Femtosecond dynamics of the forbidden carotenoid S₁ state in light-harvesting complexes of purple bacteria observed after two-photon excitation

Abstract

Time-resolved excited-state absorption intensities after direct two-photon excitation of the carotenoid S₁ state are reported for light-harvesting complexes of purple bacteria. Direct excitation of the carotenoid S₁ state enables the measurement of subsequent dynamics on a fs time scale without interference from higher excited states, such as the optically allowed S₂ state or the recently discovered dark state situated between S₁ and S₂. The lifetimes of the carotenoid S₁ states in the B800-B850 complex and B800-B820 complex of Rhodopseudomonas acidophila are 7 ± 0.5 ps and 6 ± 0.5 ps, respectively, and in the light-harvesting complex 2 of Rhodobacter sphaeroides ≈1.9 ± 0.5 ps. These results explain the differences in the carotenoid to bacteriochlorophyll energy transfer efficiency after S₂ excitation. In Rps. acidophila the carotenoid S₁ to bacteriochlorophyll energy transfer is found to be quite inefficient (φ_ET1 <28%) whereas in Rb. sphaeroides this energy transfer is very efficient (φ_ET1 ≈80%). The results are rationalized by calculations of the ensemble averaged time constants. We find that the Car S₁ → B800 electronic energy transfer (EET) pathway (≈85%) dominates over Car S₁ → B850 EET (≈15%) in Rb. sphaeroides, whereas in Rps. acidophila the Car S₁ → B850 EET (≈60%) is more efficient than the Car S₁ → B800 EET (≈40%). The individual electronic couplings for the Car S₁ → BChl energy transfer are estimated to be approximately 5–26 cm⁻¹. A major contribution to the difference between the energy transfer efficiencies can be explained by different Car S₁ energy gaps in the two species.

Plants and some bacteria have achieved remarkably high efficiencies of solar light conversion in photosynthesis. Recently, high-resolution crystal structures of some peripheral light-harvesting complexes of photosynthetic purple bacteria (1–3) have become available, enabling us to study the basic principles of the highly efficient collection of solar energy (4–8). In the light-harvesting complexes of purple bacteria, such as light-harvesting complex 2 (LH2) of Rhodobacter sphaeroides or Rhodopseudomonas acidophila, carotenoids (Cars) play important roles as light-harvesting and photoprotective pigments, as they do in the chloroplasts of higher plants (9, 10). In Rb. sphaeroides >95% of the photons absorbed by the Cars are transferred as excitation energy to the reaction center; in the strain 7050 of Rps. acidophila, which is the strain used in this report, the corresponding number is ≈70% (9, 11, 12). In the subunits of the B800-B850 complex of Rps. acidophila there is one Car (rhodopin glucoside) molecule per two bacteriochlorophyll (BChl) molecules in the B850 ring and one BChl in the B800 ring (1). Nine of these subunits comprise the LH2 ring, B800-B850 complex, of Rps. acidophila. Spectroscopic and biochemical reports suggest that the structures of the B800-B820 complex of Rps. acidophila and LH2 of Rb. sphaeroides (with the Car spheroidene) are similar (13, 14).

