Emissive spin-0 triplet-pairs are a direct product of triplet-triplet annihilation in pentacene single crystals and anthradithiophene films.

Singlet fission and triplet-triplet annihilation represent two highly promising ways of increasing the efficiency of photovoltaic devices. Both processes are believed to be mediated by a biexcitonic triplet-pair state, 1(TT). Recently however, there has been debate over the role of 1(TT) in triplet-triplet annihilation. Here we use intensity-dependent, low-temperature photoluminescence measurements, combined with kinetic modelling, to show that distinct 1(TT) emission arises directly from triplet-triplet annihilation in high-quality pentacene single crystals and anthradithiophene (diF-TES-ADT) thin films. This work demonstrates that a real, emissive triplet-pair state acts as an intermediate in both singlet fission and triplet-triplet annihilation and that this is true for both endo- and exothermic singlet fission materials.


Introduction
Photon up-and down-conversion are two of the most promising strategies for pushing photovoltaic efficiencies beyond the Shockley-Queisser limit 1 . Achieving efficient spectral conversion nevertheless remains challenging. Triplet-triplet annihilation and singlet fission in molecular systems offer an enticing solution 2 . These processes involve conversion between high-energy singlet (spin-0) excitons and pairs of low-energy triplet (spin-1) excitons 3,4 , thereby effectively turning a single high-energy photon into two low-energy excitations, or vice versa.
The conversion from singlet to triplets is widely accepted to proceed via a correlated triplet-pair state usually denoted 1 (TT) in a process described by S 1 → 1 (TT) → (T..T) → T 1 + T 1 5-7 . 1 (TT) is a biexciton state with overall spin-0 (singlet), yet its spin wavefunction can be approximated as a superposition of pairs of individual triplet excitons [8][9][10][11] . Spectral signatures of this state are widely debated in part because the main method used to study it, transient absorption spectroscopy, provides very similar signatures for 1 (TT), (T..T) and free triplets. Calculations [12][13][14] suggest that this is particularly true in the visible spectral region where most experiments are performed. In addition, paramagnetic resonance techniques [15][16][17] are blind to spin-zero states such as 1 (TT).
Instead, the simplest and most explicit probes of the 1 (TT) state are direct ground state absorption or photon emission. While many authors have assigned features from emission spectra to 1 (TT) [18][19][20][21][22][23][24][25][26][27] , recent work by Dover et al. 28 calls these assignments into question. In particular, they argue that the redshifted spectral features are not direct intermediates to singlet fission, i.e. 1 (TT), but emission from trap states which instead hinder singlet fission, as previously reported [29][30][31][32] . This is important because a lack of spectral signature of 1 (TT) implicitly questions the existence of 1 (TT) as a real, bound intermediate state 18

