3450
J. Phys. Chem. 1994,98, 3450-3458
Ultrafast Transient Absorption Spectroscopy of the Solvated Electron in Water Y. Kimura, Joseph C. Alfano, P. K. Walhout, and Paul F. BBrbara' Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455 Received: August 25, 1993; In Final Form: October 25, 1993"
Ultrafast near-infrared (N1R)-puIpp/variable wavelength probe transient absorption spectroscopy has been performed on the aqueous solvated electron. The photodynamics of the solvated electron excited to its p-state are qualitatively similar to previous measurements of the dynamics of photoinjected electrons at high energy. This result confirms the previous interpretation of photoinjected electron dynamics as having a rate-limiting bottleneck at low energies presumably involving the p-state. The absorption transients of our NIR-pump experiments obtained probing between 540 and 1060 nm reveal complicated dynamics that cannot be strictly reproduced using a two-state kinetic model, necessitating modification of the two-state model to include groundstate transient solvation and local heating following electronic relaxation. This modified kinetic model was found to quantitatively reproduce the observed spectral dynamics, yielding an excited-state lifetime of 3 10 f 80 fs and a 1.1 f 0.2 ps time scale for ground-state cooling and solvation. This model preserves a two-state electronic relaxation but adds ground-state relaxation dynamics. Excited-state solvation has been neglected in the model, and it remains to be proven whether the observed relaxation processes result from solvation in the ground state, the excited state, or both. The excited p-state absorption spectrum of the aqueous solvated electron was found to be red-shifted from the ground-state absorption, peaking at wavelengths longer than 1060 nm, in agreement with previous work. The fraction of the energy deposited in the slow solvent modes is unknown and may be small. The NIR-pump data presented here are complementary both to previous UV-pump experiments and to molecular dynamics simulations in developing a consistent picture of the dynamics of aqueous electrons.
I. Introduction The study of excess electrons in liquids has been an area of interest since the first observation of solvated electrons in liquid ammonia in 1864.'" Aqueous solvated electrons were first observed about 30 years ago in the pulsed radiolysis of water and were characterized as having a broad, intense, featureless absorption in thevisible and near-infrared (NIR) spectral region? Excess electrons are a primary photoproduct in aqueous pulse radiolysis experiments, and they play an important role in the complicated radiation chemistry of water. Solvated electrons also are important in solution photochemistry and photoelectrochemistry. Upon ionization of a solvent molecule, the ejected electron is highly energetic and is delocalized in the conduction band of water. This delocalizedelectron subsequentlylocalizes in a solvent trap and electronicallyrelaxes. Concomitant with the localization and relaxation, the solvent adjusts so as to solvate the rapidly changing charge distribution. The first time-resolved dynamical studies of electron localization and solvation were conducted in alcohols.1s21 These studies revealed an initial absorption in the IR region that slowly evolved to the known equilibrated ground-state absorption spectrum. The time scalefor this spectral evolution in various alcoholscorresponds very well to the dielectric relaxation time due to solvent rotation, suggesting that solvationcontrols the long-time spectral dynamics of electron relaxation. The dynamics of electron localization, electronic relaxation, and solvation of the aqueous solvated electron have also been inve~tigated.~~-3' The time-dependent absorption spectrum following electron ejection in bulk water by multiphoton ionization revealed the existence of a presolvated precursor species characterized by a red-shifted IR absorption band, which evolved to the known equilibrated aqueous electron spectrum on a subpicosecond timescale.2gJOJ3 This spectral evolutiondid not proceed via a continuous blue shift of the absorption maximum; instead, the IR absorption band decayed concurrently with the rise in Abstract published in Aduance ACS Absrracrs. March 1, 1994.
