Excitonic States in Photosystem II Reaction Center - The Journal of

J. Phys. Chem. B 2005, 109, 23051-23060

23051

Excitonic States in Photosystem II Reaction Center Nikolaj Ivashin† and Sven Larsson* Department of Chemistry, Chalmers UniVersity of Technology, S-412 96 Go¨teborg, Sweden ReceiVed: May 26, 2005

The excited states of a structurally well-determined photosystem II (PSII) reaction center are obtained using an effective Hamiltonian for the interaction between the Qy states. The latter are calculated using the timedependent density functional theory (DFT) method in DFT-optimized geometries, but with conserved side group orientations. Of particular importance is the orientation of the vinyl group of ring I. Couplings are calculated using actual transition charge distributions via the INDO/S model. Good agreement with experimental spectra is obtained. The lowest excited state is mainly located on the inactive B-side, but with a large component on PA too, making charge separation to HA possible at low temperature. The “trap state” and triplet state are localized on the inactive B-side. Since the spin singlet Qy states of the reaction center are all within a rather small energy range, the state with the highest component of BA*, on the blue side of the Qy absorption, has a rather high Boltzmann population at room temperature. The charge-transfer states, however, have a rather large spread and cannot be calculated accurately at present. The orientation of the phytyl chains is important and has as a consequence that the energy for the charge-separated BA+HA- state is significantly lower than the corresponding state on the B-side. It follows that the BA* and PA* states are both possible origins for a fast charge separation in PSII.

I. Introduction The structure of photosystem II (PSII) of a cyanobacterium (Synechococcus elongatus) was first determined by Zouni et al.1 A better resolved structure was recently obtained (3.5 Å) by Ferreira et al.2 (Figure 1). The reaction center (RC) contains four chlorophyll a (chl a) molecules (PA, PB, BA, and BB) and two pheophytin a (pheo a) molecules (HA and HB) in its core (Figure 2). PA and PB correspond to the “special pair” in bacterial RCs. Lower indices A and B correspond to the subunits D1 and D2, respectively (L and M, respectively, in bacterial RCs). In D1 and D2 of PSII there are also two peripheral chl molecules close to the subunits CP43 and CP47. The latter two chromophores are here called AA and AB. In the refined structure2 details such as orientation of side groups of the chl and pheo molecules appear. Provided, of course, that these details are reliable, it is now possible for the first time to connect protein structure with electronic structure, spectra, excitation energy transfer (EET), charge separation, and electron transfer (ET) properties. The cation radical remaining after the charge separation process oxidizes TyrZ of the D1 subunit on the nanosecond time scale. TyrZ in its turn oxidizes a water molecule in the oxygenevolving manganese complex. The corresponding Tyr of the D2 subunit, called TyrD, is a cationic radical under working conditions.1-3 If the ET chain is interrupted when the electron has reached HA, then the electron recombines with the hole, and a triplet state is formed at a lower energy than that of the original singlet state. It was shown using electron paramagnetic resonance (EPR) * Author to whom correspondence should be addressed. Phone: 46-317723058. Fax: 46-31-7723858. E-mail: [email protected]. † Permanent address: Institute of Molecular and Atomic Physics, National Academy of Sciences, Nezalezhnasti Ave. 70, 220072 Minsk, Belarus. E-mail: [email protected].

that the triplet state resides in either of the accessory chlorophylls, BA or BB.4,5 P680* was originally believed to be a single excitation of PAPB. Later it has become clear that charge separation occurs from an accessory chlorophyll.6 This type of charge separation is known also from bacterial RCs.7 Fourier transform infrared spectroscopy has been used to show that the cation radical remaining after charge separation and the triplet state remaining after charge recombination are not localized on the same cofactor.8,9 Diner et al. suggested that the A-side is the active side.10 It was also shown that one branch is in fact inactive.11 Since TyrZ is on the A-branch, it appears reasonable that the A-branch is the active branch. Charge separation takes place from BA* or possibly PA* or (PBPA)*. The initial hole may move to PA, so that the electronic state realized after some picoseconds may be PA+BAHA-. Other problems are the composition of the Qy absorption (the Franck-Condon states) and the nature of the activation barrier for charge separation. It has long been suspected that the spin singlet, excited Qy states are in fact quantum mechanical superpositions of the local Qy states of many individual chl and pheo molecules.12-21 Work before 2002 has been summarized in useful reviews.18,19 The aim of the present paper is to find a structural basis for the character of the excitonic Qy states and for the asymmetry of the charge separation process. In addition we will discuss the localization of the triplet state. In most theoretical applications an effective Hamiltonian is used where the off-diagonal matrix elements or couplings are obtained from the Fo¨rster expression.22 Since chl and pheo have approximately the same Qy energies and since detailed protein structures have not been available until the Ferreira paper,2 it has been reasonable to use identical diagonal matrix elements. The models are referred to as multimer (MM) models. In the present paper we will apply an extended MM model where the inhomogeneities are included in ab initio calculations. A

10.1021/jp0581734 CCC: $30.25 © 2005 American Chemical Society Published on Web 11/09/2005

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Figure 1. Photosystem II reaction center of Thermosynechococcus elongatus.1

Figure 2. Chlorophyll a. In pheophytin a the Mg2+ ion is replaced by two protons in the trans position.

