Chemical Physics Letters 393 (2004) 184–191 www.elsevier.com/locate/cplett
Dependence of singlet-energy transfer on the conjugation length of carotenoids reconstituted into the LH1 complex from Rhodospirillum rubrum G9 Junji Akahane a, Ferdy S. Rondonuwu b, Leszek Fiedor Yasutaka Watanabe b, Yasushi Koyama a,* a
a,c
,
Department of Chemistry, Faculty of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan Department of Physics, Faculty of Science and Technology, Kwansei Gakuin University, 2-1 Gakuen, Sanda 669-1337, Japan c Faculty of Biotechnology, Jagiellonian University, ul. Gronostajowa 7, 30-387 Krakow, Poland
b
Received 8 April 2004; in final form 27 May 2004 Available online 2 July 2004
Abstract A set of carotenoids, i.e., neurosporene, spheroidene, lycopene, anhydrorhodovibrin and spirilloxanthin, having the number of conjugated double bonds n ¼ 9, 10, 11, 12 and 13, were incorporated into the LH1 antenna complex from Rhodospirillum rubrum G9, and the carotenoid–bacteriochlorophyll (Cars–BChl) singlet energy-transfer efficiencies were determined by subpicosecond time-resolved absorption spectroscopy to be 78%, 75%, 46%, 40% and 36%, respectively. In carotenoids with n ¼ 9 and 10, all the 1Bþ u , 1Bu and 2Ag channels were open, whereas in carotenoids with n ¼ 11–13 the 1Bu and 2Ag channels were closed, causing a sudden drop in the efficiency on going from n ¼ 10 to 11. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction In purple photosynthetic bacteria, all-trans carotenoids (Cars) are selectively bound to the antenna complexes and play an important function of light harvesting, which includes the absorption of photons by Car and subsequent singlet-energy transfer to bacteriochlorophyll (BChl) [1–4]. The approximate C2h symmetry of the all-trans conjugated chain gives rise to low-lying singlet-excited states including the 1Bþ u , 2Ag , 1Bu and 3Ag states, the latter two of which were recently identified by measurement of resonance-Raman excitation profiles [5–7]. Fig. 1 shows an energy diagram for the four singlet-excited states. According to the selection-rule based on the Pariser’s signs, + and ), optical transitions are allowed between a pair of electronic states having different signs, whereas internal conversions are allowed between a pair of those having the *
Corresponding author. Fax: +81-79-565-9077. E-mail address:
[email protected] (Y. Koyama).
0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.06.021
same sign [8,9]. Therefore, the 1Bþ u state can be directly populated by the optical transition from the ground state, whereas the 2A g , 1Bu and 3Ag states by subsequent internal conversion processes from the 1Bþ u state. As a result, Cars can transfer the excitation energy through plural channels from all those low-lying singlet states, a fact which is most probably the reason for the natural selection of the all-trans configuration by Cars in the antenna complexes [10–13]. The excited-state dynamics of Cars and BChl a in the LH2 complexes from Rhodobacter sphaeroides G1C, Rhodobacter sphaeroides 2.4.1, Rhodospirillum molischianum and Rhodopseudomonas acidophila containing Cars with n ¼ 9, 10, 11 and 11, respectively, were examined by visible and near-infrared time-resolved absorption spectroscopy [14]. The time constants of the Car–BChl singlet-energy transfer through three channels (1Bþ u ! Qx , 1Bu ! Qx and 2Ag ! Qy ) and those of singlet–triplet conversion (1Bu ! T1 ) were determined to evaluate the energy flow. Sums of singlet-energy transfer through the three channels, i.e., 88%, 84%, 51%
J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191
n 13 12
11
185
2. Experimental 10
9
8
2.1. Preparation of the reconstituted LH1 complexes +
1Bu
Energy / 103 cm−1
20
−
3Ag
Qx −
1Bu 15
−
2Ag
Qy 10
0.04
0.05 1 / (2n + 1)
Fig. 1. The dependence of the 1Bþ u -, 3Ag -, 1Bu - and 2Ag -state energies of Cars on the number of conjugated double bonds, n. The linear relation of the 1Bþ u energy, as a function of 1/(2n þ 1), was determined by 1A the use of the 1Bþ u (0) g (0) absorptions of neurosporene, spheroidene, lycopene, anhydrorhodovibrin and spirilloxanthin that were reconstituted into the LH1 complex from Rsp. rubrum G9 (Fig. 2). The linear relations of the 3A g , 1Bu and 2Ag energies are based on Eqs. (1)–(4) of [7]. The Qx and Qy energies of B880 BChls in the LH1 antenna complexes are also shown for comparison.
