Allyl radical molecular orbitals

In the allyl radical threep orbitals overlap to form a set of tt molecular orbitals that encompass all three carbon atoms. 

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 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. 

The Stability of the Allyl Radical 13.3A Molecular Orbital Description of the Allyl Radical... 

Figure 13.2 Combination of three atomic p orbitals to form three n molecular orbitals in the allyl radical. The bonding n molecular orbital is formed by the combination of the three p orbitals with lobes of the same sign overlapping above and below the plane of the atoms. The nonbonding n molecular orbital has a node at C2. The antibonding n molecular orbital has two nodes between Cl and C2, and between C2 and C3. The shapes of molecular orbitals for the allyl radical calculated using quantum mechanical principles are shown alongside the schematic orbitals.

Figure 13.3 The n molecular orbitals of the allyl cation. The allyl cation, like the allyl radical, is a conjugated unsaturated system. The shapes of molecular orbitals for the allyl cation calculated using quantum mechanical principles are shown alongside the schematic orbitals. 

Removal of an electron from an allyl radical gives the allyl cation => the electron is removed from the nonbonding tz molecular orbital. 

Stabilized allyl radical will be stabilized further if substituents are introduced. This stabilization occurs to different degrees in the ground state and the transition structure for rotation. In the ground state the substituent acts on a delocalized radical. Its influence on this state should be smaller than in the transition structure, where it acts on a localized radical. In the transition state the double bond and the atom with the unpaired electron are decoupled, i.e. in the simple Hiickel molecular orbital picture, the electron is localized in an orbital perpendicular to the jt(- c bond. 

Problem 8.28 (a) Apply the MO theory to the allyl system (cf. Problem 8.26). Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (b) Insert the electrons for the carbocation C,H, the free radical C,H, and the carbanion CjH, and compare the relative energies of these three species. 

Are the carbon-carbon bond distances in allyl cation, allyl radical and allyl anion all similar, or are they significantly different The three molecules differ mainly in the number of electrons they assign to one particular molecular orbital. (This is the lowest-unoccupied molecular orbital (LUMO) in allyl cation, and the highest-occupied molecular orbital (HOMO) in allyl radical and allyl anion.) Examine the shape of this orbital. Are the changes in electron occupancy consistent with the changes in CC bond length Explain. 

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. 

Unpaired spin in a delocalized 7T-system tends to follow a parity-type distribution, with alternation of the sign of 7T-spin density due to polarization. As shown in Scheme 2, the odd alternant allyl radical has its major spin density confined to the 7T-atoms at each end within the simple Hiickel molecular orbital... 

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... 

Q Show how to construct the molecular orbitals of ethylene, butadiene, and the allylic Problems 15-35 and 36 system. Show the electronic configurations of ethylene, butadiene, and the allyl cation, radical, and anion. 

The cation, radical and anion have the same a framework 1.4, with fourteen bonding molecular orbitals filled with 28 electrons made by mixing the Is orbitals of the five hydrogen atoms either with the 2s, 2px and 2py orbitals of the three carbon atoms or with the sp2 hybrids. The allyl systems are bent not linear, but we shall treat the % system as linear to simplify the discussion. 

The n system is made up from the three pz orbitals on the carbon atoms. The linear combination of these orbitals takes the form of Equation 1.9, with three terms, creating a pattern of three molecular orbitals, tpi, ip2 and 3. In the allyl cation there are two electrons left to go into the n system after filling the a framework (and in the radical, three, and in the anion, four). 

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