Thermally Activated Superradiance and Intersystem Crossing in the

Jun 25, 2009 - Juni 135, D-10623 Berlin, Germany, Institute of Theoretical Physics, ... Berlin Institute of Technology, Hardenbergstrasse 36, 10623 Be...
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9948

J. Phys. Chem. B 2009, 113, 9948–9957

Thermally Activated Superradiance and Intersystem Crossing in the Water-Soluble Chlorophyll Binding Protein T. Renger,*,† M. E. Madjet,† F. Mu¨h,† I. Trostmann,‡ F.-J. Schmitt,§ C. Theiss,§ H. Paulsen,‡ H. J. Eichler,§ A. Knorr,| and G. Renger⊥ Institute of Chemistry and Biochemistry, Free UniVersity Berlin, Fabeckstrasse 36a, D-14195 Berlin, Germany, Institute of General Botany, Johannes-Gutenberg-UniVersity, Mu¨llerweg 6, D-55099 Mainz, Germany, Institute of Optics and Atomic Physics and Max Volmer Laboratory for Biophysical Chemistry, Berlin Institute of Technology, Straβe des 17. Juni 135, D-10623 Berlin, Germany, Institute of Theoretical Physics, Nonlinear Optics and Quantum Electronics, Berlin Institute of Technology, Hardenbergstrasse 36, 10623 Berlin, Germany ReceiVed: March 1, 2009; ReVised Manuscript ReceiVed: May 20, 2009

The crystal structure of the class IIb water-soluble chlorophyll binding protein (WSCP) from Lepidium Virginicum is used to model linear absorption and circular dichroism spectra as well as excited state decay times of class IIa WSCP from cauliflower reconstituted with chlorophyll (Chl) a and Chl b. The close agreement between theory and experiment suggests that both types of WSCP share a common Chl binding motif, where the opening angle between pigment planes in class IIa WSCP should not differ by more than 10° from that in class IIb. The experimentally observed (Schmitt et al. J. Phys. Chem. B 2008, 112, 13951) decrease in excited state lifetime of Chl a homodimers with increasing temperature is fully explained by thermally activated superradiance via the upper exciton state of the dimer. Whereas a temperature-independent intersystem crossing (ISC) rate is inferred for WSCP containing Chl a homodimers, that of WSCP with Chl b homodimers is found to increase above 100 K. Our quantum chemical/electrostatic calculations suggest that a thermally activated ISC via an excited triplet state T4 is responsible for the latter temperature dependence. I. Introduction We have recently reported an exciton model to describe the linear and nonlinear optical properties of the recombinant class IIa water-soluble chlorophyll binding protein (WSCP) complexes from cauliflower (Brassica oleracea) reconstituted with different types of chlorophyll (Chl).1,2 This model is based on the assumption that the two chlorophylls form an “open sandwich” dimer as proposed by Hughes et al.3 When taking into account lifetime broadening, vibrational sidebands, and static disorder, our calculations of the linear optical spectra revealed a tilt angle of 25°-36°1 between the chlorine ring planes, which is about half the value originally suggested.3 In a parallel study, the crystal structure of class IIb WSCP of Lepidium Virginicum was published and showed a tilt angle of 27°.4 The two types of class II WSCP differ in the number of chlorophylls: type IIa complexes from cauliflower bind two chlorophylls per tetrameric protein matrix, whereas type IIb from L. Virginicum binds four. In the latter case, the Chl molecules are arranged in two “open sandwich” dimers (Figure 1). A comparison of the “open sandwich” dimer of class IIb WSCP with the one proposed for Chl a homodimers of class IIa WSCP on the basis of the calculation of optical spectra1 is shown in Figure 2. The opening angles between pigment planes are 27°4 and 25°1 (panel a). The center-to-center distance between the two Chl a in the crystal structure is 10.0 Å, whereas * To whom correspondence should be addressed. E-mail: rth@ chemie.fu-berlin.de. † Free University Berlin. ‡ Johannes-Gutenberg-University, Mainz. § Institute of Optics and Atomic Physics, Berlin Institute of Technology. | Institute of Theoretical Physics, Nonlinear Optics and Quantum Electronics, Berlin Institute of Technology. ⊥ Max Volmer Laboratory for Biophysical Chemistry, Berlin Institute of Technology.

Figure 1. Structure of class IIb WSCP of L. Virginicum.4 The complex is a homotetramer in which each protein monomer (shown in blue, red, orange, and gray) binds one Chl a molecule (shown in green). The four Chl a are arranged in two “open sandwich” dimers in binding sites 1/2 and 3/4. The phytyl chains of the chlorophylls form the hydrophobic core of the tetramer.

that in the model is only 7.4 Å (panels a and b). Compared to the model dimer, the pigments in the crystal structure dimer are translated away from each other in a direction perpendicular to the plane of panel a (as shown in panel b). Another difference concerns the fact that the molecular y axes (dashed lines in panel c) of the two pigments in the crystal structure are parallel, whereas they form an angle of 12° in the model. One aim of the present work is to investigate whether the optical spectra of class IIa WSCP complexes from cauliflower can be described by using the crystal structure data of the “open sandwich” dimer in class IIb WSCP of L. Virginicum4 and the parameters of our earlier exciton model.1 This investigation will serve as a critical check of our former conclusion1 that, despite the differences between the two WSCP types with respect to the number of bound chlorophylls, the local binding motif is very similar in both cases.

10.1021/jp901886w CCC: $40.75  2009 American Chemical Society Published on Web 06/25/2009

Water-Soluble Chlorophyll Binding Protein

Figure 2. Comparison of the “open sandwich” Chl a homodimer in the crystal structure of class IIb WSCP4 with that inferred from the calculation of optical spectra1 of class IIa WSCP. In panel a, a side view on the plane that defines the opening angle of the dimer is presented; b shows a view perpendicular to panel a, from the open side of the dimer, and the view in panel c was chosen such that the molecular y axes (dashed lines) of the two pigments overlap as closely as possible.

