10410

J. Phys. Chem. B 1998, 102, 10410-10419

Excited States of the Photosynthetic Reaction Center of Rhodopseudomonas Wiridis:
SAC-CI Study
J. Hasegawa,† K. Ohkawa,† and H. Nakatsuji*,†,§
Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering,
Kyoto UniVersity, Sakyo-ku, Kyoto 606-8501, Japan, and Institute for Fundamental Chemistry, 34-4 Takano
Nishi-hiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan
ReceiVed: July 2, 1998; In Final Form: September 16, 1998

The excitation spectrum of the photosynthetic reaction center (PSRC) of Rhodopseudomonas (Rps.) Viridis is
assigned by using the SAC(symmetry adapted cluster)-CI(configuration interaction) method. All thechromophores included in the PSRC, bacteriochlorophyll b dimer (special pair, P), bacteriochlorophyll b in
L- and M-branches (BL and BM), bacteriopheophytin b in L- and M-branches (HL and HM), menaquinone(MQ), ubiquinone (UQ), and four different hemes, c-552, c-554, c-556, and c-559 in c-type cytochrome
subunit, were calculated within the environment of proteins, waters, and the other chromophores which weredealt with by the point-charge electrostatic model. We have assigned successfully all the peaks in theexperimental spectrum in the energy range from 1.2 to 2.5 eV. The assignment was done by comparing the
SAC-CI theoretical spectrum with the experimental one in excitation energy, oscillator strength, linear
dichroism data (angle of transition moment), and other experimental information available. Almost all the
peaks were red shifted due to the effect of proteins. The present assignment of the spectrum would give abasis for future photoexperimental studies of the PSRC.

I. Introduction
The initial step of solar energy conversion to chemical energy
is performed in the photosynthetic reaction center (PSRC) of
green plants and some bacteria.1 The functions of the PSRC
are of global significance and offer quite challenging subjects
to be clarified by means of science and technology. For the
PSRC of Rhodopseudomonas Viridis (Rps. Viridis), the X-ray
structure was reported by Deisenhofer et al.2 Figure 1 shows
the three-dimensional arrangement of the chromophores involved. An excitation of special pair (P, bacteriochlorophyll b
dimer) by a light absorption or by an energy transfer fromantenna molecules is the first step of the photosynthesis andcauses a primary electron transfer in the PSRC.1 This electrontransfer occurs quite efficiently only through the L-branch up
to ubiquinone (UQ),3,4 and the positive charge of P is reduced
by an electron transfer from the cytochrome c subunit.
In the upper side of Figure 2, the absorption and linear
dichroism (LD) spectra of the PSRC of Rps. Viridis reported
by Breton5 are shown. The spectra show complex but beautiful
structures in the region from about 1050 nm to about 450 nm.
The peaks in the absorption spectrum are numbered by I-XIV
in order of increasing energy. The LD spectrum gives theinformation on the angle of the transition moment of the excitedstate from the principal pseudo-C2 axis of the PSRC. Breton5also reported the absorption and LD spectra for the PSRC withthe primary donor chemically oxidized (state P+), which arealso shown in the lower part of Figure 2. Recently, van
Grondelle and co-workers reported the results indicating new
pathways of the electron transfer starting from the excited stateof bacteriochlorophyll of Rhodobacter sphaeroides (Rb. sphaeroi* To whom correspondence should be addressed.
† Kyoto University.
§ Institute for Fundamental Chemistry.

des).6,7 This implies a possibility of an existence of an entirely
different electron-transfer pathway involving different excitedstates of chromophores. In such studies, a precise knowledge
on the nature of the excited states in the excitation spectrum of
PSRC is very important. Thus, the assignment of the PSRC
spectrum shown in Figure 2 and the knowledge on the naturesof the excited states involved would provide us a starting point
for future photochemical studies involving the PSRC.
Previously, some semiempirical calculations for the excitation
spectrum were reported.8-10 These works qualitatively reproduced the experimental features of the spectrum and brought
important information about the excited states. Nevertheless,
it is necessary to perform more reliable theoretical assignment
by ab initio method because of a limited accuracy of thesemiempirical method they used.
Recently, the ab initio electronic structure theory has achieved
chemical accuracy, and applications of such methods to large
systems, such as biochemically important systems, constitute achallenging frontier of quantum chemistry. Among suchtheories, the SAC(symmetry adapted cluster)11/SAC-CI(configuration interaction)12method is very promising.12-14 It
describes almost all kinds of electronic states of molecules ingood accuracy including electron correlations: it is applicableto the ground and excited states of molecules from singlet toseptet spin multiplicities. The method has been applied to manydifferent kinds of molecules in many different fields ofchemistry, and through such applications, the reliability and theusefulness of the method have been established.13,14 Recently,
the SAC/SAC-CI method has been successfully applied tolarger molecules, including porphyrin compounds, such as freebase porphin,15 Mg porphin,16 iron-porphyrin,17-19 bacteriochlorin and pheophytin,20 phthalocyanine,21 etc., and its potential
applicability to the excited states of such moderately large
systems has been confirmed.

10.1021/jp982869y CCC: $15.00 © 1998 American Chemical Society
Published on Web 11/05/1998

PSRC of Rhodopseudomonas Viridis

J. Phys. Chem. B, Vol. 102, No. 50, 1998 10411

Figure 1. Structure of the chromophores in the PSRC of Rps. Viridis. The nuclear coordinates are taken from ref 2.

In this paper, we aim to assign the absorption spectrum of
the PSRC of Rps. Viridis shown in Figure 2 by means of the
SAC/SAC-CI method and we want to understand the excitedelectronic structures of the PSRC. We performed calculations
for the ground and excited states of all the chromophores
involved in the PSRC of Rps. Viridis in the environment of theproteins and waters, which are approximated by the point-charge
electrostatic model. The chromophores for which calculations
were performed in this paper are special pair (P) (Mg2C50N8O4H36), which is bacteriochlorophyll b dimer, bacteriochlorophyll b (MgC24N4O2H16 ) in L- and M-branches (BL and BM),bacteriopheophytin b (C24N4O2H18) in L- and M-branches (HLand HM), menaquinone (MQ) (C16O2H16), ubiquinone (UQ) (C14O4H18), and four different hemes, c-552 (FeC26N8H18), c-554,
c-556, and c-559 (FeC25N6SH21) in the c-type cytochrome
subunit, where the latter three hemes have the same chemical
formula but have different geometries and different protein
environments. The chromophores in the L- and M-branches
are arranged almost symmetrically. We also calculate theexcited states of bacteriochlorophyll b monomer to understandthe spectrum of the dimer, P. A short communication of thisstudy has been published elsewhere.22
The calculational details are described in the next section andthe excited electronic structures of special pair are investigated10412 J. Phys. Chem. B, Vol. 102, No. 50, 1998

