Competition between triplet pair formation and excimer-like recombination controls singlet ﬁssion yield

Using a reﬁned magneto-optical transient experiment, Huang et al. show that the excimer-like delayed ﬂuorescence can act as a competitive loss channel for triplet pair generation. The suggested experimental protocol in this work may help resolve the debate about the roles of intermediate states in singlet ﬁssion. SUMMARY The ultimate goal for singlet ﬁssion is that each photo-excited singlet exciton, S 1 , will result in two triplet excitons with unity yield. However, the singlet ﬁssion is now recognized to be complicated, involving bright/dark excited states of different spin multiplicity. Identifying the role of such states is vital to optimize singlet ﬁssion yield but difﬁcult due to their elusive spectral signature. Here, we develop an experimental protocol based on a reﬁned magneto-op-tical probe to access the fast time evolution of various excited states. In diphenylhexatriene crystal, the S 1 is found to undergo two competing processes—to form one of the two dark triplet pair intermediates having different exchange energies or to form a bright state, S x , exhibiting excimer-like delayed photoluminescence. Our result provides a clear picture of a competition event in singlet ﬁssion, which is beneﬁcial for the development and tailoring of singlet ﬁssion materials with high yield. exothermic case, in which the formation of the triplet pair state acts as an efﬁcient competing trap state, reducing optical transition yield. Later in the article, we show that a self-consistent rate-modeling analysis of temperature-dependent Tr-MFE provides further support for the endothermicity of the singlet ﬁssion process in DPH monoclinic organic crystals.


