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In Unit 12, we saw the double bond as a place in alkenes where reaction can occur: electrophilic or free-radical addition. But in addition to providing a site for addition, the double bond exerts powerful effects on certain reactions taking place elsewhere in the molecule. This is where the double bond exercises its role not as a functional group, but rather as a substituent. Previous effects of substituents have included those of alkyl groups: polar effects, steric effects, and (unspecified until now) effects on the stability of free radicals and alkenes. We have also considered the inductive effect of halogens. Most of the substituent effects of the double bond stem form the structural feature known as conjugation: the location of the pi orbital in such a way that it can overlap other orbitals within the molecule. And to implement our discussion, we shall also make use  of the structural theory of resonance.    

Free-Radical Substitution vs. Addition

Let's consider the reaction of propylene with HCl.

We have seen previously that propylene undergoes electrophilic addition.

With HBr in the presence of peroxides, it undergoes free-radical addition. 

But propylene also contains a methyl group, and this modifies the reactions taking place at the double bond. Because of the methyl group, the electrophilic addition takes place faster than with ethylene itself, and gives exclusively isopropyl chloride. Also because of the methyl group, the free-radical addition occurs faster than with ethylene, and gives exclusively n-propyl chloride. Thus, the methyl group substituent affects both reactivity and orientation of attack. 

Let us consider an alternative point of view, with the methyl group not as a substituent, but rather as the site of the attack. The methyl group has an alkane-like structure -- so we might expect it to undergo alkane-like reactions. This includes free-radical substitution of a halogen. But the propylene molecule presents two sites for the attack: the double bond and the methyl group. It turns out that we can direct our attack to one of these sites by a proper choice of reaction conditions. 

1) If we wish to direct the attack of halogen to the alkyl portion of an alkene, then we choose conditions that are favorable for the free-radical reaction of alkanes: high temperatures and UV light in the gas phase.

2) If we wish to direct the attack of halogen to the double bond, then we choose conditions that are favorable for the occurrence of heterolytic reactions: low temperatures, absence of light in the liquid phase.

Orientation and Reactivity

The alkyl groups in alkenes, then undergo substitution by halogens in precisely the same manner as alkanes do. But attached to these alkyl groups there is substituent: the double bond. Just as the alkyl groups affect the reactivity of the double bond, so the double bond affects the reactivity of the alkyl groups. Halogenation of many alkenes has shown that:

1) H atoms attached to doubly bonded C atoms (vinylic H atoms) are very difficult to abstract. Thus they undergo very little substitution.

2)  H atoms attached to C atoms adjacent to doubly-bonded C atoms (allylic H atoms) are even easier to abstract than tertiary H atoms. Thus they are particularly reactive toward substitution. 

We can now expand the reaction sequence of the ease of abstraction of H atoms (in alkanes):

                                          allylic  >  3°  >  2°  >  1°  >  CH4  >  vinylic 

Substitution in alkanes proceeds by the same mechanism as substitution in alkanes.

Evidently, the vinyl radical is formed very slowly and the allyl radical is formed very rapidly. We can now expand the sequence for the ease of formation of free radicals (in alkanes).

                                          allyl  >  3°  >  2°  >  1°  >  CH3.  >  vinyl 

In accordance wit hour rule correlating the ease of formation of free radicals with their relative stabilities, we can now expand the sequence for the relative stability of free radicals as follows:

allyl  >  3°  >  2°  >  1°  >  CH3.  >  vinyl 

In some way, then the double bond affects the stability of certain free radicals. It exerts a similar effect  on the incipient radicals of the transition state, and thus affects the rate of their formation. The double bond therefore helps to determine both the orientation of free-radical substitution in an alkene, and the relative reactivities of different alkenes. Thus, for example, the cyclic alkene cyclohexene is brominated almost exclusively at the allylic position (as shown) and reacts much faster than the saturated hydrocarbon cyclohexane despite a probability factor of 12: 4 favoring attack on the saturated compound.

