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Australia. ReceiVed: January 2, 2007; In Final Form: May 9, 2007. The Qy absorption spectrum of Photosystem-I from Thermosynecochoccus elongatus (form...
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J. Phys. Chem. B 2007, 111, 9923-9930

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Assignment of the Qy Absorption Spectrum of Photosystem-I from Thermosynechococcus elongatus Based on CAM-B3LYP Calculations at the PW91-Optimized Protein Structure Shiwei Yin,† Mats G. Dahlbom,† Peter J. Canfield,† Noel S. Hush,‡ Rika Kobayashi,§ and Jeffrey R. Reimers*,† School of Chemistry, The UniVersity of Sydney, NSW 2006, Australia, School of Molecular and Microbial Biosciences, The UniVersity of Sydney, NSW 2006, Australia, and Supercomputer Facility, The Australian National UniVersity, Canberra ACT 2600, Australia. Australia ReceiVed: January 2, 2007; In Final Form: May 9, 2007

The Qy absorption spectrum of Photosystem-I from Thermosynecochoccus elongatus (formerly Synecochoccus elongatus) is calculated using the CAM-B3LYP density functional and INDO schemes based on a quantummechanically refined structure for the entire photosystem obtained using the PW91 density functional. These methods present a priori predictions of the absorption and linear dichroism spectra and include protein electrostatic effects, short range inductive effects, long-range and short-range exciton couplings, and superexchange effects involving aromatic residues and carotenes. CAM-B3LYP is used as it is the only known density functional that correctly describes the Q bands of chlorophylls, all other methods contaminating them with erroneous charge-transfer excitations. A critical feature is found to be the use of fully optimized heavyatom coordinates, with those obtained from just X-ray crystallography providing a poor description of the electronic properties of the chromophores. The result is a realistic first-principles prediction of the observed absorption band that identifies the nature of the red-shifted chlorophylls as well as the energies of the reactioncenter chlorophylls and the exciton couplings acting between them. The “special pair” appears more like a dimer of dimers than a self-contained functional unit, with the exciton couplings between its members and the accessory chlorophylls exceeding the internal coupling.

1. Introduction Photosystem-I (PS-I) is one of the two photosynthetic systems in oxygen-evolving organisms. The two light-harvesting complexes are coupled in series in order to reach the high potential needed to split water.1 Long before any of these systems were structurally determined using modern techniques, it was known that the number of chlorophylls needed to perform the oxygen respiration was of the order of 2500, a result that ultimately leads to the idea of photosynthetic units or photosystems.2 The structure for PS-I was finally achieved at a resolution highenough to locate almost all of the heavy atoms in 2001.3 It is known that the reaction center special pair (P700) is different from the corresponding units in the other plant photosystem, photosystem-II (PS-II) and in the bacterial reaction center (BRC). P700 is a heterodimer consisting of one Chl-a and one Chl-a′ molecule, with Chl-a′ being the C13-epimer of Chl-a; these are usually denoted PB and PA, or alternatively ecB1 and ecA1, respectively. The remainder of the PS-I reaction center is comprised of the accessory chlorophylls ecA2 and ecB2 and the electron acceptors ecA3 and ecB3. PS-I is a large system by molecular standards; it is a trimer formed from monomers each containing ca. 50000 atoms involved in 12 protein chains, 96 chlorophylls, 4 lipids, 22 β-carotenes, 3 iron-sulfur clusters, and 1 calcium ion, as well as a shared putative sodium ion.3,4 Before and after the structure of PS-I was established there have * Author to whom correspondence should be addressed. E-mail: [email protected]. † School of Chemistry, The University of Sydney. ‡ School of Molecular and Microbial Biosciences, The University of Sydney. § The Australian National University.

been many studies of the function of the PS-I system by such experimental methods as FTIR spectroscopy,5-11 EPR and ENDOR,12 optical spectroscopy,15-19 as well as theoretical20-26 approaches, and many issues have been addressed. One of the main features of photosynthesis is the so-called “energy funnel” hypothesis that describes the way harvested optical energy is conveyed to the reaction center prior to primary charge separation. This hypothesis depicts the known operation of the photosynthetic apparatus in BRCs and could possibly form a general mechanism for the operation of all naturally occurring photosystems.1 In BRCs, the special pair dimer absorbs light at lower energy than does any other chromophore, and the flow of energy from any chlorophyll or pigment in the antenna or charge-separation units to the special pair is thus an exothermic process that is thought to “funnel” the energy to the special pair. This hypothesis seems not to be sufficient to explain the operation of PS-I, however, since for it spectroscopic studies have unambiguously shown that some pigments absorb at lower energy than the special pair (ca. 1.77 eV or 700 nm), with the observed absorption spectrum showing a significant “red tail” of absorption at low energies down to 1.70 eV. As a result, uphill energy transport is required in order that charge carriers are produced once light energy is either adsorbed by, or transferred to, the red-tail absorbers. There is, however, no consensus regarding the number of red-shifted chlorophylls and their identity or species variation. Many studies have investigated energy transport in PS-I, considering whether or not it is stochastic in nature as well as focusing on the identification of the red pigments.18,23,24,27 There are convincing experimental findings, however, that these red pigments are not part of the

