Molecular stacking controlling coherent and incoherent singlet fission in polymorph rubrene single crystals

Singlet fission (SF) is an appealing process where one photoexcited singlet transforms to two triplets, which can overcome thermalization energy loss and improve solar cell efficiency. However, it remains unclear how intermolecular coupling, which is subject to molecular stacking, controls SF pathways and dynamics. Here, we prepared polymorph rubrene single crystals with different stacking geometries, including orthorhombic (Orth.), triclinic (Tri.), and monoclinic (Mono.) phases. By micro‐area ultrafast spectroscopy, we find that Orth. and Tri. phases with closer π‐π stacking exhibit co‐existing coherent and incoherent SF channels while loosely stacked Mono. phase shows only incoherent SF. Furthermore, incoherent SF is thermally activated in Orth. but barrierless in Mono. and Tri. phases. Quantum mechanical calculation reveals that different electronic coupling strength in different phases leads to different SF dynamics. This study demonstrates that molecular stacking governs SF dynamics through electronic coupling, providing guidance for designing efficient SF materials via crystal structural engineering.

two-photon photoemission spectroscopy studies by Zhu et al. indeed have demonstrated that TT is populated nearly instantaneously in crystalline pentacene and tetracene. [12,13][18][19][20][21] Another one is incoherent mechanism where S 1 has to slowly "hop" to TT nonadiabatically or relax to TT adiabatically, depending on the coupling strength between S 1 and TT. [22]In a certain system, both coherent and incoherent SF channels could coexist and be tuned. [14,23,24][30] An unambiguous study on correlating the inherent molecular stacking with SF dynamics to unravel the role of electronic coupling remains lacking and challenging.
33] Fortunately, by controlling crystallization process, rubrene molecules can form single crystals with different phases thus stacking geometries, including orthorhombic (Orth.),triclinic (Tri.), and monoclinic (Mono.)phases, respectively. [34]his provides an ideal platform to quantitatively study how stacking geometry controls the inherent SF process via electronic coupling degree of freedom with-out changing molecules.While the SF process in Orth.phase rubrene has been reported previously showing the coexistence of ultrafast coherent process and thermally activated slow incoherent process, [35] to the best of our knowledge, SF properties in Tri. and Mono.phases have not been reported so far.Here, we successfully prepared optical thin polymorph rubrene microcrystals with Orth., Tri. and Mono.phases, respectively and investigated the SF process by micro-area ultrafast transient absorption spectroscopy.We found distinctly different SF dynamics and the temperature dependence, which was further rationalized by quantum mechanical calculations.

RESULTS AND DISCUSSION
Three rubrene microcrystals with Orth., Tri. and Mono.phases were prepared according to previously reported meth-ods (see SI1). [34,36] In Figure 1A Figure 1B shows the optical images of the hexagonal Orth., ribbon-shaped Tri. and rhombic Mono.phase rubrene single crystals with a few micrometers in lateral size and submicrometer thickness.The X-ray diffraction patterns of these micro-size crystals can be safely indexed to their corresponding crystalline phases (Figure S1).The selected area electron diffraction patterns on each individual micro-size crystal further verify its high crystallinity (Figure 1B inset and S2).suggests weaker intermolecular interaction.On PL spectra, Orth.phase shows three vibronic peaks with the dominating one locating at 601 nm.Tri.phase exhibits a broad and structureless PL peak at 582 nm.Mono.phase possesses two obvious emission peaks at 572 nm and 615 nm, respectively.The different PL features suggest distinct excited state electronic configurations in three crystals with different molecular stacking. [37,38]n order to investigate the SF process in these polymorph rubrene microcrystals, we performed micro-area femtosecond transient absorption spectroscopy (fs-TA). [39,40]The schematic of experimental setup is shown in Figure 2A where both pump and white light continuum probe beams are focused on a single micro-crystal by microscope objective, to guarantee the excited states dynamics from individual welldefined single crystals (see SI3).Because the triplet excited state absorption is along the long axis while the singlet ground state absorption along short-axis, we set the polarization of probe beam along the long axis of rubrene to maximize photoinduced absorption (PIA) of triplets and minimize the spectral overlap from ground state bleaching (Figure S3).
