Chain Dynamics Cause the Disappearance of Spin-Correlated

© Copyright 1996 by the American Chemical Society

VOLUME 100, NUMBER 33, AUGUST 15, 1996

LETTERS Chain Dynamics Cause the Disappearance of Spin-Correlated Radical Pair Polarization in Flexible Biradicals Malcolm D. E. Forbes,* Nikolai I. Avdievich, Jonathan D. Ball, and Gregory R. Schulz Venable and Kenan Laboratories, Department of Chemistry, CB 3290, UniVersity of North Carolina, Chapel Hill, North Carolina 27599 ReceiVed: January 23, 1996; In Final Form: June 5, 1996X

X-band time-resolved electron paramagnetic resonance (TREPR) spectra of 1,16- and 1,21- acylalkyl biradicals, obtained in toluene solution at low temperatures (187-253 K), are reported. The spectra show a strong temperature dependence in their patterns of chemically induced electron spin polarization. The spin-correlated radical pair (SCRP) mechanism dominates at high temperatures, while the radical pair mechanism (RPM) is the main pattern at lower temperatures. It is postulated that the SCRP spectrum is suppressed at the lower temperature due to molecular motion on a time scale which modulates the exchange interaction (J) between the unpaired electrons. Simultaneously the RPM is enhanced by this motion. Average values of J calculated from end-to-end distance distributions for the C21 biradical show that in the absence of this dynamic effect, an intense SCRP spectrum would be present at the lower temperature. The results demonstrate that the interpretation of average J couplings may be difficult in temperature regions where these motional effects dominate the appearance of the spectrum.

In photochemical reactions that produce geminate radical pairs (RPs) in environments with restricted diffusion, the spin angular momenta of the unpaired electrons can play a large role in the observed lifetimes of the intermediates and in the product distributions.1 Examples of such systems include surface-bound RPs,2 radical ion pairs bound by a Coulombic potential,3 ionpair complexes,4 micelle-confined RPs,5 RPs produced in cyclodextrin host-guest complexes,6 and covalently linked biradicals.7 The rate of diffusion of the radical centers with respect to each other is also an important parameter affecting these observations. Phenomena such as magnetic field effects on lifetimes8 and chemically induced electron spin polarization9 (CIDEP) are also observed because of the interplay of spin and diffusive dynamics in the confined RP. The application of timeresolved optical10 and electron paramagnetic resonance11 (EPR) techniques to these systems has provided new structural and * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, July 15, 1996.

S0022-3654(96)00245-6 CCC: $12.00

kinetic information to be obtained and allowed the mechanisms of these reactions to be better understood. The time scale of EPR spectroscopy and the magnitude of the magnetic interactions in organic RPs make the technique sensitive to motional effects. Chemical exchange processes in RPs12 or modulation of the exchange interaction (J) in stable biradicals13 have been studied by steady-state EPR spectroscopy for more than 30 years. However, dynamic effects in timeresolved EPR (TREPR) spectra of confined RPs, which exhibit non-Boltzmann spin-state populations due to CIDEP mechanisms, have only recently been studied. New experimental results and theoretical developments from our laboratory14 and others15 have shown that the effect of motion on different time scales presents challenges in the interpretation of magnetic field effects16 and TREPR spectra of biradicals and micellar RPs and that more sophisticated theories and computational methods are required for adequate simulation of the observed phenomena.17 There are four distinct mechanisms of CIDEP in confined RPs and biradicals. The triplet mechanism (TM) arises due to © 1996 American Chemical Society

13888 J. Phys. Chem., Vol. 100, No. 33, 1996

Letters SCHEME 1

Figure 1. Polarization patterns for a radical pair consisting of a methyl radical •CH3 with hyperfine coupling constant aH and a second radical R• which has no hyperfine interaction. (A) RPM polarization shown for a triplet precursor and a negative exchange interaction, J, which leads to an E/A multiplet (low-field E, high-field A) for the methyl radical, and no polarization for R•. (B) SCRP polarization showing the splitting of each transition in (A) into E/A doublets with separation 2J.

