J. Phys. Chem. B 2000, 104, 11395-11408
11395
Energy Transfer in the B800 Rings of the Peripheral Bacterial Light-Harvesting Complexes
of Rhodopseudomonas Acidophila and Rhodospirillum Molischianum Studied with Photon
Echo Techniques
Jante M. Salverda,† Frank van Mourik,†,‡ Gert van der Zwan,§ and Rienk van Grondelle*,†
Department of Biophysics and Physics of Complex Systems, VU Amsterdam, The Netherlands,
Institut de Physique de la Matière Condensée, Faculté des Sciences, BSP, UniVersité de Lausanne,
Switzerland, and Department of Analytical Chemistry and Applied Spectroscopy, Faculty of Exact Sciences,
VU Amsterdam, The Netherlands
ReceiVed: June 5, 2000; In Final Form: August 23, 2000
Eenergy transfer in the B800 ring of the LH2 antenna of the purple bacteria Rhodopseudomonas (Rps.)
acidophila and Rhodospirillum (Rs.) molischianum was studied at room temperature using three-pulse echo
peak shift (3PEPS) and transient grating (TG) techniques. From the transient grating experiments, we found
the B800 f B850 energy transfer rates to be 600-700 fs for both species. The anisotropy of the TG signal
decays in about 1 ps for both species, which is ascribed to B800 f B800 energy transfer. The occurrence of
B800 f B800 energy transfer was further substantiated by 3PEPS experiments. When measured over the
whole B800 band, the initial peak shift of about 30 fs exhibited a fast <100 fs decay to about 10 fs due to
the coupling to protein phonons, followed by a slow phase of about 1 ps, during which the peak shift decayed
to 1-3 fs. Polarized 3PEPS experiments systematically resulted in smaller peak shift values for the third
pulse polarized perpendicular to the first two than for the third pulse parallel to the first two. Furthermore,
frequency-resolved 3PEPS experiments performed on LH2 of Rs. molischianum showed a large difference in
peak shift decay rates when tuning over the B800 band. The “blue” peak shifts did not decay after the initial
sub-100 fs phase, while “red” peak shifts decayed much faster than the whole band signal. All these observations
confirm the presence of B800 f B800 energy transfer. Simulations using the Brownian oscillator model
allowed the determination of an equilibration rate of 1100 fs for Rps. acidophila and 800 fs for Rs.
molischianum. For a model in which the spectral equilibration in a ring occurs by single hopping steps between
adjacent pigment molecules, these times correspond to 2.2 ps (Rps. acidophila) and 1.6 ps (Rs. molischianum)
for a single step. Strong oscillations with a predominant frequency of 162 cm-1 are observed in the peak shift
decays of both species.
1. Introduction
1.1. Light Harvesting and the B800 Ring. In photosynthesis,
solar photons are converted into a stable transmembrane charge
separation with a quantum efficiency of 90% or higher. To
obtain such a high efficiency, all steps involved have to be
extremely fast: charge separation occurs within 100 ps after a
photon is absorbed.1,2 Light is harvested by antenna complexes,
membrane-bound proteins with photoactive cofactors such as
(bacterio)chlorophyll and carotenoid pigments. The antennae
transfer their excitation energy to a reaction center (RC) where
initial charge separation is followed by a sequence of stabilizing
electron-transfer steps.
Photosynthetic purple bacteria are frequently used for studying
excitation transfer in photosynthesis due to their relative
simplicity and their suitability for genetic engineering. The
different complexes involved in the process can be isolated to
a high degree of purity while retaining their stability, and the
* Corresponding author. Department of Biophysics and Physics of
Complex Systems, VU Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands. E-mail rienk@nat.vu.nl.
† Department of Biophysics and Physics of Complex Systems, VU
Amsterdam.
‡ Institut de Physique de la Matière Condensée, Université de Lausanne.
§ Department of Analytical Chemistry and Applied Spectroscopy, VU
Amsterdam.
structure of several of the pigment-protein complexes involved
is known to atomic resolution. Purple bacteria contain two types
of light-harvesting antennaesthe core antenna LH1, which
surrounds the RC, and the peripheral antenna LH2. The crystal
structure of the RC was resolved more than 10 years ago for
the two species Rhodopseudomonas (Rps.) Viridis3 and Rhodobacter (Rb.) sphaeroides.4,5 A few years ago, the structures of
the LH2 antennae of Rhodopseudomonas (Rps.) acidophila6 and
Rhodospirillum (Rs.) molischianum7 became known to a resolution of ∼2 Å, which generated an enormous increase of interest
in the study of these complexes. For the LH1 antenna, only
low-resolution models have been published so far.8,9 The
absorption spectra of the different components are carefully
tuned from 800 to 850 nm for LH2, 875 nm for LH1, and 870
nm for the primary electron donor pair (P) of the RC. Energy
transfer occurs from LH2 to LH1 on a picosecond time scale,10,11
followed by relatively slow transfer from LH1 to the RC in
several tens of picoseconds.12-14
In this study, we will look at energy transfer in the peripheral
antenna LH2. From the X-ray structure, this antenna is seen to
consist of a ring of R-helical polypeptides, which are noncovalently bound to each other. The ring lies in the plane of the
membrane with the R helices more or less perpendicular to it.
For both Rps. acidophila and Rs. molischianum, the basic unit
10.1021/jp002034z CCC: $19.00 © 2000 American Chemical Society
Published on Web 11/01/2000
11396 J. Phys. Chem. B, Vol. 104, No. 47, 2000
is a heterodimer of an R and a β polypeptide, which binds three
bacteriochlorophylls (BChl) and one or two carotenoids (Car).
Rps. acidophila contains nine of these basic units, and Rs.
molischianum contains eight. Two of the BChls per basic unit
(the Rβ-heterodimer) are sandwiched between the R and β
polypeptide rings, with their tetrapyrrole planes perpendicular
to the membrane plane. Together, all 18 (Rps. acidophila) or
16 (Rs. molischianum) of these BChls form a tightly coupled
ring, which typically absorbs at 850 nm and is denoted as B850.
Per basic unit one BChl is positioned at the outside of the ring,
between the β polypeptides. The ring of 9 or 8 of these weakly
coupled BChls, absorbs at 800 nm and is called B800. In the
case of Rps. acidophila, the B800 pigments lie parallel to the
membrane plane; in the case of Rs. molischianum, they are tilted
by 30°. From CD measurements [Frese et al., unpublished], it
appears that all purple bacteria belong to one of two classes
with different B800 orientations, which are represented by these
two species.
As seen in the structure, the B850 pigments are in close
contact with each other, with a center-to-center distance of about
9 Å within the basic unit and close to 10 Å between the
neighboring BChls from different units. Because of these short
distances, the excitonic coupling between the transition dipoles
of the lowest excited state, Qy, which lie in the plane of the
ring, is rather large, about 300 cm-1.15,16 This coupling tends
to delocalize the excitation over the whole B850 ring, but this
effect is counteracted by dynamic and static disorder, for
instance, in the site energies. The combined effect of electronic
coupling and disorder results in a delocalization of the excitation
over a few (2 or 3) pigments.17-21 Energy transfer or, in the
excitonic picture, relaxation to the lowest exciton levels, takes
place in ∼100 fs, according to fluorescence depolarization,22
pump-probe,23,24 and three-pulse (photon) echo peak shift
(3PEPS)25 measurements. For LH1, a variety of experiments
has shown that the energy transfer events occur on very similar
time scales.25-28
The B800s are as far as 20 Å apart from each other and 17
Å from the nearest B850, causing the excitation to be localized
on monomeric BChls. Energy transfer from B800 to B850 is
well established to occur in 600-800 fs at room temperature
for many different species.29-31 At low temperature, it is
somewhat slower, with rates found between 1.1 and 1.8 ps30,32-34
but probably close to 1 ps at 77K.33 It has been a subject of
much discussion in recent years whether any energy transfer
occurs between the B800s before the excitation is transferred
to B850. At low temperature, energy transfer between B800
pigments is relatively well established and has been observed
by several authors. Originally, B800 energy transfer was
proposed on the basis of the observed polarization of the B800
emission.35 From spectrally resolved pump-probe studies,30,33,36,37 a variation in decay rate over the B800 band was
found, with the fastest rate, ∼0.5 ps, at the blue side and the
slowest, ∼1.5 ps, at the red side. Also, a finite rise time was
observed in the bleaching of the red edge of the B800 band
following excitation in the blue edge. These findings were
confirmed by spectral hole-burning studies,32,38,39 in which a
variation of the hole width over the B800 absorption band was
found. Clearly, inhomogeneity plays a very important role.
