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Triplet spin dynamics of bacteriochlorophyll-a from transient EPR lineshape analysis
Volume 113, number 2
CHEMICAL PHYSICS LETTERS
11 January 1985
TRIPLET SPIN DYNAMICS OF BACTERIOCHLOROPHYLL-a FROM TRANSIENT EPR LINESHAPE ANALYSIS ~ Oded GONEN 1, Ayelet REGEV 2 , Haim LEVANON Department of Physical Chemistry, and the Fritz Haber Research Center for Molecular Dynamics 3, The Hebrew University, Jerusalem 91904, Israel Marion C. T H U R N A U E R Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, USA James 1L NORRIS and Gerhard L. CLOSS Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, USA and Department of Chemistry, University o f Chicago, Chicago, Illinois 60637, USA Received 5 November 1984
A study of the transient photoexcited triplet of bacteriochlorophyll-ain a glass matrix at 60 K utilizing light modulation EPR spectroscopy is reported. In view of widely deviating results for the triplet sublevel depopulation rates, this problem was engaged via EPR lineshape analysis rather than direct kinetic measurements. This method also yields the relative population and spin-lattice relaxation rates.
1. Introduction Magnetic resonance techniques play an important role in probing the processes which occur during the primary events in photosynthesis [ 1 - 3 ] . Much o f the information gained from studying the triplet state of the primary electron donor which can be observed in in vivo bacterial photosynthetic systems has come from comparison of the magnetic properties of the triplet state of the in vitro system at low temperatures This research was supported by the Israel Academy for Sciences and Humanities (HL) and the US-Israel BSF (HL), US-DOE Contract Numbers W31 109 ENG-38 (Argonne), and National Science Foundation CHE 821 8164 (University of Chicago). 1 In partial fulfillment of the requirements for a Ph.D. degree at the Hebrew University of Jerusalem. 2 In partial fulfillment of the requirements for an M.Sc. degree at the Hebrew University of Jerusalem. 3 The Fritz Haber Research Center is supported by the Minerva GeseUschaft for die F/Srschung, GmbH, Munich, FRG.
in solid matrices [ 2 - 6 ] . Those systems have been studied by both EPR spectroscopy [4,6] and various variants of the optical detection of magnetic resonance (ODMR) techniques [1,5,7]. The properties of interest are the magnitude (and signs) of the zero-field splitting (ZFS) parameters and the dynamics of the population, depopulation and relaxation o f the triplet sublevels. A useful approach has been to apply triplet information obtained from in vitro preparations to the complex in vivo systems utilizing the time scale and orientational sensitivity of magnetic resonance techniques to probe electron and energy transfer together with the structure o f the primary electron donor [2,3,
5]. Recently, a kinetic study employing absorbancedetected magnetic resonance (ADMR) o f the triplet sublevel decay has been published [1]. The decay rate constants found in this pulsed method are significantly faster than those known before for in vitro BChl-a utilizing cw ODMR [7]. Comparing the two results mentioned above yields a discrepancy o f a factor o f 5 117
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between the depopulation rates. In an attempt to resolve this disagreement we engage the problem in a method differing both in experimental technique and theoretical approach. This work describes a light modulation EPR study of photoexcited spin polarized triplet state of BChl-a in solid solution at moderately low temperature. This experimental method has the advantage of applicability at temperatures higher than the ~ 2 K required for ODMR and may be viewed as a bridge between the entirely steady-state measurement and the fast timeresolved work. In accordance with a lineshape analysis model developed recently [8] we determine the complete triplet spin dynamics of BChl-a in vitro from the EPR triplet spectrum without performing any EPR kinetic measurements.
2. Experimental BChl-a was prepared by a method described previously [2]. The samples, ~ 1 0 3 M BChl-a dissolved in toluene with a trace of pyridine (to ensure producing monomeric species), were degassed and sealed under vacuum in 4 mm outer diameter pyrex tubes. Laser photolysis experiments have been carried out on frozen solution of Bchl-a (6.8 X 10 - 6 M)dissolved in toluene :ethanol (1 : 1) at 138 K. This solvent composition and experimental temperature were chosen to mainrain a clear glass, essential to this optical experiment. The basic computer-controlled laser photolysis apparatus is similar to that described elsewhere [9]. In this study however, we have utilized the Tektronix unit (7912AD programmable digitizer and 4052 Tektronix computer) to control the experiment. The pumping light source was the second harmonic (X = 532 rim) of a N d - Y a g laser (Quanta Ray DCR- 1A). The EPR spectrometer used was a Varian E- 12, the cryostat was an Air-Products Helitran LTD-3-110, which maintained a temperature of 60 K. Photoexcitation was by xenon arc (Eimac 150 W) electronically modulated at 500 Hz with rise time o f ~ 5 0 / I s . The EPR signal from the 100 kHz lock in amplifier was fed into a second phase sensitive detector in reference with the light modulation frequency. A detailed description of the light excitation and signal detection is given elsewhere [ 10]. The exciting light was passed through a 5 cm water cell and a Coming 3-73 cut-off filter 118
11 January 1985
(~pass > 390 nm). The experimental results were digitized by a Nicolet Explorer III-A digital oscilloscope interfaced to a microcomputer on-line with the experiment, and processed off-line on a VAX 11/750. Lineshape analysis was carried out on the digitized spectra using the IMSL package subroutine ZXMWD (global minimum of a function of N parameters with constraints).
