Multiexciton quintet state populations in a rigid pyrene-bridged parallel tetracene dimer

Abstract

The multiexciton quintet state, ⁵TT, generated as a singlet fission intermediate in pairs of molecular chromophores, is a promising candidate as a qubit or qudit in future quantum information science schemes. In this work, we synthesize a pyrene-bridged parallel tetracene dimer, TPT, with an optimized interchromophore coupling strength to prevent the dissociation of ⁵TT to two decorrelated triplet (T₁) states, which would contaminate the spin-state mixture. Long-lived and strongly spin-polarized pure ⁵TT state population is observed via transient absorption spectroscopy and transient/pulsed electron paramagnetic resonance spectroscopy, and its lifetime is estimated to be >35 µs, with the dephasing time (T₂) for the ⁵TT-based qubit measured to be 726 ns at 10 K. Direct relaxation from ¹TT to the ground state does diminish the overall excited state population, but the exclusive ⁵TT population at large enough persistent density for pulsed echo determination of spin coherence time is consistent with recent theoretical models that predict such behavior for strict parallel chromophore alignment and large exchange coupling.

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Introduction

Singlet fission (SF) is a process in which the photoexcited singlet (S₁) transforms into two low-energy triplets (T₁), and it has been widely investigated to improve the photovoltaic conversion efficiency.^1–5 The singlet-coupled triplet pair, ¹TT, is a spin-entangled biexciton state that forms in every SF reaction via internal conversion from S₁. For the past decade or so, researchers have been focusing on generating maximum decorrelated T₁ through ¹TT for solar cell applications.^4,6 Here, in contrast, we prevent ¹TT from decaying to T₁ and drive the intersystem crossing from ¹TT to ⁵TT manifolds in a highly state-selective fashion for quantum information science (QIS) applications by designing and synthesizing a parallel rigid organic dimer. The SF-born ⁵TT manifold is regarded as a novel platform to make a quantum bit, or qubit, due to its strong spin polarization via optical excitation and the ability to perform fast quantum gate operations with microwave pulses.⁷ As an S = 2 manifold, it also has the potential to operate in a qudit scheme. Furthermore, results from time-resolved electron paramagnetic resonance spectroscopy (TREPR), and pulsed EPR in both monomer thin films^8–11 and organic dimers^12–16 have verified ⁵TT formation and laid the groundwork for understanding the spin evolution.

Considering the angular momentum coupling between the triplets in (TT) states, nine possible (TT) states can be constructed, including ¹TT (one spin sublevel), ³TT (three spin sublevels) and ⁵TT (five spin sublevels). The state selectivity from ¹TT to ⁵TT requires symmetry of the spin-exciton Hamiltonian, H = JS_A·S_B + H_A + H_B, where J represents isotropic exchange energy between the spin on each chromophore, and H_A,B are the anisotropic terms for dipolar interaction within chromophore A and B, The fine–structure interaction, governing the interconversion between the nine states, perturbs the spin-exciton Hamiltonian and makes the eigenstates of the Hamiltonian not ^2S+1TT_{M (−S≤M≤S)} states but the combination of them. However, under conditions of large J, these interactions are typically negligible. The parallel JDE model⁷ of the spin-exciton Hamiltonian assumes the two chromophores to be identical and parallel to share the same coordinate axis. Under these conditions, the conversion from ¹TT to ⁵TT while isolating ³TT is guaranteed by the Hamiltonian symmetry. Also, based on the parallel JDE model selection rules only the transition from ¹TT to ⁵TT₀ (m_s = 0) and ⁵TT_±2 (m_s = ±2) are allowed when the external magnetic axis and the molecular axis are aligned. Further, the relative kinetics of the ¹TT → ⁵TT₀ and ⁵TT_±2 transitions are proportional to the zero-field parameters D² and E², respectively, leaving the ⁵TT₀ pathway as dominant because D ≥ 3E by definition. All accessible dimer geometries must be included in this analysis, and for flexible systems, particularly about the bridge, significant conformational diversity can result. This motivates the use of both chromophore and bridge with limited flexibility to simplify the spin evolution pathways.

In this work, the rigid parallel organic dimer consists of two silylacetylene-substituted tetracene chromophores bridged with pyrene, TPT, and the structure can be seen in Fig. 2b. A similar dimer, APA, where two silylacetylene-substituted anthracenes are bridged with pyrene, has previously been characterized with UV-Vis and computational chemistry analysis.¹⁷ Electronic coupling between the two chromophores is weak, yet the interaction between the anthracenic moiety and the pyrene bridge is strong, making the S₁ energy of the chromophore to be between that of silylacetylene-substituted anthracene and tetracene. For TPT, the properties of the tetracene moiety can also be tuned by the pyrene bridge to mimic a combination of silylacetylene-substituted tetracene and pentacene. We will demonstrate that the mixed nature of the chromophore excited state facilitates the formation and preservation of ⁵TT. This stands in contrast to other flexible-bridged pentacenic dimer systems wherein independent triplets are the primary long-lived product (whether directly from ⁵TT or via intersystem crossing from ³TT), rather than ⁵TT as the surviving species.^13,14,18,19 Another rigid-bridged pentacene dimer was recently reported to almost exclusively form ⁵TT₀, but the apparent yield was low.¹² Our results reveal the first non-pentacene dimer to form a high yield of exclusively ⁵TT that persists to µs.

Results

Synthesis of TPT

Shown in Fig. 1 and S1,† the synthetic routes to TPT and PT involve intermediates 1 and 3, which have previously been reported.¹⁷ Reaction of 1 with 1,4-anthraquinone and KI yields the pyrenebis(tetracenequinone) 2. The addition of lithiated n-octyldiisopropylsilyl (NODIPS) acetylene followed by the addition of tin(II) chloride in aqueous HCl gives TPT. The synthesis of PT likewise consisted of the addition of 1,4-anthraquinone to 3 to yield pyrene-tetracenequinone 4, followed by addition of lithiated NODIPS-acetylene. Removal of Br from the diol intermediate 5 was initially attempted using a Pd catalyst at 100 °C, however these conditions resulted in apparent decomposition of the starting material and none of the target product was recovered. Debromination of 5 was ultimately achieved through metal–halogen exchange at low temperature, and subsequent addition of aq. HCl and tin(II) chloride to yield the aromatized product PT.

Fig. 1 Synthetic scheme for TPT.

