J. Phys. Chem. 1994,98, 2706-2712
2706
Transient EPR of Light-Induced Spin-Correlated Radical Pairs: Manifestation of Zero Quantum Coherence Gerd Kothe,' Stefan Weber, and Ernst Ohmes Department of Physical Chemistry, University of Stuttgart, Pfaffwaldring
55, D- 70569 Stuttgart, Germany
Marion C. Thurnauer and James R. Norris Chemistry Division, Argonne National Laboratory. Argonne, Illinois 60439 Received: November 9, 1993'
Light-induced spin-correlated radical pairs in plant photosystem I are studied by high time resolution transient
EPR following pulsed laser excitation. The time evolution of the transverse magnetization is monitored at various static magnetic fields. This implies a two-dimensional variation of the signal intensity with respect to both the magnetic field and time axis. Zero quantum coherence between two of the four eigenstates of the radical pairis observed at early times after the laser pulse. Model calculations, based on the stochastic Liouville equation, provide detailed information about the spin dynamics of correlated radical pairs.
Introduction The transient nutation technique, introduced by Torrey,l is a well-established method in time-resolved EPR. Combination of this technique with pulsed laser excitation has provided valuable information about short-lived paramagnetic ~pecies.~-l~ In contrast to steady-state methods, transient EPR measures the time evolution of the magnetization. This property is of particular importance for the study of light-induced species where large initial electron spin polarization occurs due to spin-selective population processes. Under proper conditions the time resolution of transient EPR compares favorably with pulsed methods.10 Moreover, no restriction exists with respect to excitation bandwidth. Finally, the full time development of the magnetization is obtained undiminishedby any microwave detection dead time. Apparently, transient EPR is particularly suited for the study of spin-correlated radical pairs16 generated as short-lived intermediates in a variety of photoreactive systems.8-12J4a15 The basic EPR spectrum of a spin-correlated radical pair, created in a singlet or a triplet configuration, consists of four peaks arranged as two doublets with equal splittings determined by the spin-spin coupling between the radi~als.89~J~J~ Both doublets have one component emissive and the other absorptive, reflecting the nonequilibrium populations of the four-electron spin states. There is also a coherent superposition of two of the four spin states1*-20-a zero quantum coherence21*2Lwhichcan manifest itself as quantum beats in an EPR experiment with adequate time res0lution.l2*~~ This coherence arises when the initial configuration of the radical pair is not an eigenstate of the radical pair Hamiltonian. In this paper we present a high time resolution transient EPR study of spin-correlated radical pairs formed by photoinduced charge separation in plant photosystem I. The fast chargeseparation chemistry of photosynthesis provides an ideal system for investigatingthe quantum beat phenomenon. In fact, quantum beats of the type considered here have been detected only in fully deuterated photosynthetic systems. The time evolution of the transverse magnetization is evaluated for various static magnetic fields. Manifestations of zero quantum coherence are observed at early times after laser excitation. Calculations of the time profiles, based on the stochastic Liouville equation, provide Abstract published in Advance ACS Abstracts, February 1 , 1994.
