Electronic States, Absorption Spectrum and ... - ACS Publications

J. Phys. Chem. B 1999, 103, 8739-8750

8739

Electronic States, Absorption Spectrum and Circular Dichroism Spectrum of the Photosynthetic Bacterial LH2 Antenna of Rhodopseudomonas acidophila as Predicted by Exciton Theory and Semiempirical Calculations J. Linnanto,* J. E. I. Korppi-Tommola, and V. M. Helenius Department of Chemistry, UniVersity of JyVa¨skyla¨, P.O. Box 35, FIN-40351 JyVa¨skyla¨, Finland ReceiVed: December 31, 1998; In Final Form: June 15, 1999

A new approach that uses a combination of semiempirical configuration interaction method and exciton theory to calculate electronic energies, eigenstates, absorption spectrum and circular dichroism (CD) spectrum of the LH2 antenna of Rhodopseudomonas acidophila is introduced. A statistical simulation that uses experimental homogeneous line widths was used to account for the inhomogeneous line width of the observed spectrum. Including the effect of orbital overlap of the close-lying pigments of the B850 ring and the effect of the pigment protein interaction in the B800 ring allowed a successful simulation of the experimental absorption and CD spectra of the antenna at room temperature. Two experimental parameters, the transition energy and the magnitude of the transition dipole moment of monomeric bacteriochlorophyll a (Bchl a), were used in the calculation. The dielectric constant of the protein matrix was taken as 2.1 [0]. The questions of localization lengths of the excitonic states and the energy transfer mechanism between the B800 and the B850 rings are discussed in light of the results obtained.

Introduction Photosynthetic organisms make use of solar energy to create free chemical energy that is used in their metabolic reactions. The initial process of bacterial and green plant photosynthesis is absorption of a photon by pigment molecules of a lightharvesting antenna. In the second phase, the excitation is transferred to a reaction center where the excitation energy is turned into a stable charge separation.1-4 The role of the lightharvesting antenna is to enhance the absorption cross section of the photosynthetic apparatus and to transfer the captured energy efficiently to the reaction center (RC). The light-harvesting antenna consists of pigment molecules that are noncovalently bound to proteins. In photosynthetic pigment-protein complexes the light-collecting pigments are chlorophylls and carotenoids. The major pigment in purple bacteria is bacteriochlorophyll a (Bchl a). Efficiency of the excitation transfer and charge separation depends on the properties of the pigment molecules and their spatial organization in the protein. The protein environment also modifies the energy levels of the pigment molecules, providing nature a possibility for optimization of the photosynthetic process. Usually the photosynthetic antenna of purple bacteria consists of two types of light-harvesting-antenna complexes. The lightharvesting complex I (LH1) (the core antenna complex) surrounds the reaction center, whereas the LH2 complex (a peripheral antenna complex) is further away from the RC. Recently the X-ray crystal structures of peripheral pigmentprotein complexes (LH2) of Rhodopseudomonas (Rps.) acidophila5 and Rhodospirillum (Rs.) molishianum6 have become available in 2.5 Å resolution. In addition, a 8.5 Å7 electron microscopy projection map of LH1 of Rhodospirillum (Rs.) rubrum and a 7 Å projection map of LH2 of RhodoVulum (RhV.) sulfidophilum8 have been resolved. * Corresponding author. E-mail: [email protected]

The basic unit of the LH2 antenna complex is a pair of membrane-spanning helical polypeptides R and β (each about 50 residues) that bind one B850 Bchl a each (B850 refers to absorption wavelength in nanometers). The B850 pigments are coordinated to a conserved histidine residue located in the hydrophobic transmembrane section of the polypeptide. In LH2 the R-peptide binds an additional Bchl a (B800) near the surface of the intracytoplasmic membrane. Carotenoids are present in a 1:1 or 1:2 ratio to Bchl.9 Crystallized LH2 of purple bacteria consists of eight (Rs. molishianum) or nine (Rps. acidophila and RhV. sulfidophilum) Rβ-polypeptide pairs in a cylindrical arrangement where the R-polypeptides form the inner part of the cylinder and β-peptides are located on the outer side.5,6 The B850 pigments are enclosed between the Rβ-pairs. The inner radius of LH2 cylinder is 14-18 Å in diameter. The helical β-apoproteins are arranged radially with respect to the R-apoproteins to form an outer cylinder of radius 34 Å. The 18 B850 Bchl a molecules of the LH2 complex of Rps. acidophila form a continuous overlapping ring where the Mg-Mg distance between the adjacent Bchl a molecules alternates repeatedly between 8.9 and 9.6 Å.1 The porphyrin planes of the B850 chlorophylls are perpendicular to the plane of the membrane.5 The B800 Bchl a molecules are located between the β-polypeptides. The distance between the Mg atoms of these pigments is 21.2 Å. The Mg-Mg separations of Bchl a of B800 and the two nearest Bchl a’s of B850 are 17.6 (R-apoprotein), and 18.3 Å (β-apoprotein). In the following, we will refer to the two Bchl a’s of the B850 ring as B850R and B850β. An RβB850 Bchl a dimer with the Mg-Mg distance of 9.6 Å is referred to as a protomer (D1 in Figure 1). The arrangement of the Bchl a molecules in the LH2 antenna is shown in detail in Figure 1. The arrows indicate the directions of Qy transition dipoles of Bchl a monomers. The absorption maximum of the B850 pigments of Rps. acidophila is at 859 nm and that of the B800 pigments is at

10.1021/jp9848344 CCC: $18.00 © 1999 American Chemical Society Published on Web 09/28/1999

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Figure 1. Schematic structure of LH2 antenna of Rps. acidophila. The Bchl a molecules with the central magnesium atom are shown. D1 refers to a protomer and D2 refers to the dimer between adjacent protomers. The directions of the Qy transition dipole vectors are indicated by vectors. Upper part consists of 18 B850 pigments; below are shown the 9 B800 pigments.