0022-3654/94/2098-3450504.50/0
intensity of the absorption band corresponding to the relaxed, equilibrated electron,29 as was confirmed by the existence of an isosbestic point.33 This IR-absorbing precursor is believed to be the lowest electronicallyexcited state of the aqueous electron.33.38 (The lowest excited state is traditionally referred to as the "pstate", while the electronic ground state is approximately spherically symmetric and is referred to as the "s-staten.42) The time for the initially ejected delocalized electron in the conduction band to relax into the lowest excited p-state was reported as 1 1030 and 180 f 40 fs.33 According to this two-state mode1,33.3* the p-state then relaxes to the ground s-state via a radiationless transition. The p-state lifetime was reported as 24030 and 540 f 50 fs.33 The excited-state lifetime for an electron in deuterated water (D20) was reported either as 250 fs31 or as 35% slower than in H20,34indicating a modest isotope effect. (Reference 34 does not fully analyze the absorption rise time to give the p-state lifetime in D2O.) This two-state model
- l/Tl
e-uppcr
state
1ITl
epstate
e-*-,tat,
was successful in reproducing the experimental data, and the effects of transient solvation and local heating following the electronic relaxation were believed to be relatively unimportant in the spectral dynamics. Some of the details of the spectral dynamics, however, could not easily be reproduced by a strictly two-state model.30 The structure of the electron-solvent system, the resulting electronic energy levels, and the nature of the broad, intense near-IR absorption of the solvated electron have been areas of intense activity for nearly 50 years.3841 These studies have been motivated not only by the importance of solvated electrons in various photochemical and photophysical processes but also by the fact that it is the simplest aqueous anion. Since the "solute" contains only a single electron, this system is accessibleto a variety of high-level computational techniques, effecting a high degree of contact between theory and experiment. The early work in this area treated the electron as a particle in a sphere and also included the effects of the polarization energy 0 1994 American Chemical Society
Solvated Electron in Water
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3451
and surface tension of the cavity.3W1 The theory was improved by applicationof Landau polaron theory to the solvated electron.42 A major focus of this research was in examining the width of the aqueous electron optical absorption band, which was found to result partially from the fluctuation in the radius of the solvent cavity. The technique of adiabatic molecular dynamics (MD) simulation was subsequently employed to investigate the nature of the broad, featureless equilibrated absorption band of water.38.52~53~59This broad absorption band was found to be dominated by electronic transitions from the s-like ground state to the three nondegenerate low-lying plike excited states.52 The large width (0.8 eV) of the absorption band was found to reflect the nondegeneracy of the three p-states, as well as fluctuations in the radius of the solvent cavity.52 Adiabatic simulations were also used to probe the dynamics of electron solvation following the injection of an excess electron into a solvent ~avity3~953 or the sudden change in electronic state of the electr0n.5~ The ground-state absorption spectrum,38.53-57 the energies of the individual electronic the electron radius of gyration (i.e., the width of the electron wave f~nction),5~ and the electronic transition dipole moment between the s-state and p-states7 were all used as probes of the aqueous solvation dynamics. All of these solvation probes reveal that electron solvation in water proceeds on two time scales-a fast, “inertial” component that occurs on a 20-30 fs time scale and accomplishes most of the solvation and a second, slower component occurring on a 200-500 fs time scale, on the order of the water longitudinal dielectric relaxation time as well as the experimentally measured solvation times.62 This inertial component, which has also been seen in MD simulations of solvation around a suddenly formed charge,63d6as well as in e~periment?~ has been attributed to free rotation or “free streaming” of the solvent molecules, where solvent-solvent forces play no role.57964966368 In aqueous electron solvation, the fast inertial response slows by a factor of 4 2 upon solvent deuteration, indicating that it is a result of angular solvent motion having an inertial ~haracter.5~ The statistical averaging in these simulations was insufficient to determine whether the slow, 200-500 fs component also exhibits an isotope effect;57 however, the longitudinal relaxation time of D2O is known to be -20% longer than in perprotio water. Experimentally, the slow relaxation time in water is observed to exhibit a small isotope effect.62 Simulations show that although most of the spectral evolution of solvation of the electron is achieved by the fast, 2030 fs inertial response of the solvent, some observable spectral dynamics are observed to occur on the slower, 200-500 fs time scale of the slow solvation ~omponent.38-53.5595~ Finally, nonadiabatic MD simulations have probed