Results and discussion
In order to study 1 (TT) produced via SF or TTA, we focussed on two materials as model systems: diF-TES-ADT (diftes) and pentacene. We chose to focus on diftes (molecular structure in Fig. 1a) as our endothermic model system for several reasons. Firstly, compared with tetracene, it has a simple brickwork crystal structure 33 , confirmed by our grazing incidence wide-angle X-ray scattering (GIWAXS) from a polycrystalline film in Fig. 1b (see also Supplementary Fig. 1). In addition there is no known polymorphism or other phase transition between 100 K and room temperature 18,34 . Secondly, we found diftes to be air-and photo-stable and were able to reliably make thin films with highly reproducible optical behaviour. Thirdly, distinct emission signatures have previously been attributed to 1 (TT) 18 . Fig. 1c shows the absorption and emission spectra of a diftes thin film. At room temperature the spectra arise from the vibronic progression of the S 0 ↔ S 1 transition. At low temperature however, the emission spectrum is dominated by a feature previously assigned to 1 (TT) 18 . We note that the ground state absorption spectrum does not change significantly with temperature ( Supplementary Fig. 6).
We also chose to study pentacene (Fig. 1d) Figure 2 | Long-lived emissive 1 (TT) states in diftes thin films at 100 K. Time-gated emission spectra of a diftes thin film at 100 K. Immediately after excitation S 1 fluorescence is observed; structured 1 (TT) emission then persists, spectrally unchanged, for tens of microseconds. The highest energy band of the 1 (TT) emission coincides with twice the diftes triplet energy minus one vibrational quantum (0.17 eV), consistent with a Herzberg-Teller intensity borrowing mechanism 18 . dipole moment of 1 (TT) at its equilibrium nuclear geometry is zero due to the symmetry of its wavefunction.
In fact, this is a zero-order approximation: 1 (TT) can couple to a symmetry-breaking vibrational mode, allowing it to mix with the nearby S 1 state. Since S 1 is a bright state, the transition dipole moment of 1 (TT) becomes non-zero to first order. This mechanism is known as Herzberg-Teller intensity borrowing 39 (or equivalently as the Albrecht B-term in Raman spectroscopy 40 ). Since coupling to a vibration is required, the 0-0 peak of 1 (TT) emission is expected to be suppressed. Thus the luminescence spectrum of 1 (TT) is expected to form a vibronic progression, with the first visible peak (the 0-1 phonon replica) lying at approximately 2 × E T 1 − ω vib , i.e. twice the triplet energy minus one vibrational quantum 11,18,41 . In the case of diftes, twice the triplet energy of 1.08 eV 18 minus one vibrational quantum (0.17 eV) exactly matches the first peak of the delayed fluorescence (vertical line in Fig. 2), entirely consistent with Herzberg-Teller emission from the 1 (TT) state.
To determine whether 1 (TT) is formed from bimolecular TTA as well as through SF 18 , we turn to the PL dynamics. Fig. 3 shows false-colour maps of time-resolved PL (TRPL) measured at three different excitation densities at 100 K (other temperatures 77-291 K in Supplementary Information Section 4). We extracted the S 1 and 1 (TT) spectral components using the Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) algorithm 28,42 (full details in Section 4 of the Supplementary Information). The extracted spectra are shown to the right of the PL maps and the dynamics in the bottom panel.
The TRPL maps demonstrate an increase in relative emission intensity beyond 10 ➭s as the excitation density increases. On these timescales triplet excitons are the dominant excited states 18 and delayed emission can be reasonably attributed to bimolecular triplet-triplet annihilation (TTA) 43,44 . If TTA populates 1 (TT) by first forming S 1 28 , we would expect to see a small S 1 contribution to the PL spectrum on these timescales.
Importantly, we do not observe any such contribution, suggesting that the initial products of TTA are triplet-pair states rather than S 1 states ( Supplementary Fig. 24). To confirm this, we examine the emission dynamics in more detail.
The excitation density dependent dynamics in Fig. 3d shows 3 distinct regions. During region I, the PL intensity decays exponentially with a single time constant of ∼ 25 ns (dashed red line). In region II, the decay becomes non-exponential but shows no dependence on excitation density. Region III marks the onset of the excitation density dependence, with higher densities leading to more intense emission.
This behaviour can be qualitatively explained as follows. During region I, emissive 1 (TT) states formed from sub-nanosecond SF ( Supplementary Fig. 13) either decay to the ground state or form long-lived 'dark' This qualitative description is backed up by kinetic modelling (Fig. 4). We find that we need to explicitly include two distinct triplet-pair populations in our rate model to reproduce our emission dynamics (Fig. 4a). This is only slightly different to the original Merrifield model 45 . We separate out the S 1 and 1 (TT) states (electronically coupled triplet-pairs) and take Merrifield's '(TT)' to be (T..T) l (weakly interacting tripletpairs), see Fig. 4a. There are nine (T..T) l states (l = 1, 2, ..., 9) whose singlet character is given by the  Supplementary Fig. S16). c, Measured (markers) and simulated (lines) effect of magnetic field on the room temperature PL of a single crystalline domain of diftes. Error bars were calculated from the small differences in measured PL intensity between spectra obtained while sweeping up in magnetic field and those obtained while sweeping back down. The differences arise principally from small fluctuations in laser intensity. The kinetic scheme from panel a reproduces all features of the measured effect at both time delays. d, Time-gated spectra of a diftes thin film at 250 K, 4, 20 and 100 ns after excitation with an initial excitation density of 10 17 cm −3 . Excimer emission is clearly present at 20 ns in addition to contributions from S 1 and 1 (TT). Excimers are therefore distinct from 1 (TT) in diftes. The excimer spectrum (black line) was obtained by subtracting the normalised PL at 500 ns from that at 20 ns.