The functional importance of WSCP is not yet clarified. WSCP biosynthesis is stimulated under stress conditions (heat, drought), and WSCP is capable of extracting chlorophylls from solution and from the thylakoid membrane.5 The binding of Chl critically depends on the presence of the central Mg2+ ion.6 Upon binding of chlorophylls to the protein, WSCP oligomerizes preferentially to a tetramer. The phytyl chain of the chlorophylls was reported to be essential for this process.6 One characteristic feature of WSCP complexes is the lack of carotenoids (Cars). Despite the absence of Cars, the yield of singlet oxygen formation by the reaction of ground state triplet oxygen with photoinduced triplet chlorophylls was found to be 4 times smaller in WSCP than for chlorophylls in solution.6 This effect supports the idea7 that WSCP might function as a protective Chl binding protein during either biosynthetic or degradative pathways of chlorophylls in plants. On the basis of the crystal structure, two basically different mechanisms were suggested to be responsible for the photoprotection in WSCP:4 (i) hampered physical contact between the Chl molecules and molecular oxygen originating from the close protein structure and (ii) quenching of the excited state of Chl either due to electron exchange with nearby aromatic residues (Tyr-75 and Trp-156) or by pigment-pigment coupling in the dimer. On the basis of fluorescence lifetime measurements, singlet quenching can be ruled out, which leaves only the diffusion barrier hypothesis (i) as a possible mechanism.8 Our fluorescence data8 revealed that, different from the antenna system of plants,9 the excited state lifetimes of the chlorophylls in WSCP monotonically increase with decreasing temperature. This increase can be qualitatively understood by taking into account the different oscillator strengths and thermal populations of the low- and high-energy exciton states.8 Here, we aim to provide a quantitative explanation of the fluorescence data,8 including the determination of rate constants for intersystem crossing (ISC). This analysis will also allow us to answer the mechanistically relevant question: Does ISC occur directly between the states S1 and T1 (in contrast to the nomenclature

J. Phys. Chem. B, Vol. 113, No. 29, 2009 9949 for the singlet states, the lowest triplet state is denoted T1), or are higher excited triplet states of the chlorophylls involved? In an earlier study, Petke et al.10 concluded on the basis of quantum chemical calculations of excited states of Chl a: “The relative locations of S1 and T1-T3... implies that not only T1, but also T2 and T3 may be actively involved in the mechanism of such processes as intersystem crossing...”. The triplet absorption spectra of Chl a and Chl b exhibit a strong band in the 500 nm region.11 Furthermore, a weak band has been reported for Chl a at 1200 nm.12 Taking into account the T1-S0 energy differences of Chl a (10 310 cm-1) gathered from the phosphorescence maxima,13 the 1200 nm transition T1 f Tn should lead to a state Tn that is higher in energy than the S1 state by more than 4000 cm-1 and, therefore, cannot participate in ISC. From an analysis of absorbance and fluorescence spectra of Chl a in different solvents and the peridinin-chlorophyllprotein, Knox et al.14 inferred an intensity borrowing from an electronic state that is just below the S1 state and concluded that the most likely identity of this state is an excited triplet state. Unfortunately, no further information about low-lying triplet states of Chl is available from the literature. We address this question by performing quantum chemical/electrostatic calculations on the energies of the S1 and the T1-T5 states of Chl a and Chl b and by relating these energies to data on the excited state decay of WSCP.8 The present work is organized in the following way: First, a short summary is given of the theory used for the description of the spectra and excited state decay. Next, the theory is applied to calculate linear absorbance and circular dichroism spectra of WSCP complexes, reconstituted with Chl a or Chl b. Afterward, results are presented on excited state decay times and the temperature dependence of ISC in the Chl a and Chl b homodimers formed in these complexes. Finally, the results are discussed, and conclusions are drawn. II. Theory A. Description of Optical Spectra. As described in detail previously,1,15 the homogeneous absorbance and circular dichroism spectra are obtained as

Rhom(ω) ∝ ω

∑ |µM|2DM(ω)

(1)

∑ RMDM(ω)

(2)

M

and

CDhom(ω) )

M

where b µM is the transition dipole moment, RM is the rotational strength, and DM(ω) is the line shape function of exciton state |M〉. The rotational strength, RM (in units of Debye-Bohr magnetons (D-β)), is given as16

RM ) 1.7 × 10-5

(M) (a) b µa × b µ b) ∑ c(M) a cb Eeg Rab×(b

(3)

a,b

It contains the exciton coefficients c(M) k , the electronic transi(a) tion energy Eeg (in units of cm-1) of the monomers a ) 1, 2, Ra - b Rb (in units of nm) connecting the centers the vector b Rab ) b of the monomers, and the local transition dipole moments b µa

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and b µb (in units of D) of the two monomers. The intrinsic CD of Chl is neglected.3 The line shape function DM(ω) reads15

DM(ω) )

1 2π

∫

λ)

∞

dt ei(ω-ω˜M)teGM(t)-GM(0)e-|t|/τM -∞

(4)

where the function GM(t) ) γMMG(t) containing the γMM in eq 9 and the function

G(t) )

∫0∞ dω{(1 + n(ω)) J(ω) e-iωt + n(ω) J(ω) eiωt} (5)

describes vibrational sidebands that reflect the modulation of the S0 f S1 transition energy of the chlorophylls by the protein vibrations. This modulation is described by the spectral density J(ω) ) Σξ gξ2 δ(ω - ωξ) in eq 5. The same coupling constants are assumed for both monomers; that is, gξ ) gξ(1) ) gξ(2). The n(ω) in eq 5 is the Bose-Einstein distribution function

n(ω) )

1 pω/kT

e

(6)

-1

that is the mean number of vibrational quanta excited at a given temperature T. The dephasing time τM-1 in eq 4, describing lifetime broadening due to exciton relaxation, reads

τM-1 )

∑ 2γMK C˜ (Re)(ωMK)

(7)

K

where ωMK ) (εM - εK)/p is the transition frequency between the exciton states |M〉 and |K〉 and

˜ (Re)(ω) ) πω2{(1 + n(ω)) J(ω) + n(-ω) J(-ω)} C

(8)

(K) (M) (K) -R ∑ c(M) a ca cb cb e

R(ω) ) 〈Rhom(ω)〉dis

(13)

CD(ω) ) 〈CDhom(ω)〉dis

(14)

and

The disorder average is performed by a Monte Carlo method as described previously.1 B. Radiative Lifetime. The radiative lifetime of an excited state is inversely proportional to the square of the transition dipole matrix element of the transition to the ground state and the third power of the transition frequency.21 In the excitonically coupled Chl dimer in WSCP, exciton relaxation occurs on a sub 100 fs (homodimers) or sub 10 ps (heterodimers) time scale;1,2 that is, it is fast compared to the measured nanosecond decay of the fluorescence.8 Hence, the overall radiative decay time is given as

