singlet exciton fission 
 is the quantum mechanical process by which 
 a singlet exciton splits into two distinct spin triplet excitons . 
 the triplets are initially coupled into an overall singlet state , 
 conserving spin and allowing for extremely fast and highly efficient 
 triplet formation . this phenomenon has recently become the object of 
 intense study due to its proposed use for carrier multiplication in 
 solar cells . singlet fission has already 
 been successfully harnessed in devices , in some exceptional cases with an internal quantum efficiency near 
 200% . the record external quantum efficiency in 
 these systems of 135% is the highest achieved for any photovoltaic 
 technology , demonstrating the great potential of singlet fission devices . further practical advances will demand a more thorough understanding 
 of the underlying mechanism of singlet fission , as well as how it 
 relates to intermolecular structure . for example , it has been shown 
 in amorphous films of diphenyltetracene that long - range order is not 
 required for efficient triplet formation , but other studies on disordered systems highlight the importance 
 of specific local interactions . these local interactions , 
 and particularly the strength of intermolecular coupling , have been 
 proposed to play a central role in determining the rate and dominant 
 mechanism of singlet fission  nonadiabatic or adiabatic  in 
 a new model covering all acenes . this significant progress has occurred almost exclusively within 
 a relatively narrow class of materials : tetracene , pentacene , and 
 their derivatives . property 
 relationships and singlet fission mechanisms needed to develop new 
 materials and broaden the library of candidate chromophores . one class 
 of materials with significant promise for singlet fission is the polyenes , which are characterized by a low - lying ( dark ) 
 excited state of the same ag symmetry as the ground state . the theoretical basis for fission in these materials lies in the symmetry 
 of this state , which has an equivalent description as a weakly coupled 
 pair of triplet excitons , suggesting the possibility of intramolecular 
 singlet fission . however , as we have previously shown in poly(3-dodecylthienylenevinylene ) , 
 intramolecular singlet fission does not actually proceed via the expected 
 2ag state but occurs directly from the initially photoexcited 
 1bu exciton . in carotenoids , 
 too , singlet fission has been observed ; these polyenes are evidently 
 too short to support intramolecular triplet pair formation but undergo 
 singlet fission in biological complexes with proteins or in self - assembled aggregates . it is not clear how 
 the original 2ag mediated mechanism can be extended to 
 these materials , as the model is fundamentally intramolecular in nature . wang and tauber have suggested that singlet 
 fission in carotenoid aggregates does not involve the 2ag state , but no studies have been made with sufficient time resolution 
 to confirm this hypothesis . here we use broadband transient 
 absorption spectroscopy from the 
 tens of femtoseconds to microseconds time scales to investigate the 
 singlet fission process in aggregates of the carotenoid astaxanthin 
 ( figure 1a ) . we study a series of five distinct 
 aggregates to determine both the role of intermolecular structure 
 and the interplay between triplet formation and internal conversion 
 to the 2ag state . direct formation from 
 1bu ( figure 1d)observed 
 in the intramolecular polymer system reported previously . the initial rate of triplet formation is seen 
 to only weakly correlate with the strength of intermolecular coupling 
 with a fastest time constant of only 65 fs , among the fastest of any 
 reported system . these results raise important questions about the 
 electronic structure and intermolecular interactions of the polyenes 
 and also point the way toward a universal mechanism for ultrafast 
 singlet fission . ( b ) normalized 
 uv  vis absorption of five stable aggregates of axt in 9:1 water : dmso 
 ( i and ii ) or 4:1 water : acetone ( iii  v ) as well as monomeric 
 axt in acetone ( dashed ) . ultrafast internal conversion from 1bu to 2ag is followed by fast nonradiative decay to the ground state . ( d ) 
 model of singlet fission and triplet annihilation in carotenoid aggregates , 
 as measured here . upon aggregation , the 1bu state no longer 
 couples to 2ag . the 2ag state is lower in energy 
 than the triplet pair and enables efficient recombination back to 
 the ground state . type - a 
 gelatin and c60 fullerene were purchased from sigma - aldrich . enantiomerically pure 3s,3s- , 3s,3r- , and 3r,3r - astaxanthin for circular dichroism 
 measurements were purchased from carotenature . axt monomer solutions 
 were prepared at a concentration of 100 m 
 in acetone or dmso and heated at 50 c until clear . the series 
 of five distinct , stable aggregate solutions ( figure 1a ) was prepared as follows . for aggregate i a 420 m 
 solution of axt in dmso at room temperature was mixed in a 1:9 ratio 
 with water at 5 c . aggregate ii was prepared by mixing a 1000 
 m solution of axt in dmso at 80 c in a 1:9 ratio with 
 water at 80 c . the three red - shifted aggregates were prepared 
 instead from acetone stock solutions heated to 65 c , and to 
 impart long - term colloidal stability , type - a gelatin aqueous solutions 
 at 50 c were used instead of pure water . the organic : aqueous mixing ratio for all three species was 1:4 . 