the nature of the radiationless decay of the excited p-state to the ground s - ~ t a t e . ~The ~ , ~nonadiabatic ~,~~ relaxation and solvation of an electron initiated at an energy of 2 eV above the vacuum level were investigated using a quantum treatment of the electron immersed in classical rigid simple point charge (SPC) water.54 These calculations yielded an excited-state lifetime of 1 ps. The calculated absorption transients revealed an intense IR absorption band at early times due to excited-state absorption, which decayed with a concomitant increase in the ground-state absorption band, as evidenced by the presence of an isosbestic point at times greater than 150 fs. Recently, this work has been exterlded to use a classical flexible SPC water solvent.55 The excited-state lifetime was computed to be 164 fs, indicating that the internal degrees of freedom accelerate the nonradiative relaxation rate relative to a rigid solvent bath.55 Once electronic relaxation has occurred to produce a ground-state electron, solvation was again observed to occur with two time scales-a fast 20-30-fs inertial component containing most of the amplitude and a slower 200-fs component, as seen in previous adiabatic ~ i m u l a t i o n s . ~ The ~ J ~ nonradiative ~~~ rate for the equilibrated
-
-
p-state was also evaluated using a Golden Rule expression.6’ This work predicted a rate of 120 fs for water and -220 fs for D20, with an uncertainty of 3040%. In this paper we report results of direct NIR-pump/probe spectroscopyof the solvated electron. Previousexperimentalwork discussed above employed a two-laser pulse sequence, where an ultraviolet (UV) pump pulse excited the photoelectron to the conduction band and a probe pulse monitored the spectral dynamics.23-37 In this work, we employ a three-laser pulse sequence, where a UV synthesis pulse generates excess electrons and, after a few nanosecond delay, an NIR pump pulse promotes the equilibrated ground-state electron to the excited pstate, with a tunable probe pulse monitoring subsequent spectral dynamics. This work is complementary to the previous UV-pump experiments. The NIR-pump experiments described here do not yield the important information about the localization and trapping of delocalized electronsor the dynamicsof electron-tion geminate recombination obtained from previous UV-pump work29-37; however, these IR-pump experiments may be better suited to probe the p-state to s-state radiationless transition and explore the spectral manifestations of solvation and solvent heating following electronic relaxation. The NIR-pump/probe absorption transients of the aqueous electron presented in this paper show dynamics that cannot be accounted for using a strictly two-state model. The data are interpreted using a model that incorporates the effects of groundstate solvation and cooling, yielding an excited-state lifetime of 3 10 f 80 fs, a ground-state cooling and solvation time of 1.1 f 0.2 ps, and an excited-state absorption spectrum characterized by a broad red-shifted absorption band peaking at wavelengths longer than 1060nm. Experimentsusing D20 suggest that solvent isotopic substitution has little effect on the observed spectral dynamics. These experimental results are discussed in light of both previous experimental work and recent MD simulations. It is particularly appropriate to include this paper in a special issue journal issued in honor of Joshua Jortner, who has contributed greatly to our understanding of the solvated electron.
11. Experimental Section The ultrafast transient absorption spectrometer used in these experiments has been described in detail elsewhere.69 An Ar+pumped Tisapphire oscillator produced pulses of 90-fs duration, which were amplified using chirped pulse amplification.”J In this technique, the 90-fs oscillator pulses were temporally lengthened to 130 ps in a grating stretcher and amplified in a Nd:YLF-pumped (527 nm, 6 W, 2 kHz) Tixapphire regenerative amplifier. The injection and cavity dumping of the seed pulses into the amplifierwere controlled by an electroopticPockels cell. After amplification the cavity-dumped pulses were temporally recompressed with a grating pair to yield pulses of 130-fs duration, centered at 780 nm, with an energy of 200 pJ at a repetition rate of 2 kHz. The experimental pulse sequenceconsisted of a synthesispulse, a pump pulse, and a probe pulse. About 45% of the amplified output pulse was separated and frequency-doubled in KD*P to produce the ultraviolet (UV) synthesis pulse (390 nm, 25-30 FJ), which was used to generate solvated electrons via either multiphoton ionization of the neat solvent or electron detachment of aqueous iodide anions. After a delay of -4.4 ns, a 780-nm pump pulse (1-25 pJ) was used to excite the equilibrated ground-state aqueous electrons to one of the excited pstates. At a specific delay (-30 to 100 ps), the system was interrogated by a variable wavelength probe pulse (56&1060 nm) obtained from frequency selection of white light continuum generated in quartz. Water (HPLC grade, EM Science), D2O (Cambridge Isotope Laboratories, 99.5% isotopic purity), or aqueous solutions of KI (5-50 mM, Mallinkrodt) were circulated in a 1-mm flow cell such that each pulse sequence encountered a fresh sample volume.