0022-3654f 94f 2098-2106%04.50f 0
valuable information about the spin dynamics in light-induced spin-correlated radical pairs. Theory
In this section we summarize a model for transient EPR of spin-correlatedradicl pairs and define the model parameter~.~&l~ Specifically, we consider a sudden, light-induced generation of the radical pair with a spatially fixed geometry. Particular emphasis is given to the slow-motional regime where anisotropic magnetic interactions dominate. Spin Hamiltonian. The total spin Hamiltonian H(Q,t) of the radical pair can be divided in five parts:
H(Q,t) = HZ(n)
+ H R ( Q , t ) + H E X + HD(n) + HHF(n)
(l)
The first term, describing Zeeman interactions of the electron spins SI, i = 1,2, with the static magnetic field BO= (O,O,Bo)is given by
where j3 and &, i = 1,2, are the Bohr magneton and the g tensor of radical i, respectively. In the presence of a rotating microwave field B1 = (B1 cos ut,BI sin ut, 0) the Hamiltonian includes the radiation term: HR(Q,t)
= @B1'kl(Q)'S1 + g2(n)*s,l
(3)
where B1 denotes the magnitudeof the microwave radiation. Note that H R ( Q , ~is) explicitly time dependent. The next two terms of eq 1 account for the isotropic and anisotropic spin-spin coupling of the radical pair: HEX
J(QT - Qs)
(4)
where J and D(Q)are the electron-exchange interaction and dipolar coupling tensor, respectively. The last term of the Hamiltonian 1 describes the magnetic interactions between 0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 10, 1994 2101
Spin-Correlated Radical Pairs electron and nuclear spins. For weakly coupled radical pairs this part of the Hamiltonian can be written 892'
ail, =
and
'/, 1 V s, L(Q) may be dropped. The relaxation superoperator R accounts for all relaxation processes neglected in truncating HrX(0)and L(Q). Generally, the elements of R can be related to the residual relaxation times TIand T2 by
RSST,T~R T , T=~ 1/T2
(20)
--
RSST,T,= RT,T+SS RSST-T= RT-T-SS RT,T,T,T, RT,T,T~T~ = RT,T,T-T- RT-T-T~T, = RT,T,T-T-= RT-T-T,T,= 1/Ti (21)
--
RT-T,T-T, = RT,T-T,T- RT,T,T,T, RT,T~T,T, R T S T S RSTST-= RSTJT,= RTJTJ = -l/T2 (22) The remaining diagonalelementsof R are given by the stationary condition, i.e.
= 0;
i , j E(S,To,T+T-)
(23)
1
Finally, we have to specify the chemical kinetics superoperator
K. For a first-order process of the decay of the radical pair, the elements of K can be written as203 Kijkl
= Kikajl
+ K& Kij
i, j , k, 1
= -'/z(ksQs
T+,T-) (24)
+ kTQ~)ij
(25)
where ks and kT are the decay rates from the singlet and triplet radical pair state, respectively. For simplicity, we assume
k, = kT = 1/T
(26)
where 7 is the lifetime of the radical pair. Formally, integration of eq 19 leads to pr(Q,t)
= exp(-[(i/h)Hm(Q)
+ L(Q)- R - K]tj-p'(Q,O) (27)
where D and E denote the zero-field splitting parameters of the radical pair. (Ilk is the isotropic hyperfine coupling constant of nucleus k in radical i:
where pr(Q,O) is the initial condition of the density matrix at the time of the sudden generation of the radical pair. Only in the case of primary radical pairs do we expect pure initial spin states: p'(Q,O)
= P,(Q)4,;
i
= S,T
(28)
2708 The Journal of Physical Chemistry, Vol. 98, No. 10, 1994
Kothe et al.
determined by the spin multiplicity of the excited precursor. For all following pairs, the pure singlet might be admixed with some triplet character and vice versa.32 In these cases pl(S2,O) can be evaluated by solving eq 19 for the lifetime of the precursor radical pair. Evaluating the trace of p'(t).(q + g)finally gives the observable EPR signal of the transient nutation experiment as
WO = Tr[p'(t)*(g + 5391
(29)
P'(t) = JP'(Q,t) d n
(30)
where pl(n,t) is obtained by solving eq 27. The corresponding diagonalization of the exponent may be accomplished using the Rutishauser alg~rithm.'~Integrating M(r)over an appropriate time window and plotting this integral as a function of BOyields the transient EPR spectrum. Inhomogeneous broadening is considered by convolution with a Gaussian, characterized by the line width A&.