1 1 ) τrad τ*

〈∑f O 〉

ab/Rc

· cb(K)

where · are exciton coefficients, Rab is the center-tocenter distance between pigments a and b, and Rc is the correlation radius of protein vibrations that characterizes the decay in correlation between site energy fluctuations at different sites in the protein.17,18 We take Rc ) 5 Å, as determined ˜ M, between the before.1,19 The 0-0 transition frequency, ω ground state and the Mth exciton state in eq 4 is given by15

∑ γMK C˜(Im)(ωMK)

(10)

K*M

with the exciton transition frequency ωM ) εM/p and20

˜(Im)(ωMK) ) 1 P C π

M

M

(15)

M

dis

(9) OM )

ω ˜M ) ωM - γMMλ/p +

(12)

of protein modes. The exciton energies εM and exciton coefficients cm(M) are obtained by diagonalization of a 2 × 2 matrix (a) of that contains in the diagonal the local transition energies Eeg the two monomers a ) 1, 2 and in the off-diagonal the excitonic coupling V12. The inhomogenously broadened absorbance and circular dichroism spectra R(ω) and CD(ω), respectively, are finally obtained by averaging the expressions for the homogeneous spectra in eqs 1 and 2 over disorder in local electronic transition energies

a,b

ca(M) ·

∫0∞ dω pω J(ω)

where fM ) exp{-εM/kT}/∑N exp{-εN/kT} describes a Boltzmann population of the exciton states (M ) 1, 2), τ* is the radiative lifetime of the Chl monomers, and the factor

and

γMK )

Here, P denotes the principal part of the integral, and λ is the reorganization energy

˜(Re)

∫-∞∞ dω ωCMK -(ω)ω

(11)

µM2

(16)

µS0fS12

describes the redistribution of dipole strength between the exciton states of the dimer. Here, µS0fS12 is the dipole strength of the Chl monomer, and µM2 is that of the exciton state |M〉 of the dimer. From the conservation of sum oscillator strength, that is, µM)12 + µM)22 ) 2µS0fS12, it follows that OM may vary between 0 and 2 and O1 + O2 ) 2. The 〈...〉dis denotes an average over disorder in site energies, as before. C. Rate of Intersystem Crossing. The rate constant of ISC between an exciton state |M〉 and the states, where one of the two chlorophylls (a ) 1, 2) is in a triplet state and the other is in the ground state, S0, is given as

2 kMfaT ) |c(M) a |

(a) 2 |VS-T |

p2

∫-∞∞ dt e-iω

(a) M,Tt

˜

˜

eG(t)-G(0)

(17)

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(a) (a) where ωM,T ) ωM - ETg /p is the transition frequency between exciton state |M〉 and the state, where monomer a is in the triplet ˜ (t) is similar to the G(t) in eq 5, but contains state. The function G instead of the spectral density J(ω) of the S0 f S1 transition that of the S1 f T transition and also the high-frequency intramolecular vibrational degrees of freedom of the chlorophylls. The ISC lifetime of exciton state M is obtained as

(M) τISC ) (kMf1T + kMf2T)-1

(18)

Taking into account the conservation of excitation probability, |c1(M)|2 + |c2(M)|2 ) 1, the fact that the energy differences between the exciton states and the triplet state and that between the localized excited states and the triplet states are similar (i.e., (a) (a) (a) (a) ≈ ωe,T ) (E(a) ωM,T e - ET )/p) and that the local coupling VS-T (a) ) VS-T and the local transition frequencies, ωe,T ) ωe,T, are the (M) is same for both monomers (a ) 1, 2) in a homodimer, the τISC seen to be approximately equal to the ISC lifetime of the local excited states (M) (e) τISC ≈ τISC

(19)

(e) -1 ) is given as where (τISC

(e) -1 (τISC ) )

|VS-T | 2 2

p

∫-∞∞ dt e-iω

e,Tt

˜

˜

eG(t)-G(0)

(20)

The overall ISC lifetime of the dimer,

τISC-1 )

(M) -1 (e) -1 ) ) (τISC ) ∑ fM(τISC

(21)

M

(e) , since ΣMfM ) 1. then also becomes equal to τISC This result has consequences for the weight of triplet formation relative to radiative transition, w ) τISC-1/τrad-1 in the dimer with respect to that in the monomer. By using eqs 15 and 21, it is seen that

wdimer /wmonomer )

〈∑f O 〉 M

M

-1

M

) τrad /τ*

(22)

dis

equals the ratio between the radiative lifetime of the dimer (eq 15) and the monomer (τ*). Equation 22 implies that the triplet yield is enlarged by the excitonic coupling if the dipole strength of the high-energy exciton state is larger than that of the lowenergy one, and it is decreased in the opposite case. Please note (e) that the explicit expressions for kMfaT in eq 17 and for 1/τISC in eq 20 were used only to obtain the equality in eq 21. The actual value for τISC will be determined below from a fit of the experimental excited state decay data. III. Results The parameters of our exciton model that were determined (a) in ref 1 are (i) the local transition energies Eeg of the S0 f S1 transitions of Chl a and Chl b in WSCP that correspond to wavelengths of 675 and 658 nm, respectively, at low temperature (T e 77 K) and 677 and 660 nm, respectively, at high temperature (T ) 300 K); (ii) the inhomogeneous width, 170 cm-1, of the distribution function for the site energies, and the Huang-Rhys factor, S ) 0.8, of the local pigment-protein

Figure 3. Calculated (solid and dashed lines) absorbance (upper panels) and circular dichroism (lower panels) spectra of class IIa WSCP with Chl a homodimers (left panels) and Chl b homodimers (right panels) and experimental data (symbols). The experimental data of Chl b homodimers, measured at 77 (O) and 300 K (9), were taken from ref 1. Those of Chl a homodimers were measured in the present work at 300 K by using the same setup as in ref 1. In the calculations, the crystal structure data of class IIb WSCP4 were used to obtain the excitonic coupling and the direction of optical transition dipole moments.

