Theory of Coronoid Hydrocarbons

Coronoid systems, which are defined in the subsequent chapter, have chemical counterparts in what we shall call coronoid hydrocarbons. Different other terms have been introduced in organic chemistry, some of which also being used in the present chapter. All the compounds to be considered here belong to the conjugated hydrocarbons. Typical coronoid hydrocarbons are polycyclic (aromatic) and consist of benzenoid rings. They are macrocyclic in contrast to the benzenoid hydrocarbons.

In this chapter some fundamental characteristics of the coronoid systems are described. Special attention is paid to several invariants and relations between them. Furthermore, several classification schemes for coronoids are put forward.

By enumeration of coronoid systems the counting of all possible non-isomor-phic systems within a class of coronoids is understood. Usually (but not always) the number of hexagons (h) is the leading parameter. The primitive coronoid with h=S (Fig. 2.1) is the smallest coronoid and unique with this number of hexagons. The numbers of non-isomorphic coronoid systems with h — 9, 10 and 11 are 5, 43 and 283, respectively. These numbers increase rapidly, roughly by a factor between 6 and 7 for every h unit, but yet they are known for several additional h values (see below, throughout this chapter). We are not only interested in the grand total of coronoid systems, but also in subdivisions into different classes. In this connection one speaks about classification. This aspect is especially important for large h values.

As a supplement to the references to previous work listed in Section 5.1 we give here the references to some works which include special treatments of primitive coronoids and their enumeration: Cyvin SJ, Cyvin, Brunvoll and Bergan (1987); Cyvin SJ, Brunvoll and Cyvin (1988; 1989a; 1989d); Brunvoll, Cyvin BN, Cyvin, Gutman, Tošić and Kovačević (1989); Cyvin SJ, Brunvoll, Cyvin, Tošić and Kovačević (1989); Cyvin (1989); Gutman and Cyvin (1989b); Cyvin SJ, Brunvoll, Cyvin, Bergan and Brendsdal (1990).

The generation of regular coronoids is described in Paragraph 5.4.2. These systems are divided into classes according to the below scheme, which contains the presently applied abbreviations in parentheses.

A classification of coronoids according to the corona hole is especially instructive. Firstly, we shall be concerned about the enumeration of all coronoids with a given hole and different (increasing) numbers of hexagons (h). Secondly, a detailed subdivision into classes within the whole set shall be reported for the different h values.

In the preceding chapters the classification of the coronoids into cataconden-sed and pericondensed systems is taken into account. This means a classification according to n_i = 0 and n_i > 0, respectively, where n_i is the number of internal ver-tices. A more detailed classification of the pericondensed coronoid systems according to the values of n_i is also possible. This kind of classification, which is the subject of the present chapter, is of a particular chemical interest because it is virtually an enumeration of the chemical isomers. Some enumerations of this kind for coronoid systems, beyond the catacondensed coronoids, have been reported (Cyvin SJ and Brunvoll 1989; Dias 1990; Cyvin SJ, Brunvoll and Cyvin 1990b).