801 nm at room temperature (RT).10 At low temperature the main absorption maximum is shifted to 870 nm while the B800 band remains almost unshifted.11 The circular dichroism spectrum consists of a negative peak at 875 nm, a positive peak at 854 nm, a positive peak that is not well resolved around 812 nm, and a negative peak at 797 nm (RT). The fwhm of the absorption lines is about 400 cm-1 at RT. An energy transfer rate of 600-700 fs (RT) from the B800 pigments to B850 pigments has been observed by time-resolved spectroscopic methods.12,13 During past few years a wealth of studies of spectroscopical properties of LH2 complex has been published.2,11,13-18 The structure that is known to atomic detail provides an excellent starting point for theoretical calculations. Sauer et al.2 were the first to calculate the spectrum of LH2 of Rps. acidophila after the publication of the crystal structure by McDermott et al.5 In their work chromophore-chromophore interactions were calculated by using point monopole approximation. As a starting point, the Bchl a transition energy was set at 12 500 cm-1 corresponding to absorption wavelength of the B800 ring, where the excitonic interactions are small. To match the experimental spectrum of the B850 band, the transition energies of the B850 molecules were scaled to 12 260 cm-1. The same kind of approaches has been used in most previous calculations.2,11,16,19-21 Calculations of Sauer et al.2 revealed many of the main features of the LH2 spectrum. The polarization of the allowed transitions in the plane of the membrane and the assignment of the B800 and B850 absorption bands to the corresponding pigment pools were confirmed. In addition, the experimentally observed red shift of the zero crossing of the CD spectrum due to the lowest exciton state was explained. The next level of calculation was presented by Cory et al.,20 who carried out an INDO/S calculation of B800 (8 pigments) and B850 antenna (16 pigments) of Rs. molischianum,20 so far the largest semiempirical calculation on bacterial antenna. For calculation of the B850 antenna the bacteriochlorophyll a molecule was approximated by a reduced structure containing 44 atoms. The approach included estimation of choromophore-chromophore interactions at semiempirical level and used the known crystal structure. No pigment-protein interactions were included in the calculation. Computed energy levels do not seem to predict the experimental transition energies very well. An approach to calculate energy transfer properties of LH2 has been presented by Krueger et al.22 Chromophore-chromophore interactions, which determine the spectral transition energies, were calculated by using a transition density cube method (TDC). The charge densities of bacteriochlorophyll a were calculated by using ab

Figure 2. Structure and the numbering of atoms of the bacteriochlorophyll a molecule.

initio method and the known crystal structure. Interaction energies were evaluated by integrating the electrostatic energies over the charge distributions of the two interacting chromophores. No spectral simulation was presented. A variety of intra- and inter-dimer interaction energies and monomeric transition energies have been used in the literature. Calculated values for intra- and inter-dimer interaction energies from 230 to 806 cm-1 and from 110 to 566 cm-1, respectively, have been reported. 2,11,13-16,20-23 Qy transition energies that have been used range from 751 to 843 nm. Magnitudes of transition dipole moment of monomeric Bchl a from 6 to 11 D and orientation N(A)TN(C) have been used in previous studies (Figure 2).24,25 Values of the dielectric constant used to describe the permittivity of the protein matrix have ranged from 1 to 3 [0]. At atomic scale, the macroscopic dielectric constant is not a good description of the medium. The variation of  affects both the Coulombic interaction between two dipoles and the magnitude of the dipole moment.26,27 However, the correction for the interaction energy is not likely more than 10% when the dielectric constant is changed from 1 to 2.26 In general the absorption spectrum of the LH2 complex has been described with reasonable accuracy, but difficulties have been encountered in calculating the CD spectrum. A symmetry-based analysis of the exciton level structure of the LH2 antenna has led to a useful classification of the exciton states.17,28 In the present paper the C9 symmetry of the LH2 antenna of Rps. acidophila is used for classification of the computed eigenstates. If the basic repeating unit of the antenna is taken to be an RβB850 dimer (and treating B800 states separately), then the nine excitonic energy levels can be classified in increasing energy as A (a totally symmetric lowest exciton level), E1 (a degenerate level with strong oscillator strength), and three doubly degenerate E states. If the basic unit of the LH2 antenna ring is taken to include all three Bchl a molecules (B800, B850R, B850β), the symmetry of the states is changed. In this case the state lowest in energy is A followed by 25 higher energy states and ending at the 27th exciton state with A symmetry. The A states have only weak oscillator strength because the transition is polarized parallel to the C9 symmetry axis, but the transition dipoles of the Bchl a’s are oriented perpendicular to the C9-axis. Although in a real

Properties of the LH2 Antenna of Rps. acidophila inhomogeneous system the exact C9 symmetry is broken, the classification provides a useful conceptual model of the system. A correct prediction of the energy difference between the lowest A state and the E state is a good test of a theoretical calculation. Experimentally it has been observed that the low-lying 1A state carries a few percent of the oscillator strength of the 1,2E1 state and the energy difference is about 200 cm-1 at 4 K and about 100 cm-1 at RT.29 The transition energy of the Qy band of a single Bchl a molecule in solution corresponds to a wavelength of 773 nm (diethyl ether), and it is only slightly solvent dependent. In the LH2 antenna complex, the absorption bands are observed at 800 and 850 nm. We do not think that any special pigmentprotein interaction in the LH2 antenna would shift the transition energy of monomeric Bchl a well over 800 nm. When an RβBchl a pair is isolated by a detergent from the LH1 antenna of, e.g., Rs. rubrum, the absorption maximum is shifted from 870 to 820 nm.30 In this B820 particle the red shift is mostly produced by exciton interaction of the two Bchl’s, still coordinated to R- and β-polypeptides. With higher detergent concentration the Rβ-apoproteins are separated and a new absorption band at 777 nm appears. The 777 nm absorption results from a monomeric Bchl a that is still coordinated to a histidine residue of the apoprotein. This example demonstrates that there is no reason to assume that the protein environment of LH2 itself would produce a large shift of transition energy. On the basis of high-pressure studies it has been suggested31-33 that the red shift of B850 pigments is mainly due to coupling between the electronic states of the pigments. Our calculations strongly support this view and indicate that the red shift of the B800 pigments is mainly induced by the local protein environment, where the pigments are embedded. In the present paper, we use a semiempirical configuration interaction approach combined with exciton theory (CIEM, configuration interaction exciton method). Our method differs from the pioneering semiempirical approach of Scherer and Fisher34 used for calculation of optical spectra of bacterial reaction centers. In our model the adjacent B850 molecules are treated as a supermolecule and the transition energies are calculated semiempirically. In this way the orbital overlap between the nearest neighbor B850 molecules is taken into account, which is not included in the traditional Frenkel exciton theory.35 The interaction energies were calculated from energy differences of the Qy transitions of the monomer and the dimer, respectively. In this way we avoid including uncertainties involved in calculation of the energies of the higher excited states of the dimer. For non-neighbor interactions the point dipole approximation is applied as usual. The monomer transition energies were fixed to values obtained from semiempirical calculation with linear calibration to experimental values using the method of Petke.36 The magnitude of the transition dipole of the monomeric Bchl a was kept at the experimental value of the monomeric Bchl a solution. The energy levels, eigenfunctions, and absorption and circular dichroism (CD) spectra of the LH2 complex of Rps. acidophila were calculated. As a criterion for usefulness of our method, we considered its ability to predict the experimental absorption and CD spectra. Theoretical Background We consider the system of a perfectly ordered aggregate without exciton-phonon coupling and with only one relevant molecular electronic transition from the ground to the excited state. In this case, the Hamiltonian for the description of

J. Phys. Chem. B, Vol. 103, No. 41, 1999 8741 excitations in molecular aggregates has the well-known form35

H ˆ )

