Reaction mechanism Woodward-Hoffmann rules

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

The concerted mechanism shown above is allowed by the Woodward-Hoffmann rules. The TS involves the tt electrons of the alkene and enophile and the cr electrons of the allylic C-H bond. The reaction is classified as a [tt2 + tt2 + cr2] and either an FMO or basis set orbital array indicates an allowed concerted process. 

Woodward and Hoffmann provided an understanding of pericyclic reaction mechanisms based on conservation of orbital symmetry. A few years later, Ross et al. [118] coined the term pseudopericyclic for a set of reactions they discovered, which were not explained by the Woodward-Hoffmann rules (like the oxidation of tricyclic... 

However, despite their proven explanatory and predictive capabilities, all well-known MO models for the mechanisms of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman treatment [4-6] share an inherent limitation They are based on nothing more than the simplest MO wavefunction, in the form of a single Slater determinant, often under the additional oversimplifying assumptions characteristic of the Hiickel molecular orbital (HMO) approach. It is now well established that the accurate description of the potential surface for a pericyclic reaction requires a much more complicated ab initio wavefunction, of a quality comparable to, or even better than, that of an appropriate complete-active-space self-consistent field (CASSCF) expansion. A wavefunction of this type typically involves a large number of configurations built from orthogonal orbitals, the most important of which i.e. those in the active space) have fractional occupation numbers. Its complexity renders the re-introduction of qualitative ideas similar to the Woodward-Hoffmann rules virtually impossible. 

The SC descriptions of the electronic mechanisms of the three six-electron pericyclic gas-phase reactions discussed in this paper (namely, the Diels-Alder reaction between butadiene and ethene [11], the 1,3-dipolar cycloaddition offiilminic acid to ethyne [12], and the disrotatory electrocyclic ring-opening of cyclohexadiene) take the theory much beyond the HMO and RHF levels employed in the formulation of the most popular MO-based treatments of pericyclic reactions, including the Woodward-Hoffmann rules [1,2], Fukui s frontier orbital theory [3] and the Dewar-Zimmerman model [4-6]. The SC wavefunction maintains near-CASSCF quality throughout the range of reaction coordinate studied for each reaction but, in contrast to its CASSCF counterpart, it is very much easier to interpret and to visualize directly. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

On the other hand, Takacs and coworkers added organometallic reducing agents to the reaction mixture and promoted the formation of low-valent iron(O) bipyridine complexes. The mechanism of the low-valent iron-catalyzed Alder-ene reaction involves coordination of the two starting materials within the ligand sphere of the iron, which makes the Woodward-Hoffmann rules for such reactions obsolete [11]. Thereby, the scope of the reactions was broadened so that alkenes and 1,3-dienes could also be used as educts in a formal [4 + 4]-cycloisomerization (Scheme 9.3) [12]. Intriguingly, the diastereoselectivity of the cydopentane products can be influenced by either the application of the 2Z-isomer 3 or the 2 E-isomer 4. Especially the E-isomers 4 gave almost exclusive cis selectivity [13]. 

The alkene metathesis reaction was unprecedented - such a non-catalysed concerted four-centred process is forbidden by the Woodward-Hoffmann rules - so new mechanisms were needed to account for the products. Experiments by Pettit showed that free cyclobutane itself was not involved it was not converted to ethylene (<3%) under the reaction condition where ethylene underwent degenerate metathesis (>35%, indicated by experiments involving Di-ethylene) [10]. Consequently, direct interconversion of the alkenes, via an intermediate complex (termed a quasi-cyclobutane , pseudo-cyclobutane or adsorbed cyclobutane ) generated from a bis-alkene complex was proposed, and a detailed molecular orbital description was presented to show how the orbital symmetry issue could be avoided, Scheme 12.14 (upper pathway) [10]. 

This intuitive parallel can be best demonstrated by the example of electrocye-lic reactions for which the values of the similarity indices for conrotatory and disrotatory reactions systematically differ in such a way that a higher index or, in other words, a lower electron reorganisation is observed for reactions which are allowed by the Woodward-Hoffmann rules. In contrast to electrocyclic reactions for which the parallel between the Woodward-Hoffmann rules and the least motion principle is entirely straightforward, the situation is more complex for cycloadditions and sigmatropic reactions where the values of similarity indices for alternative reaction mechanisms are equal so that the discrimination between allowed and forbidden reactions becomes impossible. The origin of this insufficiency was analysed in subsequent studies [46,47] in which we demonstrated that the primary cause lies in the restricted information content of the index rRP. In order to overcome this certain limitation, a solution was proposed based on the use of the so-called second-order similarity index gRP [46]. This... 

