Magnetic field effects in the radical ion pair recombination of fixed

Anna G. Matveeva, Fyodor B. Sviridenko, Valery V. Korolev, Leonid V. Kuibida, Dmitri V. Stass, Leonid A. Shundrin, Vladimir A. Reznikov, and Günter G...
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J. Phys. Chem. 1995,99, 13930-13937

Magnetic Field Effects in the Radical Ion Pair Recombination of Fixed-Distance Triads Consisting of Porphyrins and an Electron Acceptor Udo Werner? Yoshio Sakaguchi, and Hisaharu Hayashi* Molecular Photochemistry Laboratory, The Institute of Physical and Chemical Research (RIKEN), Wako, Saitama 351-01, Japan

Go Nohya, Ryusho Yoneshima, Satoshi Nakajima, and Atsuhiro Osuka Department of Chemistry, Faculty of Science, Kyoto University, Kyoto 606, Japan Received: March 15, 1995; In Final Form: May 31, 1995@

Absorption decay curves and their magnetic field effect (MFE) are investigated for intramolecular radical ion pairs (RIPS)consisting of a porphyrin cation and a diimide anion. These groups are linked with rigid structures containing a second porphyrin, which helps to achieve a high yield of the ion pairs after photoexcitation. The decay of these radical ion pairs occurs by direct return electron transfer. The decay curves show biphasic behavior with lifetimes in the region 0.1-2 ps, according to the length of the molecular bridge. By means of the MFE we understand that the previously described biphasic behavior is caused by intersystem crossing in the RIP. The magnetic field changes the rate of the hyperfine-induced intersystem crossing and enhances the biphasicity. A scheme for the transitions is given, and numerical simulations reproduced the results satisfyingly. The dependence on the magnetic field strength points to an MFE of the hyperfine-type with small field strengths being very effective. The compounds with medium linker lengths show a saturationtype curve with a half width of 12 or 7 G for two types of cations. These values could be reproduced by applying hyperfine-coupling constants of component anion and cation radicals. The compound with the shortest molecular linker shows a J-resonance feature in its field dependence. The maximum is found at 4 G, pointing to a 2 G value of the exchange interaction for its RIP-separation of 23 A on average.

Introduction Multicomponent molecules, designed after the model of the bacterial reaction center, are currently being investigated by a number of research groups with the long-term goal of storing solar energy in the form of chemicals with high energy contents. The systems investigated here follow the model of the reaction center quite closely. They use a system of linked porphyrins to transfer the energy from the primarily excited electron donor group zinc porphyrin via the intermediate porphyrin to the attached electron acceptor. The energetics of these functional groups are specifically selected to optimize the efficiency of long-distance charge separation and energy storage. It was shown that molecules of this type can use the excitation energy effectively to produce intramolecular radical ion pairs (RIPS) with long lifetimes.' While former investigations concentrated on the synthesis of the compounds and the mechanism leading to the production of the final ion air,^.^ we report about the decay routes of this ion pair in this paper. The produced ion pair can in principle be used as an energy source for further chemical steps. A lifetime as long as possible is desirable for this purpose. The lifetimes are mostly defined by the recombination of the final RIP due to direct electron back-transfer. Through the study of the influence of an external magnetic field on the reaction, particularly on the lifetime of the final RIP, we can obtain further insight into the mechanisms of the reaction. This knowledge might be used to further improve the energy-harvesting properties of this scheme and gain some control by the easily adjustable parameter magnetic field

'

Present address: MPI fur biophysikalische Chemie, Abt. 010, Am Fassberg, 37077 Gottingen, Germany. @Abstractpublished in Advance ACS Absrracts, August 15, 1995.

