2214
J. Phys. Chem. 1988, 92, 2214-2219
the number of distinct spectral features necessary to describe this data set, the results obtained provide additional confirmation of the plausibility of the model. The existing discrepancies-e.g., some unobserved vibronic peaks at 4.2 K on the P- band, precise line shapes in the 830-nm region at 297 K-indicate that further refinement of the model is needed to obtain full quantitative agreement. However, the level of accuracy of the assumed vibronic Hamiltonian is probably not sufficient to warrant such refinement at this time. We next discuss some consequences of the assumptions made concerning the excited electronic manifold. As stated above, inclusion of CT states at various energies has little effect on the inhomogeneously broadened line shapes as long as the oscillator strength is assumed negligible and the exchange matrix elements are not substantially larger than the vibronic line width (-400 cm-I for the P-band). A significantly stronger CT interaction has been suggested by Parson and W a r ~ h e l as * ~a mechanism for shifting the P- band to the red. Such a model implies that the electronic input parameters for our simulations (particularly t3, t4, and J.) would have different values from those used here. We plan to investigate the consequences of employing this parameter set in future work.
While unambiguously distinguishing the Parson-Warshel hypothesis from the alternatives may not be possible, we can at least check the consistency of their assumptions in a full vibronic line shape calculation. The model used here forms the basis for our simulations of photochemical hole-burning experiment^.'^,'^ The agreement obtained provides quantitative support for the validity of these simulations. In the future, we intend to continue refining of the model and hope to compute observables which can be compared with additional experiments so as to increase the level of reliability of the calculations.
Acknowledgment. This work was supported by a grant from the National Science Foundation. R.A.F. is an Alfred P. Sloan Foundation Fellow and a Camille and Henry Dreyfus TeacherScholar. We thank J. Deisenhofer for sending us the most recent set of refined X-ray crystallographic coordinates for the chromophores of the Rps. viridis reaction center and Arnold Hoff for useful discussions concerning the long-wavelength shoulder on the 990-nm absorption band. We thank the University of Texas Center for High Performance Computing for use of their Cray X-MP computer.
Theoretical Studies of Photochemlcal Hole Burning in Photosynthetic Bacterial Reaction Centers Youngdo Won and Richard A. Friesner* Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712 (Received: July 28, 1987; In Final Form: October 27, 1987)
Using the vibronic coupling model for the bacterial reaction center developed in the previous paper, simulationsof photochemical hole-burning experiments on reaction centers from Rps. viridis and Rb. spheroids are carried out. Coupling of the P* long-wavelength absorption band to a nearly resonant charge-transfer (CT) state is shown to be capable of explaining the anomalously broadened hole spectra. The effects of parameter variation (e.g., CT site energy and exchange coupling) on the results are explicitly determined. Comparisons are made with an alternate model proposed by Small.
I. Introduction In the previous paper' (henceforth designated l), a theoretical model for the excited-state manifolds of the chromophores in the bacterial reaction center was constructed and compared with a variety of optical experiments. In general, good quantitative agreement was obtained, indicating that our model is, at the very least, consistent with the available experimental data. Some cross-checking of reliability was also possible via the simultaneous analysis of several different experiments. In this paper, the identical model is used to simulate photochemical hole-burning (PHB) experiments on the RCs from the photosynthetic bacteria Rps. viridis and Rb. ~ p h a e r o i d s . ~ A ?~ brief report of our results has appeared previo~sly.~The present work systematically examines the effects of variation of diagonal site energies and interaction matrix elements and calculates the effects of the burn laser frequency upon the hole position and width. In addition, our proposal is contrasted with the model of Hayes and Small,6 which is shown to lead to incorrect predictions for the ordinary low-temperature (4.2 K) absorption spectrum (1) Won, Y.;Friesner, R. A. J . Phys. Chem., preceding paper in this issue. (2) Boxer, S. G.; Lockhart, D. J.; Middendorf, T. R. Chem. Phys. Lett. 1986, 123,476. ( 3 ) Boxer. S . G.; Middendorf, T. R.; Lockhart, D. J. FEES Lett. 1986,200, -37
AJ I .
( 4 ) Meech, S. R.;Hoff, A. J.; Wiersma, D. A. Chem. Phys. Lett. 1985, 121, 287. (5) Won, Y.; Friesner, R. A. Pmc. Natl. Acad. Sci. L7.S.A. 1987.84, 551 1. (6) Hayes, J. M.; Small, G. J. J . Phys. Chem. 1986, 90, 4928.
