Heavy-atom structures

Based upon the results described in the previous section, we define a scaling fector pg for each of the fiuee (maximiun) principal axes by 

Note that [I g ]j is an exact Watson as can be seen from Eqs. (42), 

Overall, the r distances are within 0.001 A of rg except for one case in which the difference is 0.0011 A. For the nine distance parameters of Table 15, the average 1 r - rg deviation is 0.0006 A. 

TABLE 15. structures for some heavy-atom linear molecules.  

0015 A (compared to the r deviation of0.00016 A). ForN20, the small coordinate of the cental nitrogen leads to a terrible pure r structure. If the usual expedient of recomputing the central nitrogen 

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So the disparity between intensities of Friedel pairs in the anomalous scattering data set establishes their phases in the nonanomalous scattering data set. The reflection whose phase has been established here corresponds to the vector Fhp in Eq. (6.9). Thus the amplitudes and phases of two of the three vectors in the Eq. (6.9) are known (l)FHp is known from the anomalous scattering computation just shown, and (2) FH is known from calculating the heavy-atom structure factors after locating the heavy atom by Patterson methods. The vector Fp, then, is simply the vector difference establish-... 

Figure 7. A vector diagram illustrating the effects of heavy atom anomalous scattering on the reflections hkl (denoted +) and filci (denoted —). Fpn is the average structure factor amplitude for the heavy atom derivative of the protein. FJ Ih imaginary part of the heavy atom structure factor amplitude which arises from anomalous scattering. Because FJl always advances the phase by fI/2, FpH (+) and Fpn (—) are no longer equal. The measured difference between these amplitudes can be used fbr phase determination.

Figure 13 Heavy-atom structure of [BioHi2lnMe2]", (Numbered as for B,oHi4 ...

Heavy atom derivatives of a macromolecular crystal can be prepared (Green, Ingram and Perutz 1954) which for a minimum of two derivatives (and the native crystal) and in the absence of errors, leads to a unique determination of the phase ahkt in equation (2.7) (figure 2.13(a)). This requires the site and occupancy of the heavy atom to be known for the calculation of the vector FH (the heavy atom structure factor). In the absence of any starting phase information the heavy atom is located using an isomorphous difference Patterson synthesis P(u,v,w) where the isomorphous difference is given by... 

Ring expansion is a common result of the reactions of cyclopolyphosphines and arsines with metal carbonyls e.g., Mo(CO)g combines with either cyclo-(MeP)5 or cyclo-(PhAs)g to form [Mo(CO)3]2[>/ , /<-cyclo-(RE)9] whose heavy-atom structure is that of trishomocubane, CnHi4, the same structure as found in and... 

Figure 6.7 Harker Construction Solution of the X-ray crystallographic phase problem for each hkt-reflection by Harker construction. Heavy atom structure factor F (hkl) is completely solved by Patterson Function and plotted on complex plane (white) along with known modulus FBH(hkl). The second known modulus Fb(AW) is then included on a second complex plane yellow. Intersection points characterise the two possible solutions for Fi hkl) and two possible solutions for cni hkl) or ccp ), one of which is usually eliminated by inspection or with the aid of a second heavy atom derivative.

Special difficulties arise when the heavy-atom structure, taken separately, contains one more symmetry element (usually a center of symmetry) than the overall structure. The first Fourier synthesis of the electron density then shows two light-atom structures along with the heavy-atom structure. In order to calculate the second Fourier. synthesis, the heavy-atom structure is then used together with only that part of the light-atom structure that can be assigned with high confidence to just one of the two light-atom structures indicated in the Fourier synthesis. The additional symmetry element vanishes in the next Fourier synthesis, and the structure analysis proceeds in the usual way. 

Referring to figure Bl.8.5 the radii of the tliree circles are the magnitudes of the observed structure amplitudes of a reflection from the native protein, and of the same reflection from two heavy-atom derivatives, dl and d2- We assume that we have been able to detemiine the heavy-atom positions in the derivatives and hl and h2 are the calculated heavy-atom contributions to the structure amplitudes of the derivatives. The centres of the derivative circles are at points - hl and - h2 in the complex plane, and the three circles intersect at one point, which is therefore the complex value of The phases for as many reflections as possible can then be... 

MIR), requires the introduction of new x-ray scatterers into the unit cell of the crystal. These additions should be heavy atoms (so that they make a significant contribution to the diffraction pattern) there should not be too many of them (so that their positions can be located) and they should not change the structure of the molecule or of the crystal cell—in other words, the crystals should be isomorphous. In practice, isomorphous replacement is usually done by diffusing different heavy-metal complexes into the channels of preformed protein crystals. With luck the protein molecules expose side chains in these solvent channels, such as SH groups, that are able to bind heavy metals. It is also possible to replace endogenous light metals in metal-loproteins with heavier ones, e.g., zinc by mercury or calcium by samarium. 

Structure 1 is clearly tending toward cis hydroxycarbene. The other endpoint exhibits quite large bond distances between both hydrogens and the associated heavy atom. The hydrogens themselves are close enough to be bonded. This structure is a point on the path to H2 + CO. 

The determination of the structure of adenine hydrochloride (see Volume 2, Section IV,K, of article IV by Katritzky and Lagowski) is an example of extremely accurate X-ray crystallography whereby the positions of individual hydrogen atoms were located. An example of the deduction of structure from bond lengths between heavy atoms is provided by Penfold s investigation of pyrid-2-thione. ... 

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. 

Scheme 3). The qualitative energy levels (Scheme 4) show the number of valence electrons necessary to obtain closed-shell electronic structures. Each orbital in the. y-orbital set is assumed to be occupied by a pair of electrons since the 5-orbital energies are low and separate from those of the p-orbital ones, especially for heavy atoms. The total number of valence electrons for the closed-shell structures... 

The structure was solved by the multiple isomorphous replacement technique using four heavy atom derivatives uranyl acetate, plati-nous chloride, tetramethyllead acetate, and p-chloromercury benzoate. All four derivatives gave interpretable heavy atom Patterson syntheses. The heavy atom sites could be correlated between the de-... 

Structure factors corresponding to 3,195 reflections between lOA and 1.7A were calculated for each of 50 coordinate sets at each temperature. Only the 246 heavy atoms of the hexamer were included in the structure factor calculations hydrogen atoms were not included in the refinement. 

The state of research on the two classes of acetylenic compounds described in this article, the cyclo[ ]carbons and tetraethynylethene derivatives, differs drastically. The synthesis of bulk quantities of a cyclocarbon remains a fascinating challenge in view of the expected instability of these compounds. These compounds would represent a fourth allotropic form of carbon, in addition to diamond, graphite, and the fullerenes. The full spectral characterization of macroscopic quantities of cyclo-C should provide a unique experimental calibration for the power of theoretical predictions dealing with the electronic and structural properties of conjugated n-chromophores of substantial size and number of heavy atoms. We believe that access to bulk cyclocarbon quantities will eventually be accomplished by controlled thermal or photochemical cycloreversion reactions of structurally defined, stable precursor molecules similar to those described in this review. 

Multiple isomorphous replacement allows the ab initio determination of the phases for a new protein structure. Diffraction data are collected for crystals soaked with different heavy atoms. The scattering from these atoms dominates the diffraction pattern, and a direct calculation of the relative position of the heavy atoms is possible by a direct method known as the Patterson synthesis. If a number of heavy atom derivatives are available, and... 

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