Optical spectra and origin of transitions

Fig. 2a shows molar extinction spectra for PT and TPT. To the red, the vibronic peaks ranging from 500 nm to 625 nm are attributed to the short axis polarized S₁ ← S₀ transition of the tetracene moieties. The peak for the S₁ ← S₀ 0–0 vibronic transition of PT is centered at 603 nm, located in between that of TIPS-tetracene and TIPS-pentacene,^20,21 measured to be at 530 nm and 638 nm, respectively. The ∼70 nm redshift from TIPS-tetracene and ∼40 nm blueshift from TIPS-pentacene for PT (0.28 eV and 0.11 eV, respectively)²⁰ result from the limited extension of the acene system.¹⁷ Comparing PT and TPT, as seen in Fig. 2a, for the S₁ ← S₀ transition, TPT has extinction coefficient ∼2 times that of PT. The fact that the extinction coefficient of a dimer is 2 times of the monomer suggests that the TPT is in a weakly coupled regime in terms of the interaction between the two chromophore units. This is further substantiated by the only ∼2 nm redshift for 0–0 transition from PT to TPT. Furthermore, the ratio of 0–0 to 0–1 absorption/emission intensity (I_0–1/I_0–0) for TPT and PT are both ∼1.4 as can be seen in Fig. S7.† However, for the long-axis S₃ ← S₀ transition of the chromophores around 315 nm, the extinction coefficient of TPT is less than two times of PT, suggesting some perturbation of higher-lying excited states. The extinction coefficient of the expected pyrene peaks in TPT is enhanced by roughly 5 times from the pyrene itself and from PT.

Fig. 2 Molar extinction spectra for both PT (blue line) and TPT (red line) in toluene. The molar extinction spectrum for pyrene in cyclohexane is in yellow.

The vibronic peaks for PT and TPT within the 350 nm to 425 nm window, as indicated by TDDFT calculations, originate from a singlet excitation with contributions from both pyrene and tetracene segments. In PT, this excitation has two similarly weighted natural transition orbital (NTO) pairs that, as shown in Fig. S5a,† resemble tetracene HOMO → pyrene LUMO and pyrene HOMO → tetracene LUMO, respectively. As a result, the net charge transfer from pyrene to tetracene, compared to charge redistribution within these fragments, is negligible. This is confirmed by the two-fragment charge transfer matrix (Fig. S5b†) in which off-diagonal (diagonal) elements represent inter-fragment charge transfer (charge redistribution). The transition densities of this excitation are shown in Fig. S5c† with a transition dipole moment of 3.82 a.u. polarized along the long-axis (the directions along which the transition density switches its sign). This is in contrast to the vibronic peaks from 500 nm to 625 nm (S₁ ← S₀) that result from the local excitation of tetracene with a transition dipole moment polarized along the short-axis.¹⁵

Similar to PT, the excitation responsible for vibronic peaks from 350 nm to 425 nm in TPT is polarized along the long axis (Fig. S5f†). The NTOs (Fig. S5d†) also largely resemble frontier molecular orbitals of pyrene and tetracene, featuring bidirectional charge transfer from the pyrene segment to both tetracene segments. This is corroborated by the three-fragment charge transfer matrix (Fig. S5e†) in which one-direction charge transfer contributions between pyrene and tetracene fragments largely cancel each other, resulting in a small net charge transfer from pyrene to tetracene fragments. The addition of another tetracene segment leads to an increased transition dipole moment of 7.80 a.u. for this excitation, approximately double of that in PT. This is in good agreement with the experimentally observed extinction coefficient ratio (4 : 1) between TPT and PT.

The associated peaks for pyrene in cyclohexane²² are measured to be from 300 nm to 350 nm. The peak centered ∼315 nm for PT and TPT corresponds to the S₃ ← S₀ transition of the tetracene moieties. NTOs of this excitation of PT are shown in Fig. S6a.† The two equally weighted NTO pairs resemble pentacene HOMO−2 → pentacene LUMO and pentacene HOMO → pentacene LUMO+2, respectively, as the extension of the acene system with the pyrene bridge mimics a pentacene unit. This is primarily a local excitation at the acene fragment, as indicated by the large diagonal element in its fragment charge transfer matrix (Fig. S6b†), with moderate bidirectional charge transfer yielding a small net charge transfer from tetracene to pyrene. Fig. S6c† shows the transition densities with a dipole moment of 4.45 a.u. along the long axis. Both NTOs and transition densities are similar to that of the ¹B_b state of pentacene.²³

The situation is more complicated for TPT. As shown in Fig. S6d,† another NTO pair (the third one), resembling pyrene HOMO → tetracene LUMO, appears with non-negligible contributions. Similar contributions were made to the hole and electron densities from the three fragments, leading to small differences among elements in the fragment charge transfer matrix (Fig.S6e†). Unlike the case in the previous section, where transition densities of TPT are roughly that of PT duplicated by a mirror plane along the 2, 7 positions of pyrene, transition densities of this excitation (Fig. S6f†) cannot be produced as such, likely due to the aforementioned additional NTO pair. The transition dipole moment is calculated to be 4.20 a.u. which is similar to that of PT, agreeing with the similar extinction coefficients for PT and TPT observed experimentally.

Davydov splitting, caused by interchromophore interaction of transition dipoles in a singlet fission dimer, should also be mentioned, especially for the rigidly bridged dimer. Davydov splitting for both S₁ ← S₀ and S₃ ← S₀ transitions have been observed from both norbornyl-bridged tetracene and pentacene dimers.^20,21 For TPT, the two tetracene chromophores are held firmly at 180° from each other to form a planar dimer. Due to the flat structure of the molecule and the parallel nature of the two tetracene chromophores, the Davydov splitting for long-axis (S₃ ← S₀) and short-axis (S₁ ← S₀) transitions are not observed in Fig. 2a.

