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Dienes are compounds with two carbon–carbon double bonds. Their nomenclature was dis-cussed along with the nomenclature of other alkenes in Sec. 4.2A. Dienes are classifiedaccording to the relationship of their double bonds. In conjugated dienes, two double bondsare separated by one single bond. These double bonds are called conjugated double bonds.

Cumulenes are compounds in which one carbon participates in two carbon–carbon doublebonds; these double bonds are called cumulated double bonds. Propadiene (common name al-lene) is the simplest cumulene. The term allene is also sometimes used as a family name forcompounds containing only two cumulated double bonds.

Conjugated dienes and allenes have unique structures and chemical properties that are thebasis for much of the discussion in this chapter.

Dienes in which the double bonds are separated by two or more single bonds have struc-tures and chemical properties more or less like those of simple alkenes and do not require spe-cial discussion. These dienes will be called “ordinary” dienes.

H2C CA CH2A

propadiene(allene)

one carbon involved in two double bonds

H2C CHLA CH CH2Aconjugated double bonds

1,3-butadiene(a conjugated diene)

676

Dienes, Resonance,and Aromaticity

15

15

15_BRCLoudon_pgs5-0.qxd 12/9/08 12:22 PM Page 676

15.1 STRUCTURE AND STABILITY OF DIENES 677

In this chapter, you’ll see that the interaction of two functional groups within the same mol-ecule—in this case two carbon–carbon double bonds—can result in special reactivity. In partic-ular, you’ll learn how conjugated double bonds differ in their reactivity from ordinary doublebonds. This discussion will lead to a consideration of benzene, a cyclic hydrocarbon in whichthe effects of conjugation are particularly dramatic. The chemistry of benzene and the effects ofconjugation on chemical properties will continue as central themes through Chapter 18.

15.1 STRUCTURE AND STABILITY OF DIENES

A. Stability of Conjugated Dienes. Molecular Orbitals

The heats of formation listed in Table 15.1 provide information about the relative stabilities ofdienes. The effect of conjugation on the stability of dienes can be deduced from a comparisonof the heats of formation for (E)-1,3-hexadiene, a conjugated diene, and (E)-1,4-hexadiene, anunconjugated isomer. Notice from the heats of formation that the conjugated diene is 19.7kJ mol_1 (4.7 kcal mol_1) more stable than its unconjugated isomer. Because the double bondsin these two compounds have the same number of branches and the same stereochemistry, thisstabilization of nearly 20 kJ mol_1 (5 kcal mol_1) is due to conjugation.

One possible reason for this additional stability could be the differences in the s bonds be-tween isomeric conjugated and unconjugated dienes. For example, comparing the isomers

H2CACHCH2CH2CH2CH CH2A

1,6-heptadiene(an ordinary diene)

Heats of Formation of Dienes and Alkynes

DH°f (25 °C, gas phase)Compound Structure kJ mol_1 kcal mol_1(E )-1,3-hexadiene 54.4 13.0

(E )-1,4-hexadiene 74.1 17.7

1-pentyne HC'CCH2CH2CH3 144 34.5

2-pentyne CH3C'CCH2CH3 129 30.8

(E)-1,3-pentadiene 75.8 18.1

1,4-pentadiene H2CACHCH2CHACH2 106 25.4

1,2-pentadiene H2CACACHCH2CH3 141 33.6

2,3-pentadiene CH3CHACACHCH3 133 31.8

H

H CH3

$$ $$CCAH2C CHA

H

H CH3

$$ $$CCAH2C CHCH2A

H

H CH2CH3

$$ $$CCAH2C CHA

TABLE 15.1


678 CHAPTER 15 • DIENES, RESONANCE, AND AROMATICITY

1,4-hexadiene and 1,3-hexadiene, we find that two sp2–sp3 s bonds in the unconjugated dieneare traded for one sp2–sp2 and one sp3–sp3 s bond in the conjugated diene.

We learned in Sec. 14.2 that s bonds with more s character are stronger than those with less scharacter. Two sp2–sp3 s bonds in the unconjugated diene, then, are “traded” for a strongerbond (the sp2–sp2 bond) and a weaker bond (the sp3–sp3 bond). These bond-strength effects al-most cancel; one estimate is that these effects account at most for 5–6 kJ mol_1 (1.2–1.4kcal mol_1) of the enhanced stability of the conjugated diene.