and 54%, in the four antenna complexes nicely explained the overall singlet energy-transfer efficiencies that were determined by comparison of fluorescence-excitation to electronic-absorption spectra, i.e., 92%, 89%, 53% and 51%. The sudden drop of the efficiency, on going from n ¼ 10 to 11 was explained in terms of the lowering of the 1B u - and 2Ag -state energies with respect to those of the Qx and Qy states of BChl, respectively (see Fig. 1). In the present investigation, we have applied the same method to the LH1 complex from Rsp. rubrum G9 (a carotenoidless mutant) into which the set of five different Cars, i.e., neurosporene, spheroidene, lycopene, anhydrorhodovibrin and spirilloxanthin with n ¼ 9; 10; 11; 12; and 13, respectively, was incorporated (reconstituted). We have addressed the following two specific questions: (1) Does the sudden drop in the energy-transfer efficiency on going from n ¼ 10 to 11 take place in the reconstituted LH1 complex as well? How about the efficiencies in the reconstituted LH1 complexes containing Cars with n ¼ 12 and 13? (2) How does the expansion of the ring size from LH2 (8 or 9 subunits) to LH1 (16 subunits) affect the efficiency?
A set of all-trans Cars with n ¼ 9–12 including neurosporene, spheroidene, lycopene and anhydrorhodovibrin were isolated as described previously [15]. The preparation of spirilloxanthin (n ¼ 13) was also described [7]. A reaction center-free LH1 complex from Rsp. rubrum G9 was prepared as described elsewhere, and each Car was incorporated, the details of which will be published elsewhere [16]. Briefly, the chromatophore membrane of Rsp. rubrum was solubilized with 0.3% N,N-dimethy-N-dodecylamine-N-oxide (LDAO) and centrifuged to obtain a crude LH1 complex containing a trace of reaction center, which was dialyzed to precipitate pure LH1 complex absorbing at 874 nm (B874 LH1). B874 LH1 was solubilized with 0.6% LDAO into a mixture of dimeric and monomeric LH1 complexes (B820 and B777 LH1). Each Car in acetone solution was added to the mixture, and then, the reconstituted LH1 complex was purified by DE52 column chromatography. 2.2. Subpicosecond time-resolved absorption spectroscopy Each reconstituted LH1 complex was suspended in 0.6% n-octyl-b-glucopyranoside at a concentration of OD ¼ 5 at the 1Bþ 1A u (0) g (0) absorption. Each LH1 preparation was excited at the 1Bþ 1A u (0) g (0) absorption with a photon density of 9.6 1013 photon cm2 . The setup and the experimental conditions of subpicosecond time-resolved absorption spectroscopy using 120 fs pump and probe pulses were described elsewhere [14,17]. 2.3. The singular-value decomposition and global fitting The detailed procedure of singular-value decomposition (SVD) and global fitting was described previously [18], and references therein. Four major components of physical significance were extracted by SVD from the spectral data matrix of each reconstituted LH1 complex, consisting of 419 180 data points along the 420–700 nm spectral and the )6 to 6 ps delay time scales. Then, global fitting was performed by the use of a branched relaxation scheme consisting the 1Bþ u ! 1Bu ! 2Ag ! 1Ag singlet internal conversion and the 1Bu ! T1 singlet–triplet conversion both in Car, and the 1Bþ u ! Qx , 1Bu ! Qx and 2Ag ! Qy singlet-energy transfer channels from Car to BChl in order to obtain the species-associated difference spectra (SADS) and the time-dependent changes in population of the 1Bþ u , 1Bu , 2Ag and T1 states of Car. The time constants of singlet energy-transfer channels were self-consistently refined by the use of the time profile of the bleaching of the Qy absorption.