10.1021/jp070030p CCC: $37.00 © 2007 American Chemical Society Published on Web 08/02/2007

9924 J. Phys. Chem. B, Vol. 111, No. 33, 2007 inner antenna closest to the reaction center, which then suggest that they are somewhere on the outer perimeter of the photocenter.17 The availability of a quality atomically resolved X-ray structure3 for PS-I from Thermosynecochoccus elongatus (formerly28 Synecochoccus elongatus) allows for the use of computational methods to estimate the absorption energies of each chromophore in the system as well as the interactions acting between the chromophores. Such data may be used to predict the absorption spectrum, hence determining the absorption energy of the special pair and the identity of the molecules that form the red tail, as well as allowing for calculations of the energy-transport dynamics of the system. In this work, we evaluate the energies and couplings but focus on the first of these aspects only: the assignment of the absorption spectrum. Several previous studies21,22,24,27 have similarly modeled the absorption spectrum using the available X-ray coordinates of the heavy atoms. However, the molecular mechanics methods used in X-ray structure refinement to add high-resolution (i.e., on the 0.01 Å scale) information to the raw experimental results work very well for protein chains but lead to distorted structures for chlorophylls and other chromophores.4,29 As calculated properties such as energies and couplings are very sensitive to high-resolution structural information, more reliable means of calculating the properties of the chromophores are required. Cyanobacerial PS-I exists typically as a trimeric unit, and we have recently performed a global optimization4 of the entire trimeric PS-I structure using state-of-the-art density functional theory (DFT) techniques in a linear-scaling implementation utilizing the ONIOM method via Gaussian 03,30 with all key short-range structural properties obtained using the PW91 density functional.31 This approach provides an accurate depiction of the high-resolution structural information for all aspects of the photosystem, including the chlorophyll and carotenoid chromophores. In addition to such significant quantitative improvements, the optimization procedure also isolated a variety of qualitatively inaccurate features in the original structure, the most relevant of which is an incorrect description of the Chl-a′ molecule PA. Although this molecule is clearly identified as being Chl-a′, the X-ray coordinates were inadvertently fitted to a model for Chl-a. As a result, all previous calculations for the properties of PA using the X-ray heavy-atom coordinates have yielded extremely poor results, rendering impossible the identification and understanding of the special pair and its function. Other enhancements to the X-ray structure include the identification of residues that mutated between gene sequencing and structural determination, the identification of the nature of the junction between the three strands of the trimer, and improvements to the Ramachandran plots describing protein torsional angles in atypical regions of the protein.4 Our calculations evaluate both the energy of each chromophore in situ but neglecting the interactions with the other chromophores, as well as the interactions between all chromophores. Previously, Damjanovic et al.23,24 have used the intermediate neglect of differential overlap32 (INDO) method to estimate these same properties. INDO provides an efficient semiempirical computational scheme that is in fact specifically designed to make predictions of this type. Other approaches have concentrated on evaluation of the interactions, known as exciton couplings, using the Fo¨rster point-dipole approximation24,26,27,33 and its generalized extended-dipole variant.24,27 The point-dipole approximation is known to be inadequate as the

