J . Phys. Chem. 1993,97, 134-142
134
Early Formation of Electron-Radical Pairs in a Polar Protic Liquid: Evidence of Ultrafast Concerted Electron-Proton Transfers Y. Gauduel,' S. Pommeret, and A. Antonetti Laboratoire d'Optique Appliqude, CNRS URA 1406, INSERM U275, Ecole PolytechniqueENS Techniques Avancdes, 91 120 Palaiseau, France Received: July 2, 1992; In Final Form: October 13, 1992
Ultrafast reaction dynamics of nonequilibrium electronic states in pure liquid water (D20vs H20)have been investigated using ultraviolet femtosecond laser pulses and time-resolved spectroscopy in the visible and near infrared regions. In pure light and heavy water (D20> 99.95%) a t 294 K, ultrashort lived electronic states have been discriminated and assigned to the existence of transient couplings between a subexcitation electron and neoformed prototropic species (X30+ and OX,with X = H or D). Contrary to the formation and relaxation of infrared electrons (prehydrated states), the appearance and lifetime of the hybrid electronic states in the near infrared region [X30+:e-:OX, with X = H or D]is drastically influenced by an H/Disotopic substitution. The formation of electron-radical pairs would bedependent on ultrafast reaction of a molecular cation with surrounding water molecules (X20+ X20 X30+, OX). The temporal electron-radical pair formation/ion-molecule reaction ratio is about 2Il2 times greater in D20 than in H20. Nonequilibrium electronic configurations are dependent on ultrafast reorganization of water molecules initiated by short-lived prototropic species. These transient structural fluctuations would favor electron localization by self-trapping phenomena. In light water, the present study demonstrates that the deactivation frequency of electron-radical pairs (e---OH, e - - - H 3 0 + ) n ~ 2 ~ is similar to the estimate of an H-OH decay channel of excited water molecules (0.29 X 1013s-l vs 0.33 X 1013 SI). Additional spectroscopic data obtained in D2O demonstrate that the probability to obtain electron solvation from neutralization of electron-radical pairs is very low a t ambient temperature. The existence of a competitive process involving a common precursor of the presolvated electron and electron-radical pairs is unlikely. Transient couplings between hybrid electronic states and a polar solvent would be dependent on the protic character of the water molecules and ultrafast reorganization of the hydrogen-bonded network around short-lived prototropic entities. The photoejection of electrons under the energy band gap of water is discussed considering the existence of concerted electron-proton transfer and the role of dynamical properties of this protic solvent.
+
-
1. Introduction In condensed media, reaction dynamics may be observable on the time scale of molecular motions, Le., on a subpicosecond time scale. One of the main fundamental questions on chemical reactivity is to explain how the microscopic structure of molecular liquids assist or impede a charge-transfer reaction. During the last 10 years, significant advances in the understandingof chemical dynamics have been obtained. These advances encompass simultaneous progress in experimental and computational chemistry.l+ One key point concerns the knowledge of primary processes involved in single charge transfer. In molecular liquids, the photoejection of subexcitation electrons and the subsequent dynamics of electron localizationand solvation can help to extend, at the microscopic level, our understanding of solvent effects on single charge transfer reactions. Femtosecond spectroscopic investigations of pure water and ionic aqueous media have been performed to discriminate primary events that occur following energy deposition' and to learn about the dynamics of ionmolecule reactions,s electron localization and h y d r a t i ~ n , ~and .'~ geminate electron-radical pair recombination.' 1-12 Recent nearinfrared femtosecond spectroscopy has been focused on photochemical processes for which electron couplings with an aqueous environment would involve ultrashort lived interactions with neoformed prototropic species.I3 These experimental data on electronic relaxation and early electron-radical pair recombinations permit to test the validity of quantum statistical studies using path integral molecular dynamics and classical Monte Carlo simulations.l4-I8 The ultraviolet multiphotonic ionization of water molecules leads to the formation of several transient species: localized and
* Author
to whom correspondence should be addressed.
solvated electronic states and prototropic species (eqs 1-3). Immediately after the femtosecond excitation of water molecules at 294 K by ultraviolet pulses (pump 310 nm, 4 eV), an instantaneous species ( T I 99.95%) was produced by Centre d'Etudes Nuclbires of Saclay and was used without further treatment. Oxygen was removed from the samples by tonometry at atmospheric pressure using pure nitrogen gas. The femtosecond investigations were performed a t 294 Kin a continuously vibrating fixed-volume Suprasil cell (2-mm path length) so that using a laser pulse repetition rate of 10 Hz each laser pulse excites a new region of the sample. The theoretical studies on time-dependent electronic populations in light and heavy water have been performed on a Sparc Station 1+ (Sun OS 4-0-3). Time-resolved data obtained in the visible and near infrared spectral regions are characterized by very low signal values (AAmax 0.05). The analyses of transient signals have been conducted considering the convolution of the pumpprobe pulses temporal profile and a kinetic model for the expected signal rise dynamics. More precisely the induced absorbance a t a specific test wavelength (A) and for a time delay (T) between the excitation and the probe beams is defined as the sum of the contribution A?(T) of all transient species:
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In the particular case of a small signal the time dependence of the different populations during the pumping and probing follows the relationship
136 The Journal of Physical Chemistry, Vol. 97, No.
Gauduel et al.
