The allyl radical

The allyl radical has an unpaired n electron in a doublet ground state. For the allyl radical (linear chain with N = 3), expansion of the Hiickel 

The electron distribution of the n electrons in the allyl radical ground state is  

According to these equations, the Hiickel distribution of the three n electrons is uniform (one electron onto each carbon atom, alternant hydrocarbon33), while the unpaired electron of a spin is 1/2 on atom 1 and 1/2 on atom 3, with zero probability of being found at atom 2. This spin distribution is however incorrect, since ESR experiments and theoretical VB calculations show that, if the unpaired electron has a spin, there is a nonvanishing probability of finding some (3 spin at the central atom. 

The difference 0.828 is an attractive stabilizing energy called the delocalization energy of the double bond in the allyl radical. 

Quite interestingly the behavior of the allyl radical and its cyclized counterpart the cyclopropyl radical is completely different from that of the homoallylic-methylcyclopropyl system. It does not seem that cyclized products resulting from the allyl radical have ever been observed. The opening of the cyclopropyl radical is, however, also a very slow process. Nevertheless, opening of substituted cyclopropyl radicals is observed when the substituents highly stabilize the allylic radical. In the same way photolytic cleavage of cyclopropanes is facilitated when each of the radical centers formed is stabilized.  

10 Four simple three-electron systems Table 10.1. C2v characters. 

The effect of the C2 operation is easily determined since C2 = OxzOyz- There is, of course, a completely parallel set of relations for the 2 py set of orbitals. Writing out the corresponding relations for the 2 d orbitals is left to the interested reader. 

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Stabilizing resonances also occur in other systems. Some well-known ones are the allyl radical and square cyclobutadiene. It has been shown that in these cases, the ground-state wave function is constructed from the out-of-phase combination of the two components [24,30]. In Section HI, it is shown that this is also a necessary result of Pauli s principle and the permutational symmetry of the polyelectronic wave function When the number of electron pairs exchanged in a two-state system is even, the ground state is the out-of-phase combination [28]. Three electrons may be considered as two electron pairs, one of which is half-populated. When both electron pahs are fully populated, an antiaromatic system arises ("Section HI). 

We begin by considering a three-atom system, the allyl radical. A two anchor loop applies in this case as illush ated in Figure 12 The phase change takes place at the allyl anchor, and the phase-inverting coordinate is the asymmetric stretch C3 mode of the allyl radical. Quantum chemical calculations confiiin this qualitative view [24,56]. In this particular case only one photochemical product is expected. 

The allyl radical plays an important role in many photochemical transformations, as further discussed in Section IV. 

Both resonance forms of the allylic radical must be equivalent... 

Alkenes react with N bromosuccimmide (NBS) to give allylic bromides NBS serves as a source of Br2 and substitution occurs by a free radical mechanism The reaction is used for synthetic purposes only when the two resonance forms of the allylic radical are equivalent Otherwise a mixture of isomeric allylic bromides is produced... 

Resonance theory can also account for the stability of the allyl radical. For example, to form an ethylene radical from ethylene requites a bond dissociation energy of 410 kj/mol (98 kcal/mol), whereas the bond dissociation energy to form an allyl radical from propylene requites 368 kj/mol (88 kcal/mol). This difference results entirely from resonance stabilization. The electron spin resonance spectmm of the allyl radical shows three, not four, types of hydrogen signals. The infrared spectmm shows one type, not two, of carbon—carbon bonds. These data imply the existence, at least on the time scale probed, of a symmetric molecule. The two equivalent resonance stmctures for the allyl radical are as follows ... 

The presence of free radicals can invert this rule, to form anti-Markovnikov products. Free-radical addition in this fashion produces a radical on the central carbon, C-2, which is more stable than the allyl radical. This carbon can then experience further addition. For example, acid-catalyzed addition of... 

Reaction Mechanism. High temperature vapor-phase chlorination of propylene [115-07-17 is a free-radical mechanism in which substitution of an allyhc hydrogen is favored over addition of chlorine to the double bond. Abstraction of allyhc hydrogen is especially favored since the allyl radical intermediate is stabilized by resonance between two symmetrical stmctures, both of which lead to allyl chloride. 

The allyl radical would be expected to be planar in order to maximize n delocalization. Molecular structure parameters have been obtained from EPR, IR, and electron diffraction measurements and confirm that the radical is planar. ... 

Ketones in which the double bond is located in the p,y position are likely candidates for a-cleavage because of the stability of the allyl radical that is formed. This is an important process on direct irradiation. Products then arise by recombination of the radicals or by recombination after decarbonylation. 

The second set of illustrations show the spin density plotted on the electron density isosurface the spin density provides the shading for the isodensity surface dark areas indicate positive (excess a) spin density and light areas indicate negative (excess P) spin density. For example, in the allyl radical, the spin density is concentrated around the two terminal carbons (and away from the central carbon). In the Be form, it is concentrated around the substituent, and in acetyl radical, it is centered around the C2 carbon atom. 

