Propenyl cation, radical, anion

The SHM predicts the propenyl cation, radical and anion to have the same resonance energy (stabilization energy). Actually, we expect the resonance energy to decrease as we add ji electrons why should this be the case ... 

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. 

Figure 14-3 The Aufbau principle is used to fill up the tt molecular orbitals of 2-propenyl (allyl) cation, radical, and anion. In each case, the total energy of the TT electrons is lower than that of three noninteracting p orbitals. Partial cation, radical, or anion character is present at the end carbons in these systems, a result of the location of the lobes in the 772 molecular orbital.

The resonance formulations for the three 2-propenyl species indicate that it is mainly the two terminal carbons that accommodate the charges in the ions or the odd electron in the radical. The molecular-orbital picture is consistent with this view The three structures differ only in the number of electrons present in molecular orbital tt2, which possesses a node passing through the central carbon therefore, very little of the electron excess or deficiency will show up at this position. The electrostatic potential maps of the three 2-propenyl systems show their delocalized nature. (The cation and anion have been rendered at an attenuated scale to tone down the otherwise overwhelming intensity of color). To some extent, especially in the cation and anion, you can also discern the relatively greater charge density at the termini. Remember that these maps take into account all electrons in all orbitals, a and tt. 

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