I, 1993
with
e(#) = J-+,O)ZpR(t+ T')lnpU(t) dt dT'
(7)
In these expressions, I is the interaction length, CA(7')is the normalized correlation between the probe and the pump pulse, and and Ciare the molar extinction coefficient and the concentration of species i , respectively. The transient signal triggered by a pump beam (IF."),through a nonlinear phenomena (n order), is defined by the expression
t
The transient induced signal can be probed by a test pulse with representing the temporal delay between the pump (IPu) and probe (IPR)pulses. Consequently, the time-resolved discrimination of the physical phemomena A ( t ) follows the relationship:
I
T
With the variable change t = t - ( 7 by the expression
+ t ? , S'(t) will be defined
The first term represents the response of the molecular system and the second one the correlation function between the pump and the probe pulses. For a biphotonic ionization process of a water molecule, n equals 2. The absorption spectroscopy kinetics have been analyzed by a kinetic model which takes into account the existence of primary photophysical events (reactions 1-4). Starting from the virtual excited states of water molecules, we assumed the existence of two channels for the photoejection and relaxation of the electron. Some of these early steps (reactivity of water cation, electron localization and solvation, electron-radical pair formation, and geminate recombination) have been previously investigated in pure light water by femtosecond ultraviolet, visible, and infrared spectroscopy.*-9~l2J3The different characteristic times ( T I - T ~ ) are directly discriminated by femtosecond spectroscopic experiments. In the present femtosecond spectroscopic investigations, the computed fits of the experimental traces are obtained considering symmetric biexponential pump and probe pulses. The time broadening factor occurring when the pump and the probe wavelengths overlap with different group velocities is measured on sample for which an Yinstantaneousnresponse can be defined:
The time-resolved data are analyzed taking into account the determination of the zero time delay and the refractive index effect. This last point is of particular importance at very short time when we consider the chirp of the zero time delay that occurs between two samples (H20 and D2O) having refractive indexes nl(w)and nz(w). The temporal delay between the two samples of optical length I will be
Figure 1 illustrates the direct measurement of a refractive index effect for two aqueous samples (H20 and D20 > 99.95%) at 294 K when Xpu = 310 nm and XPR = 660 nm. A temporal delay of 80 fs for 2-mm optical length can be clearly determined. Figure 2 represents, for a short temporal window (2 ps full scale) and two test wavelengths (720 and 820 nm), the rise time of an induced absorption in light and heavy water. At 720 nm, the signal corresponds to the formation of the fully hydrated
4.21 .I
"
4.5
"
0
"
0.5
"
I
'
I
1.5
T" (PSI Figure 1. Direct measurement of a refractive index effect at 660 nm and 294 K for aqueous samples, with a 2-mm path length (H20vs DzO), following the femtosecond ultraviolet excitation (3 10 nm) and photobleaching of a dye (blue nil). The measured temporal delay between light and heavy water equals 40 fs/mm.
electrons for which the energy of the lowest optical transition equals 1.7 eV. One of the key points for the analysis of femtosecond data in the red spectral region concerns the existence of an early recombination reaction. The experimental rise time at 720 nm is fitted with a kinetic model which includes electron solvation dynamics and the early geminate recombination between prototropic species and hydrated electrons: e,- + (XjO+, 0x1 X20 OX-. Over a very short temporal window (2 ps), the recombination process cannot be directly observed (Figure 2). However, as it has been previously shown at shortest test wavelength (660 nm) this early recombination reaction can influence the appearance time of the induced absorption signal.lZb The normalized induced absorption in the red spectral region (AC~'~O(T)) consists of the linear combination of two populations of fully relaxed hydrated electrons: one assigned to a long-lived hydrated electron (e-hyd)nrwmband theother toone which performs an early recombination (e-hyd)rwmb with prototropic species (eq 13, where (ehyd)r represents (e-hyd)rwmb, and (ehyd)nr represents (e-hyd)nrccomb): Recently, we have suggested that following the
+
-
femtosecond photoionization of water molecules, electron-radical pairs (e-,-.OH, e-,...H30+) would execute a one-dimensional walk before undergoing an ultrafast neutralization reaction.I2 During this ultrafast reactional process, the time-dependence of the hydrated electrons population can be expressed as follows:
In expression 14, 1/Td represents the jump frequency of the recombination process. The times Tj and T4 (eq 15) are characteristic of the electron solvation process through a twostate activated model. In HzO and D20,the femtosecond infrared spectroscopy of a transient electronic state (prehydrated electron) permits us to discriminate these characteristic times Tj and T4. The experimental data obtained at 720 nm are in agreement with previous results at 660 nm or 410 nm (Table I). The broad visible spectral band exhibits no spectral inhomogeneity due to the presence of several electronic states and can be only assigned to hydrated electrons. The best computed fits of experimental data indicate that the two times (T3 and T4) are not significantly
