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J. Phys. Chem. 1996, 100, 1488-1493
High-Pressure Studies on the Excited-State Intramolecular Charge Transfer of 4-(N,N-Dimethylamino)triphenylphosphine in Alcohols Kimihiko Hara,* Noritsugu Kometani, and Okitsugu Kajimoto Department of Chemistry, Faculty of Science, Kyoto UniVersity, Sakyo-ku, Kyoto 606-01, Japan ReceiVed: August 7, 1995; In Final Form: October 11, 1995X
The influence of solvent viscosity on the intramolecular charge-transfer (CT)-state formation in the excited S1 state for 4-(N,N-dimethylamino) triphenylphosphine (DMATP) in alcohol solvents has been investigated by measuring the steady-state and time-resolved fluorescence spectra at high pressures. The kinetic mechanism of the intramolecular CT reaction has been examined as a function of solvent shear viscosity. In the lower viscosity region the reaction is controlled by the solvent relaxation. With increasing pressure, the reaction path shifts toward the “high-viscosity regime” in which the molecule moves along the nonrelaxed path on the free energy surface. The viscosity dependence of R = 0.33, where R is the power law parameter, can be interpreted as the extreme value in which the reaction is controlled by the dynamic solvent effect due to intrinsic collisional interaction of barrier crossing. The coupling between the intramolecular CT-state formation dynamics of DMATP and the solvent relaxation dynamics is discussed.
Introduction For the present molecule, 4-(N,N-dimethylamino)triphenylphosphine (DMATP), dual fluorescence has been observed in polar solvents.1 The emission at long wavelength has been attributed to “twisted intramolecular charge-transfer (TICT)” band.1 Here, the dimethylaniline moiety is the donor part, and the diphenylphosphine moiety is the acceptor part. The mechanism responsible for the TICT-state formation is supposed to involve an intramolecular twisting process in the S1 excited state.
hidden by the comparatively large shift of the activation barrier among different solvents. In this paper we examine the coupling between the dynamics of the intramolecular charge-transfer-state formation in DMATP and the solvent relaxation dynamics by changing the solvent viscosity in single alcohol solvents using the high-pressure method. It is shown that the pressure tunes the solvent viscosity for the intramolecular CT-state formation of DMATP in linear alcohol solvents in the excited state. Experimental Section
The kinetics of the TICT-state formation has been tackled by several researchers.2-5 Contrary to the early expectation,3 it has recently been reported that no simple correlation between the TICT-state formation rate and solvent viscosity has been observed for the case of DMABN in a series of polar solvents with different viscosity.6,7 By using a high-pressure method, we have been studying the influence of solvent viscosity on various barrier crossing processes involving large amplitude twisting conformational changes due to bulky aromatic groups such as TICT-state formation,8,9 intramolecular excimer formation,10 and photoisomerization.11,12 In particular, the observation of a weak dependence of the barrier crossing rate on solvent viscosity has been discussed. The use of high pressure is a favorable method for studying the solvent dynamics, because it enables us to change the solvent viscosity for a single solvent greatly and continuously without serious modification of the solvent-shell structure.13,14 According to the solvent change method ordinarily used for changing solvent viscosity, the small viscosity dependence on the charge-transfer (CT) reaction is likely to be * To whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, January 1, 1996.
