Collisional relaxation of apocarotenals: identifying the S* state with vibrationally excited molecules in the ground electronic state S 0 * †

In recent work, we demonstrated that the S* signal of b -carotene observed in transient pump–supercontinuum probe absorption experiments agrees well with the independently measured steady-state difference absorption spectrum of vibrationally hot ground state molecules S 0 * in solution, recorded at elevated temperatures (Oum et al. , Phys. Chem. Chem. Phys. , 2010, 12 , 8832). Here, we extend our support for this ‘‘vibrationally hot ground state model’’ of S* by experiments for the three terminally aldehyde-substituted carotenes b -apo-12 0 -carotenal, b -apo-4 0 -carotenal and 3 0 ,4 0 -didehydro- b , c -caroten-16 0 -al (‘‘torularhodinaldehyde’’) which were investigated by ultrafast pump–supercontinuum probe spectroscopy in the range 350–770 nm. The apocarotenals feature an increasing conjugation length, resulting in a systematically shorter S 1 lifetime of 192, 4.9 and 1.2 ps, respectively, in the solvent n -hexane. Consequently, for torularhodinaldehyde a large population of highly vibrationally excited molecules in the ground electronic state is quickly generated by internal conversion (IC) from S 1 already within the first picosecond of relaxation. As a result, a clear S* signal is visible which exhibits the same spectral characteristics as in the aforementioned study of b -carotene: a pronounced S 0 - S 2 red-edge absorption and a ‘‘finger-type’’ structure in the S 0 - S 2 bleach region. The cooling process is described in a simplified way by assuming an initially formed vibrationally very hot species S 0 ** which subsequently decays with a time constant of 3.4 ps to form a still hot S 0 * species which relaxes with a time constant of 10.5 ps to form S 0 molecules at 298 K. b -Apo-4 0 -carotenal behaves in a quite similar way. Here, a single vibrationally hot S 0 * species is sufficient in the kinetic modeling procedure. S 0 * relaxes with a time constant of 12.1 ps to form cold S 0 . Finally, no S 0 * features are visible for b -apo-12 0 - carotenal. In that case, the S 1 - S 0 IC process is expected to be roughly 20 times slower than S 0 * relaxation. As a result, no spectral features of S 0 * can be found, because there is no chance that a detectable concentration of vibrationally hot molecules is accumulated.