semiempirical method is used for the couplings, and this allows us to go beyond the Fo¨rster approximation.22 Several experimental groups have studied electrochromic shifts and other electric field effects to determine the composition of the Qy states.23-27 For example, it is possible to obtain a spectrum where the electron transferred from HA to the plastoquinone QA is trapped on QA. Since HA is the closest chromophore, it is assumed that this inserted negative charge

mainly affects the HA spectrum.25 Our results do not agree with this interpretation, however. Reducing QA leads to changes not only in the nearby spectrum, thus invalidating some of the previous conclusions. Time-resolved energy transfer or charge separation spectra have been obtained by many groups.28-36 Excitation in the red end of the Qy spectrum leads to two resolved components with time constants 2.6 and 120 ps at 20 K, with an apparent activation energy of 20-80 cm-1.28 The structural background is still unknown, and it is still unclear if we are dealing with two cleanly activated processes. The multitude of excited states in the same energy range makes it difficult to describe the charge separation process in detail. One useful way has been to modify HB using NaBH4 to a similar pigment (131-hydroxo-131-deoxo pheophytin a) that absorbs at a slightly higher energy.11,26,27,36,37 The charge separation process speeds up as a result of this replacement,37 possibly due to increased A-side components among the lower excited states. II. Theory and Methods A. Quantum Chemical Calculations. We have used computational methods at a different level of accuracy. Hydrogen atoms are added to the crystallographic structure using molecular mechanics (MM+) of HyperChem.38 Other programs from the HyperChem set have also been used (see below). At a higher level of accuracy we used the B3LYP density functional

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method39 within Gaussian 98,40 with the 6-31G* basis set, to optimize the structures of chl a, pheo a, and 131-hydroxo-131deoxo pheophytin a. Calculations of spectra have previously been carried out by Sundholm,41,42 Parusel and Grimme,43 and Linnanto and KorppiTommola.44 Although excitation energies calculated by the INDO/S method45 agree well with measured spectra,44 we believe that differences in excitation energies are more accurately reproduced with a method such as time-dependent density functional theory (TD/DFT),46 usually considered to be an ab initio method. In TD/DFT, in principle, all singly substituted Slater determinants are included. Although Sundholm used a special basis set for the spectrum,41 we decided to use 6-31G* for both geometry optimization and the spectrum. We carried out calculations where the side groups are constrained in their crystallographically determined positions, different for different chromophores. Studies of this type have been performed before on bacterial RCs.47 In the present work, however, the nonconstrained part of the structure was optimized for each chromophore. This updating of the geometry proved to be necessary to obtain consistent results for the spectrum. In the calculation of the spectrum of 131-hydroxo-131-deoxo pheo a, agreement with the experimental result was obtained only if the structure was fully geometry optimized using DFT and the spectrum was calculated using TD/DFT. The INDO/S method does not reproduce the blue shift even on the DFToptimized structure. B. Absorption Spectra of Multiple Chromophore Systems. The applicability of ab initio methods such as TD/DFT is in practice limited to a single chl or pheo. The semiempirical INDO/S method permits considerably larger systems to be treated, but the accuracy is considerably improved if DFT methods are used. We therefore decided to use an effective Hamiltonian for the Qy transitions where the inhomogeneities are included in the diagonal matrix elements via TD/DFT calculations on each separate monomer. This effective Hamiltonian model is a Fo¨rster model 22,48 (Dexter model49 for triplets) that corresponds to partial diagonalization of the full Hamiltonian, leaving a final N-dimensional configuration-interaction (CI) problem for N chromophores. The small interaction between a Qy state and the higher excited states (Qx, etc.) on another chromophore is neglected. The diagonal matrix elements of the Hamiltonian operator are thus the Qy energies, calculated using TD/DFT for each monomer in the constrained geometry. The calculation of the off-diagonal matrix elements between the Qy states on different sites only includes two chromophores at a time. We used the HyperChem version38 of INDO/S in the present calculation. This application of a semiempirical or ab initio method is often incorrectly done with neglect of the protein structure. More details are therefore given below. C. Calculation of Off-Diagonal Matrix Elements. The Fo¨rster expression for the coupling between two chromophores is defined by

U)

[

F1 3 b µ .µ b - (µ b .R B )(µ b2.R B) F2 1 2 R3 1

]

(1)

where b µ1 and b µ2 are transition dipole moments of the two chromophores. Fo¨rster derived eq 1 with the F-factors F1 ) 1 and F2 ) n2, where n is the refractive index of the medium.22 The polarization of the Qy transitions (µ b1 and b µ2) and the distance (R) between the chromophores must be known. This and the assumption of equal diagonal matrix elements define the standard MM model, here called MM-1.

The use of transition dipoles is only justified if the distance between the chromophores is very large. A generalization to small distance can be obtained if the derivation is based on the actual CI expansion with the correct expression for the wave functions. Let us first assume that the monomer states are formed from highest occupied molecular orbital (HOMO) to lowest unoccupied molecular orbital (LUMO) singly substituted Slater determinants, φi f φa on one chromophore and φj f φb on the other. Since the substitution can be either in a or b spin orbitals, there are two possible Slater determinants. To obtain an eigenfunction of the S2 spin operator, one has to spin project, i.e., combine the two possible Slater determinants with a plus or minus sign between them. The off-diagonal matrix element in eq 1 has F1 ) 2 for singlet states and F1 ) 0 for triplet states. Fo¨rster used a nonprojected Slater determinant and therefore obtained the singlet-triplet average value F1 ) 1. In the literature this error is often incorrectly compensated for by using F2 ) 1 instead of the correct F1 ) 2 and F2 ) n2 ≈ 2 if the medium between the chromophores cannot be included. F1 is derived for singlets and triplets using spin projection on singly substituted Slater determinants50

diagonal singlet 〈1Φia|H|1Φia〉 - 〈1Φ0|H|1Φ0〉 ) a - i - (ii|aa) + 2(ia|ia) (2) diagonal triplet 〈3Φia|H|3Φia〉 - 〈3Φ0|H|3Φ0〉 ) a - i - (ii|aa) (3) where i and a are orbital energies of occupied and virtual spin orbitals, respectively.

off-diagonal singlet 〈1Φia|H|1Φjb〉 ) 2(ai|jb) - (ab|ji) (4) off-diagonal triplet 〈3Φia|H|3Φjb〉 ) -(ab|ji)

