J. Phys. Chem. 1996, 100, 1993-1995
1993
Strong Modulation of the Exchange Interaction in a Spin-Polarized, Aryl Ether-Linked 1,14-Biradical Nikolai I. Avdievich and Malcolm D. E. Forbes* Venable and Kenan Laboratories, Department of Chemistry, CB# 3290, UniVersity of North Carolina, Chapel Hill, North Carolina 27599 ReceiVed: October 25, 1995X
The time-resolved electron paramagnetic resonance spectrum of a 1,14-bis(alkyl)biradical linked via the para position of an aryl ether moiety has been studied. Previously the spectrum obtained at 50 °C could not be simulated using spin-correlated radical pair (SCRP) theory. It is successfully simulated here by adding modulation of the exchange interaction (J) to the fitting routine as a T2 relaxation mechanism. Inclusion of this line-broadening effect allowed an accurate value of the exchange interaction to be determined for this temperature. Comparison of this J value with that obtained in previous work for the meta isomer of the same biradical showed that the dominant mechanism of J coupling is through-solvent rather than through-bond. The magnitude of the J modulation matrix elements in the two isomers are discussed as are their temperature dependencies.
In a recent paper1 we presented the experimental and simulated time-resolved electron paramagnetic resonance (TREPR) spectra of biradical 1a (shown in Scheme 1) obtained in n-octane solution at two temperatures. The purpose of that work was to attempt to differentiate between two coupling mechanisms for the spin exchange interaction J: through-bond (TB) and throughsolvent (TS). It has been shown in another of our papers2 that the TB and TS mechanisms have opposite temperature dependencies for flexible alkane chain biradicals. While the TS coupling becomes greater at higher temperatures, the TB mechanism dominates at the lower ones. This means that a temperature dependence of the TREPR spectrum provides an excellent way to test the dominant mechanism of J coupling in these structures. As demonstrated in additional published work from our laboratory, construction of biradical precursors with double bonds3,4 or conjugated π-systems1 can change both mechanisms simultaneously. Figure 1A shows the X-band TREPR spectrum of biradical 1a at 50 °C, obtained by laser flash photolysis of precursor ketone 1. All experimental details regarding the collection of this data are given in ref 1. To get a better idea of which electronic coupling mechanism is dominant, our previous experiments were also performed on the meta isomer of 1a, and the temperature dependencies of the TREPR spectra were also studied for both isomers.1 At higher temperatures (105 °C), good quality simulations of spectra from 1a were obtained using SCRP theory in its most basic form. By comparison to the meta isomer, it could be concluded that the dominant mechanism was TS at 105 °C. However, at lower temperatures, a very poor quality fit was obtained, as shown in Figure 1B. It is more accurate to state that we were unable to simulate the spectrum of 1a at 50 °C. At that temperature, however, we could stimulate the spectrum from the meta isomer very well. In this paper we demonstrate that the inclusion of J modulation (caused by conformational motion) as a relaxation mechanism into the SCRP simulation routine allows us to resolve this situation and reach excellent agreement between the experimental and simulated spectra of biradical 1a at 50 °C. The comparison of the J value obtained by this method, with * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 15, 1996.
