# Singlet fission

Singlet fission is a spin-allowed process, unique to molecular photophysics, whereby one singlet excited state is converted into two triplet states. The phenomenon has been observed in molecular crystals, aggregates, disordered thin films, and covalently-linked dimers, where the chromophores are oriented such that the electronic coupling between singlet and the double triplet states is large. Being spin allowed, the process can occur very rapidly (on a picosecond or femtosecond timescale) and out-compete radiative decay (that generally occurs on a nanosecond timescale) thereby producing two triplets with very high efficiency. The process is distinct from intersystem crossing, in that singlet fission does not involve a spin flip, but is mediated by two triplets coupled into an overall singlet. It has been proposed that singlet fission in organic photovoltaic devices could improve the photoconversion efficiencies.

## History

The process of singlet fission was first introduced to describe the photophysics of anthracene in 1965. Early studies on the effect of the magnetic field on the fluorescence of crystalline tetracene solidified understanding of singlet fission in polyacenes.
Acenes, Pentacene and Tetracene in particular, are prominent candidates for singlet fission. The energy of the triplet states are smaller than or equal to half of the singlet (S$_1$) state energy, thus satisfying the requirement of S$_1$ ≥ 2T$_1$. Singlet fission in functionalized pentacene compounds has been observed experimentally. Intramolecular singlet fission in covalently linked pentacene and tetracene dimers has also been reported.
The detailed mechanism of the process is unknown. Particularly, the role of charge transfer states in the singlet fission process is still debated. Typically, the mechanisms for singlet fission are classified into (a) Direct coupling between the molecules and (b) Step-wise one-electron processes involving the charge-transfer states. Intermolecular interactions and the relative orientation of the molecules within the aggregates are known to critically effect the singlet fission efficiencies.
The limited number and structural similarity of chromophores is believed to be the major obstacle to advancing the field for practical applications. It has been proposed that computational modeling of the diradical character of molecules may serve as a guiding principle for the discovery of new classes of singlet fission chromophores. Computations allowed to identify carbenes as building blocks for engineering singlet fission molecules.

## Mechanisms

Singlet fission (SF) involves the conversion of a singlet excited state (S$_1$) into two triplet states (T$_1$). The process can be described by a two-step kinetic model (see Figure 1):
1. Formation of a correlated triplet pair state $^1$(T$_1$T$_1$) from the singlet excited state:
    S$_1$ + S$_0$ → $^1$(T$_1$T$_1$)
2. Separation of the triplet pair into two individual triplet states:
    $^1$(T$_1$T$_1$) → T$_1$ + T$_1$
The rate of singlet fission, denoted as k$_{SF}$, can be expressed using Fermi's Golden Rule:
    k$_{SF}$ = (2π/ℏ) | ⟨ $^1$(T$_1$T$_1$) ∣ H$_{el}$ ∣ S$_1$ ⟩ |$^2$ d
where H$_{el}$ is the electronic coupling Hamiltonian, and d represents the density of states. This equation shows that electronic coupling and state density determine the efficiency of singlet fission.

## Implications

Efficient singlet fission requires materials where the energy of the singlet state E (S$_1$) is at least twice the energy of the triplet state E (T$_1$):
    E (S$_1$) ≥ 2 × E (T$_1$)
The energetic requirements for singlet fission can be met by acenes (e.g., tetracene, pentacene), perylene derivatives, and diketopyrrolopyrroles (DPPs). Crystal morphology, molecular packing, and minimizing defects influence performance. For instance, single-crystal tetracene displays coherent quantum beats from spin-state interactions, whereas polycrystalline films exhibit less coherence due to defects. Single-crystal tetracene has slower singlet decay times (200–300 ps) compared to polycrystalline films (70–90 ps). In polycrystalline films, excitons can diffuse to defect-rich regions, creating “hotspots” that enhance singlet fission, with excimer-like emissions reflecting the influence of structural defects on SF rates. When materials do not meet the energetic requirements for singlet fission, other relaxation pathways occur such as fluorescence, non-radiative decay, or intersystem crossing to a single triplet state dominate, leading to lower efficiency in photovoltaic applications.

## Role of spectroscopy

Ultrafast and time-resolved spectroscopic techniques, including transient absorption and time-resolved fluorescence spectroscopy, allows determination of the rates of singlet exciton decay and the formation of triplet states. Transient absorption techniques capture the rapid conversion of singlet excitons into triplet pairs, highlighting the efficiency of singlet fission in various material morphologies. Using time-resolved fluorescence spectroscopy, one can observe coherent quantum beats resulting from spin-state interactions in triplet pairs.

## Possible applications

Singlet fission has the potential to enhance solar cell efficiency beyond the Shockley–Queisser limit, especially for organic photovoltaics. Applications extend to other fields, including light-emitting devices.