Fourier map

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. [Pg.312]

We originally proposed NNM to be present in metallic beryllium [30] based on analysis of the X-ray diffraction data measured by Larsen and Hansen [24], Based on Fourier maps and elaborate multipole least-squares modeling, indisputable evidence... [Pg.40]

With data averaged in point group m, the first refinements were carried out to estimate the atomic coordinates and anisotropic thermal motion parameters IP s. We have started with the atomic coordinates and equivalent isotropic thermal parameters of Joswig et al. [14] determined by neutron diffraction at room temperature. The high order X-ray data (0.9 < s < 1.28A-1) were used in this case in order not to alter these parameters by the valence electron density contributing to low order structure factors. Hydrogen atoms of the water molecules were refined isotropically with all data and the distance O-H were kept fixed at 0.95 A until the end of the multipolar refinement. The inspection of the residual Fourier maps has revealed anharmonic thermal motion features around the Ca2+ cation. Therefore, the coefficients up to order 6 of the Gram-Charlier expansion [15] were refined for the calcium cation in the scolecite. [Pg.300]

The location of the hydrogen atoms in hydrogen bonded systems is often difficult to ascertain. When X-ray diffraction is used there is an experimental limitation to face, as it is usually difficult to locate the very light H-atom in Fourier maps and, even when this is possible, the technique can provide information on electron density centroids rather than on the position of the light nucleus. Neutron diffraction is required for an unambiguous location of the H-atom. In ionic hydrogen bonds the situation may occur where a knowledge of the proton position in a donor-acceptor system is necessary to know whether proton transfer, i.e. protonation of a suitable base, has occurred or not. [Pg.32]

In neutron diffraction studies, the Fourier map does not show significant negative scattering density around the terminal Au-oxo oxygen 035, a result similar to the previous neutron diffraction on the terminal Pt-oxo complex 1, thus ruling out the possibility that a... [Pg.257]

About 1915 W.H. Bragg suggested to use Fourier series to describe the arrangement of the atoms in a crystal [1]. The proposed technique was somewhat later extended by W. Duane [2] and W.H. Zachariasen was the first who used a two-dimensional Fourier map in 1929 for structure determination [3], Since then Fourier synthesis became a standard method in almost in every structure determination from diffraction data. [Pg.235]

Figure 5. Changing the sign of the amplitude from minus to plus causes a phase shift of 180° in the Fourier map. Every cosine wave with a positive amplitude starts at the origin of the unit cell with a maximum (high potential) cosine waves with negative amplitudes on the other hand produce low (zero) potential at the origin.

When the 4 strongest independent reflections (in total 6 reflections including symmetry-related ones) are added, the map already shows some indication of where the atoms should be located within the unit cell (Fig. Ig). After the strongest 1/3 (11) of all the independent reflections has been included, all the atoms appear in the map (as white dots) (Fig. Ih). The map generated from all the 33 unique reflections (Fig. li) is only slightly better, because the 22 reflections further added in are weaker and so do not contribute very much to the Fourier map. The weak reflections are, however, equally important as the strong ones in the last step of a structure determination, the refinement. [Pg.281]

Usually several figures of merit are calculated for a given phase set and these are combined to given an overall figure called a CFOM, the solution(s) with the best CFOM are selected and used to compute a Fourier map. [Pg.326]

Although low-resolution difference Fourier maps for oxy-Hr and deoxy-Hr show little change in the protein structures, some of the iron center properties are significantly altered in deoxy-Hr. The differences provide a rationale for an oxygen-binding mechanism. The Mossbauer spectrum for deoxy-Hr has a single quadrupole doublet with an isomeric shift typical of high-spin ferrous iron (8 = 1.14 mm/sec AEq = 2.76 mm/sec) (Clark and Webb, 1981). As for met-Hr the two iron environments are similar, yet differ in coordination number for exam-... [Pg.242]

Fig. 9a and b. Difference Fourier maps calculated from Laue diffraction data showing maltoheptose bound in phosphorylase b. The Laue map shown in a is calculated with a subset of 9029 unique data at 2.5 A resolution. A positive contour at half maximal peak height is shown, b is an enlargement of a and shows 4 of the 7 sugar units, the 3 central units have the highest occupancies. Side chain movements produce the two extra lobes of density. (Figures courtesy of J. Hajdu)... [Pg.48]

