Open Journal of Applied Sciences, 2013, 3, 1-5
http://dx.doi.org/10.4236/ojapps.2013.33B001 Published Online July 2013 (http://www.scirp.org/journal/ojapps)
Incoherent Oscillations Accompanying Charge Separation
in Photosynthetic Re ac tion Cent er s
A. G. Yakovlev1, V. A. Shuvalov1,2
1A.N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Mos c ow , Rus si a
2Institute of Basic Biological Problems, Russian Academy of Sciences, Moscow, Russia
Received May 2013
ABSTRACT
Early events of charge separation in reaction centers (RCs) of bacterial photosynthesis are modeled by kinetic equations
with time-dependent rate constants. An illustrative case of regular motion along a “slow” coordinates leading to oscilla-
tions in the kinetics is examined. Different schemes of charge separation are investigated. A good fitting of experimen-
tal kinetics of native Rba. sphaeroides RCs is achieved in the fiv e states model P*1BAHA ↔ P*2BAHA ↔ I ↔ P+
A
B
−
HA
↔ P+BA
A
H
−
with two excited states
*
1
P
BAHA and
*
2
P
BAHA and three charge separated states I, P+
A
B
−
HA and P+BA
A
H
−
(P is a primary electron donor, bacteriochlorophyll dimer, BA and HA are an electron acceptor, monomeric bacterioch-
lorophyll and bacteriopheophytin in active A-branch, respectively). In the model only the first excited state is directly
populated by optical excitation. The emission of the two excited states is assumed to be at 905 and 940 nm, respectively.
The intermediate state I is assumed to absorb at 1020 nm as well as the P+
A
B
−
HA state. The model explains the deep
oscillations in the kinetics of the
*
1,2
P
stimulated emission and of the
A
B
−
absorption. In the simpler schemes without
the I state or with only one excited state the accordance with the experiment is achieved at unreal parameter values. A
possible nature of the I and
*
2
P
BAHA states and a possible incoherent nature of the oscillations are discussed.
Keywords: Photosynthesis; Charge Separation; Reaction Center; Electron Transfer
1. Introduction
In reaction centers (RCs ) of purple bacteria Rhodobacter
(Rba.) sphaeroides primary charge separation consisted
in electron is transferred from excited dimer of bacteri-
ochlorophyll P* to monomeric bacteriochlorophyll BA
within ~3 psec and from
A
B
−
to bacteriopheophytin HA
within ~1 psec at room temperature (for reviews see
[1,2]). Then electron is transferred to primary quinone
QA within ~200 psec. At cryogenic temperatures these
reactions are accelerated by 2 - 3 times. Excitation of
RCs by broadband femtosecond light pulses leads to os-
cillations in the kinetics of P* emission [3] and of
A
B
−
absorption [4] with a frequencies at 10 - 400 cm−1 (peak
at 130 - 150 cm−1). These oscillations are observed in
various native and mutant RCs in a wide range of tempe-
ratures. According to modern ideas, a vibrational or elec-
tronic (or bo th) coherence is a possible explanation of the
oscillatory phenomena in the kinetics of the excited and
charge separated states. A periodical motion of a vibra-
tional wavepacket [5] or a quantum beats between the
levels with close energies [6] can produce the damped
oscillations in the populations of the RC states. Analysis
of the coherent electron transfer was performed on the
base of Redfield theory in [7] and in the dispersed pola-
ron model [8]. The oscillations in the P* stimulated
emission band were theoretically studied by an approach
of single electronic transition coupled to one or two vi-
brational modes [9-11]. At room temperature the quan-
tum coherence should be destroyed very quickly due to
thermal motions [12]. On the other hand, the molecular
dynamics calculations revealed a number of classical
vibrational modes in RCs at 20 - 200 cm–1 [13]. These
modes can reflect the nuclear motions in protein matrix
as well as inside the RC pigments. A classical stochastic
Langevin equation was used to calculate the oscillatory
dynamics of the P* ↔ P+
A
B.
−
Reaction controlled by
protein relaxation [14] in modified RCs with blocked
electron transfers to HA.
