5188
J. Phys. Chem. 1996, 100, 5188-5199
Ultrafast Study of the Photodissociation and Recombination of Aqueous O3Peter K. Walhout, Carlos Silva, and Paul F. Barbara* Department of Chemistry, UniVersity of Minnesota, Minneapolis, Minnesota 55455 ReceiVed: NoVember 17, 1995; In Final Form: January 17, 1996X
The photodissociation of the strongly solvated radical O3- (generating O2 and O-) has been studied in aqueous solution by femtosecond pump-probe spectroscopy. The near-UV absorption band of O3- exhibits a prompt bleach due to photolysis (390 nm excitation), which is followed by a partial recovery (3.5 ps) that is assigned to delayed geminate recombination. The transient spectrum of O3- shows no evidence of excess vibrational energy content, indicating that vibrational relaxation of O3- occurs on a faster time scale than the recombination process (3.5 ps). This overall picture is in strong contrast to the standard prototype for solution recombination reactions, i.e. the widely investigated photodissociation of I2 in nonpolar solvents. For I2, photodissociation and prompt recombination (∼0.3 ps) lead to hot I2 molecules that relax on the tens of picoseconds time scale. The extremely fast vibrational relaxation and the slow recombination of O3- in water apparently stem from strong solute-solvent interactions for both O3- and O-. The O3- behavior may in fact be a common situation for polar reactions in polar solvents. In these studies, O3- was generated via a known reaction by photolysis of an oxygenated basic solution of hydrogen peroxide. The quantum yield of cage escape for O3photodissociation has been measured to be 0.50 ( 0.02, assuming that the long-lived bleach is due entirely to cage escape. The long-lived bleach may, however, also be due to other photophysical pathways that involve long-lived, low-lying O3- excited states. Both the apparent cage escape yield and recombination dynamics are identical within experimental error in H2O and D2O. The rotational reorientation time of O3- has been measured to be 2.3 ps.
Introduction experimental1-23
theoretical24-34
and work on the Recent photodissociation, geminate recombination, and subsequent vibrational relaxation of small molecules in clusters and solution has greatly advanced our understanding of the solute-solvent interactions involved in condensed-phase nonequilibrium dynamics. An obvious role of the solvent in condensed-phase photodissociation is the caging effect, which can dramatically decrease the quantum yield of photodissociation relative to the gas phase.21-23,34-37 While photodissociation yields typically approach zero in a solid matrix,21,37 in solution the highly dynamical nature of the solvent and the solute-solvent interactions leads to a wide array of caging effects. The most widely studied condensed-phase photodissociation system is I2 in nonpolar solvents.1-5,21,22,38-42 Visible excitation of I2 leads to a predissociative state which undergoes a collisionally-induced curve-crossing to a dissociative state. During the separation process of the atoms in the dissociative state, the solvent induces prompt geminate recombination to the ground state and A/A′ excited states for a large fraction of the initially dissociated I pairs. One main conclusion is that the caging effect should be ascribed primarily to the initial collision with the solvent.3,21-23 The promptly recombined ground-state I2 molecules are formed with a large excess of vibrational energy due to the formation of the bond. The subsequent vibrational relaxation of the hot I2 has been extensively studied by ultrafast spectroscopy1-5 and successfully modeled by theory and simulation.1,38 The vibrational relaxation is well-described by relatively simple theories that emphasize short-range solute-solvent interactions and ignore (i) quantum mechanical nuclear effects associated with the solvent and solute and (ii) the dependence of the solute’s electronic structure on the configuration of the solvent. * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-5188$12.00/0
A different and more complex view of photodissociation/ recombination has arisen in the study of the photodissociation of I2-.16-20,27-29 The electronic structure of this ion is strongly coupled to the instantaneous configuration of the surrounding solvent during the photodissociation. This coupling results in a solvent-induced charge flow between the photofragments and leads to a qualitatively different description of the photodissociation than that for an uncharged species in nonpolar solvents. Even in the absence of charge flow, the vibrational relaxation of charged (and polar) solutes has been observed and predicted to be accelerated by long-range electrostatic solute-solvent interactions.25-27,43,44 Charge flow further enhances this acceleration.28 To continue the study of these radical ion-polar solvent interaction effects, we have performed and report herein photodissociation experiments on the transient aqueous ozonide radical, O3-, which is a