0022-365419512099-13930$09.0010

strength. A magnetic field effect was also found for the natural photosynthetic reaction center as extracted from Rhodopseudomonas sphaeroide~~.~ or spinachS6 A second, not less important goal was to use the unique properties of these molecules to measure the exchange interaction between the unpaired electrons on the opposite ends of the molecule by means of the magnetic field effect (MFE). The mechanisms, which lead to an influence of weak magnetic fields on the reactions of photochemically produced radical ion pairs, are described in detail in the literature7,*and will be outlined only very briefly here. The MFE can be explained principally by the influence of the magnetic field on the spin development in the separated unpaired electrons in the radical pairs. The development of these spins comes into effect when the pair is going to recombine again: For pairs in an overall triplet configuration (T-RIPS)the recombination to the singlet ground state is forbidden. T-RIPS reach favorably the lowest triplet state of the donor moiety (if this triplet state lies energetically below the ion pair state), or they have to undergo a second intersystem crossing to recombine. Thus recombination rates and RIP-lifetimes become magnetic field dependent. The important mechanisms for this study are the hyperfinecoupling (hfc)-induced MFE and the J-resonance. In the MFE of the hfc-type, the singlet-triplet (S-T)-conversion of the radical pair is achieved by the differences of hyperfine interaction in the surrounding nuclei of both unpaired electrons, which lead to dephasing. While in zero field the hyperfine coupling can induce intersystem crossing between the singletRIP (S-RIP) and all three triplet levels of the RIP, the conversion reduces to that between the singlet state and the To-state when a magnetic field higher than the hyperfine coupling (gpB > 0 1995 American Chemical Society

Radical Ion Pair Recombination of Fixed-Distance Triads M h f c ) is applied. This can be observed as an increase of the recombination rate or as a decrease in triplet yield. The J-resonance-feature was found until now only in linked RIPs and in a mutant reaction enter.^ The mutual movements of the ion pair are restricted in these cases to certain distance regions. With this region in a suitable range (1-2.5 nm) the exchange interaction J between the unpaired electrons has a magnitude similar to the Zeeman energy applicable through an external magnetic field. The exchange interaction leads to a zero-field-splitting of 2J between the triplet and singlet total spin states of the RIP, resulting in a somewhat decreased S-Tconversion when no field is applied. At a certain field value a level-crossing of the T--state with the singlet state occurs, leading to an enhanced singlet-triplet-conversion at the field strength B,, = 21Jl/gp, followed again by a decreasing conversion at higher fields. The idea to use the MFE of linked RIPs to measure the distance dependence of the exchange interaction came already with the first findings of the J-resonance-feature in MFEcurves.I0 In the first approaches a direct identification between the field value of the resonance maximum (giving the exchange interaction 2151) and the most probable distance between the radical ions was assumed to be possible. In a more detailed analysis," however, it was shown that dynamical influences shift these values. A safe assignment can only be made with compounds of a very restricted distance or, ideally, completely rigidly linked pairs. On the other hand, some compromises with respect to the rigidity of the linker had to be made in former approaches. That is due to the fact that in most acceptor-donor bifunctional molecules the electron transfer rate tends to vanish when a long separation together with a rigid chain are used. The molecules used here have three obvious advantages for evaluating this type of curve: (i) Their high rigidity leads to a limited distance distribution. (ii) They deliver high yields of RIPs despite the fixed long distance between the intramolecular ions. (iii) The hyperfine interaction constants of the ions are very small and the ion pair lifetime is rather long. Both together lead to particularly sharp features in the magnetic field dependences. Other studies concerning the magnetic field effect in porphyrin-containing linked c o m p o ~ n d s have l ~ ~ ~little ~ similarity to the results reported here, due to the completely different nature of the linkers and electron acceptors used.

