Mechanistic insight into internal conversion process within Q-bands of chlorophyll a

The non-radiative relaxation of the excitation energy from higher energy states to the lowest energy state in chlorophylls is a crucial preliminary step for the process of photosynthesis. Despite the continuous theoretical and experimental efforts to clarify the ultrafast dynamics of this process, it still represents the object of an intense investigation because the ultrafast timescale and the congestion of the involved states makes its characterization particularly challenging. Here we exploit 2D electronic spectroscopy and recently developed data analysis tools to provide more detailed insights into the mechanism of internal conversion within the Q-bands of chlorophyll a. The measurements confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of a previously unidentified ultrafast (40 fs) intermediate step, involving vibronic levels of the lowest excited state.

More recent interpretations state that Q x and Q y transitions, far from being independent transitions, are strongly mixed. Since Q x is nearly resonant with the vibronically active mode of Q y at 1500 cm −1 , the x-polarized intensity is split nearly equally into two components and thus it is distributed over the entire Q-band system [33][34][35] .
More hints about the nature of the states can be obtained through the analysis of the 2DES maps, where different electronic transitions can be distinguished and mapped at different positions in the 2D plots. Two sets of measurements have been performed using two different exciting bandwidths. In the first set, the exciting laser spectrum was tuned to cover mainly the S 0 → S 1,0 (Q y (0, 0)) transition to characterize the relaxation dynamics of the lowest excited state. In the second set, the exciting laser spectrum was moved towards higher energies to capture the relaxation dynamics between S 2 and S 1 states. It is now known that the particular choice of the exciting band has dramatic consequences on the shape of the 2DES spectra and on the amplitude distribution of the signal relative to vibrational coherences, because the finite bandwidth acts like a spectral filter with non trivial effects 36,37 . The interpretation of the experimental data has therefore been supported by theoretical simulation of the 2DES responses, accounting for the effective spectral shape and time convolution of the exciting pulses 38 .