0022-3654/88/2092-2214$01.50/0
(at least as formulated in ref 6). Finally, some comments concerning the implication of our results for charge separation dynamics are made in the conclusion. The essential idea in what follows is that the excited states of the special pair dimer (P*) interact strongly with a nearby charge-transfer (CT) state. The questions of what constitutes sufficiently strong P*-CT exchange coupling and how small the energy gap must be are explicitly investigated by determining the resultant predictions for the PHB spectra. Within the limitations of the approximations in the computational methods and the vibronic coupling model, we are able to provide some insight into these questions. The range of parameter values obtained appears to be physically reasonable for both electronic and vibronic constants. We study models in which the C T state is at either higher or lower energy than P*. The former is likely to correspond to an internal dimer CT state suggested by several workers,s while the latter could represent some sort of electron transfer to the neighboring BChl (although note that the diagonal energies of either of these states could in fact be almost anything, due to shifts induced by the protein environment). Either model is capable of explaining the available frequency domain experimental data. (7) Friesner, R.; Wertheimer, R.Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 2138. (8) Parson, W. W.; Scherz, A,; Warshel, A. In Antennas and Reaction Centers of Photosynthetic Bacteria-Structures, Interactions and Dynamics; Michel-Beyerle, M. E., Ed.; Springer Series in Chemical Physics; SpringerVerlag: Berlin, 1985; Vol. 42, pp 122-130.
0 1988 American Chemical Society
Theoretical Studies of Photochemical Hole Burning Hence, from the results of this study, we are unable to choose between these alternatives. 11. Reaction Center Model and Theory The basic underlying model to be used in this paper has been described previously in paper 1. The only modification is addition of a CT manifold. Extensive numerical experiments (not shown below) indicate that, of the electronic states utilized in paper 1, only the SP Qylevels contribute significantly to absorption in the 990-nm region. Consequently, in our analysis of the PHB results, we employ a restricted model consisting of the two SP manifolds and a C T state. The parameters of the SP molecules are identical with those in paper 1 for the bacterium Rps. uiridis except that the SP site energy is slightly altered to reproduce the experimental peak position correctly despite a somewhat different set of electronic interactions. For the calculations on Rb. sphaeroides, we empirically adjust the site energy and dimer exchange interaction to obtain agreement with the absorption spectrum of that system. The results are not critically dependent upon the precise values of these numbers. The diagonal energy of the states and coupling to one SP excited state (we assume that CT configurations have a preferential overlap with one local exciton configuration, because charge separation proceeds in only one directiong) are explicitly varied over a range of physically reasonable values. We next consider various proposals as to the identity of the C T state. In our dynamical simulation model,' it was assumed that this state was the configuration P'B-, where B is the BChl between P and H. Recent femtosecond experimentslOsl' cast substantial doubt on whether the state P+B- is actually an intermediate in the initial charge separation. However, it has not been unambiguously established that an intermediary C T state of lower ' ~ avoid prejudicial asenergy than P can be ruled o ~ t . ' ~ 9 To sumptions, we consider a state P I - , where I simply represent some initial charge-accepting configuration, e.g., the H associated with the L subunit, the accessory BChls, or some intermediary admixture of them of the form P+B6-H6-. With the C T state unidentified, either experimentally or in a model study, we investigate its characteristics by varying the corresponding parameter values. The range of the diagonal energy of this CT state would be from the P+ equilibrium energy, -8000 cm-I,l4 to 400 cm-' below the P- component based on a delayed fluorescence measurement.ls An alternative C T state that has been suggested is an internal charge-separated state of the SP dimer, PL+PM-,represented as PLS8At present, this hypothesis is somewhat more consistent with the femtosecond dynamics results of ref 10 and 11 than the P+Imodel. QCFF-PI calculation results for an isolated BChl dimer model based on the X-ray coordinates of the Rps. uiridis R C place the lowest internal C T state at 14440 cm-1.8 Since substantial charge stabilization is expected in a protein matrix, this value is an upper bound for the P* state energy. The site energy of P* will therefore be varied from the value slightly above the P- state to 14440 cm-'. Note that in our model we consider only one interacting CT state and neglect the possible analogous CT state which could be found with the opposite symmetry, e.g., PL-PM+.This treatment assumes that one C T configuration is preferentially mixed into the SP Qy manifold, presumably due to its exchange interaction and diagonal energy values. Such an assumption does not, of course, constitute an a priori demonstration of the origin of the asymmetry of the primary charge separation reaction, although (9) Deisenhofer, J.; Michel, H.; Huber, R. Trends Biochem. Sci. (Pers. Ed.), 1985. . 10. 243. (10) Martin, J.-L.; Breton, J.; Hoff, A. J.; Migus, A,; Antonetti, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 957. (1 1) Breton, J.; Martin, J.-L.; Migus, A,; Antonetti, A,; Orszag, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 5121. (12) Woodbury, N. W.; Becker, M.; Middendorf, D.; Parson, W. W. Biochemistry 1985, 24, 7521. (13) Shuvalov, V. A.; Duysens, L. N. M. Proc. Natl. Acad. Sci. U.S.A. ~
1~
1986,83, 1960. (14) Dutton, P. L.; Kaufmann. K. J.: Chance, B.; Rentzeuis, P. M. FEBS Lett. 1975, 60, 275. (15) Shuvalov, A. V.;Parson, W. W. Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 957.
