9020
J. Phys. Chem. 1991, 95, 9020-9023
Excited-State Absorptlon in Bacteriochlorophyll a -Protein from the Green Photosynthetlc B8Ct@ri~tn Prosfhecochhrls aestuarii: Reinterpretation of the Absorption Difference Spectrum Herbert van Amerongen and Walter S. Struve* Ames Laboratory and Department of Chemistry, Iowa State University, Ames, Iowa 5001 I (Received: May 23, 1991; In Final Form: July 19. 1991)
Excited-state absorption arising from transitions between singly and doubly excited exciton components in strongly coupled photosynthetic antennae profoundly influences the absorption difference spectra observed in pumpprobe. spectroscopy. Model calculations of the absorption difference spectrum in the BChl a-protein complex from P. aestuarii are compared with the experimental spectrum.
Introduction Ultrafast pump-probe experiments have been used by several grou.ps'-s as a technique for investigating the excited-state dynamics and electronic excitation transport (EET) in photosynthetic antenna systems. Some studies have monitored photobleaching decays (ground-state recovery) in antennae composed of spectroscopically similar chlorophyll or bacteriochlorophyll chromophores. The time-dependent anisotropy functions associated with these decays have been attributed to photobleaching depolarization caused by EET between chromophores with contrasting transition moment orientations. Ultrafast timeresolved absorption difference specrra have been less frequently characterized and are seldom analyzed in terms of quantitative models. It appears desirable to be able to interpret these spectral changes in terms of energy flow among energetically inequivalent chromophores and/or exciton components. Spectral evolution can also arise in principle from exciton localization due to loss of coherence in an initially prepared antenna excited state. In a pumpprobe study of the BChl a-protein complex from the green photosynthetic bacterium Prosthecochloris aestuarii, we reported that its photobleaching spectrum at 2 ps was heavily biased toward the low-energy end of the Qy band systema6 Since the Qy spectrum in this strongly coupled antenna system' was no longer uniformly bleached at this time, this was seen as evidence for ultrafast exciton localization. In a more recent pumpprobe study of the 740-nm Qy region of BChl c aggregates in chlorosomes from the green bacterium Chlorofexus aurantiacus, we observed strongly bipolar absorption difference spectra." These spectra, dominated by excited-state absorption and photobleaching a t wavelengths shorter than -725 nm and longer than -735 nm, respectively, are reminiscent of similar spectra observed in antennae from Chlorobium limicola, Chlorofexus aurantiacus? and Rhodobacter sphaeroides.1° An analysis of our spectra in terms of linear exciton models led us ( I ) (a) Beck, W. F. Bull. Am. Phys. Soc. 1991,36, 341. (b) Beck, W. F.; Debrecreny, M.; Yan, X.; Sauer, K. In Ulrrajbsr Phenomena VII (Roceedings of the 7th International Conference, Monterey, CA, May 14-17, 1990); Harris, C. B., Ippen, E. P., Mourou, G.A., Zewail, A. H., Eds.; SpringerVerlag: Berlin, 1990; p 535. (2) Wasielewski, M. R.; Fenton, J. M.; Govindjee, Phorosynrh. Res. 1987, 12, 181. (3) Nuijs, A. M.; Shuvalov, V. A.; van Gorkom, H. J.; Plijter, J. J.; Duysens, N . M. Biochim. Biophys. Acra 1986, 850, 310. (4) Gillbro, T.; Sundstrbm, V.; Sandstrbm, A.; Spangfort, M.; Andersson, B. FEBS 1985, 193, 267. (5) Causgrove, T. P.; Yang, S.;Struve, W. S. J . Phys. Chem. 1989, 93, 6844. (6) Lyle, P. A.; Struve, W. S. J . Phys. Chem. 1990, 94, 7338. (7) Pearlstein, R. M.; Hemenger, R. D. Proc. Narl. Acad. Sci. U.S.A. 1978, 75, 4920. (8) Lin, S.; van Amerongen, H.; Struve, W. S. Biochim. Biophys. Acta, in press. (9) Vos, M.; Nuijs, A. M.; van Grondelle, R.; van Dorssen, R. J.; Gerola, P. D.; Amesz, J. Biochim. Biophys. Acra 1987, 891, 275. (IO) van Dorssen. R. J.; Hunter, C. N.; van Grondelle, R.; Korenhof, A. H.; Amesz, J . Biochim. Biophys. Acra 1988, 932, 179.
