Generalized Woodward-Hoffmann rules

The selection rules for chemical reactions derived by using symmetry arguments show a definite pattern. Woodward and Hoffmann generalized the selection rules on the basis of orbital symmetry considerations applied to a large number of systems [89], Two important observations are summarized here we refer to the literature for further details [90, 91], 

There are a number of other methods used to predict and interpret chemical reactions without relying upon symmetry arguments. It is worthwhile to compare at least some of them with symmetry-based approaches. 

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. 

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. 

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The generalized Woodward-Hoffmann rule suggests that a synchronous addition of disulfonium dications at the double C=C bond of alkenes would be a thermally forbidden process and so would be hardly probable. Simulation of the frontal attack by ethylene on l,4-dithioniabicyclo[2.2.0]hexane 115 gave no optimal structure of an intermediate complex. On the other hand in the lateral approach of the reactants, orbital factors favor attack of the double bond by one of the sulfonium sulfur atoms of the dication. This pattern corresponds to SN2-like substitution at sulfur atom as depicted in Figure 5. Using such a reactant orientation, the structure of intermediate jc-complex was successfully optimized. The distances between the reaction centers in the complex, that is, between the carbon atoms of the ethylene fragment and the nearest sulfur atom of the dication, are 2.74 and 2.96 A, respectively. 

According to the generalized Woodward-Hoffmann rule, the total number of (4q + 2)s and (4r)0 components must be odd for an orbitally allowed process. Thus, Eq. (14) is an allowed, and Eq. (13) a forbidden sigmatropic rearrangement. The different fluxional characteristics of tetrahapto cyclooctatetraene (52, 138) and substituted benzene (36, 43, 125) metal complexes may therefore be related to orbital symmetry effects. 

The generalized Woodward-Hoffmann rules for cycloaddition are summarized below. 

One central point should emerge from the later sections in this cliapter and from Chapters 5 and 6, and that is the complete agreement between the general Woodward-Hoffmann rule and the whole body of the experimental results. The rule pre-dates much of the experimental data obtained on pericyclic reactions so that it does have important predictive value. The essential correctness of the rule is therefore not in question, but its theoretical basis has been the subject of much controversy. The main theoretical explanations that have been advanced are discussed in this chapter and in Chapter 5. 

The general Woodward-Hoffmann rule for pericvciic reactions A ground state pericydic change is symmetry-allowed when the total number of (4q -f- 2)s and (4r components is odd the converse applies to photo-pericyclic reactions. ... 

Problem 4.1 Show for the reactions given in Fig. 4.3 that the frontier orbital method leads to the same predictions as the general Woodward-Hoffmann rule. 

Both the Woodward-Hoffmann and Fukui frontier orbital analyses lead to the same results as the general Woodward-Hoffmann rule, and both therefore correctly predict the topology of pericyclic processes. Although there are serious objections to this approach, nevertheless it is a very useful mnemonic device for illustrating the stereochemistry of the orbital interactions that occur in pericyclic changes as predicted by the general Woodward-Hoffmann rule. 

The general Woodward-Hoffmann rule is, of course, in complete agreement with the data presented in Table 4.1 because the general rule itself was formulated on the basis of such results. 

In the non-linear approach (b) the carbene orbitals are interacting in an antarafacial manner, and the polyene orbitals can interact either suprafacially or antarafacially as before. The disrotatory process this time relates to a Mobius system, and the conrotatory process to a Hiickel system. The nonlinear cheletropic reaction with conrotation will be preferred for the case (m +2) = 4n + 2), and with disrotation for the case (rn + 2)- 4n. Theffi conclusions are in full agreement with those obtained using the general Woodward-Hoffmann rule. 

When it is realized that a Hiickel transition state involves zero or an even number of inversions and that an anti-Hiickel transition state has an odd number of inversions, then the direct and complete correspondence of the Dewar theory and general Woodward-Hoffmann rule (p. 100) is clearly apparent. 

It should be evident, therefore, that the analytical method developed by Dewar is conceptually simple, is straightforward in its application, even to unsymmetrical systems, and has as its basis a more satisfactory theory. It suffers from one disadvantage, however, when compared with the general Woodward-Hoffmann rule. It cannot be used so readily as a predictive theory all of the various possible reaction processes have to be separately analysed,... 

Relatively few reactions in this category have come to light, and detailed mechanistic studies tend to be lacking. The interpretation of these processes in terms of the general Woodward-Hoffmann rule may yet prove to be incorrect in several cases. For this reason this section is given but brief coverage. 

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