# Calculating excitation energies of a molecule

I am trying to calculate the excitation energies for the first three transitions of a molecule which is made up by a chain of k phenyl rings, where k shall be between 1 and 8. The angle between each rings shall be $\pm 30^\circ$. You can see a picture of the molecule with $k=8$ rings below. I have calculated the first three transistion energies using Gaussian. You can see them in the table below. Now I want to calculate them by hand using a very simplified model. Since there is a linear correlation of $E(\frac{1}{k})$ a good model would be the particle in a box. Therefore I tried to use such a model, but unfortunately the difference between my energies is way to high. I used $$E_{n+1}-E_n = (2n+1)\frac{h^2}{8m(kl)^2}$$ as formula where k shall be the number of phenyl rings and l ($\simeq 2.1\mathring{A}$) shall be the diameter of one ring. You can see my results I obtained by using this formula in the table below. How could I improve my calculations?

• Do you mean the difference between levels of your particle in a box model? Or the difference between your particle in a box model and the Gaussian calculations? It would help to see a similar table of the particle in a box values. One thing I notice is your formula for the particle in a box energy difference seems wrong. I would think where you have $kl$ it should be $(kl)^2$. – Tyberius Jul 12 '18 at 3:28
• I added the table with the results I obtained by hand as well as $(kl)^2$ which I just forgot. Thanks for the correction. – p_punkt Jul 12 '18 at 5:51
• You seem to imply there is only one electron in your box. – Ivan Neretin Jul 12 '18 at 6:01
• The particle in a box is a very crude model. For example the choice for the length is somewhat arbitrary. Then there is no elecetron-electron interaction. you could try to approximate thjs by some additional energy offset, but how would one choose it? You could try to fit these parameters, but it will always be a very simple approximation to a complex system. – Feodoran Jul 12 '18 at 6:40
• also the box would work best for a.completely conjugated pi system, Hückel could be more heloful here. but your 30 degree angle complicates things. – Feodoran Jul 12 '18 at 6:50