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1 Vibronic Coherence in Oxygenic Photosynthesis Franklin D. Fuller 1, Jie Pan 1, Andrius Gelzinis 2,, Vytautas Butkus 2,, S. Seckin Senlik 1, Daniel E. Wilcox 1, Charles F. Yocum 4, Leonas Valkunas 2,, Darius Abramavicius 2 and Jennifer P. Ogilvie 1 * 1 Department of Physics and Biophysics, University of Michigan, 450 Church St, Ann Arbor MI Department of Theoretical Physics, Faculty of Physics of Vilnius University, Sauletekio Avenue 9, Building, Vilnius, Lithuania Center for Physical Sciences and Technology, Gostauto 9, Vilnius, Lithuania 4 Department of Molecular, Cellular and Developmental Biology and Department of Chemistry, University of Michigan, Ann Arbor MI Table of Contents SI.1 Additional experimental and data analysis details.. 2 SI Figure 1... SI.2 Generation of experimental coherence amplitude maps. 4 SI Figure SI. Simulations of coherence amplitude maps. 6 SI Figure... 7 SI Figure SI Figure SI Figure SI Figure SI Figure SI.4 Simulation of charge transfer dynamics..12 NATURE CHEMISTRY 1

2 SI Figure 9.. SI Table SI Table References SI.1 Additional experimental and data analysis details Tris-washed BBY particles were extracted from commercially available spinach 1, following which the D1-D2-cyt b559 reaction centers were isolated using the approach of van Leeuwen et al. 2. Prior to use the samples were diluted with a sucrose-free Bis-Tris solution and concentrated with a spin filter (Millipore). Glycerol was added to produce a glycerol:buffer ratio of 2:1 (v/v), and the sample was vacuum degassed to remove dissolved oxygen prior to being sealed in an optical cell with a sample thickness of 80 µm and an OD of ~0.2 at 680 nm. The 2DES measurements were made using a hybrid diffractive optic and pulseshaping based 4,5 approach that combines the advantages of background-free detection with the precise time-delays and phase-cycling capabilities of a pulse-shaper 6. The laser source consists of a Ti:Sapph oscillator (MaiTai SP) seeding a regenerative amplifier (Spectra Physics Spitfire Pro). The 4 mj, 500 Hz, ~40 fs, 800 nm output is split and feeds two non-collinear optical parametric amplifiers 7 (NOPAs) tuned to 680 nm (SI Figure 1 shows the pump and probe spectra used in the experiment, and the sample absorption spectrum). One beam, referred to here as the pump, is sent through a precompensating grism 8 and then into an acousto-optic pulse shaper (Dazzler, Fastlite) where it is compressed and split into two pulses with a programmable inter-pulse delay and phase. The second NOPA is compressed using a separate prism and is delayed by t 2 with respect to the pump pulses using a conventional delay stage. The pump and probe NATURE CHEMISTRY 2

3 beams are directed into a diffractive optic imaging system where the crossing angle at the sample is approximately 1 degree. The pulse durations measured at the sample were 12 fs and fs for pump and probe respectively. The radiant exposure of each pump pulse was 0.55 J/m 2 and 0.68 J/m 2 for the probe pulse, which corresponds to a 4% excitation probability per reaction center per pulse for both pump and probe, low enough to avoid exciton annihilation effects 9. The elimination of scatter from the 2DES data was achieved by a combination of a six phase-cycling scheme with the addition of chopping the probe pulse. For each 2D spectrum t 1 was scanned to a maximum delay of 00 fs in increments of 1.85 fs. The coherence delay t 1 was phase-locked 10 at nm, such that the shortest period of any ω 1 frequency within the pump bandwidth was 12.9 fs, yielding >.4x Nyquist sampling of the excitation axis. The waiting time delay was scanned in 10 fs steps to a maximum delay of 1920 fs. The first 80 fs were not analyzed to avoid pulseoverlap effects. The frequency resolution of the reported Fourier transform spectra is 18 cm. SI Figure 1 shows the pump and probe spectra used in the experiments, as well as an absorption spectrum of the PSII RC sample. The 2DES spectra were phased to pump-probe data using the projection slice theorem 11. 2DES spectra were also compared with previously published data acquired in the pump-probe geometry 12,1 to confirm accurate phasing of the data. SI Figure 1: Linear absorption spectrum of PSII RC at room temperature (black curve), and the employed excitation (red filled curve) and probe (grey filled curve) laser spectra. NATURE CHEMISTRY