3. Theory The expression for the EPR triplet lineshape of a randomly distributed sample away from thermal equilibrium is given in a parametric form [8]: rrl2 lrt2
I(B) o: ~ f i=1,2 0 /=i+l
f
pi/(O, qs) Tij(O,q5) sinOdOdqS,
0
(1)
where 0, q5 are the usual angles the external magnetic fieldB make with the molecular axes, Pi/(O, O) is the transition probability between levels] ~ i and Ti/(0, ~b) is the time-averaged population difference between adjacent levels after the creation of the triplet. The summation is over the two possible transitions and because of the symmetry the integration is carried over one octant of space. The transition probability Pij (0, qs) is a function of the ZFS parameters ID I and IE] and the linewidth 1/T2. In our experiment the light driving the system is modulated at a frequency coL and the EPR spectrum is the first harmonic component obtained via a second phase sensitive detector with respect to coL' Therefore, after time averaging the population difference along the canonical orientations p = (OliN, Y, Z) becomes [6,8]: - f2)-- ~-
t(pKT'l
cos(q~+-- ~ ) ]
t(pKT"~
I(5 TP3=c//tT
J 4(co~LL+X~)I/~2
(f2
ap t~pKT"~
J~;)+~--~
cos(q5 -- g') 4(002 + ~2_)1/2
] 4( 2+ -2+1w2 cos(qs+ -- xI,)
(2)
where the fi reflect the thermal populations, ,I, is the
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detector phase angle, X_+ are the two rate constants associated with the population and depopulation of a certain sublevel, W is the s p i n - l a t t i c e relaxation rate (assumed equal for all intersublevel transitions * and q~+ are defmed by tan G_ = --COL/X+_ -
(3)
In a high magnetic field the population and depopulation rates of the lower and upper sublevels are equal an and will be designated A 1 and k l , respectively; the rate constant o f the middle level will likewise be A 0 and k 0. Thus the population and depopulation rates are given by _1
K T = l ( 2 k l + k0),
A T-g(2A 1 +A0),
KKT = k 1 - k 0 ,
- 3 ~
o.AT = A 1 - A 0 ,
-
(4)
l<~a<~l/2.
At the canonical orientations O~p and Kp also obey the requirements [6,8] ~O~p = 0
GKp =0,
and
p=(BIIX,
Y,Z), (5)
and the kinetic parameters for the population Ap/A T and depopulation kp at zero field are obtained via the relations [6,8]
Ap=~-(1-2O~p)AT
and
kp=~(3-2Kp)K T .
11 January 1985
be possible and the kinetic parameters should be extractable from the light modulated cw EPR spectr~
4. Results and discussion
The experimental BChl-a EPR triplet spectra are given in fig. 1. These spectra are shown together with the simulated curves calculated from eq. (1) using best fit parameters obtained by numerical optimization as described below. The parameters needed to simulate those spectra fall into three categories: (a) The Pi/(O, ¢) term: it incorporates the ZFS splittings parameters IDI and [El which are extracted directly from the spectrum, and the linewidth ( l / T 2 ) obtained by the simulation. (b) Instrumental parameters: temperature, light modulation frequency w L and the detector phase angle ,I~. The first two are determined directly off the instruments, the phase however, is arbitrary in the sense that only phase differences can be measured, their absolute values are determined b y optimization of eq. (1). (c) Triplet dynamics parameters: •p, ap, W, KT,
I
T
v
I
x;x,',, v
v
v
(6)
X+ and X_ are given by X_ = K T ,
~,+ = K T + 3W.
(7)
The general population difference at any given orientation Tij(O, ¢) is a weighted sum of the canonical population differences between a pair o f levels when the high external magnetic field is directed along one o f the canonical orientations X, Y, Z [8]:
Ti/(O' ¢) : / X 1 2
+
T'Y'm2i/+ ~/j n2 ,
"ID
\
"1:3
(8)
where l, rn, n aie the direction cosines B makes with the molecular axes. Eq. (8) enables the application o f the kinetic information obtained at the six canonical orientations to the whole spectral range [8]. It is evident therefore, that the reverse procedure should also * In this treatment we do not include the double quantum relaxation T_+induced by the dipole mechanism. However, in the high field approximation as reflected in the present study, this transition may not enter the calculation because those two subleveis are populated with equal rates.
