Valence bond theory provides a model of bonding that is widely used by organic chemists despite the fact that experimental and theoretical data clearly indicate that one of the central tenets of this theory is incorrect, namely that the electron density associated with a covalent bond is restricted to the region of space between the two bonded nuclei. While this assumption is a good first approximation, there are many examples of reactions that demand a more sophisticated approach. Resonance theory was devised primarily to account for the fact that a large body of experimental data suggested that electron density was more delocalized than valence bond theory suggests. This topic begins with a brief review of some of that experimental data and continues with a discussion of additional results that are inconsistent with the valence bond model.
s-p Overlap: Hyperconjugation
As Figure 1 recalls, the relative stability of a series of a carbocation is influenced by the substituents attached to the positively charged carbon.
These trends have been rationalized in terms of extended orbital overlap. Figure 2 illustrates the overlap of the empty p orbital with one of the three C-H s bonds of the methyl group that is attached to the positively charged carbon atom in the ethyl carbocation. This type of s-p overlap is referred to as hyperconjugation.
Hyperconjugation-Delocalization of s Electrons
The implication of the double-headed arrow in Figure 2 is that the electron pair shown in red is not localized between the C and H atoms, but is also shared with the adjacent carbon atom. Since valence bond theory does not allow for this type of bonding, it is not able to explain the differences in carbocation stabilities.
Exercise 1 Does the overlap shown in Figure 2 increase or decrease the electron density in the C-H bond?
Exercise 2 Given your answer to Exercise 1, would you expect the methyl C-H bond strength in propene, CH3CH=CH2, to be greater than or less than the methyl C-H bond strength in propane, CH3CH2CH3?
A similar argument was invoked to rationalize the relative reactivities as well as the relative stabilities of alkenes.
In our discussion of the Sn1 mechanism we saw that the rate of solvolysis of alkyl halides increases as the stabilities of the carbocationic intermediates increase. Thus, the fact that the rate of hydrolysis of methyl chloromethyl ether, CH3O-CH2Cl, is approximately 1014 times faster than that of chloromethane, H-CH2Cl must mean that the carbocationic intermediate formed in the first reaction is much more stable than the one produced in the latter. This increase occurs despite the fact that the group electronegativity of CH3O is greater than that of H, i.e. on the basis of its inductive effect, the methoxy group should destabilize the carbocation. However, the methoxy group has a Jeckyl and Hyde quality to it: before the reaction begins, it withdraws electron density from the reaction center; as the carbocation forms, the methoxy group becomes an electon donor, sharing a non-bonding pair with the adjacent electron deficient center as shown in Figure 3.
Resonance-Delocalization of p Electrons
Exercise 3 How many conformations about the C-O bond are there such the a pair of electrons in a non-bonding orbital may overlap with the vacant p orbital of the carbocation formed in the hydrolysis of methyl chloromethyl ether?
Exercise 4 Draw structures of the resonance hybrid and the two resonance contributors inplied by Figure 3.
This type of kinetic evidence for n-p orbital overlap is also observed in systems having a multiple bond adjacent to the reaction center, i.e. in the solvolysis reactions of allylic and benzylic halides.
The rate of solvolysis of allyl chloride, CH2=CH-CH2Cl, is 58 times greater than that of methyl chloride; benzyl chloride, C6H5-CH2Cl, reacts over 650 times as fast. The rationalization of these results is similar, and is reiterated in Figure 4 for the solvolysis of benzyl chloride.
p-p Overlap Revisited
As the C-Cl bond breaks, the hybridization of the benzylic carbon (the carbon atom attached to the aromatic ring) changes from sp3 to sp2. The p orbital on the benzylic carbon aligns with the pi system of the aromatic ring. Side-to-side overlap of these orbitals allows electron density to be transferred from the ring into the vacant p orbital as indicated by the arrows in the figure.
Now let's consider additional evidence that argues for delocalized bonding.
Bond Dissociation Energies
The energy required to cleave a bond homolytically is known as the bond dissociation energy. Table 1 summarizes the bond dissociation energies associated with the homolytic cleavage of three types of primary C-H bonds and three types of primary C-Cl bonds.
