Direct methods of structure solution

Chemists use a wide range of physical techniques for studying the structures and reactions of the molecules they are interested in. One of the skills they need is the ability to choose and exploit the most appropriate technique for studying the particular molecules of interest. X-ray crystallography is the ultimate arbiter of chemical structure and in many cases it is now the method of choice the use of automated data collection and direct methods of structure solution have reduced many problems to a routine level. However, crystallography has many limitations beyond the obvious need for crystals it cannot tell us anything about solutions, however pure they may be, or conformational equilibria, or complex mixtures or reaction kinetics. For this type of information, the chemist must turn to other physical techniques, such as some form of spectroscopy. 

I learnt a great deal about direct methods of structure solution at the excellent schools that Michael Woolfson and Lodovico Riva di Sanseverino organized, first in Parma... 

Model building has played an important role in crystal structure solution since its earliest days, and particularly before the advent of direct methods of structure solution from single crystal diffraction data. In the field of... 

A generic algorithm of employing direct methods to structure solution may be summarized in the following steps ... 

The residual difference after a successful DDM refinement or/and decomposition can be considered as a scattering component of the powder pattern free of Bragg diffraction. The separation of this component would facilitate the analysis of the amorphous fraction of the sample, the radial distribution function of the non-crystalline scatterers, the thermal diffuse scattering properties and other non-Bragg features of powder patterns. The background-independent profile treatment can be especially desirable in quantitative phase analysis when amorphous admixtures must be accounted for. Further extensions of DDM may involve Bayesian probability theory, which has been utilized efficiently in background estimation procedures and Rietveld refinement in the presence of impurities.DDM will also be useful at the initial steps of powder diffraction structure determination when the structure model is absent and the background line cannot be determined correctly. The direct space search methods of structure solution, in particular, may efficiently utilize DDM. 

Newsam, J. M., Deem, M. W., and Freeman, C. M., Direct space methods of structure solution from powder diffraction data. Accuracy in Powder Diffraction II, NIST, May 1992. 

The generation of carbocations in strongly acidic media, and the characterization of their structure by NMR in the 1950s was a breathtaking accomplishment that led to the award of the Nobel Prize in Chemistry to George Olah. Over the past 50 years NMR spectroscopy has evolved as the most important experimental method for the direct study of structure and dynamics of carbocations in solution and in the solid state. Hans-Ullrich Siehl provides an excellent review of computational studies to model experimental NMR spectra for carbocations. This chapter provides an example of how the fruitful interplay between theory and experiment has led to a better understanding of an important class of reactive intermediates. 

The relatively recent development27 of the direct methods of crystal structure analysis has produced a great increase in the number of crystal structures reported in the literature, particularly with regard to the possible hydrogen bonds (also for biological molecules). Hence, the classical spectroscopic data on hydrogen bonding in solution are backed up by X-ray diffraction analysis data. 

The traditional approach for structure solution follows a close analogy to the analysis of single-crystal XRD data, in that the intensities 1(H) of individual reflections are extracted directly from the powder XRD pattern and are then used in the types of structure solution calculation (e.g. direct methods, Patterson methods or the recently developed charge-flipping methodology [32-34]) that are used for single-crystal XRD data. As discussed above, however, peak overlap in the powder XRD pattern can limit the reliability of the extracted intensities, and uncertainties in the intensities can lead to difficulties in subsequent attempts to solve the structure. As noted above, such problems may be particularly severe in cases of large unit cells and low symmetry, as encountered for most molecular solids. In spite of these intrinsic difficulties, however, there have been several reported successes in the application of traditional techniques for structure solution of molecular solids from powder XRD data. 

The reason why it is not usually possible to employ this direct method for the solution of crystal structures has already been indicated at the beginning of Chapter VII it is that we do not usually know, and cannot determine experimentally, the phases of the various diffracted beams with respect to a chosen point in the unit of pattern. However, for certain crystals we can from the start be reasonably certain of the phase relations of the diffracted beams, or can deduce them from crystallographic evidence, and in these circumstances we can proceed at once to combine the information, either mathematically or by experimental methods in which light waves are used in place of X-rays. Otherwise, it is necessary to find approximate positions by trial, the approximation being taken as far as is necessary to be certain of the phases of a considerable number of reflections as soon as the phases are known, the direct method can be used. 

Few methods are available for the direct determination of coordination geometry, bond lengths, and bond angles for complexes in solution, although such information is important, for example, for the interpretation of thermodynamic and dynamic data. Complexes, which can be found also in crystals where their structures can be easily determined by diffraction methods, are usually assumed to have the same structure in solution, although the different environment can be expected to influence bond lengths and coordination geometry. But many complexes, which are stable in solution, do not occur in the solid state, where structures with infinite rather than discrete complexes may be preferred. Direct determinations of structures in solution are, therefore, needed and methods that can provide such information are all based on diffraction. 

Despite many advances in analytical methods in recent years, the structural characterization of materials that only occur as microcrystals less than about 30 l in diameter remains difficult and laborious. High resolution electron microscopy in the lattice imaging mode is by far the most powerful tool in giving the direct evidence of structural details essential for modelling clues, as has been demonstrated in the cases of recent zeolite structure solutions of theta-l/ZSM-23 (26) and beta (27), in addition to ECR-1. X-ray diffraction methods provide the essential confirmatory data, and sorption molecular probing and various well established spectroscopic methods are useful ancillary tools. 

It is worth noting that practically all non-traditional methods for solving crystal structures have been initially developed for both powder and single crystal diffraction data to manage intrinsic incompleteness or poor quality that cannot be improved experimentally. Despite a variety of structure solution approaches, traditional direct phase determination methods appear to be the most common and successful when powder diffraction data are adequate. Patterson methods also work quite well but they require the presence of a heavy atom and, perhaps, more extensive crystallographic expertise. The non-traditional methods are generally employed when other techniques fail and their use is somewhat restricted by both the complexity and limited availability of computer codes. 

The application of transient kinetic methods to the solution of enzyme mechanisms has increased dramatically due to recent advances in instrumentation and in the overexpression and purification of new enzymes. Transient kinetics are becoming the method of choice for evaluation of site-directed enzyme mutants and for detailed questions regarding the relationships between protein structure and observable function. In conjunction with advances in methods of structural and genetic analyses, transient-state kinetic analysis forms the basis for what might be called the new enzymology. ... 

In theory single crystal methods can be effectively used for structure solution from powder diffraction X-ray data. However, in powder diffraction the number of peaks involved are limited, and hence the data-to-parameter ratio is very small, due to the transfer of the three-dimensional data to one dimension, namely, 26. In spite of the inherent shortcomings, conventional crystallographic methods such as Direct, Patterson and maximum entropy methods have been successfully applied to powder diffraction data. The most popular program, which uses reciprocal space methods for structure solution is EXPO. ... 

The direct methods of solving inverse problems in SEES spectroscopy have been used, taking into account oscillations of two types, for Cu MW SEES spectra [45 7]. Satisfactory agreement of the results obtained with the bulk atomic pair correlation functions and with the results of the solution of the inverse problem in EXAFS and EELFS spectroscopy makes it possible to conclude that to obtain correct structural information from the SEES experimental data it is essential to take into account oscillations of two types, which rules out the application of the Fourier transformation and necessitates the direct solution of the inverse problem. The use of Tikhonov regularization as a method for solving the inverse problem in SEES spectroscopy is the subject of Section 6. Up to now, extraction of atomic structure parameters through direct calculation of the SEFS spectrum has not been performed. 

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