The Aromatic Transition Structure

The easiest explanation is based on the frontier orbitals—the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied orbital (LUMO) of the other. Thus if we compare a [2 + 2] cycloaddition 6.133 with a [4 + 2] cycloaddition 6.134 and 6.135, we see that the former has frontier orbitals that do not match in sign at both ends, whereas the latter do, whichever way round, 6.134 or 6.135, we take the frontier orbitals. In the [2 + 2] reaction 6.133, the lobes on C-2 and C-2 are opposite in sign and represent a repulsion—an antibonding interaction. There is no barrier to formation of the bond between C-l and C-l, making stepwise reactions possible the barrier is only there if both bonds are trying to form at the same time. The [4 + 4] and [6 + 6] cycloadditions have the same problem, but the [4 + 2], [8 + 2] and [6 + 4] do not. Frontier orbitals also explain why the rules change so completely for photochemical reactions, as we shall see in Chapter 8. 

Applying frontier orbital theory to unimolecular reactions like electrocyclic ring closures and sigmatropic rearrangements is inherently contrived, since we are looking at only one orbital. To set up an interaction between frontier orbitals, we 

The second explanation is based on the frontier orbitals—the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied orbital (LUMO) of the other. Thus if we compare a [2 + 2] cycloaddition 6.172 with a [4 + 2] cycloaddition 6.173 and 6.174, we see that the former has frontier orbitals that do not match in sign at both ends, whereas the latter do, whichever way round, 6.173 or 6.174, we take the frontier orbitals. 

The frontier orbital treatment for vinyl cation cycloadditions, such as those of ketenes, has some merits. It satisfyingly shows that the bond forming between C-l and C-l develops mainly from the interaction of the LUMO of the ketene (n of the C=0 group) and the HOMO of the alkene 6.178, and that the bond between C-2 and C-2 develops mainly from the interaction of the HOMO of the ketene (i/j2 of the 3-atom linear set of orbitals analogous to the allyl anion) and the LUMO of the alkene 6.179. 

Hydroboration is another case where the frontier orbital pictures 6.180 and 6.181 reinforce the perception that the two bonds are formed independently. The former illustrates the electrophilic attack by the borane, and the latter the nucleophilic attack by the borane, simultaneously explaining the regioselectivity for an X-substituted alkene. 

Nevertheless, frontier orbital theory, for all that it works, does not explain why the barrier to forbidden reactions is so high. Perturbation theory uses the sum of all filled-with-filled and filled-with-unfilled interactions (Chapter 3), with the frontier orbitals making only one contribution to this sum. Frontier orbital interactions cannot explain why, whenever it has been measured, the transition structure for the forbidden pathway is as much as 40 kJ mol 1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. We shall return later in this chapter to frontier orbital theory to explain the much weaker elements of selectivity, like the effect of substituents on the rates and regioselectivity, and the endo rule, but we must look for something better to explain why pericyclic reactions conform to the Woodward-Hoffmann rules with such dedication. 

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At this point, it is appropriate to draw a parallel with the straightforward MO explanations for the aromaticity of benzene using approaches based on a single closed-shell Slater determinant, such as HMO and restricted Hartree-Fock (RWF), which also have no equivalent within more advanced multi-configuration MO constructions. The relevance of this comparison follows from the fact that aromaticity is a primary factor in at least one of the popular treatments of pericyclic reactions Within the Dewar-Zimmerman approach [4-6], allowed reactions are shown to pass through aromatic transition structures, and forbidden reactions have to overcome high-energy antiaromatic transition structures. 

All the reactions described so far have mobilized six electrons in the transition structure. Other numbers are possible, notably a few [8+2] and [6+4] cycloadditions involving ten electrons in the cyclic transition structure. It is no accident, as we shall see in the next chapter, that these reactions have the same number of electrons (4n+2) as aromatic rings. 

Table 8 summarizes the results of the calculations of the C2h symmetric chair and the C2v symmetric boat transition structures [83]. The local spin density approximation predicts a tight transition structure, comparable to the one obtained by the MP2(fc)/6-31G method, but fails to reproduce the experimental activation energies [84], The use of the gradient-corrected BLYP functional yields loose, aromatic-type transition structures and improved activation energies for the chair transition structures. The activation energy for the boat transition structure is, however, too low by 9-10 kcal/mol as compared to the experimental value of 44.7 kcal/mol [85]. The activation energies for the chair and the boat transition structures obtained by the Becke 3LYP method are in... 

The aromaticity of the calculated transition structure has also been confirmed by calculation of the magnetic susceptibility Jiao H, Schleyer PvR (1994) J Chem Soc Faraday Trans 90 1559... 

To explain the increase in the rate of the cyclobutene opening 6.292 —> 6.293, we need to remember that the conrotatory pathway will have a Mobius-like aromatic transition structure, not the anti-aromatic Hiickel cyclobutadiene that we saw in Fig. 1.38. We have not seen the energies for this system expressed in 8 terms, nor can we do it easily here, but the numbers are in Fig. 6.42, where we can see that a... 

Whereas methylenecyclopropanes only react with highly electron-deficient dienophiles in a [ 2n + 2fT) + 2n] fashion, alkenylidenecyclopropanes 1 readily undergo this cycloaddition type. A number of comprehensive and elaborate investigations with various alkenylidenecyclopropanes and 4-phenyl-l,2,4-triazoline-3,5-dione indicate that these reactions are concerted and proceed via [( 2j+,25+ 2 J -I-, 2 J transition states, involving the terminal double bond in an eight-electron Mobius aromatic transition structure 4. 

To provide a baseline from which to compare the substituted system, we first compute the n energy of the unsubstituted starting material on the left in Fig. 6.53 a and the fully aromatic version of the corresponding transition structure on the right. The starting material will have the n energy of two independent % bonds,... 

The best-known equation of the type mentioned is, of course, Hammett s equation. It correlates, with considerable precision, rate and equilibrium constants for a large number of reactions occurring in the side chains of m- and p-substituted aromatic compounds, but fails badly for electrophilic substitution into the aromatic ring (except at wi-positions) and for certain reactions in side chains in which there is considerable mesomeric interaction between the side chain and the ring during the course of reaction. This failure arises because Hammett s original model reaction (the ionization of substituted benzoic acids) does not take account of the direct resonance interactions between a substituent and the site of reaction. This sort of interaction in the electrophilic substitutions of anisole is depicted in the following resonance structures, which show the transition state to be stabilized by direct resonance with the substituent ... 

Probably the most important development of the past decade was the introduction by Brown and co-workers of a set of substituent constants,ct+, derived from the solvolysis of cumyl chlorides and presumably applicable to reaction series in which a delocalization of a positive charge from the reaction site into the aromatic nucleus is important in the transition state or, in other words, where the importance of resonance structures placing a positive charge on the substituent - -M effect) changes substantially between the initial and transition (or final) states. These ct+-values have found wide application, not only in the particular side-chain reactions for which they were designed, but equally in electrophilic nuclear substitution reactions. Although such a scale was first proposed by Pearson et al. under the label of and by Deno et Brown s systematic work made the scale definitive. 

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