Week #7 (Due Sunday, Feb.29)

 

1. For ethylene calculate the expansion coefficients for the molecular orbitals using Huckel theory

Different signs indicates change in phase and presence of node consistent with an anti-bonding orbital

1. Compute the electron density on each atom

Only lowest molecular orbital occupied (E=-1) and n=2

So

both have same amount of electrons and hence system has no charge

2. Compute the bond order

consistent with one pi bond

2. As was done in class for the allyl cation, compute for the radical and anion:

 

Radical:

1. Bond order on each atom

 

2. Electron density on each atom

Anion:

a.     Bond order on each atom

b.     Electron density on each atom

Excess electron density on outer carbons consistent with anionic nature of system

For both the radical and anion the bond orders are the same as the cation as the second molecular orbital has no contribution from the central atom and hence no additional overlap with the end carbons is present.