Characterization of Vibrational Coherence in Monomeric

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Spectroscopy and Photochemistry; General Theory

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy Veronica R. Policht, Andrew Niedringhaus, and Jennifer P. Ogilvie J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b02691 • Publication Date (Web): 30 Oct 2018 Downloaded from http://pubs.acs.org on November 3, 2018

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The Journal of Physical Chemistry Letters

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by TwoDimensional Electronic Spectroscopy Veronica R. Policht, Andrew J. Niedringhaus, and Jennifer P. Ogilvie* Department of Physics, University of Michigan, Ann Arbor, Michigan 48108, United States AUTHOR INFORMATION Corresponding Author *Email: [email protected]

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ABSTRACT Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna Matthews Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model. TOC Figure


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Photosynthesis, the process wherein sunlight is converted into usable chemical energy by plants and other photosynthetic organisms, is responsible for the majority of life on Earth. In the initial steps following the absorption of sunlight, energy is rapidly and efficiently transferred between large pigment-protein complexes (PPC) where it is converted into a long-lived charge separation1. The main pigments involved in the excitation energy transfer (EET) and charge separation (CS) processes in bacterial photosynthesis are bacteriochlorins. Bacteriochlorophyll a (BChla) is the most prominent pigment in the Bacterial Reaction Center (BRC) protein of several species of purple bacteria as well as the Fenna-Matthews-Olson (FMO) antenna complex of green sulfur bacteria. For decades, spectroscopists and theorists have worked to better understand EET and CS processes in these systems, both studying the complexed PPCs1,2 and monomeric samples of the constituent pigments3,4 like BChla. Despite this intense research, many questions remain regarding the physical mechanisms that underlie the rapidity (fs – ps timescales) and efficiency of the primary steps of EET and CS, which can approach quantum efficiencies of unity1. Following the first observation of coherences in a PPC using two-dimensional electronic spectroscopy (2DES) in the FMO complex in 2007 by Engel, et al.5, the origin and role of long-lived oscillatory coherences in EET and CS in PPCs has gripped the interest of the photosynthetic community. Coherent dynamics have been observed in a wide variety of systems using ultrafast spectroscopy techniques, including a variety of photosynthetic proteins including BRCs6–25, the Photosystem II D1D2 reaction center26–28, various antenna protein complexes5,29–35, and monomeric molecular systems36, including photosynthetic pigments29,37–44. There have been numerous theoretical studies which have sought to characterize the origin of these coherences by modeling the spectroscopic signatures of electronic, vibrational, and vibronic coherence to be expected in 2DES


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experiments45–51. A number of studies have explored the effect of vibrational-electronic resonances on enhancing the processes of EET49,52–54 and CS26,27,55,56. While many studies have observed coherences in bacterial PPCs there have not been many complementary studies of the constituent monomer pigments. Of the studies that have been conducted thus far, there is disagreement as to whether or not coherences exist or are prominent in monomeric BChla. The earliest room temperature coherence studies of monomeric BChla using ultrafast transient absorption (TA) spectroscopy did not resolve prominent coherent oscillations57. Not long after this initial study, another TA study of BChla resolved a single low-frequency mode at 4.2 K but failed to see coherences at room temperature29. In contrast, a 3-pulse photon echo study observed several coherent modes in BChla at room temperature in several different solvents which were in the same frequency regime as low-frequency coherences observed in BRCs37,38. The first 2DES study of BChla looked for coherences in several different solvents and concluded that two weak coherences at 550 & 730 cm-1 were present but that solvent contributions dominated the signals41. This study was used to strengthen the assignment of coherence in the FMO complex as electronic in origin41. Similarly the earliest TA study of BChla which did not resolve coherences was used in the interpretation that BRC coherences were intermolecular in origin8. Coherences have previously been observed in Chlorophyll a (Chla), the plant analogue of BChla. An ultrafast pump probe study of Chlorophyll a (Chla) showed a large number of oscillatory modes that were interpreted as intramolecular vibrations40 and several 2DES studies of coherence in Chla observed strong coherence modes and reached similar conclusions42,43. The vibrational properties of BChla and Chla are similar, with Huang-Rhys factors for strong vibrational modes on Qy in both molecules on the order of S≅0.0158,59. In a difference fluorescence line-narrowing

experiments of BChla59 (Chla58) the Huang-Rhys factors for the 565 (573) and 727 (745) cm-1