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993
Early Formation of Electron-Radical Pairs 1.2
localized in the vicinity of prototropic species (water cation: X20+ or its derivatives, hydronium ion: X 3 0 + and hydroxyl radical: OX). The total absorbance of the test pulse Aa,8,:0(r)has been described by an expression which considers the evolution of the different populations of electrons (Ci(t))during the excitation and probe pulse:
L
1-
0.1
-
0.6
-
T v
0,41 0.2
137
The linear combination of the different contributions is defined as follows:
I
t
Aa,8,:'(t) = Aa:hz(t) 4- Aa,820 prchyd( 1 )
+ Aa:!:adpair(t)
(17)
with 1.2
1 mo > 99.95%
1
0.1
0.2
0
-._
1
4.5
0.5
0
1
1.5
TIME (ps)
Figure 2. Appearance time of normalized induced absorption in pure light and heavy water at 294 K for two test wavelengths (720 and 820 nm). The photoexcitation of water molecules is performed with femtosecond ultraviolet pulses (excitation: 310 nm, 4 eV). The experimental data are analyzed considering the different contributions of electronicstates for each test wavelength. The smooth lines represent the computed best fits. In the red spectral region, the signal is due to fully hydrated electrons whose fraction recombinequickly with prototropic species (X30+and OX, X = H or D). The different characteristic times (T3, T4,and Td) are reported in Table I. In the near infrared region (820 nm), the rise time of the signal implicates the contribution of the fully hydrated electrons and the existence of two nonequilibrium electronic states (e-prshydand electron-radical pairs). The H / D isotopic substitution (H20 vs D2O > 99.95%) significantly affects the characteristictimes of the electron-radical pairs (X30+:e-:OX). For explanation, see the text and Table I.
modified by an isotope substitution: T3(D2O)/T3(H20) = 1.04; T4(D20)/T4(H20)= 1.08. However, theanalysisofexperimental data at longer times (Figures 3 and 4) underlines that an H / D isotopic substitution modifies the recombination time (Td)and the percentage of the early electron decay (eq 14). The different kinetic parameters obtained from spectroscopic data are reported in Table I. Let us, at this stage, consider the effects of an isotopic substitution on the dynamics data in the isosbestic spectral range, i.e., in the near infrared. At 820 nm, the results obtained for different temporal windows (Figures 2, and 3, and 4) show the existence of a significant H / D isotope effect. To analyze the time-dependent absorption a t short (2 ps) and longer time scales (4 and 10 ps), we have to consider the contributions of (i) infrared prehydrated electrons, (ii) fully hydrated electrons for which a fraction rapidly recombines with prototropic species (XjO+ or OX), (iii) nonequilibrium electronic state assigned to a neoformed electron-radical or electron-ion pairs [X30+:e-:OX, with X = H or D]. This last transient species has been recently identified in light water at r w m temperature and would correspond to the case for which the photogenerated electrons would be initially
where eprehyd represents e-prehyd, ehyd represents e-hyd, and e-rad pair represents e--rad pair. The factors of normalization used in the computed fits of the different experimental data require that 8, b2 P3 = 1. The different frequency factors of primary events (reactions 1-4 and eqs 14 and 15) are reported in Table I. The careful analysis of the rise time of the signal at 820 nm permits us to discriminate the existence of a significant H / D isotope substitution effect on the formation time (Ts= l/k5) and the mean lifetime (T6 = l/k6) of the near infrared nonequilibrium electronic configurations (X30+:e-:OX, with X = H or D). More precisely, Figures 2 and 3 demonstrate that this transient state appears with a time constant of 130 f 20 fs in light water and 320 f 20 fs in D2O. The computed best fits of the experimental data clearly demonstrate also the effect of an H / D isotopic substitution on the behavior of the transient near infrared signal (Figures 2 and 3). At 820 nm, the total relaxation process corresponds to a complex nonexponential decay including transient components (eqs 16-20). The contribution (8,) of the hybrid electronic state (eq 4) is greater in D20 than in H20 (Table I). Figure 4 and Table I permit us to fully compare the influence of an H / D isotopicsubstitutionon theearly behavior of the induced absorption in the red and near infrared spectral regions. At 720 nm the relaxation phenomenon has been assigned to the existence of a one-dimensional random walk law for which a proton jump time (Td)is defined (Table I). Figure 4 shows that in H20 and D20 a non-negligible fraction of the near infrared signal (820 nm) disappears faster than at 720 nm. This fact demonstrates that the relaxation phenomena observed in the isosbestic spectral range (820 nm) cannot only be assigned to the existence of an early geminate recombination between fully hydrated electrons and prototropic species. The experimental data obtained in the near infrared region underline the existence of an additional short-
+ +
Gauduel et al.
