A multisolution method of phase determination by combined maximization of entropy and likelihood. II. Application to small molecules

Optimizing the input parameters for powder charge flipping

Over the past few years, the powder charge-flipping algorithm has proved to be a useful one for structure solution from powder diffraction data, so a semi-systematic study of the effect of the different input parameters on its success has been performed. Two data sets were studied in these tests: a zirconium phosphate framework material and D-ribose. TheSuperflipinput parameters tested were the reflection overlap factor, the intensity repartitioning frequency, the isotropic displacement parameter, the threshold for charge flipping and the number of cycles/runs. By varying the values of these parameters within sensible ranges, an optimized set could be found for the zirconium phosphate case, but no combination of parameters allowed the D-ribose structure to be solved. Reasoning that starting with nonrandom phases might help, an approximate (but incorrect) structure was generated using the direct-space global-optimization method implemented in the programFOX. This structure was then used to calculate initial phase sets forSuperflipby allowing the calculated phases to vary in a random fashion by a user-defined percentage. With such phases and reoptimized input parameters, some fully interpretable solutions with the correct symmetry could be produced, even with fairly low resolution data. Unfortunately, it was not possible to recognize these solutions using theSuperflip Rvalues, so other criteria were sought. Both cluster analyses and maximum entropy calculations of the solutions were performed, and the latter, in particular, look very promising. A set of guidelines derived from these two structures could be applied successfully to a further two inorganic and seven organic structures.

Electron Crystallography of Phthalocyanines

It is shown that it is possible to obtain structural information from small (<100 nm) phthalocyanine crystals by using crystallographic direct phasing methods applied to electron diffraction data. This technique is both quantitative and does not suffer from the difficulties associated with high-resolution electron microscopy. Structural information has been obtained from both tetra- and octa chloro-copper phthalocyanines, and the results compared with the hydrogenated and perchloro members of the series.

Electron crystallography of MWW zeolites – filling the missing cone

Given that many zeolites crystallize in habits that lead to preferred orientation, and that there is a ±60° tilt limitation in many electron microscope goniometer stages, collection of a three 3-D electron diffraction data set from these materials is severely restricted. To overcome this, preparative measures must be taken to produce other sample orientations. Using a number of MWW framework zeolites (MCM-22, MCM-22P, MCM-49, ITQ-1) as examples, thin-sectioned views onto the edge stacking of lamellar layers can be prepared by a number of methods. While ultamicrotomy is a traditional approach to this problem, sections are often very thick and sparsely distributed. Other extreme mechanical processing techniques, such as extrusion and jet milling produce numerous thin crystals with the desired orientation. Dealumination, initiated by steaming, calcination or low pH, also yields a similar result. Additional intensity data from the ‘missing cone’ in addition to those obtained by tilting hexagonal plate crystals provides a more complete data set and hence a more easily interpreted structure analysis. Crystallographic phase determination by maximum entropy and likelihood, followed by Fourier refinement, yields a structural model very close to that of the known MWW framework.

Electron crystallography of aluminum alloy phases

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.

Electron crystallography on polymorphic organics

Organic materials, such as non-linear optical active compounds (1-(2-furyl)-3-(4-aminophenyl)-2-propene-1-one (FBAPPO) and 1-(2-furyl)-3-(4-benzamidophenyl)-2-propene-1-one (FAPPO)), polymeric materials like the metal coordinated polyelectrolyte (Fe(II) [ditopic bis-terpyridin] (MEPE)) or polymorphic materials (e.g. Cu-phthalocyanine), which do not crystallize big enough for single crystal x-ray structure analysis have been investigated by electron diffraction (ED) at 100 and 300 kV acceleration voltage. Sample preparation (direct crystallization, ultra sonication, ultra microtomy), diffraction strategies (selected area diffraction, nano diffraction, use of double-tilt rotation holder), data collection and data processing as well as structure solution strategies have been chosen dependent on the different requirements of the compounds under investigation. Structure analysis was carried out by simulation using ab initio quantum-mechanical methods like density functional theory (DFT), semi-empirical approach (MNDO/AM1/PM3) and force field packing energy calculations (DREIDING). The structure models resulting from simulation were refined kinematically as rigid bodies. Subsequently, refinements by multi-slice least squares (MSLS) procedures taking dynamical scattering into account were performed. The described combination of different methods which was used successfully on crystallizable materials is also adaptable to insoluble organic materials (e.g. pigments) and polymorphic systems.