Figure 2B shows the 2D color plot of fs-TA spectra of Orth.phase crystal under excitation of 535 nm, which exhibits three prominent negative PIA bands centered at 435, 477, and 508 nm, respectively.The representative spectra at different delay times are shown in Figure 2C (Figure S4A).The TA spectrum of rubrene molecules in toluene where SF cannot occur is also plotted in Figure 2C (grey line, extracted from Figure S5).By comparing rubrene solution and crys-tals, we can attribute the PIA at 435 nm, which shows up instantly, to the excited state absorption of singlet (S 1 →S n ), the PIA feature at 508 nm, which appears gradually, to triplet species and the PIA at 475 nm to the overlap of S 1 and TT (see Figure S4). [31,32,35]The nice correlation between the S 1 decay and triplet formation in picoseconds clearly indicates the occurring of SF process in rubrene crystals.Intersystem crossing can be excluded because of negligible efficiency and much slower rate in rubrene. [41]The possible interferences from polaron or oxygen-related defects which induces broad PIA band between 550 and 800 nm or emission peak at 650 nm, respectively, are also negligible (Figure S4 and Figure 1C). [31,33]n SF process, triplet species could involve different electronic configurations at different stages, including initial correlated triplet pairs (TT), subsequential spatially separated but spin−entangled triplet pairs (T⋅⋅⋅T) and ultimate free triplets (2×T). [9]In general, it is hard to distinguish them on TA spectroscopy due to similar spectral features, and the detailed assignments could be diverse across different literatures. [32,35,42][44][45][46] The TT formation kinetics at room temperature is plotted in Figure 2D (dark blue circle) and exhibits a distinct biphasic behavior with an ultrafast rising component within the instrument response function time (<150 fs) and a much slower rising component with a lifetime of ∼22 ps, consistent with previous studies by fs-TA and 2D electronic spectroscopy. [32,35]This biphasic formation dynamics in Orth.phase has been attributed to the ultrafast coherent SF process and thermally assisted incoherent SF process, respectively. [35]o study the temperature effect on SF dynamics, we conducted fs-TA measurements from 80 to 300 K.The full sets of TA spectra are shown in Figure S6, and the TT formation kinetics at different temperatures are compared in Figure 2D.Interestingly, while the ultrafast coherent process exhibits no temperature dependence, the slow incoherent rising process depends on temperature significantly, with slower formation at lower temperature, indicating the presence of thermal activation barrier for S 1 state to TT state along the incoherent pathway. [35]ame fs-TA measurements were performed on Tri. and Mono.phase crystals, which have never been investigated before.The corresponding contour plot of the TA spectra at room temperatures are shown in Figure 3A,B, respectively.The spectral evolutions are shown in Figure S4C,E.Same as Orth.phase, the TA spectra of Tri.phase (Figure 3A) show similar three prominent PIA bands.The TT formation kinetics at 510 nm (Figure 3C) also exhibits an instantly rising component and a slow component, indicating the coexistence of ultrafast coherent and slow incoherent SF in Tri.phase.An exponential fitting on the TT formation kinetics yields a lifetime of 13 ± 1 ps for the slow incoherent SF process, which is faster than that in Orth.phase.Interestingly, unlike Orth.phase, the SF process especially the incoherent components in Tri.phase shows no temperature dependence between 80 and 298 K (Figure 3C).
The TA spectra of Mono.phase are shown in Figure 3B, which depict a narrow and double-peak feature for PIA of singlet state and a slightly blue-shifted PIA peak at 503 nm for TT state.Unlike Orth.and Tri.phases with biphasic behavior, the TT formation in Mono.phase can be well described by a single exponential process with a lifetime of 24 ± 0.7 ps (Figure 3D), indicating only slow incoherent process.By varying temperature between 80 and 298 K, the TT formation kinetics in Mono.phase also show no variations (Figure 3D).
