J. Phys. Chem. 1990, 94, 5795-5801 observedzz and it seems plausible that a similar stereospecific interaction will also exist between malononitrile and dichloromethane.z3 It appears that nuclear multispin relaxation may provide a very sensitive probe of intermolecular association. Other work is in progress to explore this potential. Finally, it must be mentioned that solutesolute intermolecular interactions are not necessarily negligible for the 1.02-1.04 m employed in these studies. Indeed, if one considers only the mole fraction of hydrogen in solutions H and D,corrected values of c(H) and c(D) are 0.8 12 and 0.062, implying R 6.7. Although not strictly correct, it could be argued that mutual relaxation between two pairs of methylene protons would approximate a random-field interaction because the amount of additional multispin order created would be slightz4and would not impact directly upon the spectral parameters measured in this study. Similarly, it must be recognized that a pair of three-level systems brought into mutual contact is more effective at inducing spin relaxation than an encounter with a simple thermalized dipole. Based upon these observations, the observed value for R is certainly reasonable and seems to indicate specific intermolecular interactions are operative.
-
(22) Bougeard, D.; Le Calve, N.; Pasquier, B. Ber. Bunsen-Ges. Phys. Chem. 19877, 91, 1273. (23) Green, R . D. Hydrogen Bonding by C-H Groups; MacMillan Press: London, 1974. (24) Blicharski, J. S.;Nosel, W.; Schneider, H. Ann. Phys. 1971, 27, 17.
5795
Although the present study does not attempt to disentangle effects due to solutesolute intermolecular dipolar relaxation or chlorineproton interactions, relatively simple extensions of this work would enable the researcher to do so. For example, studies done at different solute concentrations would result in the unambiguous separation. With this information, and having the magnitude of the cross-correlated random-field term (JHH,),one could build a microscopic model of solutesolute, solutesolvent interaction that would complement conventional studies nicely. Conclusion
This study provides yet one more example of how multispin relaxation studies can provide exacting descriptions of the microdynamical behavior of relatively small spin groupings in mobile environments. For the system studied, it was discovered quite suprisingly that the reorientational motions of malononitrile in dichloromethane solution approximate symmetric top behavior-yet the molecular symmetry axis and the principal axis of the rotational diffusion tensor are not coincident. It is also suggested that multispin relaxation can serve as a sensitive probe of one of the most ubiquitous yet least exploited mechanisms of nuclear spin relaxation-the intermolecular dipolar interaction. It is important to recognize that the proposed methodology differs radically from typical isotopic substitution methods and examines nuclear spin relaxation at a different level of sophistication. Registry No. CH2(CN),, 109-77-3; dichloromethane, 75-09-2.
Conformational and Environmental Effects on Bacteriochlorophyll Optical Spectra: Correlatlons of Calculated Spectra with Structural Results E. Gudowska-Nowak,la* M. D. Newton,*,le and J. Fajer*Jb Department of Applied Science and Chemistry Department, Brookhaven National Laboratory, Upton, New York 1 1 973 (Received: January 18. 1990)
Recent structural data for porphyrins and (bacterio)chlorophylIshave demonstrated the skeletal flexibility of the chromophores. Experimental redox and optical results for puckered porphyrins have also established that such conformational variations can affect the highest occupied and lowest unoccupied molecular orbitals of the chromophores and thereby modulate their light-absorption properties. The concept is applied to the bacteriochlorophyll a (BChl) antenna protein complex from Prosrhecochloris aestuarii, whose structure has been solved by X-ray diffraction ( J . Mol. Biol. 1986, 288, 443). INDO/s calculations, based on the crystallographic data for the seven individual BChls that comprise the antenna complex, yield absorption maxima that reflect the observed conformational variations and clearly establish that skeletal differences can influence the optical properties of the chromophores. Additional effects due to axial ligands, substituent orientations, and neighboring residues are also assessed.
I. Introduction
Current X-ray studies of antenna2 and reaction center3-5 bacteriochlorophyll (BChl) proteins are unveiling the molecular architecture used by photosynthetic bacteria to harvest and transduce light into chemical energy. The cumulative structural (1) (a) On leave from Jagellonian University, Krakow, Poland. (b) Department of Applied Science. (c) Chemistry Department. (2) Tronrud, D. E.; Schmid, M. F.; Matthews, B. W. J . Mol. Biol. 1986,
188, 443. (3) Deisenhofer, J.; Michel, H. Science 1989, 245, 1463 and references
therein. (4) Chang, C. H.; Tiede, D.; Tang, J.; Smith, U.; Norris, J. R.; Schiffer, M. FEES Lett. 1986, 205, 82. ( 5 ) Yeates, T. 0.; Komiya, H.; Chirino, A.; Rees, D. C.; Allen, J. P.; Feher, G.Proc. Nail Acad. Sci. W.S.A. 1988, 85, 7993.