Introduction
Photoexcitation of a carotene in the blue-green spectral region provides access to its optically bright second electronically excited state S 2 (1 1 B u + ).The subsequent dynamics of carotenoids in solution and in light-harvesting arrangements have been interpreted in the framework of various kinetic models involving different electronic states, with several of them still being the subject of considerable debate. 1,2The simplest model for the intramolecular nonradiative relaxation of a carotenoid considers only two consecutive internal conversion (IC) steps via the S 1 (2 1 A g À ) to the S 0 (1 1 A g À ) state, as shown in Fig. 1(A).In this simplest case, modeling the optical response of such a kinetic system would require only three species-associated spectra (SAS) for S 0 , S 1 and S 2 and the time constants t 2 and t 1 for the two IC processes.
However, the situation is indeed much more complicated: firstly, the SAS of all species S i (i = 0-2) depend on the excess energy in the respective state: ''Vibrationally hot'' molecules S i * show characteristic and complex spectral changes, including an increase of absorption at the red edge of the electronic band and a decrease of absorption maxima.][5][6][7] Due to collisional energy transfer (CET) to the surrounding solvent molecules, the SAS will change with a characteristic time constant t CET , typically in the range 7-15 ps for standard organic solvents. 4,6,7n addition, it has to be kept in mind that a simple single exponential decay of a transient absorption signal due to CET can only be expected if the absorption coefficient of the relaxing molecule linearly depends on its internal energy and at the same time the average energy transferred per collision hDEi linearly depends on internal energy. 4econdly, even for a fixed energy in an electronic state, the way the energy is distributed among the different vibrational modes might severely affect the appearance of the SAS.For instance, IC of a carotene from S 2 to S 1 initially produces an excited S 1 state with a non-statistical energy distribution.The energy will ''randomize'' over time, eventually leading to a statistical distribution (provided the electronic state lives long enough).This process is well-known as ''intramolecular vibrational redistribution (IVR)''. 5,8It is accompanied by considerable spectral changes of the SAS 9,10 because energy will be ''reshuffled'' between optically ''dark'' and ''bright'' modes.
Thirdly, the IC time constants t i (i = 1, 2) may also vary with internal energy in the respective state S i .For instance, it is well known from molecular beam experiments that IC rate constants increase with excess energy, e.g. by two or more orders of magnitude in the case of azulene in the S 2 and toluene in the S 1 state, when their excess energy is raised from 0 to 10 000 cm À1 . 11,12 complete description of such a kinetic system is complicated, because the SAS of each species S i smoothly changes with its internal energy (as probably also does its lifetime).
We recently introduced a simplified kinetic treatment where such spectral changes are modeled by using time-dependent SAS.This way, IVR in S 1 and collisional relaxation of the hot ground state S 0 * of b-carotene derivatives was successfully described. 6,7lternatively, following an Occam's razor approach, one may resort to a simplified kinetic scheme with a sufficient number of species (with static SAS) and time constants to describe the essentials of the dynamics, leading us to the scheme in Fig. 1(B): after photoexcitation to S 2 , a ''hot'' S 1 ** species 9,10 is quickly formed by IC (typically t 2 o 200 fs). 1 S 1 ** experiences fast IVR forming an isoenergetic S 1 * species with a different spectrum.For b-carotene derivatives in n-hexane, one expects a time constant t IVR,1 in the range 400-600 fs. 7Collisional relaxation t CET,1 is expected to be much slower than IVR, as already mentioned, in the 7-15 ps range.Therefore, the sequential relaxation scheme within S 1 should be accurate enough.
The relaxation processes within S 1 compete with electronic relaxation to the ground electronic state by IC.As noted above, IC of the isoenergetic S 1 ** and S 1 * species is possibly faster than for the relaxed S 1 species, because of their higher internal energy.Nevertheless, due to the fact that energy dependent t 1 values are not yet experimentally available for carotenoids, we assume here the same IC time constant t 1 for all three S 1 species.IC accesses a vibrationally ''hot'' S 0 species, denoted as S 0 **.Especially for short lifetimes t 1 of the S 1 state, description of the spectral development of the hot ground state by a single spectrum might not be sufficient, and therefore we also consider here a slightly cooled-down species S 0 *.Note that the spectral shape of the hot ground state species in reality smoothly varies with excess energy. 4,5Relaxation of a carotenoid by collisional energy transfer to the solvent is then described by two collisional cooling time constants t CET,0a and t CET,0b , respectively.The scheme in Fig. 1(B) will serve as the basis for describing the carotenoid systems studied here.
It should be noted that additional spectral features have been observed which have been assigned to different intermediates formed during the electronic relaxation of carotenoids.For instance, the S* signal was observed which is still under debate. 2,6,7,13Others and we identify this S* signal as the vibrationally hot ground electronic state (S 0 **/S 0 *) discussed above, 6,7,[14][15][16][17][18] Alternatively, S* has been either described as an electronically excited state, [18][19][20][21][22][23][24] different S 0 conformers, 25,26 or the vibrationally hot S 1 state. 27n our previous investigations of b-carotene and 13,13 0 -diphenylb-carotene, we presented strong evidence that the S* spectral features found in broadband transient absorption experiments arise from the characteristic absorption of vibrationally ''hot'' carotene molecules in S 0 which are generated by IC from the S 1 state, i.e. the S 0 **/S 0 * species in Fig. 1(B). 6,7These species showed the typical ''hot band'' absorption on the red edge of the S 0 -S 2 absorption band and a characteristic ''finger-type'' structure in the S 0 -S 2 ground-state bleach (GSB).Both result from the subtraction of the ''cold'' (298 K) GSB spectrum from the transient ''hot'' spectra of the S 0 **/S 0 * molecules.This interpretation was strongly supported by the result of steadystate temperature-dependent absorption spectra, which nicely reproduced the difference spectra in the transient absorption experiments, including the ''hot band'' absorption and the ''finger-type'' structure. 6ere, we provide additional strong support for this mechanism and the relaxation scheme in Fig. 1(B) by a systematic study of S 0 **/S 0 * spectral features for three all-trans apocarotenals featuring increasing conjugation lengths (Fig. 2).This way, the S 1 lifetime and thus the time constant t 1 for generating S 0 **/S 0 * population via IC from S 1 can be precisely varied in wide ranges. 1,28On the other hand, it is a well-known fact that time constants of collisional relaxation t CET in solution do not strongly depend on the type of the vibrationally excited molecule (e.g.10-13 ps in the case of azulene in n-alkanes). 4,6,7Therefore one should be able to ''tune'' the intensity and spectral shape of the S 0 * state spectral features by variation of the conjugation length of the apocarotenal.As will be shown below, we indeed observe exactly such a behavior in the apocarotenal systems and therefore believe that the spectral features of S* arise from vibrationally hot molecules in the ground electronic state.