Electron crystallography: imaging and single-crystal diffraction from powders

The study of crystals at atomic level by electrons – electron crystallography – is an important complement to X-ray crystallography. There are two main advantages of structure determinations by electron crystallography compared to X-ray diffraction: (i) crystals millions of times smaller than those needed for X-ray diffraction can be studied and (ii) the phases of the crystallographic structure factors, which are lost in X-ray diffraction, are present in transmission-electron-microscopy (TEM) images. In this paper, some recent developments of electron crystallography and its applications, mainly on inorganic crystals, are shown. Crystal structures can be solved to atomic resolution in two dimensions as well as in three dimensions from both TEM images and electron diffraction. Different techniques developed for electron crystallography, including three-dimensional reconstruction, the electron precession technique and ultrafast electron crystallography, are reviewed. Examples of electron-crystallography applications are given. There is in principle no limitation to the complexity of the structures that can be solved by electron crystallography.

Electron crystallography of organic materials

The application of electron crystallography to the study of organic materials is reviewed, mainly in context of the author's own experience. Direct methods for crystallographic phase determination have been shown to be very effective for ab initio structure analyses with electron diffraction intensities, permitting the elucidation of previously uncharacterized crystal structures. Fruitful applications areas have included chain-folded linear polymers, pigments, polydisperse linear chain arrays and, surprisingly, the subgroup assembly of certain proteins.

Comparison of electron diffraction data from non-linear optically active organic DMABC crystals obtained at 100 and 300 kV

During the recent past, we have synthesized a new class of molecules with intramolecular two-dimensional charge transfer upon excitation. The present report presents such a molecule, 2,6-bis(4-dimethylamino-benzylidene)-cyclohexanone (DMABC), with an unusually high value of the second-order non-linear optical (NLO) coefficients. In order to optimize the macroscopic NLO properties of the compounds, it is necessary to relate their first hyperpolarizability tensors at a molecular level to those at a crystal bulk level. This requires a complete structure determination and refinement. However, the growth of sufficiently large single crystals, which are needed for structural analysis and refinement by X-ray methods, is a time consuming and sometimes impossible task. We have performed a complete structural analysis by electron diffraction combined with simulation methods and with maximum entropy and log likelihood statistics. In order to improve the quantitative analysis, a 300 kV data set using an on-line CCD camera was added and the best attainable R-values were compared with those from 100 kV data using film emulsions. Details regarding the maximum attainable resolution for both data sets are discussed as well as the problems which arise from the limited dynamic range in photographic emulsions as compared to a 14 bit CCD camera. Once the crystal structure was known, quantum-chemical methods were used to calculate non-linear optical susceptibility tensor components and these were related to the macroscopic coefficients of the crystalline quadratic non-linearity tensor. In the present work, both ab initio and semi-empirical quantum-chemical calculations were employed.

Electron crystallography in surface structure analysis

Surface structure analysis is an important area of research, and in recent years notable advances have been made in this field, both in improved techniques for studying surfaces and in methods of analyzing them. This review aims to summarize the techniques available, particularly those relating to electron microscopy, and also to outline one of the newest areas of development, the application of direct methods to surface structure analysis.

Electron crystallography and non-linear optics

Electron crystallography can be used to obtain specific information about molecular parameters such as the polarisability, dipole moment, and hyperpolarisability. In this, work we show how a combination of quantum mechanics and simulation methods can be used to solve several unknown organic structures and how the calculated molecular parameters can be used to predict the corresponding physical properties of the crystals.

Maximum entropy methods in electron crystallography

The maximum entropy (ME) method of solving crystal structures in two or three dimensions from electron diffraction data is described. Applications to organic and inorganic molecules, membrane proteins and surface structures are outlined, and the power of the ME formalism to deal with incomplete and error prone data is demonstrated.

Applications of the maximum entropy method to powder diffraction and electron crystallography

A new multisolution phasing method based on entropy maximization and likelihood ranking, proposed for the specific purpose of increasing the accuracy and sensitivity of probabilistic phase indications compared with conventional direct methods, has been implemented and applied to a wide variety of problems. The latter comprise the determination of small crystal structures from X-ray diffraction data obtained from single crystals or from powders, and from electron diffraction data, both with and without partial phase information obtained by image processing of electron micrographs; the ranking of phase sets for a small protein; and the improvement of poor quality phases for a larger protein at medium resolution under constraint of solvent flatness. The main components of the method are (1) a tree-directed search through a space of trial phase sets; (2) the saddlepoint method for calculating joint probabilities of structure factors, using entropy maximization; (3) likelihood-based scores to rank trial phase sets and prune the search tree; (4) a statistical analysis of the scores for automatically selecting reliable phase indications. Their use is illustrated here on structure determinations from powder X-ray diffraction data and from electron diffraction data.

Computational challenges for macromolecular structure determination by X-ray crystallography and solution NMR-spectroscopy

Macromolecular structure determination by X-ray crystallography and solution NMR spectroscopy has experienced unprecedented growth during the past decade.