Nonalternant systems

Returning now to normal chemical equilibria, our next problem is to extend the treatment of Section 4.3 to nonalternant hydrocarbons. This can be done (see Sections 3.12 and 3.13, pp. 93 and 96), if the nonalternant systems in question can be derived from alternant ones by intramolecular or inter-molecular union. 

Consider, for example, the deprotonation of cyclopentadiene (5) to the anion (6) by base. 

We can derive (5) and (6) by intramolecular union from 1,3-pentadiene (7) and the corresponding anion (8), 

The n energy of reaction for conversion of (7) to (8) by reaction with the base B is given [see equation (3.44)] by 

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Although Hiickel molecular orbital theory is not completely consistent in its application to nonalternant systems such as the pentalenyl dianion, it does implicate a certain degree of stabilization for this species. If the transannular bond introduces little or no perturbation, then the pentalenyl dianion is seen to be closely related to the cyclooctatetraene dianion. Katz and his co-workers successfully developed a... 

Systems categorized. The electronic structure of hydrocarbons is very convenient to describe if the latter are subdivided into two classes of alternant and nonalternant systems, AS and NAS in the abbreviated form. 

The estimated stabilization energies from the HOSE model are in line with those obtained in other ways. It was shown that HOSE correlates well with the Hess and Schaad resonance energies (correlation coefficient R = 0.991 for 22 alternant TT-electron hydrocarbons R= 0.937 for 12 nonalternant hydrocarbons). In the last case, the Hess and Schaad RE values were given for nonalternant hydrocarbons whereas geometries used to calculate the HOSE values originated from substituted species. Since the substituent effect in nonalternant systems is quite considerable, these aspects will be discussed later. 

Tropolone is another famous nonalternant system whose aromaticity has long been disputed. Recent studies of its anion and two conformers of protonated tropolone have given us a good opportunity to analyze how the aromaticity is affected by the protonation. The HOMA for tropolone is equal to 0.642. Its anion is definitely less aromatic, HOMA = 0.176, whereas cis and trans conformers of protonated... 

In the PMO approximation, the n energy of a conjugated system is referred to that of the analogous AH from which it is derived by replacement of carbon atoms by heteroatoms or by internal union to form a nonalternant system. We follow the same procedure here. Our treatment of a family of reactions will therefore involve the following steps ... 

Analysis of the effect of internal union to form analogous nonalternant systems. 

Antiaromatic ground states of nonalternant monocyclic hydrocarbons will be aromatic with reference to the excited singlet states of their open-chain analogs nonaromatic (radical), nonalternant systems will be nonaromatic with reference to the excited singlet states of their open-chain analogs. Complete the proof that the rules for aromaticity in anti-Hiickel systems hold for the excited states of monocyclic Hiickel systems. 

In the case of nonalternant systems, however, the parallel between neutral molecules and the corresponding radical cations breaks down. Consider, for example, heptafulvene (Fig. 7.9b). Heptafulvene can be derived by union of tropylium with CH3" (Fig. 7.9b). Likewise, the open-chain analog of heptafulvene, octatetraene (Fig. 7.9d) can be derived by union of the odd AH cation heptatrienylium with CH3 (Fig. 7.9c). Since both heptafulvene and octatetraene are classical conjugated polyenes, their total n energies should be the same. 

Hence, naphthalene, phenanthrene, pyrene, and biphenylene are alternant hydrocarbons, while azu-lene, pyracylene, and its isomers are non-alternant conjugated hydrocarbons. The idea of classification of hydrocarbons as alternant and non-alternant goes back to Coulson and Longuet-Higgins and the early days of HMO theory. An important property of alternant hydrocarbons, as opposed to non-alternant, is that for alternant systems all HMO eigenvalues come in pairs Xu while this is not the case for nonalternant systems. It is interesting to mention that this particular mathematical property of alternant... 

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