selective population of the triplet sublevels in the precursor ketone.18 It is sensitive to the environment in that its magnitude is a function of the rotational correlation time of the precursor,19 but the effect is weak for the ketones studied here. Because it is not observed, the TM is not considered further. The magnitude of the radical pair mechanism (RPM) depends on the time scale over which the members of the RP can diffuse to and from regions where J is widely different.20 The radicaltriplet pair mechanism21 (RTPM) can be important in systems where the triplet state of the precursor molecule interacts with a doublet state radical, but that cannot happen here because we are working at very low concentrations of biradical (no more than 10-5 M) and the data are collected at short delay times. The last type of polarization is the spin-correlated radical pair (SCRP) mechanism,22 from which the average exchange interaction, 〈J〉, can be obtained by spectral simulation under certain conditions. The polarization pattern expected from the RPM and SCRP mechanisms for a simple RP with three equivalent hyperfine couplings on one of the radicals is shown in Figure 1. Both of these mechanisms manifest themselves in the spectra with different intensities and line shapes and positions and are easily modeled in the absence of motional effects such as J modulation. As we have demonstrated in several previous papers, modulation of J by conformational or diffusive motion can alter the SCRP spectral appearance to such an extent that standard simulation programs no longer work.14a We have also shown that the meaning of 〈J〉 is challenged when measurement takes place in systems exhibiting complex molecular motion on the EPR time scale.14b In this paper we report a new manifestation of motional effects in the TREPR spectra of flexible biradicals. The structures under investigation are shown in Scheme 1. The syntheses of the precursor ketones 1 and 223 and the production and detection of the biradicals 1a and 2a, obtained upon photolysis of toluene solutions of these ketones,11 are described in previous publications. The resulting acylalkyl biradicals have chain lengths of 16 and 21, respectively, for 1a and 2a.24 Decarbonylation is slow at the temperatures of our experiments and so the acylalkyl structures are the only ones we will consider in our analysis. We have previously studied 〈J〉 values for several C16 chain length biradicals because of the high sensitivity of their spectra to temperature.25 Evidence for J modulation effects in TREPR spectra at low temperatures has been reported

SCHEME 2

only for short (C10) biradicals. In all other reports of Jmodulated TREPR spectra, the effects were observed at high temperatures (313 K and higher).14a Theory predicts that both the RPM and SCRP mechanisms should be operative in systems where the radicals are allowed to diffuse to and from each other, but SCRP polarization is usually dominant because of the larger population difference in the spin states. This difference is created by selective reaction of RPs having a large fraction of singlet character.22 Scheme 2 shows how this arises for one nuclear sublevel of a biradical originating from a triplet precursor. For small 〈J〉 values, the singlet and middle triplet level mix quantum mechanically to become two new states, ψ2 and ψ3. The allowed transitions which lead to the E/A doublets are shown as arrows. The new states have substantial singlet character and are depleted rapidly by chemical reaction of the ends of the biradical, which occurs by cyclization or by disproportionation. This leads to relative populations in the four levels of 1/3, 0, 0, and 1/3 from top to bottom in Scheme 2. If there is no chemical reaction, the SCRP intensity is reduced by a factor of 2, as the populations become 1/ , 1/ , 1/ , and 1/ . However, this is the maximum effect that 3 6 6 3 chemical reaction can have on the SCRP intensity. Although it was not interpreted as such at the time, competition between SCRP and RPM mechanisms in a biradical TREPR spectrum at low temperatures was probably observed in a study of a very long (C26) acylalkyl biradical from our laboratory.26 In that paper, in addition to strong SCRP polarization, a small contribution from the RPM was observed at 227 K. This marked the first time that the RPM intensity overcame the SCRP enough to be observed in the TREPR spectrum when the SCRP polarization was also present. We now wish to reconsider these earlier data and discuss two phenomena which may be responsible for the reduction of SCRP intensity in the C26 spectrum. One is that the chemical reaction rate may be slowing down due to fewer encounters of the biradical ends, leading to smaller population differences as described above. However, as discussed above, the maximum decrease in intensity by this mechanism is a factor of 2. Also, for us to see no chemical reaction at all on the 100 ns time scale, the reencounter rate of the biradical would have to slow down to about 106 s-1, a rather small value for an alkyl chain.