0022-3654/96/20100-1488$12.00/0
The purified sample of DMATP was provided by Prof. W. Rettig of Humboldt University and was used as received. All solvents used were spectroscopic grade. They were checked for fluorescent impurities. Sample solutions were degassed using repeated freeze-pump-thaw cycles. All of the measurements reported for this study were obtained using ∼10-5 M solutions, which is a low enough concentration to ensure that intermolecular contributions are negligible.15 The high-pressure optical cell with sapphire windows and emission equipment for steady-state fluorescence spectra have been described previously.9,16 The solution was inserted into the inner quartz capsule of the high-pressure cell in a glovebox filled with N2 gas. The effect of pressure was measured up to 500 MPa, and all measurements at high pressures were carried out at 298 K. Picosecond time-resolved fluorescence spectra were measured by the method of time-correlated single-photon counting (TCSPC). The experimental arrangement of the laser system was reported previously.17 The third harmonic radiation of a modelocked Ti:sapphire laser (Spectra-Physics, Tsunami Model 3950) was used as the excitation light source. The excitation wavelength was 280 nm. The Ti:sapphire laser, which was pumped by a continuous wave (cw) argon ion laser, produced a 840 nm light pulsed of 1.5 ps duration and had a repetition rate of 82 MHz. The third harmonic radiation (THG) was generated by overlapping the fundamental and second harmonic radiation (SHG).18,19 For the THG and SHG crystals, LiIO3 and BBO were employed, respectively. The pulse repetition rate was decreased to 8.2 MHz by using an electrooptic light modulator (Con Optic, Model 1305). A Hamamatsu R2809© 1996 American Chemical Society
Excited-State Intramolecular CT of DMATP
Figure 1. Fluorescence and absorption spectra of DMATP in hexane (- -) and ethanol (s). They were normalized to the maximum intensity.
J. Phys. Chem., Vol. 100, No. 5, 1996 1489
Figure 2. Fluorescence spectra of DMATP in ethanol at 298 K excited at different wavelength (λex): (- -) 260 nm; (s) 280 nm; (- - -) 300 nm. They were normalized to the maximum intensity.
02u microchannel plate (MCP) photomultiplier tube was used for detection. The overall instrument response function has a full width at half-maximum (fwhm) of approximately 30 ps at the excitation wavelength of 280 nm. Data were stored in a computer (NEC PC 9801) equipped with an MCA system. The transient data are fit with sums of functions that are convoluted with the instrument response function. The iterative nonlinear leastsquares algorithm was performed on an Epson PC-486GR computer. Data were collected until ∼104 counts were accumulated in the peak channel. The precision of the fluorescence lifetime is estimated as ∼5%. Results Absorption and Fluorescence Spectra. Figure 1 shows the normalized absorption and fluorescence spectra of DMATP in hexane and in ethanol at 298 K. As reported by Vogel et al.,1 the fluorescence spectra in polar solvents like alcohols consist of two bands. One is the emission from the locally excited (LE) state at the wavelength around 345 nm ((νmax)LE ) 29 800 cm-1), and the other is from the intramolecular charge-transfer state at the wavelength around 470 nm ((νmax)CT ) 21 200 cm-1). The important features are (1) that the half-width of the absorption band is about twice as large as that of the LE fluorescence band, indicating that the ground-state potential well is broader than the LE-state potential well and (2) that the absorption spectrum in the polar solvent has a tail in the lower energy region. Furthermore, as seen in Figure 2, it is found that the fluorescence spectrum is dependent on the excitation wavelength (λex). The excitation at the longer wavelength (λex ) 300 nm) causes the relative increase in the intensity of the CT band, as compared with the excitation at shorter wavelength (λex ) 260 nm). The LE- and CT-peak locations are unchanged with λex. These results lead to the conclusion that the absorption band in polar solvents is conformed by an overlap of two transitions; S0 f LE and S0 f CT. Namely, the direct excitation to the CT state is possible in polar solvents, although it seems relatively slight. The lower energy absorption tail is assigned to the S0 f CT band. Pressure Effect on the Fluorescence Yield Ratio. Figure 3 shows the normalized fluorescence spectra of DMATP in ethanol at various pressures. The long-wavelength CT band decreases relatively with increasing pressure. The shift of the CT band with pressure is fairly small, as compared with those of the TICT bands reported for various TICT-forming molecules.20 Figure 4 shows the fluorescence yield ratio of the
Figure 3. Fluorescence spectra of DMATP in ethanol at several pressures: (s) 0.1 MPa; (- -) 150 MPa, (- - -) 300 MPa; (- -) 450 MPa. They were normalized to the maximum intensity.