With the results above, we now compare the SF properties in three different phase rubrene crystals in Figure 4. Figure 4A plots the fractions of coherent and incoherent contribution in TT formation process, according to their relative amplitudes on PIA kinetics.For Orth. phase, more than half of the TT (65%) is produced via thermally assisted slow incoherent process while coherent channel contributes 35%.For Tri. phase, coherent (55%) and incoherent SF (45%) have nearly equal contributions.In contrast, Mono.phase exhibits solely incoherent SF process.Furthermore, Figure 4B shows the logarithm plot of the slow incoherent SF rate (k SF ) as a function of reciprocal of temperature (T).Circles are the experiment data and dash lines are the linear fits.While Tri. and Mono.phases show no temperature dependence, Orth.phase can be well described by an Arrhenius relationship lnk SF = lnk 0 − E a /k BT with an activation energy E a of 29 ± 5 meV.This value is consistent with previous report in Orth.phase. [35]The dramatically different SF properties in different rubrene crystal phases indicate the critical role of intermolecular interaction.[49] To capture the microscopic insights, we have calculated the electronic coupling (V ij ) between these states in different phases at equilibrium configuration (i.e., 0 K) and its fluctuation (σ ij ) at 300 K using a simplified rubrene dimer model (see SI4 and Table S1-S3 for details).
Figure 4D shows the electronic coupling strength between different states in Orth., Tri. and Mono.phases at equilibrium molecular configurations.For Orth. phase, even though LE and CT states (V LE-CT ) exhibit a large electronic coupling of hundreds of meV, electronic coupling between direct LE and TT (V LE-TT ) and between CT and TT (V CT-TT ) are strictly zero.This is due to the high structural symmetry (C 2h ) of Orth.phase where the transfer integrals between antisymmetric highest occupied molecular orbital (HOMO) and symmetric lowest unoccupied molecular orbital (LUMO) in adjacent molecules are perfectly cancelled. [16,35]Thus, in principle, coherent SF hardly happens in Orth.phase through either direct or indirect pathway at zero temperature.For Tri. phase, the direct LE-TT coupling (V LE-TT ) is nonzero but rather small (<1 meV) while V LE-CT and V CT-TT for CT mediated pathway show appreciable strength of tens to hundreds of meV.This implies that SF in Tri.phase could proceed coherently through the CT-mediated pathway (i.e., LE→CT→TT).For Mono. phase, the couplings between different electronic states are all very small (<7 meV), therefore the coherent SF process is unfavorable.
The calculated electronic coupling strength at equilibrium molecular configuration explains experimentally observed presence of coherent SF in Tri.phase and absence in Mono.phase, respectively but contradicts with coherent SF process in Orth.phase.As already demonstrated previously, the high C 2h symmetry in Orth.phase can be broken by low frequency intermolecular vibrations, enhancing electronic couplings and facilitating the ultrafast coherent SF. [18,35] Therefore, we further calculated the fluctuations of electronic couplings (σ ij ) at 300 K to capture the effect of thermally induced vibronic coupling.As shown in Figure 4E, σ ij for direct coupling between LE and TT (σ LE-TT ) in all three phases are negligible thus the direct LE→TT pathway can only occur incoherently, regardless of temperature.On the other hand, Orth.phase shows tens of meV for σ LE-CT and σ CT-TT for CT mediated pathway.Considering large V LE-CT but zero V CT-TT at equilibrium configurations, this indicates that molecular vibration at 300 K dramatically enhances V CT-TT , promoting the CT mediated coherent SF in Orth.phase.Similarly large σ ij along CT mediated pathway are also observed in Tri.phase.This, together with substantial V LE-CT and V CT-TT F I G U R E 5 The proposed singlet fission (SF) mechanism in different phase rubrene crystals.In Orth.(top) and Tri.(middle) phases, charge transfer (CT) mediates the coherent TT formation, which is unfavorable in Mono.phase (bottom).The direct conversion from LE to TT is incoherent.already at equilibrium configurations, supports CT-mediated coherent TT formation in Tri.phase.As for Mono.phase, V ij and σ ij between different states are all too small such that only incoherent SF could occur.
