For the synthetic organic chemist, the development of a general procedure that leads to the formation of carbon-carbon bonds is considered a laudable achievement. A general method that results in the simultaneous formation of two carbon-carbon bonds is worthy of a Nobel prize. In 1950, two chemists, Otto Diels and Kurt Alder, received that accolade for their discovery of a general method of preparing cyclohexene derivatives that is now known as the Diels-Alder reaction.
The Diels-Alder reaction is one type of a broader class of reactions that are known as pericyclic reactions. In 1965 two other Nobel laureates, Robert B.Woodward and Roald Hoffmann, published a series of short communications in which they presented a theoretical basis for these well known, but poorly understood pericyclic reactions. Their theory is called orbital symmetry theory. Subsequently other chemists published alternative interpretations of pericyclic reactions, one called frontier orbital theory, and another named aromatic transition state theory. All of these theories are based upon MO theory. In this topic we will use the Diels-Alder reaction to illustrate aspects of each of these theories.
The essential nature of the Diels-Alder reaction is summarized by Equation 1, where the substituents attached to the reactants have been omitted for clarity.
Figure 1 presents two examples of Diels-Alder reactions that have played vital roles in the total synthesis of biologically important molecules. The first example involves a synthesis of the steroid cortisone reported by R. B. Woodward in 1951. The second synthesis was performed by another Nobel laureate, E. J. Corey in 1969. In both cases many steps were required after the Diels-Alder reaction. The carbon atoms of the reactants are numbered to allow their identification in the final product.
Figure 1 demonstrates the practical side of the Diels-Alder reaction. Now let's take a look at the theoretical side, starting with orbital symmetry theory.
Orbital symmetry theory was a new paradigm in chemistry. As such it required new language. New words and new concepts had to be defined. The new vocabulary included the following words and terms:
The first term is the general reaction type described by orbital symmetry theory. The next four terms are specific types of pericyclic reactions. This discussion is limited to the first type, namely cycloaddition reactions. The term orbital correlation diagram describes the theoretical device that Woodward and Hoffmann developed to interpret pericyclic reactions. According to orbital symmetry theory the symmetry of the orbitals of the reactants must be conserved as they are transformed into the orbitals of the product. Consider the simplest example of a cycloaddition reaction, the head-to-head coupling of two ethene molecules to form cyclobutane as shown in Equation 2.
Figure 3 defines the conditions implied by the term head-to-head, namely that the reactants approach each other in parallel planes with the pi orbitals overlapping in the head-to-head fashion required for the formation of sigma bonds (shown in red in Equation 2). The sigma-bonded atoms of each ethene lie in the two parallel planes shown in black in the figure. The p orbitals on each carbon lie in the vertical plane which is shown in blue. The two planes shown in red are symmetry planes. Plane 1 bisects the C-C bond of each ethene, while plane 2 lies half way between the two planes shown in black.
According to the conventions of orbital symmetry theory, the reaction shown in Figure 3 is classified as a p2s + p2s cycloaddition, where p indicates that the reaction involves a p system, the number 2 is the number of electrons in the reacting p system, and the letter s stands for suprafacial: if one lobe of a p orbital is considered as the top face, while the other lobe is called the bottom face, then a suprafacial interaction is one in which the bonding occurs on the same face at both ends of the p system. The alternative to a suprafacial interaction is an antarafacial reaction: in this case bonding occurs on the top face at one end of the p system and on the bottom face of the other. We will consider these ideas again when we discuss the Diels-Alders reaction.
In classifying an orbital as symmetric (S) or antisymmetric (A) with respect to a symmetry plane, it is necessary to compare the phase of the lobes of the orbitals on each side of the symmetry plane:
The phase may be indicated by shading or by labeling one lobe of an orbital + and the other -.
Molecular orbital theory describes the formation of the product in reaction 2 in terms of linear combinations the molecular orbitals of the reactants. Each reactant has two pi molecular orbitals of interest, y1 and y2. There are four combinations of these pi orbitals possible: y1A + y1B, y1A - y1B, y2A + y2B, and y2A - y2B, where the subscripts A and B are used to distinguish one ethene from the other. These combinations transform into the four sigma molecular orbitals in the product: s1A + s1B, s1A - s1B, s2A + s2B, and s2A - s2B. The diagram depicting the correlation of the reactant and product orbitals is shown in Figure 4. The numbers 1 2 in the diagram refer to the symmetry planes 1 and 2 in Figure 3.
The horizontal dashed line in the figure represents the energy level of an isolated p orbital. The most important feature to note about this admittedly complex diagram is that the linear combination y1A - y1B of the reactants correlates with, i.e. has the same symmetry, SA, as the s2A + s2B combination in the product. This is the central postulate of orbital symmetry theory: orbitals in the reactants must transform into product orbitals that have the same symmetry. Since the s2A + s2B orbital in the product is a high energy orbital, there must be a high activation energy for the formation of the product. Hence reaction 2 is said to be symmetry forbidden.
Since orbital correlation diagrams for more reactions involving more atoms are necessarily more complex, we will not deal further with this approach to pericyclic reactions. Rather we will examine an alternative theory known as Frontier Orbital Theory.