0022-3654/91/2095-9020$02.50/0
to recognize that the presence of strong exciton coupling virtually guarantees the appearance of intense excited-state absorption (ESA) at wavelengths near those of the static spectrum. This antenna ESA is unrelated to the ESA of the corresponding monomer chromophore. It stems instead from transitions between singly excited antenna states (in which a single Qyexcitation is delocalized among N Chl or BChl chromophores) and doubly excited antenna states (in which two Qtexcitations are shared by the N chromophores). The doubly excited exciton components lie a t energies that are approximately twice those of the singly excited components. The resulting ESA spectrum thus overlaps the static spectrum. Its details differ from those of the static spectrum, because the electric dipole intensities in the latter spectrum become redistributed in transitions between the singly and doubly excited antenna states. The net absorption difference spectrum can therefore be strongly bipolar. We have successfully used simple exciton models to simulate the principal features of the difference spectra observed in C. aurantiacus" and R . sphaeroides.I I In this work, we briefly describe our exciton model for ESA in photosynthetic antennae." For illustrative purposes, we treat the calculation of the ESA spectrum for a linear J-aggregate containing N chromophores. We then apply the model to calculations of theoretical absorption difference spectra for FennaMatthews-Olson (FMO)trimers of the BChl a-protein from P. aestuarii. At the present level of approximation, computation of the ESA spectrum requires no additional parameters beyond those employed in the calculation of the static spectrum.'* The resulting Qyabsorption difference spectrum for a 300 K Boltzmann distribution of populations in the coherent singly excited component states is dominated by intense photobleaching at wavelengths near the Qyband maximum (-812 nm) and by ESA at wavelengths shorter than -795 nm. If the system is assumed to evolve instead into a Boltzmann distribution of excitations localized on single BChl chromophores, a similar difference spectrum results. Hence, the thermalized difference spectra alone do not appear to be sensitive to exciton localization in this antenna. Exciton Theory for ESA in J-Aggregates In the zeroth-order exciton theory for the singly excited states in an antenna containing N chromophores, the wave function
for the nth exciton component is expanded in the basis of N localized singly excited states O f f )=
N- I
rI4,
r#)i*
j#i
( I I ) van Amerongen, H. Unpublished work. (12) Pearlstein, R. M. Bull. Am. Phys. SOC.1991, 36, 341.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 22, 1991 9021
Excited-State Absorption in BChl a-Protein where 4, and $Ji* denote the ground and Qyelectronic states on chromophore i. In the simplest description of J-aggregates,” all of the diagonal Hamiltonian matrix elements in this basis are assigned the value a,the Q,,energy of an isolated chromophore. The off-diagonal interaction energies are assumed to be negligible between non-nearest-neighbor chromophores and are assigned the uniform value fl for all pairs of nearest neighbors. It can be shownI3 that diagonalization of this Hamiltonian leads to the singly excited exciton component energies
Eil) = a f 26
COS
(N ; 1)’
ff
f
28COS(*).
