Tables, connection

A connection table has been the predominant form of chemical structure representation in computer systems since the early 1980s and it is an alternative way of representing a molecular graph. Graph theory methods can equally well be applied to connection table representations of a molecule. 

A connection table can be extended by adding otlier lists, such as lists of tbe free electrons and/or with the charges on the atoms of the molecule. Thus, in effect, all the information in a BE-matrix can also be stored in a connection table [40]. 

If the indexing of the atoms is changed, the CT will have a different appearance. Thus, the representation of a chemical structure in a CT is unambiguous but not unique, which can only be achieved by canonicalization (see below). 

Almost all chemical information systems work with tlicir own special type of connection table. They often use various formats distinguishing between internal and external connection tables. In most cases, the internal connection tables arc redundant, thus allowing maximum flexibility and increasing the speed of data processing. The external connection tables are usually non-redundant in order to save disk space. Although a connection table can be cprcsented in many different ways, the core remains the same the list of atoms and the list of bonds. Thus, the conversion of one connection table format into another is usually a fairly straightforward task. 

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To learn more about connection tables and matrix representations of chemical structures... 

Formula, Boolean, Matrices, Connection Table, Mashcode, etc. 

The WLN was applied to indexing the Chemical Structure Index (CSI) at the Institute for Scientific Information (ISI) [13] and the Ituiex Chemicus Registry System (ICRS) as well as the Crossbow System of Imperial Chemical Industries (ICl). With the introduction of connection tables in the Chemical Abstracts Service (CAS) in 1965 and the advent of molecular editors in the 1970s, which directly produced connection tables, the WLN lost its importance. 

A major disadvantage of a matrix representation for a molecular graph is that the number of entries increases with the square of the number of atoms in the molecule. What is needed is a representation of a molecular graph where the number of entries increases only as a linear function of the number of atoms in the molecule. Such a representation can be obtained by listing, in tabular form only the atoms and the bonds of a molecular structure. In this case, the indices of the row and column of a matrix entry can be used for identifying an entry. In essence, one has to distinguish each atom and each bond in a molecule. This is achieved by a list of the atoms and a list of the bonds giving the coimections between the atoms. Such a representation is called a connection table (CT). 

There are many ways of presenting a connection table. One is first to label each atom of a molecule arbitrarily and to arrange them in an atom list (Figure 2-20). Then the bond information is stored in a second table with indices of the atoms that are connected by a bond. Additionally, the bond order of the corresponding coimection is stored as an integer code (1 = single bond, 2 = double bond, etc.) in the third column. 

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 2-22. Non-redundant connection table of ethanal. Only non-hydrogen atoms are considered bonds with the lowest indices are counted once (see Figure 2-21).

MDL Molfile. mol Molfile the most widely used connection table format ummmdli.com 50... 

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. 

The task is now to take one of the numberings as the standard one and to derive a unique code from it, which is called canonicalization. This can be accomplished by numbering the atoms of a molecule so that it is represented later by only one connection table or bond matrix. Such a unique and reproducible numbering or labeling of the atoms is obtained by a set of rules. 

Deficiencies in Representing Molecular Structures by a Connection Table... 

The concept of connection tablc.s, a.s shown. so far, cannot represent adequately quite a number of molecular structures. Basically, a connection table represents only a single valence bond structure. Thus, any chemical species that cannot he described adequately by a single valence bond (VB) structure with single or multiple bonds between two atom.s is not handled accurately. 

Figure 2-47. The bonding in organometallic coinplexes (e.g., ferrocene) cannot be expressed adequately by a connection table,...

Representation of such a system by a connection tabic having bonds between the iron atom and the five carbon atoms of either one of the two cyclopentadienyl rings is totally inadequate. A few other examples of structures that can no longer be adequately described by a standard connection table are given in the Section 2.G.2. 

Benzene has already been mentioned as a prime example of the inadequacy of a connection table description, as it cannot adequately be represented by a single valence bond structure. Consequently, whenever some property of an arbitrary molecule is accessed which is influenced by conjugation, the other possible resonance structures have to be at least generated and weighted. Attempts have already been made to derive adequate representations of r-electron systems [84, 85]. 

Enol ethers (Figure 2-58a) have two electron pairs on the oxygen atom in two different orbitals, one delocalized across the two carbon atoms, the other strictly localized on the oxygen atom (Figure 2-58b). Ionization ftom either of these two orbitals is associated with two quite different ionization potentials, a situation that cannot be handled by the present connection tables. 

The species produced through ionization of an electron from a ir-orbital (such as from a C-H or a C-C bond of an alkane in mass spectrometry) cannot be represented at all by a connection table, yet the RAMSES notation can account for it as shown in Figure 2-59. 

Figure 2-59. Singly occupied j -systems are highly reactive intermediates that occur in MS experiments. They cannot be handled adequately by a) a connection table description, but are easily accommodated by b) RAMSES.

Ferrocene (Figure 2-61a) has already been mentioned as a prime example of multi-haptic bonds, i.c, the electrons tlrat coordinate tire cyclopcntadicnyl rings with the iron atom are contained in a molecular orbital delocalized over all 11 atom centers [811, for w hich representation by a connection table having bonds between the iron atom and the five carbon atoms of cither cyclopcntadicnyl ring is totally inadequate. 

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. 

In contrast to canonical linear notations and connection tables (see Sections 2.3 and 2.4), fragment codes arc ambiguous. Several different structures could all possess an identical fragment code, because the code docs not describe how the fragments arc interconnected. Moreover, it is not always evident to the user whether all possible fi aginents of the stmetures ai e at all accessible. Thus, the fragments more or less characterise a class of molecules this is also important in generic structures that arise in chemical patents (sec Section 2.7.1)... 

Hash coding is an established method in computer science, e.g., in registration procedures [94, 95. In chemoinformatics the structure input occurs as a sequence of characters (names) or numbers (which may also be obtained, e.g., from a connection table (see Section 2.4) by conversion of a structure drawing). Both names and numbers may be quite large and may not be usable as an address... 

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]. 

The connectivity information can be given either implicitly by approximating bonding distances between the atoms, or explicitly by a connection table (bond list as shown in Figure 2-20 and 2-25. 

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. 

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