Figure 4. Plot of the fluorescence yield ratio as a function of solvent viscosity: (O) ethanol; (0) 1-propanol; (4) 1-butanol; ()) 1-octanol). The solid line represents the best fit of the data to eq 4 for 1-butanol with R ) 0.31 and for 1-octanol with R ) 0.35.
CT state to the LE state, ΦCT/ΦLE, of DMATP in ethanol, 1-propanol, 1-butanol, and 1-octanol as a function of solvent shear viscosity, η, in double logarithmic scale. They were
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determined from the area ratio of emission bands, which were separated by assuming a Gaussian form for each emission. The high-pressure viscosity data were obtained from the literature.13,14 As seen in the figure, the yield ratio decreases with solvent viscosity and the rate of the decrease is in the order of ethanol > 1-propanol > 1-butanol ∼1-octanol. The difference in ΦCT/ΦLE values among different alcohols at a given solvent viscosity indicates the barrier energy shift with solvent polarity. Temperature Effect on the Fluorescence Yield Ratio. We have also measured the temperature dependence of the yield ratio at atmospheric pressure. The CT band decreases relatively with decreasing temperature. This behavior is similar to what occurs when the pressure is increased. We obtained an apparent activation energy of 2.2 kJ/mol for ethanol and 3.0 kJ/mol for 1-butanol. The resulting activation energy, Ea, is considerably smaller than the activation energy of the viscous flow of the solvent, Eη (cf. 13.4 kJ/mol for ethanol and 19.7 kJ/mol for 1-butanol).2 The barrier energy increases with solvent viscosity. The same result of Ea < Eη has also been reported.21 However, it would be premature to conclude that the reaction is barrierless. Lifetime of the CT-State Formation. Fluorescence response curves of DMATP in 1-butanol at 0.1 and 400 MPa are representatively shown in Figure 5a,b. They were monitored at the LE emission maximum; (λmax)LE ) 345 nm. The excitation wavelength is 280 nm, at which wavelength the molecules are predominantly excited to the LE state. In order to obtain the dynamics of the population decay of the LE state, the fluorescence response decay curves were fit to the following multiexponential function:
I(t,λ) ) ∫-∞[∑Ai exp(t - τ)/τi]G(τ) dτ t
(1)
In this equation Ai and τi are the amplitude and the time constant for the ith component of the multiexponential fit. G(τ) is the instrumental response function. equation 1 indicates that the intensity I(t,λ) is expressed as a convolution of the instrumental response and a multiexponential decay. The line through the data points in Figure 5 is the best fit three exponential decay. However, for 1-butanol at 400 MPa the decay curve becomes more like the double exponential form. In 1-octanol and in compressed 1-butanol they approach the form of double exponential functions. By using Ai and τi values obtained from the fitted curves, the average lifetime τa can be determined by
τa ) ∑τiAi
(2)
i
TABLE 1: Average Survival Time (τa) Obtained from Fitting the LE-State Fluorescence Response Curves to Triple Exponential Functionsa with Longitudinal Dielectric Relaxation Times of Solvent (τL) and Average Solvation Times 〈τs〉 for Comparison solvent
where Ai is the fraction which is normalized as ∑iAi ) 1. Here, τa is related to the survival probability Q(t), i.e., τa ) ∫Q(t) dt, which measures the time dependence of the population of the reacting state.22 When the decay rate from the LE state to the ground state is sufficiently slow, as in the present case, the inverse of τa is correlated to the average rate constant of the CT formation (kCT), namely,
kCT ) τa-1
Figure 5. Fluorescence decay curves for DMATP in 1-butanol detected at 345 nm ((a, top panels) 0.1 and (b, bottom panels) 400 MPa). Excitation wavelength is 280 nm. Solid lines running through the data are best fits to multiple exponential functions with the whole component corresponding to DMATP fluorescence. Above each curve is shown the residuals for the fitted decays.
