Jones M., Fleming S.A. Organic Chemistry

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20.7 A Molecule with a Fluxional Structure 1069

But now perhaps you notice the threefold rotational axis in bullvalene. Remove

the color and the three double bonds become indistinguishable. In fact, there is a

Cope rearrangement possible in each of the three faces of the molecule, and every

Cope rearrangement is degenerate; each re-forms the same molecule (Fig. 20.67).

This point is much easier to see if you use a model.

Cope rearrangement

Turn 90⬚

axis

FIGURE 20.67 Bullvalene has a

threefold rotational axis: All three

double bonds are equivalent.The

Cope rearrangement can occur in

each of the three faces of the

molecule and is degenerate in

every case.

That’s quite interesting, but now begin to look at the structural consequences

for bullvalene. As Cope rearrangements occur, the carbons begin to move apart! This

wandering of atoms is shown in Figure 20.68 using dots to track two arbitrary adja-

cent carbons. The figure only begins the process, but it can be demonstrated that

the Cope rearrangement is eventually capable of completely scrambling the 10 CH

units of the molecule.

As long as the Cope rearrangement is fast, bullvalene has no

fixed structure; no carbon has permanent nearest neighbors, but is instead bonded

on time average to each of the 9 other methine carbons. It has a fluxional structure.

Cope

bottom

face

Cope

Redraw-arrow

for location purposes

back

face

Cope

bottom

face

FIGURE 20.68 A sequence of Cope rearrangements serves to move carbon atoms throughout the molecule.

WORKED PROBLEM 20.20 At somewhat above room temperature the

H NMR

spectrum of bullvalene consists of a single broad line at δ 4.2 ppm. Explain.

ANSWER If all the carbon–hydrogen bonds are the same on time average, the

NMR spectrum must consist of a single line. We see the averaged spectrum.

In an early paper, Doering noted that a sequence of 47 Cope rearrangements sufficed to demonstrate that

two adjacent carbons could be exchanged without disturbing the rest of the 10-carbon sequence, and that there-

fore all 1,209,600 possible isomers could be reached. No claim was made that this represented the minimum

path. A later computer-aided effort by two Princeton undergraduates (Allan Fisher and Karl Bennett) located

a sequence of 17 Cope rearrangements that could do the same thing.

1070 CHAPTER 20 Reactions Controlled by Orbital Symmetry

–

ANSWER Exchange at the α position is routine.

–

WORKED PROBLEM 20.21 Explain why the ketone below exchanges all its hydro-

gens for deuteriums when treated with deuterated base.

However, simple ketones are in equilibrium with their enol forms, and the enol of

this molecule is a substituted bullvalene. The Cope rearrangement makes all the

carbons equivalent, and thus, on time average, all carbon–hydrogens will eventu-

ally come to occupy the exchangeable α position.

Repetition leads to exchange of all the hydrogens for deuterium.

OCope

–

Now this hydrogen

can exchange

Naturally, efforts at synthesis began as soon as the prediction of the properties of

bullvalene appeared in the chemical literature.Long before the efforts at a rational syn-

thesis were sucessful, the molecule was discovered by Gerhard Schröder (b. 1929), a

German chemist then working in Belgium. Schröder was working out the structures

of the several dimers of cyclooctatetraene, and in the course of this effort irradiated

one of the dimers. It conveniently fell apart to benzene and bullvalene (Fig. 20.69).

)(C

)

hν

FIGURE 20.69 Schröder’s accidental

synthesis of bullvalene.

20.8 How to Work Orbital Symmetry Problems 1071

Schröder was alert enough to understand what had happened, and went on to a

highly successful career that included an examination of the properties of bullvalene

and substituted versions of this molecule. Doering’s predictions were completely

confirmed by Schröder’s synthesis. Other neutral, completely fluxional organic mol-

ecules have not appeared, although the phenomenon of fluxionality appears to be

rather more common in organic cations and organometallic compounds.

(a)

(b)

PROBLEM 20.23 Provide mechanisms for the following reactions:

Summary

The Cope rearrangement, a [3,3] sigmatropic shift, is far more than just a chem-

ical curiosity. It is a general reaction of almost all 1,5-hexadienes, and occurs

almost no matter how the skeletal hexadiene form is perturbed and disguised.

