Femtosecond vibrational dynamics and relaxation in the core light-harvesting complex of photosynthetic purple bacteria

llOctober 1996

CHEMICAL PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 261 (1996) 165-174

Femtosecond vibrational dynamics and relaxation in the core light-harvesting complex of photosynthetic purple bacteria Mirianas Chachisvilis, Villy SundstriSm Department of Chemical Physics, Chemical Center, Land University, P.O. Box 124, S-221 O0 Lurid, Sweden

Received 20 June 1996; in final form 29 July 1996

Abstract

Using 50 fs light pulses we have observed the wavelength dependent phase shifts of oscillatory transients in the transient absorption kinetics of the LHI complex from purple bacteria at 77 K. We applied the density operator formalism in Liouville space in combination with Redfield relaxation theory to calculate the transient absorption response of the model system consisting of three electronic states and one vibrational mode linearly coupled to the thermal bath. This enabled us to estimate relative displacements of the potential energy surfaces in the higher excited states of the LHI complex and investigate the influence of coherence transfer processes.

1. Introduction Recent experimental progress in femtosecond laser spectroscopy has made it possible to observe coherent nuclear motions in a variety of systems in the condensed phase. Oscillations following an excitation with a femtosecond pulse, have now been observed in molecules and clusters [1 ], solids [2], large dye molecules in solution [3], bacteriorhodopsin [4], bacteriochlorophyll a (BChl a) in solution [5], photosynthetic reaction centers [6-8], heine proteins [9] and light-harvesting pigment-protein complexes [10-12]. In this Letter we report on spectrally resolved femtosecond pump-probe measurements on the core light-harvesting complexes ( L H I ) from the p h o t o s y n t h e t i c bacteria Rhodobacter ( Rb.) spaeroides and Rhodospirillum ( R . ) rubrum. The available structural data suggest that the LH1 complex from these bacteria has a highly symmetric ring

structure built up from smaller units, each of which contains one ot and one [3 polypeptide binding two BChl a molecules [13,14]; the number of units in the reconstituted complex of R. rubrum is 16 [13]. Although the high resolution structure is not available yet, there are indications that the dimer nature of the smallest unit is at least partly preserved upon aggregation into a full LH1 complex [15,16]. The dipoledipole interaction between the BChl a molecules leads to excitation energy delocalization and migration within LH1 on a time-scale of = 100 fs as inferred from the transient anisotropy decays measured by femtosecond fluorescence upconversion and pump-probe techniques [10,12,17]. In the course of these experiments, coherent oscillations of the signal (main frequency -- 104 c m - i, damping time = 300 fs) following the excitation with a femtosecond pulse, were discovered and interpreted as a coherent nuclear motion in the excited state. Our present obser-

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M. Chachisvilis, V. Sundstri~m/ Chemical Physics Letters 261 (1996) 165-174

vation of the wavelength dependent phase shifts further confirms the vibrational origin of the oscillatory features. In this Letter we will concentrate on the nuclear motions in the LH1 complex by describing, it with a

!

|

I

I

i

i

I

model system consisting of three electronic states and one nuclear degree of freedom. We tentatively assign the above three states to the ground, singly excited and doubly excited electronic manifolds of a BChi a exciton coupled aggregate, thereby assuming

i

i

i

i

I

i

i

i

i

i

~

I

855 nm_

J

860 n m

L

869 n m

< <3 !

874 nm

878 n m 883 n m 892 n m 901 n m

0.0

0.5

1.0

1.5

2.0

Delay, ps Fig. 1. Pseudo two-colour kinetics of the LH1 complex of Rhodobacter sphaeroides measured with ~- 50 fs pulses at different detection wavelengths at 77 K. The laser pulses were centered at 864 nm.

M. Chachisvilis, V. Sundstr6m / Chemical Physics Letters 261 (1996) 165-174

that the vibrational and excitonic wave functions are separable. This aggregate can be viewed as a BChl a miniexciton, which in the most simple case would be a dimer but which could also be larger. From femtosecond spectra of LH2 we recently concluded that

i

i

!

