Bond alternation in annulenes

We have so far calculated NBMO coefficients by using the simplified form of Longuet-Higgins rule in which all carbon-carbon jS s are assumed equal this in effect assumes that the CC bonds all have similar lengths. Since the CC 71 bond becomes stronger the shorter it is (Section 1.13), and since the TT-bond energy of such a bond is - 2)8, )8 must be numerically greater the shorter is the CC bond. 

We have seen (Section 3.9) that the bond lengths in open-chain polyenes alternate. The CC resonance integral must then have a larger value ()8 ) for pairs of atoms forming double bonds than ()8 ) for pairs of atoms 

In order to compare the energies of linear and cyclic polyenes in which the bond lengths alternate, we must study the union of methyl with an odd AH radical in which the bond lengths alternate. Consider, for example, allyl  

The values of the NBMO coefficients are given by the rigorous form of Longuet-Higgins rule [equation (3.9)] 

The alternation of bond lengths in the allyl radical means that j8 is greater than P. Thus C is less than unity. 

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The origins of the chemical shifts are probably not sufficiently well understood (as yet), to allow a quantitative discussion of aromatic character in the annulenes. If such a concept is considered meaningful it would probably best be defined in terms of the degree of bond alternation therein, which is of pivotal importance to the jr-electron properties (see Sections B and C). Apart from theoretical calculations, a number of physical methods have demonstrated their ability to estimate the extent of bond alternation in annulenes (crystallographic analysis, electronic/vibronic spectral analysis, diamagnetic anisotropy/susceptibility exaltation measurements and of course n.m.r.), see ref. > for a full discussion. (Furthermore the known correlation between n.m.r. vicinal coupling constants and carbon-carbon bond orders is of potential utility in any determination of bond alternation 65>). 

Prior to this discussion of experimental n.m.r. data, a brief theoretical outline of annulene chemistry will be included, which begins with a consideration of the phenomenon of bond alternation in the next section. An understanding of bond alternation is necessary as it augments Hiickel s rule in delineating more precisely the relationship between the annulenes and the corresponding linear polyenes. A section will then be devoted to a consideration of some of the more important experimental parameters (other than magnetic properties) which have been studied in relation to aromaticity. 

More recently, Dewar and Gleicher 2o> have carried out SCF calculations for the annulenes (with experimental geometries). From the calculated resonance energies they conclude that the onset of bond alternation in the An + 2) series should begin with [26]annulene, which they predict to be non-aromatic (see Table 1 and Fig. 2). Note, however, that the calculated difference in resonance energy between [22] and [26]an-nulene only amounts to about 7 kcal/mole in such large molecules this could easily be overshadowed by steric requirements. 

This non-mobile spectrum shows [18]annulene to be aromatic, a fact which follows from Huckel s theory, together with the finding 118> that this molecule is almost planar, displacement of the carbon atoms from the mean plane being less than 0.1 A. Further X-ray crystallographic analysis 114> shows that there is no bond alternation in this molecule, (but not all bonds are exactly the same length). 

The results for [16] annulene are similar. The compound was synthesized in two different ways, both of which gave 103, which in solution is in equilibrium with 104. Above -50°C there is conformational mobility, resulting in the magnetic equivalence of all protons, but at — 130°C the compound is clearly paratropic there are 4 protons at 10.565 and 12 at 5.35 5. In the solid state, where the compound exists entirely as 103, X-ray crystallography shows that the molecules are nonplanar with almost complete bond alternation The single bonds are 1.44-1.47 A and the double bonds are 1.31-1.35 A. A number of dehydro and bridged... 

In agreement with the Hiickel rule those annulenes and dehydroannulenes which contain (4 n + 2) 77 electrons and a reasonably planar carbon skeleton appear to be aromatic. Aromaticity in annulenes is usually equated with positive resonance energy and the absence of bond alternation. The most direct method of measuring bond alternation is by single crystal X-ray diffraction. Unfortunately this method has been applied in only a few cases. 

The [16]annulene is nonplanar, with almost complete bond alternation. The single bonds (1.454 A) are alternately trans and gauche, and the double bonds (1.337 A) cis and trans. The average torsion angle at a gauche C—C bond is 41°. The molecule is therefore relatively flat with S4 noncrystallographic symmetry, and the structure confirms the lack of aromaticity in this [4n] annulene. 

A simple consequence of the above is the large vertical resonance energy of the distorted benzene in Figure 6 and its aromatic magnetic behavior both computed and measured.32 169-171 In fact, as emphasized by Choi and Kertesz,87 even when the aromatic [nj-annulenes undergo bond alternating distortion, their magnetic properties are still those of an aro-... 

The above arguments are quite general and applicable to other bond-alternated ground states in aromatic molecules (e.g., the distorted [18]-annulene produced with the bicyclic annelations224 as well as in other antiaromatic annulenes and other species... 

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