The Journal of Physical Chemistry, Vol, 92, No. 8, 1988
2215
it does conform to a physical model which is consistent with this observation. Recent semiempirical calculation of Plato and coworkers28 using the protein residues to perturb the BChl dimer do suggest preferential mixing of one (asymmetric) C T state in to the QySP manifold, in agreement with our model assumptions. From a mathematical point of view, these two proposed states play an identical role in the excited-state Hamiltonian, each being characterized by a set of vibronic coupling constants, an energy gap A = ECT- EP., and an exchange coupling matrix element J. For the remainder of this paper, we adopt this picture and will discuss a generic interacting C T state in terms of its parameter values. Distinguishing between the two above physical models will require analysis of additional experiments and different types of calculations. Note that our modeling of the strongly coupled, low-frequency interactions of P differ from that reported in ref 5. We now utilize two modes (one of 50 cm-' and one of 100 cm-I), which modulate the S P exchange interaction, as opposed to one such mode and one librational mode. The vibronic coupling constants of these modes are adjusted to reproduce the experimental hole width at one bum laser frequency. As pointed out in ref 5, the C T manifold eliminates the zero-phonon line but does not determine the overall hole width. The magnitude of this width can only be explained by strong, low-frequency coupling of the magnitude assumed here. The specific choice of strongly coupled low-frequency modes is at this point rather arbitrary; a wide variety of parameter sets would yield results equivalent to the ones which follow. We have chosen the present model because it seems reasonable to introduce some dispersion into the low-frequency spectrum of P. However, this feature is not crucial to reproducing the experimental results. It remains to specify the parameters of the C T state. These include the C T vibronic coupling constants, exchange interaction, and diagonal energy. For lack of a better estimate, we scale the vibronic coupling constants of the C T manifold to 3 times their value in the Qy excited state of the BChl monomer, in rough agreement with the calculations of Warshel.I6 The latter two parameters will be explicitly varied in what follows. In paper 1, inhomogeneous broadening was incorporated into the imaginary part of the energy, y, which was then parameterized to fit the observed absorption line widths. Here, we wish to study the homogeneous line shapes and associated PHB spectra. Consequently, we set y equal to 1 cm-' (for numerical convenience; a smaller value would not affect the results) and explicitly utilize a Gaussian distribution of site energies to calculate the absorbed PHB spectrum via a convolution with the homogeneous line shape. This procedure is the same as is used in ref 5. Homogeneous optical absorption line shapes are computed from the Green's function matrix elements G,,(E) via the f ~ r m u l a ~ * " ~ ' ~
We assume that only the SP molecules possess oscillator strength in the long-wavelength band (Le., the C T states have no oscillator strength independently) and obtain the appropriate transition dipole vectors from the X-ray crystal coordinates of the Rps. uiridis RC9,'9320and assumptions concerning the monomer transition dipole vectors, as in paper 1. We adopt the same geometry for the SP in the R C from Rb. sphaeroides. A recent molecular replacement study reveals the structure of the Rb. sphaeroides R C at 3.7-A resolution, which shows that the chromophore organization of the RC is highly homologous to the one of the Rps. uiridis RC.2' (16) Warshel, A. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 3105. (17) Lagos, R.; Friesner, R. A. J. Chem. Phys. 1984, 81, 5899. (18) Won, Y.; Lagos, R.;Friesner, R. J . Chem. Phys. 1986, 84, 6567. Miki, K.; Huber, R.; Michel, H. J . Mol. (19) Deisenhofer, J.; Epp, 0.; Bioi. 1984, 180, 385. (20) Deisenhofer, J.; Epp, 0.; Miki, H.; Huber, R.; Michel, H. Nature (London) 1985, 318, 618. (21) Chang, C.-H.; Tide, D.; Tang, J.; Smith, U.; Norris, J.; Schiffer, M. FEBS Lett. 1986, 205, 82.