Figure 2. (a) Absorption and (b) linear dichroism (LD) spectra of
PSRC of Rps. Viridis.5 (c) Absorption and (d) LD spectra of PSRC ofRps. Viridis with P in its oxidized state (P+).5 Intensity is in a relativeunit.

in some detail in the subsequent section, comparing with theexcited states of the monomer. The detailed discussions on theassignments of the peaks in the experimental excitation spectrumof the PSRC are then given. The assignments are done byutilizing the information on the peak position, intensity, thelinear dichroism (LD) data and other available experimental
observations. The protein effects are discussed in some detail,and the conclusion of the present study is given in the lastsection.
II. Computational Details
The structure of the PSRC of Rps. Viridis2 is shown in Figure
1. The SAC/SAC-CI calculations are performed for all thechromophores involved in the PSRC. The X-ray crystal-

Hasegawa et al.
lographic structure2 (1PRC in Brookhaven Data Bank23) wasused for the geometries of the chromophores, and therefore, all
the chromophores were treated without symmetry. For calculational efficiency, some substituents in the chromophores were
replaced with hydrogens, except for the substituents which can
π-conjugate with the rings. The adopted models are shown in
Figure 3, where the labeling of the atoms and the rings areindicated. Such simplification was shown to be acceptable inour previous calculations.20 Though the chemical structures of
the three models of the hemes, c554, c556, and c559 are thesame, their geometries and the protein environments are different
in the X-ray structure.
Common basis sets are taken for all the chromophores. For
C, N, and O atoms, Huzinaga’s (63/5)/[63/41] sets24 and for H
atoms, the (4)/[4] set,25 are used. For Mg, Huzinaga’s (533/5)/[53111/311] set24 plus two p-type polarization functions (ζ) 0.045 and 0.143) and d-type polarization functions (ζ ) 1.01)
are used. For S, Huzinaga’s (533/53)/[5321/521] set24 plus
p-type anion basis (ζ ) 0.041) and d-type polarization function(ζ ) 0.421) are used. For Fe, Huzinaga’s (5333/53/5)/[53321/
53/41] set plus p-type basis (ζ ) 0.082) are used.
The effects of the proteins and waters (consisting of about
30 000 atoms) are introduced by a point charge model. The
geometries of the heavy atoms in the PSRC are taken from the
X-ray structure2 (1PRC in Brookhaven Data Bank23). The
positions of the hydrogens are estimated by using the molecularmodeling software SYBYL.26 The published charges27,28 are
put on all the atoms of proteins and waters. The ionized form
is adopted for the ionizable residues, ASP, LYS, ARG, and
GLU. For the other chromophores surrounding the chromophore under consideration, the Mulliken charges calculated
from the Hartree-Fock orbitals are put on the constituent atomic
positions.
The polarization effect of proteins may also be important for
the excited state whose dipole moment is much different fromthat of the ground state. It is taken into account by using thecontinuum model expressed by the interaction of the dipole
moment µ of the molecule under consideration with the solvent
reaction field, represented by the refractive index η and theeffective radius of the spherical cavity a,29,30 namely by∆E ) -

η2 - 1〈µ〉‚〈µ〉a (2η2 + 1)
3

(2.1)

where ∆E is the polarization energy. We used the value of

Figure 3. Calculational models for P, B, H, UQ, MQ, c-559, c-556, c-554, and c-552. For P, only monomer is shown. Some substituents were
replaced by hydrogens if they do not π-conjugate with the rings. Labeling of the atoms and groups for P, B, and H is also defined.

PSRC of Rhodopseudomonas Viridis

J. Phys. Chem. B, Vol. 102, No. 50, 1998 10413

TABLE 1: Number of MO, Active Space, Threshold, and Dimension in the SAC/SAC-CI Calculationsa
chromophore

P

BM

BL

HM

HL

MQ

UQ

c-554

c-556

c-559

c-552

no. of MO
578
282
282
258
258
160
174
318
318
318
318
active spaceb 90 × 220
43 × 91
42 × 9042 × 84
42 × 84
27 × 53
30 × 61
95 × 151
95 × 151
95 × 151
94 × 154
(310)
(134)
(132)
(126)
(126)
(80)
(91)
(246)
(246)
(246)
(246)
ground state
thresholdc 3 × 10-6
1 × 10-5 1 × 10-5 1 × 10-5 1 × 10-5 1 × 10-5 1 × 10-5 2 × 10-5
2 × 10-5
2 × 10-5
2 × 10-5
dimension
befored 196 049 700 7 149 870 7 661 654 6 228 684 6 228 684 1 023 165 1 677 195 102 911 030 102 911 030 102 911 030 102 911 030
aftere 37 549
7 570
7 582
7 298
7 983
5 021
4 347
21 64622 676
21 48525 833Ecorrf-0.157 52 -0.122 77 -0.115 46 -0.134 99 -0.150 73 -0.135 38 -0.887 80 -0.185 68 -0.204 48 -0.178 45-0.252 80
excited state
1 × 10-6 1 × 10-6 1 × 10-6 1 × 10-6 1 × 10-6 1 × 10-6 2 × 10-5
2 × 10-5
2 × 10-5
2 × 10-5
thresholdc 2 × 10-7
dimension
befored 196 049 700 7 149 870 7 661654 6 228 684 6 228 684 1 023 165 1 677 195 102 911 030 102 911 030 102 911 030 102 911 030
aftere 226 726
37 14045 18840 96843 16528 63032 94868 81370 68763 05270 703aCalculations with protein model. b Number of occupied MOs time the number of unoccupied MOs. The number in parentheses is the total
number of active MOs. c Energy thresholds for the perturbation selection. d Number of linked operators before the perturbation selection. e Numberof linked operators after the perturbation selection. f Correlation energy for the ground state in hartrees.