Despite intensive investigation of the underlying mechanisms (8, 10, 12, 15–20), many aspects of the electronic energy transfer (EET) from the Cars are still poorly understood. The electronic states of Cars often are described by analogy to polyenes (Fig. 1): Their ground state (S₀) and first excited state (S₁) both possess A_g⁻ symmetry, their second excited state (S₂) possesses B_u⁺ symmetry in the idealized C_2h point group. Only the S₀ ↔ S₂ transition is optically dipole-allowed. Excitation of S₂ is followed by very rapid (τ₂₁ ≈100–200 fs) internal conversion (IC) to S₁, which means that a significant fraction of the excitation energy flows through this state (21). However, because the S₁ → S₀ transition is dipole-forbidden it remains a challenge to elucidate the mechanism that promotes Car S₁ to Chl EET. Neither the Förster (22, 23) nor Dexter theories (24) provide satisfactory predictions (15, 20). To explore this issue, several authors have deconvoluted Car S₁ → BChl EET time constants, τ_ET1, from pump-probe or up-conversion data obtained after excitation of the Car S₂ state in different species. A few examples of time constants derived in this way are: peridinin to chlorophyll a (Chl a) EET in the peridinin-Chl a-protein (PCP) from Amphidinium carterae (PCP; 3.1 ps), spheroidene to BChl EET in Rb. sphaeroides (2.0 ps) and okenone to BChl a ET in Chromaticum purpuratum (3.8 ps and 0.5 ps) (19, 25, 26). However, the best way to find direct evidence for Car S₁ → BChl EET and to determine its contribution to the overall Car → BChl EET is to excite Car S₁ exclusively and thereby measure τ_ET1 and φ_ET1 directly without any convolution with S₂ state dynamics. This approach becomes even more important considering the recent identification of another dark state in spheroidene at ≈17,600 cm⁻¹ between the S₁ and the S₂ states of Cars (18). This state has B_u⁻ symmetry and is thought to play an important role in facilitating the Car S₂ → Car S₁ IC (27). However, a transition A_g⁻ ↔ B_u⁻ is neither one-photon allowed nor two-photon allowed and therefore does not contribute to our two-photon results.

Figure 1.

(Upper) Energy diagram for LH2. Black arrows indicate energy pathways occurring in the TPE pump probe experiment. Gray arrows indicate additional energy pathways in conventional one-photon experiments. OPE, One-photon excitation. Fl., Fluorescence. τ_ET2, Time constant for Car S₂ → BChl EET [≈50 fs (30)]. τ₂₁, Time constant for Car S₂ → S₁ IC [≈135 fs (30)]. τ_ET1, Time constant for Car S₁ → BChl EET. τ₁₀, Time constant for Car S₁ → S₀ IC. τ_S1, (τ_ET1⁻¹ + τ₁₀⁻¹)⁻¹ lifetime of the Car S₁ state measured in this work. (Lower) TPE spectrum of LH2 of Rb. sphaeroides (line with symbols), one-photon absorption spectrum (dashed line). Data taken from ref. 28. TPE-wavelengths for the TPE pump probe experiment are indicated with double arrows.

An elegant way to populate S₁ directly is by two-photon excitation (TPE) because transitions between states of A_g symmetry are two-photon allowed. Recently we have found evidence for Car S₁ → BChl EET in Rb. sphaeroides by measuring the Car TPE spectrum through the steady-state BChl fluorescence (see Fig. 1) (28). We obtained similar results in the light harvesting complex LHCII of higher plants and green algae (29).

In this work we report fs time-resolved excited-state absorption (ESA) of the Car S₁ state in three light-harvesting complexes of purple bacteria observed after TPE of this state. We report resuts for the B800-B850 and B800-B820 LH2s of Rps. acidophila and the LH2 of Rb. sphaeroides. To understand the mechanism that promotes this EET, we model the dynamics by using a theory that calculates the ensemble average energy transfer rates using as inputs the site energy disorder and the electron–phonon coupling of the chromophores as well as the excitonic nature of the acceptors.