1

∑n nBˆ +n Bˆ n + 2m*n ∑ Jmn(Bˆ +mBˆ n + Bˆ +n Bˆ m)

(1)

where n ) ∆n + Dn + δn, ∆n is the electronic energy difference between the ground state and excited state of the molecule n, Dn is the so-called environmental shift,37 δn is the shift induced by the surrounding matrix (e.g., solvent, protein), Jmn is the matrix element of the interaction operator between the molecules m and n, and the Bˆ n operators are Pauli creation (Bˆ +) and annihilation (Bˆ ) operators for excitons at molecule n. These operators commute for different molecules (n * m), whereas for any single molecule they obey the Pauli anticommutation relation.38 The lowering operator Bˆ n corresponds to a transition of the molecule n from the excited state to the ground state, and the raising operator Bˆ + n corresponds to a transition from the ground state to the excited state. The molecular wave function representing the ground state of the nth molecule will be denoted as |0n〉, and the first and only one excited state of the nth molecule in this model will be designated as |1n〉 ) Bˆ + n |0n〉. We assume that the overlap between wave functions associated with different molecules may be neglected as well as the possibility of electron exchange between molecules. In this case the wave function of the ground state of the aggregate in the zero approximation will have the form N

|0〉agg ) |01,02,...,0N〉 )

|0i〉 ∏ i)1

(2)

and the state where only one molecule m is excited is represented in the zero approximation by the wave function m-1

|1m〉agg ) [

∏ i)1

N

|0i〉] ) Bˆ + ∏ m |0〉agg i)m+1

|0i〉] X |1m〉 X [

(3a)

The eigenstates of the system are of the form N

|Ψe〉 )

∑cen|1n〉agg

(3b)

n)1

Using the wave functions of eq 3, the Hamiltonian (eq 1) may be written in matrix form with matrix elements:

ˆ |1n〉agg ) n Hnn ) agg〈1n|H

(4)

Hnm ) agg〈1n|H ˆ |1m〉agg ) Jnm, n * m

(5)

Using these matrix elements, and the property Jnm ) Jmn, the exciton energies, e.g., in the dimer case have the form

1 E1,2 ) (1 + 2 ( x(1 - 2)2 + 4J122) 2

(6)

The coupling Jnm can be approximated at large distances by a well-known point dipole model.

Jnm ≈ Jdip nm )

[

]

bn‚R µ n‚µ bm 3(µ Bnm)(µ bm‚R Bnm) 1 b 4π R 3 Rnm5 nm

(7)

where b µn is effective transition dipole moment vector in

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molecule n and26,27

b µn )

+2 0 b µ 3 n

(8)

b µ0n is transition dipole moment vector for vacuum ( ) 1), B Rnm is the position vector between the two dipoles, Rnm is the distance between these dipoles, and  is the dielectric constant. Calculation of the Absorption and CD Spectra. Geometries of hydrogen atoms of the substructures of crystal structure of LH2 complex of Rps. acidophila (strain 10050) were optimized by using the semiempirical PM3 method.39 The non-hydrogen atoms were fixed to the crystal coordinates. The optimization was done on a Silicon Graphics O2 workstation by using SPARTAN (version 5.0) (Wavefunction Inc.) software.40 Single point ZINDO/S41-43 semiempirical singly excited configuration interaction (CIS) calculations of substructures were performed by using HyperChem44 software running on a Pentium PC with 128 MB of RAM. Single point PM3 semiempirical singly excited and double excited configuration interaction (CISD) calculations were performed by using the SPARTAN software. The coordinates used to define the positions, and orientations of individual Bchl a molecules were obtained from the X-ray crystallographic analysis having a resolution of 2.5 Å and an R value of 0.227 at room temperature.5 The interaction between adjacent LH2 complexes was neglected. The intensities of the absorption and CD bands were calculated by using eqs 9 and 10, respectively: N

µe2 ) Re ) 1.7 × 10-5

∑ |µbn||µbm|[µˆ n‚µˆ m]cencem n,m)1

(9)

N

∑ νn|µbn||µbm|Rnm[Rˆ nm‚[µˆ m × µˆ n]]cencem n,m)1

(10)

where b µn is the effective transition dipole moment vector in molecule n, µˆ n is the unit vector in the direction of that transition, B Rnm is the position vector between the two dipoles, Rnm is the distance between the dipoles, νn is the energy (in cm-1) of the transition on the nth molecule, and cen is the nth element of the eigenvector for the eth exciton state.45 To calculate the excitonic spectra of LH2 antenna complex of Rps. acidophila at room temperature, four different approaches were adopted. For comparison, the energy levels were first calculated by applying the frequently used dipole-dipole approximation between all the 27 Bchl a pigments of a single LH2 complex (case A). In the second level of approximation the calculation was improved by calculating the interaction energy Jnm (eq 6) between the neighboring B850 Bchl a molecules semiempirically (case B). The calculation was further improved (case C) by calculating semiempirically the transition energy of each monomer (B800, B850R, and B850β) with a selected part of the protein. The result was then used to recalculate the Jnm. In the last phase (case D) diagonal- and off-diagonal disorder was included in the calculation to account for the inhomogeneous line width of the experimental spectrum. The Dn term of eq 1, the environmental shift, was left out of the calculation since within the approximation used an exact evaluation of this parameter is not possible. In the following, each method of calculation is described in detail. Case A: The B800 and B850 absorption and CD band positions and intensities were calculated by using the conventional dipole-dipole approximation to describe the excitonic interaction between the pigments. The structural parameters were

