13 November 1998

Chemical Physics Letters 296 Ž1998. 499–504

Excited states and electron transfer mechanism in thephotosynthetic reaction center of Rhodopseudomonas Õiridis:SAC–CI study
H. Nakatsuji a,b,) , J. Hasegawa a , K. Ohkawa aa

Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto UniÕersity, Sakyo-ku, Kyoto
606-8501, Japanb
Institute for Fundamental Chemistry, 34-4 Takano Nishi-hiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan
Received 14 July 1998; in final form 20 August 1998

AbstractThe symmetry adapted cluster ŽSAC. –configuration interaction ŽCI. method has been utilized to assign the excited states
in absorption and linear dichroism spectra and to clarify the mechanism of the unidirectionality in the electron transfer of thephotosynthetic reaction center of Rhodopseudomonas Õiridis. We have calculated the ground, excited, ionized, andelectron-attached states of all the chromophores in the reaction center. The protein effects were included with the use of thepoint-charge model. q 1998 Elsevier Science B.V. All rights reserved.

1. Introduction
Ab initio electronic structure theory has achievedchemical accuracy even for large molecules w1x andthe elucidation of biochemically important phenomena by such methods constitute a challenging frontierof quantum chemistry. In this Letter, the SAC Žsymmetry adapted cluster. –CI Žconfiguration interaction.
method w2–4x, which describes almost all kinds ofground and excited states of molecules in good
accuracy including electron correlation w1,5x, has been
applied to the photosynthetic reaction center ŽPSRC.
of Rhodopseudomonas Ž Rps.. Õiridis w6x in order togive a definite assignment of the excitation spectrum
w7x and to clarify the mechanism of the electron)

Corresponding author. E-mail: hiroshi@sbchem.kyoto-u.ac.jp

transfer ŽET. and the origin of its unidirectionality.
This is by far the highest-level calculation modern
quantum chemistry can achieve.
Fig. 1 compares the absorption and linear dichroism ŽLD. spectra of the PSRC of Rps. Õiridis observed by Breton w7x with those calculated by theSAC–CI method. All the chromophores included in
the PSRC w6x Žbacteriochlorophyll b dimer Žspecialpair, P., bacteriochlorophyll b in L- and M-branchesŽB L and B M ., bacteriopheophytin b in L- and Mbranches ŽH L and H M ., menaquinone ŽMQ.,ubiquinone ŽUQ., and four different hemes, c-552,c-554, c-556, and c-559, in the c-type cytochrome
subunit. were calculated within the environment ofproteins, water, and the other chromophores whichwere dealt with by the point charge electrostatic
model. The peaks numbered from I to XIV in theobserved spectrum are assigned by the dotted lines tothe SAC–CI ones. This assignment was done using

0009-2614r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved.
PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 1 0 3 4 - 3

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H. Nakatsuji et al.r Chemical Physics Letters 296 (1998) 499–504

H. Nakatsuji et al.r Chemical Physics Letters 296 (1998) 499–504

501

Fig. 2. Electronic factors, < H IF < 2 Ž=10y9 in a.u.. for the electron transfers in the PSRC of Rps. Õiridis Žthe upper value is in the protein
model compared with the experimental value Žgiven in parentheses w9x. and the lower one is in the gas phase.. Energy levels colored green
are experimentally estimated values w10x and the black ones were calculated by the SAC–CI method.

the excitation energy, oscillator strength, LD angle,
and other experimental information available. In particular, the comparisons with the spectra w7x of thechemically oxidized PSRC Žin which P and hemes
are oxidized. and of the PSRC of Rhodobacter Ž Rb..
sphaeroides Žwhich does not have a cytochrome csubunit. were very useful. The average discrepancy
from the experimental peak positions is 0.13 eV Ž3kcalrmol.. The protein effects were to red-shift thepeaks for most states. The present assignment of thespectrum would give a basis for future photo-experimental studies of the PSRC.
The SAC–CI wavefunctions of the chromophores
were then utilized to clarify the electronic mechanism of the ET from the initial photo-excited P ) toH and the origin of its unidirectionality in the PSRC.
The ET rate is expressed by Marcus and Sutin w8x as
a product of the electronic and thermodynamic nuclear factors. Fig. 2 shows the electronic factorsŽtransfer integrals., < H IF < 2 Ž=10y9 in a.u.., calculated in the environment of the proteins and in thegas phase. The values in parentheses are those estimated from the experimental data w9x. The energy
levels of the two lower states in the L-branch coloredgreen are the experimentally estimated values w10x,
but for others, the SAC–CI values were used. We
assume here the sequential mechanism, since theenergy levels of the intermediate states were experimentally estimated to be lower than that of P ) w10x.
The calculated electronic factors Žincluding protein

Fig. 1. Absorption and linear dichroism spectra of the PSRC. Ža. Theoretical excitation spectrum calculated by the SAC–CI method. Žb.
Experimental absorption and linear dichroism spectra w7x. Žc. Theoretical linear dichroism spectrum calculated by the SAC–CI method.