Another aspect of wave function instability concerns symmetry breaking, i.e. the wave function has a lower symmetry than the nuclear framework. It occurs for example for the allyl radical with an ROHF type wave function. The nuclear geometry has C21, symmetry, but the Cay symmetric wave function corresponds to a (first-order) saddle point. The lowest energy ROHF solution has only Cj symmetry, and corresponds to a localized double bond and a localized electron (radical). Relaxing the double occupancy constraint, and allowing the wave function to become UHF, re-establish the correct Cay symmetry. Such symmetry breaking phenomena usually indicate that the type of wave function used is not flexible enough for even a qualitatively correct description. 

Active Figure 10.3 An orbital view of the allyl radical. The p orbital on the central carbon can overlap equally well with a p orbital on either neighboring carbon, giving rise to two equivalent resonance structures. Sign in afwww.thomsonedu.com to see a simulation based on this figure and to take a short quiz. 

In molecular orbital terms, the stability of the allyl radical is due to the fact that the unpaired electron is delocalized, or spread out, over an extended 7T orbital network rather than localized at only one site, as shown by the computer-generated MO in Fig 10.3. This delocalization is particularly apparent in the so-called spin density surface in Figure 10.4, which shows the calculated location, of the unpaired electron. The two terminal carbons share the unpaired electron equally. 

In addition to its effect on stability, delocalization of the unpaired electron in the allyl radical has other chemical consequences. Because the unpaired electron is delocalized over both ends of the nr orbital system, reaction with Br2 can occur at either end. As a result, allylic bromination of an unsymmetrical alkene often leads to a mixture of products. For example, bromination of 1-octene gives a mixture of 3-bromo-l-octene and l-bromo-2-octene. The two products are not formed in equal amounts, however, because the intermediate allylic radical is... 

Higuchi, J.,/. Chem. Phys. 26, 151, (i) Comparative calculations of the allyl radical. MO-LCAO with Cl. 

The allyl radical is better stabilized by resonance with the adjacent double bond than the cyanomethylene radical and is, therefore, less reactive. 

One contributing factor, which seems to have been largely ignored, is that the ring closed radical (in many cases a primary alkyl radical) is likely to be much more reactive towards double bonds than the allyl radical propagating species. This species will also have a different propensity for degradative chain transfer (a particular problem with allylamines and related monomers - see 6.2.6.4) and other processes which complicate polymerizations of the monoencs. 

However, a very unexpected situation is found24 for the phenyl allyl sulphone (53), for which a one-electron cleavage occurs in aprotic non-aqueous solvents. The allyl radical is apparently not electroactive at the cleavage potential, and forms the dimer. Therefore, in this one-electron bond scission no strong base is formed and the isomerization into the vinylic isomer is not observed (Figure 9). Similarly, the cleavage of phenyl propargyl... 

This is generally attributed to resonance stabilization of the allylic radical ... 

The reaction is usually quite specific at the allylic position and good yields are obtained. However, when the allylic radical intermediate is unsymmetrical, allylic rearrangements can take place, so that mixtures of both possible products are obtained, for example. 

Later, successful determination of the molecular structure of the free allyl radical was achieved by high-temperature electron diffraction, augmented by mass spectrometry studies (Vaida et al., 1986). The structural parameters obtained for the allyl radical were rcc 142.8 pm, rcH 106.9 pm, accc 124.6°, ccH 120.9°. This was the first electron diffraction study of an unstable organic molecule. 

The allyl radical [115] trapped in an argon matrix can be photolytically (A = 410 nm) converted into the cyclopropyl radical [116] (Holtzhauer er a/., 1990). Dicyclopropane and cyclopropane were formed when the photolysed matrix was warmed from 18 to 35 K. The intermediate [116] was shown to be a cr-type (Cs symmetry) and not a rr-type symmetry) radical. Normal coordinate analysis of the radical [116] has been carried out and the IR band at 3118 cm has been assigned to the stretching vibration of the C—H bond at the radical centre. 

The increase of the exocyclic C—C bond stretching frequency from 1208 cm in toluene to 1264 cm in the benzyl radical and the simultaneous decrease of the C—C ring bond stretching frequencies (from 1494 and 1460cm to 1469 and 1446cm , respectively) result from electron density delocalization in the benzyl system. Furthermore, the force constant value for the C—C bond in the C6H5CH2 radical (5.5 X 10 N m ) is between the values for the ordinary C—C bond (4.5 x 10 N m ) and the double C=C bond (9.0 X 10 N m ) and is close to the corresponding force constant in the allyl radical (5.8 x 10 N m ). 

As a result, the radical is stabilized to the extent of about 20 kcal. Two structures of nearly equal energies can be written for the allyl radical resulting from the addition of butadiene ... 

The observation that in the case of PCSO there is no formation of propanol while allyl alcohol is formed from ACSO agrees with the resonance stabilization of the allyl radical and hence weaker bond for S-allyl than for S-propyl. The yield of allyl alcohol from irradiation of ACSO is considerably greater than that from S-allyl-L-cysteine, probably due to energy delocalization by the four p electrons of the S atom. 

The choice of diallylphtalate as the cross-linker is somewhat surprising, because allylic compounds are not very reactive in radical polymerizations due to the stability of the allyl radicals. 

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