J. Phys. Chem., Vol. 99, No. 38, 1995 13931

0

M1;ZnP-1,4 benzene-HP-Pim

0

0

S1; ZnP-1.3benzene-HP-Pim

0

0

C H 2 N ~ N C I H l l

0

0

M3; DP- 1.4 benzene-ZP-Pim

Experimental Section The synthesis of the compounds used in this study was described or will be described el~ewhere.'.~Schemes of the molecules are shown in Figure 1. The short names of the compounds are given in the figure. The letters refer to the overall length of the compound (S M L), while the numbers are just counters. The lengths of the compounds, i.e. the centerto-center distances between the end groups, are given in Table 1. They were estimated with a molecular model and verified by three-dimensional computer modeling. In the case of XL1 the name refers to the long linker structure, although the RIPdistance is only in the medium range. In Figure 1, the general design consists of (from the left to the right) a porphyrin or diporphyrin part working as electron donor, a spacer consisting of one or more phenyl rings, a second porphyrin part (containing Zn centers or not), a phenyl as second spacer, and the electron acceptor. Abbreviations for the functional parts used in the text are as follows: ZnP, the lefthand side of M1, M2, XL1, and S1, working as the cation in the final RIPs; HP, the middle porphyrin of M1, M2, and XL1; HP', the middle porphyrin as in S1, L2, and M4; HP' is the same as HP only lacking the attached alkyl groups; ZP', the

L1; DP-diphenyl-ZP-Pim L2; DP-diphenyl-HP-Pim M4; DP-1,4 benzene-HP-Pim

Figure 1. Structures of the investigated compounds. The compounds L2 and M4 are not included, since they equal L1 and M3, respectively, only their bridging porphyrin is metal free.

same as HP' but with a Zn center atom (M3 and Ll); DP, lefthand group in M3, M4, L1, and L2. The groups working as the electron acceptor and anion in the RIPs are 1,4,5,8naphthalenetetracarboximide (Nim) in M2 and pyromellitimide (Pim) in all the other compounds. The setup used is a flash photolysis apparatus described p r e v i o ~ s l y .The ~ ~ excitation was carried out with the second harmonic of a Nd:YAG laser at 532 nm with a pulse width of 5 ns. The excitation energy was chosen as small as possible,

Werner et al.

13932 J. Phys. Chem., Vol. 99, No. 38, 1995

TABLE 1: Center-to-CenterDistances of the Intramolecular Radical Ions As Estimated Three Dimensionally with a CPK-Model sample s1 M1 M2 M3, M4 L1, L2 XL 1

dav{(A) 22.4 24.2 24.4 24.5 28.0 24.6

d,b (A) 21.4

dmax(A)

24.3

24.1

23.9

25.3

23.4

is the average of d, and d, or, in the case of only one possible conformation, its distance. d,, and d, refer to the extrema1 distances in the case when different conformations are possible. to prevent deformations of decay curves due to nonlinear effects and side products out of two-photon absorption. Each displayed curve or point in the MFE-curves is the average of 20-50 single shots. No changes due to irreversible photochemical processes were observed for any of the samples. The recording device is a Hewlett Packard HP54522A digital oscilloscope with 0.5 ns time resolution and 8-bit amplitude resolution. The magnetic field was produced by a Tokin SEE-1OW electromagnet and measured by an F. W. Bell 9200 gaussmeter. The hall probe was placed in the surroundings of the excited sample volume. However, in the range of the very small fields of interest here, the local remanent fields could not completely be compensated. For that reason measurements were carried out in series going from negative to positive magnetic fields. Since the polarity of the field plays no role for the observed MFE, the point of symmetry in the achieved curves was taken as the zero position. It had an offset of maximally 0.7 G (1 G = 0.1 mT) to the displayed zero field. As a conclusion of the comparison of repeated measurements, we assume the reproducibility of magnetic field values to be within 0.5 G. The sample was temperature controlled at a temperature of 22.5 "C, if not stated differently. Samples were weighed and dissolved in the solvents as purchased (Kanto Chemicals tetrahydrofuran, dehydrated, for organic synthesis; Merck dimethylfoxmamide, Uvasol, for W spectroscopy) in a concentration of 2.5 x mol d ~ n - and ~, the solutions were poured into a quartz cuvette of 10 mm optical path length. They were bubbled with a stream of dry nitrogen in a glovebox for 15-20 min. The measurements were carried out within 2 h after sealing the cuvettes. Odave

