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V. J. Koester and F. K. Fong
Exciton Interactions in the Symmetrical Dimeric Aggregate of Chlorophyll a Monohydrate' Vaughn J. Kodstert and Francis K. Fong" Department of Chemistry, Purdue University, West Lafayette, Indiana 4 7907 (Received February 17, 1976) Publication costs assisted by fhe National Science Foundation
In this paper we present a theoretical expression for exciton interactions in C2 symmetrical Chl a dimers with special emphasis on the theoretical analysis of the red absorption band of the in vitro A700 (700-nm absorbing) dimeric aggregate of chlorophyll a monohydrate. The treatment is based on the point dipole approximation in first-order perturbation theory. The comparison between theory and experiment is based on established molecular parameters relevant to the unique Cz symmetrical (Chl a.HzO)z aggregate structure.
Introduction The hydrated aggregates of Chl a have been the subject of several recent studies from this laboratorya2These studies have been motivated by a number of recent developnients that have led to the conclusion that the most probable primary molecular adduct in the photosystem (PS) I reaction center photoactive aggregate P7OO3is a C2 symmetrical dimer of Chl a m ~ n o h y d r a t e .Recent ~ ! ~ experiments on the photogalvanic effects of Chl a and quinhydrone half-cell reactions have shown that the onset of photoactivity in Chl a is probably the photoactivation of a charge transfer state in Chl a-HzO aggregates.6 The purpose of the present paper is to characterize the optical properties in the proposed P700 dimer (Chl aH2O)z using the point dipole approximation in exciton theory. Exciton calculations for biological model systems have been concerned with a variety of possible aggregate interactions and consequent energy transfer processes.7-9 Possible exciton effects for unsymmetrical dimeric chlorophyll models have been considered in an earlier study.lO It has been concluded2a from the observed experimental effects of water titration and temperature on the optical and redox properties of Chl a-HzO aggregates that the in vitro 700-nm (A700) absorbing adduct (Chl a.HzO), is probably the in vivo P700 PSI aggregate. The computer deconvolution of the red absorption band of A700 into spectral components appears to be interpretable in terms of the expected exciton interactions.2aEarlier treatment of exciton interactions in the C2 symmetrical dimer (Chl a.Hz0)2 did not include the effects arising from the relatively minor horizontal displacement between the Mg atoms of the two chlorin We present in this work a theoretical expression for exciton interactions in C2 symmetric Chl a dimers that properly account for the effects arising from the parallel Mg displacements of the chlorin planes. The treatment is applicable not only to the symmetrical hydrated dimer (Chl a.H20)2 but also to the anhydrous dimer Chl a2 that is also believed to assume4ba C2 symmetrical aggregate configuration. Deconvolutions of optical data along with experimentally determined molecular structural data and the unique geometrical restrictions of the C2 symmetric dimer configurations make possible a satisfactory comparison between theory and experiment.
+ Present address: Graduate School of Biomedical Sciences, University of Texas Health Science Center, Dallas, Tex. 75235. The Journal of Physical Chemistry, Vol. 80, No. 20, 1976
Exciton Interactions in Cz Symmetric Chlorophyll Dimers I t has been shown in the original treatment of exciton interactions in the C p symmetric dimer (Chl a-HzO)z that the symmetric l\kl(A) and antisymmetric l\kl(B) singlet exciton components are separated in energy by two times the dipole-dipole (dd) coupling ~ a r a m e t e r ~ ~ , ~ e2H2
E = 3cos 0 R12
-
where the Chl subunit singlet-singlet (SO SI)transition moments e,ii subtend angles of &0/2 with respect to the C2 z axis, Rl2 is the distance between the two parallel chlorin planes, and A and B are respectively the symmetric and antisymmetric representations in the C2 point group. Also derived was the 3\k1(A)and 3\k1(B)triplet exciton splitting attributable to the dd i n t e r a c t i ~ n ~ ~ ? ~ K
= 0.4E(6/A)2
(2)
where the factor 6/A is determined within each subunit by the spin-orbit coupling interaction and the energy separation between S1 and the lowest triplet TI. In (1)and (2), effects arising from the horizontal displacement of the Chl a chlorin planes have been neglected for the sake of simplicity. From (1)and (2) the antisymmetric exciton components l\kl(B) and 3Ql(B) will be lower in energy than the corresponding symmetric components l\kl(A) and 3\k1(A)for 0 < 7r/2 and positive
E.
Taking into consideration the relative displacements between the two Chl a molecules in the C2 symmetrical structure of (Chl a.HpO)n (see Figure l),it is easy to show from the standard theoryll for dd exciton interaction that the coupling energy is given by (3) where (4)
and Rl2 and R I are the center-center and perpendicular interplanar distances, respectively. The indices 1 and 2 are dummy indices for the two partner Chl a molecules. Solutions to (3) represent all possible exciton splittings resulting from parallel translations of the molecular planes in the Cz sym-
2311
Dimeric Aggregate of Chlorophyll a Monohydrate P
0.0 0.2 0.3 0.4
0.5 0.6
0.7
Figure 1. Scaled modei representation of the C2 symmetrical A700 dimer (Chl a.HzO)z displaying the reciprocal ester CO--H(H)O.-Mg linkages. R12 and RI are the center-center and perpendicular distances (- _ -), respectively. The subunit transition moment efi is oriented according to the polarization of the 66 1-nm transition in monomeric chlorophyll a in ether (see text).
