Primitive single coronoid

Single corofusenes can be produced in copious amounts by additions of hexagons to primitive single coronoids all the five addition modes (viz. 5 cf. Vol. I—Fig. 2.2... 

Here = 0, 1, 2, 3, 4, 5, and each of these values is associated with a characteristic shape of the circular coronoid. These shapes were already known at least to Balaban (1971), who investigated their important role in the studies of annulenes cf. also a later work in this area (Cyvin SJ, Brunvoll and Gutman 1990). The same shapes are also encountered under the studies of certain primitive single coronoids called hollow hexagons (Cyvin SJ, Brunvoll and Cyvin 1989d Cyvin SJ, Brunvoll, Cyvin, Bergan and Brendsdal 1991), where the extremal property = hOj ax( ) corona hole is of interest. A detailed treatment of this topic is offered in Vol. 

In other words, the added hexagons constitute a primitive single coronoid. The circumscribed coronoid C is designated... 

Then, according to the last equation in Volume I, I—(9.9), a primitive single coronoid around the hole (ho, nfl) has h = h (and = 0). This of course presupposes that the corona hole benzenoid, which is characterized by (h , can be circumscribed. The foUowing restrictions are vaUd for primitive single coronoids. 

The occurrence of corona holes is cumulative in the following sense. All the holes which occur in the basic (primitive and non-primitive) single coronoids with h hexagons each, are also found in single coronoids with more than h hexagons. A detailed account on the numbers of single coronoid isomers with the different classes of holes (identified by endrded numerals), is furnished by Table 4. 

Fig. 5.5. Excising of three catacondensed single coronoids. From top primitive coronoid coronoid with an outside feature coronoid with an inside feature.

This principle implies that the one-contact additions (i) are sufficient for generating all the non—primitive catacondensed single coronoids with h + 1 hexagons from the catacondensed single coronoids with h hexagons. This property is clearly sound since the number of internal vertices (n ) should not be allowed to increase during the additions. The same property may also be inferred from the positions of the pertinent formulas in Table 5.3 (first formula... 

It is also needed to consider corona hole benzenoids which cannot be circumscribed. Such corona holes are associated with the non-primitive basic single coronoids (Vol. 1-8, especially 1-8.3). The well known smallest non-primitive basic coronoid (I-8.2.2 and I—Fig. 8.2) has h = 12. Its corona hole (benzo[c]phenanthrene) has ho = 4, 71 0 = 0. Here again h = h, where h is defined in (2), but n-= 1. The next-smallest non-primitive basic coronoid, which has h = 13, is also well known (references as above). Its corona hole (pentahelicene) has ho = 5, nfl = 0. In this case h = h — 1 and n = 0. The two smallest non—primitive basic coronoids are depicted in the following (cf. also the top row of I-Fig.8.1). 

These two cases exemplify corona hole benzenoids with a cove and a fjord, respectively. They are representative for all the non—primitive basic single coronoids with h = 12, 13 and 14 (I-Fig. 8.2), which are those of the prime interest in this section. For the sake of clarity we repeat the relevant rules in strict formulations. For 12 < h < 14 the non-primitive basic single coronoids are of two kinds, (a) The corona hole benzenoid possesses exactly one cove then h = h n = 1. (b) The corona hole possesses exactly one fjord then h = h — 1, = 0. 

The corona holes, represented as benzenoids, of all basic single coronoids for 8 < h < 14 (primitive and non-primitive) are depicted in Fig. 1. The encircled numerals identify the different classes with characteristic combinations of nfi and h. Table 3 includes a listing of the corona holes in question or the appropriate basic single coronoids, which amounts to the same. 

The situation is not so simple for the non—primitive basic single coronoids with h > 15. Already for h = 15 there is one instance not covered by the cases (a) and (b) above. It is depicted below (left-hand drawing). 

---