INTRODUCTION
Singlet fission, the process whereby a pair of triplet excitons is generated from a single singlet exciton formed by the absorption of one photon, has great potential for future optoelectronics that rely on exciton multiplication. [1][2][3] Over the past decade, our understanding of fundamental physics underlying the singlet fission has been advanced with the aid of careful analyses regarding spin physics, 4-13 electronic coupling, and electronic configuration. [13][14][15][16][17][18][19][20][21][22][23][24] However, the singlet fission yield in converting a photoexcited singlet exciton into two separated triplet excitons, [T + T], is still far from perfect. The difficulty of this task can be attributed to the complex nature of the singlet fission process. It involves many bright or dark excited states of different spin multiplicity along the singlet fission pathway that can be either essential or detrimental for generating free triplet excitons. 5, 8,10,[13][14][15][16][17]22,23,[25][26][27][28][29][30][31][32] Special attention has been paid to the triplet pair states of multi-chromophore nature that are often called TT states. 15,22,28,30,32,33 Transient absorption/coherent vibrational studies suggest the TT states as the intermediates necessary for generating free triplet excitons. 28,32 The direct optical transition from TT to the ground state may also be probed as they gain a non-vanishing oscillator strength through a Herzberg-Teller-type mechanism 15 or breaking of symmetry in the case of intramolecular singlet fission in conjugated polymers. 34 These lead to excimer-like delayed photoluminescence (delayed PL). The excimer delayed PL has often been found in several tetracene derivatives 15,32,33 and in 3,6-bis(thiophen-2-yl)diketopyrrole derivatives. 35 However, the assignment of the excimer as a TT state and as a singlet fission precursor has been questioned by Dover et al., 16 who argued based on kinetic analysis that the excimer in 5,12-bis((triisopropylsilyl)ethynyl)tetracene (TIPS-tetracene) behaves as a trap state. 16 We note that these discrepancies may stem partly from the state of the matter being probed (e.g., solid-state films 32 versus solution), 16 in which the excited states important for singlet fission may not necessarily be the same. Looking more broadly, delayed PL akin to the excimer emission in TIPS-tetracene is also found in tetracene crystals at low temperature, which was assigned to emission from defect states. 25,27 This complexity underlines the need to clarify the exact role of different excited states in the singlet fission pathway and for a better experimental protocol to differentiate them. Such knowledge is vital for the design and tailoring of materials to allow high singlet fission yield. It will then facilitate strategic design for both materials and optoelectronic device architectures.
To this end, spin-sensitive probes such as magneto-optical experiments and electron spin resonance (ESR) have been proven to be useful techniques in identifying TT intermediates through their characteristic spin-spin interactions. [4][5][6][7][8]10,11,[36][37][38][39][40][41][42][43] In transient ESR (Tr-ESR) studies, the distinctive spin-resonance pattern was used to identify a set of TT intermediates with different exchange coupling strengths. 8,10,12,36 The coexistence of two triplet intermediates is also evident from magneto-optical studies of 1,6-diphenyl-1,3,5 hexatriene (DPH) crystals, as revealed by the magnetic field effect (MFE) on the steady-state PL. 6 Time evolution of Tr-ESR spectra provided a hint for the kinetic evolution between strongly interacting TT states and those that are spatially separated and non-interacting, 8,10,42 and on time-varying exchange coupling between pair of triplet excitons. 44 However, a complication in assigning the spin kinetics associated with TT intermediates to the delayed PL kinetics arises due to the different detection time windows of the two techniques. In typical Tr-ESR, the initial evolution of states within t < 2-50 ns is obscured by the instrumental response. This is problematic since the dynamic evolution of TT states, excimers, and other trap states is expected to occur on this timescale, taking crystalline film, disordered films, and solution of TIPS-tetracene at low temperatures as examples. 16,32,33 Here, we present a refined magneto-optical mapping of Tr-PL, allowing us to probe the temporal evolution associated with two singlet excitons and two TT intermediates with a time resolution better than 2 ps. In combination with temporally and spectrally resolved PL measurements under selective optical excitation, the Tr-MFE allows us to differentiate between the dark intermediate TT and the bright singlet trap states responsible for the redshifted delayed PL. Our results demonstrate that the initially excited S 1 in the short polyene crystal shown in Figure 1A undergoes two competing processes, as represented in Figure 1B: (1) to form two TT intermediates with different exchange energies and (2) to form the bright trap state S x that cannot regenerate TT pairs and, therefore, is detrimental to the overall singlet fission yield. Temperature-dependent Tr-MFE suggests endothermic singlet fission. Based on detail rate analysis, the endothermic step is between S 1 and the strongly exchange-coupled TT pairs [TT], whereas the dissociation from [TT] into a weakly exchange-coupled state [T . T] is exothermic. These two TT intermediates, together with S 1 and S x , are dynamically linked due to cyclic singlet-exciton fission and triplet exciton refusion, which occur within 4 ns. The two triplet states, [T . T] and [T + T], differ as the former can undergo geminate refusion with a faster timescale and the latter is a long-range spatially separated state. Our results thus provide a more complete picture of the competing roles of the dark intermediate multi-exciton states ll OPEN ACCESS and the trap states in determining singlet fission yield and offer a measurement protocol to differentiate them.
DPH polyene monoclinic crystals, as shown in the Figure 1A, were chosen as a typical example due to an advantage in the magneto-optical experiment. Their MFE patterns associated with both [TT] and [T . T] are expected within the range of applied magnetic fields B < 6 T. 6,36,45 These field conditions are accessible via a commercially available superconducting magnet. The MFE patterns of [TT] and [T . T] could be predicted using a classic Merrifield dynamic model with known spin Hamiltonian parameters, and the result is shown in Figure S1 for triplet conformation of both parallel and herringbone type. It shows the characteristic drops in PL yield, resulting from the singlet-quintet (S-Q) anti-crossing within the [TT] spin manifolds at B = 2.2 and 4.65 T. For the [T . T], the simulation predicts a well-known low-field MFE pattern in the range of B < 2 T. These two characteristic MFE patterns serve as fingerprints to identify the [TT] and [T . T] states in various magneto-optical experiments. 6,7,9,11,43,45,46 RESULTS AND DISCUSSION Delayed PL in DPH monoclinic crystal Spectrally resolved Tr-PL at different temperatures was used to probe the dynamic evolution and population decay of the bright exciton states. Figures 2A and 2B show two-dimensional spectral/temporal PL profiles of the DPH crystal under 375-nm photoexcitation (S 0 / S 1 ) at 200 and 8 K, respectively. Two exciton species can be identified by the observation of different exciton lifetimes at the long-and short-wavelength ranges of the probed spectral window. This is evident from the different PL spectra at t = 0.  states becomes faster at 8 K, with a timescale of $80 ps. We attribute this to a coherence effect appearing at the temperature below 80 K (see further discussion in the Note S1 and Figure S2).
The delayed PL from S x is of interest, as it resembles excimer delayed PL in TIPS-tetracene solid films and solution, 16,32,33 where there is controversy over whether it acts as a TT intermediate or a trap state. To examine the origin of S x in DPH, we proceeded with fast magneto-Tr-PL experiments. This technique is capable of modulating excited species occupying different spin states through singlet fission/triplet refusion events, and detecting their evolution within the lifetime of the delayed PL.

