a = b = 20.091 Å, c = 110.056 Å) to yield a structure with a 12-ring:10-ring ratio of 1:15. Disorder of the 12-rings results in a three-dimensional 10-ring channel system with large isolated pockets. The structure helps to clarify the material’s catalytic activity.

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.

Structure refinement using precession electron diffraction tomography and dynamical diffraction: theory and implementation.

Accurate structure refinement from electron-diffraction data is not possible without taking the dynamical-diffraction effects into account. A complete three-dimensional model of the structure can be obtained only from a sufficiently complete three-dimensional data set. In this work a method is presented for crystal structure refinement from the data obtained by electron diffraction tomography, possibly combined with precession electron diffraction. The principle of the method is identical to that used in X-ray crystallography: data are collected in a series of small tilt steps around a rotation axis, then intensities are integrated and the structure is optimized by least-squares refinement against the integrated intensities. In the dynamical theory of diffraction, the reflection intensities exhibit a complicated relationship to the orientation and thickness of the crystal as well as to structure factors of other reflections. This complication requires the introduction of several special parameters in the procedure. The method was implemented in the freely available crystallographic computing system Jana2006.