(3)
The average lifetimes (τa) calculated at the emission maximum of the LE state (345 nm) in several alcohol solvents are listed in Table 1. Discussion Kinetic Scheme for the CT-State Formation. From the experimental observations we can deduce the reaction scheme
ethanol 1-propanol 1-butanol 1-octanol
pressure (MPa)
τa (ps)
τLb (ps)
0.1 350 0.1 450 0.1 400 0.1 100
64.3 68.7 94.3 134.9 132.3 126.4 159.0 240.5
32.5c 75.0c 104.5c
〈τs〉 (ps)
56.6e 75f
375.0d
a Measurements were made at 298 K. b Values at 298 K. c Obtained from ref 24. d Calculated from literature data of 0 and ∞ (see refs 25 and 26). e The average solvation time obtained from the time-dependent Stokes shift with coumarin probe (see ref 34). f Present data obtained from the time dependent Stokes shift.
of the intramolecular CT-state formation of DMATP in alcohol solvents in the excited state. The schematic free energy surface of the excited state for explaining the mechanism of the CT formation is shown in Figure 6, in which the reaction coordinate is divided into a nuclear coordinate and a solvent coordinate,
Excited-State Intramolecular CT of DMATP
J. Phys. Chem., Vol. 100, No. 5, 1996 1491 TABLE 2: Power Law Parameter, r solvent
R
solvent
R
ethanol 1-propanol
0.71a 0.44a
1-butanol 1-octanol
0.31,a 0.32b 0.35a
a
Figure 6. Schematic picture of the excited-state free energy surface for the intramolecular CT-state formation in DMATP in polar solvent, representing the pressure tuning effect. I and II represent the reaction paths for the low- and high-viscosity regimes, respectively, and (F) is the Franck-Condon state.
as has been proposed in the Sumi-Marcus model.23 Here, we can suppose that the longitudinal relaxation time (τL) can be used as a measure of the solvent dipolar relaxation time. The τL values,24-26 which are defined by τL ) τD∞/0, are also given in the table for comparison. This characteristic time is based on a dielectric continuum model and does not include any molecular aspect of the solvent. However, it is often used as a measure of the dipolar orientational or polarization relaxation time of solvent. In the “low-viscosity regime”, where kCT 1-propanol > 1-butanol ∼ 1-octanol to give a limiting value of 0.31-0.35. This result is considered to reflect the shift of the reaction path from the intermediate viscosity regime to the high-viscosity regime (II) with increasing solvent viscosity. The slight change of activation energy (Vide supra) may be correlated with this shift of the reaction path. This phenomenon could be called a “pressure tuning” effect of the solvent viscosity for the CT reactions in alcohols. It should be noted that the indicated shift of the reaction path is caused by the stronger viscosity dependence on τL of alcohols; as indicated by τL(η) ∝ ηR with the exponent R that is larger than 1 (e.g., R ) 1.24 for ethanol).28,29 We have observed the similar shift behavior for the excited-state intramolecular CT formation in 4,4′-diaminodiphenyl sulfone (DAPS) in alcohols.30 On the other hand, in Figure 7, the rate constant of the CT formation (kCT) of DMATP in alcohols, which is defined by the inverse of the average survival time of the LE state (τa-1), is plotted against solvent viscosity. It is found that kCT behaves analogously to the result of the yield ratio (cf. Figure 4), although the dispersion of the kCT data is relatively larger than that of the yield ratio. The solid line in Figure 7 represents the leastsquares fitting with R ) 0.32 in the higher viscosity region. This value is coincident with that obtained from the yield ratio in 1-butanol of the high viscosity region and 1-octanol. Therefore, the averaged value of R = 0.33 at the viscosity region larger than ca. 3.0 mPa s is considered as belonging to the high-viscosity regime. In this extreme the intramolecular CT reaction proceeds through a nonrelaxed path independent of the solvent coordinate. The viscosity dependence should be the dynamic solvent effect on barrier crossing originated from the collisional interaction between the solute and solvent. As
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Figure 9. Time-dependent Stokes shift C(t) of the CT band in 1-butanol. The solid line represents the fitted curve.