1.427 for η (bulk property of cyclohexane) and 6.5 Å for a.9
The dependence on the value of η was checked by using thevalue for benzene, 1.498, and was confirmed to be small.
In the SAC/SAC-CI calculations, the orbitals whose energies
are within -0.7 to +0.7 au are chosen for the active space, inwhich at least 2p electrons are correlated. From our experiences,
this criteria would be enough to reproduce the low-lying excitedstates of the porphyrin compounds.14-22 In Table 1, we havesummarized the number of the active orbitals. For P, which is
the largest molecule in the present calculation, the 90 occupied
and 220 unoccupied orbitals (total 310 orbitals) are taken as
active MOs from 578 SCF MOs. For the four hemes in thecytochrome c unit, only the inner 1s cores are taken as frozen
orbitals, so that the active space is wider and the calculational
accuracy is better for these hemes.
All single excitation operators are included in the linked termof the SAC/SAC-CI calculations and the perturbation selection15,31 is carried out for double excitation operators. For the
ground and excited states of the porphyrin compounds, theenergy thresholds, 1 × 10-5 and 1 × 10-6 au are used,
respectively. For the ground, excited, and ionized states of P,
the thresholds of 3 × 10-6, 2 × 10-7, and 3 × 10-6 au,
respectively, are used. For the hemes in cytochrome c unit,
the threshold is 2 × 10-5. The dimensions of the SAC/SACCI calculations are shown in Table 1, where the correlationenergies for the ground states of these compounds are also
summarized. The numbers of the doubly excited configurations
are comparatively smaller than our previous calculations,because the aim of the present calculation is only for the states
lower than about 3 eV. Therefore, the correlation energies
calculated for these molecules are relatively small in comparison
with our previous results.
For the Hartree-Fock SCF calculations, the HONDO version
8 program32 was used and for the SAC/SAC-CI calculations,
the SAC-CI 9633 and SAC 85 programs34 were used. Parallel
computation algorithm was adopted for the integral transformation step which was the most time-consuming step in the present
calculations.
We also calculated the linear dichroism (LD) spectrum forthe system. The expression for the LD is given by8|µ|2⊥ - |µ|2| ) (1 -3 cos2 θ)|µ|2(2.2)

where θ is the angle between the transition moment µ of thestate and the pseudo-C2 axis. The signs, “⊥” and “|”, denote
to be perpendicular and parallel, respectively, to the pseudo-C2

Figure 4. Electronic spectra of BChl b monomer. (a) Experimental
absorption spectrum.35 (b) Theoretical SAC-CI spectrum.

axis. The plus region corresponds to 90° > θ > 55°, and theminus region corresponds to 55° > θ > 0°.
III. Excited States of Special Pair
The largest compound in the present calculations is the special
pair, P, which is a dimer of bacteriochlorophyll b (BChl b).
The ground and excited electronic structures of P are rather
easily understood by comparing with those of the monomer.
For this reason, we first show the results for BChl b monomer.
Figure 4 shows the experimental35 and SAC-CI theoretical
spectra of BChl b monomer, and Table 2 shows the data forthe excited states. The SAC-CI results reproduce well the
excitation energy and the direction of the oscillator strength
observed for BChl b monomer. The average error in the
excitation energy is 0.14 eV. The first excited state, 21A, ischaracterized as the HOMO to LUMO (π-π*) excitation towhich the HOMO-1 to LUMO+1 (π-π*) excitation slightly
mixes. In the free base porphin (FBP),15 these HOMO to
LUMO and HOMO-1 to LUMO+1 excitations were almost
degenerate and their contributions to the transition moment
almost canceled each other, resulting in a very small oscillator

10414 J. Phys. Chem. B, Vol. 102, No. 50, 1998

Hasegawa et al.

TABLE 2: Excited States of BChl b Monomer Calculated by the SAC/SAC-CI Methodstatemain configurationb (C > 0.2)

21A
31A
41A

-0.91(HfL)+0.21(H-1fL+1)-0.88(H-1fL)-0.32(HfL+1)-0.89(H-2fL)-0.15(H-3fL)

SAC/SAC-CI
excitationenergy (eV)exptlaexcitationenergyc (eV)oscillator
strengthc

1.52
2.34
3.53

0.395
0.179
0.0129

y
x
x

1.60
2.15

y
x

a
Reference 35. b H and L denote HOMO and LUMO, respectively. c “x” and “y” are the directions of the transition moment which are paralleland perpendicular to the axis along the two reduced pyrrole rings.

TABLE 3: Ground and Excited States of Special Pair (P) Calculated by the SAC/SAC-CI Methodstatecharactera

X1A
21A
31A
41A
51A
61A
71A
81A
91A

Ex
Ex
Ex
CT
CT
Ex
CT
CT

net charge
PLb
PMb-0.075-0.179-0.019-0.197-0.6740.506
0.043-0.675
0.539

0.075
0.179
0.019
0.197
0.674
-0.506-0.0430.675-0.539dipolemoment (debye)δEPolc(eV)in gas phase

5.45
3.60
7.55
5.75
18.00
22.25
8.48
16.65
20.00

+0.01
-0.01
0.00
-0.05
-0.22
-0.02
-0.10
-0.18

1.42
1.63
2.18
2.22
2.52
2.61
3.15
3.34

excitation energy (eV)in protein Ad
in protein Be
1.40
1.62
2.10
2.37
2.57
2.48
2.96
3.37

1.41
1.61
2.10
2.31
2.35
2.46
2.86
3.19

exptlf1.25 (I)1.46 (II)1.88 (VII)2.23 (XI)a Ex and CT denote exciton and charge-transfer excited states, respectively. b P and P denote bacteriochlorophyll monomer constructing P.
L
M
Change in the excitation energy due to the polarization effect of proteins. d Excitation energy including protein effect represented by the pointcharge electrostatic model. e Excitation energy including protein effect represented by the point-charge electrostatic model plus continuum model.
f Reference 5.
cstates (2 and 31A states) of the monomer split into eight states(four Ex and four CT states) in the dimer P.
The first excited state of P, the 21A state, is calculated at
1.40 eV and shows a red shift caused by the dimerization. A
reason of the red shift is that the HOMO-LUMO energy gap
decreases by the dimerization due to the HOMO-HOMO and
LUMO-LUMO interactions between the two monomers. Table
3 shows the amount of charge transfer in the ground and excitedstates of P. In the ground state, PL is slightly negative, while
PM is slightly positive. In the excited states, the CT state isclearly characterized by a large amount of charge transfer, givinga large dipole moment. This polarized electronic structure of
the CT state would cause a large geometric relaxation of P in
the CT excited state.
Table 3 and Figure 5 shows the effects of the proteins on the
excitation energy, but they are discussed in a later section.
Figure 5. Energy levels of the excited states of BChl b monomer anddimer (special pair P) calculated by the SAC-CI method comparedwith the experiments.5,35 Ex and CT denote exciton and charge transfer
states, respectively, and A and B in the parentheses denote the symmetry
representations to which the excited states of P approximately belong.

strength.21,36 In the case of BChl b, the reductions of the double
bonds in the pyrrole rings cause a destabilization of the
HOMO-1 and LUMO+1 energy levels, resulting in a breakdownof the quasidegeneracy, which leads to a larger intensity thanthat of FBP. The second excited state, 31A, is characterized as
HOMO-1 to LUMO (π-π*) excitation. The directions of thetransition moments of the 21A and 31A states are perpendicularand parallel, respectively, to the axis along the two reduced
pyrrole rings.
The electronic structures of the ground and excited states of
P are easily understood by comparing with those of themonomer. In Figure 5, the calculated lower excited states of P
are compared with those of the monomer, BChl b. We see thateach monomer state splits into four by dimerization: two exciton(Ex) states and two charge-transfer (CT) states. The dotted lines
from the monomer to the dimer show this splittance. The two
Ex states are lower than the two CT states. Thus, the two Q