Figure 5 summarizes the proposed SF mechanisms in polymorph rubrene crystals.According to our calculations, LE and TT states are nearly isoenergetic and CT is higher in all three phases (see Table S1-S3).For Orth. and Tri.phases, ultrafast coherent SF occurs through CT mediated super-exchange pathway because of the substantial electronic coupling between LE and CT and between CT and TT, even though the energy of CT state is higher than LE and TT. [23,50,51]This is consistent with typical SF materials such as pentacene derivatives that CT promotes the ultrafast transition from LE to TT. [16,47] For Mono. phase, only slow incoherent TT formation can occur due to the weak electronic couplings between these states.To further explore whether the incoherent SF process with time constant of tens of picoseconds occurs through direct LE→TT or indirect LE→CT→TT pathway, we estimated the associated activation barrier using Marcus theory which has been extensively applied to predict incoherent fission rate of weak coupling systems (Figure S7). [22,52]In Mono.phase, the activation barrier for indirect pathway is about one order of magnitude larger than direct pathway (Table S4), thus incoherent SF process in Mono.phase preferably occurs through direct LE→TT coupling.This is also supported by the absence of any intermediate state for LE to TT incoherent transformation on TA spectroscopy because the long-lasting CT or polaron would have induced broad and structureless PIA band at between 550 nm and 800 nm (Figure S4). [31]Moreover, if CT participates in the incoherent SF, the slow incoherent SF rate should be different among Orth., Tri. and Mono.because of their distinct CT-involved electronic couplings (Figure 4D,E). [22,52]However, similar incoherent TT formation with lifetimes of ∼20 ps at room temperature is observed in three different phases, further suggesting the direct LE→TT pathway for incoherent SF process.For direct LE→TT pathway, although the electronic couplings (V LE-TT ) are weak in these crystals, two-electron transfer controlled SF is still possible benefiting from the nearly degenerate LE and TT as previously demonstrated by theoretical simulation. [16,35]ccording to the scheme described by Michl et al., the electronic couplings between pairwise states are closely related to the spatial overlap of four frontier molecular orbitals on the two chromophores in dimer. [1,2]Therefore, the different TT formation behaviors resulting from different electronic coupling can be ultimately traced back to different stacking geometries in three rubrene crystals. [33,53]As the planes of tetracene backbone and side phenyl groups are nearly perpendicular and HOMO and LUMO of rubrene molecule mainly locate on the tetracene backbone, the electronic coupling is determined by π-π stacking distance and the degree of long and short axis displacements between neighboring tetracene backbone. [37]As shown in Figure 1A, compared to Orth. and Tri.phases, Mono.phase shows the largest π-π stacking distance and long-and short-axis displacements.In addition, the calculated band structure is clearly dispersed for Orth.and Tri.phases but nearly flat in Mono.phase. [37]Both the apparent molecular stacking and the calculated band structure indicate that the intermolecular interaction in Mono.phase is the weakest, consistent with the computational trend in Figure 4. Consequently, the weak electronic couplings induced by limited superposition of relevant electronic states causes incoherent SF mechanism in Mono.phase.On the other hand, Orth.phase and Tri.phase exhibit similar π-π stacking and parallel slipping without short axis displacement, leading to similar electronic coupling strength and SF behavior with both coherent and incoherent components.As demonstrated previously, lowfrequency torsional modes with tetracene backbones twisting around the long axis facilitate the coherent SF in Orth.phase. [35]The similar molecular stacking of Orth.phase and Tri.phase might induce distinct intermolecular vibronic modes.Future explore is expected to deeply investigate the nature of molecular packing-related coherent SF.