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J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191
879 883
(b)
877
(c)
882
(d)
881
(e)
883
(f)
589
442 469 502
374
589
458 486 522
372
588
486 513 548
375
587
484 512 548
375
589
469 498 530
377
OD / arbitrary
(i) Comparison of electronic absorption spectra. Fig. 2 shows the electronic absorption spectra of the LH1 complexes reconstituted with the five different Cars and the native LH1 complex from Rsp. rubrum S1 containing spirilloxanthin. The present technique of reconstitution can be evaluated by spectral comparison between the reconstituted and the native LH1 complexes containing spirilloxanthin (spectrum e and spectrum f). The wavelengths of the 1Bþ 1A u (v ¼ 0, 1, 2) g (0), vibronic transitions of the reconstituted LH1 complex, i.e., 548, 512 and 484 nm, are very similar to, but sometimes shorter than, those of the native LH1 complex, i.e., 548, 513 and 486 nm, a fact which indicates that the reconstitution was successful but not perfect at all. The Qx and Qy absorptions of B880 BChls can also be used as a sensitive probe for intermolecular interaction between BChl and Car; their wavelengths in the reconstituted LH1 (587 and 881 nm) are almost the same as, but slightly shorter than, those in the native LH1 (588 and 883 nm), leading us to the same conclusion. The LH1 complexes reconstituted with different Cars can be characterized by comparison of electronicabsorption spectra a–e. Since the red shift of the 1Bþ u absorption of Car and that of the Qy absorption of BChl upon binding of each Car to the LH1 reflect the dispersive interaction between the p conjugated system of Car and the surroundings, and therefore, they can be used as a measure of completeness of reconstitution. The shift of the 1Bþ 1A u (0) g (0) absorption of Car upon binding to the LH1 complex, in reference to that in n-hexane solution, was 16, 15, 17, 16 and 21 nm for neurosporene, spheroidene, lycopene, anhydrorhodovibrin and spirilloxanthin. On the other hand, the Qy absorption of BChl shifts from 770 nm in acetone solution to 879, 883, 877, 882 and 881 nm in the LH1 complexes reconstituted with the above set of Cars. The set of reconstituted LH1 complexes can be classified into two groups; one, reconstituted with spheroidene, anhydrorhodovibrin and spirilloxanthin with the methoxy group(s) giving rise to longer wavelengths of Qy absorption (881–883 nm), and the other, reconstituted with neurosporene and lycopene with no methoxy group giving rise to shorter wavelengths of Qy absorption (877–879 nm). (ii) Evaluation of the overall singlet-energy-transfer efficiencies by comparison of fluorescence-excitation to electronic-absorption spectra. Fluorescence-excitation spectra of the reconstituted LH1 complexes were recorded in the 400–650 nm region (data not shown). The overall efficiency of Car–BChl singlet energy-transfer can be evaluated, in principle, by comparison of the
(a)
589
3.1. Characterization of the reconstituted LH1 complexes by electronic-absorption and fluorescence-excitation spectroscopy
425 452 483
375
3. Results and discussion
400
600 800 Wavelength / nm
1000
Fig. 2. Electronic absorption spectra of the LH1 antenna complexes reconstituted with (a) neurosporene, (b) spheroidene, (c) lycopene, (d) anhydrorhodovibrin and (e) spirilloxanthin. (f) The electronic absorption spectrum of the native LH1 complex from Rsp. rubrum S1, containing spirilloxanthin as the major component, is also shown.