IV. Assignment of the Excitation Spectrum of the PSRC
The absorption and the LD spectra of the PSRC of Rps. Viridis
observed by Breton5 and those calculated by the SAC-CI
method are compared in Figure 6. These spectra were redrawn
from those in Figure 2 such that the horizontal axes are given
in eV. The experimental absorption spectrum has at least
fourteen peaks in the energy range of 1.25-2.5 eV. As in
Figure 2, the experimentally observed peaks in the absorption
spectrum are numbered from I to XIV and the dotted lines show
the present assignments. The excitation energy, oscillator
strength, and the LD data, which is the angle of the transition
moment from the C2 axis, are shown in Table 4. The present
assignments are carried out based on the excitation energy,
oscillator strength, LD data, and other experimental information
available. The average discrepancy from the experimental peak
positions is 0.13 eV.
The first band I at 1.25 eV has been attributed to the Qy stateof P, since no such low-lying peak exists in the experimental
absorption spectra of B and H monomers (see Table 2, forexample), and since the PSRC including P+ (chemicallyoxidized) does not have this peak.5 In the present calculation,

PSRC of Rhodopseudomonas Viridis

Figure 6. Absorption and linear dichroism spectra of the PSRC. (a)SAC-CI theoretical excitation spectrum. (b) Experimental absorption
and linear dichroism spectra.5 (c) SAC-CI theoretical linear dichroism
spectrum.

the peak positions of the BM(21A) and P(21A) states arecalculated at 1.35 and 1.41 eV, respectively. As for the peak
position, the BM(21A) state is closer to the experimental value,
while for the oscillator strength and LD data, the P(21A) stateis closer to the experimental values. We think that theexperimental data for the PSRC including P+ is decisive andtherefore assign P(21A) state to Band I of the experimental
spectrum.
The main configuration of P(21A) state consists of HOMO(H) to LUMO(L) (π-π*) excitation with a small mixing of
H-1 to L+1 excitation. As seen in Table 3, the P(21A) state ischaracterized as an exciton (Ex) state where the two Qy states(HfL excitation) of the monomers couple and, therefore,
belongs to the B symmetry of the pseudo-C2 symmetry of thespecial pair. The calculated intensity 0.607 is about twice aslarge as that of the monomer 0.395, which is already large owing
to the partial hydrogenation of the porphyrin double bond as

J. Phys. Chem. B, Vol. 102, No. 50, 1998 10415
shown in the preceding section. This enhancement is due tothe Ex character of the state; the additive contribution of theintensities of the two monomers. It is noteworthy that this strong
intensity has an important biological implication in the photoexcitation process of the PSRC. Compared with the groundstate P(X1A) of special pair, about 0.1 electron is transferredfrom PM to PL as seen in Table 3, so that P(21A) state has asmall CT character.
Band II at 1.46 eV is observed as a red-shifted shoulder of
an intense band III.5 This peak has been attributed to the excitedstate of P, since it vanishes in the absorption spectrum of P+ of
the oxidized PSRC shown in the lower part of Figure 2.5 In
the oxidized state, not only P but also the hemes in thecytochrome unit are oxidized. Therefore, we propose here that
this band II consists of two states, IIa and IIb, which are thefirst excited state of the c-552 heme calculated at 1.50 eV andthe P(31A) state calculated at 1.61 eV. We propose thisassignment by the following reasons. First, band II disappears
for the PSRC including P+, so that the candidates are P andhemes. Second, comparing the spectra of the PSRC’s of Rps.
Viridis and Rb. sphaeroides given by Breton,5 we notice thatthe intensity of the LD spectrum of peak II is stronger in theformer than in the latter. This may indicate that peak II of Rps.
Viridis consists of two states, while that of Rb. sphaeroides
consists of one state. Due to our SAC-CI calculations, thefirst excited state of c-552 is at 1.53 eV with the oscillator
strength of 0.124 (stronger) and with the LD angle of 43.3°,
while the P(31A) state is at 1.61 eV with the oscillator strengthof 0.09 (weaker) and the LD angle of 36.9° inconsistent withthe observed peak position at 1.46 eV and the large negative
LD peak whose angle was estimated to be about 30°.5 Further,
the energy separation between the first and second excited statesof P are 0.20 eV by SAC-CI which is comparable with theexperimental value 0.21 eV.
The main configuration of P(31A) state is H-1 to L (π-π*)
excitation with a small in-phase mixing of H to L+1 excitation,
which is characterized as an exciton coupling of the monomer
Qy states (H to L excitation). The intensity of this state is muchsmaller than that of P(21A) state, though these two states areboth Ex states. The reason is that, in the dimer of pseudo-C2
symmetry, the P(31A) state belongs to the A symmetry in which
the transition from the ground state is allowed only along thedirection along the C2 axis, but the H to L excitation of themonomer has only a small intensity component in this direction.
The next very strong peak centered at 1.49 eV, band III, also
seems to be composed of the two states: a stronger peak with
the LD angles θ of about 70° and a weaker shoulder peak inhigher energy with a smaller LD angle. We designate thesetwo peaks as peak IIIa and IIIb, respectively. Both of these peaks
still exist in the spectrum of the oxidized PSRC, and therefore
they should originate from either B or H. We assign peaks IIIa
and IIIb to the first excited Qy states of BM and BL, respectively,
since they are calculated at 1.35 and 1.45 eV, respectively, andsince the calculated LD angles 67.2° and 64.3° for BM and BL,
respectively, are close to the experimentally observed values.
We assign bands IV (1.54 eV) and V (1.57 eV) to the firstexcited states of HL (21A) and HM (21A) calculated at 1.59 and1.75 eV, respectively. These states originate from the Qy stateof H whose main configuration is H to L (π-π*) excitation.
This assignment is supported from both the oscillator strengthand the θ value of the LD spectrum. The peak IV is stronger
than the peak V, but both are weaker than band III. Correspondingly, the calculated oscillator strengths are 0.323 and0.283 for HL(21A) and HM(21A), respectively, but they are10416 J. Phys. Chem. B, Vol. 102, No. 50, 1998

Hasegawa et al.