Pump-supercontinuum probe (PSCP) spectroscopy
0][31][32] The apocarotenal sample was excited by a NOPA (l pump = 490 or 500 nm, beam diameter ca.250 mm, energy ca.1.0-1.5 mJ pulse À1 ) and probed by a supercontinuum (350-770 nm, beam diameter ca.150 mm), with the relative polarization set at magic angle.The pump-probe intensity cross-correlation time was ca.90 fs, with a time zero accuracy of ca. 10 fs.To avoid any influence of photoinduced sample degradation, 10-15 mL of an apocarotenal solution in n-hexane was circulated through a flow cell (path length 400 mm, window thickness 200 mm), so that the sample volume was exchanged after each pump-probe experiment (repetition frequency 920 Hz).Solutions with an OD (at maximum, 400 mm path length) of 0.333 (b-apo-12 0 -carotenal), 0.174 (b-apo-4 0 -carotenal) and 0.752 (torularhodinaldehyde) were employed.For these conditions, the transient absorption signals were in the linear regime, as confirmed in separate experiments.Steady-state absorption spectra of the sample solutions were recorded on a Varian Cary 5000 dualbeam spectrometer.

Global analysis procedure
The PSCP spectra were chirp-corrected by using the transient response of the pure n-hexane solvent.The spectra were then subjected to kinetic modeling.Each data set, which consisted of 512 kinetic traces, was analyzed globally using the kinetic schemes discussed below.Each species-associated spectrum was represented by a sufficiently large number of Gaussian functions, and only the known S 0 spectrum was kept fixed.During the fitting procedure, all parameters (position, width, height of the Gaussian functions and time constants of the kinetic model) were optimized simultaneously to arrive at the best fit, which also considered the experimentally determined time resolution by a convolution procedure.  of the apocarotenals, suggesting a reduction of the S 0 -S 2 energy gap.At the same time, the structure of the electronic band becomes more pronounced.The latter can be explained by a reduced influence of the terminal b-ionone ring on the absorption properties of the carotenes, as suggested by Christensen et al.: 33 according to their ''distribution of conformers'' model, conformations featuring different torsional angles C5-C6-C7-C8 (Fig. 2) of the b-ionone ring with respect to the rest of the polyene system, result in different ''effective conjugation lengths'', and thus a distribution of transition energies.The impact of this effect will be much weaker for a larger number of conjugated double bonds, thus the spectra will show more structure and appear more resolved.

