Particle on a ring model for polyacenes

Abstract

The particle on a ring model has been limited to circular systems, and there is no application of the particle on a ring model to molecules like naphthalene and anthracene, or more generally to polyacenes. When a circle is no longer a valid approximation of the delocalization for the π electrons, the model fails to correctly predict absorption maxima. This article addresses this specific shortcoming of the particle on a ring model by considering an elliptical path of delocalization for the π electrons in polyacenes. By finding an approximate radius for the ellipse from the major and minor axes of an ellipse, it has been shown that the calculated absorption maxima (λmax) values corresponding to the π-π* transitions are in good agreement with the literature values and with the computed TD-DFT results. Thus, a new perspective of particle on a ring model has been established for use in undergraduate quantum mechanics and spectroscopy courses.