The Journal of
Physical Chemistry
0 Copyright, 1988, by the American Chemical Society
VOLUME 92, NUMBER 9 MAY 5,1988
LETTERS Dynamic Solvent Effects on Intramolecular Electron-Transfer Reactions: Fluctuation Time Scales and Population Decays John D. Simon**+and Shyh-Gang Su Department of Chemistry and the Institute for Nonlinear Studies, University of California, San Diego, La Jolla, California 92093 (Received: February 5, 1988)
Time-resolved picosecond emission spectroscopy is used to examine the kinetics of intramolecular charge transfer in bis(4-aminophenyl) sulfone in ethanol solutions as a function of temperature. The population decay of the local excited state is compared to both an exponential decay and a decay of the form Z ( t ) = sin-' (e-'Irs); the latter function has been proposed to be applicable in the limit of solventantrolled electron-transfer reactions and is found to provide a good fit to the experimental data. The calculated decay times, T ~are , similar to the longitudinal relaxation time of the so!vent, T ~defined , by T~ = ~~t,,,,,,/t,,.
Introduction The effect of solvent fluctuations on rates of electron-transfer reactions has been the subject of many recent experimental and theoretical studies.I-l1 For reactions which are controlled by solvent motions, the rate constant is predicted to be inversely proportional to the solvent relaxation time. However, the evaluation of the relevant solvent relaxation time is currently a subject of much debate. Most theoretical models describe the solvent as a dielectric continuum, using a Debye description for the frequency-dependent dielectric constant e ( ~ ) . In this case, the solvent fluctuation time scale is given by the longitudinal relaxation time, TL = rDtm/eo.12In a series of papers by Kosower and co-worke r ~ , ~rate * ~ constants ~ - ~ ~ for the excited-state intramolecular electron-transfer reactions of TNSDMA and related molecules in alcohol solutions were found to correlate with TL-I. In addition to solvent fluctuations, there have k e n several recent reports which demonstrate that intramolecular vibrational motion can have a dramatic effect on the chemical reaction rate.9g11Experimental studies on a variety of molecules indicate that these effects can play a significant role in modulating the influence of solvent 'NSF Presidential Young Investigator 1985-1990, Alfred P. Sloan Fellow 1988-1990.
0022-365418812092-2395$01 SO10
dynamics; in particular, contributions from vibrational modes can lead to reaction rates which are in excess of T L - I . " ~ ~ ~ Electron-transfer rates of 7L-I are expected for molecular system which have essentially no barrier (AG* < k7') for reaction. For (1) Rips, I.; Jortner, J. J . Chem. Phys. 1988, 88, 818. (2) Sparpaglione, M.; Mukamel, S. J . Chem. Phys. 1988, 88, 1465. (3) Simon, J. D.; Su,S.-G. J . Chem. Phys. 1987, 87, 7016. (4) Huppert, D.; Kosower, E. M. Annu. Reu. Phys. Chem. 1986, 37, 127. (5) Kahlow, M. A.; Kang, T. J.; Barbara, P. F. J . Phys. Chem. 1987, 91,
6452. (6) McManis, G. E.; Golovin, M. N.; Weaver, M. J. J . Phys. Chem. 1986, 90, 6563. (7) Hynes, J. T. J . Phys. Chem. 1986, 90, 3701. (8) Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986, 84, 4272. (9) Nadler, W.; Marcus, R. A. J . Chem. Phys. 1987, 86, 3906. (10) Hicks, J. M.; Vandersall, M. T.; Sitzman, E. V.; Eisenthal, K. B. Chem. Phys. Lett. 1987, 135, 413. (1 1) Su, S.-G.; Simon, J. D., accepted for publication in J . Chem. Phys. (12) Frohlich, H. Theory ofDielectrics; Oxford University Press: Oxford, 1949. (13) Huppert, D.; Kanety, H.; Kosower, E. M. Faraday Discuss. Chem. SOC.1982, 74, 161. (14) Kosower, E. M.; Dodiuk, K.; Tanizawa, K.; Ottolenghi, M.; Orbach, N. J . A m . Chem. SOC.1975, 97, 2167. (15) Kosower, E. M. J . A m . Chem. SOC.1985, 107, 1114.