In the present work the incoherent charge separation
dynamics of native Rba. sphaeroides RCs is modeled by
the kinetic equations with time-dependent rate constants.
This approach is based on the Marcus theory [15]. An
aim of the work was to study a possibility of incoherent
origin of the oscillatory phenomena observed at early

A. G. YAKOVLEV, V. A. SHUVAL OV
2
times of charge separation.
2. Model
According to Marcus theory [15], electron or energy
transfer reaction occurs at the intersection of the potential
energy surfaces of the initial and final states of the sys-
tem. In harmonic approximation these surfaces are para-
boloids shifted one from another: Uin = 1/2mω2x2 +
1/2MΩ2X2; Ufin = 1/2mω2 (x – x0)2 + 1/2MΩ2(X - X0)2 +
ΔG. Here x and X are effective coordinates of fast (ther-
mal) and s low (relaxation) motion, respe ctively; m and M
are effective masses, ω and Ω are self-frequencies, x0 and
X0 are the potential surface displacements along the x and
X coordinates, ΔG is the free energy change of the reac-
tion. In the high-temperature limit, the rate constants of
the forward and backward reaction can be written as fo l-
lows:
( )( )
f0 bf
exp; exp.
BB
KKEkT KKGkT=−=
Here the activation energy E = 1/4λ(1 + G/λ)2; the
energy gap G = ΔG + λ1 − 2 λ1X/X0; the fast reorganiza-
tion energy λ = 1/2m
2
0
x
; the slow reorganization energy
λ1 = 1/2MΩ2
2
0
X
; kB is the Boltzmann constant; T is a
temperature; K0 is a constant. After an averaging over the
fast coordinate x the dynamics of the energy gap G(t) and
of the activation energy E(t) is determined by the dy-
namics of the slow coordinate X(t). Thus, the rate con-
stants Kf,b are time-dependent in this approach. In our
model we examine a simplest illustrative case of damped
cosine dependence of X on time. We studied the schemes
of three (P*BAHA ↔ P+
A
B
−
HA ↔ P+BA
A
H
−
), four (
*
1
P
BAHA ↔
*
2
P
BAHA ↔ P+
A
B
−
HA ↔ P+BA
A
H
−
) and five
(
*
1
P
BAHA ↔
*
2
P
BAHA ↔ I ↔ P
+
A
B
−
HA ↔ P+BA
A
H
−
)
states. The coordinates of each reaction were assumed to
be independent. The incoherent dynamics of relative
populations of these states was described by kinetic equ-
ations.
3. Results and Discussion
3.1. The Modeled Kinetics
The results of the modeling of the five states scheme (Fi-
gure 1) are shown in Figure 2 for native RCs of Rba.
sphaeroides. The calculation parameters are as follows:
temperature Т = 90 K, energy difference
0
12
G
= 35 cm–1,
0
23
G
= 85 cm–1,
0
34
G
= −400 cm–1,
0
45
G
= −900 cm–1;
reorganization energy λ12 = 80 cm–1, λ23 = 100 cm–1, λ34 =
450 cm–1, λ45 = 1500 cm–1; reactio n rate
0
12
K
= 26 psec–1,
0
23
K = 34 psec–1, 0
34
K = 12 psec–1,
0
45
K
= 40 psec–1;
G12(t) = 5 0 cm–1 exp(–3.5t)(sin(30.5t − 1.2) + sin(25. 5 t −
1.2)); G23(t) = 60 cm–1exp(−2t)(sin(22.5t − 0.1) +
sin(27.5t − 0.1)) + 20 cm–1 exp(−9t); G34(t) = –600
cm−1exp(−5t) + 320 cm–1exp(−0.5t)sin(12t − 2.4); G45(t)
Figure 1. An illustrative scheme of the energy levels of the
states at zero oscillations.
Figure 2. The modeled kinetics of the relative populations of
the
*
1
P
BAHA,
*
2
P
BAHA, I, I + P+
A
B−
HA and P+BAA H
−
states
of the native Rba. sphaeroides RCs. For details see the text.