well-studied species in radiation chemistry. Extensive prior studies of O3- have been made by pulse radiolysis45-48 and flash photolysis,49,50 where it has been found to be a key intermediate in the aqueous decomposition of ozone. This is of interest in waste water treatment51 and is also relevant to the behavior of ozone in atmospheric water droplets.52,53 This study of O3- represents the first femtosecond pumpprobe study of the photodissociation and geminate recombination of a triatomic radical anion in solution. I3-, a nonradical, is the only other charged triatomic in solution whose photodissociation has been studied with comparable time-resolution.13,14 From a solution dynamics standpoint there are many features of O3- which make it an interesting radical to examine. O3has more concentrated charges (smaller atomic radii), which should increase the polar solute-solvent interactions. O3- has higher vibrational frequencies which should enhance quantum mechanical vibrational relaxation effects. Finally, O3- has a lower dissociation energy in water, which should enhance © 1996 American Chemical Society
Photodissociation and Recombination of Aqueous O3-
J. Phys. Chem., Vol. 100, No. 13, 1996 5189
Figure 1. Energy level diagram for the ground and excited states of O3- and their possible dissociation products in the gas phase (from Hiller et al).57 The vertical arrow labeled hν depicts excitation of the 2A state with a 390 nm photon in the experiment. 2
dynamical coupling of the solvent’s configuration and the electronic structure of the solute. Gas-phase studies of O3- 54-57 coupled with ab initio theoretical studies58,59 indicate that excitation of the 1 2A2 r X 2B absorption band between ∼2.1 and 2.5 eV directly photo1 dissociates O3- into O2 and O-. The diffuse structure appearing in the photodissociative continuum of the absorption spectrum has been interpreted according to the models for a symmetric triatomic of Pack60 and Heller61 as arising from excitation of the bound excited-state symmetric stretch of the dissociating molecule. While this symmetric vibration is excited following promotion of the ground-state wave packet to the inner wall of the 2A2 excited-state potential energy surface, simple dissociation proceeds along the unbound asymmetric stretch coordinate. The various gas-phase results are summarized in Figure 1. The 430 nm absorption spectrum observed in water and the similar nearUV band seen in matrix isolation studies62-64 and metal ozonide crystals65 correspond to the 1 2A2 r X 2B1 transition probed in the gas-phase photodestruction studies.58,59 We therefore assume that aqueous O3- directly dissociates upon absorption of 390 nm light, which eliminates many complications in data interpretation that result from exciting to predissociative and bound states. Effects from the competing photodestruction channel O3- + hν f O3 + e- will be neglected in this paper, as the photodetachment cross section is over an order of magnitude smaller than the photodissociation cross section.56,57 In principle, all three product channels in Figure 1 would be energetically accessible in this study, but we will assume that the lowestenergy channel dominates. In fact, the major conclusions of the paper would be unchanged if the higher-energy channels also occurred with some significant yield (see below). Crude potential energy curves (Figure 2) for the dissociation (O3- f O2 + O-) in the gas phase and water can be estimated from available data in the literature. A striking effect of the strong solvent interactions on the O3- potential energy surface is the tremendous relative stabilization of the photofragments O- + O2 in solution compared to the gas phase. The gas-phase value for dissociation along the asymmetric stretch is De ) 1.7 eV.56,66 In contrast, the corresponding stabilization free energy between reactants and products in water is only ∼0.34 eV, as calculated from the equilibrium constant.45 This is attributed to the high energy of solvation for O-, estimated to be 5.1 eV from a simple Born model.67 The two dissociation channels shown correspond to O- (2P) and either O2(3Σg-) (lower energy)
Figure 2. (upper panel) Morse potential energy surfaces for the ground 2B electronic state of O - in the gas phase (dashed line) and in water 1 3 (solid line) plotted vs the asymmetric dissociation coordinate. The surfaces were calculated using experimental values for the dissociation energies and asymmetric vibrational frequencies. (lower panel) 2A2 excited state of O3- in water, which is accessed from the aqueous 2B1 state in the experiment by a 390 nm pump photon. The two dissociation channels shown correspond to O-(2P) and either O2(3Σg-) (lower energy) or O2(1∆g) (higher energy). The dashed curve represents the 2B2 excited state, which may be bound. While the 0-0 energy of this dark state has been calculated, the displacement and dissociation energy are not known, so this diagram only schematically illustrates possible crossings with the other curves.