Results The transformations leading to the formation of the final RIPS were investigated in previous and parallel investigations by transient absorption measurements in the picosecond and nanosecond time scale described e l s e ~ h e r e . ~The ~ ~scheme ~'~ of the RIP formation is given and explained in Figure 2, for the example of ZnP-HP-EA (EA = electron acceptor). Excitation (a) of the ZnP moiety to its first excited singlet state is followed by energy transfer (b) to the bridge porphyrin, electron transfer (c) between this porphyrin and the electron acceptor, and hole transfer (d) from the bridging porphyrin to the electron donor porphyrin. This scheme results in the longlived intramolecular radical ion pair in its initial overall singlet state. The hyperfine interaction converts (e) a part to the overall triplet state with a magnetic field dependent rate. The pair cannot recombine from the triplet state (indicated by the dashed arrow g), because the triplet state of ZnP lies energetically above the RIP. Return electron transfer brings the molecule back to the ground state. While the processes leading to the RIPproduction (a-d in Figure 2 ) occur within a few nanoseconds, the lifetime of the RIPs is several hundred nanoseconds. This scheme is valid for all the compounds with somewhat varying energies of the intermediate states. An exception are

(ZnP)- HP-EA

Figure 2. Scheme of the pathway of radical ion pair formation shown for the example of ZnP-HP-EA, Arrows: a, excitation of the ZnP

moiety to its first excited singlet state; b, energy transfer to the bridge porphyrin; c, electron transfer between this porphyrin and the electron acceptor; d, hole transfer from the bridging porphyrin cation to the electron donor porphyrin; e, hyperfine-driven intersystem crossing in the RIP, magnetic field dependent; f, retum electron transfer back to the ground state; g, (energetically unfavorable) retum electron transfer to produce the lowest triplet state. The RIPs on both sides of mow e are the long-lived species, monitored in the decay curves and MFEcurves. The singlet spin state of the system is preserved through steps a-d, so that the RIP is born with singlet-correlated spins in its unpaired electrons. the P' (porphyrin without attached alkyl groups)-containing compounds. In these compounds the different energetics leads to a difference as follows: The electron transfer occurs between the P' group (P'*) and the electron donor. The negative charge on P' is then transferred to the electron acceptor, resulting in the same final ion pair as above.Is The transient absorption was measured in the absorption band of the radical anion, which differs for the two electron acceptors used. The characteristic peaks] are seated at 715 nm for Pimand 680 nm for Nim-. It was often more favorable to measure either in the range 600-680 nm for Pim- and Nim- or at around 475 nm for Nim-, although the absorbance is weaker there. This is as a consequence of the used setup, which has a much better signal-to-noise ratio at wavelengths shorter than 680 nm. Other criteria for the choice of the measuring wavelength were the transparency for the monitoring light, which decreases below 600 nm and the fluorescence of ZnP at 640 nm. Checks with both types of acceptors showed that the decay times were unchanged at the characteristic bands compared to the wavelengths in the ranges given above. Also the effects of the magnetic field were the same in both spectral regions. No magnetic field effect was found in the fluorescence emission of the samples by measuring without monitoring light. The recorded emission is ascribed to the primary fluorescence of the excited porphyrin moiety. Decay curves for the compound M4 are shown Figure 3a. Similar curves were observed for all the compounds with medium length, i.e. Ml-M4. Each of the curves can be represented by a biphasic decay, with a fast decaying part in the beginning and a slower one following. The application of a magnetic field enhances this feature by accelerating the fast decay part and slowing down the slow one. A more general description (valid for compounds S1, Mn, and L2) of the changes caused by a magnetic field, compared to B = 0, is as follows (cf. Figures 3 and 6): (i) The amplitude at the initial peak is equal or a little ( C i k Uik, uik being the hyperfine coupling constants, it should resemble a resonance curve:I9 low values for high and low fields, and a peak coming up at the “resonance” gpB = 21JI. In contrast to that prediction, all MFE-curves found until now resemble that shown in Figure 4 for J = 0 and that shown in Figure 5 for a nonvanishing J. The experimental results never showed a resonance where R,,, exceeds 50%, and no curves were found where R,,,= 0, rather R,,,became some 60%. This might be due to the fact that the experiments didn’t fit the above conditions: J is either not fixed or too small or the RIP decay is too fast. Some refinement was added to the theory to explain the deviation by a distribution of J-values, leading to an averaging of the curves belonging to fixed Ss, which in consequence led to good agreement between experiment and simulation^.'^,^^*^^