(5)

In eqs 2-5 the matrix elements are expressed in the Mulliken notation

(ij|kl) )

∫

φi(r b1)φj(r b1)φk(r b2)φl(r b 2) dV1 dV2 r12

(6)

We assume that the two orbitals φi and φa in the substitution φi f φa (or the two orbitals φj and φb in the substitution φj f φb) are on the same center. The Mulliken matrix elements are of four standard types

one-center, Coulomb (ii|aa) )

∫

Fii(r b1)Faa(r b 2) dV1dV2 r12 (7)

one-center, exchange (ia|ia) )

∫

φi(r b1)φa(r b1)φi(r b2)φa(r b 1) dV1dV2 (8) r12

two-center, Coulomb (ai|jb) )

∫

Fai(r b1)Fjb(r b2) dV1dV2 r12 (9)

two-center, exchange (ab|ji) )

∫

Fab(r b1)Fji(r b 2) dV1dV2 r12 (10)

The one-center Coulomb matrix element of type (ii|aa) is large since it is a one-center repulsion between two positive charge

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distributions Fii and Faa ((ii|aa) ≈ 2-5 eV). The one-center matrix element (ia|ia) tends to be considerably smaller since Fia, formed by multiplying orbitals φi and φa, can be positive or negative in different parts of space. Since (ia|ia) > 0, singlets are higher than triplets. In the two-center Coulomb matrix element (ai|jb) the charge distributions Fai and Fjb can be thought of as forming transition charge densities for the transitions i f a and j f b, respectively, on different centers. Taylor expansion of (ai|jb) gives a leading dipole-dipole term

∫

[

]

Fai(r b1)Fjb(r b2) 3 dV1 dV2 ) b µ 1.µ b2 - 3(µ b1.R B )(µ b2.R B ) (11) r12 R

This is identical to Fo¨rster U of eq 1 (with F1/F2 ) 1). The Fo¨rster method is thus an approximation to a semiempirical or ab initio calculation of the matrix element. The latter includes “monopoles”, which are important at a short distance between the chromophores. The integrand of eq 5 is a two-center exchange matrix element. It involves two orbital products, Fab ) φaφb and Fij ) φiφj. Each is a product of two orbitals centered on different chromophores. This product is a “normal” overlap charge at a small distance between the centers but contains a factor exp(-cR), where R is the distance between the centers and c is a number of order unity depending on which atomic orbitals are involved. If the c values are the same in the two products, (ab|ji) is small for R tending to zero and is further multiplied by an exponential exp(-2cR) for larger distances R. This (Dexter) matrix element is the only off-diagonal matrix element in the case of triplets (eq 5). The latter therefore interact only at the contact distance between the chromophores (R close to zero).49,50 From eq 4 follows F1 ) 2 and F2 ) 1 for singlets. The Fo¨rster matrix element, however, has F1 ) 1 and F2 ) n2 ≈ 2. The Fo¨rster derivation is for a single Slater determinant, and therefore an average between singlets (F1 ) 2) and triplets (F1 ) 1) is obtained. Consequently the Fo¨rster matrix element is approximately a factor of 4 smaller than the corresponding CI matrix element derived in quantum chemical ab initio methods as well as semiempirical methods such as INDO/S and CNDO/ S. The latter methods are correctly spin projected (F1 ) 2) but refer to the in vacuo case (F2 ) 1). Using F1 ) 1 for singlets is definitely wrong but is most often in the literature compensated for by another error, that of using F2 ) 1 instead of more correctly F2 ) n2 if there is a medium between the chromophores. The off-diagonal matrix elements used in quantum chemical calculations are consequently too large if a protein medium is present between the chromophores but cannot be included in the calculation. In practice this factor may be even larger in the case of INDO/S or CNDO/S, but this is due to “ordinary” problems with semiempirical methods (for example, overestimation of oscillator strengths). There is further uncertainty in using a refractive index for a protein. All of these inconsistencies in the theoretical calculation of chromophore interactions provide motivation for using an empirical scale factor (see below). Each off-diagonal matrix element corresponds to an excitonic interaction matrix element between the Qy states in a CI involving only two chromophores. The couplings are obtained backward from the INDO/S energy levels and coefficients. The sign of the coupling cannot be obtained in this simple way, and therefore the Fo¨rster matrix element22 is also calculated. The calculated couplings are given in Figure 3. These matrix

Figure 3. Calculated EET couplings for the PSII reaction center in units of cm-1.

TABLE 1: Calculated Wavelength (λ) (Vertical Excitation) of the First Excited (Qy) State Using the TD/DFT Method on Structures Fully or Partly Optimized Using DFT B3LYPa system cofactor

1

2

PA PB BA BB HA HB AA AB

567.5 567.5 567.5 567.5 569.8 569.8 567.5 567.5

568.1 572.6 558.8 570.1 562.4 565.1 560.9 560.6

3

4

vinyl angle

561.2 572.2 564.8 567.6

573.2 582.2 567.5 581.2 565.1 572.0 570.4 564.2

146 157 -87 152 92 -59 106 112

a System 1 is full optimization; the dihedral angle for chl a is 143.8° and for pheo a 142.0°; system 2 has the vinyl and ether group dihedral angles frozen; system 3 is the same as system 2 but including a neighboring (nonoptimized) phytyl tail; system 4 has optimized structures, freezing all angles and dihedrals.