coefficients |C l S | 2 which give their degree of overlap with the singlet (see Supplementary Information Section 6.1). This is equivalent to the currently accepted description of SF: S 1 ↔ 1 (TT) ↔ (T..T) l ↔ T 1 + T 1 . We note that, as pointed out in a recent review 10 , the nomenclature used in the literature can be confusing.
Merrifield assumed that triplet-pairs have no electronic interaction (orbital overlap). In other words, the triplet-pair '(TT)' state described by Merrifield is identical to what we describe as (T..T). Others write 1 (TT) and implicitly include both the electronically coupled 1 (TT) and weakly-interacting (T..T) 18,46 .
We use this scheme (Fig. 4a) to model our data with additional inclusion of spin-lattice relaxation 8 and non-radiative triplet decay from (T..T) l (i.e. (T..T) l → T 1 ). Both of these are found to have little effect.
The governing rate equations are below and the resulting kinetics are shown in Fig. 4b.
In these equations square brackets denote concentrations of species in units of cm  Merrifield's model was originally developed to describe magnetic field-dependent fluorescence. Our kinetic scheme should, therefore, also be able to describe these effects, which arise as the |C l S | 2 coefficients vary with magnetic field according to the spin Hamiltonian 47 . Fig. 4c therefore shows a plot of ∆PL/PL as a function of magnetic field at two different delay times, measured at room temperature on a drop-cast sample (Supplementary Fig. 26, Methods, Supplementary Information Section 7). We then used our kinetic model to simulate the expected magnetic field dependence. The model (lines in Fig. 4c), reproduces the shape, magnitude and zero-crossing at both delay times.
We note that in our model, the magnetic field dependence arises specifically from 1 (TT) ↔ (T..T), which occurs on longer timescales than ultrafast singlet fission (S 1 ↔ 1 (TT)). Thus kinetic schemes that do not explicitly include both of these steps cannot correctly simulate the time dependence of the magnetic field effect, as demonstrated in Supplementary Fig. 30.
The kinetic scheme proposed by Dover et al. 28 includes an emissive excimer-like state that acts as a singlet trap rather than an intermediate to SF, but does not include any intermediates between S 1 and 2 × T 1 . This model is not applicable here: the magnetic field-dependent PL requires the presence of 1 (TT) and (T..T) intermediates. Since 1 (TT) is a singlet state and thus expected to be emissive 11,18,41 , we find no reason to assume that trap states are responsible for the emission we observe.
In fact, at a temperature of 250 K, we do observe distinct excimer-like emission in addition to 1 (TT) and S 1 emission (Fig. 4d). Whilst we do not wish to speculate further on the behaviour of the excimers, since we observe them only at this particular temperature and low excitation density, we reiterate that they are distinct from 1 (TT) in this system. This suggests that, while excimers may be present in singlet fission systems [28][29][30][31][32]48 , they are not by themselves direct evidence of 1 (TT).
Having demonstrated that emissive triplet-pairs are populated through bimolecular TTA in a polycrystalline endothermic SF material, we now turn to our highly ordered, exothermic model system: single crystals of pentacene. Previous reports of pentacene photoluminescence are scarce, and the spectral assignments 49,50 were made before the recent boom in singlet fission research. We therefore start by revisiting this literature and find evidence that the observed emission is consistent with 1 (TT). We further show, using fluence-and time-dependent measurements, that the 1 (TT) emission arises from bimolecular TTA.
Redshifted emission in pentacene single crystals arises from 1 (TT) rather than selftrapped excitons. Fig. 5a shows delayed emission from single crystals of pentacene (micrographs in Fig. 5b). Despite the sub-100 fs, near-200% conversion of singlets to triplets in crystalline pentacene 35,51 , we were able to measure weak photoluminescence from the crystals at 77 K. Just as for diftes, we found an instrument limited conversion from the S 1 fluorescence at around 690 nm to a redshifted feature that includes a peak at around 740 nm. Due to poor spectral sensitivity beyond around 820 nm ( Supplementary Fig. 5), we cannot resolve the spectral shape at longer wavelengths and can only say that some emission is present in this region. This poor sensitivity, coupled with the weakness of the PL signal make the assignment of the redshifted feature considerably more challenging than for diftes.
We therefore begin by comparing our emission spectra to those previously measured 49,50,52 (Fig. 5c,   Supplementary Fig. 33). The features that we observe are consistent with previously reported emission spectra of pentacene single crystals 49,50 and high-quality 20 nm thin layers 52 , all of which report bands at around 1.85 eV, 1.65 eV, 1.5 eV and 1.35 eV. In Fig. 5c we plot the delayed emission measured in this work alongside that reported at 4 K and 100 K in Ref. 52 which we judge to be the least affected by artefacts, particularly self-absorption. A comparison with other reported spectra is presented in Fig. S33.
