Aromatic and Antiaromatic Transition States

The appearance in the previous section of the 4 + 2 and 4r formulas brings to mind the criteria for aromatic and antiaromatic systems discussed in Chapter 1. Furthermore, the HOMO-LUMO interaction patterns discussed in Section 11.2 are reminiscent of those used in Section 10.4 to analyze aromatic stabilization. In this section, we trace the connection between aromaticity and pericyclic reactions, and show how it leads to a third approach to the pericyclic theory. 

Returning to the interaction diagram for the ground-state allowed ir2s + -n4s cycloaddition, 33, we see immediately that it is equivalent to that (34 or 35) for 

26 Woodward and Hoffmann, The Conservation of Orbital Symmetry, p. 169. It is understood that reactions forbidden in the ground state are allowed in the excited state and vice versa. 

The next step in the analysis is to provide an unambiguous method of recognizing systems of the Hiickel or anti-Hiickel type. We introduce first the idea of a phase inversion.3 In the orbital interaction diagram, each interaction joining lobes of opposite sign constitutes a phase inversion. A change of sign within an orbital does not constitute a phase inversion. In 42, for example, there 

Pericyclic reactions that pass through aromatic transition states are allowed in the ground state those that pass through antiaromatic transition states are ground-state forbidden.36 

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Delocalization energy (this is related to aromaticity and antiaromaticity) Transition state structures and energies (see the hedge below)... 

PMO-treatment of Cheletropic Reactions Cheletropic reactions can be easily explained on the basis of aromatic and antiaromatic transition states by PMO-method. Transition states in each mode of linear and non-linear approach of carbene both suprafacially and antarafacially to n-system are drawn below ... 

While the initial formulation of homoaromaticity pre-dated the introduction of orbital symmetry by some eight years the two concepts are inextricably linkedThis is most evident when pericyclic reactions are considered from the perspective of aromatic or antiaromatic transitions states and the Huckel/Mobius concept. The inter-relationship can be demonstrated by the electrocyclic reaction shown in Scheme 1. ... 

The single-parameter X-model is now extended to a parametric description of complex reactions with an arbitrary number of reaction parameters. Let p( 3) be the number of reaction partn s (reactants, products or intermediates) the reaction lattice is then isomorphic to the lattice Pip + 1) 2 with a diagram of a higher dimensional cube (6.32). Accordin y, the dynamic sublattice is isomorphic to P(p) = 2 and thus contains at least one element of the non-roechanistic dimension A (see Ch. "Generalized reaction lattice"). Ck>nsequently, the choice of the reaction path is no longer unique - in contrast to the sin e-parameter X model for pericyclic reactions with a well defined reaction path (via an aromatic or antiaromatic transition state.). The formal algebraic description of... 

We term the in-phase combination an aromatic transition state (ATS) and the out-of-phase combination an antiaromatic transition state (AATS). An ATS is obtained when an odd number of electron pairs are re-paired in the reaction, and an AATS, when an even number is re-paired. In the context of reactions, a system in which an odd number of electrons (3, 5,...) are exchanged is treated in the same way—one of the electron pairs may contain a single electron. Thus, a three-electron system reacts as a four-electron one, a five-electron system as a six-electron one, and so on. 

There is another usefiil viewpoint of concerted reactions that is based on the idea that transition states can be classified as aromatic or antiaromatic, just as is the case for ground-state molecules. A stabilized aromatic transition state will lead to a low activation energy, i.e., an allowed reaction. An antiaromatic transition state will result in a high energy barrier and correspond to a forbidden process. The analysis of concerted reactions by this process consists of examining the array of orbitals that would be present in the transition state and classifying the system as aromatic or antiaromatic. 

The selection rules for cycloaddition reactions can also be derived from consideration of the aromaticity of the transition state. The transition states for [2tc -f 2tc] and [4tc -1- 2tc] cycloadditions are depicted in Fig. 11.11. For the [4tc-1-2tc] suprafacial-suprafacial cycloaddition, the transition state is aromatic. For [2tc -F 2tc] cycloaddition, the suprafacial-suprafacial mode is antiaromatic, but the suprafacial-antarafacial mode is aromatic. In order to specify the topology of cycloaddition reactions, subscripts are added to the numerical classification. Thus, a Diels-Alder reaction is a [4tc -f 2 ] cycloaddition. The... 

Applying these rules in pericyclic reactions it has been shown and a generalization given that thermal reactiom occur via aromatic transition states while photochemical reactions proceed via antiaromatic transition state. A cyclic transition state is considered to be aromatic or isoconjugate with the corresponding aromatic system if the member of conjugated atoms and that of the n... 

R. C. Dougherty, J. Amer. Chem. Soc., 93, 7187 (1971) has argued that systems whose ground states are aromatic have antiaromatic excited states and vice versa, and that therefore the universal criterion for allowed pericyclic reactions, both ground and excited-state, is that the transition state be aromatic. The uncertainty of our present knowledge of excited states nevertheless indicates that the more restricted statement given here is to be preferred. 

According to Zimmermann [101] and Dewar [102], the allowedness of a concerted pericyclic reaction can be predicted in the following way A cyclic array of orbitals belongs to the Hiickel system if it has zero or an even-number phase inversions. For such a system, a transition state with An+ 2 electrons will be thermally allowed due to aromaticity, while the transition state with An electrons will be thermally forbidden due to antiaromaticity. 

NICS methods (NICS(O) and NICS(l)) have found widespread use in evaluating relative aromatic and antiaromatic characters for a variety of systems—aromatic transition states, ° antiaromatic dications,and aromatic bowls ... 

