Single crystals electron density determination

Dijfraction by single crystals electron density determination... 

X-Ray diffraction from single crystals is the most direct and powerful experimental tool available to determine molecular structures and intermolecular interactions at atomic resolution. Monochromatic CuKa radiation of wavelength (X) 1.5418 A is commonly used to collect the X-ray intensities diffracted by the electrons in the crystal. The structure amplitudes, whose squares are the intensities of the reflections, coupled with their appropriate phases, are the basic ingredients to locate atomic positions. Because phases cannot be experimentally recorded, the phase problem has to be resolved by one of the well-known techniques the heavy-atom method, the direct method, anomalous dispersion, and isomorphous replacement.1 Once approximate phases of some strong reflections are obtained, the electron-density maps computed by Fourier summation, which requires both amplitudes and phases, lead to a partial solution of the crystal structure. Phases based on this initial structure can be used to include previously omitted reflections so that in a couple of trials, the entire structure is traced at a high resolution. Difference Fourier maps at this stage are helpful to locate ions and solvent molecules. Subsequent refinement of the crystal structure by well-known least-squares methods ensures reliable atomic coordinates and thermal parameters. 

The crystallinity of organic pigment powders makes X-ray diffraction analysis the single most important technique to determine crystal modifications. The reflexions that are recorded at various angles from the direction of the incident beam are a function of the unit cell dimensions and are expected to reflect the symmetry and the geometry of the crystal lattice. The intensity of the reflected beam, on the other hand, is largely controlled by the content of the unit cell in other words, since it is indicative of the structural amplitudes and parameters and the electron density distribution, it provides the basis for true structural determination [32],... 

EDSA of thin polycrystalline films has several advantages First of all the availability of a wide beam (100-400 pm in diameter) which irradiates a large area with a large amount of micro-crystals of different orientations [1, 2]. This results into a special t5q)e of diffraction patterns (DP) (see Fig.l). Thus it is possible to extract from a single DP a full 3D data set of structure amplitudes. That allows one to perform a detailed structure analysis with good resolution for determining structure parameters, reconstruction of ESP and electron density. 

At —30°C in THF, in the presence of anthracene a single-electron transfer from 118 to anthracene occurs, with the formation of insoluble (Ci4Hio)2Mg(THF)6 (equation 12) . A further reaction with MgCl2 affords the radical anion complex [Mg2Cl3(THF)6] [CiaHio] " (119). An X-ray crystal-structure determination of 119 clearly shows the presence of anthracene radical anions as distinct species in the crystal lattice (Figure 58) . The bond lengths and the deformation of the electron density of the anthracene radical anion clearly show that in 119 the LUMO is occupied by one electron . 

In Bragg s way of looking at diffraction as reflection from sets of planes in the crystal, each set of parallel planes described here (as well as each additional set of planes interleaved between these sets) is treated as an independent diffractor and produces a single reflection. This model is useful for determining the geometry of data collection. Later, when I discuss structure determination, I will consider another model in which each atom or each small volume element of electron density is treated as an independent diffractor, represented by one term in a Fourier series that describes each reflection. Bragg s model tells us where to look for the data. The Fourier series model tells us what the data has to say about molecular structure. 

Characterization of the Surfaces of Catalysts Measurements of the Density of Surface Faces for High Surface Area Supports. - It has always been a tenet of theories of catalysis that certain reactions will proceed at different rates on different surface planes of the same crystal. Experiments with metal single crystals have vindicated this view by showing that the rate of hydrogenolysis of ethane on a nickel surface will vary from one plane to another. In contrast the rate of methanation remains constant for the same planes.4 Because of this structure sensitivity of catalytic processes there is a requirement for methods of determining the number of each of the different planes which a catalyst and its support may expose at their surfaces. Electron microscopy studies of 5nm Pt particles supported upon graphite show them to be cubo-octahedra with surfaces bound by (111) and (100) planes.5 Similar studies of Pd and Pt prepared by evaporation reveal square pyramids of size 60-200 A bounded by incomplete (111) faces.6... 

G.J.H. Vannes, A. Vos, Single-crystal structures and electron density distributions of ethane, ethylene and acetylene. I. Single-crystal X-ray structure determinations of two modifications of ethane. Acta Cryst. B 34, 1947-1956 (1978)... 

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