Model crystallization

As mentioned above, the preferred computational methods for modeling crystals have changed over the years. Below is a list of basis function schemes, with the most often used appearing first ... 

O Hara, M. and Reid, R.C., 1973. Modelling Crystal Growth Rates from Solution. Englewood Cliffs Prentice-Hall. 

Figure 5.6. Cell types that may be used in modeling crystal formation...

Enzyme Cellular Location Reaction Cofactor Phase OSAR Pharmacophore Homology models Crystal structures... 

Keywords Chain folding Computer modeling Crystal growth Crystal-melt interfaces Molecular dynamics Polymer crystallization... 

Sanchez and DiMarzio identified [41] a crossover regime 11 [Fig. 1.15(c)], where g is more rapid than in 1 and less than in 111. On the basis of the LH model, crystallization kinetics in these three regimes are obtained as follows. 

Let us assume that the constituent units of both a crystal and that of growth are simple cubes. This kind of model crystal is called a Kossel crystal, and is shown in Fig. 3.9. The 100 face is completely paved by the unit, and the surface is atomically flat. This face is called the complete plane. The 111 face, however, consists of kinks, as can be seen in Fig. 3.9, and has an uneven surface, and so it is called an incomplete plane. In contrast to [111], [110] corresponds to a face consisting entirely of steps. Kossel did not give a particular name to this t3TJe of crystal face. 

A. Roosen and J.E. Taylor. Modeling crystal growth in a diffusion field using fully-faceted interfaces. J. Computational Phys., 114(1) 113—128, 1994. 

Metalloenzymes pose a particular problem to both experimentalists and modelers. Crystal structures of metalloenzymes typically reveal only one state of the active site and the state obtained frequently depends on the crystallization conditions. In some cases, states probably not relevant to any aspect of the mechanism have been obtained, and in many cases it may not be possible to obtain states of interest, simply because they are too reactive. This is where molecular modeling can make a unique contribution and a recent study of urease provides a good example of what can be achieved119 1. A molecular mechanics study of urease as crystallized revealed that a water molecule was probably missing from the refined crystal structure. A conformational search of the active site geometry with the natural substrate, urea, bound led to the determination of a consensus binding model[I91]. Clearly, the urea complex cannot be crystallized because of the rate at which the urea is broken down to ammonia and, therefore, modeling approaches such as this represent a real contribution to the study of metalloenzymes. 

Perhaps the most rigorous attempts to model crystal growth developed... 

Given a state of interest /q) (normalized to 1) and a model crystal Hamiltonian H, we consider the Green s function... 

Here we comment briefly on a two-band model crystal with a single energy gap. A schematic picture for the density of states is shown in Fig. 3. Following the notations of Turchi et al., we denote by E, j, 3, 4 the energy bounds, by W the half-width of the total spectrum, and by G the half-width of the gap. 

HgureS. Schematic representation of the density of states of a two-band model crystal with a single energy gap. The notations used are the same of Tiudii et al. ... 

The regular orbit displayed in Figure 2.7, is the geometry on the unit sphere such that the bond length , the Euclidean distance between adjacent vertices, is constant. This restriction is not necessary from a symmetry viewpoint it may be relaxed subject only to the requirement that the local four, three and two-fold symmetries are maintained. One important example of such a relaxation occurs for the regular orbit of the Oh Crystallographic point group. In the simplest model crystal of Oh point symmetry, the primitive cubic array, for example, as in cubium, lattice points are distributed as dictated by the lattice vector Rmnp such that... 

As a first example, consider the growth of a cubic lattice about the origin. For the simple primitive lattice , most familiar as the structure of the model crystal cubium , the cubic array... 

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