Experimental Procedures

LH2 of Rb. sphaeroides was prepared from the Rb. sphaeroides strain 2.4.1 by using previously described methods (28). LH2s of Rps. acidophila were isolated from Rps. acidophila strain 7050 by using the methods described in refs. 9 and 30. β-Carotene (Acros, New Jersey) was dissolved in octane by sonicating for ≈10 s and centrifuging for 4 min at ≈8,000 g. The solutions had an optical density of ≈1 per mm at the maximum of the absorption. The samples were flowed through a 1-mm path-length quartz cell and maintained at 4°C under a nitrogen atmosphere. To reduce scattering further, a 0.45 μm filter was added to the flow cycle. The pump-pulses [≈10 nJ, 85 fs full width half maximum (FWHM), 250 kHz] and white-light probe pulses were both provided by a Coherent 9450 optical parametric amplifier. Excitation light intensity fluctuations were monitored with a power meter connected to a computer. To minimize population via one-photon excitation caused by the probe-white light we blocked the dominant 800-nm component with a highly reflective laser mirror and filtered the probe wavelength with a 555 ± 5-nm interference filter before the sample cell. The pump beam was focused with an f = 5-cm achromatic lens and the probe beam with an f = 10 cm. Only about <25% of the intensity of both beams was blocked by a 50-μm pinhole. Our instrument response function had a FWHM of ≈90 fs. The signal was detected by using a photodiode and lock-in amplification. To suppress white-light fluctuations with a frequency similar to the pump-chopper frequency, a part of the white light was measured with a separate photodiode and lock-in amplifier also triggered by the chopper. Subtracting this trace resulted in an improvement of the signal-to-noise ratio of more than a factor of 5. The polarization dependence was measured by using a 1,310-nm λ/4 and λ/2-waveplate in the excitation beam. Results without a waveplate were identical to those with λ/2-waveplate.

Results

β-Carotene in octane solution, a Car with known properties and similarities with spheroidene (31), was used to test the experimental setup. From one-photon pump probe data it is known that ESA from the S₁ of Cars has a maximum close to 550 nm, therefore we chose this wavelength as the detection wavelength in all experiments (32). The excitation wavelength was ≈1,310 nm, which is close to the 0–0 transition of the S₁ two-photon absorption of the Car (Fig. 1.). The changes in the probe intensity after TPE were typically on the order of 0.1%. A monoexponential fit to the transient absorption data gave a time constant of 9 ± 0.2 ps, in excellent agreement with the reported S₁ lifetime of β-carotene (31).

Two experiments were used to confirm that the pump was a two-photon process. First, the power dependence of the signal intensities were found to have a quadratic dependence on the excitation power (Fig. 2b). The fit suggests a power dependence with an exponent of 2.2 ± 0.3. Second, we measured the dependence of the signal on the polarization of the two-photon pump pulse (33). In one-photon spectroscopy the signal depends only on the relative orientation of linear polarized pump and probe fields. In two-photon spectroscopy, the signal is in general different for linear, circular, or any elliptical polarization of the pump beam. The polarization ratio, Ω = S_circ/S_lin, defined as the ratio of the signal obtained with circularly and with linearly polarized excitation, depends on the symmetries of the excited- and ground-state wave functions. Therefore this experiment can be used not only to verify the two-photon nature of the signals, but also to identify the symmetry of the two-photon excited molecule via its polarization ratio Ω. This can be used to confirm that we have indeed excited the Car in the light-harvesting complexes. The result, shown in Fig. 2c, gives Ω = 0.84 ± 0.07, which is identical within error to the literature value of Ω ≈ 0.8 for all-trans diphenyloctatetraene and diphenylhexatriene (34).

Figure 2.

(a) Time dependence of ESA (λ_det = 550 nm) of β-carotene in octane (squares) observed after TPE (λ_exc = 1,310 nm). Monoexponential fit: 9 ± 0.2 ps (solid line). (b) Power dependence of ESA. Power fit: Exponent = 2.2 ± 0.3 (solid line). (c) Relative intensity of ESA excited with linear and circular polarized light (Ω = 0.84 ± 0.07). The “coherence spike” is very large in the two-photon experiments (off scale) and has a quadratic dependence on the excitation power and a linear dependence on the Car concentration. No spike was seen with a pure buffer sample. In experiments with chlorophyll a, which has no two-photon allowed states, the coherence spike was found to be substantially smaller in magnitude (data not shown).