Anyway, it seems surprising that the new example of a J-resonance-feature described here has again the same general shape as all the other examples before. The very small hyperfine coupling constant and the almost fixed distance are ideal conditions for exhibiting the “pure” resonance curve. However, in the case of SI the exchange interaction will be too small to reach a clear separation of the saturation and resonance behavior of the MFE-curves. Therefore we consider it most challenging to find a varied compound with a somewhat shorter distance in the 18-20 8, region and hyperfine coupling constants as small as here. Combined with the strong distance restriction, it could turn out to be the fiist candidate to show the “theoretical” MFEc&e with J-resonance. Calculation of BID. It is possible to obtain a semitheoretical value of the half width of the MFE, B1/2, when the hyperfine coupling constants of both radicals are known. First an effective Bi for both radicals is calculated by a semiclassical appr~ach:~’ (4) where Uik is the hyperfine coupling constant and I k the spin quantum number of nucleus k. For the anion group we use as a first approach the hyperfine coupling constants of pyromellitimide.28 Because in this reference data NH instead of NCH2 groups are present, we estimate the uik for the NCH2 groups by a comparison of the values found for maleimideZ9 with those for N-eth~lmaleimide.~~ Doing that, we assume that the overall pattern of spin distribution remains unchanged. The used values are given in Table 4. Finding literature values for ajk turned out to be even more difficult for the cation group. We will use the hyperfine coupling constants for zinc tetrapr~pylporphyrin.~~ In that compound there are eight H’s (in the frst CH2 of four propyl groups) with non-neglible influence on the hfc. Meanwhile, these positions in ZnP are substituted by two H’s and two phenyl groups. Phenyl groups were found to have no hfc-infl~ence.~‘For the two single hydrogens we use the hfc-constants found for a magnesium p~rphyrin.~’ Using the values as listed in Table 4 and IH = ‘12 and IN = 1, one obtains the effective magnetic fields B1 = 5.82 G for the porphyrin cation and B:! = 2.81 G for Pim-.

Radical Ion Pair Recombination of Fixed-Distance Triads To estimate Bl/2 we use an empirical equation given by Steiner, which proved to be the most suitable in the range of small hyperfine coupling constants,’ compared to that of Weller:

J. Phys. Chem., Vol. 99, No. 38, 1995 13937 (STA) and the German Alexander-von-Humboldt Stiftung. HH thanks the MR (magnetic resonance) Science Project on Chemical Dynamics from RIKEN for financial support.