Yin et al. size of the chlorophyll molecules, molecules that are represented as point dipoles in the model, is large compared to the separations between the molecules, but the INDO and extendeddipole methods are known to be effective in the description of BRC photophysical processes.34 In this work, we reconsider INDO, Fo¨rster point dipole, and generalized Fo¨rster methods, and in addition, we also consider application of DFT-based methods. DFT methods are firstprinciples-based approaches that require the specification of the (approximate) density-functional to be used. In general, they are more accurate than INDO but suffer from systematic problems regarding the treatment of charge-transfer absorption bands such as the N bands of chlorophylls and porphyrins.35,36 Although this, in principle, is not a problem as we are concerned herein only with the properties of the low-energy Qy band, in practice, application of DFT is hindered as it incorrectly places N bands in the vicinity of Qy, making difficult interpretation of the calculated results. However, a new density functional, CAM-B3LYP,37 has been developed that corrects for this otherwise general failure of modern DFT functionals;38 we apply this method to predict the energies of the chromophores and the key couplings that act between all close-lying chlorophylls. 2. Methods A. Effective Exciton Hamiltonian for PS-I. As the observed energy gap between the lowest-energy singlet excited-state of chlorophylls, Qy, and the second lowest excited state, Qx, is much larger than the observed width of the Qy band, we only consider the Qy band in this work. Also, as no chlorophyll in one of the trimeric PS-I units interacts with more than one trimeric replica of any particular chlorophyll, we introduce an effective-monomer model for the interactions. All interactions with non-chlorophyll chromophores are either ignored or treated implicitly through the use of effective chlorophyll-chlorophyll exciton coupling parameters. These approximations allow the energetics of PS-I excited states to be described in terms of a Hamiltonian H containing 96 basis states |i〉 depicting single Qy excitation on chlorophyll i. The diagonal elements of this matrix are exciton site energies Ei and off-diagonal elements are exciton couplings Hij. B. Electronic Structure Calculations. INDO/S calculations32 are performed using our own package,39 whereas CAMB3LYP37 calculations are performed using the development version of Gaussian 03.40 Most calculations are performed at the DFT optimized structure of the PS-I trimer,4 though some are also performed with their heavy atoms constrained at the trimer X-ray coordinates3 for comparison. Only exciton couplings acting between chromophores whose closest Mg-Mg separations are less than 20 Å are explicitly calculated. The phytyl chains of the Chl molecules are replaced with methyl groups in all calculations. C. Exciton Couplings from Fo1 rster Coupling Models. In these approaches, the site energies Ei are taken from the electronic structure calculations, whereas the couplings Hij are evaluated using41

Hij )

µi‚µj - 3(µi‚Rij)(µj‚Rij) 4π0|Rij|3

(1)

where µi is the calculated transition dipole moment vector of the Qy band of the ith molecule and Rij is the vector between the magnesium atoms of the two Chls. Also, in a generalized transition-charge approach, the coupling is written as a sum over

PS-I Absorption Spectrum

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[ ][

the Qy transition charges q located on atoms R of molecule i and β of molecule j as34

Hij )

qRqβ

∑ Rβ 4π |R 0

Rβ|

(2)

Hjk )

-

∑

i *j,k

S′ H S′ ji H ik S′ S′ (H S′ jj + H kk)/2 - H ii

]

using 1/0 1/0 1/0 i ) 〈φi |Hi|φi 〉

D. Energies and Exciton Couplings from the INDO Calculations. The site energies from the INDO calculations are taken as either the energies of the monomers evaluated in the absence of their environment or those evaluated in the presence of the external electric field emanating from the remainder of PS-I. This external field is obtained from AMBER charges for the protein residues combined with charges obtained from analysis of the electrostatic potential calculated for all other moieties,4 using a dielectric constant of  ) 2 to model the fast dielectric relaxation processes of the environment;42 all of the atomic charges used have been previously published.4 The exciton couplings are evaluated using model systems comprising the two Chls of interest as well as all non-chlorophyll chromophores containing delocalized π electrons located within 10 Å of any atom within these two Chls. First, the HartreeFock orbitals for each supramolecular system are determined and then localized to each chromophore by rotation within the occupied and virtual orbital manifolds (such a procedure creates a slightly incomplete localization but does not affect the calculated transition energies). The single-excitation manifold is then constructed and partitioned into excitations representing localized excitations on each chromophore as well as chargetransfer excitations between chromophores. The blocks of the single-excitation matrix HS representing localized excitations are then diagonalized, exposing vectors j and k corresponding to the two Chl Qy transitions, etc. The entire coupling matrix is then transformed into the basis of these localized-excitation vectors, producing the state interaction matrix HS′. The matrix element HS′ jk thus represents the through-space exciton coupling (complete with all terms including both the Fo¨rster and Dexter contributions) between the localized Qy transitions on each chromophore. The superexchange effects of nearby non-Chl chromophores on enhancing this exciton coupling is then included through the Larsson decomposition43

HS′ jk

H H 1 + 0j + Vi′j Hij Hd ) Hii Hij ) i Hji 0i + 1j + Vij′ ji jj

(3)

Significant technical issues arise during this procedure owing to the arbitrary nature of the phase of the molecular-orbital and configuration-interaction wavefunctions produced, with the result that different phasing for each chlorophyll may be produced in the various independent dimer calculations performed. To ensure that all calculated exciton couplings adhere to the same sign convention, reference molecular orbitals and excited-state wavefunctions are determined for each monomer. In each dimer calculation, all phases are then set to match this definition. E. Energies and Exciton Couplings from the CAM-B3LYP Calculations. The required properties are extracted by performing calculations for the isolated monomers, these monomers in the external electric field originating from neglected pairs of PS-I (see previous subsection) and from calculations containing pairs of chlorophyll molecules. Following Fo¨rster, the excitoncoupling hamiltonians for the dimers Hd are expressed as41

