STRUCTURE SOLUTIONS

As mentioned above, structure solution may be difficult for twins where every reflection is affected by the twinning, and especially for those with similar domain sizes. For small molecules, normal direct methods are often able to solve twinned structures even for perfect twins, provided that the correct space group is used. The program SHELXD is even able to utilize the twin law and the fractional contribution (Uson and Sheldrick, 1999). 

The Patterson function of a twinned stmcture is the sum of the Patterson functions of both domains. Therefore procedures using Patterson methods are in principle possible. There are several examples in the literature of stmctures solved by molecular replacement using twinned data (e.g. see Breyer et al, 1999). 

For partially twinned structures, mathematical detwinning is possible if the fractional contribution is not too close to 0.5. The intensities Ji and J2 measured from a twinned crystal are the sum of the two intensities Ii and h of both domains weighted by their fractional contribution a  

This detwinned data can be used for structure solution, whereas refinement should be performed against the original data, because for a approaching 0.5 detwiimed intensities become very inaccurate. 

There are also examples of structures solved by MAD/SAD using twirmed or detwiimed data (e.g. see Rudolph et al 2003). However, care should be exercized in detwinning anomalous diffraction data in order to avoid mixing the positive and negative Friedel mates (Dauter, 2003). 

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. 

Where a material can only be prepared as a fine crystalline powder, powder diffraction methods are needed, and for these the determination of the phases of the diffraction peaks is more problematic. Often a good model structure is 

Once the basic structure has been determined, bond valences can be used to resolve a number of problems of interpretation. Diffraction experiments can identify the location of each atom, but cannot identify its oxidation state. In most structures the oxidation state is determined by the requirements of electroneutrality (Rule 11.1), but in some structures more than one assignment is possible. Bond valence sums can usually resolve this ambiguity. 

T = tetrahedral site, 0 = octahedral site, p gives the proportion of the ion on the site. The last column gives the inversion parameter, i. 

Equations (13.1) and (13.2) can be used when only two species occupy a given site but sometimes several different species are found to occupy the same site, particularly in minerals. In this case it is necessary to use all available evidence 

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M Falciom, MW Deem. A biased Monte Carlo scheme for zeolite structure solution. I Chem Phys 110 1754-1766, 1999. 

The first six chapters of this book deal with the basic principles of protein structure as we understand them today, and examples of the different major classes of protein structures are presented. Chapter 7 contains a brief discussion on DNA structures with emphasis on recognition by proteins of specific nucleotide sequences. The remaining chapters illustrate how during evolution different structural solutions have been selected to fulfill particular functions. 

For many proteins, it is possible to generate structures of protein-ligand complexes quite rapidly. It is therefore not uncommon for many hundreds of structures to be determined in support of a drug discovery and optimization project. The major challenge for this level of throughput is informatics support. It is also this type of crystallography that is most in need of semiautomated procedures for structure solution and model building (see Section 12.6). 

The free electron resides in a quantized energy well, defined by k (in wave-numbers). This result Ccm be derived from the Schroedinger wave-equation. However, in the presence of a periodic array of electromagnetic potentials arising from the atoms confined in a crystalline lattice, the energies of the electrons from all of the atoms are severely limited in orbit and are restricted to specific allowed energy bands. This potential originates from attraction and repulsion of the electron clouds from the periodic array of atoms in the structure. Solutions to this problem were... 

Once a structure of the desired protein has been solved, it is a very rapid process to produce subsequent high-quality structures and, in fact, some groups have even linked various scripts together, or modified software tools to provide much more automated software aids to repeated crystal structure solution, such as when solving multiple ligand complexes of the same protein [7]. 

Hybrid MPC-MD schemes may be constructed where the mesoscopic dynamics of the bath is coupled to the molecular dynamics of solute species without introducing explicit solute-bath intermolecular forces. In such a hybrid scheme, between multiparticle collision events at times x, solute particles propagate by Newton s equations of motion in the absence of solvent forces. In order to couple solute and bath particles, the solute particles are included in the multiparticle collision step [40]. The above equations describe the dynamics provided the interaction potential is replaced by Vj(rJVs) and interactions between solute and bath particles are neglected. This type of hybrid MD-MPC dynamics also satisfies the conservation laws and preserves phase space volumes. Since bath particles can penetrate solute particles, specific structural solute-bath effects cannot be treated by this rule. However, simulations may be more efficient since the solute-solvent forces do not have to be computed. 