4 SI.2 Generation of experimental coherence amplitude maps In order to resolve low frequency modes, population kinetics were removed using a global exponential fit 14. It was found that a single variable life time (266 fs) and two long fixed life times (2 ps and 10 ps) gave an adequate description of the population kinetics for the entire 2D spectrum over the ~2 picosecond scan range of the experiment. The waiting time trace for each frequency-frequency point in the 2D spectrum, after exponential kinetics were removed, is then Fourier-transformed along the waiting time, and the amplitude of the Fourier transform is plotted at the frequency of interest to generate the coherence amplitude map. Fourier spectra were zero-padded to 1024 units after a one-sided Tukey window was applied in the time domain. SI Figure 2 shows the coherence amplitude maps for modes not shown in the main paper (91 cm, 854 cm, 974 cm ). Both the 854 cm and 974 cm modes are close in frequency to reported vibrational modes. While both of these maps show predominantly vibrational features (see SI Figure 7) the dominant peaks in the 854 cm and 974 cm coherence maps are in different locations, appearing either on the main or lower diagonal respectively. The work of Butkus et al. 16 has shown that differences in Huang Rhys factors can strongly influence the peak distribution in coherence maps, and this may offer an explanation for the differences observed here. NATURE CHEMISTRY 4

5 ω2: 91.2 cm 16 b 16 ω2: 854 cm c 0.9 ω2: 974 cm 0.8 Detection frequency in cm x10 a Excitation frequency in cm x Excitation frequency in cm x Excitation frequency in cm x10 17 SI Figure 2: Coherence amplitude maps (filled contours) derived from the real rephasing 2D spectra at ω2 values corresponding to peaks in the summary spectrum (Figure 2d). Coherence amplitude maps at a) 91 cm, b) 854 cm and c) 974 cm. For each map dashed black lines indicate the diagonal and parallel lines offset from the diagonal by ±ω2 and -2ω2. Overlaid open contours show the real rephasing 2D spectrum, averaged over waiting time t2. Note that unequal axis ranges are used in panels b and c to facilitate viewing of features below the diagonal that are expected within the vibrational and vibronic models depicted in SI Figure 7. Coherence amplitude maps at other peaks in the summary spectrum are shown in the main paper in Figure. SI. Simulations of coherence amplitude maps The dimeric special pair of the PSII RC (initially without the CT state) was considered in simulations of coherence amplitude maps. Here we used the exciton-vibronic model for calculating the 2D spectra as described in detail in previous work16,17. Each of molecules in the special pair is represented by two shifted harmonic oscillators, using parameters close to those in our previous simulations of the 2DES of the PSII RC18. For a single vibration per molecule the corresponding system Hamiltonian in the site basis is then # 1& H s = ε n + δε n W s b n + b n B n B n + W % b n b n + ( + J B m B n $ 2 ' m n n=1 n=1 { ( )} (1) where b n and b n are the respective annihilation and creation operators for molecular vibrations; B n and B n are the corresponding operators for the electronic excitations. ε1 and ε 2 are the site energies of the special pair molecules PD1 and PD2, which were taken to be 280 cm and 210 cm respectively18. J is the resonant coupling constant, taken to be 120 cm, reduced somewhat compared to our previous work. W is the vibrational NATURE CHEMISTRY 5 5

