Pericyclic reactions Woodward-Hoffmann rules

What do molecular orbitals and their nodes have to do with pericyclic reactions The answer is, everything. According to a series of rules formulated in the mid-1960s by JR. B. Woodward and Roald Hoffmann, a pericyclic reaction can take place only if the symmetries of the reactant MOs are the same as the symmetries of the product MOs. In other words, the lobes of reactant MOs must be of the correct algebraic sign for bonding to occur in the transition state leading to product. 

Roald Hoffmann (1937—) was born in Zloczow, Poland, just prior to World War II. As a boy, he survived the Holocaust by hiding in the attic of a village schoolhouse. In 1949, he immigrated to the United States, where he received an undergraduate degree at Columbia University and a Ph.D. at Harvard University in 1962. During a further 3-year stay at Harvard as Junior Fellow, he began the collaboration with R. B. Woodward that led to the development of the Woodward-Hoffmann rules for pericyclic reactions. In 1965, he moved to Cornell University, where he remains as professor. He received the 1981 Nobel Prize in chemistry. 

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

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. 

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... 

In the present chapter, however, because the problem is considered from a retrosynthetic point of view, we will distinguish only between heterolytic and homolytic disconnections -to which we will refer to as "retro-annulations"- and concerted or "pericyclic (or cheletropic) cycloreversions". In the same way that Woodward-Hoffmann rules [2] apply to pericyclic reactions, the Baldwin rules [3] may be said to apply to heterolytic as well as to homolytic "monotopic" annulations (see Table 6.1). Although in the preceding Chapter (see 5.5) we have already described some radical "monotopic" annulations, later on in this Chapter (see 6.1.3) and mainly in Chapter 7 we will refer to some new methods, syntheses and strategies which have been developed recently. 

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. 

The interpretation of chemical reactivity in terms of molecular orbital symmetry. The central principle is that orbital symmetry is conserved in concerted reactions. An orbital must retain a certain symmetry element (for example, a reflection plane) during the course of a molecular reorganization in concerted reactions. It should be emphasized that orbital-symmetry rules (also referred to as Woodward-Hoffmann rules) apply only to concerted reactions. The rules are very useful in characterizing which types of reactions are likely to occur under thermal or photochemical conditions. Examples of reactions governed by orbital symmetry restrictions include cycloaddition reactions and pericyclic reactions. 

The formation of alicyclics by electrocyclic and cycloaddition reactions (Section 9.4) proceeds by one-step cyclic transition states having little or no ionic or free-radical character. Such pericyclic (ring closure) reactions are interpreted by the Woodward-Hoffmann rules in the reactions, the new a bonds of the ring are formed from the head-to-head overlap of p orbitals of the unsaturated reactants. 

Fortunately, all the conclusions that can be drawn laboriously from correlation diagrams can be drawn more easily from a pair of rules, known as the Woodward-Hoffmann rules, which distil the essence of the idea into two statements governing all pericyclic reactions, one rule for thermal reactions... 

The Woodward-Hoffmann rule for thermal pericyclic reactions ... 

The following reactions use two or more pericyclic steps. Identify all the reactions, and draw reasonable looking transition structures obeying the Woodward-Hoffmann rule. 

In this primer, Ian Fleming leads you in a more or less continuous narrative from the simple characteristics of pericyclic reactions to a reasonably full appreciation of their stereochemical idiosyncrasies. He introduces pericyclic reactions and divides them into their four classes in Chapter 1. In Chapter 2 he covers the main features of the most important class, cycloadditions—their scope, reactivity, and stereochemistry. In the heart of the book, in Chapter 3, he explains these features, using molecular orbital theory, but without the mathematics. He also introduces there the two Woodward-Hoffmann rules that will enable you to predict the stereochemical outcome for any pericyclic reaction, one rule for thermal reactions and its opposite for photochemical reactions. The remaining chapters use this theoretical framework to show how the rules work with the other three classes—electrocyclic reactions, sigmatropic rearrangements and group transfer reactions. By the end of the book, you will be able to recognize any pericyclic reaction, and predict with confidence whether it is allowed and with what stereochemistry. 

The Diels-Alder reaction is a concerted reaction in which four re-electrons from the diene and two re-electrons from the dienophile participate in the transition state. The Woodward-Hoffmann Rules provide a theoretical framework for these reactions.24 They suggest that those reactions are thermally allowed which have 4n + 2 pericyclic electrons, i.e. 6, 10, 14, etc. The Diels-Alder reaction is an example where n = 1, i.e. (4 + 2) re-electrons. 

The Woodward-Hoffmann rules also allow the prediction of the stereochemistry of pericyclic reactions. The Diels-Alder reaction is an example of (re4s + re2s) cycloaddition. The subscript s, meaning suprafacial, indicates that both elements of the addition take place on the same side of the re-system. Addition to opposite sides is termed antarafacial. The Woodward-Hoffmann rules apply only to concerted reactions and are derived from the symmetry properties of the orbitals involved in the transition state. These rules may be summarised as shown in Table 7.1. 

There is no doubt that the principles usually known as the Woodward-Hoffmann rules have provided a most valuable insight into our understanding of organic reactivity, and in particular of pericyclic reactions. Their applications in organic... 

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],... 

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. 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

Kenichi Fukui and Roald Hoffmann won the Nobel prize in 1981 (Woodward died in 1979 and so couldn t share this prize he had already won the Nobel prize in 1965 for his work on synthesis) for the application of orbital symmetry to pericyclic reactions. Theirs is an alternative description to the frontier orbital method we have used and you need to know a little about it. They considered a more fundamental correlation between the symmetry of all the orbitals in the starting materials and all the orbitals in the products. This is rather too complex for our consideration here, and we shall concentrate only on a summary of the conclusions—the Woodward-Hoffmann rules. The most important of these states ... 

Whether they go in the direction of ring opening or ring closure, electrocyclic reactions are subject to the same rules as all other pericyclic reactions—you saw the same principle at work in Chapter 35 where we applied the Woodward-Hoffmann rules both to cycloadditions and to reverse cycloadditions. With most of the pericyclic reactions you have seen so far, we have given you the choice of using either HOMO-LUMO reasoning or the Woodward-Hoffmann rules. With electrocyclic reactions, you really have to use the Woodward-Hoffmann rules because (at least for the ring closures) there is only one molecular orbital involved. 

This rotation is the reason why you must carefully distinguish electrocyclic reactions from all other pericyclic reactions. In cycloadditions and sigmatropic rearrangements there are small rotations as bond angles adjust from 109° to 120° and vice versa, but in electrocyclic reactions, rotations of nearly 90° are required as a planar polyene becomes a ring, or vice versa. These rules follow directly from application of the Woodward-Hoffmann rules—you can check this for yourself. 

The so-called aromaticity rules are chosen for comparison, as they provide a beautiful correspondence with the symmetry-based Woodward-Hoffmann rules. A detailed analysis [92] showed the equivalence of the generalized Woodward-Hoffmann selection rules and the aromaticity-based selection rules for pericyclic reactions. Zimmermann [93] and Dewar [94] have made especially important contributions in this field. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

The Woodward-Hoffmann rules arise fundamentally from the conservation of orbital symmetry seen in the correlation diagrams. These powerful constraints govern which pericyclic reactions can take place and with what stereochemistry. As we have seen, frontier orbital interactions are consistent with these features,... 

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