-
1.0
. .
metric dimer. The ordering of exciton components is determined by the geometric factor
G = 1 - (3p2 - 1)sin2
[
!]2
(5)
which is plotted in Figure 2 for 0 5 0 5 P and values of p in the range 0 Ip I1. The So S1 transition dipole strengths for the two exciton components11
-
where the plus and minus signs refer to the symmetric and antisymmetric components, respectively, are related to the angle 0 subtended by the subunit transition moments according to the expression
D;t = e2p2(1f cos 0)
(7)
Equation 7 may be recast in the form of a ratio 0 D+ _ - cot2 D2 which will become convenient in later applications. The above results are exact in first-order perturbation theory for point dipole interactions.ll The validity of this treatment will be examined in the following by applying (3)-(8) to a correlative interpretation of the experimental behavior of the in vitro (Chl a.H20)2 dimeric species. Exciton Interactions in the Cz Symmetric Dimer (Chl a432012 We have accounted for the computer deconvoluted (Chl a.H20)2 A700 absorption band components at 699 and 713 nm in terms of exciton interactions.2aUsing the experimentally observed2aratio 3.03 rt 0.15 for the integrated 699 nm/713 nm band intensity ratio in (81, we obtain 0 60'. The observed2a energy difference of 280 cm-I between the deconvoluted components corresponds to l = 140 cm-l. The interplanar distances R L and Rl2 in Figure 1 can be estimated from interatomic distances determined from x-ray diffraction studied2 of the polymeric ethyl chlorophyllide a dihydrate aggregate. The similarities between the Chl a-HzO interactions in (Chl a-H20)2 and (Chl a.2H201, have been described earlier.4c,5In Figure 1,we observe that the Mg atoms and H20 oxygens lie in a plane perpendicular to the C2(z) axis with the (H)HO-.Mg bonds directed perpendicular to the
8 (degrees) Figure 2. The relationship between exciton splitting and geometrical configuration for C2 symmetric chlorophyll dimers. Regions above and below the zero line correspond to positive and negative values of 6, respectively. Relative transition dipole strengths for the symmetric (-) and antisymmetric (- - -) exciton components are represented in the bottom portion of the figure. The angle 6' = 60' with the corresponding intensity ratio 3:l is obtained for the hydrated dimer (Chl a.H20)*.
chlorin planes. The bonding interactions within (Chl a.H20)2 may be envisaged to be equivalent to a symmetrical addition of a Chl a molecule to a monomeric unit of Chl a.2HzO.4c These interactions are accordingly seen to be equivalent4c to the subunit interactions in the ethyl chlorophyllide a.2H20 polymeric aggregate,12 in which the two water oxygens are respectively -2.4 and -3.6 8, from the chlorin plane and are separated by -2.8 h;. The 2.4-A value corresponds to the water molecule bonded to the Mg atom. For the unique C2 symmetrical (Chl a.H20)2 structure given in Figure 1,we obtain R L = 6.0 A, Rl2 = 6.5 A, and p = 0.92. Using these molecular parameters, we arrive at G = 0.62 and e2p2 = 12 D2 from (5) and (3), respectively. The subunit transition dipole strength e2y2 , 12 D2 corresponds to a transition dipole length of y = 0.73 h;, with which we compute the subunit oscillator strengthl3
where h is Planck's constant, m is the electron mass, c is the speed of light, and cv is the transition frequency. In the numerical computation of (9), we have used the chlorophyll monomer absorption v = 1.51 X lob4cm-l. Discussion The subunit transition dipole strength e2p2 = 12 D2 and dipole length p = 0.73 h; calculated for (Chl a-H20)2are on the order of the corresponding experimental values 21.7 D2 and 0.96 A for monomeric chlorophyll a in ether.14 There are two factors that may contribute to the apparent discrepancy: (1) The subunit oscillator strength f = 0.09 of (Chl a.H20)2 may be expected to differ somewhat from that (0.155) of monomeric Chl a in ether.l4 (2) The inherent difficulties encountered in applying the point-dipole exciton theory for finite intersubunit distances Rlz. In the present case, the calculated The Journal of Physical Chemistry, Vol. SO,No. 20, 1976
2312
V. J. Koester and F. K. Fong
subunit dipole length w = 0.73 A corresponds to Rlz = 6.5
A.
