Heavy atom method

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 relative stereochemistry of stephadiamine (16) was clarified by X-ray diffraction analysis, using the direct method, and the absolute configuration was solved by the heavy-atom method, using the N-p-bromobenzoyl derivative (6). Stephadiamine (16), a C-norhasubanan alkaloid, is not regarded as a hasubanan congener in the strict sense, but as a new member of oe-amino acid derivatives (6). 

The method, also called heavy atom method, consists in introducing a heavy atom in the molecule. Then X-rays with a wave length close to the X-ray absorption of the heavy atom is introduced. As a result a phase shift is superimposed on the ordinary diffraction pattern and configuration is then deduced. The method was first employed in 1951 by Bijvoet et al. to examine sodium rubidium tartrate who concluded that it is possible to differentiate between the two optically active forms. In other words it was possible to determine the absolute configuration of the enantiomers. Since then the absolute configurations of about two hundred optically active compounds have been elucidated by their correlation with other substances of known configuration. 

As discussed in section 2.3, the electron diffraction intensities need to be corrected before being employed for structure analysis. An empirical method has been set up to correct simultaneously all kinds of distortions in the diffraction data by referring to the heavy atom method and the Wilson statistic technique in X-ray crystallography. After correction, the intensity of each diffraction beam can approximately lead to the modulus of the corresponding structure factor [26]. 

Various methods have been used to circumvent the phase problem. The earliest method was based on trial-and-error procedure and works well for relatively simple molecules (diatomic and tri-atomic). The most successful method has been the heavy atom method, wherein an electron-dense atom (for example, bromine or... 

Erythromycin A, a widely used, macrolide, antibiotic substance, was crystallized as the hydriodide dihydrate. It would be expected that the iodine atom would be used as the heavy atom in solving the structure, and, indeed, the authors tried the heavy-atom method first.68 Unfortunately, the iodine atom lies on a crystallographic mirror-plane, and so this method failed. Because erythromycin con-... 

Both direct and heavy-atom methods have been used to determine structures of substituted coumarins. Examples include 4-hydroxycoumarin and its 3-bromo derivative (65AX927, 66AX646) and the 7,8- and 6,7-dihydroxycoumarins, daphnetin and esculetin, respectively <76AX(B)946, 77AX(B)283). In the last compounds, hydrogen bonds link the molecules in the crystal. The stacking distances are comparable to those for other substituted coumarins <75AX(B)1287). A study of the structure of 7-hydroxy-4-methylcoumarin contains... 

The crystal and molecular structure of l-(2-pyridyl)-3-benzoyl-6-bromoindolizine has been obtained by the heavy atom method.129 The larger than normal 0=0 distance (1.32 A compared with 1.22 A for a carboxy group) suggests significant contributions from charged canonical forms. 

The most demanding element of macromolecular crystallography (except, perhaps, for dealing with macromolecules that resist crystallization) is the so-called phase problem, that of determining the phase angle ahkl for each reflection. In the remainder of this chapter, I will discuss some of the common methods for overcoming this obstacle. These include the heavy-atom method (also called isomorphous replacement), anomalous scattering (also called anomalous dispersion), and molecular replacement. Each of these techniques yield only estimates of phases, which must be improved before an interpretable electron-density map can be obtained. In addition, these techniques usually yield estimates for a limited number of the phases, so phase determination must be extended to include as many reflections as possible. In Chapter 7,1 will discuss methods of phase improvement and phase extension, which ultimately result in accurate phases and an interpretable electron-density map. 

Although the heavy atom method has been successful in establishing many structures, particularly those of alkaloids since alkaloids have a propensity for crystallizing as halide salts, there had been an urgent need to develop a procedure for phase determination that was not dependent on the presence of a heavy atom in a crystal. Such a procedure, now commonly called the direct method of phase determination, has been devised. Karle and Hauptman 13) recognized that the number of unique reflections measured in an X-ray pattern is 25-50 times greater than the number of unknowns in a crystal, the unknown quantities being the three coordinates... 

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... 

Interpretation of interatomic vectors. Use of known atomic positions for an initial trial structure (a preliminary postulated model of the atomic structure) can be made, by application of Equations 6.21,4 and 6.21.5 (Chapter 6), to give calculated phase angles. Methods for obtaining such a trial structure include Patterson and heavy-atom methods. Such methods are particularly useful for determining the crystal structures of compounds that contain heavy atoms (e.g., metal complexes) or that have considerable symmetry (e.g., large aromatic molecules in which the molecular formula includes a series of fused hexagons). The Patterson map also contains information on the orientation of molecules, and this may also aid in the derivation of a trial structure. 

In a minimum-function map, the origin of the Patterson map is put in turn on each of the known symmetry-related positions of a heavy atom that has already been located from a Patterson map. On each superposition of the origin of the Patterson map onto the various symmetry-related heavy-atom positions, the lowest value at each superimposed grid point in the pairs of maps is recorded. This superposition process is repeated until the structure is revealed. In this way the lighter atoms can be located. The method is an alternative to the heavy-atom method just described and has proved useful in many cases. 

From the Patterson and heavy-atom methods, once the direction of the first vector to be selected has been assigned, the origin of the unit... 

Heavy-atom method Relative phases calculated for a heavy atom in a location determined from a Patterson map are used to calculate an approximate electron-density map. Further portions of the molecular structure may be identified in this map and used to calculate better relative phases, and therefore a more realistic electron-density map results. Several cycles of this process may be necessary in order to determine the entire crystal structure. 

The application of the Patterson technique to locate strongly scattering atoms is often called the heavy atom method (which comes from the fact that heavy atoms scatter x-rays better and the Patterson technique is most often applied to analyze x-ray diffraction data). This allows constructing of a partial structure model ( heavy atoms only), which for the most part define phase angles of all reflections (see Eq. 2.107). The heavy atoms-only model can be relatively easily completed using sequential Fourier syntheses (either or both standard, Eq. 2.133, and difference, Eq. 2.135), sometimes enhanced by a least squares refinement of all found atoms. 

Another application of simulated annealing is in the real-space search problem of crystallography. This problem arises when the initial electron density map obtained by the heavy-atom method is so poor that no obvious tracing of the polypeptide chain is even partly possible. Typically one expects to see connected tubes of electron density corresponding to mainchain atoms strung along the polypeptide backbone. When the heavy-atom phases are poor, much of this connectivity is lost and the remaining bubbles of isolated density are impossible to interpret. Frequently, when a crude approximation of the expected model is already available from other unrelated sources, this otherwise fatal situation can be overcome. 

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