Week #8 (Due Sunday, March 7)
For this exercise you will need to download the program ÔhmoÕ from http://www.unb.ca/fredericton/science/chem/ajit/hmo.htm It is similar in format to Dr. GilbertÕs program.
1. For cyclopropylene (C3H3) radical:
a. Construct the Huckel matrix in terms of alpha and beta.
b. Use ÔhmoÕ to find the energies for the neutral case.
i. Construct the orbital electron occupation diagram using the aufbau principle
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_e__
_e_e_
ii. Record the energy of the pi system
Epi=3alpha+3beta
b. Find the expansion coefficients for the lowest energy molecular orbital using algebra (Show your work)
c. Using the expansion coefficients from ÔhmoÕ 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)
bond order (c1-c2)= 2*(.577)*(.577) + .5*(.211)*(-.789) + .5*(.789)*(-.211)=.499
bond order (c2-c3) = .502
bond order (c1-c3) = .502
Half a pi-bond between each carbon atoms
electron density (c1) = 2*(.577)2+.5*(.211)2+.5*(.789)2=.999=1
electron density (c2) = .999=1
electron density (c3) = .998=1
As would expect for neutral radical equal electron density throughout
Discuss/Explain the values in terms of pi-bonding and the neutrality of the molecule.
d. Use ÔhmoÕ to find the energy for the anion and cation.
Epianion=4*alpha+2*beta
Epication=2*alpha+4*beta
i. Display the orbital electron occupation diagram using the aufbau principle
Anion
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_e_e_
_e_e_
Cation
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_e_e_
ii. Which is more stable the cation, neutral or anionic species? For alpha=0 and beta=-1, the cation is more stable (has lower energy)
2. Use ÔhmoÕ 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? Longer. Higher pi bond order between end carbons versus center bonds which agrees with experiment.