Ultrafast dynamics of torularhodinaldehyde
We commence with the PSCP transient absorption data for torularhodinaldehyde in n-hexane, shown in Fig. 4. The carotene was excited at 500 nm (S 0 -S 2 band).The top panel shows the dynamics around t = 0. We observe a pronounced bleach of the ground electronic state centered at 510 nm.In addition, absorption features appear in the 570-770 nm range.We assign these to S 2 -S n excited state absorption (ESA), in agreement with our earlier PSCP experiments on other carotene systems. 6,7,31he wavelength range below 450 nm appears to be spectrally silent, however, based on the inverted steady-state absorption spectrum, shown in the bottom panel as a dotted orange line, it is clear that there must be superimposed broad and unstructured S 2 -S n ESA in this wavelength range compensating the bleach.
In the middle panel, the spectral development up to 0.45 ps is depicted.One observes the rise of a strong S 1 -S n ESA band above 560 nm, as a result of S 2 -S 1 internal conversion (IC) with a time constant t 2 = 200 fs, obtained from a global analysis procedure.The value is reasonable, compared with our earlier values found for b-carotene derivatives (160 fs), yet it could be also shorter, as the spectral dynamics could be ''contaminated'' by fast relaxation processes of the nascent S 1 ** state due to IVR.While there is a slight narrowing of the S 1 ESA band, a separate time constant t IVR,1 cannot be reliably determined.The region below 450 nm remains spectrally silent.This suggests that there is an S 1 -S n ESA band which must be similarly unstructured and weak as in the case of the S 2 state.
The bottom panel shows the dynamics on longer timescales.Starting from 0.5 ps (black line), the absorption band decays in a non-uniform way: the peak centered at 600 nm quickly disappears, and what remains is a relatively broad absorption in the range 550 to 650 nm, see e.g. the green spectrum at 4 ps.We assign this process to IC from S 1 with a time constant t 1 = 1.2 ps.In addition, the peaks in the bleach region are more and more sharpening.Based on our previous findings for b-carotene derivatives, 6,7 we assign the remaining spectral features to the almost pure difference spectrum of vibrationally hot S 0 molecules which are generated by the fast IC process.The shape of this spectrum is explained as follows: first, a spectral hallmark of such species is a ''hot-band'' absorption (resulting from absorption of the population in the ''Boltzmann tail'') which should appear on the red edge of the room-temperature electronic spectrum (compare Fig. 3).Indeed, a pronounced absorption ''bump'' is located between 570 and 650 nm, see also the inset in the bottom panel of Fig. 4 for the spectra at 10 ps (blue line) and 18 ps (red line).The structured bleach in the 470-570 nm region results from another typical spectral property of vibrationally hot molecules, namely a decrease of spectral maxima and increase of spectral minima compared to room temperature spectra, see e.g.previous temperature-dependent gas-phase studies of the electronic spectra of azulene and anthracene by Schwarzer and co-workers 5 and our previous temperature dependent study of b-carotene steady-state absorption spectra in solution. 6Subtraction of the room-temperature steady-state absorption spectrum from a transient spectrum will therefore result in a pronounced undulatory structure in the bleach region.This is also clearly seen in the inset of the bottom panel in Fig. 4 for the spectra at 10 and 18 ps.The ''modulation depth'' of the maxima and minima in the two transient spectra is much stronger than for the room temperature spectrum (orange dotted line in the bottom panel).Its short S 1 lifetime makes torularhodinaldehyde a textbook example for studying S 0 * collisional energy transfer of carotenoids in solution.As shown in more detail below, collisional relaxation in the ground electronic state can be modeled best by employing two ''hot'' species S 0 ** and S 0 * in the global kinetic analysis, relaxing with time constants of 3.4 and 10.5 ps, respectively.The second time constant agrees well with our previous findings for b-carotene derivatives in the same solvent: 11.9 ps for b-carotene 6 and 10.4 ps for 13,13 0 -diphenyl-bcarotene. 7 In the latter two cases, the S 0 * state features were weaker, because of the seven times larger S 1 lifetime (t 1 = 8.7 and 9.2 ps, respectively), and the correspondingly smaller S 0 * transient absorption features.The cooling time constant of S 0 * of torularhodinaldehyde also compares well with vibrational relaxation time constants of smaller organic molecules, such as azulene, where one finds t CET,0 = 10-13 ps for a series of alkanes. 4

Photoinduced dynamics of b-apo-4 0 -carotenal
To further test the aforementioned generation and cooling mechanism of S 0 * molecules, we examined the photoinduced dynamics of b-apo-4 0 -carotenal in n-hexane.This carotenoid possesses the same type of chromophore as torularhodinaldehyde, yet the conjugated polyene system is slightly shorter.This should lead to a longer S 1 lifetime, as already suggested by results from our previous single-wavelength pump-probe studies in various solvents. 28SCP spectra are shown in Fig. 5.In the top panel, the earlytime dynamics around t = 0 are similar to those for torularhodinaldehyde, with pronounced S 0 -S 2 bleach features centered at 500 nm and weak S 2 -S n ESA above 600 nm.In the middle panel, the formation of S 1 -S n ESA is observed, with a time constant t 2 = 180 fs, again very similar to torularhodinaldehyde.However, we note that the peak of the bleach and the S 1 ESA are shifted to the blue by ca.840 cm À1 and 570 cm À1 , respectively, a result of the shorter conjugation length of b-apo-4 0 -carotenal.
The bottom panel depicts the behavior on longer time scales.The decay time of the S 1 ESA band (peak at 590 nm) is t 1 = 4.9 ps.The time constant of the S 1 -S 0 * IC process is thus by a factor of four larger than for torularhodinaldehyde.This becomes particularly clear in the inset, where the blue spectrum at 10 ps still shows a remainder of the S 1 ESA peak at 590 nm (in contrast to Fig. 4) overlapped by the characteristic signature of the vibrationally hot S 0 * molecules formed by the IC process.The ''S 0 * part'' of the transient spectrum at 10 ps shows the same fingerprints as in Fig. 4: a ''hot band'' absorption at 560 nm and a bleach which is much more structured than the ground state bleach of cold S 0 molecules.Importantly, the blue-shift of the S 0 * state difference spectra (840 cm À1 ) is identical to the blue-shift of the S 0 -S 2 steady-state absorption spectra, in agreement with the assignment to a hot groundstate species.The decay time of the S 0 * state feature obtained from global spectral analysis is t CET,0 = 12.1 ps, in line with the S 0 * collisional cooling time of torularhodinaldehyde.