32

+

B,,, = (31B,2 B221)1’2 That results in Bl/2 = 11.2 G for compounds SI, M1, and M2. Of course this value is only a rough estimation, due to the uncertainties connected with the used ark and also the empirical nature of eq 5 . For the explanation of the smaller B1/2 values for the compounds with DP as cation, compared with ZnP, we assume that the spin distribution in the cation is similar to that in a porphyrin dimer. Thus, the spin may equally spread over both porphyrin parts of the cation. As a general rule, it was observed that the hyperfine constants of dimers are a little bit smaller than half of those of the monomers.33 Applying this rule (a factor of 0.4 to ark and the double number of nuclei) for the calculation for B112 of the DP+ cation gives Bl(DP+) = 3.3 G. Using this value in eq 5 results in = 7.5 G for the compounds containing DP+ as cation. Both values agree quite nicely with the experimentally found value, as can be seen by the comparison given in Table 3. Concerning the comparison of ZnP and DP, the agreement of theory and experiment may be seen as a proof for the dimer nature of the DP+ cation. The marked difference between the MFE-curves found here and that described p r e v i ~ u s l y ’ ~for . ’ ~compounds of porphyrin linked to electron acceptors is explained by two properties of these systems: (i) Because T-RIPS are also initially produced from triplet porphyrins, their MFE-curves can be explained by the (spin) relaxation m e ~ h a n i s m . ~Consequently .~~ their B1/2 values are much larger than those caused by the hyperfine coupling mechanism. (ii) The flexible linker is shorter and allows mutual motions. This leads to shifted and broader distance distributions and dynamical effects. Consequences of the latter point are described in detail in ref 11. Conclusions The effect of an externally applied magnetic field on the decay curves of porphyrin-porphyrin-diimide triads shows that the biphasic behavior is due to conversions between the singlet and the triplet state of the total spin of the intramolecular radical ion pair. Simulations demonstrated that the curves could reproduce when the decay of singlet-RIPS to the ground state has a rate comparable to that of the singlet-triplet-interconversion. The S-T-interconversion rate is governed by the hyperfine interaction and can be reduced by a magnetic field to roughly one-third. Comparison of experimental and theoretical values for Bl/2 did not only confirm the hyperfine interaction as the source for the MFE? but also led to a recognition of a porphyrin dimer acting as cation in the DP-containing compounds. MFE-curves show a sensitivity to very low fields such as 7 G , due to the small hyperfine coupling constants in both radical ions. The appearance of a MFE is strongly related to the lifetime of the RIPS,in the way that an influence of the magnetic field can only be detected when the lifetime is not too long. In the compound with the shortest interradical distance, the MFE showed the J-resonance feature but (in spite of its particularly small hfc-constants) fails to exhibit a “resonance” shape of the MFE-curve. Acknowledgment. UW wishes to acknowledge the STA Fellowship of the Japanese Science and Technology Agency