-
-
Kimura et al.
3452 The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 0
0
?
?
(TI
v
n
0
T ? m W
2
n
8 0
I
C
,
6
TIME (ps) Figure 1. Comparisonof the pumpprobe absorption transient of solvated
electrons between neat water (points) and 50 mM KI solution (solid line) obtained probing at 640 and 1000 nm. The sample reservoir (100-500 mL) was changed repeatedly to minimize the accumulation of unwanted chemical species. The transients at some wavelengths were corrected for an artifact seen at t = 0 that likely resulted from phase modulation interactions of the pump and probe beams, causing “signal” to be seen at early times ( t < 0.3 ps) even when the synthesis pulse was blocked. The correction procedure entailed substracting the transient obtained upon blocking the synthesis pulse from that obtained when all three beams are present. The magnitude of this artifact was in all cases less than about 20% (and usually less than 10%) of the electron signal levels at corresponding times. Thus, when plotted on the scale shown in Figures 2 4 , the corrected and uncorrected transients are nearly indistinguishable. The artifact, however, causes some very minor modifications in the parameters extracted from our spectral modeling procedure, and thus the corrected transients were used as inputs into the spectral model. The isotopic purity of the D20 samples was checked before and after the experimental runs by NMR spectroscopy and found to be at or above the stated isotopic purity. Typical AOD values at the peak of the transients were about 0.01, which corresponds to a change in transmittance of 2%. 111. Results
In our initial experiments on the aqueous solvated electron,’’ the excess electron was generated via multiphoton ionization of neat water, most likely a three-photon proce~s.7~ A representative absorption transient of an electron in neat water is shown in Figure 1. Addition of acid to the solutions was observed to quench the transient signal, confirming the assignment of these transients as originating from the aqueous solvated electron, as described elsewhere.71.73 In order to probe the electronic relaxation and assess the effects of solvation and solvent cooling, it is necessary to obtain very high signal-to-noise absorption transients. Consequently, dilute solutions of KI in water were employed. The resulting iodine anion has an intense charge-transfer-to-solvent transition in the UV centered near 235 nm;74consequently, the UV synthesis was able to generate excess electron via resonantlyenhanced two-photon electron photodetachment of I-. In this manner, signal-to-noise levels about 5 times higher than in neat water could be obtained. With the exception of the improved signal levels, the resulting absorption transients were found to be identical to those obtained in neat water as is illustrated in Figure 1, indicating that the ionic species do not perturb the electron spectral dynamics. The signal levels increased nonlinearly with KI concentration; the results are described elsewhere.73
-E
TIME (ps)
Figure 2. Pumpprobe absorption transients of the solvated electron in
aqueous 50 mM KI solution, probing at the blue edge of the electron absorption band. The solid lines are results of the spectral simulations described in the text. The instrumental responsefunction obtainedusing the optical Kerr effect in water is 0.3 ps fwhm and is shown in the top spectrum. Maximum AOD values were about 0.01, which corresponds to a change in transmittance of 2%.
0
T
? m
W
I
-E
I
I
I
I
I
TIME (ps)
I
I
I
6
Figure 3. Pumpprobe absorption transients of the so ated electron in aqueom50mMKIsolution,probingat thecenteroftheelectronatworption band. Maximum AOD values were about 0.01, which corresponds to a transmittance of 2%.
Representative pumpprobe absorption transients of aqueous solvated electrons probing between 540 and 1060 nm are shown in Figures 2 4 . Transients probing on the blue edge of the groundstate absorption band show a fast, instrument-limited reduction in optical density, or bleach, followed by a bleach recovery that
Solvated Electron in Water
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3453
0 ?
