Conservation of orbital symmetry theory

Chapter 29 discusses pericyclic reactions—reactions that occur as a result of a cyclic reorganization of electrons. In this chapter, you will learn how the conservation of orbital symmetry theory explains the relationships among reactant, product, and reaction conditions in a pericyclic reaction. 

The conservation of orbital symmetry theory states that in-phase orbitals overlap during the course of a pericyclic reaction. The conservation of orbital symmetry theory was based on the frontier orbital theory put forth by Kenichi Fukui in 1954. Although Fukui s theory was more than 10 years old, it had been overlooked because of its mathematical complexity and Fukui s failure to apply it to stereoselective reactions. 

Roald Hoffmann and Kenichi Fukui shared the 1981 Nobel Prize in chemistry for the conservation of orbital symmetry theory and the frontier orbital theory. R. B. Woodward did not receive a share in the prize because he died two years before it was awarded, and Alfred Nobel s will stipulates that the prize cannot be awarded posthumously. Woodward, however, had received the 1965 Nobel Prize in chemistry for his work in organic synthesis. 

Poland in 1937 and came to the United States when he was 12. He received a B.S. from Columbia and a Ph.D. from Harvard. When the conservation of orbital symmetry theory was proposed, he and Woodward were both on the faculty at Harvard. Hoffmann is presently a professor of chemistry at Cornell. 

According to the conservation of orbital symmetry theory, whether a compound will undergo a pericyclic reaction under particular conditions and what product will be formed both depend on molecular orbital symmetry. To understand pericyclic reactions, therefore, we must now review molecular orbital theory. We will then be able to understand how the symmetry of a molecular orbital controls both the conditions under which a pericyclic reaction takes place and the configuration of the product that is formed. 

The two lobes of up orbital have opposite phases. When two in-phase atomic orbitals interact, a covalent bond is formed two out-of-phase orbitals interact to create a node. The conservation of orbital symmetry theory states that in-... 

The conservation of orbital symmetry theory states that in-phase orbitals overlap during the course of a pericychc reaction. 

The theory of electrocyclic reactions was first presented in a form that focused on the HOMO by (a) R. B. Woodward and R. Hoffmann, J. Amer. Chem. Soc87, 395 (1965), and later in the form described here (b) R. Hoffmann and R. B. Woodward, Accts. Chem. Res, 1, 17 (1968). See also (c) R. B. Woodward and R. Hoffmann, The Conservation of Orbital Symmetry, Verlag Chemie, Weinheim/ Bergstr., Germany, and Academic Press, New York, 1970. 

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... 

In 1965, the American chemists R. B. Woodward and R. Hoffmann ( conservation of orbital symmetry or Woodward-Hoffmann rules) and Japanese chemist K. Fukui ( frontier orbital theory ) proposed theories to explain these results as well as those for other 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.)... 

For many years, pericyclic reactions were poorly understood and unpredictable. Around 1965, Robert B. Woodward and Roald Hoffmann developed a theory for predicting the results of pericyclic reactions by considering the symmetry of the molecular orbitals of the reactants and products. Their theory, called conservation of orbital symmetry, says that the molecular orbitals of the reactants must flow smoothly into the MOs of the products without any drastic changes in symmetry. In that case, there will be bonding interactions to help stabilize the transition state. Without these bonding interactions in the transition state, the activation energy is much higher, and the concerted... 

New kinetic and stereochemical information on these two cycloadditions and two degenerate molecular rearrangements has become available, and a comprehensive theory relating some general postulates on conservation of orbital symmetry during concerted chemical processes to their stereochemical features has been advanced and impressively developed 118,142) ... 

The discovery of handedness, or chirality, in crystals and molecules brought the symmetry concept nearer to the chemical laboratory. All this, however, concerned more the stereochemist, the structural chemist, the crystallographer, and the spectroscopist rather than the synthetic chemist. Symmetry used to be considered to lose its significance as soon as the molecules entered the chemical reaction. Orbital theory and the discovery of the conservation of orbital symmetry have encompassed even this area. It was signified by the 1981 Nobel Prize in chemistry awarded to Kenichi Fukui and Roald Hoffmann (Figure 1-1) for their theories, developed independently, concerning the course of chemical reactions [6],... 

The conservation of orbital symmetry dictates that electrocycUc reactions involving An electrons follow a conrotatory pathway while those involving 4 -l-2 electrons follow a disrotatory pathway. For each case, two different rotations are possible. For example, 3-substituted cyclobutenes can ring open via two allowed conrotatory but diastereomeric paths, leading to E- or Z-1,3-butadienes, as shown in Scheme 4.11. Little attention was paid to this fact until Houk and coworkers developed the theory of torquoselectivity in the mid-1980s. They defined torquoselec-tivity as the preference of one of these rotations over the other. 

Although Otto Diels and Kurt Alder won the 1950 Nobel Prize in Chemistry for the Diels-Alder reaction, almost 20 years later R. Hoffmann and R. B. Woodward gave the explanation of this reaction. They published a classical textbook, The Conservation of Orbital Symmetry. K. Fukui (the co-recipient with R. Hoffmann of the 1981 Nobel Prize in Chemistry) gave the Frontier molecular orbital (FMO) theory, which also explains pericyclic reactions. Both theories allow us to predict the conditions under which a pericyclic reaction will occur and what the stereochemical outcome will be. Between these two fundamental approaches to pericyclic reactions, the FMO approach is simpler because it is based on a pictorial approach. Another method similar to the FMO approach of analyzing pericyclic reactions is the transition state aromaticity approach. 