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vibrational modes were measured to be 0.0081 (0.018) and 0.0266 (0.035). Given these similarities it might be expected that coherences would be present in BChla as they were seen in Chla. To this effect, a recent 2DES study of coherences on the red edge of the BChla Qy band showed several coherences which were assigned to vibrational origins44, however only a few low-frequency modes were observed due to the low bandwidth of the pulses used. Given the discrepancy in observations of coherences over the years and the need for proper comparison with signals seen in the PPCs, it is necessary to establish benchmark signatures of coherence in BChla. Here we present broadband 2DES on monomeric BChla dissolved in isopropanol at 77 K. In this study we observe many prominent coherences which correspond well with known vibrational modes of BChla. To characterize the distribution of coherence in the 2DES data we present coherence maps (also called Fourier maps)60 for comparison with a simple displaced oscillator (DO) model for purely vibrational coherence45,46. Our data shows that vibrational coherences are indisputably present on monomeric BChla molecules. We also find some deviations from the expected behavior based on the simple DO model of purely vibrational coherence. These results serve as important benchmarks of coherence for improving our understanding of the more complex PPCS such as FMO and the BRC.


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Figure 1 Real Absorptive 2D spectrum of Bacteriochlorophyll a in isopropanol at 77 K and t2 = 200 fs. The 77 K linear absorption spectrum (blue) is shown along with the pump (top, gray) and probe (right, gray) spectra used in the experiments. The pump pulse is centered to the blue of Qy so as to better access high-frequency excited state coherences while the probe spectra is centered about Qy. Figure 1 shows the 77 K real absorptive 2DES spectrum and the 77 K linear absorption spectrum of BChla in isopropanol along with the pulse spectra. This experiment used isopropanol as the solvent because it has been suggested that the dielectric constant is similar to that experienced by BChla molecules in the BRC. Isopropanol is a 5-coordinating solvent where one solvent molecule is ligated to the Mg2+ ion of each BChla61. In contrast, 6-coordinating solvents have two solvent molecules ligated to the Mg2+ on either side of the bacteriochlorin plane. As a control study for solvent dependence, we also performed 2DES at 77 K on BChla in ethanol, a predominantly 6-


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coordinating solvent62 with a significantly different resonance Raman (RR) spectrum from isopropanol, the results of which are presented in the SI and show similar results to what is presented in the main text. The 77 K real absorptive 2DES spectrum of BChla (Figure 1) shows a strong positive peak corresponding to ground state bleach (GSB) and stimulated emission (SE) of the Qy band, which shows large inhomogeneous broadening along the diagonal, as well as negative excited state absorption (ESA) signals above the diagonal and positive ground state bleach (GSB) signatures below the diagonal. The lifetime of the Qy excited state is on the order of tens of nanoseconds63, significantly longer than the 3.5 ps scan analyzed here. The Qy band retains the inhomogeneous broadening for the entire 3.5 ps scan, indicating slow spectral diffusion. In order to analyze the weak oscillatory signals corresponding to coherences, we first perform a global kinetic fit to the 2DES data set, fitting to a sum of complex exponentials. The exponential decay terms are then subtracted from the data and the oscillatory residual is Fourier transformed with respect to t2 to the coherence frequency, ω2. Figure 2 shows the Frobenius or Fourier spectrum calculated by taking the Frobenius norm of the pseudo-three dimensional frequency solid. The Frobenius spectrum shows several prominent peaks sitting atop a noise pedestal. Comparison of the peak frequencies from the Frobenius spectrum with known vibrational modes for monomeric BChla measured via resonance Raman64– 66

shows that they are consistent with these modes being vibrational in origin. For several of these

peaks there are small differences in the frequency observed in the 2DES experiment versus the vibrational spectroscopy experiments, however many of the observed modes in Figure 2 are within the experimental resolutions of our experiment and the RR experiments referenced. This Frobenius spectrum shows reproducible peaks frequencies when compared across data sets from different experimental runs and when compared against different solvents (Figure S6), within the