Figure 7. Plot of kCT against solvent viscosity: (O) ethanol; (0) 1-propanol; (4) 1-butanol; ()) 1-octanol.
transients at various fluorescence wave numbers. Note that the CT spectrum shows an evidence of time-dependent red shifting, which is roughly analogous to the time-dependent Stokes shift observed for polar molecules as relaxation occurs. At times longer than 500 ps the spectra are indistinguishable from the completely relaxed spectrum, except for a slow excited-state population decay. The time-dependent Stokes shift can be analyzed to quantify the dynamics of solvation using the solvent relaxation function C(t):34-36
C(t) )
Figure 8. Reconstructed time-resolved fluorescence spectra at different delay times at 298 K in 1-butanol: (s) 10 ps; (- -) 50 ps; (- ‚ -) 100 ps; (‚‚‚) 500 ps. The curves were obtained by the best fits of two Gaussians to the fluorescence decay data.
a result kCT can be written by
kCT ) A′η-0.33kTST
(5)
where A′ is a viscosity-independent constant and kTST is the rate constant defined by transition-state theory (TST). The R value of 0.33 is too weak a viscosity dependence to apply the Kramers theory.31 Another approach for describing this barrier crossing dynamics, such as frequency-dependent friction, seems to be taken into account.11,32 We can conclude for the CT formation of DMATP that the intramolecular conformational change, if any, is not so large in amplitude motion as has been suggested in the TICT mechanism.1 This is in contrast to the excited-state CT formation in triphenylmethane derivatives in which a much larger viscosity dependence (R ) 0.7) has been observed and synchronous twisting of three phenyl rings has been suggested.33 Time-Resolved Fluorescence Spectra. Figure 8 portrays time-resolved fluorescence spectra of DMATP at 298 K in 1-butanol at 0.1 MPa in the time range of 10-500 ps. At early times the emission spectrum is more like the LE state, but the CT character increases with time. The spectral lines are obtained by two Gaussian fits to the individual fluorescence
ν(t) - ν(∞) ν(0) - ν(∞)
(6)
Here, ν(0), ν(t), and ν(∞) represent the wave numbers of the intensity maximum of the fluorescence spectrum immediately after excitation, at a time t after excitation, and at a time sufficiently long to ensure the excited-state solvent configuration is at equilibrium. In the case of a pure Debye solvent, C(t) is predicted to decay exponentially with a time constant τL.37,38 Recently, the solvent relaxation dynamics has been recorded for some solvents by the time-dependent Stokes shift.34-36 Nonexponential time dependence has been observed. The resulted response times for some alcohols have been characterized by an average solvation time, 〈τs〉, which is slightly longer than τL. However, for 1-alkanols the value of 〈τs〉 is not available except for 1-propanol 56.6 ps at 295 K. Figure 9 represents the time-dependent Stokes shift obtained from the intensity of the time-resolved fluorescence spectra (cf. Figure 8). A good fit to a double exponential function is observed with the experimental data. The resulting decay data for C(t) showed two characteristic time constants, i.e., 34.6 ps (77%) and 215 ps (23%). This behavior is considered to reflect the fact that the dielectric response of linear alcohols is generally