obtained from the crystal structure of the LH2 complex of Rps. acidophila (strain 10050).5 Excitonic energies were computed by diagonalizing a 27 by 27 H matrix. The diagonal elements Hnn of H (eq 4) were taken as S1 r S0 transition energies of monomeric Bchl a molecules (773 nm, Qy band of Bchl a in diethyl ether at room temperature46,47). Off-diagonal elements Hnm of H (eq 5) were calculated by using eq 7. The value of transition dipole moment vector (µ b0) of Bchl a was taken to be 6.13 D in the direction along N(A)-N(C), and  was taken to be  ) 2.1 [0]. Case B: In the second approach (CIEM) the values of nearest neighbor interaction matrix elements of the B850 ring were estimated by considering both possible Rβ-Bchl a dimers as a single supermolecule. By using this method, the spatial extension of the transition densities and overlap between the wave functions with nearest neighbor molecules were taken into account. To begin with, the hydrogen atoms were added in the crystal structure, and the geometry of the Bchl a’s with the nearest amino acids were optimized by using the semiempirical PM3 method. The non-hydrogen atoms were kept fixed. In the second stage the transition energies of the two different Bchl a dimers together with the histidines that are binding noncovalently to Mg atoms of Bchl a of B850 were calculated. The method of calculation was the semiempirical configuration interaction (CIS) ZINDO/S method with all possible singly excited configurations from HOMO-14 to LUMO+14. Using the obtained transition energies, the interaction matrix elements Jnm between the nearest neighbor Bchl a molecules of the B850 ring were estimated from the eq 6. The diagonal elements Hnn of H (eq 4) were kept as the transition energies of monomeric Bchl a molecules (773 nm). The non-neighbor pigment interaction was obtained by using the point dipole approximation as usual. Case C: In this case the diagonal elements Hnn of H (eq 4) (transition energies of the B800, B850R, and B850β) were estimated by using semiempirical configuration interaction (CIS) ZINDO/S method. The nearest neighbor coupling energies were estimated from eq 6 as in case B, the difference being that the monomer energies were calculated separately instead of using the experimental value of 12 937 cm-1 (773 nm). All possible singly excited configurations from HOMO-14 to LUMO+14 were taken into account. The transition energies of the B850 Bchl a monomers were calculated with the histidine residues. The B800 monomer was calculated with the nine nearest amino acids, the part of phytyl tail of B850 that is in close vicinity of B800, and part of the carotenoid (Figure 3). In this way, the effects of surrounding protein environment were included in the calculation. The size of the complex was limited by the computer memory. Since the next nearest amino acids are further away, we do not expect any major effect on the transition energy even if they were included. In addition, the transition energy of B800 monomer with the surrounding amino acids was calculated by using semiempirical configuration interaction (CISD) PM3 method with all possible singly and double excited configurations from HOMO-4 to LUMO+4. The second method of calculation produced essentially the same result as (CIS) ZINDO/S, indicating that the result is not just a property of the ZINDO/S Hamiltonian. The transition energies of the monomers used in the calculation were obtained from a leastsquares fit of the computed (vacuum) and the experimental transition energies of monomeric Bchl a.36 Finally, the absorption and CD spectra of the LH2 complex were calculated by using two different sets of directions of the Qy transition dipole moment vectors. In the first case the directions of the Qy

Properties of the LH2 Antenna of Rps. acidophila

J. Phys. Chem. B, Vol. 103, No. 41, 1999 8743

Figure 3. Stereoview of Bchl a of the B800 ring together with the protein surroundings (incuding a fraction of a rhodopsin-glucoside carotenoid and two B850β phytyl tails) that was included in the semiempirical calculation of the monomer transition energy.

transition dipole moment vectors were kept in the N(A)-N(C) direction as usual. In the second case, the directions of these vectors were taken from the ZINDO/S calculations. The ZINDO/S calculation resulted in transition dipoles that are about 3° (B800) or 4-5° (B850R,β) off the porphyrin plane. Case D: The last step was a simulation of absorption and CD spectra of LH2 antenna of Rps. acidophila at RT. Computation included uncorrelated random variation of the values of the matrix elements that leads to inhomogeneous broadening of the spectral lines. The transition dipoles were kept fixed. One spectral simulation consisted of 8000 iterations where eigenvalues of the 27 × 27 Hamiltonian (eq 1) were solved. Homogeneous widths of 210 cm-1 (B800) and 188 cm-1 (B850) were used for each transition. The variation was generated by using a Gaussian distribution of random energy disorder. The diagonal disorder (fwhm) was 200 cm-1 (B800) and 220 cm-1 (B850), and the off-diagonal disorder was 10% of the value of the matrix element. These line widths are similar to experimental values reported in the literature13,28,48-54 and represent maximum values that still keep the zero crossing of the computed CD spectrum around the experimental value of 864 nm. As a final refinement, the transition energies of the monomers were lowered by 35 cm-1, which was about 0.3% of the value of the transition energy of the B800 monomer. This value was obtained from the energy difference between the calculated and experimental position of the B800 band. The nearest neighbor interaction energies in the B850 ring were 531 and 590 cm-1. Results and Discussion Four different approaches (cases A-D) were used to calculate the CD and absorption spectra of the LH2 antenna complex of Rps. acidophila at RT. With each method, additional features were introduced in the model and an increasingly accurate description of the system was produced. Throughout the discussion, the main absorption bands are referred to as B800 and B850 and the corresponding states are named according to their symmetry in a homogeneous system. The lowest exciton state (with little oscillator strength) is of A symmetry and the lowest but one is of E1 symmetry. The 1,2E1 state is responsible for the B850 absorption band.

Figure 4. Exciton stick spectra of LH 2 complex and simulated spectra with a 350 cm-1 Gaussian line width. The experimental spectra (room temperature) are shown by dashed line for comparison. (a) Case A, (b) case B, (c) case C; see text for details of computation in each case.

Case A. Conventional point-dipole interaction between the chromophores was assumed. In this approach the exciton interaction energies Jnm between the nearest neighbor Bchl a of B850 are 346 cm-1 (within the protomer) and 249 cm-1 (between the protomers). The exciton interaction energies between non-neighboring pigments are of the order of 30-40 cm-1 as shown previously by Sauer et al.2 The absorption intensity is concentrated mainly on four exciton states, two of which are red shifted only (33 cm-1) to 775 nm. The other two states are red shifted to 811 nm, corresponding to a displacement of 616 cm-1 from the Qy transition energy of the monomeric Bchl a at 773 nm (12 937 cm-1). These four components form two absorption bands of Figure 4a. Each of these transitions includes one doubly degenerate energy level. The energy separation of the two absorption bands is 583 cm-1 (Table 1). The transition from the ground state to the 1A state, which has

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TABLE 1: Comparison of Methods Used for Calculation of the Absorption and CD Spectra of LH2 Antenna of Rps. acidophila at Room Temperaturea ∆ν (cm-1) case A

δb (cm-1) 0

B

0 -385 -189 -107 -420 -224 -142

C D exptl

Jnmc (cm-1) DD 249 346 DD 712 771 DD 562 622 DD 531 590

λ(B800) (nm) 3,4E1

λ(B850) (nm) 1,2E1

λ(B875) (nm) 1A

3,4E1-2A

1,2E1-1A

3,4E1-1,2E1

775

812

817

17

86

583

775

871

882

17

140

1426

799

862

871

18 (19)d

125 (127)d

910

801

858

801

858-859

828 g100

830-843

a

The first column indicates the approximations used (cases from A to D, see text). The experimental values, if available, are given in the last row. b Shift induced by the protein surrounding (eq 1). c Coupling between the pigments: DD indicates dipole-dipole coupling between nonadjacent pigments (eq 7). Numbers indicate coupling between adjacent pigments within the protomer and between the protomers (see Figure 1). d The values calculated by the ZINDO/S transition dipole directions.