167

for this complex the size of the miniexciton is 4 _ 2 BChl a molecules. The situation is probably similar in LH1. For the purpose of demonstration we choose a dimer as the miniexciton in the present calculations. This approach is supported by the fact that the

!

i

!

|

858 n m 863 n m 867 nm

i

i

:

:

i

872 n m

876 n m

i

881 nm

i

i

886 n m 890 n m 895 n m

900 n m 909 nm

904 nm

0.0

0.5

1.0

Delay, ps Fig. 2. Pseudo two-colour kinetics o f the L H I c o m p l e x o f Rhodospirillum wavelengths at 77 K. The laser pulses were centered at 8 7 6 rim.

rubrum measured with = 50 fs pulses at different detection

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M. Chachisvilis, V. Sundstrfim / Chemical Physics Letters 261 (1996) 165-174

dipole-dipole coupling in the dimer is likely to be on the order of = 450 c m - l (as implied by the structure of a similar system [18]) while the hole burning studies indicated that the electron-phonon coupling is relatively weak (Huang-Rhys parameter S---0.3 [19]). We have chosen to use the reduced density operator to describe the system. This enabled us to include energy dissipation effects in a systematic way by using Redfield relaxation theory [20] and to calculate the transient absorption spectra and kinetics of the system by employing Liouville space formalism [21], which treats the interactions with optical fields in a perturbative way.

2. Experimental Pseudo two-colour (dispersed) pump-probe measurements [22] were performed using the output of a mode-locked Ti:Sa laser (Tsunami, Spectra-Physics). The pulse repetition rate was reduced to 400 kHz, using a pulse picker (Spectra-Physics), in order to prevent pile up effects in the experiments. Recompression after the pulse picker resulted in transform limited pulses of typically = 50 fs time duration. Pump and probe pulses were formed from these with an intensity ratio of approx. 25:1, and = 1 nJ/pulse in the pump. After traversing the sample the probe was sent through a monochromator and the spectrally resolved pump induced intensity change of the probe beam was detected with a photomultiplier tube (Hamamatsu R-636) at a spectral resolution of 2 nm. The angle between the pump and probe polarizations was set to the magic angle (54.7°). Experiments were performed on a membrane preparation [10] in glycerol/buffer 1:1 solution, at 77 K, in a 1 mm cuvette. The optical density of the sample was --~ 0.5 at the absorption maximum at 77 K.

3. Experimental results In Fig. l we present transient absorption kinetics of the LH1 complex from Rb, spaeroides in a membrane environment measured at different detection wavelengths using the pseudo two-colour pump-probe technique. Similarly, Fig. 2 shows analogous data for the LH1 antenna of R. rubrum. In both cases the excitation pulse was centered on the

blue side of the absorption band; the FWHM of the pulse spectrum was approx. -- 294 cm- l ( r = 50 fs). We remind that the LH1 complex has a single near-infrared absorption band located at 884 nm and 891 nm for Rb. spaeroides and R. rubrum, respectively (at 77 K). The transient absorption signal is dominated by the excited state absorption (ESA) on the short-wavelength side of the absorption spectrum and by the ground state bleaching (BL) and stimulated emission (SE) at longer wavelengths. The initial part of the kinetic traces in the pulse overlap region exhibits coherent transients, typical for the pseudo-two colour pump-probe signal; it has been shown recently, both experimentally and theoretically, that these are primarily due to the electronic coherence induced by the pump and probe pulses [22]. The kinetics further display small but clear oscillations with a main period of = 320 fs (~ = 104 cm-~); the period is the same for Rb. spaeroides and R. rubrum and agrees with the values reported earlier from integrated pump-probe and fluorescence upconversion studies [5,10,12,17] Oscillations are observed in both the signal dominated by the ESA and the B L / S E . The phases of these oscillations are wavelength dependent. We have used the second maximum position in the kinetic traces to determine the phase shift, since the oscillatory signal in the zero delay region is strongly obscured by the coherent electronic transients (the arrows in Fig. 1 and Fig. 2 mark the second maximum position in the oscillatory pattern). The shift is largest (0.15-0.3rr) in the kinetics measured at shortest and longest detection wavelengths. It is also important to notice that the amplitude of oscillations is zero (or significantly reduced, so that it is not noticeable with our signal to noise ratio) at some specific detection wavelength near the isosbestic point (at 878 nm in case of Rb. spaeroides and at 890 nm in case of R. rubrum). It is tempting to attribute this effect to a mutual cancellation of the oscillatory signals coming from the ESA and the SE; we will use this observation to determine the relative displacement of potential energy surfaces in the excited states (vide infra).

