J . Phys. Chem. 1989, 93, 1633-1637 monitored in this dynamic gel system. In the future, combining matrix molecules with fibrillar collagen or hydroxyapatite seed crystals will greatly expand the potential of the dynamic gel system.
Acknowledgment. I especially thank Mr. Andrew J. Burstein for designing the gel system, and Dr. A. Veis and Dr. L. Rosenberg for supplying the macromolecules tested in this study. The assistance of Mr. Tony Labastierre and the staff of the Department
1633
of Pathology at the Hospital for Special Surgery, who helped in the preparation and evaluation of the electron micrographs, and of Mr. Darryl Jonas, Ms. Pegeen Mularchuk, Ms. Mary Mckeveny, Mr. Wil Armentano, and Mr. Michael Maresca is gratefully acknowledged. This work was supported by NIH Grant DE 04141. Registry No. Ca, 7440-70-2; PO:-,
14265-44-2.
Long-Range Electron Transfer within the Hexamer of the Photosynthetic Reaction Center Rhodopseudomonas viridis P. 0. J. Scherer and Sighart F. Fischer* Technische Universitat Munchen, Theoretische Physik, 0-8046 Garching, FRG (Received: April 22, 1988; In Final Form: June 30, 1988)
Quantum calculations of the INDO-SCI type are performed for the hexamer of the central prosthetic groups of the reaction center Rhodopseudomonas uiridis. The lowest electronic excitations including 28 charge-transfer states are analyzed with regard to their configuration interactions.
Introduction In photosynthetic reaction centers such as Rps. Viridis or Rb. sphaeroides a very rapid charge separation takes place after excitation of the bacteriochlorophyll dimer P. The first detected charge-separated state P+HL- is formed in 2.8 ps'J and has the negative charge on the bacteriopheophytine HL. This pigment is separated from P by about 17 A. Between P and HL an accessory bacteriochlorophyll BL is located so that it can mediate the electron transfer. These pigments belong to the so-called L branch of the protein. An almost symmetrically arranged pair BM and HM on the so-called M branch seems to be inactive in the charge-separation process. Since the structure of the reaction centers Rps. viridis3 and Rb. sphaeroides4 has been resolved, several attempts have been made to understand its function from a quantum mechanical point of vie^.^-^ The high interest in these systems is motivated by the observations that the charge separation is extremely efficient (lOO%)'O and the energy loss into the surrounding medium is relatively small (less than 20%). Once it becomes clear which structural features are essential for the function, it might be possible to construct artificial systems with similar properties that could be useful for solar energy conversion and energy storage. In this article we present quantum calculations for the full hexamer consisting of four bacteriochlorophyll monomers BM, PL, PM, and BL as well as two bacteriopheophytins HM and HL together with four histidines, which are attached to the Mg atoms (1) Martin, J. L.; Breton, J.; Hoff, A. J.; Migus, A.; Antonetti, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 957. (2) Breton, J.; Martin, J. L.; Migus, A.; Antonetti, A.; Orsay, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 5121. (3) Deisenhofer, J.; Epp, 0.;Huber, R.; Michel, H. J. Mol. B i d . 1984, 180, 385. Michel, H.; Epp, 0.; Deisenhofer, J. EMDO J. 1986, 5, 2445. (4) Allen, J. P.; Feher, G.; Yeates, T. 0.;Komiya, H.; Rees, D. C. Proc. Natl. Acad. Sci. U.S.A. 1987, 84, 5730. (5) Fischer, S. F.; Scherer, P. 0. J. Chem. Phys. 1987, 115, 151. (6) Scherer, P. 0. J.; Fischer, S. F. Chem. Phys. Lett. 1987, 141, 179. (7) Kuhn, H. Phys. Rev. A : Gen. Phys. 1986, 34, 3409. (8) Warshel, A.; Creighton, S.; Parson, W. W. J . Phys. Chem. 1988, 92, 2696. (9) Michel-Beyerle, M. E.; Plato, M.; Deisenhofer, J.; Michel, H.; Bixon, M.: Jortner, J. Bimhim. Biophys. Acta 1987, 932, 52. (IO) Wraight, C. A.; Clayton, R. K. Biochim. Biophys. Acta 1974, 246, 333.