In Fig. 3a the time dependence of the ESA is shown for the LH2 of Rb. sphaeroides and the B800-B850 and B800-B820 LH2 of Rps. acidophila observed after TPE at 1,310 nm. All traces show a decay on the ps time scale to a constant offset, which persists over the entire dynamic range accessible with our setup (≈400 ps). The results of fits to OD(t) = y₀ + Ae^−t/τ_S1 are summarized in Table 1. A relatively fast decay with a time constant of τ_S1 ≈ 1.9 ± 0.5 ps is observed for Rb. sphaeroides, whereas both complexes of Rps. acidophila show a significantly slower decay (τ_S1 ≈ 7 ± 0.5 ps and τ_S1 ≈ 6 ± 0.5 ps). The observed τ_S1 for Rb. sphaeroides is in very good agreement with the value recently reported by Koyama and coworkers (19). As Fig. 3b shows, the preexponential factor A has a quadratic dependence on the excitation power, the solid line in Fig. 3b being fit by an exponent of 2.2 ± 0.3. We assign the decay component as the lifetime, τ_S1, of the S₁ state of the Cars in the light-harvesting complexes. Further confirmation of this assignment is provided by the polarization dependence shown in Fig. 3c. In both species the observed polarization ratio is very similar to those observed for β-carotene and polyenes (34) in solution (Ω = 0.84 ± 0.04 for Rb. sphaeroides and Ω = 0.80 ± 0.04 for Rps. acidophila).

Figure 3.

(a) Time dependence of ESA (λ_det = 550 nm) along with monoexponential fits with constant offset of the B800-B850 complex (□, τ_S1 = 7 ± 0.5 ps) and the B800-B820 complex (▪, τ_S1 = 6 ± 0.5 ps) of Rps. acidophila and LH2 of Rb. sphaeroides (○, τ_S1 = 1.9 ± 0.5 ps) observed after TPE (λ_exc = 1,310 nm). The traces have been normalized and offset from each other by 0.2. (b) Power dependence of the prefactor in the monoexponential fit to the data of Rb. sphaeroides (○). Power fit: Exponent = 2.2 ± 0.3 (solid line). (c) Power dependence of the constant offset in the fit to the data of Rb. sphaeroides (○). Solid line: Linear fit. (d) Relative intensity of the fluorescence obtained after TPE (λ_exc = 1,310 nm) with linear and circular polarized light of B800-B850 of Rps. acidophila (□, Ω = 0.80 ± 0.04) and LH2 of Rb. sphaeroides (○, Ω = 0.84 ± 0.04).

Table 1.

Fitting results for the kinetic data in Figs. 2–4 and the corresponding polarization ratios

λexc/nm	1310				1200
Species	β-carotene	Rb. sphaeroides	Rps. acidophila B800–B850	Rps. acidophila B800–B820	Rb. sphaeroides	Rps. acidophila B800–B850	Rps. acidophila B800–B820
τS1/ps	9  ± 0.5	1.9  ± 0.5	7  ± 0.5	6  ± 0.5	3  ± 0.5	7  ± 0.5	7.5  ± 0.5
A/%	100	41	38	34	46	45	46
y0/%	0	59	62	66	54	55	54
Ω	0.84  ± 0.07	0.84  ± 0.04	0.80  ± 0.04	—	—	—	—

OD(t) = y₀ + ; Ω = S_circ/S_lin. 

The constant offset y₀ has a linear dependence on the excitation power (Fig. 3c). No constant offset can be seen with pure buffer as sample. This result can be explained as a direct excitation of triplet states. It is not surprising that, with the given field intensities, the probability of directly exciting a spin forbidden transition via one-photon excitation is similar to the probability of exciting the S₁ state via TPE. However, because no offset has been observed with Cars in solution, we must assume that it is the triplet state of the BChl that can be seen in the transient absorption of the light-harvesting complexes. This interpretation is supported by the fact that the ESA of the triplet states of BChl has a maximum close to the detection wavelength of 550 nm and that the triplet states are the only states with an energy corresponding to one-photon excitation at 1,310 nm (35). For the interpretation of the S₁ state dynamics the triplet state excitation can be neglected, because the overall population of excited states is very small.