Experiments and Methods Sample Preparation. Frozen, packed cells of fully (99.7%) deuterated whole algae Synechococcus lividus were suspended in deuterated Tricine buffer (pH = 7.5). About 5 mL of the sample was circulated through a 1-mm (inner diameter) quartz capillary located in the symmetry axis of the microwave resonator. EPR Measurements. The basic concept of the EPR experiment is similar to that described previou~ly.l~.~~ A modified X-band spectrometer (Bruker ER-200 D) was used, equipped with a fast microwave preamplifier (36 dB, 1.8-dB noise figure) and a broadband video amplifier (bandwidth 200 Hz-200 MHz). The sample was irradiated in a home-built split-ring resonator with 600-ps pulses of a nitrogen laser (PTI PL 2300, 337.1 nm, 1.6 mJ/pulse) at a repetition rate of 15 Hz. The split-ring resonator exhibits a high filling factor at low Q (unloaded Q C 500) and provides an easy means of sample irradiation. The time-dependent EPR signal was digitized in a transient recorder (LeCroy 9450 digital oscilloscope,waveform processing package WP-01) at a rate of 2.5 4 1 2 bit sample. The time resolution of the experimental setup is in the 10-ns range. Typically, 5 12 transients were accumulated at off-resonance conditions and subtracted from those on resonance to get rid of the laser background signal. Two different modes of operation, controlled by a personal computer, were employed. The time profile of the transients was either monitored at a given magnetic field or the transient EPR spectrum was recorded for a fixed time window after the laser pulse. In the latter mode the magnetic field was set by a modified Bruker field controller and measured by an NMR gaussmeter (Bruker ER 035 M). As demonstrated in the next section, the best overall view of the full data set is obtained from a twodimensional plot of the signal intensity versus the time and magnetic field axis. Computations. A Fortran program package, based on the theoretical approach outlined in the previous section,was employed to analyze the transient EPR experiments. The programs calculate EPR time profiles and line shapes of spin-correlated radical pairs with a spatially fixed geometry. The corresponding diagonalizations were accomplished using the Rutishauser algorithm according to Gordon and Messenger.33For this purpose, Fortran routines have been adapted from the literature33934 and modified.19 Experimental Results Suspensions of fully deuterated whole algae Synechococcus lividus were irradiated with 600-ps pulses from a nitrogen laser and the time evolution of the transverse magnetization was
2.48Second, it converts the zero quantum coherence into observable single quantum precessions,18,21,22significantlyvarying withB0.I2Jg Because of hyperfine interactions, rapid averaging of these oscillations is expected even in case of narrow-band microwave excitation, as usual in transient EPR. Thus, manifestations of zero quantum coherenceare likely to be observed only immediately after the laser pulse. Transient Line Shapes. We first explore the effect of zero quantum coherence on the transient spectra. Figure 2 shows selected line shapes of P7,33+A1- at various times after the laser pulse. One sees that the early spectrum is much broader than thelatter ones. Moreover, the spectralshapechangessignificantly with time. A detailed analysis reveals that lifetime broadening dominates the early spectrum whereas zero quantumprecessions modulate the line shapes at intermediate times. Note that all transient spectra are faithfully reproduced by our model. As expected, the stochastic Liouville equation adequately describes the complex spin dynamics of correlated radical pairs. Indeed, simulation of a set of transient spectra provides a critical test for all parameters extracted from the EPR experiments.46 Coherent Oscillations. We now explore how zero quantum coherence manifests itself in the time evolution of the transverse magnetization. Figure 3 depicts selected time profiles for the secondaryradical pair, P7m+A1-. The transients refer to a constant microwave field and six different BOpositions. Apparently, all transients exhibit oscillatory behavior at early times after the laser pulse. As noted above, the frequency of these oscillations is independent of B1 but significantly varies with BO. Basically, these oscillations represent quantum beats detected in the transverse m a g n e t i z a t i ~ n . ~Yet, ~ - ~ ~the conventional transient EPR experiment does not give the frequency of the zero quantum precession directly because the coherence transfer, required to observe this precession, is modulated by Torrey oscillations.22 Therefore, it was proposed to perform a delayed nutation experiment, in which the zero quantum coherence is allowed to evolve freely during a variable time period after the laser pulse.22 However, such an experiment, posing considerable technical problems associated with the rapid switching of the microwaves, has not yet been reported. Detection of quantum beats for the light-induced radical pairs in photosynthetic systems provides unambiguous confirmation of the applicability of the correlated radical pair mechanism.83.1I,16,17