Results and Discussion
The results obtained in the first set of measurements (Fig. 1a-c and Supplementary Fig. S2) confirm the dynamic evolution of the Q y (0, 0) band already reported in the literature 22,23 . The beating analysis highlighted, in particular, the contribution of three frequencies of 260, 420 and 745 cm −1 ( Supplementary Fig. S4), corresponding to the vibrational modes more strongly coupled with the S 0 → S 1 transition, in agreement with previous measurements 22,23 and with the resonant Raman analysis 39 . The 2DES response, including the amplitude distribution of beatings at different frequencies, was simulated modelling the system with two electronic states (S 0 and S 1 ). The nuclear degrees of freedom were incorporated into the lineshape function associated to the electronic transition 40 . Frequencies and reorganization energies of the coupled vibrational modes were obtained from hole-burning experiments of chla in ether 35 . Following standard nonlinear response function theory, the lineshape function was used as input to calculate the nonlinear response functions, linear absorption spectrum and 2DES spectra (see Supplementary Fig. S1).
The shape of the signals and the amplitude distribution of the main beating modes in the experimental 2DES maps reveal intensity patterns in full agreement with the two-level simulations (Fig. 1c), confirming that the 2DES response in this spectral region can be fully justified considering only the lower energy excited state S 1 .
More interesting results come from the second set of measurements. The evolution of the 2DES map in time reveals two different diagonal features at early times ( Supplementary Fig. S5): a signal centered at 15500 cm −1 that corresponds to the blue tail of the S 1 state, whose dynamics has been investigated in the previous set, and a second diagonal contribution appearing around 16360 cm −1 . This peak is characterized by an ultrafast dynamics with amplitude halving in about 120 fs. In addition, 2DES maps are characterized by the presence of a strong lower diagonal cross peak between the recognized diagonal contributions, featuring a lively dynamics in the first hundred of femtoseconds after photoexcitation.
Differently from the previous set of data, in this case, the experimental behavior could not be fully justified by simulations including only the S 0 and S 1 states (Fig. 1e,f), suggesting that the higher energy diagonal signal cannot be interpreted as a vibronic state of S 1 . In agreement with the band attribution reported in refs 32, 33, 35, this signal has then be attributed to a second excited state, S 2 . The ultrafast dynamics moving the signal density from the higher to the lower diagonal cross peak and giving rise to the oscillating cross peak feature is thus depicting the S 2 → S 1 internal conversion. Below we report the analysis of the 2DES spectra that supports this attribution.
The attention has been focused first on the non oscillatory decay dynamics. The time evolution of the signals has been analyzed using a recently proposed methodology based on a global fitting of the whole 2DES dataset with complex multi-exponential functions 41 .
Briefly, the decay of the total complex signal at each point of the 2D map is fitted with a global function written as sum of N complex exponentials capturing simultaneously the population decay contributions and the oscillating components associated to coherent dynamics. The corresponding amplitudes plotted in a 2D map as a function of emission and excitation frequency build the so called 2D-DAS (decay associated spectra) and 2D-CAS (coherence associated spectra), respectively. This methodology provides a remarkably higher reliability in the identification of ultrafast decays and quickly damped oscillations with respect to other procedures since it fits simultaneously oscillating and non-oscillating components 41 . Moreover, this method allows retrieving at the same time the frequencies, damping times and amplitude maps for all the fitted components considering simultaneously real and imaginary parts (i.e. the full complex dataset). In order to minimize the possible contamination of coherent artifacts at early times, the fitting procedure has been applied to the data after exclusion of the first 30 fs.
The analysis revealed that non oscillating dynamics is dominated by two time components, with time constants 170 fs and 2 ps, respectively. The corresponding 2D-DAS are reported in Fig. 2.
The 2D-DAS associated to the faster time constant reveals a very complex pattern. When the dynamics of a single transition of an isolated chromophore is investigated, time constants of hundreds of femtoseconds are typically associated to spectral diffusion processes, characterized by 2D-DAS with a well-defined signal amplitude distribution 41 , accounting for the rounding of the peak as the population time increases 23 . This is what has been recorded in the first set of measures ( Supplementary Fig. S3(a)). The 2D-DAS of Fig. 2a presents a completely different behavior, suggesting a more complex dynamic process, likely involving more than one excited state. Negative (positive) features in 2D-DAS appear in regions of the 2D plots where the signal is rising (decaying) with the associated time constant. The negative signals in Fig. 2a can be justified invoking a rising population in a lower energy state, located where S 1 is expected to contribute, as verified in the first measure set. The higher energy portion of the diagonal reveals instead a weak positive signal which is associated to a decaying feature that is located at energy compatible with the S 2 state. We can therefore attribute this ultrafast time component to the relaxation of the population from S 2 to S 1 within the Q-bands.
A closer look to the 2D-DAS reveals however a more complicated distribution, especially in the spectral region corresponding to an excitation frequency of 16360 cm −1 (Fig. 2b): the signal amplitude along this coordinate shows, indeed, several sign changes. This evidence suggests the presence of complex relaxation dynamics between S 2 and S 1 states, involving several processes and intermediate states. Thus, the relaxation process is not characterized by a unique decaying component, but, more likely, by a distribution of components with possibly different time constants. In agreement with previous theoretical and experimental findings 30,35 , the effective time constant for the overall process is found to be 170 fs.
More details can be extracted from the oscillatory dynamics. After removing the non-oscillatory decaying part of the signal, the resulting oscillating residues have been Fourier transformed to generate the so-called Fourier maps 15,[42][43][44][45][46] . Not surprisingly, we could verify, also in this case, the presence of the vibrational frequencies already emerged in the first set and attributed to vibrational coherences of S 0 and S 1 states. The overall beating behavior of the 2DES signal in this spectral region is however dominated by a quickly damped oscillating signal centered at about 700 cm −1 , whose Fourier map is shown in Fig. 3a, and contributing predominantly at coordinates (16360, 15660) cm −1 (blue dot in Fig. 3a) and, to a lower extent, on the symmetric upper diagonal position (green dot in Fig. 3a).
The dephasing dynamics of this oscillating signal has been characterized through two different approaches recently developed 41,47 . First, the same global fitting method employed to characterize the non-oscillating dynamics has been applied. The results confirm that the main oscillating component is a damped coherence with frequency centered at about 700 cm −1 and dephasing time of 40 fs (see also Supplementary Fig. S6).
A more direct visualization of the beating dynamics can be obtained studying the oscillating residuals with a time-frequency transform (TFT) method 47 . Figure 3b  The position and the dynamic behavior of these signals can be explained invoking relaxation pathways that involve coherences between S 2 state and vibronic states of the first excited state, S 1,n , as illustrated in Fig. 4c. the central frequency of the coherent signal roughly corresponds to a superposition between S 2 and a vibronic state at about 510 cm −1 above the vibrational ground state of S 1 , the full manifold of vibrational levels is involved, as sketched by the color scale in Fig. 4a,b.
On the other hand, also in agreement with previous 2DES measurements 22 , no signatures of a S 2 -S 1,0 coherent dynamics have been found. This seems to indicate that, overall, the internal conversion leading to the relaxation of the excitation at the bottom of the Q-band (S 1,0 ) is an incoherent process with a timescale of about 170 fs. Nevertheless, the vibronic states of S 1 are strongly involved as intermediates in the relaxation process. The timescale of these intermediate steps cannot be fully captured looking directly at the population dynamics ( Fig. 2) but an upper limit for the associated time constants can be estimated considering the dephasing time of the S 2 -S 1,n superpositions prepared by the laser excitation, in the order of 40 fs. Given the fast timescale involved, this time constant could be affected by a large uncertainty. However, the crucial point of this analysis is the experimental detection of a quickly decaying signature of the S 2 -S 1 mixing, possibly justifying the fast interconversion between the two states. It is interesting to note that the quick Q x (S 2 ) decoherence captured by our data was already theoretically predicted and justified in terms of Q x -Q y mixing 35 .
The following internal conversion mechanism can thus be proposed: following excitation on the high energy side of the Q-bands, the excitation energy is quickly (about 40 fs) redistributed among vibronic states of the S 1 level before being eventually directed to the bottom of the band in 170 fs.