Vi′j ) 〈φi1φj0|V|φi1φj0〉, Vij′ ) 〈φi0φj1|V|φi0φj1〉 Hij ) 〈φi1φj0|V|φi0φj1〉, Hji ) 〈φi0φj1|V|φi1φj0〉

(4)

where φ1/0 and 1/0 indicate excited and ground state wavei i functions and energies, respectively, for the ith chlorophyll monomer, Vi′j indicates the Coulombic interaction between the excited-state of the i-th Chl and the ground state of the jth Chl, and Hij is the exciton coupling. This dimer Hamiltonian can be diagonalized by the rotation matrix C

C)

[

cos θ -sin θ sin θ cos θ

]

(5)

expressed in terms of the basis-vector rotation angle θ, leading to

tan 2θ )

2Hij Hii - Hjj

(6)

and

W1/2 )

Hii + Hjj Hij ( 2 sin 2θ

(7)

where W1/2 are the two eigenvalues of dimer Hamiltonian, equated to the two calculated Qy transition energies from the CAM-B3LYP calculations. We assume that the transitionmoment polarizability is small so that the transition moment vectors of the dimer µ1 and µ2 can be written in terms of transition moment vectors µi and µj of the monomers rotated as

[] [][

][ ]

µ1 µi cos θ -sin θ µi ) C ) µ2 µj µj sinθ cos θ

(8)

Obtaining the best fit of the CAM-B3LYP dimer transition moments to the rotated CAM-B3LYP isolated monomer moments yields θ from eq 6 andVi′j and Vij′ from eqs 7 and 4. Once all dimer calculations are complete, the final Chl site energy for Chl i is determined using

Ei ) 1i - 0i +

Vi′j ∑ j*i

(9)

F. Linear Dichroism Calculations. Linear dichroism spectra depicting the difference in absorption A⊥ perpendicular to the membrane normal (ie., the C3 axis of the trimer) and parallel to it A|

1 LD ) A⊥ - A| 2

(10)

are evaluated from the calculated transition moments. 3. Results A. Simulated Spectra. The site energies and exciton couplings evaluated by the various computational methods are given in full in Supporting Information, while simulated spectra

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Yin et al.

Figure 1. Comparison of the observed Qy absorption spectrum of PS-I from Thermosynechococcus elongatus at 4 K33 with calculated spectra: (a) INDO calculations for isolated Chl monomers at their X-ray3 and optimized4 geometries, as well as after treatment of exciton coupling without (dimers only) and with (full) inclusion of superexchange, (b) CAM-B3LYP calculations of isolated molecules at their X-ray3 and optimized4 geometries, with corrections for the external protein electric field only as well as all environmental effects, and (c) CAM-B3LYP calculations including exciton coupling obtained using a Fo¨rster treatment, explicit short-range computation, and this plus long-range Fo¨rster contributions.

based on this data are compared in Figure 1 to the observed spectrum33 of PS-I at 4 K. The calculated spectra are broadened using a Gaussian window to model inhomogeneous broadening effects using

A(ν) )

ν 2xπσ

96

Mi ∑ i)1

2

[

exp -

]

(hν - Ei - ∆E)2 2σ

2

(11)

where σ is the standard deviation of the Gaussian, ∆E is a small frequency shift used to align the calculated and observed band energies, and Ei and Mi are the energy and transition moment, respectively, of the ith eigenvector of the exciton-coupling Hamiltonian H. The value of the shifts used are ∆E ) 0.065 eV for INDO and -0.285 eV for CAM-B3LYP, values compatible with the absolute errors expected in calculated band transition energies. The broadening used is σ ) 0.012 eV for CAM-B3LYP and 0.010 eV for INDO. The calculated spectra shown in Figure 1 include the total spectra obtained using the full calculation method as well as spectra obtained using specific aspects only. For example, Figure 1a provides the full INDO simulation at the optimized protein geometry4 plus that obtained using the monomer energy distribution Ei only (i.e., ignoring the local field effects as well as the exciton couplings Hij) plus that obtained using the original X-ray heavy-atom coordinates. Also, Figure 1b shows CAM-

