Peri-condensed benzenoids

An excised internal structure or insular structure is a structure obtained by excising out the set of connected internal vertices usually associated with a strictly peri-condensed benzenoid hydrocarbon [3,13]. A strictly peri-condensed benzenoid PAH6 has all its internal third degree vertices mutually connected, has no cata-condensed... 

If a benzenoid excised internal structure is 1-factorable, 2-factorable, strictly peri-condensed, has one or more bay regions, and/or has one or more selective... 

Rank order is increasing from top to bottom and left to right. Fig. 2. Scheme for recursive enumeration of some peri-condensed benzenoids... 

Rule 1. Whenever the excised internal structure has an eigenvalue of zero, then the nonbisanthrene-like strictly peri-condensed benzenoid structure also has an eigenvalue of zero. 

Phenylenyl monoradical (C13H9) is a strictly peri-condensed PAH6 with the methyl radical as an excised internal structure and both have e = 0. The diradical C22H12 isomer, triangulene, is a strictly peri-condensed benzenoid hydrocarbon and has trimethylenemethane diradical as an excised internal structure both triangulene and trimethylenemethane diradicals have two eigenvalues of s = 0. 

Fig. 2 Cata- and peri-condensed benzenoid hydrocarbons with Clar structure...

Distributions of pyrolytic PAFls are characterized by the dominance of the non-alkylated species shown in Fig. 7.3. Particularly abundant are the highly peri-condensed compounds—such as pyrene, the benzopyrenes, benzo[gfe]perylene and coronene—that result from extensive angular fusion of benzenoid systems.The presence of such PAF1 distributions in the aromatic... 

Both graphite and diamond in practice are not infinite, but finite nets and therefore have dangling bonds at the peripheries of single crystals normally, these bonds have hydrogen atoms attached to them. Consequently one may consider graphite to be an "honorary polycyclic peri-condensed benzenoid hydrocarbon", and diamond to be an "honorary adamantanoid or diamondoid hydrocarbon"... 

We will show that the interatomic distances and their powers offer a better characterization of molecular shapes. The shape of an object is defined by its exterior, surface, or contour in the case of 2D objects. Hence, when characterizing molecular shape one should consider only the interatomic separations between atoms at the molecular periphery, excluding atoms in the interior part of the structure. In the case of cflto-condensed benzenoids, all carbon atoms are on the periphery, hence the shape profile and the molecular profile of such compounds are the same. In the case of peri-condensed benzenoids, only carbon atoms at the periphery will be taken into account. 

If we extend the similarity/dissimilarity analysis to all benzenoids having P = 18 (including contours of peri-condensed systems 6-12), using shape profiles for their characterization we find as the least similar pairs ... 

We want to discuss the differences of the characterization of benzenoid hydrocarbons by the molecular profiles and by the shape profiles. Let us consider pen-condensed benzenoids more closely. In Table 24 are listed for the selected peri-condensed benzenoids (illustrated in Figure 28) the numerical values for the molecular... 

In the former only the carbon atoms on the molecular periphery contribute in the construction of the average interatomic distances and the average powers of the distances. For cata-condensed benzenoids, both and S are identical, but for peri-condensed benzenoids there is a difference between the two sets of descriptors. When we use 5 descriptors in the regressions of the Chromatographic retention indices we obtain ... 

A comparison with the corresponding values of equations (3)-(5) shows that the descriptors D, D, D, in which the atoms in the interior as well as those at the periphery contribute, are superior in describing Chromatographic indices of benzenoids. The superiority of over 5 descriptors becomes even more pronounced if we limit the analysis only to peri-condensed benzenoids for which the descriptors "D and differ. In Table 27 we compare the regressions using the shape descriptors and the full descriptors... 

Although the alkane and alkane-like substances are the most important, no series of compounds has received as much interest in generating isomer series as has the polyhexes, with much being done on various classes of benze-noids. For example, isomer series are available for benzenoids of a variety of classes, including peri-condensed, cata-condensed, essentially disconnected,helicenes, ° resonant sextets, quinones, coronenes, "" and pyrenes.Recently, with the aid of a new lattice... 

Peri-condensed benzenoid hydrocarbons or perifusenes can have one or more inner carbon atoms common to three rings, that is, their dualist graph has three-membered cycles. As a well-known rule, Kekulean alternant systems must have even numbers of inner carbon atoms, whereas Kekulean non-altemants may have either even or odd numbers of inner carbon atoms. In Part 3. Perifusenes (Balaban and Randic 2004c) all possible benzenoid perifusenes having four, five and six benzenoid rings were displayed and examined. In Fig. 8.15 we show some of them. 

The EC values of alternant non-benzenoids have not been discussed till now. We shall limit the discussion to cata-fused non-benzenoids having two or three condensed rings with ring sizes equal to 4, 6, or 8, and to peri-condensed non-benzenoids with the above ring sizes having at most four rings. Figure 8.19 craitains structures of systems that are discussed in this section. 

Fig. 9.11 The Wiswesser codes for peri-condensed polyhexes with a single inner vertex representing carbon skeletons of rather unstable benzenoids with five six-membered rings C21HJ3...

At first, it seems that the generation of the numeric Kekule stmctures for peri-condensed benzenoids is also straightforward. For example, this is shown in the case of benzo[a]pyrene. Its geometric and numeric Kekule stmctures are given in Figs. 9.16 and 9.17. 

It should be noted that the numeric code is a linear code in which the codes for peri-condensed benzenoids are built in the same way as the Wiswesser codes. For example, the numeric code for the Kekule structure VI (see Fig. 9.17) is 45335. 

However, it appears that there exist peri-condensed benzenoids with distinct geometric Kekule structures but with the identical numeric Kekule structures (Gutman et al. 2004 Vukicevic et al. 2004). The smallest example of such a case is pyrene. In Fig. 9.18, we give its six geometric Kekule stmctures and in Fig. 9.19 its six numeric Kekule structures. Note, stmctures denoted by B and C possess identical numeric codes. Therefore, there is no one-to-one correspondence between geometric and numeric Kekule stmctures for some peri-condensed benzenoids. In such cases the recovery of geometric stmctures requires the amendment of the numeric codes. 

In Fig. 9.21, we show how a pair of peri-condensed benzenoid with identical numeric codes can be recovered from their perimeter codes. As an illustrative example, we selected numeric code 5 5 2 2 5 5 which is identified to belong to a pair of Kekule structures of dibenzo[, op]naphthacene. 

Fig. 7.2. Forms of single coronoid isomers. Abbreviations 71 normal 0 non—Kekulean, with the A values indicated as subscript - 0. When the associated benzenoid is strictly peri condensed, the contour of its excised internal structure is given by heavy lines.

Dias JR (1990b) Benzenoid Series Having a Constant Number of Isomers — 2 — Topological Characteristics of Strictly Peri-Condensed Constant-Isomer Benzenoid Series. J Chem Inf Comput Sci 30 251... 

The concept of numeric Kekule structures is used for coding and ordering Kekule structures of cfltfl-condensed benzenoids. In the case of peri-condensed benzenoids, the numeric code of Kekule structures is not discriminative enough since there are Kekule structures with identical numeric codes. In that case, an additional code is needed—Milicevic et al. (2004) tested the use of the Wissweser coding system for benzenoid hydrocarbons, and Lucid et al. (2011) tested the perimeter codes. 

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