composed of three regions of Debye dispersion. For 1-butanol it is reported that the three relaxation times (τD1, τD2, and τD3) are 2.35, 27.0, and 668 ps.25 The resulting two time constants seem to correspond to τD2 and τD3. The fast component is likely to be missing due to the limited time resolution of the present apparatus. Thus, the average solvation time, 〈τs〉, is determined to be 75 ps. This value is coincident with the value of kCT-1 ()75.7 ps), although it is considerably smaller than τL. In consequence, the fact that kCT ∼ τL-1 in 1-butanol at atmospheric pressure indicates that the reaction path is still in the region controlled by the solvent relaxation. For further detailed discussion in this
Excited-State Intramolecular CT of DMATP respect, the accurate values of solvation time and its viscosity dependence would be inevitable. Concluding Remarks In this paper, the steady-state and picosecond time-resolved fluorescence spectroscopy has been used to examine the role of the solvent dynamics to the excited-state intramolecular CT dynamics of DMATP in alcohol solutions as a function of pressure. The following observations and conclusions can be made. The power law parameter, R, in eq (4) has been used as a measure of the strength of solvent viscosity dependence. The R value obtained from the fluorescence yield ratio, ΦCT/ΦLE, decreases with the change of solvent into the higher alcohol to give a limiting value of 0.31-0.35. This result just corresponds to that of the rate constant of the CT formation, kCT, determined from the inverse of the average survival time, (τa)-1. The excited-state intramolecular CT formation of DMATP in alcohols can be well-explained by the scheme represented on the free energy surface of the excited state, shown in Figure 6. Increasing the pressure in a single alcohol solvent or changing the solvent to a higher alcohol such as 1-octanol produces the shift of the reaction path toward the high-viscosity regime from the intermediate viscosity regime where the reaction is controlled by the solvent relaxation. This could be called as the pressure tuning effect of the solvent viscosity for the excitedstate CT formation in polar solvents. This is caused by the strong viscosity dependence on the solvent relaxation time. The viscosity dependence of R ) 0.33 observed at the highviscosity regime is considered as the intrinsic dynamic solvent effect for barrier crossing. Such a weak viscosity dependence could not be determined unless the high-pressure measurement in a single solvent has been carried out. From the time-dependent Stokes shift for the CT emission band of DMATP in 1-butanol, the solvent relaxation time (〈τs〉) has been determined as 75 ps, which is almost equal to the τL value (105 ps). This may substantiate the supposition that τL is used as a measure of the solvent relaxation time. Acknowledgment. We are grateful to Prof. Wolfgang Rettig of Humboldt University for providing a sample of DMATP. This research was supported in part by a Grant-in-Aid for Scientific Research No. 06214213. Additional support was provided by the Shouwa-Houkoukai Foundation. References and Notes (1) Vogel, M.; Rettig, W.; Heimbach, P. J. Photochem. Photobiol., A: Chem. 1991, 61, 65.