TABLE 4: Singlet Excited States of Chromophores in the Photosynthetic Reaction Center of Rhodopseudomonas Viridis
SAC-CI (gas phase)chromophoresa state

exptl.f

SAC-CI (in protein)

excitationenergy oscillator(eV)strength state

main configurationb (|C| g 0.3)

excitation energy
linear excitation
lineardichroism
energyc shiftd oscillator dichroism energye(eV)(eV) strength
(deg)
(eV)
(nm) (peak) (deg)e

P
c-552
P
BM
BL
HL
HM
c-552

21A
21A
31A
21A
21A
21A
21A
31A

1.42
1.53
1.63
1.42
1.52
1.65
1.67
1.82

0.673
0.160
0.067
0.335
0.372
0.317
0.284
0.013

21A 0.88(HfL)
21A -0.66(H-1 fL)+0.57(HfL)
31A -0.85(H-1 fL)
21A -0.92(HfL)
21A 0.92(HfL)
21A -0.87(HfL)-0.34(H-1 fL+1)
21A -0.87(H-1 fL)
31A 0.68(HfL)+0.56(H-1 fL+1)

1.41
1.50
1.61
1.35
1.45
1.59
1.75
1.83

-0.01
-0.03
-0.02
-0.07
-0.07
-0.06
+0.08
+0.01

0.607
0.124
0.090
0.363
0.406
0.323
0.283
0.110

85.1
43.3
36.9
67.2
64.3
33.7
28.6
38.3

P
c-556
BM
BL
c-556
P
P
P
HL
HM
c-554
c-559
c-552
UQ
P
P
MQ

41A
21A
31A
31A
31A
51A
61A
71A
31A
31A
21A
21A
61A
21A
81A
91A
21A

2.18
2.26
2.32
2.41
2.30
2.22
2.52
2.61
2.67
2.67
2.40
2.45
2.46
3.85
3.15
3.34
3.52

0.100
0.034
0.125
0.140
0.023
0.070
0.083
0.181
0.103
0.090
0.036
0.014
0.150
0.018
0.006
0.009
0.000

41A -0.89(H-2 fL)
21A -0.58(HfL)-0.42(H-1 fL+1)
31A 0.88(H-1 fL)
31A -0.87(H-1 fL)-0.30(H-1 fL+1)
31A -0.71(HfL+1)+0.49(H-1 fL)
51A -0.88(HfL+1)
61A -0.83(H-1 fL+1)
71A 0.70(H-3 fL)-0.37(H-2 fL+1)
31A -0.84(H-1 fL)-0.44(H-1 fL+1)
31A 0.82(H-1 fL)+0.47(H-1 fL+1)
21A 0.80(HfL)-0.50(H-1 fL+1)
21A 0.81(HfL)+0.45(H-1 fL+1)
61A 0.77(H-2 fL)+0.47(H-3 fL)
21A 0.92(HfL)
81A 0.80(H-2 fL+1)+0.38(H-3 fL)
91A 0.78(H-3 fL+1)+0.37(H-3 fL)
21A 0.74(H-4 fL)+0.45(HfL)

2.10
2.23
2.17
2.23
2.27
2.31
2.35
2.46
2.66
2.67
2.38
2.44
2.44
2.86
2.86
3.19
3.44

-0.08
-0.03
-0.15
-0.18
-0.03
+0.09
-0.17
-0.15
-0.01
0.00
-0.02
-0.01
-0.02
-1.01
-0.29
-0.15
-0.08

0.088
0.047
0.149
0.148
0.020
0.038
0.120
0.144
0.091
0.113
0.035
0.058
0.059
0.001
0.013
0.018
0.002

61.0
44.6
79.8
77.1
62.2
87.4
71.5
25.3
61.6
53.6
46.1
64.1
45.4
76.8
35.6
84.7
58.0

1.25
1.46
1.46
1.49
1.49
1.54
1.57
1.75
1.81
1.88
1.99
2.04
2.06

990
850
850
834
834
805
789
709
684
660
615
607
600

(I)
(IIa)
(IIb)
(IIIa)(IIIb)
(IV)
(V)
(VI)
(VII)
(VII)
(VIII)
(IX)
(X)

90
30
30
70
70
40
40

2.23
2.28
2.32
2.36

556
544
534
525

(XIb)g(XII)(XIII)(XVIa)

30
70
70

2.38

520 (XVIb)

30
70
70

a P, B, and H denote special-pair, bacteriochlorophyll, and bacteriopheophytin, respectively. L and M denote L- and M-branches, respectively.
b H and L denotes HOMO and LUMO, respectively. c Excitation energy including protein effect by a point charge electrostatic model. For P, thepolarization effect of protein is also included by a contiuum model. d Energy shift in excitation energy between in protein and in gas phase. Plusand minus signs denote blue and red shifts, respectively. e Angle of the transition moment vector with the pseudo-C2 axis of the reaction center.
f Reference 5. g For peak XI , see text.
asmaller than those of BM(21A) and BL(21A), 0.363 and 0.406,
respectively. The calculated LD angles are 33.7° for HL and
28.6° for HM, which correspond well with the experimental
angles around 40° for both, large negative values in the LD
spectrum.5 The present result supports the energetic order of
HL and HM proposed previously,37 and this order is considered
to be due to the difference in molecular geometry between HLand HM since the gas phase result shown in Table 4 shows thesame order of the states as that in protein. Note, however, thatthe protein effect enlarges the difference. This assignment is
consistent with the experimental result that an illumination of
λ > 900 nm light to the PSRC bleached these peaks due to thephotoreduction of the L-branch chromophores.37 Last, we notethat the spectrum of Rb. sphaeroides is somewhat different fromthe present spectrum: there is only one strong band in this regionin contrast to the present two bands. This is perhaps due to thedifferences in the geometry of HL and HM and in the protein
environment between these two PSRCs.
A small peak VI, is observed at 1.75 eV in the absorption
spectrum and its LD has a negative contribution as seen from
Figure 6. To the best of our knowledge, no assignment has
been made for this peak. Actually, the assignment of this peakis rather difficult, since the peak itself is so weak and it seems
to exist also in the absorption spectrum of the chemicallyoxidized PSRC (Figure 2).5 In our present SAC-CI calculation,
the second excited state (31A) of c-552 is calculated at 1.83 eVwith a negative LD component. Though this result wellaccounts for the spectrum of the reduced PSRC, it may
contradict with the spectrum of the oxidized one. Maybe wehave to perform calculations for the excited states of the cationsof P and the hemes in the c-type cytochrome unit for the final
assignment. We note that, in the level of the Koopmans
theorem, the third excited state of c-552+ is calculated to be

