29 May 1998
Chemical Physics Letters 288 Ž1998. 833–840
Ultrafast events in the electron photodetachment from the hexacyanoferratež II/ complex in solution Stanislas Pommeret ) , Ryszard Naskrecki 1, Peter van der Meulen 2 , Marjorie Menard, Georges Vigneron, Thomas Gustavsson ´ CEA r Saclay, DSM r DRECAMr SCM, URA 331 CNRS, 91191 Gif-sur-YÕette Cedex, France Received 8 January 1998; in final form 24 March 1998
Abstract Following excitation of the hexacyanoferrateŽII. complex in water with a 40 fs laser pulse at 267 nm, the absorption of the hydrated electron rises with a global time constant of 510 fs, whereas the characteristic absorption of the hexacyanoferrateŽIII. appears almost instantaneously. A transient absorption band around 490 nm is tentatively assigned to the charge-transfer-to-solvent ŽCTTS. state of the hexacyanoferrateŽII.. Its ultra-rapid decay Ž< 60 fs. is due to the electronic repulsion between the electron and its parent core. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction Electron solvation has been the subject of many experimental investigations w1–18x ever since its discovery 35 years ago in pulse radiolysis experiments w19x. Shortly afterwards, the spectrum of the solvated electron in water was also evidenced in flash photolysis experiments in iodide w1x and hexacyanoferrateŽII. w2–6x solutions. With advances in laser technology, several attempts have been made to time-resolve the electron solvation process using the hexacyanoferrateŽII. complex as an electron donor w7–9x. The first experimental time-resolved study of
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Corresponding author. E-mail:
[email protected] Permanent address: Institute of Physics, Adam Mickiewicz University, Umultowska 85, 60-780 Poznan, Poland. 2 Present address: Department of Physics I, KTH, Royal Institute of Technology, S-100 44 Stockholm, Sweden. 1
the electron photodetachment of a 10y3 M hexacyanoferrateŽII. aqueous solution was performed by Rentzepis et al. w7x. Using picosecond pulses at 265 nm, they concluded that the solvation process occurs through at least one intermediate step. The absorption of the intermediate state was located in the infrared part of the spectrum. These authors reported characteristic times for the solvation process of 2 and 4 ps, respectively, both of which were at the limit of their time resolution. Somewhat later, Wiesenfeld and Ippen w8x reinvestigated the time dependency of the solvation process using sub-picosecond pulses at 307 nm. In a 0.48 M solution of heaxacyanoferrateŽII. in water, they found that the overall electron solvation process occurs in less than 300 fs. Using wellknown electron scavengers such as nitrite, nitrate and acetone they demonstrated that the absorption observed at 615 nm was indeed due to the hydrated electron. The first real femtosecond time-resolved study of
0009-2614r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 8 . 0 0 3 7 1 - 6
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the photodetachement of hexacyanoferrateŽII. in water was carried out by Gauduel et al. w9x. Using 100 fs laser pulses centred at 310 nm, they excited a 0.45 M aqueous solution of hexacyanoferrateŽII.. Like Rentzepis et al. w7x, they found two characteristic electron solvation times and proposed that the solvation process occurred through at least one intermediate step. The first time constant Ž110 fs. was associated with the formation of an intermediate species Žthe pre-solvated state or ‘wet’ electron. and the second time constant Ž240 fs. was ascribed to the relaxation of the pre-solvated state towards the fully hydrated electron. Since they were identical to the times obtained for electron solvation in pure water w10x Ž110 and 240 fs. they concluded that ‘‘the existence of the presolvated state of electron is neither influenced by the method of electron photoejection nor by the ionic strength of the polar medium in the range of 0–0.45 M w9x’’. q Finally, using electron scavengers like NOy 3, H 2q and Cd Mialocq et al. w11x showed that the absorption rise observed in the red part of the visible spectrum following a picosecond laser excitation at 267 nm of a solution of hexacyanoferrateŽII. in water is due to the hydrated electron. In the present Letter we will present our results obtained by exciting a 10y2 M aqueous solution of hexacyanoferrateŽII. with 40 fs ultraviolet laser pulses at 267 nm. The improved time-resolution, as compared to the studies of Wiesenfeld and Ippen w8x and of Gauduel et al. w9x, as well as the observation of the transient absorption spectrum over a large wavelength interval allows us to obtain a more detailed picture of the photodetachement process. In particular, it leads to the discovery of a thus far unobserved ultra-short-lived intermediate state which we propose to be of charge-transfer-to-solvent ŽCTTS. character. Moreover, the different excitation wavelength used in the present study enables us to address the dependence of the charge separation process on the amount of energy initially put into the system Žsee e.g. Table 1 in Ref. w20x..
