Woodward-Hoffmann general rule

In previous sections we have seen how the CM model may be utilized to generate reaction profiles for ionic reactions, and it is now of interest to observe whether the same general principles may be applied to the class of pericyclic reactions, the group of reactions that is governed by the Woodward-Hoffmann (1970) rules. In other words, the question we ask is whether the concept of allowed and forbidden reactions may be understood within the CM framework. 

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. 

This type of condensation is of great interest in connection with the Woodward-Hoffmann selection rules for symmetry-allowed concerted suprafacial and antarafacial cycloaddition reactions.284 The generalized rules for cycloaddition of an m- to an n-electron system predict that the concerted supra-supra or antara-antara dimerization is allowed in the excited state (i.e., photochemically) when m + n = 4q, and in the ground state (i.e., thermally) when to + n = 4q + 2, where to and n are the numbers... 

The above molecular orbital theory is always widely used either quantitatively by performing explicit calculations of molecular orbitals or qualitatively for rationalizing various kinds of experimental or theoretical data. As nicely shown by Gimarc (1979) in his comprehensive book Molecular Structure and Bonding, qualitative MO theory allows an approach to many chemical problems related to molecular shapes and bond properties. Its most important achievement is the determination of reaction mechanisms by the well-known Woodward-Hoffmann (1970) rules and the general orientation rules proposed by Fukui (1970). 

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. 

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

A general rule for determining the stereochemical course of concerted reactions has been put forward by R.B. Woodward and R. Hoffmann. 

These reactions are characterized by the phenomenon that the frontier orbitals of the reactants maintain a defined stereochemical orientation throughout the w hole reaction. Most noteworthy in this respect, is the principle of orbital symmetry conservation ( Woodward-Hoffmann rules la), but the phenomenon is much more general, as shown by the following examples of Self-Immolative Stereoconversion or Chirality Transfer . This term describes processes by which a stereocenter in the starting material is sacrificed to generate a stereocenter in the product in an unambiguous fashion. This is, of course, the case in classical SN2-displacements. 

A second point that needs to be clarified is why allowed reactions actually have a barrier at all. In fact, some so-called allowed reactions possess particularly high barriers so that they hardly proceed. One such case, discussed by Houk et al. (1979), concerns the allowed trimerization of acetylene to yield benzene. Despite being extremely exothermic (AH° = — 143 kcal mol ) this reaction appears to have an activation barrier in excess of 36 kcal mol"1. Since the orbitals of the reactants correlate smoothly with those of the products, in accord with the Woodward-Hoffmann rules, the origin of barrier formation in allowed reactions generally, needs to be clarified. 

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 general rule for all pericyclic reactions was formulated by Woodward and Hoffmann ([3], p. 169). A ground-state pericyclic change is symmetry allowed if the total number of (An + 2)s and (Am)a components is odd. 

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. 

The Generalized Woodward Hoffmann Pericyclic Selection 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],... 

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. 

Group Transfer Reactions. There are so few of these reactions that a fully general rule for them can wait until the next section, where we see the final form of the Woodward-Hoffmann rules. For now, we can content ourselves with a simplified rule which covers almost all known group transfer reactions. When the total number of electrons is a (4 +2) number, group transfer reactions are allowed with all-suprafacial stereochemistry. 

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