4. Theory In this section we will describe the method used to calculate the pump-probe response from the model

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M. Chachisvilis, V. SundstrOm / Chemical Physics Letters 261 (1996) 165-174

/

that the transition dipole moments are independent of vibrational degrees of freedom (Condon approximation); the dipole operator (in tetradic notation) is given by: I1.)) = 1.a2112)) + 1.21121)) + 1.23123)) + 1.32132)). (4)

I1>

Fig. 3. Displaced potentialenergy surfaces of the model system used for calculations.

system consisting of three electronic states and one vibrational degree of freedom coupled to the surrounding bath which induces vibrational relaxation and dephasing (see Fig. 3). The dispersed pseudo two-colour pump-probe signal is defined as the difference in the spectrum of the probe field with respectively pump-on and pump-off, S( to, 7-) = [Epr( w, r)l 2 -[Epr ( to)l 2

=2~ImEpr(to)e(3)*(to,r),

(1)

where Epr(tO) and p(3)* (09, 7") are the Fourier transforms of the probe field and the third-order polarization, respectively. 12 is the central frequency of the probe field, 7" is delay time between pump and probe pulses. In the following we employ the density operator formalism in Liouville space [21] to calculate the optical response the system. The third order polarization is given by the expectation value of the dipole operator 1., p(3) = ( ( 1.1 P ( 3 ) ( t ) ) ) ,

(2)

where p(3)(t) is the third order term in the perturbative expansion of the Liouville equation. The molecular Hamiltonian is defined as follows,

H= ~_,[i)Hi(il,

(3)

i where H i ( i = 1, 2, 3) represent the vibrational Hamiltonian of the system in its electronic state li). The interaction with the electric field is treated in the electric dipole approximation and we also assume

We introduce the electronic dephasing in a simple phenomenological way by adding non-diagonal relaxation terms to the Liouville equation in order to describe the decay of electronic coherences of the lower and upper transitions (dephasing rates 3q2 and "}/23); it should be mentioned that this is a reasonable approximation since in the condensed phase the electronic dephasing rate is usually much faster than the vibrational one. We also neglect decay of population of the excited electronic state 12). Following Yan et al. [23] the expression for the third order polarization is obtained by expanding the Liouville equation 3 i -~tp= --~Lp (here L = [ H .... l) to the third order in material-field interaction and making the rotating wave approximation. Additionally it is assumed that the pump pulse can be approximated with a 8(t) function, since in our experiments the pulse was by a factor of --6 shorter than the dominating vibrational period. Under these assumptions and using Eq. 2-4 we obtain, p(3)(t ) =

i

h-3

/'t

,

,

4

4 dtEpr( t ){ 1.12 e

-

"~,2(,-

t')

X ((IIGlz ( t - / ' ) G 2 2 (t a)[ p ( - o o ) ) ) + t,42 e- ~12(/- t') × ((l[G,2(t - , ' ) G , , ( t ' ) l p ( - m ) ) ) --1.~2 ~Z223 e-'V23(t-t')

× ( ( l l G 3 z ( t - t ' ) G = ( t ' ) [ p( - o e ) ) ) } ,

(5) where G,.j is the Liouville space Green function [21], 1 is the unit operator, Epr(t) is the temporal envelope of the probe field and p ( - ~ ) is the initial density operator describing the system in the lowest electronic state and in thermal equilibrium with the bath. The three terms in Eq. 5 can be interpreted as the SE, BL and ESA contributions, respectively.