An interesting observation is that the incoherent SF process through LE→TT pathway requires thermal assistance in Orth.phase but not in Tri. and Mono.phases.The detailed origin is unclear yet.One possible reason is that Mono.and Tri.phases have lower symmetry and always have non-zero electronic couplings between nearly isoenergetic LE and TT (Figure 4D).Thus, unlike Orth.phase, their SF process does not rely on the thermally activated symmetry-breaking. [18,35]Similar temperature independent incoherent singlet fission has also been observed in rubrene thin film, rubrene derivatives, and other polyacenes (e.g., tetracene film). [46,54,55]Baronas and co-authors attributed the weak temperature dependence in crystalline t-butyl substituted rubrene with monoclinic phase to energetic driving force (E S1 > E TT ). [33]Zhu and co-authors proposed that the energy barrier in endothermic tetracene could be overcome through coherent coupling and entropic gain. [13]

CONCLUSION
In summary, we investigated the SF dynamics via controlling the stacking geometries using polymorph rubrene single crystals, including Orth., Tri. and Mono.phases.Consistent with previous studies, Orth.phase exhibits a coherent SF process via CT mediated pathway and a coexisting incoherent process by direct LE and TT coupling.Tri.phase exhibits similarly coherent and incoherent biphasic SF behavior.In contrary, Mono.phase only shows incoherent SF process without ultrafast coherent channel.Interestingly, unlike thermally assisted incoherent SF process in Orth.phase, the incoherent SF processes in Tri. and Mono.phases are temperature independent.According to quantum mechanical calculation, the distinctly different SF behaviors correlate well with electronic coupling strength which further originates from the stacking geometries including symmetry, π-π stacking distance and lateral displacements between neighboring molecules.This finding unambiguously demonstrates that in parallel to the energetics, crystal structural engineering provides another way to design molecular systems with efficient SF performance.For example, instead of conventional Orth.phase, Tri.phase with lower symmetry and less intermolecular displacement provides larger fraction of coherent SF process and moreover, temperature independent incoherent process, which is beneficial for SF-based optoelectronic devices.

F I G U R E 1
Structural and optical characterization.(A) Diagram of stacking geometries, (B) optical images and (C) steady-state absorption (solid line) and photoluminescence (dash line) spectra of polymorph rubrene crystals.From left to right: Orth., Tri. and Mono.phases, respectively.Insets in (B) are the corresponding selected area electron diffraction (SAED) patterns on a single crystal.Scale bar in (B): 2 μm.
, we show the simplified stacking geometries by extracting the nearest molecular pair in each crystal structure.All crystals show obvious displacement along long axis direction, 5.94-8.68Å.Along the short axis direction, Orth.and Tri.phases show negligible displacement while Mono.slips by 5.22 Å.Three structures show similar intermolecular distance along the π-π stacking direction, with Mono.phase being the farthest one.The dihedral angles of tetracene backbone and phenyl groups are as large as 80-90 • in three phases, indicating that the side phenyl groups have minimal contribution to the conjugation of rubrene molecule.
Figure 1C displays the steady-state micro-area absorption (solid line) and photoluminescence (PL, dash line) spectra on each phase single crystals.The onset of the absorption band locates at near 560 nm (2.21 eV) for Orth.and Tri.phase.and 548 nm (2.26 eV) for Mono.phase.The similar absorption onset of Orth.and Tri.phases indicates similar intermolecular interaction, which is correlated with molecular stacking while the blue-shifted absorption onset of Mono.

F I G U R E 2
Femtosecond transient absorption (fs-TA) spectra for Orth.phase crystal.(A) Schematic of micro-area fs-TA spectroscopy.(B) Contour plot of the fs-TA spectra as a function of wavelength and delay time for Orth.crystal.(C) Representative TA spectral evolution at indicated delay time.The TA spectrum of S 1 (grey line) is extracted from rubrene solution in toluene.The split of horizontal axis is due to the switch of probe range.(D) Temperature dependence of triplet pair (TT) formation kinetics at ∼510 nm.The split of time axis at 4 ps is to turn the linear axis to log axis.

F I G U R E 3
Femtoseconds transient absorption (fs-TA) spectra for Tri. and Mono.phase crystals.Contour plot of the fs-TA spectra as a function of wavelength and delay time for (A) Tri. and (B) Mono.phase crystals.TT formation kinetics of (C) Tri. and (D) Mono.phase crystals at different temperatures.

F I G U R E 4
Summary of singlet fission (SF) properties in different phase rubrene crystals.(A) The fraction of coherent or incoherent components in TT formation.(B) Logarithm plot of the rate of incoherent component as a function of reciprocal of temperature.Dashed lines are the fits to the Arrhenius model.(C) Scheme showing direct SF where the initial singlet excited state (LE) is converted to TT directly and indirect SF where charge transfer (CT) state mediates the TT formation.(D) Electronic couplings (V ij ) between different excited states at equilibrium structures.(E) Fluctuation of the electronic couplings (σ ij ) at 300 K.