3554
J. Phys. Chem. 1995,99, 3554-3565
Dynamic Solvent Effect on Betaine30 Electron-Transfer Kinetics in Alcohols Philip J. Reid and Paul F. Barbara* Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 Received: September 28, 1994; In Final Form: December 12, 1994@
The electron-transfer kinetics of Betaine-30 (B-30), which have been widely studied in polar, aprotic solvents, are investigated for the first time in alcohols with femtosecond pump-probe spectroscopy. In alcohols, B-30 is believed to have a multidimensional solvent coordinate with components corresponding to solvent/solute hydrogen bonding. The observed back-electron transfer (b-ET) times are compared to predictions of the phenomenological electron-transfer model of Walker et al., which has previously been shown to work well for polar, aprotic solvents. This model fails for alcohols, presumably due to hydrogen-bonding interactions. However, if the model is modified to include a fast component of solvation corresponding to changes in hydrogen bonding, it agrees well for the linear alcohols over a large temperature range. Experimental evidence suggests that the newly identified component of the solvent coordinate should be associated with solvent/ solute hydrogen-bonding displacements, rather than the inertial response of the solvent. The new experimental results in alcohols, combined with the previous results in polar, aprotic solvents, c o n f m and broaden the previous conclusion that both solvation dynamics and vibrational effects are important in the electron-transfer kinetics of B-30.
Introduction The role of dynamical solvent effects in electron transfer has been under intense investigation since the early 1 9 8 0 ~ . l Early -~~ theoretical work predicted that electron-transfer rates should be proportional to the inverse of the solvent longitudinal relaxation time (ZL)as follows: 1
kET= - exp(-A&lkT) ZL
where A@ is the free energy of activation for the electron transfer, T is the temperature, and k is Boltzmann’s constant. Equation 1 is based on the assumption that the solvation dynamics are diffusional or overdamped with characteristic exponential relaxation. Within this approximate model, the longitudinal relaxation time (ZL) is related to the dielectric relaxation time, ZD,by the well-known continuum theory result:
where and EO are the optical or infinite frequency and static dielectric constants, r e ~ p e c t i v e l y . ~Recent . ~ ~ theoretical and experimental results have demonstrated the complex role that solvation dynamics play in electron-transfer reactions. Experimental measurements of solvation times have indicated that in some liquids, especially small, polar solvents, the solvent response is characterized by two different time scales for relaxation in contrast to the above discussion. The first relaxation component is an initial inertial response with Gaussian temporal behavior characterized by a time ~ i . ~ The ~ - second ~ ~ component corresponds to slower, diffusional relaxation with an average time constant rS. This diffusive component can be nonexponential; however, the average zS is typically close to the continuum prediction Z L . The ~ ~relative ~ ~ importance of the inertial and diffusional components of solvation will vary with the particular solvent being considered. For example, the solvation dynamics of water and acetonitrile are characterized
* To whom correspondence should be addressed.
* Abstract published in Advance ACS Abstracts, February 15, 1995. 0022-365419512099-3554$09.00/0
