Band Structure of the Rhodobacter sphaeroides Photosynthetic

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Band Structure of the Rhodobacter sphaeroides Photosynthetic Reaction Center from Low Temperature Absorption and Hole-Burned Spectra Olga Rancova, Ryszard J Jankowiak, Adam Kell, Mahboobe Jassas, and Darius Abramavicius J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b02595 • Publication Date (Web): 06 Jun 2016 Downloaded from http://pubs.acs.org on June 8, 2016

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The Journal of Physical Chemistry

Band Structure of the Rhodobacter sphaeroides Photosynthetic Reaction Center from Low Temperature Absorption and Hole-Burned Spectra Olga Rancova,1 Ryszard Jankowiak,2,3,* Adam Kell,2 Mahboobe Jassas,2 and Darius Abramavicius1,* 1

Department of Theoretical Physics, Vilnius University, Sauletekio al 9-III, 10222 Vilnius, Lithuania; 2Department of Chemistry and 3Department of Physics, Kansas State University, Manhattan, KS 66506, US Abstract Persistent/transient spectral hole burning and computer simulations are used to provide new insight into the excitonic structure and excitation energy transfer of the widely studied bacterial reaction center (bRC) of Rhodobacter (Rb.) sphaeroides. We focus on site energies of its cofactors, electrochromic shifts induced in chemically oxidized (P+) and charge-separated (P+QM−) states. Theoretical models lead to two alternative interpretations of the H-band. Based on our experimental and simulation data, we suggest that the bleach near 813-825 nm in transient HB spectra in the P+QM− state, often assigned to the upper exciton component of the special pair, is mostly due to different electrochromic shifts of the BL/M cofactors. From the exciton compositions in the charge neutral (CN) bRC, the weak 4th excitonic band near 780 nm can be denoted as PY+, i.e., the upper band of the special pair, which in CN bRC behaves as a delocalized state over PM and PL pigments that weakly mixes with accessory BChls. Thus, the shoulder in the absorption of Rb. sphaeroides near 813-815 nm does not contain the PY+ exciton band.

--------------------------*Corresponding authors; RJ: Phone: 785-532-6785. E-mail: [email protected]; DA: Phone: 00370-5-236-62-81. E-mail: [email protected].

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I. Introduction

The Rhodobacter (Rb.) sphaeroides bacterial reaction center (bRC) is the most thoroughly studied protein complex among all photosynthetic reaction center (RC) complexes.1-3 For a recent and comprehensive overview of the electronic structure and charge separation (CS) mechanisms in bRCs, see ref 4. The photosystem core in Rb. sphaeroides is a RC complex dimer surrounded by the light-harvesting 1 complex (LH1) and the PufX protein.5-7 The RC of this bacterium is a type-II RC, which contains a ‘special pair’ bacteriochlorophyll a (BChl a) dimer (called ‘P’) bound by RC L and M proteins on the periplasmic side of the membrane. 8 The special pair (‘PL/M’) is flanked by two accessory BChls (called ‘B’) bound to the L (in the BL site) and M (in the BM site) proteins, which are the periplasmic ends of two cofactor branches often called L and M, respectively (see Figure 1). Two bacteriopheophytin a (BPheo a) molecules (called ‘H’ in the HL/M sites) are located between the accessory BChls and two quinones (QL/M), which are bound near the cytoplasmic side of the bRC. An iron (Fe2+) ion is located between QL and QM, and a carotenoid is bound near the BM pigment.9 Sometimes, the special pair PL/M is referred to as PA/B, and other cofactors are labeled as BA/B and HA/B.4,10,11

Figure 1. The RC of Rb. sphaeroides contains a ‘special pair’ BChl a dimer (PL/PM), flanked by two accessory BChls (BL/M), two BPheo a molecules (HL/M), and two quinones (QL/M). Atomic coordinates based on X-ray crystallography data (PDB ID: 2J8C).12 Forward ET follows the pathway: PL/M → BL → HL → QM → QL.2,3,4,11


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The absorption spectrum of the wild type (WT) bRC in the Qy absorption region shows three separate bands conventionally named P, B, and H (going from low to high energy), which are usually associated with the corresponding pigments. As the two special pair pigments strongly interact, it is assumed that they produce two excitonic bands where the lower energy band carries most of the intensity due to the mutual orientation of the transition dipole moments of the pigments. Thus, the so-called P-band in the absorption spectrum of bRC is also called the lower excitonic band of the special pair pigments, denoted as PY–. Correspondingly, the higher excitonic component is denoted by PY+. The electron transfer (ET) reaction is initiated when light is absorbed by P; i.e., PL/M chromophores, or by energy transfer to P from the surrounding LH1. Electrons are transferred through the L-branch pigments, from the special pair through BL13 and then to HL, before passing to QM and finally to the QL quinone. 14 The back reactions at each step are 2-4 orders of magnitude slower than the forward reactions, resulting in a quantum yield near unity. Figure 1 shows the cofactor arrangement in the WT bRC of Rb. sphaeroides based on the crystal structure (PDB ID: 2J8C).12

Polarization-dependent two-dimensional electronic spectroscopy (2DES) applied to the B-band of the oxidized bRC15 resolved two excited states attributed to each of the two branches; it was proposed that ultrafast energy transfer (on a time scale of ~100 fs) occurs between the B cofactors on the two branches. Additionally, the lifetime of the B-band is of the same order of magnitude. These data demonstrate the complexity of excitation energy transfer (EET) dynamics in bRCs. At low-temperatures (5 K) a complementary insight may be provided by highresolution, frequency-domain spectroscopies, i.e., hole-burning (HB) spectroscopy. 16 , 17 For example, in bRCs resonant holes obtained via transient HB spectra can directly provide ET times since these photosynthetic bRCs show negligibly small persistent HB.

In this work, we characterize chemically oxidized and charge neutral (CN) WT bRC of Rb. sphaeroides in light of various persistent and transient HB spectra obtained at 5 K. In order to explain the structure of these spectra, we perform computer simulations of low-temperature


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absorption spectra of: i) CN bRC; ii) chemically oxidized bRC; and iii) bRC in the CS state P+QM− via nonresonant (transient) HB spectra. To the best of our knowledge such holes have not been fitted before even though experimental P+QM− spectra in such a broad spectral range were often reported.18-20 Only the frequency-dependent resonant holes burned within the P-band have been described theoretically so far.19-21 The revised parameters obtained recently for the P-band of Rb. sphaeroides21 provide important input and significant constraints in our simulations reported below. Fitted site energies and electrochromic shifts of the B and H chromophores, as well as EET between bands in oxidized bRCs, is compared to the corresponding values measured via persistent HB spectra.

II. Experimental Methods.

Preparation and purification of the WT bRCs from Rb. sphaeroides are described in detail in ref 22. The samples were kindly provided by Drs. T. Beatty and R. Saer from the Department of Microbiology and Immunology, University of British Columbia, Vancouver, Canada. For absorption and HB measurements, samples were diluted with 45:55 (v/v) buffer:glass solution. The glass-forming solution was 55:45 (v/v) glycerol:ethylene glycol. Postassium ferricyanide was added to chemically oxidize bRC samples (concentration ~ 0.1 M). Details about the measurement setup are described elsewhere.23 A Bruker HR125 Fourier transform spectrometer was used to measure the absorption and HB spectra with resolutions of 2-4 cm-1. The laser source for nonresonant HB at 496.5 nm was produced from a Coherent Innova 200 argon ion laser. Tunable wavelengths came from a Coherent CR899 Ti:Sapphire laser (line width 0.07 cm1

) pumped by a Spectra-Physics Millenia Xs diode laser (532 nm). Laser power in the

experiments was precisely set by a continuously adjustable neutral density filter. All experiments were performed at 5 K in an Oxford Instruments Optistat CF2 liquid helium cryostat, with sample temperature read and controlled by a Mercury iTC temperature controller. All samples preparation was carried out in the dark or under dim green light. Very low probing light (~650 nW/cm2) was used in FTIR spectrometer to measure absorption spectra. The latter ensured negligible white light bleach of the P-band.

