Refinement heavy atom positions

The goodness of fit achieved in a refinement is defined by Eq. (4.27). Its evaluation for each of the subsets of data requires partitioning the unknowns between the two sets. Some, such as the scale factors, will be dependent on one subset only other, such as heavy-atom positional parameters, will be determined by both sets of data. Information on the relative dependency is contained in the matrix B, the elements of which are the sums of the contributions from the X-ray and neutron observations. We may write... 

You can see that as the number of real atoms increases, the number of Patterson atoms, and with it the difficulty of this problem, increases rapidly. Computer programs can search for solutions to such problems and, upon finding a solution, can refine the atom positions to give the most likely arrangement of heavy atoms. 

Refine the heavy-atom positions by difference Fourier maps. 

When we analyze the list of residual electron density peaks in the file zr5-08.res, the final model of this refinement, we find that Q( 1) and Q(2) are significantly higher than all the other maxima. Q(l) corresponds to 1.38 electrons and is located 0.66 A away from Zr( 1), not far from the location of the deepest hole. This could be an artefact arising from Fourier truncation, but absorption effects can also lead to spurious electron density close to heavy atom positions. It is difficult to decide which of the two effects holds responsibility for Q(l), but it is clear that we cannot do anything about it. Q(2) represents 1.13 electrons and sits on the crystallographic fourfold. It... 

In (CgHg ) P-Au-Mn(CO)g there is an approximately linear bond system P-Au-Mn, This is the normal stereochemical form that would be expected for an Au(I) atom forming two bonds. Considerable difficultly arose in the structure determination. The crystal is non-centrosymmetric and, as a further complication, contains two crystallographically different molecules with a pseudosymmetry of the heavy atom positions higher than that of the space-group. In this situation the common methods of crystal structure refinement are severely hampered. Nevertheless all atoms have been located. The distance Au-P may be used to get, by difference, a covalent radius applicable to the gold atom and hence, from the Au-Mn distance, a radius for Mn is found, A more suitable compound is the variant... 

JT-Ray studies on the F a fragnients prepared by papain and pepsin fragmentation of human myeloma IgG immunoglobulins are being carried out by Poljak et /. The preparation of heavy-atom derivatives has involved considerable difficulties. A 6A electron-density map has been computed, which shows two clear domains (unpublished work) and is clearly of good quality. The data have been collected to 3.S A resolution, refinement of the heavy-atom positions of the derivatives has been completed, and an electron-density map computed. 

The uranyl heavy atom parameters were then used to calculate Fj and Fj two sets of phases for the protein were calculated - one for each possible heavy atom enantiomorph - by the method of single isomorphous replacement with the inclusion of anomalous scattering data. The value of E" was initially calculated from the r.m.s. error in the least squares refinement for the centric zone, and E" was made equal to E/3. The phases, were used to compute difference Fouriers with coefficients (Fp - Fp exp.iap for the other derivatives. The phases calculated from uranyl positions gave a clear indication of the heavy atom positions of other derivatives which agreed well with those positions determined from the Patterson functions. The enantiomorphic set of uranyl positions gave no clear indication of the heavy atom positions. Thus, the correct enantio-morphs and relative origins for derivatives were established. We then carried out a series of phase refinement cycles (16,17). 

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. 

Determination of Structure. Analysis of a Patterson map indicated two sets of heavy atoms in genera) positions, a result incompatible with the preconceived opinion of the composition of the materia). For this reason the subsequent analysis was carried out using the diffraction data to establish the composition. The peaks for the heavy atoms were of appropriate relative height to correspond to Xe and As, and other peaks were found which corresponded to six F atoms around the As atom. Fourier maps phased with these eight atoms revealed the seventh fluorine atom. Another smaller peak was tested as a possible fluorine atom, but it was rejected by the least-squares refinement. A later electron density map, prior to the absorption correction and with R - = O.IO, showed no other peaks... 

Since the intensities of the standards were observed to diminish (finally to 85% of their original values) in a regular and nearly isotropic manner, the data were scaled linearly between each pair of standards. Associated with this decrease we also noted a decrease in the parameters b and y (which were in the end reduced by 0.02 A and 0.21 from their initial values). Broadening of the scans of file standards from 0.10 to 0.35 was also observed. The positions of the heavy atoms were determined from a three-dimensional Patterson synthesis. These positions were subjected to least-squares refinement as xenon atoms, after which it was possible to separate the antimony atoms by exploiting temperature factor differences. The positions were then further refined. A difference Fourier revealed positions for 12 of the 14 fluorine atoms. Least-.squares refinement of these positions was followed by another difference Fourier which revealed the positions of the final two fluorine atoms. Refinement of all these positions, with anisotropic temperature factors, resulted in a conventional/ factor of 0.06. Wei ting sch es were as previously described. ... 

The structure was solved by heavy-atom methods at the U.C. Berkeley CHEXRaY facility using full-matrix least-squares refinement procedures detailed elsewhere. Systematically absent reflections were eliminated from the data set, and those remaining were corrected for absorption by means of the calculated absorption coefficient. A three-dimensional Patterson synthesis gave peaks that were consistent with Xe atoms in Wyckoff position 4c and Ge atoms in 4a in space group Pnmb (see Pnma, No. 62). Three cycles of... 

The positional parameters of the heavy atoms provided by DM are submitted to automatic Rietveld refinement to improve their accuracy. The distances between the heavy atoms are analyzed to derive (or confirm) the cation connectivity (tetrahedral or octahedral). Let us suppose that two cations, say Cl and C2 (see Figure 8.10), have been located. The bridge anion Al, bonding Cl to C2, is expected to lie on the circle intersection of the two coordination spheres, centred in Cl and C2. A random point on the circle is chosen as a trial location of Al it is a feasible atomic position. The positions of the other anions A2, A3, A4 may be (randomly) fixed by a random rotation of the Cl polyhedron about the... 

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