Figure 5. Exciton stick CD spectra of LH 2 complex and simulated spectra with a 350 cm-1 Gaussian line width. The experimental spectra (room temperature) are shown by dashed lines for comparison. (a) Case A, (b) Case B, (c) case C; see text for details of computation in each case.

less than 1% of the dipole strength of the strongest transition, is predicted to 817 nm (12 235 cm-1). The energy difference between the 1A state and the 1,2E1 state is 86 cm-1. The CD spectrum consists of two pairs of lines, one pair centered at about 775 nm with energy separation of 17 cm-1 and one pair around 815 nm with energy separation of 86 cm-1 (Table 1). The signs of the CD lines with increasing wavelength are: + + - (Figure 5a). As expected, the result of point dipole calculation does not predict the experimentally observed LH2 absorption or CD spectrum correctly. The calculated B800 and B850 absorption bands are predicted to 775 and 812 nm (Table 1), far from the experimental values of 801 and 859 nm at RT.2,11,55 Furthermore, the energy separation of these two bands in the calculated spectrum is 583 cm-1, compared to the experimental value of 830-843 cm-1 at RT.2,56 Though the calculated values are not correct, the general shapes of the absorption and CD spectra are in agreement with the experimental result.

Figure 6. Calculated and experimental spectra of Bchl a dimers at room temperature. The calculated spectrum of the B850 ring protomer is indicated with a solid line (s), the spectrum of the dimer between the protomers with a dotted line (‚‚‚), and the experimental spectrum of a B820 dimer of LH1 of Rs. rubrum with dashed line (- -). Homogeneous Gaussian width of 540 cm-1 was used to dress the stick spectra. The feature around 777 nm in the experimental spectrum is due to the residual monomer in the preparation.

Case B. The next step is to improve the calculation of the nearest neighbor interaction energies. The transition energy and the transition dipole moment of single Bchl a’s were fixed to experimental values. Both possible Rβ-heterodimers were treated as supermolecules and their interaction energies calculated semiempirically. The Qy transition energies of the two dimers of B850 are 822 nm (12 165 cm-1) within the Rβ-protomer and 818 nm (12 225 cm-1) between the adjacent Rβ-protomers (Figure 6). The transition energies of the dimers (E1 in eq 6) and the monomer transition energy of 12 937 cm-1 (both 1 and 2 in eq 6) yield exciton interaction energies Jnm of 771 cm-1 (within the protomer) and 712 cm-1 (between the protomers). The calculated absorption intensity is again concentrated mainly on four exciton states, and as in case A, these four components form two absorption bands (Figure 4b). The positions of these absorption bands are at 775 nm (a red shift of 33 cm-1 from the monomer absorption, corresponding to the B800 transition) and at 871 nm (a red shift of 1459 cm-1, the

Properties of the LH2 Antenna of Rps. acidophila B850 transition). The energy separation between the two transitions is 1426 cm-1, and the energy difference between the 1A and the 1,2E1 state is 140 cm-1. The CD spectrum consists of two pairs of lines, one pair centered around 775 nm with energy separation 17 cm-1 and one pair around 876 nm with energy separation of 140 cm-1 (Table 1). The sequence of signs of the CD lines is identical with that obtained in case A (Figure 5b). An improved representation of the B850 pigments is obtained, when each Rβ-dimer is treated semiempirically as a supermolecule. In this case the B850 band is red shifted by 170 cm-1 and the B800 band is blue shifted by 427 cm-1 from the corresponding experimental values. The energy separation of the two bands in the calculated spectrum is 1426 cm-1, twice the experimental value. With the CIEM calculation an acceptable red shift of the B850 absorption is obtained. However, the calculation does not give the correct transition energy for the B800 band. Because the interaction between the B800 pigments or between the B800 and B850 pigments is weak, the interaction shifting the B800 absorption from the monomeric transition energy of Bchl a has to be a pigment-protein interaction. In the following (case C) the relevant part of the protein surrounding of all three Bchl a’s (B800, B850R, and B850β) is incorporated into the calculation. Case C. The transition energy of each of the three Bchl a pigments with nearby amino acids was calculated semiempirically. Resulting Qy transition energies of the three monomers were 12 552 cm-1 (B800), 12 748 cm-1 (B850β), and 12 830 cm-1 (B850R), which correspond to 797, 784, and 779 nm on the wavelength scale, respectively. Compared with the Qy transition energy of monomeric Bchl a (12 937 cm-1), shifts induced by the surroundings (eq 1) of the Bchl a monomers are -385 cm-1 (B800), -189 cm-1 (B850β), and -107 cm-1 (B850R) (Table 1). The exciton interaction energies (from eq 6) between the nearest neighbor Bchl a’s of the B850 ring are 622 cm-1 (within the Rβ-protomer) and 562 cm-1 (between the protomers). The calculated absorption intensity of the whole LH2 complex is again concentrated on four components. These components give rise to two absorption bands, one at 799 nm and the other at 862 nm (Figure 4c). The red shifts of these bands are 420 and 1330 cm-1 from the transition energy of the monomeric Bchl a (12 937 cm-1). The energy separation of these two bands is 910 cm-1, and the energy difference between the low-energy exciton state 1A and the 1,2E1 state is 125 cm-1. The CD spectrum consists of two pairs of lines (Figure 5c). One pair is centered at 800 nm, with energy separation of 18 cm-1, and one pair on 867 nm, with energy separation of 125 cm-1. If directions of the Qy transition dipole moment vectors calculated by the ZINDO/S method are used instead of the N(A)-N(C) direction, the absorption band and CD band positions remain almost the same. The intensities of both positive and negative CD lines in B850 region increase about 10-15%. The energy difference between the low-energy exciton state 1A and the 1,2E1 state is 127 cm-1 in this case. The spectral band positions obtained in case C are very close to experimental values at RT. The transition energy of the B800 monomer with the nearest amino acids is 797 nm, almost exactly the experimental value. It seems obvious, then, that the red shift of the B800 band is to a large extent due to pigment-protein interaction. This interpretation is consistent with the holeburning data that indicate that exciton effects are unimportant for the B800 molecules and thereby for the B800 band.32 The computed transition energies of the B850 Bchl a’s with the

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Figure 7. Exciton states from cases A, B, and C (see computational details in text). The numbering of the states is in the order of increasing energy. The symmetries of the states are shown. The states with high oscillator strength are marked with an asterisk (*). Also marked in the figure are the energy differences in cm-1 between the highest (3A) and lowest state (1A) of the exciton manifolds, the differences between the 1A and the degenerate 1,2E1 states, and the energy difference between the 1,2E1 and the 3,4E1 states. The latter two pairs of states give rise to B850 and B800 absorption bands, respectively.