elements are scaled by a single factor, designed to give optimum agreement with the experimental spectrum. We will refer to the model described above and used here as the MM-2 model. In comparison to the previously used MM-1 model, it includes inhomogeneities and an improved calculation of the off-diagonal matrix elements. Further improvements may involve higher monomer states, including Qx and charge-transfer states. In bacterial reaction centers the diagonal matrix elements are more different, and the coupling matrix elements therefore of less significance, except in the special pair. In the latter case, however, there is no protein structure between the chromophores. In that case the approximation n2 ) 1 is a reasonable one.51 III. Results A. Monomer Spectra. The results (Table 1) for fully optimized structures agree well with the results of Sundholm.41,42 The lowest transitions are about 80 cm-1 lower for chl a than those for pheo a, while the oscillator strength is about 50% higher for the former chromophore. In the next step we calculated the spectrum with the side groups in the positions obtained from crystallographic coordinates.2 The remaining coordinates were optimized using DFT B3LYP. In the subsequent TD/DFT calculations rather large differences in excitation energy were obtained depending on the orientation of the side groups (Table 1). The difference between the BA and BB chromophores is mainly due the vinyl

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TABLE 2: Calculated States of Neutral RC Using the MM-2 Model (See Text)a coefficients

energy (cm-1)

PA

BA

HA

PB

BB

HB

AA

AB

17 318 17 539 17 637 17 737 17 775 15 288 15 294 15 430

50 -15 72 10 37 3 1 -28

-6 -15 43 5 -16 -2

6 8 -33 -5 86 13 2 35

-70 -62 17 -7 24 2

50 -66 -32 -45 -14 -1 -2 7

-14 36 27 -88 3 4 -2

0 0 2 0 13 -99

-1 3 -2 -3 2 1 100

87

-19

1

oscillator strength

θ

1.57/1.56 0.94/0.86 0.5/0.48 0.44/0.32 0.44/0.30 1.05/1.03 1.0/1.02 0.77/0.79

87.3/88.2 20.5/31 115.2/114.6 107/97.1 78.2/87.5 21/24.5 28.7/29.8 92/95.3

a

Coefficients, multiplied by a factor 100, on chromophores of RC. The scale factor for couplings is 0.5. Two figures are given for the oscillator strength and for θ. The first assumes fchl/fphe ) 1.64 (solution) and the second fchl/fphe ) 2.5 (protein).

group of ring I and to a lesser extent the methoxy carbonyl group of ring V. To reduce the computing costs we replaced the methyl and ethyl groups by hydrogen atoms. Spot checks confirmed that this has no effect on the order of the Qy energies. We also neglected the small influence of doming, the axial ligand, and Mg2+ distance from the plane. Thus quite generally we find lower excitation energies on the inactive B-side than on the A-side, and this is mainly due to the orientation of the vinyl groups. A perpendicular orientation leads to a difference in conjugation compared to the in-plane orientation. Looking closer at the difference between BA and BB we see that the former cofactor has a LUMO higher by 0.06 eV while its HOMO is higher only by 0.02 eV. The explanation lies in the orientation of the vinyl group. In the coplanar case the vinyl π* molecular orbital (MO) interacts with the macrocycle π system to lower the LUMO energy for the whole π system. The bond lengths are also slightly changed due to side group orientation, and this gives a second-order correction in the absorption spectrum. B. Spectrum of the RC. INDO/S calculations were carried out on different subsystems to obtain a first idea about which factors are important for the localization of the Qy excitonic states. The calculation included four chl’s and two pheo’s, with truncation of the phytyl chains, in all 442 atoms and 1312 electrons. The lowest state is mainly located on the B-side, consistent with the different orientations of the vinyl groups in the respective chromophores. The two lowest states have large transition moments. The total width of the Qy band, however, is more than twice as large as found experimentally. This is expected since the coupling is overestimated by approximately a factor of 2 in INDO/S, as explained above. The calculated spectrum using the effective Hamiltonian is given in Figure 4 with the scale factor equal to 0.5. There are two low-lying multiple chromophore states with large, almost perpendicular transition moments. The lowest state has large components on PA, PB, and BB (Table 2). The second lowest state has large components particularly on the B-side. An important reason for the width of the Qy band is inhomogeneity. The highest state has mainly BA character since the vinyl group in BA is turned almost perpendicular to the molecular plane. Interestingly the peripheral AA and AB chlorophylls also have high energies, for the same reason. Still the energy variation between the Qy states is small, and therefore the distribution of excitations on all cofactors possible is at room temperature.52 C. HOMO and LUMO Energies. HOMO and LUMO energies are given in Table 3. Generally the variation among them is larger than that between excitation energies. There is a substantial change when the nearby phytyl chain is included in the calculation (middle column, Table 3). If the positive charge of TyrD is included, then even larger changes are obtained,

Figure 4. Calculated spectrum of PSII, including the two peripheral chl a (see text for explanation). The scale factor is 0.5. The full width at half-maximum is 5 cm-1 for sticks and 130 cm-1 for the broadened spectrum.

TABLE 3: Calculated HOMO and LUMO Energies (eV) for Different Sizes of Systemsa system 1

2

3

cofactor -HOMO -LUMO -HOMO -LUMO -HOMO -LUMO PA PB BA BB HA HB Bb Hb

5.045 5.014 5.062 5.084 5.130 5.199 5.035 5.117

2.587 2.577 2.570 2.631 2.572 2.648 2.576 2.587

5.003 5.123 5.140 5.157

2.529 2.686 2.585 2.612

5.805 6.115 5.728 5.861 5.599 5.766

3.343 3.694 3.245 3.403 3.040 3.213

a The system 1 structure has been optimized using as a constraint the orientation of the vinyl group and methoxy-carbonyl group of ring V. In system 2 the closest phytyl chain is included. System 3 includes a positive charge on TyrD. b Optimization without constraints.

depending on how close the chromophore is to TyrD (right column, Table 3). In principle, oxidation potentials for the positive ions can be obtained from HOMO energies, while energies of chargetransfer states can be obtained from HOMO-LUMO energy differences, using the Born approximation (see the next section). Unfortunately, accurate calculation of oxidation potentials is not possible with methods known to us at the present. The main problem is that even if a very large part of the protein around the chromophore is included there will still remain long distance effects due to charges. The lowest HOMO energy of Table 3