The second and major reason for the greater stability of conjugated dienes is the overlap of 2porbitals across the carbon–carbon bond connecting the two alkene units. That is, not only does pbonding occur within each of the alkene units, but between them as well. Fig. 15.1a shows thealignment of carbon 2p orbitals in 1,3-butadiene, the simplest conjugated diene. Notice that the2p orbitals on the central carbons are in the parallel alignment necessary for overlap.

As we learned when we considered p bonding in ethylene (Sec. 4.1B), the overlap of 2porbitals results in the formation of p molecular orbitals. The overlap of j 2p orbitals resultsin the formation of j molecular orbitals. In the case of a conjugated diene, j = 4. Therefore,four molecular orbitals (MOs) are formed. For a conjugated diene, half of the MOs are bond-ing—they have a lower energy than an isolated 2p atomic orbital. The other half are anti-bonding—they have a higher energy than an isolated 2p orbital. These four MOs for 1,3-bu-tadiene, the simplest conjugated diene, are shown in Fig. 15.1b. Each MO of successivelyhigher energy has one additional node, and the nodes are symmetrically arranged within thep system. The MO of lowest energy, p1, has no node, and the second bonding MO, p2, hasone node between the two interior carbons. The antibonding MOs, p 3* and p 4*, have two andthree nodes, respectively. (The asterisk indicates their antibonding character.)

1,3-Butadiene has four 2p electrons; these electrons are distributed into the four MOs. Be-cause each MO can accommodate two electrons, two electrons are placed into p1 and two intop2. These two bonding MOs, then, are the ones we want to examine to understand the bondingand stability of conjugated dienes. Consider first the energies of these bonding MOs. These areshown to scale relative to the energies of the ethylene MOs (Fig. 4.6, p. 126). The energy unitconventionally used with pMOs is called beta (b), which, for conjugated alkenes, has a valueof roughly –50 kJ mol_1 (–12 kcal mol_1). By convention, b is a negative number. The p1 MOof butadiene has a relative energy of 1.62b, and p2 has a relative energy of 0.62b. Each p elec-tron in butadiene contributes to the molecule the energy of its MO. Therefore, the two electronsin p1 each contribute 1.62b or a total of 3.24b, and the two electrons in p2 contribute 2 X(0.62b) = 1.24b. The total p electron energy for 1,3-butadiene, then, is 4.48b.

To calculate the bonding advantage of a conjugated diene, then, we compare it to thep-electron energy of two isolated ethylene molecules. As Fig. 15.1 shows, the bonding MO ofethylene lies at 1.00b; the two bonding p electrons of ethylene contribute a p-electron energyof 2.00b, and the p electrons of two isolated ethylenes contribute 4.00b. It follows that the en-ergetic advantage of conjugation—orbital overlap—in 1,3-butadiene is 4.48b – 4.0b= 0.48b.This energetic advantage must result from p1, which is the MO with lower energy than thebonding MO of ethylene.

Half of the total p-electron density in 1,3-butadiene is contributed by the two electrons in p1and half by the two electrons in p2. Consider now the nodal structure of these two molecular

H2C CH CH CH CH3CH2

1,4-hexadiene(unconjugated)

H2C CH CH CH CH3CH2

1,3-hexadiene(conjugated)

sp2–sp3 sp2–sp3 sp2–sp3 sp2–sp2 sp2–sp3 sp3–sp3



orbitals. The p2 MO has a node that divides the molecule into two isolated “ethylene halves;”thus, the electrons in this MO contribute some isolated double-bond character to the p-electronstructure of 1,3-butadiene. However, the p1 MO has no node; consequently, the electron densityin this MO is spread across the entire molecule. The electrons in p1 for this reason are said to bedelocalized. In particular, this MO contributes to bonding between the two central carbons—the

(b)

(a)

ENER

GY

2p atomic orbitals p2

p3

p1

p4*

*

–1.62b

+1.62b

–0.62b

energy of theethylene bonding MO

(+1.00b)

energy of theethylene antibonding MO

(–1.00b)

+0.62b

0b

p molecular orbitals

Figure 15.1 An orbital interaction diagram showing p molecular orbital (MO) formation in 1,3-butadiene. (a)Arrangement of 2p orbitals in 1,3-butadiene, the simplest conjugated diene.Notice that the axes of the 2p orbitalsare properly aligned for overlap. (b) Interaction of the four 2p orbitals (dashed black lines) gives four pMOs. Nodalplanes are shown in gray. Notice that nodes occur between peaks and troughs in the MOs, indicated by blue andgreen, respectively. The four 2p electrons both go into p1 and p2, the bonding MOs. The violet arrows and num-bers show the relative energies of the MOs in b units. (Remember that b is a negative number.) The relative ener-gies of the ethylene MOs are shown in red.



carbons connected by the “single bond.” The delocalization of p electrons across the centralsingle bond is also evident from the EPM of 1,3-butadiene.