III. Experimental Results


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3.1. Absorption spectra of CN and oxidized WT bRC. Curves a and b in Figure 2 show the absorption spectra of the CN and chemically oxidized (with ferricyanide, vide supra) bRC of Rb. sphaeroides, respectively; both spectra were obtained at 5 K with 2 cm-1 spectral resolution. Note that our oxidized sample does not have contribution from the unoxidized P-band. Since thermal broadening is significantly reduced at 5 K, the bands corresponding to the P, B, and H cofactors in the Qy region are well resolved in the CN bRC spectrum. To avoid CS induced by white light interrogation during absorbance measurements, i.e., to ensure the correct intensity of the P-band in comparison with the B and H bands, extremely low light intensity (~650 nW/cm2) was used to measure absorption and HB spectra. Comparison of these spectra reveals the following: i) the special-pair P-band (PY− excitonic component with a maximum at 11,155 cm-1) and the shoulder near 12,300 cm-1 (often assigned in the literature to the special pair upper excitonic component PY+;24-28 vide infra) are absent in the oxidized bRC; ii) the BL/M and HL/M bands shift to higher and lower energies, respectively, in the oxidized case in agreement with literature data;29,30 and iii) there is no indication that other cofactors apart from P are oxidized. It has been established previously that the site energy of BM is lower than that of BL, while the site energy of HL is lower than that of HM.4,15,28,31-33

T=5K

PL/PM

b a

BM/BL

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Absorbance

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HL/HM 0

*

* 11000

12000

13000

14000

Wavenumber (cm-1)


5


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Figure 2. 5 K absorption spectra of CN (curve a) and chemically oxidized (curve b) bRC of Rb. sphaeroides. Spectra are normalized to the maximum of the BL/M band. The asterisks indicate possible locations of two P+ states calculated for the oxidized bRC.34

The absorption spectrum of bRC with chemically oxidized primary electron donor (curve b) may also have contributions from various excited states of P+ (vide infra), which could quench the excitation energy of BL/M pigments, as proposed in ref 34. The locations of the two major states within the spectral range of interest (i.e., P4+ and P5+ calculated in ref 34 at room temperature) are indicated in Figure 2 by two asterisks below the absorption spectra. The simple absorption spectra hide the existing complexity of structure and excitation dynamics in these systems. To provide more insight on the qualitative understanding of EET and CS, as well as the spectral location of molecular excitations (including possible P+ transitions), we employ below nonphotochemical persistent and photochemical transient HB spectroscopy. 3.2. Electrochromic shifts. Absorption spectra of ferricyanide oxidized bRCs (P+), as well as bRCs in the CS state (P+QM−), will differ from those of the CN bRC due to various excited states of P+ and/or P+/QM− charges present. The electrochromic shifts are best reveled via absorption difference spectra, as shown in Figure 3. Namely, curves a and b (normalized at the PY− bleach near 898 nm) correspond to the P+QM− related electrochromic shifts in the CS state and partly oxidized bRCs (P+ induced), respectively. The absorption difference in the 780-850 nm region is associated with changes in the B band area, whereas the 730-780 nm region is associated with changes in the H band area. The features in the B/H band regions indicate blueshift/redshift of the bands marked by arrows in Figure 3. Curve c shown in the insert is the difference between normalized (at the P-band) spectra a and b and reveals the approximate shifts induced by an electron on QM (i.e., QM−). As expected, the latter induces an additional red-shift of H and a blue-shift of B bands. Note, that in Figure 3 the transient HB spectrum in the CS state is compared with the difference between CN bRC and partly oxidized bRC, to allow normalization of the difference spectra at the major bleach of the PY− band near 898 nm.


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B H

T=5K H band

B band

P band

Figure 3. Absorption difference spectra obtained for the CN bRC. Spectra a and b (normalized at the bleach of the P band) correspond to P+QM− and P+ induced bleach/electrochromic shifts, respectively. Curve c = a – b shows the extracted QM− induced electrochromic shift (see text).

3.3. Persistent holes burned in the oxidized bRC within the B band. Frame A in Figure 4 shows the absorption and persistent HB spectrum obtained at a burning frequency of 12,561 cm-1 (λB = 796.1 nm) for fluence f = 60 J/cm2, where f = I·tB with I and tB corresponding to laser intensity and burn time, respectively, for chemically oxidized bRC. Spectrum a′ (blue) shows part of the low-energy absorption spectrum (multiplied by a factor of 13) in the 11,500-12,200 cm-1 spectral range to reveal the existence of a very weak band near 12,005 cm-1 (833 nm), which, based on theoretical calculations reported in ref 34, could correspond to the P4+ state. As mentioned above, the absorption spectrum does not contain the P-band, but due to its oxidation, bands B and H are electrochromically shifted. The broad B-band near 12,469 cm-1 (802 nm) in Figure 4 accounts mostly for the absorption of the BL/M pigments, though mixing with the various P+ states cannot be excluded, as discussed below. The persistent hole (curve b in frame A, multiplied by a factor of 46) shows a zero-phonon hole (ZPH) at λB. The insert shows the expanded ZPH and its Lorentzian fit with a fwhm of ~6 cm-1. The shape of curve b clearly indicates that EET takes place, as reflected by the broad bleach, apparently contributed to by bleach of both BL and BM molecules. The latter suggests that the B-band consists of two excitons contributed to by both BL and BM molecules, i.e., it is strongly excitonically mixed (see section 4.2 for modeling data). Curve c (green) in Figure 4B shows the persistent (nonphotochemical)


7


HB spectrum burned resonantly into the B-band contributed mostly by BM molecules at 12,398 cm-1 (λB = 806.6 nm). This spectrum was obtained with f = ~180 J/cm2. The percent hole depth at λB is 1.3%.

A

802 nm

+ P5 ?

+

P4

a΄

a

BM BL

0

b

* -0.05

~833nm 92%

0.005

λB λB

0

∆ Absorbance

Absorbance

0.15

∆ Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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e

B d

c

*

-0.005 ~833 nm -0.01

-0.015 12000

12500

13000

13500 -1

Wavenumber (cm )

Figure 4. Curve a is the 5 K absorption spectrum of chemically oxidized bRC. Spectra b and c are the persistent HB spectra obtained with λB of 796.1 nm (12,561 cm-1) and 806.6 nm (12,398 cm-1), respectively. The insert in frame A shows the fit of the ZPH with a Lorentzian of fwhm of ~6 cm-1. The sum of two Lorentzian curves d (fwhm ~90 cm-1) and e (fwhm ~7 cm-1) in frame B fits well the bleach observed in curve c at the burning frequency, i.e., 12,398 cm-1.

The sharp ZPHs (obtained with 2 cm-1 resolution) in frames A and B suggest that there are also molecules that act as local traps (see also data shown in Figure 10). However, the broad hole at λB in curve c (see red curve d) has a Lorentzian shape with a fwhm of ~90 cm-1 which provides Γhom = 45 cm-1 (as Γhom = ½ ΓZPH).16,17 This Γhom corresponds to a fast process with τEET of ~120 fs, which may reflect fast relaxation from the lowest exciton, contributed to by BL/M, to P4+. In curve c, in contrast to curve b shown in frame A, the fast EET is clearly revealed as there is no overlap with the broad antihole with the maximum near 12,620 cm-1, however, the fast component is likely present in spectrum b as well.


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Interestingly, burning into BL pigments (absorbing at higher energies within the B-band) and BM pigments (absorbing at lower energies in the B-band) at λB = 806.6 nm (12,398 cm-1) and

λB = 796.1 nm (12,561 cm-1), respectively, reveals broad bleaches at 12,005 cm-1 (~35%) and near 13,280 cm-1 (~1.5%) indicated by the asterisk. The former and latter bleaches are likely associated with the P4+ and P5+ states, respectively, calculated theoretically in ref 34 for oxidized bRC. The P4+ state was associated with charge transfer (CT) and internal conversion transitions; thus, excitation quenching by the P4+ state cannot be excluded. The bleach near 13,280 cm-1 could correspond to a strongly mixed state between the P5+ and HM pigments, while the derivative type change near 13,120 cm-1 (762.2 nm), indicated by the double arrow in frame A, could be related to a red electrochromic shift of HL (vide infra) or a new absorption band of P+ in the oxidized sample. The latter cannot be excluded as the narrow feature observed in the H-band could correspond to the P5+ band itself. Therefore, we will also consider this scenario while modeling the spectrum. Figure 5 shows the persistent HB spectrum obtained with 12,005 cm-1 (λB = 833.0 nm), i.e., into the band assigned above to the P4+ state. The absorption spectrum of oxidized bRC (curve a in Figure 5) is shown for easy comparison with the HB spectrum, whose ∆ Absorbance was multiplied by a factor of 44 (curve b). Again, a broad bleach (with hole depth estimated to be ~15%) is observed, suggesting that this state is, to a large extent, homogeneously broadened. Note that similar bleaches were observed for λB = 796.0 and 806.0 nm (see Figure 4). The similarity indicates that irrespective of λB, the system evolves into the same long-lived state, which induces more electrochromicity in addition to the chemical oxidation. That is, persistent HB spectra obtained for oxidized WT bRC suggest the P4+ state could be the acceptor of excitation energy from the BL/M pigments. Additionally, P5+ together with HM, and in part HL, might contribute the broad mixed state, which is bleached near 13,280 cm-1.