6 frequency and s is the Huang-Rhys factor. Vibrational reorganization energy Ws is the same for both molecules and is therefore not included in the Hamiltonian. δε n is the Gaussian-distributed energy off-set. A value of s=0.04 was used for the Huang-Rhys factor, which is in close agreement with the proposed values from the FLN data 19. The standard deviation of the energy disorder distribution was set to =80 cm and the results were averaged over 2000 realizations. The finite width experimental laser spectrum was taken into account by multiplying the corresponding contributions to the Feynman diagrams by the Gaussian function exp ( Ω ω i ) 2 / 2σ 2, where the central wavelength and width of laser pulse spectrum are Ω=879 cm and σ=1025 cm, respectively and ω i is the frequency of the i th excitonic transition 20. Coherence amplitude maps were created from a set of simulated 2D spectra with waiting times 0 t 2 2 ps at every 10 fs. Time traces of each spectral point were fitted by a threecomponent exponential function and later the residuals were Fourier transformed with a Gaussian spectral window. The Frobenius norm was calculated as the function of the Fourier frequency ω 2 (see SI Figure ), illustrating that multiple peaks appear when the simple dimer is coupled to single vibrational modes. This phenomenon can also be visualized by considering how the manifold of singly excited states depends on the particular vibrational modes that are coupled to the special pair dimer and the strength of the resonant coupling J. SI Fig. 4 shows the manifold of singly excited states as a function of resonant coupling between the special pair dimer for the case of a 250 cm vibrational mode, a 49 cm vibrational mode and both modes simultaneously. At a particular value of resonant coupling J, the difference between the energy levels will give rise to peaks in the Frobenius spectrum that reflect the different coherences that can be σ D ( ) NATURE CHEMISTRY 6

7 excited among different pairs of states. Peak amplitudes become additionally scaled by the corresponding Franck Condon overlap integrals. We note that the experimental and simulated coherence maps shown in Figures and 4 in the main text and in SI Figures 2, 5, 6 and 8 were derived from the real rephasing 2D spectra and therefore should not contain new frequencies that could arise from taking an absolute value. Analyzing the real nonrephasing spectra revealed the same frequencies, with a different (ω 1, ω ) distribution. SI Figure : Frobenius norm dependence on coherence frequency ω 2 in simulations of the special pair dimer and a single vibrational mode at frequency W=91, 251, 9 and 70 cm (no CT state is included here). Note that each simulation shows peaks at several frequencies. The corresponding coherence amplitude maps at the major peaks in each simulation are shown in SI Figure 5. The sum over all four simulations is given by the black curve. NATURE CHEMISTRY 7

8 a 250 cm 1 mode only b 9 cm 1 mode only c 250 cm 1 & 9 cm 1 modes Energy, cm cm Resonant coupling J, cm 1 Resonant coupling J, cm 1 Resonant coupling J, cm 1 SI Figure 4: Energy level dependence on the resonant coupling strength. Cases when the 250 cm or 9 cm vibrational mode is solely included (a and b, respectively) and both modes included (c). Indicated on the 9 cm mode simulation is the energy level splitting that gives rise to the 10 cm coherence. Other energy level splittings give rise to other coherences at different frequencies in the Frobenius spectra shown in SI Fig. for the 250 cm and 9 cm modes and in SI Fig.5 for the two mode case. The corresponding coherence amplitude maps for the peaks in the Frobenius spectra are shown in SI Figs. 5 and 6. The coherence amplitude maps of real rephasing spectra at different population frequencies ω 2 obtained from simulations that considered single modes coupled to the special pair (W=91 cm, 251 cm,9 cm and 70 cm ) are presented in SI Figure 5. Additional coherence amplitude maps from simulations that explicitly included both the 251 cm and 9 cm modes are presented in SI Figure 6. NATURE CHEMISTRY 8

9 SI Figure 5: Simulated coherence amplitude maps (filled contours) derived from the simulated real rephasing 2D spectra for the special pair dimer model with a single vibrational mode of frequency W (no CT state included). Each row of the figure shows the coherence amplitude maps at the major peaks (along ω 2 ) for a given frequency W (see SI Figure ). a: W=91 cm, b: W=251 cm, c: W=9 cm and d: W=70 cm. The dashed black lines indicate the diagonal and parallel lines offset from the diagonal by ±ω 2 and -2ω 2. Overlaid open contours show the real rephasing 2D spectrum, averaged over waiting time t 2. NATURE CHEMISTRY 9

