MDMD simulations were performed on neat NODIPS-Tc, and a 50% w/w mixture with toluene. The neat liquid is essentially immobile on experimental timescales, with a structural decorrelation time on the order of 100 μs. However, the structural decorrelation of the mixture was 104 times faster, with a time constant of about 10 ns (Extended Data Fig. 1).The simulations predict that the closest nearest-neighbour interaction of both the neat liquid and the mixture are at a distance of 3.8 Å, with a π-stacking angle of about 60°. The second nearest configuration has the chromophores π-stacked in a perpendicular arrangement at a distance of 4.4 Å (Extended Data Fig. 2). These two arrangements occur as distinct peaks in the configurational probability distributions in the neat liquid, which merge into a single peak/ridge in the mixture (angular–radial distribution functions in Supplementary Figs. 9c and 10c). Configurations expected to be prone to excimer formation, with anti-parallel or parallel transition moments, are found at larger distances of around 5.6 and 6.5 Å, respectively, in both simulations.TRPLThe room temperature TRPL of neat NODIPS-Tc liquid is shown in Fig. 1b. Each spectrum is normalized by its integral, accentuating the changes that occur as the spectrum evolves over time. At early times (0–8 ns, epoch 1), the emission is dominated by the photo-generated S1 state, rapidly red shifting into an 1Ex-dominated spectral shape in epoch 2 (8–80 ns). The S1 emission appears H-aggregated39, with the 0–0 band suppressed to a greater extent than in more dilute (yet optically thick) samples measured under identical conditions (Extended Data Fig. 3). This observation is consistent with the predominance of π-stacked nearest neighbours in the molecular dynamics simulations. For comparison, the steady-state absorption and photoluminescence spectra of dilute NODIPS-Tc solution are shown in Fig. 1a. The expected effect of self-absorption on the spectra is shown in Extended Data Fig. 4.The early time spectral slices spanning epochs 1 and 2 are plotted in Fig. 1c. There is a rapid shift of the iso-emissive point (IEP) in the first few nanoseconds, which then settles down near 620 nm. As with TIPS-Tc, in NODIPS-Tc, both SF and TF pathways are thermally accessible19,40. After 100 ns, in epoch 3, the annihilation of SF-generated triplets dominates the spectrum. Spectral slices spanning all epochs are plotted in Fig. 1d.The presence of a stable IEP after a few nanoseconds in the area-normalized spectra suggests that there are two major spectral components. The IEP deviates in the first few nanoseconds, indicating that there is probably a third component. To quantify the presence of a third component, we implemented principal component analysis (PCA).PCAThe PCA of the dataset is shown in Fig. 2a. A scree plot41 showing the percentage variance explained by each principal component (PC) and the cumulative variance is plotted in Fig. 2b. It is important to note that PCA does not generate the spectra of species, and as the PCs are necessarily orthogonal, they can exhibit differently signed spectral regions. PC1 represents the average spectrum and PC2 accounts for the principal spectral changes, with the S1 component diminishing and the 1Ex component growing in time. The variance attributed to each PC drops steadily before an elbow appears at PC4, indicating the onset of insignificant factors41. The eigenvector of PC4 is very noisy. Since three spectra are required to reproduce the deviation from a single IEP in Fig. 1c, and there is no evidence of a significant fourth component, we proceed on the basis that there are three spectral components in the neat sample. The PCA and scree plots for the mixtures with toluene (75%, 50% and 30% w/w) are shown in Extended Data Fig. 5. The third component is not in evidence in these samples as shown by PCA, although the PC3 eigenvector seems to contain spectral information.Fig. 2: PCA on TRPL of neat NODIPS-Tc.a, Eigenvectors of the first four PCs. b, Scree plot of variance per cent and cumulative variance per cent of the first six PCs.The number of PCs may be equated with the number of kinetically and spectrally distinct emissive species. As such, three PCs suggests at least three emissive species. Clearly, during the transition from epoch 1 to 2, the red-shifted 1Ex emission grows at the expense of the bluer, S1-like spectrum. Since the initially prepared state is S1 and the IEP deviates and then settles in the first few nanoseconds, there must be a rapid quasi-equilibrium established between the S1 state and another species. We propose that this third spectral component is due to emission by an excitonically coupled chromophore pair, which is spectrally distinct from 1Ex. We assign this species to the exchange-coupled triplet pair state, 