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Figure 5. Linear dichroism spectrum. The same parameters are used as in Figure 4.

should give a hint as to which positive cofactor ion is the most stable one. In any case the hole may transfer within the RC before TyrZ is oxidized. The time for ET between two cofactors should be in the picosecond range, judging from our experience from bacterial RCs. It is thus possible that an initial hole on, for example, BA is filled from the HOMO on PA. In the presence of TyrD+ it seems from Table 3 that PB has the highest oxidation potential, and thus PB always keeps its electron. D. Linear Dichroism Spectrum. Germano et al.36,37 compared linear dichroism (LD) spectra of natural PSII RC to spectra where the pheophytins HA or HB are selectively changed to 131-hydroxy-131-deoxo pheophytin. We use the expression f(1 - 3 cos2 θ) for the LD, where f is the oscillator strength relative to the chlorophyll molecule and θ is the angle between the transition moment µ of the monomer state and the pseudoC2 axis. This expression for LD is taken from earlier studies.51,53 The calculated LD spectrum gives us the transition moment orientation of the Qy band relative to the membrane plane (or C2 axis perpendicular to it). Transitions oriented at an angle smaller than 54.7° with respect to the normal to the membrane plane have negative LD and vice versa. Figure 5 shows a positive band on the red side and a negative band on the blue side, and this is in agreement with the experimental spectrum.37 The shoulder of the negative band corresponds to the excitonic state with a large contribution from HB. The modeled intensity decreases if we account for the fact that the extinction coefficient for pheophytin is lower in protein than that in solution.37 The positive peak on the blue side belongs to BA. In the experimental spectrum the BA peak appears to be hidden behind the negative LD peak that arises mainly from peripheral AA and AB. This hints that the BA* state is calculated at a slightly too high energy. IV. Discussion A. Qy Absorption Energy of the Monomers. It is clear from our calculations that the side group orientations, the presence of axial ligands, and to a lesser extent the presence of charges in the environment affect the energy and composition of the Qy exciton states of the RC. A full understanding of the absorption spectrum of PSII, and therefore also the subsequent charge separation, is thus possible only with knowledge of the refined structure.2 The calculated difference in site energy between the lowest and the highest is 14 nm. The experimental width is 17 nm at 6 K.36 We have identified the vinyl side group of ring I

Ivashin and Larsson as the main cause of the inhomogeneity. BA and the peripheral pigments AA and AB have the highest excitation energy, and PB and BB the lowest. The reason is the almost perpendicular orientation of the vinyl groups of the former cofactors. What is the reason for the different orientations and how reliable are the crystallographic data for PSII? As expected there is no significant difference between the coordinate sets of the two PSII monomers.2 However, there are differences between the coordinate sets of Ferreira et al.2 and Biesiadka et al.,54 particularly for the vinyl group orientation in BB. Since the latter work4 does not give the full coordinate sets, it is not useful for us. By comparing column 2 and 3 in Table 1 we find that the phytyl group is not of any direct importance to the spectrum but interacts via spatial constraints and to some extent π-interactions with the vinyl group. Also in other parts the coordinate set of Ferreira et al. looks convincing and acceptable as a basis for our studies. Direct evidence for the correctness of our assignment of the blue absorption to AA and AB may be obtained from spectra where one of these peripheral chl’s is missing.55,56 Clearly in the latter case absorption is missing at the blue end of the Qy spectrum, consistent with the data in Tables 1 and 2. The vinyl group orientations thus lead to asymmetry in the Qy absorption that may be important for the efficiency of PSII. It appears likely that evolution selected efficient photosystems by optimizing the orientation of the side groups in the protein. At first sight this asymmetry seems strange since charge separation appears to take place from the blue side of the Qy band while for bacterial RCs it is the opposite way. B. Main Features of the RC Qy Spectrum. Although there are very significant inhomogeneities, our results show that the excited singlet states are delocalized on several chl and pheo molecules of RC, except the peripheral cofactors, which are monomeric. This agrees in general terms with the conclusions from other sources, including site-selected fluorescence spectroscopy. It is clear from Table 2 that there is no dimeric “special pair” state at low energy as is the case in bacterial RCs. Remarkably the new coordinates2 show that the center-to-center distance between the magnesium ions is only slightly longer (0.15 Å) than the corresponding distance in bacterial RCs. (However, the distance between the chl planes is significantly longer in PSII.) The appearance of two delocalized states at low energy with high intensity and with approximately perpendicular transition moments agrees well with time-dependent anisotropy data.57 The lowest states are localized mainly on the B-side (Table 2) and contain rather little HA character. Small components of HA and HB agree with an estimation from the small intensity of a characteristic mode in the line-narrowed emission spectra of PSII.15 Konermann and Holzwarth described the Qy spectrum on the basis of weakly interacting monomer energies (with the exception of the P-dimer)32 and obtained delocalized Franck-Condon states despite weak coupling. Delocalization should be even greater with adequate interaction matrix elements. It is possible though that some localization occurs soon after excitation. There are good reasons for disagreement between our data and some experimental or theoretical results. The most obvious reason is that most previous calculations of the spectrum assume equal site energies. An exception is a paper of Raszewski et al. where the best possible attempt at the time was made to employ inhomogeneities known from the literature.21 Unfortunately the data used were based on assignments that now appear doubtful, perhaps due to incorrect interpretation of electrochromic shifts (see below). The varying orientations of the vinyl groups in