138 The Journal of Physical Chemistry, Vol. 97, No. I , 1993
TABLE I: Influence of an H/D Isotopic Substitution on the Frequency of Primary Events and the Lifetimes of Transient Species in Pure Liquid Water at 294 K parameters" (P) HzO D20 (P)D ~ O(PI / H~O ref formation (X20+) (kl = l / T l ) relaxation (XzO+)(k2 = 1/T2) electron prehyd (k3 = 1 / T3) electron hyd (k4 = 1/T4)
jump frequency (1 / Td) percentage recomb (7%) [f-hydlCr55%/[e-hydlGrOl
Test Wavelength: 410 nm > 1014 1 0 1 3 S-1 0.58 x 1 0 1 3 S K I Test Wavelength: 1250 nm 0.9 x 1 0 1 3 S-1 0.83 x 1013 S-I 0.42 X 10l3s-I 0.40 x 1 0 1 3 S-1 Test Wavelength: 720 nm 0.83 X 10l2s-I 0.45 X 10l2s-I 55 49 0.9 0.95
> 1014 SSI
lifetime X,O+ ( 1 / n lifetime OX (1 / T )
Test Wavelength: 820 nm 0.77 x 1013 SKI 0.31 x 1 0 1 3 S-I 0.29 x 1013 S-I 0.13 x 1013 S K I 0.34 0.38 N M R Studies 1.17 X 10I2 s-I 0.71 X 10l2 s-I 0.55 X 10l2s'I 0.20 x 10'2 s-I
T5/ T2 Tsl T3 T5/ T4 T6/ 7-4 T6/ T(x@+)
1.30 1.18 0.54 1.42 0.40
encounter pair (k5 = l/Ts) neutralization (k6 = 1 /T6) P3
Temporal Ratio 1.88 2.66 1.28 3 0.53
0.58
8
0.92 0.96
9, 12
0.54 0.89
present study
0.40 0.45
present study
0.6 1 0.37
37
1.44 2.25 2.37 2.1 1
present study
The parameters include the behavior of prototropic species (water cation, hydronium ion, and hydroxyl radical), electron solvation dynamics, the early geminate recombination reactions, and the electron-radical pairs formation. (1
lived electronic component for which the frequency of the neutralization process (reaction 4 ) is significantly dependent on the protic character of the solvent: k6 = l/T6 = 0.29 X l o i 3s-I in H2O and 0.13 X 1013 s-l in D2O. 3. General Discussion
a. PhotochemicalGeneration of Subexcitation Electrons and Early Neutralization Reactions. The influence of an H/D isotopic substitution on the formation and lifetime of nonequilibrium electronic states in water at 294 K has been investigated by femtosecond absorption spectroscopy in the near infrared. Regarding the different kinetic data summarized in Table I, several important points must be considered and discussed. From a general point of view, the H / D isotopic substitution drastically influences the frequency of (i) the ion-molecule reaction, (ii) the solvent cage formation around neoformed prototropic species (hydronium ion and hydroxyl radical), and (iii) the early geminate recombination between the hydrated electron and neoformed prototropic species. Let us consider, first, the analysis of the early recombination reaction occurring between the hydrated electron and prototropic species (OH and H30+) for which a proton jump would occur with a frequency A over a distance b (diffusive motion by a finite process). For instance, taking into account the high mobilities of the hydronium ion and e-hyd(DHIOt= 9 X cm2 s-I vs De-,,, = 4.75 X 10-5 cm2 S - ~ , ~ O the J ~ proton jump model emphasizes the role of the dynamical structure of the electron-ion pair recombination and would involve the time dependence of hydrogen bond polarization. We can consider a limiting caseof the ultrafast neutralization reaction for which the diffusion coefficient of the hydrated proton (H30+)is defined by the expression D = (Ab2)/ 6)O and the reaction radius R2 = 5 A. In this hypothesis, for a mean H3O+ lifetime of 10-l2 s we obtain a proton jump distance 6 of 2.19 A. That means that an electron-ion pair which has an initial separation length L = R2 6 of about 7 Acan relax through a single proton jump (unidirectional dvfusive motion by afinite process). This initial length (7 A) is also equivalent to the Onsager distance over which structural characteristics of the solvent must be remembered.40 The proton jump rate, suspected to be linked to the neutralization process (geminate recombination), is found to be significantly influenced by an H / D isotopic substitution
+
(Table I). In agreement with previous pulse radiolysis experiments, this would demonstrate that the initial spatial distribution of photogenerated hydrated electrons and prototropic species is slightly broader in D2O than in H20.31-41 The initial yield of hydrated electrons generated by femtosecond ultraviolet excitation of water molecules can be dependent on the rate of energy scattering within the vibrational modes of neutral water m 0 1 e c u l e s ~ ~ or J ~on ~ ~the I transient solvent configurations due to prototropic entities. To examine this last point, we have performed a simulation of the time dependence of different electronic populations in H2O and D20 considering (i) the correlation functions between pump and probe beams, (ii) the early photochemical processes described by eqs 1-4 and 14, and (iii) the experimental times measured in the infrared, near infrared, visible, and ultraviolet regions. The computed simulations of the transient populations of electrons (prehydrated states, electron-radical pair, and fully relaxed hydrated states) are reported in Figure 5 . The curves are not normalized in order to compare the effects of an H/D isotopic substitution on the different populations. After a very short time ( t < 4 ps) this figure shows that in H20 and D2O the ultrashort lived infrared electron population (prehydrated state) exhibits a maximum at t 300 fs. An H / D isotopic substitution does not modify either the temporal dependence of this nonequilibrium electronic population or its maximum value (C(cprehyd)max). It is interesting to notice that the population of fully relaxed hydrated electrons absorbing in the red spectral region is never at equilibrium. As previously discussed, this situation is due to the influence of prototropic species through an early one-dimensional walk geminate recombination (eq 14). Computed data reported in Figure 5 demonstrate that within the first 2 ps, the spectroscopic contribution of the hydrated electron detected in H20 (D20) corresponds to 90% and (95%)of a saturated population (Cchyd In other words, H / D isotopic substitution modifies the early yield of photogenerated hydrated electrons in the liquid phase, and 10% (5%) of hydrated electrons cannot be detected at these early times. This fact demonstrates that the direct observation of an isosbestic point is prohibited. Additional data reported in Figure 5 exhibit
-
The Journal of Physical Chemistry, Vol. 97, No. 1. 1993 139
Early Formation of Electron-Radical Pairs
T h D q " d Ekmnk Swn
h Llghtnd
6 j
a
t 820nm
t
-1 --
4
4
I
2
0
4
6
D
Pump: 310 nm
294K
1
0.6
t
I
I
[ - I
I
15
20
0.4
02
0
--.5
0
5
10
2
.