0022-3654/96/20100-1993$12.00/0
SCHEME 1
that obtained at higher temperature in the previous paper, will allow a definite conclusion to be made about the dominant mechanism of J coupling at this temperature. A description of the J modulation relaxation mechanism and its inclusion into our established SCRP simulation program has recently been presented by Avdievich and Forbes.5 The theory developed in that work led to eq 1 for the contribution by this mechanism to
T1-1 ) 2 〈V2〉τeq2/Ω2
(1a)
T2-1 ) 2〈V2〉τe(1 ( J/Ω)
(1b)
q ) βeB0(g1-g2)/2 + (∑aimiz-∑ajmjz)/2
(1c)
Ω ) (q2 + J2)1/2
(1d)
the electronic relaxation times T1 and T2. Here 〈V2〉 is the average value of the matrix element of the modulation of the exchange interaction, τe is the correlation time of that modulation, and Ω and q are defined using constants and magnetic parameters that have their conventional meaning in SCRP theory.5 The positive and negative signs in eq 1b correspond to “allowed” and “forbidden” biradical EPR transitions, respectively. The simulated spectrum for biradical 1a at 50 °C, shown in Figure 1C, was calculated by taking into account J modulation relaxation by adding line broadening to each EPR transition according to eq 1. The parameters used in the simulation are listed in the Table 1. It is clear from Figure 1 that inclusion of the extra line broadening due to J modulation into the conventional SCRP simulation routine allows us to obtain © 1996 American Chemical Society
1994 J. Phys. Chem., Vol. 100, No. 6, 1996
Letters
Figure 1. (A) Experimental X-band TREPR spectra of biradical 1a in n-octane at a delay time of 1.0 µs after the laser flash at a temperature of 50 °C. Simulated spectra of biradical 1a obtained (B) without and (C) with the inclusion of J modulation relaxation. The parameters used in the simulations are listed in Table 1.
TABLE 1: Parameters Used for Simulation of TREPR Spectra of 1aa temp (°C) J (MHz) 50 105 50 105
ken (s-1)
-35 e1.0 × 109 -185 2.0 × 109 -61.5 5.0 × 109 -185 2.0 × 109
line 〈V(t)2〉τeb (G) widthc (G) 0 0 13.6 30.6
3.5 2.5 1.5 2.5
Figure 1B (this work) 2A (ref 1) 1C (this work) not shown
a g factors and hyperfine couping constants are taken from ref 1. The value of τe was 2 × 10-11 s for all simulations. c Line width in the absence of J modulation. b
excellent agreement between the calculated and experimental spectra. It is interesting to note that the effect of J modulation is not present in the spectrum of 1a obtained at 105 °C. From an earlier simulation of the higher temperature spectrum, we can obtain only the upper limit for the parameter 〈V2〉τe. This upper limit represents the maximum value of the modulation that does not change the high temperature spectrum (see Table 1). The J value obtained at 50 °C is about 3 times less than that for 105 °C. The TS coupling is supposed to be stronger at higher temperatures,4 and so it is of interest to ask if we have less TS or more TB coupling at the lower temperature. With an accurate J value for the lower temperature from our new simulation we can now make a direct comparison with data obtained for the meta isomer of 1a at the same temperature.1 This comparison shows that the para isomer is still much more weakly coupled than the meta one, and so we conclude that TS coupling still dominates at this temperature. This is in line with several previous observations in our laboratory: In long-chainlength biradicals at elevated temperatures, TS coupling is dominant, and only at very low temperatures (below -50 °C) is there a chance of observing a significant TB component to J. Low-temperature spectra of 1a and its constitutional isomers are presently being pursued. As discussed in ref 5, the two parameters in eq 1, 〈V2〉 and τe, have opposite temperature dependencies. The correlation time τe decreases with increasing of the temperature, while the matrix element 〈V2〉 increases. The latter is caused by broadening of the end-to-end distance distribution, which leads to an increase in the weighing of conformations with short distances between the two radical centers. The difference in the temperature dependence in the spectra of 1a indicates that we may be able to determine, semiquantitatively, the optimum conditions
