Diffraction methods structure reliability

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 methods available for structure determination are surveyed. Those that are applicable to the gas phase, i.e. electron diffraction and rotational spectroscopy, are suitable mainly for small molecules. Data for the crystalline phase are usually relatively straightforward to obtain, but acquiring reliable structural data for silicon compounds as liquids or in solution by diffraction methods or liquid crystal NMR spectroscopy remains a challenge. 

As described in Chapter 11, bond valences can play a role in modelling but, since most crystal structures can still not be predicted ab initio, diffraction methods remain the most common and reliable technique for determining the structures of those compounds that can be prepared as single crystals large enough for study by X-ray or neutron diffraction. 

Allied with the diffraction methods, such as low-energy electron diffraction (LEED) and photoelectron diffraction (PED), which can also be applied in single-crystal research, these advances have led to much better interpretations of the vibrational spectra of chemisorbed hydrocarbons in terms of the structures of the surface species. The new results have in turn led to the possibility of reassessing more reliably earlier interpretations of the infrared or Raman spectra of adsorbed hydrocarbons on the finely divided metal samples (usually oxide supported) that are more closely related to working solid catalysts. Such spectra are more complicated because of the occurrence of a variety of different adsorption sites on the metal particles, with the consequence that the observed pattern of absorption bands frequently arises from overlapping spectra from several different surface species. 

In this case, the phase problem reduces to a question of the sign of the structure factor. Since the sign of the structure factor can be evaluated more reliably than the phase angle, the electron density in a centrosymmetric crystal can be evaluated more accurately than that in an acentric crystal (93), Equation (2) implies that total, time-averaged electron density can be determined by the diffraction method. 

Tabic l.l gives those crystal data for the C,S polymorphs that have been obtained using single crystal methods. The literature contains additional unit cell data, based only on powder diffraction evidence. Some of these may be equivalent to ones in Table 1.1, since the unit ceil of a monoclinic or triclinic crystal can be defined in different ways, but some are certainly incorrect. Because only the stronger reflections are recorded, and for other reasons, it is not possible to determine the unit cells of these complex structures reliably by powder methods. The unit cells of the T, Mj and R forms are superficially somewhat different, but all three are geometrically related transformation matrices have been given (12,HI). 

Today, however, polynuclear carbonyls are of primary interest. Their structure is frequently so complicated that it cannot be derived from the vibrational spectra by applying selection rules. Only certain structural elements, such as terminal and bridging CO groups, can be identified. Reliable information about the structure of these species can only be obtained by X-ray diffraction methods. 

This paper will discuss the state of the art in 3D structure refinement using empirical, semi-empirical and ab initio methods. We believe that the success story of liquid state NMR in protein structure elucidation is going to continue within the solid state (or membrane environment) if chemical shifts can be successfully exploited. Neutron and X-ray diffraction methods owe their success to a simple formula that connects the measured reflex intensities with the nuclear positions or the electron density, respectively. The better we understand how chemical shifts change with the three-dimensional arrangement of atoms, the more reliably we can construct molecular models from our NMR experiments. As we can in principle determine up to six numbers per nucleus if we perform a full chemical shift tensor analysis, we need to address the question whether whole CS tensor or at least its principal values can be used in structure calculations. 

It should be emphasized that in some cases the electron diffraction method fails to provide reliable structural information, because the interatomic distances have nearly the same values. Thus, it has been shown that in the case of the SOF4 molecule, four models, which differ by 10° in their FSF and FSO angles, could account for the experimental pattern. The choice between these models was made on the basis of additional considerations. These complications are probably responsible for the difference between the microwave and electron-diffraction values for the... 

We anticipate two advantages of using the more realistic electron densities obtained by the AFDF methods. More reliable theoretical electronic charge densities calculated for each assumed nuclear geometry in the course of the iterative structure refinement process will improve the reliability of comparisons with the experimental di action pattern. In particular, AFDF electron densities are expected to serve as more sensitive and more reliable criteria for accepting or rejecting an assumed structure than the locally spherical or possibly elliptical electron density models used in the conventional approach. We also expect that the more accurate density representations within the QCR-AFDF framework will facilitate a more complete utilization and interpretation of the structural information contained in the observed X-ray diffraction pattern. 

The definitive method for determining static structures is X-ray diffraction. Indeed, the 1976 Nobel Prize in Chemistry was awarded to Professor William N. Lipscomb for his work in determining structures of the boron hydrides by diffraction methods. However, it must be remembered that packing forces and solvation effects may change the preferred structure between solid state and solution. Another technique, which combines theory and experiment, has established a reliability on a par with X-ray diffraction for confirming structures. It is called the ab /n/n o/IGLO/NMR method (see NMR Chemical Shift Computation Structural Applications for an extensive discussion of calculated NMR chemical shifts) and combines calculated chemical shifts for a number of possible structures with the experimentally measured chemical shifts in solution. 

A most suitable test is provided by X-ray diffraction (XRD). Generally, a number of reflections are selected and the sum of their intensities prior to and after the solid-state reaction compared. However, the absolute intensities frequently change they may increase or decrease depending on the contributions of charge-compensating, in-going and out-going cations to the structure factors of the reflections. Nevertheless, this method provides reliable results provided these effects are adequately considered (cf. [54]). The XRD tests showed that in the cases described above (Sect. 5.1) no loss of crystallinity had occurred. 

Another powerful tool for the structural elucidation of free radicals is X-ray diffraction analysis, which provides unique and reliable information about the structures of the radical species in the crystalline form. Needless to say, the use of such an informative method is limited to the case of stable (isolable) radicals only. 

The electrostatic valence rule has turned out to be a valuable tool for the distinction of the particles O2-, OH- and OH2. Because H atoms often cannot be localized reliably by X-ray diffraction, which is the most common method for structure determination, O2-, OH- and OH2 cannot be distinguished unequivocally at first. However, their charges must harmonize with the sums pj of the electrostatic bond strengths of the adjacent cations. 

The chemical bonding and the possible existence of non-nuclear maxima (NNM) in the EDDs of simple metals has recently been much debated [13,27-31]. The question of NNM in simple metals is a diverse topic, and the research on the topic has basically addressed three issues. First, what are the topological features of simple metals This question is interesting from a purely mathematical point of view because the number and types of critical points in the EDD have to satisfy the constraints of the crystal symmetry [32], In the case of the hexagonal-close-packed (hep) structure, a critical point network has not yet been theoretically established [28]. The second topic of interest is that if NNM exist in metals what do they mean, and are they important for the physical properties of the material The third and most heavily debated issue is about numerical methods used in the experimental determination of EDDs from Bragg X-ray diffraction data. It is in this respect that the presence of NNM in metals has been intimately tied to the reliability of MEM densities. 

It has grown increasingly apparent that the non-crystalline portions of cellulose structures may play as important a role in the properties and behavior of cellulosic materials as the crystalline parts. X-ray diffraction studies have greatly extended knowledge of crystalline cellulose but in the case of the amorphous or disordered fraction the methods of study have necessarily been indirect and not completely reliable. 

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