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The Journal of Physical Chemistry, Vol. 92, No. 8, 1988
Won and Friesner
0.0 E n e r g y (cm-’)
E n e r g y (cm”)
1.0
1.0
b
b
E n e r g y (cm’)
E n e r g y (cm”)
Figure 1. (a) Homogeneous line spectrum of the isolated SP manifold. All parameters are described in section I1 except J = 0; i.e., no coupling to CT states exists. (b) Photochemically modified absorption spectrum for the isolated SP system (solid line) calculated ( J = 0) via eq 2. C = 0.107 and wL = 11 253 cm-I. The spectrum with T = 0 (dashed line) is shown for comparison. The inhomogeneous width is 300 cm-I.
Figure 2. (a) Homogeneous line shapes from a CT state coupled model system. The CT state manifold is appropriately constructed by using A = -500 cm-’ and J = 240 cm-I. (b) Photochemically modified absorption (solid line) spectrum for the P+I--P* system. All parameters are as in Figure 1, except J = 240 cm-’. The C = 0 spectrum (dashed line) is
Once the homogeneous line shapes are calculated, the hole spectra can be obtained by incorporating the appropriate experimental conditions. After the irradiation with the burn laser of frequency wL and intensity I for a bum time T , the photochemically modified absorption spectrum I,(E) can be generated from the convolution integral of the homogeneous line shapes with a ~ ~ Gaussian line width Gaussian energy distribution, P ( E - E ~ ) .The is adjusted to reproduce the low-temperature absorption spectra in the 990-nm region for the case of Rps. uiridis.5 Because the P870 of R b . sphaeroides absorption band overlaps with the accessory BChl band^,^^^ we obtain the corresponding energy distribution parameter directly from fitting the hole spectra. The expression used to evaluate I#) is then
of the long-wavelengthdimer absorption only, the precise geometry is not of critical importance, so the use of the Rps. viridis X-ray coordinates is acceptable. All parameters, unless otherwise stated, are those described above. Figure l a displays the homogeneous absorption spectrum of the SP dimer manifold with the electronic coupling to C T states set to zero. A sharp ZPL is present, followed by a progression of Franck-Condon peaks due to molecular vibrations. This calculation predicts that a narrow hole would be observed if the SP dimer could be decoupled from the rest of the electron-transfer system. A narrow, sharp zero-phonon hole is observed (Figure 1b in the modified absorption spectrum after irradiation with a burn laser at wL = 11 253 cm-’. In the following discussion, we couple the SP Qymanifold to a C T state. The crucial electronic parameters of this state are the energy gap, A, between the SP and C T site energies, and the exchange coupling strength J . The decoupled spectrum of Figure 1 corresponds to J = 0. When the SP excited states are coupled in an appropriate way to a C T state, a broad line profile without sharp features is generated as shown in Figure 2a. A typical set of C T energy parameter values which are sufficient to obliterate the ZPL of the dimer spectrum are employed in Figure 2; the energy gap, A = -500 cm-I, and the C T state coupling to the P* state, J= 240 cm-’ . Qualitatively indistinguishable results are obtained from many other parameter sets. Strong coupling to any C T state suppresses the ZPL and produces a broad and featureless homogeneous line shape. Figure 2b displays the modified absorption spectrum of the above system after irradiation with a burn laser at wL = 11 253 cm-’, which reveals no sharp holes. This qualitative result remains true as wL is tuned across the absorption band and is insensitive to the precise values of intramolecular and intermolecular vibronic coupling constants. That is, strong, quasiresonant coupling to a C T manifold is capable of destroying the narrow zero-phonon hole observed in the usual photochemical hole-burning experiments with organic glasses.23
I,@) = S m p ( E!-Eo) exp [ CZH(EL-E’-Eo)]IH(E-E’-EO) d E ’ -m
(2) where EL = hwL and C is a constant depending on the experimental conditions, the absorption cross section 0 , and the photochemical quantum yield %, i.e.