Photoluminescence

In Fig. S7 and S8,† S₀ ← S₁ 0–0 emission peaks for TPT and PT are found to be 2.04 eV and 2.05 eV, respectively. Similar S₁ energies for dimer and monomer suggests minimal electronic delocalization between the two tetracenic chromophores for TPT. However, the emission quantum yield Φ_emifor TPT is significantly smaller than PT, measured to be 6% and 100%, respectively. Photoluminescence kinetics for PT, obtained via time-correlated single photon counting (TCSPC), are displayed in Fig. S9b.† The relationship between Φ_emi and the kinetics of S₁ can be described with the formula: where k_r and k_nr represent radiative and nonradiative S₁ decay coefficient, respectively. We obtain 1/k_r to be 23 ± 0.02 ns from fitting the TCSPC measurement to a single exponential decay under conditions where Φ_emi is 100%. We show that 1/(k_r + k_nr) is 22.6 ± 0.2 ns from TA (vida infra) in Fig. S10a and b,† consistent with the measured Φ_emi of 100%. For TCSPC traces of TPT, shown in Fig. S9c and d,† we can see an early decay from the fast fission process and a slow decay with a lifetime fitted to be 21.2 ± 0.02 ns, which is similar to the S₁ lifetime from PT (Fig. S9a and b†). We assign the low emission quantum yield of TPT as due to the efficient singlet fission process, which will be verified below.

Femtosecond transient absorption (fsTA). TPT is excited by a ∼100 fs optical pulse centered at 600 nm, where the S₁ ← S₀ 0–0 transition is located. As shown in Fig. 3a, the transient absorption spectrum evolves from the earliest species (S₁, delay time = 1 ps in blue) to the later species (putative ¹TT, delay time = 5388 ps in red) in 2-MeTHF at room temperature. An excited state absorption (ESA) feature of the S₁ state (blue) rises immediately upon excitation from S₀ to S₁, and it appears in both visible (VIS) and near-IR (NIR) regions. In the VIS region, S₁ ESA consists of a broad band from 430 nm to 550 nm with relatively sharp peaks at 462 nm and 539 nm, corresponding to the S_n ← S₁ transition. A dip centered at 560 nm is associated with the ground state bleach (S₀ ← S₁). The other band centered at 648 nm from 600 nm to 800 nm is assignable to a S₅ ← S₁ transition. In the NIR region, a weak band from 900 nm to 1000 nm is from the S₄ ← S₁ transition, and a larger peak centered at 1345 nm is attributed to the S₃ ← S₁ transition.²⁴ The decay of the S₁ features can be seen in Fig. 3b. At 460 nm, the S₁ state decays to an offset within ∼ 10 ps, and kinetics at both 646 nm and 1339 nm show a similar decay as at 460 nm, suggesting they all originate from the S₁ state. While the S₁ state decays, it evolves to ¹TT, and two isosbestic points at 478 nm and 553 nm indicate direct conversion between these species. In the visible region, a characteristic triplet ESA with a main peak at 539 nm and a shoulder peak at 502 nm appears, which we relate to TT_n ← TT₁. A kinetically correlated band between 600 nm and 800 nm can also be assigned to the TT_n ← TT₁ transition, and another relatively sharp triplet peak centered at 974 nm is found that has been previously verified as a signature of the triplet state.²⁵ As depicted in Fig. 3b, the decay of the S₁ state gives rise to the ¹TT state completely within about 10 ps, which can be most clearly followed as a rise at 540 nm. The biexciton formation time is extracted from the global fit of the biexponential function to be 4.5 ± 0.02 ps. In contrast, no triplet-like features are found in TA for PT, Fig. S10.†

Fig. 3 (a) Spectra at selected delay times for fsTA of TPT in 2-MeTHF at room temperature. Dots represent the raw data, and the solid lines represent the fit. (Inset) Spectra in visible region only. (b) Kinetic traces at selected wavelengths from (a). (c) Spectra at selected delay times for nsTA of TPT in 2-MeTHF at room temperature. (Inset) Spectra in visible region only. (d) Kinetic traces at selected wavelengths from (c).

Applying the (A → B → 0) model based on the biexponential fitting result, we determined the species associated spectra (SAS) for S₁ and ¹TT, which can be seen in Fig. S11.† The S₁ ESA from TPT shows a similar spectral shape compared to the S₁ ESA from PT. In Fig. S11a† the redshift from S₁(TPT) to S₁(PT) at ∼465 nm and ∼1350 nm is apparent, suggesting S_n delocalization is facilitated by the bridge, to be discussed further below. Turning to the triplet, the spectral shape of the ¹TT ESA features approximately aligns with those of the T₁ measured through anthracene sensitization, as shown in Fig. S11b and S15.† However, a blueshift in the visible peak and a redshift in the NIR region (974 nm → 987 nm) is apparent from ¹TT to T₁.

At 77 K, the biexciton formation time increases to 8.3 ± 0.1 ps (Fig. S12†). The spectral shape of the triplet shows only a minor redshift at 77 K compared to room temperature, shown in Fig. 4a. The slowing of the fission process at 77 K suggests that singlet fission of TPT is thermally activated; selected kinetic traces for both temperatures in VIS and NIR regions are shown in Fig. S13a and b.† As a thermally activated yet reversible singlet fission process, the equilibrium between S₁ and ¹TT is also temperature dependent. The S₁ ESA remaining on ns timescales in the normalized fsTA time trace at room temperature and at 77 K (1345 nm and 1356 nm in Fig. 3b and S12b,† respectively) are measured to be ∼0.065 and ∼0.042, respectively, which are the signal portions relative to maximum S₁ signal at early times. The 6.5% remaining S₁ ESA amplitude is consistent with the emission quantum yield measurement mentioned above (∼6%).

Fig. 4 (a) Normalized ¹TT spectra at different temperatures. (b) Arrhenius plot for the ¹TT decay rate coefficient at two different concentrations.

Nanosecond transient absorption (nsTA). In Fig. 3c and d, we show the remaining species after 5 ns, ¹TT, which decays on a ns–µs timescale at room temperature. However, ¹TT does not decay completely to S₀ – a small but non-negligible offset remains in the visible region at later time. Considering the long-lasting unknown species, fitting the nsTA spectra with a single exponential function is not sufficient. Here, we fit the nsTA data globally with a bi-exponential function, to represent both ¹TT and the other species initially labeled X. In Fig. 3c, the characteristic triplet peak at 540 nm and the shoulder at 502 nm decay to the long-lasting X, with peaks at ∼520 nm and a shoulder at ∼556 nm. τ_1TT obtained from the global fit is 197.4 ± 1.5 ns. However, τ_X from the fit is inaccurate due to the relatively small signal, which is <5% of ¹TT. Therefore, we report only the lower limit of τ_X to be ∼35 µs. While a lower limit, the lifetime is markedly below that determined for T₁ using sensitization experiments where we observe >150 µs. At 77 K, the ¹TT ESA shows similar spectral features as the ESA in room temperature, except with a ∼10 nm redshift. The X ESA observed at room temperature can also be seen in the later time at 77 K in Fig. S12c.† Therefore, we again fit the nsTA at 77 K with the bi-exponential function. The τ_1TT extracted from the global fit is 286.2 ± 5.3 ns, which is longer than 197 ns measured at room temperature.

