1. Write down the determinate that would result from solving the Huckel MO for the pi electrons in the cyclopropene cation. Explain where it comes from.

Show that E=a-b, E=a-b, E=a+2b are solutions to this determinate. [You may do this inductively]. What will the orbital diagram for this system look like with two electrons in it? [ Remember the actual value of b is negative].

2. Show how the variation theorem applies to the equation:

<E> = (c_a²H_AA + 2c_ac_bH_AB + c_b²H_BB)/(c_a²+c_b²)

Show how it leads to two simultaneous equations in c_a and c_b when solved for the minimum energy.

3. Huckel MO theory.

a) Write down the secular determinate that must be solved for benzene when the Huckel MO theory is applied to it.

b) From memory, what are the solutions of this determinate and how do these solutions explain resonance energy in this compound.

4. The lowest two Huckel molecular orbials for butadiene are:

y1 = .371 p1 + .6 p2 +.6 p3 + .371 p4

y2 = .6 p1 + .371 p2 -.371 p3 -.6 p4

where p1 is the p orbital on atom 1 perpendicular to sigma bond backbone and is normalized to itself and is orthogonal to p2, p3, and p4.

a) Show that y2 is normalized.

b) Show that y1 and y2 are orthogonal.

c) A third orbital has the following form:

y3 = 0.6p1 +c p2 + c p3 +0.6 p4

Calculate what c is.

5. Use mathcad to ealculate the energy states for the following pi system: cyclopentadiene anion. Please print out a hard copy and on it put your name and indicate draw the energy diagram for this pi system.