or O2(1∆g) (higher energy). The dashed curve represents the excited state, which may be bound.58 While the transition energy of this dark state has been calculated,58 the displacement and dissociation energy are not known, so this diagram only schematically illustrates possible crossings with the other curves. Direct spectroscopic evidence for extraordinarily strong O3-water interactions was recently demonstrated in a Raman study of O3- by Su and Tripathi, leading the authors to represent the aqueous O3- as [O3(H2O)n]-.67 They observed that the Raman transition of the O3- symmetric ν1 stretch (1058 ( 2 cm-1) in H2O was partially broadened by unresolved shoulder bands at multiples of ∼16 cm-1. Interestingly, a significant narrowing of the Raman line width was observed in D2O due to a closer spacing of the shoulders. It was postulated that these closelyspaced shoulders which changed with solvent could be associated either with combination bands of a low-frequency solutesolvent intermolecular vibration coupled to ν1 or with variations in the “hydration number” n of the [O3(H2O)n]- complex which slightly modify ν1. The strong coupling of O3- to the solvent also was manifested in a higher frequency of the symmetric ν1 2B 2
5190 J. Phys. Chem., Vol. 100, No. 13, 1996 stretch (1058 cm-1) relative to the ν1 measured in matrix isolation studies (1020-1030 cm-1)62,63,68,69 and gas-phase studies (980 cm-1).56,66 The O3- ion solvated in water partially shares its radical antibonding electron with surrounding water molecules, thereby strengthening the two O-O bonds relative to both the gas phase and the solid matrix, where interactions with the environment are diminished. According to contemporary theory of vibrational relaxation of polar solutes in polar solvents, the ozonide ion in solution also represents a very different system than either I2- or I3-. Both I2- and I3- have significantly smaller vibrational frequencies (115 cm-1 for I2- and ν1, ν2, ν3 ) 111, 70, 143 cm-1 for I3-) than O3- (ν1, ν2, ν3 ) 1058,67 550,66 88066 cm-1). The dissipative friction exerted by a polar solvent such as water on vibrations e200 cm-1 is, according to theory, dominated by translational motions of the solvent. In this frequency range, long-range electrostatic interactions play only a moderate role in the relaxation process.25-27 However, for solutes with vibrations near 1000 cm-1, such as O3-, theory predicts that a librational band of water should play a dominant role in the vibrational relaxation. This relaxation rate should be greatly enhanced for charged species as a result of long-range electrostatic interactions.26 This paper reports the first ultrafast experiments on O3-, which itself is a reactive species. It has been generated in situ in this study via a known photochemical reaction initiated by photolysis of an oxygenated basic solution of hydrogen peroxide. The photodissociation and recombination are studied by recording the transient absorption signal at various wavelengths in the 1 2A2 r X 2B1 band of O3- in H2O and D2O at 20 °C, including a study of the polarization anisotropy of the transient data. The main experimental results of the paper are (i) the 1 2A r X 2B band of O - exhibits an instantaneous reduction 2 1 3 in absorption (bleach) upon photoexcitation of O3-, (ii) the bleach partially recovers (∼50%) on the 3.5 ps time scale, and (iii) the 1 2A2 r X 2B1 band shape does not significantly evolve. Detailed modeling of the vibronic structure of O3- strongly indicates that the absence of spectral evolution of the O3- band means that the vibrational relaxation occurs on a time scale that is much shorter than the time scale for geminate recombination (3.5 ps). These O3- results, which are in striking contrast to the photodissociation of I2 that was described above, point toward a more complex and potentially richer picture of condensed phase chemical dynamics than has been conventionally assumed. Experimental Section The experiments reported in this paper utilized a Ti:sapphirebased amplified laser system.17 A mode-locked Ti:sapphire oscillator based on the design of Murnane and Kapteyn70 was pumped by 4.25 W from an Ar+ laser (Spectra Physics 2060), producing 3 nJ, 90 fs pulses centered at 780 nm with a frequency of 90 MHz. These pulses were amplified at 2 kHz using the technique of chirped-pulse amplification.71 The pulses from the oscillator were temporally stretched and seeded into a Ti:sapphire regenerative amplifier, which was pumped by a Nd:YLF laser (527 nm, 6.0 W, 2 kHz, Quantronix 532-DP). After amplification and pulse compression, the 2 kHz output consisted of ∼130 fs, 780 nm, 170 µJ pulses. Pump-probe transient absorption experiments were performed utilizing a three-pulse sequence. The fourth harmonic of a second Nd:YLF laser (263.5 nm, 120 ns pulse width, 150 mW, 2 kHz, Quantronix 527-DP-H) was used to dissociate HO2- in alkaline solution, producing O- and OH.50 The amplification process in the Ti:sapphire regenerative amplifier