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M. Chachisvilis, V. Sundstrbm / Chemical Physics Letters 261 (1996)165-174

We have chosen to evaluate the propagation using the Green function in two different ways, depending on whether indexes i and j are equal or not. In the case when i # j the propagation describes quantum evolution of the system in the electronic coherence state, decay of which is taken care of by the dephasing factors e x p ( - T i j ( t - t')) in Eq. 5. The calculation of this evolution is greatly facilitated by assuming that the time-scale for vibrational relaxation and dephasing in any electronic state under consideration is slow compared to the electronic dephasing. The propagation under the corresponding Green function is then simply performed according to the definition,

Gij(t)p=exp

(i)

(i)

- - h H , t pexp ~-H/, .

(6)

When i = j, the system is in a population state and consequently its quantum evolution involves only nuclear degrees of freedom. Notice, that since p( - 0¢) describes the system in the equilibrated ground state, the propagation under Gjl(t) in the second term of Eq. 5 need not to be evaluated at all as a consequence of impulsive excitation. Thus we are left with only nuclear evolution in the excited state 12). It is at this point that we include energy dissipation effects into the model. We follow Redfield's approach [20], which treats the system-bath coupling perturbatively; we remind here that the general result of this theory is that all density operator elements become coupled among themselves via the so called Redfield tensor R. The Redfield relaxation theory assumes that the bath correlation time r c is much shorter compared to the timescale of the dynamics of the system. The required propagation on the excited state potential surface can then be performed using the following Green function, G22( t ) = e t',

(7)

where I. is a tetradic operator with its elements defined as follows, Lij. m n = - iooij6in6mj + R i j . . . .

(8)

here wi / = ( H 2 ) i i - (H2)jj. The first term in Eq. 8 describes the free evolution of the system under the vibrational Hamiltonian of the first excited state. The second term accounts for the dissipative influence of the thermal bath; physically it induces processes like population relaxation, pure dephasing, transfer of

coherences and coupling between populations and coherences (see for instance Ref. [24]). A formal expression for the Redfield tensor elements in terms of correlation functions of system-bath interaction operator elements can be found in Ref. [20]. To be more specific we assume that coupling between the system and the bath is linear in system and bath coordinates, which means that only one-phonon processes will be considered. This amounts to discarding the two-phonon contribution to pure dephasing processes, which seems to be a reasonable assumption in the case of vibrational transitions in the condensed phase. Additionally, the so called secular approximation is invoked, which neglects non-resonant terms (e.g., transfer between populations and coherences). It has recently been shown by Walsh and Coalson [25] that in the case of weak coupling this approximation yields a fairly good agreement with exact calculations. Under these assumptions the following elements of the Redfield tensor are nonzero, population transfer:

Rii.jj=[]2(J-(¢oji)

+J+(wij)).

(9a)

population relaxation:

Rii.,, = - ( Ri- ,i-1., + Ri+ ,i+ ,.ii).

(9b)

dephasing: I

e i j , ij = -~( Rii. i i ~- g jj, j j ) ,

(9c)

coherence transfer:

R ij. jm = (ivlQljv)(mvlQIJv)(J-(oj,,j)

-FJ+(ooij)), (9d)

where Q denotes the system coordinate and [i v) are the eigenstates of the vibrational Hamiltonian H 2. Following Jean and Fleming [24], we assume that the bath correlation functions decay exponentially with a correlation time r c. This results in the following simple expression for spectral densities,

J + ( OOij) = f2r¢( 1 + e -+13n,o,j)- ' , where f2 is the squared amplitude of bath fluctuations. This form of spectral densities assures that the system is relaxing to the thermal equilibrium according to the Boltzmann distribution.