 aggregate iii used an axt concentration of 250 m and a 5 mg / ml 
 gelatin solution . the axt stock concentration for aggregate iv was 
 375 m , with a gelatin concentration of 2.5 mg / ml . aggregate 
 v was prepared with the same acetone stock as aggregate iv and a higher 
 gelatin content of 10 mg / ml , and the solution was heated at 65 c 
 for an additional 10 min after mixing . time - resolved measurements 
 were only performed on aggregates that were stable for > 1 week . sub - picosecond transient absorption ( ta ) measurements were performed 
 on a previously reported setup with slight 
 modifications . narrow - band ( 10 nm ) excitation pulses were 
 generated in an optical parametric amplifier ( topas , light conversion 
 ltd . ) coupled to the output of a 1 khz regenerative amplifier ( spectra - physics 
 solstice ) . to ensure that ta spectra reflected specific aggregate 
 types rather than mixtures of species , pump photon energies were scanned 
 across the aggregate absorption bands ( vertical lines in figure 1a ) , with typical pump fluences below 4  10 photons / pulse - cm . because excessive pump fluence 
 results in spurious ultrafast effects , all measurements were also 
 performed at lower fluence , and the fluence dependence was studied 
 in detail for all samples ( see below ) . the sample transmission was 
 probed using broadband pulses generated in two home - built non - collinear 
 optical parametric amplifiers ( nopas ) roughly spanning 0.752.5 
 ev . the probe beam was split to provide a reference 
 signal not affected by the pump to mitigate any laser fluctuation 
 effects , and both were dispersed in a spectrometer ( andor , shamrock 
 sr-303i ) and detected using a pair of linear image sensors ( hamamatsu , 
 g11608 ) driven and read out at the full laser repetition rate by a 
 custom - built board from stresing entwicklungsbro . the differential 
 transmission ( t / t ) was then 
 measured as a function of probe photon energy and pump  probe 
 delay . this setup afforded a temporal resolution of approximately 
 120 fs . the same setup was employed for nanosecond ta , using the frequency - doubled 
 ( 2.33 ev ) nanosecond output of a q - switched nd : yvo4 laser as the excitation 
 source . high - time - resolution measurements were also performed on a 
 similar setup , in which both the pump and probe beams were generated 
 by home - built nopas generating sub-30 fs ( pump ) and sub-10 fs ( probe ) 
 pulses using chirped mirror compression . the spectra in figure 1a demonstrate the 
 great potential of astaxanthin ( axt ) aggregates for a study of structure this system is noteworthy both for the 
 large number of distinct aggregates formed and the wide range over 
 which the primary absorption band can be tuned  approximately 
 1.2 ev  through simple control of water content , temperature , 
 and gelatin stabilization . axt also appears to be unique in having 
 two blue - shifted structures and the strongly red - shifted aggregate 
 v , which is unlike any other reported carotenoid aggregates . we consider that the uv  vis absorption spectra shown here 
 represent distinct aggregate types , rather than mixed populations . 
 because these aggregates form through gradual transitions from one 
 species to the next ( see supporting information , 
 figures s1 and s2 ) , it is easy to generate mixtures of species 
 through slight changes in preparation conditions . in all cases , the 
 uv  vis spectra of such samples can be decomposed into the species 
 shown in figure 1a . to control for the possibility 
 of aggregate mixtures , we performed ta measurements with selective 
 excitation across the absorption band ( see below and supporting information , figures s6s10 ) . only aggregate the determination of the structure of carotenoid aggregates is 
 a long - standing problem , and the diversity of intermolecular packing attained here highlights 
 its complexity . from the uv  vis absorption spectra alone , little 
 can be determined about the relevant intermolecular parameters . in 
 the absence of vibronic structure at room temperature likewise , the degree of red- or blue - shift , a gauge of 
 the strength of exciton coupling , can not be determined precisely due 
 to significant solvatochromism ( see supporting 
 information , figure s3 ) . aggregate i is strongly blue - shifted and exhibits significant 
 narrowing of the absorption band aggregate ii exhibits a weaker blue - shift 
 as well as a change in shape that would be consistent with a decrease 
 in the 00/01 peak ratio , making it most likely a weakly 
 coupled h - aggregate . aggregate iii is a borderline case which would 
 typically be described as a j - aggregate , but on the basis of spano s 
 analysis of lutein aggregates , it may 
 equally be a very weakly coupled h aggregate . the appearance of a 
 pronounced 00 peak and strong red - shift in aggregates iv and 
 v is characteristic of j - aggregation , which is presumed to be the 
 primary interaction in these species . aggregates similar to i are almost exclusively formed by carotenoids 
 with at least one hydroxyl group on the terminal rings , pointing to 
 the importance of intermolecular hydrogen bonding . the observed sensitivity of the formation of i to ph is consistent 
 with this motif . furthermore , the absorption spectrum of crustochrin , 