In Fig. 4 the time-resolved data of the Car S₁ ESA for all species are shown analogously to Fig. 3a but with TPE at 1,200 nm. As can been seen from Fig. 1, an excitation wavelength of 1,200 nm corresponds to the blue edge of the TPE spectrum of the light-harvesting complexes. The kinetics are very similar to the kinetics observed after TPE at 1,310 nm. We observe a relatively fast decay with the time constant τ_S1 ≈ 3 ± 0.5 ps for Rb. sphaeroides, whereas both complexes of Rps. acidophila show a significantly slower decay: τ_S1 ≈ 7 ± 0.5 ps and τ_S1 ≈ 7.5 ± 0.5 ps. However, the data, especially from Rb. sphaeroides, are not fit as well by a monoexponential decay as the data for TPE at 1,310 nm. This is possibly related to the 2,000 cm⁻¹ of excess vibrational energy resulting from 1,200-nm excitation compared with 1,310 nm. Another difference between the data observed with TPE at 1,200 nm and that at 1,310 nm is the significantly smaller relative magnitude of the constant offset (see Table 1). We will use the time constants observed with excitation at 1,310 nm for our subsequent analysis.

Figure 4.

Time dependence of ESA (λ_det = 550 nm) along with monoexponential fits with constant offset of the B800-B850 complex (□, τ_S1 = 7 ± 0.5 ps) and the B800-B820 complex (■, τ_S1 = 7.5 ± 0.5 ps) of Rps. acidophila and LH2 of Rb. sphaeroides (○, τ_S1 = 3 ± 0.5 ps) observed after TPE (λ_exc = 1,200 nm). The traces have been normalized and offset from each other by 0.2.

Discussion

Efficiencies of the Energy Transfer Via the Car S₂ and the Car S₁ States.

The significantly quenched Car S₁ lifetime observed after direct TPE of Rb. sphaeroides, τ_S1 ≈ 1.9 ± 0.5 ps, compared with the lifetime of spheroidene in solution, τ₁₀ ≈ 9 ps (31), provides clear evidence for efficient Car S₁ → BChl EET. We calculate τ_ET1 for Rb. sphaeroides, assuming τ₁₀ is unchanged, to be τ_ET1 = (τ_S1⁻¹ − τ₁₀⁻¹)⁻¹ ≈ 2.4 ± 0.5 ps. The unquenched S₁ lifetime of the Car in Rps. acidophila, rhodopin glucoside, has been determined by Frank and coworkers (36) to be τ₁₀ ≈ 4.1 ps. We measured τ_S1 ≈ 6–7 ps in the antenna complex, indicating that Car S₁ → BChl EET is negligible in Rps. acidophila. Even if the time constant for IC of rhodopin glucoside in the protein is as long as τ₁₀ ≈ 9 ps, like the corresponding value for β-carotene or spheroidene in solution, the Car S₁ → BChl EET time τ_ET1 could not be faster than 25 ps, and the Car S₁ → BChl EET efficiency φ_ET1 then would be φ_ET1 = (τ_S1⁻¹ − τ₁₀⁻¹) τ_S1 < 28%.† The same calculation for Rb. sphaeroides, using the value τ₁₀ = 9 ps for spheroidene, yields a Car S₁ → BChl EET efficiency of φ_ET1 ≈ 80%.