= 0; time t is given in psec. The calculated kinetics of the
states are similar with the experimental ones at t > 150
fsec [2-4,16]. A decay of the P* stimulated emission at
905 and 940 nm (the
*
1
P
BAHA and
*
2
P
BAHA states in
the model, respectively) and a bleaching of the HA ab-
sorption band at 760 nm (the P+BA
A
H
−
state) occur
within ~1.5 psec in native RCs at 90 K. These processes
are accompanied by the formation of the
A
B
−
absorption
band at 1020 nm. The modeled sum of the I and P+
A
B
−
HA
populations is close to the experimental kinetics of the
A
B
−
absorption band. This means that the I state absorb
at 1020 nm. The pronounced damped oscillations with
the ~220 fsec period are observed in the kinetics of the
P* stimulated emission and of the
A
B
−
absorption. The
main contribution to the
A
B
−
oscillations is provided by
the I state. The oscillatio ns are completely damped with-
in ~600 fsec. The P* oscillation s at 905 and 940 nm have
the opposite phases, while the
A
B
−
absorption oscillates
in phase with the P* oscillations at 940 nm.
3.2. The Parameters of the Calculations
The parameter values used in the model are in accor-
dance with the extensive theoretical and experimental
studies reviewed in [1,2,5,14]. According to different
estimations, in Rba. sphaeroides RCs the Р+A B−HA and
P+ВА
A
H
−
energy levels are placed below the P*BAHA
energy level by 300 - 700 and 900 - 2000 cm–1, respec-
tively. In our model the energies of the
*
1
P
BAHA,
P*2BAHA and I states are different by less than 100 cm–1.
( 5)
( 4)
( 3)
( 2)
( 1)
P
+
B
A
H
A_
P
+
B
A_
H
A
Ι
P*
2
B
A
H
A
P*
1
B
A
H
A
0,0 0,4 0,8 1,2
0,0
0,4
0,8
Ι
P
+
B
A
H
A_
Ι + P
+
B
A_
H
A
P*
2
B
A
H
A
P*
1
B
A
H
A
Population, rel. un.
Time, ps

A. G. YAKOVLEV, V. A. SHUVAL OV
3
The rates of the forw ard and backward reactions between
these states oscillate with approximately opposite phases
(Figu r e 3 ). Such correlation between the dynamics of the
forward and backward reactions leads to the deep oscilla-
tions in the populations.
The molecular dynamics calculations estimate the re-
organization energy of the P*BA → Р+ВА– and Р*HA →
Р+HА– reactions by ~700 cm–1 [17] and ~2000 cm–1 [18],
respectively. In our model the fast reorganization energy
of the I → P+
A
B
−
HA (450 cm–1) and P+
A
B
−
HA →
P+BAHA– (1500 cm–1) reactions is much greater than that
of the
*
1
P
BAHA →
*
2
P
BAHA (80 cm–1) and
*
2
P
BAHA → I
(100 cm–1) reactions. This means the small displacement
between the potential surfaces of the
*
1
P
BAHA,
*
2
P
BAHA
and I states.
If we assume X/X0 = 1 for convenience, then the slow
reorganization energy λ1 = 25, 40, 460, 0 cm–1 for the
*
1
P
BAHA ↔
*
2
P
BAHA,
*
2
P
BAHA ↔ I, I ↔ P+A
B−HA and P+
A
B
−
HA ↔ P+BA
A
H
−
reactions, respectively. Thus, the
main part of the slow reorganization is corresponded to
the I ↔ P+A
B−HA reaction, and the noticeable part of this
reorganization (160 cm–1) is corresponded to the aperi-
odic motion.
In the model the values K0 = 26, 34, 12 and 40 cm–1
were used for the
*
1
P
BAHA ↔ P*2BAHA,
*
2
P
BAHA ↔ I, I
→ P+
A
B
−
HA and P+BA–HA → P+BA
A
H
−
reactions, respec-
tively. In the adiabatic approximation these K0 values are
corresponded to the effective frequency υ = 400 - 1300
cm–1. In the nonadiabatic approximation in high tempera-
ture limit these K0 values together with the λ values give
the electron coupling energy for the above mentioned
reactions V = 74, 89, 77 and 190 cm–1. The estimations of
the V value for the P*B ↔ P+
A
B
−
and P+
A
B
−
↔ P+
A
H
−
reactions are varied from 5.4 cm–1 [19] to 80 cm–1 [20]
and from 15 cm –1 [21] to 480 cm–1 [20], respectively.