 a carotenoprotein predominant in yellow lobster carapace , is almost 
 identical to that of aggregate i , and the two share similar raman 
 signatures . however , that protein has 
 never been crystallized , and little is known about the orientation 
 or coupling of the axt molecules in this material . aggregates such 
 as ii are preferentially formed by carotenoids with carbonyl but no 
 hydroxyl groups ; it is likely that in 
 this species the supramolecular structure is primarily mediated through 
 the c ho motif described by bartalucci et 
 al . for crystals of axt and canthaxanthin . strongly red - shifted axt aggregates such as iv and v have long been 
 studied in the context of lobster coloration . the primary carotenoprotein 
 in lobster carapace , crustacyanin , exhibits a similarly pronounced 
 red shift . recent studies attribute the bulk of this effect 
 to planarization of the axt molecules within the protein so that the 
 terminal rings lie in trans conformation , with a consequent extension 
 of the conjugation length . indeed , the 
 spectra of iv and v each closely match different portions of the reported 
 absorption of a crystal of an all - trans axt derivative . we thus consider species iv and v to contain 
 all - trans axt , with packing similar to the reported crystal structure . the fact that each aggregate agrees so well with a separate section 
 of the crystal spectrum indicates the presence of two polymorphs in 
 the solid state . the uv  vis absorption and circular dichroism 
 data ( supporting information , figure s4 ) at hand are 
 insufficient to reliably determine the intermolecular packing in these 
 aggregates , and further structural characterization is needed . for 
 our purposes here , it is sufficient to rank them by approximate strength 
 of intermolecular coupling : i > v > iv > , we first examine the excited 
 state processes of monomeric axt in pure organic solution . because 
 the carotenoids exhibit pronounced solvatochromism ( suporting information , figure s3 ) , monomer solutions were 
 prepared in both acetone and dmso . the key results of ta measurements 
 on axt monomers excited at the absorption maximum are presented in 
 figure 2 . our ta results are presented throughout 
 in units of t / t , in which 
 the absorption of photogenerated states appears negative . positive 
 features can reflect either increased transmission of the probe through 
 the sample due to bleaching of the ground state or probe amplification 
 arising from stimulated emission . the results for the two solvents were almost identical save for a 
 slight red - shift of all photoinduced absorption ( pia ) features in 
 dmso ( figure s3 ) , so only the acetone data 
 will be addressed here . axt shows the characteristic polyene behavior 
 illustrated in figure 1c and can be described 
 in terms of just two states . ( a ) selected sub - ps 
 ta timeslices 
 following excitation at 2.6 ev with 26 j / cm . the initial 
 1bu pia can only be clearly observed within the pump pulse 
 duration ( black ) , and it decays to form the well - known 2ag pia in the visible region . the region below 1.1 ev is magnified 
 10 to show the weak 2ag  1bu pia . ( b ) the corresponding decay kinetics ( lines ) show direct , instrument - limited 
 conversion from 1bu to 2ag and rapid decay to 
 the ground state . these processes are completely independent of pump 
 fluence over nearly 2 orders of magnitude ( symbols , data normalized 
 with respect to pump intensity ) the data for 0.78 ev are magnified 
 by a factor of 4 for clarity . within the instrument response ( black trace ) , a sharp pia 
 can be 
 detected between 1.0 and 1.5 ev , accompanied by a positive feature 
 around 2.25 ev which agrees well with steady - state photoluminescence 
 spectra and can be assigned to stimulated emission . these are the 
 signatures of the initial 1bu exciton , which decays with 
 instrument - limited kinetics to the dark 2ag state ( green 
 traces ) . this state shows a pronounced pia peaked at 2.05 ev as well 
 as a weak pia tail at the low - energy edge of the available spectral 
 range , assigned to the 2ag  1bu transition . as in other polyenes , after fast thermalization 
 the 2ag state decays uniformly and nonradiatively back 
 to the ground state through efficient coupling to the vibrational 
 manifold . we thus treat the monomer decay as following the simple 
 model of 1bu  hot 2ag  2ag  1ag ( ground state ) . the entire 
 spectral range can be fitted well with three time constants : 
 an instrument - limited 120 fs constant describing the internal conversion 
 from 1bu , a 200 fs thermalization within the 2ag manifold and a 5 ps final decay to the ground state . this behavior 
 is completely independent of pump fluence for all spectral features 
 over nearly 2 orders of magnitude ( figure 2b ) . there is no sign of or apparent need for intermediate states 
 between 1bu and 2ag to explain these results , 
 as confirmed with sub-30 fs ta measurements ( see below ) . it should 
 be stressed that there is also no sign of triplet formation by singlet 
 fission or any other process at any pump photon energy ; individual 
 carotenoid molecules are evidently too small to support triplet pair 
 states . ta measurements were 
 performed on all five aggregates at four or more pump photon energies . 