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Figure 5. Spectra a and b correspond to 5 K absorption and persistent HB spectra with λB = 833.0 nm (12,005 cm-1). The bleach near 833.0 nm is about 15%.

3.4 Transient HB spectra for the WT bRC of Rb. sphaeroides. Figure 6 (frame A) shows two transient P+QM− HB spectra obtained at 5 K. Curves a and b were obtained with λB = 496.5 and 796.0 nm, respectively. Frame B shows the same spectra normalized at the P-band bleach. The spectra are very similar indicating that in both burn cases the system goes into the same final CS state. Additionally, the absence of a sharp ZPH for λB = 796.0 nm denotes the short lifetime of the exciton state within the B-band.

0.1

B

A 0

∆ Absorbance

∆ Absorbance

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a b

-0.1 WT bRC T=5K

-0.2 750

800

850

Wavelength (nm)

900

750

800

850

900

Wavelength (nm)

Figure 6. Transient P+QM− HB spectra obtained with λB = 496.5 nm (curve a) and 796.0 nm (curve b). Both spectra were obtained for WT bRC of Rb. sphaeroides at 5 K.


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In order to reveal the properties of various HB spectra we theoretically describe the system under consideration in the next section. Using an excitonic model we perform a search of the model parameters based on absorption and HB spectra, which results in two new models for the bRC.

IV. Simulations of absorption spectra of bRC in CN, oxidized, and CS states 4.1. General description. The simulations of bRC spectra are based on the exciton concept. CT states make small direct contribution to the spectra so they are neglected and only molecular excitations are taken into consideration. Six chromophores of the bRC are resonantly coupled standing for the electronic system. All vibrational degrees of freedom of the pigmentprotein complex constitute the thermal bath, which is modeled by a set of harmonic oscillators in the present simulations. These simplifications allow us to restrict the number of unknown parameters and focus on the excitonic properties of the system. The system is described by the Frenkel exciton Hamiltonian35-37 = ∑ | | + ∑ | | ,

(1)

where is the site energy (electronic excitation energy) of pigment m, is the resonant (excitonic) coupling between the site excitations. Additionally, this system interacts with the harmonic bath and the optical field. The system interaction with the bath oscillators representing the protein environment and inter- and intra-pigment thermal vibrations causes fluctuations of the excitation energies. The fluctuations of different sites are assumed to be uncorrelated in the present simulations. Spectral densities ′′() characterize the frequency-content of the fluctuations. Additionally, in the present simulations we use the spectral density factors fi to adjust system-bath coupling strengths for different sites, then ′′ () = ′′() (see Supporting Information for details). The system-bath interaction causes relaxation and dephasing processes, creating homogeneous broadening of the spectral lines.

Interaction with the optical field is included perturbatively using the dipole approximation. Each molecule is then characterized by its transition dipole vector . The linear


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absorption (LA) spectrum is obtained by a cumulant expansion approach in the excitonic basis. = In this basis the electronic (system) part of the Hamiltonian is diagonal, in accord with , which yields exciton energies with and wavevectors . The absorption spectrum in this case is given in the exciton representation by () = ∑ | |

() ;

(2)

where is the transition dipole moment for exciton e: = ∑ with being the excitonic wavevector components;

()

is the spectral lineshape. The fluctuating terms

(system-bath coupling) are also transformed into the exciton representation and after the transformation are split into diagonal and off-diagonal exciton fluctuations. The off-diagonal fluctuations are included perturbatively to second order within the secular Redfield theory level. Diagonal fluctuations are included via cumulant expansion, which modulate the optical oscillations by a lineshape function " (#) and thus take into account the time-dependent pure dephasing. The resulting lineshape of the e-th exciton is: ()

2

= ℜ %3 &# exp*+# − + # − " (#) − -̅ # − #/0 1,

(3)

here the function " (#) describes the spectral line broadening of exciton e due to the linear coupling with the thermal fluctuations of the nuclei, 0 is the exciton lifetime due to exciton relaxation, and -̅ is an additional damping constant which effectively accounts for the nonlinearity of the system-bath coupling and causes the line broadening of the zero-phonon line.38 The function " (#) can be written as

" (#) = 25 % &(∑| |6 77 ())

89:;8?@ BB A CA

DE CF − 1 − +#H,

(4)

while the exciton lifetime is given by 0I9 = ∑7 7 (∑ |7 | | | ′′ (7 )) 81 + coth 8

NCOPO


BB.

(5)

12

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Here R is the inverse temperature in energy units; 7 is the transition energy from exciton e' to e.

The above-described spectrum is homogeneous in a sense that it does not take into account static variations of protein conformation (i.e., inhomogeneity) in the ensemble. In the present simulations we assume that only the site energies are randomly shifted in the ensemble. The site energies in the Hamiltonian (Eq. (1)) are the mean values of Gaussian distributions, each having its own variance. We thus define N variances ST . The final simulated spectrum is then the ensemble-average of a set of realizations of the Frenkel exciton Hamiltonian subject to the site energies disorder. The absorption spectra were numerically computed using the package Spectron.39

In order to explore the excitonic band structure of the molecular aggregate, we also

evaluate the composition of exciton e, i.e., we present the squared components 〈V V 〉XYZ[X[ of the excitonic wavevector averaged over the ensemble of realizations of site energy disorder. These values show contribution of each pigment of the complex to excitonic state e. Another quantity we are interested in is the exciton delocalization \ , effectively showing how many pigments contribute to the particular exciton. It is given by the participation ratio \ = ∑

9

_ ^ |]O^ |

.

(6)

Thus, when \ = 1, the exciton is localized on one pigment. The other limiting case is \ = `, meaning the exciton is completely delocalized over all N pigments in the system.

We aim to allow minimal changes in the site basis parameters while calculating the absorption spectra of different charged states of the bRC. The optimization of the parameters is performed sequentially; repeating it for the CN and oxidized states of the bRC. The CS state giving the transient HB spectrum (see Figure 9) is then modeled on the basis of the oxidized state model. Further we discuss the parameters of the oxidized and CN states separately for clarity.


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4.2. Absorption of oxidized bRC. A general description of parameters is detailed in the Supporting Information. Here we start with the description of most simple system – the chemically oxidized RC. Oxidation of the special pair changes its chemical state and consequently the electronic transitions. The special pair cation also creates an electrostatic field affecting the optical properties of other pigments. Earlier experiments and modeling showed that the electron density distribution within the special pair is asymmetric in the electronic ground state

40 - 42

, suggesting that upon oxidation the hole is mostly localized on the PL pigment,

especially at low temperature. We also take advantage of the calculated (INDO/MRCI-S) properties of the special pair cation P+ states.34 The authors of ref 34 present five main P+ states associated with the transitions mainly having CT or triplet transition characteristics. The three lowest energy states have only minor effect on the absorption spectra in the region of interest (10,500 – 14,000 cm-1). The fourth state, P4+, though seemingly appearing in the spectrum as a very weak shoulder near 12,000 cm-1 (see Figure 4), was associated with CT and internal conversion transitions, thus it is not included in our excitonic model. The fifth of these states, denoted as P5+, has a main contribution from the dipole transition of PM, with calculated values of the transition dipole moment similar to those of the monomeric BChls BM and BL and its transition energy is in the range of B and H pigments. The calculated oscillator strength of this transition is very similar to those of B pigments. The calculations of the absorption spectrum of oxidized bRC in ref 34 showed that the P5+ state has a noticeable effect on the spectrum. Hence we include this state in our model.