The three redshifted bands in the PL spectrum at 4 K (purple line in Fig. 5c) appear to form a vibronic progression. If all these bands arise from the same electronic state, the 0-1 and 0-2 peaks should follow a standard Franck-Condon progression whilst the 0-0 may be either enhanced or suppressed, depending on symmetry constraints 53 . We therefore fitted the two lowest energy peaks of the 4 K spectrum to the 0-2 and 0-1 bands of a Franck-Condon progression. We used the in-plane C-H bending mode at 1180 cm −1 as the main vibrational mode coupled to the electronic transition. Resonance Raman experiments have shown that this mode is resonant with both the S 1 fluorescence and the peak at 1.65 eV 54 . It also matches the separation between the 0-1 and 0-2 vibronic replicas in our polarised absorption measurement (Fig. 1f).
Strikingly, the emission band at 1.65 eV coincides with the 0-0 peak of the resulting progression (dashed line in Fig. 5c), provided that its intensity is partially suppressed, as expected for emission enabled by Herzberg-Teller intensity borrowing. Within this context, intensity borrowing from S 1 , which is expected to become superradiant below ∼ 10 K 11,38,55,56 , may explain the observed temperature dependence of the 0-0 peak 49,52 . The 0-0 energy is slightly below that of two triplets in pentacene 57 (vertical line, Fig. 5c). The energy and spectral shape are therefore consistent with emission from 1 (TT).
Historically however, various alternative sources for the redshifted emission in pentacene have been proposed, namely defects 50 and self-trapped excitons 49,50,52 . It is also possible that excimers contribute to the redshifted emission. While difficult to rule out, we highlight that excimeric emission has been reported in several polyacenes and other SF materials 25,[28][29][30]32,58 , yet in every case the spectrum is broad, featureless and quite unlike the narrower, well resolved progression of peaks under consideration here.
Defects in single crystals may include extrinsic impurities or intrinsic vacancies or edge states. In the case of pentacene single crystals, extrinsic defects are reported to give rise to dominant emission at 1.5 eV 50 , overlapping with the 0-1 vibronic feature described above. While we cannot rule out extrinsic defect emission in this spectral region, we expect it to be minimised in our crystals, grown using a two-stage sublimation of triple-sublimed starting material (see Methods). We focus instead on the 1. 65  However, we argue in the following that self-trapped excitons are highly unlikely to be present in pentacene. The dimensionality of the exciton is important because it determines the relationship between the slope extracted from Urbach tails and the exciton-lattice coupling, which in turn governs self-trapped exciton stability 73 . For a given slope, a 2D lattice gives weaker exciton-lattice coupling than a 3D one. In order to assign the non-S 1 emission in tetracene to self-trapped excitons, Matsui et al. were forced to invoke a 3D lattice, despite the evidence that excitons are 2D in tetracene 37,62,74 . Thus the assumption that selftrapped excitons are the source of the emission is built into their assignment (of the emission to self-trapped excitons), which we find to be a somewhat circular argument.
Taking the more physically realistic 2D lattice, self-trapped excitons should be unstable in both anthracene and tetracene 62 , and the predicted trend in exciton-lattice coupling 75 would match widely accepted calculations of electron-lattice coupling by Brédas et al. 76,77 . Following this trend, exciton-lattice coupling should be even weaker in pentacene than in tetracene 76 , although to our knowledge it has never been de-  The dashed lines of Fig. 6d,e show the non-fitted, normalised 1 (TT) behaviour predicted by the model used to describe the transient absorption data. All parameters, including the fluence scaling, remained the same as for Fig. 6a,b. The match to our time-gated fluence dependence is remarkable and as expected the slope of -2 in Fig. 6d is also reproduced. It is perhaps surprising that this independent model prediction and our data are so similar, given the difference in measurement temperature between Fig.s 6a,b and d,e (the crystal dimensions and excitation source are comparable). For polycrystalline organic semiconductors, triplet transfer becomes slower at low temperature 81,87 , as we observed for our diftes films. However, charge carrier mobility, and therefore expected triplet transfer rate 87 , is independent of temperature for single crystal pentacene [88][89][90] . The room temperature model is therefore valid for our low-temperature PL data, and the excellent match confirms that 1 (TT) is populated directly through bimolecular TTA. S 1 cannot be involved in this process since it lies too high in energy.
We have shown that a weakly emissive 1 (TT) state is formed directly from bimolecular TTA in pentacene single crystals. Considerably brighter 1 (TT) emission is found in a range of acenes including diftes 18 , tetracene 19,20 , TIPS-tetracene 24 and rubrene 18 . The increase in 1 (TT) brightness between pentacene and diftes is explained by the reduced energy gap between 1 (TT) and S 1 , which increases the Herzberg-Teller mixing. A consistent picture thus emerges of biexcitonic 1 (TT) intermediates that emit light through a Herzberg-Teller mechanism. Crucially for spectral upconversion, we have demonstrated here that such states are directly formed through bimolecular TTA.

