Coherent-potential-approximation study of excitonic absorption in orientationally disordered molecular aggregates

TL;DR

This paper applies the coherent-potential approximation to study how orientational and energetic disorder in molecular chains affect excitonic optical properties, providing analytical formulas and validating them against numerical results.

Contribution

It introduces a CPA-based model for excitonic absorption in disordered molecular aggregates, accounting for various disorder types and deriving asymptotic relations.

Findings

CPA accurately predicts absorption linewidths under disorder.

Derived formulas relate disorder strength to coherence length and linewidth.

Model agrees well with numerical diagonalization results.

Abstract

We study the dynamics of a single Frenkel exciton in a disordered molecular chain. The coherent-potential approximation (CPA) is applied to the situation when the single-molecule excitation energies as well as the transition dipole moments, both their absolute values and orientations, are random. Such model is believed to be relevant for the description of the linear optical properties of one-dimensional $J$ aggregates. We calculate the exciton density of states, the linear absorption spectra and the exciton coherence length which reveals itself in the linear optics. A detailed analysis of the low-disorder limit of the theory is presented. In particular, we derive asymptotic formulas relating the absorption linewidth and the exciton coherence length to the strength of disorder. Such expressions account simultaneously for all the above types of disorder and reduce to well-established form when no disorder in the transition dipoles is present. The theory is applied to the case of purely orientational disorder and is shown to agree well with exact numerical diagonalization.