The Conservation of Symmetry during Reactions

In addition to the static stereochemical features across planes, about axes, and through points (discussed above and seen in realized organic compounds), an understanding of the stereochemical relationships often found to exist in the dynamic relationship between reactants and products is vital to organic chemistry. Such an understanding allows detailed predictions, for example, of products, to be made  

By way of example, consider the following observations reported in 1958 when (Z)-3,4-dimethylcyclobutene is heated, it undergoes decomposition to (Z,E)-2,4-hexadiene (exclusively ). Furthermore, when ( )-3,4-dimethylcyclobutene is heated. 

Interestingly, many examples of such reactant-product specificity are known. Their analysis led Woodward and Hoffmann to propose that these and other elec-trocydic processes occur in a fashion, which conserves symmetry. 

Indeed, it is clear that it is the conservation of symmetry that rules the path the reactions take. This powerful predictive tool operates using the following concepts  

Overlap of orbitals of like sign corresponds to bonding and overlap of orbitals of unlike sign corresponds to antibonding (see Chapter 1). 

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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... 

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. 

Robert Woodward, worked out the rules for the conservation of orbital symmetry during chemical reactions in which ring compounds are formed from chain structures (cyclization), and bonds break and form simultaneously. With Kenichi Fukui, he was awarded the 1981 Nobel Prize in chemistry for this work, which has proved to be seminal. 

Figure 4.50. A cartoon depiction of the conservation of orbital symmetry during a Diels-Alder reaction between ethene (ethylene, H2C=CH2) and trans-,trans-, or ( ,i )-2,4-hexadiene (CH3-CH=CH-CH=CH-CH3).The stereochemistry of the starting materials is conserved.

These results are interesting because neither the frontier orbital method nor arguments based on the conservation of orbital symmetry during reactions can account for the difference between the two modes of the Cope rearrangement. According to these theories, rearrangement via boat and chair transition states should be equally allowed. 

Longuet-Higgins and Abrahamson and has been rather generally adopted. This is based on the idea that if a molecule has symmetry and if the symmetry is conserved during a reaction, the wave function will tend to retain similar symmetry. Thus if the molecule has a plane of symmetry, and if the wave function is initially symmetric with respect to reflection in that plane, and if the plane of symmetry is retained throughout a reaction, then the wavefunction must remain symmetric. In the MO approximation, it can be shown that similar restrictions apply to MOs. This has led to the interpretation of pericyclic reactions in terms of the conservation of orbital symmetry during them. 

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

The key to understanding the mechanism of the concerted pericyclic reactions was the recognition by Woodward and Hoffmann that the pathways of such reactions were determined by the symmetry properties of the orbitals that were directly involved. Their recognition that the symmetry of each participating orbital must be conserved during the... 

The interpretation of chemical reactivity in terms of molecular orbital symmetry. The central principle is that orbital symmetry is conserved in concerted reactions. An orbital must retain a certain symmetry element (for example, a reflection plane) during the course of a molecular reorganization in concerted reactions. It should be emphasized that orbital-symmetry rules (also referred to as Woodward-Hoffmann rules) apply only to concerted reactions. The rules are very useful in characterizing which types of reactions are likely to occur under thermal or photochemical conditions. Examples of reactions governed by orbital symmetry restrictions include cycloaddition reactions and pericyclic reactions. 

What should be correlated In an orbital correlation diagram, the shapes and energies of orbitals are examined to see if the electronic structure of the reactants could be smoothly converted into the electronic structure of the products, each defined by the structures and occupancies of their respective orbitals. The nodal characteristics of orbitals are very resistant even to rather large perturbations and will tend to be conserved in chemical reactions. If an element of symmetry, for example, a mirror plane, is maintained during the course of the reaction, the nodal characteristics separate the orbitals into two sets, the members of one set being symmetric with respect to reflection... 

A total synthesis of vitamin B12 was announced in 1972, as the result of a collaborative effort between R. B. Woodward (Harvard) and A. Eschenmoser (Zurich). The synthesis was completed after 11 years of effort involving 100 co-workers from 19 countries. A number of important techniques and reactions of synthetic value were developed during the course of this work, including the principle of conservation of orbital symmetry (the Woodward-Hoffman rules, Section 21-10). The biochemical action of vitamin B12 is considered in Chapter 31. 

Free atoms are spherically symmetrical, which implies conservation of their angular momenta. Quantum-mechanically this means that both Lz and L2 are constants of the motion when V = V(r). The special direction, denoted Z, only becomes meaningful in an orienting field. During a chemical reaction such as the formation of a homonuclear diatomic molecule, which occurs on collisional activation, a local held is induced along the axis of approach. Polarization also happens in reactions between radicals, in which case it is directed along the principal symmetry axes of the activated reactants. When two radicals interact they do so by anti-parallel line-up of their symmetry axes, which ensures that any residual angular momentum is optimally quenched. The proposed sequence of events is conveniently demonstrated by consideration of the interactions between simple hydrocarbon molecules. 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angular momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal symmetry of mechanics. 

The theory of such reactions was put forward in 1969 by the American chemists Robert Bums Woodward (1917-79) and Roald Hoff-marm(1937- ), and is concerned with the way that orbitals of the reactants change continuously into orbitals of the products during reaction and with conservation of orbital symmetry during this process. See also... 

The most important observation in the smdy of pericyclic reactions is the existence of conservation of molecular orbital symmetry throughout the transformation, meaning thereby that the symmetric orbitals are converted into symmetric orbitals whereas antisymmetric orbitals are converted into antisymmetric orbitals. In this approach, symmetry properties of various molecular orbitals of the bonds that are involved in the bond breaking and formation process during the reaction are considered and identified with respect to C2 and m elements of symmetry. These properties remain preserved throughout the course of reaction. Then a correlation diagram is drawn in which the molecular orbital levels of like symmetry of the reactant are related to that of the product by drawing lines. 

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