1
0
1
2
3
4
5
Figure 5. Simulated effect of an H/D isotopic substitution on the early concentration of transient electronic populations (Cj(t))generated by femtosecond photoionization ofwater moleculesat 294 K. Thesimulations are performed using experimental characteristic times (Ti = l/ki, i = 1-6) asreported inTableI. To favor thecomparison between thedifferent electronic populations in water, the curves are computed considering that D20*) the initial virtual population of excited water molecules (HzO*, equals 1.
I 4
.
(PSI
TIME (PSI Figure 3. Influence of an isotopic substitution on the early behavior of the induced absorption a t 820 nm. The smooth lines represent the best computed fits of the experimental traces. The relaxation of the signal is non-monoexponential and results from the contribution of two primary processes (i) an electron recombination with prototropicspecies (e--X30+, e-.-OX) for which a one-dimensional proton jump (Td) is defined and (ii) the deactivation of electron-radical pairs (OX:e-:X30+). In this later case, the mean lifetime of the electron-radical pairs (T6) is two times longer in deuterated water than in light water (Table 1).
l t 0.8
i
I
12,
O1
0.6
WI(*
TIME (pr) Figure4. Comparison between the early decay of the induced normalized absorption at 720 and 820 nm following the femtosecond photoionization of pure light or heavy water (294 K) by ultraviolet pulses (310 nm).
the significant effects of an isotopic substitution on the population of hybrid electronic states in the near infrared. These results will be discussed at length in the following paragraphs. b. Early Electron Localization and the Protic Character of Water. Numerous discussions can be mentioned concerning the photon energy required to perform vertical Born-Oppenheimer ionization of liquid water at ambient temperature.32.42-44 Using picosecond pulses, the production of hydrated electrons can be observed around 6.5 eV, Le., 2 eV lower than the estimate of the
ionization potential (8.76 eV).44 This experimental data would suggest that ultrafast internal energy exchange and cage effects, which are not considered in the macroscopic ionization threshold, can affect the early charge separation and quantum yield. It is interesting to notice that thevalue, 6.5 eV, isvery near theenergy of the first electronically excited state (AIBI) whose photodecomposition gives OH (XII) and H(2S).4s Experimental studies on the photophysics of liquid water have suggested the existence of a low-energy channel under the energy band gap for which the excitation energy required to produce hydrated electrons and prototropic species equals 5.78 eV.32333 This charge-transfer process would compete with the direct dissociation of the -A state (1 bl 3sal) and involve transitions from a favorable site geometry to permit the thermodynamic cycle of an autoionization process. Our previous femtosecond investigations of transient electronic states in the near infrared are in agreement with the existence of such a low-energy photochemical ~hanne1.I~The initial electron-radical pair distribution (e-...0H:e-...H30+)nH*~ would be highly dependent on initial energy transfer on water molecules, early electron scattering, and finally the microscopic environment created by the primary water molecular cation (H2O+) or its byproducts. A limiting case has been previously studied in concentrated acid aqueous solutions for which [H20/HCI] = 5.46 In this concentrated solution the femtosecond investigations had permitted us to identify a transient absorption band peaking at E,,, = 1.32 eV and exhibiting a red shift of 0.4 eV in comparison with the spectrum of a fully solvated electron in bulk. This band has been assigned to the existence of transient couplings that would correspond to an unrelaxed electron in the solvation area of the hydronium ion. The present study clearly demonstrates the existence of an H/D isotopic substitution effect on the different steps of a lowenergy photochemical channel. Femtosecond ultraviolet excitation of water molecules through a two-photon process (2 X 4 eV) can represent sufficient energy to initiate,via latticevibrations, ultrashort-lived configurations, i.e., electron-radical pairs, compressed by solvent molecules. The kinetic data obtained in the red and near infrared regions in the present work confirms that the femtosecond ultraviolet excitation of water molecules initiates the formation of early electron-radical pairs (e--X30+; e--OX),x,o, X = H or D) through transient couplings between electrons and prototropic species. In light and heavy liquid water,
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140 The Journal of Physical Chemistry, Vol. 97, No. I, 1993
the early steps of the ion-molecule reaction (equation 2) are faster than the formation of electron-radical pairs (reaction 4). Table I shows that the T5/T2 ratio of these two steps is 21/2times greater in D2O than in H20. This means that very transient favorable structured environments for electron localization can be triggered by the presence of neoformed prototropic species (X20+or its derivates). In this hypothesis, excess electrons would get localized or trapped through energy scattering linked to an energetic vibrational mode and a vibration frequency (H-OH vs D-OD). Ultrafast nuclear motions such as proton transfer can favor the existence of local solvent cage configurations whose microscopic structure would be dependent on a concerted phenomenon occurring between electrons, the hydrogen-bond lattice, and prototropic species. c. Positive Hole Migration and