0022-3654/90/2094-5795$02.50/0
results have revealed the organization of the chromophores and their protein microenvironment, i.e., axial ligands, neighboring and have Provided the impetus and basis residues, hydrogen for theoretical ca~cu~ations Of optical, redox and ESR properties, Stark effects, and vectorial electron transfer in BChls, antennas, and reaction center^.^-'^ (6) (a) Thompson, M. A.; Zerner, M. C . J . Am. Chem. SOC.1988, 110, 606. (b) Thompson, M. A.; Zerner, M. C., Fajer, J. J . Phys. Chem. 1990, 94, 3832. (7) Plato, M.; Mijbius, K.; Michel-Beyerle, M. E.; Bixon, M.; Jortner, J. J . Am. Chem. SOC.1988, 110, 7279. (8) Barkigia, K. M.; Chantranupong, L.; Smith, K. M.; Fajer, J. J . Am. Chem. SOC.1988, 110, 7599. (9) Hanson, L. K.;Fajer, J.; Thompson, M. A,; Zerner, M. C. J . Am. Chem. SOC.1987, 109, 4128.
0 1990 American Chemical Society
5796
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
Gudowska-Nowak et al. Y
R= C H , ~R ’ = c H ~ c H ~R,‘!=CH,OC
0
0
R’”=HOC C H ~ C H ~
0 c Figure 1. Schematic view of the backbone and arrangement of the BChls in one subunit of P.aestuarii. Reproduced with permission from: Fenna, R. E.; Matthews, B. W. Brookhaven Symp. Biol. 1976, 28, 174. Copyright 1976 Brookhaven National Laboratory.
Calculations of optical spectra for (B)Chl aggregates in proteins have often utilized exciton theory in which transitions for the monomers that comprise the arrays are arbitrarily shifted in order to obtain satisfactory agreement with experiment.1h222These shifts are attributed to generic protein effects that include axial ligands, nearby charges, T-T interactions with aromatic residues, and hydrogen bonding. Monomeric BChls do indeed exhibit shifted absorption maxima in vivo, but the “solvation” effects listed above do not offer a complete basis for the extent of these shifts.22 More recently, attention has focused on consequences of conformational distortions of the porphyrin skeleton, imposed by the protein in vivo, or by analogous steric interactions in vitro. These considerations are based on the expanding body of structural information that is becoming available for porphyrins and saturated hydroporphyrins such as chlorins, bacteriochlorins, isobacteriochlorins, and (bacterio)~hlorophylls.~~~~~~*~~ For example,
R= C H ~R’=H ,
,
R”=CH 3 o c
,
R”’=H
R=R’=R “=R.’”=H
0 model c , with CH3C replaced by H
Figure 2. Definition of structural models a-d for BChl a.
