Stochastically Realized Observables for Excitonic Molecular Aggregates

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 N ( )3 for N dye molecules. Our approach scales much more efficiently as N N ( log( )), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, 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.

Bridging the Gap between H- and J-Aggregates: Classification and Supramolecular Tunability for Excitonic Band Structures in 2-Dimensional Molecular Aggregates

“…As shown in Figure 1 and pervious works, these parameters lead to the subtle variations in excitonic band structure. 23,34 The absorptions of these 2D aggregates range from 587 nm (TDBC) to 1050 nm (Cy7-DPA), shown in Figure 3b. The narrow lineshape with a high energy tail observed across all aggregates is characteristic of extended 2D aggregate structures, and is also seen in other 2D aggregates of perylene bisimides.…”

“…sheet-like and tubular aggregates. [21][22][23] Examples of non-Kasha behavior have also been observed in polydiacetylene, poly (3-hexylthiophene) and other conjugated polymers, referred to as segregated "HJ" aggregates, wherein interchain and intrachain couplings have opposite signs. 24,25 In some cases, different forms of couplings can cancel out, resulting in a null aggregate with no excitonic shift in optical spectra in spite of a significant excitonic bandwidth.…”

Bridging the Gap between H- and J-Aggregates: Classification and Supramolecular Tunability for Excitonic Band Structures in 2-Dimensional Molecular Aggregates

“…As shown in Figure 1 and pervious works, these parameters lead to the subtle variations in excitonic band structure. 23,31 The absorptions of these 2D aggregates range from 587 nm (TDBC) to 1050 nm (Cy7-DPA),…”

“…We screen large parameter space of possible aggregate packing parameters (slips) and disorder values using the stochastic sampling methods for the DOS, and Chebyshev kernels the absorption spectra, following Bradbury et al 23 The stochastic density of states is calculated by taking a random superposition of all eigenstates, projecting it down onto a specific energy in the spectrum, and then averaging over many random samplings. This approach is computationally less expensive than diagonalizing large Hamiltonians and allows for rapid screening of several aggregate geometries with realistic sizes (~ 10 6 monomer units).…”

“…sheet-like and tubular aggregates. [21][22][23] Examples of non-Kasha behavior have also been observed in polydiacetylene, poly(3-hexylthiophene) and other conjugated polymers, referred to as segregated "HJ" aggregates, wherein interchain and intrachain couplings have opposite signs. 24,25 In some cases, different forms of couplings can cancel out, resulting in a null aggregate with no excitonic shift in optical spectra in spite of a significant excitonic bandwidth.…”