coupling. The spectral density is given by1 J(ω) ) SJ0(ω), where the normalized J0(ω) was inferred before15 from fluorescence line narrowing spectra of B777 complexes and successfully applied to a number of other complexes,1,22,23 including WSCP.1 The earlier structural model1 is replaced here by the crystal structure of an “open sandwich” dimer of L. Virginicum (binding sites 3/4 in Figure 1; note that the results obtained for the second dimer in binding sites 1/2 are practically identical). The ab initio TrEsp transition monopole method24 and an effective dipole strength of 4.0 D for Chl a and 3.6 D for Chl b were used as outlined in ref 1 to calculate the excitonic couplings V12 resulting in 77 and 69 cm-1 for Chl a and Chl b homodimers, respectively. These values are only slightly smaller than the 84 cm-1 (Chl a) and 72 cm-1 (Chl b) obtained with our previous structural model.1 In light of the factor of 1.3 larger center-to-center distance between the pigments in the crystal structure4 with respect to that in the structural model,1 the near equality of the coupling values is surprising. In fact, in point-dipole approximation, the coupling in the model dimer is larger by a factor of 2.4 than in the crystal structure dimer, as expected. However, the point-dipole approximation is found to break down for the model dimer, and the corrections roughly compensate for the factor of 2.4. A. Optical Spectra. In Figure 3, the linear absorbance spectra of Chl a and Chl b homodimers, calculated by using the crystal structure of class IIb WSCP, are compared with the corresponding experimental data. The spectra of class IIa WSCP from cauliflower reconstituted with Chl b only were reported in ref 1, whereas those of samples reconstituted with Chl a only are new results of the present study obtained as described previously.1,8 As in the former study,1 quantitative agreement is obtained between calculated and experimental absorbance spectra for the low-energy region. The deviation at higher energies is due to excitations of intramolecular vibrational transitions and of the next-higher electronic state (Qx transition), which were not included in the present calculations. The temperature dependence of the linear absorbance spectrum of Chl b homodimers can be described by using the same Huang-Rhys factor, S ) 0.8, for the protein vibrations as in ref 1. There is quantitative agreement between theoretical and experimental CD spectra of Chl a WSCP over the whole spectral range. In contrast, the experi-

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Figure 4. Disorder-averaged rotational strength 〈R-〉dis (eq 3) as a function of the angle β between the Qy transition dipole moment and the y axis of Chl a of the low energy exciton state of the two “open sandwich” dimers (in binding sites 1-2 and 3-4) in Figure 1. The horizontal dashed lines mark the experimental value determined by Hughes et al.,3 and the vertical dashed lines point to the corresponding values of β. The inset shows the same quantity for a larger range of β values.

mental CD spectrum of Chl b WSCP is nonconservative and seems to contain some intrinsic negative CD of Chl b, which is not taken into account in the present exciton theory (for a more detailed discussion of this point, see ref 1). To correctly describe not only the shape of the experimental CD spectrum of Chl a homodimers but also their rotational strength |R(| ) (0.8 ( 0.1) D-β, determined by Hughes et al.,3 a slight in-plane rotation of the Qy transition dipole moment by 6-8° away from the y axis of the chlorophylls toward their 131-keto group is necessary (Figure 4). We note, however, that except for the absolute values of the CD spectra, the results obtained by using β ) 0° differ only marginally from those obtained for β ) 6-8°. The nonconservative form of the CD spectrum of Chl b homodimers does not permit a reliable determination of the angle β for the Chl b molecules in this dimer. B. Excited State Decay. The experimentally observed inverse decay time constant (τ)-1 is the sum of the rate constants for ISC and radiative transition:

1 ) τ

〈 ( ∑ fM M

OM 1 + τ* τISC

)〉

dis

)

1 1 + τISC τ*

〈∑f O 〉 M

M

M

Figure 5. Correlation of measured8 and calculated (eq 23) excited state decay times at different temperatures between 10 and 300 K for Chl a homodimers (left panel) and Chl b homodimers (right panel). A temperature-independent τISC ) 6.7 ns was assumed in the calculations for both types of dimers. The solid lines indicate the case of perfect correlation.

Figure 6. Natural logarithm of the ISC rate constant, calculated from eq 24, as a function of inverse temperature for Chl a homodimers (O) and Chl b homodimers (9). The solid line shows a fit using eq 27 (see discussion).

5). In striking contrast, there is a systematic deviation between calculated and experimental values for Chl b homodimers (right panel of Figure 5). In this case, the temperature dependence of 〈ΣMfMOM〉dis is not sufficient to explain the experimental data. Note that a variation of τISC, the only free parameter, would not change the slope of the correlation plot. To evaluate a possible temperature dependence of the ISC rate, we rearrange eq 23 as

dis

(23)

The above equation relates the lifetime of excited states in the WSCP to our exciton model that provides the temperaturedependent factor 〈ΣMfMOM〉dis and to the rate constants for ISC (1/τISC) and spontaneous emission (1/τ*) of uncoupled Chl a in the protein environment. Since the refractive index of a protein is similar to that of typical organic solvents, the radiative lifetime, τ*, of Chl a is also similar in the protein and the solvent. The widely accepted textbook value of τ* ) 15 ns for Chl a was first determined by Brody and Rabinowitch25 together with the value τ* ) 23 ns for Chl b from an analysis of the absorbance spectrum of Chl a and Chl b in ethyl ether, using a method suggested by Lewis and Kasha.26 We apply these τ* values in the present analysis and provide an error estimate of these values in the discussion section. For Chl a homodimers, an excellent agreement results between experimental and calculated decay times at different temperatures (between 10 and 300 K), when using the above τ* value, the 〈ΣMfMOM〉dis obtained from our exciton model and a temperature-independent τISC of 6.7 ns (left panel of Figure

1 1 1 ) τISC τ τ*

〈∑f O 〉 M

M

(24)

M

dis

The natural logarithm of the resulting 1/τISC is shown in Figure 6 as a function of the inverse temperature for both types of homodimers. As expected, the ISC rate of Chl a homodimers does not depend on temperature, whereas that of Chl b homodimers increases with temperature above 100 K and is virtually temperature-independent below 100 K. IV. Discussion A. Class IIa WSCP and Class IIb WSCP Share the Same Chl Binding Motif. The fact that the optical spectra of class IIa WSCP in Figure 3 can be described by using the crystal structure data of an “open sandwich” dimer of class IIb WSCP provides further support for our conclusion1 that both classes contain the same Chl binding motif. Interestingly, class IIb WSCP of L. Virginicum binds four chlorophylls, whereas class IIa WSCP of cauliflower binds only two. These two chlorophylls

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TABLE 1: Coulomb Couplings (cm-1) between the Ground State Charge Densities of the Macrocycles of Chl a in Different Binding Sites 1-4 of Class IIb WSCP (see Figure 1) Calculated with Two Different Methods: DFT/B3LYP and HF (in parentheses) 1 2 3

2

3

4

-647 (-859)

26 (36) 18 (40)