We now turn to the temperature dependent kinetics of ¹TT and X based on the biexponential fit introduced above. From the global fit of nsTA, we normalize the ESA of ¹TT to the maximum of the triplet peak, which is shown in Fig. 4a. The triplet feature redshifts by 10 nm from 296 K to 77 K. Fig. 4b is the Arrhenius plot for the decay rate coefficient of ¹TT, 1/τ_1TT, measured at two different concentrations: 2.2 µM and 22 µM. The agreement between τ_1TT and the nearly constant spectral shapes at the two concentrations (cf., Fig. S17 and S18† for concentration and temperature dependence) indicates that the environment for molecules in the solutions is similar, and that aggregation is not playing a significant role in the photophysics. However, the data from 130 K to 77 K show a stark change in slope compared with temperatures higher than 130 K, indicating a violation of the expected Arrhenius trend. The change occurs very near the glass transition of 2-MeTHF at ∼137 K. Despite this abrupt change in temperature-dependent decay kinetics of ¹TT, the spectral amplitude of the long-lived X does not show much temperature dependence from 77 K to 296 K, as seen in Fig. S14b.†

Electron paramagnetic resonance (EPR). We directly measured the spin-active species via TREPR upon exciting the frozen TPT/2-MeTHF solution with a pulse centered at 600 nm as shown in Fig. 5. In Fig. 5a, the X-band EPR signal ranges from 280 mT to 380 mT, and it shows a spin polarization pattern of aeaae. The triplet EPR spectrum obtained by optically exciting PT in heavy-atom solvent at 76 K is shown in Fig. S16.† There the separation between the emissive and absorption peaks suggests D, the zero-field splitting parameter, to be 1260 MHz. In Fig. 5a, the separation between the inner peaks at 325 mT and 340 mT is 420 MHz, which is D/3, indicating the two peaks represents transitions between m_s = ±1 and m_s = 0 in ⁵TT.¹¹ There are outer peaks at ∼310 mT and ∼355 mT, and the split is equal to D. Thus, these peaks could be related to the transitions between m_s = ±1 and m_s = 0 in the T₁ manifold or transitions between m_s = ±2 and m_s = ±1 in the ⁵TT manifold. To rule out the possibility of aggregate induced EPR signals, we measure EPR spectra at 76 K for a concentrated solution of PT in 2-MeTHF (220 µM), and compare these to data collected for TPT under the same experimental conditions but at a lower (66 µM) concentration (Fig. S17a and b†). In Fig. S17a,† the ⁵TT signal generated in PT/2-MeTHF can only arise from aggregation (because there is only one tetracene chromophore to harbor a triplet), and the EPR signal intensity is <10% of the TPT/2-MeTHF sample. In addition to the small intensity, the ⁵TT spectral shape for PT/2-MeTHF is distinct from that of TPT/2-MeTHF. A factor of 6 reduction in the TPT concentration was also introduced and found to produce no significant perturbation to the EPR signals (Fig. S17c†). The lack of significant change to the steady-state absorption of TPT at low temperature (Fig. S17c†) further substantiates that the EPR signal in Fig. 5 originates from singlet fission of an ensemble of isolated TPT and contains little influence from aggregation.

Fig. 5 (a) Normalized TREPR 2D plot for TPT in 2-MeTHF at 77 K. (b) Normalized EPR spectra from (a) at the selected delay times.

To support our assignment for the EPR signal mentioned above, pulsed EPR experiments were conducted on TPT in 2-MeTHF at 10 K. Transient nutation traces were obtained with the pulse sequence shown in Fig. 6a at both 308 mT and 338 mT, and the data are shown in Fig. 6c. The Fourier transformed results (Fig. 6d) indicate extracted frequencies that are centered at 32.5 MHz and 40 MHz for the 308 mT and 338 mT nutation experiments, respectively. The ratio of these frequencies (0.81 : 1) is a close match to the ratio (i.e., 0.816 : 1). Based on the equation where B₁ is the microwave field strength and m_s represents spin quantum number, the EPR signal at 308 mT can be assigned to a transition between m_s = ±2 and m_s = ±1, while the signal at 338 mT is associated with the transition between m_s = ±1 and m_s = 0, all within the ⁵TT manifold.

Fig. 6 (a) Pulse sequence for the transient nutation measurement, where T is 300 ns, τ is 148 ns, the π/2 pulse is 6 ns, π pulse is 12 ns, and the delay after flash (DAF) is t₀ + dt, where dt = 30 ns. (b) Pulse sequence for the T₂ measurement. (c) The nutation traces at 308 mT and 338 mT for TPT in 2-MeTHF at 10 K. (d) Fourier transformed data from (c). (e) Net spin magnetization decay trace at 338 mT for TPT in 2-MeTHF at 10 K using the pulse sequence in (b).

To measure the spin dephasing lifetime (T₂), we operate on the spin states corresponding to the EPR signal at 338 mT with the Hahn echo pulse sequence shown in Fig. 6a. The transient net spin magnetization decay trace is displayed in Fig. 6d, obtained by modifying the relaxation time between the pulse, π pulse, and the echo. The decay trace is fit with a single exponential function leading to a determination of T₂ = 726 ns at 10 K.