M. Chachisvilis, V. Sundstr~m / Chemical Physics Letters 261 (1996)165-174

The initial propagation of the density operator with the Green function ( G 2 2 ( t ) ) of the first excited electronic state was performed using the short-iterative-Arnoldi method in Liouville space (see [26]), while subsequent coherent evolution under G12(t) or G32(t) was evaluated in Hilbert space to reduce the time needed for calculations. We have used a Gaussian function for the temporal shape of the probe field.

171

--~ ~

x2

503cm 1 422 cm -t 301 cm -I

i

187 cm -1

5. Numerical simulations and discussion In Fig. 4 we show the pseudo two-coiour pumpprobe kinetics calculated using the model system shown in Fig. 3 and parameters appropriate for comparison with the experiment. The 50 fs probe pulse is centred + 200 cm-~ above the ground-excited state transition frequency. It was assumed that the dimensionless displacement in the first excited state is 8e = 0.7 (S e = 0.24) while in the second excited state, it is 8~ = 0. The vibrational frequency too = 104 cm -1 was taken from the experimental data (see Fig. 1, 2 and ref. [5], [10]). For the electronic dephasing rates of the lower and upper transitions, 712 and ')/23 we used 1/110 fs -I and 1 / 6 0 fs -I, respectively; this choice is supported by the experimental observation that in these systems the transient anisotropy relaxation occurs on the 50-150 fs time scale (see ref. [17], [27]) which sets the lower limit for the dephasing rates. The 0 - 0 electronic energy gap for the upper pair of levels (2 and 3) is taken to be by V = 430 cm- 1 larger than that of the lower pair of levels (1 and 2). This configuration can, e.g., represent the exciton coupled dimer with head to head or head to tail orientation of the transition dipole moments of the constituent monomers and V as interaction energy between them (in this case ].LI2= P~23 ). Furthermore, we have assumed that the monomeric transition energy is inhomogeneously broadened and can be described by a Gaussian distribution function with the FWHM of 100 c m - l (the calculated kinetics are not significantly affected by increase of this value up to 400 c m - l ) . The system-reservoir coupling constant f2"r¢ was set to 1 / 7 4 fs-i (to fit the experimentally observed decay rate), which gives 1/85 fs -1 for the population relaxation rate from the first excited to the zero

!

i

0

200

400

x2

600 800 Delay, fs

-98 cm -I

1000

1200

Fig. 4. Calculated pseudo two-colour pump-probe kinetics of the model system shown in Fig. 3. The numbers denote the detection wavelength relative to the 0 - 0 transition between the ground and first excited state. The curves corresponding to the far wings of the pulse spectrum are scaled to ease the inspection. The dashed lines represent kinetics calculated using the Redfield tensor without coherence transfer terms. For the parameters used see the text.

vibrational state at 77 K. The one-phonon population relaxation rate between the higher states grows linearly with the quantum number of the state, according to Eq. 9a. It is assumed that initially the system is in the electronic ground state in thermal equilibrium with the reservoir at 77 K. The calculated kinetics (Fig. 4) are quite similar in their general features to the experimental results presented in Fig. 1 and Fig. 2. The signal at the higher frequencies is dominated by the ESA while at the lower frequencies mainly the S E / B L contribute. At most of the detection frequencies the pump-probe response is modulated with the main vibrational period 2,rr/to 0. Also, we note that there is a fre-