2. Experimental The laser pulses used in the experiment were delivered by a modified ŽMC2. Ti:Sapphire laser
oscillator ŽCoherent, Mira., pumped by an argon ion laser ŽCoherent, Innova 310. and amplified in a Ti:Sapphire regenerative amplifier ŽAlpha 1000 US, BM Industries.. This laser source produces pulses of 40 fs Žfull width at half maximum ŽFWHM. assuming a sech2 pulse shape. around 800 nm with a pulse energy of about 750 mJ at a repetition rate of 1 kHz. A detailed description of the laser system as well as all experimental procedures involved will be given elsewhere w21x. Here we will briefly mention only the most important features. The electron photodetachment process from hexacyanoferrateŽII. in aqueous solution was investigated using the transient absorption pump–probe technique and 267 nm laser pulses obtained by frequency tripling the output of the Ti:Sapphire based laser system. Energies of up to 100 mJ per pulse could be obtained in the frequency tripling w21x. A white light continuum, generated by focusing a small fraction of the 800 nm Ti:Sapphire fundamental in a thin rotating fused silica disk, served as a probe. After the sample, the continuum was dispersed by a spectrograph and detected by a 1024 = 512 pixel CCD camera ŽPrinceton Instruments.. The input spectrograph slit ŽJobin–Yvon 270 M. was set to 0.25 mm. In order to improve the signal-to-noise ratio, the readout rate of the CCD camera was raised to about 30 Hz using a chopper to modulate the light beam w21,22x. Only reflective optics are being used in the set-up to minimise undesirable effects due to group velocity dispersion ŽGVD.. The zero-time delay was derived from two-photon absorption ŽTPA. measurements in a 150 mm thick glass microscope slide using the second harmonic at 400 nm and the white light continuum w21,23x. To illustrate our approach, we have plotted transient TPA signals for six different probe wavelengths in Fig. 1. In these experiments the microscope slide was mounted at the position of the sample flow cell. From these measurements it is easily seen that in the spectral region of interest, between about 410 and 650 nm, the time origin shifts by about 200 fs. These numbers can be used to correct the recorded kinetics at various wavelengths for the GVD effects and determine an unique zerotime origin. The transient absorption spectra of the hexacyanoferrateŽII. were then reconstructed. Moreover, these TPA transient optical densities show that
S. Pommeret et al.r Chemical Physics Letters 288 (1998) 833–840
Fig. 1. Two-photon absorption in a glass microscope cover slide Ž150 mm thick. using a 40 fs FWHM pump pulse at 400 nm and a white light continuum. The peak power density of the 400 nm pump pulse is 10 15 Wrm2 .