Conclusions
We have shown here that 1 (TT) is an emissive, and real, intermediate state in both singlet fission and TTA, resolving a recent controversy in the literature. We find that 1 (TT) emission in our systems is distinct from excimer-like features. This work provides the first direct spectroscopic evidence that the strongly exchangecoupled 1 (TT) triplet-pair state can be directly formed from bimolecular triplet-triplet annihilation in both nominally endothermic and single crystal exothermic systems. In addition, we have shown that emission previously assigned to self-trapped excitons instead arises from 1 (TT).
Magnetic resonance techniques are blind to spin-zero states. Yet these states, including the strongly exchange-coupled 1 (TT), can be easily detected using photoluminescence spectroscopy. We find that we  Correspondence and requests for materials should be addressed to J.C.

Competing interests
The authors declare no competing interests.

Methods diftes thin film preparation
diF-TES-ADT (diftes) was synthesised following previously reported procedures 33 and dissolved in anhydrous toluene at a concentration of 15 mg ml −1 . Thin films were prepared by spin-coating from solution onto pre-cleaned quartz-coated glass at a speed of 1200 rpm for 40 s. Film thickness was measured to be ∼ 60 nm using stylus profilometry (Dektak, Bruker). All thin film preparation was carried out in a nitrogen-filled glovebox.
Samples for TRPL measurements were not encapsulated since the measurement took place in an inert helium atmosphere. In general, exposure to light and air was kept to a minimum and all samples were stored in a nitrogen-filled glovebox. For transient absorption and magnetic field effect measurements, the sample was encapsulated inside the glovebox using a thin glass coverslip and a 2-component epoxy resin (Araldite).

Morphological characterisation of diftes thin films
Grazing incidence wide-angle X-ray scattering (GIWAXS) measurements were taken using a Xenocs Xeuss 2.0 system with a liquid Ga MetalJet X-ray source (Excillum). The 9.243 keV X-ray beam was collimated with two sets of slits and the sample chamber, flight tube and detector were held under vacuum to minimise additional scatter. Scattered X-rays from the sample surface were collected with a Pilatus3R 1M hybrid photon counting detector (Dectris) at a distance of 330 mm and a grazing incidence angle of 0.18➦. Geometry was refined with a AgBe calibrant after which azimuthal integrations of the data were performed with a full pixel-splitting algorithm to account for issues with detector resolution and binning at small angles 93 .
The 2D data was corrected and processed with the GIXSGUI MATLAB toolbox 94 . Powder XRD patterns and crystal packing images for diftes were simulated in Mercury, using previously reported crystallographic information files 33,95 . Analysis of the processed GIWAXS data is presented in Supplementary Fig. 1b.
Atomic force microscopy (AFM) measurements were performed in tapping mode using a scanning force microscope (Veeco Dimension 3100) with a nanoscope 3 A feedback controller. The AFM tips were TESPA-V2 probes (Bruker) with a resonance of around 320 kHz and spring constant of 42 N m −1 . Gwyddion 2.54 software was used to process the AFM images (levelling by mean plane subtraction, row alignment, horizontal scar correction, zero correction for the height scale). An AFM image of one of the diftes films is shown in Supplementary Fig. 1c.