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M. Chachisvilis, V. Sundstrfim / Chemical Physics Letters 261 (1996)165-174

quency dependent phase shift of these oscillations, observed in both the kinetics dominated by the ESA and B L / S E . The shift is minimal (as determined by the second maximum position in the oscillatory pattern) at a detection frequency = 98 cm-1 and increases when the detection is shifted to either lower or higher frequencies, as expected for the configuration of potential energy surfaces depicted in Fig. 3. The direct comparison with experiment is complicated in the zero-delay region because the calculations are performed using 8 pulse excitation which results in a different shape of the coherent transients typical for the pseudo two-colour pump-probe signal [22]. Fig. 4 also displays two kinetic traces (at 301 c m - l and 98 c m - l , dashed lines) calculated using the Redfield tensor without coherence transfer terms (Eq. 9d). It is evident that inclusion of coherence transfer processes leads to a substantial retention of the vibrational coherence in the signal and to a non-exponential decay of the amplitude of vibrational modulation. Physically the coherence transfer can be envisaged as the emission of the vibrational quantum from the system into the bath (creation of a virtual bath phonon) accompanied by the simultaneous re-absorption of the same bath phonon by the system. Due to the coherence transfer process mainly the initial decay phase is slowed down; this can be easily understood by noticing that relaxation leads to a reduction of the number of coherences (non-diagonal density matrix elements) that contribute to and result in diminished importance of the coherence transfer processes. Non-exponentiality arises due to the fact that each non-diagonal density matrix element is coupled via the coherence transfer terms to the adjacent elements along the corresponding subdiagonal of the density matrix. When the coherence transfer is not included the decay of the amplitude of the oscillations can well be described by a single exponential function. It is important to notice that the oscillatory modulation is nearly absent in the kinetic trace calculated close to the isosbestic point, at 187 cm-1 above the ground state absorption maximum; the existence of such a detection frequency strongly depends on the nuclear displacement 8f of the second excited state. Our specific choice of the relative displacements of the excited states is motivated by the fact that only in

-Am, a.i

t = 2 "l

t = I/2 l

t=T

t -T/2

t=0

- ! 000

-500

0

500

1000

1500

Frequency, cm l Fig. 5. Calculated transient absorption spectra o f the model system (Fig. 3) at different delay times t after excitation. Time is running from bottom to top. The adjacent spectra are separated by T/IO, where T = 2 " r r / t o 0. F o r the other parameters used, see text.

case of 8e > 8f it is possible to find the detection wavelength at which oscillations due to the SE and ESA cancel each other. The underlying reason for this is that in this configuration the motion of the initially prepared excited state wavepacket results in opposite frequency shifts of the transient SE and ESA maxima. When 8e < 8f such a detection wavelength does not exist because the frequency shifts have the same sign. A few calculations done with slightly larger values of 8f (~< 0.4) showed that in this case it is still possible to find a detection frequency with complete cancellation of the main vibrational frequency; larger values of 8e result in a different value of this frequency (e.g., 195 cm- i for ~f = 0.2, and 211 cm- l for 6f = 0.4) and in a smaller

M. Chachisvilis, V. Sundstrbm / Chemical Physics Letters 261 (1996) 165-174

amplitude of oscillations in the kinetics dominated by the excited state absorption. In Fig. 5 we show the transient absorption spectra of the model system calculated using the same parameters as for Fig. 4, except that the values of the dimensionless displacement 6e and system-reservoir coupling constant f2~-c are increased to 1.5 (Se = 1.12) and 1/140 fs -1, respectively, to make the spectral changes more pronounced. A 8 function is used for the probe pulse in these calculations. At zero delay-time the transient spectrum is characterised by a positive signal region at --- 100 cmwhich is due to the BL and SE and a negative signal region at -~ 400 cm-1 caused by the ESA. The subsequent time evolution of the transient spectrum reflects the dynamics of the initial excited state wave-packet. Clearly, the positive and negative bands exhibit out-of-phase oscillatory shifts. At long delay times the ESA band is up-shifted by -- Sehto= 117 cm-~ due to vibrational relaxation towards thermal equilibrium in the excited state. The temporal evolution of the positive band is more complex since it involves contributions from both the ground and excited state (second and third terms in Eq. 5). As a result of the impulsive excitation the ground state contribution (the BL) does not depend on the delay time (see above, section 4), therefore the time evolution comes from the SE reflecting the time-dependent S~ - SO energy difference at the position of the excited state wave-packet. This leads to e.g., appearance of a double peak most clearly seen in the transient absorption spectrum at t = 0.4T; the first peak at + 100 cm -~ is the bleach and the second peak at - 2 1 6 cm -~ is due to the SE from the non-stationary wave-packet near its turning point. At sufficiently long delay times when the dephasing of the wave-packet has occurred, the positive signal is simply a superposition of the relaxed fluorescence and BL. The question which remains to be answered is: why does the displacement of the potential energy surface of the second excited state appear to be smaller than that of the first excited state? To deal with this problem one has to consider the nature of these states. If we tentatively assign the 104 cmoscillation to an intradimer mode, then within our dimer model the ground and doubly excited states (states I1) and 13) in our notation) are given by the