the FWHM of the pump–probe cross-correlation function is equal to about 60 fs and is almost independent of the probe wavelength. It is interesting to note that a gaussian of 65 fs FWHM is obtained by calculating the autocorrelation of a gaussian of 40 fs FWHM. Since we have used a thin non-linear optical crystal Ž0.1 mm, BBO. and only reflective optics it is reasonable to assume that the time resolution of our experiment is not affected when we change the pump wavelength from 400 to 267 nm. The solutions were flowed in a fused silica cell with a 0.1 mm optical path length. The pump energy was set to 20 mJ per pulse and the pump beam diameter was 2 mm FWHM. The pump power density was thus 1.6 10 14 Wrm2 assuming a 40 fs pulse at 267 nm. At this relatively low power density we did not detect any measurable transient signal in pure water. For the electron photodetachment experiments the potassium hexacyanoferrateŽII. concentration was 10y2 M, giving an optical density of 0.23 at 267 nm in the 0.1 mm thick sample cell. The 90 cm3 total
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sample volume of the solution was changed every 30–40 min in order to minimise the build-up of photoproducts. From the UV-visible absorption recorded after each change of the solution, it was established that under our experimental conditions the only photoproduct formed was the oxydized hexacyanoferrateŽIII. complex w2,5x. After 40 min of laser photolysis, only about 0.5% of the initial hexacyanoferrateŽII. concentration was converted to hexacyanoferrateŽIII.. Potassium hexacyanoferrateŽII. ŽK 4 FeŽCN. 6 . ŽProlabo, ) 99%. was used without further purification. Water obtained from a purification system ŽWaters Millipore. had a resistivity greater than 18 M V my1 . The experiments were carried out at room temperature Ž208C. and under atmospheric pressure. The data were analysed using a fitting program based on the Marquart algorithm w24x which performs a global fit of the transient optical densities as a function of both the delay time and the wavelength. The program neglects coherence effects, i.e. the pump and probe pulses are assumed to be non-overlapping w25x. The finite duration of the pump and probe pulses has been taken into account by convoluting the spectra calculated assuming impulsive excitation and probing with the experimental pump–probe cross-correlation function. The resolution of the spectrograph dispersing the continuum probe was assumed to be infinite. As input the program required the number of bands, their type Žgaussian or lorentzian. and a first guess of the spectroscopic parameters describing them Žspectral position, height and width.. In addition, the program needs a prescription defining how these spectroscopic parameters evolve in time Že.g. exponential, linear or constant. and an initial estimation of the parameters describing these changes Že.g. rate constants.. Subsequently, all parameters were optimised simultaneously to achieve the best fit with the complete set of the time-resolved spectra. The program is described in more detail elsewhere w22,26x. The required CPU time depended strongly on the number of data points and the number of freely varying parameters. For example, fitting a 2D map Ž DOD as a function of the time and the wavelength. consisting of 140 time steps and 200 wavelengths with 16 free parameters took more than 5 h CPU time on a Sun Ultra1 workstation.
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3. Results and discussion In Figs. 2 and 3 we present spectrally resolved kinetics and time-resolved spectra, respectively, of a 0.01 M aqueous solution of potassium hexacyanoferrateŽII.. These data have been recorded using steps of 13.3 fs Ž4 mm. fs with each scan consisting of 110 steps after GVD correction Ž150 before.. Total accumulation amounted to 1200 recorded spectra per step with a readout frequency of 28 Hz Žeach spectra correspond approximately to 15 laser shots. and the laser time needed for the experiment was approximately 2 h. The two most prominent features in these data are the rapid rise of the band centred at about 420 nm, and the much slower rise of an intense band whose maximum lies to the red of the spectral region considered Ž400–650 nm.. The band at 420 nm is easily identified as belonging to the hexacyanoferrateŽIII. complex w2,27x, whereas the band in the red part of the spectrum can be associated with the fully hydrated electron w3,4,7–9,18x. Apart from these two bands which are relatively well understood, a third,
Fig. 2. Experimental Žsymbols. and fitted Žsolid lines. kinetics of the transient optical density at several representative wavelengths. The 10y2 M potassium hexacyanoferrateŽII. solution in water is excited using pulses centred at 267 nm with a FWHM of 40 fs.