Magneto-Tr-PL and MFE mapping: dynamic evolution of [TT] and [T . T] states
A schematic diagram of magneto-Tr-PL experiments is shown in Figure 3A. Here, the laser excitation and Tr-PL detection are parallel to the B field. The crystal surface normal is rotated 45 away from the optical axis to minimize laser scattering into

OPEN ACCESS
the Tr-PL detection. This orientation also facilitates our later measurements under a quasi-resonant excitation condition. Figure 3B shows spectrally integrated Tr-PL (415-600 nm) measured at 200 K with a pulsed optical pumping to the S 1 state (375-nm excitation), at B = 0 T and 1.9 T. The fast and slow components of the Tr-PL are from S 1 and S x states, respectively. The magnetic field response of the Tr-PL seen in Figure 3B is known to be a result of dynamic singlet fission and/or triplet-triplet refusion involving TT pair states. 38 Figure S1, can be clearly seen in the MFE spectra at long delay times (t = 4 ns) in Figure 4B for T = 100 K and 200 K. The temporal evolution of the MFE fingerprints is clearly visible in Figure 4A within the marked magnetic field ranges. To quantify the temporal evolution of the two MFE fingerprints independently without interference, we intro-  Figures 4C and 4D.
We now consider the dynamics of the associated exciton species from the Tr-MFE results. We note that the origin of the Tr-MFE differs from other spin-sensitive transient probes. While techniques such as Tr-ESR monitor TT states (S > 0), formed directly from the singlet fission and/or indirectly via triplet-triplet annihilation in a bimolecular manner, Tr-MFE monitors these states through luminescence precursors such as S 1 and/or S x . Therefore, finite MFE requires a complete circle of singlet fission and triplet  Figures 4C and 4D, imply that a quasi-steady-state condition involving these two TT intermediates is established on similar timescales. In previous magneto-optical studies of DPH crystals at room temperature, 6,43,45 the MFE pattern was modeled by a stepwise process. 6 Nonetheless, we can conclude that the generation and recombination of the two TT intermediates happen within 4 ns, which is similar to the time window in which the delayed PL from S x is detected.
Next, we turn to the temperature dependence of the Tr-MFE. As can be seen from Figure 4, MFE becomes diminished as the temperature decreases from 200 to 8 K. Such observation may suggest an endothermicity of the singlet fission in the DPH monoclinic crystal. 38 Alternatively, it could indicate that the energy of the triplet pair states is below that of S 1 . In this case, triplet refusion becomes improbable at low temperature, and, therefore, exothermic triplet pair states act as the non-radiative trap states. However, we argue that the exothermic case is not likely due to the following evidence. According to the temperature-dependent continuous wave (CW)-PL measurements shown in Figures S2A and S2B, an increase in optical transition yield from singlet states is observed at low temperatures. This rather supports the first endothermic scenario, in which the non-radiative competing singlet fission pathway is suppressed at low temperatures. At the same time, it goes against the show that a self-consistent rate-modeling analysis of temperature-dependent Tr-MFE provides further support for the endothermicity of the singlet fission process in DPH monoclinic organic crystals.