Discussion

Despite evidence of some spectral shifts and transition dipole enhancement for the electronic transitions involving the pyrene bridge caused by interaction with the tetracenic chromophores, the overall picture still implicates weak coupling in the TPT dimer. Interaction between the tetracene and pyrene could be large, yet the coupling between the two tetracene chromophores through the pyrene bridge is relatively low based on the only weakly perturbed S₁ ← S₀ transition. Upon excitation from S₀ to S₁, TT is formed with a risetime of 4.5 ps at room temperature and 9.3 ps at 77 K. Due to the fast observed rate, internal conversion from S₁ to ¹TT is the most likely reaction pathway.²⁶ The temperature dependence suggests that singlet fission of TPT is a thermally activated process, which could in principle be an indication of a slightly endothermic energy balance between S₁ and ¹TT. However, the apparent equilibrium between S₁ and ¹TT, which has been observed in tetracenic systems,^{20,25,27–29} strongly favors ¹TT in TPT, suggesting instead the overall reaction is exoergic. Because we observe no other species besides S₁ and ¹TT on the ns timescale, the equilibrium indicates that the singlet fission yield is about 94%, as the S₁ emission quantum yield is measured to be 6%. The singlet fission yield for pentacene dimers in most cases is close to 100%,^{13,14,20,30–39} and is typically higher than tetracene dimers, which is lower than 50% in general.^16,20,40,41 For tetracene dimers bridged with a norbonyl ring studied by Gilligan et al.,²⁰ TIPS-BT1 and TIPS-BT1′, an equilibrium constant between S₁ and ¹TT was found to be 0.1 and 1, respectively. The small equilibrium constant of the tetracene dimers is due to the similar energetics of S₁ and ¹TT. On the other hand, the pentacene dimer, TIPS-BP1, has an equilibrium constant of 10²–10⁵ and the emission quantum yield is <0.01, indicating strong exothermicity from S₁ to ¹TT. From this perspective, TPT behaves closer to pentacene than tetracene, commensurate with its S₀–S₁ energy red-shift.

Given the slight exothermicity, the relatively fast fission rate for TPT compared with other weakly coupled tetracenes is not surprising. The rate falls below that of the fastest pentacene dimer systems with sub-ps singlet fission rates, and in those cases strong electronic coupling between chromophores can be implicated for accelerating the rate. In TPT however, the bridge does not evidently lead to strong chromophore–chromophore coupling, as judged by the unperturbed and only slightly shifted S₁ ← S₀ absorption bands. Only higher-lying absorption bands show evidence of mixed-state behavior involving charge redistribution, but these are not directly excited nor involved in singlet fission during our measurements. Nevertheless, models of singlet fission originally developed by Ratner, Michl, et al.⁴² clearly show a role for virtual CT states in the SF process through the mediated mechanism. Modulating the importance of CT state involvement using solvent polarizability or polarity could be insightful, although here poor solubility in many solvents prevents a systematic study.

Now we turn to the eventual fate of ¹TT. From nsTA data, the decay lifetimes of ¹TT are 197 ns and 276 ns at 296 K and 77 K, respectively, indicating the decay of the ¹TT state is also a thermally activated process. One of the decay pathways for ¹TT is internal conversion to S₀, which can be seen from the dominant ground state bleach recovery on the ns timescale (Fig. 3d at 560 nm and Fig. S12d† at 568 nm, yellow traces). The other decay pathway could be from ¹TT to ⁵TT, and we suggest here that nsTA data are consistent with the EPR data in this regard. In addition to the distinct ⁵TT peak pattern with primary separation of D/3, the TREPR signals are further characterized to be from the pure ⁵TT state using nutation frequencies from pulsed EPR at 10 K (Fig. 6). Importantly, these data lack any clear contribution from T₁. This then suggests that the longer-lived species identified in nsTA experiments – what was referred to earlier as species X – is due to ⁵TT. Because we can now verify the long-lived species common to EPR and TA is ⁵TT, we suggest that ⁵TT has unique spectral features compared with ¹TT, which can be seen in Fig. S14a.† Distinct ESA features for ¹TT and ⁵TT were also observed by Pace et al.⁴³ A more definitive method for connecting ⁵TT photoinduced absorption and spin signatures involving optically detected magnetic resonance^44,45 is planned.

To gain a full kinetic picture, kinetic simulations are performed based on the scheme shown in Fig. 7. Comparison of the relative state populations as a function of time are shown in Fig. S21.† The long-lived ⁵TT appears in nsTA throughout the temperature range with no obvious temperature dependence. For ¹TT, we assume that the competing pathways (¹TT → S₀, ¹TT →⁵TT) could both play some role in dictating the temperature dependence of TT deactivation. One possible mechanism for reduced ¹TT → S₀ decay at low temperature involves the constraint of the solvent environment that severely restricts the molecular motion of TPT upon freezing, decelerating relaxation from the ¹TT state to the S₀ state. The exact dynamics involved in the transition is unclear, as is the role that the aforementioned CT states might play, but the lower polarizability of the frozen solution may modulate their involvement. While ¹TT → S₀ is delayed as the solvent is gradually frozen to solid, ¹TT → ⁵TT may also be slowed. The exact mechanism responsible here is again unknown, but it may be that large J fluctuations required to promote the transition⁷ and caused by thermally induced motions are suppressed, reducing the observed rate of ¹TT → ⁵TT population flow.

Fig. 7 (a) The kinetic scheme for TPT in 2-MeTHF upon excitation centered at 600 nm. (b) Resulting rate coefficients from a fit of the kinetic scheme to TA data. k_fiss was determined from fsTA data, and k_5TT was given an upper bound based on estimated decay on a µs timescale. Φ_emi was fixed based on fluorescence quantum yield. k_SQ and k_1TT were varied in the fit of nsTA to match the ¹TT and ⁵TT populations. Further details of the fit are in the ESI.†

Despite the coincidence of long-lived signals assignable to ⁵TT in TA and EPR, there is a lifetime mismatch between the long-living ESA from nsTA (τ > 35 µs) and the ⁵TT signal from TREPR that decays in ∼3 µs. The EPR signal arises from spin polarization, proportional to the population difference between the magnetic spin states.⁴⁶ Consequently, the decay of the EPR signal does not signify the disappearance of population from the state, but instead the decrease of the population difference between the corresponding states. Namely, although the ⁵TT signal from TREPR decays in ∼3 µs due to spin-lattice relaxation, the ⁵TT population lifetime can still be much longer. We fit the kinetic trace for TREPR spectra at 338 mT with a set of ordinary differential equations based on the scheme in Fig. S19c.† The normalized population for ¹TT and ⁵TT states is shown in Fig. S19a.† The population difference between ⁵TT(0) and ⁵TT(1), representing the spin polarization between the two states, follows the kinetic trace for TREPR spectra at 338 mT, including the sign flipping at ∼2500 ns. Furthermore, the fitted lifetimes of ¹TT and ⁵TT roughly correlate with the lifetimes obtained from nsTA. From the ODE fit, τ₁₁, τ₁₀, τ_SLR, τ₁, and τ₀ are 106.6 ns, 446.3 ns, 2 µs, 19.1 µs, and 38.4 µs, respectively. From nsTA, τ_1TT is 276 ns (similar to the average of τ₁₁ and τ₁₀, the two ¹TT decay pathways), and τ_5TT is >35 µs, consistent with the average of τ₁ and τ₀, the ⁵TT decay pathways from different spin sublevels.

