Organic Chemistry at Penn State: Allyl

Here is the display of π orbitals of the allyl system. The allyl π system is built out of three atomic p orbitals on the adjacent carbon atoms, one orbital per carbon. The mixing of these three orbitals results in three molecular orbitals, arranged here from the lowest energy (bottom) to the highest energy (top). The interactive models do not show the sign of the wavefunction on the orbital lobes correctly (an error in Chime), but you can easily correct for that by comparing them with the correctly colored picture on the left.

The number of π electrons in the allyl system can vary. The three most important cases to consider are the allyl cation, the allyl radical and the allyl anion. Here, for illustration purposes, these species are generated from propene, which already has a π bond (two p orbitals) and the third p orbital is "generated" by breaking one of C-H bonds of the CH₃ group. In the allyl cation (formed by a hydride abstraction from propene) there are only two π electrons, and only the lowest-energy orbital is occupied. Thus, in the allyl cation π₁ is the HOMO, and π₂ is the LUMO. In the allyl radical (formed by a hydrogen atom abstraction from propene) there are 3 π electrons, and the highest occupied orbital (HOMO) is the middle orbital (π₂), sometimes also called a SOMO (Singly Occupied Molecular Orbital). For the allyl radical π₃ is the LUMO. The allyl anion (formed by a proton removal from propene) has 4 π electrons, and π₂ is the HOMO and π₃ is the LUMO.

The allyl system illustrates the advantages of using the MO description to properly account for the delocalized electrons. Instead of "artificial" resonance structures, a set of molecular orbitals spanning the whole carbon skeleton is used to spread electron density over more than two atoms at a time. This delocalization leads to more sharing of electron density and lowering of the energy of the system.