0 1988 American Chemical Society
2396 The Journal of Physical Chemistry, Voi. 92, No. 9, 1988
Letters
SCHEME I
T w i s t e d Intramolecular Charge Transfer S t a t e
Loco1 Exclted State ( L E )
k
" I
N/
I
electron transfer
""I
APS
(320-370 nm)
reactions with small free energy barriers, faster relaxation modes of the solvent as well as intramolecular vibrations could play a large role in determining the reaction rate. The agreement between T ~ - I and the rate of electron transfer in TNSDMA reported by Kosower and co-workers suggests that there is no reaction barrier in that system. It is important to point out that the observed correlation with T L involved setting c, equal to the square of the optical index of refraction. However, the solvents studied, the linear alcohols, generally show more complicated dielectric dispersion that described by the Debye form for c ( ~ ) . In general, three regions of Debye dispersion are observed, each being attributed to rotational motions of the solver~t.~'~~* The longest time motions, associated with the making and breaking of hydrogen bonds in molecular aggregates, make the dominant contribution to the dielectric constant. As a result, several recent papers have proposed that E,, the high-frequency dielectric constant for this For region of dispersion, should be used in calculating short-chain alcohols, cmw is greater than n2 (for ethanol at room temperature ,e, - n2 = 2.5); thus, there is a significant difference in the magnitude of T L depending on which value is used to represent the high-frequency dielectric constant. In addition, whether or not T~ is a good gauge of solvent dynamics for chemical reactions in associated solvents is still an unanswered question. Several workers have tried to directly measure solvent fluctuation time scales by studying the time-dependent fluorescence Stokes shift (TDSS) of polar molecules dissolved in polar solutions.16J+22 In general, the Stokes shifting times are longer than TL, the deviations becoming greater with increasing solvent polarity. Given the similarity between barrierless intramolecular chargetransfer processes and the relaxation reflected by the TDSS, one would expect that, for such systems, the electron-transfer rate should be equivalent to the inverse of the spectral relaxation time. Such a correlation was recently reported by Barbara and coworkers5 for the intramolecular charge transfer in bianthryl in various polar aprotic solvents. Stokes shift measurements have been carried out in the alcohol solution studies by Kosower and co-workers; the solvation relaxation times obtained are also longer than T~ ( = ( ~ , , , , / E ~ ) T ~ ) .In light of the observations of Barbara et al., one might have expected to observe correlations between electron-transfer rates and solvation times in alcohol. However, the electron-transfer rates are significantly faster. Most studies to date focus on the average time required for the electron-transfer process. However, additional insight into the role of solvent fluctuations can be obtained by examining the nature of the time-dependent decay of the reactant population. Marcus and co-workers have proposed functional forms for the population decay under conditions where both solvent motion and intramolecular vibrational motion affect the reaction ~
~
(16) Simon,'J. D.; Su,S.-G., to be submitted for publication in J . Phys.
Chem. (17) Garg, S . K.; Smyth, C. P.J. Phys. Chem. 1965, 69, 1294. (18) Davies, M. In Dielectric Properties and Molecular Behavior; Hill, N. E., Vaughan, W. E., Price, A. H., Davies, M., Eds.; Van Nostrand-Reinhold: New York, 1969. (19) Castner, E. W., Jr.; Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987,86, 1090. (20) Simon, J. D.; Su,S.-G. J . Phys. Chem. 1986, 90,6475. (21) Maroncelli, M.; Fleming, G. R. J . Chem. Phys. 1987, 86, 6221. (22) Nagaragan, V.; Brearley, A. M.; Kang, T. J.; Barbara, P.F. J. Chem. Phys. 1987, 86. 3183.
intra-
1 molecular
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I
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.
~
~
I
3
~
0
~
200
400
, 6
Time (ps) Figure 1. Emission intensity at 330 nm for APS in ethanol at -30 " C (-) plotted as a function of time. The data reflect the population decay of the LE state. The best fit of a single exponential function (--) and the function I(f) = sin-' (exp(-t/Ts)) (-) are plotted for comparison.
Different decay behavior is predicted depending on the relative importance of these two contributions to the reaction process. In the limit of solvent-controlled chemical reactions (the narrow reaction window limit in ref 9), the population decay, Q(t), is not described by an exponential function but by the equation
Q ( t ) = (2/a) sin-' (eTr/'S) In this limit, the time constant, T ~ corresponds , to the solvent relaxation time. In this letter, the dynamics of charge transfer in bis(4aminopheny1)sulfone( A P S ) are examined in ethanol solution over the temperature range -50 to +20 OC. The reaction process is depicted in Scheme I. Excitation populates the local excited (LE) state. In polar solvents, rapid charge transfer occurs to form the twisted intramolecular charge-transfer (TICT) state. The charge separation is stabilized by twisting around the sulfur-phenyl bond.23-25 The data reveal that the population decay of the LE state (the reactant state) is found to be better described by eq 1 than by a simple exponential decay. In addition, the time constant of the fitted curve, T ~ is, close to the longitudinal relaxation time of the solvent, defined by T~ = rDcmw/cO. Experimental Section
A detailed description of the picosecond emission spectrometer has been recently p~blished.~ All decays were measured by using magic-angle polarization. APS was purified by repeated recrystallization from ethanol. Static emission spectra were recorded by using a I/.,-m monochrometer (SPEX) and a Reticon (E.G.G. Model 1420) detector. The sample cell was housed in a brass flow block which was temperature controlled by a closed cycle recirculator. Temperatures between -50 and +20 O C can be obtained. (23) Su, S.-G.; Simon, J. D. J . Phys. Chem. 1986, 90,6475. (24) Su,S.-G.; Simon, J. D. Chem. Phys. Lett. 1986, 132, 345. (25) Rettig, W.; Chandross, E. A. J . Am. Chem. SOC.1985, 107, 5617.