3000 3200 3400 3600 Magnetic Field (Gauss) Fig. 1. EPR triplet spectra of Bchl-a at 60 K (differing only in relative instrumental phase) at exciting light modulation frequency of 500 Hz, microwave power of 1.5 mW and modulation amplitude of 32 G. The smooth line superimposed on the each trace is a computer simulation using eq. (I) with the parameters in table 1 and 1/1"2 of 8 G. The true phase of each simulation is indicated on the trace. 119
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which are determined by the optimization. Altogether there are nine parameters sought for by the optimization procedure. These are three sublevel population and three depopulation rates (Ap, kp), the s p i n - l a t t i c e relaxation rate W, the total triplet decay rate K T and the phase angle xp. In the general case o f simulating an experimental spectrum it is possible to construct eight independent equations to solve for them; these are the six line intensities at the canonical fields and eq. (5). It is therefore necessary for one parameter to be known a priori for a unique solution. The chosen parameter is the total triplet decay rate K T which can be obtained by different measurement techniques. In fact, K y was measured independently by laser photolysis at 138 K. The differential t r i p l e t triplet absorption spectrum, 46 ~ts after the laser pulse, is shown in fig. 2 and a typical first-order triplet decay curve at 495 nm is also presented (insert). Qualitatively, the spectrum is in line with that reported previously in pyridine at room temperature [11] and the calculated first-order decay rate K T = 4400 s -1 was used in the EPR lineshape analysis. To solve for these eight unknown parameters a minimum o f the sum o f squares of the differences between the intensities o f an experimental and the calculated (via eq. (1)) spectra is required. However, from (8) it is clear that the whole EPR triplet spectrum is a 1.0
t-',, k_ 0 0') J~
Time
÷+ 4- ÷÷ ++
._> ÷
÷÷÷
÷ ÷ ÷ ÷
÷÷
÷ ÷
÷
0.0 400
500
600
700
)',(rim)
Fig. 2. Differential triplet-triplet absorption spectrum of Bchla (6.8 X 10 -6 M) in a glass matrix (ethanol : toluene) at 138 K. Insert is the absorption decay of Bchl-aT at 495 nm, the smooth curve superimposed on the experimental points is a first-order decay simulation with a rate of 4400 s- 1. Laser photoexcitation is at 530 rim. 120
manifestation of the information found in the six canonical fields by substituting (2) into (8) and back into eq. (1). It is therefore sufficient to optimize for these six intensity differences, via
m i n (\canonical C (Intexp - Int(parameters)calc.)2). (9) fields The optimization is subject to constraints inherent to the nature o f the desired parameters namely: (a) The s p i n - l a t t i c e relaxation rate W is a bound parameter in the range [0... 105 s-1]. The upper limit was chosen in accordance with known values of similar molecules, e.g. chlorophylls and porphyrins [2,3]. (b) The three depopulation rate parameters np are reduced to two via eq. (5). Choosing arbitrarily to optimize for KX and ~ y eq. (4) translates into: - 3 ~< Kx ~< 3 / 2 , m a x ( - 3 - KX, - 3 ) ~< •y ~< rain(3/2 - Kx, 3/2).
(10)
This is due to the need to accommodate KZ = -(K X + Ky ) into eq. (4). (c) Population rate parameters ap. Similar to the K treatment above we get:
- 1 <~aX <~ 1/2, m a x ( - 1 - e¢x, - 1 ) <~ay <~ min(1/2 - e¢x , 1/2).
m
o
n'-
11 January 1985
(11)
Again due to the need to accommodate c~Z -- - ( a X + a y ) into eq. (4). (d) The phase angle q~ is bound in [0...360°]. In the actual calculation, two spectra (differing only by a known phase shift) are optimized simultaneously, thus effectively eight parameters are extracted from fourteen equations. In our case, this procedure was carried out on two such pairs both of which converged to the same parameter values. Fig. 1. shows the traces resulting from the simulation via eq. (1), based on the best fit parameters obtained from the optimization of eq. (9)(see table 1). Superimposed on the simulated traces are the experimental spectra which absolute phases were computed from the offset between the relative value given by the instrument and the value given by the optimization. The expression for the line intensities at the canonical orientations eq. (2) clearly indicates a strong depen-
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CHEMICAL PHYSICS LETTERS
?