Letters

Figure 2. X-band TREPR spectra of (A) biradical 1a and (B) biradical 2a taken in toluene at 0.1 µs delay time at the temperatures indicated. Each spectrum is shown scaled up below each raw dataset to show the peripheral structure.

A second possibility is that the chain dynamics are taking place on a time scale where modulation of J is lowering the intensity of the SCRP transitions. Basically, what happens is that the collapse of the E/A SCRP doublets begins to take place not only because the static distribution of end-to-end distances is changing but also because the motion of the radicals affects the line widths and positions, i.e., the time scale over which J is averaged. The net result is a splitting of the doublets that is a function of the interradical motion. Collapse of the doublets will lead to a decrease in the SCRP intensity. Simultaneously, while the RPM line positions and widths are unaffected by this motion, the intensity of the RPM polarization can be increased because of increased viscosity at lower temperatures, as noted in the early theoretical work on CIDEP.8 We believe that the spectra reported here and in ref 2f fall into this category, i.e., that the observed effect is attributed to more of an increase in the RPM than a decrease in the SCRP. It is interesting to note that an appropriate rate of change in J can enhance the RPM intensity in two ways: (1) by allowing the biradical to pass more often through regions of end-to-end distance where spin wave function evolution (S-T0 mixing) can take place;27 (2) by ensuring that the RPs spend less time in regions of large J, where the RPM is destroyed by dephasing. Observation of these phenomena is unique to time-resolved magnetic resonance methods and provides additional ways to probe the diffusive dynamics of RPs. Unfortunately, due to solubility problems, experiments at lower temperatures (below 220 K) on the C26 biradical were not possible. Here we present two new cases of temperature-dependent biradical TREPR signals. One of these shows the low-temperature extreme of diffusive dynamics and RPM/SCRP competition: the nearly complete disappearance of SCRP intensity in a flexible biradical. The TREPR spectra of biradicals 1a and 2a at two different temperatures are shown in Figure 2. All of the spectra are shown first as raw data and then scaled up so that the transitions

J. Phys. Chem., Vol. 100, No. 33, 1996 13889 on the perimeter can be more easily discerned. Apart from chain length and temperature, all experimental conditions for the collection of these datasets (solvent, concentration, light intensity, microwave power) were identical.28 Immediately discernible in the spectra at higher temperatures is the classic SCRP polarization pattern of E/A doublets. Such a pattern also indicates that the value of 〈J〉 is small in this system (less than the hyperfine coupling terms). At the lower temperatures for both biradicals, the polarization pattern more closely resembles the RPM, with low-field lines showing E polarization and the high field lines showing absorption. This pattern was observed with better resolution but poorer signal-to-noise ratio at delay times of 1.0 µs. The effect is very pronounced for the C21 chain length (2a), where the spectrum more closely resembles that expected for two noninteracting monoradicals than a biradical (cf. Figure 1A). In fact, in the lower temperature spectrum of 2a, the only remaining trace of the SCRP spectrum is the small splitting in the central lines, due primarily to the acyl fragment. The spectrum of 1a shows features of both SCRP and RPM spectra, and this indicates that chain length, in addition to temperature, is important in determining the contribution of each mechanism. The magnitude of this phenomenon is unprecedented at these temperatures. In previous steady-state EPR work on stable nitroxide biradicals,29 spectra were sometimes obtained that appeared as if the biradical transitions had almost completely disappeared, but because of the use of phase-sensitive detection, the resulting first-derivative line shapes provided enough sensitivity to show that while they were very broad, some biradical transitions were still present. Furthermore, the dynamic effects observed in those structures were generally observed at high temperatures. In our time-resolved work, we have now observed the effects of biradical J modulation in four separate cases: (1) a C25 biradical at 313 K (large 〈J〉, high T),14a (2) a C10 biradical at 233 K (large 〈J〉, low T),14a (3) a 1,14-aryl ether-spaced biradical at 323 K (small 〈J〉, high T),14b and (4) the C21 biradical reported here at 193 K (small 〈J〉, low T). The effects are not always manifested by line broadening. In the work reported here, the intensities and line positions are more strongly affected, which will be discussed in more detail below. Over this range of 〈J〉 values, chain lengths, and temperatures, observation of these phenomena specifically highlights the advantages of studying spin-polarized species using the TREPR technique. Simulations of the spectra shown in Figure 1 are presently not possible. Although one mechanism dominates in each spectrum, all of them show components of both SCRP and RPM polarization patterns, and so line shapes and intensities are not satisfactorily reproduced by either simulation routine. What is needed is a program that simultaneously solves the spin and diffusion problem for both the SCRP and RPM mechanisms. Development of the theory for this has been reported by Norris and co-workers,30 Hore and Hunter,31 and Shushin.32 Because of the multiple nuclear hyperfine interactions and the many distances (and therefore J values) available to these biradicals, a program based on these theories that can accommodate our complex structures is not presently available. It is instructive to present a brief description of the dynamic effects here in order to highlight differences between the phenomena observed at low temperature with small 〈J〉 values and those reported in our previous work.14 In ref 14a, we treated J modulation as a T2 relaxation process and showed that a correction to the line width could be made for each transition in the SCRP spectrum.14a This correction has the general form shown in eq 1.

