Allylic radical, molecular orbital resonance

Allylic radicals are stable for the same reason that allylic carbocations are stable (Section 8.13). Like an allylic carbocation, an allylic radical has two resonance forms. One form has the unpaired electron on the left and the double bond on the right, and one form has the unpaired electron on the right and the double bond on the left (Figure 12.1). Neither structure is correct by itself the true structure of the allyl radical is a resonance hybrid of the two. In molecular orbital terms, the unpaired electron is delocalized, or spread out, over an extended tt orbital network rather than localized at only one site. Thus, the two terminal carbons share the unpaired electron. 

The radical is much more stable if both stmctures exist. Quantum mechanical theory implies that the radical exists in both states separated by a small potential. Moreover, both molecular orbital theory and resonance theory show that the allyl carbocation is relatively stable. 

In the allyl cation, with two tt electrons, and in the anion, with four -n electrons, there are two in M(V Note that the nonbonding >Pmo2 is concentrated at the ends of the chain the molecular orbital pictures for these species thus correspond closely to the resonance pictures (see 8, 9, 10, p. 6), which show the charge or unpaired electron to be concentrated at the ends. 

Conjugated compounds undergo a variety of reactions, many of which involve intermediates that retain some of the resonance stabilization of the conjugated system. Common intermediates include allylic systems, particularly allylic cations and radicals. Allylic cations and radicals are stabilized by delocalization. First, we consider some reactions involving allylic cations and radicals, then (Section 15-8) we derive the molecular orbital picture of their bonding. 

The right-hand column of Figure 15-11 shows the electronic structure for the allyl radical, with three pi electrons in the lowest available molecular orbitals. Two electrons are in the all-bonding MO (iri), representing the pi bond shared between the Cl—C2 bond and the C2—C3 bond. The unpaired electron goes into tt2 with zero electron density on the center carbon atom (C2). This MO representation agrees with the resonance picture showing the radical electron shared equally by Cl and C3, but not C2. Both... 

The allyl radical has two electrons in the bonding tt molecular orbital, so these electrons are spread over all three carbon atoms. The third electron is in the nonbonding MO. The molecular orbital diagram shows that the third electron is shared equally by the end carbons, with none of the electron density on the middle carbon. This is in agreement with what the resonance contributors show Only the end carbons have radical character. 

At its essence, a conjugated system involves at least one atom with ap orbital adjacent to at least one tt bond. The adjacent atom with the p orbital can be part of another ir bond, as in 1,3-butadiene, or a radical, cationic, or anionic reaction intermediate. If an example derives specifically from a propenyl group, the common name for this group is allyl. In general when we are considering a radical, cation, or anion that is adjacent to one or more TT bonds in a molecule other than propene, the adjacent position is called allylic. Below we show the formula for butadiene, resonance hybrids for the allyl radical and an allylic carbocation, and molecular orbital representations for each one. 

An explanation of the stability of the allyl radical can be approached in two ways in terms of molecular orbital theory and in terms of resonance theory (Section 1.8). As we shall see soon, both approaches give us equivalent descriptions of the allyl radical. The molecular orbital approach is easier to visualize, so we shall begin with it. (As preparation for this section, it may help the reader to review the molecular orbital theory given in Sections 1.11 and 1.13.)... 

We see, then, that resonance theory gives us exactly the same picture of the allyl radical that we obtained from molecular orbital theory. Structure C describes the carbon-carbon bonds of the allyl radical as partial double bonds. The resonance structures A and B also tell us that the unpaired electron is associated only with the Cl and C3 atoms. We indicate this in structure C by placing a 8 beside Cl and C3. Because resonance structures A and B are equivalent, the electron density from the unpaired electron is shared equally by Cl and C3. 

The lone electron of the allyl radical is associated with the rr-nonbonding MO, which places electron density on carbons 1 and 3 only. This localization is shown clearly in the unpaired electron density map in Figure 8.6. Thus, both the resonance model and molecular orbital theory are consistent in predicting radical character on carbons 1 and 3 of the allyl radical but no radical character on carbon 2, consistent with the experimental observation. Importantly, when there is a difference, the reaction will occur to generate the alkene product that is most stable—in other words, with the more highly substituted double bond. 

PROBLEM 12.20 Add electrons to both the resonance and molecular orbital descriptions in Figure 12.47 to form the allyl anion, radical, and cation. 

Although satisfactory for allyl cation. Figure 10.1 is insufficient for species with more than two tt electrons because the tt orbital in (c) can accommodate only two electrons. Molecular orbital (MO) theory, however, offers an alternative to resonance and valence-bond theory for understanding the structure and reactions of not only allylic cations, but radicals (three rr electrons) and anions (four tt electrons) as well. In a simplification known as the Hiickel, or ir-electron, approximation the tt MOs are considered as separate from... 

Benzylic carbocations, radicals, and anions resemble their allylic counterparts in being conjugated systems stabilized by electron delocalization. This delocalization is describable in resonance, valence bond, and molecular orbital terms. 

The resonance forms of the two allyl radicals used as models for the reactions are shown as a transition state in the following equation. An allyl radical contains three 7t electrons, two in 7ti and one in the K2 molecular orbital. Therefore, the frontier molecular orbital is TZ2- h h antisymmetric. The bond that is broken must generate 2p atomic orbitals with lobes of the same sign directed toward each other. The bond to be formed must occur between 2p atomic orbitals with lobes of the same sign directed toward each other. This can be accomphshed using the HOMO of one radical to form a O bond with the HOMO of the other radical. 

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