?
0
fn
v
n
8 n
2
m
v
-2
n
8
C
-'
6
TIME (ps)
Figure 4. Pumpprobe absorption transients of the solvated electron in aqueous 50 mM KI solution, probing at the red edge of the electron absorption band. Maximum AOD values were about 0.01, which corresponds to a transmittance of 2%.
TABLE 1: Multiexponential Fit Parameters for Transient Pump-Probe Absorption Signals of the Aqueous Solvated Electron' AI 0.97 0.91 0.90 0.96 1.00 0.87 0.85 0.81 0.62 1.00
TIME (ps)
Figure 5. Comparison of the transient absorption spectra of solvated electrons in H20 at 740 nm (solid line) and D20 at 720 nm (points).
C
560 640 700 740 750 800 860 900 lo00 1060
6
0
TI
(PSI
Az 0.03 0.09
0.45 0.38 0.31 0.28 0.29 0.27 0.11 0.07 0.57 0.67
0.10 0.04 0.00 -0.13 -0.15 -0.19 0.39
TZ(PS)
(7)
(PSY
1.92 2.45 2.21 2.35
0.48 0.54 0.47 0.35 0.29
1.57 1.55 1.65 1.37
C
0.00
0.82 0.67
+
"Data were fit to the functional form AOD = A I exp(t/q) A2 exp(r/r2!,where(All+(A~J-1. ( 7 ) =Alrl+A272. e isno not defined
*
for transients that exhibit nonmonotonic behavior.
consists of a fast component containing most of the amplitude and a slower component decaying on a picosecond time scale. Table 1 summarizes the results of fitting these absorption transients to a sum of two exponential functions convoluted with our instrument response function. (Note that these multiexponential fits are not shown in Figures 2-4; rather, the solid line in these figures results from the spectral model described in the next section.) The bleach recovery times aredifferent for different probe wavelengths. Absorption transients obtained probing on the red edge of the ground-state absorption band are shown in Figure 4. These transients are similar to those shown in Figure 2, but they are inverted. The transients on the red edge of the absorption band show a fast, instrument-limitedincreasein optical density, followed by a decay of this increased absorption on several time scales. The results of fitting those data to a sum of exponentials are summarized in Table 1. Once again, the time scale of the spectral dynamics is different for different probe wavelengths. Finally, absorption transients probing at the intermediate spectral region are shown in Figure 3. These transients show complicated, nonmonotonic behavior, having a bleach at early
times, followed by a bleach recovery which overshoots to yield a transient increased absorption that decays on a picosecond time scale. As discussed in the next section, these transients indicate a breakdown in the two-state model used to interpret previous data,3023indicatingthat, in additionto the nonradiativerelaxation, other processesmust play a role in theobserved spectral dynamics. Experiments examining the absorption transients as a function of pump beam power have also been performed. Varying the pump power by a factor of 10 causes no change in the absorption transients at most wavelengths. Absorption transients in the spectral region near 860 nm, however, show a modest change in appearance at the highest pump powers employed in these experiments (-25 pJ). At very high pump intensities, the ratio of the initial bleach to the maximum of the transient increased absorption is modestly larger than at lower pump intensities. This enhancement of the initial bleach at high pump powers may result from a "cycling" of population, where an s-state electron absorbs a photon, electronically relaxes, and then absorbs a second photon during the duration of the pump pulse. At all pump power intensities studied, the 860-nm transient maintains its characteristic appearance of an instrument-limited bleach followed by a transient increase in absorption. It should be noted that the lowest-power 860-nm transient is in slightly better agreement with the 860-nm transient extracted from our spectral model than the high-power transient shown in Figure 3. The net effect of the power-dependent behavior in the intermediate wavelength region is to cause a small uncertainty in the parameters extracted from our spectral model that is likely less than the uncertainty resulting from other sources (see section IV). These powerdependent phenomena form an interesting area of study in their own right and are currently under further investigationn73 Figure 5 shows the absorption transient for solvated electrons in deuterated water (D20) probing at 720 nm. Overlaid on this transient is a transient for electrons in perprotio water (H20) probing at 740 nm. There is a 15-nm blue shift in the ground s-state absorption spectrum in going from Hz0 to D2O; consequently, both of the transients in Figure 5 probe the same portion of the absorption bands. The two transients are identical within the precisionof our measurements,suggesting that solvent isotopic substitution does not significantly effect the observed spectral dynamics. It should be noted that due to both the spectral shift of the absorption maximum in H2O and D2O and to the finite time resolution of our spectrometer, a deuterium isotope effect on the excited-state lifetime of as large as 25% would be difficult for us to observe. Thus, if an isotope effect exists, it must be small. This conclusion is in agreement with previous measurement~.",~ The ~ complete results of our pump-probe experiments on the solvated electron in deuterated water are presented el~ewhere.