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Figure 2: Frobenius spectrum of the real rephasing signal of Bacteriochlorophyll a in isopropanol at 77 K. The spectrum is normalized by the integrated amplitude. Several prominent peaks are labeled with their frequency. Blue lines above the spectrum indicate vibrational frequencies measured by resonance Raman64–66. The resonance Raman spectra of BChla features many prominent modes. In order to stringently compare our observed coherence frequencies, we select only those peaks in the Frobenius spectra above the background pedestal and search for matching vibrational modes from the RR experiments within our experimental resolution of Δω2 = 9.96 cm1

and the reported resolutions in the RR studies.

experimental Δω2 resolution, with peak amplitudes sensitive to the bandwidth of the pump and probe spectra. The two lowest frequency peaks in Figure 2 are below the lowest resolved frequency in the RR experiments we are comparing against64–66. The normal vibrational modes of BChla Qy state have been calculated by Rätsep, et al. and the prominent modes identified in Figure 2 are assigned to skeletal stretching, in-plane bending, and torsional vibrational modes59. Normal vibrations of BChla Qx states have also been assigned previously to skeletal vibrational modes67. In order to better assign an origin to the coherence signals present in the BChla data we plot the amplitude distribution of specific coherence frequencies as a function of the excitation and detection frequencies in coherence maps (Figure 3). Figure 3 shows both the real rephasing signal coherence maps, which show the same signatures in both ±ω2, along with the separated -ω2 and


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+ω2 coherence maps from the complex rephasing signal. The ±ω2 Frobenius spectra of the complex rephasing signal is shown in Figure S1. Analyzing the complex rephasing signals allows us to better separate out distinct signals which may overlap in (ω1,ω3) but which oscillate with different signs. Analyzing coherences in this way was initially proposed by Seibt, et al.68 and first performed by Song, et al.69 and has been used in several recent coherence studies of PPCs16,35. Analyzing the complex signals also allows us to differentiate ground and excited state vibrational frequencies (see Figure S1). Presenting the coherence data in coherence maps allows us to compare more directly to toy models for coherence of different origins. Coherences with a purely vibrational origin, where the coherence is between two vibrational states on the same electronic state are frequently described by a displaced harmonic oscillator (DO) model (Figure 4)45,46. This model includes two electronic states (|g⟩ and |a⟩) each with two vibrational levels where the excited electronic state is displaced along the nuclear coordinate, q, by dimensionless displacement d. A similar model was used in the initial observations of coherences in the BRC using ultrafast TA spectroscopy6. Given the simplicity of this model, we can easily determine which light-matter interaction pathways result in coherence during t2. There are eight rephasing coherence pathways, represented by double-sided Feynman diagrams in Figure 4, which are distributed in five distinct peaks in the 2D coherence map forming a characteristic “chair” pattern. The nonrephasing signal also has 8 pathways but we focus on the rephasing signals for signal-to-noise reasons.


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Figure 3: Real rephasing (left column), -ω2 and +ω2 of the complex rephasing (center and right column, respectively) coherence maps for several prominent modes in Bacteriochlorophyll a in isopropanol. Diagonal lines are drawn at -ω1 = ω3 and at several values of -ω1 = ω3 ± n×ω2 to guide the eye for comparison to the displaced harmonic oscillator model in Figure 4.


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Figure 4 Toy model for purely vibrational coherences45,46. A displaced harmonic oscillator model consisting of two electronic states (|g⟩ and |a⟩) with two vibrational states of frequency Ω (|a⟩ and |a’⟩) are displaced along the nuclear coordinate q by displacement d. This simple model yields eight possible rephasing light-matter interaction pathways resulting in coherences during t2, illustrated with double-sided Feynman diagrams (below). These signals yield a characteristic chair-pattern in the real rephasing signal when plotted in a 2D coherence map (top, right), two of which oscillate at +ω2 (red symbols) and six which oscillate at -ω2 (black symbols). The first coherence map shown in Figure 3 is at ω2 = 158 cm-1, which is a weak peak in the Frobenius spectrum (Figure 2). This coherence map is shown for the purpose of comparison to a prominent mode observed in several coherence studies of FMO of about 160 cm-1 5,32,70 and shows three diagonally-elongated peaks along the guiding diagonal lines, similar to other more prominent low-frequency coherences (Figure S3). The high-frequency modes ω2 = 572 & 741 cm-1 show the best agreement with the DO model, showing nearly all the expected signatures with the exception of the signature located at (-A,A-Ω) in Figure 4. The ω2 = 901 cm-1 mode also shows signals with the expected distribution (Figure 3) but with decreased signal strength in the off-diagonal signatures. The complex rephasing coherence maps allow us to further separate out pathways