Fig. 3. Experimental Žsymbols. and fitted Žlines. time-resolved spectra at various delay times. The 10y2 M potassium hexacyanoferrateŽII. solution in water is excited using pulses centred at 267 nm with a FWHM of 40 fs.
rather broad and low-intensity absorption is detected at very early times. This can actually be observed in the kinetic traces ŽFig. 2. between 450 and 550 nm. This band has hitherto remained unobserved and in the following we will propose that it can be interpreted as the CTTS band of the hexacyanoferrateŽII. complex. In Fig. 4 we have plotted the kinetics at several representative wavelengths illustrating the behaviour at somewhat longer times. In this case each scan consisted of 100 points and the stepsize was 0.1 ps Ž30 mm.. This figure shows that after completion of the initial dynamics in about 1.5 ps all further reactions take place on a much slower time scale. In this respect we would like to briefly discuss the hexacyanoferrateŽIII. band at about 420 nm w2x observed in the ordinary absorption spectra of the irradiated solution after each sample change. Of course, the appearance of the hexacyanoferrateŽIII. band in the spectra after irradiation strongly supports a scheme in which the absorption of a UV photon by the hexacyanoferrateŽII. complex leads to ejection of a photoelectron w2,5–9x. Matheson et al. w2x have suggested that the appearance of the hexacyanoferrateŽIII. band in these spectra is due to the fact that some of the photoelectrons do not recombine
S. Pommeret et al.r Chemical Physics Letters 288 (1998) 833–840
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formed, together with the quasi-free photoelectron Ži.e. the electron just after charge separation.. Schematically this can be represented as follows: Fe Ž CN .
4y hn ™ 6
CTTS Tsep
¶• ß™
4y
Fe Ž CN . 6 1
T2 g
TCTTS
4y
Fe Ž CN . 6 CTTS
5
3y
™ Fe Ž CN . 6 q ey qf .
Fig. 4. Experimental Žsymbols. kinetics of the transient optical density at several representative wavelengths. The 10y2 M potassium hexacyanoferrateŽII. solution in water is excited using pulses centred at 267 nm with a FWHM of 40 fs.
Ž 1.
Note that, since the characteristic absorption band of FeŽCN.5 H 2 O 3y at about 440 nm w6,30x could not be detected in the spectra of the irradiated solution, we have neglected the photoaquation reaction w6x. Previous femtosecond time-resolved studies w9,10,12,15,17,18x have indicated that the solvation of the quasi-free electron occurs, at least, in two stages: T1
T2
y y ey qf ™ e pre ™ es
with the parent hexacyanoferrateŽII. complex but react according to: ey Ž aq . q ey Ž aq . ™ H 2 q 2OHy. The rate constant for this reaction equals about 10 10 moly1 l sy1 w2x, which means that on a timescale of about 10 ps it is hardly contributing to a decline in the ey concentration. The amount of hexacyanoferrateŽIII. in solution after irradiation indicates that the FeŽCN. 63yq ey™ FeŽCN. 64y recombination reaction may be about an order of magnitude faster, but, by femtosecond standards, it remains a rather slow reaction as well. This is completely consistent with the curves presented in Fig. 4 and with findings of other researchers w7–9,11x. Based on the original ideas put forward by Shirom and Stein w5,6x, we have performed a global fit of the data shown in the Figs. 2 and 3. For ease of discussion we shall first briefly introduce the model of Shirom and Stein w5x concerning the electron photodetachment of the hexacyanoferrateŽII. complex. Absorption of a photon at 267 nm most likely leads to the population of the 1 T2 g state, corresponding to a ligand field d–d transition w28,29x. The 1 T2 g state subsequently decays into the FeŽCN. 64y CTTS state. Finally, an electron is ejected from the CTTS state and the hexacyanoferrateŽIII. complex is
Ž 2.
where ey pre represents the pre-solvated or ‘wet’ electron and ey s is the final solvated electron. Together, Eqs. Ž1. and Ž2. provide a detailed representation of the chain of events following UV photoexcitation of the hexacyanoferrateŽII. complex. However, in order to be able to present a simple, but physically attractive, picture, and at the same time keep the number of parameters to be fitted to an absolute minimum, we have chosen to base our fit on the following simplified scheme: 4y hÕ
Fe Ž CN . 6
Tsep 4y)
™ Fe Ž CN . 6 Tsol
3y
3y
™ Fe Ž CN . 6 q ey qf
™ Fe Ž CN . 6 q ey s
Ž 3.