The Journal of Physical Chemistry, Vol. 98. No. IO. 1994 2711
Spin-Correlated Radical Pairs
TABLE 1: Parameters Used in the Calculation of Transient EPR Experiments of the Light-Induced Radical Pairs P,w+Al- in Deuterated Plant Photosystem 1 g tensors'
PiW+
AI-
4 . 2 . 0 0 3 04 g 2 on2 62 i o n 2 32
$,2.005 64 g ,2.on4 94 g?,2.002 17
2
geometr
hyperfine interactions
1 ps Tz,500 ns
T,
microwave field o,9.8562 GHz B1,0.03 mT
Data from high-field EPR s t ~ d i e s . 4 ~Estimated *~~ on the basis of a low-resolution X-ray str~cture.'~Data from pulsed EPR and ENDOR s t u d i e ~ . ~Evaluated ?~~ from the BOdependence of the initial oscillations.46 The lifetime T and the relaxation times TIand Tz of the radical pair have been determined from the BI dependence of the time profiles.I2 Inhomogeneous broadening is considered by convolution with a Gaussian of line width A B 0 = 0.125 mT.4J0 @
frequency being equal to the difference in energies of two of the eigenstates of the radical pair. Thorough investigation of this coherence allows a more detailed characterization of the shortlived intermediates of bacterial and plant photosynthesis.
4
Acknowledgment. Financial support by the US.Department of Energy, Office of Basic Energy Sciences,Division of Chemical Sciences (Contract W-31-109-ENG-38) and by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. J.R.N. greatly acknowledges support from the Humboldt foundation. E"
Figure 6. Energy level diagram for a spin-correlatedradical pair, created in the singlet state. Full arrows: single quantum coherences. Curly arrow: Zero quantum coherence. tl = energy of eigenstate i.
Moreover, analysis of the beat frequencies provides a direct measurement of a number of important magnetic and structural parameters. In Figure 3 we compare experimental and calculated time profiles for the secondary radical pair, P,w+Al-. Generally, the agreement between observed and simulated transients is good. In particular, the initial oscillatory behavior is faithfully reproduced by the calculations. Notice that all time profiles start out with a horizontal slope. Then, amplitude and phase vary depending on the field position. Finally, 130 ns after the laser pulse all coherent oscillations are averaged by residual hyperfine interactions in the fully deuterated sample. This result shows that high time resolution is required for a successful EPR detection of zero quantum coherence. Two-Dimensional Spectra. The Occurrence of zero quantum precessions is immediately apparent from a two-dimensional representation of the transient EPR experiment. Figure 4a shows the Fourier transform of the time profiles as a function of gPBo/h for P700+AI-.The modulus of the complex Fourier transform is plotted with contours 5% of the maximum amplitude. Basically, two distinct contributions can be distinguished in the 02 domain: Isotropic Torrey oscillations at g@Bl/h= 1 MHz and anisotropiczero quantumprecessionr, modulated by transient nutations.22 Note that precession frequencies up to 24 MHz can be extracted from the contour plot. The pronounced variation of the precession frequencies across the powder spectrum (00 dimension) has been used to evaluate the geometry of the underlying radical pair.4 Figure 4b shows a best-fit simulation of the two-dimensional experiment using the parameters of Table 1. Generally, a good agreement is achieved between the experimental and calculated contour plot.
Apparently, analysis of zero quantum precessions as a function of the external field can provide detailed information on the spatial arrangement of the radicals in a spin-correlated pair.
Conclusion Using high time resolution transient EPR we have been able to detect signals from the zero quantum coherence of spincorrelated radical pairs generated by pulsed laser excitation of a photosynthetic system. Compared to Torrey oscillations, the zero quantum coherence provides more direct information, its
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