0022-3654/89/ 2093-1633$01.50/0 . , I
,
of the four bacteriochlorophylls. The monomers PLand PMform the dimer P. The results indicate that the rapid charge separation may be an outcome of a special molecular engineering of the pigments. Due to an energetically close arrangement of the lowest unoccupied orbitals a certain delocalization of these orbitals is achieved. This delocalization depends on the coupling between localized orbitals as well as their relative energy differences. Here we show that the energy spacing of these self-consistent field (SCF) orbitals affects the configuration interaction (CI) between the excited states in a very sensitive way. Within our calculations charge-transfer states such as P'HLare treated as excited configurations in the same way as the initially excited dimer state P*. We analyze the final interaction responsible for a transition from P* to P'HL- in terms of oneparticle interactions, CI coupling constants, and energy differences between orbitals as well as those between states. Compared to the energy differences, the extracted coupling constants should be less sensitive to further refinements of the coordinates and model assumptions about the calculated reaction center complex. We consider three mechanisms, the direct electron transfer from P* to P+HL-and two indirect transfers invoking P+BL- or BL'HLas intermediates. We show how the energetics can favor one or the other. It is interesting to note that the direct coupling becomes relatively large in the basis of partially delocalized orbitals. To understand this new result, it is essential to distinguish between orbital tuning and the energetics of states.
Methods We included 518 atoms (1400 atomic orbitals of the s and p type). We used a modified version of the QCPE 372 program (INDO-SCI). The parametrization was chosen as in ref 11. However, we preferred to takefy = 1 to have y = e Z / Rfor large distances. The Mg atoms were treated in the sp approximation. The Slater exponent for Mg was taken from ref 12. For distances larger than 2.8 8, the resonance integrals Pij were reduced as in ref 13. (11) Ridley, J.; Zerner, M. Theor. Chim. Acto. 1973, 32, 111. (12) Gordon, M. S.; Bjorke, M. D.; Marsh, F. J.; Korth, M. S . J. Am. Chem. SOC.1978, 100, 2670.
0 1989 American Chemical Society
1634
The Journal of Physical Chemistry, Vol. 93, No. 4 , 1989 -2
- -3 5 h
p-4 a a. c
B - -5 n
I
1 -
sponding orbitals completely localized on any one of the pigments or the dimer as q,and the expansion coefficients as c k , and get in low-order perturbation theory.
6 -
t-
4-
$k p+p*I
P H,
-
P+H;
i
r
L
0
-6
Scherer and Fischer
t
t Figure 1. Energy diagram for the six highest occupied and the six lowest unoccupied orbitals of the hexamer.
For such large systems it is important to choose a reasonable guess for the initial wave functions of the S C F iteration. The generally used extended Hiickel wave functions do not give convergent results. Therefore, we first calculated wave functions for smaller parts of the system, Le., for the three pairs PLPM, BLHL, and BMHM. Convergence of 10-5-1 0-6 eV (maximum deviation of orbital energy between two successive iterations) can be achieved with 10-15 iterations, where each iteration takes about 15 min CPU time on a CDC 995 E. At present the configurations had to be restricted as the computing time is limited; 80 configurations took about 5 h. We treated the special pair as one molecule and took into account transitions from its six highest occupied molecular orbitals (HOMOs) to its four lowest unoccupied (LUMOs). For the other four pigments BL, BM, HL, and HM we kept transitions from its three HOMOs to its two LUMOs (six transitions for each pigment). From the charge-transfer states between the pigments, in addition to those within the special pair, we kept 28 formed between the 6 HOMOs and 6 LUMOs of the hexamer. Energetics of the HOMOs and LUMOs In Figure 1 the six HOMOs and the six LUMOs of the hexamer are shown. The degree of localization of one orbital on one pigment relative to a neighboring pigment is represented by the location of the center of the bars. It appears that only the four orbitals localized on the special pair dimer are substantially distributed among two pigments, here PM and PL. The energies between the three LUMOs localized on PL,BL, and HL respectively differ by less than 600 cm-'. The corresponding orbital energies of BM and HM on the M branch are somewhat further separated from the lower orbital energy of the special pair. As we compare the LUMOs with the HOMOs, we find that they are spread in energy over a much larger range. In particular those of the HL and HM are about 4000 cm-I below the HOMO of the whole system, which is localized on the special pair. Such an arrangement of the orbitals has significant consequences. The evaluated close energetic proximity of the LUMOs leads to enhanced delocalization among them, while the HOMOs are essentially localized. The engineering of the reaction center is in our calculation and might be in reality such that the energetic prerequisites for delocalization are best established on the L branch. We note further that the energy difference between the HOMO and the LUMO of HM as compared to HL is considerably larger. This is already an indication that the lowest excited state of H M becomes higher in energy than that of HL. Since the fine tuning of the evaluated orbital energies may be accidental in the sense that it changes once the protein environment is included more completely, we want to present a more general analysis based on perturbation theory. We denote the six LUMOs largely localized on a pigment or the dimer as $k and corre(13) Plato, M.; Trankle, E.; Lubitz. W.; Lendzian, F.; Mobius, K . Chem. Phys. 1986, 107, 185.