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oscillating with opposite sign. Of the 8 pathways predicted from the DO model (Figure 4) two oscillate with +ω2 and 6 with -ω2. This behavior is present in the high-frequency coherence maps in Figure 3, strengthening our assignment that these coherences are due to intramolecular vibrations. Regarding the decreased signal strength of some signatures in the high-frequency coherence maps, several previous studies have discussed the filtering42,71 or even distorting72 effects that laser bandwidth can have on coherences probed. The effects we see in the coherence maps, where expected signatures are attenuated in amplitude or missing from the maps shown in Figure 3, are related to the limited bandwidth of the pump spectrum (Figure 1). The pump spectrum in the experiment of BChla in ethanol (Figure S5) was tuned so as to better access these belowdiagonal signals which are attenuated in Figure 3, with the tradeoff of attenuated signatures at ω1 = -(A+Ω) (Figure S8). While the high-frequency coherence maps in Figure 3 match the expected 2D distribution predicted by the DO model well, the ω2 = 158 cm-1 and other low-frequency coherences prominent in the Frobenius spectrum (Figure S3) show distinct deviations from this model, suggesting that the DO model is insufficient to fully describe coherences in BChla. The coherence maps for ω2 = 202 and 349 cm-1 in Figure S3 show significant signal between the diagonal lines, which would indicate a vibronic coherence based on simulations of a mixed vibrational-electronic system50,51. It is however unlikely that these low frequency modes could be related to vibronic coherence, as Qy is well isolated from the next nearest electronic transition (Qx is ~4000 cm-1 to the blue) and the samples are prepared with low enough concentration to assume each molecule is an isolated monomer. Additional signatures not predicted in the DO model are present in the ω2 = 901 cm-1 in Figure 3 which features a nodal line in the diagonal peak where there is expected to be a maximum. The


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nodal signature appears similar to destructive interference signals recently observed in coherence maps of the BRC in a study by Paleček, et al.16 where such features were attributed to ultrafast energy transfer between the pigments of the BRC. In the case of the spectrally isolated Qy band of monomeric BChla we do not expect any energy transfer to occur, nor do the population dynamics show evidence for energy transfer. We can confirm that these signatures are due to destructive interference by looking at the complex rephasing coherence signal in Figure 3 which shows signal maxima along the diagonal. The nodal feature is also present in many weak coherence modes with similar destructive interference behavior as the ω2 = 901 cm-1 mode. There is also a nodal line in the ω2 = 349 cm-1 coherence map in Figure S3, but this seems to be due to a lack of amplitude on the diagonal rather than destructive interference effects. In an attempt to understand these nodal features, we have considered possible solvent effects, including excitation of solvent vibrations via coordinated solvent ligands73,74. As a control study we performed 2DES of BChla in ethanol, finding very similar results to the isopropanol studies, suggesting that solvent effects do not explain the observed nodal signature. The BChla in ethanol results are summarized in the SI along with additional discussion of deviations from the DO model. Understanding the origin of the nodal signals and other deviations from the DO model is a work in progress that will be facilitated by ongoing theory collaborations. We note that the relative amplitudes and some of the frequencies of the dominant coherences found in our monomer data differ from those reported in 2DES studies of BChla-containing photosynthetic proteins. In the Fenna-Matthews-Olson (FMO) complex, initial reports indicated frequencies ranging from ~170-500 cm-1 present in analysis of a particular cross-peak location in the 2D spectrum5. More recent work in which coherences were characterized using coherence maps and polarization to suppress purely vibrational contributions has reported dominant