Bond Dissociation Energies
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In the first set of reactions, the dissociation of the C-H bond in propane serves as the reference. The bond dissociation energy of 101 kcal/mol is typical of a primary C-H bond in an alkane. The fact that cleavage of the C-H bond in propene requires 15 kcal/mol less energy may be rationalized from two perspectives, both of which may be appreciated by inspection of Figure 5.
Rationalizing Your Weaknesses
Before the reaction occurs, the hyperconjugative interaction depicted by the arrow implies that there is greater electron density in the C-C internuclear region than valence bond theory allows. As electron density shifts from between the C and H atoms toward the two carbon atoms, the strength of the C-H bond necessarily decreases. While this might seem like a destabilizing interaction, it is not. Whenever electrons are delocalized, they experience greater nuclear attractions, and their energy decreases.
Cleavage of the C-H bond produces an allylic radical. The allylic carbon is now sp2 hybridized. The change in hybridization occurs in order to maximize the overlap of the p orbital on the allylic carbon with the pi system of the adjacent double bond. This affords the greatest nuclear attraction for all three electrons in the pi system. Figure 6 presents this rationalization in terms of the standard resonance contributors. Note the use of the single-barbed arrow to indicate the movement of a single electron.
The Resonance Picture
Exercise 5 Draw structural diagrams similar to those in Figure 5 for each of the other reactions shown in Table 1.
Exercise 6 Which of the resonance structures shown in Figure 6 makes the greater contribution to the hybrid structure for the allylic radical? A B They make equal contributions.
Before we move on to other evidence for delocalized bonding, let's consider the potential energy diagram shown in Figure 7. It compares the relative energy changes associated with homolysis of the C-H bonds in propane and propene.
Rationalizing Relative Bond Dissociation Energies
The curve at the left of the figure represents the changes in potential energy that attend the homolytic cleavage of a primary C-H bond in propane. The difference in potential energy between propane and propene is indicated by the red bar labeled 1. This difference may be attributed to the hyperconjugative interaction shown in the structure at the left of Figure 5. A comparable interaction is not possible in propane. The difference in potential energy between the propyl radical and the alllylic radical is indicated by the red bar labeled 3. Resonance stabilization of the allylic radical, as shown in Figure 6, is not possible for the propyl radical. Since resonance stabilizes the allylic radical, it must also stabilize the transition state leading to that radical, although not by as much. The red bar labeled 2 indicates the stabilization of the transition state for the formation of the allylic radical relative to the propyl radical. Greater stabilization of the transition state means that the primary C-H bond of propene will be cleaved faster than the primary C-H bond of propane, a fact that is also consistent with the relative bond dissociation energies.
Reactions of Allylic Systems
There are many reactions that illustrate the delocalized nature of bonding in allylic systems. Representative examples of reactions involving allylic cations, anions, and radicals are shown below.
Reactions Involving Allylic Cations
Equations 1 and 2 describe two nucleophilic substitution reactions that proceed by an Sn1 mechanism.
Exercise 7 The fact that the same products are formed in the same relative amounts suggests that a common intermediate is involved in reactions 1 and 2. Draw the structure of that intermediate. Draw the structures of the carbocations that are initially formed in these two reactions. Then draw appropriate resonance contributors.
Electrophilic addition of HCl to 1,3-butadiene produces a mixture of 1-chloro-2-butene and 3-chloro-1-butene as shown in Equation 3.
Although the starting material is not an allylic system, the carbocationic intermediate generated by protonation of this material is.
Exercise 8 In 1,3-butadiene, C-1 is identical to C-4 and C-2 is indistinguishable from C-3. Given the results shown in Equation 3, does protonation of 1,3-butadiene occur preferentially at C1(C4) or C2(C3)?
Exercise 9 Draw resonance structures for the carbocation that is formed by protonation of C-1 of 1,3-butadiene. Draw the structure of the resonance hybrid that is formed in this reaction.
