Numbering the atoms of a molecule

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. 

Various methods have been developed for a unique and unambiguous numbering of the atoms of a molecule and thus for deriving a canonical code for this molecule [76]. Besides eigenvalues of adjacency matrices [77], it is mainly the Morgan Algorithm that is used [79]. 

Basically, two different methods arc commonly used for representing a chemical struchiive in 3D space. Both methods utilize different coordinate systems to describe the spatial arrangement of the atoms of a molecule under con.sidcration. The most common way is to choose a Cartesian coordinate system, i.e., to code the X-, y-, and z-coordinates of each atom, usually as floating point numbers, For each atom the Cartesian coordinates can be listed in a single row. giving consecutively the X-, )> , and z-valnc.s. Figure 2-90 illustrates this method for methane. 

Internal fluctuations are caused by the discrete nature of matter. The density of a gas fluctuates because the gas consists of molecules fluctuations in a chemical reaction arise because the reaction consists of individual reactive collisions current fluctuations exist because the current is made up of electrons radioactive decay fluctuates owing to the individuality of the nuclei. Incidentally, this explains why the formulas for fluctuations in physical systems always contain atomic constants, such as Avogadro s number, the mass of a molecule, or the charge of an electron. 

Spatial autocorrelation is a quantitative measure of the probability of finding objects of defined properties within a distance of interest [9, 10]. The concept of autocorrelation is mainly applied in fields such as geography, economics, ecology or meteorology to describe the spatial distribution of features. The idea of a molecular descriptor based on the autocorrelation concept was first introduced into the field of cheminformatics by Moreau and Broto in 1980 [11] with the ATS (autocorrelation of a topological structure) descriptor. For this approach, the atoms of a molecule were represented by properties such as atomic mass or partial charge. The distance between atoms was measured as the number of bonds between the respective atoms (topological distance). 

Fig. 4.24 The SHM charges on the atoms of a molecule can be calculated from the number of electrons in each occupied MO and the coefficients of these MOs. The predicted dipolar nature of methylenecyclopropene has been ascribed to a cyclopropenyl-cation-like resonance contributor...

A number of practical problems are involved, however, most particularly in the interconversion of absolute and relative stereochemical descriptors because a substructure query does not show all the atoms of a molecule, it is not normally possible to... 

The atoms of a molecule can be partitioned into equivalence classes on the basis of a single property or a set of properties. The value of each class for the property(s) will be called the initial canonical value. The set of properties could include the atomic number, predominant in the Cahn-Ingold-Prelog system if this is used to number the atoms of the molecule, or the number of ligand atoms, which is the property... 

A more general picture involves complex motion of all the atoms of a molecule. This over-all complex motion can be resolved into a small number of basic motions, which can be designated as the fundamental vibrations of the molecule. It can be shown that in order to resolve the complex motion of a nonlinear molecule of N... 

Their boiling points increase with the number of carbon atoms. For molecules of low carbon numbers, the addition of a carbon increases the boiling point about 25°C. Further additions result in a smaller increase. The density increases with the molecular weight 0.626 kg/1 for pentane which has 5 atoms of carbon, 0.791 kg/1 for pentacosane which has 25 carbon atoms, but the density is always much lower than 1. 

With such a matrix representation, the storage space is dependent only on the number of nodc.s (atoms) and independent of the number of bonds. As Figure 2-14 dcmon.stratcs, all the e.sscntial information in an adjacency matrix can also be lound in the much smaller non-rediindant matrix. But the adjacency matrix is unsuitable for reconstructing the constitution of a molecule, because it does not provide any information about the bond orders. 

The most well-known and at the same time the earliest computer model for a molecular structure representation is a wire frame model (Figure 2-123a). This model is also known under other names such as line model or Drciding model [199]. It shows the individual bonds and the angles formed between these bonds. The bonds of a molecule are represented by colored vector lines and the color is derived from the atom type definition. This simple method does not display atoms, but atom positions can be derived from the end and branching points of the wire frame model. In addition, the bond orders between two atoms can be expressed by the number of lines. 

The length or dimension of the RDF code is independent of the number of atoms and the size of a molecule, unambiguous regarding the three-dimensional arrangement of the atoms, and invariant against translation and rotation of the entire molecule. 

When writing the constitution of a molecule it is not necessary to concern your self with the spatial orientation of the atoms There are many other correct ways to represent the constitution shown What is important is to show the connectiv ity OCCN (or its equivalent NCCO) and to have the correct number of hydrogens on each atom... 

Section 2 4 In molecular orbital theory the molecular orbitals (MOs) are approxi mated by combining the atomic orbitals (AOs) of all of the atoms m a molecule The number of MOs must equal the number of AOs that are combined... 

First the peak for the molecular ion M for all compounds that contain only car bon hydrogen and oxygen has an m z value that is an even number The presence of a nitrogen atom m the molecule requires that the m z value for the molecular ion be odd An odd number of nitrogens corresponds to an odd value of the molecular weight an even number of nitrogens corresponds to an even molecular weight... 

One of the major difficulties with molecular mechanics procedures (MMh- or otherwise) is that they almost always fail. That is, you find that force constants are not available for the molecule of interest. This is both the strength and weakness of molecular mechanics it uses atom types to introduce specific chemical environments for the atoms within a molecule (to obtain accuracy in the calculations) but then requires knowledge of force constants specific to that chemical environment (as specific as stating that an atom is in a five-member ring containing one oxygen and one carbon, for example). As the number, N, of atom types rises the number of force constants needed to describe all possible occurrences of these atom type becomes very large. For torsions, for... 

HyperChem quantum mechanical calculations are ab initio and semi-empirical. Ab initio calculations use parameters (contracted basis functions) associated with shells, such as an s shell, sp shell, etc., or atomic numbers (atoms). Semi-empirical calculations use parameters associated with specific atomic numbers. The concept of atom types is not used in the conventional quantum mechanics methods. Semi-empirical quantum mechanics methods use a rigorous quantum mechanical formulation combined with the use of empirical parameters obtained from comparison with experiment. If parameters are available for the atoms of a given molecule, the ab initio and semi-empirical calculations have an a priori aspect when compared with a molecular mechanics calculation, letting... 

---