Nonequilibrium Electronic States. The femtosecond spectroscopic investigations of primary events in water permit us to underline several important points. They concern the role of neutral or charged neoformed prototropic species in (i) the initiation of ultrashort lived favorable traps for fast electron localization and (ii) the solvent cage effect around a positive hole (X20+). These two aspects can be linked to the influence of the positive hole migration on the time dependence of the early electron-hole or electron-pair couplings in water. Previous experimental investigations have permitted us to estimate that the migration frequency of the hole (H20+) was about 21 times greater than that for the ion-molecule reactions.47 In our femtosecond photochemical conditions, that means that a resonant proton transfer (X20+ X20 X 2 0 X20+) would occur with a frequency of k{ = 21k2, i.e., -2.1 X 1014s-I in H2O and 1.23 X 1014 s-I in D20. In light water, this value remains comparable to the estimates of the vibrational frequency of the H-OH bond Y H ~ = H 1.15 X lOI4 It is interesting to discuss more at length the relationship that exists between an H / D effect on the ion-molecule reaction (reaction 2) and the formation time of nonequilibrium electronic states in the near infrared (reaction 4). The water cation-molecule reaction observed in the near ultraviolet occurs with a transition probability of about loi3 SI, i.e., few vibrational X-OX period^.^^,^^ The limiting factor for the cleavage rate constant of the water cation X20+ would be due to the dynamics of hydrogen bond formation and the weak activation energy of the ultrafast proton transfer with adjacent water molecules along the hydrogen bond. The influence of an H / D isotopic substitution on the T s / T2 ratio permits us to conclude that the subexcitation electron would probably test several configurations in the vicinity of prototropic species before reaching a near infrared localized state. A limiting step in the formation of neoformed encounter pairs would correspond to proton movements during an ultrafast ionmolecule reaction. Our femtosecond data show that the migration of the water cation in D20 is about 30% larger than that in H20. A similar H / D isotope effect is obtained on the Ts/ T2 ratio. This result suggests that a positive hole migration can be, at a microscopic level, a determining factor for the existence of transient coupling between electrons and prototropic species. This does not exclude the possibility that the electron can continue to influence the local environment of prototropic species with polarization of hydrogen bonds through proton dispersion forces.SO.51 The significant change observed for Ts between light and heavy water underlines the role of a concerted mechanism in the low photochemical channel for which a proton transfer and an electron trapping would be involved to get an hybrid electronic state (Rydberg state or neoformed encounter pair). It is interesting to notice that the formation time ratio ( T s ( D ~ O ) / T S ( H ~ O ) 2.4 isverysimilartotheratioof thepredissociation rateof Rydberg states which has been shown to be dependent on rotational sublevels and to exhibit a significant isotope effect: T(C-)D~O/ T(C-)H~O.= 2.4.52 Indeed, as previously suggested, short-lived configurations of solvent molecules resulting from electronic excitation would be equivalent to Rydberg states whose adjacent
+
-
+
Gauduel et al. water molecules can influence their behavior.13 Initial configurations including several water molecules would correspond to a favorable local trap for which cooperative effects on electron ejection may be probable under the energy band gap of water. d. Different Modes of Electronic Relaxation. At this stage, an important point concerns the comparison between thedynamics of formation (T3)and relaxation (T4) of infrared electrons through a two-state activated model with those of neoformed electronradical pairs (7‘s and T6). In pure light water at ambient temperature, femtosecond spectroscopic data show that the formation time of an early electron-pair (T5) remains similar to the dynamics of electron localization (Tj): Ts(H)/ Tj(H) = 1.18 (Table I). From these data, the existence of a common precursor for the infrared electron (prehydrated electron) and the neoformed encounter pair could be suggested.I3 The present study, by using isotopic substitution, permits us to clarify an important point on the electronic relaxation in water. It has been recently shown that an isotopic substitution does not significantly affect the dynamics of the electron hydration.12 By contrast, the electron-radical pair formation is longer in DzO thaninHzO(TS(D)/TS(H) = 2.4). Moreover,inD20(>99.95%), the Ts(D)/T3(D) ratio is two times more than that in H2O (2.25). This means that two photochemical channels exist in pure water. The presolvation of excess electrons and the formation of electronradical pairs do not involve similar responses of the water molecules. If the energy distribution of preexisting traps is defined by fluctuations in the density of the ~olvent,I5-22-~~.53 then ultrafast structural liquid reorganization initiated by short-lived prototropic species would favor an electron localization by self-trapping phenomena. Indeed, we can conclude that the existence of a competitive process from a common precursor of a presolvated electron and electron-radical pairs is unlikely. Femtosecond spectroscopic investigations of charge transfer in pure deuterated water permit us (i) to determine whether or not several photochemical