The coupled coherent and incoherent motion of excitons and its influence on the line shape of optical absorption

Abstract

We treat the coupled coherent and incoherent motion of Frenkel excitons by a model calculation. The model contains the four parametersa (distance of neighbouring atoms),J (exchange interaction integral), γo (describing the strength of the local energy fluctuations) and γ1 (a measure of the fluctuations of the exchange interaction integral, i.e. nonlocal fluctuations). Calculation of the optical absorption of systems with two differently oriented molecules/unit cells results in the Davydov-splitting given by Δ=8J and the linewidth given by Γ=γo+γ1. From the equation of motion of the density matrix we derive a diffusion equation. The diffusion constant is given by $$D = \frac{{a^2 }}{\hbar }\left( {2\gamma _1 + \frac{{J^2 }}{{\gamma _1 + \Gamma }}} \right)$$ . Comparison with experiment yields γo=70cm−1, γ1=0.1 cm−1 at room temperature and Γ<1 cm−1 at 4.2 °K. Using these numerical values and the criterium of Haken and Strobl we derive that at room temperature the exciton motion is incoherent and may be described by a hopping process whereas at low temperature it is coherent.