Patterns of atoms

Qaessens et al. extended and automated this procedure and tested it on three proteins of known structure. The selection of the best-matching fragment of a given sequence length is based on three successive comparisons of fewer and fewer fragments with the input fragment. First, the end-to-end dis- 

These searches based on adjacent C , atoms are very fast in operation because they make use of the faa that a necessary, but not sufficient, condition for two sets of atoms to have the same structure is that the sum of the interatomic distances is the same. This observation allows rapid rejection of nonhits that can then be checked in more detail if required.  

A more computationally demanding search of patterns of atoms in a protein occurs when a protein must be inspected for the presence or absence of an arbitrary pattern of atoms in three-dimensional space, i.e., the atoms can be in any possible topological relationship to each other. 

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LEED is a very specific tool for examination of the geometric pattern of atoms on a surface. In electrochemistry, it has been used to study surface reconstruction. 

In discussing gross atomic charges it must be realized that a given pattern of atomic charge densities in a molecule can be imposed by several factors. We identify three effects responsible for a molecular charge distribution ... 

The unit of pattern ( unit cell ). A crystal consists of a large number of repetitions of a basic pattern of atoms. Just as in many textile... 

The concept of hybridization of AOs to give new hybrid AOs involved in the bonding patterns of atoms is a useful and practical way to describe the way in which functional groups are constructed. It provides a rationale for the structure as well as the geometry and electron distribution in functional groups and molecules in which they are found. It can also be used to predict reactivity patterns of functional groups based on these considerations. 

For a limited discussion of fractal geometry, some simple descriptive definitions should suffice. Self-similarity is a characteristic of basic fractal objects. As described by Mandelbrot 58 When each piece of a shape is geometrically similar to the whole, both the shape and the cascade that generate it are called self-similar. Another term that is synonymous with self-similarity is scale-invariance, which also describes shapes that remain constant regardless of the scale of observation. Thus, the self-similar or scale-invariant macromolecular assembly possesses the same topology, or pattern of atomic connectivity, 62 in small as well as large segments. Self-similar objects are thus said to be invariant under dilation. 

In general, during the preparation of metallic catalysts, more than one type of crystallographic planes are uncovered, each of which exposes a characteristic pattern of atoms, for example, the crystallographic planes (111), (110), (100), and (010) [27],... 

Fortunately, the imino forms of A and C and the enol forms of G and T occur rarely. Most A C and G T mispairs observed to date in high-resolution crystal structures (e.g., References 22 and 23) associate through a wobble configuration (14), with the bases sheared past one another relative to the Watson-Crick configuration (Table 1 and Fig. 1). These structural perturbations (Table 1 and Table 2) alter the patterns of atomic charges and accessibihty that are presumably required for protein recognition and enzymatic action (see discussion below). 

The discovery of the periodic structure of the elements by Dmitri Ivanovich Mendeleev, shown in Fig. 9.1, must be ranked as one the greatest achievements in the history of science. And perhaps the most impressive conceptual accomplishment of quantum mechanics has been its rational account of the origin of the periodic table. Although accurate computations become increasingly more difficult as the number of electrons increases, the general patterns of atomic behavior can be predicted with remarkable accuracy. A modem version of the periodic table is printed on the inside back cover. 

Unlike the polarization of the base atom in a regular hydrogen bond interaction, the dipolar polarization of a noble gas atom is towards the hydrogen. In the relatively weak complex of HF with N2, the change in the polarization of the base N away from H is very small. This interaction is transitional between the two patterns of atomic polarizations that result from the mutual penetration of closed-shell systems with little or no accompanying charge transfer, the features common to van der Waals and hydrogen-bonded interactions. 

A few examples are known of crystal structures based on more complex nets. Borocarbides MB2C2 are formed by scandium and the rare-earth metals, and they consist of layers of composition B2C2 interleaved with metal atoms. In the compounds of the 4f metals the layer is the 4 8 layer, the pattern of atoms being similar to that of Fig. 3.27(b), the open and shaded circles now representing B and C atoms. The scandium compound is of special interest as the only example at present known of the layer consisting of equal numbers of 5-gons and 7-gons. 

Autocorrelation coefficients are used to transform a pattern of atom properties into a representation that allows comparison of molecules without needing to find the correct atom-by-atom superposition [60, 61]. Any atom property P (atomic charge, Hpophilicity parameter, topological or electrotopological index, etc.) can be used as input... 

Patterns of Atomic Structure The Size of Orbitals MiniLab 7.2 Electrons in Atoms... 

Fig. 9 Displacement pattern of atoms around an isolated vacancy in a 95 atom supercell [2] (reprinted with permission)...

Mental models pattern of atoms, ions, molecules o electrons, wave-particle, dualism... 

Lesk AM. Detection of three-dimensional patterns of atoms in chemical structures. Commun ACM 1979 22 219-224. 

The basic assumption in this model is that the shape of a molecule is a function of the number of atoms and their adjacency relationships (bonding scheme). The pattern of atoms and bonds is represented by a molecular skeleton or graph in which all hydrogen atoms are excluded, called the hydrogen-... 

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