and eigenvectors of a matrix

Check that is works for the matrix, H =

0 1 0

1 0 1

0 1 0

By showing that

H v(k) = e(k) v(k)

for the e(k) eigenvalue and the v(k) eigenvector

2) Take alpha=0, and beta = -1,

Use Huckel MO theory to calculate eigenvalues

and eigenvectors for the following organic molecules:

butadiene

hexatriene

dodecene i.e. C_{12}H_{14}

benzene

naphthalene : a tricky one!!! just do it!

Do an MO calculation for the cyclic compound C_{4N+2}H_{H4N+2}

for several values of N.

BUT assume that alternating bonds have two

different beta values:

beta_1 = 1.2 and beta_2 = 0.8

Calculate the HOMO LUMO gap, and plot the gap

vs chain length N

Compare this to the results when there is only one

beta value of beta=1.