J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191
intensity of the 1Bþ 1A u (0) g (0) transition in the fluorescence-excitation spectrum to that in the absorption spectrum after normalizing the peaks due to the Qx ground transition. We evaluated the overall efficiency, to be 88%, 73%, 35%, 34% and 35% for neurosporene, spheroidene, lycopene, anhydrorhodovibrin and spirilloxanthin, respectively. The probable errors were evaluated to be approximately 5%. 3.2. Subpicosecond time-resolved absorption spectra of the reconstituted LH1 complexes Fig. 3 shows the time-resolved absorption spectra of the reconstituted LH1 complexes; the ground state absorption spectra are shown on the top for comparison. In the visible region, spectral patterns due to the three different singlet-excited states of Cars appear in the orþ der: (1) the 1Bþ u state showing the 1Bu ! 1Ag (ground) stimulated emission, (2) the 1Bu state showing a broad transient absorption accompanied by the 1Bþ u stimulated emission and (3) the 2A g state showing a sharp and strong transient absorption accompanied by the bleaching of the 1Bþ 1A u g absorption. The spectral changes indicate internal conversion in the sequence of 1Bþ u ! 1Bu ! 2Ag ! (1Ag ). Accompanying the rise of the 2Ag -state transient absorption, the Tn T1 (13 Bu ) transient absorption increases in intensity, reflecting the branched 1B u ! T1 singlet–triplet conversion. In the near-infrared region, spectral patterns due to the two singlet states of BChl are seen in the order, (1) the Qx state showing a flat transient absorption and a dip due to the bleaching of the ground-state Qy absorption, and then, (2) the Qy state showing an Sn Qy transient absorption characteristic of the ring-type aggregate of BChl molecules [19] accompanied by the stimulated emission and/or the bleaching of the groundstate absorption. The spectral changes reflect the Qx ! Qy internal conversion; those states can be populated by singlet-energy transfer from Cars. The generation of the T1 state looks less pronounced in the longer-chain Cars (anhydrorhodovibrin and spirilloxanthin) rather than in the shorter-chain Cars (neurosporene and spheroidene), an observation which is in contrast to the case of Cars free in solution [20]. On the other hand, the decay of the Qy bleaching looks faster in longer-chain Cars than in shorter-chain Cars. If we ascribe the recovery of the Qy bleaching to the generation of the T1 -state BChl, the faster decay of T1 Car can be ascribed to the triplet–triplet annihilation reaction between Car and BChl. 3.3. Excited-states dynamics of Cars in the reconstituted LH1 complexes (i) The results of the SVD and global-fitting analyses. Fig. 4 shows the results of analyses for the reconstituted
187
LH1 complexes. The models used in the analyses are shown in Fig. 5. The species-associated difference spectra (SADS) for different Cars (top panels) can be characterized as follows: (1) In all Cars, the SADS of the 1Bþ u state consist of stimulated emission with some contribution of transient absorption. (2) The SADS of the 1B u state exhibit a broad absorption accompanied by bleaching of the ground-state absorption. Interfer ence between the spectral patterns of the 1Bþ u and 1Bu states remains to be removed. (3) The SADS of the 2A g state exhibit the characteristic strong and sharp transient absorption accompanied by bleaching of groundstate absorption. (4) The SADS of the T1 state exhibit clear vibrational progression of transient absorption and bleaching. The time-dependent changes in population (central panels) can be characterized as follows: In all Cars, se quential rise and decay in the order, 1Bþ u ! 1Bu ! 2Ag ! are clearly seen. The decay in the 1Bu state accompanies simultaneous rise of the 2A g and the T1 state, showing the branched relaxation starting from the 1B u state. The internal conversion processes speed up in longer-chain Cars. In this short time range (<5 ps), the relative population of the T1 state is higher in longerchain Cars, although it tends to decay subsequently. The fitting to the time profile of the Qy bleaching (the bottom panels) can be compared, or contrasted, as follows: (The observed time profile (noisy line) and the fitting curve (smooth line) are in almost complete overlap in each reconstituted complex. The residual of observed minus fitting is shown on the top). The time profiles of the shorter-chain Cars (n ¼ 9 and 10) are completely different from those of the longer-chain Cars (n ¼ 12 and 13); lycopene ðn ¼ 11Þ is somewhat in-between. The former Cars exhibit a slower rise phase suggesting the presence of both the fast and the slow transfer channels of singlet energy, whereas the latter Cars exhibit only a fast rise phase, suggesting the presence of only the rapid singlet-energy transfer channel. Further, the former Cars exhibit constant bleaching, whereas the latter Cars exhibit the recovery of the bleaching; an additional decay component was added in the fitting. Obviously, the bleaching recovery reflects the triplet-triplet annihilation reaction between the Car and BChl molecules as mentioned in Section 3.2. (ii) Singlet-energy transfer from Car to BChl and triplet generation in Car. Fig. 5 shows the time constants determined for the three possible channels of Car–BChl singlet-energy transfer and the generation of the Car T1 state in the reconstituted LH1 complexes. The time constants of singlet internal conversion in Cars and BChl were transferred from those determined in solution [20]. Those pathways whose time constants exceeded 40 ps (practically infinite in the present time scale) are shown in broken lines. Introduction of the 1B u ! Qy channel never succeeded the fitting to the time profiles of
188 J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191 Fig. 3. Subpicosecond time-resolved absorption spectra, in the visible and near-infrared regions, of the LH1 antenna complexes reconstituted with (a) neurosporene, (b) spheroidene, (c) lycopene, (d) anhydrorhodovibrin and (e) spirilloxanthin. The ground-state absorption spectra are also shown on the top for comparison.
J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191
189
Fig. 4. The results of singular-value decomposition followed by global fitting of the spectral data matrix in the visible region, including the SADS and 3 the time-dependent changes in population for the 1Bþ u , 1Bu , 2Ag and T1 (1 Bu ) states (upper two panels), and the results of fitting to the time profile of the bleaching of the Qy absorption (bottom panels, the residual for the fitting is also indicated) for the LH1 complex reconstituted with (a) neurosporene, (b) spheroidene, (c) lycopene, (d) anhydrorhodovibrin and (e) spirilloxanthin. Both global fitting procedures were based on the scheme shown in Fig. 5.
the Qy bleaching, and therefore, its possibility was excluded. Dependence of singlet-energy transfer on the conjugation length of Car can be characterized as follows: (1) energy transfer through the 1Bþ u channel slows down slightly when n increases; (2) energy transfer through the 1B u channel slows down slightly on going from n ¼ 9 to 10, and then, becomes (practically shut down) on going from n ¼ 10 to 11, because this channel becomes an uphill energy transfer. No energy transfer through this channel takes place at all in n ¼ 12 and 13, because the 1B u energy becomes far below the Qx energy. (3) Energy transfer through the 2A g channel speeds up by 1.6 times on going n ¼ 9 to 10, but it stops on going from n ¼ 10 to 11, 12 and 13. The above trends that singlet-energy transfer is suppressed when the energy gap between the donor and the acceptor states is decreased are found not only in the previous investigation on LH2 but also in the present investigation on LH1. This observation remains
unexplained. On the other hand, the generation of T1 state from the 1B u state of Car systematically speeds up when n increases following the energy-gap law. Table 1a lists the efficiencies of Car–BChl singletenergy transfer and the triplet generation in Car in the reconstituted LH1 complex, which can be summarized as follows: (1) the singlet-energy transfer through the 1Bþ u channel decreases slightly but systematically with n; (2) the energy transfer through the 1B u and 2Ag channels decrease on going n ¼ 9 to 10. Both channels become closed in n ¼ 11–13; (3) as a result, a sum of the three channels slightly decreases on going from n ¼ 9 to 10, substantially decreases on going from n ¼ 10 to 11, and slightly decreases further on going from n ¼ 11 to 12 and 13. The sums of the singlet-energy transfer roughly parallel to the overall efficiencies independently determined by the use of fluorescence-excitation and absorption spectra (see Section 3.1); (4) the generation of the T1 state increases accordingly, when n increases.