As for the EPR spectral shape of the ⁵TT state, according to the literature,^7,12 it depends on the molecular geometry and the alignment between molecular axis and magnetic axis. For the organic dimers with the two chromophores aligned in parallel as in TPT, the population within the ⁵TT state should be symmetric regarding m_s = 0, that is, P(m_s = −1) = P(m_s = 1) and P(m_s = −2) = P(m_s = 2), where P represents population. Because of the symmetric population distribution for the ⁵TT manifold, the arrangement of features in the EPR spectrum should be approximately symmetric, accordingly. However, in Fig. 5, the spectrum throughout the magnetic field range is mostly positive and is asymmetric with respect to B₀ (334 mT). Absorptive spin polarization for ⁵TT has been observed^10,14–16 and discussed in other systems. The transition from ¹TT to ⁵TT is mediated by the fluctuation of exchange energy, in films or aggregates caused by triplet migration. This process is discussed by Kobori et al.^10,47 in disordered TIPS-pentacene thin films and aggregated TIPS-pentacene solutions. In their chemically induced dynamic electron polarization (CIDEP) model, SQ₀ mixing takes place when the coupling of the triplet pair is weakened via triplet migration. Meanwhile, SQ₋₂ and SQ₋₁ become populated via level crossing at the corresponding distances between the triplet pair, and through zero-field splitting, population is trapped in ⁵TT₀, ⁵TT₋₂, and ⁵TT₋₁, resulting in absorptive spin polarization of ⁵TT. No triplet migration is possible in TPT, nor are large-scale nuclear motions, so we disfavor this mechanism. Instead, we suggest that large and rare fluctuations in J produce ⁵TT populations. We compare TPT behavior with predictions for planar but flexible pentacene dimers studied by MacDonald et al.,⁴⁸ who interpret net-absorptive quintet peaks in CW EPR and symmetric ⁵TT spectra in pulsed-EPR to arise from SQ-mixing (i.e., low J, fast decoherence)⁴⁹ and stochastic processes (high J, slower decoherence),⁵⁰ respectively. These regimes may be simultaneously available in their ensemble due to conformational flexibility, absent in TPT. The fact that cw-EPR and echo-detected X-band spectra for TPT roughly match (Fig. 5b and S20a,† both are net-absorptive with similar shapes), confirms that quintets are not likely forming via low-J SQ mixing because such net-absorptive quintets should be strongly suppressed by the echo detection process. Therefore, net-absorptive X-band spectra seemingly arise in the stochastic regime due to asymmetrically-populated quintets not subject to fast decoherence, whereas the population becomes more symmetric at Q-band (Fig. S20b†). This type of field-dependent mechanism requires further theoretical investigation, and we note that the full collection of cw- and pulsed-EPR at different field strengths are needed to develop a complete picture.⁵¹

One of the primary goals for QIS applications with the ⁵TT state is to increase the dephasing time, T₂, and the population of purely spin-polarized ⁵TT sublevels. In this study, abundant ⁵TT is produced such that the ⁵TT state can be monitored by both nsTA and EPR. Higher ⁵TT yield has been reported in monomer thin films^8–10,43,51 or weakly coupled dimers,^{13–16,18,19} but it inevitably comes with isolated T₁ because the interchromophore interaction can become weak enough to enable the spin mixing and decorrelation process to T₁.^14,19 The ¹TT decay pathways for these cases are proposed to be ¹TT → ⁵TT ⇌ T₁ + T₁ or through intersystem crossing from ⁵TT to ³TT, generating T₁ in two steps. However, TPT is an example of a weakly coupled dimer from the pure electronic coupling standpoint (and as judged by steady-state spectroscopy), where there is no evidence for isolated triplets generated through ⁵TT. The features that could give rise to this behavior are the rigid bridge, the co-planar orientation, and the near-resonance of mixed chromophore-bridge electronic states. The outcome of these characteristics is an unusually large J at the equilibrium geometry, which is one of the keys to generate spin-polarized ⁵TT without coexistence of T₁, stated in the parallel JDE model.⁷ For the weakly coupled dimers and the monomer thin films that generate T₁, J is estimated to be <100 GHz,^{10,13,15,16,43,51} and sometimes close to 0 GHz, indicating the energies of ¹TT, ⁵TT and 2*T₁ are about the same. For TPT, from broken symmetry DFT calculation as described in detail in the ESI,†J is calculated to be −512 GHz, where the absolute value is higher than the weakly coupled chromophores mentioned above, and the negative sign suggests ⁵TT to be lower in energy than ¹TT. We thus hypothesize that the exchange energy of TPT is strong enough to slow the formation of uncorrelated T₁, given that there are limited intramolecular degrees of freedom available to promote the ⁵TT → (T₁ + T₁) transition, unlike dimers with flexible bridges.

The dephasing time, T₂, of the ⁵TT manifolds is measured to be 726 ns, and it is long enough for us to demonstrate more than 4 Rabi oscillating cycles with the pulsed microwave setting mentioned previously. At 338 mT, for example, the EPR signal corresponds to the transition between m_s = 0 and m_s = 1 in ⁵TT, and with pulsed microwaves, we can rotate the population between the two magnetic spin states, therefore demonstrating this two-level system as a qubit.

Conclusion

We design a parallel pyrene-bridged tetracene dimer, TPT, with coupled triplet spins for purposes of demonstrating pure spin polarization production relevant to QIS applications. Excited states are calculated to involve both tetracene and pyrene, yet the lowest singlet transitions are only weakly perturbed from the PT to TPT, suggesting minimal interchromophore communication across the bridge. The interaction between tetracene chromophores is optimized to allow the singlet-quintet mixing and trap the population in the ⁵TT state while preventing the production of T₁. We have observed ⁵TT with optical transient absorption spectra, which is rarely reported, through kinetic and temperature-dependent measurements that correlate with observations of ⁵TT using EPR. We characterize the qubits in ⁵TT manifolds with TREPR and pulsed EPR, and the dephasing time approaches the µs timescale. The pure ⁵TT state produced in large population is a highlight of this work; however, to generate high-quality qubits for QIS applications, we not only need a large population solely in the ⁵TT state, but also pure spin-polarized ⁵TT state. Toward this end, we suggest aiming future efforts to align all TPT dimers with their principal magnetic axis along an applied magnetic field direction.