Excitonic States in PSII RC the new crystallographic coordinates2 provide a new source of information that, of course, was absent in earlier calculations. We have to keep in mind that the composition of the excited states in the Qy manifold given in Table 3 refers to FranckCondon states (with the ground-state geometry). After excitation there will be some relaxation of the geometry. For example, in an excited state with a large component of PA or PB the distance between the two chromophores may change. Within single chl or pheo molecules the bond lengths between atoms C, N, or O may change slightly. The orientation of the vinyl group may change. As a result the composition of the excited states changes, very likely toward a greater localization. This is particularly important for almost degenerate states and if the coupling is low (triplet states). Therefore the equilibrated states may have a rather different composition compared to that given in Table 2. Looking at the two lowest states, it is not unlikely that the two already rather close PA or PB cofactors form a sort of exciplex state, while the almost degenerate state becomes exclusively localized on the inactive B-side. The latter state would not be involved in fast ET since it is far from HA.26 The experiments of Peterman et al.15 were carried out at 5 K, when the charge separation rate is very small. In the absence of quenching mechanisms, the fluorescence rate from the trap state is high at a low temperature. It is therefore very likely that the “trap state” is situated on BB.33,58 Our result that HA does not contribute on the red side is supported by the high-resolution emission data of Peterman et al.15 and the site-selection data by Konermann et al.59 The results from a comparison between intact and RC preparations where one of the peripheral chromophores is missing support our assignment of the blue part of the spectrum.60 From our results it is not completely excluded, however, that the trap state is localized on PB. The difference in the localization of the vinyl group is too small to make it possible to say for sure which of BB* or PB* has the lowest energy. In a calculation of the spectrum of PSI, including its antenna system, Damjanovic´ et al.61 used a methodology similar to ours. Thus the couplings were calculated using the INDO/S method as well as with the Fo¨rster model (using n ) 1). The spin factor of 2 was left out from the coupling as is appropriate if F2 ) n2 ) 1 is used. Thereby the calculated couplings should be rather similar to ours. In fact the detailed analysis carried out by Damjanovi et al.,61 showing considerable consistency between different procedures, indicates that also our methodology is reliable. An important difference between our methods is that we optimized the ground-state structures before the spectrum was calculated, with conserved side groups. This procedure improves considerably our geometries compared to the crystallographic coordinates, which are probably obtained using less perfect quantum chemical methods. If the crystallographic structure is not reoptimized, then the trends in the spectrum, for example, due to the vinyl group orientation, are wiped out almost completely. Provided of course that the latter group is correctly given in the crystallographic raw data for PSII, we are convinced that our results are reliable even if the degree of resolution is still low. C. Triplet Spectrum. The lowest triplet state was calculated in the optimized geometry with conserved side group orientation, using the DFT method (Table 5). The triplet energies correlate well with the energies of the lowest singlet excited state calculated using TD/DFT. Hence the two lowest triplet states are also located on the inactive B-side within 100 cm-1. The BA* triplet is about 250 cm-1 higher than the lowest triplet on the B-side.

J. Phys. Chem. B, Vol. 109, No. 48, 2005 23057 TABLE 4: Calculated Wavelength (λ) of the First Excited (Qy) State Using the TD/DFT Method on Structures Optimized with Vinyl and Ether Group Dihedral Angles Frozen Using DFT B3LYPa system cofactor

1

2

3

4

PA PB BA BB HA HB

568.1 572.6 558.8 570.1 562.4 565.1

568.4 572.6 559.0 570.1 562.2 565.2

568.3 574.0 559.6 569.8 562.5 565.3

569.5 571.9 559.5 570.0 565.2

5 581.4b 560.4 573.1 562.8 565.8

a

System 1 has no charges; in system 2 QA is reduced; in system 3 TyrD is oxidized; in system 4 HA is reduced; in system 5 PA is oxidized. In all cases a charge is put in the center of the molecule, and the spectrum of the respective chlorophyll is recalculated in the presence of this charge. b This result is without significance (see text for explanation).

TABLE 5: Calculated Triplet State Vertical Excitation Energy

a

cofactor

∆ (eV)

PA PB BA BB HA HB chla pheoa

1.509 1.493 1.524 1.505 1.547 1.552 1.508 1.542

Without constraints.

In charge recombination experiments an EPR-detectable triplet, excitation is formed that may transfer subsequently to a neighboring cofactor by the Dexter mechanism.49 It has been shown that the π macrocycle of the triplet state is oriented 30° toward the membrane plane, which means that it has to be on BA or BB.4,5,8 The most popular idea is that the triplet is on the BA side, but the evidence is not convincing and is in conflict with our results. Furthermore, on purely experimental grounds one concludes that the singlet trap state is located on the B-side.33 It is generally expected that the lowest singlet state and the lowest triplet state are localized on the same chromophore. There is also other evidence that this is the case.15 Noguchi et al. have used Fourier transform IR spectroscopy and later time-resolved infrared spectroscopy to study formation, transfer, and decay processes where the triplet state is involved.8 Their conclusion, consistent with EPR work, is that the triplet is localized to one of the accessory chl a’s, probably BA. One argument for BA and not BB is based on the spectral indication of a hydrogen bond. Comparison to bacterial RC made it likely that this hydrogen bond was on the A-side. In fact the new crystallographic data2 shows that it is on the B-side. If charge separation occurs from BA*, then BA+ is created and may survive for some time. Charge recombination may therefore lead to an initial triplet state on BA. The triplet decay rate increases considerably if QA is negatively charged, and this fact has been used to support the appearance of the triplet state on BA.8 We may therefore suggest that the triplet lifetime on BA is quite long in any case, particularly since the state energy is only 250 cm-1 above the lowest triplet state. In any case our results do not support that 3BA* is the lowest energy excited state. Another argument that appears to support the triplet on BA idea is that the slow triplet decay rate speeds up in the presence of oxygen, due to the formation of singlet oxygen.62,63 This