~x
05 ..=
+I
+I
+i
! t'-q tt'> '~" +I
¢~
0 rm
+I
+I
11 January 1985
dence on the light modulation frequency CoL. Inspection of the experimental curves in fig. 1 shows that changing the detector phase angle by zr/2 (from the optimal phase of a certain fine) does not suppress the complete spectrum but rather affects simultaneously only a pair of lines of a particular orientation. This implies that although CoL, 500 Hz in our experiment, does not satisfy CoL >~ I/KT (needed for all fines to have the same zr/2 phase difference with the driving light), it is still fast enough to eliminate phase shifts between the transitions within a particular orientation. Since W, as obtained from the simulation, is not negligible at this temperature then its substitution in eq. (3) yields )t+ >> k_ and consequently ~+ "~ ~ . Therefore, there is no experimental value o f ' I ' in eq. (2) that will make all six amplitudes at the canonical fields vanish simultaneously at this coL . The triplet sublevels decay rates obtained from the lineshape analysis are given in table 1. These values correspond t o K y of 4400 s -1, lying among 10 × 103 [1], 2.1 X 103 [7], and 3.3 X 103 s -1 [12] obtained previously by independent methods. Such discrepancy may be due to different ligation states of Bchl-a in the sample affecting both the triplet lifetime and the ZFS factors. Indeed, Blanken and Hoff [ 1] report a significant dependence o f k X and k y on the polarity of the solvent whereas k Z they note is independent of such effects, consistent with the result obtained here for this rate (see table 1). Nevertheless, it should be pointed out that the simulation analysis described above, by employing the kinetic parameters (KT) obtained by Blanken and Hoff [1], could not simulate the experimental cw spectra• On the other hand, the values of Clarke et al. [7] enable quite easily such a reconstruction. The former case is to be anticipated, because ?t+, X >~ COL thus ~b+ ~ ~b_ (eq. (3)) and there should exist a xI, that can suppress the whole spectrum, in contradiction with the experimental results (fig. 1). Since no EPR kinetic measurements are performed in this method the dynamic parameters are purely computer obtained results by numeric~l analysis. The accuracy therefore cannot be judged from the instrumental measurements but is assessed from the residual sum of squares from eq. (9) to be -+20% versus 5 - 1 0 % in the direct methods for the determination of the depopulation rates [ 1,7]. However, comparing these results with those reported in the past, reveals that the trend k y ~ k X ~ k Z for BChl-a is common to all methods. In conclusion this study demonstrates the ability 121
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to d e t e r m i n e the c o m p l e t e triplet sublevel spin dynamics f r o m E P R o b t a i n e d by the relatively slow light m o d u l a t i o n E P R spectroscopy w i t h o u t the need to carry out elaborate kinetic measurements.
Acknowledgement We are grateful to Professor R.W. Fessenden (Radiat i o n L a b o r a t o r y , University o f N o t r e D a m e ) for programming the c o m p u t e r - c o n t r o l l e d laser photolysis during his visit to Jerusalem under the Lady Davis Program.
References [1 ] H.J. Blanken and A.J. Hoff, Chem. Phys. Letters 96 (1983) 343. [2] M.C. Thurnauer, Rev. Chem. Intern. 3 (1979) 197. [3] H. Levanon and J.R. Norris, Chem. Rev. 18 (1978) 185; in: Molecular biology and biophysics, Vol 35. Light reaction path of photosynthesis, ed. F.K. Fong (Springer, Berlin, 1982) pp. 155-195.
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[4] M.C. Thttrnauer, J.J. Katz, and J.R. Norris. Proc. Natl. Acad. Sci. US 72 (1975) 3270. [5 ] R.H. Clarke, R.E. Cormors, T.J. Schaafsma, J.F. Kleibeuker and R.J. Platenkamp, J. Am. Chem. Soc. 98 (1976) 523. [6] H. Levanon and S. Vega, J. Chem. Phys. 61 (1974) 2265. [7] R.H. Clarke, R.E. Connors and H.A. Franck, Biochem. Biophys. Res. Commun. 71 (1976) 671; R.H. Clarke, R.E. Connors, H.A. Frank and J.C. Hoch, Chem. Phys. Letters 45 (1977) 523. [8] O. Gonen and H. Levanon, J. Phys. Chem. 88 (1984), to be published. [9] P.K. Das and S.N. Bhattacharyya, J. Phys. Chem. 85 (1981) 1391. [10 ] H. Levanon, in: Multiple electronic resonance, eds. M. Dorio and J.H. Freed (Plenum Press, New York. 1979) ch. 13. [11] L. Pekkarinen and H. Linschitz, J. Am. Chem. Soc. 82 (1960) 2407. [12] J.F. Kleibeuker and T.J. Schaafsma, Chem. Phys. Letters 29 (1974) 116; J.F. Kleibeuker, R.J. Platenkamp and T.J. Schaafsma, Chem. Phys. 27 (1978) 51.