10 SI Figure 6: Simulated coherence amplitude maps (filled contours) derived from the simulated real rephasing 2D spectra for the special pair dimer model with two vibrational modes of frequency W=250 cm - 1 and W=40 cm (no CT state included). Each row of the figure shows the coherence amplitude maps at the major peaks (along ω 2 ) found in the Frobenius spectrum (bottom right). In addition, the coherence map for the small peak at 120 cm is shown in the main paper in Fig. 4a. The dashed black lines indicate the diagonal and parallel lines offset from the diagonal by ±ω 2 and -2ω 2. Overlaid open contours show the real rephasing 2D spectrum, averaged over waiting time t 2. NATURE CHEMISTRY 10

11 SI Figure 7: Cartoon maps depicting the rephasing signals expected for two different models. a) A model for vibrational coherence consisting of two displaced harmonic oscillators, with a single vibrational mode of frequency ω produces a chair shape 21. When disorder is included the signals are smeared along the diagonal lines indicated by D+, D, D- and D b) A vibronic model consisting of a coupled electronic dimer with a single vibrational mode on each electronic state (after Butkus et al. 17 ). The blue squares show the chair signals analogous to the vibrational case, for each excitonic state A and B. The red stars indicate the position of purely electronic coherence signals. The green circles indicate signals generated via vibronic processes that involve interactions between both excitonic states A and B as well as a vibrational quantum. Unlike the vibrational signals, these are found outside and between the diagonal lines D+, D, D- and D--. SI Fig. 7 shows cartoon coherence maps for the vibrational (displaced oscillator) model 21 with disorder (left) and the vibronic model 17 (right). To distinguish between vibronic coherent dynamics and purely vibrational dynamics, we note that in the vibronic case the coherence amplitude maps exhibit a number of peaks that do not fall on the four parallel diagonal lines (D--, D-, D, and D+) depicted in SI Fig. 7b. Coherent dynamics of pure vibrational origin do not, even in the presence of inhomogeneous broadening, give rise to peaks off these diagonal lines, as seen in SI Fig. 7a. Labeling the peaks that fall between the D+ and D lines as X, between the D and D- lines as Y and between the D- and D-- lines as Z, in SI Fig. 8 we show several of the coherence maps that highlight some of the vibronic signatures. These are strongest in the 251 cm and 9 cm maps which is expected due to their closer proximity to the energy level splittings. NATURE CHEMISTRY 11

12 Detection frequency in cm x10 X X Y z Excitation frequency in cm x10 16 c Detection frequency in cm x10 b a Detection frequency in cm x10 X Y X Y z Excitation frequency in cm x10 X X z Y Excitation frequency in cm x10 17 SI Figure 8: Coherence maps with vibronic features labeled as detailed in SI Fig. 7. a) 251 cm map, b) 9 cm map and c) 70 cm. SI.4 Simulation of charge transfer dynamics Next we performed calculations of the density matrix evolution for a three state system two states represent the special pair molecular excitations and the third state corresponds + PD1 to the PD2 CT state. The site energies and coupling for the special pair were used as described above for the simulations of the coherence amplitude maps. The energy for the CT state was taken to be 200 cm and it was coupled to each of the special pair molecules with J=45 cm. Here we want to control the decay time of vibrational coherences. For this purpose we describe the vibrational modes by its Lorentzian Fourier spectrum in the so-called spectral density function. Each electronic state is coupled to a two mode environment, thus the spectral density is 2 λlγω 2 λ H ωw 2 Γ C (ω ) = ω + γ (ω 2 W 2 )2 + Γ 2ω 2 '' (2) The first mode corresponds to a Debye spectral density with parameters λl=40 cm and γ=40 cm as used previously18. This mode is responsible for Markovian relaxation. The second mode corresponds to a damped vibrational mode. Its damping parameter is either Γ=10 cm (~1 ps vibrational coherence decay time), representing a weakly damped NATURE CHEMISTRY