Walhout et al. TABLE 1: Biexponential Fits to Transient-Absorption Dataa λprobe (nm)
(100%) A1/(A1 + A2)b
τ1 (ps)
410 430 430d 430e 440 460 480 520
51 ( 5c 50 ( 2 69 ( 1 68 ( 2 46 ( 4 43 ( 5 47 ( 3 34 ( 4
3.6 ( 0.2 3.4 ( 0.2 2.0 ( 0.1 2.1 ( 0.1 3.4 ( 0.2 3.4 ( 0.8 3.9 ( 0.9 3.9 ( 1.0
a Data obtained with pump and probe polarizations oriented at the magic angle (54.7°) unless otherwise noted. b The ∆OD data were fit to a biexponential function of the form {A1 exp(-t/τ1) + A2 exp(-t/τ2)} X g(t), where g(t) is the instrument response function. τ2 was held constant at 10 ns to fit the long-time residual bleach. c The reported errors are the estimated standard deviations for the set of data at each wavelength. d Parallel polarizations of pump and probe; pump energy ) 10.5 µJ. e Parallel polarizations of pump and probe; pump energy ) 4.7 µJ.
was electronically delayed 2 µs, allowing for the creation of O3- from the diffusional reaction of O- and O2.50,72 The delayed amplified laser output was split and used to perform a pump-probe experiment on the transient O3- radical. The 50 µJ pulses were frequency doubled in β-BBO to produce 390 nm, 15 µJ pump pulses which were used to photoexcite the O3- transient radical, while a temporally delayed probe pulse was used to interrogate the change in absorbance of the sample. The 400-1100 nm tunability of the probe pulses was achieved by creating a white-light continuum in quartz and selecting a 20 nm portion with a circular variable interference filter (CVF, from Optical Coating Laboratories, Inc.). The transient data actually represent a smaller bandwidth, however, as individual 10 nm interference filters were required at each wavelength in front of the silicon photodiode detectors to eliminate a weak background continuum and fluorescence impurity induced by the 390 nm pump pulses. The instrument response of the system was typically 300 fs, as measured by the optical Kerr effect in water. A calcite polarizer was placed after the CVF to attain clean linear polarization of the probe light, while a 1/2 wave plate was used to rotate the linear polarization of the pump beam 0°, 54.7°, or 90° relative to the probe polarization for acquisition of parallel, magic angle, and perpendicular data, respectively. In obtaining the anisotropy data, parallel and perpendicular data scans were interleaved throughout the experiment to minimize the effects of long-term power fluctuations. The power of the pump pulses was monitored constantly as a function of polarization and was found always to be identical within 5%. In addition, the long-time residual offsets in the parallel and perpendicular transient data were tail-matched when necessary to compensate for any minor differences in pump power. Typical 390 nm pump pulse energies at the sample were 4-10 µJ. The transient ∆OD data did not exhibit a significant pump power dependence in this range (see Table 1). The absorption spectrum of the O3- transient species was obtained by blocking the pump pulses, chopping the 263.5 nm synthesis pulse at 1 kHz, and monitoring the ∆OD of the probe pulses as a function of wavelength. The reliability of this method was demonstrated in earlier studies.20 As in past experiments on this apparatus, all the transients were corrected for an artifact which is manifested by a spike in ∆OD intensity centered at zero pump-probe temporal delay. This artifact is due to phase modulation arising from interactions between the pump and probe pulses when they are temporally overlapped in the sample. The correction was accomplished by subtraction of the artifact obtained without the 263.5 nm
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Figure 3. Absorption spectra of equilibrated, ground-state O3- in H2O (b) and D2O (O) at 298 K. Data points were obtained by chopping the 263.5 nm synthesis light and measuring the ∆OD of the variablewavelength probe pulse. Also plotted is the spectrum obtained from the pulse radiolysis experiment of Sehested et al.46 (- - -) and the best fit to this spectrum (s) using eq 1 to calculate the absorption crosssections for O3- in its lowest vibrational state.