Using the known values for the overall Car → BChl EET quantum yield, φ_OA, together with the values of φ_ET1 we are able to calculate the energy transfer efficiencies for Car S₂ → BChl EET, φ_ET2. The overall EET efficiency is the sum of both efficiencies, weighted by their population probabilities: φ_OA = φ_ET2 + φ_ET1φ₂₁, where φ₂₁ is the quantum efficiency for Car S₂ → Car S₁ IC, φ₂₁= τ₂₁⁻¹/(τ_ET2⁻¹ + τ₂₁⁻¹) = 1 − φ_ET2 (see Fig. 1). We now assume that φ_OA differs from 100% entirely owing to Car S₁ → Car S₀ IC. The quantum yield for Car S₁ → Car S₀ IC is φ₁₀ = (1 − φ_ET1)φ₂₁. Therefore φ_OA also can be written as φ_OA = 1 −[(1 − φ_ET1) × φ₂₁] = 1 + (φ_ET1 − 1) × φ₂₁. Substituting φ₂₁ = 1 − φ_ET2 into this equation gives φ_ET2 = 1 − [(φ_OA − 1)/(φ_ET1 −1)]. Thus we estimate φ_ET2 > 75% for Rb. sphaeroides and φ_ET2 > 60% for Rps. acidophila. The contributions of the Car S₁ → BChl EET to φ_OA are φ_ET1 × φ₂₁ < 20% for Rb. sphaeroides and φ_ET1 × φ₂₁ < 10% for Rps. acidophila. The results of these quantum efficiency calculations are summarized in Table 2.

Table 2.

Calculated Car S₁ → BChl energy transfer time constants and efficiencies

Species	τS1/ps*	τET1/ps	φET1	φOA(9,11)	φET2	φET1φ21	φ21
Rb. sphaeroides	1.9 ± 0.5	2.4 ± 0.5	80%	>95%	>75%	<20%	<25%
Rps. acidophila	6.5 ± 0.5	>25	<28%	∼70%	>60%	<10%	<40%

φ_OA = φ_ET2 + φ_ET1φ₂₁. 

^*Measured in this work. 

The Mechanism of Car S₁ → BChl Energy Transfer.

The mechanism of electronic coupling that promotes Car S₁ → BChl EET usually has been discussed in light of the relative merits of Förster versus Dexter energy transfer theories (22, 24, 37). In general, the coupling may be partitioned into a Coulombic contribution V^Coul, operative at all separations, and a short-range contribution V^short that explicitly depends on interpenetration of the donor and acceptor molecular orbitals. Thus V = V^Coul + V^short. However, V^short has been shown previously to be insignificant for interactions between the pigments in LH2 (20, 38).

The transition density cube (TDC) (17) method is very useful for calculating V^Coul when the donor and acceptor molecules are closely proximate relative to molecular dimensions, because local interactions between the donor and acceptor transition densities determine the overall coupling. Such details are lost when averaging over wavefunctions to give transition moments. In algebraic form the difference between the dipole approximation and the TDC method is given by

1

for discrete charges q_i at position r_i on donor molecule D and charges q_j at position r_j on acceptor A. r_ij = r_i − r_j, and R_DA is the center-to-center separation of D and A.

Zhang et al. (19) suggested that the Car S₁ → BChl couplings are dominated by Coulombic interactions, V^Coul, determined by mixing between the Car S₁ and Car S₂ states. This would result in a Car S₁ → BChl transition density with spatial properties resembling the transition density of the Car S₂ → BChl transition. If this is the case, scaling down of the Car S₂ → BChl electronic couplings, determined previously using the transition density cube method (17), should provide a reasonable estimate of the Car S₁ → BChl couplings. The scaling factor is determined by the state mixing between the Car S₁ and Car S₂ states. If Coulombic interactions dominate the Car S₁ → BChl couplings, small differences in the positions of the pigments will not affect the couplings as much as for short-range interactions. We therefore assume for the species investigated in this work that the estimated couplings are similar.

In recent work Scholes and Fleming (8) showed that the BChl B800 → B850 EET can only be elucidated by introduction of site energy disorder before solving the eigenvalue problem for the B850 acceptor aggregate in each individual LH2, because the assumption of identical B850 eigenstates for each LH2 gives incorrect values for the ensemble average rate, τ_ET⁻¹. We anticipate that a quantitative description of the Car S₁ → BChl EET will require a similarly detailed theory.

