1242

Chemistry Letters Vol.34, No.9 (2005)

Excited States and Electron-transfer Mechanism in the Photosynthetic Reaction Centerof Rhodobactor sphaeroides: SAC-CI Theoretical Study
Jun-ya Hasegawa and Hiroshi NakatsujiyDepartment of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University,
Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8510
yFukui Institute for Fundamental Chemistry, Kyoto University,
Takano-Nishihiraki-cho 34-4, Sakyo-ku, Kyoto 606-8103(Received June 21, 2005; CL-050792)
The SAC-CI calculations clarify the natures of the excitedstates and the electron-transfer (ET) processes in the photosynthetic reaction center (PSRC) of Rhodobactor (Rb.) sphaeroides.
The absorption spectrum was assigned with the averaged error of0.11 eV. The electronic factors calculated from the SAC-CI wave
functions clariﬁed the mechanism of the unidirectionality of theET in Rb. sphaeroides. It is controlled by the ET step from bacteriochlorophyll (B) to bacteriopheophytin (H), not from the special pair (P) to B as in the Rhodopseudomonas (Rps.) viridis reported previously: the electronic factor of the A-branch ET is
20 times larger than that of the B-branch. An analysis clariﬁedthat the unidirectionality originates from the inter-chromophore
distances, and further that the hyperconjugations of the methylgroups with the  electrons of the chromophores have primarycontributions to the electronic factor.

Light-induced transmembrane ET in the PSRC is a key stepof the energy production in the green plants and bacteria.1 The
structure and function of these PSRCs resemble each other. InRb. sphaeroides, the PSRC protein contains seven chromophores: bacteriochlorophyll-a dimer (Special Pair, P), two bacteriochlorophyll-a monomers (BA and BB ), two bacteriopheophytina monomers (HA and HB ), and two ubiquinones (QA and QB ).
Figure 1 shows the chromophore alignment in the PSRC, whichhas pseudo-C2 axis. An excited electron at P is sequentially transferred only along the A-branch as indicated in Figure 1.2 This ET
is also well-known to be highly eﬃcient. In our previous study on
the ET in a bacterial PSRC of Rhodopseudomonas (Rps.) viridis,
the unidirectionality of the ET was explained by the electronic
factor calculated with the SAC-CI wave functions: The electronic
factor for the ET from P to BA was 15 times larger than that fromP to BB .3,4 Decomposition analysis clariﬁed that the origin of theasymmetric electronic factor is in the interchromophore distance shorter thanbetween P and B.3,4 That of the A-branch is 0.5 A
that of the B-branch. However, in Rb. sphaeroides, the P to B distance is similar in the two branches,5 suggesting another origin. In
this study, the excited states and electron transfer in the PSRC ofthe Rb. sphaeroides were examined by SAC-CI6 method, and theresults were compared with those for Rps. viridis.
The structure of the PSRC was taken from a X-ray structure(1OGV5). For the computational model of the chromophores, thesubstituents lying between the chromophores were kept in themodel. The coordinates of the chromophores were optimized
with B3LYP/6-31G level. The eﬀect from the rest of the protein
was treated by a point charge model using AMBER force ﬁeld.7
The SAC-CI calculations was performed for each chromophores
with D95 basis sets8 for the H, C, O, and N atoms, and (533/5)[52121/41] sets9 for the Mg atoms. All valence orbitals werecorrelated in the SAC-CI calculations. For P, the orbitals withthe energy of 33  33 eV were taken into the active space.
The perturbation selection was performed for the double excitation operators with the threshold of 1  105 and 1  106 a.u.
for the ground and excited states, respectively. See Supporting
Material for the detail of the calculations.
In Table 1, the excited states of the PSRC calculated by theSAC-CI method are summarized. The results are compared withthe experimental data. Total 15 states were calculated in the energy region of 1.3–2.8 eV, and the 6 peaks in the experiments
were consistently assigned and their nature were clariﬁed. Therms error in the SAC-CI excitation energy was 0.11 eV, indicating that the present assignments are reliable. This assignment
provides a starting point for future photochemical studies of thePSRC. The ﬁrst peak, which is important as the initial state ofthe ET, is assigned to the ﬁrst excited state of P. From HOMO
to LUMO excitation dominates 50% of the weight in the wavefunction.
Using these SAC-CI wave functions, we calculated theelectronic factor jHIF j2 in the ET rate constant.
2ð1Þ
jHIF j2 ðFCÞhFC is Frank–Condon factor which describes the contribution
from the nuclear dynamics. We note that the ET rate constantis proportional to the electronic factor. The details of the calculation method are found in the previous paper.4 The results are summarized in Figure 2. The energy levels of the states weretaken from a previous experimental study.11 For the ET from Pto B, the calculated electronic factors for the A- and B-branches
are very close to each other: 3:93  103 and 3:63  103 cm2 , respectively. However, for the ET from B to H, the electronic factor
for the A-branch ET is 20 times larger than that for the B-branch:
10:5  103 and 0:52  103 cm2 , respectively. For the Rps. virikET ¼

Figure 1. Chromophores in the PSRC of Rb. sphaeroides.