Allylic Rearrangement

Besides the fact that the allyl radical is extremely stable, the free-radical substitution at allylic positions can lead to allylic rearrangement. E.G. when 1-octene is treated with N-bromosuccinimide, there is obtained not only the expected 3-bromo-1-octene. But also (and in larger amounts) 1-bromo-2-octene (both Z and E). It is an allylic H atom on C3 that is abstracted,

but in much of the product , bromine appears on C1. Whenever the structure permits, such allylic rearrangement occurs, and according to a well-defined pattern (as shown). Thus the allylic radical reacts to give two different products:

1) The halogen has become attached to the C atom that lost the H atoms

2)  The halogen has become attached to the C atom at the other end of the 3C unit - the C=C-C allylic system. 

Examination of the structures involved shows us that such rearrangement involves no migration of atoms or groups. Only the double bond appears in a different position from the one it occupied in the reactant structure.

Symmetry of the Allyl Radical

The allyl radical is a symmetrical molecule. If the allyl radical actually possessed the classical structure that we have so far proposed for it:

It would be unsymmetrical about the central carbon atom. It would contain two different types of bonds: 1) a long, single, weaker bond, and  2) a short, stronger double bond. An ESR spectrum , however, reflects the structure of a free-radical by what it shows about the H atoms in the molecule. Among other things, how many different types of H atoms the free-radical contains.

In the classical structure, the two vinylic H atoms on the terminal C atom would be non-equivalent, since one is cis and the other is trans to -CH2. The two H atoms in the CH2 group would be equivalent. The vinylic H atom on the central C atom would be different still. Thus, we would expect 4 different types of H atoms.   

In fact, however, the spectrum measured reveals only 3 types of H atoms. Thus, each vinylic H atom at one end of the molecule has an exact counterpart at eh other end. The two ends of the molecule are equivalent. Both C-C bonds are identical. The allylic radical is perfectly symmetrical about the central C atom.

In order to explain this enigma, we turn now to the theory of resonance.

The Theory of Resonance

It may be helpful at first to list a few of the general principles of resonant structures in chemistry (not to be confused with the physical resonance of standing waveforms), and then to discuss these principles in terms of the structure of the allyl radical.

1)  Whenever a molecule can be represented by two or more structures that differ only in the arrangement of the electrons -- that is, by structures that have the same arrangement of atomic nuclei -- there is resonance. The molecule is a hybrid of all these structures, and cannot be represented satisfactorily by any one of them. Each of these structures is said to contribute to the hybrid.

2)  When these contributing structures are of about the same stability -- that is, they have about the same energy content -- then resonance is important. The contribution of each structural variation to the hybrid depends upon the relative stability of each individual structural variation. The most stable structures make the largest contributions, and vice versa.

3)  The resonance hybrid is more stable that any of the contributing structures. This increase in stability is the difference between the energy content of the hybrid and the proportionately weighted sum of all the individual structural variations. The difference is called the resonance energy. The more nearly equal in stability the contributing structures, the greater the resonance energy.

Allyl Radical as a Hybrid

The allyl radical is thus a resonance hybrid of the two structures I and II.

This means simply that the allyl radical does not correspond to either I or II, but rather to a structure intermediate between I and II. Furthermore, since I and II are equivalent in all ways, the resonance hybrid is equally related to I and II. That is to say, I and II both make equivalent contributions to the hybrid.

This does not in any way imply that the allyl radical consists of molecules half of which correspond to I and half to II. Nor does it mean than an individual molecule changes back and forth between I and II. Rather, all molecules are identical -- each with an intermediate structure between that of I and II.

The resonance theory further tells us that the allyl radical does not contain one C-C single bond and one C-C double bond (as in I or II). But rather it contains two identical bonds, each one intermediate between a single and double bond. This hybrid bond has been described as a 1.5 bond. It is said to possess one-half single-bond character and one-half double-bond character. The density of electrons holding the central C atom to each of the others is intermediate between that of a single bond and a double bond.

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We might represent this symmetrical hybrid molecules as in III, where the broken lines represent half bonds. The odd electron is not localized on one C atom or the other -- but rather, it is delocalized, or equally distributed over both terminal C atoms.

A major result of the resonance theory is that the allyl radical is more stable than either of the contributing structures. The difference in energy between the allyl radical and the contributing structures is referred to as the resonance energy (~10 kcal/mol). 

