Heptatrienyl systems

Problem 15.10 Show the relative energy levels of the seven n molecular orbitals of the cycle-heptatrienyl system. Indicate which of the seven orbitals are filled in the cation, radical, and anion, and account for the aromaticity of the cycloheptatrienyl cation. 

The second step, which yields vitamin D3, is a thennal [1,7] sigmatropic shift of a hydrogen atom. Based on the symmetry of the HOMO of a heptatrienyl system, the transfer of the hydrogen must occur antarafacially. Both the number of single bonds and the number of atoms provide sufficient ffexibihty for this reaction to occur. 

Fig. 4.2 illustrates the first few members of the series of equilibria of conjugated ions. In cations, they are the equilibria between the allyl 4.11 and the cyclopropyl cation 4.12, the pentadienyl 4.13 and the cyclopentenyl cation 4.14, and the heptatrienyl 4.15 and cycloheptadienyl cation 4.16, In anions, they are between the allyl 4.17 and the cyclopropyl anion 4.18, the pentadienyl 4.19 and the cyclopentenyl anion 4.20, and the heptatrienyl 4.21 and cycloheptadienyl anion 4.22. There are heteroatom-containing analogues, with nitrogen and oxygen lone pairs rather than a carbanion centre, and the systems can again have substituents and fused rings. 

With substituted conjugated systems, such as heptatriene (314) and butadiene nitrile (319), a similar kind of selectivity is shown with maleic anhydride (315)259 and isoprene (318)260 respectively, they give the lower energy adducts (316 and 320), rather than the alternatives (313 and 317). Once again a frontier orbital treatment, in its simplest form, has little to offer. We need the coefficients in the two compounds (314 and 319), but in neither case do we have them to hand. To avoid doing a calculation for the triene (314), we could add a little of the coefficients of the HOMO of the heptatrienyl anion (p. 123) to those of the HOMO of hexatriene. Similarly, for butadiene nitrile (319), we could... 

Claisen rearrangements introduce the complication of oxygen lone pairs within the rearranging system, rather than as substituents on the perimeter. They may be ignored and the transition structure treated as benzene-like, or they may interrupt the conjugation, and the transition structure is then like a heptatrienyl anion.915 Predictions based on the simple theory above, whichever of these models is taken, match most of the substituent effects, and more elaborate treatments with calculations account for the anomalous accelerating effect of a donor substituent at C-6.916... 

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