Predict the molecular orbitals and identify the HOMO and LUMO orbitals of the following cation.

The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.

a. Use resonance forms to show which three carbon atoms bear the unpaired electron.

The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.

b. How many MOs are there in the molecular orbital picture of the pentadienyl radical?

c. How many nodes are there in the lowest-energy MO of the pentadienyl system? How many in the highest-energy MO?

d. Draw the MOs of the pentadienyl system in order of increasing energy

The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.

f. Show how your molecular orbital picture agrees with the resonance picture showing delocalization of the unpaired electron onto three carbon atoms.

The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.

g. Remove the highest-energy electron from the pentadienyl radical to give the pentadienyl cation. Which carbon atoms share the positive charge? Does this picture agree with the resonance picture?

The pentadienyl radical, H₂C=CH–CH=CH–CH₂•, has its unpaired electron delocalized over three carbon atoms.

h. Add an electron to the pentadienyl radical to give the pentadienyl anion. Which carbon atoms share the negative charge? Does this picture agree with the resonance picture?

Answer the following questions for the MOs of 1,3-butadiene:

a. Which are $\pi$ bonding MOs, and which are $\pi$* antibonding MOs?

b. Which MOs are symmetric, and which are antisymmetric?

c. Which MO is the HOMO and which is the LUMO in the ground state?