Ultrafast dynamics of b-apo-12 0 -carotenal
So far, we have presented transient spectra for two apocarotenals where t 1 o t CET,0 , i.e. the S 0 * species are formed faster than they are cooled by collisions.As a result, pronounced transient spectral features of S 0 * were clearly identified.We now turn to an example, where t 1 c t CET,0 .In such a case, cooling of S 0 * molecules by collisions with solvent molecules is much faster than their generation from S 1 .Thus, a detectable concentration of vibrationally hot S 0 * species in the ground electronic state is never accumulated and spectral features of S 0 * should be absent.
Experimentally, such conditions are established by further shortening the polyene chain of an apocarotenal, which largely increases t 1 , 28,34,35 whereas the time constant for collisional energy transfer t CET is much less sensitive to such a structural modification, as demonstrated by the results for torularhodinaldehyde and b-apo-4 0 -carotenal in this paper and previous experiments on a range of organic molecules. 4,36Here, we therefore choose b-apo-12 0 -carotenal which features a rather short conjugation length.In our previous preliminary studies on this molecule we found a lifetime t 1 of ca.200 ps, 34,35 therefore one expects t 1 E 20Át CET,0 in this case.
PSCP spectra of b-apo-12 0 -carotenal in n-hexane (l pump = 490 nm) are presented in Fig. 6.The behavior at early times in the top panel is shown for the same delay times as in Fig. 4  and 5.Because of the much shorter conjugation length, the pronounced S 0 -S 2 ground state bleach appears in the range 360-470 nm, in agreement with the steady-state absorption spectrum (Fig. 3).We note that the center peak at 430 nm is due to anti-Stokes Raman scattering of the C-H stretching modes of n-hexane and only present during temporal overlap of the pump and probe pulses.Above 470 nm, one observes S 2 -S n ESA features, again blue-shifted compared to torularhodinaldehyde and b-apo-4 0 -carotenal.
In the middle panel one finds that the S 2 -S n ESA quickly disappears due to ultrafast IC (t 2 = 105 fs) and is replaced by a pronounced S 1 -S n ESA band.The S 1 state undergoes further internal relaxation, as indicated by the green, blue and red lines for delay times of 0.50, 1 and 10 ps, respectively.The ESA band becomes sharper, and especially the peak at 510 nm rises.We assign these dynamics to two processes: fast IVR of the initially prepared S 1 ** species with a time constant t IVR,1 = 0.44 ps to form S 1 *.The value is in very good agreement with values previously obtained by us for IVR timescales of b-carotene derivatives. 6,7The second, slower, process is collisional deactivation of S 1 * by the n-hexane solvent with a time constant of t CET,1 = 8.3 ps.Note that the latter process is analogous to the S 0 * -S 0 relaxation discussed above, however the initial vibrational excess energy of the S 1 * molecules is of course lower and therefore the ''hot band'' dynamics in the S 1 state is less pronounced.Still it is clearly detectable for b-apo-12 0 -carotenal because its S 1 lifetime is much larger than for torularhodinaldehyde and b-apo-4 0 -carotenal.
In the bottom panel, one follows the slow S 1 -S 0 IC process from the internally almost relaxed S 1 state with a time constant of 192 ps.The S 1 -S n ESA band decays and at the same time the ground state bleach is filled up.There is an isosbestic point at 460 nm and, in contrast to the other two apocarotenals, we do not find indications for spectral features of S 0 *.