by a large fraction of the solvent response originating from inertial solvation (>SO%), while in alcohols (especially higher alcohols) the inertial component tends to be much smaller (1*is the FC factor involving the nth ground-state vibronic channel, and Ai$-, is the potential energy barrier for internal conversion to the nth vibrational level of the ground state given by
A&*,,
=
sol + AGO- m s o l + 'Lcl,vib
nhvQM + Acl,vib)2
(9)
Reid and Barbara
3560 J. Phys. Chem., Vol. 99, No. 11, 1995
TABLE 4: Kinetic Parameten from Fitting Transient Spectra
292 270 250 213
-0.34 -0.36 -0.31 -0.47
Ethanol (550 nm) 0 . 9 f 0 . 5 0.55 4.5 f 0 . 5 1.0 f 0 . 6 0.57 7 . 0 f 2.5 0.9 f 0.5 0.69 14.0 f 2.6 1.1 f 0 . 6 0.53 4 2 . 0 f 4.5
292 270 250 213
-0.42 -0.41 -0.42 -0.36
Ethanol (640 nm) 2.1 f 0 . 2 0.43 18.9 f 2 . 0 3.9 f O . 6 0.44 18.1 i 4 . 5 1.4 f 0 . 8 0.32 20.3 f 10.5 0.6 f O . 5 0.34 32.8 f 12.0
292 269 240 210 180
-0.42 -0.43 -0.30 -0.30 -0.45
1-Propanol (550 nm) 1.3 f 0 . 4 0.52 6.7 f 1.7 -0.06 28.5 f 6 . 4 1.3 $0.4 0.54 14.0 f 4 . 0 -0.03 30.0 f 21.5 1.OfO.5 0.61 25.5 f 3.5 -0.09 42.0 f 10.4 0.8 + O S 0.47 48.2 f 15.2 0.23 7 3 . 0 f 17.5 1 . 0 f 0 . 6 0.55 191.0 f 10.6
292 270 250 213
-0.35 -0.32 -0.44 -0.37
1-Propanol (640 nm) 2.0f0.9 1.4 f 1.1 0.49 7.0 f 2.5 1.0 f 0.6 0.57 2.0% 1.6 1.5 f 5 . 5 0.38 5.7 f 3.5 0.8 f 0 . 5 0.15
-0.11 12.3 f 2.0 -0.07 34.6 f 5.5
0.15 0.15 0.26 0.30
0.16 0.11 0.18 0.48
1-Butanol (396 nm) 9.5 f 0.2 16.5 f 1.2 20.0 f 2.1 82.9 f 5.3 158.5 f 4.5 1-Butanol (550 nm) 5.9 5 0 . 3 -0.08 292 -0.33 0.7 f 0.2 0.59 1 . 0 f 0 . 4 0.57 11.1 f 1.5 -0.05 273 -0.38 0.8 f 0 . 4 0.60 16.9 f 0.9 -0.06 262 -0.34 1.0. f 0 . 4 0.59 3 5 . 9 f 0 . 4 -0.06 237 -0.35 0.5 f 0.4 0.53 99.7 f 5.0 -0.08 211 -0.39 292 265 255 218 193
292 278 250 22 1 292 278 250 22 1
65.5 f 7.7 98.9 f 15.0 100.5 f 28.2 120.0% 27.6
51.4 f 3.3 87.6 f 5.5 93.0 f 16.5 1 5 0 . 2 f 18.5
1.00 1.00 1.00 1.00 1.00
292 -0.50 276 -0.42 257 -0.39 24 1 213 292 272 240 200
hpr= 396 nm
1-Butanol (640 nm) 3.6 f 0 . 2 0.43 2.7 f 0.1 5.4 f 1.2 0.42 2.0f0.1 5.8 f 1.3 0.41 4.5 f 0.6 0.39 27.1 f 2.5 0.25 20.3 f 2.7
0.07 0.16 0.20 0.61 0.75
45.6 f 6.1 109.0f 15.0 126.3 f 9 . 5 130.0 f 25.0 138.3 f 14.5 63.0 f 1.5 97.4 f 0 . 4 118.8 f 4 . 5 173.0 f 17.3 169.0 f 4.9
1-Butanol (720 nm) 0.77 2.9 f 0.2 0.23 35.0 f 1.3 0.88 4.5 f 0.8 0.12 75.5 f 5.4 1.00 14.8 f 0.3 1.00 118.0 2.4 1-Pentanol(550 nm) -0.39 0.7 f 0 . 2 0.55 7.8 f 0 . 4 -0.06 90.0% 11.2 -0.31 0.8 f 0.4 0.62 1 5 . 0 f 3.8 -0.07 158.0 f 17.2 -0.26 0.9 f 0 . 4 0.72 35.4 f 2.6 -0.02 83.0 f 28.5 0.75 96.0 f 9.5 -0.25 134.5 f 33.6 1-Pentanol(640 nm) -0.51 3.3 f 1.2 0.42 4.5 f 1.0 0.07 87.0% 9.5 4.2 f 1.5 0.13 98.1 f 2.5 -0.48 5.8 f 3.0 0.39 -0.47 3.5 f 3.0 0.40 7.0 f 2.5 0.13 152.7 f 23.0 0.31 13.8 f 5.5 0.69 171.0 f 18.0
*
where VQM is the frequency of the quantized vibrational degree of freedom (2350 cm-’ for the simulations presented here) and is the classical vibrational reorganization energy. The important aspect of this model is that it reproduces the electron-transfer dynamics at low temperatures where the solvation time is much longer than the b-ET time. In this limit, the electron transfer proceeds through vibronic channels which function as individual Gaussian sinks with a width dictated by the classical vibrational reorganization energy. Therefore, the electron transfer can occur through nuclear degrees of freedom in the absence of solvent fluctuations which typically drive the reaction at higher temperatures.