Barkigia et a].* have demonstrated the crystallographically significant deformations possible for a series of homologous bacteriopheophorbides d as well as for sterically crowded porphyrins. Deisenhofer et aL3 noted that the BChl b subunits that comprise the special pair or primary donor of Rhodopseudomonus viridis consist of different conformers, and Matthews and co-workers2 specifically called attention to the variety of conformations exhibited by the BChls that comprise the antenna complex of the green bacterium Prostkecochloris aestuarii (Figure 1 ), We thus consider here the role of such conformational variations in modifying the highest occupied (homo) and lowest unoccupied (lumo) molecular orbital levels of the chromophores and thereby modulating their light-absorption properties. We focus on the BChl complex of P . aestuarii whose sequencing and structure in the crystalline phase have been solved by X-ray diffraction,2 and which exhibits a series of low-energy absorption maxima that range from 793 to 825 nm in a low-temperature g l a ~ s . ~ * -The ~ ’ seven BChls a that comprise the protein subunits fall into two distinct conformational classes.2 We report here INDO/s calculations2*
(IO) Warshel, A.; Parson, W. W. J. Am. Chem. SOC.1987, 109, 6143. ( I I ) Parson, W. W.; Creighton, S.; Warshel, A. J. Am. Chem. SOC.1989, 1 1 1 , 4277. (12) LaLonde, D. E.; Petke, J. D.; Maggiora, G.M. J . Phys. Chem. 1989, 93. 608. ( I 3) See also: The Photosynthetic Bacterial Reaction Center; Breton, J., Vermeglio, A., Eds.; Plenum Press: New York, 1988: Treutlein. H.; Schulten, K.; Deisenhofer, J.; Michel, H.; Briinger, A,; Karplus, M. Ibid. p 139. Scherz, A,; Rosenbach-Belkin, V. Ibid. p 295. Parson, W.; Warshel, A,; Creighton, S.; Norris, J. Ibid. p 309. Scherer, P. 0. J.; Fisher, S. F. Ibid. pp 319,425. Pearlstein, R. M. Ibid. p 331. Won, Y.; Friesner, R . A. Ibid. p 341. Hanson, L. K.; Thompson, M.A.; Zerner, M. C.; Fajer, J. Ibid. p 355. Plato, M.; Lendzian, F.; Lubitz, W.; Trankel, E.; Mobius, K. Ibid. p 379. (14) For a recent review, see: Friesner, R. A.; Won, Y. Biochim. Biophys. Acta 1989, 977, 99. (15) Scherer, P. 0. J.; Fisher, S. F. Chem. Phys. Lett. 1987, 137, 32. ( I 6) Scherz. A.; Parson, W. W. Biochim. Biophys. Acta 1984, 766, 666. ( I 7) Pearlstein, R. M. In Photosynthesis; Amez, J., Ed. Elsevier Science: New York, 1987; p 299. ( I 8 ) Pearlstein, R. M. In Photosynthetic Light-Harvesting Systems; Schecr. H.; Schneider, S., Eds.; Walter de Gruyten: Berlin, 1988; p 555. 119) Lous, E. J.; Hoff, A. J. Proc. Natl Acad. Sci. U.S.A. 1987,84,6147. (20) Eccles. J.; Honig, B.; Schulten, K. Biophys. J . 1988, 53, 137. (21) Vasmel, H.; Amesz, J.; Hoff, A. J. Biochim. Biophys. Acta 1986,852, 159.
( 2 2 ) Hanson, L. K . Photochem. Photobiol. 1988, 47, 903. (23) Eschenmoser, A. Ann. N Y.Acad. Sri. 1986, 471, 108.
(24) Strouse, C. E. Proc. Natl Acad. Sci. U.S.A. 1974, 71, 325. Chow, H. C.; Serlin, R.; Strouse, C. E. J . Am. Chem. SOC.1975, 97, 7230. Serlin, R.; Chow, H. C.; Strouse, C. E. Ibid. 1975, 97, 7237. Kratky, C.; Dunitz, J. D. Acta Crystallogr.. Sect. B 1975, 832, 1586; 1977, B33, 545. Kratky, C.; Dunitz, J. D. J . Mol. Biol. 1977, 113, 431. Kratky, C.; Isenring, H. P.; Dunitz, J. D. Acta Crystallogr., Sect. B 1977, B33, 547. (25) Smith, K. M.; Goff, D. A.; Fajer, J.; Barkigia, K. M. J . Am. Chem. SOC.1982, 104, 3747; 1983, 105, 1674. Fajer, J.; Barkigia, K. M.; Fujita, E.; Goff, D. A.; Hanson, L. K.; Head, J. D.; Horning, T.; Smith, K. M.; Zerner, M. C. In Antennas and Reaction Centers of Photosynthetic Bacteria; Michel-Beyerle, M. E., Ed.; Springer-Verlag: Berlin, 1985; p 324. Barkigia, K. M.; Fajer, J.; Chang, C. K.; Young, R. J. Am. Chem. SOC.1984, 106, 6457. Waditschatka, R.; Kratky, C.; Juan, 8.;Heinzer, J.; Eschenmcser, A. J . Chem. SOC.,Chem. Commun. 1985, 1604. Suh, M. P.; Swepston, P. N.; Ibers, J. A. J . Am. Chem. SOC.1984, 106, 5164. Stolzenberg, A. M.; Glazer, P. A.; Foxman, B. M. Inorg. Chem. 1986.25, 983. Barkigia, K. M.; Smith, K. M.; Fajer, J. Recl. Trau. Chim. Pays-Bas 1987, 106, 218. Kratky, C.; Waditschatka, R.; Angst, C.; Johansen, J. E.; Plaquerent, J. C.; Schreiber, J.; Eschenmoser, A. Helu. Chim. Acta 1985, 68, 1312. Strauss, S . H.; Silver, M. E.; Long, K. M.; Thompson, R. G.; Hudgens, R. A.; Spartalian, K.; Ibers, J. A. J . Am. Chem. SOC.1985, 107, 4207. Barkigia, K. M.; Fajer, J.; Chang, C. K.; Williams, G. J. B. J. Am. Chem. SOC.1982, 104, 315. Alden, R. G.; Crawford, B. A.; Doolen, R.;Ondrias, M. R.; Shelnutt, J. A. J. Am. Chem.