Single-molecule spectra taken at 1.2 K40-43 demonstrate this
inhomogeneity straightforwardly, as the spectrum of a single
LH2 molecule around 800 nm is shown to consist of several
narrow (∼1 nm) peaks at wavelengths ranging from 785 to 810
nm. Remarkably, in these spectra, no variation of the line width
Salverda et al.
over the B800 band was observed, in contrast to the pumpprobe30,33,36,37 and hole-burning32,38,39 results.
At room temperature, the occurrence of B800 intraband
transfer is much more a matter of debate. Different techniques
and models are needed to deal with B800 T B800 energy
transfer compared with cryogenic temperatures. Due to the large
homogeneous line width of the pigments (∼150 cm-1 44) at room
temperature, frequency-selective excitation is seriously hampered. Furthermore, both uphill and downhill energy transfer,
if any, will proceed at comparable rates. In polarized pumpprobe experiments, several authors36,45,46 find anisotropy decay
times which they attribute to B800 T B800 energy transfer.
Hess et al.45 and Kennis et al.46 find a value of 0.8-1.2 ps for
this time, whereas Ma et al.36 find faster rates of 400 to 800 fs
at varying wavelengths. Hess et al.45 and Joo et al.44 observe
isotropic transient absorption decay times of ∼300 fs, which
they attribute to vibrational relaxation. In their 3PEPS experiment, Joo et al.44 detect a ∼600 fs peak shift decay time, but
they attribute this to B800 f B850 transfer. Jimenez et al.22
find a decay time of 350 fs for the anisotropy of B850
fluorescence after B800 excitation, which they interpret as due
to B800 intraband energy transfer. By others, Jimenez’s
observation is cited as evidence both for2 and against44 B800
intraband transfer. Altogether, the picture is confusing both with
respect to the presence of B800 T B800 transfer and the time
which should be attributed to it. For a review of this debate,
see also Sundström et al.2
In this study, we describe a set of 3PEPS experiments on the
B800 band of LH2 of Rps. acidophila and Rs. molischianum.
To search specifically for evidence of B800 intraband energy
transfer, we use both polarized and frequency-selective detection
of the echo signal. A transient grating (TG) experiment was
also performed at both polarizations, with and without frequencyresolved detection.
1.2. The Three-Pulse Echo Peak Shift and Transient
Grating Methods. In the 3PEPS experiment, a sequence of
three laser pulses, each with a slightly different direction of
propagation k1, k2, or k3, is focused onto the sample. We will
describe the principle of this experiment using the impulsive
limit. A fourth pulse, the photon echo, is emitted in the direction
k3 - k2 + k1 at a time τ after the third pulse, with τ being the
delay between the first two pulses. The time-integrated intensity
of the echo is measured as a function of the delay τ, with the
delay T between the second and third pulse, also known as
population time, as a parameter. The distance of the maximum
of this signal (further referred to as the echo) from τ ) 0, the
peak shift, is then determined as a function of T. The decay of
the peak shift with T reflects all processes which lead to
frequency changes of the excited pigments, described as
∆ω(t), within the spectral window of the used pulses. This can
be explained by the following argument. Pulses 1 and 2 generate
a frequency-dependent modulation of the excited-state population within the laser bandwidth, a so-called frequency grating,
which has spacing proportional to 1/τ. The modulation depth
and width of this grating will be affected by changes in the
transition frequencies of the pigments within the laser bandwidth, rather like in a transient hole-burning experiment. The
amplitude of the grating also decays due to population transfer
to pigments absorbing outside the laser window, but this does
not affect the peak shift. Because the intraband frequency
changes efface a fine grating more easily, an increasingly widespaced grating is needed to survive when longer T values are
used. As a more widely spaced grating corresponds to a smaller
delay between pulses 1 and 2, this means that the echo intensity
Peripheral Bacterial Light-Harvesting Complexes
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11397
maximum gets closer to zero τ. Thus, the decay of the peak
shift as a function of T reflects the loss of correlation, averaged
over all pigments, between the excitation frequency at the time
of pulse 2 and the frequency at the time of pulse 3. We note
that for the case of nonzero pulse widths, the overlap of the
pulses in time, leading to different time ordering, must explicitly
be accounted for (see section 4). The fluctuating frequency ωi(t) of each pigment i can be described as
ωi(t) ) ωeg + ∆ωi(t) + i
(1.1)
with ωeg the ensemble average of the transition frequency, ∆ωi(t) the fluctuation of the transition frequency for pigment i, and
i the static deviation of wi(t) from average, i.e., the inhomogeneous broadening. The average frequency correlation of the
ensemble is then described by the two-point frequency correlation function
M(t) )
⟨∆ω(0)∆ω(t)⟩
⟨∆ω(0)2⟩
(1.2)
The transient grating technique is a special case of the threepulse echo, with the first two pulses set at τ ) 0 and the signal
intensity scanned as a function of the population time T. The
first two pulses now create a spatial population grating in the
sample due to interference between the beams which intersect
at a small angle. The decay of this grating reflects the loss of
excited-state population from within the laser spectrum. This
spatial grating is also created in the 3PEPS experiment, of
course, but in that experiment, the amplitude decay, which is
caused by population transfer, is not considered (as mentioned
above). Also at nonzero delays between pulses 1 and 2, the
phase of this grating will be different for each frequency, leading
to canceling contributions.
The 3PEPS technique, originally developed for the study of
solid-state dynamics, became increasingly popular in the field
of liquid dynamics as sub-100 fs lasers were developed. For
monomeric solutes in solvents, the peak shift decay reflects the
coupling of the solute electronic transition to various solvent
relaxation processes. From 3PEPS and other experiments, these
solvent relaxation processes were shown to occur over a whole
range of time scales,47,48 thereby demonstrating the limited
usefulness of the standard (Bloch) model, which factors all
dynamics in an infinitely fast homogeneous contribution and
an infinitely slow inhomogeneous contribution. Several more
sophisticated models were developed, such as the Kubo theory49
and the Brownian oscillator model,50-53 which will be used here.
In the Brownian oscillator model, each frequency-affecting
process is defined by its characteristic time scale and the strength
of its coupling to the electronic transition. Several studies on
dye molecules in liquids have shown how relaxation processes
can be identified with this technique.54,55
In the case of pigment protein complexes, the protein will
act as a solvent, reacting to the excitation of the pigment via
electron-phonon coupling. Further contributions to the decay
of the frequency correlation function M(t), such as inter- and
intramolecular vibrations of the excited pigments, also have to
be taken into account. The most important difference between
a pigment in a protein and a solute in a solvent is the coupling
between the pigments leading to energy transfer. In the most
often used approach,25,44,56 the energy transfer is incorporated
by taking ωi(t) (eq 1.1) to describe a two-level electron-hole
system which migrates among the pigments, rather than a single
fixed pigment. During the migration, the electron-hole pair
samples the inhomogeneous distribution, so the i term in eq
1.1 becomes a time-dependent quantity. The diffusive character
of energy transfer implies an exponential decay term of M(t),
which is added to the sum of Brownian oscillators. In fact, the
electron-hole system is analogous to a solute in a liquid, with
the exponential term analogous to an overdamped oscillator.
This analogy, which allows for the use of modeling methods
derived for liquid systems, explains how the Brownian oscillator
(BO) model came to be used for photosynthetic systems.
However, it is unclear whether this is physically justified.
Recently, a different approach to third-order nonlinear spectroscopy, using exciton annihilation and creation operators, was
developed by Mukamel and co-workers,57 which can be applied
to strongly coupled systems such as B850 and LH1. For more
weakly coupled systems such as B800, a model was developed
by Yang and Fleming,58 which describes the system as two twolevel systems, a donor and an acceptor, with uncorrelated
frequency fluctuations. In this paper, we will employ the more
widely used “old” model. We will discuss the validity of the
obtained results by comparing them to calculations based on a
simplified form of the formalism of Yang and Fleming.
1.3. This Study. As mentioned above, in this work, we
specifically search for evidence of B800 intraband transfer. We
have attempted to separate a possible energy transfer contribution to the 3PEPS signal from protein dynamics contributions
by measuring at both parallel and perpendicular polarization of
the third pulse. If any energy transfer takes place, we expect to
see a difference in peak shift decay between both polarizations,
since energy transfer will change the polarization drastically
because of the different orientations of the pigments involved.