 due to the overall similarity of the aggregate ta data , only the representative 
 aggregates ii ( weak h - aggregate ) and iv ( strong j - aggregate ) will 
 be discussed in detail here . the spectra of other aggregates and other 
 pump photon energies can be found in the supporting 
 information , figures s5s10 . comparison of the ta spectra 
 for aggregate ii in figure 3a , b with the monomer 
 data in figure 2 reveals two immediate differences : 
 the pia bands are broader and much less pronounced in ii , and the 
 final decay is significantly slower . as will be shown below in figure 4 , the final state in this aggregate is the triplet . its pia is dominant well before 3 ps ( see below ) , and the spectrum 
 decays without further evolution out to the s time scale . the 
 only spectral changes that can be clearly discerned occur on an ultrafast 
 instrument - limited time scale : much like in monomeric axt the initial 
 excited state absorbs in the nir , seen as a broad , weak pia in the 
 earliest ta spectrum . as shown in figure 3c , 
 the decay of the nir band is matched by the decay of the slight ground - state 
 bleach ( gsb ) observed around 2.4 ev . this kinetic reflects the sub - ps 
 formation of triplet pia , which strongly overlaps with the ground - state 
 absorption and results in a negative overall signal . ( a ) selected timeslices 
 from sub - ps ta of ii excited at 2.6 ev . the prompt decay of the broad 
 nir pia is the only significant spectral change in the entire measurement 
 range and reflects internal conversion from the initial 1bu state . ( b ) timeslices from ns ta show continued uniform decay of 
 the state formed within 3 ps . ( c ) integrated decay kinetics from sub - ps 
 ta reveal instrument - limited decay of the gsb and nir pia ( solid lines ) 
 to form the final state . ( d ) equivalent sub - ps measurement of iv excited 
 at 2.3 ev , showing similar rapid decay of the initial band in the 
 nir and formation of the final state within 3 ps , which ( e ) uniformly 
 decays on the s time scale . ( f ) integrated decay kinetics from 
 sub - ps ta of iv show an instrument - limited internal conversion from 
 the initial state ( thin solid line ) similar to ii . the slower rise 
 at 1.94 ev reflects a gradual shift of the crossing point between 
 gsb and pia , related to the generation of vibrationally excited ground 
 states following nonradiative decay of triplet pairs . ( a ) integrated decay 
 kinetics from all 
 species , at the peak of pia , following excitation at 2.3 ev . all aggregates 
 ( solid ) show an enhancement of the final state lifetime of 5 orders 
 of magnitude , relative to the monomer ( dashed ) . ( b ) comparison of 
 the ta signal at 100 ns for all five aggregates reveals the same pia 
 signature in each , combined with a gsb related to the uv ( c ) 
 comparison of the absorption edge ( dashed ) and long - lived ta signal 
 ( solid ) of monomer axt following triplet sensitization ( green ) and 
 aggregate ii . the similarity of shape confirms the assignment of the 
 long - lived aggregate state to triplets , produced via singlet fission . on first inspection the ta results 
 for iv in figure 3d the most prominent difference is the sharp positive t / t band above 2.0 ev . this signal perfectly 
 matches the position of the vibronic peaks observed in steady - state 
 absorption ( figure 1a ) and can be assigned 
 to gsb of the aggregate . as in figure 3a , an 
 ultrafast decay from the initial 1bu state can be inferred 
 from the instrument - limited loss of the pia in the nir along with 
 a matching rise of pia in the visible and a slight blue - shift of the 
 gsb edge . the final state in this aggregate  again formed on 
 ultrafast time scales  is the same as in aggregate ii , namely 
 triplet excitons . indeed , all five aggregates form triplets 
 on ultrafast time scales , 
 with most spectral evolution complete by 1 ps . in a system such as 
 aggregated axt , with no heavy atoms and no significant intersystem 
 crossing yield in free solution , we detect none of the signatures 
 of 2ag , such as 2ag  1bu pia 
 below 1 ev , or of any other excited state within the 120 fs 
 temporal resolution of this measurement . we thus propose that intermolecular 
 singlet fission in this polyene system occurs directly from the 1bu exciton , the same mechanism we observed for intramolecular 
 singlet fission in poly(3-thienylenevinylene ) . figure 4 compares the final state observed 
 in each aggregate following excitation at 2.33 ev . we first highlight 
 the dramatic enhancement of the final state lifetime upon aggregation , 
 by roughly 5 orders of magnitude . only thermal effects or the formation of charged species or triplet 