Pentacene single crystal growth
Pentacene (≥99.995%, triple-sublimed grade) was purchased from Merck. Single crystals were grown by physical vapour transport 96,97 (PVT). A horizontal PVT furnace (Trans Temp, Thermcraft) was used for the growth, and the apparatus was enclosed to prevent possible photo-degradation.
First sublimation Quartz tubes used inside the PVT furnace were first cleaned with soap and a succession of solvents before being baked at 325 ➦C for 16 h and allowed to cool fully. 79 mg of starting material was placed at the end of the furnace and the whole assembly was purged under flowing ultra high purity argon gas (99.999%, 50 cm 3 min −1 ) for 21 h. This gas flow was then maintained for the entirety of the first sublimation.
The temperature of the starting material was next raised to 137 ➦C for 2.5 h and finally set at 289 ➦C and left for 3 d before being allowed to cool to room temperature. During the first sublimation, pentacene crystals were observed in the hottest part of the crystallization zone ∼220-260 ➦C, with orange, green and yellow impurities forming in the cooler parts as shown in Supplementary Fig. 2.
Second sublimation The purple pentacene crystals grown in the first sublimation were used as the starting material for the second sublimation. The remaining quartz tubes were cleaned and baked as before, and again the whole assembly was purged with argon for 17 h, this time at a flow rate of 30 cm 3 min −1 ). The temperature was next held at 137 ➦C for 2 h, then set to 289 ➦C for sublimation. After 1 d of sublimation, pentacene crystals were observed in the crystallization zone within a temperature range of ∼220-260 ➦C. No impurities were observed during the second sublimation.
Pentacene single crystal characterisation Following the second sublimation, pentacene single crystals were selected and laminated onto pre-cleaned quartz-coated glass. Bright-field, dark-field and cross-polarised images were recorded using a white-light microscope (Olympus BX51) and are shown in Supplementary   Fig. 3a-i. No image processing was used for the micrographs. Crystal thickness was measured by taking a step profile using AFM (Dimension Icon, Bruker fitted with Scanasyst-Air tips); these results are displayed in Supplementary Fig. 3k-l.
Supplementary Fig. 4 shows a surface scan of crystal 2, recorded using the same AFM instrument as for the thickness measurements. Terraces with an average step height of 1.6 nm were found, corresponding to the c-axis of the pentacene crystal 37 and confirming that, as expected 38 , the platelet-shaped crystals grew in the a-b plane.
The polarised absorption measurement reported in the main text was performed on crystal 1, since this was the largest but thinnest of the crystals. Time-resolved PL measurements were performed on crystals 2 and 3, these being the largest and most perfect respectively.
The crystals were not encapsulated, but exposure to air and light was kept to a minimum and the crystals were stored in a nitrogen-filled glovebox.

Steady-state absorption and PL measurements
Room temperature ground state absorption of thin film samples was performed using a UV-visible spectrophotometer (Cary60, Agilent). For temperature-dependent absorption and PL, the sample was mounted in a closed-cycle helium cryostat (OptistatDry BLV, Oxford Instruments). White light for absorption measurements was provided by a deuterium-halogen lamp (DH2000-BAL, Ocean Optics) and excitation for PL measurements was provided by a 405 nm CW laser diode (Thorlabs). Spectra were recorded using a fibrecoupled spectrometer (HR2000+ES, Ocean Optics). A 435 nm longpass filter (GG435, Schott) was placed before the detector for PL measurements.
The polarised absorption of the pentacene single crystals was measured by focussing light from a tungsten lamp through a variable linear polariser and onto the crystal using a 100 mm focal length lens. Transmitted light was collected with a 50× Mitutoyo Plan Apo SL infinity-corrected objective and delivered to a spectrometer (Andor). The grating used in the spectrometer is blazed at 500 nm and has a groove density of 150 lines per mm.