The qualitative agreement of our model with the expe-
rimental data can be achieved in the wide range of the
parameters that indicates the stability of the model against
the parameter fluctuations. The two-fold change of the
Figure 3. The calculated dependences of the forward K12,
K23 and backward K21, K32 reaction rates (1–
*
1
P
BAHA, 2–
*
2
P
BAHA, 3–I) on time for the native Rba. sphaeroides RCs. For
details see the text.
energy differences, reaction rates or reorganization ener-
gies causes minor quantitative changes in the kinetics
shown in Figure 2.
3.3. Different Rea ct ion Schemes
Calculation shows that the simplest scheme of three
states P*BAHA ↔ P+
A
B
−
HA ↔ P+BA
A
H
−
produces more
smooth oscillations than it is in experiment. In this
scheme very large amplitude of the energetics changes
~1000 cm–1 is necessary to obtain the oscillation ampli-
tude comparable with experimental one. It is clear that
this scheme does not explain the out-of-phase oscillations
of the P* stimulated emission at 905 and 940 nm. These
out-of-phase oscillations can be explained by the scheme
of four states
*
1
P
BAHA ↔
*
2
P
BAHA ↔ P+A
B−HA ↔
P+BA
A
H
−
. In this scheme the oscillatory behavior of the
P+
A
B
−
HA state can be explained if to assume that the
energetics of the
*
2
P
BAHA ↔ P+A
B−HA reaction oscil-
lates with unreal amplitude ~1 400 cm–1 or that the P+
A
B
−
HA energy level is higher than the
*
1
P
BAHA and
*
2
P
BAHA levels. The last assumption contradicts to the
number of theoretical and experimental works [5,17,22,
23]. An insertion of the intermediate state I between the
*
2
P
BAHA and P+A
B−HA states helps to explain the oscil-
latory kinetics of the
A
B
−
absorption if to suppose that
the I energy is close to the
*
2
P
BAHA energy and that the I
state has spectral properties of the A
B−.
3.4. A Possible Na t ure of the
*
2
P
BAHA and I
States
In our model the
*
2
P
BAHA state is presumably associated
with the P* stimulated emission band at 940 nm. This
band is spectrally and temporally differ from the initially
excited P* emission band at ~905 nm (
*
1
P
in the model)
and is clearly observed in native and mutant RCs at room
and low temperatures [3,24]. In the experimental ΔA
spectra the 940-nm emission band forms a long-wave-
length tail of the broadband negative signal mainly con-
sisted of the P absorption band bleaching at ~870 nm.
The nature of 940-nm emission band is not well unders-
tood. The visible and IR transient spectroscopy indicates
that this band may be ascribed to the state with partial
charge separation inside the dimer P [24-26]. From the
other hand, the hole burning experiments at low temper-
atures show an absence of the P* conversion into another
state on a time scale much shorter than 1 psec [27,28].
The possible charge transfer character of the P* state
may be a result of the electron-spin density shift from PA
to PB in P* calculated by quantum-mechanical methods
[29]. The appearance of the delayed 940-nm feature in
the P* emission spectra may originates from vibrational
relaxation or electronic relaxation (or both) or fro m exci-
tation energy redistr ibution over vibrational modes in the
0,0 0,2 0,4 0,6
0
10
20
30
K
12
K
23
K
21
K
32
K, 1/psec
Time, psec

A. G. YAKOVLEV, V. A. SHUVAL OV
4
P* state. It is clear that further studies are need in this
question.