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Fig. 3. Geometries of the chromophores and the MO populations for ŽA. the LUMOs of B and H in M- and L-branches and ŽB. theLUMOŽP. –LUMOŽB L . pair and the HOMOŽP. –LUMOŽB L . pair which are the MO pairs responsible for the ET and CR processes,respectively. The sign of the population indicates the phase of the orbital.

H. Nakatsuji et al.r Chemical Physics Letters 296 (1998) 499–504

effect. for the ETs from P ) to B and from B to H in
the L-branch are 25.2 and 104.4, respectively, which
are in good agreement with the experimentally estimated values of 21 and 72, respectively, and aremuch larger than the corresponding values for theM-branch of 1.7 and 15.9, respectively. The calculated branching ratio, < H L < 2r< H M < 2 f 15 in proteinsŽ< H L < 2r< H M < 2 f 35 in the gas phase., is large enoughto explain the experimental branching ratio k Lrk M) 5 w11x. These ETs occur mainly through the lowest
unoccupied molecular orbitals ŽLUMOs. of P, B, andH.
A competitive reaction to the ET from B to H isthe charge recombination ŽCR. reaction from Pq By H
to the ground state of PBH. This CR is essentially atransfer of an electron from the LUMO of B L to thehighest unoccupied molecular orbitals ŽHOMO. of P.
The electronic factor calculated for the CR is 1.0
which is much smaller than that for the chargetransfer ŽCT., 104.4, so that CR is much less preferable to ET: the branching ratio here to the CR is
1.0r105.4, ; 1% of that of the ET, which corresponds well with the so-called efficiency Žquantumyield. of the photosynthesis.
The L-branch selectivity is explained by theasymmetry of the electronic factors. Namely, theL-side route is much wider than the M-side one.
Therefore, we have analyzed the electronic factors insome detail and found that this asymmetry originates
mainly from a small structural asymmetry of thePSRC: the L-side chromophores are closer locallythan the M-side ones, though the average separations
are almost the same. Fig. 3A shows the geometriesof B and H and the populations of the LUMOs of theB–H pairs in the M- and L-branches. The analysis ofthe transfer integrals has revealed that the transfer
between ring I of B and ring I of H is dominant inboth branches, but since the inter-ring distance is
˚ in the L-branch than in the M-branch,closer by 0.5 A
the ET occurs more easily in the L-branch. Note thatthe B–H center-to-center distance is almost the same
between both branches. A similar argument also
holds for the ET from P ) to B.
The smallness of the CR rate, on the other hand,
is attributed to the difference in the electron localization between the LUMO and HOMO of the specialpair. In Fig. 3B, the populations of the LUMO andHOMO of P and the LUMO of B are shown. The503

populations of PM and PL are different in the HOMOand LUMO w12x. In PM , which is closer to B L , theLUMO population is localized in the lower area,
while the HOMO population is localized in the upperarea, so that the effective distance between P and L
is much less in the LUMOŽP. –LUMOŽB L . pair thanin the HOMOŽP. –LUMOŽB L . pair. Therefore, although the ET occurs easily, it is difficult for CR to
take place.
The role of the proteins is decisive as the three-dimensional arrangement of the chromophores in theL- and M-branches is supported by them. However,the protein effects accounted for by the electrostatic
point-charge model were found to be very small.
Nature offered a duality in the electron path, but
now only one is utilized. Since we could attribute theprimary origin of the L-branch selectivity of the ET
to a bio-structural factor – the local closeness of thechromophores in the L-region relative to the M-region – we propose a mutation experiment which
would make the M-side chromophores locally closer
than the L-side ones, since this should result in an
occurrence of the M-side ET. This would certainly
be an exciting experiment, and would lead to theclarification of many other facts. More details of thepresent study will be published in the near future
w13,14x.

2. Method
All calculations were carried out using the geometries of the chromophores and proteins as determinedby X-ray crystallography w15,16x. Huzinaga et al.’sbasis sets w17x plus some anion and polarization
functions w18x were commonly used in the calculations of all the chromophores. The proteins andwaters were replaced by the point charge modelusing the published charges w19x. The polarization
effect of proteins was considered only for P. In theSAC–CI calculations, the active MOs were selected
such that at least p-orbitals of C, N, and O and thevalence orbitals of the other atoms should be included. For the hemes in the cytochrome subunit,only the inner 1s orbitals were frozen, so that theaccuracy is better for the hemes. The dimensions ofthe SAC–CI calculations were reduced by doing
perturbation selections for double linked operators:

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the thresholds are similar to the previous ones w20x.
The calculations were done using the HONDO8
program w21x for the self-consistent field ŽSCF. –MO
calculations and SAC–CI 96 program w22x for theSAC–CI calculations. Other details of the calculations are described in Refs. w13,14x.

Acknowledgements
This study has been supported in part by a Grantin-Aid for Scientific Research from the Ministry ofEducation, Science, Culture, and Sports, and by theNew Energy and Industrial Technology Development Organization ŽNEDO.. One of the authors ŽJH.
gratefully acknowledges the Research Fellowshipfrom the Japan Society for the Promotion of Sciencefor Young Scientists.

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