Moreover, we applied frequency-resolved detection of the echo
signal. Possible downhill energy transfer between B800s would
then show up as a difference between blue and red detected
peak shift decays. Furthermore, a transient grating experiment
was carried out as an alternative way of looking at B800 excitedstate dynamics. Also in this experiment, frequency-selective and
polarized detection of the signal was applied. From the polarized
transient grating signals, we have calculated the anisotropy
decay, which is taken to reflect B800 f B800 energy transfer.
The overall decay of the transient grating will display the B800
population decay due to B800 f B850 energy transfer.
In the following section, we will discuss the experimental
setup and methods. In section 3, we will discuss the results
qualitatively. After introducing the mathematics of the models
used in section 4, we will proceed to present simulations of the
measured peak shift curves, which will allow for more quantitative statements. Concluding remarks will follow in section 5.
2. Experimental Procedure
The experimental setup is shown in Figure 1. A standard
3PEPS configuration was used, similar to that described
elsewhere.25,44 As a source of ultrashort pulses, we used a
commercial 20 fs Titanium Sapphire laser (Coherent MIRA
Seed). A cavity dumper (Coherent) was built into the laser cavity
to reduce the repetition rate from 76 MHz to 150 kHz. The rate
has to be reduced to avoid the buildup of carotenoid triplet states,
which live for about 1 µs. Together with the use of a flow cell,
lowering the repetition rate also reduces possible heat damage
to the sample.
The wavelength of the laser can be tuned from 770 to 840
nm by changing the position of the mode-locking slit across
the beam profile. For our experiment, the central wavelength is
tuned to 800 nm to match the absorption of B800. In Figure 2,
the laser spectrum is shown together with the absorption
spectrum of the LH2 of Rps. acidophila which was used for
11398 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Figure 1. Experimental setup. An Ar+ laser pumps a cavity-dumped
Ti:sapphire laser, which yields 30 fs pulses with a wavelength of 800
nm and a bandwidth of 30 nm. The beam is split twice to obtain three
pulses, which can be delayed with respect to each other. The three
beams are focused into the same spot in the sample, each beam entering
at a slightly different angle. The two photon echoes exit the sample
under two separate angles determined by the geometry of the incident
beams (see text) and are detected by two photodiodes, each connected
to a lock-in amplifier.
Salverda et al.
integrated fashion by photodiodes. To reduce noise, we connected the diodes to lock-in amplifiers, for which a chopper in
beam 2 is used as reference. The original beams are blocked
after the sample to reduce scattering onto the detectors.
For the polarized measurements, waveplates are positioned
in all three beams to set their polarization. The orientation of
the waveplate in beam 3 can be varied with a motorized rotator.
Frequency selection is achieved by placing interference filters
in front of the detecting photodiodes. Two filters with bandwidths of 7 nm and central wavelengths of 818 and 797 nm are
used. The filters were tilted with respect to the beam to set the
wavelengths of maximum transmission to 810 and 790 nm,
respectively. The time resolution is not affected by the
bandwidth reduction because the filter only lengthens the echo
signal, which is already detected time-integrated.
The sample consists of detergent isolated LH2 complexes of
Rps. acidophila strain 10050 and Rs. molischianum, isolated
and purified as described elsewhere.6,7 The complexes are
dissolved in a standard phosphate buffer with 20 mM HEPES
and a pH of 8. Some excess detergent was added to a total of
0.2% LDAO to avoid aggregation. To remove any remaining
large aggregates, we placed a sub-0.45 µm filter into the flow
circuit. The sample is circulated through the flow circuit at a
speed of 20-30 cm/s by a peristaltic pump. The maximum
absorbance is 0.3, chosen to balance the intensity of the signal
against deformation of it from reabsorption and against the use
of large amounts of the sample. To check if any photodamage
had occurred, we measured the absorption spectrum before and
after the experiments. No changes could be detected.
3. Results
Figure 2. Absorption spectrum (solid line) of the detergent-isolated
LH2 of Rps. acidophila (strain 10050) and laser spectrum (dotted line).
our experiments. The pulse spectrum has a width (fwhm) of
about 30 nm and amply covers the B800 absorption band, so
no selection effects are to be expected. An autocorrelation of
50 fs is measured, implying that the pulses are nearly transformlimited when a Gaussian pulse shape is assumed. At the sample,
the total energy per shot is about 2 nJ.
Directly after the laser, an external LaKL21 prism compressor
corrects for the group velocity dispersion (GVD) of the setup.
After compression, the beam is split in three with beam splitters,
with all beams having approximately equal energy. All three
beams are delayed by travelling via retroreflectors on translation
stages. Pulses 1 and 2 travel via motorized translation stages
(Newport stepper motor MM3000), so their delays can be varied.
After the delay path, the three beams are aligned parallel to
each other at a distance of about 1 cm, forming an equilateral
triangle, and they are focused onto the sample. The sample is
contained in a quartz flow cuvette of only 0.2 mm path length
to ensure that no reabsorption takes place after the focus, where
the echo signal is generated. For a more accurate determination
of the peak shift, the echo corresponding to pulse 2 (with
wavevector k2) is also detected. The echoes with vectors kS )
k3 + k2 - k1 and kS′ ) k3 - k2 + k1 are detected in a time-
Three-pulse echo (3PE) signals were measured for both Rs.
molischianum and Rps. acidophila at about 50 values of the
population time T, with the third pulse at parallel polarization.
For the third pulse perpendicular, the 3PE signals were measured
at three values of T. For each value of the population time, a
number of fast scans was averaged to obtain a good signal-tonoise ratio. For Rs. molischianum only, the 3PEPS experiment
was repeated with selective detection of the blue and red edges
of the B800 band, both at parallel polarization of the third pulse.
Transient grating signals were measured for both polarizations
and with and without frequency selection, for Rs. molischianum
and Rps. acidophila.
3.1. Transient Grating. In Figure 3, transient grating (TG)
curves are shown for both species at all combinations of
polarization and detection frequency. In each plot, the curves
for both polarizations are shown together, with the parallel signal
being the largest. At T ) 0, the ratio between the parallel and
perpendicular signals is about 9:1.
All transient grating traces decay almost monoexponentially.
At early times, a coherent coupling artifact is superposed on
the transient grating signal, with a relative amplitude varying
from one measurement to the next. A very small oscillatory
contribution, which is not further considered here, can be
discerned during the first 1000 fs of the decay. Within 1 to 2
ps, the signals decay to a constant, finite level as B800 transfers
its excitation to B850. Because excited B850 (denoted as B850*)
displays excited-state absorption around 800 nm, it generates
also a small TG signal, which does not decay on the time scale
of the experiment. This contribution is larger at longer wavelengths, so it shows up most clearly in the 810 nm signals. Since
the B850* grating results from absorption, it has an opposite
phase to the grating constituted by the B800 bleaching,
Peripheral Bacterial Light-Harvesting Complexes
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11399
Figure 3. TG signals obtained for LH2 of Rps. acidophila (A-C) and Rs. molischianum (D-F). The signals were measured with a 790 nm filter
(A,D) or a 810 nm filter (C,F) placed behind the sample or without a filter (B,E). In each plot, the signal obtained with all pulses polarized parallel
(large) is shown together with the signal obtained with the third pulse polarized perpendicular to the first two (small).
TABLE 1: Exponential Fits of Transient Grating Signals
wavelength (nm)
Rps. acidophila
Rs. molischianum
Figure 4. Monoexponential fits (dotted line) to the TG signals (solid
line) measured without a filter for Rps. acidophila (a) and Rs.
molischianum (b). In each graph, both parallel and perpendicular
polarizations are shown (see Figure 3). To avoid contamination by the
coherent coupling artifact, the fits ignored the first 100 fs after T ) 0.
leading to a shallow minimum at around 1.5 ps, when both
contributions are comparable in size and cancel each other.