ff
f
where the eigenvalue 0 exists only if N is odd. The expansion coefficients c,,, in eq 1 are given by the analytic expression (4)
In the specialized case of a J-aggregate, all of the chromophore transition moments p are parallel and are oriented so that the nearest-neighbor interaction energies are negative (8 < 0). The intensities I,, of the absorption bands arising from transitions between the ground state and singly excited exciton component q,,may then be computed from
At the same level of approximation, the doubly excited exciton levels
may be expanded in the N ( N - 1)/2 basis functions
a ~=)4,*4j*kYf 4k +ij
for j
> i; i = 1, ..., N - 1
(7)
that describe pairs of Q,,excitations localized on chromophores i and j . The diagonal energies in this basis are assi ned the uniform value 2a. The off-diagonal energy 2B) equals 8 if (a) one of the chromophores ( i j ) is the same as one of the chromophores (k,O and (b) the remaining two chromophores are nearest neighbors in the one-dimensional aggregate. It vanishes otherwise. It may then be shown that the N(N- 1)/2 eigenvalues for the doubly excited exciton components are8
(@f)lv@i,
EL2) = 2 a
+ 2fl[ COS
(&)
+ COS
(&)I
(8)
where p runs from 1 to ( N - 1) and q runs from (p + 1) to N for given p. These eigenvalues and the corresponding eigenvectors (not shown) can be used to compute the intensities Iia of transitions between singly and doubly excited exciton components with energies Efl) and G2), respectively, using an equation analogous to eq 5 : I/,n = Ixcijbnpq6jpfiq12 JW
(9)
Here 6 is the Kronecker delta. The resulting photobleaching and E& spectra have been discussed in detail* in connection with modeling the absorption difference spectrum of the BChl c antenna in chlorosomes from Cblorofexus auranriacus. In particular, the ground-state photobleaching is dominated by the transition between the ground state and the lowest singly excited exciton component. The strongest ESA transition from the latter level occurs to the lowest doubly excited exciton component and is blue-shifted from the photobleaching spectrum. Hence, this exciton model correctly predicts the bipolar feature of the absorption (13) McRae, E. G.;Kasha, M. J . Chem. Phys. 1958, 28. 721.
difference spectrum observed in the BChl c antenna from C. aurantiacus.8
Exciton Theory for ESA in FMO Trimers In photosynthetic antennae with arbitrary architecture, the diple-dipole couplings 6,in the N X N Hamiltonian matrix for the singly excited states may be evaluated using a Weiss point monopole expansiod4 if the chromophore electronic structure and organization are known. The X-ray structure of the BChl aprotein, first characterized by Matthews, Ten Eyck, and Fenna,” was later refined by Tronrud, Schmid, and Matthews.I6 The basic structural unit of the BChl a-protein is a trimer of identical protein subunits, whose folded &sheets each enclose seven BChl a chromophores. The diagonal matrix elements Hii, which nominally represent the BChl a site energies in the absence of couplings between chromophores, cannot be evaluated a priori without detailed knowledge of protein-chromophore interactions. Hence, the earliest simulations of electronic spectra in this antenna took the approach of evaluating realistic off-diagonal interactions using the known geometry and then searching for combinations of input diagonal energies H,, that would simultaneously yield good fits to both the absorption and CD ~ p e c t r a .Since ~ the dipole-dipole interactions between chromophores belonging to different subunits are smaller than the largest couplings between chromophores within the same subunit, these calculations were restricted to diagonalization of a 7 X 7 Hamiltonian,’ yielding exciton states that are delocalized over only one subunit of the FMO trimer. Phenomenological variation of the (unknown) energies Hii failed to produce any wave functions that