Since the phase angles cannot be measured in X-ray experiments, structure solution usually involves an iterative process, in which starting from a rough estimate of the phases, the structure suggested by the electron density map obtained from Eq. (13-3) and the phase computed by Eq. (13-1) are gradually refined, until the computed structure factor amplitudes from Eq. (13-1) converge to the ones observed experimentally. 

Structural aspects were discussed, but not heavily, in the first edition. The complexity of new compounds (and macromolecules) now being investigated has driven many of the technological advances in X-ray crystallographic data collection and structure solution over the last two decades. Small-molecule (m.w. < 1,000 g mol-1) structure determinations are now routinely carried out, and Co complexes constitute a significant proportion of these. Indeed, the incorporation of crystal structures in most papers reporting new synthetic coordination chemistry is now a standard feature much more so than at the time of CCC(1987) (Figure 1). Inevitably, most of the new compounds described herein have been the subject of crystal structure determinations, rather... 

The development and application of multidimensional solid state homo- and heteronuclear correlation (HETCOR) NMR techniques have lead to an increasingly important role in structure solution of zeolitic materials and have had many practical applications in the detailed structural characterization of completely siliceous zeolites[6,7] and AlPOs.[8-ll] However, HETCOR NMR is not readily applicable to aluminosilicates... 

Zeolite structures sometimes remain unsolved for a long time, because of either their complexity, the minute size of the crystallites or the presence of defects or impurities. One extreme example of stacking disorder is provided by zeolite beta [1,2], Different stacking sequences give rise to two polymorphs (A and B) in zeolite beta that always coexist in very small domains in the same crystal. Not only do the small domains make the peaks in the powder X-ray diffraction pattern broad and thereby exacerbate the reflection overlap problem, but the presence of stacking faults also gives rise to other features in the diffraction pattern that further complicate structure solution. 

On the crystal structure solution and characterization of ECS-2, a novel microporous hybrid organic-inorganic material... 

The electron crystallography method (21) has been used to characterize three-dimensional structures of siliceous mesoporous catalyst materials, and the three-dimensional structural solutions of MCM-48 (mentioned above) and of SBA-1, -6, and -16. The method gives a unique structural solution through the Fourier sum of the three-dimensional structure factors, both amplitude and phases, obtained from Fourier analysis of a set of HRTEM images. The topological nature of the siliceous walls that define the pore structure of MCM-48 is shown in Fig. 28. 

Although definitive structural solutions for any of the prion domain filaments have yet to be achieved, the body of experimental data is growing and it is possible that the fold and packing of prion domains in HET-s filaments differ qualitatively from those in Ure2p or Sup35p filaments (Section VI). 

The structural solution for the vast majority of OM proteins is provided in the form of the (3-strand, a secondary fold, which allows portions of the polypeptide chain to organise as a (3-barrel. In this cylindrical structure, hydro-phobic residues point outwards and hydrophilic residues are located inside, which can allow the formation of a water-filled channel [30 33]. 

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

EDXRD is a very powerful technique, although limitations include the requirement for synchrotron radiation. This Hmits the number of experiments that can be performed, due to the high cost and low availabihty of synchrotron beam time. Because of the large voliune of the reaction vessel and the geometry of the instrument, the peak resolution of the energy dispersive data is also rather poor (AE/E). This means that although it is possible to accurately monitor the course of a reaction, using the data for ab initio structure solution or structure refinement is precluded. 

All of them assume that the data are at least pseudo-kinematic, and use techniques that are robust against systematic and random errors. The list is not exhaustive and new techniques are still being developed, but it covers more than 95% of published structures. We will examine each technique in turn, but postpone the routine application of solution methods at this stage since it teaches us very little about how structure solution methods actually work. 

Model building remains a useful technique for situations where the data are not amenable to solution in any other way, and for which existing related crystal structures can be used as a starting point. This usually happens because of a combination of structural complexity and poor data quality. For recent examples of this in the structure solution of polymethylene chains see Dorset [21] and [22]. It is interesting to note that model building methods for which there is no prior information are usually unsuccessful because the data are too insensitive to the atomic coordinates. This means that the recent advances in structure solution from powder diffraction data (David et al. [23]) in which a model is translated and rotated in a unit cell and in which the torsional degrees of freedom are also sampled by rotating around bonds which are torsionally free will be difficult to apply to structure solution with electron data. 

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