 excitons would be expected to yield such long lifetimes . the only 
 long - lived features are found in the visible spectral region ( figure 4b ) . the agreement of the pia bands on the low - energy 
 side of the spectrum is striking , and the differences at higher energies 
 can be accounted for as different gsb contributions , related to the 
 shape of the ground - state absorption spectra . this comparison not 
 only confirms that the same long - lived species is present in every 
 sample but also ensures that it is an excited state of the primary 
 aggregate type observed in uv  vis absorption rather than a 
 minority population . the close spectral overlap of the pia bands allows 
 us to rule out pump - induced thermal modulation , as it is highly unlikely 
 for this effect to produce the same red - absorbing species in five 
 widely varied aggregate structures with absorption edges varying by 
 1.5 ev . we can also rule out charge formation , as the characteristic 
 nir absorption bands of carotenoid anions and cations are absent in 
 all cases . these considerations already enable an assignment of the terminal 
 long - lived state to triplet excitons , and for further confirmation 
 we use the triplet sensitization technique of sasaki et al . briefly , a mixed solution of axt and c60 in toluene was excited at 2.33 ev with the long - delay ta setup . 
 within the pump pulse duration , we observe the decay of axt singlets 
 and formation of triplet excitons on c60 ( supporting information , figure s11 ) . on a hundreds of picoseconds 
 time scale , the triplet excitons undergo triplet energy transfer to 
 axt , resulting in the sharp characteristic pia of carotenoid triplets 
 ( figures 4c , green , and s11 ) . comparison with our long - delay spectra , using only aggregate 
 ii for clarity , shows a similar overall shape . however , the long - lived 
 signal in aggregates is slightly broader and red - shifted by 0.2 
 ev . a small red - shift for carotenoid triplet absorption in aggregates 
 or complexes has been previously observed and can be partially attributed to the change in dielectric environment 
 upon aggregation . moreover , the shift is comparable to that observed 
 in the ground state absorption edge ( dashed lines ) , which may indicate 
 that gsb also contributes to the apparent red shift . as for 
 the spectral broadening , it is actually a consequence of 
 singlet fission . the same phenomenon has been observed in poly(3-dodecylthienylenevinylene ) and in polydiacetylene . in the latter work it was proposed that the initial geminate triplet 
 pairs still interact following singlet fission , though they are no 
 longer fully coupled into a singlet state . these interactions perturb 
 the triplet energy levels , leading to a broadening and further red - shift 
 of the pia . the agreement of our results with a similar system and the reasonable match between the long - lived spectrum and the 
 triplet reference are sufficient to conclude that the final state 
 in all axt aggregates is triplet excitons . the match of this 
 triplet pia across the entire aggregate series 
 is striking and merits further consideration . we recall that optically 
 allowed transition varies by 1 ev between aggregates i and 
 v , demonstrating the strong effect of aggregation on the singlet excited 
 state . on the other hand , the most significant effect on the t1tn absorption band in figure 4 is the mere fact of aggregation : all aggregates share approximately 
 the same redshift of this band relative to the sensitized monomer 
 triplet . this result is a likely consequence of the highly localized 
 nature of carotenoid triplets . whereas the precise nature of the nearest - neighbor 
 coupling within the aggregates can strongly influence singlet absorption , 
 the triplet only reflects bulk - type dielectric effects . on the basis 
 of this behavior , we can be confident that the energy of the triplet 
 exciton does not change through aggregation . ( a ) integrated decay kinetics of ii following sub - ps excitation at 
 2.6 ev . the same multiexponential function fits the decay at all fluences , 
 requiring the recombination process to be entirely geminate . lifetimes 
 ( 0.9 , 6 , and 49 ps ) are not assigned to individual processes but rather 
 reflect the wide distribution of triplet pair decay rates . ( b ) integrated 
 decay kinetics of ii on longer time scales , following ns excitation 
 at 2.3 ev , show strong fluence dependence indicative of non - geminate 
 tta . though all of the aggregates undergo 
 the same process of singlet fission , the kinetics in figure 4a reveal clear differences in the subsequent fate 
