Ground form benzenoid

A higher member (of benzenoids) is a drcumextremal benzenoid (and itself an extremal benzenoid). A ground form is an extremal benzenoid which is not drcumextremal. Assume that (Nq 5q) is a formula for a ground form benzenoid G. Then the formulas Nq 5q), (N 5 ),., N 5, . are said to form a constant-isomer series when (N 5 pertains to k-iold drcumscribed G. All these formulas are known to have the same number of benzenoid isomers. 

The associated benzenoid to G is a ground form benzenoid, while the associated... 

The value of x gives the following information about B. (i) x > 0 B is a nonextremal benzenoid. If it can be circumscribed x times, then x-circum—B is a ground form benzenoid (which is extremal), and there always exists (at least) one isomer Be N 5 which can be circumscribed arbitrarily many times, (ii) x = 0 B is a ground form benzenoid. (iii) x < 0 B is a higher member (drcumextremal benzenoid), and specifically an x —fold circumscribed ground form. 

How can we know whether a benzenoid with the formula C HS is a member (ground form or higher member) of a one-isomer series The relation... 

The general expression for the formulas of the ground forms of constant-isomer benzenoid series in the Balaban picture was worked out from the formula (b) of Sect. 8.1. The new pair of parameters <5 was introduced to be consistent with the description in Sect. 8.2. The net result reads [51]... 

In Table 3 a number of formulas for the ground forms of constant-isomer benzenoid series are listed. 

It is useful to have some concrete pictures of the ground forms for constant-isomer benzenoid series, in continuation of Fig. 10 for the one-isomer series. Some of them are displayed in our main reference [8] and more of them elsewhere [20, 43], the latter citation [43] containing detailed documentations to previous works. All the complete sets from these sources are collected in Fig. 11 (without too much overlap with the previous chapter [8]). 

Fig. 12. The C52Hig (h = 18) benzenoid isomers, first higher members of a constant-isomer series (ground forms in Fig. 11)...

F5g. 13. Parts of the ground forms for constant-isomer series of benzenoids (25 < h < 41) they should be supplemented with circumscribed benzenoids according to the text... 

Application of the Special Aufbau Procedure to Ground Forms of Constant-Isomer Benzenoid Series... 

Let again G represent the ground forms of a constant-isomer series for benzenoids, of which the formula is C HS or (n s). In the following treatment... 

Table 6. Three-parameter codes for (n s) and (n — 3 s — 1), where (n s) represents the ground forms of a constant-isomer benzenoid series...

If C H5 has an excised internal structure [8, 32-34, 38], then its formula is C 2s+6Hs 6 in accord with Eq. (26). This is also the formula which appears in point (c ) of the special aufbau procedure (Sect. 11). In general an excised internal structure may be a non-benzenoid. Several examples of this phenomenon are found in Fig. 10. In connection with Eq. (27), however, when the excised internal structures of not too small ground forms (G) of constant-isomer benzenoid series are going to be considered, we shall only encounter benzenoids as such systems. Therefore, all we need to known about the definition of an excised internal structure here, is if G = circum-G0, then the benzenoid G° is the excised internal structure of G. Let again (n s) be the formula of G, and correspondingly (n° s°) of G°. Then... 

The answer to the above question is therefore Look up the formula for the ground forms with the same 5 as in G, but one unit less in j. Subtract C2, which means moving two places up and one place to the right in the periodic table for benzenoids. 

The cardinality of C HS, which represents the j, 8 ground forms (h > 13) for constant-isomer series of benzenoids, is given by... 

The isomers with the formulas in Table 8 were enumerated by computer aid as far as possible. These systems are excised internal structures (G°) of ground forms for constant-isomer series of benzenoids when they are benzenoids themselves. They were classified according to A values and the symmetry groups to which they belong. The results are listed in Tables 9 and 10 for the even- and odd-carbon atom formulas, respectively. The documentation (given by footnotes) therein follow the previous review [8],... 

Fig. 17. The smallest ground form of constant-isomer benzenoid series which is an improper snowflake C99oH78 (h = 457)...

Let a constant-isomer series of benzenoids be identified by the symbol j, 5 cf. Sect. 9.4 and Table 3. Strictly speaking this symbol was specifically used for the ground forms. However, the discussion of the present section is not restricted to these systems since the properties under consideration (A and symmetry) do not change by circumscribing. Let the partial cardinality for j, <5 at a given A value be written y, 5, A. Then the Dias paradigm in a strict sense, as will be used presently, is expressed by ... 

Table 6.1. Fonnula for the first (smallest) ground forms of single coronoids (G) and their associated benzenoids (A) ...

Careful product and kinetic studies for selected electron-deficient alkenes, electron-rich dienes and vinyl-substituted aromatic systems have provided some clarification of the [2 + 2] versus [2 + 2] cycloaddition issue. The thermodynamically favored product can often be anticipated on structural grounds. Reactions of TCNE with vinyl-substituted benzenoid aromatics, protoporphorins or heteroaromaticsgive [2 + 2] products, but for some styrenes the [2 + 4] addition may be kinetically favored. p-Methoxystyrene and TCNE react to form a charge-transfer complex which leads reversibly to the Diels-Alder product, and eventually to the finally isolated [2 + 2] adduct. An isomer of di-cyclopentadiene shows the same pattern, with the initially formed Diels-Alder adduct giving rise to a [2 + 2] adduct. 

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