References and Notes (1) Osuka, A.; Zhang, R.-P.; Maruyama, K.; Ohno, T.; Nozaki, K. Bull. Chem. SOC.Jpn. 1993, 66, 3773. (2) Osuka, A.; Nagata, T.; Kobayashi, F.; Zhang, R.-P.; Maruyama, K.; Mataga, N.; Asahi, T.; Ohno, T.; Nozaki, K. Chem. P hys. Lett. 1992, 199, 302. (3) Osuka, A.; Zhang, R.-P.; Maruyama, K.; Mataga, N.; Tanaka, Y.; Okada, T. Chem. Phys. Lett. 1993, 215, 179. Osuka, A.; Nakajima, S.; Maruyama, K.; Mataga, N.; Asahi, T.; Yamazaki, I.; Nishimura, Y.; Ohno, T.; Nozaki, K. J . Am. Chem. SOC. 1993, 115, 4577. (4) Blankenship, R. E.; Schaafsma, T. J.; Parson, W. W. Biochim. Biophys. Acta 1977, 502, 255. (5) Hoff, A. J. Q . Rev. Biophys. 1981, 14, 599. (6) Rademaker, H.; Hoff, A. J.; van Grondelle, R.; Duysens, L. N. M. Biochim. Biophys. Acta 1980, 592, 240. (7) Steiner, U. E.; Wolff, H.-J. Photochemistry and Photophysics; CRC Press: Boca Raton, FL, 1990; Vol. I, Chapter 2. Steiner, U. E.; Ulrich, T. Chem. Rev. 1989, 89, 51. ( 8 ) Hayashi. H. Photochemistry and Photophysics; CRC Press: Boca Raton, FL, 1990; Vol. I, Chapter 2. (9) Hoff, A. J.; Gast, P.; van der Vos, R.; Vriese, J.; Franken, E. M.; LOUS,E. J. Z . Phys. Chem. (Munich) 1993, 180, 175. (10) Staerk, H.; Kiihnle, W.; Treichel, R.; Weller, A. Chem. Phys. Letr. 1985, 118, 19. (11) Staerk, H.; Busmann, H.-G.; Kiihnle, W.; Treichel, R. J . Phys. Chem. 1991, 95, 1907. (12) Werner, U.; Kiihnle, W.; Staerk, H. J . Phys. Chem. 1993,97,9280. (13) Staerk, H.; Kiihnle, W.; Weller, A,; Werner, U. Z . Phys. Chem. (Munich), in press. (14) Werner, U.; Wiessner, A,; Kiihnle, W.; Staerk, H. Photochem. Photobiol. 1995, 85, 77. (15) Saito, T.; Hirata, Y.; Sato, H.; Yoshida, T.; Mataga, N. Bull. Chem. SOC.Jpn. 1988, 61, 1925. (16) Nakamura, H.; Uehata, A.; Motonaga, A.; Ogata, T.; Matsuo, T. Chem. Lett. 1987, 543. (17) Sakaguchi, Y.; Hayashi, H. J . Phys. Chem. 1984, 88, 1437. (18) Osuka, A.; Nakajima, S.; Mataga, N.; Okada, T.; Taniguchi, S.; Ohno, T.; Nozaki, K.; Yamazaki, I.; Nishimura, Y. Submitted to J . Am. Chem. SOC. (19) Schulten, K.; Bittl, R. J . Chem. Phys. 1985, 84, 5155. (20) Baumann, D.; Ulrich, T.; Steiner, U. E. Chem. Phys. Lett. 1987, 137, 113. (21) We want to thank one of the reviewers for a remark regarding this. (22) Turro, N. J. Modem Molecular Photochemistry; Benjamin Cummings Publishing Co.: Menlo Park, NJ, 1978; pp 354 and 590 ff. (23) Werner, U.; Staerk, H. J . Phys. Chem. 1993, 97, 9274. (24) Werner, H.-J.; Schulten, Z.; Schulten, K. J. Chem. Phys. 1977,67, 646. (25) Bittl, R.; Schulten, K. J . Chem. Phys. 1989, 90, 1794. (26) Busmann, H A . ; Staerk, H.; Weller, A. J . Chem. Phys. 1989, 91, 4098. (27) Schulten, K.; Wolynes, P. G. J . Chem. Phys. 1978, 68, 3292. (28) Russell, G. A,; Malatesta, V.; Morita, T.; Osuch, C.; Blankespoor, R. L.; Trahankovsky, K. D.; Goettert, E. J. Am. Chem. SOC. 1979, 101, 2112. (29) Magnetic Properties of Free Radicals; Landolt-Bomstein New Series; Hellwege, K.-H., Ed.; Vol. 9, Part d, p 69. (30) Fujita, I.; Hanson, L. K.; Walker, F. A,; Fajer, J. J . Am. Chem. SOC.1983, 105, 3296. (31) Fajer, J.; Borg, D. C.; Forman, A,; Dolphin, D.; Felton, R. H. J . Am. Chem. SOC.1970, 92, 3451. (32) Weller, A.; Nolting, K.; Staerk, H. Chem. Phys. Letr. 1983, 96, 24. (33) Yoshimi, H.; Kuwata, K. Mol. Phys. 1972, 23, 297 and refs 1-5 therein. (34) Hayashi, H.; Nagakura, S. Bull. Chem. SOC. Jpn. 1984, 57, 322.

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