Data availability

Crystallographic data for TPT has been deposited at the Cambridge Structural Database under deposition number 2299672. TDDFT log files have been uploaded as part of the ESI.†

Author contributions

LL performed all spectroscopic experiments and analysis, supervised by JCJ and NHD, and wrote the experimental portions of the manuscript. JCJ assisted with spectroscopic experiments and advised on the data analysis and manuscript writing with NHD. JEA designed the target molecules and the experimental approach, and JEA and TS devised the appropriate chromophores for singlet fission studies. TS performed and optimized the synthesis and conducted appropriate structural characterization. QA contributed conceptualization and investigation of calculation methodology and wrote portions of the manuscript. CR supervised and conceptualized computational efforts and contributed to reviewing and editing the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Work on transient absorption and time-resolved electron paramagnetic resonance spectroscopy was supported by the Solar Photochemistry Program of the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Biosciences, and Geosciences. We acknowledge funding for steady-state spectroscopy and aggregation studies from the National Science Foundation (CHE-2102713). Q. A. and C. R. acknowledge funding from the National Science Foundation through the Designing Materials to Revolutionize and Engineer our Future (NSF DMREF) program under award number DMR 1627428, and thank the University of Kentucky Center for Computational Sciences and Information Technology Services Research Computing for their fantastic support and collaboration and use of the Lipscomb Compute Cluster and associated research computing resources. We thank Sean Parkin, University of Kentucky X-ray crystallography facility, for obtaining the TPT crystal structure. This work was authored by Alliance for Sustainable Energy, Limited Liability Company, the manager and operator of the National Renewable Energy Laboratory under Contract No. DE-AC36-08GO28308. The views expressed in the article do not necessarily represent the views of the Department of Energy or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid‐up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes.

