Fourier difference map

The procedure is called hybrid electronic maps (or the over-fit ) method. Figure 5.23, and can be obtained, for example, by non-refining (i.e., non-minimizing) completely the D factor of (5.60), so generating a structure such as Eq. (5.61), yet unrefined, therefore being called as the structure by omission, this is compared (by superimposing) with the density difference (or synthesis of the Fourier maps differences)... 

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. 

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-... 

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)... 

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. 

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. 

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. 

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. 

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-... 

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. 

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). 

P(3) bond distance. The largest residual electron-density peak in the final difference Fourier map is at that position and a hydrogen atom H(l) can be placed there with some confidence. 

The utility of La Placa s and Ibers technique is illustrated in the structure determination of H3Mn3(CO)i2 18) (Fig. 2). In this compound, the H atoms are suspected to lie in bridging positions in the equatorial plane. A conventional difference-Fourier map of this plane (Fig. 3a) shows a number of potential hydrogen peaks surrounded... 

Although the La Placa/Ibers procedure has been criticized 19 subsequent experiments have shown that it is effective in many instances. One should not expect it to work every time, but it does seem to improve significantly one s chances of finding H atoms, and it is a useful technique for distinguishing noise from true H peaks. In a recent publication, Dapporto and co-workers 2°1 have pointed out that Fourier maps (as opposed to the conventionally-used difference Fourier maps) can sometimes be more useful in revealing H positions, especially if the space group is centrosymmet-ric. 

Often, H coordinates determined from a difference-Fourier map are difficult to refine in the subsequent least-squares process. In our experience, the success or failure in the refinement can sometimes be critically dependent on the particular choice of variables in the cycles immediately following the introduction of the H positions 18L... 

Although the direct location of H atoms from X-ray data is often possible, success is notoriously unpredictable. In some cases H atom positions will be readily apparent from difference-Fourier maps, while in other cases one has to apply the tricks mentioned in this section to ferret them out. A good R index does not necessarily guarantee that the search for H atoms will be successful conversely, structures with less impressive R indices will sometimes produce acceptable H positions6). Then there is the problem that H coordinates do not always converge during least-squares refinement. Even when they do, there is no guarantee that the refined positional parameters will be any better than the raw peak positions obtained from... 

Fig. 5. Difference-Fourier maps corresponding to the six non-crystallographic mirror planes of the Re4 tetrahedron. In each section, the two dots on the left represent Re atoms, the dot in the center represents the centroid of the tetrahedron, and the dot on the right corresponds to the mid-point of a Re-Re bond...

Lastly, it should be pointed out that there are often significant differences between H positions determined by X-ray analysis and those determined from neutron data. Neutron diffraction provides true nuclear positions, whereas X-ray diffraction measures the electron density distribution. Thus, X-ray Fourier maps often give H peaks that, because of the perturbing influence of the M-H bonding electrons, appear closer to the M atoms than they really are A thorough analysis of this effect has... 

The unsaturated (56e ) molecule H4Re4(CO)i2 12) (Fig. 2) was discussed earlier in connection with methods of locating H atoms with X-ray data (Sect. A. II.). A symmetry-averaged H position was located from a composite difference Fourier map (Fig. 6), which corresponds to an unrefined Re-H distance of 1.77 A. This distance is, as is the case with most M-H bond lengths derived from X-ray data, probably 0.1—0.2 A shorter than its true value. 

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