B3LYP results obtained using only the monomer contributions by various treatments of the local environment, whereas Figure 1c adds to this various treatments of the exciton coupling. The first feature of note from Figure 1 is that at the X-ray structure the Qy transition energies of the isolated monomers are overestimated by on average 0.1 eV, according to the predictions of both computational methods. In addition to this shift, the relative chlorophyll transition energies change significantly within the bands, making the X-ray coordinates unsuitable for investigation of the roles and nature of individual chlorophylls. In particular, the lowest-energy chromophore at the X-ray structure is the Chl-a′ molecule ecA1, whereas after optimization, this absorption moves toward the band center. Overall, the monomeric Qy bandwidth contracts by ca. 20% after optimization of the Chl coordinates. Figure 1 also shows the results of addition of environmental effects and exciton couplings to the calculated Chl Qy transition energies. As similar effects are found from both the INDO and CAM-B3LYP calculations, only the full calculation including all contributions is shown for INDO, whereas the contributions of various environmental effects and exciton-coupling approaches are detailed for CAM-B3LYP. The local electric field emanating from the protein interacts with the Qy transitions, slightly broadening the absorption band. However, a more profound effect is found to be the inductive interaction of nearby Chl molecules, an effect independent of exciton coupling that acts to lower transition energies by ca. 0.02 eV. Also, although some Chl molecules absorb at low energies, forming a “red tail” to the absorption band purely as a result of the geometric distortions that the Chl’s undergo in the protein matrix, this inductive effect results in two discernible low-energy bands. The primary effect of turning on the exciton coupling is to push the absorption of the red-shifted Chls even further to the red, and as a result, the calculated CAM-B3LYP Qy band structure closely parallels that observed. Similar results are displayed in Figure 1c for all of the methods used to estimate the electron coupling: dipole couplings estimated using the Fo¨rster equation, eq 1, for all Chls, those extracted from the CAM-B3LYP Chl dimer calculations for all dimers separated by less than 20 Å, and those obtained using the CAM-B3LYP results for these short-range interactions combined with the Fo¨rster values for the remainder. The similarity of these results justifies the approach taken in not explicitly evaluating the very long-range exciton couplings. Also, Figure 1a shows the results of the INDO calculations with and without inclusion of superexchenge exciton coupling through the neighboring chromophores (carotenoids and aromatic residues). Results labeled “dimers only” neglect superexchange altogether, whereas those labeled “full” include superexchange (see eq 3) through both aromatic residues and Chls; the actual exciton couplings, including the separate effects of the aromatic residues and carotenes are provided in the Supporting Information. Although individual exciton-coupling coefficients change by up to 100 cm-1, having significant effect if the precise absorption of particular chromophores is required, the net effect on the absorption spectrum is small. The largest changes are for the interactions between Chls. A04-A03, A11A03, A14-A02, A31-A30, A34-A33, B07-A32, B13-A14, and B25-B24. B. Linear Dichroism. Calculated and observed linear dichroism (LD) spectra are shown in Figure 2. The calculated spectra are based on the 0 K optimized structure4 of PS-I, whereas the observed absorption at 4 K33 is shown along with the observed absorption and LD spectra at 295 K.27 Positive values indicate

PS-I Absorption Spectrum

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Figure 2. CAM-B3LYP and INDO calculated 0 K absorption and linear dichroism (LD) spectra for PS-I of Thermosynechococcus elongatus are compared to observed absorption spectra at 4 K33 and 295 K27 as well as observed LD spectra at 295 K.27

a predominance of absorption polarized in the membrane plane, whereas negative numbers indicate a predominance of out-ofplane absorption. As the absorption is essentially isotropic, the LD signal is quite weak and sensitive to a great many of the parameters in the exciton-coupling model, including fine details of the calculated transition moment vectors, the monomer state energies, and the exciton couplings. Parameter variations may easily induce order-of-magnitude changes in the amplitude of the calculated LD spectrum, as well as changing its sign in narrow frequency regions. Given these features, the calculated spectra provide remarkably good predictions of the observed LD spectra. Experimentally, the LD is positive and enhanced compared to the net absorption in the region of the red tail, with a maximum of ca. 10% of the total absorption strength at a frequency significantly below the absorption maximum. The observed LD also falls to just below zero for the blue tail of the observed absorption band. The LD spectra predicted by the INDO and CAM-B3LYP calculations are quite similar to each other: the calculated LD is positive over the red tail and band center, in good qualitative agreement with the observed spectrum, but instead of falling to near zero in the region of the blue tail, they fall significantly negative. Most significantly, the CAM-B3LYP calculations give quantitative agreement with the observed spectrum through the key region of the red tail and the (red-shifted) band maximum. Detailed analysis of the red-tail region is reserved for the next section where the INDO and CAM-B3LYP predictions are shown to arise from very similar origins. In this region the most significant difference is the predicted absorption frequency of the strongly LD-positive Chl. B15; Figure 2 clearly supports the CAM-B3LYP interpretation. Alternatively, the INDO and CAM-B3LYP calculations differ significantly in their description of the origins of the blue tail. In general, negative LD in the blue tail region may arise from any of the Chls. A40, B22, B34, B39, J01, L02, and M01, Chls. whose Qy absorption is polarized nearly parallel to the membrane normal. The INDO calculations strongly couple Chls. B22, B23, and B34, generating the blue tail, whereas the CAM-B3LYP monomer energies force the absorption of Chls. B39, L02, and M01 into the blue tail. It is