As a first approximation, single exponentials were fit to all
transient grating signals. To avoid contamination of the time
constant by the coherent coupling artifact, the curves were fit
from 100 fs onward. An infinite second lifetime was included
to account for the B850* absorption. Examples of the fits are
shown in Figure 4 for the TG signals measured at both
polarizations without frequency selection. The results of the fits
to all 12 curves are given in Table 1. Decay of the gratings
takes place in 300-400 fs, corresponding to a 600-800 fs
790
whole band
810
790
whole band
810
τpar (fs)
τperp (fs)
320
310
290
380
360
300
550
420
310
530
350
XXX
excited-state lifetime of B800. For Rps. acidophila, this value
agrees well with rates found by others at room temperature.36,46
For Rs. molischianum, only B800 f B850 transfer rates
measured at low temperature have been published so far.39 The
room-temperature rate of ∼700 fs, which we obtain in this work,
is remarkably similar to the rates known for Rps. acidophila
and Rb. sphaeroides, considering the difference in orientation
of the B800 pigments. Compared to the Rps. acidophila structure
(to which the Rb. sphaeroides structure is probably similar
[Frese et al., unpublished]), the chlorin rings of the B800s in
Rs. molischianum are tilted out of the membrane plane by 30°
and rotated by 90°, corresponding to a 30° tilt and a 90° rotation
of the Qy transition. Calculations show that both configurations
have an orientation factor of the same magnitude [Wendling,
M., personal communication]. When the Förster equation is used
together with the point dipole approximation, the calculated
coupling strength between B800 and B850 should be similar in
both species, which is in line with our findings. At a distance
of ∼17 Å between the pigments, the point dipole approximation
should be allowed.60 However, for the absolute value of the
rate to be reproduced reasonably well, it is crucial that the
excitonic and vibronic structures of the B850 band and
11400 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Salverda et al.
its disorder are included properly.39,60
From the blue to the red edge of the B800 band, the decay
seems to get slightly faster. This could reflect better energy
transfer B850 from the red B800s. However, it is most likely
due to the larger B850* contribution in the 810 nm traces. Thus,
the point at which the two gratings cancel is reached earlier,
leading to an apparently faster decay. Because of the large
interference minimum, which is neglected in the fit, the residuals
are also largest for the red curves. The Rs. molischianum TG
signal with perpendicular polarization could not even be fit at
all.
The transient grating signals measured at perpendicular
polarization mostly decay more slowly than those detected
parallel, even with the B850* contribution being relatively
stronger at perpendicular polarization. This trend is most obvious
in the 790 nm traces with parallel decay times of 300-400 fs
and perpendicular decay times of ∼550 fs. This suggests that
energy transfer between the B800s, changing the orientation of
the excited state, does occur. To look at this in more detail, we
have made an analogy between the transient grating and the
more common pump-probe experiment. Both of these reflect
population decay, with the transient grating approximately
quadratic and the pump-probe linear in the population. Because
of interference terms, the transient grating is not exactly
quadratic with either the B800 or B850 population, but for the
moment, we will ignore this. To look at the polarization change
as a measure of energy transfer between differently oriented
pigments, one calculates the anisotropy, r, of a pump-probe
signal as
IVV - IVH
r)
IVV + 2IVH
(3.1)
The decay time constant, τdep, of the anisotropy can be related
to the hopping time, τhop, with
τdep )
τhop
4(1 - cos2R)
(3.2)
with R ) 360/N and N the number of pigments (or effective
sites) in a ring. Note that this expression only holds true when
the anisotropy decay is wavelength independent. For the
transient grating, the equivalent of this anisotropy is obtained
by replacing IVV and IVH in eq 3.1 with the square root of the
transient grating signals TGVV and TGVH (note that in the TG
experiment, the first subscript refers to the polarization of the
first two pulses, while the second subscript is the polarization
of the third pulse). We expect this to yield a better result than
the pump-probe equivalent because in the TG signal the small
B850 contribution is positive whereas in the pump-probe
experiment this contribution is negative. In the pump-probe
signal, this leads to a zero-crossing where the anisotropy is not
defined.
The resulting anisotropy decays are shown in Figure 5 for
the TG decays measured without frequency selection together
with monoexponential fits. The results of fits for all six
anisotropy traces are given in Table 2. The anisotropies decay
in about 1 ps from an initial value of ∼0.4 to a final value of
∼0.05. We think that the anisotropy decay can be taken to
represent mostly B800 T B800 transfer. The B850 signal is
also depolarized, but it is too small to contribute much on a
sub-picosecond time scale, especially for the blue and whole
band signals. For the two curves shown in Figure 5, we find a
decay time of 700 fs for Rps. acidophila and 900 fs for Rs.
Figure 5. Anisotropy of the TG signals (solid line) measured without
a filter and the monoexponential fits (dotted line) for Rps. acidophila
(a) and Rs. molischianum (b). The anisotropies were calculated from
the square roots of the TG signals, as described in the text.
TABLE 2: Exponential Fits of Transient Grating
Anisotropy
residual
wavelength (nm) τ (fs) amplitude anisotropy
Rps. acidophila
Rs. molischianum
790
whole band
810
790
whole band
810
807
700
486
1127
929
496
0.38
0.41
0.61
0.34
0.44
0.59
0.02
0.07
0.04
0.04
0.02
0.02
molischianum. These times correspond well with pump-probe
anisotropy decay times found by others for B800 at room
temperature,45,46 which they also ascribed to B800 T B800
transfer. The initial anisotropy we observe is close to the
theoretical maximum value of 0.4, which indicates that any
possible ultrafast (sub-100 fs) dynamics does not lead to
depolarization. For Rs. molischianum, the final value of ∼0.03
is clearly lower than that for Rps. acidophila, ∼0.08. With the
Rs. molischianum B800 Qys tilted at an angle of about 30° with
respect to the membrane plane, an anisotropy lower than 0.01
should be expected after equilibration between the B800s has
taken place. Transfer to B850, with its Qy transition almost in
the membrane plane, should lead to an increase again at later
times. In Figure 5b, a slight increase can be seen, but the fits
do not take this into account. For Rps. acidophila, the final
anisotropy is close to the minimum of 0.1 for randomization
within a plane.
3.2. Three-Pulse Echo Peak Shift. Typical examples of 3PE
scans are shown in Figure 6. The left plot shows the signal at
T ) 0 fs and the right plot the signal at T ) 200 fs. Also shown
are the Gaussian fits used to determine the peak shift value. As
can be seen in Figure 6, the shape of the signal is not entirely
Gaussian at very short times T. We estimate that this results in
an uncertainty of 2-3 fs in the value of the peak shift. At
intermediate times, the Gaussian fits match the signal almost
perfectly, thereby decreasing the uncertainty. However, at long
times T, the low signal intensity makes the fits less reliable
again, so the uncertainty is considered to be 2-3 fs over the
whole range for the sake of simplicity.
In Figure 7, the peak shift curves measured at parallel
polarization are shown. The peak shift decay is similar for both
species, with Rs. molischianum decaying slightly faster and to
a lower final value. The initial peak shift is ∼30 fs for both
species. This relatively high value suggests that the coupling
between pigment and protein is weak compared to the coupling
between a dye and a liquid solvent. For dyes in solvent, an initial
Peripheral Bacterial Light-Harvesting Complexes
Figure 6. Examples of three-pulse photon echo (3PE) signals (solid
line) obtained for LH2 of Rs. molischianum. Shown are two scans in
which the integrated echo intensity is measured as a function of the
delay τ between the first two pulses for the delay times T ) 0 fs (a)
and T ) 200 fs (b). The peak shift values were obtained from these
curves by fitting them with Gaussians (dotted line; see also the text).
Figure 7. Peak shift decay as a function of the population time T
measured over the total B800 band. The curves show the peak shift
for the parallel polarization of the third pulse obtained for LH2 of Rps.
acidophila (dotted line) and Rs. molischianum (solid line). The points
show the peak shifts measured at three selected population times, with
the third pulse polarized perpendicular to the first two, for Rps.
acidophila (4) and Rs. molischianum (b)
peak shift of 10-15 fs is generally obtained with comparable
pulse lengths.54,55 In that case, the dephasing is so fast compared
to the pulse duration that the measurement at T ) 0 already
probes a partially relaxed situation. In our experiment, dephasing
due to electron-phonon coupling is probably responsible for
the decay of the peak shift from the initial value of 30 fs to
about 10-12 fs on a sub-100 fs time scale.
After the initial dephasing, a slower decay process leads to a
peak shift value of a few femtoseconds in less than a picosecond.
This decay process is partly obscured by pronounced oscillatory
features. For both species, these oscillations look very similar
in amplitude and frequency. In section 4, we will discuss these
oscillations more extensively.