1(TT), as reported in the solid state24,33,35,36,42,43.Spectral decompositionThe kinetic scheme is illustrated in Fig. 3a. In epoch 1, there is a rapid onset of equilibrium between S1 and 1(TT), which then equilibrates with the 1Ex state in epoch 2. Dissociation of 1(TT) states (SF) generates a pool of free triplets, which then undergo mutual annihilation (TF) in epoch 3.Fig. 3: Photoluminescence kinetics.a, The kinetic scheme shows the quasi-equilibrium formed between the S1 state, 1Ex and strongly exchange-coupled 1(TT) state, and their connection to separated triplets. The external magnetic field, B, modifies the Gibbs free energy of activation for SF, giving rise to the MFE on photoluminescence. b, Jablonski diagram of involved states. c, Spectra of each epoch and the steady-state (SS) spectrum. d, Spectra of each emissive species.The spectra of the three epochs, σ1−3, are shown in Fig. 3c, and are linear combinations of the species-associated spectra, σS, σTT and σEx. Epoch 1, σ1, is clearly σS dominated, and epoch 2 is σEx dominated. Epoch 3 closely resembles the steady-state emission spectrum, indicating that TF principally populates the S1 state after transiting the 1(TT) state. Subsequent emission is equivalent to the steady-state spectrum. Since σ3 is generated by 1(TT) states, it will naturally have a higher proportion of 1(TT) emission than σ1 or σ2.The spectral evolution that occurs in the first nanoseconds suggests that the 1(TT) spectrum, σTT, is slightly red shifted compared with the photo-generated S1 state spectrum, σS, but does not have the same intensity in the deep-red region as the 1Ex state spectrum, σEx. As such, we may isolate σTT by assuming that the bluest emission is due to the S1 state and the reddest emission is due to the 1Ex state. Subtracting contributions due to σS, and the excimer-dominated spectrum σ2, from σ3 results in the σTT spectrum displayed in Fig. 3d. The other species-associated emission spectra, σS and σEx are also displayed in Fig. 3d.MagnetophotoluminescenceTo shed further light on the spectral characteristics of the 1(TT) state, we performed magnetic photoluminescence experiments. Though not directly observable through photoluminescence, there must also be a bichromophoric state in which the exchange coupling is weaker than the zero-field splitting, 1(T…T). This weakly coupled regime is included in the kinetic scheme illustrated in Fig. 3a. For aligned chromophores, at zero-field there are three out of nine triplet pair sublevels with singlet character (\(\left\vert xx\right\rangle ,\left\vert\, yy\right\rangle\) and \(\left\vert zz\right\rangle\), where the triplet basis is \(\{\left\vert x\right\rangle ,\left\vert\, y\right\rangle ,\left\vert z\right\rangle \}\)). As a magnetic field is applied, these states mix with other sublevels and the number of levels with singlet character increases, essentially increasing the entropy of the 1(T…T) state. At higher fields where the basis transforms into \(\{\left\vert -\right\rangle ,\left\vert 0\right\rangle ,\left\vert +\right\rangle \}\), only two of the nine weakly coupled substates have singlet character, \(\left\vert 00\right\rangle\) and \((\left\vert +-\right\rangle +\left\vert -+\right\rangle )/\sqrt{2}\), and the entropy of the state is diminished37,44,45,46. Low entropy of an intermediate is accompanied by a higher free energy of activation, and thus rate constants are effectively manipulated by the magnetic field (Supplementary Information). This effect of the magnetic field on the free energy of the 1(T…T) state is illustrated schematically in Fig. 3a.The effect of increasing the free energy of the 1(T…T) state is to attenuate SF, and thus enhance photoluminescence. In Fig. 4a, we see that at fields as high as 210 mT, for the neat sample, the photoluminescence is enhanced by about 3.6% (ΔPL/PL). Furthermore, we see that at low fields, the photoluminescence is diminished, which is characteristic of chromophores that exhibit hindered rotational diffusion on the timescales of SF and TF47. This is less evident but persists in the 75% w/w sample. In the 50% w/w sample, both the effect of hindered rotation and the SF rate are diminished, giving rise to a smaller positive MFE at all fields. This is consistent with the results of the MD simulations, which showed that the mobilities were 104 times higher in the 50% w/w mixture than the neat liquid.Fig. 4: The MFE on photoluminescence of NODIPS-Tc.a, The effect of magnetic field (0–210 mT) on the integrated photoluminescence (PL) of NODIPS-Tc at three concentrations. b, The wavelength dependence of the MFE on the photoluminescence of NODIPS-Tc at 210 mT magnetic field. The vertical axis is expressed as the percentage photoluminescence change (ΔPL/PL). For comparison, the ratio of the TF spectrum from epoch 3 (σ3) to the