Generation of Crystal Structures

For the construction of a molecular couple related by a center of symmetry (/couple), only the location of the center of symmetry in the space surrounding the molecule needs to the found for the S and G strings, the molecular orientation, the distance between the center of mass and the symmetry element, as well as the screw or glide translation period, must be found. Thus, the search for the / couples is much quicker than the search for S or G strings. The search for the cell translation periods is longest for triclinic structures. In summary, crystal structures are generated as follows  

1) set up a geometrical model of the molecule, with standardized H-atom positions if the molecule has conformational degrees of freedom, optimize the molecular conformation, or consider in turn each of the plausible molecular conformations  

2) calculate D, and estimate the ranges for the shortest and longest cell parameters as in 12.4.3 calculate (or use Thbles 12.4 and 12.5) and estimate the cell volume per molecule as Vc = Km/0.7  

3) calculate and estimate the value of (PPE) at 7 A according to the correlations in Table 12.3 alternatively, use the atomic increments in Tkble 12.4  

4) recognize the stable I couples, S and G strings try to use chemical intuition or the empirical rules applying to molecular arrangement in crystals (e.g. HB vs. stack as in 13.4.2.1) use any other available structural or spectroscopic information on similar compounds. A subsequent search of translational periods produces structures in space groups Pi, P2i and Pc  

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Both thermodynamic and kinetic factors need to be considered. Take, for instance, acetic acid. The liquid contains mostly dimer but the crystal contains the catemer and no (polymorphic) dimer crystal has ever been obtained. Various computations (R. S. Payne, R. J. Roberts, R. C. Rowe, R. Docherty, Generation of crystal structures of acetic acid and its halogenated analogs , J. Comput. Chem, 1998, 19,1-20 W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, J. Kroon, Crystal structure predictions for acetic acid , J. Comput. Chem., 1998, 19, 459-474) show the relative stability of the dimer. Perhaps the dimer is not formed in the crystal because it is 0-dimensional and as such, not able to propagate so easily to the bulk crystal as say, the 1-dimensional catemer. 

Payne R S, R J Roberts, R C Crowe and R Docherty 1998. Generation of Crystal Structures of Acetic Acid and Its Halogenated Analogs. Journal of Computational Chemistry 19 1-20... 

With five torsion angles (Fig. 6.5), sulopenem is a challenging compound for CSP calculations. Because of the flexibility, an initial exploration for likely conformations in the solid state needs to be conducted first before the computer generation of crystal structures. 

Figure 18 CSD information that can contribute to the three main stages in crystai structure prediction (a) the generation of 3D molecular models, (b) the generation of crystal structure packings, and (c) the final ranking of crystal structures.

Mancia, E., et al. How coenzyme Biz radicals are generated the crystal structure of methylmalonyl-coen-zyme A mutase at 2 A resolution. Strueture 4 339-350, 1996. 

In all cases, broad diffuse reflections are observed in the high interface distance range of X-ray powder diffraction patterns. The presence of such diffuse reflection is related to a high-order distortion in the crystal structure. The intensity of the diffuse reflections drops, the closer the valencies of the cations contained in the compound are. Such compounds characterizing by similar type of crystal structure also have approximately the same type of IR absorption spectra [261]. Compounds with rock-salt-type structures with disordered ion distributions display a practically continuous absorption in the range of 900-400 cm 1 (see Fig. 44, curves 1 - 4). However, the transition into a tetragonal phase or cubic modification, characterized by the entry of the ions into certain positions in the compound, generates discrete bands in the IR absorption spectra (see Fig. 44, curves 5 - 8). 

A crystal is an orderly array of atoms or molecules but, rather than focusing attention on these material units, it is helpful to consider some geometrical constructs that characterize its structure. It is possible to describe the geometry of a crystal in terms of what is called a unit cell a parallelepiped of some characteristic shape that generates the crystal structure when a three-dimensional array of these cells is considered. We then speak of the lattice defined by the intersections of the unit cells on translation through space. Since we are interested in crystal surfaces, we need to consider only the two-dimensional faces of these solids. In two dimensions the equivalent of a unit cell is called a unit mesh, and a net is the two-dimensional equivalent of a lattice. Only four different two-dimensional unit meshes are possible. 

Fig. 5. The important interactions of Zanamivir (1) with the active site of influenza virus A sialidase.70 This figure was generated from crystal structure data (PDB-1NNC) using LIGPLOT.63...

The most thermophilic variant of j/NB esterase, 8G8, has only thirteen mutations compared to the wild-type esterase, making it 97% identical to the wild-type esterase sequence, with a root-mean-square deviation of only 0.44 A between the two C backbone structures. As with the 5-6C8 organophile structure, the catalytic triads of 8G8 and wild-type / NB esterase are superimposable. This high sequence and structural identity, in conjunction with the availability of crystal structures for both the wild type and thermophile, affords an interesting opportunity to study the structural basis for thermostability. Thermophile 8G8 is the product of eight generations of directed evolution, screening for retention of activity... 

It is consequential from these considerations that polymorphism occupies an extraordinarily relevant place in the solid-state sciences. Even the smallest step ahead in understanding the reasons for polymorphism, and of how to bend it to our wishes/needs, might represent a quantum leap in structural sciences with enormous conceptual, practical and economic consequences. One way to tackle this problem is the computational generation of theoretical crystal structures [11], which often goes under the epithet of crystal structure prediction. Even though this is a very important area of research, it will be touched upon only marginally in this chapter and mainly in connection with experimental results. 

Abstract Methods, evolutionary and systematic search approaches, and applications of crystal structure prediction of closest-packed and framework materials are reviewed. Strategies include developing better cost functions, used to assess the quality of the candidate structures that are generated, and ways to reduce the set of candidate structures to be assessed. The crystallographic coordinates for new materials, available only as a powder sample, are often intractable from diffraction data alone. In recent years, steady progress has been made in the ability to solve previously unknown crystal structures of such compounds, the generation of known structures (inferring more confidence in such approaches) and the prediction of hypothetical yet-to-be-synthesised structures. 

In the next section the ideas behind several methods, including the GA and a simulated annealing (SA) approach [19,20], then their implementation used to generate ionic crystal structures are reviewed. This will contain an introduction to the types of move class operators and the various types of cost functions used to modify the current trial structure(s) and to assess the quality of the trial structures, respectively. In the third section recent applications of the GA and SA approaches to closest-packed ionic systems and then to open-framework crystal structures are reviewed. 

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