Reactions Involving Allylic Anions
When the Grignard reagent generated from 1-bromo-2-butene is treated with aqueous acid, a mixture of 1-butene and 2-butene is formed. Furthermore, the product distribution in this mixture is the same as that obtained by acidification of the Grignard reagent produced from 3-bromo-1-butene. Equations 4 and 5 compare these results.
Exercise 10 Assuming that the C-Mg bond is ionic (a false assumption), draw the structure of the carbanion corresponding to the Grignard reagent shown in Equation 4. Then draw the resonance contributor for this carbanion. Do these two resonance structures have the same energy? Draw similar structures for the carbanion that corresponds to the Grignard reagent shown in Equation 5.
Exercise 11 Which isomer is more stable 1-butene or 2-butene?
Exercise 12 Does the product distribution shown in Equations 4 and 5 suggest that these reactions are kinetically controlled or thermodynamically controlled?
Reactions Involving Allylic Radicals
In the presence of a peroxide catalyst, alkenes undergo free radical bromination upon treatment with N-bromosuccinimide NBS). The NBS serves as a souce of bromine atoms, and the mechanism involves initiation, propagation, and termination that is characteristic af free radical substitution reactions. Equation 6 shows the results of bromination of 1-butene with NBS.
Compare this result with the outcome of Equation 3.
Exercise 11 Assuming that the initiation step of reaction 6 involves abstraction of an allylic hydrogen atom by an alkoxy radical, RO., write equations for each of the steps involved in the conversion of 1-butene to 1-bromo-2-butene.
Reactions Related to Allylic Systems
A Look Back
In our initial discussion of the pKa scale as well as in our more recent discussions of reactions of ketones and aldehydes and the aldol reaction we have seen that a hydrogen atom attached to a carbon a to a carbonyl group is more acidic than a comparable hydrogen in an alkane. The structural element that is responsible for this enhanced acidity is the same as that which is responsible for the experimental results we have considered in this topic, namely orbital overlap. Figure 8 compares the orbital diagrams commonly used to describe the intermediates that are formed in these systems.
The Bottom Line
The electrons that occupy the various orbitals shown in the figure have been omitted in order to emphasize the fact that it is the geometry of the orbitals that is important in the stabilization of reaction intermediates. The number of electrons that occupy those orbitals is not important. Learning to recognize situations involving this type of orbital array will simplify your mastery of such seemingly diverse reactions as electrophilic addition, free radical substitution, and, looking ahead, nucleophilic 1,4-addition reactions.
We have seen that sodium borohydride is a useful reagent for the reduction of the carbonyl group. For example, NaBH4 readily reduces cyclohexanone to cyclohexanol as shown in Equation 7.
This reaction involves the 1,2-addition of the "elements of" dihydrogen to the carbonyl group of the ketone.
Now compare the result of reaction 7 with that shown in Equation 8. Here the formation of cyclohex-2-en-1-ol is just what you would expect from 1,2-addition of the "elements of" dihydrogen to carbonyl group. The formation of cyclohexanone, on the other hand, appears to be 1,2-addition of the "elements of" dihydrogen to the C-C double bond. But looks can be deceiving.
Closer inspection of the starting material reveals the the C-C double bond is conjugated to the carbonyl group. This orbital interaction leads to a polarization of the double bond as indicated in Figure 9.
Resonance Interactions in Cyclohex-2-en-1-one
The extended orbital overlap implied by arrows 1 and 2 provides a pathway for electron density to be drawn away from C-3 toward the oxygen atom. The positive charge makes the electron deficiency on C-3 apparent in resonance contributor B in the figure. As Figure 10 demonstrates, delivery of a single hydride ion to C-3 generates ion C. Protonation of the oxygen atom this ion yields enol D. At this point the "elements of" dihydrogen have been added to the 1st and 4th atoms of a conjugated system that extends over four atoms. Hence the formation of enol D, and by extension the formation of the cyclohexanone, is described as a 1,4-addition reaction. We will consider other examples of 1,4-additions in our discussion of Michael additions.
1,4-Addition of "the elements" of Dihydrogen
Exercise 12 Draw an orbital picture of resonance structure B similar to those shown in Figure 8. Put the appropriate number of electrons into each of the p orbitals that form this conjugated system.