channels can lead to electron solvation and (ii) to extend the knowledge on primary reactions between electrons and prototropic species. From a general point of view, the characteristic times of the two-state activated model for electron solvation in the infrared and the visible regions are not significantly different in H20 and D20.10b By contrast, a significant H / D effect on the mean lifetime of the nonequilibrium electronic state is observed in the near infrared. An increase in the lifetime of the hybrid state is not associated with the appearance of a time delay for the fully solvated electron. Indeed, additional kinetic data on the H / D isotope substitution permits us to discriminate the existence of two well-defined relaxation processes for electronic states in the infrared and near infrared regions: (Ts/T4)D/(Ts/T4)H = 2.11. In other words it is likely that electronic relaxation does not occur in the same way when the excess electron is localized far from or in the vicinity of neoformed prototropic species. That also means that the probability to obtain electron solvation from neutralization reactions of electron-radical pairs (reaction 4) is very low. This is confirmed by the valueof the (T5/T4)o/(T5/T4)Hratio (2.37) which underlines the existence of a discrepancy between a nonadiabatic relaxation of an infrared electron and an electronradical pair deactivation. It is interesting to compare the relaxation frequency of hybrid electronic states assigned to electron-radical pairs [(XjO+: e-:OX)h,d] with the estimate of the lifetime of excited molecules produced by ultrafast recombination between an unrelaxed electron and a primary water cation: e- + X20+ [X20*],,x2o 2X20. In the absence of surrounding water molecules, the deactivation of [X20*] can be estimated by the formula of Henly and Johnson:s4
-
- -
-
for which E* equals the exciting energy of neutral molecules (-6.25 eV) and Edis 5.1 1 eV. The H-OH decay channel
Early Formation of Electron-Radical Pairs occurs with a time constant of 3 X lO-I3s, Le., a frequency of 0.33 X IO13 s-1. Data reported in Table I demonstrate that the deactivation frequency of electron-radical pairs in H2O is similar to this estimate (k6 = l/T6 0.29 X l o i 3s-I a t 294 K). This means that the early rearrangement of water molecules during deactivation of an encounter pair can be equivalent toa relaxation of an excited state of neutral water configurations [ H 2 0 * ] n ~ 2 ~ . Considering that we cannot obtain direct spectroscopic information on the ultrafast quasi free electron-water cation reaction (H20+ e- H20*, r 10-14s) it is not easy to determine the quantum yield of electron solvation from virtual excited states of water molecules. This point is more complex if we consider the existence of different statistical populations of hybrid electronic states in the near infrared. e. Lifetimes of EncounterPairs and the Efficiency of ElectronProton Reactions. The femtosecond spectroscopic identification of ultrashort lived electron-radical pairs in liquid water (H2O or D20) suggests that excitation transfer following early energy deposition is dependent on local structural configurations due to the existence of adjacent water molecules for which resonant energy transfer between large "Rydberg" type orbitals and surrounding water molecules can occur. The fact that significant H / D effects are observed on the appearance time of electronradical pairs suggests that an autoionization process would be faster in H20 than in D20. The relaxation of hybrid electronic states in the near infrared is significantly influenced by an isotopic substitution T6(D)/T6(H) = 2.2. As previously shown, it is noticeable that the relaxation of an electron-radical pair is always longer than the infrared electron lifetime (Figure 2). The present results permit us to underline the existence of dual electron relaxation modes following an autoionization process or a vertical ionization of water molecules. In the latter case, it has been previously shown that a fully hydrated electron can recombine with prototropic species early according to a finite process, i.e., a proton jump.'? As far as the behavior of a nonequilibrium electron subsequent to a low photochemical channel process (autoionization process) is concerned, the relaxation process corresponds to an ultrafast neutralization reaction. The existence of neoformed encounter pairs (e-:X30+:OX) can be dependent on the dynamics of the rearrangement of water molecules in the vicinity of prototropic entities. The reorganization of water molecules may require the breaking of the hydrogen bonds which concern important parameters such as the OH stretch mode. The cleavage rate constant of an electron-radical pair occurs on a similar time scale to that of the H-bond mean lifetime or the average lifetime of the hydrated p r ~ t o n . ~ ~ - j ~ Let us discuss the relationship that can exist between the lifetime of the transition state and the efficiency of the electron-proton reaction. In water, the probability of reaction of a dry electron with a hydrated proton is very low and the reactivity of hydrated electrons with the hydronium ion (reaction 22) exhibits a rate constant of 2.3 X 1010 M-1 5-1.39,5*39 This value is about 30% of the estimate for a diffusion-controlled process using a reaction radius of 5 A and diffusion coefficients of 9 X cm2 s-I and 4.7 X 10-5 cm2 s-l for hydronium ion and hydrated electron, r e ~ p e c t i v e l y . 3 ~ ~This ~ ~ ~last ~ ' reaction will not be diffusioncontrolled but influenced by the activation rate constant k,,,.