The Nazarov cyclization is an example of a 47r-electrocyclic closure of a pentadienylic cation. The evidence in support of this idea is primarily stereochemical. The basic tenets of the theory of electrocyclic reactions make very clear predictions about the relative configuration of the substituents on the newly formed bond of the five-membered ring. Because the formation of a cyclopentenone often destroys one of the newly created centers, special substrates must be constructed to aUow this relationship to be preserved. Prior to the enunciation of the theory of conservation of orbital symmetry, Deno and Sorensen had observed the facile thermal cyclization of pentadienylic cations and subsequent rearrangements of the resulting cyclopentenyl cations. Unfortunately, these secondary rearrangements thwarted early attempts to verify the stereochemical predictions of orbital symmetry control. Subsequent studies with Ae pentamethyl derivative were successful. - The most convincing evidence for a pericyclic mechanism came from Woodward, Lehr and Kurland, who documented the complementary rotatory pathways for the thermal (conrotatory) and photochemical (disrotatoiy) cyclizations, precisely as predicted by the conservation of orbital symmetry (Scheme 5). 

For excellent discussions of this method, see Woodward, R.B. Hoffmann, R. The Conservation of Orbital Symmetry, Academic Press, NY, 1970 Angew. Chem. Int. Ed. 1969, 8, 781 Jones, R.A.Y. Physical and Mechanistic Organic Chemistry 2nd ed., Cambridge University Press, Cambridge, 1984, pp. 352-366 Klumpp, G.W. Reactivity in Organic Chemistry, Wiley, NY, 1982, pp. 378-389 Yates, K. Hiickel Molecular Orbital Theory, Academic Press, NY, 1978, pp. 263-276. 

The linear response function [3], R(r, r ) = (hp(r)/hv(r ))N, is used to study the effect of varying v(r) at constant N. If the system is acted upon by a weak electric field, polarizability (a) may be used as a measure of the corresponding response. A minimum polarizability principle [17] may be stated as, the natural direction of evolution of any system is towards a state of minimum polarizability. Another important principle is that of maximum entropy [18] which states that, the most probable distribution is associated with the maximum value of the Shannon entropy of the information theory. Attempts have been made to provide formal proofs of these principles [19-21], The application of these concepts and related principles vis-a-vis their validity has been studied in the contexts of molecular vibrations and internal rotations [22], chemical reactions [23], hydrogen bonded complexes [24], electronic excitations [25], ion-atom collision [26], atom-field interaction [27], chaotic ionization [28], conservation of orbital symmetry [29], atomic shell structure [30], solvent effects [31], confined systems [32], electric field effects [33], and toxicity [34], In the present chapter, will restrict ourselves to mostly the work done by us. For an elegant review which showcases the contributions from active researchers in the field, see [4], Atomic units are used throughout this chapter unless otherwise specified. 

A key to understanding the mechanisms of the concerted pericyclic reactions was the recognition by Woodward and Hoffmann that the pathway of such reactions is determined by the symmetry properties of the orbitals that are directly involved. Specifically, they stated the requirement for conservation of orbital symmetry. The idea that the symmetry of each participating orbital must be conserved during the reaction process dramatically transformed the understanding of concerted pericyclic reactions and stimulated much experimental work to test and extend their theory. The Woodward and Hoffmann concept led to other related interpretations of orbital properties that are also successful in predicting and interpreting the course of concerted... 

A pericyclic reaction such as the Diels-Alder reaction can be described by a theory called the conservation of orbital symmetry. This simple theory says that pericyclic reactions occur as a result of the overlap of in-phase orbitals. The phase of the orbitals in Figure 8.4 is indicated by their color. Thus, each new a bond formed in a Diels-Alder reaction must be created by the overlap of orbitals of the same color. Because two new a bonds are formed, we need to have four orbitals in the correct place and with the correct color (symmetry). The figure shows that, regardless of which pair of HOMO and LUMO we choose, the overlapping orbitals have the same color. In other words, a Diels-Alder reaction occurs with relative ease. The Diels-Alder reaction and other cycloaddition reactions are discussed in greater detail in Section 29.4. 

This alternation of chemical behavior, 67t-system versus 47t-system, thermal versus photochemical, has at its core the quantum effeas that dictate the symmetries of molecular orbitals. In 1964, Roald Hoffmann (1937- ) was 27, had completed his Ph.D. at Harvard two years earlier, and was in the second year of an appointment as a Harvard junior fellow. The renowned Woodward (who would win the Nobel Prize in chemistry in 1965) discussed his observations on electrocyclic reactions with Hoffmann. Although Kenichi Fukui had developed frontier molecular orbital theory more than a decade earlier and many related theoretical ideas were percolating in the chemical community, it was Woodward and Hoffmann who published, in 1965, their intellectual synthesis as a book titled The Conservation of Orbital Symmetry. Their theory explained a broad spectrum of concerted reactions and made bold predictions that were later verified. 

Opposite page) Molecular orbital picture diagrams rationalizing the Diels-Alder reaction between 1,3-butadiene and ethylene (top) using A) the conservation of orbital symmetry (Woodward and Hoffmann) B) frontier molecular orbital theory (Fukui). 

---