As it was mentioned above, the I state was introduced
into the model for better fitting of the experimental
A
B
−
absorption kinetics at 1020 nm. The population dynamics
of the I state is close to the oscillatory component of the
experimental
A
B
−
absorption band dynamics. The cal-
culated sum of the I and P+
A
B
−
HA populations is close to
the experimental A
B− kinetics. These results indicate
that the I state may contain
A
B
−
or ВА
δ–. One may spe-
culate that I is the state with charge transfer character
between P* and BA. To distinguish the I and P+A
B−HA
states in experiment is very difficult because of their
spectral and temporal closeness. No clear experimental
evidence of the I state existence is available now.
In our opinion, an advantage of the schemes with the
*
2
P
BAHA and I intermediates consists in the high rates of
the reactions in which these states are involved. The
*
2
P
BAHA and I states act as fast mediators between the in-
itially excited (
*
1
P
BAHA) and charge separated states. A
stabilization of electron occurs lately in the P+
A
H−
state
and partially in the P+
A
B
−
state.
3.5. A Nature of the Oscillations
In our model the oscillations in the populations are
caused by external modulation of the reaction energetics.
A nature of this modulation is beyond the scope of the
model. The nuclear motion (not only inside P) can be a
possible source of this modulation. Shortly after the ex-
citation of P by broadband femtosecond pulse the nuclear
motion has a coherent character. When the coherence is
rapidly damped this motion may continue incoherently
due to the nuclear inertia. One can speculate that the in-
coherent motion may exist a longer timescale than the
coherent one, but the latter produces the greater ampli-
tude of the oscillations. The observed oscillations may
reflect both the coherent and incoherent motion. The
presented model shows th at at t > 150 fsec the oscillatory
features observed in the kinetics of the excited and
charge separated states can be explained by incoherent
modula t ion of the reaction energetics.
4. Acknowledgements
We are grateful to L.G. Vasilieva and A.Ya. Shkuropatov
for preparing RC samples. We acknowledge the partial
financial support of the Russian Foundation for Basic
Research.
REFERENCES
[1] W. W. Parson and A. Warshel, “Mechanism of Charge
Separation in Purple Bacterial Reaction Centers,” In: C. N.
Hunter, F. Daldal, M. C. Thurnauer and J. T. Beatty, Eds.,
The Purple Phototrophic Bacteria, Springer Science +
Business Media B.V., Dordreht, 2009, pp. 355-377.
http://dx.doi.org/10.1007/978-1-4020-8815-5_19
[2] V. A. Shuvalov, “Primary Light Energy Conversion in
Reaction Centers of Photosynthesis,” Nauka, Moscow,
2000.
[3] M. H. Vos, M. R. Jones, C. N. Hunter, J. Breton, J.-C.
Lambry and J.-L. Martin, “Coherent Dynamics during the
Primary Electron-Transfer Reaction in Membrane-Bound
Reaction Centers of Rhodobacter sphaeroides,” Bioche-
mistry, Vol. 33, 1994, pp. 6750-6757.
http://dx.doi.org/10.1021/bi00188a002
[4] A. G. Yakovlev, A. Ya. Shkuropatov and V. A. Shuvalov,
“Nuclear Wavepacket Motion Producing a Reversible
Charge Separation in Bacterial Reaction Centers,” FEBS
Letters, Vol. 466, 2000, pp. 209-212.
http://dx.doi.org/10.1016/S0014-5793(00)01081-4
[5] V. I. Novoderezhkin, A. G. Yakovlev, R. van Grondelle
and V. A. Shuvalov, “Coherent Nuclear and Electronic
Dynamics in Primary Charge Separation in Photosynthet-
ic Reaction Centers: A Redfield Theory Approach,” The
Journal of Physical Chemistry B, Vol. 108, 2004, pp.
7445-7457. http://dx.doi.org/10.1021/jp0373346
[6] D. S. Shchepetov, D. S. Cher navsky , V. V. Gorokhov, N.