This analysis shows that electron delocalization, which is not adequately conveyed byLewis structures, is responsible for the additional stability associated with conjugation. To putit another way, conjugation results in additional bonding that makes a molecule more stable.

The energetic advantage of conjugation is called the delocalization energy. This name col-orfully describes its origin—the delocalization of electrons in p1. Because b is negative, delo-calization energy is energy the molecule “doesn’t have.” The delocalization energy of 1,3-bu-tadiene is 0.48b, which, as we have seen, is the difference between the p-electron energies of1,3-butadiene and two isolated ethylenes.

B. Structure of Conjugated Dienes

The length of the carbon–carbon single bond in 1,3-butadiene reflects the hybridization of theorbitals from which it is constructed. At 1.46 Å, this sp2–sp2 single bond is considerablyshorter than both the sp2–sp3 carbon–carbon single bond in propene (1.50 Å) and the sp3–sp3

carbon–carbon bond in ethane (1.54 Å).

Recall from Secs. 4.1A and 4.2 that, as the fraction of s character in the component orbitals in-creases, the length of the bond decreases.

Conjugated dienes such as 1,3-butadiene undergo rapid internal rotation about the centralsingle bond of the diene unit. 1,3-Butadiene has two stable conformations. The most stableconformation is the s-trans conformation. (The s-prefix emphasizes that this refers to rota-tion about a single bond.) This conformation is sometimes called the anti conformation. Thesecond conformation is the gauche or skew conformation. These conformations and theirrelative standard free energies are shown in Fig. 15.2a; Newman projections are shown in Fig.15.2b. (The s-trans conformation is shown in Fig. 15.1 as well.) In the s-trans conformation,the 2p orbitals of all carbons are coplanar and can overlap. In the gauche conformation, the 2porbitals of one double bond are twisted 38° relative to those of the other, at the cost of some

H2C CH CH CH2AA AALL1.34 Å 1.34 Å1.46 Å

15.1 The conjugated triene (E)-1,3,5-hexatriene has six pmolecular orbitals with relative energies61.80b, 61.25b, and 60.44b. (a) Sketch these MOs. Indicate which are bonding and whichare antibonding. (b) Tell how many nodes each has. (c) Show the position of the nodes in p1,p2, and p*6.

15.2 Calculate the delocalization energy for (E)-1,3,5-hexatriene.

PROBLEMS

EPM of 1,3-butadiene

p-electron densityacross the C —C single bond



orbital overlap. The partial loss of overlap accounts for the higher energy of the gauche con-formation. The energy barrier between the two conformations, which is greatest at 102°,largely reflects the complete loss of overlap at this angle. The third conformation shown inFig. 15.2a, the s-cis conformation, is unstable. In this conformation, the 2p orbitals are copla-nar, but van der Waals repulsions between two of the hydrogens (shown in Fig. 15.2a) desta-bilize this conformation; in the gauche conformation, the offending hydrogens are furtherapart. Despite the instability of the s-cis conformation, it is important in some reactions ofconjugated dienes (Sec. 15.3).

15.3 Draw the s-cis and s-trans conformations of (2E,4E)-2,4-hexadiene and (2E,4Z)-2,4-hexadi-ene. Which diene contains the greater proportion of s-cis conformation? Why?

PROBLEM

HHCH CHH2C CH2

s-trans, or anti,conformation

gauche, or skew,conformation

H

H

CH

CH

H2C

H2 C

38°

24 kJ mol–1

(5.8 kcal mol–1)

11 kJ mol–1

(2.7 kcal mol–1)

15 kJ mol–1

(3.6 kcal mol–1)

(a)

(b)

0° 142°102° 180°angle of rotation

s-trans conformation gauche conformation

STA

ND

AR

D F

REE

EN

ERG

Y

s-cisconformation

van der Waalsrepulsions

anti gauche s-cis

Figure 15.2 (a) The conformations of 1,3-butadiene and their relative standard free energies. Internal rotationoccurs about the central carbon–carbon single bond (green arrow; rotation angles are shown in green along thehorizontal axis). (b) Newman projections of the two stable conformations obtained by sighting along the centralcarbon–carbon single bond, as shown by the eyeball in (a).