 of the triplets . to better understand this behavior , we begin by evaluating 
 the dependence of these kinetics on pump fluence in detail for aggregate 
 ii ( see supporting information , figures s13 and 
 s14 for qualitatively similar results for the other aggregates ) . we first consider the ps - ns regime ( figure 5a ) , during which the triplet pia spectrum decays uniformly with at 
 most a slight narrowing ( figure 3a ) . the multiexponential 
 decay we observe on these time scales is far too short for the intrinsic 
 triplet lifetime . instead , in agreement with studies of zeaxanthin 
 aggregates we attribute this behavior to 
 annihilation processes , specifically triplet  triplet annihilation 
 ( tta ) . this is a highly efficient process  though some fraction 
 of the triplets survives out to s time scales , at least 90% 
 of the excited population annihilates between 1 ps and 1 ns . at the 
 same time , this initial tta regime is completely independent of pump 
 fluence and must thus correspond to the annihilation of geminate triplet 
 pairs . these facts enable an important insight into the energetics 
 of singlet fission in carotenoids . according to the conventional 
 energy scheme 1bu > 2ag > 2t1 > t2 , only one pathway for tta 
 is permitted : t1 + t1  t2 + s0  t1 + s0 . such a model 
 could potentially explain a prompt loss of 50% of the triplet population 
 through geminate tta , but any further losses would depend on intrinsically 
 slow triplet diffusion . this latter process would be strongly dependent 
 on excitation density , which can not be reconciled with the fast , fluence - independent 
 decay observed here . the usual treatment of 
 tta assumes a randomized population of triplets , such that pairs of 
 triplets can couple and annihilate into an overall spin singlet or 
 spin triplet state . the triplet pair produced through fission is 
 by definition coupled into a spin singlet , so tta is only possible 
 back to a singlet state until the coherence is broken by spin thus , fast geminate 
 recombination of the type t1 + t1  t2 + s0 should not be possible , even if it is energetically 
 favorable . instead , the only available pathway for geminate 
 tta that passes 
 through another electronic state is t1 + t1  
 s1 ( i.e. , 2ag ) + s0 . this process 
 would be completely independent of excitation density and could proceed 
 on a range of time scales , governed by the couplings in the distribution 
 of triplet pair states formed . in short , this model of tta very closely 
 matches the results presented in figures 5a 
 and s13 on axt aggregates . it 
 is generally accepted that 1bu > 2ag > 
 2t1 > t2 , with a relatively small gap between 
 2ag and 2t1 . however , triplet energies are notoriously 
 difficult to measure , particularly in the absence of phosphorescence , 
 and if the t1 energy were even slightly higher , the state 
 ordering would become 1bu > 2t1 > 2ag . on the longer time scales shown in figure 5b , the relatively few triplets that survive the 
 initial tta regime 
 are stabilized and do not appear to undergo geminate recombination . 
 instead , they are free to diffuse and decay with a strong fluence 
 dependence , a clear indicator of non - geminate tta . at lower fluences the final decay still converges well to a single exponential decay 
 of 1.25 s , which is reasonable as the intrinsic triplet 
 lifetime , but at the highest excitation density the triplet decay 
 is distinctly nonexponential over the entire range . it is important 
 to note here that the fluence behavior is more complicated than in 
 standard bimolecular recombination , as the ability of the triplets 
 to annihilate depends not only on the rate of triplet diffusion but 
 also on the distribution of aggregate sizes , both quantities unknown 
 but likely to vary across the aggregate series . with this understanding 
 of tta in axt aggregates the fastest initial 
 decay is observed for the aggregates i and v that exhibit the strongest 
 intermolecular coupling  as would be anticipated , the triplet 
 pairs formed by singlet fission are similarly more strongly coupled 
 and annihilate quickly . conversely , the 
 decay over the first 1 ns is slowest in the relatively weakly coupled 
 aggregate ii . the dependence on excitation density and strong variation 
 in absorption cross - section between aggregates preclude direct comparison 
 of the longer - time decay kinetics , though all exhibit a similar characteristic 
 lifetime of order 1 s . as noted above , the process 
 of singlet fission identified in figure 3 is 
 largely complete within the instrument response of the sub - ps ta experiment . 
