Well it is a Huckel MO matrix and you are correct in thinking I wanted the eigenvalues - this is why I do not usually make up problems.  I think I will need to come up with a new question for my pchem class - I appreciate your help.

Here is the file.

Download 7904_h2_parameters.mws
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Ideally - I want the form of the line fitted to the LUMO (Set 2 data) to graphically mirror the form of the equation from Set 1.  My fits are projecting the wrong slope for this data - it should have an increasing slope - see paper.  Any ideas on how to reflect the fit line from Set 1 to Set 2?

The problem I am doing is a fit over HOMO/LUMO data obtained from TDDFT.  The equation I using to fit comes from Kuhn and has the form of

E = E_0*sqrt(1+k'/k_0*cos(Pi/(N+1)))

where E_0 is the transition energy, N is the number of double bonds, and k'/k_0 is an adjustable parameter relating he coupling between oscillators and is typically on the order of -0.45.

This equation has been shown to fit over the data (Chem. Mater. Vol. 19, No. 20, 2007, p. 4949).

I was able to fit the HOMO using this expression without difficulty which is the first set of data in the *mws.

The big picture: I am trying to determine the long chain limit for a set of polymers and so using the equation above to fit the data is critical.

My plot problem:

I fit the data using N.  However, the actual plot is performed using E vs. 1/N.