Thus, a given pair of electrons may serve to bind together more than two nuclei. It is this ability of electrons to participate in multiple bonds, this delocalization of electrons, that results in stronger bonds and increased molecular stability.      

Allylic rearrangement is a natural consequence of the hybrid character of an allylic radical. The terminal carbons of the 3-carbon allylic system are exactly equivalent in the allyl radical itself, and very similar in an unsymmetrically substituted allylic radical. When halogen reacts with such a radical, it can become attached to either of these terminal C atoms. Where the structure permits, this attachment to either end is shown by the formation of two different products as shown here.   

In the case of the unsubstituted radical itself, the same product is obtained whichever end receives the halogen, and so no rearrangement is seen. But there can be little doubt that here, too, both carbons are subject to attack.

Let us next consider the bond orbitals in the allyl radical. Since each carbon is bonded to three other atoms, it uses sp2 orbitals. Overlap of these orbitals with each other and with the s orbitals of five H atoms gives the molecular skeleton shown here, with all bond angles 120 degrees. In addition, each C atom has a p orbital which consists of two equal lobes, one lying above and one lying below the plane of the sigma bonds. The p orbital is occupied by a single electron.

Equivalent To:

The p orbital of one C atom can overlap the p orbital of an adjacent C atom, thus permitting the electrons to pair up and a bond to be formed. In this manner, we would arrive at either of the contributing structures, I or II, with the odd electron occupying the p orbital of the remaining C atom. But the overlap is not limited to a pair of p orbitals as it was in ethylene. The p orbital of the middle C atom overlaps equally well the p orbitals of both the C atoms to which it is bonded. The result is two continuous pi electron clouds, one lying above and one lying below the plane of the atoms.

*Note: Since no more than two electrons may occupy the same orbital (Pauli exclusion principle) these pi clouds are actually made up of two orbitals. One of these, containing two pi electrons, encompasses all three C atoms. The other, containing the third (odd) pi electron, is divided equally between the terminal C atoms.

We saw earlier that the methyl radical may not be quite flat (see Unit 1: Methane). I.E. Hybridization of carbon in the methyl radical may be intermediate between sp2 and sp3. For the allyl radical, however (and for many other free radicals), flatness is clearly required in order to permit the overlap of p orbitals that leads to stabilization of the radical.

Chemists use the term conjugated to describe molecules containing alternating single and double bonds. The special properties of these molecules were attributed to the interaction of the pi orbitals of two or more double bonds. This overlap is much like what we have just described for the "double bond" of an allyl radical with the p orbital containing the odd electron. The allyl radical is, then, a conjugated molecule.

The Allyl Cation

I. Resonance Hybrid Structure

Let us turn now to heterolytic reactions, and see how this is affected by the presence of a double bond in the substrate molecule. Since carbocations are key intermediates in much of heterolytic chemistry, let us begin by examining the structure of the allyl cation.

The structure of the allyl cation is depicted in precisely the same manner as that of the allyl radical. The only difference is that: instead of an odd electron (or dot) there is a positive sign to indicate an electron deficiency. On the basis of this resonance structure, there are several predictions we might make about the properties of the allyl cation.

1) Resonance gives rise to considerable stabilization of the molecule. 

2) The allyl cation is about as stable as a secondary carbocation. 

3) The allyl cation is symmetrical about the central carbon atom.

All of these predictions are borne out by experimental data.

II. Nucleophilic Substitution: SN1 

Let us next consider what we might expect of a reaction in which allylic cations are intermediates: nucleophilic substitution of the S_N1 kind. Consider, for example, the solvolysis of allyl chloride,

or the reaction of allyl alcohol with a hydrogen halide.

Let us assume for the moment that these reactions proceed by the S_N1 mechanism. According to this mechanism, the rate-determining step is heterolysis to give a carbocation.

And, as we have seen it is the nature of this carbocation that largely controls the course of the reaction.  In these cases, since the substrates are allyl substrates, the intermediate

cation will be the allyl cation. From what we have just learned about the allyl cation, what can we predict about these S_N1 reactions ?