CHEMICAL PHYSICS LETTERS
11 January 1985
TRIPLET SPIN DYNAMICS OF BACTERIOCHLOROPHYLL-a FROM TRANSIENT EPR LINESHAPE ANALYSIS ~ Oded GONEN 1, Ayelet REGEV 2 , Haim LEVANON Department of Physical Chemistry, and the Fritz Haber Research Center for Molecular Dynamics 3, The Hebrew University, Jerusalem 91904, Israel Marion C. T H U R N A U E R Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, USA James 1L NORRIS and Gerhard L. CLOSS Chemistry Division, Argonne National Laboratory, Argonne, Illinois 60439, USA and Department of Chemistry, University o f Chicago, Chicago, Illinois 60637, USA Received 5 November 1984
A study of the transient photoexcited triplet of bacteriochlorophyll-ain a glass matrix at 60 K utilizing light modulation EPR spectroscopy is reported. In view of widely deviating results for the triplet sublevel depopulation rates, this problem was engaged via EPR lineshape analysis rather than direct kinetic measurements. This method also yields the relative population and spin-lattice relaxation rates.
1. Introduction Magnetic resonance techniques play an important role in probing the processes which occur during the primary events in photosynthesis [ 1 - 3 ] . Much o f the information gained from studying the triplet state of the primary electron donor which can be observed in in vivo bacterial photosynthetic systems has come from comparison of the magnetic properties of the triplet state of the in vitro system at low temperatures This research was supported by the Israel Academy for Sciences and Humanities (HL) and the US-Israel BSF (HL), US-DOE Contract Numbers W31 109 ENG-38 (Argonne), and National Science Foundation CHE 821 8164 (University of Chicago). 1 In partial fulfillment of the requirements for a Ph.D. degree at the Hebrew University of Jerusalem. 2 In partial fulfillment of the requirements for an M.Sc. degree at the Hebrew University of Jerusalem. 3 The Fritz Haber Research Center is supported by the Minerva GeseUschaft for die F/Srschung, GmbH, Munich, FRG.
in solid matrices [ 2 - 6 ] . Those systems have been studied by both EPR spectroscopy [4,6] and various variants of the optical detection of magnetic resonance (ODMR) techniques [1,5,7]. The properties of interest are the magnitude (and signs) of the zero-field splitting (ZFS) parameters and the dynamics of the population, depopulation and relaxation o f the triplet sublevels. A useful approach has been to apply triplet information obtained from in vitro preparations to the complex in vivo systems utilizing the time scale and orientational sensitivity of magnetic resonance techniques to probe electron and energy transfer together with the structure o f the primary electron donor [2,3,
5]. Recently, a kinetic study employing absorbancedetected magnetic resonance (ADMR) o f the triplet sublevel decay has been published [1]. The decay rate constants found in this pulsed method are significantly faster than those known before for in vitro BChl-a utilizing cw ODMR [7]. Comparing the two results mentioned above yields a discrepancy o f a factor o f 5 117
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between the depopulation rates. In an attempt to resolve this disagreement we engage the problem in a method differing both in experimental technique and theoretical approach. This work describes a light modulation EPR study of photoexcited spin polarized triplet state of BChl-a in solid solution at moderately low temperature. This experimental method has the advantage of applicability at temperatures higher than the ~ 2 K required for ODMR and may be viewed as a bridge between the entirely steady-state measurement and the fast timeresolved work. In accordance with a lineshape analysis model developed recently [8] we determine the complete triplet spin dynamics of BChl-a in vitro from the EPR triplet spectrum without performing any EPR kinetic measurements.
2. Experimental BChl-a was prepared by a method described previously [2]. The samples, ~ 1 0 3 M BChl-a dissolved in toluene with a trace of pyridine (to ensure producing monomeric species), were degassed and sealed under vacuum in 4 mm outer diameter pyrex tubes. Laser photolysis experiments have been carried out on frozen solution of Bchl-a (6.8 X 10 - 6 M)dissolved in toluene :ethanol (1 : 1) at 138 K. This solvent composition and experimental temperature were chosen to mainrain a clear glass, essential to this optical experiment. The basic computer-controlled laser photolysis apparatus is similar to that described elsewhere [9]. In this study however, we have utilized the Tektronix unit (7912AD programmable digitizer and 4052 Tektronix computer) to control the experiment. The pumping light source was the second harmonic (X = 532 rim) of a N d - Y a g laser (Quanta Ray DCR- 1A). The EPR spectrometer used was a Varian E- 12, the cryostat was an Air-Products Helitran LTD-3-110, which maintained a temperature of 60 K. Photoexcitation was by xenon arc (Eimac 150 W) electronically modulated at 500 Hz with rise time o f ~ 5 0 / I s . The EPR signal from the 100 kHz lock in amplifier was fed into a second phase sensitive detector in reference with the light modulation frequency. A detailed description of the light excitation and signal detection is given elsewhere [ 10]. The exciting light was passed through a 5 cm water cell and a Coming 3-73 cut-off filter 118
11 January 1985
(~pass > 390 nm). The experimental results were digitized by a Nicolet Explorer III-A digital oscilloscope interfaced to a microcomputer on-line with the experiment, and processed off-line on a VAX 11/750. Lineshape analysis was carried out on the digitized spectra using the IMSL package subroutine ZXMWD (global minimum of a function of N parameters with constraints).