J. Phys. Chem., Vol. 100, No. 5, 1996 1493 (2) Lippert, E.; Luder, E.; Boos, H. In AdVances in Molecular Spectroscopy; Margini, A., Ed.; Pergamon Press: Oxford, U.K., 1962; p 443. (3) Grabowski, Z. R.; Rotkiewicz, R.; Siemiarczuk, A.; Cowley, D. J.; Baumann, W. NouV. J. Chim. 1979, 3, 443. (4) Rettig, W. Angew. Chem., Int. Ed. Engl. 1986, 25, 971. (5) Lippert, E.; Rettig, W.; Bonacis-Koutecky, V.; Heisel, F.; Miehe, J. A. AdV. Chem. Phys. 1987, 68. Rettig, W. In Modern Models of Bonding and Delocalization; Liebman, J. F., Greeberg, A., Eds.,; Cambridge, U.K., 1988, Chapter 5, p 229 and references cited therein. (6) Hicks, J. M.; Vandersall, M. T.; Sitzmann, E. V.; Eisenthal, K. B. Chem. Phys. Lett. 1987, 135, 413. Hicks, J. M.; Vandersall, M. T.; Babarogic, Z.; Eisenthal, K. B. Chem. Phys. Lett. 1985, 115, 18. (7) Simmon, J. D.; Su, S.-G. J. Phys. Chem. 1990, 94, 3656. (8) Hara, K.; Obara, K. Chem. Phys. Lett. 1985, 117, 96. (9) Hara, K.; Arase, T.; Osugi, J. J. Am. Chem. Soc. 1984, 106, 1968. (10) Hara, K.; Yano, H. J. Phys. Chem. 1988, 90, 4265; J. Am. Chem. Soc. 1988, 110, 1911. (11) Hara, K.; Akimoto, S. J. Phys. Chem. 1991, 95, 5811; High Pressure Res. 1992, 11, 55. (12) Hara, K. In High Pressure Liquids and Solutions; Taniguchi, Y.; Senoo, M.; Hara, K., Eds.; Elsevier Applied Science: Oxford, U.K., 1994; p 67. (13) Bridgman, P. W. Collected Experimental Papers, Vol. IV; Harvard University Press: Cambridge, MA, 1964; p 2043. (14) Matsuo, S.; Makita, T. Int. J. Thermophys. 1989, 10, 833. (15) Kometani, N. M.S. Thesis, Kyoto University, 1994. (16) Hara, K.; Morishima, I. ReV. Sci. Instrum. 1988, 59, 2397. (17) Hara, K.; Kometani, N.; Kajimoto, O. Chem. Phys. Lett. 1994, 225, 381. (18) Skripko, G. A.; Bartoshevich, S. G.; Mikhnyuk, I. V.; Tarazevich, I. G. Opt. Lett. 1991, 16, 1726. (19) Nebel, A.; Beigang, R. Opt. Lett. 1991, 16, 1729. (20) Hara, K.; Rettig, W. J. Phys. Chem. 1992, 96, 8307. (21) Braun, D.; Rettig, W. Chem. Phys. 1994, 180, 231. (22) Nadler, W.; Marcus, R. A. J. Chem. Phys. 1987, 86, 3906. (23) Sumi, H.; Marcus, R. A. J. Chem. Phys. 1986, 84, 4894. Nadler, W.; Marcus, R. A. J. Chem. Phys. 1987, 86, 3906. (24) Su, S.-G.; Simon, J. D. Chem. Phys. Lett. 1989, 158, 423. (25) Garg, S. K.; Smyth, C. P. J. Phys. Chem. 1965, 69, 1294. (26) Su, S.-G.; Simon, J. D. J. Chem. Phys. 1988, 89, 908. (27) Bulgarevich, D. S.; Kajimoto, O.; Hara, K. J. Phys. Chem. 1995, 99, 1335b. (28) Mandel, H.; Frood, D. G.; Saleh, M. A.; Morgan, B. K.; Walker, S. Chem. Phys. 1989, 134, 441. (29) Castner, E. W.; Bagchi, B.; Maroncelli, M.; Webb, S. P.; Ruggiero, A. J.; Fleming, G. R. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 363. (30) Hara, K.; Bulgarevich, D. S.; Kajimoto, O. Unpublished data. (31) Kramers, H. A. Physica 1940, 7, 284. (32) Hara, K.; Kiyotani, H.; Bulgarevich, D. S. Chem. Phys. Lett. 1995, 242, 455. (33) Vogel, M.; Rettig, W. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 1241. (34) Maroncelli, M.; Fleming G. R. J. Chem. Phys. 1987, 86, 6221. (35) Barbara, P. F.; Jarzeba, W. AdV. Photochem. 1990, 15, 1. (36) Jarzeba, W.; Walker, G. C.; Johnson, A. E.; Barbara, P. F. Chem. Phys. 1991, 152, 57. (37) van der Zwan, G.; Hynes, J. T. J. Phys. Chem. 1985, 89, 4181. (38) Bagchi, B.; Oxtoby, D. W.; Fleming, G. R. Chem. Phys. 1984, 86, 257.
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