synthesis laser, i.e. no O3- present, from the data obtained with the synthesis laser. The artifact in these experiments constituted over 50% of the initial ∆OD bleach observed. This is a larger fraction than that seen in earlier transient-absorption experiments performed on this laser system due to the necessity in this study of placing an additional 10 nm band-pass interference filter before the detectors. Typical samples consisted of 0.03 M H2O2 (30% solution in water, Baker) in water (EM Science, HPLC grade), which was made pH ) 13 with NaOH (Fisher). No significant difference was observed using 0.1 M KOH (EM Science). Oxygenation of the solution was achieved by a constant flow of O2 (Airgas). The isotopic study was performed using D2O (Cambridge Isotope Labs.) and NaOD (Aldrich), though H2O2 was still used as a precursor in the isotope experiment. The effect of the peroxide solution protons on the deuterated experiment was negligible, however, as they amounted to only ∼0.3% of the number of deuterons in the system. Results In Situ Preparation of O3- and the Sequence of Pulses. Pump-probe transient absorption experiments were performed utilizing a three-pulse sequence. The first pulse in the sequence was a 263.5 nm synthesis pulse that was used to dissociate HO2in alkaline solution, producing O- and OH. O3- was subsequently produced by the diffusional reaction of O- and O2.50,72 The synthesis pulse was followed by a delay of 2 µs (allowing for the creation of O3-) and then a pump-probe pulse pair. The pump pulse was used to photoexcite the O3- transient radical, while a temporally delayed probe pulse was used to interrogate the change in absorbance of the sample. Figure 3 compares the absorption spectrum of the H2O solution obtained 2 µs after arrival of the 263.5 nm synthesis pulse with the known spectrum of O3-, which peaks at 430 nm,46,48,67 verifying the identity of the transient species studied. The procedure for making the O3- radical relied on saturating the aqueous solution with O2 (∼3 mM), so that O- could be depleted via its reaction with O2. O3- is the only anticipated species that absorbs at 430 nm in this solution, so a sensitive test of whether our observed ∆OD signal was due to O3- was to purge the solution
Figure 4. Pump-probe transient absorption data of O3- at probe wavelengths of 410, 430, and 440 nm. The instrument response function is 0.3 ps fwhm and is shown in the upper panel. The 390 nm pump light, generated by frequency doubling the amplified Ti:sapphire fundamental, was linearly polarized at the magic angle (54.7°) relative to the linearly polarized probe light. Also shown are the biexponential fits (s) to the data with parameters given in Table 1. Typical pump energies were 10 µJ per pulse.
with N2. This was accomplished, and the 430 nm signal disappeared. A further test was performed by adding acid to the solution to lower the pH below the pKa of OH (11.9). This eliminated the presence of O- in the solution, which also caused the 430 nm ∆OD signal to disappear. The absorption spectrum of O3- in D2O is also shown in Figure 3, with no apparent isotope effect. Summary of the Transient Data. The transient absorption data of O3- in water are shown in Figures 4 and 5. These data have been recorded with linearly polarized pump and probe beams with the planes of polarization oriented at the magic angle (54.7°) to remove contributions to the transients from rotational reorientation of O3-. The transients are all fit to a biexponential decay, with the second time constant fixed to an unresolvably slow recovery (to represent the long-time residual offset in the data). The offset was determined to be constant out to delays of 0.5 ns. The data are a result of excitation of O3- by a 390 nm pump pulse. The pump-probe transients show a fast, instrumentlimited reduction in optical density (bleach), followed by an exponential partial recovery to give the long-time residual bleach at the various probe wavelengths. As seen in Table 1, the time constant of the partial recovery does not vary significantly with probe wavelength, being ∼3.5 ps in all cases. Table 1 also shows the relative amplitudes for the biexponential fits. The
5192 J. Phys. Chem., Vol. 100, No. 13, 1996
Walhout et al.
Figure 6. Pump-probe transient absorption data of O3- in H2O (s) and D2O (b) probing at 430 nm at the magic angle (54.7°) with respect to the pump polarization. The data sets were obtained back-to-back to avoid long-term drifts in laser conditions.