Figure 3. Total absorption spectrum calculated using all contributions as evaluated using CAM-B3LYP as well as some of its projections onto individual chlorophyll contributions.

hence clear that the calculations do not provide a robust description of the nature of this part of the absorption band. Adjustment of the parameters to match the observed spectra is in principle possible, but such a fitting procedure is significantly underdetermined. We note, however, that replacement of the INDO exciton coupling parameters for Chls. B22, B23, and B34 with those from CAM-B3LYP reduces the error in the blue tail by half. C. Nature of the Red Tail. Insight into the nature of the red-shifted chlorophylls is obtained from the eigenvectors of the full CAM-B3LYP exciton-coupling Hamiltonian H; key results are sketched in Figure 3, and details of the critical eigenvectors are provided in the Supporting Information, Table S3. Four low-energy states are identified, and these can be correlated with the observed red-tail spectral features at 1.73 eV (719 nm). A further seven Chls are also red-shifted further than is ecA1, and these can be associated with the absorption at 1.75 eV (710 nm) and the shoulder observed at 1.77 eV (700 nm). The six lowest-energy states predicted by CAM-B3LYP and by INDO are very similar, although their relative internal orderings vary. As mentioned previously, the most significant difference is for Chl. B15, predicted to be the most red-shifted Chl. by INDO but predicted by CAM-B3LYP to be a contributor to the 1.77 eV shoulder instead. We discuss in detail only the CAM-B3LYP results as these show excellent resemblance to the experimental absorption and LD spectra in the region of the red tail. In Figure 3, the total absorption calculated using CAMB3LYP with all terms included is shown and compared to component absorptions attributable to some key individual

9928 J. Phys. Chem. B, Vol. 111, No. 33, 2007 chlorophylls, including the 12 lowest-energy absorbing molecules and all six chlorophylls from the central reaction center. Indeed, this figure shows the component spectra for all Chls. that have in excess of 10% of their absorbance at below 1.79 eV. The red tail at 1.73 eV (719 nm) is seen to arise from exciton coupling between the B31-B32 and A32-B07 Chl pairs, whereas the higher-energy peak and shoulder arise from Chls. A03, A12, A14, A17, A27, B15, and B25. All previous methods3,21,23,24,26,27,33 that have been used to identify the red pigments have indicated A32-B7 as contributing. This feature involves the interaction of pigments in different monomers and is absent in the spectra of monomeric PS-I units. Byrdin et al.27 and Vaitekonis et al.26 using Fo¨rster-coupling calculations also identify the B31-B32 pair, though often the involvement of B33 with this pair has also been postulated. We find, as has been indicated previously by Damjanovic et al.,23,24 that the electrostatic and environmental effects are more significant than the exciton couplings in determining the nature of the red pigments, and hence differences between our results and earlier ones3,21 that did not include these effects consistently for pairs such as B31-B32 are to be expected. However, Damjanovic et al.23,24 in their thorough investigations failed to identify B31B32 but found B24-B25 and B37-B38 to be important instead. Although there are some differences between the treatments of electrostatic effects between their treatment and the current one, the predicted differences are attributed to their use of the crude X-ray heavy-atom coordinates in their calculations. When our results are compared to those obtained through fitting a large range of available spectral data by Bru¨ggemann et al.,33 the most significant difference appears to be that the A38-A39 pair that they identify is not predicted to make a prominent contribution to the red tail. D. Energy-Funnel Hypothesis. Shown also in Figure 3 are the absorption bands attributed to the reaction center Chls ecA1, ecA2, ecA3, ecB1, ecB2, and ecB3. Of these, only the absorption of the Chl-a′ molecule ecA1 significantly overlaps with the observed red shoulder at 1.77 eV (700 nm). The other component of the special pair P, ecB1, adsorbs at 0.25 eV higher energy while the remaining chromophores adsorb between the center and the blue tail of the observed band. It is thus predicted that excitonic energy reaching the reaction center will be funneled toward the special pair and in particular ecA1. As the absorption of ecA1 overlaps significantly with that of the 7 Chls that contribute to this shoulder, rapid flow of excitonic energy from them through the reaction center is anticipated. Also, as the upper excitonic components of the two pairs A32-B07 and B31-B32 that form the red tail lie above the absorption of ecA1, it is feasible that low-frequency phonon modes that reduce the exciton coupling and hence drive exciton localization could facilitate exciton transfer to the special pair. However, it is clear that the energy-funnel model developed for bacterial reaction centers does not apply to PS-I, as has been concluded by previous studies.3,21,23,24,26,27,33 A more comprehensive expose´ of the energy-funnel hypothesis is provided in Figure 4, which shows the trimeric photosystem color coded with different monomers used to display different spectral properties. These properties are the frequency of lowest absorption and highest absorption of each Chl judged to be the frequencies at which the absorbance reaches/passes 10% of its maximum in Figure 3. The A32-B07 and B31B32 pairs that form the red tail are most easily recognized in this figure through their red coloring in the lowest-frequency section and their brown-red coloring in the highest-frequency section. If the energy-funnel hypothesis described this figure,