19 (42) 30 (42) -565 (-755)

are bound in an “open sandwich” geometry very similar to that of the chlorophylls in the two dimers of class IIb WSCP in Figure 1. It seems that specific interactions favor the formation of strongly coupled Chl dimers (at binding sites 1/2 and 3/4 in Figure 1), rather than the formation of WSCP complexes with chlorophylls in more distant binding sites (e.g., 1/3 and 1/4). To study the role of the Chl molecules in the formation of tetramers, we have analyzed the Coulomb coupling between the ground state charge densities of the macrocycles of the chlorophylls in the four putative binding sites (see Figure 1) using two different quantum chemical methods. Details of these calculations are given in the Supporting Information (SI). As seen in Table 1, there is a strong attractive coupling between chlorophylls forming the “open sandwich” dimers (1/2 and 3/4) and a weak repulsive coupling between the chlorophylls in more distant binding sites (1/3, 1/4, 2/3, 2/4). This marked difference could well explain our conclusion on preferential formation of “open sandwich” dimers in class IIa WSCP.1,2,8 Accordingly, the following scenario appears to be realistic: The formation of WSCP tetramers is initiated by dimer formation of two monomeric subunits that bind one Chl molecule each. Subsequently, two additional monomeric subunits of the protein without bound Chl are attached, most likely driven by the hydrophobic interaction between the subunits. However, it remains an open question whether the latter two subunits are arranged in the same way as in class IIb WSCP, where each subunit of the tetramer contains a Chl molecule. It is tempting to speculate that instead of filling the two empty binding sites with water molecules, there is an energetically more favorable conformation of the tetrameric complex in class IIa WSCP. A definite answer to this question awaits the crystal structure analysis of class IIa WSCP of cauliflower. At present, we cannot exclude the possible existence of a minority of complexes with weakly coupled chlorophylls as inferred from transient absorption data.2 To decide whether the angle β ) 6-8° inferred from the rotational strength of the exciton transitions in Figure 4 really reflects a deviation between the direction of the Qy transition dipole moment and the y axis of Chl a or rather a small structural difference in the “open sandwich” dimers of L. Virginicum and cauliflower, measurements of the CD spectrum of L. Virginicum would be helpful. If the exciton transitions in the latter WSCP type exhibit a rotational strength similar to cauliflower, then direct evidence would be obtained for an in-plane rotation of the Qy transition dipole moment of Chl a. Such a rotation has been discussed in the literature for many years.27-30 Different values were reported for the orientation of this transition dipole moment ranging from β ) -20°27 to β ) 15°.28 Recently, values were gathered for β ) (4.5 ( 2.5)° determined from an analysis of time-resolved fluorescence anisotropy measurements on the peridinin-Chl a complex29 and β ) -(12 ( 3)° determined by femtosecond polarization resolved visible pump-infrared probe spectroscopy on Chl a in a toluene-d8 solution.30 (A

Figure 7. Radiative lifetime, τrad (eq 15), of the Chl a homodimer in WSCP as a function of temperature in units of nanoseconds and in units of the radiative lifetime of the Chl a monomer τ* ) 15 ns.

positive (negative) sign of β indicates a rotation toward (away from) the 131-keto group.) Quantum chemical calculations, using either time-dependent density functional theory (TDDFT) with the hybrid B3LYP exchange correlation (XC) functional31 or the Hartree-Fock method and configuration interaction with single excitations (HF/CIS) predict β ) 0°24 for Chl a in vacuum. We note that L. Virginicum represents an ideal model system to determine this angle, since the molecular y axes of the pigments are parallel (panel c of Figure 2) and the rotational strength of parallel dipole moments vanishes (eq 3 and Figure 4). B. The Temperature Dependence of the Excited State Decay Rate of Chl a WSCP Is Explained by Thermally Activated Exciton Superradiance. The present exciton model fully accounts for the temperature dependence of the excited state decay times measured on Chl a homodimers (left panel of Figure 5). At elevated temperatures, the thermal population of the high-energy exciton state opens a fast radiative relaxation channel. The population of the upper exciton state decays much faster than that of the low-energy one because of the larger oscillator strength of the former, an effect called superradiance. The difference in oscillator strength is a direct consequence of the relative orientation of monomer transition dipole moments (vide supra). The influence of the excitonic coupling on the radiative lifetime, τrad (eq 15), and thereby on the relative yield of formation of unwanted triplet states (eq 22) of the dimer is seen in Figure 7 as a function of temperature. The strongest enlargement of the radiative lifetime and the triplet formation by a factor of about 4 is seen at low temperatures, where only the low energy exciton state is populated. The thermal population of the superradiant high-energy exciton state at higher temperatures then leads to a decrease in the triplet yield and the radiative lifetime to reach a value of about 1.4 times the monomer value (horizontal line in Figure 7) at physiological temperature. It can be concluded that the excitonic interaction in the “open sandwich” dimers is not responsible for the 4-times-lower yield of formation of singlet oxygen with respect to the yield measured in solution.6 In fact, even at physiological temperatures, the excitonic coupling increases the triplet yield; that is, working in the opposite direction. So the question arises why the chlorophylls in WSCP are not arranged in an “in-line” geometry, since this would make the lower exciton state superradiant and thereby decrease the triplet yield. It seems that nature accepted this loss but gained protection by packing the chlorophylls closely in the core of the WSCP, thus creating a diffusion barrier for oxygen, as was proposed before.4,8 Probably, a closer packing is possible if the chlorophylls are arranged as “open sandwich” rather than “in-line” dimers.

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The present quantitative agreement between the measured and calculated decay times of Chl a homodimers (left panel of Figure 5) provides further and independent evidence for our conclusion on the same Chl binding motif in class IIa and IIb WSCP. The former conclusion, which was based on the description of optical spectra, critically depends on the use of the correct line shape function.1 The present conclusion is more direct, since it depends only on the oscillator strength of the exciton transitions and their energy gap. To obtain an error estimate of our method, we have used the radiative lifetime τ* in eq 23 as a fit parameter that is determined from linear regression. Interestingly, the best correlation between experimental and calculated values is obtained for τ* ) 17 ns, which is somewhat larger than the 15 ns from Brody and Rabinowitch.25 To understand possible origins of the discrepancy, we have repeated the regression procedure (using eq 23) after varying the angle R between the transition dipole moments of the two chlorophylls in WSCP. If this angle is increased by 9° with respect to its value in the crystal structure of class IIb WSCP, the τ* ) 15 ns of Brody and Rabinowitch25 is reproduced. Hence, one origin of the discrepancy could be a somewhat larger opening angle between the two chlorophylls in IIa WSCP as compared to that of the dimers 1/2 and 3/4 in IIb WSCP. We note that increasing the opening angle by 9° even slightly improves the fit of the absorbance spectrum of Chl b homodimers in Figure 3. Another source of uncertainty could be the value τ* ) 15 ns itself. We have refined the procedure that Brody and Rabinowitch25 used to extract the value of τ*. Instead of integrating the absorbance spectrum, we have taken the value of the dipole strength of the 0-0 transition determined by Knox32 as a function of the refractive index n as d0(n) ) 20.2 + 23.6(n 1) (in units of D2) and estimated the part of the dipole strength that is contained in the high-frequency intramolecular vibronic transitions from fluorescence spectra. From the d0(n) and the sum of the Huang-Rhys factors of intramolecular modes Σ ) 0.36, determined for the monomeric low-energy Chl a in the CP29 complex by Ra¨tsep et al.,33 we have estimated the total dipole strength, d (in units of D2), of the Qy-transition of Chl a as

d(n) ) eΣd0(n) ) 1.43(20.2 + 23.6(n - 1))