for observation of the J modulation effect in SCRP spectra. We now present a model that provides useful definitions of the relevant parameters. The analysis can be performed in the terms of a two-site model, with J ) J1 in the first site and J ) 0 in the second site. Rate constants for the transitions between site 1 and site 2 and vice versa are then τ1-1 and τ2-1, respectively. The value of τ2-1 is defined for biradicals as the reencounter rate constant. Numerical estimations of τ1 and τ2 are given in our previous paper.5 For a medium chain-length biradical, typical values are about 2 × 10-11 s for τ1 and 1 × 10-9 s for τ2. For most cases τe in eq 1 can be assumed to be equal to τ1. As derived in our earlier paper, in the two-site model the average exchange interaction value 〈J〉 is equal to J1τ1/τ2. The theory of spin exchange and J modulation relaxation for the steady-state EPR spectra of stable nitroxide biradicals was developed many years ago by Luckhurst,6 Johnson,7 and others.8 Also, in theoretical work by Shushin,9 the collapsing of the lines in SNP and RYDMR spectra due to fast singlet-triplet dephasing was also discussed. In the terminology of these theories, the conditions for the fast and slow exchange can be written as J1τ1 > qτ2 and J1τ1 < qτ2, respectively, only if we add the additional condition that J1τ1 < 1. Application of this condition means that we are working in a region where Redfield theory is valid. Here q, as defined in eq 1c, represents the local magnetic field difference (or the difference in Larmor frequency) between any two members of the electron-nuclear spin ensemble. Conditions for fast and slow exchange can then be written for a general spin state as 〈J〉 > q and 〈J〉 < q, respectively. Taking into account the fact that maximum broadening is supposed to be observed in the middle of this range, we arrive at a useful criterion for the efficiency of the broadening due to J modulation relaxation:
〈J〉 ∼ q
(2)
Since the value of 〈J〉 is determined by a combination of static and dynamic parameters, it is not surprising that eq 2 contains no explicit terms involving the dynamic parameters of the exchange process. It must be realized that this criterion (eq 2), obtained using a simple two-site approximation, gives an estimation only of the region of efficiency for the J modulation effect. It is an especially coarse approximation for systems with a large number of hyperfine coupling constants. The experimental TREPR spectra of the meta isomer of 1a did not exhibit J modulation broadening. Comparison of J modulation effects in the para and meta biradicals is possible only if the mechanism of the coupling is the same for both structures. We have established above in our comparison of the 〈J〉 values at each temperature that this is indeed the case. The absence of any J modulation for the meta isomer is in agreement with the criterion established in eq 2, because the absolute 〈J〉 values are more than 500 MHz at both experiments, which is larger than any q value in that biradical. The consequences of dynamic effects in systems that have a distribution of possible J values have been discussed by Bittl et al. in theoretical work aimed at explaining magnetic field effects in flexible, biradical-like charge separated states.10 A very detailed theory explaining such effects in magnetic resonance spectra of spin-correlated micellized radical pairs has also been presented by Shushin.11 Here we have demonstrated that a very simple model can adequately account for such effects in SCRP spectra and further that this model provides a useful criterion for predicting the maximum effect. Other examples of the maximum J modulation region have been observed in our laboratory and will be published in a separate paper.12
Letters Acknowledgment. This work was supported by the National Science Foundation through Grant CHE9522007 and through the NSF Young Investigator Award Program (Grant CHE9357108). References and Notes (1) Forbes, M. D. E. J. Phys. Chem. 1993, 97, 3396. (2) Forbes, M. D. E.; Closs, G. L.; Calle, P.; Gautam, P. J. Phys. Chem. 1993, 97, 3384. (3) Forbes, M. D. E. J. Phys. Chem. 1993, 97, 3390. (4) Forbes, M. D. E.; Bhagat, K. J. Am. Chem. Soc. 1993, 115, 3382.
J. Phys. Chem., Vol. 100, No. 6, 1996 1995 (5) Avdievich, N. I.; Forbes, M. D. E. J. Phys. Chem. 1995, 99, 9660. (6) Luckhurst, G. R. Mol. Phys. 1966, 10, 543. (7) Johnson, C. S. Mol. Phys. 1967, 12, 25. (8) Parmon, V. N.; Zhidomirov, G. M. Mol. Phys. 1974, 27, 367. (9) Shushin, A. I. Chem. Phys. Lett. 1991, 181, 274. (10) (a) Bittl, R.; Schulten, K. J. Chem. Phys. 1986, 84, 9. (b) Bittl, R.; Schulten, K. Chem. Phys. Lett. 1988, 146, 58. (11) Shushin, A. I. J. Chem. Phys. 1994, 101, 8747. (12) Forbes, M. D. E.; Avdievich, N. I.; Ball, J. D., manuscript in preparation.
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