The Conservation of Orbital Symmetry Woodward-Hoffmann Rules

The Conservation of Orbital Symmetry (Woodward-Hoffmann Rules) 

Abstract A discussion on conservation of orbital symmetry and its application to select pericyclic reactions is presented. Initially, effort is made to explore the symmetry characteristics of the cr, cr, n and n molecular orbitals (MOs). This is followed by a description of the MOs and their symmetry characteristics for allyl cation, allyl radical, allyl anion, and 1,3-butadiene. This concept is applied to n2 + n2, n4 + it2 (Diels-Alder) and electrocyclic reactions. 

Keywords Conservation of orbital symmetry rules Mirror plane symmetry C2 symmetry n2 + n2 reaction Electrocyclic reactions - n4 + n2 reaction 

In the projected synthesis of vitamin B12, the plan called for the construction of a key intermediate by the stereospecific cyclization of a stereochemically well-defined 1,3,5-triene to the corresponding 1,3-cyclohexadiene. From the inspection of molecular models, Woodward and his colleagues were confident that the minimization of angle strain coupled with appropriate orbital overlap would favor a conrotatory cyclization. While the reaction was indeed found to be highly stereospecific, it took the disrotatory path instead. To explain the observed contradiction, it was necessary to recognize a new control element that Woodward and Hoffmann christened conservation of orbital symmetry [2, 3]. 

Reactions occur readily when there is congruence between the orbital symmetry characteristics of the reactants and the products, and only with difficulty when that congruence does not obtain. In other words, the orbital symmetry is conserved in concerted reactions. How exactly is the orbital symmetry conserved and what are its further ramifications are important issues which we will examine in detail by considering a few examples. For a better grasp of the subject, let us first understand orbitals and their interactions in relation to n and cr bond formation. 

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In 1965, American chemists R. B. Woodward and R. Hofimarm ( conservation of orbital symmetry Woodward-Hofimann Rules) and Japanese chemist K. Fukui ( frontier orbital theory ) proposed theories to explain these results as well as those for other related reactions. Woodward won the Nobel Prize in Chemistry in 1965 for his synthetic work. In 1981, after the death of Woodward, Hoffmann and Fukui shared the same prize for the theories discussed here. 

Woodward-Hoffmann rule org chem A concept which can predict or explain the stereochemistry of certain types of reactions in organic chemistry it is also described as the conservation of orbital symmetry. wCid-ward haf-mon, rul ... 

Roald Hoffmann, bom Zloczow, Poland, 1937. Ph.D. Harvard, 1962, Professor, Cornell. Nobel Prize 1981(shared with Kenichi Fukui Section 7.3.5) for work with organic chemist Robert B. Woodward, showing how the symmetry of molecular orbitals influences the course of chemical reactions (the Woodward-Hoffmann rules or the conservation of orbital symmetry). Main exponent of the extended Hiickel method. He has written poetry, and several popular books on chemistry. 

McWeeny has written a tribute to the valence-bond theory pioneers of 1927-1935.362 Shavitt has outlined the history and evolution of Gaussian basis sets as employed in ah initio molecular orbital calculations.363 Hargittai has interviewed Roald Hoffmann (b. 1937)364 of Cornell University and Kenichi Fukui (1918-1998)365 of Kyoto University, who were jointly awarded the Nobel Prize in Chemistry in 1981. Fukui developed the concept of frontier orbitals and recognized the importance of orbital symmetry in chemical reactions, but his work was highly mathematical and its importance was not appreciated until Robert Woodward (1917-1979) and Hoffmann produced their rules for the conservation of orbital symmetry from 1965 onwards.366... 

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,... 

Woodward-Hoffmann rules These rules are based upon the principle of the conservation of orbital symmetry, and are used to predict which concerted reactions are allowed and which are forbidden. 

To see where false rigor can get us in trouble, let s first examine another use of symmetry. Near the end of the book The Conservation of Orbital Symmetry, in which Woodward and Hoffmann described their rules for understanding pericyclic reactions, the authors included a section entitled "Violations" (Woodward Hoffman, 1970). The first, single-sentence paragraph proclaims "There are none "... 

Woodward saw organic synthesis as a way to advance science and to solve practical problems. One need only look to his vitamin Bj2 work to illustrate this. A reaction that Woodward had planned to use as part of the early stages of the synthesis of vitamin B12 gave a prodnct with nnexpected stereochemistry, leading the perplexed Woodward to look for similar reactions in the organic literatnre. He found them, and with Roald Hoffmann, a theoretical chemist at Harvard, formulated what are now known as the Woodward-Hoffmann mles for the conservation of orbital symmetry. These rules explained the ontcomes of a series of seemingly unrelated chemical reactions and correctly predicted the outcomes of many others. For his con-tribntions to the orbital symmetry rules, Hoffmann shared the 1981 Nobel Prize in chemistry with Kenichi Fukui of Japan, who had reached similar conclnsions independently. Woodward died before the 1981 Nobel Prize was awarded, and had he lived longer, he certainly would have received his second Nobel Prize. 

For further details of the Woodward-Hoffmann rules and their application to a wide variety of organic reactions, see R. B. Woodward and R. Hoffmann, Angew. Chem. Intern. Ed., 8, 781 (1969) The Conservation of Orbital Symmetry, Academic Press, New York, 1970 R. E. Lehr and A. P. Marchand, Orbital Symmetry, Academic Press, New York, 1972. 

We are now set to analyze the above transformation in terms of the fundamental rule of the conservation of orbital symmetry as proposed by Woodward and Hoffmann. The orbitals of cyclobutene that are directly... 

Woodward and Hoffmann based their original derivation of their rules on Fukui s frontier orbital theory and have subsequently relied on arguments based on the conservation of orbital symmetry. Both these approaches suffer from deficiencies (which will be discussed at the end of this chapter) so we will rely here on an earlier treatment by M. G. Evans, which is both simpler and better. 

The first insight on the mechanism of pericyclic reactions was provided by Woodward and Hoffmann in their famous monograph The Conservation of Orbital Symmetry. The basic idea is that reactions occur readily (are thermally allowed) when there is congruence between the orbital symmetry characteristics of the reactants and the products, while they occur with difficulty (are thermally forbidden) when that congruence does not pertain. In short, orbital symmetry is maintained in concerted reactions. This has been proved by Pearson by means of perturbation theory. While the Woodward and Hoffmann rules determine which reactions are allowed and which are forbidden, they do not establish what the real mechanism of the process is. Although this initial view of pericyclic reactions has been very much debated, it forms the basis of the important progress made in the understanding of these reactions. 

The Woodward-Hoffmann method [52], which assumes conservation of orbital symmetry, is another variant of the same idea. In it, the emphasis is put on the symmetries of molecular orbitals. Longuet-Higgins and Abramson [53] noted the necessity of state-to-state correlation, rather than the orbital correlation, which is not rigorously justified (see also, [30,44]). However, the orbital symmetry conservation rules appear to be very useful for most themial reactions. 

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... 

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. 

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. 

Much of what we have said about the electronic factors controlling whether a cycloaddition reaction can be concerted or not originally was formulated by the American chemists R. B. Woodward and R. Hoffmann several years ago, in terms of what came to be called the orbital symmetry principles, or the Woodward-Hoffmann rules. Orbital symmetry arguments are too complicated for this book, and we shall, instead, use the 4n + 2 electron rule for-normal Hiickel arrangements of tt systems and the An electron rule for Mobius arrangements. This is a particularly simple approach among several available to account for the phenomena to which Woodward and Hoffmann drew special attention and explained by what they call conservation of orbital symmetry.- ... 

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