histidine residue are close to the experimental value of 777 nm of the B777 complex.57 The B777 complex is a detergent isolated monomeric Bchl a molecule bound to R- or β-polypeptide of the LH1 antenna.58 Resonance Raman spectroscopy shows that the central magnesium atom in the B777 Bchl a molecule is still 5-ligated, indicating that the ligation to the histidine residue is still present.59 If the transition energies of the three Bchl a’s are calculated with the geometry of the crystal structure, but without the nearest amino acids, the Qy transition energies correspond to a wavelength of 774 nm. Therefore it is concluded that the protein environment does not change the geometry of the Bchl a to the extent that the transition energy would change significantly. It is concluded that the environment of the Bchl a molecule in the protein has an effect on the charge distribution rather than on geometry. Figure 7 summarizes the exciton energy levels of cases A, B, and C. The symmetry of each state is indicated in Figure 7. The states are numbered in order of increasing energy. The states with large oscillator strength (1,2E1 and 3,4E1) are marked with an asterisk (*). Also marked in the figure is the energy difference between the highest (3A) and lowest state (1A) of the exciton manifold. The energy differences between 1A and degenerate

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Figure 8. Simulation of absorption and CD spectrum of LH2 antenna of Rps. acidophila at room temperature. For details of the simulation, see case D in the text. Also shown is the experimental spectrum (dashed line) of Frese et al.10

TABLE 2: Symmetries, Energies, Relative Oscillator Strengths, and Rotation Strengths of the States Used for Spectral Simulationa state symmetry

energy (cm-1)

rel int (au)

R (au)

exciton length ( std dev

1A 1E1, 2E1 1E2, 2E2 1E3, 2E3 2A 3E1, 4E1 3E2, 4E2 3E3, 4E3 1E4, 2E4 3E4, 4E4 5E4, 6E4 5E3, 6E3 5E2, 6E2 5E1, 6E1 3A

11 524 11 644 11 911 12 251 12 462 12 481 12 514 12 543 12 547 12 625 13 014 13 324 13 573 13 732 13 787

0.00 1.00 0.00 0.00 0.02 0.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01

-0.15 0.22 -0.03 -0.01 0.86 -1.00 0.09 0.02 0.00 0.01 0.00 0.00 0.00 -0.03 0.02

11.1 ( 2.5 9.5 ( 1.9 11.1 ( 0.7 11.0 ( 3.0 2.2 ( 0.7 2.2 ( 0.8 2.5 ( 0.7 2.4 ( 0.7 2.7 ( 0.8 1.9 ( 0.6 11.0 ( 1.0 10.8 ( 0.8 10.4 ( 1.2 9.2 ( 1.7 10.5 ( 1.9

a Exciton lengths are average values of 8000 iterations. Exciton length N is defined as (eq 3b) L(e) ) ∑n)1 Cen4.

1,2E1 states and between the 1,2E1 and 3,4E1 states giving rise to B850 and B800 absorption bands, respectively, are shown as well. Simulation of the Absorption and CD Spectra of LH2. The last step of calculation (case D) is a simulation of the absorption and CD spectra of Rps. acidophila at room temperature (Figure 8). Homogeneous line width is added to the calculated exciton stick spectrum, and the actual inhomogeneous absorption and CD spectrum is simulated by introducing diagonal and nondiagonal disorder to the exciton Hamiltonian. Table 2 lists the states that are used as a basis for simulation. In addition, the energies, relative intensities, and rotational strengths are included. In the last column of Table 2 average participation ratio of each state is shown. A good agreement with the experimental spectra is obtained. The absorption band positions at 801 and 858 nm are produced exactly. Also the intensity ratio of the absorption bands is well predicted. The absorption band profile differs somewhat from

the experimental one. The zero crossing of the CD spectrum is perfectly fitted. One nanometer difference remains between the band positions of the simulated and experimental CD spectra. There is a discrepancy between the intensities of the experimental and the predicted negative CD bands at 874 nm. The experimental CD is almost conservative in the 850 nm region, whereas the calculated negative CD is too weak. If the CD spectrum is calculated without the B800 pigments or the B800B850 interaction energy is reduced by 50%, a nearly conservative CD is obtained. In the present calculation the B800-B850 interaction energies were estimated by using dipole-dipole interaction and a too weak CD signal in the 874 nm region was obtained. This is an indication of overestimation of the point dipole approximation in predicting the strength of this interaction. The 1A state giving rise to the negative CD at 874 nm has a small positive contribution from the B800 pigments. Reducing this contribution results in a more negative CD spectrum that resembles more closely the experimental spectrum. Both the absorption and CD spectra show a deviation between the simulated and experimental spectra around 820-840 nm. In the case of the absorption spectrum, this is partly due to a nonzero background that seems to rise toward the higher energy side of the spectrum. In the case of the CD spectrum, the excitonic interaction produces the main features of the spectrum. The model used for spectral simulation does not include vibronic bands or exciton phonon coupling. A low-temperature absorption spectrum shows that the intensity between 820 and 840 nm is strongly reduced as compared to RT.60 The temperature dependence indicates that thermally populated vibronic or phonon-coupled excitations are involved in this spectral region. Zero Crossing of the CD Spectrum. The CD spectrum of LH2 of Rps. acidophila at room temperature consists of a negative peak at 797 nm with zero crossing at 805.5 nm and a positive and a negative peak at 854 and 874 nm with zero crossing at 864.5 nm. The zero crossing of the 850 feature is red shifted from the absorption maximum at 858 nm by 7 nm.61 The red shift of the zero crossing is most easily explained by taking into account the whole 850 ring, as pointed out by Sauer et al.2 and Koolhaas et al.61 In a homogeneous B850 ring of 18