satisfactorily simulated the absorption and CD spectra. This result prompted speculation that simple exciton calculations could not reproduce the major features of antenna electronic spectra. Efforts were then directed toward improving estimates of the single-chromophore energies Hi, by studying energetic effects of BChl conformational changes17and by attempting to model the protein-chromophore interactions.I8 It was also suggested that FMO trimers in the solutions studied spectroscopically may aggregate in a mode different from that in crystals; &sheets belonging to different trimers were hypothesized to be in such close contact that interactions between BChl chromophores inside the respective subunits became significant.I8 Very recently, spectral hole-burning studiesI9 provided compelling evidence that the Qyabsorption spectrum of this antenna exhibits more than seven exciton components and hence that the laser-prepared excited state must be delocalized over more than one subunit of an FMO trimer. The energy distribution of the exciton levels observed in hole burning was inconsistent with that predicted by Pearlsteinis for aggregates of FMO trimers with strong interactions (- 100-200 cm-’) between subunits belonging to different trimers. Hence, Johnson and Small suggestedIgthat the observed spectra must arise instead from interactions between subunits belonging to the same FMO trimer. By symmetry, such exciton states would be delocalized over the entire trimer. Subsequently, straightforward extension12of the single-subunit exciton calculation’ to all 21 chromophores in an isolated FMO trimer, based on trial variations of the single-site BChl a energies Hii, yielded greatly improved simulations of the Qyabsorption and CD spectra. Since the evaluation of the ESA spectrum requires no information beyond that used in the computation of the singly excited exciton states, this calculation provides a basis for the present simulation of the absorption difference spectrum. The interaction energies Fj used in our computations were evaluated by Pearlstein.I2 The diagonal energies Hii for the BChl (14) Weiss, C., Jr. J . Mol. Specrrosc. 1972, 44, 37. (15) Fenna, R. E.;Ten Eyck, L. F.; Matthews, B. W. Biochem. Eiophys. Res. Commun. 19’17, 75, 751. (16) Tronrud, D. E.; Schmid, L. F.; Matthews, B. W. J . Mol. Eiol. 1986, 188, 443. (17) Gudowska-Nowak, E.; Newton, M. D.; Fajer, J. J . Phys. Chem. 1990, 94, 5795. (1 8) Pearlstein, R. M. In Phorosynrheric Lighr-Huruesring Systems; Scheer, H., Schneider, S., Eds.; De Gruyter: Berlin, 1988; p 555. (19) Johnson, S.G.; Small, G.J. J . Phys. Chem. 1991, 95, 471.
9022 The Journal of Physical Chemistry, Voi. 95, No. 22, 1991
van Amerongen and Struve
24.8 244
a
12.0 12.4
I
780
800
820
WAVELENGTH (nm)
-
0L
I
Figure 2. Calculated absorption difference plus stimulated emission spectra for the FMO trimer from Prosthecochloris aestuarii. Curves 1, 2, and 3 show prompt (unrelaxed) spectra for excitation at 780,800, and 820 nm, respectively; the dashed curve is the spectrum for a 300 K Boltzmann distribution in the singly excited exciton components. Vertical scale calibration correspondsto representing the absorption band for the Q?transition of an isolated BChl (I chromophoreby a Gaussian spectrum with a height of unity.
I
I
Xhm)
Figure 1. Schematic energy level diagram for singly and doubly excited
exciton components in BChl a-protein complex from Prosthecochloris aestuarii, computed from basis sets confined to excitations on BChls 1-7 in one subunit of the FMO trimer. Arrows show all transitions from the ground state and strongest transitions from the lowest singly excited exciton component; numbers show relative intensities. Transitions from higher exciton components are omitted for clarity. The resulting stick spectrum is shown at the bottom, where dashed and continuous lines indicate photobleaching and ESA intensities, respectively.