The results of the perpendicular polarization measurements
are also shown in Figure 7 as separate points. All six points lie
below the curves measured at parallel polarization. Furthermore,
this difference is somewhat larger at later times. Apparently, a
population is probed by the perpendicular polarization measurements whose change of transition frequency is larger than that
for the population probed at parallel polarization. The easiest
explanation for this observation is that the population probed
with the third pulse perpendicular has been formed after energy
transfer between pigments with different orientations has taken
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11401
Figure 8. Peak shift decay as a function of the population time T
measured for the LH2 of Rs. molischianum with frequency-selective
detection. All three experiments were performed with parallel polarization of the laser pulses only. The peak shift decay detected at 790 nm
(dashed line) is shown together with the peak shift decay measured at
810 nm (dotted line). The measurement without filter (solid line) is
shown for comparison.
place. From the transient grating measurements, it is clear that
the B850 excited state absorption is too small to show up clearly
in the 3PEPS signal at these population times, all three of which
are below 1 ps. Therefore, we conclude that energy transfer
must be taking place between different B800 pigments.
In Figure 8, frequency-selective peak shift decay curves for
the B800 ring of LH2 of Rs. molischianum are shown. The
curves for the blue edge, 790 nm, and the red edge, 810 nm,
are both averages of two measuring sessions. The uncertainty
in these curves is about 3 fs, judging from the difference between
these two sessions.
The difference between the three signals in Figure 8 is
remarkable, with the blue curve not showing any decay after
the initial drop to about 10 fs. By contrast, the red peak shift
curve decays faster than the peak shift measured over the whole
band. This difference shows that it is unlikely that a protein
relaxation process can be responsible for the picosecond decay
of the peak shift from ∼10 fs to a few femtoseconds; otherwise,
this decay would show up at all wavelengths. Most likely, at
790 nm, pigments are detected which absorb to the blue of the
maximum and have not yet transferred their energy to more
red pigments. We estimate the difference between the energy
transfer rate from 790 to 810 nm and the back rate to be at
least a factor of 2 at room temperature, so downhill energy
transfer is still dominant. Support for our energy transfer
hypothesis comes from the observation by Yu et al.61 that the
B820 subunit of the LH1 antenna, in which no energy transfer
occurs, also has a large residual peak shift, like the peak shift
observed by us at 790 nm. The peak shift of the intact LH1
antenna, which does show energy transfer, decays to 1 or 2 fs
on a time scale of a few hundred femtoseconds.25 The peak
shift decay curve measured for B820 by Yu et al. actually looks
remarkably similar to the 790 nm peak shift curve for B800
shown in Figure 8.
In summary, from the peak shift measurements shown in
Figures 7 and 8, we conclude that the B800 energy transfer
takes place at room temperature and that it is responsible for
the peak shift decay to a value of a few femtoseconds on a ∼1
ps time scale, which is seen in the non-frequency-selective
measurements.
4. Simulations and Discussion
In this section, we present numerical simulations of the
measured signals discussed in the previous section. All simula-
11402 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Salverda et al.
The response functions are expressed as functions of g(t), with
R1 ) R4 ) exp{-g*(t1) + g(t2) - g*(t3) - g(t1 + t2) g(t2 + t3) + g*(t1 + t2 + t3)} (4.6)
R2 ) R3 ) exp{-g(t1) + g*(t2) - g*(t3) + g(t1 + t2) +
g*(t2 + t3) - g(t1 + t2 + t3)} (4.7)
Figure 9. Schematic outline of the pulse sequence in the 3PEPS
experiment. The parameters as used in the numerical integration are
indicated (see text).
tions of the peak shift curves are based on the nonlinear response
theory described by Mukamel.62 To obtain the frequency
correlation function M(t) used in this formalism, we used two
simple models, the Brownian oscillator (BO) model50-53,62 and
the modified electron-hole (MEH) model,58 which will be
described below. The transient gratings were only simulated
with a simple model describing B800 f B850 transfer, without
any reference to nonlinear response theory. This model will be
described in more detail in section 4.2. In section 4.1, we will
first review the key features of the nonlinear response formalism
as it was used in the numerical code for the 3PEPS simulations.
4.1. Three-Pulse Echo Simulation Method. Photon echo
and transient grating signals are two of many third-order
nonlinear responses of a medium to applied external electric
fields. For both signals, we have three incident optical pulse
electric fields E1, E2, and E3, each of which has a single
interaction with the medium. These three interactions result in
a reactant polarization of the sample, the third-order polarization
P(3). The 3PE signal S(τ,T) is proportional to the square of this
polarization in the direction kS ) k3 - k2 + k1, measured timeintegrated as
S(τ, T) )
∫-∞∞|P(3)(t,τ,T)|2 dt
(4.1)
A diagram showing the pulse sequence and the definition of
the relevant time intervals is shown in Figure 9. The third-order
response of the sample to electric fields is determined by the
third-order response functions R1 - R4 and their complex
conjugates [see ref 62 for details]. These functions allow us to
calculate the polarization P(3) (see below). They can be related
straightforwardly to the frequency correlation function M(t). At
high temperature, when all fluctuations ∆ω are much slower
than ∆ωL ) kT/p, this function has the form
M(t) )
⟨∆ω(0)∆ω(t)⟩
⟨∆ω(0)2⟩
(4.2)
as mentioned in the Introduction. From M(t), we can calculate
the line shape function g(t)
∫0t(∫0τ M(τ2) dτ2) dτ1 + iλ∫0t(1 - M(τ1)) dτ1
g(t) ) ⟨∆ω2⟩
1
(4.3)
The time variables used in these expressions, t1, t2, and t3, are
the intervals between the three interaction points and the time
t at which the echo is emitted (see the diagram in Figure 9).
With the three fields E1, E2, and E3 peaking at times -τ - T,
-T, and 0, respectively, we calculate the polarization as follows:
4
P(3)(kS,t,τ,T) )
∫0∞∫0∞∫0∞(∑Ri(t1,t2,t3)E3(k3,t - t3)E2
i)1
(k2,t + T - t3 - t2) × E1(k1,t + T + τ - t3 - t2 t1)) dt1 dt2 dt3 (4.8)
For nonzero pulse duration, we thus have to integrate over the
pulse profiles. From eq 4.1 and the ensemble averaging (over
all molecular orientations) of the response functions Ri, we now
find the echo signal S(τ,T). The transient grating is a special
case of this formula, obtained from eq 4.8 with τ ) 0. With
two polarizations e1 and e2 for the first two pulses and the third
pulse, respectively, the direction of P, eP, can be calculated
eP ) e2 + 2e1(e1‚e2)
This leads to a polarization-dependent prefactor for S(τ,T), given
by
|e2 + 2e1(e1‚e2)|2 ) 1 + 8(e1‚e2)2
⟨∆ω2⟩
λ)
2kT
M(t) ) {⟨∆ωg2⟩e-(t /τg ) +
2
2
∑i ⟨∆ωi,e2⟩e-(t/τ
∑j ⟨∆ωj,o2⟩e-(t/τ
i,e)
cos(ωjt + φj)}
+
1
∑k ⟨∆ωk ⟩
(4.11)
2
(4.4)
The line shape function g(t) is directly related to the absorption
line profile σ(ω) via the Fourier transform
σA(ω) ∝ Re
(4.10)
For the third pulse parallel to the first two, this factor equals 9,
while for the third pulse perpendicular to the first two, we get
1. This explains the 9:1 ratio of intensities of the initial transient
grating and three-pulse echo signals. This, of course, leads to
an initial value of 0.4 for the TG anisotropy, as defined in section
3.1.
To calculate the frequency correlation function M(t) for our
system, we used two approaches, which will be described below.
As a basis, we used the Brownian oscillator (BO) model
described in the Introduction, which takes M(t) to be the sum
of a number of independent contributions from damped oscillators. A Gaussian term was added to describe the fastest decay
component of M(t), which is due to electron-phonon coupling,
giving
j,o)
with 2λ the Stokes’ shift, related to ∆ω via
(4.9)
∫-∞∞e-i(ω - ω )te-g(t) dt
eg
(4.5)
In this equation, the subscripts g, e, and o denote the Gaussian,
exponential, and oscillatory contributions, respectively. The
sums over i and j are partial sums over the exponential or
oscillatory terms, whereas the sum over k includes all processes
which contribute to M(t). The ⟨∆ω2⟩ factors describe the
ensemble-averaged coupling strength of each process. Note that
Peripheral Bacterial Light-Harvesting Complexes
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11403
the sum over k of ⟨∆ω2k ⟩ could still be related to the Stokes’
shift as described in eq 4.4, although more commonly, the
energy transfer contribution is excluded from the Stokes’ shift.