Based on these data we set up Frenkel exciton Hamiltonian parameters of the oxidized special pair pigments as follows: PL is ionized, which shifts its site energy away from the absorption region. Its energy becomes arbitrary, essentially it is below 10,000 cm-1 and it does not affect the absorption spectrum. Ionized PL is hence uncoupled from the rest of the excitonic system. PM (P5+), however, is allowed to experience electronic excitation in the same range as the B and H pigments, and remains coupled to the rest of the system as calculated by the TrEsp method.43 The coupling matrices of chemically oxidized, CS, and CN bRCs are shown in Table 1. The transition dipole moments necessary for the calculation of the absorption spectrum were obtained using the atomic coordinates of the chromophores from the structural data of bRC12 and the atomic partial charges of the Qy transition are the same as in the calculations of the


14

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excitonic couplings. The obtained transition dipole moments were then scaled to experimental values of the BChl and BPheo transition dipoles ratio. Spectral densities used in simulations are described in the Supporting Information and shown in Figure S1. Here we only mention that the complete spectral density function of the special pair pigments ′′a () is a sum of three terms: 1) a log-normal term for phonon part;21 2) the Lorentzian term for the special pair marker mode;21 and 3) the intramolecular high-frequency modes. 44 The spectral density for all other pigments ′′b () includes the same terms for phonon and high-frequency modes, but it has no marker mode term.

Table 1. Two Frenkel exciton Hamiltonians used for fitting the absorption spectra of the oxidized or CS (left), and CN (right) bRC.

Oxidized/CS

CN

EPM

EPM

0

EPL

-20

0

EBM

-119

0

18

EBL

27

0

-7

104

EHL

-11

0

104

-7

3

EHM

VP

EPL

-20

-119

EBM

-119

-17

18

EBL

27

-9

-7

104

EHL

-11

24

104

-7

3

EHM

There is no obvious experimental reference to set the energy and fluctuation parameters of the PM pigment to simulate the P5+ state of the special pair cation. However, notice the pronounced narrow peak appearing on the low energy side of the H-band in the absorption spectrum of the WT bRC upon oxidation (Figure 2). At the same time in the absorption spectrum of the CN WT bRC the H-band looks completely featureless (Figure 2). We suggest that the prominent feature of the H-band in the absorption spectrum of the oxidized bRC could be due to the P5+ transition of the special pair cation. As a result, we purposely fit the parameters of PM in such a way that it considerably contributes to the H-band. Thus, for the oxidized bRC, we fit the


15


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Page 16 of 41

values of the site energies: ac , dc , de , fc , and fe ; the factors of the spectral density: ac , dc , de , fc , and fe ; and the standard deviations of the Gaussian distribution of the site energies of the pigments Sac , Sdc , Sde , Sfc , and Sfe evaluating the mean square deviation of the calculated absorption spectrum from the experimental one. Initial values of all spectral density factors are = 1, and site energy disorder S = 55 h I9. In our model the site energies contain the reorganization energies. Detailed accounts of parameters are described in the Supporting Information.

Regarding the simulations, we report below the results of our best two models. In Model A, we assume that the fluctuation parameters ac (homogeneous broadening) and Sac (inhomogeneous broadening) of PM (P5+) are the same in the oxidized and CN states of bRC. In Model B, the putative P5+ band is narrow (ac and Sac are reduced) and directly produces the peak in the H-band at approximately 13,100 cm-1. Since the special pair is oxidized we assume that the spectral density of the PM pigment is the same as that of the B pigments ′′b (), i.e., it does not have the special pair marker mode at 125 cm-1 (see Figure S1). The resulting sets of fitted parameters for Models A and B are presented in Tables 2 and 3 ("Oxidized") and the corresponding absorption spectra of the oxidized bRC in Figure 7 are near-perfect matches to the experiment.

Figure 7. Absorption spectra of the oxidized WT bRC Models A and B. Red line - experimental (same as in Figure 2), blue line - calculated using the parameters presented in Tables 1, 2 and 3 part "Oxidized".


16

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Other color lines show separate calculated excitonic bands. Their composition is presented in Table 4 part "Oxidized". Thin cyan vertical lines mark burn frequencies 12,561 cm-1 and 12,398 cm-1 used to obtain persistent HB spectra of Figure 4.

Table 2. Model A parameters of the WT bRC: site energies E (cm-1) of the Frenkel exciton Hamiltonian (Table 1) and the environment related parameters f (dimensionless) and σ (cm-1) for the absorption spectrum of the oxidized (Figure 7), CN with ijk = lmm noIp and VP = 750 cm-1 (Figure 8), and CS (Figure 9) states.

PM

PL

BM

BL

HL

HM

Oxidized Model A Ei

13,360

7,770

12,605

12,665

13,240

13,445

qr

1.84a

1.84a

1.25a

0.95a

0.95 a

1.35 a

sr

88

88

65

65

20

40

Ei

11,920

12,420

12,535

12,625

13,295

13,500

qr

1.84b

1.84b

1.25a

0.95a

0.95 a

1.35 a

sr

88

88

65

35

40

65

CN Model A

CS Model A Ei

13,370

qr

1.84

sr

88

a

7,770 1.84

a

88

12,615 1.25

a

30

12,710 0.95

a

65

13,165 0.95

a

30

13,365 1.35 a 50

-----------------------a

denotes factor to the spectral density t′′u (v); b denotes factor to the spectral density t′′k (v).

Table 3. Model B parameters of the WT bRC. See caption of Table 2 for explanation.

PM

PL

BM

BL

7,770

12,630

HL

HM

Oxidized Model B Ei

13,215

qr

1

sr

30

a

1

a

30

1.45 50

a

12,680 1.1

a

50

13,365 1.1 50

a

13,540 1.65 a 50

CN Model B


17


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Page 18 of 41

Ei

11,920

12,420

12,560

12,650

13,315

13,540

qr

1.84b

1.84b

1.45 a

1.1 a

1.1 a

1.65 a

sr

88

88

50

20

30

50

13,155

7,770

12,640

CS Model B Ei qr

1

sr

45

a

1

a

30

1.45 30

a

12,725 1.1

a

70

13,335 1.1

a

50

13,510 1.65 a 50

The absorption spectra of the oxidized WT bRC in Figure 7 are obtained as a sum of the spectra of the calculated excitonic bands shown in the figure as well. The spectra are obtained as ensembles of 4000 realizations of the static energy disorder. The intensities of all bands are normalized to fit the intensity of the B-band to the experimental one. The B-band is very simple, as it consists of two excitonic bands coming from BL and BM pigments. The ensemble-averaged

components 〈V V 〉XYZ[X[ of the excitonic bands contributing to the absorption spectrum and exciton participation numbers Le (Eq. (6)) are shown in Table 4 ("Oxidized") (the 1st exciton is absent both in the spectra and in Table 4 of the oxidized bRC, as it corresponds to the ionized PL site, which does not contribute to the absorption spectrum in the region of interest). As it turns out the 2nd and 3th excitons, which make up the B-band, have strong mixing between BL and BM pigments with exciton delocalization close to 2 in both models. This is due to PM, which acts as an intermediate. However, PM does not contribute to the B-band considerably. Even more interesting is the structure of the H-band. The modeled spectra demonstrate that in both Models A and B the H-band comprises three excitonic bands, and the 4th exciton is responsible for the fine feature at approximately 13,100 cm-1 in the absorption spectra. However, the composition of this exciton is different in the models. In Model A, the 4th exciton has a main contribution from HL (Table 4) and the band is moderately intense, while in Model B this excitonic band is intense and originates from PM, effectively representing the P5+ state of the special pair cation. In Model A the 5th and 6th excitons are delocalized over PM and HM and the 5th excitonic band overlaps with the 4th band, enabling this narrow band to appear in the spectrum. In Model B the 5th and 6th excitons are highly localized on HL and HM, respectively. In the models of the CN bRC the 5th and 6th excitons originate from HL and HM (vide infra). Thus, in


18

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Model A the compositions of the 5th and 6th excitons change upon oxidation, whereas in Model B, they remain the same. It appears that oxidation of the special pair produces different effects in the two models. z

Table 4. Exciton compositions presented by the exciton wavevector components Vwxy V and exciton participation numbers Le of oxidized, CN, and CS bRC for Models A and B. All values are obtained by taking into account the static energy disorder and are averaged over 4000 realizations. Oxidized Model A