(3) We estimate C from the experimental conditions described in ref 2 and 3 and adjust it to give the integrated depletion of the absorption spectrum by approximately 7% as in the reported experimental data. The photochemical hole spectra is then defined as A
m =
- I,=o(E)
(4)
111. Results
We study a variety of SP-CT models of the Rb. sphaeroides R C (for which experimental results with better signal-to-noise ratio are available3) by calculating homogeneous line shapes. The Rps. viridis RC,model study yields similar conclusions. In a study (22) Friedrich, J.; Haarer, D. Angew. Chem., Int. Ed. Engl. 1984, 23, 113.
shown for comparison.
(23) Volker, S.; Macfarlane, R. M. J . Chem. Phys. 1980, 73, 4476
Theoretical Studies of Photochemical Hole Burning 4.0 r
The Journal of Physical Chemistry, Vol. 92, No. 8, 1988 2217
#
1,o
0. 0 Energy (em")
Figure 3. Homogeneous line shapes from the P*-PtI- model system without P mode contributions. All the other parameter are as in the system of Figure 2.
......_..... .'
\
7
11000 12000 Energy (em')
Figure 5. Homogeneous absorption spectra as a function of A. P*-P+Imanifold with J = 240 cm-' is used in the calculations. A values are shown in the figure.
1.0
0.0
0.0
11000 12000 Energy (cm-')
Y
Figure 4. Homogeneous absorption spectra as a function of A. Pt-P* manifold with J = 240 cm-' is used in the calculations. A values are shown in the figure.
Figure 6. Homogeneous absorption spectra as a function of J . Pt-P* manifold with A = 2000 cm-' is used in the calculations. J values are shown in the figure.
In our RC modeling, we have postulated the importance of SP intermolecular vibrations (P modes), which represent the relative motions of the SP BChls. The significance of the intermolecular modes can be shown in a control calculation without those modes (Figure 3). A coupled system with an energy gap of -500 cm-I and only intramolecular vibronic coupling is used to demonstrate the relevant effect. Although a homogeneous line shape without any sharp features is obtained, the resultant homogeneous line width is only -50 cm-'. No matter how broad a Gaussian distribution is incorporated in the hole spectra calculation from the homogeneous line shapes, it would be impossible to obtain a broad hole of -450 cm-' and retain the correct 4.2 K absorption spectrum. We next investigate the effect of varying the C T site energy gap A = Em - Ep. Figure 4 presents the homogeneous line shapes generated by values of A varying from +500 to 10 000 cm-I. Up to about A = 2000 cm-I, a broad, featureless line shape is observed; when convoluted with the inhomogeneous Gaussian distribution, a hole spectrum similar to that in Figure 2b is produced. For higher energy gaps, the C T manifold is moved out of resonance, and the ZPL reappears. The limiting value of 2000 cm-I should be regarded only as a crude estimate, due to uncertainties in both the parameter values and the computational method. Rigorously accurate calculations utilizing a basis set of several hundred thousand ~ t a t e s are ~ ~ currently 2~ in progress; these confirm qualitatively the results shown here but will allow a better quantitative assessment of the resonance condition.
+
(24) Nauts, A,; Wyatts, R. E. Phys. Rev. A 1984, 30, 872. (25) Moiseycv, N.; Fricsner, R. A.; Wyatt, R. E. J. Chem. Phys. 1986,85,
331.
11000 12000 Energy (em-')
TABLE I: Electronic Parameters for the Model System Hamiltonian" species
P* energy
J.
Ja
Ab
J
Rb. sphaeroides Rps. viridis
11 925 11045
500 872
350 612
2000 2000
240 240
"Energies are given in wavenumbers. b A = E,.