3. Theory The expression for the EPR triplet lineshape of a randomly distributed sample away from thermal equilibrium is given in a parametric form [8]: rrl2 lrt2
I(B) o: ~ f i=1,2 0 /=i+l
f
pi/(O, qs) Tij(O,q5) sinOdOdqS,
0
(1)
where 0, q5 are the usual angles the external magnetic fieldB make with the molecular axes, Pi/(O, O) is the transition probability between levels] ~ i and Ti/(0, ~b) is the time-averaged population difference between adjacent levels after the creation of the triplet. The summation is over the two possible transitions and because of the symmetry the integration is carried over one octant of space. The transition probability Pij (0, qs) is a function of the ZFS parameters ID I and IE] and the linewidth 1/T2. In our experiment the light driving the system is modulated at a frequency coL and the EPR spectrum is the first harmonic component obtained via a second phase sensitive detector with respect to coL' Therefore, after time averaging the population difference along the canonical orientations p = (OliN, Y, Z) becomes [6,8]: - f2)-- ~-
t(pKT'l
cos(q~+-- ~ ) ]
t(pKT"~
I(5 TP3=c//tT
J 4(co~LL+X~)I/~2
(f2
ap t~pKT"~
J~;)+~--~
cos(q5 -- g') 4(002 + ~2_)1/2
] 4( 2+ -2+1w2 cos(qs+ -- xI,)
(2)
where the fi reflect the thermal populations, ,I, is the
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detector phase angle, X_+ are the two rate constants associated with the population and depopulation of a certain sublevel, W is the s p i n - l a t t i c e relaxation rate (assumed equal for all intersublevel transitions * and q~+ are defmed by tan G_ = --COL/X+_ -
(3)
In a high magnetic field the population and depopulation rates of the lower and upper sublevels are equal an and will be designated A 1 and k l , respectively; the rate constant o f the middle level will likewise be A 0 and k 0. Thus the population and depopulation rates are given by _1
K T = l ( 2 k l + k0),
A T-g(2A 1 +A0),
KKT = k 1 - k 0 ,
- 3 ~
o.AT = A 1 - A 0 ,
-
(4)
l<~a<~l/2.
At the canonical orientations O~p and Kp also obey the requirements [6,8] ~O~p = 0
GKp =0,
and
p=(BIIX,
Y,Z), (5)
and the kinetic parameters for the population Ap/A T and depopulation kp at zero field are obtained via the relations [6,8]
Ap=~-(1-2O~p)AT
and
kp=~(3-2Kp)K T .
11 January 1985
be possible and the kinetic parameters should be extractable from the light modulated cw EPR spectr~
4. Results and discussion
The experimental BChl-a EPR triplet spectra are given in fig. 1. These spectra are shown together with the simulated curves calculated from eq. (1) using best fit parameters obtained by numerical optimization as described below. The parameters needed to simulate those spectra fall into three categories: (a) The Pi/(O, ¢) term: it incorporates the ZFS splittings parameters IDI and [El which are extracted directly from the spectrum, and the linewidth ( l / T 2 ) obtained by the simulation. (b) Instrumental parameters: temperature, light modulation frequency w L and the detector phase angle ,I~. The first two are determined directly off the instruments, the phase however, is arbitrary in the sense that only phase differences can be measured, their absolute values are determined b y optimization of eq. (1). (c) Triplet dynamics parameters: •p, ap, W, KT,
I
T
v
I
x;x,',, v
v
v
(6)
X+ and X_ are given by X_ = K T ,
~,+ = K T + 3W.
(7)
The general population difference at any given orientation Tij(O, ¢) is a weighted sum of the canonical population differences between a pair o f levels when the high external magnetic field is directed along one o f the canonical orientations X, Y, Z [8]:
Ti/(O' ¢) : / X 1 2
+
T'Y'm2i/+ ~/j n2 ,
"ID
\
"1:3
(8)
where l, rn, n aie the direction cosines B makes with the molecular axes. Eq. (8) enables the application o f the kinetic information obtained at the six canonical orientations to the whole spectral range [8]. It is evident therefore, that the reverse procedure should also * In this treatment we do not include the double quantum relaxation T_+induced by the dipole mechanism. However, in the high field approximation as reflected in the present study, this transition may not enter the calculation because those two subleveis are populated with equal rates.