The model we have used for our calculation is described in detail in ref. 8. Briefly, the ensemble average rate of energy transfer is given by

2

where V_δα is the electronic coupling between the donor state δ and eigenstate α of the acceptor in an individual LH2, calculated by using the electronic couplings in the monomeric site representation, V_est.^Coul(m). P_δ is a normalized population factor, and J_δα(ɛ) is the spectral overlap factor for states δ and α, J_δα(ɛ) = a_α^hom(ɛ)f_δ^hom(ɛ). The superscript “hom” specifies that these line shapes are determined only by fluctuations of the bath that have characteristic frequencies faster than that of the EET. Slower fluctuations (e.g., static disorder) are accounted for by the Monte Carlo averaging procedure denoted by the angular brackets in Eq. 2. The bandwidth of a_α^hom(ɛ) and the disorder parameters were derived from three pulse-echo peak shift measurements.

Estimation of the Electronic Couplings Mediating the Car S₁ → BChl EET.

We modified the B800 → B850 EET model by extending the acceptor Hamiltonian by two diagonal elements representing the two B800 BChl in the closest neighborhood to the Car. We used the mirror image of the Car S₁ TPE spectrum of Rb. sphaeroides (28) for the donor-fluorescence, f_δ^hom(ɛ). To estimate the electronic couplings in the monomeric site representation, V_est.^Coul(m), we varied the scaling factor for the electronic coupling and the Stokes shift of the mirror image in such a way that the calculation always produced the observed time constant of τ_ET1 ≈ 2.4 ps, Inset in Fig. 5a. The Car S₁ state 0–0 transition in Rb. sphaeroides has been determined to be around 14,000 cm⁻¹ (28, 31, 39–41). As can be seen from the inset in Fig. 5a, the electronic couplings scaling factor remains very similar (≈0.15) when the 0–0-transition is varied over a wide range. The resulting individual couplings range from 5 cm⁻¹ to 26 cm⁻¹ (monomeric site representation, see Table 3). The range of these values is in very good agreement with estimates for the necessary couplings from Zhang et al. (19) and Damjanovic et al. (20). Recently, one of us (C.-P.H.) calculated the Coulombic Car S₁-BChl couplings by using the transition density cube method and time–dependent density functional wavefunctions. The individual couplings obtained in the ab initio calculation are in very good agreement with the couplings estimated by the scaling-down procedure (Table 3). Analysis of these results provides strong evidence that scaling down the Car S₂-BChl couplings is appropriate because the Car S₁-BChl Coulomb couplings are dominated by a small mixing of a strongly dipole allowed Car S₂-like configuration as proposed by Zhang et al. (19).

Figure 5.

(a) Acceptor DOS in LH2 of Rb. sphaeroides calculated with (solid line) and without introducing disorder (short dashed line) before solving the eigenvalue problem for the acceptor aggregate along with Car S₁ emission (long dashed line). Note that the shown DOS is not weighed by electronic coupling. For details see text. (Inset) Electronic coupling scaling factor (see text) needed to reproduce the experimentally observed time constant τ_ET1 as a function of the 0–0 transition of the Car S₁ emission. (b) Same results for the B800–B850 complex of Rps. acidophila. (Inset) Calculated time constants τ_ET1 as a function of the Car S₁ state 0–0 transition.

Table 3.

Car S₁-BChl Q_y couplings in the monomeric site representation estimated by scaling down Car S₂-BChl Q_y couplings, V_est.^Coul, and calculated via ab initio methods, V_TDDFT^Coul

	B800A*	B800B*	αB850B†	βB850B†	αB850C†	βB850C†
Vest.Coul/cm−1	26	7	5	7	16	12
VTDDFTCoul/cm−1	31	10	5	9	32	18

^*Couplings between Car S₁ and the B800 Chl molecules in the notation of ref. 17. 

^†Couplings between Car S₁ and the B850 Chl molecules in the notation of ref. 17. 

