Collective aspects of singlet fission in molecular crystals

Abstract

We present a model to describe collective features of singlet fission in molecular crystals and analyze it using many-body theory. The model we develop allows excitonic states to delocalize over several chromophores which is consistent with the character of the excited states in many molecular crystals, such as the acenes, where singlet fission occurs. As singlet states become more delocalized and triplet states more localized, the rate of singlet fission increases. We also determine the conditions under which the two triplets resulting from fission are correlated. Using the Bethe Ansatz and an entanglement measure for indistinguishable bipartite systems, we calculate the triplet-triplet entanglement as a function of the biexciton interaction strength. The biexciton interaction can produce bound biexciton states and provides a source of entanglement between the two triplets even when the triplets are spatially well separated. Significant entanglement between the triplet pair occurs well below the threshold for bound pair formation. Our results paint a dynamical picture that helps to explain why fission has been observed to be more efficient in molecular crystals than in their covalent dimer analogues and have consequences for photovoltaic efficiency models that assume that the two triplets can be extracted independently.

Vibronic exciton theory of singlet fission. III. How vibronic coupling and thermodynamics promote rapid triplet generation in pentacene crystals

“…In addition to both types of vibronic coupling, we identify a thermodynamic mechanism unique to crystalline environments as a driving force for singlet fission. A similar idea was previously proposed to explain experiments on tetracene, 37 and subsequently explored theoretically 38,39 albeit without non-perturbative vibronic coupling. We here show thermodynamics to drive the conversion between vibronically resonant singlet and triplet states in crystalline pentacene at a time scale consistent with the experimentally determined fission rates.…”

“…Perhaps more significant, however, is the contrast in collective characteristics between singlet and triplet excitons. 39 Whereas triplets remain largely localized, singlet states tend to delocalize over a considerable number of molecules in crystalline environments. 53 For pentacene, the resulting Davydov splitting induces an energetic separation between singlet states, while most of the oscillator strength is concentrated in the lower Davydov component, S 1 .…”

Polymorphism influences singlet fission rates in tetracene thin films

“…semiconductor nanocrystals, 5 with the added potential of molecular and crystallographic control through chemical synthesis. While much theoretical 6 – 14 and experimental 15 – 21 work has focused on the mechanism of SF, it has only been utilized in a few PV device moieties. 22 – 25 From the limited number of applications, it is clear that taking full advantage of SF requires a more complete understanding of the mechanism and a wider array of systems supporting efficient SF.…”

Polariton-Assisted Singlet Fission in Acene Aggregates

“…Its interaction with the singlet excitons is described by the light-matter Hamiltonianwhere in the second line we have introduced a delocalized Fourier basis for the singlet excitons |k = (5) is the collective light-matter coupling and Ω is the so-called Rabi splitting. Importantly, the singlet excitons are optically bright, in contrast to the dark TT states [25]. Because of this property, our model does not feature a TT term analogous to Eq.…”

“…The singlet-TT electronic coupling is (assuming periodic boundary conditions |T −1 T 0 = |T N −1 T 0 ): [25]…”