The connectivity table

The generation of equivalents (e.g. in a toluene molecule on an inversion centre) may be prevented by assigning a negative part number. If necessary, bonds may be added to or deleted from the connectivity array using the B l ND or fre E instructions. To generate additional bonds to symmetry equivalent atoms, EQIV can be used. 

Oftentimes the short highways can be travelled on auto pilot, and carriage return becomes the most important, if not the only, key on the computer. Referring to the decimal value of the carriage return key in the ASCII character set, we could call this the Highway 13—and that is not what this book is about. This book is about the outdoor adventure of roaming the rough roads of refinement, those perilous paths of 

A critical point in this process is the evaluation of the model, as the model should only be altered if a change improves its quality. There are several mathematical approaches to define a function which is assumed to possess a minimum for the best possible model in the world of small molecules (typically less than 2(X) independent atoms) the least-squares approach is by far the most common method, while for protein structures other methods Ufce maximum likelihood have also been employed. The program SHELXL, on which this book focuses, is predominantly a program for small-molecule structures and the least-squares refinement is the only method on which we need to concentrate. The concept is simple by means of Fourier transformation, a complete set of structure factors is calculated from the atomic model. The calculated intensities are then compared with the measured intensities, and the best model is that which minimizes M  

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Lines 4—18 form the connection table (Ctah), containing the description of the collection of atoms constituting the given compound, which can be wholly or partially connected by bonds. Such a collection can represent molecules, molecular fragments, substructures, substituent groups, and so on. In case of a Molfile, the Ctah block describes a single molecule. 

The first line of the connection table, called the counts line (see Figure 2-21), specifies how many atoms constitute the molecule represented by this file, how many bonds arc within the molecule, whether this molecule is chiral (1 in the chiral flag entry) or not, etc. The last-but-onc entry (number of additional properties) is no longer supported and is always set to 999. The last entry specifics the version of the Ctab format used in the current file. In the ease analyzed it is V2000". There is also a newer V3000 format, called the Extended Connection Table, which uses a different syntax for describing atoms and bonds [50. Because it is still not widely used, it is not covered here. 

RAMSES is usually generated from molecular structures in a VB representation. The details of the connection table (localized charges, lone pairs, and bond orders) are kept within the model and are accessible for further processes. Bond orders are stored with the n-systems, while the number of free electrons is stored with the atoms. Upon modification oF a molecule (e.g., in systems dealing with reactions), the VB representation has to be generated in an adapted Form from the RAMSES notation. 

Conversion in both directions needs heuristic information about conjugation. It would therefore be more sensible to input molecules directly into the RAMSES notation. Ultimately, we hope that the chemist s perception of bonding will abandon the connection table representation of a single VB structure and switch to one accounting for the problems addressed in this section in a manner such as that laid down in the RAMSES model. 

Figure 2-73. The stereo part" (right) of a tetrahedral C-atom inciuded in the connection table of an SMD file.

A molecule editor can draw a chemical structure and save it, for example as a Molfile. Although it is possible to include stereochemical properties in the drawing as wedges and hashed bonds, or even to assign a stereocenter/stereogroup with its identifiers R/S or E/Z), the connection table of the Molfile only represents the constitution (topology) of the molecule. 

The additional stereoinformation has to be derived from the graphical representation and encoded into stereodescriptors, as described above. The stereodescriptors are then stored in corresponding fields of the connection table (Figure 2-76) [50, 51]. 

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

The representation of a chemical reaction should include the connection table of all participating species starting materials, reagents, solvents, catalysts, products) as well as Information on reaction conditions (temperature, concentration, time, etc.) and observations (yield, reaction rates, heat of reaction, etc.). However, reactions are only Insuffclently represented by the structure of their starting materials and products,... 

The connection table of the query object (similarity probe) is processed to obtain the set of atom pairs, and then the database file is scanned to evaluate the similarity between the query and each of the database structures. The maximum number of structures that the program will select is specified, as well as the minimum similarity score that a database compoimd must show to be selected. Within these limits, the program will select from the database the structures that are most similar (with the highest similarity value) to the query and will create an output file of compoimd numbers and similarity values, sorted by decreasing similarity, for the selected compounds. 

The method of building predictive models in QSPR/QSAR can also be applied to the modeling of materials without a unique, clearly defined structure. Instead of the connection table, physicochemical data as well as spectra reflecting the compound s structure can be used as molecular descriptors for model building,... 