where Tsep is the time needed for the charge separation, Tsol is the global time for the electron solvation, and FeŽCN. 64y ) is an intermediate state before the charge separation. We have thus lumped together the FeŽCN. 64y 1 T2 g and FeŽCN. 64y CTTS states, and have neglected any signals due to the pre-solvated electron. The latter step is easily justified since the absorption maximum of the pre-solvated electron lies in the infrared w10,12,18x, outside the wavelength range considered here Ž400–650 nm.. For a free electron, represented by a plane wave, photon ab-
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sorption or emission is dipole forbidden, and signals due to the quasi-free electron are therefore anticipated to be of low intensity. Moreover, these signals, if any, may be expected to lie outside the probed wavelength region w18x. Consequently, we have not included any bands related to the quasi-free electron in the fit. Hence, we are left with only three bands associated with, respectively, the hexacyanoferrateŽIII. complex, the fully solvated electron, and the FeŽCN. 64y ) intermediate. We want to stress that without this last species, i.e. the FeŽCN. 64y ) , a satisfactory fit at very early times could not be obtained. A fit of the experimental 2D data set assuming three bands and allowing all spectroscopic parameters to vary freely leads to the following results. The hexacyanoferrateŽIII. band is found to be well represented by a gaussian centred at 422 nm and with a FHWM of 0.57 eV. This band appears instantaneously, i.e. within the FWHM of the experimental pump–probe cross-correlation function, and has an ‘infinite’ lifetime. The band of the fully solvated electron is best described by a lorentzian centred at 716 nm with a FWHM of 1.03 eV. The height of this band is increasing according to Ž1 y expŽytrt .. with a global time constant t of 510 " 20 fs. We did not find any indication of time-dependent changes in the peak frequency or the FWHM of both bands. The spectroscopic parameters obtained for these bands agree quite well with values available in the literature w2,31x, in particular if one realises that only the red half of the hexacyanoferrateŽIII. band and only the blue tail of the band of the solvated electron fall within the wavelength region probed in the present study. Jou and Freeman w31x reported that at 298 K the blue part of the absorption band of the solvated electron can be represented by a Lorentzian centred at 719 nm with a half width at half maximum of 0.49 eV. In their flash photolysis experiments Matheson et al. w2x obtained a peak position of approximately 410–420 nm and a FWHM of 0.62 " 0.08 eV for the hexacyanoferrateŽIII. band. As expected from the model of Shirom and Stein w5x, there is a one to one and correspondence between the amounts of ey s FeŽCN. 63y in solution shortly after the excitation pulse. If we take a value of 10 5 My1 my1 for the extinction coefficient of hexacyanoferrateŽIII. at 422 nm w27x and a value of 1.85 10 6 My1 my1 for the extinction coefficient of the solvated electron at 722
Ž . 3y nm w19,31x the concentrations of ey s and Fe CN 6 are found to be equal at the end of the solvation process, i.e. no electrons are lost during the solvation process. The third band, corresponding to the FeŽCN. 64y ) intermediate, is lorentzian shaped with a maximum at about 490 nm and a FWHM of 1.4 eV. It appears and disappears within the FWHM of the pump–probe cross-correlation function, i.e. Tsep < 60 fs. Note that it is unlikely that this band is associated with the solvated electron since it has never been observed in previous time-resolved studies on electron solvation w9,10,12,16–18x. Gauduel et al. w32x and Long et al. w33x observed a transient signal which they attributed to the water cation, but no such contribution is expected in the experiments presented here because no signal was observed in neat water. It is thus very appealing to attribute this transient band to an excited state of FeŽCN. 