1.91 eV, which might explain this peak still existing in the
spectrum of the oxidized PSRC.
Band VII is composed of at least two states from the LD
spectrum.5 A peak at 1.81 eV was proposed to be assigned to
HL anion, since the intensity of this peak increase in theabsorption spectrum of the photoreduced PSRC.37 We therefore
calculated the electron attached states of HL and obtained theexcitation energy for X2A to 22A (L to L+1) transition at 1.4
eV. The discrepancy of 0.4 eV is somehow large and probably
due to a geometric relaxation of the ground state of the anion,
which was not taken into account in this calculation. Further,
we note that the intensity of this band decreases when the PSRC
is chemically oxidized.5 Then, the second excited state (31A)of c-552 calculated at 1.83 eV may also be assigned to thisband: this is another possible assignment of c-552(31A).
A blue-side shoulder (1.88 eV) of band VII was proposed to
be a Qx component of P from the circular dichroism (CD) spectraof the oxidized PSRC.5 We attribute P(41A) state calculated at
2.10 eV to this shoulder. The calculated LD data shows a smallplus, which is consistent with the experimental one shown in
Figure 6. The energy separations from the first singlet excitedstate of P in the theory and experiment5 are 0.70 and 0.63 eV,
respectively, which are close. The P(41A) state is certainlyclassified to the Qx component, since the main configuration of
the state, H-2 to L (π-π*) excitation, originates from themonomer 31A state, H-1 to L excitation.
Band VIII at about 1.99 eV is a featureless red-side shoulderof band IX. The LD experiment showed a characteristic large
negative component as seen in Figure 6 (θ = 30°).5
Breton assigned band VIII to P and the consistent assignment
would be P(71A) state calculated at 2.46 eV. Although thediscrepancy of the peak position from the experiment, 0.44 eV,
is very large, the calculated small angle (25.3°) is close to thePSRC of Rhodopseudomonas Viridis
experiment.5 Another assignment of band VIII is 21A state ofc-556 calculated at 2.23 eV (just at 556 nm), which also has asmall calculated LD angle of 44.6°. The discrepancy here is
0.21 eV. Both of these assignment is consistent with the factthat band VIII disappears when the PSRC is oxidized.5 We
prefer the second assignment since the discrepancy is smallerand since the P(71A) state is preferentially assigned to band XI
at 2.23 eV (556 nm) whose LD angle was also observed to besmall (30°).
The band IX and X observed at 2.04 and 2.07 eV are
attributed to the Qx states of BM(31A) and BL(31A) calculated
at 2.17 and 2.23 eV, respectively. The present assignment to
the Qx states is consistent with the previous ones,5,37 but Breton
assigned BL, to band IX in contrast to the present assignment.
Experimentally, the LD angle is around 70° but it is larger forband IX than for band X and this is reproduced by the present
assignment. The energy ordering of the Qx states of BL andBM calculated in protein is the same as that in a gas phase,
which indicates that the different molecular structures of BL
and BM are the origin of the ordering of the states.
In the blue shoulder region of band X, some states may exist(Figure 6) and c-556(31A), P(51A), and P(61A) states wereobtained in our calculation. The intensities of these states are
smaller than those of the QX states of BM and BL, and theyshould give positive contribution to the LD spectrum. This
assignment has some support from the experiment, since thebands IX and X of the oxidized PSRC involving P+ have smaller
intensity than those of the reduced PSRC.5 The main configuration of P(51A) and P(61A) states are H to L+1 and H-1 to L
(π-π*) excitations, respectively, which are the CT coupling
between monomer Qx states. Net charges shown in Table 3
clearly show their CT character; 0.67 and 0.51 electrons aretransferred from PM to PL and from PL to PM, respectively. The
P(61A) state has relatively large intensity in comparison withother CT states: it borrows its intensity from the Ex state (21A)
through a configuration mixing.
Bands XI observed at 2.23 eV (556 nm) was attributed toheme c-559.5 However, band XI would have two components,
since the sharp peak (XIb) vanishes and a shoulder (XIa) remains
in the absorption spectrum of the oxidized state (P+).5 The sharp
one has a characteristic large negative LD. We assign P(71A)
state to this sharp component, since our SAC-CI calculation
gives very small LD angle (25.3°) and a large oscillator strength
to this state. P(71A) state has the main configuration characterized by H-3 to L (π-π*) excitation, and is classified as the Qx
component of the excited state of P, since this transition
originates from the monomer H-1 to L excitation. In the present
calculation, the first excited state of c-556(21A) calculated at
2.23 eV (556 nm) with a small negative LD value has been
assigned to band VIII. The first excited state of c-559 (21A),
which was experimentally assigned to band XI, is calculated at
higher energy, 2.44 eV, with a plus LD contribution and witha small oscillator strength (0.058). It is assigned in the present
calculation to a component of peak XVI, as discussed below.
For the shoulder of the band XI, which still exists in the oxidized
states, the excited states of hemes in their oxidized states might
be the origin, since they are produced by the chemical
oxidation.5 Here, c-559+ is certainly the most probable origin
since it has an excitation energy at 2.25 eV estimated at thelevel of the Koopmans theorem. Other calculated excitationenergies of the heme cations in this energy region are 2.44 and2.55 eV for c-552+, 2.34 and 2.57 eV for c-554+, 2.49 and 2.67
eV for c-556+, and 2.45 eV for c-559+.

J. Phys. Chem. B, Vol. 102, No. 50, 1998 10417
Band XII and XIII observed at 2.28 and 2.32 eV are attributed
to the QX states of HL and HM, respectively. The illuminatedresult37 indicated this energy order. Our result is 2.66 eV for
HL and 2.67 eV for HM, and the energy splitting is obtained as
the protein effect: the gas-phase energy levels of HL and HM
are the same. This ordering is also supported by the calculated
LD angles: the angle of the lower energy state is larger thanthat of the higher energy state in accordance with the LD
spectrum shown in Figure 5.
The excited states of the hemes, c-554(21A), c-559(21A), andc-552(61A) are calculated at 2.38, 2.44, and 2.44 eV, respectively. Their characters are H to L, H to L, and H-2 to L
excitations, respectively, and c-554(21A) and c-552(61A) havenegative LD components. In the experimental spectrum, weobserve a negative LD region, band XIV, at the blue-side
shoulder of band XIII, and at 2.36 and 2.38 eV we see small
peaks having negative LD components. We therefore assign
c-554(21A) and c-552(61A) states, respectively, to these peaks.
The LD angle of c-554(21A) is a bit larger than that of c-552(61A), in accordance with experiment.
In the energy region higher than 2.7 eV, four excited states
UQ(21A), P(81A), P(91A), and MQ(21A) are calculated by the
SAC-CI method, but all the states have very small intensities.
P(81A) and P(91A) states calculated at 2.96 and 3.37 eV are
intramolecular CT states as shown in Table 3. UQ(21A) statecalculated at 2.86 eV is H to L (π-π*) excitation. Note a verylarge protein effect on this state which is discussed below. MQ(21A) state calculated at 3.44 eV is n-π* excited state withwhich H to L (π-π*) excitation strongly mixes.
V. Protein Effect on the Excited States
In the present SAC-CI calculations of the ground and excitedstates of the chromophores, the proteins, waters, and the otherchromophores involved in the PSRC were represented by the
point charge model. For P, we further considered the polarization effect of the protein medium as shown in Table 3. In Table
4, the excitation energies and the oscillator strengths of thechromophores calculated in the gas phase are compared withthose calculated in the environment of the proteins. The
geometries of the chromophores are the X-ray structures, also
common for both gas-phase and in-protein calculations. Table
4 also shows the energy shift caused by the protein environment.
Almost all the states are red shifted by an inclusion of the protein
effect, though some states, P(51A) state in particular, are blue
shifted. The calculated energy shifts are less than 0.2 eV, except
for UQ, since the orbital-energy gaps are not so much affectedby the protein potential.
For UQ, the excitation energy is red shifted by as large as
1.01 eV by the proteins, since the HOMO is more largely
destabilized by the protein potential than the LUMO. Theenergy shifts of the HOMO and LUMO are +1.73 and +0.79
eV, respectively. The reason of a larger shift of the HOMO isthat the orbital has a large amplitude in the negative-potential
region generated by GLU L 212. Unfortunately, the excitation
peak of UQ is not identified in the experimental spectrum, since
the absorption band of UQ must be hidden by the strong broad
bands composed of the Soret bands of the porphyrins.
The excitation energy shifts of B’s are relatively large incomparison with those of the other chromophores. Parson etal.38 compared the absorption spectra of the RC and bacteriochlorophyll b in ether solvent and observed red shifts of the Qy
and Qx bands. The present calculation gave the red shifts of-0.07 eV for the Qy bands of BL and BM and -0.15 and -0.18

