Catacondensed Single Coronoids

Let Q be a catacondensed (n. = 0) single coronoid with h hexagons it has the formula Ah 2h Q f 2s s Q circumscribed. Then one finds easily from 

Assume now that Q is a catacondensed single coronoid without inside feature(s) cf. Vol. I-8.2.1. Then, as mentioned in Par. 5.4.5, = e(Q) consists of the inner perimeter. We shall 

Since also m = 0 for primitive coronoids, one obtains with the aid of eqn. (45) for 

It is recalled that 25 + 6 = (see above). The first parentheses on the right-hand side of (47) is valid for Q as assumed originally, viz. a catacondensed single coronoid without inside feature(s). In other words, 

This is immediately obvious because the excising will strip Q for the outside feature(s), which consist(s) of one or more catacondensed appendages. It is also possible to verify eqn. (48) in a formal way by computing m, the number of fusing edges, and exploit the more general equation for 5 inherent in (45). Let Q and Qt be the same coronoid except for the possible outside feature(s) in Q. Then 5 is the same in Q and Qt. Let the number of hexagons in Q and Qt be h and ht, respectively. Then 

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Firstly, if an excised coronoid Cq, viz. c(Cq), is not itself a coronoid, then the circumscribing of c(Cq) is not defined, and Cq becomes automatically a core coronoid. The two last systems of the top and bottom rows of Fig. 4.2 (viz. C32H16 and C48H20) examples. In particular, every catacondensed coronoid is a core coronoid belonging to the category under consideration. If Q is a catacondensed single coronoid vdthout an inside feature (cf. Vol. I), then e(Q) consists of the inner perimeter of Q. 

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

The formula for a catacondensed single coronoid is C2 H h = s/2). Then the formula index, in accordance with eqn. (15), can be written... 

Catacondensed Systems. The catacondensed single coronoids fall outside the scope of Principle 6.3. Instead, we have the following rules. 

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... 

Principle 6.4 All catacondensed (n = 0) single coronoid isomers are obtained by (a) attaching one unit to all dl possible positions and (b) including all the... 

There are 31177 catacondensed and 422769 pericondensed single coronoids with h = 15. This adds one row to Vol.I-Table 5.2. As another coarse classification, it was arrived at 172212 Kekulean and 281734 non-Kekulean systems. 

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