Week #8 (Due Sunday, March 7)

 

For this exercise you will need to download the program åhmoπ from http://www.unb.ca/fredericton/science/chem/ajit/hmo.htm It is similar in format to Dr. Gilbertπs program. 

 

1.     For cyclopropylene (C₃H₃) radical:

a.     Construct the Huckel matrix in terms of alpha and beta.

b.     Use åhmoπ to find the energies for the neutral case.

                                                                                                               i.     Construct the orbital electron occupation diagram using the aufbau principle

                                                                                                                 ii.     Record the energy of the pi system

c.     Find the expansion coefficients for the lowest energy molecular orbital using algebra (Show your work)

 

d.     Using the expansion coefficients from åhmoπ and the equations from class compute the bond orders and electron densities for the molecule. To account for the two degenerate MOs assume half of the highest energy electron is in each degenerate orbital (i.e n₂=.5=n₃ in the expression for bond order/density) (Show your work) Discuss/Explain the values in terms of pi-bonding and the neutrality of the molecule.

e.     Use åhmoπ to find the energy for the anion and cation.

                                                                                                               i.     Display the orbital electron occupation diagram using the aufbau principle

                                                                                                                 ii.     Which is more stable the cation, neutral or anionic species?

2.     Use åhmoπ to predict whether or not the central bond in butadiene is longer or shorter than the other two. Does your prediction based on Huckel theory agree with experiment?