10418 J. Phys. Chem. B, Vol. 102, No. 50, 1998
eV for the Qx bands of BL and BM, respectively, which arecomparable with the experimental values, -0.11 eV for the Qy
bands of B's, -0.11 eV for the Qx bands of BM, and -0.08 eV
for the Qx bands of BL.5,35 The reason of the red shift isaccounted for by the orbital-energy change as in UQ. The Qy
and Qx bands of B’s are due to the HOMO to LUMO and
HOMO-1 to LUMO excitations, respectively. The orbitalenergies of BL and BM are destabilized by the negativeelectrostatic potentials due to ASP M 182 and ASP L 155,
respectively. But, the energy shifts of the LUMO’s for BL and
BM are smaller than those of the HOMO’s and HOMO-1’s by
about 0.2 eV, since the LUMO regions are more distant fromthis negative potential region in both BL and BM.
The oscillator strengths are also affected by the protein
environment, but the effects are not monotonic as seen from
Table 4: some peaks become more intense but the others
become less intense. The effects are not small, as expected,
because the oscillator strengths of the porphyrins are generally
the results of the two large canceling contributions.21,36
For P, we have considered the effect of proteins expressedby the point-charge model and the polarization model and theresults are shown in Table 3 and Figure 5. As seen from theseresults, the polarization effect is very small for the Ex states,
since the induced dipole moments are small. For this reason,
the polarization effects were calculated only for P. A remarkably large polarization effect is seen for P(61A) state whichbecomes lower than P(71A) states after the polarization effectis included: otherwise the ordering of P(61A) and P(71A) states
are reversed. P(61A) state is the CT state and therefore is muchstabilized by the polarization effect.
VI. Summary and Conclusion
The excitation spectrum of the PSRC of Rps. Vridis has atleast 14 distinct bands in a narrow energy range from 1.25 to
2.4 eV. We calculated the excitation spectrum and the LD
spectrum of this PSRC theoretically by the SAC-CI method
and gave the assignment of all the peaks. We used the excitationenergy, oscillator strength, LD angle, and other information
available. In particular, the comparisons with the spectra of
the chemically oxidized PSRC, in which P and hemes areoxidized, and of the PSRC of Rb. sphaeroides were very useful.
Our final assignment is summarized in Table 4 and Figure
6. Band I at 1.25 eV(990 nm) is assigned to P(21A) QY state.
Band II at 1.46 eV(850 nm) is considered to be composed of
the QY states of c-552 and P(31A). Band III at 1.49 eV (834nm) consists of the two states, BM(21A) and BL(21A), and bands
IV and V at 1.54 eV (805 nm) and 1.57 eV (789 nm) are
assigned to HL(21A) and HM(21A) state, respectively. The
c-552(31A) state may be assigned to a small peak VI at 1.75
eV (709 nm) or to peak VII at 1.81 eV (684 nm), though themain peak at 1.81 eV is due to H-. Band VII at 1.85 eV (660nm) is assigned to P(41A) QX state. Band VIII at 1.99 eV (615nm) has a negative LD component and disappears by chemical
oxidation and assigned to c-556(21A) state, different from theassignment to P(71A) state. Band IX and X at 2.04 eV (607nm) and 2.06 eV (600 nm) are assigned to BM(31A) and BL(31A). Band XI at 2.23 eV (556 nm) has a large negative LD
peak and is assigned to P(71A) having a small LD angle θ. The
c-556(31A) state also composes this peak. Band XII and XIIIat 2.28 eV (544 nm) and 2.32 eV (534 nm) are due to HL(31A)and HM(31A). The small peaks XIVa and XIVb having negative
LD components at 2.36 eV (525 nm) and 2.38 eV (520 nm)
are assigned to c-554(21A) and c-552(61A) state. The c-559(21A) state also exists in this peak XIV. Some other states not