(25)

From the Einstein coefficient of spontaneous emission, taking into account propagation effects of the light in the dielectric medium with refractive index n,34,35 the radiative lifetime τ* is obtained as

τ* )

3πε0pc3

1 n d(n) (Eeg /p) 3

(26)

If the value n ) 1.35 (ethyl ether) of the analysis of Brody and Rabinowitch25 is used (and the Eeg ) hc/(676 nm) for the transition energy of Chl a), a value of τ* ) 17.8 ns results. A likely reason for the discrepancy in the value of 15.2 ns reported by Brody and Rabinowitch25 is the possibility that the integral over the absorbance spectrum as determined in ref 25 might contain a contribution from the next-higher electronic state of Chl a (Qx transition) that overlaps with the vibronic excitations of the lowest electronic state. It may well be that the actual refractive index in a protein is larger than that of ethyl ether. We estimate n2 to be in the range

Figure 8. The black line shows the τ* values, as determined from linear regression using eq 23, as a function of the variation of the angle between the transition dipole moments of the two chlorophylls ∆R, where ∆R ) 0 represents the crystal structure geometry of class IIb WSCP. The dashed lines indicate τ* values estimated from eq 26 for a range of optical dielectric constants, n2 (see text and Appendix), and the dotted line the literature value, τ* ) 15.2 ns.25

from 1.82 to 2.04 (average 1.93), on the basis of measurements of the oscillator strength of protein-bound and solvent-extracted Chl a by Mu¨h and Zouni.36 Details of this estimation are given in the Appendix. These n2 values correspond to radiative lifetimes τ* ranging from 16.2 to 17.8 ns, a range that is fully consistent with the τ* ) 17 ns obtained from the decay data analysis performed for the crystal structure of class IIb WSCP (∆R ) 0 in Figure 8). To remove the remaining uncertainty, it would be helpful to measure the temperature-dependent excited state lifetime of class IIb WSCP, for which the crystal structure is known. With these data at hand, the present analysis would allow a direct determination of the natural lifetime τ* and also allow us to conclude whether there is a small deviation in the opening angle between class IIa and class IIb WSCP. C. The ISC Rate of Chl b Homodimers Is TemperatureDependent. Since a variation of τISC, which is the only free parameter of the calculations in Figure 5, does not change the slope of the correlation plot, the discrepancy between measured and calculated excited state decay times for Chl b homodimers (right panel of Figure 5) demonstrates that the exciton effect cannot explain the observed strong temperature dependence of the decay. A radiative lifetime, τ* ) 8.5 ns, would be required that is smaller by almost a factor of 3 than the literature value, τ* ) 23 ns.25 Variation of the angle between the Qy transition dipole moments leads to a maximum τ* value of only about 10 ns (obtained for parallel transition dipole moments), which is still too small and, in addition, results in optical spectra that deviate strongly from the experimental data. A possible explanation of the strong temperature dependence of excited state lifetimes in Chl b homodimers is a temperaturedependent ISC rate (Figure 6). This explanation raises the question: Why should the ISC rate be temperature-independent for Chl a homodimers and increase with temperature for T > 100 K in the case of Chl b homodimers? Early quantum chemical calculations by Petke et al.10 on the excited state energies of Chl a suggest that ISC from the first excited singlet state, S1, involves not only the lowest triplet state, T1, but also higher excited triplet states, T2 and T3. The states T3 and S1 were found to be nearly degenerate.10 To check for the possibility of thermally activated ISC via higher excited triplet states, we have calculated the S0-S1 and the S0-Tn energies of Chl a and Chl b by using TDDFT with different exchangecorrelation (XC) functionals. These functionals differ in the extent of exact (Hartree-Fock-type) exchange. The latter varies

Water-Soluble Chlorophyll Binding Protein

Figure 9. Quantum chemical energies of the S1 state and the Tn states (n ) 1-5) of Chl a (left part) and Chl b (right part) using methods that differ in the amount of HF exchange correlation (for details, see the SI).

between 20% (B3LYP XC-functional) and 65%, as discussed in detail in the SI. Note that a larger extent of exact exchange means that a smaller amount of dynamic correlation of electrons is taken into account. For comparison, we also show results obtained with the wave function-based HF/CIS method, which contains 100% exact exchange, but the fewest dynamic correlation effects. The quantum chemical energies of the S1 and T1-T5 states obtained with the different methods for Chl a and Chl b are compared in Figure 9. The results are shown as a function of the relative contribution of the HF exchange part in the XCfunctional. In the case of Chl a, the two lowest triplet states, T1 and T2, are energetically well below the S1 state, whereas the state T3 is only slightly below or, in the case of HF/CIS, nearly degenerate with S1. These results are in line with the earlier data by Petke et al.10 and with a recent proposal by Knox et al.14 Interestingly, the S1-T3 energy gap is larger in Chl b than in Chl a (Figure 9). Therefore, it seems unlikely that ISC is thermally activated via T3 in Chl b and not in Chl a. However, a candidate for thermally activated ISC in Chl b (and not in Chl a) appears to be the state T4. Whereas the T4-S1 energy gap obtained for Chl a is much larger than the thermal energy at room temperature (kT ≈ 200 cm-1), that of Chl b is smaller for some methods and even becomes negative for the B3LYP XC-functional. A quantitative evaluation of the energy gap also requires one to take into account the influence of the protein environment. We have recently developed a combined quantum chemical/electrostatic method for calculating relative shifts in transition energies of pigments in pigment-protein complexes.23 To obtain an order-of-magnitude estimate of the shift of the energies of the S1 and T4 states due to the protein environment, we applied this method, using the protein coordinates of class IIb WSCP.4 Briefly, first, the ab initio electrostatic potentials φ of the charge densities of the S0, S1, and T4 states of Chl b in vacuum were calculated using density functional theory (DFT) for the ground state, S0, and time-dependent DFT for the excited states with the BHHLYP XC-correlation functional (containing 50% HF exchange). These potentials were fitted by atomic partial charges that were afterward applied in electrostatic free energy calculations, including the whole protein in atomic detail. From the relative shift in free energy that occurs when the partial charges of the different states