Figure 5. Pump-probe transient absorption data of O3- at probe wavelengths of 460, 480, and 520 nm. The 390 nm pump light was linearly polarized at the magic angle (54.7°) relative to the linearly polarized probe light. Also shown are the bi-exponential fits (s) to the data with parameters given in Table 1.
ratio A1/(A1 + A2) is seen to decrease slightly as the probe wavelength is moved to the lower-energy edge of the O3absorption spectrum. Interference from the 390 nm pump scatter and the diminished intensity of the white-light continuum prevented probing of the blue edge of the band at wavelengths shorter than 410 nm. At probe wavelengths longer than 520 nm the transient optical density was less than the detection sensitivity (∼1 × 10-4 ∆OD). Figure 6 compares the transient ∆OD data of O3- in H2O and D2O probing at 430 nm. From Figure 3 we know that there is no spectral shift between the two solvents, so any difference between the transients would be indicative of an isotope effect in the photodynamics. No isotope effect is observed in either the time scale for bleach recovery or the ratio of amplitudes A1/A2 within experimental error (e20%). Assignment of the Spectral Dynamics. The photodissociation of a variety of small molecules, e.g. I2, has been studied by ultrafast pump-probe spectroscopy and typically exhibits a set of spectral characteristics and dynamics which we now summarize for comparison to the O3- data. In these related systems the geminately recombined molecules are formed with excess vibrational energy, which is subsequently dissipated by the solvent as the molecules relax. Transient electronic spectroscopy exhibits specific spectral features due to the excess vibrational energy and subsequent relaxation. These features are a direct consequence of the dependence of the absorption spectrum (Franck-Condon profile) of the solute on excess energy. The “hot” solutes, as compared to the equilibrated
solutes, typically exhibit (i) less absorption near the center of the equilibrated spectrum and (ii) much more absorption at the red edge of the equilibrated spectrum due to hot bands. Consequently, ∆OD transients recorded at the extreme red edge of the spectrum show increased absorption (positive ∆OD) at early times followed by recovery during vibrational relaxation to a slightly negative ∆OD value. The negative value at long times is due to permanent photodissociation, i.e. cage escape. The pump-probe transients near the center of the band are complimentary to the red-edge transients. Immediately after the geminate recombination a decreased absorption (negative ∆OD) is observed due to both the loss of molecules to photodissociation and the smaller absorption at the center of the band by hot recombined molecules. The magnitude of the negative ∆OD decreases as vibrational relaxation occurs. At long times a permanent bleach is observed due to cage escape. Surprisingly, the transient spectral behavior that is outlined in the preceding paragraph is not observed for O3-. The O3∆OD data of Figures 4 and 5 show no clear evidence of excess vibrational energy and/or vibrational relaxation. In particular, the transients near the red edge do not exhibit a positive ∆OD, which is the clearest signature of hot bands. Also, the absorption near the center of the O3- band does not exhibit a complimentary relationship to the transients at the red edge that is seen for vibrational relaxation. In fact, Table 1 indicates that the time scale of bleach recovery and the relative amplitudes are actually not very sensitive to the probe wavelength. There are at least two possible explanations for the observed spectral behavior of O3-. First, vibrational excitation of the triatomic O3- molecule may not cause sufficient broadening and/or red-shifting of the 430 nm electronic absorption band to detect in this experiment. Second, vibrational relaxation of the delayed geminately recombined molecules may be much faster than the rate of geminate recombination such that the fraction of hot molecules is small at all times. There is no prior theoretical or experimental evidence to our knowledge which might support the first explanation. Many small molecules in the gas-phase and solution show a discernible red shift and/or broadening of the electronic absorption spectrum upon vibrational excitation, such as I2, I2-, I3-, H2O,73-75 O3,76,77 OCS,78 and CH2.79 In fact, theoretical estimates of the absorption spectrum for hot O3- molecules verify that the absorption spectrum of this molecule does significantly red shift and broaden as a result of vibrational excitation (see below). Given the body of evidence that the absorption spectrum of O3- does indeed red shift and broaden upon vibrational