In S_N1, it is the rate of formation of the carbocation that determines the overall rate of reaction. We have so far seen that rate of formation of carbocations generally parallels their relative stability. We have also concluded that the allyl cation is about as stable as a secondary carbocation. We therefore expect that allyl substrates will react about as fast  by S_N1 as secondary substrates.

This is, indeed, the case. In general, secondary substrates react much faster by S_N1 than primary substrates. In nucleophilic substitution, then, the allyl cation - like the secondary cation - is formed perhaps a million times as fast as its saturated analog, the n-propyl cation.

The presence of alkyl substituents at either end of the allylic system increases the reactivity still further. 

One more prediction: We expect that S_N1 reactions of allylic substrates can show allylic rearrangement. In the second step of S_N1, the combining of the carbocation with the nucleophile should take place at either terminal carbon of the allylic system. Thus, structure permitting, there will be two different products.

For results, consider the conversion of the isomeric allylic chlorides (IV and V) into the ethyl ethers (VI and VII). In a concentrated solution of sodium ethoxide in ethanol, each chloride reacts by second-order kinetics. Thus, IV gives exclusively VI, and V gives exclusively VII.

If, now, the same chlorides are heated in ethanol in the absence of added base, the course of the reaction changes dramatically. Thus, whichever allylic substrate one starts with, both ethers are found in the product. Under solvolytic conditions, the reaction shifts to the

S_N1 mechanism. And as we predicted, allylic rearrangement occurs.

III. Nucleophilic Substitution: SN2 

In nucleophilic substitution by S_N2, is has been found, allyl substrates are roughly as reactive as saturated primary substrates. The chief factor governing S_N2 reactivity is steric hindrance, and the allyl group is about as bulky as an unbranched primary substituent group.

In a sense, the allyl group has the best of both worlds: a capacity for charge dispersal comparable to that of a secondary group, but without the bulkiness that would hinder direct nucleophilic attack.

IV. Substitution in Vinylic Substrates 

Let us continue our examination of of the effect of the double bond on nucleophilic substitution by looking at vinylic substrates -- i.e. those substrates in which the leaving group is attached to one of the doubly bonded C atoms.

We have seen previously that toward nucleophilic substitution in general, vinylic halides are very much less reactive than their saturated counterparts. Fundamental to the understanding of these compounds is the fact that they contain an unusually strong C-H bond. For example, it takes approximately 16 - 18 kcal more energy to break the C-H bond in a vinyl halide than in the corresponding ethyl halide.

Now, whether nucleophilic substitution occurs by S_N1 or S_N2, the rate-determining step involves the breaking of the C-H bond. The C-H bond in vinyl halides is stronger, and thus the reaction is slower. Not surprisingly, the difficulty of generating vinyl cations by heterolysis has been a distinct challenge to organic chemists. 

Vinylic cations can readily be made through solvolysis of the S_N1 kind if two conditions are met. 1) The leaving group is an extremely good one. 2) The vinylic group contains electron-releasing substituents.   

Most commonly used for this purpose is the "super" leaving group, trifluoromethane-sulfonate, -OSO2CF3, commonly known as triflate. 

The powerfully electron-withdrawing fluorine atoms (through a dispersal of negative charge) help to stabilize the triflate anion, CF3SO2O-, and make the parent acid CF3SO2OH one of the strongest Lowry-Bronsted acids known (much stronger than H2SO4 or HClO4). The triflate anion is, correspondingly, an extremely weak base, and one of the best leaving groups in organic chemistry. The electron-releasing substituents in the vinylic moiety are very commonly aryl groups. But alkyl groups are sufficient to allow reaction by S_N1.

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Dienes: Structure & Properties

Dienes are alkenes that contain two C=C double bonds. What we shall discover applies equally well to compounds that contain more than two double bonds. Dienes are quite similar to alkenes. But in certain cases, the properties resulting from the presence of the double bond are modified by the presence of the second double bond. Dienes are divided into three classes according to the arrangement of the double bonds.

1) Double bonds that alternate with single bonds are conjugated.

2) Double bonds that are separated by more than one single bond are isolated. 