P. Grishanova, V. Z. Paschenko and A. B. Rubin, “The
Nature of Oscillations in the Kinetics of Electron Transfer
in the Reaction Center of Purple Bacteria,” Doklady Bio-
chemistry and Biophysics, Vol. 425, 2009, pp. 87-90.
http://dx.doi.org/10.1134/S1607672909020082
[7] J. M. Jean and G. R. Fleming, “Competition between
Energy and Phase Relaxation in Electronic Curve Cross-
ing Processes,” Journal of Chemical Physics, Vol. 103,
1995, pp. 2092-2101. http://dx.doi.org/10.1063/1.469684
[8] K. Ando and H. Sumi, “Nonequilibrium Oscillatory Elec-
tron Transfer in Bacterial Photosynthesis,” The Journal of
Physical Chemistry B, Vol. 102, 1998, pp. 10991-11000.
http://dx.doi.org/10.1021/jp982659l
[9] X. Gu, M. Hayashi, S. Suzuki and S. H. Lin, “Vibrational
Coherence and Relaxation Dynamics in the Primary Do-
nor State of the Mutant Reaction Center of Rhodobacter
capsulatus: Theoretical Analysis of Pump -Probe Stimu-
lated Emission,” Biochimica et Biophysica Acta, Vol.
1229, 1995, pp. 215-224.
http://dx.doi.org/10.1016/0005-2728(94)00197-D
[10] S. H. Lin, M. Hayashi, S. Suzuki, X. Gu, W. Xiao and M.
Sugawara, “Theoretical Analyses on Femtosecond Time-
Resolved Spectra of Initial Electron Transfer of Photo-
synthetic Reaction Centers at Low Temperatures,” Che-
mical Physics, Vol. 197, 1995, pp. 435-455.
http://dx.doi.org/10.1016/0301-0104(95)00186-R
[11] J. A. Leegwater, “Theory of Coherent Oscillations in the
Photosynthetic Reaction Center,” The Journal of Physical
Chemistry, Vol. 99, 1995, pp. 11605-11611.
http://dx.doi.org/10.1021/j100029a044
[12] A. Lucke, C. H. Mak, R. Egger, J. Ankerhold, J. Stock-
burger and H. Grabert, “Is the Direct Observation of Elec-
tronic Coherence in Electron Transfer Reactions Possi-
ble?” Journal of Chemical Physics, Vol. 107, 1997, pp.
8397-8408.

A. G. YAKOVLEV, V. A. SHUVAL OV
5
http://dx.doi.org/10.1063/1.475040
[13] W. W. Parson, Z. T. Chu and A. Warshel, “Oscillations of
the Energy Gap for the Initial Electron-Transfer Step in
Bacterial Reaction Centers,” Photosynthesis Research,
Vol. 55, 1998, pp. 147-152.
http://dx.doi.org/10.1023/A:1005992121305
[14] D. A. Cherepanov, L. I. Krishtalik and A. Y. Mulkidja-
nian, “Photosynthetic Electron Transfer Controlled by
Protein Relaxation: Analysis by Langevin Stochastic Ap-
proach,” Biophysical Journal, Vol. 80, 2001, pp. 1033-
1049. http://dx.doi.org/10.1016/S0006-3495(01)76084-5
[15] H. Sumi and R. A. Marcus, “Dynamical Effects in Elec-
tron Transfer Reactions,” Journal of Chemical Physics,
Vol. 84, No. 9, 1986, pp. 4894-4914.
http://dx.doi.org/10.1063/1.449978
[16] A. G. Yakovlev, A. Ya. Shkuropatov and V. A. Shuvalov,
“Nuclear Wavepacket Motion between P* and P+BA– Po-
tential Surfaces with a Subsequent Electron Transfer to
HA in Bacterial Reaction Centers at 90 K. Electron Trans-
fer Pathway,” Biochemistry, Vol. 41, 2002, pp. 14019-
14027. http://dx.doi.org/10.1021/bi020250n
[17] A. Warshel and W. W. Parson, “Dynamics of Biochemi-
cal and Biophysical Reactions: Insight from Computer Si-
mulations,” Quarterly Review of Biophysics, Vol. 34,
2001, pp. 563-679.
http://dx.doi.org/10.1017/S0033583501003730
[18] W. W. Parson, Z. T. Chu and A. Warshel, “Electrostatic
Control of Charge Separation in Bacterial Photosynthe-
sis,” Biochimica et Biophysica Acta, Vol. 1017, 1990, pp.