In eq 4.11, one exponential will describe energy transfer with
rate τi,e, but possibly, exponentials can be used to describe other
processes such as overdamped vibrational relaxation of the
pigment or spectral diffusion of the protein. However, in our
simulations, we only needed an exponential for the energy
transfer, with rate τe, with coupling strength ωe equal to the
inhomogeneous broadening. The (damped) oscillatory terms in
eq 4.11 represent specific vibrational modes of the chromophore
and bath molecules. A nonzero phase shift φj was needed to
account for the vibrations being set in motion before T ) 0 by
the first pulse.
The assumption on which the BO model is based, that all
processes are independent, is obviously oversimplified. In a
proper description, the rate of losing frequency information via
one-pigment relaxation should be added to the rate of transferring the excitation to a neighboring pigment via energy transfer.
If the frequency of the neighboring pigment is assumed to be
uncorrelated to that of the originally excited pigment, M(t)
becomes zero as soon as energy transfer occurs. The M(t) of
the originally excited pigment, described with the BO model,
should then be multiplied with its population amplitude. This
approach was later described as the “modified electron-hole
model” (MEH) by Yang and Fleming58 (note that in ref 58, the
BO model is termed the “electron-hole” or EH model, hence
the additive “modified”). As Yang and Fleming explain, this
model is not physically correct because the system is still
described as a single two-level system. In a more exact approach
in the same paper, they describe energy transfer as a jump from
a donor to an acceptor, both of which contribute to the echo
signal. At early (sub-100 fs) times and for systems with many
processes on the same time scale, the exact model and the MEH
model differ significantly, but for B800, within the time range
we are interested in, the deviation is expected to be minimal.
We obtain for the MEH model
M(t) ) Mmon(t)e-(T/τET)
(4.12)
with Mmon(t) describing the originally excited monomeric
pigment and e-(t/τET) the decay of its population through energy
transfer with rate τET. With Mmon(t) from eq 4.11, we have
M(t) ) e-(t/τET){⟨∆ω2g⟩e-(t /τg ) +
2
2
∑j ⟨∆ωj,o2⟩e-(t/τ
j,o)
∑i ⟨∆ωi,e2⟩e-(t/τ
cos(ωjt + φj)}
i,e)
+
1
∑k
(4.13)
⟨∆ω2k ⟩
which leads to a decay of the peak shift τ* with population
time T
τ*(T) ) τ*mon(T)e-(T/τET)
(4.14)
To compare both methods, we will first simulate our measured
peak shift decays with the BO model. With the obtained
parameters, we will calculate τ*mon(T), which will include a non
decaying term with the same coupling strength as that of the
exponential which was used to describe energy transfer in the
BO model. This nondecaying term represents the inhomogeneous broadening. The monomeric peak shift decay obtained
this way will be multiplied with an exponential e-(t/τET), with
τET equal to the exponential decay time τe from the BO model
simulations. If necessary, the parameters will be adapted slightly
to obtain a better fit.
To calculate the peak shift for a given set of parameters, we
first calculated g(t) as a numerical function via a straightforward
integration program. A separate program is used to calculate
R1 - R4 from g(t). The polarization P(3) is calculated from R1
- R4 with a Monte Carlo routine, in which a large number of
random t1, t2, and t3 combinations is used to perform the
integration over the pulse profiles. In this calculation, the cases
for which t1, t2, and t3 correspond to a reversal in the timeordering of the pulses are explicitly considered. Note that also
in this case the phase-matching condition must be fulfilled. For
example at kS ) k3 + k2 - k1, the 3PE signal corresponding to
the time-order pulse 3 first, then pulse 1, then pulse 2 will also
be detected. Just as in the measurements, the echo profile S(τ)
is calculated for a limited number of T values, and the peak
shift τ*(T) is determined by fitting a Gaussian to S(τ). The
resulting peak shift curve is compared to the experimental curve.
Unfortunately, a run with one set of parameters takes approximately 20 min; therefore optimization has to be performed
by hand. To avoid the canceling effects which can result from
using too many parameters, we have attempted to limit the
various contributions to M(t) to one Gaussian, one exponential
(or constant), and one oscillation. Once a set of parameters is
obtained which reproduces the peak shift satisfactorily, the
absorption spectrum can be calculated from g(t) with eq 4.5.
Note that the population decay due to the B800 f B850 transfer,
which should not influence the peak shift, is not incorporated
in this simulation. Therefore, the same method could not be
used for the simulation of the TG signals. Those are performed
with a model that only considers population decay and will be
described below.
4.2. Transient Grating. We have tried to estimate the effect
of the B850 excited-state absorption contribution to the shape
of the TG signal and the B800 f B850 transfer time which
could be derived from this signal. A very simple model was
used with
ITG(T) )
∫B800(B800(λ)e-(T/τ
B800)
-
B850*(1 - e-(T/τB800)))2 dλ (4.15)
The B800 spectrum B800(λ) was taken to be a Gaussian, and
the B850* absorption was taken to be independent of wavelength
within the range of interest, taken from about 775 to 825 nm in
this simulation to cover the B800 band completely. The energy
transfer time, denoted as the B800 excited-state lifetime τB800
and the amplitude of B850* relative to the peak amplitude of
B800(λ) could be varied. For the transfer time, the value
obtained from the single-exponential fits in section 3.1 is taken
as a starting point. Note that now the real B800 f B850 transfer
time is used, as opposed to half this time, which came out of
the exponential fits.
The transfer times we find are clearly at least 10%, and often
30%, larger than the times found from the exponential fits. The
larger the B850* contribution is, the bigger this difference. For
the parallel signals, with no frequency selection, we have a
transfer time of 800 fs for Rps. acidophila and 1000 fs for Rs.
molischianum. In Table A1 of the Appendix, the transfer times
and B850* amplitudes are given for all transient grating curves.
In Figure A1 of the Appendix, examples of TG simulations are
shown. In section 3.1, we found 600 fs for Rps. acidophila and
700 fs for Rs. molischianum, which must be lower limits to the
real values. However, we want to stress that the values obtained
from the simulations using eq 4.15 are also only an indication.
11404 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Salverda et al.
TABLE 3: 3PEPS Simulations of Whole Band Signals with
the BO Model
component
Rps. acidophila
Gaussian
exponential
oscillation 1
oscillation 2
Rs. molischianum Gaussian
exponential
oscillation
∆ωa
(cm-1) τb (fs) ωc (cm-1) φd (rad)
130
150
70
50
130
130
70
80
1100
700
1300
80
800
500
162
30
0.7
2.0
162
0.7
a
Coupling strengths ∆ωg, ∆ωe, and ∆ωo,1 (and 2) (see eq 4.11). b Decay
times τg, τe, and τo,1 (and 2). c Oscillation frequency ω1 (and ω2). d Phase
shift φ1 (and φ2).
Figure 10. Simulation of the 3PEPS experiments measured without a
filter and with all pulses polarized parallel for LH2 of Rps acidophila
(experiment, -‚-; simulation, ‚‚‚) and Rs. molischianum (experiment,
s; simulation, ---). Simulations were based on the Brownian oscillator
model, as described in the text.
The simulations do not reproduce the signals perfectly. The
interference dip in the simulations is much too pronounced. The
explanation for this is that the wavelength dependence of both
B850* absorption and the energy transfer rate should have been
taken into account in eq 4.15. Because of this dependence, the
minimum occurs at different times for different wavelengths.
Also, the multiexponential character of the curves caused by
anisotropy decay due to B800 T B800 transfer was ignored.
With the simple model used here, it is somewhat arbitrary at
which time point the simulations are allowed to start deviating
from the measurements, which leads to an according uncertainty
in the parameters. Despite these shortcomings, we think it can
be safely concluded that the single exponential fits give a good
lower limit to the energy transfer times. The real values are
probably wavelength-dependent and, on average, about 20%
larger.
4.3. Three-Pulse Echo Peak Shift. In Figure 10, simulations
of the 3PEPS curves are shown which were obtained with the
BO model. The simulations for LH2 of both Rs. molischianum
and Rps. acidophila are shown together with the measured
curves. The parameters which correspond to these simulations
are given in Table 3.
For Rs. molischianum, a M(t) consisting of one Gaussian,
one exponential, and one oscillation was sufficient to obtain a
reasonable correspondence with the experimental curve. For Rps.
acidophila, a second, low-frequency oscillation was required.