0
50
100 150
Time (ps) Figure 8. Transient absorption spectra of Betaine-30 in 1-butanol obtained with a pump wavelength of 600 nm and a probe wavelength of 396 nm. Temperatures given in the figure correspond to the sample temperature at which the data were obtained. The kinetics determined at this probe wavelength provide a measure of the back-electron transfer time in the absence of ground-state solvation. Application of the Walker et al. Model to B-30 Normal in Alcohols. The b-ET kinetics were modeled using the Walker et al. model outlined in the previous section. The parameters used in these simulations are presented in Table 2. The quantized vibrational mode frequency, reorganization energies, and electronic coupling matrix element were determined from analysis of the static absorption spectrum. The solvation times used in the simulations were obtained from measurements of ts where this information was available or by the longest longitudinal relaxation time where ts values were not reported as described above. Initial attempts at modeling the electron-transferkinetics were performed by placing the initial excited-state population at X = 1 along the solvent coordinate. The ground- and excitedstate minima are at X = 1 and 0, respectively. This approach is consistent with previous modeling of the B-30 b-ET in polar, aprotic solvents. However, with this initial condition, we were unable to model the observed Arrhenius behavior for any value of the electronic coupling matrix element. The inability of this model, in which all the solvation dynamics are treated as diffusional, to reproduce the observed kinetics is not that surprising. In normal alcohols, the possibility exists for specific solventholute hydrogen-bonding interactions which would not
Betaine-30 Electron-Transfer Kinetics in Alcohols
3.5 4- 4.5
5
J. Phys. Chem., Vol. 99, No. 11, 1995 3561
5.5
1O O O / l ( K) Figure 9. Comparison of the experimental (W) back-electron transfer time with the theoretical predictions from the Walker et al. model. Two excited-state survival times are presented, t~ (6) and are defined in the text by eqs 10-12.
tg
(A),which
be well modeled as overdamped. The presence of inertial solvation dynamics would also be inconsistent with the diffusional solvation model employed here.31-33,43 The introduction of an instantaneous displacement of the excited-state population to X = 0.7 along the solvent coordinate resulted in good agreement between the calculated and observed b-ET kinetics. A comparison between the experimental and theoretical b-ET times is presented in Figure 9. The decay rate is defined by the two survival times as follows:
and tg =
1 S tS(t) dt ZA
where
With these definitions, ZA is sensitive to the early-time dynamics where ZB reflects the later-time behavior. The difference between ZA and ZB provides a measure of the nonexponentiality of the kinetics. In the simulations presented here, T A e ZB at temperatures close to ambient, demonstrating that the b-ET kinetics are well described as exponential. However, the kinetics are predicted to become more nonexponential at lower
temperatures although this behavior is not observed experimentally similar to the behavior in polar, aprotic solvents.57 The reason for the discrepancy between theory and experiment is unclear. In these simulations, only the instantaneous displacement in position along the solvent coordinate (A‘) and the electronic coupling matrix element were varied with the remainder of the parameters defined from analysis of the static absorption spectra. Best fit was obtained with Vel = 1800 cm-’ consistent with the determination of the electronic matrix element presented above. This good agreement is demonstrated in Figure 2B which presents the theoretical b-ET rates with respect to zs as defined in eq 3. Further comparison of the experimental b-ET times to ZA and ZB is given in Figure 9 with numeric results presented in Table 1. It is important to note that only minor adjustments in Vel and position along the solvent coordinate were required to accurately reproduce the b-ET rate. The ability to model the observed kinetics with this analysis demonstrates that, in addition to diffusive solvation, a second solvation process must be operative. The necessity of including an initial displacement of the excited-state population provides evidence for the mechanistic role of solventlsolute, hydrogen-bonding interactions. Inertial solvation dynamics are believed to be of minimal importance in normal alcohols in that these dynamics represents -20% of the relaxation in methanol and decrease in importance in higher a l ~ o h o l s . ~ *Furthermore, * ~ ~ , ~ ~ a constant, 30% initial excitedstate displacement was sufficient to model the b-ET kinetics in all of the alcohols studied here. Both of these observations are inconsistent with this initial, fast relaxation originating from inertial solvation dynamics. However, the instantaneous displacement can reflect changes in solventlsolute hydrogen bond interactions. In B-30, photoexcitation results in the evolution of the phenolate