Spectra of graphs and semi-conducting polymers

We study the band gap in some semi-conducting polymers with two models: Huckel molecular orbital theory and the so-called free electron model. The two models are directly related to spectral theory oil combinatorial and metric graphs. Our numerical results reproduce qualitatively experimental results and results from much more complex density-functional calculations. We show that, several trends can be predicted from simple graph models as the size of the object tends to infinity.