3)  Double bonds which share a carbon atom are cumulated, and the compounds are called allenes.

The chemical properties of a diene depend upon this arrangement of its double bonds. Isolated double bonds exert little effect on each other, and hence each reacts as thought it were the only double bond in the molecule. Except for the consumption of larger amounts of reagents, then, the chemical properties of non-conjugated dienes are identical with those of simple alkenes. (We will not be looking very closely at allenes). We shall focus our attention on conjugated dienes, which differ from simple alkenes in four ways:

1) They are more stable

2) They are the preferred products of elimination

3)  The undergo 1,4-addition (both electrophilic and free-radical)

4) Toward free-radical addition, they are more reactive.

Conjugated Dienes

We next focus our attention on the four key C atoms of any conjugated diene system. We ordinarily write the C1-C2 and the C3-C4 bonds as double, and the C2-C3 bond as single:

                                                      C1 = C2 - C3 = C4

This would correspond to an orbital picture of the molecule in which pi bonds are formed by overlap of the p orbitals of C1 and C2, and overlap of the p orbitals of C3 and C4 (see a below).

In the allyl radical and cation, we saw that resonance resulted form the overlap of the p orbital of a C atom with p orbitals on both sides. We might expect that, in the same way, there could be a certain amount of overlap between the p orbitals of C2 and C3 (see b above).

The resulting delocalization of pi electrons makes the molecule more stable. Each pair of electrons attracts - and is attracted by - not just two carbon nuclei, but four.

Using the language of conventional valence-bond structures, we say that a conjugated diene is a resonance hybrid of I and II. The dotted line in II represents a formal bond, and simply means that an electron on C1 and an electron on C4 have opposite spins. I.E. They are paired.

To the extent that II contributes to the structure, it gives a certain double-bond character to the C2-C3 and C3-C4 bonds. More importantly, it makes the molecule more stable than we would expect I (the most stable contributing structure) to be.

Formation of a bond releases energy and stabilizes a system. I.E. Multiple bonds increase molecular stability (all other factors being equal). Thus, we might expect II with 10 bonds to be less stable than I with 11 bonds. The resonance energy for such a hybrid of non-equivalent structures should be less than that of a hybrid made up of equivalent structures. The structure of a conjugated diene should resemble I more than II, since the more stable structure makes the larger contribution to he hybrid.

Consistent with partial double-bond character, the C2-C3 bond in 1,3-butadiene is O.O5 angstroms shorter than a pure single bond. The resonance energy of a conjugated diene is only 2-4 kcal/mol, compared with 10 kcal/mol for the allyl radical. In this manner, sp2-sp3 hybridization makes the C2-C3 bond short and strong.

*Note: For an alternative explanation of this increased stability, see an explanation of hyperconjugation in alkenes.

The most important diene, 1,3-butadiene (used to make rubber substitutes) is obtained industrially in large quantities by the cracking of hydrocarbons.

Electrophilic 1,4-Addition

When 1,4-pentadiene is treated with bromine under conditions which favor the formation of the dihalide, there is obtained the expected product, 4,5-dibromo-1-pentene. Addition of more bromine yields 1,2,4,5-tetrabromopentane.

This is typical of the behavior of dienes containing isolated double bonds. the double bonds react independently, as though they were in different molecules.

When 1,3-butadiene is treated with bromine under similar conditions, there is obtained not only the expected 3,4-dibromo-1-butene, but also 1,4-dibromo-2-butene. Treatment with HCl yields not only 3-chloro-1-butene, but also 1-chloro-2-butene. Hydrogenation yields not only 1-butene but also 2-butene.

Study of many conjugated dienes and many reagents show that such behavior is typical. In addition to conjugated dienes, a reagent may attach itself not only to a pair of adjacent C atoms (1,2,-addition), but also to the C atoms at the two ends of the conjugated system (1,4-addition). Very often the 1,4-addition product is the significant one.

To explain this, let us recall that electrophilic addition is a two-step process, and that the first step occurs in the way that yields the more stable carbocation. Applying this principle to the addition of HCl to 2,4-hexadiene:

These products show that hydrogen adds to C2 to yield carbocation I, rather than to C3 to yield carbocation II.