The strongest oscillation, present in both, has a frequency of
162 cm-1 and was taken from Joo et al.44 Note that for this
frequency the high-temperature limit does not apply, as pω/kT
) 0.77 ≈ 1. The error introduced is negligible, although in the
real part of the line shape function g(t) (eq 4.3), an (implicit)
factor of 2kT/pω (2.56) should be replaced by coth(pω/2kT)
(2.72). From the five oscillations of Joo et al., we have included
only this one, the strongest, in our calculations. Oscillations of
similar frequency have been observed in many photosynthetic
complexes.28,63,64 Some of these modes, including our 162 cm-1
mode, are found to be very weak in monomeric Bchl. Also, it
depends heavily on the technique whether any oscillations are
seen. For the systems we have studied, pump-probe experiments were carried out in our laboratory, which show no
oscillations at all [Wendling et al., unpublished results]. In our
transient grating results, these oscillations are also virtually
absent.
The second oscillation in the Rps. acidophila simulation, with
a frequency of 30 cm-1, was included only to achieve a better
fit, especially around the “bump” at ∼1 ps. The experimental
Rs. molischianum curve also has a higher amplitude at ∼1 ps
than that of the simulation, but we found this difference to be
too small to add the second component. Low-frequency modes
of 30 and 12 cm-1 were seen in the RC of Rb. sphaeroides by
Streltsov et al.65 in a pump-probe experiment and attributed
to protein motions. However, another explanation is that the
observed bump in the peak shift at 1 ps is related to the
preferential removal of more relaxed pigments (with smaller
M(t)) out of the spectral window of the laser due to a relatively
fast excitation transfer to B850. The echo signal from the
remaining, slower pigments with higher peak shifts then
becomes more dominant.
The Gaussian contribution corresponds to a decay of the peak
shift from about 30 to 10 fs within the first 100 fs. As mentioned
in section 3, we think that this initial dephasing is caused by
electron-phonon coupling between the pigment and protein.
The coupling strength of this term represents a kind of
“homogeneous” line width. The simulated decay curve was not
extremely sensitive to the value of the time constant, found to
be ∼80 fs, especially when the amplitudes of the Gaussian and
exponential were varied simultaneously. In general, some
exchange between all different parameters was possible, despite
our attempts to limit the number of contributions. Also, it should
be noted that we have concentrated on reproducing the first 1
ps of the signal, since the 1-2 ps part consists of only a few
points.
The exponential contribution reproduces the peak shift decay
from ∼10 to 2-3 fs on the time scale of 1 ps. As argued in
section 3, we propose that this decay is caused by energy transfer
between B800 pigments. The coupling strength of this term can
be interpreted as inhomogeneous broadening.25,44 The exponential term then describes the sampling of this inhomogeneous
distribution by energy transfer between pigments of different
energies. In our fits, we find amplitudes ∆ωe of about 150 cm-1.
This corresponds to the experimentally determined inhomogeneous width (standard deviation) of the B800 band.32,40,43 Our
experimental result then implies that the full inhomogeneous
width of the B800 band is sampled within a single ring, since
it is highly unlikely that ring-to-ring energy transfer occurs
within less than 1 ps.10
For the time constants of the exponential, we find a value of
800 fs for Rs. molischianum and a somewhat larger value of
1100 fs for Rps. acidophila. For the latter, good simulations
were also obtained with values of 1200 or 1300 fs. Both time
constants correspond well to the values of 0.8-1.2 ps found
by other authors with pump-probe anisotropy.45,46
To interpret these decay times, we base ourselves on a nearestneighbor hopping model with a single hopping time τhop. For
hopping in a ring with N pigments, it can be analytically
Peripheral Bacterial Light-Harvesting Complexes
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11405
TABLE 4: 3PEPS Simulations of Frequency-Selected
Signals with the BO Modela
Rs. molischianum
790 nm
Rs. molischianum
810 nm
a
Figure 11. Simulation of the 3 PEPS experiments for the LH2 of Rs.
molischianum with selective detection at 790 nm (experiment, -‚-;
simulation, ‚‚‚) and 810 nm (experiment, ---; simulation, -‚-). The
experiment without a filter (s) is shown for comparison. Simulations
were based on the Brownian oscillator model as described in the text.
calculated that equilibration in the ring occurs with N time
constants ranging from τhop/4 to 2τhop.27,66 These time constants
should show up in M(t) and, thus, in the peak shift decay. The
time constant with the largest amplitude, τhop/2, is the only one
which can be identified from our data. Our exponential decay
times then correspond to hopping times of 1.6 ps for the B800
ring of LH2 of Rs. molischianum and 2.2 ps for B800 of Rps.
acidophila. It is peculiar that we extract a faster time for LH2
of Rs. molischianum than for Rps. acidophila from the peak
shift experiments, while from the transient grating anisotropy,
it was exactly the opposite. In the 3PEPS curves, Rs. molischianum is clearly seen to decay faster. On the other hand, in
Table 2, all decay times point in the direction of faster anisotropy
decay for Rps. acidophila, which is the more striking as the
change in anisotropy per neighbor-to-neighbor step will be
smaller with 9 rather than 8 pigments per ring. A second
measurement on Rs. molischianum, not selected because of a
high noise level, could be fit with a 700 fs time.
For the points measured at perpendicular polarization of pulse
3, no simulations could be carried out because the experiments
were only performed for three values of the population time.
Some support for our result that the perpendicular peak shift
decays faster can be obtained from Joo et al.,44 who have
measured their complete 3PEPS data set only at perpendicular
polarization of pulse 3 to reduce noise from scattering. With
the BO model simulation method, they find an exponential decay
constant of 600 fs, notably smaller than our values from parallel
polarization measurements. Although we note that their data
were measured on Rb. sphaeroides and it is not certain that the
B800 T B800 energy transfer occurs at a similar rate in this
species, it seems likely that the difference in polarization
explains the relatively fast time constant.
Simulations of the frequency-selected peak shift decays
measured on Rs. molischianum are shown in Figure 11. The
parameters are given in Table 4. Again, we have included a
single Gaussian and one or two oscillations. For the red peak
shift curve, detected at 810 nm, we have included a decaying
exponential which represents energy transfer. For the blue curve,
detected at 790 nm, an exponential term with an “infinite” (1
ns) lifetime was included to reproduce the large final level of
∼10 fs. For both curves, the initial peak shifts are not as well
matched as those for the whole band data. This was done
deliberately, since very small or large coupling strengths would
otherwise be needed for both the Gaussian and the exponential,
which would correspond to unreasonably small or large
homogeneous and inhomogeneous line widths.
component
∆ω
(cm-1)
τ (fs)
Gaussian
exponential
oscillation 1
oscillation 2
Gaussian
exponential
oscillation
160
150
80
40
100
150
90
60
1 ns
500
2000
80
300
500
ω
(cm-1)
φ (rad)
162
15
1.5
2.0
162
0.7
See Table 3 for details on the parameters.
The strongest oscillation is the same 162 cm-1 mode which
was described above. For the blue curve, a low-frequency mode
of 15 cm-1 had to be added. The explanation for this mode is
probably the same as that for the Rps. acidophila simulation
described above. The pigments with smaller M(t) are removed
from the laser spectral window by energy transfer to B850 or
more red B800s or by vibrational relaxation to a lower
frequency. The complete absence of the 800 fs exponential
decay process from the simulation of the 790 nm peak shift
curve is a strong support for our proposal that this particular
decay is caused by B800 T B800 energy transfer.
For the 810 nm curve, a decay time of 300-500 fs (dependent
on how we accounted for the negative end value in the
experiment) rather than 800 fs was found for the exponential
contribution. We do not think that this should be interpreted as
an energy transfer rate which is 2-3 times faster between red
B800s than between all B800s on average. Rather, this fast time
reflects the shortcomings in our analysis, which does not account
for “uncorrelated” (i.e., with zero M(t)) excitations arriving on
the red pigments by energy transfer. The faster apparent rate
may be understood as the sum of two rates: one due to the
creation of excited-state population with zero frequency correlation after energy transfer from blue B800s and another due
to the energy transfer among red B800s. In the case that both
these contributions are of comparable magnitude, this would
lead to an apparent doubling of the rate.
For the red curve, the agreement between simulation and
experiment is clearly not so good at later times. This mismatch
is a result of the fact that the experimental peak shift becomes
negative at T > 1 ps approximately, which is possibly due to a
small deviation from the ideal geometry in the experiment. If
the curve is corrected with a constant to obtain a positive peak
shift at all times, zero is reached at notably later population
time, and a decay time of 400 or 500 fs is found.