~3 IV. Modeling of Spectral D ~ M ~ C S Strictly Two-State Model. To identify the underlying dynamical processes in the relaxation of the excited electron, it is
3454
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994
necessary to develop a model that can reproduce the observed spectral dynamics. Previous experiments were successfully modeled using a strictly two-state model, neglecting the spectral effects of transient solvation and solvent heating. For the data presented here this model reduces to
This model predicts that all probe wavelengths should show identical temporal behavior. Thus, the time scale of the bleach recovery obtained probing at all wavelengths on the blue edge of the absorption band should be equal and identical to the time scale of the transient increased absorption decay obtained for probe wavelengths on the red edge of the absorption band. The wavelength where the ground and excited state have the same molar extinction coefficient should act as an isosbestic point, and there should be no dynamical behavior at this probe wavelength. Finally, all observed spectral dynamics should be monotonic. The predictions of this strictly two-state model are not in accord with our experimental observations. As can be seen in Table 1, different probe wavelengths show different time scales for the dynamics. For example, the bleach recovery at the extreme blue edge of the ground-state absorption band (e.g., 640 nm) is nearly 2 times slower than that obtained closer to the absorption maximum (e.g., 750 nm), in contrast to the predictions of the two-statepredictions of the two-state model. Even more dramatic evidenceof the two-state model breakdown is seen by the absence of an isosbestic point. Probing in the spectral region where the ground and excited states have a similar extinction coefficient (800-900 nm), an isosbestic point is not seen. Instead, complicated, nonmonotonic behavior is observed (see Figures 4 and 5). Such temporal behavior cannot be accounted for using a strictly two-state model. Model with Ground-State Solvation and Cooling. In light of the breakdown of the previous model, we have modified the strictly two-state model to incorporate the effects of transient solvation and local heating followingthe electronic relaxation. The kinetic model is
- - hu
e-s-state
1/72
1/71
e-pstatc
e-*s-state
wntinuous shift
e-s-state
where e-*s-sratc represents a ground-state electron that is not fully solvated and/or has a sudden increase in the local temperature of the surrounding solvent environment. This model assumes that solvation in the excited state plays no role in the spectral dynamics. While this assumption is not strictly true, MD simulations show the excited state to be much less sensitive to transient solvation effects than the ground state.57 It remains to be proven whether the observed relaxation processes seen in the data (vide infra) result from solvation in the ground state, the excited state, or both. Additionally, this model assumes only a single rate for the electronic relaxation. Because of the inhomogeneity in the solvent cavities, a range of energy gaps exist between the s- and pstates. Radiationless transition theory predicts that the rate of an electronic nonradiative process is inversely related to the energy gap between the electronic states. While a single rate for all electrons thus is not rigorously correct, simulations suggest it to be a reasonable assumption.54.55.61 Finally, the effectsof site selection,or “holeburning”,are neglected in this model, as simulations show these effects to be small and essentially unobservable at times longer than 300 fs.53 In order to simulate the spectral dynamics with this model, the absorption spectrum of each species in the model must be known. The absorption spectrum of the equilibrated ground-state electron e-s-state is well-kn0wn.~5The excited p-state absorption spectrum was an adjustable parameter and was varied to match the experimental transients (see below). The spectroscopiccharacter