 to fully resolve the triplet formation , we performed sub-30 fs ta 
 measurements on the full set of aggregates as well as monomeric axt 
 in acetone and dmso . in dilute solution ( figure 6 ) we find that the monomer reproduces the behavior observed previously 
 using sub - ps ta , namely direct conversion of 1bu into a 
 hot 2ag state which rapidly cools . the higher time resolution 
 enables a clean determination of the 1bu  2ag internal conversion time constant , which we find to vary 
 with solvent from 105 fs in dmso to 125 fs in acetone with no discernible 
 intermediate states . it is unclear what environment is most appropriate 
 for comparison to axt molecules embedded in ( or at the surface of ) 
 aggregates , but this measurement establishes an approximate 100 fs 
 time scale with which singlet fission must compete to proceed efficiently . ( a ) transient absorption timeslices from sub-30 fs ta on monomeric 
 axt in dmso , showing smooth transition from 1bu ( pia below 
 1.5 ev ) to 2ag ( pia above 1.8 ev ) . the corresponding decay kinetics ( symbols ) in ( b ) dmso and ( c ) acetone 
 can be well described with an exponential time constant ( lines ) of 
 105 or 125 fs , respectively . iv , for which the fission 
 process can be most clearly distinguished , are presented in figure 7 . data for aggregates i and v can be found in the supporting information . in all cases , the spectra 
 agree well with the sub - ps ta measurements on the same aggregates . the initial state in all species has a pia in the nir , in the same 
 region where the 1bu state absorbs in monomeric axt . this 
 band rapidly decays , resulting in the same triplet signature identified 
 in figure 4b . to capture the time scale of 
 this process , the decay kinetics for each aggregate were globally 
 fitted with a simple biexponential function , revealing two distinct 
 temporal regimes : a sub-100 fs process that describes the formation 
 of triplet pia , and a slower ( hundreds of femtoseconds ) redshift consistent 
 with thermalization of the hot triplet pair state . these fits give 
 a singlet fission time constant of 85 , 90 , and 65 fs in aggregates 
 ii , iii , and iv , respectively , distinctly faster than the ultrafast 
 1bu  2ag internal conversion detected 
 in the monomer . to confirm the assignments from these decay 
 kinetics , the data 
 were analyzed with a spectral decomposition technique based on a genetic 
 algorithm . in aggregates ii iv , 
 the transition was best modeled with only two species ( figure 7d  f ) showing the characteristic features 
 of 1bu and the triplet described above . we observe singlet 
 fission directly from 1bu on time scales consistent with 
 the raw kinetic fitting and find no evidence of any other excited 
 states . the rates of triplet formation here are among the fastest 
 reported 
 for any intermolecular singlet fission system . this rapid fission 
 can not be explained solely by the energetic difference between singlet 
 and triplet pair states : the triplet energy should not change with 
 aggregation , while the singlet varies by over 1.2 ev . using typical 
 values , we may even expect the singlet 
 and triplet pair states to be nearly degenerate in aggregate v. the 
 two weakly coupled aggregates ii and iii are the slowest , forming 
 triplets with roughly the same time constant 90 fs . aggregate 
 iv exhibits even faster singlet fission , which we propose is related 
 to its stronger intermolecular coupling . indeed , in the two most strongly 
 coupled aggregates i and v we are unable to distinguish any state 
 prior to triplets within the temporal resolution of the measurement , 
 which was restricted in those systems to 70 fs due to scattering 
 and a strong coherent solvent response . unlike the initial rate 
 of tta , we find the rate of triplet formation 
 is only weakly dependent on the strength of intermolecular coupling . 
 indeed , the mechanism of singlet fission in these aggregates must 
 be remarkably robust : variation of the band gap over a range of 1.2 
 ev , with concomitant changes in the energetic driving force for triplet 
 pair formation , yields fission time constants that span the narrow 
 range 50100 fs . even in the most weakly bound aggregates 
 ii and iii , where singlet fission is only slightly faster than the 
 expected 1bu  2ag time scale , we detect 
 no signs of any other excited states , and we thus consider that this 
 initial step is highly efficient in all aggregates . the surprising 
 result that the ultrafast 1bu  
 2ag internal conversion channel of the monomer is completely 
 deactivated within the aggregates merits closer consideration . we 
 note that this internal conversion is generally accepted to proceed 
 via a conical intersection and is thus driven by nuclear motion . it is conceivable that the same crossing is 
 approached in the aggregates , with the important distinction that 
 the strong exciton coupling ensures a delocalized state . the predicted 
 triplet pair character of 2ag results in a short - lived 
 singlet state when it is confined to a single polyene chain , but delocalization 
 over multiple chromophores may allow sufficient separation between 
 the constituent triplets to give the state more triplet - like character . while such a model could explain the early time transient absorption 
 behavior , it is inconsistent with the energetic structure evident 
 from the analysis of tta kinetics . it may nonetheless be instructive 
 to consider in relation to other possible triplet pair states . we 
 propose instead that aggregation alters the vibrational landscape 
 and distorts the 1bu potential energy surface , such that 
 a crossing with the triplet pair state is strongly favored over that 