group to a carbonyl (Scheme 1). Intermolecular hydrogen-bonding interactions involving this functional group would be dramatically effected by transitions between the ground and excited state. Therefore, the “instantaneous” excited-state displacement along the solvent coordinate probably corresponds to rearrangement of the local hydrogen-bonding network. Furthermore, the importance of hydrogen-bonding interactions is demonstrated by the deuterium isotope effect on the b-ET rate as well as the observation of ground-state solvation dynamics in which the Arrhenius behavior is in contrast to that expected for diffusional solvation. The mechanistic implications of these results are explored in the following sections. Isotope Effect on the Back-Electron-TransferKinetics. To ascertain the influence of solutelsolvent hydrogen bonding on the b-ET kinetics, experiments were performed in propanol-d and butanol-d. In these solvents, only the hydroxyl proton is deuterated. Figure 10 presents the transient absorption data obtained in 1-butanol with a pump wavelength of 600 nm and a 396 nm probe. Best fit to a single exponential resulted in b-ET times of 11.2 f 0.3 and 9.4 k 0.13 ps for deuterated and protonated butanol, respectively. A similar isotope effect was also measured in propanol (Table 3). Finally, experiments performed with degenerate, 550 nm pump and probe wavelengths also demonstrated the presence of an isotope effect on the b-ET rate in both solvents. The observation of an isotope effect demonstrates that solvent hydrogenic motions are coupled to the b-ET. We can classify these solvent degrees of freedom as accepting modes in the electron transfer. In this limit, these modes accept energy during the excited-state internal conversion. Deuteration would serve to lower the frequency of these modes, resulting in a reduction of the b-ET rate via the Franck-Condon factors which dress the electronic coupling matrix element (eq 8). These solvent
3562 J. Phys. Chem., Vol. 99, No. 11, 1995
I
R
Reid and Barbara
br= 720 nm
Time (ps) Figure 10. Comparison of the back-electron-transfer kinetics observed in deuterated (A) and protonated (B) 1-butanol with a pump wavelength of 600 nm and a probe wavelength of 396 nm. The back-electrontransfer time increases from 9.4 to 11.2 ps upon deuteration of the exchangeable proton (Table 3).
modes probably correspond to solventholute hydrogen-bonding interactions rather than librational (rotational) hydrogenic motion. Librational degrees of freedom are believed to correspond to inertial solvation dynamics which represent a small component of the solvent response in normal alcohols (see above).zI ,33,40,74.75 Ground-State Solvation Dynamics. An analysis of the ground-state solvation dynamics has been presented in detail elsewhere; therefore, a summary of these results is presented here.55 The kinetics of the bleach recovery observed with degenerate 550 nm pump and probe wavelengths (Figures 6 and 7) provide a measure of the ground-state resolvation. At 292 K, this probe wavelength is situated on the blue edge of the charge-transfer absorption band (Amax = 555 and 570 nm in ethanol and butanol, respectively); therefore, the decrease in optical density observed after decay of the early-time, SI-S, absorption corresponds to the production of a nonequilibrium ground-state population by internal conversion from the excited state. The decay of this absorption deficit corresponds to ground-state resolvation. The kinetics observed at 292 K (z3 at 550 nm in Table 4)demonstrate that the ground-state solvation time is 12.3 ps for ethanol and 45.6ps for butanol, close to the rs of these solvents. At -270 K, the ground-state solvation times increase to 34.6and 109.0 ps for ethanol and 1-butanol, respectively. This observation is consistent with the increase in rs accompanying a reduction in temperature. Inspection of Table 4 demonstrates that a further reduction in temperature results in only a modest increase in the bleach-recovery time. At the lowest temperatures investigated, the ground-state bleach is no longer evident; however, the absorption decay is now biphasic. This change in spectral dynamics is due to the shifting of the absorption maximum of the charge-transfer band such that the probe is situated on the red edge of the SO-SI transition (Figure 4). In this case, the displaced ground-state population created by internal conversion results in an increase in optical density. This effect is further illustrated by the observation that the change from ground-state bleach to absorption occurs at a higher temperature for ethanol relative to 1-butanol, consistent with the measured temperature-dependent shift in the charge-
Time (ps) Figure 11. Transient absorption data on Betaine-30 in 1-butanol obtained with a pump wavelength of 550 nm and a probe wavelength of 720 nm. Temperatures given in the figure correspond to the sample temperature. The fast recovery of the optical density decrease corresponds to the back-electron transfer with the later-time dynamics corresponding to ground-state resolvation.