Kimura et al. of the desolvated and/or hot electron, e-*,.,ute, is somewhat arbitrary. Both transient desolvation and local heating produce a red shift in the absorption maximum relative to the equilibrated ground state. Consequently,we group these two effects together and characterize the electron as having an effective temperature T immediately after the internal conversion to the ground state, and this temperature T subsequently cools exponentially to the equilibrium bulk temperature with a time constant 7,:
where AT is the effective temperature increase immediately after electronic relaxation. An electron in a solvent environment characterized by an effective transient local temperature T is assumed to have the same absorption spectrum as an electron in water with an equilibrium temperature T. The absorption spectrum of the aqueous electron as a function of equilibrium temperature has been previously tabulated.’6 (We have neglected the temperature dependenceof emx since the reliable information could not be found.) While this treatment of the combined effects of solvation and local heating is somewhat arbitrary, the fact that both phenomenahave similarspectral manifestations(red-shifting of the ground-state spectra) suggests that this model may capture the essential features of the observed spectral dynamics. This photodynamic model was convolved with our instrument response function, and the transient change in optical density was calculated using the following expressions: AOD(A,t) = AODe(X,t)
+ AOD,(A,t)
(2)
where AOD,(h,t) = c(X)c,(A)LdsAt - s) exp[-t/~,] and AOD,(A,t) = c ( A ) ~ ~ o ‘ d t ’ e,[A,T(t,t’)lf(t’~ds s) X TC
exp[-s/7,1-
c ( ~ ~,(A,T,)J&A~ ) - 8)
where e,(A) is the p-state extinction coefficient at wavelength A, e,(A,T) is the s-state extinction coefficient at wavelength A and local temperature T, f ( r ) is the instrumental response function of our apparatus (fwhm = 0.3 ps), Tq is the bulk equilibrium temperature (306 K), c(A) is a scaling factor, and T(r,r’) is as given in eq 1. The nine absorption transients shown in Figures 3-5 probing from 540 to 1060 nm were globally fit to this model. The values of T., T ~and , AT were held identical for all nine transients, while c(A) and c,(A) were independently varied for each transient. The convergence of the fit was slow and dependent on the initial estimates, indicating the presence of multiple local minima. We explored a large range of physically reasonable initial guesses and present the results that gave the minimum residual. Fits that yielded parameters significantly different from those reported here tended to have significantly larger residuals and gave much poorer agreement with the experimental transients. The solid lines in Figures 3-5 show the results of the fits. This model appears to reproduce all of the observed spectral dynamics, including the slow (1-2 ps) component in the bleach recovery at blue wavelengths (Figure 3,the nonmonotonic behavior in the intermediate wavelength region (Figure 4), and the slow tail in the absorption decay at the redmost wavelengths (Figure 5). A second data set of nine absorption transients was fit, and the parameters from the two data sets were averaged. The parameters provided a physically reasonable picture of the relaxation of the electron. The excited-state lifetime, T,, is
Solvated Electron in Water
h
The Journal of Physical Chemistry, Vol. 98, No. 13, 1994 3455
-
--e 0.1 ps 1.0 ps -m0.5 ps +2.5 ps
20000 ?
F
-4
(ZI
0
Y
n
F
5
'
?
'E
2
10000
Y
W
I
1
500
700
I
h (nm)
I
900
1
O n
1
I
1100
500
Figure 6. Absorption spectrum of the excited p-state of the solvated electron as extracted using the photodynamic model. The broken line
shows the absorption spectrum of the ground state.
b
I
I
I
I
I
I
1100
900
700
h (nm) F i p e 7 . Transient AOD spectra obtained from the photodynamic model.
Details are given in the text. 20000>
310 f 80 fs, in reasonable agreement with previously measured values of 24030 and 540 f 50 fs.33 Since the model does not include excited-state solvation,this value of 7, may reflect effects of excited-state dynamics that continually modify the energy gap between the s- and p-states. The value of the ground-state solvation and cooling time, rS,was found to be 1.1 f 0.2 ps. This time constant is on the order of the time scale for thermal dissociation of hydrogen bonds in water (-0.5 PS).~'This time scale is also comparable to the population relaxation time of vibrationally excited water with one quantum of energy in the OH stretching mode, which has been variously reported as 0.45 f 0.15,'*
