Stochastically Realized Observables for Excitonic Molecular Aggregates

TL;DR

This paper introduces a stochastic computational method that efficiently calculates optical properties of large excitonic molecular aggregates, significantly reducing computational complexity compared to traditional diagonalization techniques.

Contribution

The authors develop a stochastic approach that scales as O(N log N), enabling rapid analysis of large 2D and nanotubular excitonic systems with millions of molecules.

Findings

The stochastic method accurately reproduces optical spectra and density of states.

It enables analysis of spatial correlations in large aggregates.

The approach significantly reduces computational time for large systems.

Abstract

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as $\mathcal{O}(N^3)$ for $N$ dye molecules. Our approach scales much more efficiently as $\mathcal{O}(N\log(N))$, enabling quick study of systems with a million of coupled molecules on the micron size scale. We calculate several important experimental observable including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.