Conclusions
In conclusion, the 2DES characterization of chla discussed in this work gives a new and detailed mechanistic insight on the relaxation and dephasing dynamics of internal conversion process within the Q-bands. The analysis of the dynamics response by means of recently developed methodologies confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of an intermediate step involving vibronic states S 1,n , in particular a state at 510 cm −1 above the vibrational ground state of electronic state S 1 . The presence of such intermediate process, suggested by the analysis of the population dynamics, could be better characterized studying the evolution of the S 2 -S 1,n coherences prepared by the laser excitation. The investigation on their dephasing dynamics provided indeed an estimate of the time constant associated with this intermediate step (40 fs). While the involvement of vibronic levels of S 1 and the overall ultrafast timescale of the relaxation process are well established facts 30 , this work represents a step ahead of the current knowledge because not only it demonstrates that vibronic states indeed contribute, but also it provides a direct quantitative proof of how they affect the process and in which timescale.
The characterization of these mechanistic details represents an important piece of information in the wider context of the photosynthetic energy transport in chla-based antenna protein complexes. Non radiative relaxation of high-energy excited states to the lowest excited state represents indeed the first stage of photosynthesis. The ultrafast timescale of this relaxation and the congestion of energy levels within the Q-band region make the full characterization of this process particularly challenging, as demonstrated by the continuous experimental and theoretical attempts appearing in the literature. We therefore expect these findings to be particularly important in the future interpretation of 2DES coherent response of biological complexes bearing chla.

Methods
Sample preparation and characterization. Chla from spinach was purchased from Sigma Aldrich and used without further purification. The sample solutions were prepared dissolving chla in MeOH with a concentration of about 50 μM, leading to an optical density of about 0.3 on the maximum of the Q-bands with a pathlength of 1 mm. In these conditions chla is not expected to form aggregates and, indeed, we verified that the normalized steady-state absorption spectrum do not show any significant modification lowering the concentration down to two orders of magnitude. Steady-state absorption spectra were acquired before and after each scan to control that no degradation of the sample occurred during the 2DES measurements.
2D electronic spectroscopy. 2DES measurements have been performed with the setup described in ref. 48.
Briefly, the output of a 800 nm, 3 KHz Ti:Sapphire laser system (Coherent Libra) is converted in a visible broad  pulse in a non-collinear optical amplifier (Light Conversion TOPAS White). The transform-limited condition for the pulses at the sample position is achieved through a prism compressor coupled with a Dazzler pulse shaper for the fine adjustment. The pulse duration is optimized through FROG measures. The pulses energy at the sample position is reduced until 7 nJ per pulse by a broadband half-waveplate/polarizer system. The 2DES experiment relies on the passively phase stabilized setup. The laser output is splitted into four identical phase-stable beams (three exciting beams and a fourth beam further attenuated of about 3 orders of magnitude and used as Local Oscillator, LO) in a BOXCARS geometry using a suitably designed 2D grating. Time delays between pulses are modulated by pairs of 2° CaF 2 wedges. One wedge of each pair is mounted onto a translation stage that regulates the thickness of medium crossed by the exciting beam and provides a temporal resolution of 0.07 fs. 2DES experiments were performed tuning the TOPAS White in two different spectral ranges as shown in Fig. 1a,d. The pulse duration and the spectral bandwidth (FWHM) are 24 fs and 610 cm −1 in the first set of measures; 18 fs and 820 cm −1 in the second set. Rephasing spectra were acquired for population times ranging from 0 to 800 fs in 5 fs increments, with each experiment repeated three times to ensure reproducibility. Data Availability. The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.