23058 J. Phys. Chem. B, Vol. 109, No. 48, 2005 would make it likely that the triplet is on the A-side where there is no quenching by carotenes.62 The reason for the absence of carotenes on the A-side is to avoid the oxidation of carotenes that competes with the oxidation of water. Carotenes have to be absent within a certain radius (maybe 20 Å) from the hole state on the A-side. However, there appears to be evidence that the carotenes are not forming triplet states on the B-side.64-66 Hence the carotenes present there may be too distant there too for the Dexter mechanism to work. In fact this hints that the role of the carotenes may be to quench singlet oxygen.65 The increased triplet decay rate in the presence of oxygen62 does not necessarily mean that the carotenes and triplet are on different sides. We conclude that the triplet formed after charge recombination may well be localized on the B-side, consistent with our results. Since large amounts of oxygen are evolved near the A-side under natural conditions, the presence of triplets there would be very destructive. There are three Met side groups67 present in the vicinity of BA but not in corresponding positions of BB.68 These groups are known to quench singlet oxygen but are destroyed at the same time themselves.69 BB therefore seems to be more resistant against singlet oxygen than BA. The lower triplet energy on the B-side may hence be an efficient way to remove part of the danger from the active side and place the source of possible singlet oxygen closer to the singlet oxygen quenchers, the carotenes. D. Electrochromic Shifts. As we have seen there are different opinions on the assignment of the experimental spectrum. It has been suggested that the red part of the absorption is mainly composed of HA absorption. The shift of the spectrum when QA is reduced is mainly at the red edge.23-25 It was argued that since HA is the chromophore closest to QA the affected part of the spectrum should be due mainly to HA. We decided to investigate this hypothesis. The monomer spectrum was calculated when a charge is placed on the center position of other groups. In this way we simulated prereduction of QA and HA and preoxidation of TyrD and PA. We used the TD/DFT method for a single chromophore, but the results are consistent with the results of Hanson et al.70 The result is given in Table 4. The changes are quite small except the change of the PB spectrum when a positive charge is placed on PA. In the latter case we see a red shift of the PB spectrum. Modeling PA+ with just a positive charge is too simplified in this case, however, due to orbital interactions between the two chromophores. In the present case the hole in fact appears distributed on both PA and PB in agreement with experimental data.71 In an improved treatment we therefore included both chromophores in an INDO calculation of (PBPA)+. We now see a blue shift instead of the red shift and also a decrease of the intensity of the Qy absorption of the positive ion. This agrees qualitatively with the experimental difference spectrum for the PSII RC core system.10 We may draw two conclusions. (1) The blue shift in the red in the Qy spectrum for PSII is not due to an electrochromic shift of the BA part of the spectrum but due to changes in the spectrum of PAPB when this dimer is ionized. This means that the results by Diner et al.10 cannot be used to conclude that the BA part of the spectrum is at the red side. (2) The point charge model works if the point charge is at a sufficiently large distance to neglect orbital interactions and delocalizations between the chromophores. In bacterial RC it apparently “works” to predict the blue shift in BA if there is a positive charge on PA. The results of Hanson et al. are the same as ours. However, if we apply the same model in the case of PSII, there is a red shift for the BA component.

Ivashin and Larsson Since there is a red shift also for PB, the point charge model predicts a red shift when the experimental shift is a blue shift. As we have seen above, a better model predicts the correct shift also for PSII. In the case of a negative charge on QA the changes are very small, although screening is not included. The calculations show that the shift is larger for PA and BA than that for HA, and this is in accordance with mutual arrangement of charge and difference in dipole moment between the ground state and the excited state. Therefore the assumption that only Qy of HA is affected is incorrect. Furthermore other experimental data suggest that the HA* character contributes very little to the lowest Qy states.15,58 Considering the change in the Qx transition of HA, the calculated shift is 57 cm-1, and the experimental shift is 6080 cm-1, and thus there is a quite good agreement with the experiments.25 The predicted shift for the Qy transition is also in the blue direction but an order of magnitude less. This also agrees reasonably well with the results of A° rsko¨ld et al.25 However, in our calculation, HA is not at the red end of the Qy band. Possibly a large part of the experimental shift is due to the antenna system. E. Charge Separation. A remaining problem is to find a structural reason for the asymmetry in charge transfer between the active (A) and passive (B) branches. In what way does the orientation of the vinyl group influence the redox properties? We know that the LUMO energy is lowered if the vinyl group is parallel to the plane, due to the increased size of the π-system. This means increased probability for BB to be negatively charged, which goes against the accepted understanding of the photosynthetic mechanism. A preliminary inspection of Table 3, column 1, shows that the LUMO of HB (-2.648 eV) is lower than that of BB (-2.631 eV) by 0.017 eV, while the LUMO of HA (-2.572 eV) is lower than that of BA (-2.570 eV) by 0.002 eV. These differences are too small to be significant, as becomes clear if we examine column 2 of Table 3 and compare to the LUMO energies when the nearby phytyl chains are included in the calculation. The LUMO energy of HB (-2.612 eV) is higher than that of BB (-2.686 eV) by 0.074 eV, while the LUMO energy of HA (-2.585 eV) is lower than that of BA (-2.529 eV) by 0.056 eV. These differences are large and probably significant and show that the final ET step from the accessory chl to pheo is much more likely on the A-side than on the B-side. HOMO and LUMO energies depend very much on environmental effects, and this makes predictions very hard. Generally the energy of a charge-transfer state tends to be higher than the energies of the lowest locally excited Qy states. The charge-transfer energy increases with the distance between the chromophores. The distance difference in the antenna system should be unfavorable for charge separation (CS), while the slightly smaller distances in the RC gives CS at about the same energies as the Qy states (for  ) n2). After solvent relaxation the charge-transfer states are stabilized ( ) s). To obtain a rough idea about the energy of charge-separated states X+Y-, we have to take the ionization energy of X and subtract the electron affinity of Y. These energies are much higher than the excitonic energies. There are corrections for the Coulomb attraction of the ion radical pair at the actual distance between the chromophores (R) as well as for the reaction field. Using the Born equation (for two charges, +1 au and -1 au), we obtain for the free energy