=
(1)
CCkn'Pn
with ck,
=
Ukn/(ck -
for k #
En)
(2)
From the computed energies f k and the coefficients ck, the most important effective "one-particle'' interactions come out as U1,3 = U3%I= -34 cm-l U2,3
U2$5= U5,2 = -4 cm-' U4,5= U5,4= -35 cm-l
= U3,2= -10 cm-'
(3)
The indexes 1-6 are chosen according to the energetic ordering and are labeled in Figure 1. From eq 3 we obtain in second-order perturbation the induced expansion coefficients
= ~ l , 3 u 3 , 2 / ( c l - c3)(c1- t2) = u2,3u3,1/(c2 - e3)(e2c1,4 = Ul,5u5,4/(cl - c5)(cl - 64) cl,2
c2,1
=
c4,1
u4,5u5,1/(c4
-
c5)(c4
-
€1)
(4)
which compared quite well with the computed values if the corresponding couplings from (3) and the orbital energies ck from the computational results are substituted. That means in zero order only the dimer orbitals (p2 and p6 are delocalized over two pigments (PLand PM)the others are almost completely localized on pigment. The localized orbitals interact via an effective one-particle Hartree-Fock potential U. The states interact via two-particle Coulombic and exchange terms in the sense of configuration interaction (CI). We will see next that the detailed tuning of the orbitals can affect the CI matrix elements substantially.
Configuration Interaction Analysis of the Direct Electron-Transfer Couplings The charge-transfer states of the hexamer are just special singly excited states that differ from the excited states of individual pigments by their smaller transition dipoles and larger permanent dipole moments. They mix via the configuration interactions. Let us denote the zero-order energies of excited states by the nature of the transition of the pigments as, for instances, Eo(P*),Eo(P'H-), --,and the CI mixed excited-state energies, by E(P*), E(P+H-), --,and further the interactions between the zero-order states evaluated with the completely localized orbitals q n by Vo(P*,P+H-) and those evaluated with the orbitals $k by V(P*,P+H-). For the direct charge-separation the CI matrix element reads V(P*,P+HL-) = 2 S d r d J $o(r) $2(r)e2/(r -
4 $o(r')
$I(/)
- J-dr dJ $02(r)e2/(r - r') $,(r') $2(r') (5)
$o denotes the HOMO of the dimer.
Substituting for obtain from ( 5 )
and $z the expansions from (1) to (4), we
V(P*,P+H,-) = VO(P*,P+HJ + C1,2( Vo(P*,P*) Vo(P+BL-,P+BL-)+ C2,1(Vo(P+HL-,P+HL-)VO(P+BL-,P'BL-)) (6) and we made use of the orthogonality condition c2,3c3,1
+
cl,Z
+ c2,l =
(7)
The last two terms contain diagonal CI energy corrections listed in Table I. Even though the expansion coefficients Cl,zand C2,1 are quite small (=10-2-10-3), we found that the last two terms of (6) are almost 2 orders of magnitude larger than the first. This is remarkable, since the first would be the only term, if one started with the common assumption that the excited state P* and the charge-transfer state P'HL- denote transitions between completely localized orbitals. From (4) and (6) it becomes clear why it is
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989 1635
Long-Range Electron Transfer TABLE I: Transition Energies, Diagonal CI Matrix Elements, and Exchange Couplings for Several Charge-Transfer States (CT)"
CT state PL'PMPL'BLBM'HMPM'PLBL'HLPL'BMPL'HLPL'HM-
CT energy after CI
diagonal CI matrix element Vo(CT,CT)
1.696 2.278 2.343 2.288 2.367 2.355 2.569 2.71 1
-1.623 -1.122 -1.264 -1.775 -1.269 -1.065 -0.760 -0.754
exchange coupling Jo 3.3 x 10-1 7.0 X 5.0 X 2.8 X 2.1 x 3.0 x 6.0 x 3.1 X
lo4 IO-* lo-' 10-3 10-5 10-7 10"
"All values are given in electronvolts. The transition to P* is denoted as PLtPM-to emphasize its charge-transfer character.