Time-resolved PL measurements
The image intensifier employs a gen. 3 VIH photocathode. The photocathode and grating largely determine the spectral sensitivity of the detector, which was measured using a calibrated light source and is plotted in Supplementary Fig. 5. The intensified CCD (iCCD) was cooled to −30 ➦C by a Peltier element during measurements. A combination of a 532 nm notch filter and 550 nm longpass filter (OG550, Schott) were used to cut out pump scatter.
The iCCD allows PL spectra to be collected (integrated) during a specified gate width. The gate opens at a specified gate delay after the laser pulse, remains open for the specified gate width during which photons are collected and then closes. This cycle is typically repeated over hundreds of laser shots for each data point and the result accumulated. This mode of operation allows for the recording of time-gated PL spectra.
In order to measure PL kinetics, the gate delay is incremented by a gate step for each data point.
However, since the PL signal decreases with time, the signal to noise ratio gets progressively worse with time. To overcome this and take advantage of the excellent sensitivity of the detector over the full range of timescales that we can measure, we record the PL kinetics in short sections, using a constant gate step and gate width for each section. The gate width is always less than or equal to the gate step. As we move further from time zero, the gate width and step used for each section are increased (gain and exposure may be increased as well). We are careful to include a temporal overlap between the end of the preceding section and the start of the following one. Backgrounds are also collected for each section.
Data processing first involves subtracting the background from every spectrum in each section. Next, at each point of overlap between sections, the second section is scaled by a constant factor until the spectra at the overlapping time exactly match in shape and intensity. In this way, the true PL kinetics can be obtained over many orders of magnitude in time and intensity whilst maintaining a good signal to noise ratio. We note that the scaling procedure means that plotting the y-axis in absolute units (such as counts) would not give a true indication of the fidelity of the data, since the counts are scaled differently for each section.
Instead the fidelity of the data should be examined by (a) looking at the raw spectra by eye and/or (b) looking at the error bars, which are given as the standard deviation of the noise across the spectral range for which the data point was averaged (±5 nm in all the data presented in this way here.) Typical values for intensifier gain and exposure time are as follows. diftes: gain of around 2000 or lower, exposure time around 1 s or lower. Pentacene: gain of around 3000-4000, exposure time 5-10 s.
Spectra presented in the main text have been corrected for the spectral sensitivity of our iCCD and for filter transmission. The spectral sensitivity of our iCCD is shown in Supplementary Fig. 5.
Measurements of average laser power P were carefully converted into values of average exciton density N using the following expression: Here, F S and F A represent the fraction of incident light scattered and absorbed by the sample respectively, Probe pulses spanning the ranges 350-700 nm and 850-1300 nm were generated by focussing a portion of the 800 nm beam through a continuously translating calcium fluoride or sapphire crystal, respectively. Pumpprobe delay was controlled using a motorized linear stage. Detection was carried out using a commercial instrument (Helios, Ultrafast Systems) equipped with CMOS and InGaAs detectors for the UV-visible and NIR probe regions respectively. The pump and probe polarizations were set to magic angle. Pump beam spot size was measured at the sample position using a CCD beam profiler (Thorlabs).

Multivariate curve resolution alternating least squares
Spectral components and their dynamics were extracted from the diftes TRPL data at each excitation density and temperature using Multivariate Curve Resolution Alternating Least Squares (MCR-ALS) 42 .
Two components only were used in each case and pure spectra were used as the initial point. Both the spectra and concentrations were forced to be non-negative using fast non-negative least squares. The spectral matrix was normalised and the algorithm run until convergence was achieved.

Kinetic modelling for diftes
Algorithms All simulations and fitting were performed using custom-made python code. The systems of rate equations were solved using the LSODA algorithm from MINPACK as implemented in SciPy's odeint.
The Levenberg-Marquardt algorithm from MINPACK as implemented in SciPy's least squares was used to globally fit the kinetic models to the exciton density-dependent data through variation of certain rate constants. The logarithm of data and simulation were taken when calculating residuals in order to treat all timescales equally. Rate constants were manually adjusted prior to fitting to ensure convergence to the global minimum.
Spin Hamiltonian Spin wavefunction overlap factors |C l S | 2 were computed using custom-made python code following the method laid out by Tapping and Huang 47 . The calculation requires knowledge of the relative orientation of adjacent molecules: this was determined from the published crystal structure of diftes 33 . The zero-field splitting parameters D and E are also needed. For diftes we took values derived from PL quantum beating (D = 1 × 10 −6 eV, E = 3 × 10 −6 eV) 18 . The strength of the triplet-triplet dipole-dipole interaction was taken as 60 neV 17 .