3000 3200 3400 3600 Magnetic Field (Gauss) Fig. 1. EPR triplet spectra of Bchl-a at 60 K (differing only in relative instrumental phase) at exciting light modulation frequency of 500 Hz, microwave power of 1.5 mW and modulation amplitude of 32 G. The smooth line superimposed on the each trace is a computer simulation using eq. (I) with the parameters in table 1 and 1/1"2 of 8 G. The true phase of each simulation is indicated on the trace. 119
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which are determined by the optimization. Altogether there are nine parameters sought for by the optimization procedure. These are three sublevel population and three depopulation rates (Ap, kp), the s p i n - l a t t i c e relaxation rate W, the total triplet decay rate K T and the phase angle xp. In the general case o f simulating an experimental spectrum it is possible to construct eight independent equations to solve for them; these are the six line intensities at the canonical fields and eq. (5). It is therefore necessary for one parameter to be known a priori for a unique solution. The chosen parameter is the total triplet decay rate K T which can be obtained by different measurement techniques. In fact, K y was measured independently by laser photolysis at 138 K. The differential t r i p l e t triplet absorption spectrum, 46 ~ts after the laser pulse, is shown in fig. 2 and a typical first-order triplet decay curve at 495 nm is also presented (insert). Qualitatively, the spectrum is in line with that reported previously in pyridine at room temperature [11] and the calculated first-order decay rate K T = 4400 s -1 was used in the EPR lineshape analysis. To solve for these eight unknown parameters a minimum o f the sum o f squares of the differences between the intensities o f an experimental and the calculated (via eq. (1)) spectra is required. However, from (8) it is clear that the whole EPR triplet spectrum is a 1.0
t-',, k_ 0 0') J~
Time
÷+ 4- ÷÷ ++
._> ÷
÷÷÷
÷ ÷ ÷ ÷
÷÷
÷ ÷
÷
0.0 400
500
600
700
)',(rim)
Fig. 2. Differential triplet-triplet absorption spectrum of Bchla (6.8 X 10 -6 M) in a glass matrix (ethanol : toluene) at 138 K. Insert is the absorption decay of Bchl-aT at 495 nm, the smooth curve superimposed on the experimental points is a first-order decay simulation with a rate of 4400 s- 1. Laser photoexcitation is at 530 rim. 120
manifestation of the information found in the six canonical fields by substituting (2) into (8) and back into eq. (1). It is therefore sufficient to optimize for these six intensity differences, via
m i n (\canonical C (Intexp - Int(parameters)calc.)2). (9) fields The optimization is subject to constraints inherent to the nature o f the desired parameters namely: (a) The s p i n - l a t t i c e relaxation rate W is a bound parameter in the range [0... 105 s-1]. The upper limit was chosen in accordance with known values of similar molecules, e.g. chlorophylls and porphyrins [2,3]. (b) The three depopulation rate parameters np are reduced to two via eq. (5). Choosing arbitrarily to optimize for KX and ~ y eq. (4) translates into: - 3 ~< Kx ~< 3 / 2 , m a x ( - 3 - KX, - 3 ) ~< •y ~< rain(3/2 - Kx, 3/2).
(10)
This is due to the need to accommodate KZ = -(K X + Ky ) into eq. (4). (c) Population rate parameters ap. Similar to the K treatment above we get:
- 1 <~aX <~ 1/2, m a x ( - 1 - e¢x, - 1 ) <~ay <~ min(1/2 - e¢x , 1/2).
m
o
n'-
11 January 1985
(11)
Again due to the need to accommodate c~Z -- - ( a X + a y ) into eq. (4). (d) The phase angle q~ is bound in [0...360°]. In the actual calculation, two spectra (differing only by a known phase shift) are optimized simultaneously, thus effectively eight parameters are extracted from fourteen equations. In our case, this procedure was carried out on two such pairs both of which converged to the same parameter values. Fig. 1. shows the traces resulting from the simulation via eq. (1), based on the best fit parameters obtained from the optimization of eq. (9)(see table 1). Superimposed on the simulated traces are the experimental spectra which absolute phases were computed from the offset between the relative value given by the instrument and the value given by the optimization. The expression for the line intensities at the canonical orientations eq. (2) clearly indicates a strong depen-
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?