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J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191 1Bu+ 1Bu-
0.18 ps
0.20 ps
1Bu+
0.20 ps
1Bu+
0.18 ps
1.2 ps 1Bu0.56 ps
Qx
Qx
1Bu-
4.2 ps 0.70 ps
1Bu+
Qy
Qy
Qx
0.15 ps 1Bu-
0.10 ps
2Ag-
Qx
0.10 ps
2AgQy
0.10 ps 1Bu-
0.33 ps 40 ps
0.42 ps
0.24 ps
0.13 ps
0.38 ps
0.10 ps 2.6 ps
0.56 ps
0.23 ps
5.0 ps
0.46 ps 2Ag-
0.10 ps
1Bu+
0.15 ps 1.3 ps
Qx
2Ag-
0.22 ps
0.28 ps Qy
(100 ps)
2Ag-
Qy (100 ps)
0.35 ps 0.30 ps
T1
T1 24 ps 2 ns
G BChl
G
spheroidene
BChl
2 ns
2 ns
1AgBChl
2 ns
1Ag-
G
lycopene
1.4 ps
2 ns
2 ns
1Ag-
T1
2.2 ps
2 ns
2 ns
1Ag-
T1
3.9 ps
2 ns
2 ns
neurosporene
T1
8.9 ps
anhydrorhodovibrin
G BChl
1Ag-
G
spirilloxanthin
BChl
Fig. 5. Relaxation schemes including (i) singlet internal conversion in Car and BChl, (ii) singlet–triplet conversion in Car, and (iii) singlet-energy transfer from Car to BChl through the 1Bþ u , 1Bu and 2Ag channels. The energies of singlet levels are transferred from those in Fig. 1, and those of T1 Car are transferred from the linear relations obtained by phosphorescence spectroscopy of the LH2 complexes [14]. The time constants of singlet internal conversion were transferred from those determined in solution for both Cars [20] and BChl [Rondonuwu et al. unpublished]. The time constants of the Car–BChl singlet-energy transfer through different channels and that of the singlet–triplet conversion in each Car have been determined in the present investigation.
Table 1 Efficiencies of Car–BChl singlet-energy transfer through the 1Bþ u , 1Bu and 2Ag channels and those of the 1Bu -to-T1 singlet–triplet conversion as determined by the SVD and global-fitting analyses of time-resolved absorption data Carotenoid ðnÞ
U(1Bþ u ) (%)
U(1B u ) (%)
U(2A g ) (%)
U(overall) (%)
Triplet (%)
(a) Reconstituted LH1 complexes Neurosporene (9) Spheroidene (10) Lycopene (11) Anhydrorhodovibrin (12) Spirilloxanthin (13)
47 47 41 39 35
11 9 2 0 0
20 19 3 1 1
78 75 46 40 36
19 20 27 29 31
(b) Native LH2 complexes Neurosporene (9)a Spheroidene (10)b Rhodopin & lycopene (11)c Rhodopin glucoside (11)d
48 46 48 48
19 18 2 2
22 20 1 4
88 84 51 54
10 12 17 16
a
Rba. sphaeroides G1C. Rba. sphaeroides 2.4.1. c Rsp. molischianum. d Rps. acidophila [14]. b
Table 1b compares, between the LH1 and the LH2 complexes, the efficiencies of Car–BChl singlet energytransfer through the three channels and triplet genera tion in Cars: (1) closing down of the 1B u and 2Ag energy-transfer channels and the resultant sudden drop in the overall energy-transfer efficiency take place on