Hasegawa et al.
included in the above descriptions exist, and compose theshoulders, etc., of the main peaks. The average discrepancy
between the calculated and experimental excitation energies is0.13 eV.
The protein effect on the excitation energy is calculated tobe red-shifts in most cases. Although we have replaced theeffects of proteins, waters and the interchromophore interactions
by the classical Coulombic interactions, the calculations reproduced the experimental values rather well, which might indicate
the adequacy of our model. However, a precise examination
for the protein effect is very much desirable and should beconsidered by a more accurate treatment of protein molecules,
which will be studied in the next stage.
The calculations of the ground and excited states of all thechromophores in the PSRC of Rps. Viridis have thus madesuccessfully by the SAC/SAC-CI method and gave a firm basis
for the assignments of the experimental spectrum observed by
Breton.5 We believe that the present assignment would offer agood starting basis for a future development in the chemistry
and biochemistry of the PSRC.
In the succeeding paper,39 we study the mechanism and theunidirectionality of the electron transfer in the PSRC of Rps.
Virides using the SAC/SAC-CI wave functions of the chromophores calculated in this and the succeeding studies.
Acknowledgment. We thank Prof. K. Miki in the Facultyof Science, Kyoto University for the information on theoxidation state of the hemes. This study was supported in partby a Grant-in-Aid for Scientific Research from the Japanese
Ministry of Education, Science, Culture, and Sports, and by the
New Energy and Industrial Technology Development Organization (NEDO). One of the authors (J. H.) gratefully acknowledges
the Research Fellowship from the Japan Society for the
Promotion of Science for Young Scientists.
References and Notes(1) Voet, D.; Voet, J. G. Biochemistry; 2nd ed.; John Wiley & Sons:
New York, 1995; Chapter 22.
(2) Deisenhofer, J.; Epp, O.; Miki, K.; Huber, R.; Michel, H. J. Mol.
Biol. 1984, 180, 385.
(3) Hörber, J. K. H.; Göbel, W.; Ogrodnik, A.; Michel-Beyerle, M.
E.; Knapp, F. W. In Antennas and Reaction Centers of Photosynthetic
Bacteria; Michel-Beyerle, M. E., Ed.; Springer-Verlag: Berlin, 1985; pp292.
(4) Hörber, J. K. H.; W. Göbel; Ogrodnik, A.; Michel-Beyerle, M. E.;
Cogdell, R. J. FEBS Lett. 1986, 198, 268.
(5) Breton, J. Biochim. Biophys. Acta 1985, 810, 235.
(6) van Stokkum, I. H.; Beekman, L. M. P.; Jones, M. R.; vanBrederode, M. E.; van Grondelle, R. Biochemistry 1997, 36, 11360.
(7) van Brederode. M. E.; Jones, M. R.; van Mourik, F.; van Stokkum,
I. H.; van Grondelle, R. Biochemistry 1997, 36, 6855.
(8) Parson, W. W.; Warshel, A. J. Am. Chem. Soc. 1987, 109, 6152.
(9) Thompson, M. A.; Zerner, M. C. J. Am. Chem. Soc. 1992, 113,
8210. Also see: Thompson, M. A.; Zerner, M. C., Fajar, J. J. Am. Chem.
Soc. 1991, 112, 5693.
(10) Scherer, O. J.; Scharnagl, C.; Fischer, S. F. Chem. Phys. 1995, 197,
333.
(11) Nakatsuji, H.; Hirao, K. J. Chem. Phys. 1978, 68, 2053.
(12) Nakatsuji, H. Chem. Phys. Lett. 1978, 59, 362; 1989, 67, 329; 1989,
67, 334.
(13) Nakatsuji, H. Acta Chim. Hung. 1992, 129, 719.
(14) Nakatsuji, H. In Computational Chemistry, ReViews of Current
Trends; Leszczynski, J., Ed.; World Scientific: Singapore, 1996; Vol. 2,
pp 62-124.
(15) Nakatsuji, H.; Hasegawa, J.; Hada, M. J. Chem. Phys. 1996, 104,
2321; Tokita, Y.; Hasegawa, J.; Nakatsuji, H. J. Phys. Chem. A 1998, 102,
1843.
(16) Hasegawa, J.; Hada, M.; Nonoguchi, M.; Nakatsuji, H. Chem. Phys.
Lett. 1996, 250, 159.
(17) Nakatsuji, H.; Hasegawa, J.; Ueda, H.; Hada, M. Chem. Phys. Lett.
1996, 250, 379.

PSRC of Rhodopseudomonas Viridis(18) Nakatsuji, H.; Tokita, Y.; Hasegawa, J.; Hada, M. Chem. Phys.
Lett. 1996, 256, 220.
(19) Tokita, Y.; Nakatsuji, H. J. Phys. Chem. B. 1997, 101, 3281.
(20) Hasegawa, J.; Ozeki, Y.; Ohkawa, K.; Hada, M.; Nakatsuji, H. J.
Phys. Chem. B 1998, 102, 1320.
(21) Toyota, K.; Hasegawa, J.; Nakatsuji, H. J. Phys. Chem. A 1997,
101, 446.
(22) Nakatsuji, H.; Hasegawa, J.; Ohkawa, K. Chem. Phys. Lett. 1998.
In press.
(23) Abola, E. E.; Bernstein, F. C.; Bryant, S. H.; Koetzle, T. F.; Weng,
J. Protein Data Bank. In Crystallographic Databases-Information Content,
Software Systems, Scientific Applications; Allen, F. H., Bergerhoff, G.,
Sievers, R., Eds.; Data Commission of the International Union of Crystallography: Chester, 1987; pp 107-132. Bernstein, F. C.; Koetzle, T. F.;
Williams, G. J. B.; Meyer, E. F., Jr.; Brice, M. D.; Rodgers, J. R.; Kennard,
O.; Shimanouchi, T.; Tasumi, M. The Protein Data Bank: a Computerbased Archival File for Macromolecular Structures. J. Mol. Biol. 1977, 112,535.
(24) Huzinaga, S.; Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.;
Sakai, Y.; Tatewaki, H. Gaussian Basis Set for Molecular Calculations;Elsevier: NewYork, 1984.
(25) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293.
(26) SYBYL, Version 6.1;TRIPOS, Inc.: St. Louis, Missouri.
(27) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K.
M.; Freguson, D. R.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman,
P. A. J. Am. Chem. Soc. 1995, 117, 5179.

J. Phys. Chem. B, Vol. 102, No. 50, 1998 10419(28) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.;
Klein, M. L. J. Chem. Phys. 1983, 79, 926.
(29) Karelson, M. K.; Zerner, M. C. J. Phys. Chem. 1992, 96, 6949.
(30) Onsanger, L. J. Am. Chem. Soc. 1936, 58, 1486.
(31) Nakatsuji, H. Chem. Phys. 1983, 75, 425.
(32) Dupuis, M.; Farazdel, A. MOTECC-91; Center for Scientific andEngineering Computations: IBM Corporation, 1991.
(33) Nakatsuji, H.; Hada, M.; Ehara, M.; Hasegawa, J.; Nakajima, T.;
Nakai, H.; Kitao, O.; Toyota, K. SAC/SAC-CI program system (SACCI96) for calculating ground, excited, ionized, and electron attached statesand singlet to septet spin multiplicities, 1998. To be submitted for
publication.
(34) Nakatsuji, H. Program system for SAC and SAC-CI calculations.
Program Library No. 146(Y4/SAC); Data Proccessing Center of Kyoto
University: Kyoto, 1985; Program Library SAC85, No. 1396; Computer
Center of the Institute for Molecular Science; Okazaki, 1986.
(35) Scherz, A.; Parson, W. W. Biochim. Biophys. Acta 1984, 766, 653.
(36) Toyota, K.; Hasegawa, J.; Nakatsuji, H. Chem. Phys. Lett. 1996,
250, 437.
(37) Tiede, D. M.; Choquet, Y.; Breton, J. Biophys. J. 1985, 47, 443.
(38) Parson, W. W.; Scherz, A.; Warshel, A. In Antennas and Reaction
Center of Photosynthetic Bacteria; Michel-Beyerle, M. E., Ed; SpringerVerlag: Berlin Heidelberg, 1985; p 122.
(39) Hasegawa, J.; Nakatsuji, H. J. Phys. Chem. B 1998, 102, 10420.