Higher member benzenoid

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... 

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

The first three benzenoids in Fig. 11 pertain to the first formula (C22H12) in Eq. (14). The next formula (C52H12) is accounted for by the first higher members of this series see Fig. 12. These three instructive forms are also found in one of the references cited above [43], Moreover, all three of them or the two Kekulean ones, have been displayed several times by Dias [32-34, 36-38, 46, 53-55]. 

The annulenes are that series of monocyclic polyolefins (C H ) containing a complete system of contiguous double bonds. While benzene (the best known member of this class of compounds) has been in evidence for some time it is only of late that interest in the higher members has become apparent. This interest has its origins in the LCAO-MO theory of re-elec-tron systems as formulated by E. Hiickel (in particular the "Hiickel rule relating aromatic stability to structure). Although the non-classical chemistry of the benzenoid hydrocarbons had previously been the subject of some conjecture, Httckel s theoretical studies provided the first satisfactory explanation of the peculiar stability of this class of compounds and, incidently, the elusiveness of cyclobutadiene. 

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 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. 

Biphenylene and trisdehydro[12]annulene are representatives of conjugated hydrocarbons with a 4 -membered ring. The pattern of their absorption spectra is completely different from that of benzenoid aromatics. Their HOMO and LUMO are derived from the two NBMOs of an ideal perimeter and both the lowest excited singlet and triplet state can be described by the configuration A ho lu- The transition is symmetry forbidden in molecules of D2h symmetry or higher. Nonradiative decay usually dominates their photophysical properties. Quantum yields of fluorescence and intersystem crossing are low.307 The LCAO version of Platt s perimeter model has been extended to treat conjugated systems with AN jt-electrons derived from [ ]annulenes.308,309... 

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