going from n ¼ 10 to 11 in both the LH1 and LH2 complexes. In the LH1 complex, the efficiency goes down further on going further to n ¼ 12 and 13; (2) the energy-transfer efficiencies through different channels as well as the overall efficiencies are smaller, whereas the amounts of triplet state generated are larger in the LH1
J. Akahane et al. / Chemical Physics Letters 393 (2004) 184–191
complex than in the LH2 complex. The pair of results constitutes the answers to the questions addressed in Section 1. Acknowledgements This work has been supported by a grant from Ministry of Education, Science, Sport and Culture (Open Research Center Project) and a grant from NEDO (New Energy and Industrial Technology Development Organization, International Joint Research Grant). References [1] H.A. Frank, R.J. Cogdell, in: A. Young, G. Britton (Eds.), Carotenoids in Photosynthesis, Chapman & Hall, London, 1993, p. 252. [2] Y. Koyama, M. Kuki, P.O. Andersson, T. Gillbro, Photochem. Photobiol. 63 (1996) 243. [3] V. Sundstr€ om, T. Pullerits, R. van Grondelle, J. Phys. Chem. B 103 (1999) 2327. [4] T. Ritz, A. Damjanoviae, K. Schulten, J.-P. Zhang, Y. Koyama, Photosynth. Res. 66 (2000) 125. [5] T. Sashima, H. Nagae, M. Kuki, Y. Koyama, Chem. Phys. Lett. 299 (1999) 187. [6] T. Sashima, Y. Koyama, T. Yamada, H. Hashimoto, J. Phys. Chem. B 104 (2000) 5011.
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[7] K. Furuichi, T. Sashima, Y. Koyama, Chem. Phys. Lett. 356 (2002) 547. [8] R. Pariser, J. Chem. Phys. 24 (1956) 250. [9] P.R. Callis, T.W. Scott, A.C. Albrecht, J. Chem. Phys. 78 (1983) 16. [10] Y. Koyama, J. Photochem. Photobiol. B: Biol. 9 (1991) 265. [11] Y. Koyama, R. Fujii, in: H.A. Frank, A.J. Young, G. Britton, R.J. Cogdell (Eds.), Advances in Photosynthesis, The Photochemistry of Carotenoids, vol. 8, Kluwer Academic Publishers, London, 1999, p. 161. [12] C.C. Gradinaru, J.T.M. Kennis, E. Papagiannakis, I.H.M. van Stokkum, R.J. Cogdell, G.R. Fleming, R.A. Niederman, R. van Grondelle, Proc. Natl. Acad. Sci. USA 98 (2001) 2364. [13] E. Papagiannakis, J.T.M. Kennis, I.H.M. van Stokkum, R.J. Cogdell, R. van Grondelle, Proc. Natl. Acad. Sci. USA 99 (2002) 6017. [14] F.S. Rondonuwu, K. Yokoyama, R. Fujii, Y. Koyama, R.J. Cogdell, Y. Watanabe, Chem. Phys. Lett. 390 (2004) 314. [15] R. Fujii, T. Inaba, Y. Watanabe, Y. Koyama, J.-P. Zhang, Chem. Phys. Lett. 369 (2003) 165. [16] L. Fierdor, J. Akahane, Y. Koyama, unpublished. [17] J.-P. Zhang, R. Fujii, P. Qian, T. Inaba, T. Mizoguchi, Y. Koyama, K. Onaka, Y. Watanabe, H. Nagae, J. Phys. Chem. B 104 (2000) 3683. [18] J.-P. Zhang, T. Inaba, Y. Watanabe, Y. Koyama, Chem. Phys. Lett. 331 (2000) 154. [19] T. Pullerits, M. Chachisvilis, V. Sundstr€ om, J. Phys. Chem. 100 (1996) 10787. [20] F.S. Rondonuwu, Y. Watanabe, R. Fujii, Y. Koyama, Chem. Phys. Lett. 376 (2003) 292.