The terms aromatic and antiaromatic have been extended to describe the stabilization or destabilization of TRANSITION STATES of PERICYCLIC REACTIONS. The hypothetical reference structure is here less clearly defined, and use of the term is based on application of the Huckel (4n+2) rule and on consideration of the topology of orbital overlap in the transition state. Reactions of molecules in the ground state involving antiaromatic transition states proceed, if at all, much less easily than those involving aromatic transition states. 

Now we would like to use a transition state ring bond order uniformity (n-molecular orbital delocalization) as a measure of its stability, and therefore the selectivity between two or more isometric transition state structures. A view that transition state structures can be classified as aromatic and antiaromatic is widely accepted in organic chemistry [54], A stabilized aromatic transition state will lead to a lower activation barrier. Also, it can be said that a more uniform bond order transition state will have lower activation barriers and will be allowed. An ideal uniform bond order transition state structure for a six-membered transition state structure is presented in Scheme 4. According to this definition, a six-electron transition state can be defined through a bond order distribution with an average bond order X. Less deviation from these ideally distributed bond orders is present in a transition state which is more stable. Therefore, it is energetically preferred over the other transition state structures. 

Application of this method to pericyclic reactions led to the generalization that thermal reactions take place via aromatic or stable transition states whereas photochemical reactions proceed via antiaromatic or unstable transition states. This is the case because a controlling factor in photochemical processes is conversion of excited state reactants into ground state products. Thus, the photochemical reactions convert the reactants into the antiaromatic transition states that correspond to forbidden thermal pericyclic reactions and so lead to corresponding products. 

In general the aromatic systems are more stable and hence less reactive especially towards an addition reaction and antiaromatic systems are more reactive. Moreover aromatic systems prefer to undergo substitution reactions rather than addition reactions (as in the cases of alkenes and alkynes). Pericyclic reactions have been analyzed via (anti) aromaticity of the transition state . ... 

Table 9 Calculated values of similarity indices of transition states with aromatic and antiaromatic reference structures for several selected pericyclic reactions.

This latter expression illuminates the connection between the avoided crossing diagrams and the orbital symmetry and related MO rules [1, 37]. It is apparent thus from Eq. (18) that B will get smaller the smaller becomes the HOMO-LUMO gap of the transition state in the general case). Since antiaromatic" transition states of forbidden reactions [37] possess small or vanishing HOMO-LUMO gaps, then according to Eq. (18) these transition states will possess much smaller B values than the aromatic" transition states of allowed reactions [7, 8]. 

Another very common sigmatropic shift is the [1,2] hydride shift associated with car-bocations (Eq. 15.30). Although not usually analyzed this way, these migrations involve a cyclic, two-electron system and are Hiickel aromatic (see margin). Viewing these reactions this way nicely rationalizes why comparable [1,2] shifts are not seen in carbanions that is, they would involve a four-electron Hiickel antiaromatic transition state. 

This argument can obviously be extended to concerted pericyclic reactions of all kinds. The transition state for any such reaction will be isoconjugate with a normal Hiickel-type cyclic polyene or an anti-Hiickel analog of one. If the transition state is aromatic, the resulting stabilization will lower its energy and so accelerate the reaction. If it is antiaromatic, the converse will be true. Since, moreover, the rules for aromaticity in Huckel-type and anti-Huckel-type systems are diametrically opposite, in each case one will be aromatic and the other antiaromatic. If, then, a reaction can follow one of two alternative pericyclic paths, one involving a Hiickel-type transition state and the other an anti-Hiickel-type transition, the reaction will prefer to follow the path in which the transition state is aromatic. If, on the other hand, only one of the two alternatives is sterically possible, the reaction will take place relatively easily if the corresponding transition state is aromatic and with relative difficulty if it is antiaromatic. In the latter case, the antiaromatic transition state will, if possible, be bypassed by a two-step mechanism in which the transition state is linear instead of cyclic [e.g., equation (5.291)]. 

So far we have considered only reactions in which the pericyclic ring contains an even number of atoms. Reactions of this kind are, however, known in which an odd-numbered ring is involved. A simple example is the Diels-Alder-like addition of 2-methylallyl cation (148) to cyclopentadiene (149) to form the methylbicyclooctyl cation (150). The transition state for this reaction is easily seen to be of Hiickel type (151) and so isoconjugate with tropylium. Since the allyl cation contains only two n electrons, we are dealing here with a six-electron system isoconjugate with the tropylium cation (147) and hence aromatic. In reactions of this kind, both the reactants and the transition state are odd. The reactions are therefore of 001 type. Since, moreover, the aromaticity or antiaromaticity of the transition state is again unrelated to the structures of the reactants or products, the reactions are of anti-BEP type and are consequently classed as 00 J. 

It is therefore inaccurate and misleading to talk about allowed and forbidden pericyclic reactions. The terms aromatic and antiaromatic pericyclic reaction are much more appropriate. It is also clear that the distinction between them has nothing to do with symmetry. It depends on the topology of overlap of the AOs in pericyclic transition states, not on the symmetries of MOs. If symmetry were involved, the distinction between allowed and forbidden reactions would be attenuated as symmetry was lost. This is not the case. The Woodward-Hoffmann rules, or the equivalent statement embodied in Evans principle, hold just as strongly in systems lacking symmetry as in symmetric systems. Indeed, if this were not the case, they would be far less useful and important. 

There are a large number of photocyclizations reactions of polycyclic aromatic systems that all proceed through antiaromatic transitions states. The cyclization " of cis-stilbene (105) and the related diarylethylene are classical examples of this reaction,... 

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