-
J. - (ECT- JR).
A parallel study is performed for the C T state lying below P* in energy. The energy gap A is varied from -500 to -4000 cm-I, which roughly corresponds to the position of the equilibrium P+ absorption band (1250 nm).14 Figure 5 displays the results of those calculations; the ZPL and other sharp features are gradually recovered by increasing the energy gap as in the results from the previous calculations. The effect of the magnitude of the C T state coupling to the P* manifold investigated by using an energy gap A = 2000 cm-I As Jis varied from 0 (Figure la) to 320 cm-', the ZPL is gradually eliminated (Figure 6 ) . Setting the parameters A = 2000 cm-l and J = 240 cm-I, we simulate the burn laser wavelength dependence of the hole spectra of Rb. sphaeroides (Figure 7) and of Rps. uiridis (Figure 8 ) . For the case of Rb. sphaeroides, the hole spectra are calculated at oL = 11 180, 11 253, 11 345, and 11 470 cm-I at 1.5 K and the amplitudes of the holes are scaled to the same magnitude as in ref 3. The corresponding homogeneous absorption spectra can be seen in Figure 6. An inhomogeneous width of 300 cm-' is incorporated in the Gaussian distribution function used in the integral of eq 2. When the laser is tuned to higher frequencies, the corresponding holes are shifted from red to blue a s reported in the experiments; the experimental burn frequencies are indicated
2218
The Journal of
Physical C h e m i s t r y ,
Vol. 92, No. 8, 1988
Won and Friesner
E n e r g y (cm-')
/
Figure 7. The hole spectrum of the RC from Rb. sphaeroides as a function of bum laser frequency. The burn frequencies are indicated with vertical arrows: 11 180, 11 253, 11 345, and 11 470 cm-I. C = 0.107 is utilized as the proper experimental conditions in the calculations, and the amplitudes of the resultant hole spectra are scaled to the same magnitude for comparison of the line shapes.
I 1 1 000
11500
I 12000
E n e r g y (cm")
Figure 9. Hole spectra of the Rb. sphaeroides RC are compared to the experimental data (dotted line) measured at 1.5 K. C = 0.107 and the inhomogeneous line width of 300 cm-I are incorporated in the calculation. Burn laser frequencies are (a) wL = 11 180 cm-', (b) wL = 11 253 cm-', (c) wL = 11 345 cm-I, and (d) wL = 11 470 cm-'
t 9500
f
+
I
10000 E n e r g y (cin-']
'053C
Figure 8. The hole spectrum of the RC from Rps. uiridis as a function of burn laser frequency. The burn frequncies are indicated with vertical arrows: 9870, 10009, and 10250 cm-I. C = 0.107 is used and the hole spectra are generated as in Figure 8.
in Figure 7 by arrows. Direct comparison of experimental and theoretical holes for each burn laser wavelength is presented in Figure 9. Note that the variation of hole width as well as peak position is accurately reproduced. This agreement arises from the model with no explicit parameter adjustment. For the case of the Rps. v i r i d i s R C at 1.4 K, the hole spectra are calculated with the laser excitations a t wL = 9870, 10009, and 10 250 cm-'. An inhomogeneous line width of 177 cm-] is incorporated in the convolution integral for this calculation (eq 2). The experiments on Rps. viridis display poorer signal-to-noise ratio than those on Rb. sphaeroides, making a comparison like that of Figure 9 difficult. Our calculations stand as predictions of what a noise-free sequence of spectra would look like.
