Structure determination, experimental diffraction

A comprehensive and critical compilation has been published relatively recently on gas-phase molecular geometries of sulfur compounds including sulfoxides and sulfones5. This book covers the literature up to about 1980 and contains virtually all structures determined experimentally, up to that date, either by electron diffraction or microwave spectroscopy. Here we shall highlight only some of the most important observations from that source5 and shall discuss recent results in more detail. 

The experimental studies on biopolymer structures are increasingly supplemented by computational approaches. First, it has to be realized that computation is a sine qua non for experimental structure determination by diffraction methods and NMR spectroscopy themselves. In addition, independent computational studies can provide useful information on structure and dynamics of biopolymers not accessible, at least currently, by experiments. With regard to base poiyads there are three fields that have to be mentioned here primarily quantum-chemical studies of nucleic building blocks, MD simulations of medium-sized nucleic acids and structural bioinformatics. 

As a general rule, the measurements yield relative intensities, i.e. integrated intensities with an arbitrary scale X, because it is difficult to know what part of the intensity of the primary beam passes through the crystal. The constant X is thus an unknown. The function g 6) is analytic and its values can be easily calculated. The calculation of the absorption factor A is carried out with a computer and, today, poses no major problem. The theory of extinction is still poorly understood, but the factor y is often close to 1. Thus, from the intensity measurements, structure amplitudes F hkl) are obtained on a relative scale, typically with a precision of the order of 1-5%. The values of F hkl) represent the experimental information about the distribution of the atoms in the unit cell. A discussion of this information forms the subject of this section. However, we will discuss neither the theory nor the practice of structure determination by diffraction. 

The situation is different for other examples—for example, the peptide hormone glucagon and a small peptide, metallothionein, which binds seven cadmium or zinc atoms. Here large discrepancies were found between the structures determined by x-ray diffraction and NMR methods. The differences in the case of glucagon can be attributed to genuine conformational variability under different experimental conditions, whereas the disagreement in the metallothionein case was later shown to be due to an incorrectly determined x-ray structure. A re-examination of the x-ray data of metallothionein gave a structure very similar to that determined by NMR. 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

Within the multichannel Bayesian formalism of structure determination, it is indeed possible to make use ofMaxEnt distributions to model systems whose missing structure can be reasonably depicted as made of random independent scatterers. This requires that the structural information absent in the diffraction data be obtained from some other experimental or theoretical source. The known substructure can be described making use of a parametrised model. 

In general, all observed intemuclear distances are vibrationally averaged parameters. Due to anharmonicity, the average values will change from one vibrational state to the next and, in a molecular ensemble distributed over several states, they are temperature dependent. All these aspects dictate the need to make statistical definitions of various conceivable, different averages, or structure types. In addition, since the two main tools for quantitative structure determination in the vapor phase—gas electron diffraction and microwave spectroscopy—interact with molecular ensembles in different ways, certain operational definitions are also needed for a precise understanding of experimental structures. 

Table 22 Structures of closo-1, 2-C2BioH- 2 (ortho-carborane) derivatives determined experimentally by X-ray diffraction unless otherwise stated with cage C(1)—C(2) bond lengths listed where possible...

Structure determination from X-ray and neutron diffraction data is a standard procedure. Starting with a rough model, the accurate structure is determined using a least-squares structure refinement, which is based on kinematic diffraction and in which the differences between calculated and experimental intensities are minimized. X-ray and neutron diffraction are not applicable to all crystals. To determine crystal structures of thin layers on a substrate or small precipitates in a matrix (see figure 1) only electron diffraction (ED) can lead you to the crystal structure. 

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