References

1. M. J. Y. Tayebjee, D. R. McCamey and T. W. Schmidt, Beyond Shockley–Queisser: Molecular Approaches to High-Efficiency Photovoltaics, J. Phys. Chem. Lett., 2015, 6, 2367–2378.
2. M. B. Smith and J. Michl, Recent Advances in Singlet Fission, Annu. Rev. Phys. Chem., 2013, 64, 361–386.
3. M. B. Smith and J. Michl, Singlet Fission, Chem. Rev., 2010, 110, 6891–6936.
4. M. C. Hanna and A. J. Nozik, Solar conversion efficiency of photovoltaic and photoelectrolysis cells with carrier multiplication absorbers, J. Appl. Phys., 2006, 100, 074510.
5. M. J. Y. Tayebjee, A. A. Gray-Weale and T. W. Schmidt, Thermodynamic Limit of Exciton Fission Solar Cell Efficiency, J. Phys. Chem. Lett., 2012, 3, 2749–2754.
6. I. Paci, et al. , Singlet Fission for Dye-Sensitized Solar Cells: Can a Suitable Sensitizer Be Found?, J. Am. Chem. Soc., 2006, 128, 16546–16553.
7. K. E. Smyser and J. D. Eaves, Singlet fission for quantum information and quantum computing: the parallel JDE model, Sci. Rep., 2020, 10, 18480.
8. D. Lubert-Perquel, et al. , Identifying triplet pathways in dilute pentacene films, Nat. Commun., 2018, 9, 4222.
9. R. D. Pensack, et al. , Observation of Two Triplet-Pair Intermediates in Singlet Exciton Fission, J. Phys. Chem. Lett., 2016, 7, 2370–2375.
10. H. Nagashima, et al. , Singlet-Fission-Born Quintet State: Sublevel Selections and Trapping by Multiexciton Thermodynamics, J. Phys. Chem. Lett., 2018, 9, 5855–5861.
11. L. R. Weiss, et al. , Strongly exchange-coupled triplet pairs in an organic semiconductor, Nat. Phys., 2017, 13, 176–181.
12. R. D. Dill, K. E. Smyser, N. H. Damrauer and J. D. Eaves Entangled, Spin-polarized Excitons from Singlet Fission in a Rigid Dimer, Nat. Commun., 2023, 14, 1180.
13. M. J. Y. Tayebjee, et al. , Quintet multiexciton dynamics in singlet fission, Nat. Phys., 2017, 13, 182–188.
14. B. S. Basel, et al. , Unified model for singlet fission within a non-conjugated covalent pentacene dimer, Nat. Commun., 2017, 8, 15171.
15. S. Nakamura, et al. , Synergetic Role of Conformational Flexibility and Electronic Coupling for Quantitative Intramolecular Singlet Fission, J. Phys. Chem. C, 2021, 125, 18287–18296.
16. Y. Matsui, et al. , Exergonic Intramolecular Singlet Fission of an Adamantane-Linked Tetracene Dyad via Twin Quintet Multiexcitons, J. Phys. Chem. C, 2019, 123, 18813–18823.
17. Q. Ai, et al. , Nanoribbons or weakly connected acenes? The influence of pyrene insertion on linearly extended ring systems, J. Mater. Chem. C, 2021, 9, 16929–16934.
18. B. S. Basel, et al. , Evidence for Charge-Transfer Mediation in the Primary Events of Singlet Fission in a Weakly Coupled Pentacene Dimer, Chem, 2018, 4, 1092–1111.
19. A. B. Pun, et al. , Ultra-fast intramolecular singlet fission to persistent multiexcitons by molecular design, Nat. Chem., 2019, 11, 821–828.
20. A. T. Gilligan, E. G. Miller, T. Sammakia and N. H. Damrauer, Using Structurally Well-Defined Norbornyl-Bridged Acene Dimers to Map a Mechanistic Landscape for Correlated Triplet Formation in Singlet Fission, J. Am. Chem. Soc., 2019, 141, 5961–5971.
21. J. D. Cook, T. J. Carey and N. H. Damrauer, Solution-Phase Singlet Fission in a Structurally Well-Defined Norbornyl-Bridged Tetracene Dimer, J. Phys. Chem. A, 2016, 120, 4473–4481.
22. H. Du, R. A. Fuh, J. Li, L. A. Corkan and J. S. Lindsey, PhotochemCAD++: A Computer-Aided Design and Research Tool in Photochemsitry, Photochem. Photobiol., 1998, 62, 141–142.
23. H. F. Bettinger, C. Tönshoff, M. Doerr and E. Sanchez-Garcia, Electronically Excited States of Higher Acenes up to Nonacene: A Density Functional Theory/Multireference Configuration Interaction Study, J. Chem. Theory Comput., 2016, 12, 305–312.
24. J. C. Dean, et al. , Photophysical characterization and time-resolved spectroscopy of a anthradithiophene dimer: exploring the role of conformation in singlet fission, Phys. Chem. Chem. Phys., 2017, 19, 23162–23175.
25. K. Miyata, et al. , Coherent singlet fission activated by symmetry breaking, Nat. Chem., 2017, 9, 983–989.
26. N. V. Korovina, N. F. Pompetti and J. C. Johnson, Lessons from intramolecular singlet fission with covalently bound chromophores, J. Chem. Phys., 2020, 152, 040904.
27. N. R. Monahan, et al. , Dynamics of the triplet-pair state reveals the likely coexistence of coherent and incoherent singlet fission in crystalline hexacene, Nat. Chem., 2017, 9, 341–346.
28. K. Miyata, F. S. Conrad-Burton, F. L. Geyer and X.-Y. Zhu, Triplet Pair States in Singlet Fission, Chem. Rev., 2019, 119, 4261–4292.
29. M. W. B. Wilson, et al. , Temperature-Independent Singlet Exciton Fission in Tetracene, J. Am. Chem. Soc., 2013, 135, 16680–16688.
30. J. Zirzlmeier, et al. , Singlet fission in pentacene dimers, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 5325–5330.
31. C. Hetzer, et al. , Chromophore Multiplication To Enable Exciton Delocalization and Triplet Diffusion Following Singlet Fission in Tetrameric Pentacene, Angew. Chem., Int. Ed., 2019, 58, 15263–15267.
32. J. Zirzlmeier, et al. , Solution-based intramolecular singlet fission in cross-conjugated pentacene dimers, Nanoscale, 2016, 8, 10113–10123.
33. S. N. Sanders, et al. , Quantitative Intramolecular Singlet Fission in Bipentacenes, J. Am. Chem. Soc., 2015, 137, 8965–8972.
34. K. C. Krishnapriya, et al. , Spin density encodes intramolecular singlet exciton fission in pentacene dimers, Nat. Commun., 2019, 10, 33.
35. H. Sakai, et al. , Multiexciton Dynamics Depending on Intramolecular Orientations in Pentacene Dimers: Recombination and Dissociation of Correlated Triplet Pairs, J. Phys. Chem. Lett., 2018, 9, 3354–3360.
36. T. Sakuma, et al. , Long-Lived Triplet Excited States of Bent-Shaped Pentacene Dimers by Intramolecular Singlet Fission, J. Phys. Chem. A, 2016, 120, 1867–1875.
37. E. Kumarasamy, et al. , Tuning Singlet Fission in π-Bridge-π Chromophores, J. Am. Chem. Soc., 2017, 139, 12488–12494.
38. T. Yamakado, Conformational planarization vs. singlet fission: Distinct excited-state dynamics of cyclooctatetraene-fused acene dimers, Angew. Chem., Int. Ed., 2018, 57, 5438.
39. S. Lukman, et al. , Tuneable Singlet Exciton Fission and Triplet–Triplet Annihilation in an Orthogonal Pentacene Dimer, Adv. Funct. Mater., 2015, 25, 5452–5461.
40. A. M. Müller, Y. S. Avlasevich, K. Müllen and C. J. Bardeen, Evidence for exciton fission and fusion in a covalently linked tetracene dimer, Chem. Phys. Lett., 2006, 421, 518–522.
41. N. V. Korovina, et al. , Linker-Dependent Singlet Fission in Tetracene Dimers, J. Am. Chem. Soc., 2018, 140, 10179–10190.
42. E. C. Greyson, J. Vura-Weis, J. Michl and M. A. Ratner, Maximizing Singlet Fission in Organic Dimers: Theoretical Investigation of Triplet Yield in the Regime of Localized Excitation and Fast Coherent Electron Transfer, J. Phys. Chem. B, 2010, 114, 14168–14177.
43. N. A. Pace, et al. , Conversion between triplet pair states is controlled by molecular coupling in pentadithiophene thin films, Chem. Sci., 2020, 11, 7226–7238.
44. G. Joshi, et al. , Optical readout of singlet fission biexcitons in a heteroacene with photoluminescence detected magnetic resonance, J. Chem. Phys., 2022, 157, 164702.
45. R. D. Dill, et al. , Near-Infrared Absorption Features of Triplet-Pair States Assigned by Photoinduced-Absorption-Detected Magnetic Resonance, J. Phys. Chem. Lett., 2023, 14, 2387–2394.
46. C. Hintze, U. E. Steiner and M. Drescher, Photoexcited Triplet State Kinetics Studied by Electron Paramagnetic Resonance Spectroscopy, ChemPhysChem, 2017, 18, 6–16.
47. S. Matsuda, S. Oyama and Y. Kobori, Electron spin polarization generated by transport of singlet and quintet multiexcitons to spin-correlated triplet pairs during singlet fissions, Chem. Sci., 2020, 11, 2934–2942.
48. T. S. C. MacDonald, M. J. Y. Tayebjee, M. I. Collins, E. Kumarasamy, S. N. Sanders, M. Y. Sfeir, L. M. Campos and D. R. McCamey, Anisotropic Multiexciton Quintet and Triplet Dynamics in Singlet Fission via Pulsed Electron Spin Resonance, J. Am. Chem. Soc., 2023, 145(28), 15275–15283.
49. M. I. Collins, M. R. McCamey and M. J. Y. Tayebjee, Fluctuating exchange interactions enable quintet multiexciton formation in singlet fission, J. Chem. Phys., 2019, 151, 164104.
50. M. I. Collins, F. Campaioli, M. J. Y. Tayebjee, J. H. Cole and D. R. McCamey, Quintet formation, exchange fluctuations, and the role of stochastic resonance in singlet fission, Commun. Phys., 2023, 6, 65.
51. B. K. Rugg, et al., Triplet-pair spin signatures from macroscopically aligned heteroacenes in an oriented single crystal, Proc. Natl. Acad. Sci. U. S. A., 2022, 119, e2201879119.

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Footnote

† Electronic supplementary information (ESI) available: Synthesis details and characterization, additional steady-state and transient optical and EPR spectroscopy, TDDFT and exchange energy calculations, details of the kinetic models and associated fits. See DOI: https://doi.org/10.1039/d3sc03153e

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