Yin et al.

Figure 4. Lowest absorption frequency and the highest absorption frequency attributed to each chlorophyll are shown color-coded, whereas the difference between these values is shown on a gray scale on which dark indicates a wide range (i.e., the chlorophyll is strongly exciton coupled).

then the central region (reaction center) of the low-frequency absorption plot would be colored red while the outer ring would be colored blue; similarly, for the high-frequency absorption plot, the central region would be colored brown while the outside would be colored violet. A remnant structure of this form is apparent in the low-frequency plot as the ecA1 in the middle of the reaction center is colored brown and is surrounded by a green ring with many blue Chls falling outside the green ring, but the presence of the red-tail Chls (colored red-brown) as well as the blue-shifted ecA3 molecule and a few other blue-shifted Chls near the reaction center significantly disturb it. Also shown in Figure 4 is a monomer shaded in gray to indicate the difference between the high-frequency and lowfrequency extents of the Chl absorptions, i.e., the extent of exciton coupling experienced by each Chl. Although early approaches to the identification of the red tail were based first on estimated values for this property,22 this figure shows clearly that other factors are also important. Most significantly, the light shading afforded the Chls in the reaction center indicates that these molecules experience weaker interactions than do the Chls in the periphery. This feature is quite different than the scenario found in bacterial reaction centers as in these the special-pair dimer from the reaction center gains its key properties through its strong internal exciton coupling. E. Exciton Coupling within the Reaction Center. Once energy is transferred to the special pair, it is the properties of the reaction center that control primary charge separation and subsequent processes. The exciton couplings involving the special pair and the adjacent accessory chlorophylls in the reaction center provide insight into the nature of these processes. These couplings, obtained from our CAM-B3LYP and INDO calculations, along with previous estimates,21,24,27,44 are listed in Table 1. For CAM-B3LYP the values given include the ones used in the spectral simulations obtained for individual dimers, the same as determined from the Fo¨rster point-dipole approximation, and the full dimer couplings corrected to include superexchange contributions from the 92 Chls that are not

PS-I Absorption Spectrum

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TABLE 1: Calculated Excitonic Couplings, in cm-1, Involving Key Chromophores in the Reaction Center of PS-I CAM-B3LYP

Chls

Fo¨rster dipole

dimers onlyb

ecA1-ecB1 ecA1-ecA2 ecA1-ecB2 ecB1-ecA2 ecB1-ecB2 ecA2-ecB2

191 -118 -14 -13 -119 32

140 -183 -49 -47 -175 52

previous estimatesa

INDO

LDSc

Fo¨rster dipole

Fo¨rster transition charges

dimers onlyb

149 -177 -103 -66 -210 50

399 -193 -35 -31 -190 -52

201 -323 -110 -100 -307 99

135 -281 -112 -106 -268 98

fulld

Fo¨rster dipoleb

Fo¨rster transition chargesf

HFg

20 -279 -134 -102 -321 100

415 -92 -25 -24 -87 157

138 -105 -27 -26 -99 31

334 -296 51 86 -303 73

a Other calculations for ecA1-ecB1: 334 cm-1 (configuration-interactions calculations44 involving 48 cm-1 (Pariser-Parr-Pople calculations21 at the heavy-atom X-ray geometry, 90 cm-1 (INDOc),24 141 cm-1 (configuration-interaction singles calculations24 obtained using spatial integrations over the transition density), 272 cm-1 (Fo¨rster dipole),21 and 240 cm-1 (Fo¨rster dipole).24 b Only pairs of Chl. dimers included in the calculaton. c Includes superexchange contributions (eq 3) from nearly aromatic residues and carotenes. d Using the Larsson decomposition scheme, eq 11, to reduce the full 96-dimensional exciton-coupling matrix down to an effective 4-Chl model; Fo¨rster dipole terms are used for long-range interactions. e From ref 27. f From ref 27. g Using four Hartree-Fock determinants per Chl at a lower-resolution X-ray geometry.45

included in this 4-Chl subsystem. These corrections are obtained using the Larsson decomposition scheme (LDS)43