The Journal of Physical Chemistry, Vol. 92, No. 9, 1988 2391
Letters TABLE I: Decay Times (Q) of the Local Excited State of A B Compared with Solvent Relaxation Times Determined from both Dielectric Relaxation and Time-Dependent Stokes Shift Data T, TL (=(n2/ Tss,a TL (=(emw/ TSIb 7s: OC ~ T D ) DS . PS &n), DS DS DS 20 10 0 -10 -20 -30 -40 -50
14 17 22 28 36 48 66 94
43 64 113 200 356 420
35 43 60 72 96 132 185 270
40 49 65 80 120 160 220 285
T
300
a,
iii
38 46 60 70 100 130 170 225
Y
Spectra relaxation times determined from time-dependent Stokes shift measurements.) bTime constant from fitting the emission decay to eq 1, &lo%. cTime constant from fitting the emission decay to a single exponential, f 10%.
The temperature in the sample cell is monitored by a thermocouple and is stable to within fl OC.
Results and Discussion The steady-state fluorescence properties of APS in alcohol solution have been discussed in detail in several recent Dual emission is observed corresponding to emission from both the LE and TICT excited states, Scheme I. Procedures for decomposing these spectra into the individual contributions from the LE and TICT states have been discussed by several researchers.26 Spectral decomposition clearly demonstrates that the emission dynamics at 330 nm reflect only emission from the L E state. Thus, by monitoring the emission at this wavelength, the population decay of the reactant state can be studied. In Figure 1, the emission decay at 330 nm for APS in ethanol at -30 O C is plotted. This data provides information on the dynamics of charge transfer in this system. The data shown in Figure 1 is a convolution of the population decay with the instrument response, G ( r ) . G ( T ) is determined directly from measuring the response of the detector to UV light scattered by a nonabsorbing sample. The data, Z(t), are then fit by an iterative nonlinear least-squares technique which minimizes the variance between the experimental data and the calculated convolution between the desired function, F ( f - T ) , and the instrument response: Z ( t ) = l '-mF ( t - s ) G ( ~d) s
Two fitted curves are compared to the data in Figure 1. The dashed line represents the best single exponential fit. Examination of the residuals for this fit shows that a single exponential function does not accurately described the population decay of the LE state. The second calculated curve is a fit of the data to the function given in eq 1. Examination of the residuals clearly shows that this function does a superior job at fitting the decay than a single exponential. Similar results are observed over the entire temperature range studied. Information on the importance of solvent fluctuations in determining the rate of reaction can be extracted from these data. From the recent theoretical development of Marcus and cow o r k e r ~ ,the ~ , ~ability of eq 1 to describe the population decay suggests that the reaction rate is being dominated by solvent motion. In this case, fluctuations in the intramolecular vibrational degrees of freedom of the molecule do not contribute to the re~~
(26) Rettig, W.; Zander, M. Ber. Bunsen-Ges Phys. Chem. 1983,87, 1443.
200
100
200
300
Longitudinal Relaxation Time (ps) Figure 2. Time constants for the decay of the LE state plotted as a function of the longitudinal relaxation time of the solvent, T L = ~ ~ c The time constants from both the single exponential fits (X) and the sin-' (exp(-r/rs)) fits (0) are plotted. In both cases, the data are in excellent agreement with the longitudinal relaxation time.
action rate and the time constant of the population decay, ss, is a direct measure of the solvent relaxation time relevant to the charge-transfer reaction. In Figure 2, the time constants from the fit of eq 1 to the LE decay data are plotted as a function of sL.The data are also given in Table I. In plotting the data in Figure 2, T~ is calculated by using e,, for the high-frequency dielectric constant (sL= ( e m w / ~ o ) ~ o ) .The solid line corresponds to T~ = sL. This plot clearly shows that, within experimental error, the time scales of the population decays, T S , are very close to T~ over the entire temperature range studied (-50 to +20 "C). For comparison, the time constants obtained from single exponential fits to the data are also plotted. Although the fit to the data is not as good as that obtained using eq 1, the time constants are essentially unchanged. The above similarity between T S and T L and the ability of eq 1 to describe the population decay suggest that there is no barrier (AG* < kT) to reaction for APS in ethanol and that the relevant solvent relaxation time can be reasonably well described by the continuum dielectric time, sL.However, as mentioned above, for reactions which have no barriers, one might have expected a correlation between the electron-transfer rates and the inverse of the solvent relaxation time obtained from time-dependent Stokes shifting studies. Spectral relaxation times have been reported for polar probe molecules in ethanol over most of the temperature range studied in this paper.3 The lifetime of the LE state of APS in ethanol is not equal to the measured Stokes shift relaxation times, sSs, Table I. The data show that, for T > -20 OC,T~ > T S ~ while , T S < sSS for T I-20 OC. This comparison suggests that the solvation times determined from Stokes shifting measurements may not be an appropriate measure of the solvent fluctuation time important in the electron-transfer process in alcohol solution. We are currently examining the electron-transfer dynamics of APS and related molecules in additional solvents in order to address these questions.
Acknowledgment, This work is supported by grants from the N S F and O N R and by the donors of the Petroleum Research Fund, administered by the American Chemical Society. J.D.S. thanks Professors Rudy Marcus and J. T. Hynes for many stimulating discussions.
~
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