173

products of the corresponding electronic wave functions of the monomers and the nuclear wave function describing the relative vibrational motion. In general, the vibrational wave functions can be slightly different for the ground and doubly excited states due to e.g. different strength of quadrupole-quadrupole interactions which can be important for closely situated pigments as in the LH1 complex. The situation is more complex for the singly excited degenerate dimer states, since they can be efficiently coupled by a dipole-dipole interaction. In the case of a symmetric dimer and one interdimer mode it can be shown (see [28]) that the eigenstates of the dimer are Ixl0"±) = I~b+-(QAB))(Ia/tA) ___laltta ) ) , where IqJA) and I~0B) are the electronic wave functions of the excited monomers, and I~b+(Qaa)) and I~b-(QAB)) are the nuclear wave functions which are the solutions to the corresponding eigenvalue equations,

(T,+U(QAB)+_V(QAB))Ick +-) = E l 6 ± ) .

(10)

Here T, is the kinetic energy operator of relative vibrational motion of two monomer molecules, U(Q AB) is the potential energy of the system in the absence of interaction and V(Q As) represents the electronic interaction between the monomer molecules. It follows from Eq. 10 that the vibrational motion in the two dimer states is affected by the coupling in different ways. The V(QAa) can be expanded around the equilibrium position with respect to the coordinate QAB. The linear term in this expansion would then introduce the shift of the potential energy surfaces and it would have opposite signs in the dimer states IV+) and IV-). The most likely candidate for V(Q ga) is a dipole-dipole interaction, but due to the close proximity of pigments in the LH1 complex other short-range interactions might be important. Further experimental investigations are necessary for more definite assignment. An alternative approach, suggested by experimental observation [5], could be to assign the 104 cm- ~ oscillation to an internal vibrational mode of the BChl a molecule. In this case the electronic interaction between monomers leads to vibronic coupling and as a consequence to formation of a complex manifold of vibrational levels [28]. In principle the formalism outlined above could be applied to calculate the

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M. Chachisvilis, V. Sundstr3m / Chemical Physics Letters 261 (1996)165-174

pump-probe response of such a system. However, we have not attempted to do so during this work due the significantly higher numerical effort involved. Summarising: in this Letter we have used a simple model consisting of the BChl a dimer and a single vibrational degree of freedom coupled to it to simulate the oscillatory transients observed in the pump-probe kinetics of the LH1 complex. The simulations using the density operator technique reasonably well reproduce the wavelength dependent phase shifts of oscillations in experimental traces and also enable us to show that the dimensionless displacement of the potential energy surface is larger in the first excited state than in the second excited state. We also show that the incorporation of coherence transfer processes into the model leads to the retention of vibrational coherence for longer delay times and to non-exponential relaxation of the amplitude of oscillations.

Acknowledgements Financial support is acknowledged from the Swedish Natural Science Research Council, the Knut and Alice Wallenberg Foundation and EEC contract SCI *-CT92-0796.

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