Oxidized Model B

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

PM

-

0.01

0.02

0.08

0.67

0.22

PL

-

0

0

0

0

BM

-

0.63

0.35

0

BL

-

0.34

0.60

HL

-

0.01

HM

-

Le

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

PM

-

0.01

0.03

0.94

0.01

0

0

PL

-

0

0

0

0

0

0

0.01

BM

-

0.61

0.38

0

0

0.01

0.04

0.02

0

BL

-

0.37

0.57

0.05

0.02

0

0.02

0.88

0.09

0

HL

-

0.01

0.01

0.01

0.96

0.01

0.01

0.01

0

0.22

0.77

HM

-

0.01

0

0

0.01

0.98

1.94

2.06

1.28

1.97

1.58

Le

1.99

2.13

1.13

1.08

1.04

-

CN Model A

CN Model B

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

PM

0.65

0.03

0.01

0.31

0

0

PM

0.65

0.03

0

0.31

0

0

PL

0.34

0.04

0.04

0.59

0

0

PL

0.34

0.04

0.04

0.58

0

0

BM

0

0.84

0.09

0.05

0

0.01

BM

0

0.89

0.04

0.06

0

0.01

BL

0

0.08

0.84

0.05

0.02

0

BL

0

0.03

0.89

0.05

0.02

0

HL

0

0

0.02

0

0.97

0

HL

0

0

0.02

0

0.98

0

HM

0

0.01

0

0

0

0.98

HM

0

0.01

0

0

0

0.99

Le

1.85

1.39

1.38

2.24

1.05

1.03

Le

1.85

1.27

1.25

2.29

1.05

1.02

CS Model A

CS Model B

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

1 ex

2 ex

3 ex

4 ex

5 ex

6 ex

PM

-

0

0.03

0.01

0.42

0.54

PM

-

0.01

0.06

0.92

0.01

0

PL

-

0

0

0

0

0

PL

-

0

0

0

0

0

BM

-

0.78

0.20

0

0.01

0.01

BM

-

0.73

0.25

0

0

0.01

BL

-

0.20

0.73

0.05

0.02

0.01

BL

-

0.24

0.67

0.07

0.03

0


19


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Page 20 of 41

HL

-

0.01

0.04

0.94

0.01

0

HL

-

0.01

0.02

0.01

0.96

0.01

HM

-

0.01

0

0

0.55

0.44

HM

-

0.01

0

0

0.01

0.98

Le

-

1.54

1.75

1.13

2.11

2.07

Le

-

1.68

1.96

1.17

1.09

1.05

4.3. Absorption of CN bRC. Next we proceed to model the absorption spectrum of the WT bRC in the CN state. For this we use the "CN" coupling matrix presented in Table 1. There are two unknown parameters of the special pair pigments: the difference of their site energies Δa and excitonic coupling VP. Once these two parameters are set, other special pair parameters are straightforwardly obtained from the experimental data: the position and the shape of the PY− band. The position of PY− defines EPM, then ae = ac + Δa . The band shape related site basis characteristics Sac , Sac , fPM, and fPL are adjusted to reproduce the experimentally obtained spectral density and distribution function of the excitonic PY− band as described in the Supporting Information. We have additionally adopted the following constraints: ac ≤ ae , ac = ae , and Sac = Sae (see Supporting Information for more details). Parameters of other pigments are inherited from the values obtained for the oxidized bRC (Tables 2 and 3 part "Oxidized"). Concerning the latter, we assume that differences of the internal electrostatic field between the CN and oxidized bRCs cause different site energy shifts of the pigments. However, we have found that the sole site energy shifts to BM, BL, HM and HL pigments, compared to the oxidized state, do not provide satisfactory agreement with the experimental absorption spectrum of the CN bRC. Thus, we allow changing of the site energy disorder parameters for these pigments, S . By fitting the experimental absorption spectrum we optimize the values of the above-mentioned parameters for particular fixed values Δa and VP. Here we present the case with Δa = 500 h I9 and VP = 750 cm-1 to illustrate the main effects obtained. In the models presented the transition dipole strength of the P pigments is reduced to 80% compared to the B pigments.

All parameters of the CN bRC are presented in Tables 2 and 3 ("CN") for Models A and B, respectively. The corresponding absorption spectra obtained with these parameters are shown in Figure 8. The spectra of the individual excitonic bands are also shown in the figure. The spectra are obtained from an ensemble of 4000 realizations of the static energy disorder. The


20

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intensities of all bands are normalized to fit the experimental intensity of the P-band. However, in Figure 8 the amplitude of the 4th excitonic band (green line) is amplified 10 times for clarity. The composition of the excitonic bands contributing to the absorption spectra and exciton participation numbers are shown in Table 4 ("CN"). The fitting yields near-perfect agreement to experiment. The lowest energy band is contributed by the special pair dimer. The configuration of B-band changes considerably in comparison with the oxidized state. While it is still composed out of BL and BM pigments, the 2nd and 3th excitons are quite localized. The 4th exciton is again due to the special pair, however its contribution to the spectrum is very small. Finally the H-band is now composed out of HM and HL pigments with completely localized excitations.

Figure 8. Absorption spectra of the CN WT bRC Models A and B with ijk = lmm noIp and VP = 750 cm-1. Red line - experimental (same as in Figure 2), blue line - calculated using the parameters presented in Tables 1, 2 and 3 ("CN"). Other color lines show separate calculated excitonic bands. Their compositions are presented in Table 4 ("CN"). The amplitude of the 4th excitonic band (green line) is amplified 10 times in the figure.

4.4. Modeling of transient HB spectrum. For the simulations of the transient HB spectrum (Figure 6) we assume that during the burn process the CN bRC is converted into the CS state. The transient HB spectrum (fd ) is then equal to the difference of the absorption spectra with the laser on and laser off (i.e., the pre-burn spectrum). Here the pre-burn spectrum corresponds to the absorption of CN bRC (~T ). Burning by the laser induces ET within bRC


21


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Page 22 of 41

creating the CS state P+QM−. To model the absorption of the CS state ( ~ ), we use the "Oxidized/CS" Hamiltonian in Table 1 and assume that the parameters should be very similar to the ones of the oxidized bRC (Tables 2 and 3). However, the electrostatic field originating from the negative charge on QM will produce additional site energy shifts of the BL/M and HL/M pigments in comparison to the oxidized bRC (see Figure 3, curve c). We also found that additional changes in the static energy disorder improve agreement with the experimental spectrum. Thus, we use the parameters of the oxidized bRC as initial values to simulate the absorption spectrum of the CS bRC. Next we adjust the site energies of the CS state Ei and the standard deviations of the Gaussian distribution of the site energies of the pigments S by minimizing the mean square deviation of the experimental and calculated difference absorption spectra fd = ~ − ~T (i.e., the HB spectrum). We use the experimental transient HB spectrum burned nonresonantly at 496.5 nm (Figure 6) as a target of the fit. The obtained HB spectra for Models A and B are presented in Figure 9 and corresponding parameters are listed in Tables 2 and 3 ("CS"), respectively. Both fits are very good. We emphasize that P+QM− HB spectra in a spectral range covering all co-factors were never described theoretically before. The composition of the excitonic bands contributing to the absorption spectrum and exciton participation numbers of the CS bRC are shown in Table 4 ("CS").

Figure 9. Transient HB spectra = t − t - the difference absorption spectra of CS and CN states of Models A and B of WT bRC. Red line - experimental (same as in Figure 6), blue line - calculated


22

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spectra. The calculated spectra are obtained with parameters presented in Tables 2 (“CS”) and 3 (“CN”), respectively. Green arrow points at a small spectral feature considered in the Discussion section.