a chromophores were those that yielded optimal fits to the static absorption and CD spectra:'* 12470 cm-' (BChls 1 and 2 in the original numbering of Fenna et al.Is), 12 500 cm-' (BChls 3 and 5),12 700 cm-' (BChl4), 12 300 cm-' (BChl6), and 12 165 cm-' (BChl 7). The Qytransition moment directions were computed from the BChl a crystallo raphic coordinates.lSJ6 The Hamiltonian matrix elements ( a,72)Iqa:?) in the doubly excited basis sets are readily expressed in terms of the matrix elements Hi, and Vii in the singly excited basis; they are HP4.W
Hpq*pr
H,,,
=
=0
= HPP v q r
(loa)
+ Hqq
for 4 # for p # s, q #
t
Figure 1 shows the exciton transitions that are predicted by a calculation confined to the seven BChl a chromophores in one subunit, for which there are N(N - 1)/2 = 21 doubly excited basis functions. Transitions from the ground state to the seven singly excited exciton components are responsible for the static Qyabsorption spectrum, while transitions between singly and doubly excited components account for ESA. Only the ESA transitions originating from the lowest exciton component are shown for simplicity. The resulting stick spectrum (evaluated using eqs 5 and 9) is shown at the bottom of Figure 1, where dashed and solid lines denote photobleaching and FSA, respectively. It is dominated by ground-state photobleaching (ESA) at wavelengths longer (shorter) than -790 nm. This single-subunit calculation is presented only for ease of visualization in Figure 1, because the 210 doubly excited levels in the FMO trimer (see below) are not easily depicted in such a diagram. In more realistic calculations extended to all 21 interacting BChl a chromophores in an FMO trimer,'2J9 symmetric-mode storage of the 22 155 matrix elements arising from the 210 doubly excited basis functions was automated with an algorithm based on eqs 10. Theoretical absorption difference spectra were evaluated by arbitrarily assigning a uniform Gaussian profile (200 cm-' fwhm) to each of the photobleaching and ESA transitions. In addition, stimulated emission (which is detected in pump-probe experiments
780
800 WAVELENGTH (nm)
820
Figure 3. Calculated difference plus stimulated emission spectrum for
an FMO subunit with a Boltzmann distribution of excitations localized
on single chromophores.
because the direction and polarization of the emitted photon coincide with those of the stimulating probe photon) was included in the simulations. The pertinent Einstein coefficients, denoted by Bod for absorption from the vibrationless ground state to Qy vibrational level u' and by Bdt,o for stimulated transitions from the vibrationless Qystate to vibrational level in the electronic ground state, obey the sum rule
Accordingly, the stimulated emission from each exciton component was represented by a 200-cm-' Gaussian line shape with height equal to that of the corresponding absorption component, weighted by the population in that exciton component. The energy shift A between the absorption and stimulated emission components was varied between 40 and 80 cm-I, in agreement with the shift observed between the fluorescence line-narrowed spectrum and the lowest energy exciton component;19 changes in A over this range had little effect on the spectra. Figure 2 contrasts the prompt (unrelaxed) absorption difference plus stimulated emission spectra for trimers excited at 20-nm intervals from 780 to 820 nm, with the thermalized spectrum for a 300 K Boltzmann distribution of singly excited exciton components. These spectra bear a strong family resemblance to corresponding spectra (not shown) obtained from the single-subunit calculation. (Such similarity implies that absorption difference spectra alone cannot determine whether the exciton states are delocalized over an entire FMO trimer or localized inside one subunit.) All of these spectra are dominated by a strong photobleaching peak centered at -807-814 nm. An additional calculation was carried out under the contrasting assumption of a Boltzmann distribution of excitations
J. Phys. Chem. 1991,95, 9023-9024
W
0
z
1
2U
0 m
v)
a a
0
800
780
820
WAVELENGTH (nm)
Figure 4. Experimental difference absorption signal normalized to the square of the laser power, data points; spectrum for 300 K Boltzmann distribution in the singly excited exciton components, solid curve; spectrum for Boltzmann distribution of excitations localized on single chromophores, dashed curve. Data are from ref 6 .