Properties of the LH2 Antenna of Rps. acidophila Bchl a’s the low-energy transition (to 1A state) becomes forbidden in the absorption spectrum but has significant rotational strength in the CD spectrum. This results in a negativegoing CD feature that is red shifted with respect to the absorption spectrum. Koolhaas et al.21 report that a B800-less mutant of Rhodobacter (Rb.) sphaeroides shows a minor negative CD peak at 780. Their interpretation is that this is a high energy exciton component of the B850 band. To explain the estimated 1:10 intensity ratio of peak heights at 780 and 870 nm, the directions of the transition dipole angles of the B850 pigments had to be changed (about 5°) in their calculation as compared those of Rps. acidophila. We note that our results show that the Qy transition of B850 Bchl a in the LH2 complex is not exactly in the porphyrin plane. The histidine residue coordinated to the Mg atom of the R- and β-Bchl a’s changes the direction of the transition dipole about 4-5° from the usual N(A)-N(C) direction. The B800 transition moment with the protein is about 3° off the N(A)-N(C) direction. Therefore, a change in the CD intensity ratio can be induced by the protein environment without the need of actually moving the chlorophyll plane. There is no corresponding spectral feature at 780 nm in our simulation of CD spectrum of Rps. acidophila. A minor negative peak in the simulation is observed around 750 nm. Our calculation does not take into account vibrational modes that may have an effect on the CD spectrum. Hole-burning results show the B850 band has satellite bands from 200 to 920 cm-1 on the high-energy side. These were initially assigned to vibronic bands, although later assignment of these features to higher exciton states has been favored.33,53 Spectrum of an rβ-Bchl a Dimer. The semiempirical calculation of a RβB850 protomer produces a spectrum that peaks at 822 nm. An absorption band at 818 nm is calculated for the Bchl a dimer of adjacent protomers. It is interesting to note that the Rβ-Bchl a dimer isolated from a LH1 complex (B820) of Rhodospirillum (Rs.) rubrum absorbs around 820 nm, depending on the detergent used in the isolation (Figure 6). The fact that absorption band position observed for B820 and the one calculated for the protomer are almost identical is not surprising, since the structures of the corresponding dimers of the LH1 and LH2 are closely related. The experimental CD spectrum of the B820 dimer of Rs. rubrum at room temperature shows a higher exciton component in the wavelength region 776-783 nm.57,62-64 The higher exciton component is also observed in the fluorescence excitation spectrum.58,64 The higher exciton component of the two dimers is according to calculation at 717 nm for the dimer within the Rβ-protomer and at 753 nm for the dimer of adjacent protomers. The computed CD spectrum of the RβB850 protomer has the same sign sequence as that of the B820 dimer of Rs. rubrum, only the higher energy CD band is predicted at a wrong position. To explain the difference between the energies of the excited exciton states, more accurate calculation of higher exciton states and detailed structural information of the B820 dimer are needed. Pigment-Protein and Pigment-Pigment Interactions. The local protein environment has an effect on the pigment transition energies and therefore on the exciton states of the system. Figure 7 demonstrates how the exciton energy level manifold is changed when the simple dipole-dipole calculation (case A) is replaced with CIEM calculation (cases B and C). The effect of the local protein environment is taken into account in case C. The most profound effect by the protein is induced in the states originating from the B800 pigments (2A to 3,4E4). These states are shifted more than 350 cm-1 to lower energy (Figure

J. Phys. Chem. B, Vol. 103, No. 41, 1999 8747 7). The protein-induced shifts in transition energies of the B850R and B850β pigments reduce the width of the exciton manifold by 595 cm-1 (Figure 7). This is a consequence of a reduced nearest neighbor interaction energy Jnm, when the transition energies of the individual pigments become unequal. Figure 9 illustrates the effect of pigment-protein and pigment-pigment interactions. The transition energy of the ZINDO/S calculation of a single Bchl a molecule fixed to the experimental value of 12 937 cm-1 is shown on the left column of Figure 9a. When the interaction with the protein matrix δn (eq 1) is taken into consideration, the transition energy of each pigment is shifted to lower energy. The local environment of the B800 pigment shifts its energy by 420 cm-1 to 12 517 cm-1. The transition energies of the B850R and B850β pigments are shifted towards lower energy by 142 and 224 cm-1 by the histidine residue of the polypeptide. The dipole-dipole coupling Jnm between the B800 pigments results in nine excitonic energy levels that are spread over only 95 cm-1 (Figure 9b). Coupling between the pigments in the B850 ring results in an energy level structure where the 18 exciton levels are spread over 2263 cm-1 (Figure 9a). When the interaction between the B800 and B850 pigments is taken into account (LH2 in Figure 9), the energy levels that belong initially to B800 pigments move closer to each other, spreading now over 87 cm-1. The energy levels that were initially part of the B850 system shift away from the B800 energy levels. The B800-B850 interaction has no effect on the spread of the entire exciton manifold. Point Dipole Approximation. The point dipole approximation (case A) produces an exciton manifold of 1230 cm-1 in width, about half of what is predicted by the CIEM approach (cases B and C). The difference is due to the coupling energy between the B850 neighboring pigments. The semiempirical calculation gives much higher interaction energies than the point dipole approximation. This indicates that the Bchl a pigments of the B850 ring are so closely packed that the overlap of the molecular orbitals of the neighboring monomers contributes significantly to the interaction energy. The problem with the point dipole approximation has been accounted for in the literature by shifting the transition energies of the Bchl a molecules, increasing the transition dipole moments, and/or by improving the model for pigment-pigment interaction.2,22,60,61 One way of taking into account the spatial size of the transition density of Bchl a is to use point monopole model instead of point dipoles. Point monopoles obtained from π-electron wave functions of a dicarbonyl-substituted tetrahydroporphin25 have been applied for spectral simulation of LH2.2 Other parameters used for this simulation were  2.1 [0], transition dipole 6.13 D, and the transition energies corresponding to 800 nm (B800) and 816 nm (B850R,β). The resulting interaction matrix element Jnm between B850R and B850β of adjacent protomers was 273 cm-1. By using these parameters, the absorption spectrum of LH2 was quite successfully produced while the prediction of the CD spectrum failed. A more advanced model for the pigment-pigment interaction has been suggested recently.22 Starting with ab initio wave functions of the single pigments, a numerical transition density function (transition density cube, TDC) was calculated. Provided that the wave functions describe the transition correctly, it is possible to use TDCs to calculate Coulombic coupling between the pigments with high accuracy. The result of TDC method was that the coupling within the RβB850 protomer is 213 cm-1. The point monopole interaction model takes the spatial size of the transition density into account. The resulting RβB850 interaction energy is reduced compared to point dipole ap-

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Figure 9. (a) Effect of δn and Jnm terms on energy levels. In the column on the left the effect of protein interaction on the energy levels of the Bchl a molecules of the LH2 antenna is shown. Following columns show the coupling between the B800 molecules (without the B850 pigments) and the coupling between the B850 pigments (excluding the B800 pigments). LH2 column refers to the exciton manifold of the entire antenna. (b) An expanded view of the central 800 nm region of the exciton manifold. (Also marked in the figure are the energy differences in cm-1.)

proximation. The more accurate TDC method reduces the interaction energy even further. This is in contrast to our CIEM result. It seems that the problem of calculation of RβB850 pigment-pigment interaction is not in the description of transition density. Most likely the Bchl a’s of B850 are so close to each other that the interactions cannot be described as small perturbations. Our CIEM calculation, where the nearest neighbor interaction energy is taken from a semiempirical calculation, provides a feasible way of avoiding this difficulty. A semiempirical calculation of a Bchl a dimer is well manageable by current computers. The method takes into account the effect of orbital overlap that has a major effect on the interaction energies of the B850 pigments. In this way, the transition energies and the transition dipoles can be kept within experimental values, and there is no need to introduce arbitrary environmental shifts. In many cases transition energies of the B850 chromophores have been used as a variable parameter (from 751 to 843 nm), with no systematic calculation of its value, in an effort to shift the computed spectra to make a good match with the experimental spectra.2,11,16,19-21 In our case all monomeric transition energies, for the B800 pigment and both B850 pigments, were computed by the semiempirical ZINDO/S method and the environmental interactions (amino acids, phytyl tails, and carotenoids) were included in the calculation of these energies. A further difference of our work from the previous studies is that interaction energies were computed by using the supermolecule approximation of the B850 dimers and clearly higher interaction energies were obtained than have been reported by using the dipole-dipole, the point monopole, and the TDC approximations.2,11,16,19-21 Localization of Wave Functions. The function of the LH2 antenna system is to transfer the excitation energy via the LH1 antenna to the reaction center. Two limiting cases are often

