Electron diffraction structures, accuracy

To measure the goodness of fit, and to quantify the structural determination, a reliability (i -factor) comparison is used. In comparing the data and simulation of the experiment for many trial structures, a minimum R factor can be found corresponding to the optimal structure. In this way atomic positions can be determined in favorable cases to within a few hundredths of an A, comparable to the accuracy achieved in Low-Energy Electron Diffraction (LEED). 

These uncertain atoms remain to be verified by a careful structure refinement. For a structure refinement, as many reflections as possible should be included. The phases are not needed at the refinement stage, but if possible complete 3D data out to 1 A resolution should be used. Strong and weak reflections are equally important. Such data can be obtained by electron diffraction, which is not affected by the contrast transfer function of the electron microscope, but suffers from dynamical scattering. The higher the accuracy of the amplitudes, the more accurate will the atomic positions become. 

Finally, in a vast number of structure analyses we tend to ignore small structural differences. They may often be indeed unaccessible to electron diffraction. It is not always obvious, however, how such assumptions will influence the determination of principal parameters for which generally great accuracy may be claimed. Carefulness dictates the testing the influence of such assumptions and the incorporation of the results of the tests into the error estimates. It is hoped, however, that other >urces, e. g., quantum chemical calculations will aid electron diffraction by providing reliable information on the small structural differences. They may often be calculated reliably even when the actual parameters themselves may be much less reliable. 

L. S. Bartell, The status of electron scattering theory with respect to accuracy in structure analyses, in I. Hargittai and M. Hargittai (eds), Stereochemical applications of gas-phase electron diffraction, VCH Publishers, Weinheim, (1988). 

With a known mineral, as determined by electron diffraction or other technique (such as X-ray diffraction), determination of the stoichiometry and structural formula can be a suitable test for analytical precision of thin-film elemental analyses. This simple test follows the practice commonly employed for electron microprobe data in which the accuracy (and completeness) of an analysis is judged by the departure from stoichiometry calculated for a given mineral. Thus, thin-film analyses of olivines, pyroxenes, garnets, feldspars and many other common rock-forming minerals can be examined for internal consistency via a calculation of structural formulae. 

Selp HM (1973) Electron diffraction theory and accuracy. In Sutton LE (ed) Molecular structure by diffraction methods, vol 1. Chem Soc Lond, UK, Chap I, pp 7-57... 

Here we discuss structures that have been established at the atomic level revealing the exact conformation of the polypeptide chain. All were determined by X-ray diffraction analysis of a tridimensional protein crystal. Some o -helical membrane protein structures have been analyzed by electron diffraction of o-dimensional crystals, although generally with a lower accuracy. For a long time structural analyses by NMR... 

Four different experimental techniques were employed in attempts to elucidate the structure of bicyclobutane. Haller and Srinivasan obtained some structural information from the analysis of partially resolved infrared vibration-rotation bands. However, this method is not expected to give results of high accuracy, especially since some of the fundamental parameters has to be assumed. Meiboom and Snyder used NMR measurements in liquid crystals for structure determination. One limitation of this method is that only ratios of internuclear distances rather than absolute values can be determined. Also, the authors point out that their results should not be considered as final since corrections for vibration were not made. The other two methods successfully employed were electron diffraction and microwave spectroscopy The structural parameters obtained by these methods are collected in Table 1. 

In the mid-1970 s, with the availability of intense X-ray synchrotron sources, a powerful new technique. X-ray absorption spectroscopy (XAS), emerged. This is a local structural probe, the information content of which derives from electron diffraction. For a metalloprotein, the electron source and detector is the metal atom that is probed, because selective excitation is achieved by scanning a range of X-ray wavelengths particularly appropriate to the element of central interest. The selectivity and the local nature of the diffraction process give the technique its major strength. For example, metal-ligand distances can be determined to an accuracy of approximately 0.02 A. In addition, XAS does not require crystalline materials thus, aqueous protein samples are readily probed under a variety of conditions. 

There is, of course, another important structural method for gas-phase molecules, viz., electron diffraction. Here one does not probe the properties of particular quantum states by spectroscopy rather, the scattering of electrons from the atoms of a thermal distribution of molecules is studied in a fashion analogous to x-ray diffraction of crystalline solids. This leads to entirely different types of structures, for example, rg. Vibrational motions are, of course, once again the complicating factor. With appropriate corrections, electron diffraction data have led to re structures of high accuracy. The abimdant literature should be consulted for the methods of electron diffraction [11]. 

Definition of the structural parameters As the accuracy of structural techniques has improved, one has been forced to consider the differences between the nominally similar quantities provided by these techniques. The interatomic distances provided by Eq. (6a) to (8) are termed ra or rg 1-5 and are represented by the centers of gravity of the D(r) (or P(r)/r) peaks. They differ from the distances re, rg,rQ, rs, etc., by amounts in some cases substantial. Relations exist by which one type may be converted to another14 of which Eq. (9) and (10) are examples pertinent to electron diffraction. 

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