difficult to predict these electronic interactions accurately. The orbital energy differences tk - c,, enter as denominators in (4), so that a small shift of the orbital energies belonging to one pigment relative to that of another can cause large effects on the CI matrix elements. Shifts are induced by the polar residues surrounding the pigments. The most important are due to the histidines which we included already in the calculation. They transfer charge up to 0.15e to the bonded bacteriochlorophylls and bring our calculation the LUMOs into a close energetic region of the LUMOs of the bacteriopheophytins. In other words, we would not have reached a delicate orbital tuning without them. The excitation of P* induces a strong change in the electronic charge distribution. $o the HOMO of P is to 62% localized on PL, but g2is the 64% localized on PM. The resulting change in permanent dipole is 8.18 D with an angle of this vector to the transition dipole of 40'. These results compare quite well with the experiment^.'^,]^ Considering the close arrangement between the LUMOs of P and HL and the parametric dependence of the orbital energies upon the nuclear configuration and the charge distribution, one might obtain orbital crossing during the equilibration process within P*. Such an effect would increase the effective CI responsible for the charge separation. It would also induce a rapid homogeneous dephasing, which has been studied by different techniques.I6-l8
Indirect Coupling Routes Next we compare the direct coupling (6) with indirect coupling routes, which involve one or more excited (charge-transfer) states as virtual intermediates. An obvious choice for such an intermediate is the charge-transfer state P+BL-, which leads in second-order perturbation theory to the interaction term V(P* ,P+BL-,P+HL-)= V(P*,P+BL-) V(P+BL-,P+HL-)/(E(P*) - E(P+BL-)) (8) Again we can introduce the expansion (1) and obtain to first order as the main contribution V(P*,P+BL-,P+HL-) = Vo(P*,P+BL-,P+HL-)+ c1,3c3,2(Vo(P*,P*) - Vo(P+BL-,P+BL-))(Vo(P+BL-,P+BL-) VO(P'HL-,P+HL-))/(EO(P*)- Eo(P+BL-)) (9) If we combine the direct interaction from (6) with the indirect we obtain on the energy shell (E(P*) = E(P+HL-)) in agreement with the description in the local basis an interaction Vc: Vc(P*,P+HL-) = u23u3,/(Eo(p*)
- Eo(PBL-))
700
803
900
1000
wavelength l n m )
Figure 2. Absorption spectrum for the Q, region of Rps. uiridis. Open circles are the experimental data from ref 25. Bars give the calculated 10 lowest transitions.
Finally we consider the exciton charge-transfer (ECT) coupling with BL'HL- as a real or virtual intermediate. For the two-step process to be consistent with the experiment the transition P* to BL'HL- must be rate determining, and the following process BL'HL- to P+HL- must be so fast that BL'HL- cannot be resolved within 25 fs.'9,20 The charge-transfer state gets its transition dipole mostly from BL*. In the local basis we get V(P*,BL*,BL'HJ = Vo(P*,BL+)U,,/(E(BL*) - E(P*)) (1 1) which amounts to 3 cm-]. For the interaction between BL'HLand P+HL- we need to know the coupling U0,-2between the HOMOS of P and B L . We found it to be the only sizable coefficient among the HOMOS (C,,,-2 = 0.0086), and we obtain V(BL+HL-,P+HL-)= U0,-2= 12 cm-'
(12)
This is 4 times as much as the coupling for the first step. So we predict the rate to be more than 16 times as large as the ratedetermining step. Strictly speaking, the last coupling should be evaluated with the equilibium configuration corresponding to the relaxed state BL'HL-. If the energy of the state BL'HL- does not fall below P*, one has to treat BL+HL-as a virtual intermediate. If the orbital energies of B L and of HL become very close, this coupling route can dominate over the others. The interaction U2,3 between P and B L is 2.5 times larger than U2,5between P and B M . The higher value of eL(HM) relative to c~(HL)leads also to an increased energy difference between the charge-transfer states P'HM- and P'HL-. These facts may contribute to suppress the electron transfer on the M branch.