13 vibration, or Γ=100 cm, (~100 fs vibrational coherence decay time) representing a strongly damped vibration. The 10 cm damping parameter was chosen as a compromise to have the reasonably long-lived vibrational coherence (up to 1 ps) and a feasible computational time, because the time needed for numerical convergence grows sharply with the decay time. The 100 cm coherence decay rate does not pose a numerical challenge, however it is shorter than the oscillation period of the electronic coherence. It should be noted that the full quantum mechanical problem consisting of electronic and vibrational degrees of freedom is solved using the hierarchical equations of motion (HEOM) approach 22,2, which is exact for a Gaussian bath. We thus avoid perturbative calculations and can be sure that our results are correct for all the parameters used. As the exact solution does not depend on the chosen basis states, the vibronic effects of electronic-vibrational mixing are properly accounted for as well. Following the experimental data, we performed calculations for four vibrational modes. The reorganization energies for the specific modes were based on the Huang-Rhys factors of specific modes in previous modeling of the PSII RC 19, obtained from the fluorescence line narrowing (FLN) data. For the W=91 cm mode we used λ H = 4 cm (based on the 97 cm mode from FLN), for W=251 cm we used λ H =27 cm (based on 21 and 260 cm modes from FLN), for W=9 cm we used λ H =7 cm (based on 298, 42 and 88 cm modes from FLN) and for W=70 cm we used λ H =51 cm (based on 700, 722, 742, 752 and 795 cm modes from FLN). Additionally, the CT state was assigned 1.5 times bigger reorganization energy compared to the other states, as in our previous work 18. All calculated evolutions of the CT state populations and corresponding spectral densities are presented in SI Figure 9. The main results are the following. First, the 91 NATURE CHEMISTRY 1

14 cm vibrational mode has very little effect on the charge separation dynamics, as it has very small reorganization energy. Second, for both 251 cm and 9 cm vibrations, we can observe different evolutions, depending on the nature of the vibrational mode. If the mode is weakly damped, sudden increases in CT state populations can be observed. In both of these cases the vibrational frequency is close to the excitonic resonances in the system. Note that the observed effect is stronger for 77 K, which is not surprising, since coherences survive longer at lower temperatures. For the 70 cm vibrational mode, no such speed-up is observed, which should be related to the fact that this frequency is not close enough to an excitonic resonance. The observed speed-up effect is not a simple transfer rate increase, which would be expected from the traditional Redfield transfer rate formula, which says that the transfer rate is proportional to the value of the spectral density at the frequency corresponding to the energy difference between the states 24. We should emphasize that the Redfield formula is dependent on the Markov approximation, which is valid when the bath relaxes much faster than all the timescales of the system dynamics. In the case of coherent vibrational modes the bath relaxation time is longer than the excitonic coherence timescales and this assumption does not hold, and conversely, the Redfield formula does not give an accurate picture of transfer rates. NATURE CHEMISTRY 14

15 SI Figure 9: Evolutions of the P + D2 P D1 charge transfer state population with different spectral densities (shown in the last column) including single vibrational modes at frequencies a: 91 cm, b: 251 cm, c: 9 cm, d: 70 cm. Simulations were performed for special pair heterodimer and P + D2 P D1 state included in the model. Population evolution was calculated using the HEOM theory. Red line denotes incoherent (strongly damped) mode and black line denotes coherent (weakly damped) mode. Blue lines in the figures of spectral density mark optical excitonic splittings (at 272 cm, 211 cm and 61 cm ).. NATURE CHEMISTRY