J. Phys. Chem. B, Vol. 113, No. 29, 2009 9955 are introduced into the protein, a shift of the transition energy between vacuum and the protein is obtained. This energy difference is thermally averaged over the possible protonation states of the titratable amino acid residues (for details, see the SI and ref 23). In this way, the BHHLYP T4-S1 energy gap is found to decrease from 690 cm-1 in vacuum to 20 cm-1 in the protein. We consider a more detailed investigation of the energy gap shift by the protein as premature, since the vacuum energy gap value depends strongly on the applied XCfunctional, and there is no independent way to evaluate its reliability. In addition, the protein-induced shift might be different in class IIa WSCP of cauliflower and class IIb WSCP of L. Virginicum due to differences in the amino acid sequence5 and pigment content. A more quantitative estimation of the T4-S1 energy gap is obtained below from an analysis of the excited state decay data. In summary, despite the above-described uncertainties, a comparison between the quantum chemical energies obtained for Chl a and Chl b suggests that ISC in Chl a involves three channels, whereas in Chl b, an additional channel is opened at higher temperatures via thermally activated population of the T4 state. Hence, we expect the following behavior of the ISC rate constant:

〈∑f e

1 ) k1 + k2 τISC

M

M

-∆EM,T4

〉

(27)

dis

Here, fM is a Boltzmann factor (the same as in eq 15) describing a thermally equilibrated population of exciton states prior to ISC. ∆EM,T4 is the energy gap between exciton state M and the state, where one of the two monomers is in the singlet ground state and the other is in the triplet state T4; k1 and k2 are constants, and 〈...〉dis denotes an average over disorder in local transition energies. The same inhomogeneous width of ∆inh ) 170 cm-1 as for S1-S0 is assumed for the T4-S1 energy gap. The temperature dependence of the ISC rate constant in Chl b homodimers can be fitted by eq 27 with k1 ) (7.4 ns)-1, k2 ) (11.8 ns)-1, and by assuming a (mean) T4-S1 energy gap of 320 cm-1 for the two monomers (solid line in Figure 6). V. Conclusions On the basis of calculations of the spectra of Chl a and Chl b homodimers of class IIa WSCP, using the structural data of class IIb WSCP, evidence is obtained that both classes of WSCP contain a very similar Chl binding motif. Independent support for this result is gained from the explanation of the temperature-dependent fluorescence decay of Chl a homodimers. The analysis suggests that the opening angle between pigment planes in the two classes does not differ by more than 10°. The temperature dependence is quantitatively described by taking into account the different oscillator strengths of the upper and lower exciton states. The stronger temperature dependence of the excited state decay of Chl b homodimers is explained by the assumption that the ISC rate in the latter is temperature-dependent. This temperature dependence is explained by a thermally activated ISC channel, which involves the triplet state T4. In the case of Chl a, the energy gap between the S1 and T4 states is calculated to be significantly larger than for Chl b. We propose that the S1-T4 ISC channel is closed at all temperatures in Chl a homodimers, but opens up in Chl b

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homodimers for T > 100 K. A value of 320 cm-1 is obtained for the T4-S1 energy gap of Chl b in WSCP from an analysis of the decay data. Measurements of optical spectra and excited-state lifetimes of class IIb complexes are planned to decide as to whether the 6-8° in-plane rotation of the Qy transition dipole moment inferred from the rotational strength of the exciton transitions reflects a structural difference in mutual orientations of the chlorophylls between class IIa and class IIb WSCP complexes or an intrinsic property of Chl a. Furthermore, these experiments will help to pinpoint the radiative lifetime, τ*, of Chl a in WSCP. This value could then be used to decide whether the angle between pigment planes in IIa and IIb WSCP is exactly equal or differs slightly. Appendix A: Estimation of the Protein Refractive Index The protein refractive index n can be estimated on the basis of medium effects on the dipole strength of Chl a, if data are available that quantitatively correlate the optical spectra of protein-bound and solvent-extracted Chl a. Such a correlation has been established in ref 36 for cyanobacterial photosystem I as the protein and 80% acetone/20% aqueous buffer as the solvent. If d(n) is the dipole strength of protein-bound Chl a and da ) d(na) that in 80% acetone, the ratio of dipole strengths is given by

d(n) ) da

∫∆ω ω-1 R(ω) ∫∆ω ω-1 Ra(ω)

(A1)

where R(ω) and Ra(ω) are the absorbance spectra of proteinbound and acetone-extracted Chl a, respectively, on the frequency scale in the integration interval, ∆ω. Actually, ∆ω should cover the range of the Qy 0-0 transition only, but this transition is difficult to separate from the spectrum. In ref 36, the integration has been performed on the wavelength scale, and the integration interval ∆λ (550 to 800 nm) contains, in addition to the Qy 0-0 transition, the higher vibronic Qy transitions and the Qx 0-0 and higher vibronic transitions. Whereas the dipole strengths of the vibronic Qy transitions can be expected to change with solvent similarly to the Qy 0-0 transition (neglecting solvent effects on the Franck-Condon factors of the high-frequency intramolecular modes), the effect on Qx may be different. Because of the small dipole strength of the Qx transition, we neglect such differences here and use the full ∆λ. The ratio of integrals over ∆λ reported in ref 36 is 1.060 ( 0.013 (evaluated on the basis of 144 spectrum pairs). The interaction with the protein not only changes the dipole strengths of Chl a, but also shifts the transitions to lower energies with respect to the solvent. As a consequence, some vibronic Qy transitions of Chl a with λ < 550 nm in the solvent samples will be shifted into the integration interval in the protein samples, depending on the average site energy shift of Qy transitions in photosystem I. The latter can be estimated from structurebased calculations (Adolphs, J.; Mu¨h, F.; Madjet, M. E.; Renger, T.; to be published) to be -200 ( 100 cm-1 so that the lower integration limit for the spectrum of protein-bound Chl a has to be increased by 6 ( 3 nm, yielding a corrected ratio of integrals of 1.05 ( 0.03. Finally, the conversion to the frequency scale and dividing R(ω) by ω as in eq A1 decrease the ratio further, resulting in

d(n) ) 1.03 ( 0.03 da

(A2)