Exchange Coupling At this point we wish to inject a result that may throw further light on the CI coupling scheme for the electron transfer. For the charge-transfer state P+HL- the exchange coupling J , which is just half the singlet-triplet splitting of this radical pair, has been measured.21s22 The small value of 10-3-104 cm-' has played a major role in the discussion of the electron-transfer mechanism and the possible involvement of BL.23*24We can express J in terms of an integral over the orbitals $o and $, and expand #z in ( 1 ) to (4) to get in zero order Jo = Jd'
dr'$o(r) $2(r)e2/(r - r ? $o(r? $2(r? =
C,,?Jdr
(10)
dr'Po(r) Pl(r)e2/(r - r ? cpo(r? P I ( d = o.5c1,22(E(P*) - E(3P)) (13)
Using the energy difference given in Table I, we find the very small value of V, = 0.07 cm-l.
(19) Martin, J. L.; Breton, J.; Lambry,
J. C.; Fleming, G. Nuto ASI Ser.
A : Life Sci. 1988, 198.
(14) Lockhardt, D. J.; Boxer, S . G. Biochemistry, 1987, 26, 664. ( 1 5 ) Liische, M.; Feher, G.;Okamura, M. Y . Proc. Nutl. Acud. Sci. U.S.A. 1987, 84, 7537. (16) Boxer, S. G.; Lockhardt, D. J.; Middendorf, T. R. Chem. Phys. Lett. 1986, 123, 416. (17) Meech, S. R.; Hoff, A. J.; Wiersma, D. A. Chem. Phys. Lett. 1985, 121, 287. (18) Tang, D.; Jankowiak, R.; Gillie, J. K.; Small, G. J.; Tiede, M. D. J . Phys. Chem. 1988, 92, 4012.
(20) Breton, J.; Martin, J. L.; Petrich, J.; Migus, A,; Antonetti, A. FEES Lett. 1986, 209, 37. (21) Hunter, D. A.; Hoff, A. J.; Hore, P. J. Chem. Phys. Lett. 1987, 134.
6.
(22) Ogrodnik, A.; Remy Richter, N.; Michel-Beyerle, M. E.; Feick, R. Chem. Phys. Lett. 1987, 135, 576. (23) Marcus, R. A. Chem. Phys. Lett. 1987, 133, 471. (24) Bixon, M.; Jortner, J.; Michel-Beyerle, M. E.; Ogrodnik, A,; Lersch, W. Chem. Phys. Lett. 1987, 140, 626.
1636
Scherer and Fischer
The Journal of Physical Chemistry, Vol. 93, No. 4, 1989
If we incorporate configuration interaction we obtain the relation 2J = V:
E(P+BL-) - E(P*) E(P+BL-) - E(P*HL-) 1 E(P*) - E(P+HL-)
+ E(P+HL-)1 - E(3P*)
)
(14)
It differs from similar relations used b e f ~ r e by ~ the ~ ~second ' ~ ~ ~ factor, which together with the first gives the coupling square V: for the recombination from 3P+HL-to 3P* instead of that for the charge separation V:. Experimentally there is no conflict between J and Vr2 (ref 20), which indicates that only V, is not well understood.