Simplified kinetic schemes for apocarotenals in n-hexane
The transient PSCP spectra of the three apocarotenal systems were analyzed using simplified forms of the general scheme in Fig. 1(B).In the case of torularhodinaldehyde and b-apo-4 0carotenal we could not observe clear spectral indications of IVR of S 1 **, except for a very minor narrowing of the S 1 band, which did not allow us to extract a reliable value for t IVR,1 .Also, because of the short IC lifetime t 1 , spectral indications for the collisional relaxation of S 1 * are of course not present, and therefore a single S 1 species is sufficient for modeling the dynamics.
We simulate the results for torularhodinaldehyde employing the simplified sequential scheme in Fig. 7(A).Because of the very short S 1 lifetime of 1.2 ps, a substantial population of hot ground state molecules with initially high excess energy is quickly generated.Two vibrationally hot species S 0 ** and S 0 * are  This journal is © the Owner Societies 2015 employed to describe the complex change of the hot ground state spectrum resulting from vibrational cooling by solvent collisions.The corresponding SAS are shown in Fig. 8(A).Characteristic spectral changes due to collisional energy transfer are evident in the S 0 **, S 0 * and S 0 spectra (green, red and blue): the pronounced hot band at ca. 620 nm in the S 0 ** spectrum disappears upon cooling and the spectrum narrows, leading to S 0 * which then further cools down to 298 K (S 0 ).Time constants of 3.4 and 10.5 ps are found for this collisional cooling process.Such biexponential dynamics is not unusual and expected if the absorption coefficient of S 0 does not linearly depend on excess energy. 4The oscillator strength of the S 0 species is approximately conserved, as expected for a CET process.Note also that the spectral development is comparable to b-carotene derivatives, as previously reported by us in ref. 6 and 7. similar spectral behavior of vibrationally hot ground state molecules is also observed for other organic molecules, compare e.g. the temperaturedependent absorption spectra for azulene and anthracene reported in Fig. 3 and 4 of ref. 5.This experimental evidence therefore supports our assignment of the S* spectral features 2 to vibrationally hot ground state molecules.Kinetic traces for three selected wavelengths are included in Fig. 9.They show the superposition of the fast S 1 decay dynamics with the collisional relaxation of the hot S 0 **/S 0 * species resulting in the curved shape and the slow final decay of the transients.Global fit parameters are summarized in Table 1.
Our interpretation is further confirmed for b-apo-4 0 -carotenal.SAS can be found in Fig. 8(B).Because of the longer S 1 lifetime of t 1 = 4.9 ps and the therefore slower production of hot ground state molecules, collisional cooling (t CET = 12.1 ps) competes more efficiently.As a result, the PSCP spectra can be fully modeled by considering the simplified kinetic scheme given in Fig. 7(B), including only a single (cooler) hot ground state species S 0 *.Note that the resulting SAS for S 0 * is very similar to the slightly cooled S 0 * species of torularhodinaldehyde. Three selected kinetic traces are shown in Fig. 10.Here, the longer lifetime of S 1 is evident (4.9 vs. 1.2 ps for torularhodinaldehyde), and therefore the S 1 decay is not as clearly separated from the cooling process of S 0 * as in the case of torularhodinaldehyde.A summary of global fit parameters is included in Table 1.
In the case of b-apo-12 0 -carotenal, IC from the S 1 state is very slow: t 1 c t IVR,1 , t CET,1 .As a result, IVR and CET in S 1 should be clearly observable.At the same time, this also means that t 1 c t CET,0 .Therefore, the steady-state approximation for S 0 * holds, and thus the concentration of S 0 * will be very small at all times.One therefore does not expect to see any S 0 * spectral features and thus the simplified scheme in Fig. 7(C) is applied.The resulting SAS are depicted in Fig. 8(C).Characteristic spectral changes accompany the relaxation within the S 1 state: the initially formed S 1 ** species shows a broad spectrum (green line) extending to the upper wavelength limit of our spectral observation window, including a small but distinct peak at 700 nm.The main peak at 510 nm is already visible but it is small and broad, as is the rest of the spectrum.Due to fast IVR, an S 1 * species is quickly formed (t IVR,1 = 440 fs), which is internally equilibrated.This species exhibits a narrower spectrum and steeper main peak (red line).S 1 * then relaxes further by CET to the solvent to form the room temperature S 1 species (black line), with the aforementioned time constant t CET = 8.3 ps.Because of very slow IC to S 0 (t 1 = 192 ps) we do not find spectral indications for an S 0 * species which due to its extremely low concentration is below the detection limit.
Three representative kinetic traces are depicted in Fig. 11.CET in S 1 is apparent in the 501 nm transient as a characteristic round shape in the 2-30 ps range.Here the steepening of the main peak of the S 1 ESA band due to CET is superimposed by slow population loss due to IC to S 0 .Kinetic parameters obtained from the global analysis are again summarized in Table 1.
The impact of vibrationally highly excited S 0 and S 1 species for the different apocarotenals is finally highlighted in Fig. 12, where PSCP spectra (open circles) and global analysis results (lines) are shown for the fixed delay time of 10 ps.
For torularhodinaldehyde (Fig. 12(A)), the S 1 population has already completely decayed (flat magenta line), and the structured    This journal is © the Owner Societies 2015 spectrum is a result of the superposition of hot ground state absorption (mainly S 0 * (red), but also S 0 **(green)) and the bleach of room-temperature S 0 molecules (blue).For b-apo-4 0 -carotenal (Fig. 12(B)), the resulting spectrum is a superposition of remaining S 1 absorption (magenta), hot ground state absorption of S 0 * (red) and the bleach of cold S 0 molecules (blue).The S 1 and S 0 * contributions are responsible for the characteristic broad double-peak structure in the range 560-590 nm, which we similarly observed previously for b-carotene and 13,13 0 -diphenyl-b-carotene, 6,7 which feature only a slightly longer S 1 lifetime (ca. 9 ps).
In the case of b-apo-12 0 -carotenal (Fig. 12(C)), the spectrum at 10 ps contains only ESA contributions from the S 1 and S 1 * species (CET in the first electronically excited state is still ongoing), which is superimposed by the bleach of cold S 0 molecules (blue).Because of the long S 1 lifetime (192 ps) the concentration of S 0 * molecules is negligible, and therefore spectral features of S 0 * are not visible at all.