∆G ) I - A -

(eV) [a1(1 - 1) + R1 ]27.21 1.89

(12)

Excitonic States in PSII RC where  is a dielectric constant for the medium in which the chromophores are immersed. The distance between the centers is given in Å. a is the radius of a polarization sphere around the chl molecule. ∆G is in electronvolts if a and R are in Å. Disregarding problems with DFT, eq 12 is physically correct but very approximate. As we have seen a large part of the environment has to be included to get an accurate value of I A. It is not possible to define a dielectric constant for a protein. Finally the electron affinity is highly dependent on how much of the environment is included. For example, the positive charge on TyrD is considerably closer to PB than to BB. Therefore ET to BB is more difficult. Accurate calculation requires that a very large part of the system is included. Our results may be compared to the experimental results of Groot et al.33 using time-resolved transient spectroscopy and with excitation in the red side of the Qy band. They find an X-state at higher energy than the lowest Qy state (which contains a large PA component) responsible for fast charge separation. The average lifetime decreases from 2.6 ps at 20 K to 0.4 ps at 240 K. Since this charge separation is activated, it may correspond to activation of the BA* state, with ensuing fast charge separation. Groot et al.33 also found a slower charge separation process corresponding to a trap state. This trap state can hardly be any other state than the lowest energy Qy state. F. Simulation of Spectrum. The spectrum of Figure 4 is based on “raw” data, calculated as described above. The agreement with the experimental spectrum is far from perfect. This is expected since there are errors in the theoretical method and in the crystallographic data and due to the fact that only a part of the system can be included in the calculations. Some shortcomings are quite obvious. An interesting question is whether the experimental spectrum can be reproduced with the help of a few modifications. The first problem is that the calculated transition energies are too high compared to the experimental values. This is a traditional problem when the variation principle is applied to spectral properties and the basis set is incomplete. Experimental data only exist for solution spectra. To obtain consistent corrections we first calculate the difference (∆ν) between the Qy frequency for the chromophore with the structure found in the protein and the Qy frequency for the free chromophore. The solution (ether) transition frequencies (15 163.3 cm-1 for chl and 15 000.9 cm-1 for pheo) were subsequently multiplied by (1+ ∆ν/ν) to obtain a protein spectrum consistent with the solution spectrum. The “inhomogeneities” obtained may now be directly compared to the Qy spectrum. The Qy spectrum is recalculated using the coupling calculated earlier and the same scale factor F1/F2 ) 0.5. The calculated width turns out to be too large compared to the experimental spectrum. In this situation we noticed in corresponding INDO/S calculations that when a large part of the protein was included in the calculation the value of ∆ν tended to decrease. In particular inclusion of the axial ligand decreased ∆ν. When more possible sources of inhomogeneity are included, the general tendency is a small decrease of ∆ν compared to including just a few side groups (particularly the vinyl group). We therefore decided to correct the solution spectrum with the inhomogeneity factor (1 + 0.7∆ν/ν) instead of (1 + ∆ν/ν) combined with a different scale factor. The result of the new simulation fits the experimental spectrum well (Figure 6).37 There are practically no changes in the composition of the lowest Qy state. HA* and HB* are the main contributors to the next two states. The second state is still predominantly localized on the B-side. The high energy of

J. Phys. Chem. B, Vol. 109, No. 48, 2005 23059

Figure 6. Simulated spectrum (see text for explanation). The same parameters as in Figure 4 (s), with HB replaced by 131-hydroxy-131deoxo pheophytin (- - -), and with HA replaced by 131-hydroxy-131deoxo pheophytin (‚‚‚).

BA* was also conserved. In summary no results were obtained that forced us to change our conclusions. In Figure 6 we have also included the result of a calculation where HA or HB has been replaced by 131-hydroxy-131-deoxo pheophytin. The spectral changes agree well with the experimental spectra.37 V. Conclusion Using the coordinates recently determined for PSII2 we calculated the exciton spectrum for RC. As suggested by Fajer,72 the side group orientations of the chl and pheo molecules are very important as a source of inhomogeneities in the spectrum. Our calculations confirm the general result of the MM model that the Franck-Condon excited states of the RC are distributed on several chl and pheo molecules. The agreement with the experimental spectrum is satisfactory. BA* is found at a higher energy than BB*. This is consistent with at least one earlier simulation.32 It also agrees with the existence of a trap state,33 which is easier to explain if it is localized on the inactive side. The higher energy of BA* has been connected to the perpendicular orientation of the vinyl group. The energy of BA* is still low enough to permit a quite large Boltzmann population at 300 K. There is no structural difference between the pheo molecules HA and HB that suggest a lower energy for HA- than that for HB-. At this time a remaining possibility for explaining the mechanism of fast charge separation in PSII at elevated temperatures is that BA* is the only excited chromophore that is high enough in energy to perform efficient charge separation to HA. Acknowledgment. We are grateful for support from Vetenskapsrådet and the Royal Academy of Science. References and Notes (1) Zouni, A.; Witt, H. T.; Kerry, J.; Fromme, P.; Krauss, N.; Saenger, W.; Orth, P. Nature 2001, 409, 739-743. (2) Ferreira, K. N.; Iverson, T. M.; Maghlaoui, K.; Barber, J.; Iwata, S. Science 2004, 303, 1831-1838. (3) Ananyev, G. M.; Sakiyan, I.; Diner, B. A.; Dismukes, G. C. Biochemistry 2002, 41, 974-980. (4) Rutherford, A. W. Biochim. Biophys. Acta 1985, 807, 189. van Mieghem, F. J. E.; Satoh, K.; Rutherford, A. W. Biochim. Biophys. Acta 1991, 1058, 379.

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