According to Frontier Orbital Theory it is possible to determine if a pericyclic reaction is allowed or forbidden by simply considering the symmetry relationship of the frontier orbitals of the reactants. The frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). The interaction between these orbitals, a so-called HOMO-LUMO interaction, is a concept that is similar to Lewis acid-Lewis base chemistry which involves the interaction of a filled orbital of the base with an empty orbital of the acid.
According to Frontier Orbital Theory, a pericyclic reaction is allowed when the HOMO of one reactant has the same symmetry as the LUMO of the other.
We will now return to reaction 1, the Diels-Alder reaction, to illustrate this idea. Ethene has two pi orbitals which we will label y1E and y2E, the latter being the LUMO. 1,3-butadiene has four pi orbitals, y1B , y2B, y3B, and y4B, with y2B the HOMO. Figure 5 shows an idealized geometry for the approach of these frontier orbitals in parallel planes. The blue lines highlight the incipient overlap of the terminal lobes of the pi system of the diene with the orbitals of the alkene. The plane shown in red is a symmetry plane that bisects both molecules. Both the LUMO of ethene and the HOMO of 1,3-butadiene are antisymmetric (A) with respect to this plane. Since the HOMO-LUMO interaction shown in Figure 5 involves orbitals of the same symmetry, the reaction is allowed.
Using the convention we discussed earlier, the Diels-Alder reaction is classified as a p2s + p4s cycloaddition. The alkene is a 2p electron system, while the diene is a 4p electron system. As the blue lines in Figure 5 indicate, the interaction between these two p systems occurs on the top face of each lobe of the alkene and the bottom face of each lobe of the diene. Hence, the interaction is suprafacial on both components. As we will see shortly, it is useful to regard the Diels-Alder reaction as a reference point for allowed cycloadditions.
In order to use any of the three theories discussed in this topic effectively, you must be able to draw the molecular orbitals of the reactants. This is straightforward, and we will illustrate the approach with the four MOs of 1,3-butadiene. These MOs are formed by taking linear combinations of the p orbital on each of the four sigma bonded carbons. The lowest energy MO, y1= p1 + p2 + p3 + p4, has no nodes. Remember: a node is that point where the phase of a standing wave changes from positive to negative. The next orbital, y2= p1 + p2 - p3 + p4, has 1 node (the minus sign (-) indicates a node); y3 = p1 - p2 + p3 - p4, has 2 nodes and y4 = p1 - p2 - p3 - p4, has 3. The nodes in each MO are placed symmetrically. Figure 6 offers three representations of the MOs of 1,3-butadiene along with their classification as either symmetric (S) or antisymmetric (A) with respect to a symmetry plane that is perpendicular to the sigma bonded framework and bisects the C-2-C-3 bond. The red dots in MOs y2-y4 depict nodes. Notice that the symmetry of the orbitals alternates S-A-S-A as you go from one orbital to the next.
Exercise 3 Consider the following reaction: Draw a frontier orbital diagram similar to that shown in Figure 5. What type of cycloaddition is this? Is y2 symmetric or antisymmetric to a symmetry plane bisecting the C-2-C-3 bond? symmetric antisymmetric. Is this reaction allowed?
How can you decide if a pericyclic reaction involves an aromatic transition state? In our discussion of aromaticity we classified structures as aromatic or anti-aromatic based upon Hückel's rule: an aromatic molecule contains a cyclic array of orbitals in which there are 4n + 2 electrons. Consider the description of the Diels-Alder reaction shown in Figure 7.
The dashed red lines indicate bonds that are being formed in the transition state, while the dashed blue lines depict those that are breaking. Since the reaction involves the 4 pi electrons of 1,3-butadiene and the 2 pi electrons of ethene, there must be 6 electrons involved in the transition state, which, therefore, is aromatic because it conforms to Hückel's rule where n = 1. Note that this analysis assumes the geometry shown in Figure 5.
All of the theories just described involve two basic assumptions
Given these assumptions, we can state the following:
The rules are reversed when the reaction is photochemically induced:
These rules are summarized in Table 1. Note that changing just one of the variables, i.e. faciality, energy source, or number of electrons (two electrons at a time), changes an allowed reaction to a forbidden one and vice versa.
Exercise 5 What is the HOMO in the allylic cation? y1 y2 y3 What is the LUMO in the allylic anion? y1 y2 y3
Exercise 6 Indicate whether the following reactions would be allowed or forbidden
Allowed Forbidden
Exercise 7 Classify each of the following reactions as 2+2, 2+4, etc. Do not leave any spaces in your answer.
Figure 7 outlines a strategy for conversion of solar energy to chemical energy in a way that offers potential for the design of a solar energy storage device.
The idea begins with a thermally allowed Diels-Alder reaction in which the 2-pi electron component is an alkyne rather than an alkene. The product, 1, is a cyclohexadiene. Irradiation of this diene should promote an allowed intramolecular 2+2 cycloaddition, leading to the formation of the highly strained tricyclic ring system 2. Since 2 cannot revert to 1 by a thermally allowed process, it is trapped in this high energy state. Recall that our definition of a forbidden reaction merely means that it is a process that has a high activation energy. This suggests that the reverse reaction, 2 ---> 1, might be enabled with an appropriate catalyst. The requirements to implement this approach then are
Your fortune awaits.
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