A descriptor for the 3D arrangement of atoms in a molceulc can be derived in a similar manner. The Cartesian coordinates of the atoms in a molecule can be calculated by semi-empirical quantum mechanical or molecular mechanics (force field) methods, For larger data sets, fast 3D structure generators are available that combine data- and rule-driven methods to calculate Cartesian coordinates from the connection table of a molecule (e.g., CORINA [10]). 

There are a number of different ways that the molecular graph can be conununicated between the computer and the end-user. One common representation is the connection table, of which there are various flavours, but most provide information about the atoms present in the molecule and their connectivity. The most basic connection tables simply indicate the atomic number of each atom and which atoms form each bond others may include information about the atom hybridisation state and the bond order. Hydrogens may be included or they may be imphed. In addition, information about the atomic coordinates (for the standard two-dimensional chemical drawing or for the three-dimensional conformation) can be included. The connection table for acetic acid in one of the most popular formats, the Molecular Design mol format [Dalby et al. 1992], is shown in Figure 12.3. 

An alternative way to represent molecules is to use a linear notation. A linear notation uses alphanumeric characters to code the molecular structure. These have the advantage of being much more compact than the connection table and so can be particularly useful for transmif-ting information about large numbers of molecules. The most famous of the early line notations is the Wiswesser line notation [Wiswesser 1954] the-SMILES notation is a more recent example that is increasingly popular [Weininger 1988]. To construct the Wiswesser... 

An important approach to the graphic representation of molecules is the use of a connection table. A connection table is a data base that stores the available bond types and hybridizations for individual atoms. Using the chemical formula and the connection table, molecular stmctures may be generated through interactive graphics in a menu-driven environment (31—33) or by using a linear input of code words (34,35). The connection table approach may be carried to the next step, computer-aided molecular design (CAMD) (36). 

Our present reaction rule database is made up of approximately one hundred rules adapted from a microfiche generously sent to us by Gelernter (4). For a given reaction, a rule specifies the reactants (subgoal) and the product(s) (goal), in connection table format and any constraints on their composition (Figure 2a). The rules are identified by chapter and schema numbers. The connection tables are organized as follows ... 

Each goal or subgoal clause is terminated with the predicate Rxnrule whose first argument is a reaction rule identification number. After this number, the predicate uses the function LL (for linked list) to list all the atoms in the connection table. 

Historically, most chemists have modeled the structure of molecules using a highly idealized platonic representation, where atoms are represented as vertices and bonds as paths between vertices. Chemoinformatics has very successfully adopted this representation and based many of its techniques around the metaphor of the connection table , i.e., a list of all atoms and bonds, which occur in the molecule. While this approach is quite successful for well defined chemical entities, it begins to break down for rapidly interconverting isomers, for example, and is completely inappropriate for polymers. In the majority of cases, the successful application of chemoinformatics to a given problem depends on the availability of a connection table. 

The representation is unambiguous since it corresponds to one and only one substance, but it is not unique because alternative numberings of the connection table would result in different representations for the same chemical substance (the connection table representation is discussed in more detail below). In addition to being categorized according to their uniqueness and ambiguity, chemical substance representations commonly used within computer-based systems can be further classified as systematic nomenclature, fragment codes, linear notations, connection tables, and coordinate representations. 

Dittmar, Stobaugh, and Watson [8] describe the connection table utilized in the CAS Chemical Registry System. Lefkowitz [9] describes a concise form of a connection table, called the Mechanical Chemical Code, which does not explicitly identify the bonds and has attributes of both a connection table and linear notation. 

Eakin [13] describes the chemical structure information system at Imperial Chemical Industries Ltd., where registration is based on Wiswesser Line Notation. For connection tables, the unique, unambiguous representation is derived automatically, i.e., a single, invariant numbering of the connection table is algorithmically derived. 

The conversion from a connection table to other unambiguous representations is substantially more difficult. The connection table is the least structured representation and incorporates no concepts of chemical significance beyond the list of atoms, bonds, and connections. A complex set of rules must be applied in order to derive nomenclature and linear notation representations. To translate from these more structured representations to a connection table requires primarily the interpretation of symbols and syntax. The opposite conversion, from the connection table to linear notation, nomenclature, or coordinate representation first requires the detailed analysis of the connection table to identify appropriate substructural units. The complex ordering rules of the nomenclature or notation system or the esthetic rules for graphic display are then applied to derive the desired representation. 

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