Molecular Orbitals of the Allylic System

Let s take a closer look at the electronic structure of allylic systems, using the allyl radical as our example. One resonance form shows a pi bond between C2 and C3 with the radical electron on C1, and the other shows a pi bond between C1 and C2 with the radical electron on C3. These two resonance forms imply that there is half a pi bond between C1 and C2 and half a pi bond between C2 and C3, with the radical electron half on C1 and half on C3. 

Geometric structure of the allyl cation, allyl radical, and allyl anion. 

As with butadiene, we expect that half of the MOs will be bonding, and half antibonding but with an odd number of MOs, they cannot be symmetrically divided. One 

In drawing pi MO s, several p orbitals combine to give the same number of MOs half bonding and half antibonding. If there are an odd number of MOs, the middle one is nonbonding. 

The lowest-energy MO has no nodes each higher MO has one more node. 

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The molecular orbitals of the allyl system are formed by the overlap of three atomic p orbitals. Because there is an odd number of atomic orbitals, one of the molecular orbitals is a nonbonding orbital, whose energy is comparable to that of the isolated p orbitals from which it was derived. Note that if there were degenerate molecular orbitals in the allyl system, the electronic configurations of various allyl species would be different. For example, if P2 3 for the allyl system had identical energy levels, the allyl anion would have two unpaired electrons. 

We can summarize all this information in a molecular orbital energy level diagram, the n molecular orbitals of the allyl system the allyl cation... 

Fig. 2-15 Coefficients in the molecular orbitals of the allyl system (a) as sine curves, (b) in elevation and (c) in plan...

The LCAO tt molecular orbitals of the allyl system CH2=CH=CH2 are shown below. 

Schematic representation of the LCAO IT molecular orbitals of the allyl system. The "nonbonding" orbital is really antibonding but only very slightly so, because atoms 1 and 3 are rather widely separated in space.

Figure 1.8 -Molecular orbitals of the allyl system. From left to right, the electron occupancies are for the cation, radical and anion, which have two, three, and four x-electrons, respectively.

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