Dark TT intermediates and the bright recombination trap S x
The fact that the two TT intermediates and the delayed PL (assigned to S x ) are present on similar timescales may imply that the S x state is in fact a TT intermediate, provided that its optical transition is allowed via a Herzberg-Teller-type radiative transition. 15 However, the results from the Tr-MFE and the Tr-PL at 8 K do not support this assignment. At 8 K, the Tr-MFE shows that both [TT] and [T . T] could not be populated, while the S x delayed PL is clearly seen (see Figure 2B). This discrepancy provides a hint that TT intermediates and the S x are of different origins. To further justify this, magneto-Tr-PL under a selective optical excitation was used. Resonant excitation to S x was achieved by tuning the excitation wavelength to be below the S 1 absorption edge. The fluorescence spectra at delay times of t = 0.01 ns and 3 ns under 430 nm excitation at 200 K are presented in Figure 5A. The fluorescence spectra in these two temporal windows, which correspond to the time windows in which the prompt and the delayed PL are respectively expected, exhibit no spectral evolution and are similar to the decomposed spectrum of S x from Figure 2C. These confirm the resonant excitation to S x . Importantly, the S x decay curves under resonant excitation at 0, 1.5, and 4.65 T, shown in Figure 5B The disappearance of MFE under S x resonant excitation implies that the states involving in the S x radiative transition have a net zero magnetic moment. This experimental finding confirms that S x is not a TT intermediate but a singlet state (S = 0) situated at $170 meV below the S 1 state. We thus conclude that S x acts as a competing recombination hotspot and the TT intermediates remain dark.