The percarboxylic acid proton of 3-oxo-l,2-benzisothiazole-2(377)-peroxypropanoic acid 1,1-dioxide (51) (Pnma, 0—0 = 1.469, C—O—O—H = 180.0°) was located on the difference Fourier map . Hydrogen bonding in the peracid 51 (Figure 22) occurs from the peracid proton to the carbonyl O of the saccharin entity (O O = 2.618 A) to provide chains of peracid molecules that are stacked via additional C—H O contacts (not shown in Figure 22) in sheets along the b axis. [Pg.126]

The resulting compounds were evaluated by determination of their IC50 values (the inhibitor concentration causing 50% inhibition of PNP) and by x-ray diffraction analysis using difference Fourier maps. This iterative strategy—modeling, synthesis, and structural analysis—led us to a number of highly potent compounds that tested well in whole cells and in animals. [Pg.154]

Crystallographic analysis was based primarily on the results of difference Fourier maps in which the interactions between residues in the active site and the inhibitor could be characterized. During these studies, about 35 inhibitor complexes were evaluated by x-ray crystallographic techniques. It is noteworthy that the resolution of the PNP model extends to only 2.8 A and that all of the difference Fourier maps were calculated at 3.2 A resolution, much lower than often considered essential for drug design. Crystallographic analysis was facilitated by the large solvent content that allowed for free diffusion of inhibitors into enzymatically active crystals. [Pg.166]

For trypanosomal TIM we experimented with three different cocktails of 32 compounds (Table 4). Molecules were chosen in such a way that they would be compatible, soluble, cheap, and as varied as possible. Each compound was present at a concentration of 1 m M The final cocktail solutions were clear and devoid of precipitate. Since this was a pilot experiment both subcocktails were checked at each stage of the dichotomic strategy. Only the soak with cocktail 1 revealed electron density that could not be accounted for by water molecules, hereafter called peak X. The soaks with cocktails 2 and 3 led to featureless difference Fourier maps. The quality of the data and refinement can be inspected from Table 5, while Figure 9 illustrates the dichotomic search to identify peak X. An oxidized molecule of DTT, identified in the high-resolution structure of the native TIM crystals [24], served as an internal reference to judge the quality of the data and the noise level in the final difference Fourier maps. [Pg.379]

As a result of the recognized role of transition metal hydrides as l reactive intermediates or catalysts in a broad spectrum of chemical reactions such as hydroformylation, olefin isomerization, and hydrogenation, transition metal hydride chemistry has developed rapidly in the past decade (J). Despite the increased interest in this area, detailed structural information about the nature of hydrogen bonding to transition metals has been rather limited. This paucity of information primarily arises since, until recently, x-ray diffraction has been used mainly to determine hydrogen positions either indirectly from stereochemical considerations of the ligand disposition about the metals or directly from weak peaks of electron density in difference Fourier maps. The inherent limi-... [Pg.18]

Normally, if the assumed model for a crystal structure has an R value of 0.5 and resists attempts to refine to a lower residual, then the model structure is rejected as false, and a new model is tried until a fit between the observed and calculated structure factors yields an acceptable residual (R < 0.25). (Other models were tried for this complex, but they either gave Fourier maps which were uninterpretable or they converged to the present model). However, the normal crystal structure is solved with data obtained from crystals which have dimensions of the order of 0.1 mm. In the crystals available for this experiment, two of the dimensions were of the order of 0.01 mm. Thus, long exposures were required to give a small number of relatively weak diffraction spots. (Each Weissenberg photograph was exposed for five days with Cuka radiation 50 kv., 20 ma. loading, in a helium atmosphere). [Pg.257]

The Fourier maps in Figure 9 tend to indicate that the caffeine and pyrogallol molecules are roughly parallel to the x,y plane and separated from each other by half of a unit cell in the z direction which amounts to approximately 3.5 A. The closest approach between these two molecules occurs between the nitrogen atom labeled 3 (Table II) in the caffeine... [Pg.258]

The difference Fourier map shows a peak at x = y = z = 0.17 which may correspond to water molecules. Including these species in the refinement slightly decreased R, but the relevant population was not significant. [Pg.75]

SII water molecules detected on the difference Fourier map. Therefore, their coordination would be similar to that of the partially hydrated Ni2+ ions observed on SI (0.08) sites in Ni faujasite (9) and NiY zeolite (5). [Pg.78]

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