Attempts to explain the origin of spectral red shifts in Chl a aggregates relative to the 661-nm absorption in monomeric Chl a have not been successful.12 The exciton splitting centered a t 706 nm suggests that the red shift in the hydrated dimer may be due to Coulombic or exchange effects. The sign of the exciton splitting parameter from Figure 1 is positive in the region 6 < 90". Consequently the symmetric component which has the greater transition dipole intensity for 6 < 90" is on the short wavelength side of the antisymmetric component. For 6 > 90°, the transition dipole intensity for the antisymmetric component is larger and the latter can lie on either side of the symmetric component depending on the magnitude of p. The agreement between theory and experiment is consistent with the previous determination that the hydrated dimer symmetric exciton component 1*1(A) lies a t a higher energy than the antisymmetric component '*I@).
An alternative solution to (8) obtained from the observed2a intensity ratio of the exciton components yields 0 = 120". This solution appears to be less reasonable for physical reasons. CPK molecular models show that the reciprocal ester C=O. -H(H)O-Mg linkages in (Chl a.Hz0)Z are favored in configurations in which 6 = 60".15 An upper limit 6 = 80' is calculated in the dimer configuration where the carbomethoxy oxygens, HzO oxygens, and Mg atoms lie in the same plane, using the orientation of the transition moment e,ii (see Figure 1)in monomeric chlorophyll a 1 4 3and interatomic distances for ethyl chlorophyllide a.12 References and Notes (1) This research was supported by NSF Grant No. BMS7411919. (2) (a)F. K. Fong and V. J. Koester, Biochim. Biophys. Acta, 423, 52 (1976); (b) N. Winograd, A. Shepard, D. H. Karweik, V. J. Koester, and F. K. Fong, J. Am. Chem. SOC.,98, 2369 (1976); (c)V. J. Koester, L. Galloway, and F. K. Fong, Naturwissenschaften, 62, 530 (1975); (d) V. J. Koester. J. S. Polles. J. G. Koren, L. Galloway, R. A. Andrews and F. K. Fong, J. Lumin., 12, 718 (1976). (3) B. Kok, Biochim. Biophys. Acta, 48, 527 (1961). (4) (a)F. K. Fong. J. Theor. Biol., 46,407 (1974); Proc. Natl. Acad. Sci. U5A, 71, 3692 (1974); Appl. Phys., 6(2), 151 (1975); (b) F. K. Fong and V. J. Koester, J. Am. Chem. Soc., 97, 6888 (1975); (c)F. K. Fong, ibid., 97,6890 (1975). (5) For a review of recent developments,see, F. K. Fong, "Theory of Molecular
The Journal of Physical Chemistry,
Vol. 80, No. 20, 1976
Relaxation: Applications in Chemistry and Biology", Wiley-lnterscience, New York, N.Y., 1975, Chapter 9. (6) F. K. Fong and N. Winograd, J. Am. Chem. SOC.,98, 2287 (1976). (7) E. G. McRae and M. Kasha, J. Chem. Phys., 28, 721 (1958). (8)R. M. Hochstrasser and M. Kasha, Photochem. Photobiol., 3, 317 (1964). (9) R. S.Knox
in "Bioenergetlcs of Photosynthesis", Govingjee, Ed., Academic Press, New York, N.Y., 1975, Chapter 4. 10) J. C. Chang, Ph.D. Thesis, University of Rochester, Rochester, N.Y., 1972.
(a)A. S. Davydov, "Theory of Molecular Excitons", McGraw-Hill,New York, N.Y., 1962; (b) I. Tinoco, Jr., Radiat. Res., 20, 133 (1963). 12) H.-C. Chow, R. Serlin, and C. E. Strouse, J. Am. Chem. SOC.,97, 7230 11)
(1975). 13) G. Herzberg. "Molecular Spectra and Molecular Structure", Vol. 1, Van Nostrand, New York, N.Y., 1950. 14) C. Houssier and K. Sauer, J. Am. Chem. Soc., 92, 779 (1970). 15) Reference 5, p 282. 16) M. Gouterman and L. Stryer, J. Chem. Phys., 37, 2260 (1962).
Discussion S. FREED. Would you elaborate on your deconvolution experiment?
V. KOESTER. It was a computer deconvolution of the experimentally obtained absorption spectrum. M. GOUTERMAN. Are the 680-nm band in one dimer (the anhydrous) and the 700-nm band in the other, the upper exciton bands?
V. KOESTER.In the hydrated dimer A700 that is correct; for the anhydrous dimer theory predicts the upper exciton component to be weaker than the lower exciton band. M. GOUTERMAN. What is the mechanism for the red shift in the dimer? Isn't such a red shift for an upper exciton band without precedent?
V. KOESTER.That is an excellent question. I can only speculate at this point by a comparison with the spectrum of the 743-nm absorbing species. The crystal structure of ethyl chlorophyllide.2HzO has been done, and it's a polymeric species that absorbs at 743 nm. The 700-nm absorbing species also contains hydrogen bonded water, and the anhydrous species does not. If one plays with resonance structure models, one can, for hydrated chlorophyll, make resonance forms that allow ring 5 to resonate with the entire P system of the chlorin ring, that is, if one invokes an admixture of the enol form.