Since both I and II are secondary cations, why the preferential formation of one to the other ? The reason is that I is an allylic cation, since the electron deficient C atom is attached to a doubly bonded carbon. It is, then, a resonance hybrid.

As a cation that is both secondary and allylic, I is more stable than II, and is the preferred cationic intermediate. The products obtained form addition to conjugated dienes are always consistent with the formation of the most stable intermediate carbocation: an allylic cation. This requires the first step to be addition to one of the ends of the conjugated system.

In the second step cation IV combines with a chloride ion to form the product. the chloride ion can attach itself to either end of the allylic system and thus yield the 1,2 or 1,4 product.

Like allylic arrangement, the occurrence of 1,4-addition is a natural consequence of the hybrid nature of the intermediate allylic cation.

Thus, the hybrid nature of the allylic cation governs both steps of electrophilic addition to conjugated dienes.

1) Via stabilization of the cation.

2) By permitting attachment to either of two C atoms.

It is worth noting that the relative proportions of the 1,2 and 1,4 products are markedly affected by the reaction temperature.

The fact that either compound is converted into the same mixture by heating indicates that this mixture is the result of a thermodynamic equilibrium between the two isomeric compounds. The fact that the 1,4 compound predominates in the equilibrium mixture indicates that it is the more thermodynamically stable of the two isomers.

The fact that more 1,2 than 1,4 product is obtained at -80 degrees C indicates that the 1,2 product is formed faster than the 1,4 product. Since each compound remains unchanged at -80 degrees C, the proportions in which they are isolated show the proportions in which they were initially formed. As the reaction temperature is raised, the proportions in which the products are initially formed may remain the same. But there is faster conversion of the initially formed products into the equilibrium mixture.

The proportions of products actually isolated from the low-temperature addition are determined by the rates of addition. Whereas for the high-temperature addition, the proportions are determined by the equilibrium between the two isomers.

Free-Radical Polymerization

Like substituted ethylenes, conjugated dienes also undergo free-radical polymerization.

E.G. Form 1,3-butadiene, there is obtained a polymer whose structure indicates that 1,4-addition occurs predominantly.

Such a polymer differs from the polymers of simple alkenes in one very important way: each unit still contains one double bond.

Natural rubber has a structure which strongly resembles these synthetic polydienes. We could consider it to be a polymer of the conjugated diene 2-methyl-1,3-butadiene: isoprene. 

The double bonds in the rubber molecule are highly important, since - by providing reactive allylic H atoms - they permit vulcanization, the formation of sulfur bridges between different chains. These cross-links make the rubber harder and stronger, and eliminate the tackiness of the untreated rubber.

Polymerization of dienes to form substitutes for rubber was the forerunner of the modern-day plastics industry. Polychloroprene (aka Neoprene or Duprene) was the first commercially successful rubber substitute in the United States.

The properties of rubber substitutes - like those of other polymers - are partially determined by the nature of the substituent groups. In addition to Neoprene, polymers of Isoprene can be made artificially. They contain the same unsaturated chain and the same substituent (the CH3 group) as natural rubber.

But polyisoprene made by the free-radical process described here was a radical change. It differed in stereochemistry. Thus, natural rubber has the cis configuration at nearly every double bond. The artificial material was a mixture of cis and trans. Not until 1955 could a true synthetic rubber be made. What was needed was an entirely new kind of catalyst and an entirely new mechanism of polymerization. This new technology in chemical physics made it possible to carry out a stereoselective polymerization of Isoprene to a compound virtually identical to natural rubber: cis-1,4-polyisoprene.

The Isoprene Rule

The isoprene unit is one of nature's favorite building blocks. It occurs not only in rubber, but also in a wide variety of compounds isolated from plant and animal sources. E.G. Nearly all the terpenes (found in the essential oils of many plants) have carbon skeletons made up of isoprene units joined in a regular, head-to-tail fashion.   

Recognition of this fact - the so-called Isoprene rule - has been a great help in working out the structures of terpenes, as well as such distantly related compounds as cholesterol.