All sorts of chemical “spinach” can be added, often making it quite difficult to

find the bare bones of the hexadiene system, but the reaction will persist.

Moreover, as we have just seen, digging deep into the Cope reaction, following

the intellectual implications of substitution, leads to the marvelous molecule

bullvalene, without precedent in organic chemistry.

20.8 How to Work Orbital Symmetry Problems

PROBLEM SOLVING

All people and all problems are, of course, different. Nonetheless, there are some

general principles that apply, and it is worth summarizing ways to approach—

and hopefully solve—orbital symmetry problems, which are separable into three

varieties.

20.8a Electrocyclic Reactions

1. Look for rings opening or closing within a single molecule. Sound like simple advice?

Yes, it is, but in all these problems the major difficulty is one of recognition, and it is

well worth your time to be a little “too straightforward,” and to “think simple.”

PROBLEM 20.22 Why is the second step of Figure 20.69, the photochemical

fragmentation, so easy?

Fluxional molecules are the

result of electrons and atoms

moving much like the blur of a

spinning skater.

1072 CHAPTER 20 Reactions Controlled by Orbital Symmetry

2. Once you are sure that the question involves an electrocyclic reaction,draw an arrow

formalism.

3. Next, work out the molecular orbitals of the open-chain partner.

4. Count the number of electrons involved in the reaction. Be careful to take account

of any charges.

5. Knowing the number of electrons allows you to find the HOMO of the open-chain

partner.

6. Finally, work out the motion,conrotatory or disrotatory, that allows the ring to close

through a bonding—not antibonding—interaction. If there are 4n electrons

involved in the reaction, then the thermal process will be conrotatory and the

photochemical process will be disrotatory. If there are 4n  2 electrons, then the

thermal process will be disrotatory and the photochemical will be conrotatory.

20.8b Cycloaddition Reactions

1. Look for a ring forming from two molecules or breaking open to give two new mol-

ecules. When you find this situation, you know you have a cycloaddition reaction.

2. Draw an arrow formalism.

3. Work out the π molecular orbitals for the two partners.

4. Identify the HOMOs and LUMOs.

5. Examine either possible HOMO–LUMO interaction. It is generally easier to look

at ring closing, rather than ring opening. Your final answer will be good for either

direction (of course!).

6. Count the number of electrons involved in the reaction.

7. If there are 4n electrons involved,then the thermal process will require a rotation in order

to occur and the photochemical process will not. If there are 4n  2 electrons involved,

then the thermal process will not require a rotation and the photochemical will.

20.8c Sigmatropic Shift Reactions These reactions are by far the hardest

for students to “get.”

1. The major difficulty is one of recognition. Is some piece of the molecule flying

around, departing from one place and reattaching somewhere else? If so, that’s

probably a sigmatropic shift reaction. Once you are sure it is a shift, identify—

mark—the shifting atom or group.

2. Where does it depart from? Where does it arrive? Draw an arrow formalism.

3. Now let’s work out a picture of the transition state. Break the bond attaching the

migrating group to the position from which it departs in a homolytic fashion.

Neither ions nor polar transition states are involved.Ask yourself what species is left

behind? What species is migrating?

4. Work out the molecular (or atomic) orbitals for both partners.

5. Remember that the migrating group was attached through a bonding interaction.

That fact allows you to sketch in the symmetry of the HOMO of the portion of the

molecule along which the atom or group is migrating.

6. Can the migrating group reattach reasonably (can it reach?) in a bonding fashion?

If so, the reaction is allowed. If it must reattach through an antibonding interaction,

the reaction is forbidden.

7. Count the number of electrons involved in the reaction.

20.9 Summary 1073

8. If there are 4n electrons involved, then the thermal hydrogen (or other) shift must

be antarafacial in order to occur and the photochemical process will occur in a

suprafacial fashion. If there are 4n  2 electrons, then the thermal process will be

suprafacial and the photochemical process will be antarafacial.