In the simulated transient HB spectra in Figure 9, in both Models A and B, the positive peak at approximately 13,000 cm-1 is created by the 4th exciton of the CS state (Table 4, "CS") analogously with the oxidized state. The composition of this excitonic band is very similar to the oxidized case in both models, although this band is red shifted in comparison to the analogous 4th exciton of the oxidized state, largely due to QM− induced electrochromic shift of the HL site energy in Model A, or PM (P5+) site energy in Model B. The features at higher energies (positive shoulder indicated by the green arrow in Figure 9 and negative feature at approximately 13,300 cm-1) in the transient HB spectra are due to shifts of the 5th and 6th excitonic bands, which are of different origins in the two models (Table 4). That is, in Model A these states are almost equally contributed to by PM and HM, while in Model B they are localized on HL and HM. Note, that in Model A these excitons become more delocalized in comparison to the oxidized case. The 2nd and 3rd excitons are composed mainly of B pigments (Table 4). Though excitonic coupling between B pigments is rather small (Table 1), their exciton participation numbers are much higher for the oxidized or CS case than for the CN one; showing that oxidation of the special pair induces their delocalization in both present models.

4.5. Lifetimes. In our simulations all spectra are obtained from an ensemble of 4000 realizations of the static energy disorder. For the oxidized bRC, the ensemble averaged lifetime of the 3rd exciton (higher energy exciton contributing to the B-band) is ~2224 fs for Model A and ~1050 fs for Model B. However, the distribution of the lifetimes in the ensemble is very wide. In Figure 10 we present the distributions of the 3rd and 4th exciton lifetimes in the ensemble for the oxidized and CN bRC. As seen from the figure for the 3rd exciton of the oxidized bRC, nearly 40% of the lifetimes of individual realizations are shorter than 100 fs in Model A, and nearly 50% in Model B, even though the average lifetime of the 3rd exciton (oxidized bRC) is longer than 1 ps. This explains the presence of a broad hole in the persistent HB spectrum in Figure 4A. On the other hand, there are realizations when this exciton lives for over 10 ps. The latter could explain why it is possible to burn persistent ZPHs in the B-band region of the oxidized bRC. In comparison, the 3rd exciton of the CN bRC has an averaged lifetime of ~163 fs for Model A and


23


~154 fs for Model B. The distribution presented in Figure 10 for this exciton shows that only a very small number of excitons in the ensemble survive for longer than 500 fs and none for longer than 1 ps. This result is consistent with the absence of a sharp ZPH in the transient HB spectrum burned into B band (Figure 6, curve b).

Unfortunately in our model we cannot investigate the energy transfer out of the B-band in the oxidized bRC as the lower exciton of the B-band (2nd exciton in the model) cannot transfer energy, therefore its lifetime is infinite. Recall that the 1st exciton in the oxidized bRC is produced by oxidized PL and is energetically unreachable for the rest of the system. This state is

over 10 ps

5-10 ps

1-2 ps

100-500 fs

2-5 ps

0-50 fs

over 10 ps

2-5 ps

5-10 ps

1-2 ps

0.5-1 ps

Oxidized 4 ex < τ > ~ 608 fs

50-100 fs


100-500 fs 0.5-1 ps

50-100 fs

0-50 fs

Model B

over 10 ps

5-10 ps

1-2 ps

0.5-1 ps


50-100 fs

0-50 fs

2-5 ps

500

1-2 ps

100-500 fs 0.5-1 ps

0-50 fs

1000

50-100 fs

1500

over 10 ps


2-5 ps

Model A

2000

5-10 ps

2500

100-500 fs

shown neither in the spectra presented in Figure 7 nor in the exciton compositions in Table 4.

over 10 ps

5-10 ps

2-5 ps

1-2 ps

0.5-1 ps

0-50 fs

50-100 fs

Neutral 4 ex < τ > ~ 61 fs 100-500 fs

over 10 ps

5-10 ps

2-5 ps

1-2 ps

100-500 fs

Neutral 3 ex < τ > ~ 154 fs

0.5-1 ps

50-100 fs

0-50 fs

over 10 ps

5-10 ps

2-5 ps

1-2 ps

0.5-1 ps

0-50 fs

100-500 fs

Neutral 4 ex < τ > ~ 62 fs 100-500 fs

over 10 ps

5-10 ps

2-5 ps

500

1-2 ps

1000

Neutral 3 ex < τ > ~ 163 fs

0.5-1 ps

1500

50-100 fs

2000

50-100 fs

0 2500

0-50 fs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 41

0

Figure 10. The four panels on the left and right show the distributions of the 3rd and 4th exciton lifetimes of oxidized and CN (Neutral) bRC in the ensemble of simulated spectra for Model A and Model B, respectively.

V. Discussion

The photosynthetic bRC contains six Chl-type pigments only, and the absorption spectrum has three separated peaks ascribed to particular pigments. Thus, it might seem that interpretation of the spectra and their simulation is a rather straightforward task. However, there are still many unknowns, which repeatedly cause scientific interest. Though pigments in the bRC


24

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form two symmetric branches, the bRC functions as a heterodimer (in the sense of two protein branches L and M) probably due to different environmental properties within the branches. The special pair pigments demonstrate different electron density distribution even in the ground state.40,41 Furthermore, it has been suggested experimentally that the effective dielectric constant differs by approximately three times in the two branches of the bRC18 and dynamic effects in dielectric relaxation were also observed. 45 , 46 The excitonic coupling depends on the fast (optical) part of the dielectric constant and the electrochromic energy shifts on the static one. Due to this uncertainty of the dielectric properties, all parameters of the Frenkel exciton model could be somewhat different for two branches, including excitonic couplings of the pigments and couplings to the environment. This is probably why the very structured (transient) HB spectra in the P+QM− state (in a very broad spectra range) have never been described theoretically before.

Though there are structural data of rather high resolution obtained by X-ray crystallography for the bRC,12, 47 , 48 the molecular aggregate is too large for structure-based quantum chemical or electrostatic calculations to provide unambiguous information on site energies and excitonic coupling of pigments. We applied the TrEsp method43,49 to evaluate the resonant couplings between the pigments in the complex and found that the couplings between monomeric BChl a and BPheo a pigments calculated by the same method based on the different structure files12,47,48 differ by up to 25%. The special pair pigments act as a supermolecule and their coupling, evaluated using different quantum chemistry methods, also resulted in different values.42 Furthermore, the coupling seems to be temperature dependent. This feature complicates application of the predictions obtained from the quantum chemistry calculations.

Nevertheless, the data presented below and our theoretical analysis uncovers internal structural properties of the bRC, which were poorly understood previously. Even though there have been many studies regarding the excitonic structure and ET dynamics in bRCs (see ref 4 and references therein), the electrochromic shifts of cofactors in the chemically oxidized bRC and in the presence of the P+QM− state, as well as the energy of PY+, are not yet fully understood. In particular, the position of the upper exciton level is not well established even though its


25


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energy may have significant implications regarding the nature of the very fast EET in photosynthetic RCs.50

5.1. Electrochromic shifts. The comprehensive description of three states of the bRC and their comparison allows one to directly obtain electrochromic shifts of pigment site energies and consequently to evaluate the dielectric properties inside the proteins on a microscopic scale. We have evaluated site energy shifts of B and H pigments based on the available crystal structure of the bRC. Using the 2J8C structure12 we put +0.25 charges on four N atoms of PL and -0.167 charges on six C atoms of quinone QM, thus creating the electrostatic field within the bRC in the PL+QM− state. We then calculate the site energy shifts of B and H pigments by the CDC method49 using the atomic coordinates of the chromophores and the atomic partial charges of the Qy transition obtained by TD DFT B3LYP calculations.43 With = 1 we obtain the following site energy shifts: Δdc = 184 h I9 , Δde = 287 h I9 , Δfe = −133 h I9 , and Δfc = −131 h I9 . Roughly, by dividing these values by the corresponding site energy differences between charge CS and CN states obtained from spectroscopy simulations (Tables 2 and 3) we can evaluate effective dielectric constants at B and H sites for both models. Indeed, in Model A for BM and BL pigments we get /c ≈ 2.3 and /e ≈ 3.4, respectively. For the

same pigments in Model B /c ≈ 2.3 and /e ≈ 3.8. So the effective dielectric constant is larger in the L-branch in both models, in agreement with Stark spectroscopy data,18 though we do not get a three-fold difference between the values. The picture is more complicated for H pigments. From the same evaluation of the site energy shifts we get that /e ≈ 1.0 and /c ≈ 1.0 in Model A, and /e ≈ −6.6 and /c ≈ 4.4 in Model B for HL and HM, respectively. So in Model A the effective dielectric constant is approximately equal in the H binding pockets of the two branches, whereas our Model B does not fit this scenario. However, the authors of ref 18 (also45,46) interpret the H-band as originating from the absorption of H pigments only, whereas, in our models the composition and structure of H-band changes upon oxidation of P. In both Model A and B the H-band comprises three excitonic bands. In Model A, the H pigments experience a red shift of their site energies, become less disordered, and the appearing P5+ state mixes with HM. In Model B, the red shift of the H-band upon oxidation is not due to an energy shift of H pigments, but rather due to the appearance of the P5+ band of the


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oxidized special pair. Therefore, in this model the site energy of the HL pigment shifts blue instead, in contrast to ∆Absorbance obtained for P+ and/or P+QM− and shown in Figure 3. However, in the excitonic picture the 5th exciton shifts blue and the 6th exciton shifts red upon oxidation in both models.

