I was reading the explanations of electronic configurations of the Allylic Radicals, Cations and Anions in my textbook. I completely understand everything, but there is one thing that confuses me. Namely, it is said that the antibonding pi3* orbitals of allylic cations, radicals and anions have no electrons. Now my questions is, where are they? Regardless of the type of bonding, there should be 2 pi electrons in an allylic cation, 3 pi electrons in allylic radical, and 4 pi electrons in allylic anion. So the electrons should be somewhere. For example I would think that the allylic radical of pi3* is a molecule with 1 pi electron in each carbon, but because of the absence of orbital overlap they are not shared between the carbons, whereas in the case of pi2 nonbonding they are partially shared and fully shared in pi1 bonding orbitals.
In allylic species 3 orbital wave functions are interfering to form 3 molecular orbitals among which the pi antibonding molecular orbital will have the max energy. The first two mo can accomodate 4 electrons. Since pi antibonding are at a higher energy level the first 4 electrons will remain in first two mo only. Similarly in cation and radical electrons will remain in these orbitals hence the pi antibonding will always remain empty.