discussed in the literature. On one hand the excitation can be thought of as being localized on a single Bchl a or a Bchl a dimer and the excitation transfer described as hopping motion of the excitation from one site to another. On the other hand the excitation can be imagined to be delocalized over all the B850 pigments of the LH2 ring and the excitation transfer considered as relaxation between these exciton states. The actual dynamics may be an intermediate case, where the excitation is delocalized over only a part of the system. Table 2 lists an average exciton length of each state of the spectral simulation (see Table 2 for definition of exciton length). Participation number is defined as an inverse of the exciton length. According to a calculation of Pullerits et al.,26 the coherence length of an excitation in the B850 antenna of Rb. Sphaeroides is 4 ( 2 Bchl a monomers 2 ps after the exciting laser pulse. Their result is based on a simulation of the transient absorption difference spectrum and comparison with the experiment. A similar number was obtained by the same group with a more advanced model taking into account also the effect of diagonal disorder.65 Meier et al.66 incorporated exciton phonon coupling in their involved Green function formalism of pump-probe spectroscopy. A conclusion was arrived at that the absorption difference spectrum itself can be explained with a variety of parameters, including a model where there is no diagonal disorder present. In a superradiance study of the LH2 complex of Rb. sphaeroides Monshouwer et al.67 concluded that the average participation ratio is 8.3 at room temperature. It should to be noted that this participation ratio takes into account the Boltzmann population of the states together with the dipole strength of each state contributing to the emission. According to spectral simulation of the LH2 of Rps. acidophila by Koolhaas et al.,61 at least half of the whole B850 ring has to be taken into account in order to explain the red shift of the CD spectrum.

Properties of the LH2 Antenna of Rps. acidophila Also, the fact that the lowest A level of the exciton structure is only weakly allowed (carrying about 3% of the oscillator strength of the B850 absorption at 4.2 K)29 indicates that almost the entire ring contributes to the absorption spectrum. The oscillator strength of the strongly allowed E states is proportional to the exciton delocalization.16 Disorder in the structure or in the transition energies or coupling between the pigments shifts oscillator strength to the states that are forbidden in a totally symmetric case with no disorder. There is an apparent discrepancy between the exciton delocalization in the time-resolved experiments and in the calculation of static properties of the spectrum. The Green function theory of nonlinear spectroscopy applied by Meier et al.66 suggests a definition of a localization size that is different from one based on the size of the eigenstates. The definition of localization based on a density matrix formalism may show localization even if the individual eigenstates are delocalized. A time domain analysis of the effect of static inhomogeneity upon exciton dynamics of the B850 complex has been presented.68 The analysis shows that initially an extended virtual exciton state, which is a superposition of optically accessible eigenstates, can be prepared irrespective of the amount of disorder in the system. It seems that the disagreement between different partition numbers at least partly results from the theoretical viewpoint taken to describe the experimental results. When interpreting time-resolved experiments, it is essential to correctly construct the initial state from where the time evolution starts. In the following, we consider the time-independent eigenstates of the system. Our results show that the whole B850 ring has to be taken into account in calculation of the energy levels of the LH2 complex. Although the probability amplitude of a certain exciton level is concentrated only on a few pigments, the whole structure is needed to create the state involved. The time-independent wave functions show a disorder-dependent delocalization length. The effect of disorder on the localization of the wave functions has systematically been studied by Wu and Small17,28 by using symmetry-adapted basis defect patterns. Figure 10 shows an example of states for one of the 8000 simulations with random diagonal and nondiagonal disorder (case D). The original symmetry of the corresponding state of a homogeneous system state together with the actual wavelength of absorption, relative oscillator strength, and a participation ratio are indicated in Figure 10 for the five most important exciton states. The area of each circle is proportional to the coefficient cen of the pigment in the exciton wave function (eq 3b). The sign of the coefficient is indicated by black/white color. The outer ring represents the B800 pigments, while the inner circle shows the B850 pigments. The randomly selected B800 states 4E1 and 3E1 of the inhomogeneous system show that although the probability amplitude is mainly concentrated on a single molecule, there is significant amplitude over four to five Bchl a molecules (Figure 10). Therefore, even the B800 states cannot be considered localized on a single Bchl a molecule. Additionally, the B800 states show some probability amplitude on the B850 molecules. The energy transfer is from the B800 state to the states involving the B850 pigments. The first step of energy transfer most probably takes place between B800 and the states close to 820 nm in energy. These states (e.g., 2E3 of Figure 10) are very much delocalized over the B850 pigments. A correct presentation of energy transfer between the B800 states and the states near 820 nm includes pairwise couplings between all the pigments involved in the transition. From Figure 10, it is clear that it is not sufficient to calculate a transfer rate between a

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Figure 10. Selection of states taken from one simulation with random diagonal and nondiagonal disorder (case D). The original symmetry of the corresponding state of a homogeneous system together with actual wavelength of absorption, relative oscillator strength, and exciton length is indicated for each state.

single B800 molecule and a single B850 molecule. Our preliminary estimate for the energy transfer rate between B800 and B850 gives inverse rate values ranging from a few hundred femtoseconds to a few picoseconds depending on which particular sample from inhomogeneous distribution is probed. Conclusion The main results of this paper are that the absorption spectrum of LH2 antenna of Rps. acidophila can only be explained by taking into account the entire ring structure of Bchl a’s and the nearby amino acid residues in the calculations. The electronic states of the LH2 antenna result from interactions between all the 27 Bchl a pigments. The couplings between the adjacent B850 pigments cannot be described as point dipole interaction. The close distance between the pigments in the B850 ring results in orbital overlap that cannot be considered as a small perturbation between the chromophores. A new method based on semiempirical configuration interaction ZINDO/S calculation together with exciton theory is introduced, and it is shown that the approach is successful in predicting the absorption and CD spectra of the LH2 antenna of Rps. acidophila. Configuration interaction exciton method (CIEM) is not limited to semiempirical level of theory. As the computational resources improve, the CIEM method can be applied on large molecules at ab initio CI level. The method produces a simulation of the absorption and CD spectrum of LH2 by using parameters that are kept at their experimental values. In addition, the effect of protein environment on the electronic states can be taken into account. The most profound effect by the protein is induced to the B800 pigments, where the red shift is almost entirely from pigmentprotein interaction. In the case of B850 pigments, the red shift is mainly due to pigment-pigment interaction. We note that the direction of the transition dipole moment is about 3-5° above the N(A)-N(C) direction when the Bchl a is coordinated to a histidine residue. This can have a significant effect on intensities of the CD spectrum of the antenna.

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