transfer absorption band maximum (Figure 4). At lowest temperatures, the ground-state resolvation time corresponds to the longest decay times listed in Table 4. The kinetics demonstrate that the bleach recovery is weakly temperature dependent with a reduction in temperature from 275 to 210 K resulting in only a factor of 2 increase in the solvation time. Our previous analysis demonstrated that the activation energy for this process was only 1.5 kcaUm01.5~In contrast, zsincreases by roughly an order of magnitude over this same temperature range (Table 2). Further measurement of the solvation and electron-transfer kinetics in 1-butanol is provided by experiments performed with a probe wavelength at 720 nm (Figure 11). This wavelength is situated at the extreme red edge of the SO-SI transition; therefore, this experiment provides a measure of the internal conversion and solvation times. At 292 K, an instrumentresponse-limited bleach centered at zero time is observed. The bleach recovery is followed by the appearance of a groundstate absorption which decays in -40 ps (Table 4). This decay time is in good agreement with the kinetics observed at 550 nm, demonstrating that this feature corresponds to ground-state solvation where the fast bleach recovery corresponds to the b-ET. As the temperature is reduced, the bleach-recovery time increases similar to the kinetics observed at other probe wavelengths. However, the ground-state absorption component decreases in amplitude, and the decay rate of this feature increases. At the lowest temperature investigated, only the internal conversion dynamics are observed as evidenced by the 110 ps recovery time in agreement with the kinetics observed
Betaine-30 Electron-Transfer Kinetics in Alcohols
hpr= 640 nm
IR
292K
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J. Phys. Chem., Vol. 99, No. 11, 1995 3563
hpr= 640 nm
0 0
50
100
150 200
Time (ps) Figure 12. Transient absorption data on Betaine-30 in ethanol obtained with a pump wavelength of 550 nm and a probe wavelength of 640 nm. Temperatures given in the figure correspond to the sample temperature. Note that decay of the long-time absorption component, corresponding to ground-state solvation, demonstrates only a modest temperature dependence.
at 400 and 550 nm. The observation of an increase in the ground-state solvation time and a corresponding decrease in amplitude is consistent with a reduction in energy deposition into the solvent coordinate due to the increase in ts at lower temperatures. In other words, excited-state evolution along the solvent coordinate is reduced due to the increase in solvation time relative to the b-ET time. The ground-state solvation dynamics observed at this probe wavelength are consistent with diffusional solvation. In contrast to the behavior observed at 720 nm, complex ground-state solvation dynamics are observed in the transient absorption data obtained with a probe wavelength of 640 nm (Figures 12 and 13). In ethanol at 292 K (Figure 12), an instrument-response-limited increase in optical density at zero delay is observed. This feature decays to reveal the presence of a second, larger increase in optical density. The kinetics are completed by the decay of this later-time absorption. As the temperature is reduced, the early-time absorption increases in amplitude. This feature is assigned to the SI-S, transition corresponding to the presence of excited-state B-30. With a reduction in temperature, the SO-S I transition absorption maximum shifts to lower wavelengths since the larger groundstate dipole moment is preferentially stabilized relative to the excited state with the effective increase in solvent polarity at lower temperature (Figure 4). Correspondingly, we might expect higher-energy excited states with larger dipole moments to also be stabilized, resulting in a red shift in the SI-S, transition. This assignment is supported by the early-time kinetics observed in 1-butanol at 640 nm where the transient
Figure 13. Same as Figure 12, except the solvent is 1-butanol.