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frequencies of 170 cm-1 and 210 cm-1 in FMO at 77 K35. An LH1 dimer studied by Ferretti et al.55 reports dominant modes at 416 cm-1 and 546 cm-1. In comparison, our monomer data shows a peak at 414 cm-1 which is weak in the isopropanol data but strong in ethanol (Figure S6). Resonance Raman studies are unable to resolve this peak possibly due to overlap with a broad multi-peaked feature in the 300-400 cm-1 range64–66. We observe a weak peak at 555 cm-1, though again this mode is not well characterized in resonance Raman studies. Studies of LH2 have reported a coherence dominating at ~730-750 cm-1 75,76, consistent with our observation of a 741 cm-1 mode. In summary, we have characterized the coherences present upon excitation of the Qy band of BChla in isopropanol using 2DES with broadband excitation and detection (Figure 1). Given the correspondence of peaks in the Frobenius spectrum (Figure 2) to well characterized vibrational modes of BChla and the agreement of the coherence map amplitude distributions for prominent modes (Figure 3) with those expected for the DO model (Figure 4), the coherences observed in BChla are clearly vibrational in character. The characterization of the coherences in BChla is an important step in understanding the coherences present in the large pigment-protein complexes and offers strong evidence that intramolecular vibrations are prominent in ultrafast spectroscopy of BChla and must be considered in the analysis of coherences in PPCs. Having established benchmark 2DES signatures of coherence of the monomer pigments, comparisons to 2DES coherences studies of the more complex PPCs can be made to improve our understanding of electronic-vibrational coupling and its possible functional role in photosynthetic EET and CS. We note that during the review of this manuscript, Irgen-Gioro et al. published a complementary report on coherence in BChla77. ASSOCIATED CONTENT Supporting Information.


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Experimental Methods, Real and Complex Coherence Analysis, Coherence Signal to Noise Comparison, Deviations from the DO Model, Discussion of Solvent Dependence and Figures S1 – S8 (PDF) ACKNOWLEDGEMENT We thank Dewey Holten, Dave Bocian, and Kenneth Spears for helpful discussions. We gratefully acknowledge the support of the National Science Foundation through grant #PHY1607570.


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26

Wavelength (nm)

Page810 27 Theof790 Journal 31 770of Physical Letters 750 730Chemistry 710

710 730

Detection Frequency (cm-1x102)

750 770 790 810 830 850 870

ACS Paragon Plus Environment -125

-130

-135

-140

Excitation Frequency (cm-1x102)

890

Wavelength (nm)

1 2 3 4 140 5 6 135 7 8 9 130 10 11 12125 13 14 15120 16 17 115 18 19 20 21

Frobenius spectrum

The 202 Journal of Physical ChemistryPage Letters 28 of 31 572

741

349

1 2 3 4 5 06 7

901

160

ACS Paragon Plus Environment 100 200 300 400 500 600 700 800 900 1000 1100 Coherence frequency (cm-1)

Detection frequency (cm-1x102)

1

2

3

4

5

6

2

4

6

8

10 12

2

4

6

8

10

Page 29 ofThe 31 Journal of Physical Chemistry Letters 140 135

ω2 = 160 cm-1 2


4

6

ω2 = -158 cm-1

8

10

ω2 = 572 cm-1 2



1 2 130 3 4125 5 120 6 7115 8 9 10 140 11 12 135 13 130 14 15 125 16 17 120 18 19 115 20 21 22 140 23 135 24 25 130 26 27 125 28 29 120 30 115 31 32 33 140 34 35 135 36 37 130 38 39 125 40 120 41 42 115 43 44 45

4

6

4

6

8

10

15

ω 2 = 158 cm -1 20

ω2 = -572 cm-1 8

10

ω2 = 741 cm-1 2

5

10 12 14

5

10

15

10

4

6

8

10 12

ω 2 = 572 cm -1 20

ω2 = -741 cm-1 5

2

2

4

6

8

10 12

ω 2 = 741 cm -1 15

5

10

15

ACS Paragon Plus Environment -1

ω2 = 901 cm-1

ω2 = -903 cm

ω 2 = 903 cm -1

-125 -130 -135 -140 -125 -130 -135 -140 -125 -130 -135 -140 Excitation frequency (cm-1x102)

ω3

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Characterization of Vibrational Coherence in Monomeric

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