64y as was, of course, already anticipated from the beginning. Within our model, this state is the precursor of both the hexacyanoferrateŽIII. complex and the pre-solvated electron. Our time resolution does not allow us to differentiate between the FeŽCN. 64y 1 T2 g and the FeŽCN. 64y CTTS state. We therefore, somewhat arbitrarily, assign the band at 490 nm to the FeŽCN. 64y CTTS state. The important conclusion from our analysis is, however, that charge separation in the hexacyanoferrateŽII. complex is extremely fast: the hexacyanoferrateŽIII. band is formed within the FWHM of the experimental pump–probe cross-correlation function of 60 fs. We then temporarily loose track of the photoelectron as it becomes trapped in the presolvated state simply because the wetrpre-solvated electron does exhibit little absorption in the wavelength region considered in this study. Finally, we observe the reappearance of the photoelectron, this time in its fully hydrated state, with a global time constant of 510 fs. So far we have shown that the charge separation in the hexacyanoferrateŽII. complex is essentially instantaneous. The lifetime of the FeŽCN. 64y CTTS state is much shorter than 60 fs. In earlier studies w34,35x on halide ions significantly longer lifetimes for CTTS states have been found. Gauduel et al. w34x obtained a lifetime of what they identified as the CTTS ) state of Cly of 190 fs. Long et al. w35x measured a lifetime of approximately 300 fs for the
S. Pommeret et al.r Chemical Physics Letters 288 (1998) 833–840
CTTS state of iodide ions. The shorter lifetime of the FeŽCN. 64y CTTS state may be related to the particular nature of this state, as explained by Stein et al. w5x. The repulsion between the remaining FeŽCN. 63y ion core and the excited electron may be the dominating driving force behind the rapid electron ejection from the FeŽCN. 64y CTTS state. This repulsion is absent in the case of the halide ions. The global time for electron solvation of 510 fs obtained in the present study is longer than the electron solvation times reported previously using the same electron donor w8,9x. Wiesenfeld and Ippen w8x reported an upper limit to the electron solvation time of 300 fs, and Gauduel et al. w9x found two times of 120 and 240 fs, respectively. The major difference between these studies and ours is the excitation wavelength. Both Wiesenfeld and Ippen w8x and Gauduel et al. w9x used excitation pulses of about 310 nm whereas we have used pulses of 267 nm to excite the hexacyanoferrateŽII. complexes. This means that in our case the photoelectrons have an additional kinetic energy of almost 5200 cmy1 which may slow down the trapping of the electron in the pre-solvated state. Furthermore, the solvation might be influenced by the character of the initially populated CTTS state. It is well known that the quantum yield of electron formation from hexacyanoferrateŽII. complexes is extremely dependent on the initially populated state w20x. In summary, we have performed femtosecond pump–probe experiments using 267 nm excitation and white light continuum probing of hexacyanoferrateŽII. complexes in aqueous solution. The charge separation in the hexacyanoferrate ŽII. complex is found to occur faster then the FWHM of the pump– probe cross-correlation function of 60 fs, as evidenced by the instantaneous appearance of the hexacyanoferrateŽIII. band. An extremely short-lived intermediate is assigned to the FeŽCN. 64y CTTS state. This CTTS state has an absorption maximum around 490 nm and is the common precursor of the hexacyanoferrateŽIII. complex and the pre-solvated electron. The fully solvated electron appears with a global time constant of 510 " 20 fs. In order to better understand the mechanism of electron solvation, experiments are currently under way which probe in the red and near infrared parts of the spectrum Ž700–1050 nm..
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Acknowledgements The authors would like to thank Dr. J.-C. Mialocq for stimulating discussions and gratefully acknowledge support from the GDR 1017 of the CNRS.