Conclusions
We have demonstrated that three apocarotenals with very different S 1 lifetimes can be described by simplified versions of the relaxation model in Fig. 1(B), considering only three electronic species S 2 , S 1 and S 0 and additional ''distortions'' of their spectra due to internal vibrational excess energy or incomplete IVR (Fig. 7).These ''spectral distortions'' were captured in a simplified kinetic model by introducing vibrationally ''hot'' electronic species S 0 **, S 0 * and S 1 * and a not internally equilibrated S 1 ** species.The visibility of these species in transient spectra depends on the specific value of the S 1 lifetime t 1 , e.g. if it is much larger or much smaller than typical time constants for collisional relaxation (t CET E 10 ps).The spectral properties of the ''hot'' species found in our global analysis are completely consistent with experimental data in the literature for vibrationally hot organic molecules, e.g.showing a characteristic hot band absorption tail reaching by 1000-2000 cm À1 toward the red spectral range. 4,5Moreover, in our previous study of b-carotene, the difference absorption spectrum of S 0 * was independently measured in separate temperature-dependent steady-state absorption experiments and found to be very similar to the S* spectral features in the transient absorption spectra. 6The same characteristic spectral signatures are found in the current study for torularhodinaldehyde and b-apo-4 0 -carotenal, see Fig. 12(A) and (B), and this striking similarity is further highlighted in the comparison shown in Fig. S1 of the ESI.† We also believe that this model is applicable to a wide range of carotenoids.As one example, we already demonstrated in two previous studies that the photoinduced processes of two b-carotene derivatives are well described in the same way. 6,7As another example, clear S 0 *-like spectral signatures were found by Gillbro and co-workers for the longchain dodecapreno-b-carotene which features a very short S 1 lifetime of t 1 = 0.5 ps. 14Its spectral features are very similar to those of torularhodinaldehyde.
Also, various observations from previous experimental transient absorption studies of carotenoids can be traced back to vibrationally hot ground state molecules: for instance, Papagiannakis et al. 37 and Savolainen et al. 38 found that the excitation intensity modified the intensity ratio between S* and S 1 absorption signals for carotenoids bound to natural and artificial light-harvesting complexes.In both cases, the S*/S 1 absorption ratio increased when the pump energy was increased and entered the nonlinear regime.Such a behavior can be traced back to the increasing influence of a two-photon excited population with high initial excess energy.After IC, such carotenoid molecules will enter S 0 with an excess energy much higher than for an initially one-photon excited population.The S 0 ** spectrum of these molecules with high internal temperature will be considerably distorted giving rise to much stronger hot band absorption features than those of the onephoton excited S 0 * population.
In addition, Billsten et al. observed that the intensity of the S* signal of zeaxanthin was correlated with the amount of initial excess energy: 39 the S* absorption features became more pronounced when decreasing the excitation wavelength (485, 400 and 266 nm).This can be explained in the same way as above.For higher initial excitation energies, zeaxanthin will enter S 0 with much higher excess energy which gives rise to more pronounced S* absorption features.We therefore believe that extensions of our kinetic model will be only required in special cases: for instance, systems such as b-apo-12 0 -carotenal are known to exhibit significant charge transfer character in polar solvents, including the appearance of substantial stimulated emission and a drastic reduction of the S 1 lifetime: 28,34,35,40,41 the first electronically excited state is then better termed ''S 1 /ICT'', [42][43][44] but the basic model of three electronic states survives.Because formation of the S 1 /ICT state leads to a substantial change in dipole moment, solvation dynamics will induce a transient Stokes shift of the S 1 /ICT stimulated emission and possibly also excited state absorption features, as already demonstrated by us previously. 34In the simplest approach, solvation dynamics can be handled e.g. by introducing an additional S 1 species in the models of Fig. 1(B) and 7 or by introducing a time-dependence for the S 1 spectrum, as demonstrated by us previously. 6,7Short-chain apocarotenals, such as all-trans-retinal (= all-trans-b-apo-15-carotenal), might constitute another special class.In that case triplet formation (via an intermediate np* state) and trans-cis isomerization were proposed as additional channels. 41,45