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excitation, the absence of eVidence of this phenomena in the transient data strongly indicates that the bleach recoVery seen at all probe waVelengths in the transient ∆OD data is not due to Vibrational relaxation. Furthermore, since the transient data are consistent with a simple bleach and partial recovery of O3-, it seems reasonable to assign the 3.5 ps component to geminate recombination. The data indicate that the 3.5 ps component is the dominant time scale for geminate recombination and no subpicosecond geminate recombination is observed. The mechanistic implication of this extraordinarily slow time scale for geminate recombination, (as compared to I2-, for example) will be explored in the Discussion. Simulation of the Absorption Spectrum of Vibrationally Excited O3-. In order to verify that vibrationally-excited O3has an increased absorption on the red edge of the equilibrium spectrum, we have calculated electronic absorption cross sections for various vibrational states in the O3- electronic ground state that could correspond to states occupied by the vibrationallyexcited molecule following geminate recombination. We used the time-dependent semiclassical formalism80-83 to calculate the absorption cross sections, which can be written
σA(EL) )
4πELe2M2 2
3p cn
Re[∫0 〈i|i(t)〉ei(EL+i)t/pe-Γt/p dt] (1) ∞
EL and i are the energies of the incident photons and the electronic ground-state vibrational level |i〉, respectively, c is the speed of light, and n is the refractive index of water. M is the transition dipole length, which in the Condon approximation is assumed to be independent of nuclear coordinates and is therefore simply a scaling factor with an arbitrary value. 〈i|i(t)〉 is the overlap of the wave function of the initial vibrational state |i〉 with itself following excitation and propagation on the excited-state surface n for a time interval t:
|in(t)〉 ) e-iHnt/p|i〉
(2)
Equation 1 gives absorption cross sections for specific vibrational ground states |i〉. Thus, in simulating the O3- absorption spectrum at a given temperature a sum over a Boltzmann distribution of ground-state vibrational levels is performed. Solvent broadening of the spectra was treated by inclusion of the damping term exp[-Γt/p], where Γ is the homogeneous line width. The inclusion of inhomogeneous broadening did not improve the fit to the experimental spectrum, so it was omitted from the calculations shown here. To attain the width of the aqueous experimental absorption spectrum, 900 cm-1 of homogeneous solvent broadening was necessary. The ground and excited states for the symmetric and bend normal modes are assumed to be displaced harmonic oscillators with frequency changes, which allows for an analytical solution to the time-dependent overlaps 〈i|i(t)〉.84 The asymmetric normal mode time-dependent overlaps, which include wave functions for an excited-state saddle point with a negative frequency, are calculated numerically using the split-time propagator method of Feit and Fleck.85 Table 2 lists some of the parameters used in these calculations. The unitless normal coordinate displacement parameter for the electronic excited-state symmetric stretch mode was determined by fitting the relative intensities of the bands in the symmetric stretch progression to the prominent symmetric progression observed in the gas-phase photodissociation spectra. A bending
TABLE 2: Parametersa for Simulated O3- Absorption Spectra frequencies (cm-1) ′′b
ν1 ν2′′ ν3′′ ν 1′ ν 2′ ν3′
other parameters
1058c 550d 880d 815e 275e 456if
g
∆1 ∆2 E0-0 (cm-1) Γ (cm-1)
3.1 0.2 19 450 900
LEPS parameters ν02 (cm-1) 1D xy,yz (eV) 1 rxy,yz,eq (Å) 1χ -1 )h xy,yz (Å ) 3 Dxy,yz (eV) 3r xy,yz,eq (Å) 3χ -1 xy,yz (Å ) bond angle
1580 5.263 1.207 2.642 4.0 1.5 2.6 105°
ν02- (cm-1) 1D (eV) xz 1 rxz,eq (Å) 1χ (Å-1) xz 3 Dxz (eV) 3r xz,eq (Å) 3χ (Å-1) xz
1089 3.967 1.341 2.097 10.0 1.341 4.7
a The parameters listed in the table were used as inputs into the timedependent absorption cross-section calculations described in the text. b The double prime denotes the ground electronic 2B1 state, and the single prime denotes the excited 2A2 state. c Su et al.67 d Leahy et al.66 e Hiller et al.57 f Imaginary frequency obtained from a LEPS potential surface as described in the text. g ∆1 and ∆2 refer to the unitless normal mode excited-state displacement in the symmetric stretch and bend, respectively, obtained from a best fit of the calculated absorption spectrum to the experimental spectrum of Sehested et al.46 h Spectroscopic parameter determined from χRβ ) (µRβ/2DRβ)1/22πνRβ.
coordinate displacement of 0.2 was used for the spectra of Figure 7, though it is difficult to empirically determine this value. We could not completely reproduce the fine structure observed in the broad gas-phase symmetric progressions, so calculations were duplicated within a range of bending displacements up to a value of 1.3. There was no evidence for the bending mode in the aqueous Raman spectra of Su et al., though given the signal-to-noise of that data a line intensity of 0.1 of the intensity of the symmetric line would be consistent with experiment. Therefore, the relative intensities of the Raman lines were calculated in the time-dependent formalism86,87 to ensure that for any bend displacement chosen, the intensity of its Raman line was