The peak shift decay curves with energy transfersthat is,
both Rs. molischianum and Rps. acidophila without filter and
the 810 nm curve for Rs. molischianumswere simulated with
the MEH approach. The parameters from Tables 3 and 4 were
taken as a starting point. The exponential lifetime was replaced
with an infinite lifetime of 1 ns. The resulting peak shifts all
looked rather comparable to those from the simulation of the
blue curve in Figure 11. These curves were multiplied with an
exponential with decay time τET equal to the τe value in Tables
3 and 4. The measured curves were reproduced even slightly
better than with the BO model simulations. The parameters had
to be adjusted only 10% or less from the BO model values.
The energy transfer times are unchanged, 800 fs for Rs.
molischianum and 1100 fs for Rps. acidophila. The simulated
curves are shown in Figure A2 of the Appendix. The parameters
are given in Table A2 of the Appendix.
11406 J. Phys. Chem. B, Vol. 104, No. 47, 2000
Figure 12. Absorption spectrum of LH2 of Rps. acidophila (solid line)
together with a simulated absorption spectrum (dotted line) calculated
on the basis of parameters obtained from the simulation of the 3PEPS
experiment with the MEH model (see text and Appendix, Table A2).
For all four B800 peak shift curves, we have calculated the
absorption spectrum from the g(t) functions used in the
simulations. For the three curves with energy transfer, the
parameters from the MEH simulations were used. All four
spectra look very similar, which is to be expected because
similar coupling strengths were used. As an example, the
(normalized) calculated and experimental spectra of Rps.
acidophila are shown in Figure 12. The calculated spectrum is
about 20% too wide. Obviously, the coupling strength values
of the simulation, which were restricted mostly by the initial
peak shift value, are too large to match the absorption spectrum
simultaneously. A very similar problem can also be noticed in
the work of Jimenez et al.25 and Yu et al.,61 where the absorption
spectra are matched very well by their simulations but the
simulated initial peak shifts are much too high. Apparently, these
two observations can generally not be perfectly simulated with
one model.
5. Concluding Remarks
In this work, we have used the 3PEPS technique to study
energy transfer in the antenna LH2 of purple bacteria. We have
excited the B800 ring of LH2s from Rs. molischianum and Rps.
acidophila to look for energy transfer within the B800 absorption
band at room temperature. The 3PEPS technique monitors the
loss of transition frequency correlation of pigments with their
transition frequency within the laser bandwidth due to energy
transfer between these pigments or due to relaxation processes
in or near the excited single pigments.
From transient grating measurements, we have determined
the time constant of transfer from B800 to B850, which is twice
the decay rate of the TG signal. The values of 600 to 800 fs we
find for this transfer time are consistent with values reported
by many others determined with alternative techniques. The
anisotropy of the transient grating signal was determined. It
decays in 700-900 fs, which we believe to be due to B800
intraband energy transfer. This is consistent with results which
others have obtained using polarized pump-probe.
We have also shown the presence of B800 f B800 energy
transfer at room temperature by measuring the peak shift at both
parallel and perpendicular polarization of the third pulse. At
perpendicular polarization, the peak shift is lower and decays
faster. After an initial decay from ∼30 to ∼10 fs within about
100 fs population time, the parallel polarization curves show a
decay from 10 fs to a few femtoseconds on a ∼1 ps time scale,
which we attribute to energy transfer. This is supported by the
Salverda et al.
frequency-selective 3PEPS measurements we have carried out.
At 790 nm, the peak shift remains very large at ∼10 fs after an
initial decay within the first ∼100 fs. At 810 nm, the decay
after the first 100 fs is much more prominent than in the whole
band.
By simulating the echo signal using the Brownian oscillator
model, the rates for the energy transfer process could be
determined. For the peakshift decay of Rs. molischianum
measured without frequency selection, a rate of 800 fs was
found, and for that of Rps. acidophila, a rate of 1100 fs was
found. These rates correspond well with values found from
anisotropy decay studies.45,46 The determined rates should be
seen as the strongest component of a multiexponential decay
of the frequency correlation function M(t), which arises from
neighbor-to-neighbor hopping between the pigments. This single
hopping step is twice as slow as the strongest rate, so we obtain
values of 1.6 and 2.2 ps, respectively, for the two species.
Finally, we tested the BO model by simulating the peak shift
decays also with the MEH model of Yang and Fleming, which
treats energy transfer as an independent process instead of
another overdamped oscillator. These simulations yield the same
results as those using the BO model.
Appendix A
Tables and Figures for the TG Simulations and for the
3PEPS Simulations with the MEH Model. In this appendix,
we present the tables and figures mentioned in section 4.2,
Transient Grating, and section 4.3, Three-Pulse Echo Peak Shift,
MEH Model Simulations.
In Table A1 are shown the results of the simulations to the
transient grating curves. A simple model was used with
ITG(T) )
∫B800(B800(λ)e-(T/τ
B800)
-
B850*(1 - e-(T/τB800)))2 dλ (A.1)
The B800 spectrum B800(λ) was taken to be a Gaussian, and
the B850* absorption was taken to be independent of wavelength
from 775 to 825 nm. The energy transfer time, denoted as the
B800 excited-state lifetime τB800, and the amplitude of B850*
relative to the peak amplitude of B800(λ) could be varied. These
two parameters are given in the table.
In Table A2 are shown the results of the simulations to peak
shift decay curves with energy transfer for both Rs. molischianum and Rps. acidophila without filter and for the 810 nm
curve of Rs. molischianum. All curves were simulated with the
MEH model
M(t) ) e-(t/τET){⟨∆ω2g⟩e-(t /τg ) +
2
2
∑j ⟨∆ωj,o2⟩e-(t/τ
j,o)
∑i ⟨∆ωi,e2⟩e-(t/τ
cos(ωjt + φj)}
i,e)
+
1
∑k
(A.2)
⟨∆ω2k ⟩
with the terms between braces {} describing the originally
excited pigment and e-(t/τET) the energy transfer between
pigments. The parameters from Tables 3 and 4 (section 4.3)
were taken as the starting point. The exponential lifetime was
replaced with an infinite lifetime of 1 ns. These curves were
multiplied by an exponential with a decay time τET equal to the
τe value in Table 4.
Acknowledgment. This research was supported by the
Netherlands Organization for Scientific Research (NWO) via
Peripheral Bacterial Light-Harvesting Complexes
J. Phys. Chem. B, Vol. 104, No. 47, 2000 11407
References and Notes
TABLE A1: Simulations of Transient Grating Signals
wavelength
τΒ800,perp
(nm)
τB800,par (fs) ESAB850,par (fs) ESAB850,perp
Rps. acidophila
790
whole band
810
Rs. molischianum 790
whole band
810
700
800
700
1000
1000
900
0.05
0.12
0.10
0.10
0.13
0.15
1500
1500
1500
1600
∼ 1600
1500
0.16
0.25
0.3
0.17
∼ 0.3
∼ 0.4
TABLE A2: 3PEPS Simulations with the MEH Model
Rps. acidophila
τETb) 1100 fs
Rs. molischianum
whole band
τET ) 800 fs
Rs. molischianum
810 nm
τET ) 300 fs
a
component
∆ωa
(cm-1)
τ (fs)
Gaussian
nondecaying
oscillation 1
oscillation 2
Gaussian
nondecaying
oscillation
Gaussian
nondecaying
oscillation
140
150
70
50
140
140
70
120
130
90
80
(1 ns)
700
1300
80
(1 ns)
500
80
(1 ns)
500
ω
(cm-1)
φ (rad)
162
30
0.7
2.0
162
0.7
162
All parameters as used in eq 4.13 (see also Table 3).
equal to τe from Tables 3 and 4.
0.7
b
τET taken
Figure A1. Simulation (dotted line) of the TG experiment measured
(solid line) without filter and with parallel polarization of all pulses
for the LH2s of Rps. acidophila (a) and Rs. molischianum (b), as
described in the text.
Figure A2. Simulation of the 3PEPS experiments measured without
a filter for LH2 of Rps. acidophila (experiment, -‚-; simulation, ‚‚‚),
Rs. molischianum (experiment, s; simulation, ---), and the 3PEPS
experiment measured at 810 nm for LH2 of Rs. molischianum
(experiment, - - -; simulation, -‚-). Simulations were based on the
modified electron-hole model (see ref 58), as described in the text.
the Board of Earth and Life Sciences (ALW). The authors are
grateful to Markus Wendling for useful discussions and assistance in computer programming and to Petra de Gijsel for
help with typing the manuscript.
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