IV. Conclusion From the preceding calculations, we obtain a semiquantitative picture of the behavior of the predicted PHB spectrum of our vibronic coupling model as a function of the CT exchange coupling, energy gap, burn laser frequency, and vibronic coupling strength. A summary of the important results are as follows: (1) Quasiresonant mixing (la1 I 2000 cm-I, J L 80 cm-', roughly) is required to destroy the ZPL holes. Otherwise, the CT state acts only to perturbatively renormalize line positions and oscillator strengths. (2) Intermediate coupling of the Q,,state to low-frequency modes (the corresponding Huang-Rhys factor S 1) is required to explain the hole width. Such a value is also consistent with all other optical properties. (3) The wavelength and hole width dependence on the burn laser frequency is correctly predicted. The approximate Green's function theory is not rigorously reliable in computing homogeneous line shapes, so that the limiting values mentioned in (1) above are not quantitatively accurate. The large-scale recursive residue generation calculation^^^^^^ mentioned above will provide more precise delineation of the various parameter regimes. The picture presented here is in accord
-
with what one would expect from quasi-resonant mixing due to strong vibronic coupling and is qualitatively confirmed by our preliminary ultralarge basis set results. The model studied here is rather complicated, both conceptually and computationally. Is it really necessary to utilize such a complex formulation, or is the essential pictures of the hole-burning experiments captured in a simpler construction? We address this question by comparing our approach to that of Small,6 who has presented an alternate explanation of the anomalous hole width. The model described in ref 6 consists of a single displaced harmonic oscillator (DHO) of frequency 30 cm-' linearly coupled to the 990-nm transition with a reorganization energy of S 8. This results in a line spectrum of equally spaced peaks at a separation of 30 cm-I, with the intensity distributed in a Gaussian pattern. The shifting of intensity to the center of the band means that the zero-phonon line (first peak) has very little intensity and hence would not be detectable. First, we discuss the physical implication of this model. To our knowledge, the only observation of an S of this magnitude in an organic system is in weak charge-transfer organic crystals.26 If the transition has some C T character, the relative relaxation of the SP in the excited state will modulate a strong Coulombic interaction, leading to a significant change in the equilibrium position of the intermolecular separation. Thus, this mode can be identified as the "P mode" utilized in the present work. However, it is unrealisic to assign the C T state any direct oscillator strength in the 990-nm region. Evidence overwhelmingly indicates that the absorptive behavior is due to the SP Q,,state, e.g., the LD and polarized light absorption and the circular dichroism results (see paper 1). Hence, the C T character must be obtained via vibronic borrowing, as in our model. A second important point concerns the consequences of the model for the ordinary low-temperature (4.2 K) absorption spectrum. As S of 8 would eliminate the asymmetry of the 990-nm band and obscure the shoulder at 850 nm from view by broadening it. In other words, the resolution and asymmetry displayed by the 4.2 K absorption are inconsistent with a much larger direct vibronic coupling constant. A third question is whether or not one could observe sharp phonon holes if a single D H O type picture was accurate. Unlike the C T coupling, the DHO model contains no chaotic behavior, predicting a series of sharp lines. Of course,, one could hypothesize
-
(26) Haarer, D.;Philpott, M. R. In Spectroscopy and Excitation Dynamics of Condensed Molecular Systems; Agranovich, V. M.; Hochstrasser, R. M., Eds.; North-Holland: Amsterdam, Netherlands, 1983; pp 27-82.
J . Phys. Chem. 1988, 92, 2219-2223
that other medium effects would result in dispersion of the sharp phonon peaks, resulting in a more continuous line shape (e.g., each phonon line could certainly have a phonon sideband). Still, it is not at all clear that this would be sufficient to completely eliminate the sharp behavior predicted from a single-mode D H O model. The present model suffers from none of the above objections. The direct coupling to the intermolecular mode that is obtained is an intermediate value, which yields an anomalously large hole-burning line width that does not eliminate the asymmetry from the long-wavelength band. The resonant coupling does introduce chaotic spacing of levels, so that the resultant hole is broad and featureless. Finally, the electronic interactions are treated correctly, via a model which reproduces other spectroscopic data.' These arguments are by no means definitive; the D H O model could probably be modified to yield better agreement with experiment than the crude version in ref 6. Alternatively, some combinations of the two picture may be correct; e.g., the large spectral widths required to "dress" the stick spectra in the DHO model could arise from interactions with a C T state. However, the proponents of D H O model do need to show that their model can in fact be made consistent with all available experimental data. We next turn to the question of further experimental tests of hole-burning models. Recent Stark effect measurements*' support the contention that a C T state is mixed into the Qy SP manifold. A simulation of the Stark line shape with our vibronic coupling model will be undertaken in the near future. Note, however, that the mere presence of C T character in the excited state does not guarantee that the chaotic restructuring of the absorption band proposed here actually takes place. A key issue which has emerged from various theoretical perspectives is the characterization of the (hypothesized) strongly (27) Lockhart, D. J.; Boxer, S. G. Biochemistry 1987, 26, 664. (28) Plato, M., personal communication.