Fig. 1
Fig. 1 Two kinetic schemes for the interpretation of carotenoid photophysics.Horizontal and tilted arrows denote electronic transitions between different singlet states, whereas vertical arrows denote intramolecular vibrational redistribution or vibrational cooling by collisional energy transfer to the surrounding solvent.

Fig. 3 Fig. 2
Fig. 3 shows steady-state absorption spectra of the three apocarotenals in n-hexane solution at 298.15 K. Upon extension of the polyene chain, there is a clear red-shift of the S 0 -S 2 band

Fig. 4
Fig. 4 Transient PSCP absorption spectra of torularhodinaldehyde in n-hexane for excitation at 500 nm: (upper panel) À0.2-0 ps with 20 fs steps; (middle panel) 0.05-0.45ps with 50 fs steps; (lower panel) 0.5-3 ps and 4-10 ps with 0.5 ps and 2 ps steps, respectively, and 18 ps.Selected transient spectra are shown as thick colored lines for guidance.For comparison, the inverted and scaled steady-state absorption spectrum is shown in the lower panel as an orange dotted line.The inset in the bottom panel shows a magnification of the spectra at 10 and 18 ps.

Fig. 5
Fig. 5 Transient PSCP absorption spectra of b-apo-4 0 -carotenal in n-hexane for excitation at 500 nm: (upper panel) À0.2-0 ps with 20 fs steps; (middle panel) 0.05-0.50ps with 50 fs steps; (lower panel) 1-8 ps with 1 ps steps and 10, 14 and 18 ps.Selected transient spectra are shown as thick colored lines for guidance.For comparison, the inverted and scaled steadystate absorption spectrum is shown in the lower panel as an orange dotted line.The inset in the bottom panel shows a magnification of the spectra at 10 and 18 ps.

Fig. 6
Fig. 6 Transient PSCP absorption spectra of b-apo-12 0 -carotenal in n-hexane for excitation at 490 nm: (upper panel) À0.2-0 ps with 20 fs steps; (middle panel) 0.10-0.50ps with 50 fs steps, 1 ps and 10 ps; (lower panel) 20 ps and 50 ps, 100-600 ps with 100 ps steps.Selected transient spectra are shown as thick colored lines for guidance.For comparison, the inverted and scaled steady-state absorption spectrum is shown in the lower panel as an orange dotted line.

a
Pump-probe intensity cross-correlation of the experiment.b Internal conversion (IC) time constant for S 2 -S 1 , initially populating a hot S 1 state (S 1 **), which is not internally equilibrated.c Time constant for narrowing of the S 1 -S n ESA band due to IVR (intramolecular vibrational redistribution; fast process) and CET (collisional energy transfer; slow process), not clearly assignable for torularhodinaldehyde and b-apo-4 0carotenal because of the short S 1 lifetime.d Internal conversion (IC) time constant populating the vibrationally hot ground electronic state.e Time constants for collisional energy transfer in the ground electronic state.Two time constants are required for torularhodinaldehyde, whereas for b-apo-4 0 -carotenal one time constant suffices.In the case of b-apo-12 0 -carotenal, IC from S 1 is very slow: thus the concentration of S 0 * is very low and its contribution to the PSCP spectra too low to be detected.

Table 1
Kinetic parameters from global analysis for apocarotenals featuring different conjugation lengths in the solvent n-hexane