bleach observed at ambient temperature evolves into an absorption at low temperature (Figure 13). The absorption observed at later times provides a measure of the ground-state solvation dynamics. At 292 K, the decay time of this feature is -60 ps in both ethanol and 1-butanol. As the temperature is reduced, the decay time of this feature increases to -120 and -160 ps for ethanol and 1-butanol, respectively. Similar temperature evolution is observed in the other solvents studied (Table 4). The biphasic absorption decay observed at lowest temperatures corresponds to excited-state internal conversion and ground-state resolvation. Measurement of the temperature dependence of the internal conversion at 396 and 550 nm allows for an independent determination of the excited-state decay time. In butanol, the b-ET time increases from 9.2 to 82.3 ps between 292 and 218 K. These times are shorter than the decay of the longest component of the absorption decay measured at 640 nm; therefore, the longertime constant is assigned to ground-state solvation. The temperature dependence of the ground-state solvation dynamics measured at 550 and 640 nm in 1-butanol is presented in Figure 14. The longitudinal relaxation time (ZL) of this solvent is also shown, providing an estimate of zS. The figure clearly demonstrates that the observed solvation dynamics do not correlate with t ~ .Although a component of the solvent response corresponding to diffusional solvation is present, a second component of the solvation is also operative which demonstrates weaker Arrhenius behavior than that expected for
3564 J, Phys. Chem., Vol. 99,No. 11, 1995
Reid and Barbara
1OOOflemp (K) Figure 14. Comparison of the temperature dependence of the groundstate resolvation time determined at probe wavelengths of 550 and 640 nm (M), the back-electron-transfer time (O), and the longitudinal relaxation time (solid line) for Betaine-30 in 1-butanol.
I 5400
24800
Energy (cm-1) Figure 15. Simulations of the spectral evolution of B-30 in 1-butanol. The temperature for a given simulation is given in the figure. The solid curve in all simulations is the zero time spectrum, demonstrating the ground-state bleach (higher frequency band) and stimulated emission (lower frequency band) features. These features decay in time due to internal conversion from the excited state (Le,, the back-electron transfer). Curve spacings are 10 ps for the 293 K simulation. For the 255 and 218 K simulations, the curve spacings are 25, 50, 75, 100, 200, 400, 800, and 1500 ps. Note the transient absorption centered at -16 OOO cm-' corresponding to the appearance and relaxation of the nonequilibrium ground-state population resulting from the back-electron transfer. This feature decreases in amplitude as the temperature is reduced.
diffusional solvation. This point is further illustrated by Figure 15, which presents the expected spectral evolution if the solvation dynamics were exclusively diffu~ional.~~ As the figure clearly demonstrates, the amplitude of the absorption corresponding to the nonequilibrium, ground-state population created by internal conversion from the excited state should decrease by an order of magnitude with a reduction in temperature from 298 to 218 K. Furthermore, the decay time of the ground-state absorption should undergo a much larger increase with a reduction in temperature than what is observed experimentally.
