Structure determination using X-ray diffraction

Crystal structures are most often determined by diffraction of X-rays from single crystals of the sample, although structure determination from polycrystalline powders is also important, especially via neutron diffraction, as described below. As noted in the previous section, in order to generate a structure, (i.e. an image), it is necessary to recombine the beams that make up the diffraction pattern. Unfortunately, this cannot be carried out by using lenses, and the process must be done mathematically. 

The technique is simple in principle. A small crystal of the material, of the order of a fraction of a millimetre in size, is mounted in a beam of X-rays. Each plane of atoms in the crystal gives rise to a narrow diffracted beam. The position of each beam is recorded, along with the intensity of each spot. Each member of the resulting data set comprises a position, intensity and hkl index. 

The problem is then to mathematically convert the data set into an electron density map. The way in which this is done is similar to that 

Unfortunately values of F(hkl) are not available in the X-ray data set. Recall that 

The value F(hkt) is easily obtained as it is equal to the square root of the measured intensity. However, the phase angle, cj)flkh for the reflection cannot be recovered from the intensity. This fact, which has been the continued bane of structural crystallographers, is known as the phase problem. The equation for the contrast must be rewritten in terms of the known experimentally determined F(h00) values and the unknown phases, O 0() 4 200, ) 3oo etc. The equation for a one-dimensional chain is  

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Structure determination using x-ray diffraction methods provides an atomic-level description of the protein-ligand complex. In general, protein-ligand structures that are determined by diffraction methods are more precise than those determined by NMR methods. Such structures, determined by either method, are typically used as the starting point for computational methods for rational drug design... 

In order to understand the interactions between these bis-intercalating drugs and IMA more fully, we have crystallized several complexes of them and undertaken the structure determination by x-ray diffraction technique. One of the crystal forms diffracts to 1.6 A resolution with a space group of F222. The crystal structure was determined by the multiple isomorphous replacement method using three different heavy atom derivatives. The structure was refined to an R-factor of 19% and there were moderate number of solvent molecules clearly visible. The crystal... 

An examination of the stereochemistry of the H+ ion is complicated by a number of factors. Because it has no electron core, hydrogen is difficult to locate using X-rays which are scattered by electrons. In earlier structure determinations its presence was often ignored because it made no contribution to the X-ray diffraction pattern and could not therefore be located. Even when H is included in the model, its position can rarely be accurately determined and in any case the centre of its electron density is usually displaced from the nucleus towards the donor anion by around 20 pm. Accurate positions of the H+ nuclei can be found using neutron diffraction which has provided sufficient information to reveal the essential characteristics of hydrogen bond geometries, but in many of the structures determined by X-ray diffraction the positions of the H cations have had to be inferred from the positions of their neighbouring anions. 

Globular proteins have more complicated tertiary structures, often containing several types of secondary structure in the same polypeptide chain. The first globular protein structure to be determined, using x-ray diffraction methods, was that of myoglobin. 

Note the relationship of the dimethylbenzimida-zole to the ring system of riboflavin (Box 15-B). Several molecules of ammonia could be released from amide linkages by hydrolysis, but all attempts to remove the cobalt reversibly from the ring system were unsuccessful. The structure was determined in 1956 by Dorothy C. Hodgkin and coworkers using X-ray diffraction.13 At that time, it was the largest organic structure determined by X-ray diffraction. The complete laboratory synthesis was accomplished in 1972.c... 

Structural properties. The structure of metallic films can be conveniently determined using x-ray diffraction with a surface reflection pinhole technique in a vacuum camera as indicated in Fig. 20. This device resulted from extensive efforts to develop a camera that could be used to determine the surface orientation of thin metal films with a minimum of manipulation of the instrument, of exposure time and of calculation required to obtain the data on orientation from the diffraction pattern. The film (6) mounted with a Lucite spacer (7) onto the turn table (8) is activated by the shaft (10). The beam (3) enters through the... 

In the N3 bridged compounds, there is a stronger electron-electron interaction through the N/ bridging molecule between two adjacent Ni spins, than between the NO2 bridged compounds. A cluster model constructed on the basis of the accurate structure determined by X-ray diffraction is used in the DV-Xa calculation for NINAZ, NDMAZ, and NDMAP. These are typical Haldane gap materials, which include the N3-bridging ligand. 

In addition to many structure determinations by X-ray diffraction, nmr studies using 14N and 15N have allowed the comparison of NR with other N-bonded ligands like NO, NNR, etc.140... 

Fig. 5.3. Protein structure determination by X-ray diffraction. A. Crystals of porcine heart aconitase composed of 754 amino acids. The orthorhombic crystals shown are about 0.5 mm in the longest dimension. B. Film showing the diffraction pattern obtained from the above crystal. These data were used to obtain a 2.7 A resolution structure shown in two representations in panels C and D. Panel C shows the tracing of the protein backbone, with the small molecule (in red and yellow) in the central region depicting the iron-containing cofactor of the enzyme. Panel D shows the space-filling representation. (Courtesy of Dr Arthur H. Robbins, Miles Pharmaceuticals Inc. For details see A.H.Robbins and C.D.Stout (1989). Proteins Structure, Function, and Genetics 5, 289 312.)...

The purpose of this book is to introduce the reader to the methods of molecular structure determination by X-ray diffraction of crystals. This will enable the reader to appreciate those results published in the scientific literature not only in terms of the structural parameters derived, but also in terms of their precision. We will also demonstrate how useful these results can be to the chemist and biochemist. 

As techniques for structure determination by X-ray diffraction i evolved, molecules of even greater complexity could be studied. Two ilDolecules of special biological interest were penicillin, the important ntibiotic discovered by Alexander Fleming, and vitamin B12, used tin the treatment of pernicious anemia. Several possible structures had kbeen proposed for penicillin, but the / -lactam structure was considered wmlikely by Robert Robinson and John Cornforth from the point of view... 

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