Structural diagram

Based on the above-described concept of molecular structure, all configurational space of the nuclear coordinates Q q) may be divided into a finite number of 

The separation of the configurational space into structural regions may conveniently be represented in the form of a structural diagram [25, 26]. 

The structures of this type are unstable—any geometrical deformations, however small, which cause deviation from a boundary surface, destroy them. 

The topological approach has widened the concept of molecular structure (new definition of unstable structures), but especially important is that it has laid solid physical foundation under this central concept of chemistry by showing the possibility of rigorously defining the structure on the basis of the fundamental principles of quantum mechanics. This has put an end to uncertainty which hitherto prevailed in regard to this question. 

The authors of Refs. [19, 21-26] hold the view that the electron-topological approach to the analysis of molecular structure should, in principle, not be restricted to the Born-Oppenheimer approximation, however, this question is still unresolved (see Ref. [18] and other authors cited there). 

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The algorithm of calculating crack depth is realized in electropotential device Zond IGT-97 for measuring cracks depth. Its structure diagram is shown in Fig. 8 Using quasi-direct current is the device particular feature that made it possible to reduce its dimensions and weight. 

Representation of Chemical Compounds 21 Structure diagram Condensed formula... 

Figure 2-7. Different tine notations for the structure diagram of phenylalanine,...

The structure diagram is drawn and the atoms are arbitrarily numbered each atom is assigned a unique number),... 

Another approach applies graph theory. The analogy between a structure diagram and a topological graph is the basis for the development of graph theoretical algorithms to process chemical structure information [33-35]. 

Figure 2-20. A connection table the structure diagram of ethanal, with the atoms arbitrarily labeled, is defined by a list of atoms and a list of bonds.

Figure 2-32. Structure diagrams of a) phenylalanine and b) 1-isopropyladamantane c), d) different representations of 1 f ,4S,4aS,6fi,SaS-octahydro-4,8a,9,9-tetraiTiethyl-l, 6-methano-iiaphthalen-1 (2H -ol.

Figure 2-39. The empirical formula of C3H6O can be expressed by seven structure diagrams and even more compound names.

For database handling it is necessary to compare existing database entries with new ones. Consequently, database registration and retrieval are dependent on isomorphism algorithms which compare two graphs or structure diagrams to determine whether subgraphs are identical or not. 

Figure 2-62. The substituted phenyl derivative is an example of a typical Markush structure. Herein, a number of compounds are described in one structure diagram by fill-ins. Phenylalanine is one of these structures when r is COOH, is H, and X is H.

The stereochemistry is usually expressed in structure diagrams by wedged and hashed bonds. A wedge indicates that the substituent is in ont of a reference plane and a hashed bond indicates that the substituent is pointing away om the viewer (behind the reference plane). This projection is applied both to tetrahe-... 

However, care has to be taken to keep this graphical 3D information in 2D structure diagrams unambiguous. Since the reference plane can be chosen arbitrarily, there exist different possible ways of displaying the stereochemistry (Figure 2-68). 

Drawing-, text-, and structure-input tools are provided that enable easy generation of flow charts, textual annotations or labels, structures, or reaction schemes. It is also possible to select different representation styles for bond types, ring sizes, molecular orbitals, and reaction arrows. The structure diagrams can be verified according to free valences or atom labels. Properties such as molecular... 

D. Bawden, E.M. Mitchell, Chemical Information Systems - Beyond the Structure Diagram, Elhs Horwood, Chichester, UK, 1990. 

Factual databases may provide the electronic version of printed catalogs on chemical compoimds. The catalogs of different suppliers of chemicals serve to identify chemical compounds with their appropriate synonyms, molecular formulas, molecular weight, structure diagrams, and - of course - the price. Sometimes the data are linked to other databases that contain additional information. Structure and substructure search possibihties have now been included in most of the databases of chemical suppliers. 