Such an alternative reproduction of the Woodward-Hoffmann rules is not, however, the only result of the similarity approach. The formalism of the approach is very flexible and universal and the original study [33] has become the basis of a number of subsequent generalisations in which a number of problems dealing with various aspects of pericyclic reactivity were analysed and discussed [48-55], In spite of the considerably broad scope of these applications, recently reviewed in [56], the possibilities of the similarity approach are still not exhausted and its formalism is still capable of further methodological development. Our aim in this report is to present some of more recent applications of the similarity approach for the study of mechanisms of pericyclic reactions [57-59],... 

Since the detailed calculation of these matrices is sufficiently described in the original literature [33, 58], it is possible to present directly the final results first for the case of concerted reactions for which there are two alternative reaction mechanisms, conrotatory and disrotatory. The first of these mechanisms is allowed by the Woodward-Hoffmann rules while the second one is forbidden. 

If we now look at the values of the above indices, it is possible to see that the prediction of the Woodward-Hoffmann rules is indeed confirmed since the greater values of the similarity index for the conrotatory reaction clearly imply, in keeping with the expectations of the least-motion principle, the lower electron reorganisation. If now the same formalism is applied to a stepwise reaction mechanism, the following values of the similarity indices result (Eq. 21). 

The Diels-Alder reaction and related pericyclic reactions, which can be treated qualitatively by the Woodward-Hoffmann rules (Section 4.3.5), have been reviewed in the context of computational chemistry [39]. The reaction is clearly nonionic, and the main controversy was whether it proceeds in a concerted fashion as indicated in Fig. 9.5 or through a diradical, in which one bond has formed and two unpaired electrons have yet to form the other bond. A subtler question was whether the reaction, if concerted, was synchronous or asynchronous whether both new bonds were formed to the same extent as reaction proceeded, or whether the formation of one ran ahead of the formation of the other. Using the CASSCF method (Section 5.4.3), Li and Houk [40] concluded that the butadiene-ethene reaction is concerted and synchronous, and chided Dewar and Jie [41] for stubbornly adhering to the diradical (biradical) mechanism. 

This is a key difference. The Woodward-Hoffmann rules (Chapters 35 and 36) were deduced from theory, and examples were gredually discovered that fitted them. They cannot be violated a reaction that disobeys the Woodward-Hoffmann rules is getting around them by following a different mechanism. Baldwin s rules were formulated by making observations of reactions that do, or do not, work. 

All these photocyclizations are well explained in terms of an electrocyclic mechanism of nitrogen-containing, six 7r-electron conjugated system, according to the Woodward - Hoffmann rule, by postulating the intermediacy of a common trans cyclic structure from which respective types of products are formed depending on the reaction conditions either a nonoxidative, oxidative, or reductive condition. 

The effect described here seems fully capable of rationalizing the phenomena discussed. However, at least one other effect parallels the changes in polarization described in the last section. Like any qualitative quantum mechanical effect, generalizations and predictions are easily made, but experiments must be devised, or quantitative computations attempted, in order to determine whether the effect is of chemical significance. For example, the basis of the Woodward-Hoffmann rules is certainly correct, and allowed reactions appear to be 10—15 kcal/mol more favored than similar forbidden reactions in many cases. It would have been possible, in principle, that allowed reactions would have been 0.1 kcal/mol more favorable than forbidden. If such had been the case, then the Woodward-Hoffmann Rules would have been of no chemical significance The magnitude of the effects, not the correctness of the arguments, is what is in question for the phenomena discussed here. 

Organic chemists tend to be pragmatists when faced with rival MO and VB descriptions of molecular electronic structure. Many will use whichever model seems most convenient for the problem at hand. MO descriptions are widely employed in frontier orbital approaches, as in the Woodward-Hoffmann rules, and tend to be favoured when predicting excited states or photoelectron spectra. On the other hand, it is customary to represent reaction mechanisms in terms of resonance between classical VB structures with single, double etc. bonds (plus any unpaired electrons or lone pairs) and then to indicate by means of curly... 

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