Absorption Spectrum An important test for the quality of the quantum calculation is the absorption spectrum. To achieve agreement with experiments, the INDO-SCI treatment has to be corrected in at least two points: First, the transition dipole moments p and as a result also the exciton-type intermolecular interactions have to be reduced. We used in Figure 2 a reduction factor of 0.5 for p i and 0.25 for the excitonic interaction. Second, the spectrum has to be shifted to the red, since the number of CIS (80) is still small for the six pigments and since the protein environment is not included except for the four histidines. The polarization of the protein environment should lower also our charge-transfer states. We obtained the stick diagram of Figure 2 with an energy shift of 3500 cm-I for all transitions and 650 cm-I as extra shift for all excited states of P. The correlation with the experimental pointsz5 is quite satisfactory considering the fact that the monomeric transitions of BM, BL, HM, and HL are no longer independently adjusted in energy. In particular it is interesting to note that the splitting and the intensity ratio between the states of HL* relative to HM* come out in the right order. This feature is ultimately connected to the asymmetry of the dimer. The spectrum shows four states of mixed excitonic and charge-transfer character which belong essentially to P. Warshel and ParsonZ6 incorporated also charge-transfer states within a a-electron treatment. This way certain aspects of the spectrum such as the shift and charge-transfer character of the dimer band may be produced by shifting of the internal excitonic and charge-transfer states. However, we found within the a-electron model for the lowest transition P* a change in the permanent dipole that points almost in the opposite direction as compared to the INDO-SCI modeLZ7 Here the H O M O is localized to 62% on PLwhile the corresponding state within the a-electron model has stronger delocalization with a tendency to localize this orbital more on PM. The opposite applies to the corresponding LUMOs. The physical origin for this difference is found in the u-system, which together with the Mg orbitals causes the change in the charge distribution within these orbitals. For a further comparison with the exciton model it is convenient to transform the dimer orbitals to a basis of molecular orbitals, which are localized on the two pigments PL and PM. Denoting the HOMOS as m ( P M )and m(PL), the LUMOs as fi(PM) and e ( P L ) , and the corresponding zero-order orbital energies as tH(PM),cH(PL), tL(PM),and tL(PL), respectively, we find that the on-site energy differences tL(PM) - tH(PM)and tL(PL)- CH(PL) are similar. However, the intersite values cH(PL)- eH(PM)and cL(PL) - tL(PM) differ by about 1000 cm-'. Within the pure exciton model this difference does not show up. It affects, however, the charge-transfer energies, such that the transition from a ( P L ) to fi(PM) becomes the lowest transition. Within this local basis we find a relatively strong "one-particle'' S C F interaction U(PL,PM) of 1400 cm-' between the orbitals (PL(PM)and (PL(P,). The resulting mixed exciton-charge-transfer state P* gets most of the intensity from the other transitions such (25) Breton, J. J . Biochim. Biophys. Acta 1987, 810, 235. (26) Parson, W. W.; Warshel, A. J . Am. Chem. SOC.1987, 109, 6152. Warshel, A,; Parson, W. W. J . Am. Chem. Soc. 1987, 109, 6143. (27) Scherer, P. 0 .J.; Fischer, S. F. Nato ASISer. A: LifeSci. 1988,425.
as a ( P L ) fi(PL) and a ( P M ) fi(PM). These experience CI coupling via transition dipole interactions and thus form two mixed states separated by 685 cm-', out of which the lower one is essentially perpendicular polarized to the state P*. So it assumes the role of the upper exciton band. We found further that P* gets sufficient intensity (about twice as much as one monomer) only if CI with the Soret bands is included. Scherz et aLZ8pointed at experimental evidence for this intensity redistribution shift in the dimers. An exciton model without charge-transfer states29 cannot account for this effect completely, since the charge-transfer states reduce the intensity shifting from the Qy transition into the Soret band relative to that in a monomer. Analyzing the excitations within the S C F orbital basis of the full hexamer, we find that the state P*, denoted as 1 in Figure 2, is a rather pure transition cpo cpz (87%) with some admixture of BL* and BM*. States 2 and 3 have mostly character of BL* and BM*, where 2 has more BM character and BL* mixes stronger with HL* (state 4) than does BM* with HM*. Furthermore, the excitonic states 5 and 7 of P mix with HL*. Only state 6 is a rather pure excitation of HM. It is followed by 7 , the upper exciton state of P, and 8, the upper partial charge-transfer state of P. States 9 and 10 already contain contributions of the Q, regime. For a crucial test of the calculation we have to be able to predict the LD spectraZSwith the same parametrization. This goal cannot be