Problem Set 1: CH 368 (Bauld): Due Monday, February 2

1. Draw energy level diagrams
for the allyl cation, radical, and anion. Qualitatively, depict the magnitudes
and signs of the coefficients in each of these MO’s. Use the MO energies
given in the notes to calculate the resonance energies (RE; at the HMO level)
of the allyl cation, radical, and anion.

2. Calculate the charge
densities in the allyl cation and anion at all three positions of these
systems, using symmetry as a shortcut. The coefficients of the BMO are given in
the notes. The coefficients of the NBMO were given in class. They are as
follows: for C1, square root of 1/2; for C3, the negative of the square root of
1/2; for C2, zero.

3. Display the energy level
diagram for 1,3-butadiene, and qualitatively depict the magnitudes and signs of
the coefficients in each of these MO’s. Calculate the resonance energy of
1,3-butadiene using the MO energies given in the notes (the comparison is to
two ethene type double bonds).

4. Calculate the charge densities
(Q_{i}) at C1 and C2 of butadiene using the MO coefficients given in
the notes. Show all calculations.

5. Calculate the charge
densities at C1 and C2 of the butadiene anion radical and the butadiene cation
radical. Use any reasonable shortcuts which are available.

6. Calculate the odd electron
densities (r_{i}) at all positions of the allyl radical.

7. Calculate the odd electron
densities (r_{i}) at C1 and C2 or the butadiene anion
radical and cation radical.