SOC.1989, I I I , 2070. (26) Barkigia, K. M.; Gottfried, D. S.; Boxer, S. G.;Fajer, J. J . Am. Chem. SOC.1989, I I I , 6444. (27) Pearlstein, R. M.; Hemenger, R. P. Proc. &-at/ Acad. Sci. U.S.A. 1978, 75, 4920.
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990 5797
Bacteriochlorophyll Optical Spectra TABLE I: Deviation of the Conjugated BCbl Planarity BChl'
P
Framework from
class I b
Az,,,,~ A 22-atom planed N-atom planee
[hz]'/2p deg
1
1 1
class If 2 3 class [If 4 5 6 7
TABLE II: Linear Correlation Coefficients ( r ) for Out-of-Plane Deformation in the BChls"
0.07 0.12 0.13
0.08 0.22 0.21
6.7 8.7 8.5
0.14 0.10 0.15 0.10
0.15 0.14 0.22 0.24
8.4 10.4 8.7 7.1
2 3
BChl labels as defined in Figure 1. bAz is the vertical displacement ~ of the devifrom the indicated least-squares planes ( x y ) . c R m value ations (Aw) from idealized values (0' or 180') of all torsional angles w associated with atomic sequences i, j, k, I, where atoms j and k are bonded members of the set of 22 conjugated atoms. dPlane obtained by TSM.* 'Least-squares plane containing the four N atoms, each of which departs by 50.082 A from this plane (excluding BChl 2, the maximum deviation is 0.047 A). 'See ref 2.
for the seven individual BChls, based on the crystallographic data. These calculations yield absorption maxima which clearly establish that skeletal differences can significantly alter the optical properties of the chromophores. Effects of axial ligands, orientations of substituents, metals, and neighboring residues are also assessed in order to partition environmental and conformational influences on the spectral properties of the pigments. The calculations suggest that the effects of intrinsic conformational variations are at least as large as any of the former factors. The present calculations and previous results* for model porphyrins and photosynthetic reaction centers suggest that conformational variations play a significant role in determining optical (and redox) properties of porphyrin derivatives, and thus may offer attractively simple rationales, in conjunction with additional modulations imposed by protein residues or solvents, for their properties in vivo and in vitro. 11. Structural Models Coordinates for the BChls used in the calculations were based on the X-ray data of Tronrud, Schmid, and Matthews (TSM).2 The overall protein structure has been refined at 1.9 A resolution, and the resulting uncertainty in the BChl coordinates is estimated to be within 0.15 A. However, the porphyrin bond lengths and angles were constrained to lie (in the rms sense) within 0.02 A and 3.2', respectively, of idealized values. Hence, the experimental coordinates are felt to provide a useful sampling of conformational variation of the porphyrin skeleton. To help pinpoint the factors controlling the spectra, the BChl subunits were treated at several levels of structural elaboration, as indicated in Figure 2: these range from a nearly "complete" structure, model a (which contains all substituents except the phytyl group), to model b (containing the acetyl and methoxy carbonyl groups, and the methyl groups at unsaturated carbons), to model c (acetyl substituent only), to the bare skeleton, model d (with each omitted substituent replaced by a hydrogen atom at the appropriate site). In cases where a coordinating ligand was included, a subscript L is appended (aL, bL). To assess the role of the magnesium ion, bacteriopheophytin (BPheo) variants of models c and d (denoted cH and dHJ were generated by replacing Mg with H atoms at the atoms in rings 1 and 111. In addition, some calculations employed the recent high-precision coordinates obtained for methyl bacteriopheophorbide a.26 A measure of the distortion of the seven BChl frameworks is provided (Table I) by the rms deviation of the 22 conjugated atoms from the mean-molecular plane. Results are shown for the least-squares planes defined either by the conjugated atoms or
d
(28) Ridley, J.; Zerner, M. Theor. Chim. Acra 1973, 32, 11 I; 1976, 42, 223. Zerner, M.; Loew, G.; Kirchner, R.; Mueller-Westerhoff, U. J . Am. Chem. SOC.1980, 102, 589.