16 SI.5 Exciton differences from exciton models Exciton No Participating Pigments/CT states Chl D1 + Phe D1 - P D2 + P D1 - P D1 + Chl D1 - Phe D2 Chl D2 Chl D1 Phe D1 Phe D1 Chl D1 Chl D2 P D2 P D1 Chlz D2 Chlz D1 P D1 P D SI Table 1: Exciton energies and difference frequencies (in cm ) in the Gelzinis Model 18. Difference frequencies matching the observed coherence frequencies (within 10 cm ) are marked in red. NATURE CHEMISTRY 16

17 Exciton No Participating Pigments/CT states P D1 + P D2 - Chl D1 Phe D1 Phe D2 P D1 P D2 Chl D1 Phe D1 Phe D2 Chl D2 Chl D1 Phe D1 Phe D2 Chl D2 Chl D2 P D1 P D2 P D1 P D2 Chlz D2 P D1 P D2 Chlz D2 Chlz D1 Chlz D1 P D1 P D SI Table 2: Exciton energies and difference frequencies (in cm ) in the Novoderezhkin Model 25. Difference frequencies matching the observed coherence frequencies (within 10 cm ) are marked in red. NATURE CHEMISTRY 17

18 References 1 Berthold, D. A., Babcock, G. T. & Yocum, C. F. A highly resolved, oxygenevolving Photosystem-II preparation from spinach thylakoid membranes - electron-paramagnetic-res and electron-transport properties FEBS Letters 14, (1981). 2 van Leeuwen, P. J., Nieveen, M. C., van Demeent, E. J., Dekker, J. P. & van Gorkom, H. J. Rapid and simple isolation of pure photosystem-ii core and reaction center particles from spinach. Photosynthesis Research 28, 1495 (1991). Cowan, M. L., Ogilvie, J. P. & Miller, R. J. D. Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes. Chemical Physics Letters 86, (2004). 4 Myers, J. A., Lewis, K. L. M., Tekavec, P. F. & Ogilvie, J. P. Two-color twodimensional Fourier transform electronic spectroscopy with a pulse-shaper. Optics Express 16, (2008). 5 Grumstrup, E. M., Shim, S. H., Montgomery, M. A., Damrauer, N. H. & Zanni, M. T. Facile collection of two-dimensional electronic spectra using femtosecond pulse-shaping technology. Optics Express, (2007). 6 Fuller, F. D., Wilcox, D. E. & Ogilvie, J. P. Pulse shaping based two-dimensional electronic spectroscopy in a background free geometry. Optics Express 22, , doi:10.164/oe (2014). 7 Wilhelm, T., Piel, J. & Riedle, E. Sub-20-fs pulses tunable across the visible from a blue-pumped single-pass noncollinear parametric converter. Optics Letters 22, (1997). 8 Kane, S. & Squier, J. Grism-pair stretcher-compressor system for simultaneous second- and third-order dispersion compensation in chirped-pulse amplification. Journal of the Optical Society of America B-Optical Physics 14, , doi:10.164/josab (1997). 9 Donovan, B., Walker, L. A., Yocum, C. F. & Sension, R. J. Transient absorption studies of the primary charge separation in photosystem II. Journal Of Physical Chemistry 100, (1996). 10 Keusters, D., Tan, H. S. & Warren, W. S. Role of pulse phase and direction in two-dimensional optical spectroscopy. Journal of Physical Chemistry A 10, (1999). 11 Jonas, D. M. Two-dimensional femtosecond spectroscopy. Annual Review Of Physical Chemistry 54, (200). 12 Lewis, K. L. et al. Simulations of the two-dimensional electronic spectroscopy of the photosystem II reaction center. Journal of Physical Chemistry A 117, 4-41 (201). 1 Myers, J. A. et al. Two-dimensional electronic spectroscopy of the D1-D2-cyt b559 photosystem II reaction center complex. Journal of Physical Chemistry Letters 1, (2010). 14 Mullen, K. M. & Van Stokkum, I. H. The variable projection algorithm in timeresolved spectroscopy, microscopy and mass spectrometry applications. Numerical Algorithms 51, (2009). NATURE CHEMISTRY 18

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