13890 J. Phys. Chem., Vol. 100, No. 33, 1996

T2-1 ) 2〈V(t)〉2τe(1 - |〈J〉|/Ω)

Letters

(1)

Here V(t) is the time-dependent fluctuation in J, which has a correlation time associated with it, τe, related to conformational motion. Also, Ω ) (〈J〉2 + q2)1/2, where q is the local magnetic field difference between any two radical pairs. Equation 1 can be simplified by considering the limiting cases for large and small 〈J〉, which are shown in eqs 2. From eq 2 it is easy to

T2-1 ∼ 〈V(t)2〉q2τe/〈J〉2 T2-1 ∼ 〈V(t)2〉τe

for 〈J〉 > q for 〈J〉 < q

(2) (3)

see why we previously observed line broadening due to J modulation at both temperature extremes. Going to high temperatures, the correlation time for conformational motion will decrease, but the magnitude of the fluctuations will increase. Since the fluctuations are taken to the square in eq 2, the dynamic effects should be large at high temperatures. This is confirmed by the experimental results reported in ref 14. This temperature dependence is characteristic for the condition of eq 3: 〈J〉 is less than or approximately equal to q. In the other case, i.e., when 〈J〉 . q, the temperature dependence of the relaxation rate is entirely determined by the correlation time τe, since 〈V(t)2〉 and 〈J〉2 vary with temperature in a similar way. This is why we observed an increase in the J modulation effect with decreasing temperature in the C10 biradical spectra from ref 13a. It is important to note here that eqs 1 and 2 are only valid in the limit of rapid conformational motion, i.e., where the Redfield theory used to derive them is applicable. For the slow conformational motion we are most likely dealing with in 1a and 2a at these temperatures, a different theoretical model is needed, which will be discussed briefly below. The spectra in Figure 1 show a decrease in the amplitude of the SCRP component with decreasing temperature, without a line broadening effect. Such a trend is not predicted by eqs 1 or 2. For two reasons, it is difficult to use our previous perturbative approach to describe this dynamic effect. First, this former treatment did not contain the temperature or diffusional dependence of the SCRP spectral amplitude. It accounted only for the line broadening effect. Second, perturbation theory has to be used very carefully in the region of slow diffusional motion, since it may not be valid in the case of a slow exchange rate. Recently, in work by Shushin,33 a rigorous analytical treatment of the SCRP spectrum has been presented for the case of small 〈J〉 values. It was demonstrated that the amplitude and line width of the SCRP spectrum can be very sensitive to the diffusion coefficient. Adrian34 has also discussed the amplitude of SCRP spectra with regard to both static and dynamic parameters of the RP. We are presently attempting to incorporate these ideas into our simulation routines for the spectra in Figure 1. Another interesting observation in these spectra is the difference between the perimeter transitions compared to the central transitions in the low-temperature spectra for each chain length. In the C16 case, the outermost lines show the greatest change from SCRP (E/A doublet for the transition at high temperature) to RPM (nearly pure E for the lowest field transition, nearly pure A for the highest field one). In the C21 case, there is no observable SCRP component except in the center of the spectrum. This is in line with our previous observation that the transitions corressponding to the largest q for the RP are the ones most sensitive to J modulation.14a In biradicals 1a and 2a, the transitions furthest from the center of the spectrum have the largest q and do indeed show the largest

