Singlet Exciton Diffusion in Organic Crystals Based on Marcus Transfer Rates

Abstract

Exciton diffusion is a critical step for energy conversion in optoelectronic devices. This spawns the desire for theoretical approaches that allow for fast but reliable determinations of the material-dependent exciton transport parameters. For this purpose, the Marcus theory, which is widely used in the context of charge transport, is adapted to exciton diffusion. In contrast to the common approach of calculating the exciton hopping rate via the coupling and the spectral overlap, this alternative approach is less costly, because, instead of the spectral overlap, only the reorganization energy is needed. To demonstrate the capability of the approach, the diffusion constants for naphthalene, anthracene, and diindenoperylene crystals are calculated and compared with both calculations conducted with the well-established exciton hopping rate, including coupling and spectral overlap, and with experimental data. These test calculations show that Marcus-based exciton diffusion properties tend to be too small but are qualitatively correct (i.e., they seem to be useful to predict trends). Nevertheless, for reliable results, high-level quantum chemical approaches are necessary for the computation of the reorganization energies. However, they have to be calculated only once. Coupling constants, which are needed for all pairs of monomers, have a considerably smaller influence, i.e., they can be computed by a lower level approach, which makes the method even less costly.

Regimes of Exciton Transport in Molecular Crystals in the Presence of Dynamic Disorder

“…Therefore, the exciton transport in anthracene crystals is expected to take place in the incoherent regime, in agreement with several theoretical and experimental studies. [30,31,57,58] For DCVSN5 we estimate instead λ to be 0.328 eV, a figure comparable with the excitonic coupling along the antiparallel π-stacked pair (-0.200 eV) and for which one cannot assume incoherent hopping as the transport mechanism (see below).…”

“…It has been selected because it is a good model for a wide range of active donor materials in the context of organic electronics and its exciton transport properties have been experimentally [23][24][25][26] and theoretically [27][28][29][30][31] characterized. The 5 relatively strong exciton-phonon coupling, due to its small size, is already evident from the absorption spectrum.…”

The dimer-approach to characterize opto-electronic properties of and exciton trapping and diffusion in organic semiconductor aggregates and crystals

“…Employing a monomer hopping model in combination with the Marcus approach, predicts an L D value of 160 nm for a-PTCDA, which is almost an order of magnitude too large, while a reasonable value of 100 nm was computed for DIP. 100,101 This indicates that the monomer-based model misses some important effects for a-PTCDA which seem to be less important or not active in DIP crystals. Simple disorder effects, which are expected to limit the L D for amorphous systems, should be less significant because both measurements were performed on single crystals.…”

“…Consequently, a monomer based hopping model which neglects such trapping effects but carefully considers relevant intra-monomer motions can provide reasonable L D values. 100,101 Our examples given for the three perylene based aggregates PBI, PTCDA and DIP show that the dimer approach is necessary if fast trapping effects are important which involve relaxation pathways along inter-monomer coordinates leading to a population transfer to a lower lying state. Efficient trapping does not occur if the relaxation takes place in a single state because the corresponding PESs are very flat.…”

QM/MM calculations combined with the dimer approach on the static disorder at organic‐organic interfaces of thin‐film organic solar cells composed of small molecules

“…[2] A more profound understanding of these and other parameters influencing the disorder is needed to rationally design materials with favorable transport properties because small energetic disorder is decisive for efficient exciton and charge transport in molecular semiconducting thin films of optoelectronic devices. [8][9][10] Computational chemistry provides ideal tools to deepen the understanding of the origin of disorder in organic semiconducting materials because the DOS is directly accessible from the calculations. Furthermore, it is in silico also possible to extend the disorder concept to interfaces between 2 semiconducting phases, where optical absorption measurements as well as investigations of charge carrier mobilities are experimentally barely feasible.…”