Now practice! Use the schemes above to work the following three problems.

PROBLEM 20.24 Is the following reaction allowed or disallowed? Give a detailed

analysis.

PROBLEM 20.25 Is the following thermal reaction allowed or disallowed? Give a

detailed analysis.

–

CCH

–

CCH

PROBLEM 20.26 Is the following thermal reaction allowed suprafacially or

antarafacially? Give a detailed analysis.

20.9 Summary

New Concepts

The central insight of Woodward–Hoffmann theory is that

one must keep track of the phase relationships of orbital

interactions as a concerted reaction proceeds. If bonding

overlap can be maintained throughout, the reaction is allowed;

if not, the reaction is forbidden by orbital symmetry. This

notion leads to a variety of mechanistic explanations for

reactions that can otherwise be baffling. Some of these

pericyclic reactions are discussed in the section on Reactions,

Mechanisms, and Tools.

The notion of a fluxional structure is introduced through

the (CH)

molecule bullvalene. In this molecule, a given

carbon atom does not have fixed nearest neighbors, but instead

is bonded, over time, to each of the other nine carbons in the

molecule. In bullvalene, the fluxionality is the result of rapid

degenerate Cope rearrangements.

Many stereochemical labeling experiments are described in

this chapter. A careful labeling experiment is able to probe

deeply into the details of a reaction mechanism. Examples

include W. R Roth’s determination of the suprafacial nature of

the [1,5] shift of hydrogen and Doering and Roth’s experiments

on the structure of the transition state for the [3,3] sigmatropic

shift known as the Cope rearrangement.

Key Terms

antarafacial motion (p. 1055)

bullvalene (p. 1068)

conrotation (p. 1037)

Cope rearrangement (p. 1059)

cycloaddition reaction (p. 1043)

degenerate reaction (p. 1031)

disrotation (p. 1037)

electrocyclic reaction (p. 1036)

fluxional structure (p. 1063)

pericyclic reaction (p. 1031)

sigmatropic shift (p. 1050)

suprafacial motion (p. 1055)

Woodward–Hoffmann theory (p. 1031)

1074 CHAPTER 20 Reactions Controlled by Orbital Symmetry

Reactions, Mechanisms, and Tools

20.10 Additional Problems

Certain polyenes and cyclic compounds can be interconverted

through a pericyclic process known as an electrocyclic reaction.

Examples include the 1,3-butadiene–cyclobutene and 1,3-

cyclohexadiene–1,3,5-hexatriene interconversions (Figs. 20.5

and 20.16).

Orbital symmetry considerations dictate that in 4n-electron

reactions the thermal process must use a conrotatory motion,

whereas the photochemical reaction must be disrotatory. Just

the opposite rules apply for reactions involving 4n  2 elec-

trons. The key to analyzing electrocyclic reactions is to look at

the way the p orbitals at the end of the open-chain π system

must move in order to generate a bonding interaction in the

developing σ bond.

Cycloaddition reactions are closely related to electrocyclic

reactions.The phases of the lobes in the HOMOs and LUMOs

must match so that bonding interactions are preserved in the

transition state for the reaction. Sometimes a straightforward

head-to-head motion is possible in which the two π systems

approach each other in parallel planes to produce two bonding

interactions. Such reactions are typically easy and are quite

common. An example is the Diels–Alder reaction (Fig. 20.21).

In other reactions, the simple approach of HOMO and

LUMO involves an antibonding overlap. In such reactions, a

rotation is required in order to bring the lobes of the same sign

together (Fig. 20.28). Although in principle this rotation main-

tains bonding interactions, in practice it requires substantial

amounts of energy, and such reactions are rare.

Sigmatropic shifts involve the migration of hydrogen or

another atom along a π system. Allowed migrations can be

either suprafacial (leave and reattach from the same side of the

π system) or antarafacial (leave from one side and reattach from

the other) depending on the number of electrons involved in

the migration. The important point is that in an allowed shift,

bonding overlap must be maintained at all times both to the

lobe from which the migrating group departs and to that to

which it reattaches. Steric considerations can also be important,

especially for hydrogen, which must migrate using a small 1s

orbital (Figs. 20.43 and 20.44).