1.00
2 0.56 (0.54) 1.00
3 0.32 (0.42) 0.84 (0.92) 1.00
4 5 6
4 -0.43 (0.41) -0.02 (0.03) 0.01 (0.01) 1.00
class I I b 5 6 -0.37 -0.36 (0.42) (0.36) -0.12 -0.22 (0.39) (0.17) -0.15 -0.40 (0.36) (0.32) 0.58 0.72 (0.43) (0.72) 1.00 0.80 (0.65) 1.00
7 0.00 (0.26) 0.23 (0.69) 0.03 (0.55) 0.50 (-0.23) 0.46 (0.38) 0.62 (-0.21) 1.oo
7
'Based on the vertical displacements (Az) of the 22 conjugated atoms of the BChls with respect to the least-squares plane ( x y ) . The entries in parentheses are based on the least-squares plane through the four N atoms (see Table I). bConformational classes defined by TSM.2 lumo+l
-
b3g (YZ)
homo-1
+
bl,
(2)
Figure 3. Schematic representation of the molecule orbitals involved in the four-orbital model for a porphyrin. The indicated orbital designations refer to the D2*subgroup appropriate to the idealized conjugated framework of the BChl molecule (pyrrole rings I and 111 are bisected by the y z plane, and rings I1 and I V by the x z plane (see Figure 2)). The transformation properties of the four orbitals are indicated (in parentheses) by appropriate functions of the Cartesian coordinates.
by the nitrogen atoms. In the former case, the corresponding linear correlation coefficients shown in Table I1 reveal the basis on which TSM2 partitioned the seven conformers in two classes (1-3 and 4-7). Interestingly, deviations from the plane of the nitrogen atoms (results in parentheses) do not lead to any clear partitioning of the seven BChls. Table I also includes rms deviations from idealized values (0' or 180') of torsional angles involving conjugated atoms. 111. Computational Models The calculations employed the INDO/s method developed by Zerner and co-workers.6J8 Ground electronic states were obtained as closed-shell molecular orbital (MO) wave functions in the restricted Hartree-Fock (RHF) framework. Low-lying excited states were approximated by configuration interaction (CI) among configurations generated as single excitations from the R H F ground state. It is helpful in this context to consider the four-orbital model of GoutermanZ9(Figure 3), which focuses attention on the two highest lying occupied MO's (HOMO, and HOMO-1) and the two lowest lying unoccupied MO's (LUMO and LUMO 1). G ~ u t e r m a nhas ~ ~shown that single excitations involving these four orbitals provide a good CI basis for approximating the low-lying Q-bands in the visible and near-infrared region. While the BChls dealt with here have no rigorous symmetry elements, it is useful for schematic purposes to assume an idealized DZhsymmetry for the conjugated BChl framework (see Figure
+
(29) Gouterman, M. J . Mol. Spectrosc. 1961, 6, 138. The Porphyrins; Dolphin, D., Ed.: Academic Press: New York, 1978; Vol. 3, p I .
5798
The Journal of Physical Chemistry, Vol. 94, No. 15, 1990
TABLE 111: Calculated 0. Excitation Energies (nm) BChl subunit 1 2 3 4 5 6 7
TABLE I V Primary Contributions to CI Wave Function for Qy States (Model c)
structural aL 182 805 733 842 751 801 846
bL 169 800 741 842 161 803 842
b 169 795 154 841 786 803 829
c
d 125 739 134 788 749 169 793
771 799 768 840 791 808 836
percentage contribution’ C H ~
694 132 109 802 719 791 805
dH2 646 673 675 747 618 144 751
Osee Figure 2. bThe subscript L indicates inclusion of the axial ligand: histidine (imidazole nitrogen) for all BChls except no. 2 (water) and no. 5 (leucine oxygen). The imidazole ligand is bound via nitrogen N E 2 for BChl 1, 3, 4, and 6, and by NDI for BChl 1 (notation is defined in ref 21.