effect. These transitions also have the largest RPM polarization, as predicted by early CIDEP theories.9,20 It can be argued that our hypothesis regarding competition between the RPM and SCRP mechanisms is not due to molecular motion, but instead what is happening is that the distribution of end-to-end distances is simply shifting at lower temperatures to include many conformations whose contributions to 〈J〉 are much smaller than the line width of the EPR transitions (3-4 G). However, we have computed end-to-end distributions35 for the C21 biradical at both temperatures and calculated 〈J〉 from them.36 The results show that if a rapidly averaged distribution was the only determinant of 〈J〉, there should be an observable splitting of 2 G in the lower temperature spectrum of the C21 biradical. This result, along with others we have obtained for micellar RPs,37 shows that there are cases when the TREPR spectral appearance and the 〈J〉 values responsible for SCRP polarization are determined by both static and dynamic parameters. Great care must be taken in the interpretation of such spectra, particularly when the goal is to relate the 〈J〉 value to the molecular structure. This point has been recognized in an analysis of magnetic field effects in flexible, covalently bound radical ion pairs,38 but not in the context of time-resolved magnetic resonance spectroscopy. A good fit of the spectrum using the “pure” SCRP program is a good criterion for the valid use of an average J value and also for the meaningfulness of the relation of 〈J〉 to a distribution of conformations. Comparisons between 〈J〉 values in flexible systems are therefore best made within a homologous series where all the biradicals in question undergo similar chain dynamics at each temperature. Acknowledgment. The authors express their gratitude to the National Science Foundation for continued strong support of this work through the Divisions of Chemistry (Grant 9522007) and the National Young Investigator Program (Grant 9357108). References and Notes (1) Turro, N. J.; Buchachenko, A. L.; Tarasov, V. F. Acc. Chem. Res. 1995, 28, 69. (2) (a) Forbes, M. D. E.; Ruberu, S. R.; Dukes, K. E. J. Am. Chem. Soc. 1994, 116, 7299. (b) Forbes, M. D. E.; Dukes, K. E.; Myers, T. L.; Maynard, H. D.; Breivogel, C. S.; Jaspan, H. B. J. Phys. Chem. 1991, 95, 10547. (c) Forbes, M. D. E.; Myers, T. L.; Dukes, K. E.; Maynard, H. D., J. Am. Chem. Soc. 1992, 114, 353. (3) Beckert, D.; Plu¨schau, M.; Dinse, K. P. J. Phys. Chem. 1992, 96, 3193. (4) (a) Rozenshtein, V.; Zilber, G.: Rabinovitz, M.; Levanon, H. J. Am. Chem. Soc. 1993, 115, 5193. (b) Hugerat, M.; van der Est, A.; Ojadi, E.; Biczok, L.; Linschitz, H.; Levanon, H.; Stehlik, D. J. Phys. Chem. 1996, 100, 495. (5) (a) Turro, N. J.; Wu, C.-H. J. Am. Chem. Soc. 1995, 117, 11031. (b) Khudyakov, I. V.; McGarry, P. F.; Turro, N. J. J. Phys. Chem. 1993, 97, 13234. (c) Tarasov, V. F.; Ghatlia, N. D.; Buchachenko, A. L.; Turro, N. J. J. Am. Chem. Soc. 1992, 114, 9517. (6) (a) Ramamurthy, V.; Eaton, D. F. Chem. Mater. 1994, 6, 1128. (b) Barra, M.; Scaiano, J. C. Photochem. Photobiol. 1995, 62, 60. (7) (a) Forbes, M. D. E. J. Phys. Chem. 1993, 97, 3390. (b) Forbes, M. D. E. J. Phys. Chem. 1993, 97, 3396. (c) Maeda, K.; Terazima, M.; Azumi, T.; Tanimoto, Y. J. Phys. Chem. 1991, 95, 197. (d) Forbes, M. D. E.; Ball, J. D.; Avdievich, N. I. J. Am. Chem. Soc. 1996, 118, 4707. (8) (a) Korolenko, E. C.; Cozens, F. L.; Scaiano, J. C. J. Phys. Chem. 1995, 99, 14123. (b) Nakamura, Y.; Igarashi, M.; Sakaguchi, Y.; Hayashi, H. Chem. Phys. Lett. 1994, 217, 387. (9) Spin Polarization and Magnetic Effects in Radical Reactions; Molin, Yu. N., Ed.; Elsevier: New York, 1984. (10) (a) Scaiano, J. C.; Abuin, E. B.; Stewart, L. C. J. Am. Chem. Soc. 1982, 104, 5673. (b) Gould, I. R.; Zimmt, M. B.; Turro, N. J.; Baretz, B. H.; Lehr, G. F. J. Am. Chem. Soc. 1985, 107, 4607. (11) (a) Forbes, M. D. E.; Peterson, J.; Breivogel, C. S. ReV. Sci. Instrum. 1991, 62, 2662. (b) Forbes, M. D. E. Z. Phys. Chem. 1993, 182, 63. (c) Closs, G. L.; Forbes, M. D. E. J. Phys. Chem. 1991, 95, 1924. (12) (a) Bolton, J. R.; Carrington, A.; Todd, P. F. Mol. Phys. 1963, 6, 169. (b) Fischer, H. Mol. Phys. 1965, 9, 149. (13) (a) Reitz, D. C.; Weissman, S. I. J. Chem. Phys. 1960, 33, 700. (b) Buchachenko, A. L.; Golubev, V. A.; Meiman, M. B.; Rosantsev, E. G. Dokl. Akad. Nauk. SSSR 1965, 163, 1416. (c) Brie`re, R.; Dupeyre, R. M.;