Clearly, the observed kinetics at 640 and 550 nm are in opposition to the predicted behavior for diffusional solvation only. Again, the participation of solventlsolute hydrogen bonding in the ground-state solvation dynamics is consistent with the experimental observations. In this picture, rearrangement of intermolecular hydrogen bonding occurs to reestablish the ground-state population distribution along the solvent coordinate. The -100 ps relaxation time observed here is similar to the -40 ps intermolecular hydrogen-bond formation time of resorufin in polar, protic s o l v e n t ~ . ~Also, ~ , ~ ~the presence of nondiffusive component of solvation is supported by the modeling of the electron-transfer kinetics and isotope effect on the b-ET rate. Finally, similar solvation times are observed at 640 nm for all of the solvents studied here where we would expect to see large variations in the ground-state solvation time if diffusive motion dominated the solvent response. Dynamic Solvent Effect in Alcohols. Previous application of the Walker et al. model in predicting the b-ET rates for Betaine-30 (B-30) in polar, aprotic solvents demonstrated the importance of both solvent and solute degrees of freedom in determining the reaction kinetics.57 The studies presented here represent a more stringent test of this theory. In addition to the larger excited-ground state energy gap in normal alcohols, the increase in solvent reorganization energy relative to polar, aprotic solvents provides for an increase in the importance of solvation dynamics in determining the reaction rate. Specifically, the Arrhenius behavior of the b-ET kinetics, in which a factor of 40 increase in this rate was observed, shows that solvent motion is important in determining the electron-transfer kinetics at ambient temperatures. However, with a reduction in temperature such that Zb-ET < zs, the rate of internal conversion becomes determined by solute degrees of freedom exclusively. Therefore, the role of both solvent and solute fluctuations needs to be considered in describing the reaction dynamics of this inverted regime electron transfer. Although a portion of the solvation dynamics is assigned to evolution in solventlsolute hydrogen bonding, the majority of the solvent response corresponds to overdamped, diffusional solvent motion. This is evidenced by the linear correlation between the b-ET time and zs(Figure 2) and the success of the Walker et al. model in predicting the electron-transfer rates. These observations also demonstrate that, in this barrierless, nonadiabatic electron transfer, the complete frequency response of the solvent is involved in determining the reaction rate at close to ambient temperature. This is in contrast to the behavior expected for nonadiabatic electron-transfer reaction in the presence of a barrier. Theoretical work has demonstrated that significant deviations from the predictions of transition-state theory are expected when the rate of relaxation in the product or reactant potentials is comparable to the nonadiabatic relaxation rate.15,22,23*45 In the case of B-30, and inverted-regime electron-transfer reactions in general, the nonadiabatic dynamics are dominated by the barrierless vibronic channeL2 In this limit, the full frequency spectrum of the solvation dynamics is important in defining the dynamical effect of the solvent. Therefore, the mechanistic importance of fast versus slow solvent dynamics will depend on the specifics of the electrontransfer reaction being studied. At low temperatures, where solvent relaxation is restricted such that the electron-transfer time is shorter than zs,the solute vibrational degrees of freedom serve to promote the b-ET. This effect was recently explored by Bixon and Jortner.I7 In this work, the weak dependence of the electron-transfer rate on excess energy was demonstrated to arise from the presence of
Betaine-30 Electron-Transfer Kinetics in Alcohols the Franck-Condon density of states corresponding to the presence of low-frequency solute vibrational degrees of freedom. The weak Arrhenius behavior of the electron-transfer was assigned as characteristic of the involvement of solute vibrational modes in inverted regime electron-transfer processes, even in the presence of solvation. This description of inverted-regime, nonadiabatic electron transfer is similar to that of the Walker et al. model in that both theories depend on the presence of low-frequency solute vibrational modes in predicting electrontransfer rates, especially in the limit of slow solvent relaxation. However, the dramatic dependence of the b-ET rates on temperature and solvation dynamics (Tables 1 and 3) demonstrates that solvent fluctuations are also important in this b-ET.
Conclusions In this paper, the back-electron-transfer (b-ET) kinetics of B-30 in normal alcohols were investigated. The measured b-ET times were compared to the predicted rates from the Walker et al. model. This theoretical treatment was capable of modeling the Arrhenius behavior of the b-ET rate in the series of normal alcohols from ethanol to pentanol with the assumption that 30% of the solvation dynamics arise from rearrangement of solvent/ solute hydrogen bonds. This approximation is consistent with the isotope effect on the b-ET rate and the observation of ground-state solvation dynamics which which are not exclusively diffusional in nature. Finally, the success of the Walker et al. model in predicting the b-ET rates in normal alcohols as well as in polar, aprotic solvents c o n f i i s that both solvent and solute dynamics need to be considered in describing electron-transfer reactions in the Marcus inverted regime.
Acknowledgment. This work was supported by the Office of Naval Research. References and Notes (1) (2) (3) (4) 279.
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