2), and accordingly, the four orbitals in Figure 3 are assigned to the appropriate irreducible representations in the DZhsubgroup of D4,,. Symmetry with respect to the Cartesian planes is given in parentheses (these planes correspond to the Cartesian axes defined in Figure 2). In Dzh symmetry, the HOMO is the a, orbital, and the lower of the unoccupied bz8, b, pair is the bzg orbital. Hence we expect the dominant contribution to the lowest excited state to be a, bz8 (HOMO LUMO) with some contribution also from b,, bjg. Since these configurations can only be coupled to the ground state by y-polarized light under electric dipole selection rules, the transition to this state is designated Q,, The other two excitations arising in the four-orbital model are expected to provide the major contributions to the Q, transition. In the INDO/s calculations, all single excitations involving the highest 15 occupied and lowest 15 unoccupied M O s were included, thereby providing a reference level for examining the quantitative validity of the four-orbital model. The calculations yielded state and transition dipole moments, and oscillator strengths, as well as excitation energies. Primary focus in the present study is on the Qytransitions, although reference is also made to Q, results.
--
Gudowska-Nowak et al.
-+
IV. Results and Discussion A. Calibrations of the Calculations. To help assess the validity of the INDO/s method in predicting spectral features of BChl derivatives, the Q, transition energy of methylbacteriopheophorbide a (MeBPheo) was calculated. The molecule is a close analogue of BPheo a in which the esterifying phytyl chain of the latter is replaced by a methyl group (this should have little effect on the optical spectrum). The optical spectra of BPheos are less susceptible to solvent or complexation effects than BChl itself. In addition, high-precision X-ray data have recently been reportedz6 for MeBPheo. Its Q, transition is calculated at 734 nm, to be compared with observed maxima ranging from 740 to 753 nm for BPheo a (depending in the solvent) reported by Callahan and Cotton.m The maximum discrepancy between the calculated and observed Qy transitions is thus 350 cm-l or 0.04 eV (see also Table V below). Additional validation for the use of these calculations derives from the treatment of conformational variations in spectra reported by Barkigia et aI.* for a puckered porphyrin, zinc tetraphenyloctaethyl porphyrin: red shifts of 1370 and 1880 cm-’ are observed experimentally relative to the “planar” macrocycles, zinc tetraphenyl- and octaethylporphyrins, respectively, to be compared with a calculated shift of 1900 cm-’ for puckered vs planar macrocycles. B. QyTransitions in Isolated BChls a. The calculated transition energies are presented in Table 111 for each of the seven BChls at several different levels of chemical substitution, as described in section 11. Although the pattern of calculated spectral shifts is clearly complex, a number of systematic trends are apparent. Before considering these in detail, we briefly examine the calculations from the point of view of expectations based on the four-orbi tal model. (30) Callahan. P. M.: Cotton, T. M. J . Am. Chem. Soc. 1987, 109, 7001.
Q,
QY
HOMO - 1 -+ LUMO+ 1
HOMO LUMO 91.8 90.6
-+
BChl I
2 3
90.4
4
88.5 90.8 88.5 87.8
5
6 7
4.4
5.0 5.2 7.2 5.8 7.4 7.8
HOMO - I LUMO 64.0 55.8 52.7 64.0 61.8 59.6 56.4
+
HOMO LUMO+l 28.3 35.5 39.8 30.6 32.1 35.6 38.6
+
100 X square of CI coefficient. 14000 1 I
7
-E
13750
> 13500
8W 6
t
I
I
I
I
1
I
1
I
1
model d
13250
2
0 k cn
13000
2
12750 12500 1 3 90
I
3.95 400 4.05 4.10 4.15 homo / lumo ENERGY DIFFERENCE (eV)
1
4.20
Figure 4. Linear correlation between Qyexcitation energy and the difference in the HOMO and L U M O orbital energies for model d (the hollow squares refer to the seven BChls (see Figure 1)).
I . Analysis of Calculated States. Inspection of the calculated CI coefficients (Table IV) reveals that >90% of the Qyexcited state is accounted for by the HOMO LUMO excitation (for completeness, the corresponding information for the Q, transition is also included). Much of the remainder is provided by the HOMO - 1 LUMO + 1 excitation, and the individual contributions from the other 223 excitations included in the CI calculations are all