5.2. Upper excitonic band of the special pair. Another important property often discussed in the literature is the energetic position of the upper excitonic band PY+ of the special pair. Although many researchers have suggested that the PY+ energy level must contribute to the absorption near 12,300 cm-1 (~813 nm),24-27 based on our experimental data and simulations this is not the case, i.e., the bleach of the shoulder near 813 nm is mostly due to differing blue electrochromic shifts of the BL/M cofactors. From the exciton composition in the CN bRC (Table 4 "CN") one may see that the pigments of the special pair (in both models) mainly contribute to the 1st and 4th excitons. The 4th excitonic band can be denoted as PY+, i.e., the upper band of the special pair. The band appears between the B- and H-bands in our models. However, the amplitude of this band is rather low (multiplied by 10 in Figure 8), whereas the lower excitonic band of the special pair PY– (1st band in the Figure 8) is superradiant and has a rather intense, long-pronounced high-energy tail in the B-band region of the absorption spectrum. The tail spans the PY+ band spectral region as well. This high-energy tail appears in our modeling due to highfrequency modes included in the spectral density. So we speculate that the features in earlier experiments (for example ref 51 at 825 nm/12,120 cm-1) associated with the high excitonic component of P band, are due to a high frequency tail of the lower excitonic state itself. In our simulated spectra the intensity ratio of the maximum of the P-band and intensity of its highenergy tail in the region 12,000-12,500 cm-1 is approximately 10/1 in agreement with a previous estimation51 where it was ascribed to the high excitonic component. In our simulations the position of the high excitonic component corresponding to the 4th exciton is at higher energy and its intensity is very low in both models (see also subsection 5.6). As follows from our simulations (see Figure 10) the average lifetime for 4th exciton in CN bRC is ~60 fs, similar for both Models A and B. 5.3. P5+ state of the special pair cation. An outstanding feature of the present model is the interpretation of the so-called P5+ state of the special pair cation, which differs somewhat


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from the one reported in ref 34. We propose that P5+ transition is responsible for the pronounced and rather sharp peak on the low-energy side of the H-band in the oxidized bRC (Figure 2). Importantly, our attempt to model the appearance of this peak in the H-band in the oxidized state by merely shifting the site energies of H pigments did not give a satisfactory result. In Model B we speculate that the P5+ band is narrow and is directly responsible for the fine feature appearing in the H-band upon P oxidation and for the features around 13,140 cm-1 in the transient HB spectrum (Figure 9). The presence of such a state is also indicated by the persistent HB spectra shown in Figures 4 and 5. Alternatively, this feature may reflect an electrochromic shift of a narrow band of the HL pigment, as considered in Model A. In Model A we assumed PM (P5+) should have the same fluctuational parameters (i.e., homogeneous and inhomogeneous broadening) as in the CN state. Unlike in the CN state, there is no exchange narrowing in the special pair in the oxidized state, and PM produces a rather broad band in agreement with spectra a and b in Figure 4, thus favoring Model A. However, to get the above-mentioned peak in the H-band, we need to allow a substantial narrowing of H-bands (mostly HL), which is also observed in curve b of Figure 4 (see also Figure 11). Then a band involving P5+ overlaps with a narrow HL band thus enabling the latter to show-up in the spectrum. Modeling studies show that in this case the site energy of HL molecule would have to change by about -55 cm-1 (see Table 2). It is feasible that upon oxidation of the special pair the environmental properties of HL could change due to the modified internal electric field. Note that local protein internal fields do not have to be constant and may induce spectral and/or conformational changes.

5.4. Excitation lifetimes. While HB cannot directly inspect energy transfer pathways, it can provide lifetimes of the zero-point level of S1(Qy)-states due to EET which are determined by the widths of ZPHs (½ of the ZPH provides the homogeneous linewidth (Γhom)) in highresolution measurements.16,52 The ~120 fs energy transfer time revealed by persistent HB spectra in section 3.2 appears to be consistent with data obtained previously in a 77 K 2DES experiment.15 There the ~100 fs EET time between two B bands and transfer out of the lower B band by ~120 fs were observed.15 Similar τEET values were also calculated in ref 34, where


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energy transfer times between the possible BL/M donors and P4+ acceptor (using the vibronic coupling method) were 130 fs (BL → P4+) and 200 fs (BM → P4+), respectively. However, notice that in ref 34 the labeling of the BL and BM bands (possible donors) was reversed, in disagreement with many previously published data.15,28,31-33 A comparable effective decay time (i.e., ~150 fs) was also observed for the B-band in the oxidized WT bRC of Rb. sphaeroides at 70-80 K 2DES by other group,53 which is also consistent with data shown in Figures 4 and 5. All these results support our assignment of the 833 nm bleach to the P4+ state (see curve a′ in Figure 4), and our measured value of ~120 fs can be assigned to redistribution of excitation between BM, BL and P4+. This state must have a very small transition dipole and contributes to a very weak shoulder on the low-energy side of the BM band (see an asterisk below curve b in Figure 2). A similar state was observed in the oxidized bRC and assigned to a hole-transfer plus tripdoublet excitation (HT + 3Qy(L)).34 5.5. On the persistent holes burned into the B-band. An important observation from the experimental persistent HB spectra (Figure 4) is that burning in either lower or higher energy sides of the B-band results in ZPHs at λB. The latter provides evidence that long lived states (traps) exist, while the presence of broad holes indicates the existence of shorter lifetimes of the excited states. These experimental data are consistent with the wide distributions of exciton lifetimes (for both models) as illustrated in Figure 10. Unfortunately, a broad hole near 12,500 cm-1 and the ZPH at λB = 12,561 cm-1 (i.e., the burn frequency) overlaps with a broad antihole, which precludes an exact evaluation of its width and corresponding EET time. Nevertheless we can suggest that it has a fast component indicating energy transfer to the lower B state and likely other lower states. In Figure 7, showing the simulated spectra of oxidized bRC, thin cyan vertical lines mark the two experimental λB into the B-band. As seen, both excitonic B-bands are affected at either λB used in the HB experiment in Figure 4. Keeping in mind that the simulation results presented in this work are an ensemble average over static disorder and that the experimental spectra are measured on bulk sample, it is obvious that the excitation and following relaxation pictures in individual bRCs can be quite diverse due to static disorder. It has been suggested before34 that the bright P5+ transition may lend intensity to other oxidized special pair transitions (e.g., P4+

34

). The intensity sharing (common ground state)


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between the P4+ and P5+states seems to also be confirmed by spectra b and c in Figure 4, as revealed by bleaches near 833 nm (12,005 cm-1) and 762 nm (13,123 cm-1). The bleach near 13,270 cm

-1

(~754 nm) in these spectra likely corresponds to mixing of H with P+ states.