-
+
- -
ko
k m
H 3 0 ++ e-hyd [transition states] H + H 2 0 (kexp= 2.3 X 10'' M-l s-I) (22) Several years ago, Czapski and Peled62suggested the existence of a relationship between the lifetime of suspected encounter pairs ( e - p H 3 0 + ) and the rate constant of the reaction.22 The lifetime of the encounter pair would be one of the limiting factors of the electron-proton reaction. Our femtosecond study on pure liquid water emphasizes the existence, at room temperature, of nonequilibrium electronic states which can be assigned to
The Journal of Physical Chemistry, Vol. 97, No. 1, 1993 141 neoformed encounter pairs between electrons and hydrated hydronium ion (X30+)or hydroxyl radical (OX), X = H or D. The mean lifetime of these transient electronic states in pure water at 294 K (HzO and D20) is less than 1 ps (Table I). If we consider that, for a given concentration of hydrated proton, the probability of reaction between the electron and the hydronium ion is dependent on the lifetime of the encounter pair (e--. H 3 0 + ) n H 2then ~ , the ratio of the pseudo-first-order constant (kerp/ kthcor)can be expressed as follows: kcxp/kthcor
- Oa3- /
VeffEP/vTS
TTs/ TEffEp (23) TeffEP)/( / TTS) In this expression, v,ffEP = 1/ T,ffEPrepresent the frequency of formation of an efficient encounterpair. Thelimitingcases would correspond to those for which the lifetime of the encounter pair will be limited by the mean lifetime of hydrated proton (H30+)h,d. In this hypothesis, reaction 22 can be characterized either by an activation barrier or by a tunneling process. The second parameter VTS = l / T ~ srepresents the frequency of formation of efficient and unefficient pairs. To a first approximation, this frequency can be defined from the mean lifetime of the encounter pair (e-:H30+) in water. Indeed taking the values obtained by near infrared femtosecond spectroscopy, Le., TTS T6 = 340 fs and 750 fs in H2O and D20, respectively, the estimate of the ratio T T S / T ~ ~ (eq ~ E P23) equals 0.40 in HzO and 0.53 in D20. These two values are estimated by default owing to the fact that in our experimental conditions, up to now, we cannot discriminate the respective contributions of XjO+ and OX in the ultrafast neutralization process of the electron-radical pair. Consequently, the mean lifetime of the electron-radical pairs we measure a t 820 nm represents the average lifetime of two populations of pairs (e-:H30+ and e-:OH) whose formation probability would be dependent on transient microscopic structures of the solvent cage. NMR studies have shown that the lifetime of the OH (OD) radical is 2 (3.5) times longer than the lifetime of the H 3 0 + (D30+)ion.37 If we take TeffEP,to be equivalent to the average lifetime of the two prototropic species ( Tx30+ T 0 ~ ) / 2Le., , 1.12 ps in HzO and 3.35 ps in D20, then the TTS/T,rfEP ratio equals 0.26 in H20 and 0.24 in D20. These calculations on the probability of reaction via the existence of electron-radical pairs would underline that (i) the lifetime of hybrid states of electrons in water are shorter than those of isolated prototropic species in very dilute solution and (ii) that the limiting factor of the reaction between an electron and a proton is not the lifetime of hydrated hydronium ion but rather that of the short-lived electron-ion pair. Weshould wonder whether therelaxation of nonequilibrium electronic states involves intracomplex structural changes for which proton mobility, H bond mean lifetime, or average lifetime of prototropic species will be determining factors for activation energy of the reaction 22. In water, the importance of the following many-body effects must be considered: (i) the influence of the Coulomb attraction between electron and hydronium ion upon the e1ectron:OH couplings; (ii) the dynamics of couplings between proton and neutral water molecules; and (iii) the role of cooperative effects between several water molecules. These different aspects need to be considered to better understand ultrafast reactions and the microscopic structure of the solvent cage around the electron and the radicals.
(
-
+
4. Conclusions Femtosecond spectroscopic investigations of nonequilibrium electronicstates in purelight and heavy water permit us toestablish that transient local solvent configurations linked to the protic character of the solvent molecules exert a major force on electron relaxation in the bulk. Ultrashort lived cage effects are modified by a change in the energetic vibrational mode of the solvent. H / D isotopic substitution demonstrates the existence of two different relaxation channels of the excess electron. One of them
142 The Journal of Physical Chemistry, Vol. 97, No. I, I993
does not contribute to the formation of a fully hydrated electron but is involved in the formation of a hybrid electron-radical pair. An improvement in the knowledge of the relaxation processes of electron-radical pairs (electron-proton or electron-OH radical) would help to define the distribution of the charges along a convenient reaction coordinates in order to determine the displacement of the electronic clouds during the complexation mechanism. Recent advances in the theory of ultrafast geminate recombination reactions are in progress.63 The second key point of this study concerns the very fast motions that would occur in molecular complexes following the early localization of the electron within the solvation shell of prototropic species. Spectral identification of ultrashort lived intermediates during the concerted electron-proton transfer in water provide guidance for future developments on transition state theories in condensed matter.
Gauduel et al.
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