~x
05 ..=
+I
+I
+i
! t'-q tt'> '~" +I
¢~
0 rm
+I
+I
11 January 1985
dence on the light modulation frequency CoL. Inspection of the experimental curves in fig. 1 shows that changing the detector phase angle by zr/2 (from the optimal phase of a certain fine) does not suppress the complete spectrum but rather affects simultaneously only a pair of lines of a particular orientation. This implies that although CoL, 500 Hz in our experiment, does not satisfy CoL >~ I/KT (needed for all fines to have the same zr/2 phase difference with the driving light), it is still fast enough to eliminate phase shifts between the transitions within a particular orientation. Since W, as obtained from the simulation, is not negligible at this temperature then its substitution in eq. (3) yields )t+ >> k_ and consequently ~+ "~ ~ . Therefore, there is no experimental value o f ' I ' in eq. (2) that will make all six amplitudes at the canonical fields vanish simultaneously at this coL . The triplet sublevels decay rates obtained from the lineshape analysis are given in table 1. These values correspond t o K y of 4400 s -1, lying among 10 × 103 [1], 2.1 X 103 [7], and 3.3 X 103 s -1 [12] obtained previously by independent methods. Such discrepancy may be due to different ligation states of Bchl-a in the sample affecting both the triplet lifetime and the ZFS factors. Indeed, Blanken and Hoff [ 1] report a significant dependence o f k X and k y on the polarity of the solvent whereas k Z they note is independent of such effects, consistent with the result obtained here for this rate (see table 1). Nevertheless, it should be pointed out that the simulation analysis described above, by employing the kinetic parameters (KT) obtained by Blanken and Hoff [1], could not simulate the experimental cw spectra• On the other hand, the values of Clarke et al. [7] enable quite easily such a reconstruction. The former case is to be anticipated, because ?t+, X >~ COL thus ~b+ ~ ~b_ (eq. (3)) and there should exist a xI, that can suppress the whole spectrum, in contradiction with the experimental results (fig. 1). Since no EPR kinetic measurements are performed in this method the dynamic parameters are purely computer obtained results by numeric~l analysis. The accuracy therefore cannot be judged from the instrumental measurements but is assessed from the residual sum of squares from eq. (9) to be -+20% versus 5 - 1 0 % in the direct methods for the determination of the depopulation rates [ 1,7]. However, comparing these results with those reported in the past, reveals that the trend k y ~ k X ~ k Z for BChl-a is common to all methods. In conclusion this study demonstrates the ability 121
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to d e t e r m i n e the c o m p l e t e triplet sublevel spin dynamics f r o m E P R o b t a i n e d by the relatively slow light m o d u l a t i o n E P R spectroscopy w i t h o u t the need to carry out elaborate kinetic measurements.
Acknowledgement We are grateful to Professor R.W. Fessenden (Radiat i o n L a b o r a t o r y , University o f N o t r e D a m e ) for programming the c o m p u t e r - c o n t r o l l e d laser photolysis during his visit to Jerusalem under the Lady Davis Program.
References [1 ] H.J. Blanken and A.J. Hoff, Chem. Phys. Letters 96 (1983) 343. [2] M.C. Thurnauer, Rev. Chem. Intern. 3 (1979) 197. [3] H. Levanon and J.R. Norris, Chem. Rev. 18 (1978) 185; in: Molecular biology and biophysics, Vol 35. Light reaction path of photosynthesis, ed. F.K. Fong (Springer, Berlin, 1982) pp. 155-195.
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[4] M.C. Thttrnauer, J.J. Katz, and J.R. Norris. Proc. Natl. Acad. Sci. US 72 (1975) 3270. [5 ] R.H. Clarke, R.E. Cormors, T.J. Schaafsma, J.F. Kleibeuker and R.J. Platenkamp, J. Am. Chem. Soc. 98 (1976) 523. [6] H. Levanon and S. Vega, J. Chem. Phys. 61 (1974) 2265. [7] R.H. Clarke, R.E. Connors and H.A. Franck, Biochem. Biophys. Res. Commun. 71 (1976) 671; R.H. Clarke, R.E. Connors, H.A. Frank and J.C. Hoch, Chem. Phys. Letters 45 (1977) 523. [8] O. Gonen and H. Levanon, J. Phys. Chem. 88 (1984), to be published. [9] P.K. Das and S.N. Bhattacharyya, J. Phys. Chem. 85 (1981) 1391. [10 ] H. Levanon, in: Multiple electronic resonance, eds. M. Dorio and J.H. Freed (Plenum Press, New York. 1979) ch. 13. [11] L. Pekkarinen and H. Linschitz, J. Am. Chem. Soc. 82 (1960) 2407. [12] J.F. Kleibeuker and T.J. Schaafsma, Chem. Phys. Letters 29 (1974) 116; J.F. Kleibeuker, R.J. Platenkamp and T.J. Schaafsma, Chem. Phys. 27 (1978) 51.