Particle-in-a-bos model of one-dimensional excitons in conjugated polymers

A simple two-particle model of excitons in conjugated polymers is proposed as an alternative to usual highly computationally demanding quantum chemica l methods. In the two-particle model, the exciton is described as an electr on-hole pair interacting via Coulomb forces and confined to the polymer bac kbone by rigid walls. Furthermore, by integrating out the transverse part, the two-particle equation is reduced to one-dimensional form. It is demonst rated how essentially exact solutions are obtained in the cases of short an d long conjugation length, respectively. From a linear combination of these cases an approximate solution for the general case is obtained. As an appl ication of the model the influence of a static electric field on the electr on-hole overlap integral and exciton energy is considered.