Letters Lemaire, H.; Morat, C.; Rassat, A. Bull. Chim. Soc. Fr. 1965, 3290. (d) Dupeyre, R. M.; Lemaire, H.; Rassat, A. J. Am. Chem. Soc. 1965, 87, 3771. (14) (a) Avdievich, N. I.; Forbes, M. D. E. J. Phys. Chem. 1995, 99, 9660. (b) Avdievich, N. I.; Forbes, M. D. E. J. Phys. Chem. 1996, 100, 1993. (15) (a) Hore, P. J.; Hunter, D. A. Mol. Phys. 1992, 75, 1401. (b) Shushin, A. I. Chem. Phys. Lett. 1995, 245, 183. (c) Shkrob, I. A.; Felder, P.; Wan, J. K. S. J. Am. Chem. Soc. 1993, 115, 5227. (16) (a) Bittl, R.; Schulten, K. J. Chem. Phys. 1986, 84, 9. (b) Bittl, R.; Schulten, K. Chem. Phys. Lett. 1988, 146, 58. (17) Busmann, H.-G.; Staerk, H.; Weller, A. J. Chem. Phys. 1989, 91, 4098 and references therein. (18) (a) Spin Polarization and Magnetic Effects in Radical Reactions; Molin, Yu. N., Ed.; Elsevier: New York, 1984; p 224. (b) Atkins, P. W.; Evans, G. T. Chem. Phys. Lett. 1974, 25, 108. (c) Wong, S. K.; Hutchinson, D. A.; Wan, J. K. S. J. Chem Phys. 1973, 58, 985. (19) Forbes, M. D. E.; Ruberu, S. R. J. Phys. Chem. 1993, 97, 13223. (20) (a) Pedersen, J. B.; Freed, J. H. J. Chem. Phys. 1973, 58, 2746. (b) Monchick, L.; Adrian, F. J. J. Chem. Phys. 1978, 68, 4376. (c) Monchick, L. J. Chem. Phys. 1980, 72, 6258. (21) Goudsmit, G.-H.; Paul, H.; Shushin, A. I. J. Phys. Chem. 1993, 97, 13243. (22) (a) Closs, G. L.; Forbes, M. D. E.; Norris, J. R. J. Phys. Chem. 1987, 91, 3592. (b) Buckley, C. D.; Hunter, D. A.; Hore, P. J.; McLauchlan, K. A. Chem. Phys. Lett. 1987, 135, 307. (23) (a) Ketone 1: 8-cyclohexadecen-1-one (Aldrich) was hydrogenated and then tetramethylated as described in: Closs, G. L.; Forbes, M. D. E. J. Phys. Chem. 1991, 95, 1924. (b) Ketone 2: Forbes, M. D. E.; Dang, Y. Org. Prep. Proc. Int. 1993, 25, 309. (24) The conformations illustrated in Scheme 1 are arbitrary. There are many others accessible to these molecules at the temperatures of our experiments. (25) (a) Forbes, M. D. E.; Closs, G. L.; Calle, P.; Gautam, P. J. Phys. Chem. 1993 97, 3384. (b) Forbes, M. D. E.; Bhagat, K. J. Am. Chem. Soc. 1993, 115, 3382.