Although the very weak P4+ state has not been used in our modeling studies, the data shown in Figure 11 and values reported in Tables 2-4 (compare the compositions of various excitonic states in the oxidized bRC) also show that in Model A PM (P5+) is strongly mixed with HM. Regarding the transient HB spectra of the CS bRC shown in Figures 6 and 9, it appears that the absorption bands of the BL/M chromophores in the WT bRC are not strongly mixed with the PL/M pigments (see Table 4 for details). Concerning the persistent HB spectrum burned into the putative P4+ state (Figure 5), no ZPH is obtained and the hole appears very broad suggesting that this state is very short lived. Since we do not include the P4+ state in our model, we cannot directly relate simulation results with this persistent HB spectrum. One may notice, however, that the overall profiles of all three persistent HB spectra presented here are rather similar. Moreover, they resemble the shape of the transient HB spectra (Figure 6) as well. Our simulations of transient HB clearly indicate that the CS spectrum modeled in Figure 9 is mainly due to the bleach of the PY–/PY+ states and electrochromic shifts of site energies and consequently the excitonic bands. Therefore, it is likely that some additional electrochromic shifts happen while burning oxidized bRC to generate persistent HB spectra. Note, that the signals in persistent HB spectra in comparison to transient holes are very low, i.e., the spectra presented in the Figures 4 and 5 are multiplied by 46 and 44, respectively. The transient HB spectra of Figure 6 are not multiplied and reflect real ∆Absorbance changes. 5.6. Models uncertainties and why Model A appears to favor HB data. Lastly, we have to point out that our sets of parameters include some uncertainties: 1) while HB brings very high spectral resolution, distinction between homogeneous and inhomogeneous broadening of the spectral lines for higher energy pigments is not simple when exciton lifetimes are short. Consequently, we arrived at two Models (A and B) which produce very similar CN absorption spectra (Figure 8) with different set of parameters. For B and H pigments, the homogeneous broadening parameters (fi) are smaller and inhomogeneous broadening parameters (S ) are larger in Model A than in Model B (see Tables 2 and 3, "CN"). The parameters of P pigments are the


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same in both models as they are obtained directly from modeling of resonant (transient) HB spectra published in ref 21, with fixed values of Δa = 500 h I9 and VP = 750 cm-1 (the latter two values were chosen for illustrative purposes); 2) While modeling the absorption spectrum of the CN bRC, the transition dipole moments of P and B pigments (all BChl a molecules) had to be scaled in order to obtain intensities of the P and B bands compatible with the experimental spectrum. The most likely reason is that we did not include CT states (research in progress) or ultimately the whole special pair should be considered as a supermolecule with its unique set of transitions. As a result, in our model the reduction of the transition dipole moments of P pigments to 80% of B pigments is not surprising (which effectively compensates for the putative intensity loss of the P-band to dark CT states); and 3) From the present experimental data we cannot elucidate the excitonic coupling and site energy difference of P pigments uniquely. Here we present results obtained with fixed values of Δa = 500 h I9 and VP = 750 cm-1. In general, we obtained very similar features for models of the CN bRC with Δa in the range 0 − 500 h I9 and VP = 650-750 cm-1, which is more restrictive. When parameters of P pigments are set to satisfy the results obtained directly from modeling of resonant (transient) HB spectra published in ref 21, only minor changes in the values of the parameters of B and H pigments are necessary (in comparison to present values) and the overall picture remains the same (results not shown). However, we found that an excitonic coupling VP < 650 cm-1 leads to poor agreement with the experiment. Thus, the values of Δa = 500 h I9 and VP = 750 cm-1, based on multiple models tested, are most reasonable. Concerning the upper excitonic component of the special pair we find it at energies higher than 12,600 cm-1 in all models tested. Finally, the theoretical approach in the Spectron package involves tough approximations. One of them is the neglect of complex-value lifetime broadenings. It thus does not include additional band shifts coming from off-diagonal excitonic fluctuations. However, minimal tuning of transition energy parameters compensates this deficiency and provides the same quality of fits with the same physical insight (work in progress).

Given the concerns mentioned above, we note that the major uncertainties are related to site energies, fi and S parameters of PM, HM, and HL pigments in chemically oxidized, CN, and CS bRCs. We took great care to explore/gather additional information from time-domain experiments, including the most recent 2D coherent spectra, to discriminate between Models A


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and B. The 2D spectra of oxidized bRC in ref 15 were obtained in the nonrephasing phase matching direction; so the homogeneous and inhomogeneous line broadenings are not resolved. However, the two peaks in the B-band of 2D spectra for different waiting times appear rather different. This could be an argument that the properties of the B-bands are not the same supporting our models where B pigments have different environmental characteristics fi. Unfortunately, the 2D spectrum in ref 15 covers only the B-band region and no information on the H-band (i.e., the HM and HL chromophores) is available. In another 2D spectrum obtained for the oxidized bRC53 both B- and H-bands are visible, however, the diagonal peaks there are featureless and resolve the structure of neither B- nor H-bands. Figure 11 compares the bleach and electrochromic shift induced by P+ in partly chemically oxidized bRC with the calculated maxima of the 4th, 5th and 6th excitons (indicated by thick vertical lines) obtained for Models A and B. This comparison and data shown in Figures 4 and 5 appear to favor Model A since the main bleach near 748.5 nm (5th exciton) is consistent with the observed broad bleach due to PM (σ = 88 cm-1), which effectively represents the P5+ state. This bleach occurs at the maximum of the 5th exciton which is mostly delocalized over the PM (67%) and HM (22%) molecules. The maxima of the 4th and 6th excitons are located at 755.3 and 743.8 nm (black lines); these two excitons are also delocalized over PM/HL as 8/88% and PM/HM 22/77%, respectively. Qualitatively, the spectrum within the 720-780 nm is consistent with a red-shift of both HL and HM molecules. That is, the narrow derivative type spectrum near 750-770 nm is due to an electrochromic shift of the narrower band of HL (σ = 20 cm-1), whose red-shift overlaps with a red-shift of a much broader band associated with HM (σ = 40 cm-1). The maxima and composition of the 4th, 5th and 6th excitons obtained for Model B (see Table 4) are less consistent with the P+ spectrum shown in Figure 11 than Model A. Interestingly, the approximately three times larger blue shift of BL compared to BM induced by QM− is observed in both Models A and B, in agreement with the data shown in the inset of Figure 4. Also the lifetime of the 4th exciton (Figure 10) is quite similar in both models. More data from 2DES (to provide more insight into homogeneous and inhomogeneous line broadenings) and selective resonant HB into the H-band are needed to provide more insight into the electronic structure near the HL and HM chromophores.


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PL+ - induced shift of BL / BM

T=5K

Delta Absorbance (arb. units)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Model A Eigenvalues

6 4 5

0

* PY− 6 54

Eigenvalues

Model B

700

750

800

850

900

Wavelength (nm) Figure 11. P+ induced bleach and corresponding electrochromic shifts in partly chemically oxidized bRC from Rb. sphaeroides. Calculated eigenvalues ( ) of the 4th, 5th and 6th excitons for Models A and B are indicated by vertical lines. The asterisk indicates the position of the very weak upper exciton band, PY+.

VI. Conclusions

Our experimental results and their theoretical interpretation provide new insight into the excitonic structure of the widely studied bRC from Rb. sphaeroides. We were able to experimentally determine the excitonic states of chemically oxidized, CN, and CS bRC of Rb. sphaeroides. We propose two novel models that include structurally determined excitonic couplings. Although both models describe the absorption and transient HB spectra very well, the calculated exciton compositions of oxidized, CN, and CS bRCs appear to favor Model A. However, more experimental data are needed to entirely exclude Model B. Fitted site energies provide new insight into P+, CS induced electrochromic shifts, and the protein dielectric. Although many researchers have suggested that the PY+ energy level must contribute to the absorption near 12,120-12,300 cm-1 (~825-813 nm),24-28 based on our experimental data and simulations we argue that this is not the case, i.e., the bleach of the shoulder near 813-815 nm is


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mostly due to different electrochromic shifts of the BL/M cofactors. From the exciton composition in the neutral bRC we show that the pigments of the special pair mainly contribute to the 1st and 4th excitons. The 4th excitonic band can be denoted as PY+, i.e., the upper band of the special pair. Therefore, we conclude that the shoulder in the absorption of Rb. sphaeroides near 813-815 nm does not contain the PY+ exciton band, as sometimes suggested in the literature,24-28 in agreement with previously published data for the Zn-bRC.54

Acknowledgements

We acknowledge Drs. T. Beatty and R. Saer from the Department of Microbiology and Immunology, University of British Columbia, Vancouver, Canada for kindly providing the samples of WT bRC from Rb. sphaeroides. OR and DA acknowledge support from the Lithuanian Science Council (grant No: MIP-090/2015). RJ, AK, and MJ acknowledge the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the U.S. Department of Energy through Grant DE-SC0006678 (to RJ) for support. We also thank Dr. Khem Acharya for experimental help at the early stage of this work.

Supporting Information. Description and setup of the model parameters: excitonic coupling

matrix elements, site energies, spectral densities, static energy disorder.


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Band Structure of the Rhodobacter sphaeroides Photosynthetic

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