H′′jk ) Hjk -

∑ i *j,k (H

Hji Hik jj

+ Hkk)/2 - Hii

(12)

where Hjk is an element of the full exciton-coupling Hamiltonian and the sum is over all 92 Chls i other than ecA1, ecB1, ecA2, and ecB2; we also modify this expression to use a 2 × 2 matrix diagonalization instead of this perturbation scheme for contributions with small denominators. The results show that indirect couplings acting through neighboring Chls modify the apparent exciton by a maximum of 35 cm-1 for the ecB1 and ecB2 interaction. Also, the Fo¨rster point-dipole approximation is seen to produce errors of the same order for CAM-B3LYP but much larger errors for INDO, but the use of transition charges in modified Fo¨rster theory produces much more reliable results; these type of effects have also been reported from the previous exciton-coupling calculations.21,24,27,44 Finally, the INDO calculations show the influence of superexchange pathways involving non-Chl. chromophores including aromatic residues and carotenoids. The most significant effect is a 43 cm-1 increase in the magnitude of the interaction between ecB1 and ecB2, the interaction previously identified as the one most susceptible to superexchange via nearby Chls. The exciton couplings evaluated using CAM-B3LYP and INDO differ by as much as 100 cm-1. Despite this significant variation, a common pattern is revealed: the interactions between each half of the special pair with its neighboring accessory chlorophyll, i.e., ecA1-ecA2 and ecB1-ecB2 are larger than the other interactions, including the interaction within the special pair. This is an important feature concerning the structure and function of the reaction center as it depicts the reaction center as being a dimer of dimers rather than a central weakly coupled special pair, the motif that dominates the properties of bacterial reaction centers. Previous calculations27,44 have hinted at this possibility, but in these, the interactions within the special pair were calculated to slightly exceed those to the accessory Chls. The current calculations offer significant improvements through the use of more realistic Chl geometries and through the use of improved methods for deducing the exciton couplings in a complex environment. 4. Conclusions The Qy absorption spectrum of PS-I from Thermosynechococcus elongatus has been calculated a priori using the CAM-

B3LYP density functional and the INDO technique. In particular, the CAM-B3LYP results present the first first-principles calculation of the spectra, obtained based on the assumption that all Chl-Chl interactions add pairwise, allowing an orthodox exciton-coupling approach to be taken. Both methods provide a similar qualitative picture of the nature of the Qy absorption, identifying the Chl molecules that contribute to the red tail of the spectrum and its nearby shoulder. In particular, the CAMB3LYP predictions are in excellent agreement with the observed spectral band shape, as well as for the observed linear dichroism for all but the blue absorption tail. As has been previously noted, proper treatment of the long-range electrostatic interactions and short-range polarizations is as important as the treatment of the exciton couplings in determining the absorption spectrum. However, it is also demonstrated that use of precise in-situ quantum-mechanically optimized geometries is also essential for a priori estimates of the molecular electronic structure, energetics, and exciton couplings. The calculations identify the reddest pigments, absorbing at 1.73 eV (719 nm) as coupled A32-B07 and B31-B32 pairs of Chls, in common with results from most other methods that have been used for this purpose. The region of absorption of the special pair is also identified, with the Chla′ molecule ecA1 having the lowest-frequency absorption, an absorption that overlaps with those of the chlorophylls that have components of their absorption at lower energy. Although the energy-funnel hypothesis is shown to be inadequate as the special pair does not produce the most red-shifted absorption, a general qualitative trend is that the absorption energy decreases from the periphery toward the center of each monomeric PS-I unit. The exciton coupling between the ecA1 and ecB1 pigments of the special pair is found to be weaker than the couplings ecA1-ecA2 and ecB1-ecB2 between these pigments and their neighboring accessory chlorophylls. This indicates that in PS-I the concept of a “special pair” of tightly coupled chlorophylls whose properties are key to the device function cannot be sustained, the assembly appearing more like a dimer of dimers. Acknowledgment. We thank the Australian Research Council for funding the research, and the Australian Partnership for Advanced Computing (APAC) and the Australian Centre for Advanced Computing and Communications (AC3) for the provision of computer resources. Supporting Information Available: Complete version of References 30 and 40 as well as three tables detailing the calculated exciton-couplings and Chl state energies and one table

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