C. Structure and Stability of Cumulated Dienes

The structure of allene is shown in Fig. 15.3. Because the central carbon of allene is bound totwo groups, the carbon skeleton of this molecule is linear (Sec. 1.3B). A carbon atom with180° bond angles is sp-hybridized (Sec. 14.2). Therefore, the central carbon of allene, like thecarbons in an alkyne triple bond, is sp-hybridized. The two remaining carbons of the cumu-lated diene are sp2-hybridized and have trigonal planar geometry.

The two p bonds in allenes are mutually perpendicular, as required by the sp hybridizationof the central carbon atom (Fig. 15.4). Consequently, the HLCLH plane at one end of theallene molecule is perpendicular to the HLCLH plane at the other end, as shown by theNewman projection in Fig. 15.3. Note carefully the difference in the bonding arrangements inallene and the conjugated diene 1,3-butadiene. In the conjugated diene, the p-electron systemsof the two double bonds are coplanar and can overlap; all carbon atoms are sp2-hybridized. Incontrast, allene contains two mutually perpendicular p systems, each spanning two carbons;the central carbon is part of both. Because these two p systems are perpendicular, they do notoverlap. The perpendicular p orbitals of allene are reflected in the EPM of allene, whichshows areas of p-electron density above and below each double bond.

Because of their geometries, some allenes are chiral even though they do not contain anasymmetric carbon atom. The following molecule, 2,3-pentadiene, is an example of a chiralallene.

(Using models if necessary, verify the chirality of 2,3-pentadiene by showing that these twostructures are not congruent.) The two sp2-hybridized carbons are stereocenters. Thus, theenantiomers of 2,3-pentadiene differ by an internal rotation about either double bond. Becauseinternal rotation about a double bond does not occur under normal conditions, enantiomericallenes can be isolated. This is another example of a chiral molecule that has no asymmetricatoms; see Sec. 6.9.

The sp hybridization of allenes is reflected in their CAC stretching absorptions in the in-frared spectrum. This absorption occurs near 1950 cm_1, not far from the C'C stretching ab-sorption of alkynes.

mirror

AC$H3C AC CH

CH3

H

H

CH3)AC$ ACC

H

H3C )

enantiomers

EPM of allene

regions of p-electron density lieon perpendicular axes



The data in Table 15.1 (p. 677) show that allenes have greater heats of formation than othertypes of isomeric dienes. For example, 1,2-pentadiene is considerably less stable than 1,3-pen-tadiene or 1,4-pentadiene. Thus, the cumulated arrangement is the least stable arrangement oftwo double bonds. A comparison of the heats of formation of 2-pentyne and 2,3-pentadieneshows that allenes are somewhat less stable than isomeric alkynes as well. In fact, a commonreaction of allenes is isomerization to alkynes.

Although a few naturally occurring allenes are known, allenes are relatively rare in nature.

PROBLEMS15.4 Explain why there is a larger difference between the heats of formation of (E)-1,3-pentadiene

and 1,4-pentadiene (29.3 kJ mol_1 or 7.1 kcal mol_1) than between (E)-1,3-hexadiene and(E)-1,4-hexadiene (19.7 kJ mol_1 or 4.7 kcal mol_1).

15.5 (a) Draw line-and-wedge structures for the two enantiomers of the following allene.

(b) One enantiomer of this compound has a specific rotation of -30.7°. What is the specificrotation of the other?

H3C

CH2CH2CH2CH3

CO2H

CH C CL A A $)

H

H

C C1.31 Å

1.07

Å

117°

90°LLL

LLLAAA AAA

(a) (b)

HHH

HC

H

H

Figure 15.3 The structure of allene, the simplest cumulated diene. (a) Lewis structure showing the bond anglesand bond lengths. (b) A Newman projection along the carbon–carbon double bonds as seen by the eyeball. TheCH2 groups at opposite ends of the molecule lie in perpendicular planes.

sp2carbon

perpendicular2p orbitals

sp carbonsp2carbon

(a) (b)

perpendicularp orbitals

Figure 15.4 The p-electron structure of allene. The blue and green orbital colors represent wave peaks andwave troughs. (a) The component 2p orbitals of the double bonds. The central carbon is sp-hybridized and thushas two mutually perpendicular 2p orbitals. (b) The pmolecular orbitals that result from overlap of the 2p orbitalsare mutually perpendicular and do not overlap.


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