The Woodward-Hoffmann Rules

Electi ocyclic reactions are examples of cases where ic-electiDn bonds transform to sigma ones [32,49,55]. A prototype is the cyclization of butadiene to cyclobutene (Fig. 8, lower panel). In this four electron system, phase inversion occurs if no new nodes are fomred along the reaction coordinate. Therefore, when the ring closure is disrotatory, the system is Hiickel type, and the reaction a phase-inverting one. If, however, the motion is conrotatory, a new node is formed along the reaction coordinate just as in the HCl + H system. The reaction is now Mdbius type, and phase preserving. This result, which is in line with the Woodward-Hoffmann rules and with Zimmerman s Mdbius-Huckel model [20], was obtained without consideration of nuclear symmetry. This conclusion was previously reached by Goddard [22,39]. 

We have seen (Section I) that there are two types of loops that are phase inverting upon completing a round hip an i one and an ip one. A schematic representation of these loops is shown in Figure 10. The other two options, p and i p loops do not contain a conical intersection. Let us assume that A is the reactant, B the desired product, and C the third anchor. In an ip loop, any one of the three reaction may be the phase-inverting one, including the B C one. Thus, the A B reaction may be phase preserving, and still B may be attainable by a photochemical reaction. This is in apparent contradiction with predictions based on the Woodward-Hoffmann rules (see Section Vni). The different options are summarized in Figure 11. 

Along "Reaction Paths", Orbitals Can be Connected One-to-One According to Their Symmetries and Energies. This is the Origin of the Woodward-Hoffmann Rules I. Reduction in Symmetry... 

Along "reactionpaths", configurations can be connected one-to-one according to their symmetries and energies. This is another part of the Woodward-Hoffmann rules... 

The direct connection of rings A and D at C l cannot be achieved by enamine or sul> fide couplings. This reaction has been carried out in almost quantitative yield by electrocyclic reactions of A/D Secocorrinoid metal complexes and constitutes a magnificent application of the Woodward-Hoffmann rules. First an antarafacial hydrogen shift from C-19 to C-1 is induced by light (sigmatropic 18-electron rearrangement), and second, a conrotatory thermally allowed cyclization of the mesoionic 16 rc-electron intermediate occurs. Only the A -trans-isomer is formed (A. Eschenmoser, 1974 A. Pfaltz, 1977). 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The importance of orbital overlap in determining why certain chemical reactions proceed easily while other similar reactions do not go at all was first advanced by Woodward and Hoffmann, and collectively their ideas are now known as the Woodward-Hoffmann rules. Applications of these ideas can be found in Chapter 21. 

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. 

In a photochemical cycloaddition, one component is electronically excited as a consequence of the promotion of one electron from the HOMO to the LUMO. The HOMO -LUMO of the component in the excited state interact with the HOMO-LUMO orbitals of the other component in the ground state. These interactions are bonding in [2+2] cycloadditions, giving an intermediate called exciplex, but are antibonding at one end in the [,i4j + 2j] Diels-Alder reaction (Scheme 1.17) therefore this type of cycloaddition cannot be concerted and any stereospecificity can be lost. According to the Woodward-Hoffmann rules [65], a concerted Diels-Alder reaction is thermally allowed but photochemically forbidden. 

As we saw in 15-58, the Woodward-Hoffmann rules allow suprafacial concerted cycloadditions to take place thermally if the total number of electrons is 4n 4- 2 and... 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

According to the Woodward-Hoffmann rule [6, 7], conjugate polyenes with 4n and 4n+2 n electrons undergo cychzations in conrotatory and disrotatory fashions under the thermal conditions, respectively. Recently, novel cycloisomerizations were found to be catalyzed by Lewis acid and to afford bicychc products [39] as photochemical reactions do [40]. The new finding supports the mechanistic spectrum of chemical reactions. 

Hexatrienes undergo disrotatory ring closure by thermal activation to afford cyclohex-adienes in agreement with the Woodward-Hoffmann rule (delocalization band in Scheme 8) [41 3]. Photo-irradiation of hexatrienes is known to give bicylic products in a stereospecific [4n +2nJ manner (delocalization band in Scheme 8) [40] in contrast to this rule. 

Trauner and colleagues [39] recently found a striking contrast in the thermal and catalyzed reactions of a triene. Thermal reaction of a trienolate readily underwent disrotatory electrocyclization to afford cyclohexadiene (delocalization band in Scheme 8) in accordance with the Woodward-Hoffmann rule. Surprisingly, treatment of the trienolate with Lewis acid did not result in the formation of the cyclohexadiene but rather gave bicyclo[3.1.0]hexene in a [4n +2nJ manner (pseudoexcitation band in Scheme 8). The catalyzed reaction is similar to the photochemical reaction in the delocalization band. 

A part of the chemical consequences of the cyclic orbital interactions in the cyclic conjngation is well known as the Hueckel rule for aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions [14]. In this section, we describe the basis for the rnles very briefly and other rules derived from or related to the orbital phase theory. The rules include kinetic stability (electron-donating and accepting abilities) of cyclic conjugate molecules (Sect. 2.2.2) and discontinnity of cyclic conjngation or inapplicability of the Hueckel rule to a certain class of conjngate molecnles (Sect. 2.2.3). Further applications are described in Sect. 4. 

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

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. 

Cycloadditions of ketenes and alkenes have synthetic utility for the preparation of cyclobutanones.163 The stereoselectivity of ketene-alkene cycloaddition can be analyzed in terms of the Woodward-Hoffmann rules.164 To be an allowed process, the [2ir + 2-tt] cycloaddition must be suprafacial in one component and antarafacial in the other. An alternative description of the TS is a 2irs + (2tts + 2tts) addition.165 Figure 6.13 illustrates these combinations. Note that both representations predict formation of the d.v-substituted cyclobutanone. 

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. 

The cyclization of conjugated polyenes and the inverse reaction were those processes which provided superb materials 142> leading to the Woodward-Hoffmann rule 51>. 

However, as we have seen, all derivatives containing -electron systems do not behave similarly—some yield dimers and some do not, even though all should be equally allowed according to the Woodward-Hoffmann rules. 

The products (101) are presumably formed in an orbital symmetry allowed (2 + 2 + 2) 7t concerted cyclo-addition. The formation of the compounds (99) and (100) are more difficult to rationalise unambiguously. Clearly, if an intermediate such as (102) had more than a very transient existence, one would expect to isolate products derived from carbonium ion rearrangements. That no rearranged products have been isolated might be used as an argument for the violation of the Woodward-Hoffmann rules. "There are none " 68>. 

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