Self-consistent rate modeling and dynamic parameters evaluation of the trap state-induced singlet fission loss
To determine the important dynamic parameters and thus energy ordering along the singlet fission pathway, we perform detailed rate-modeling analysis of the  Figure 1. The detail analysis, values, and justification of fitting parameters can be found in Note S2 and Figure S3. In short, first, we restrict the fitting parameters to the minimum number of seven while using experimentally determined values for all of the remaining parameters. Second, we consider two conformations of the triplet pair states within the DPH monoclinic unit cells: the herringbone and the parallel configuration. Third, the fitting must have self-consistent fitting values of the Tr-MFE in all temperature ranges. Based on this fitting protocol, the analysis suggests that the singlet fission event most likely happens at the DPH pairs with a herringbone configuration, with a possible small contribution from that of the parallel configuration (see details in Note S2 and Figures S4 and S5). The fitting parameters are summarized in Table S1. In the case of herringbone structure, S 1 / [TT] has the endothermic barrier of $D SF = 13.5 meV, and the endothermicity of the states is also in line with predictions from electronic structure calculations provided in Note S3 and Tables S4 and S5. We note that the theoretical absolute value of D SF differs from the rate analysis due to intrinsic limitations of the computational model used (see Note S3 for a detailed discussion). The second step for triplet dissociation, [TT] / [T . T], is found to be exothermic with D TT = À12.4 meV, in agreement with our highly correlated wave-function-based calculations (Table S3). The [T . T] / [T + T] hopping dynamics g d TT is set to be temperature independent, following a suggestion from a previous pioneer study in thin films of 6,13-bis(triisopropylsilylethynyl)pentacene, which was attributed to long-range triplet dissociation promoted by the vibronic effect. 40,47 The 8-to 200-K Tr-MFE fittings of the triplet pairs in the herringbone conformation are plotted as the black solid lines in Figures 4C and 4D.
The trapping from S 1 to S x competes with the formation of TT intermediates, which lowers the overall singlet fission yield as S x cannot regenerate TT pairs. To evaluate the competing loss, the dynamic parameters obtained from the rate modeling were used to estimate the singlet fission yield: where g SF , g S1 , and g R are the rate constants for singlet fission, S 1 / S x trapping, and radiative recombination of S 1 , respectively. This estimation considers an ideal condition with efficient separation and collection of fission-generated triplet excitons such that re-fusion is not likely.
Nonetheless, the obtained F SF is still far from perfect. F SF is found to be 0.79 (0.94), 0.69 (0.90), and 0 (<0.3) with (without) the contribution of the trap state, S x , at 200, 100, and 8 K, respectively. This analysis shows that trapping to S x happens on a timescale comparable to that of singlet fission and therefore must be avoided to promote a high singlet fission yield.
In general, the triplet refusion shall be also considered in determining the overall fission yield. Nevertheless, F SF provides a good estimate of the efficiency of the singlet fission for devices with optimal performance. In the endothermic singlet fission process, it is natural to assume that the singlet fission rate g SF smaller than the reverse triplet fusion rate g TF . However, this does not necessarily imply a low fission efficiency. This is because the singlet fission efficiency is associated with the population flow (see Figure 1B) so that both the rate parameters (e.g., g SF , g TF ) and occupation of the states (e.g., n S1 and n [TT] for S 1 and [TT]) matter. In optimized devices, the steady-state triplet or triplet pair density is assumed to be low due to the ll OPEN ACCESS efficient carrier extraction. The large concentration ratio between singlet and triplet pairs leads to a negligible exciton flow in the reverse direction. The fission efficiency is then only limited by the branching ratio between S 1 / [TT] that fission to triplet and S 1 / S x , which we denoted as trap state-induced singlet fission loss in this work. Therefore, F SF reflects the fundamental singlet fission efficiency limited by the trap states S x .
Regarding the possible origin of S x , we consider both an excimer and crystal defects. The low emission energy and strong exciton-phonon coupling well resemble the excimer emission found in other organic crystals. 48 However, the intrinsic radiative lifetime of S x ($4.7 ns) obtained from the Tr-PL analysis is rather short to be a dimeric/multi-chromophoric transition for an excimer. For the lattice defects, we consider the lattice imperfections due to misoriented minor conformers found from X-ray diffraction (XRD). 49 These defects, however, should be restored to normal lattice sites at low temperature. 49 Therefore, this type of lattice defect cannot account for the S x delayed fluorescence, which appears at 8 K. Finally, we considered the PL of the cis-trans conformations of the molecule, which arise from rotation of the polyene carbon chain. The energy position and vibronic progression of the S 1 emission resemble the PL of the s-t-DPH conformer and those of the S x emission resemble the PL of the s-c-DPH conformer. 50 Moreover, the $170 meV redshift of S x with respect to S 1 is in very good agreement with computed vertical energies (Table S2 and Table 1 in the previous first-principles study 51 ). Thus, we tentatively attribute S 1 to the PL of s-t-DPH and S x to the minority contribution of s-c-DPH.
In summary, the competing formation of dark TT intermediates and bright recombination hotspots, S x , in singlet fission have been clearly demonstrated in DPH. S x cannot regenerate TT intermediates and, therefore, is detrimental to the overall singlet fission yield. We conclude that the TT intermediates, both with strong and weak exchange coupling, are the necessary steps for free triplet generation. The temperature effects on the Tr-MFE reveal an endothermic singlet fission. Optimizing the singlet fission yield in endothermic systems should be done by avoiding the formation of low-energy bright states. We anticipate that our experimental protocols will help in resolving the debate about the roles of intermediate states and delayed PL in singlet fission materials more generally.

EXPERIMENTAL PROCEDURES
Resource availability Lead contact Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Yuttapoom Puttisong (yuttapoom.puttisong@liu.se).

Materials availability
This study did not generate new unique reagents.

Data and code availability
The datasets generated, analyzed during the current study and the simulation code are available from the lead contact on reasonable request.

Spectral-resolved Tr-PL and transient magneto-optical experiments
Fast spectral-resolved Tr-PL was measured by a Hamamatsu Streak camera assembled with a single-grating monochromator. The optimal time resolution was better than 1 ps. The excitation source was a 76-MHz Ti:sapphire pulsed laser with a second harmonic generator to produce an excitation wavelength range of 360-430 nm. The pulse width was 150 fs. The excitation power was kept low throughout the measurement to minimize non-geminate triplet exciton re-fusion that could contribute to a long-lived delayed PL with t > 1 ms. The Tr-PL being probed in all of the experiments had an effective lifetime <13 ns, and therefore was of geminate type. The samples were placed inside a liquid-He superconducting magnet cryostat operated at T = 1.75-275 K and B = 0-10 T. The surface normal of the sample was oriented at 45 to the B field direction.