Instrument response
We took the instrument response of our iCCD into account in a somewhat crude fashion by assuming an exponentially rising population of photoexcited singlet excitons. Mathematically, this involved introducing an additional rate equation to the kinetic models for the pre-excitation ground state as follows: We calculated the initial value of [GS] according to equation 5. We then determined the value of k gen by modelling the decay of the S 1 state in pentacene single crystal 2. Since singlet fission is known to occur within 100 fs in pentacene 51 , the PL decay of S 1 is instrument-limited. We found a value of 1.8 ns −1 using this method and used it in all further modelling. We note that this is a reasonable number, given the laser pulse width of < 500 ps. The precise shape of the instrument response function (IRF) is immaterial since all the dynamics of interest occur on longer timescales. The decay of the pentacene S 1 fluorescence ( Figure 6d in the main text) gives a very reasonable idea of the IRF, since the decay constant is known to be ≤ 100 fs 51 .
This is equivalent to (for example) measuring the decay of pump scatter.
Fixed rate constants We determined the value of the singlet fission rate constant k sf from TA measurements as 10 ns −1 (Supplementary Fig. 13). Since this rate is thought to be independent of temperature 98 , we fixed it for all the modelling presented here.
We set the rate constant for conversion of 1 (TT) back to S 1 (k −sf ) to zero for temperatures of 100 K and below since little or no singlet contribution was observed in the delayed luminescence. From 150 K upwards, we estimated the rate using the following relation, which assumes a thermal equilibrium between 1 (TT) and S 1 : Here P S /P T T is the ratio of S 1 PL to 1 (TT) PL in the delayed luminescence and we took the ratio of radiative rates k ttr /k sr to be 1/40 as previously reported 18 .
Finally, we took the intrinsic lifetime of the singlet to be 12 ns, as measured using TA for dilute solutions of diftes ( Supplementary Fig. 13). We note however, that the precise values of all these rate constants have a negligible effect on the 1 (TT) population dynamics (Supplementary Information Section 6.5).
Preparation of a diftes crystal for measurement of magnetic field effects diftes was dissolved at a concentration of 5 mg mL −1 in toluene. A pre-cleaned quartz-coated glass substrate was placed in a small petri dish situated inside a larger petri dish containing 1 mL of toluene. 80 ➭L of the diftes solution was drop-cast quickly onto the substrate and the whole system covered with another glass dish. The solvent was allowed to slowly evaporate overnight. This procedure yielded large single crystalline domains many hundreds of microns in size ( Supplementary Fig. 26). The sample was made and encapsulated in a nitrogen-filled glovebox. Encapsulation was done using Araldite epoxy resin and a glass coverslip. The micrograph ( Supplementary Fig. 26) was collected using a Nikon Eclipse ME600 microscope in reflection mode with crossed polarisers. No image processing was used.

Magnetic field effect measurements
The sample was placed between the poles of an electromagnet. The measurement was performed at room temperature, since the pole separation required for low temperature measurements was much too great to achieve the required magnetic field strengths. Excitation was provided by the frequency-doubled output of a Q-switched Nd:YVO4 laser (Picolo-AOT, Innolas). The laser produces pulses at 5 kHz with temporal width < 500 ps and a wavelength of 532 nm. The photoluminescence was collected and sent via optical fibre to a spectrograph (Shamrock 303i, Andor) and time-gated intensified CCD (iStar DH334T, Andor) for detection. Magnetic field strength was measured using a gauss meter. A spot size of 50 ➭m was evaluated by translating a razor blade through the focal point. Magnetic field strength was measured using a Gauss meter.
The PL dynamics at 0 mT were measured first in order to check rate constant values for magnetic field effect modelling (see below). The effects of magnetic field on PL were measured by recording PL spectra at a series of magnetic field strengths at two different gate delays: 20-30 ns and 100-200 ns. The measured spectra were identical in shape and magnitude both while sweeping upwards and subsequently downwards in magnetic field strength ( Supplementary Fig. 27), allowing us to rule out any effects from photo-degradation or laser power fluctuations and giving us high confidence in the reproducibility of the observed magnetic field effect. Spectra were integrated along the wavelength axis and the magnetic field effect evaluated as ∆P L P L (B) = P L(B) − P L(0) P L(0) Simulation of the measured magnetic field effect The magnetic field effect was simulated using the kinetic scheme outlined in the main text and Fig. 4a.
The rate constants were varied slightly from the values used for the thin film and the zero field splitting parameters D and E were adjusted within their reported experimental errors 18 . This procedure is described in detail in Supplementary Information Section 7.

Kinetic modelling for pentacene
In Ref. 36 the triplet photoinduced absorption (PIA) was measured as a function of pulse energy and fitted to a simple bimolecular annihilation model given by: Where k tta = 1.2 × 10 −10 cm 3 s −1 and k tnr = 1/500 ns. Here we simply extended this model to include the full singlet fission process, as described in the main text. The rate equations are given by: Here f is the fraction of TTA events that form 1 (TT). We found the precise value to be unimportant, so long as it is less than unity. We used a value of 10%. We note that in Ref. 36, one of the conclusions was that not all triplet-triplet annihilation caused a loss of excited states in pentacene. Our data suggests that this is because a fraction of TTA events in fact form 1 (TT). The rate equations were solved using similar python code to that described above for diftes. Finally, the populations were convolved with a Gaussian IRF to mimic the instrument response of the different TA and PL setups. We take the triplet PIA to be proportional to [ 1 (TT)] + [T 1 ].
In order to apply this model to the experimental data, the measured laser pulse energies (units of ➭J cm −2 ) had to be converted to units of cm −3 . Ref. 36 did not report their calculation for this conversion.
We therefore obtained a constant conversion factor simply by applying the model to their fluence-dependent TA data and varying its value until the data was well reproduced by eye and the simulation matched that