steady-state (SS) spectrum (blue), we plot the ratio of σTT to the steady-state (green), the ratio of the excimer (1Ex) to the steady-state and the combination of σTT and σEx (red). The error bars represent the standard error from 20 individual measurements, errors arise due to small fluctuations in the laser diode power.The ΔPL/PL spectrum is shown in Fig. 4b. All samples exhibit peaks around 560 nm and 595 nm. Raising the free energy of the 1(T…T) state with a magnetic field should enhance the emission non-uniformly by initially returning a population to the 1(TT) state. Indeed, we would expect, as a first approximation, that the magnetic enhancement would be identical to the spectrum observed during epoch 3, where TF dominates. The ratio of the TF spectrum in epoch 3 to the steady-state spectrum is plotted in Fig. 4b (in blue). It exhibits the same shape as the ΔPL/PL spectrum. The population that returned to the S1 state by the action of the magnetic field can be expected to have an identical fate to photo-generated S1 chromophores, and thus the enhanced emission will be identical to the steady-state emission. Contributions to the ΔPL/PL spectrum from TF-generated S1 states will thus result in a featureless ΔPL/PL spectrum. Any spectral features can thus be attributed to excess 1Ex or 1(TT) states.The 1(TT)-associated spectrum σTT (Fig. 3d) is ratioed to the steady-state spectrum and plotted in Fig. 4b (in green). The ratio of the excimer spectrum to the steady-state spectrum is shown in black. Clearly, the peaks at 560 nm and 595 nm are reproduced by the 1(TT) spectrum. However, σTT cannot account for the excess emission in the red region, which must be due to excess excimer formation (compared with the steady-state spectrum). The TF spectrum exhibits a greater excimer contribution than observed in the ΔPL/PL spectrum. The differences suggest that the generation and recombination of geminate 1(T…T) pairs does not produce the same spectrum as TF from uncorrelated triplets. It may be hypothesized that the sites that are conducive to SF are those that are less susceptible to excimer formation than a randomly chosen chromophore pair. For instance, the nearest-neighbour sites identified in the MD simulations may act as SF sites that do not easily form excimers due to the hindered mutual rotation of the tetracene subunits. However, the parallel and anti-parallel pairs at longer distance may become engaged in TF through random hopping of triplet excitons and are geometrically predisposed to the formation of an excimer. These dimer geometries are depicted in Extended Data Fig. 2.MD simulations find that similar dimer geometries occur at 50% w/w in toluene. Figure 4b shows remnants of the spectral features attributed to the 1(TT) state, showing that the 1(TT) state is in evidence in concentrated solutions, but is displayed to a lesser extent. At 30%, there is no longer any evidence of this emission (Extended Data Fig. 6). Interestingly, at low magnetic fields corresponding to the dip in Fig. 4a, a spectrum showing negative 1(TT) features is observed (Extended Data Fig. 7).The shape of σTT is essentially that of a broadened and red-shifted S1 spectrum. The broadening can be attributed to a distribution of chromophore pair geometries, as predicted by the MD simulations (Supplementary Figs. 9–11). The energy of the 1(TT) state is estimated to be about 2.30 eV. Notwithstanding the triplet binding energy, this places the T1 state of the NODIPS-Tc chromophore at >1.15 eV, consistent with energy transfer experiments48. The energy of the excimer state was estimated from a van’t Hoff plot, shown in Extended Data Fig. 8. The S1 and 1(TT) emission is activated by 0.313(16) eV, placing the 1Ex state at 1.99 eV. The relative energies of these states are shown in Fig. 3b.The results in this work underscore the complexity of the excited states in the most studied SF chromophore (tetracene). In addition to unifying the debate regarding the fundamental photophysics of SF and TF in solids and solutions, our results have many implications for technologies that exploit SF and TF. First, multi-exciton logic and magnetic resonance imaging are underpinned by an understanding of spin evolution and is affected by the equilibrium in Fig. 3a. Second, the development of TF-based light-emitting diodes necessitates an understanding of all the emissive states in the system. Finally, magnetic field dependent measurements are often used to characterize SF-based solar cells5,49,50. These analyses usually assume that the magnetic field perturbs the equilibrium between (S0S1 and T1 + T1), mediated by the singlet character of the 1(T…T) pair. However, as shown in Fig. 4, this is an oversimplication, as it does not consider the interplay between these states and the coupled-pair 1(TT) and 1Ex states.
