Single anomalous dispersion

The anomalous positive ORD curve in Fig. 2b is rounded at finite values for the maximum (peak) and minimum (trough) extremities. The crossover wavelength, where a = 0, generally coincides with the wavelength of the maximum absorbance. An anomalous curve is always superimposed on a fundamental plain curve that is alluded to as the background rotation. Media confirmed to have just a single anomalous dispersion can be solved for 2,. Historically, this procedure was used to predict the wavelength maximum for an incomplete absorbance band that could not be observed in its entirety because of instrumental limitations. This particular application of ORD is now obsolete. 

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. 

Single crystals of ferroelectric TGS grown from solution generally contain domains of the two enantiomorphous phases (110). This juxtaposition of enantiomorphous domains may be explained in terms of the minor deviations of the crystal structure from a centrosymmetric arrangement. The relative concentrations of the two enantiomorphous phases in a single crystal may be determined by means of anomalous dispersion of X-rays (111,112). 

Note that an equivalent stmeture is obtained when the positions of the Zn and S atoms are interchanged, but in this case the polar direction of the crystal is reversed. This arises because Pfymc is a polar space group, and historically the polar sense of a single crystal of ZnS has been used to demonstrate the breakdown of Friedel s law under conditions of anomalous dispersion. 

Anomalous dispersion can also be used as an aid in the determination of phase angles. It was realized early on that anomalous scattering from the heavy atom in a derivative could be used to resolve the phase ambiguities if a single heavy-atom derivative is all that is available. 

Karle, J. Triplet phase invariants from single isomorphous replacement or one-wavelength anomalous dispersion data, given heavy-atom information. Acta Cryst. A42, 246-253 (1986). 

Excellent and detailed treatments of the use of anomalous dispersion data in the deduction of phase information can be found elsewhere (Smith et al., 2001), and no attempt will be made to duplicate them here. The methodology and underlying principles are not unlike those for conventional isomorphous replacement based on heavy atom substitution. Here, however, the anomalous scatterers may be an integral part of the macromolecule sulfurs (or selenium atoms incorporated in place of sulfurs), the iron in heme groups, Ca++, Zn++, and so on. Anomalous scatterers can also be incorporated by diffusion into the crystals or by chemical means. With anomalous dispersion techniques, however, all data necessary for phase determination are collected from a single crystal (but at different wavelengths) hence non-isomorphism is less of a problem. 

For more than 50 years it has been known that the barely measurable differences between Fhki and F-n-k-t contained useful phase information. For macromolecular crystals lacking anomalous scattering atoms, this phase information was impossible to extract and use because it was below the measurement error of reflections. Anomalous dispersion was, however, sometimes useful in conjunction with isomorphous replacement where the heavy atom substitutent provided a significant anomalous signal. The difference between F ki and F-h-k-i was, for example, employed to resolve the phase ambiguity when only a single isomorphous derivative could be obtained (known as single isomorphous replacement, or SIR) or used to improve phases in MIR analyses. 

Ultimately the question of electron density map quality is answered by whether we can trace a single polypeptide or polynucleotide chain through the density in a manner consistent with the known amino acid or nucleotide sequence. In doing so, we consider the agreement between amino acid side chains and the density assigned to them, whether selenium atoms in a map experimentally determined by single (SAD) or multiple anomalous dispersion... 

Despite repeated recrystallizations, both diastereomers 43a and 43b were obtained only as amorphous solids. Therefore, the first-eluted fraction (-)-43a was reduced with LiAlH4 to yield enantiopure glycol (-)-42, which was further converted to 4-bromobenzoate (-)-44 (Fig. 9.7a). By recrystallization from EtOH, (-)-44 gave good single crystals suitable for X-ray analysis, and consequently its absolute configuration was explicitly determined as S by the Bijvoet pair measurement of the anomalous dispersion effect of the bromine atom contained (Fig. 9.7b) [40]. 

The tunability of synchrotron radiation allows for data collection at or near the x-ray absorption edge of anomalous scatterers present in the protein or crystal to provide experimental phase information. Using techniques such as multi-wavelength anomalous dispersion (MAD) and single-wavelength anomalous diffraction (SAD) researchers are now able to solve macromolecular structures in a matter of days or weeks, a process that required months, or even years, a decade ago. 

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