J. Phys. Chem., Vol. 100, No. 33, 1996 13891 (26) Forbes, M. D. E.; Schulz, G. R. J. Am. Chem. Soc. 1994, 116, 10174. (27) (a) Pedersen, J. B.; Freed, J. H. J. Chem. Phys. 1973, 58, 2746. (b) Monchick, L.; Adrian, F. J. J. Chem. Phys. 1978, 68, 4376. (c) Monchick, L. J. Chem. Phys. 1980, 72, 6258. (28) The solvent was toluene, the concentration of precursor varied from 0.05 to 0.1 M, the laser pulse energy was 20 mJ maximum, and the microwave power was typically 10 mW in all experiments. Increasing the microwave power up to 120 mW had no effect on the line shapes or relative intensities of the observed transitions. (29) Hudson, A.; Luckhurst, G. R. Chem. ReV. 1968, 69, 191. (30) Norris, J. R.; Morris, A. L.; Thurnauer, M. C.; Tang, J. J. Chem. Phys. 1990, 92, 4239. (31) Hore, P. J.; Hunter, D. A. Mol. Phys. 1992, 75, 1401. (32) (a) Shushin, A. I. J. Chem. Phys. 1994, 101, 8747. (b) Shushin, A. I. Chem. Phys. Lett. 1991, 177, 338. (33) (a) Shushin, A. I. J. Chem. Phys. 1994, 101, 8747. (b) Shushin, A. I. Chem. Phys. Lett. 1991, 177, 338. (34) Adrian, F. J. J. Chem. Phys. 1995, 102, 4409. (35) a) Photinos, D. J.; Poliks, B. J.; Samulski, E. T.; Terzis, A. F.; Toriumi, H. Mol. Phys. 1991, 72, 333. (36) The calculations were carried out by averaging the function J ) J0 exp(-λ(r - r0)) over the distribution of r values. We used J0 ) 8.4 × 1010 s-1, r0 ) 3.5 Å, and λ ) 1.1 Å-1, which gave a value for 〈J〉 that matched the value from a fit of the SCRP spectrum at high temperatures for 2a. These values were then fixed and applied to the low-temperature spectrum using its distribution. (37) Forbes, M. D. E.; Avdievich, N. I.; Schulz, G. R. J. Am. Chem. Soc., in press. (38) (a) Bittl, R.; Schulten, K. J. Chem. Phys. 1986, 84, 9. (b) Bittl, R.; Schulten, K. Chem. Phys. Lett. 1988, 146, 58.

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