Free-electron-nonbonding molecular orbital

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. 

---