Syntheses

The photochemical 2  2 dimerization of alkenes.

Common Errors

hν

For many students the big problem in this material is determin-

ing the kind of reaction involved. The way to start a problem in

this area is to spend some time and thought identifying what

kind of reaction is taking place. Cycloadditions are generally

easy to find, although even here confusion exists between these

reactions and electrocyclic processes. Sigmatropic shifts can be

even harder to uncover. Often it is not easy to identify exactly

what has happened in a sigmatropic reaction. When one atom

or a group of atoms has translocated from one part of the

molecule to another, there is often a rather substantial

structural change. The product sometimes doesn’t look much

like the starting material. The temptation is to use other

reagents to make the change, but in a sigmatropic shift every-

thing is “in house.”

PROBLEM 20.27 Analyze the photochemical and thermal

[1,7] shifts of hydrogen in 1,3,5-heptatriene. Be sure to look at

all possible stereoisomers of the starting material. What kind of

[1,7] shift will be allowed thermally? What kind photochemi-

cally? How will the starting stereochemistry of the triene affect

matters? Top views of the π molecular orbitals of heptatrienyl

are given.

Energy

CH CH

–

Top views of the π

molecular orbitals

of heptatrienyl

(+ means blue,

– means green)

1,3,5-Heptatriene

C CH CH

CH CH

20.10 Additional Problems 1075

PROBLEM 20.29

The thermally induced interconversion of

cyclooctatetraene (1) and bicyclo[4.2.0]octa-2,4,7-triene (2) can

be described with two different sets of arrows. Although these

two arrow formalisms may seem to give equivalent results, one

of them is, in fact, not a reasonable depiction of the reaction.

Explain.

PROBLEM 20.28 Vitamin D

(3) is produced in the skin as a

result of UV irradiation. It was once believed that 7-dehydro-

cholesterol (1) was converted directly into 3 upon photolysis. It

is now recognized that there is an intermediate, previtamin D

(2), involved in the reaction. This metabolic process formally

incorporates two pericyclic reactions, 12and 23.

Identify and analyze the two reactions.

s-cis-3

s-trans-3

rotation

(a)

(b)

PROBLEM 20.30 Analyze the thermal ring opening to allyl

ions of the two cyclopropyl ions shown below. What stereo-

chemistry do you expect in the products? Will the reactions

involve conrotation or disrotation? Explain. Do not be put off

by the charges! They only serve to allow you to count electrons

properly.

(a)

An allyl cation

(b)

An allyl anion

–

PROBLEM 20.31 Orbital symmetry permits one of the two fol-

lowing photochemical cycloaddition reactions to take place in a

concerted fashion. What would be the products, which reaction

is the concerted one, and why?

Allyl cation

hν hν

1076 CHAPTER 20 Reactions Controlled by Orbital Symmetry

HH H

PROBLEM 20.32 The following two cyclobutenes can be opened

to butadienes thermally. However, they react at very different

rates. Which is the fast one, which is the slow one, and why?

PROBLEM 20.33 These same two cyclobutenes (Problem

20.32) react photochemically to give two monocyclic (one ring)

compounds isomeric with starting material. Predict the prod-

ucts, and explain the stereospecificity of the reaction.

PROBLEM 20.34 Benzocyclobutene (1) reacts with maleic

anhydride when heated at 200 °C to give the single product

shown. Write a mechanism for this reaction.

200 ⬚C

PROBLEM 20.35 Given your answer to Problem 20.34, explain

the stereochemistry observed in the following reaction:

C(CN)

(NC)

PROBLEM 20.36 Write a mechanism for the following reac-

tion. Note that no similar reaction appears for cis-1,3,5-hexa-

triene. It may be useful to work backward from the product.

What molecules must lead to it?

PROBLEM 20.37 Now, here’s an interesting variation on the

reaction of Problem 20.36. Diels–Alder additions typically

take place as shown in Problem 20.36, with the ring-closed

partner (A in the answer to Problem 20.36) actually doing

the addition reaction. However, the molecule shown below is

an exception, as the Diels–Alder reaction takes place in the

normal way to give the product shown. Draw an arrow

formalism for the reaction and then explain why 1 reacts

differently from other cycloheptatrienes.

