A coupled anharmonic oscillator model for optical nonlinearities of conjugated organic structures

Abstract

We present a simple model of coupled locally anharmonic oscillators which can be used to describe the optical nonlinearities in conjugated organic monomeric, oligoneric, and polymeric structures. We show that the method can very readily be used to explain the dependence of the band gap, the polarizability α, and the second hyperpolarizability γ on the number of repeat units of conjugated chain compounds by adjusting two parameters: the local anharmonicity term and the oscillator coupling constant. To illustrate the usefulness of this model, we have calculated the dependence of the band gap, the polarizability α, and the second hyperpolarizability γ, as the function of the number of repeat units for the oligomers of thiophene and benzene. The results predicted by the coupled anharmonic oscillator model are in good agreement with those of the experimental studies on thiophene and benzene oligomers recently reported by our group. In addition, the predicted power dependences of orientationally averaged 〈α〉 and 〈γ〉 on the number of repeat units are compared with those predicted by a free electron model, PPP method, sum-over-states method, and ab initio calculations.