Copyright Ó 2005 The Chemical Society of Japan

Chemistry Letters Vol.34, No.9 (2005)

1243

Table 1. Excited states of the PSRC of Rb. sphaeroides
Exptl.eSAC-CIState(Chro.a )b21 A(P)21 A(BB )21 A(BA )31 A(P)
21 A(HB )21 A(HA )41 A(P)
31 A(BA )31 A(BB )51 A(P)
61 A(P)
71 A(P)
31 A(HA )31 A(HB )81 A(P)rms fMain conﬁgurations (jCj > 0:3)

Eex .

c

Osc.

d

Eex .c0.69(H!L) + 0.42(H1!L+1) + 0.39(H1!L)0.90(H!L)
0.87(H!L)
0.65(H1!L)  0.37(H!L) + 0.33(H!L+1)
0.83(H!L)
0.85(H!L)
0.78(H!L+1) + 0.48(H1!L)
0.88(H1!L)
0.86(H1!L)
0.79(H1!L+1)  0.47(H1!L)0.79(H2!L)  0.43(H3!L+1)
0.65(H2!L+1)  0.61(H3!L)
0.86(H1!L)+0.37(H!L+1)
0.86(H1!L)+0.39(H!L+1)
0.61(H2!L+1)  0.55(H3!L) + 0.35(H2!L)

1.32
1.39
1.48
1.77
1.79
1.86
1.88
1.95
2.01
2.06
2.22
2.35
2.37
2.38
2.84
0.11

0.64
0.44
0.35
0.07
0.27
0.28
0.02
0.18
0.16
0.01
0.13
0.27
0.15
0.14
0.00

1.42
1.55
1.55
1.63
1.63
1.79
2.07
2.07

2.30
2.30aChromophore. b H and L denote HOMO and LUMO, respectively. c Excitation energy in eV. d Oscillator strength in a.u. e Ref. 10. f Root mean squear error
in the excitation.

P+BH-P+B-H

kcal/mol

P*BH

30 P+(12A)H-(12A)

P+(12A)B-(12A)

0.52 × 10

P+B-H

P*(22A) P+(12A)B-(12A)

B-branch

C13BA

BA

C133hν

100

P+(12A)H-(12A)

10.5 × 10320P+BH-

3.93 × 10 3

3.63 × 103

PBH

53.02.95Å
H106

A-branch

H106

HAHAFigure 2. Electronic factor jHIF j2 (in cm2 unit) of the ET in the PSRC ofRb. sphaeroides.

dis studied previously,3,4 the electronic factor for the A-branch
was larger than the B-branch for both ET’s from P to B and from
B to H. The present result indicates that the origin of the Abranch selectivity in Rb. sphaeroides is ascribed to the electronic
factor of the ET from B to H. A narrow path in the B-branch from
B to H makes the A-branch ET favorable.
We also calculated the electronic factor for the charge
recombination from Pþ BA  to the ground state. The result(53.0 cm2 ) is 200 times smaller than that of the ET, whichindicates that the electronic factor also controls the eﬃciencyof the ET in the PSRC.
To clarify the origin of the asymmetry in the electronic factor, we performed a decomposition analysis. Since oﬀ-diagonal
elements of the Fock matrix dominantly contributes to the electronic factor,3,4 the decomposition into atom–atom contributions
provides useful information about the detailed route of the ET.
For the ET from BA to HA , the largest contribution comes fromthe pair H106 (HA ) and C13 (BA ) as shown in Figure 3. The dis while that of the corretance between the two atoms is 2.95 A,
sponding pair is 3.96 A in the B-branch. Since the electronic interaction decays exponentially to the interchromophore distance, becomes critical. On the other hand, the disthe diﬀerence of 1 A
tance between P and B in the A-branch is very close to that of Bbranch, which results in the similar magnitude of the electronicfactor. The asymmetry in the structure is the origin of the unidirectional ET, similarly to the case of Rps. viridis.3,4
It is very interesting to note that the methyl groups play a crucial role in the ET. Figure 3 shows the donor and acceptor orbitals
in the ET from BA to HA . The analysis showed the importance ofthe amplitude on H106 (HA ) in the acceptor orbital. This is due to(a) Donor orbital (BA)(b) Acceptor orbital (HA)

Figure 3. (a) Donor and (b) acceptor orbitals in the electron transfer fromBA to HA .

the hyperconjugation between the methyl group and the -systemof HA . Such crucial contribution of the hyperconjugation seems
to be common in all ET’s in the PSRC, and should be recognized
as a general principle.
References
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Published on the web (Advance View) August 6, 2005; DOI 10.1246/cl.2005.1242