20.10 Additional Problems 1077

PROBLEM 20.38

Write an arrow formalism mechanism for

the following thermal reaction and explain the specific trans

stereochemistry. Careful here—note the acid catalyst for this

reaction.

PROBLEM 20.39 Write an arrow formalism mechanism

for the following reaction and explain the observed trans

stereochemistry:

PROBLEM 20.40 Explain the following differences in product

stereochemistry:

–

PROBLEM 20.41 Provide mechanisms for the following trans-

formations:

(b)

(a)

COOCH

OOC

PROBLEM 20.42 Provide mechanisms for the following trans-

formations. Part (a) is harder than it looks (Hint: There are two

intermediates in which the three-membered ring is gone) and

(b) is easier than it looks (Hint: What simple photochemical

sigmatropic shift do you know?).

hν

(b)

(a)

PROBLEM 20.43 In Problem 20.23 (b), we saw an example

of a [3,3] sigmatropic shift known as the Claisen rearrange-

ment. This reaction involves the thermally induced intramol-

ecular rearrangement of an allyl phenyl ether to an o-allylphenol.

(continued)

1078 CHAPTER 20 Reactions Controlled by Orbital Symmetry

(a) It might be argued that this rearrangement is not a

concerted process, but instead involves a pair of radical

intermediates. Write such a mechanism and design a

labeling experiment that would test this hypothesis.

(b) If both the ortho positions of the allyl phenyl ether are

blocked with methyl groups, the product of this rearrange-

ment is the p-allylphenol.This version of the Claisen

reaction is often called the para-Claisen rearrangement.

Explain why the rearrangement takes a different course in

this case. In addition, would the label you suggested in (a)

be useful in this case for distinguishing concerted from non-

concerted (radical) mechanisms?

PROBLEM 20.44 Propose an arrow formalism mechanism for

the following reaction. Be sure that your mechanism accommo-

dates the specific labeling results shown by the dot (

•



C).

Also, be sure that any sigmatropic shifts you propose do not

involve impossibly long distances.

COO

OOC

–

OOC

–

COO

Perhaps the role of the enzyme is to bind the predominant

pseudodiequatorial conformer 2. The enzyme–substrate com-

plex then undergoes a rate-determining conformational change

to convert the substrate into the pseudodiaxial form 1, which

rapidly undergoes rearrangement.

(a) Explain why 1 can rearrange to prephenate but 2 cannot.

(b) Suggest a reason why conformer 2 is preferred over con-

former 1. Hint: Focus on the OH. What can it do in 2 that

it cannot do in 1?

gram that illustrates the situation outlined above, that is, a

reaction in which the rate-determining step is the conver-

sion of 2 into 1. What would the Energy versus Reaction

progress diagram look like if the rate-determining step were

the conversion of 1 into prephenate?

PROBLEM 20.46 In 1907, Staudinger reported the reaction of

diphenylketene (1) and benzylideneaniline (2) to give β-lactam

3. Although this reaction is formally a 2  2 cycloaddition

reaction, there is ample experimental evidence to suggest that

the reaction is not concerted, but is instead a two-step process

involving a dipolar intermediate.

PROBLEM 20.45 We saw on page 1063 that chorismate

undergoes a [3,3] sigmatropic shift (Claisen rearrangement) to

prephenate catalyzed by the enzyme chorismate mutase. This

enzyme-catalyzed reaction occurs more than 1 million times

faster than the corresponding nonenzymatic reaction. How does

the enzyme effect rate enhancement? Both enzymatic and

nonenzymatic reactions proceed through a chairlike transition

state. However, the predominant conformer of chorismate in

solution, as determined by

H NMR spectroscopy, is the pseu-

dodiequatorial conformer 2, which cannot undergo the reaction.

CCH

CCO

C NPh

20 ⬚C

(a) Propose an arrow formalism mechanism for this cycloaddi-

tion reaction. Don’t forget to include the dipolar intermediate.