According to Knox,32 the ratio of dipole strengths can be written as

d(n) 20.2 + 23.6(n - 1) ) da 20.2 + 23.6(na - 1)

(A3)

Since the refractive indices for acetone and water are 1.36 and 1.33, respectively, we have na ) 1.35, and the refractive index, n, of the protein follows from eqs A2 and A3 as

n ) 1.39 ( 0.04

(A4)

which is reasonably between the values for polar solvents and hydrocarbons. The optical dielectric constant, n2, of the protein then is in the range 1.82-2.04. Acknowledgment. Financial support by the German Research Foundation through collaborative research center Sfb 429 (TP A1 and A9) is gratefully acknowledged. Supporting Information Available: Details of quantum chemical and electrostatic calculations, table containing atomic partial charges obtained from a fit of the electrostatic potential of the charge density of the S0 state of Chl b, obtained by either using density functional theory with the B3LYP XC-functional and a 6-31G* basis set or HF calculations with the same basis set. The partial charges for Chl a are given in the supporting online material of ref 24. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Renger, T.; Trostmann, I.; Theiss, C.; Madjet, M. E.; Richter, M.; Paulsen, H.; Eichler, H. J.; Knorr, A.; Renger, G. J. Phys. Chem. B 2007, 111, 10487. (2) Theiss, C.; Trostmann, I.; Andree, S.; Schmitt, F.-J.; Renger, T.; Eichler, H. J.; Paulsen, H.; Renger, G. J. Phys. Chem. B 2007, 111, 13325. (3) Hughes, J. L.; Razeghifard, R.; Logue, M.; Oakley, A.; Wydrzynski, T.; Krausz, E. J. Am. Chem. Soc. USA 2006, 128, 3649. (4) Horigome, D.; Satoh, H.; Itoh, N.; Mitsunaga, K.; Oonishi, I.; Nakagawa, A.; Uchida, A. J. Biol. Chem. 2007, 282, 6525. (5) Satoh, H.; Nakayama, K.; Okada, M. J. Biol. Chem. 1998, 273, 30568. (6) Schmidt, K.; Fufezan, C.; Krieger-Lieszkay, A.; Satoh, H.; Paulsen, H. Biochemistry 2003, 42, 7427. (7) Satoh, H.; Uchida, A.; Nakayama, K.; Okada, M. Plant Cell Physiol. 2001, 42, 906. (8) Schmitt, F.-J.; Trostmann, I.; Theiss, C.; Pieper, J.; Renger, T.; Fuesers, J.; Hubrich, H.; Paulsen, H.; Eichler, H. J.; Renger, G. J. Phys. Chem. B 2008, 112, 13951. (9) Huyer, J.; Eckert, H. J.; Irrgang, K. D.; Miao, J.; Eichler, H. J.; Renger, G. J. Phys. Chem. B 2004, 108, 3326. (10) Petke, J. D.; Maggiora, G. M.; Shipman, L.; Christoffersen, R. E. Photochem. Photobiol. 1979, 30, 203. (11) Linshitz, H.; Sarkanen, K. J. Am. Chem. Soc. 1958, 80, 4826. (12) Setif, P.; Hervo, G.; Mathis, P. Biochim. Biophys. Acta 1981, 638, 257. (13) Takiff, L.; Boxer, S. G. J. Am. Chem. Soc. 1988, 110, 4425. (14) Knox, R. S.; Brown, J. S.; Laible, P. D.; Talbot, M. F. J. Photosynth. Res. 1999, 60, 165. (15) Renger, T.; Marcus, R. A. J. Chem. Phys. 2002, 116, 9997. (16) Pearlstein, R. M. In Chlorophylls; Scheer, H., Ed.; CRC Press, Inc.: Boca Raton, FL, 1991; p 1051. (17) Renger, T.; May, V. J. Phys. Chem. A 1998, 102, 4381. (18) Renger, T.; May, V.; Ku¨hn, O. Phys. Rep. 2001, 343, 138. (19) Renger, T.; Marcus, R. A. J. Phys. Chem. B 2002, 106, 1809. (20) Renger, T.; May, V. Phys. ReV. Lett. 2000, 84, 5228. (21) Einstein, A. Phys. Z. 1917, 18, 121.

Water-Soluble Chlorophyll Binding Protein (22) Raszewski, G.; Renger, T. J. Am. Chem. Soc. 2008, 130, 4431. (23) Mu¨h, F.; Madjet, M. E.; Adolphs, J.; Abdurahman, A.; Rabenstein, B.; Ishikita, H.; Knapp, E. W.; Renger, T. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 16862. (24) Madjet, M. E.; Abdurahman, A.; Renger, T. J. Phys. Chem. B 2006, 110, 17268. (25) Brody, S. S.; Rabinowitch, E. Science 1957, 125, 555. (26) Lewis, G. N.; Kasha, M. J. Am. Chem. Soc. 1945, 67, 994. (27) Fragata, M.; Norden, B.; Kurucsev, T. Photochem. Photobiol. 1988, 47, 133. (28) Van Zandvoort, M. A. M. J.; Wrobel, D.; Lettinga, P.; Vanginkel, G.; Levine, Y. K. Photochem. Photobiol. 1995, 62, 299. (29) Kleima, F. J.; Hofmann, E.; Gobets, B.; van Stokkum, I. H. M.; van Grondelle, R.; Diederichs, K.; van Amerongen, H. Biophys. J. 2000, 78, 344.

J. Phys. Chem. B, Vol. 113, No. 29, 2009 9957 (30) Linke, M.; Lauer, A.; von Haimberger, T.; Zacarias, A.; Heyne, K. J. Am. Chem. Soc. 2008, 130, 14904. (31) Stevens, P. J.; Devlin, J. F.; Chabatowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623. (32) Knox, R. S. Photochem. Photobiol. 2003, 77, 492. (33) Ra¨tsep, M.; Pieper, J.; Irrgang, K.-D.; Freiberg, A. J. Phys. Chem. B 2008, 112, 110. (34) Fowler, W. B.; Dexter, D. L. Phys. ReV. 1962, 128, 2154. (35) Knox, R. S.; van Amerongen, H. J. Phys. Chem. B 2002, 106, 5289. (36) Mu¨h, F.; Zouni, A. Biochim. Biophys. Acta 2005, 1708, 219.

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