References w1x L.I. Grossweiner, E.F. Zwicker, G.W. Swenson, Science 141 Ž1963. 1180. w2x M.S. Matheson, W.M. Mulac, J. Rabini, J. Phys. Chem. 67 Ž1963. 2613. w3x S.-I. Ohno, G.-I. Tsuchihashi, Bull. Chem. Soc. Jpn 38 Ž1965. 1052. w4x A.W. Adamson, W.L. Waltz, E. Zinato, D.W. Watts, P.D. Fleischauer, R.D. Lindholm, Chem. Rev. 66 Ž1968. 541. w5x M. Shirom, G. Stein, J. Chem. Phys. 55 Ž1971. 3372. w6x M. Shirom, G. Stein, J. Chem. Phys. 55 Ž1971. 3379. w7x P.M. Rentzepis, R.P. Jones, J. Jortner, Chem. Phys. Lett. 15 Ž1972. 480. w8x J.M. Wiesenfeld, E.P. Ippen, Chem. Phys. Lett. 73 Ž1980. 47. w9x Y. Gauduel, A. Migus, J.P. Chambaret, A. Antonetti, Rev. Phys. Appl. 22 Ž1987. 1755. w10x A. Migus, Y. Gauduel, J.L. Martin, A. Antonetti, Phys. Rev. Lett. 58 Ž1987. 1559. w11x J.C. Mialocq, J. Sutton, P. Goujon, J. Chem. Phys. 72 Ž1980. 6338. w12x X. Shi, F.H. Long, H. Lu, K.B. Eisenthal, J. Phys. Chem. 100 Ž1996. 11903. w13x J.L. McGowen, H.M. Ajo, J.Z. Zhang, B.J. Schwartz, Chem. Phys. Lett. 231 Ž1994. 504. w14x Y. Kimura, J.C. Alfano, P.K. Walhout, P.F. Barbara, J. Phys. Chem. 98 Ž1994. 3450. w15x M.U. Sander, K. Luther, J. Troe, J. Phys. Chem. 97 Ž1993. 11489. w16x Y. Gauduel, J. Mol. Liq. 63 Ž1995. 1. w17x A. Reuter, A. Laubereau, D.N. Nikogosyan, J. Phys. Chem. 100 Ž1996. 16794. w18x C. Pepin, T. Goulet, D. Houde, J.-P. Jay-Gerin, J. Phys. ´ Chem. A 101 Ž1997. 4351. w19x E.J. Hart, J.W. Boag, J. Am. Chem. Soc. 84 Ž1962. 4090. w20x J.-C. Mialocq, J. Chim. Phys. 85 Ž1988. 31. w21x R. Naskrecki, P.v.d. Meulen, M. Menard, G. Vigneron, J.-C. ´ Mialocq, S. Pommeret. manuscript in preparation. w22x J.C. Mialocq, S. Pommeret, R. Naskrecki, G. Baldacchino, T. Gustavsson, Laser Appl. Life Sci. SPIE Proc. 2370 Ž1994. 253. w23x T.F. Albrecht, K. Seibert, H. Kurz, Opt. Comm. 84 Ž1991. 223. w24x W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes ŽUniversity Press, Cambridge, 1986.. w25x S. Mukamel, Principles of Nonlinear Optical Spectroscopy ŽOxford University Press, Oxford, 1995..
840
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w26x C. Prayer, These ` de Docteur en Sciences, Universite´ de Paris VI, 1997. w27x C.S. Naiman, J. Chem. Phys. 35 Ž1961. 323. w28x H.B. Gray, N.A. Beach, J. Am. Chem. Soc. 85 Ž1963. 2922. w29x J.J. Aleaxander, H.B. Gray, J. Am. Chem. Soc. 90 Ž1968. 4260. w30x D.H. Macartney, Rev. Inorg. Chem. 9 Ž1988. 101. w31x F.-Y. Jou, G.R. Freeman, J. Phys. Chem. 83 Ž1979. 2383.
w32x Y. Gauduel, S. Pommeret, A. Migus, A. Antonetti, Chem. Phys. 149 Ž1990. 1. w33x F.H. Long, H. Lu, K.B. Eisenthal, Phys. Rev. Lett. 64 Ž1990. 1469. w34x H. Gelabert, Y. Gauduel, J. Phys. Chem. 100 Ž1996. 13993. w35x F.H. Long, H. Lu, X. Shi, K.B. Eisenthal, Chem. Phys. Lett. 169 Ž1990. 165.