In Fig. 5a the calculated density of states (DOS) is shown together with the S₁-emission spectrum. Note that the DOS does not necessarily represent the acceptor states in Förster overlap calculations, because each state is coupled differently to the donor states. However, as can be seen in Fig. 5, for Rb. sphaeroides there is excellent overlap of donor and acceptor states, which explains the efficient Car S₁ → BChl EET observed in this species. Disorder causes the couplings and state orderings in the B850 excitonic states to differ significantly between individual LH2s. Nonetheless, the calculated time constant τ_ET1 ≈ 2.4 ps can be separated into a time constant for Car S₁ → B850 EET, τ_B850 ≈ 6.7 ps (15%), and a time constant for Car S₁ → B800 EET, τ_B800 ≈ 2.8 ps (85%). The corresponding time constants for Rps. acidophila are τ_B850 ≈ 11.7 ps (60%) and τ_B800 ≈ 17.5 ps (40%).

The Car S₁ State in Rps. acidophila.

We estimate the 0–0 transition energy of the Cars in Rps. acidophila by assuming that the S₁ emission spectrum only differs from that in Rb. sphaeroides by a shift to lower energies and that the couplings in both species are similar. For Rps. acidophila we used the B850 Hamiltonian reported previously, which was obtained by modeling the 77K absorption and CD spectra (8). To determine the 0–0 transition of Car S₁ in Rps. acidophila, we shifted the Car S₁ mirror image and calculated the ensemble average time constant by using the same electronic couplings obtained from our Rb. sphaeroides calculations. As can be seen from the Inset in Fig. 5b, time constants larger than the experimentally observed lifetime, τ₁₀ ≈ 7 ps, are found for 0–0 transitions ≈<12,800 cm⁻¹. This value is in very good agreement with S₁ energies of other Cars with 11 conjugated double bonds. However, because the Car S₁ lifetime, τ₁₀, is not known for rhodopin glucoside, this estimate only gives an upper limit, which is valid in the case τ₁₀ >> τ_ET1. Of course, differences in the electronic coupling also could contribute to the differences in the EET efficiencies, and in this case the 0–0 transition energy will be underestimated. As in the calculations for Rb. sphaeroides, the introduction of disorder did not result in a large difference in the calculated time constant provided we assume that electron–phonon coupling dominates the broadening of the Car S₁ spectrum. However, via some model calculations we found that if the heterogeneous broadening were to contribute significantly to the S₁ spectra, the time constants may change by more than a factor of 2. We also expect that the temperature dependence of the Car S₁ → BChl EET can be modeled only by considering Eq. 2.

Conclusions

By measuring the dynamics of the Car S₁ ESA after TPE, we determined Car S₁ → BChl EET time constants in LH2 of the purple bacteria Rb. sphaeroides and Rps. acidophila without any convolution with dynamics associated with the Car S₂ state or the recently discovered dark state between S₁ and S₂. The energy transfer efficiency was found in Rps. acidophila to be φ_ET1 < 28% and in Rb. sphaeroides φ_ET1 ≈ 80%. The Car S₁ → BChl EET was modeled by using a detailed theory that suggests that for Rb. sphaeroides the time constant for Car S₁ → B850 EET is τ_B850 ≈ 6.7 ps (15%) and for Car S₁ → B800 EET τ_B800 ≈ 2.8 ps (85%). The corresponding time constants for Rps. acidophila are τ_B850 ≈ 11.7 ps (60%) and τ_B800≈ 17.5 ps (40%). The individual electronic couplings for the Car S₁ → BChl EET are in the order of 5–26 cm⁻¹. A major contribution to the drastic difference in the efficiency φ_ET1 can be explained by a shift of the Car S₁ energy from ≈14,000 cm⁻¹ in Rb. sphaeroides to a value of ≈<12,800 cm⁻¹ in Rps. acidophila.

Abbreviations

EET

electronic energy transfer

Car

carotenoid

BChl

bacteriochlorophyll

Chl

chlorophyll

ESA

excited-state absorption

TPE

two-photon excitation

LH2

light-harvesting complex 2 of purple bacteria

IC

internal conversion

DOS

density of states