reached without allowing for further shifts of the diagonal energy differences of the local excitations, which are expected, since the protein environment is incorporated in a rather incomplete manner with the four histidines. The predicted charge-transfer states are relatively close in energy to P*. In particular we found that the state P'BL- dropped in energy as a result of the attachment of the histidines. Apparently this is due to the positive charge on the five-membered histidine ring which overcompensates for the effect of the transferred negative charge on the pigment. In Table I we listed the energies of several charge-transfer states together with the diagonal CI contributions and their exchange coupling. The state P* is denoted as PL+PM- to indicate its charge-transfer character. -+
+
-
Concluding Remarks Some of our conclusions rest critically on the choice of the initial state. One might argue that the CI interaction with other states contributes in a coherent way to the initial state.26 The situation is complicated since the state preparation depends on the excitation conditions and the internal damping mechanisms. Crudely speaking, if the width of the admixed states becomes larger than their coupling strength and their spacing relative to P*, they should no longer be part of the initially prepared state. Electron-transfer states couple particularly strongly to the polar residues and thereby receive a large width. That is our reasoning to treat the coupling of P* to the charge-transfer state P'HL- incoherently as the source for the electron transfer. The excitonic states, however, can mix coherently as can be seen from the stationary spectrum. So one ought to incorporate them in the construction of the initial state P* even for pulse excitation. We dealt with this question by a prediagonalization procedure, which involves a transformation to a local basis, a diagonalization of the intermolecular excitonic couplings, and a back transformation. For the new states we found that the admixture of B* and HL* into P* affected the electron-transfer coupling not substantially. However, the inclusion of the admixture of the Soret components from the dimer into P* increased the electron-transfer coupling from 3 to 4 The partial delocalization between the LUMOs of P and of HL is almost entirely mediated via the LUMO of B,. This may be thought of as a superexchange mechanism and leads to the admixture of the state P'BL- to P*99Z1which stands for the indirect v ~could , ~ not ~ bring this mechanism (10). In earlier ~ o r k ~we (28) Scherz, A,; Rosenbach, V.; Melkin, S. In Antennas and Reaction Centers of Photosynthetic Bacteria; Michel-Beyerle, M. E., Ed.; SpringerVerlag: Berlin, 1985; p 143. (29) Knapp, E. W.; Scherer, P. 0. J.; Fischer, S. F. Biochim. Biophys. Acta 1986,852, 295. Scherer, P. 0.J.; Fischer, S. F. Biochim. Biophys. Acta 1987, 891, 157.
J . Phys. Chem. 1989, 93, 1637-1642 mechanism in harmony with the Stark spectrum30or the temperature dependence of the charge ~eparati0n.l~ We still find that this route cannot explain the fast charge separation. For the excitonic coupling between P* and BL’HL- a delocalization between the LUMOs of B L and HL is needed. This mechanism becomes particular effective if the energies of BL’HL- and BL* are close in energy. We took the exchange coupling J of the radical pair P’HL- as evidence for orbital delocalization. We established the interrelation, (14), between the exchange-coupling J and the square of the combined electron-transfer coupling V,. This relation may be tested for artificially linked donor-acceptor systems with variable bridges, where the coupling may not be so easily affected by relaxation processes. It seems that we have reached a point where it becomes important to use further improved structural data and to incorporate more elements of the protein surrounding such as water molecules (30) Scherer, P. 0. J.; Fischer, S . F. Chem. Phys. Letf. 1986, 131, 153.
1637
to predict the orbital energy spacings more accurately. Also a self-consistenttreatment of the partial delocalization in conjunction with the nuclear reorgani~ation~’-~* should be included for the description of this class of rapid charge-separation processes. In a forthcoming paper33we will show that the Stark spectrum and the spectrum for linear dichroism can be well described if the orbital energies are properly adjusted.
Acknowledgment. We thank Dr. Plato for fruitful discussions that helped us to develop an INDO program similar to the one he is using. We also thank Dr. Deisenhofer, who provided us with the structural data. Finally, we acknowledge support by the Deutsche Forschungsgemeinschaft SFB 143 C2. (31) Fischer, S . F.; Nussbaum, I.; Scherer, P. 0. J. In Antennas and Reaction Centers of Photosynthetic Bacteria; Michel-Beyerle, M. E., Ed.; Springer-Verlag: Berlin, 1985; p 256. (32) Knapp, E. W.; Fischer, S. F. J . Chem. Phys., in press. (33) Scherer, P. 0. J.; Fischer, S. F. Chem. Phys., special issue, edited by D. Wiersma, in preparation.