 with 2ag . full clarification of this intriguing behavior 
 will likely call for both extensive new computational studies of the 
 electronic structure of coupled polyenes and a detailed exploration 
 of vibronic coupling in the aggregates . ( a ) sub-30 fs ta measurements of aggregate 
 ii in the visible and nir spectral regions show a direct transition 
 from the initial singlet ( solid ) to triplets , already evident by 150 
 fs . equivalent 
 measurements on aggregates ( b ) iii and ( c ) iv reveal similar behavior . ( d  f ) 
 species extracted with a genetic algorithm using a two - state model 
 agree well with the characteristics of 1bu and triplet 
 excitons , and no additional states are needed to describe the data . ( g  i ) integrated decay kinetics for each aggregate type ( symbols ) 
 can all be globally fitted with biexponential functions ( lines ) capturing 
 the initial singlet fission process and subsequent relaxation of the 
 triplet pair . the singlet fission time constant varies with aggregate 
 structure , from 85 and 90 fs for ii and iii to 65 fs for iv . we 
 have isolated a system of five distinct aggregates of astaxanthin , 
 allowing adjustment of the intermolecular coupling while maintaining 
 the same monomer chemical and electronic structure . our transient 
 absorption measurements demonstrated that ultrafast singlet fission 
 occurs in all aggregate types . sub - ps ta data revealed the presence 
 of only two excitonic states  the bright 1bu singlet 
 exciton and the triplet produced via singlet fission  suggesting 
 a mechanism of singlet fission directly from 1bu rather 
 than via 2ag . this model is consistent with our previous 
 high - time - resolution measurements of intramolecular singlet fission 
 in polyenes , and also agrees with the 
 proposal of wang et al . we confirmed 
 this two - state model with sub-30 fs ta , demonstrating for the first 
 time in a polyene system that intermolecular singlet fission proceeds 
 directly from the initial 1bu state . furthermore , the purely 
 geminate tta dynamics immediately following singlet fission indicate 
 that the triplet pair energy is in fact greater than that of 2ag , which instead functions merely as an efficient decay pathway 
 back to a vibrationally excited ground state . in other words , the 
 mechanisms of singlet fission and subsequent tta in polyenes are strikingly 
 similar , whether the fission event is intramolecular like in poly(3-dodecylthienylenevinylene ) or intermolecular like in axt aggregates . these 
 findings raise important questions about the role of low - lying 2ag states . the existence of such a state appears to be a useful 
 sign of the ability to undergo singlet fission , but in polymers and 
 aggregates the state not only does not participate in triplet formation 
 but actually harms the overall yield . further theoretical work 
 is required to determine how the triplet 
 pair state forms directly from 1bu , a process beyond the 
 scope of current models . turning to recent high - level calculations 
 of polyene excited states , we note that another triplet pair state , 
 1bu , is predicted to lie just below 
 the initial allowed 1bu transition . the coupling between these states would likely be strong , 
 with consequently fast relaxation into the triplet pair . comparison 
 with the more established polyacenes sheds some light onto the mechanism 
 of singlet fission discussed here . in the most strongly coupled acenes 
 ( pentacene and tips - pentacene ) , singlet fission is described as adiabatic , 
 with a rate independent of intermolecular coupling strength . for the 
 majority of the more weakly coupled acenes , however , triplet formation 
 appears to be highly dependent on intermolecular coupling . by contrast , in astaxanthin similar sub-100 
 fs singlet fission kinetics are observed in strongly ( i , v ) and weakly 
 ( ii , iii ) coupled systems with large ( i ) and small ( v ) energetic driving 
 force . this suggests that singlet fission remains in the adiabatic 
 regime in all aggregates and may reflect a unique property of singlet 
 fission in polyenes . this is perhaps not surprising given the widely 
 accepted role of conical intersections in carotenoid photophysics , 
 and it will be important to investigate how vibrational dynamics are 
 implicated in singlet fission within the aggregates . a recent study 
 of tips - pentacene , for example , has revealed that ultrafast triplet 
 formation is mediated by vibronic coupling between s1 and 
 the triplet pair state , and a similar 
 mechanism may apply here . our results also allow important insight 
 into the processes following 
 triplet generation . the observation of two distinct regimes of tta  fast 
 geminate and slow bimolecular  highlights the unique quantum 
 mechanical properties of triplet pairs generated through singlet fission , 
 which are initially entangled into an overall singlet state . the conversion 
 from geminate to bimolecular recombination reflects a combination 
 of the time scales for triplet pair separation and de - coherence and 
 triplet diffusion , affording a window to study these processes with 
 multipulse techniques or under applied fields and build a model of 
 how and why triplet pairs break apart . more broadly , this system of 
 carotenoid aggregates can serve as a platform to investigate tta and 
 how it can be controlled through material properties , which is of 
 great interest in the context of triplet - based light - emitting diodes . an understanding of such annihilation processes 
 and their interrelation with intermolecular coupling and triplet generation 
 will be essential to realize the full potential of singlet fission 
 in solar energy harvesting .