251-272.
http://dx.doi.org/10.1016/0005-2728(90)90192-7
[19] M. Plato and C. J. Winscom, “A Configuration Interac-
tion (CI) Description of Vectorial Electron Transfer in
Bacterial Reaction Centers,” In: J. Breton and A. Ver-
meglio, Eds., The Photosynthetic Bacterial Reaction Cen-
ter, Plenum, New York, 1988, pp. 421-424.
http://dx.doi.org/10.1007/978-1-4899-0815-5_41
[20] Y. Hu and S. Mukamel, “Sequential versus Superexchange
Electron Transfer in the Photosynthetic Reaction Center,”
In: J. Jortner and B. Pullman, Eds., Perspectives in Pho-
tosynthesis, Kluwer Acad. Publ., Amsterdam, 1990, pp.
171-184.
http://dx.doi.org/10.1007/978-94-009-0489-7_15
[21] A. Warshel, S. Creighton and W. W. Parson, “Electron-
Transfer Pathways in the Primary Event of Bacterial
Photosynthesis,” The Journal of Physical Chemistry, Vol.
92, 1988, pp. 2696-2701.
http://dx.doi.org/10.1021/j100320a057
[22] V. A. Shuvalov and A. G. Yakovlev, “Energy Level of
Р+В– with Respect to P* Found from Recombination Flu-
orescence Measurements in Pheophytin-Modified Reac-
tion Centers,” Membrane and Cell Biology, Vol. 12, No.
5, 1998, pp. 563-569.
[23] E. Sim and N. Makri, “Path Integral Simulation of Charge
Transfer Dynamics in Photosynthetic Reaction Centers,”
The Journal of Physical Chemistry B, Vol. 101, 1997, pp.
5446-5458. http://dx.doi.org/10.1021/jp970707g
[24] R. A. Kha typov, A. Yu. Khmelnitskiy, A. M. Khristin, T.
Yu. Fufina, L. G. Vasilieva and V. A. Shuvalov, “Primary
Charge Separation within P870* in Wild Type and Hete-
rodimer Mutants in Femtosecond Time Domain,” Bio-
chimica et Biophysica Acta, Vol. 1817, 2012, pp. 1392-
1398. http://dx.doi.org/10.1016/j.bbabio.2011.12.007
[25] V. A. Shuvalov and A. G. Yakovlev, “Coupling of Nuc-
lear Wavepacket Motion and Charge Separation in Bac-
terial Reaction Centers,” FEBS Letters, Vol. 540, 2003,
pp. 26-34.
http://dx.doi.org/10.1016/S0014-5793(03)00237-0
[26] P. Hamm and W. Zinth, “Ultrafast Initial Reaction in Bac-
terial Photosynthesis Revealed by Femtosecond Infrared
Spectroscopy,” The Journal of Physical Chemistry, Vol.
99, 1995, pp. 13537-13544.
http://dx.doi.org/10.1021/j100036a034
[27] S. G. Johnson, D. Tang, R. Jankowiak, J. M. Hayes, G. J.
Small and D. M. Tiede, “Primary Donor State Mode
Structure and Energy Transfer in Bacterial Reaction Cen-
ters,” The Journal of Physical Chemistry, Vol. 94, 1990,
pp. 5849-5855. http://dx.doi.org/10.1021/j100378a045
[28] P. A. Lyle, S. V. Kolaczkowski and G. J. Small, “Photo-
chemical Hole-Burned Spectra of Protonated and Deute-
rated Reaction Centers of Rhodobacter sphaeroides,” The
Journal of Physical Chemistry, Vol. 97, 1993, pp. 6924-
6933. http://dx.doi.org/10.1021/j100128a030
[29] M. Plato, F. Lendzian, W. Lubitz and K. Möbius, “Mole-
cular Orbital Study of Electronic Asymmetry in Primary
Donors of Bacterial Reaction Centers,” In: J. Breton and
A. Verméglio, Eds., The Photosynthetic Bacterial Reac-
tion Center II: Structure, Spectroscopy, and Dynamics,
Plenum, New York, 1992, pp. 109-118.
http://dx.doi.org/10.1007/978-1-4615-3050-3_13