Doping and Anion-Exchange Thermochemistry of Electrochemically Prepared Polypyrrole Larry S. Curtin, Marc McEllistrem, and William J. Pietro* Department of Chemistry, University of Wisconsin-Madison, (Received: May 31, 1988)
Madison, Wisconsin 53706
Solid-state voltaic cells having silver anodes and polypyrrole cathodes were employed to study the thermochemistry of halogen doping of the electrically conductive polymer, as well as the thermochemistry of dopant exchange with aqueous solvated anions. Moderately large enthalpic driving forces exist for the exchange of perchlorate in polypyrrole for halide in the aqueous phase. In addition, the activities and activity coefficients for halides in halogen-doped polypyrroles have been determined.
Within the past decade, polypyrrole (l),has emerged to be one
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of the most important and extensively studied electrically conductive polymers.’ Its convenient electrochemical preparation affords a variety of anionically “doped” materials possessing a wide range of electrical conductivities.2 Moreover, these polymers are electroactive and can be electrochemically “switched” between the oxidized, conductive state and the neutral, insulating state. This property has been exploited to produce novel ion-gate membranes3 and microelectrochemical diode^.^ (1) For comprehensive reviews of the preparation and properties of polypyrrole see: (a) Diaz, A. F.; Kanazawa, K. K. In Extended Linear Chain Compounds; Miller, J., Ed.; Plenum: New York, 1983; pp 417-441. (b) Reynolds, J. R. J . Mol. Electron. 1986, 2, 1-21. (2) (a) Dall’Olio, A.; Drascola, Y.; Varacca, V.; Bocchi, V. C. R. Seances Acad. Sci., Ser. C. 1968, 267, 433-435. (b) Diaz, A. F. Chem. Scr. 1981, 17, 145-148. (c) Murthy, A. S.N.; Shri, P.; Reddy, K. S . J. Mater. Sci. Lett. 1984, 3,745-747. (d) Asavapiriyanont, S.;Chandler, C. K.; Gunwardena, G. A.; Pletcher, D. J. Elecfroanal. Chem. 1984, 177, 229-244. (e) Wernet, W.; Monkenbush, M.; Wegner, G. Macromol. Chem., Rapid Commun. 1984, 5, 157-164. (f) Wynne, K. J.; Street, G. B. Macromolecules 1985, 18, 2361-2368. (g) Warren, L. F.; Anderson, D. P. J . Elecrrochem. SOC.1987, 134, 101-105. (3) Burgmayer, P.; Murray, R. W. J. A m . Chem. SOC. 1982, 104, 6139-61 40.
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We,5 and others,6 have recently discovered that the anions incorporated into the polypyrrole matrix during electrochemical film growth can be subsequently replaced with a large number of different anions by simply soaking the film in an aqueous or acetonitrile solution of the desired anion. We have demonstrated a potential use for this phenomenon by preparing electrochemically grown poly(pyrro1e iodide), a previously unknown materiaLs The iodide-doped polymer cannot be directly prepared by the conventional electrochemical method since the potential required for the oxidation of pyrrole is higher than the 12/1- redox couple. This anion-exchange phenomenon is thus very useful for the incorporation of potentially interesting electroactive anions into polypyrrole that would be otherwise inaccessible by direct electrochemical preparation:
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The concurrent incorporation of anions during film growth, as well as the facile anion-exchange process, indicates that the anions are fairly mobile within polypyrrole and only loosely interact with (4) Kittlesen, G. P.; White, H. 1985, 107, 7373-7380.
S.;Wrighton, M.S.J . Am. Chem. SOC.
( 5 ) Curtin, L. S.; Komplin, G. C.; Pietro, W. J. J . Phys. Chem. 1988, 92, 12-13. (6) Schlenoff, J. B.; Chien, J. C. W. J. A m . Chem. Soc. 1987, 109, 6269-6274.
0 1989 American Chemical Society