loalized on the individual chromophores. (When the excitation localizes on a particular chromophore, the computed ESA arises from exciton states delocalized over the remaining chromophores in the subunit.) The resulting spectrum, shown in Figure 3, is very similar to the thermalized coherent spectrum in Figure 2. For comparison, the experimental spectrum6 is shown in Figure 4. This was normalized in the earlier work by dividing the observed signal at each wavelength by the corresponding BChl a-protein optical density at that wavelength. A more detailed normalization, taking into account the wavelength dependence in the total probe beam attenuation and in the pump beam attenuation in the sample region before the beam intersection, has been applied in Figure 4. The localized spectrum (Figure 3) yields superficially better agreement with the experimental spectrum than the thermalized coherent spectrum (Figure 2); for example,
9023
the 795-nm zero-crossing point predicted in the coherent spectrum appears to be inconsistent with the experimental spectrum. However, these two calculated spectra are so similar in our view that they do not form a basis for judging the extent of coherence in this antenna. In summary, our exciton calculations of absorption difference spectra in P.aestuarii lead to the following conclusions: (1) ESA transitions drastically influence the absorption difference spectra in the presence of strong exciton couplings, even in antennae whose monomers do not exhibit strong ESA at wavelengths near the Q static spectrum. (2) Model calculations of the absorption d i t ference spectra, performed under assumptions of coherence over the FMO trimer versus localization on individual chromophores, yield similar agreement with the experimental spectrum. A more incisive experimental test for coherence may be afforded by a dynamic pump-probe experiment using 100-200-fs laser pulses. For example, Figure 3 offers a prediction of the spectral evolution accompanying relaxation between exciton components in the FMO trimer following excitation at 800 nm. Here, most of the spectral metamorphosis is predicted to occur at probe wavelengths shorter than -800 nm if exciton coherence is maintained; the photobleaching/stimulated emission peak at 807-81 4 nm would shift in position and broaden symmetrically. Localization of excitation followed by thermalization, however, would broaden this peak asymmetrically toward the red side (Figure 3). The required time scale for observing these spectral changes is suggested by the zero-phonon hole widths measured by Johnson and Small,Ig who reported that relaxation between exciton componnets occurs within 100 fs in this antenna. Acknowledgment. We are indebted to R. M. Pearlstein for making the BChl a-protein trimer point monopole interaction matrix available to us. The Ames Laboratory is operated for the US. Department of Energy by Iowa State University under Contract W-7405-Eng-82. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences.
COMMENTS In our original article, we showed that rcq approximately equals (1/2) d[CI-]dt. Substitution of this expression in eq 3 leads to the integrated form
Influence of Chiorlde on the Chlorlne-Formic Acid Reaction in Sulfuric Acid Sic In our article' "Kinetics of the Reaction of Chlorine with Formic Acid in Aqueous Sulfuric Acid", we assumed that chlorine is the species that oxidizes formic acid and did not consider the possibility of oxidation by hypochlorous acid. We have completed experiments that explore this possibility. This paper discusses our experiments and results. A scheme involving oxidation of HOC1 consists of an equilibrium step followed by a rate-determining step
C12 + H20 HCOOH
-
+ HOC1
HOC1
+
+ H+ + Cl-
C02 + H+ + C1-
+ H2O
(2)
which leads to the rate expression rco2 = kK[HCOOH] [ClJ /[H+] [Cl-]
(1) Hoq,
(3)
M.F.;Indu, B.: Emst, W. R.; Neumann, H.M.J . Phys. Chem.
1991, 95, 681.
0022-3654/9 1 /2095-9023%02.50/0
[C1-I2 - [Cl-]02 = 2kK[HCOOH] [Cl2]/[H+]t
(4)
To test for negative order dependence in chloride, we ran two chlorine-formic acid reaction experiments under identical conditions. In one experiment, sodium chloride was added initially to the reaction solution. In the other, sodium chloride was not added; however, some chloride formed initially because of the equilibrium, eq 1. Both experiments were run in triplicate. The experiments were conducted at 298 K with 1 M sulfuric acid and 0.59 M formic acid concentrations. Both of these reactants were present in large excess so that their concentrations remained constant. Chlorine concentration was maintained essentially constant and was monitored continuously by a UV spectrophotometer at 322 nm. Chlorine was continuously added to the solution from a cylinder through a fritted glass gas sparging tube. Chloride concentration was continuously monitored by a chloride-sensitive probe. Table I shows concentration data collected in the experiments. In experiment 2 (a, b, and c) the initial chloride concentration is, on the average, 10 times greater than that in experiment 1 (a, b, and c). Figure 1 is a plot of chloride concentration versus time 0 1991 American Chemical Society