Structure databases are databases that contain information on chemical structures and compounds. The compounds or structure diagrams are not stored as graphics but are represented as connection tables (see Section 2.4). The information about the structure includes the topological arrangement of atoms and the connection between these atoms. This strategy of storage is different from text files and allows one to search chemical structures in several ways. 

Patent databases are therefore integrated databases because facts, text, tables, graphics, and structures are combined. In patents that include chemical aspects (mostly synthesis or processing), the chemical compounds are often represented by Markush structures (see Chapter 2, Section 2.7.1). These generic structures cover many compound families in a very compact maimer. A Markush structure has a core structure diagram with specific atoms and with variable parts (R-groups), which are defined in a text caption. The retrieval of chemical compounds from Markush structures is a complicated task that is not yet solved completely satisfactorily. 

In order to transform the information fi om the structural diagram into a representation with a fixed number of components, an autocorrelation function can be used [8], In Eq. (19) a(d) is the component of the autocorrelation vector for the topological distance d. The number of atoms in the molecule is given by N. 

We denote the topological distance between atoms i and j (i.e., the number of bonds for the shortest path in the structure diagram) dy, and the properties for atoms i and j are referred to as pi and pj, respectively. The value of the autocorrelation function a d) for a certain topological distance d results from summation over all products of a property p of atoms i and j having the required distance d. 

Figure 10.3-16. Graphical representation of the chemical structure of the reactants and products of a chemical reaction a) as a 2D image b) with structure diagrams showing all atoms and bonds of the reactants and products to indicate how this information is stored in a connection table.

Fig. 17. Structural diagram (51) for sputtered layers. Zone 1 is a porous stmcture consisting of tapered crystallites separated by voids, Zone 2 shows...

The canonical jelly roll barrel is schematically illustrated in Figure 16.13. Superposition of the structures of coat proteins from different viruses show that the eight p strands of the jelly roll barrel form a conserved core. This is illustrated in Figure 16.14, which shows structural diagrams of three different coat proteins. These diagrams also show that the p strands are clearly arranged in two sheets of four strands each P strands 1, 8, 3, and 6 form one sheet and strands 2, 7, 4, and 5 form the second sheet. Hydrophobic residues from these sheets pack inside the barrel. 

Fig. 7.3. Crystal structures of some lithium etiolates of ketones. (A) Unsolvated hexameric enolate of methyl t-butyl ketone (B) tetrahydrofuran solvate of tetramer of enolate of methyl r-butyl ketone (C) tetrahydrofuran solvate of tetramer of enolate of cyclopentanone (D) dimeric enolate of 3,3-dimethyl-4-(r-butyldimethylsiloxy)-2-pentanone. (Structural diagrams are reproduced from Refs. 66-69.) by permission of the American Chemical Society and Verlag Helvetica Chimica Acta AG.

Fig. 16. Top High-rcsolution stereo SEM micrograph of the PAA oxide on 2024 aluminum. Bottom Schematic drawing of the oxide structure. Diagram from Refs. [9,59].

I. A. ZUBiETA and I. I. Zuckerman, Structural tin chemistry, Prog. Inorg. Chem. 24, 251-475 (1978). An excellent comprehensive review with full structural diagrams and data, and more than 750 references. 

F. Hulliger, Struct. Bonding (Berlin) 4, 83 -229 (1968). A comprehensive review with 532 references, 65 structural diagrams, and a 34-page appendix tabulating the known phases and their physical properties. 

Dance and K. Fisher, Prog. Inorg. Chem. 41, 637-803 (1994). A comprehensive review with 503 references, 100 structural diagrams and 40 pages of tabulated material. 

Helson HE. Structure diagram generation. In Boyd DB, Lipkowitz KB, editors. Reviews in Computational Chemistry, Vol. 13. New York Wiley-VCH, 1999. p. 313-98. 

Figure 8.1 Example of (a) a structure diagram, (b) systematic nomenclature, (c) connection table in MDL format (see URL http //www.mdli.com), and (d) SMILES for a molecule.

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