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coupled intermolecular mode (P mode) of the SP dimer. The most direct way to address this experimentally would be a resonance Raman (RR) experiment in which excitation was made directly into the SP Qy band and the low-frequency region of the R R spectrum was obtained. In the most favorable circumstances, one could extract the Franck-Condon (FC) factor of the P mode from analyzing the RR intensity (relative to, e.g., high-frequency peaks); issues of vibronic borrowing versus direct FC displacement could be studied by analyzing R R excitation profiles, which have a very different shape for A (direct FC) and B term (vibronic borrowing) scattering mechanisms. Finally, we give a brief discussion concerning the relationship of the hole-burning analysis to primary charge separation dynamics. If the interacting C T state could be identical as P'B-, the model developed here would be in complete accord with that of ref I , which proposed that the state P+B- was quasi-resonantly coupled to the SP Qy manifold. However, this model also predicts that an initial transient bleaching of B should occur instantaneously. Such a bleaching is apparently not observed in the recent femtosecond experiments of Breton, Martin, and co-workers.lOJ1 If, on the other hand, the CT state is closer in form to PL+PM-, no conflict with the dynamical results is produced. One could argue that admixture of this state would facilitate overlap with the P'B- (or P+H-) configuration, thus accounting in part for the speed and asymmetry of electron transfer. These ideas are not new, and we have not provided any sort of proof of their validity; rather, our present results are consistent with such a picture.
Acknowledgment. This work was supported by a grant from the National Science Foundation. R.A.F. is an Alfred P. Sloan Foundation Fellow and a Camille and Henry Dreyfus TeacherScholar. We thank J. Deisenhofer for sending us the most recent set of refined X-ray crystallographic coordinates for the chromophores of the Rsp. viridis reaction center. We thank the University of Texas Center for High Performance Computing for providing Cray X-MP computation time.
Time-Resotved Studies on the Dynamics of Photoinduced Formation of M(CO),(polypyridyi) (M = Mo, Cr, and W) Complexes K. Kalyanasundaram Institut de Chimie Physique, Ecole Polytechnique FgdPrale, CH- 1015 Lausanne, Switzerland (Received: July 30, 1987; In Final Form: November 3, 1987)
The dynamics of photoinduced formation of M(CO),(LL) (M = Mo(O), Cr(O), and W(0) and LL = various polypyridyl ligands such as 5-chloro-l,lO-phen, 1,lO-phen, 2,2'-bpy, and 4,4'-Mez-2,2'-bpy) from M(C0)6 and LL in benzene has been examined via pulsed laser photolysis techniques. The formation of the polypyridyl tetracarbonyl complex occurs in several steps, extending over a wide range of time scales (from a few nanoseconds to several milliseconds). Spectral evidence is presented for the formation of a pentacarbonyl monodentate polypyridine intermediate. The rate of formation of the complexes follows the order Mo(0) > Cr(0) > W(0). For a given metal carbonyl, the reactivity of various ligands follows the order 5-Clphen 3 phen > bpy 3 Me2bpy.
Introduction In recent years there has been an enormous growth in studies of photochemistry of organometallic compounds, in particular those of metal carbonyls.' Metal carbonyl derivatives containing pyridyl (L) or polypyridyl (LL) ligands exhibit low-lying metal-to-ligand charge-transfer (MLCT) states. Photophysical and (1) (a) Geoffroy, G. L.; Wrighton, M. S. Organometallic Photochemistry; Academic: New York, 1979. (b) Meyer, T. J.; Caspar, J. V. Chem. Rev. 1985, 85, 187. (c) Steigman, A. E.; Tylor, D. S. Coord. Chem. Rev. 1985, 63, 217.
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photochemical investigations of these complexes have revealed room temperature emission and also rich and diverse forms of photoreactivity. References 2-5, for example, list some recent photochemical studies on group VIB metal carbonyl polypyridyl derivatives: M ( CO)5L,2 M ( C0)4L2,3 M ( CO),( LL) ,, and (2) (a) Wrighton, M. S.; Abrahamson, H. B.; Morse, D. L. J. Am. Chem. SOC.1976, 98, 4105. (b) Boxhoorn, G.; Oskam, A.; Gibson, E. P.; Narayanaswamy, R.; Rest, A. J. Inorg. Chem. 1981, 20, 783. (c) Lees, A. J.; Adamson, A. W. J. Am. Chem. SOC.1980, 102, 6874; J . Am. Chem. SOC. 1982, 104, 3804. (d) Lees, A. J.; Adamson, A. W. Inorg. Chem. 1981, 20, 4381.
0 1988 American Chemical Society
