+ R’SH
-
-
J . Phys. Chem. 1989, 93, 161-164
+ ROH
161
Reaction 9 is very similar in nature to reaction 8 and it is thus difficult to eliminate (9) as a competing mechanism. Further, the intermediate proposed is analogous to the intermediate [RSSS(H)R] suggested for the reaction of RSS’ with RSH.37 Using bond energies of 170 kJ (0-0),435 kJ (0-H), 380 kJ (S-H), and 360 ld (S-O), we predict reaction 9 to be exothermic by approximately 245 kJ.38 Gilbert et al.” found that sulfinyl radicals resulted from reaction of thiols with the Ti3+-H202couple at pH 1-2 and their g values and hyperfine couplings (allowing for differences in rotational averaging) correlate quite well with those reported here. Although the authors reported that the
radicals produced were a result of *OHattack, their system results in HO; as well as ‘OH. Consequently reactions similar to those proposed here may have taken place. Our molecular orbital calculations and spin density distributions indicate the S-O bond in RSO’ is highly polar with substantial double bond character. We suggest that in sulfinyl radicals, the a-spin density on oxygen is 0.4 while that on sulfur is 0.6. The sulfur peroxyl radical, RSOO’, is predicted to be similar to other peroxyl radicals in its ESR parameters. Our recent results show that the cysteinethiol peroxyl radical19 has g values similar to carbon-centered peroxyl radicals but also a more equivalent distribution of the spin density between the two oxygens than found for carbon-centered peroxyl radicals39or predicted by MO theory.
(37) Nelson, D. J.; Peterson, R. L.; Symons, M. C. R. J . Chem. SOC., Perkin Trans. 2 1977, 2005. (38) The first three bond energies used here are standard values (Handbook of Chemistry and Physics, 56th ed.;CRC: 1975; p F224). The sulfinyl radical S-0 bond energy is estimated as follows. Our molecular orbital calculations yield a bond length of approximately 150 ppm for this bond. This is near the typical length of 149 pm for the S-0 bond in alkyl sulfoxides (Kucsman, A,; Kapovits I. In Bernardi, F., Csizmadia, I. G., Mangini, A,, Eds. Organic Sulfur Chemistry; Elsevier: New York, 1985; pp 192-195), which have a average S-0 bond energy of 360 kJ/mol (Oae, S., In Bernardi, F., Csizmadia, I. G., Mangini, A,, Eds. Organic Sulfur Chemistry; Elsevier: New York 1985; p 30). Thus, we estimate 360 kJ for the S-0 bond energy in sulfinyl radicals. (39) Sevilla, M. D.; Champagne, M.; Becker, D. J . Phys. Chem., in press.
Acknowledgment. This investigation was supported by PHS Grant ROlCA45424-01 awarded by the National Cancer Institute, DHHS, and by the Office of Health and Environmental Research of the US.Department of Energy. Acknowledgment is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of S.D.B. as a P R F Undergraduate Summer Fellow. Registry No. Methyl mercaptan, 74-93-1; tert-butyl mercaptan, 7566-1; n-butyl mercaptan, 109-79-5;cysteamine, 60-23- 1; dithiothreitol, 3483-12-3; methylsulfinyl radical, 25683-64-1; tert-butylsulfinyl radical, 1 17020-91-4; n-butylsulfinyl radical, 117020-92-5;cysteamine sulfinyl radical, 117020-93-6;dithiothreitol sulfinyl radical, 117020-94-7.
ROO’
[ROOS(H)R’]
R’SO.
(9)
Lifetime and Electronic Spectra of p -Methoxybenzyl Radical in the Lowest Excited Doublet State in Solution Kunihiro Tokumura,* Tomomi Ozaki, Masahiro Udagawa,+and Michiya Itoh* Faculty of Pharmaceutical Sciences and Division of Life Sciences, Graduate School, Kanazawa University, Takara-machi, Kanazawa 920, Japan (Received: May 13, 1988)
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The D, D1absorption (A, = 340 nm) and the D1 Dofluorescence (A, = 490 nm) spectra of the lowest doublet excited state (D1) of p-methoxybenzyl radical in solution were detected in the 248-nm KrF laser photolysis of p-(chloromethy1)anisole followed by the 308-nm XeCl laser pulse excitation. A long lifetime of 120 ns at room temperature and a slightly temperature-dependent nonradiative relaxation were confirmed for p-methoxybenzyl in the DI state. The rotation of the methoxy group seems to be responsible for the relaxation with an activation energy of 1.1 kcal mol-’.
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perturbation of the p-methoxy group.22 In this study, both the D, D1 absorption and the D1 Do fluorescence spectra were
Introduction Since the detection of the fluorescence of benzyl radical in the vapor phase has been reported by Schiiler et al.,I numerous fluorescence spectroscopic studies of benzyl radical in the static vapor p h a ~ e and ~ - ~in the supersonic as well as in the rigid glass a t low were reported. Complicated fluorescence spectra were suggested to be attributable to the proximity of two lowest doublet excited states (DI and D2) with small oscillator strengths for the Dl-Do and D2-Do transitions. Fluorescence lifetimes of benzyl were determined to be 0.88 ps7 in the noncooled vapor phase and ca. 1.4 ps13 in 3-methylpentane at 77 K. On the other hand, the fluorescence spectra of benzyl itself2°,21and benzyls with p-methyl and p-chloro substituents2’ in fluid solution were recently detected by transient spectroscopy employing photolysis and probe laser pulses, and an extensively temperature-dependent fluorescence lifetime was confirmed for them. It was suggestedZ0J that the proximity of D, and D2 states is also responsible for the extensively temperature-dependent nonradiative relaxation. This suggestion led us to examine the excited-state relaxation of p-methoxybenzyl, the D, and D2 states of which are assumed to be no longer close lying owing to a strong
(1) Schiiler, H.; Reinbeck, L.; Koberle, R. Z . Naturforsch., A 1952, 7 A , 421, 428. (2) Walker, S.; Barrow, R. F. Trans. Faraday SOC.1954, 50, 541. (3) Schuler, H.;Stockburger, M. Spectrochim. Acta 1959, 13; 841. (4) Watts, A. T.; Walker, S . J . Chem. SOC.1962, 4323. (5) Cossart-Magos, C.; Leach, S . J. Chem. Phys. 1972, 56, 1534. (6) Cossart-Magos, C.; Leach, S . J . Chem. Phys. 1976, 64,4006. (7) Okamura, T.; Charlton, T. R.; Thrush, B. A. Chem. Phys. Lett. 1982, 88, 369. (8) Heaven, M.; Dimauro, L.; Miller, T. A. Chem. Phys. Lett. 1983,95, 347. (9) Fukushima, M.; Obi, K. Abstr. Jpn. Symp. Mol. Struct. Spectra 1986, 182; 1987, 582. (10) Johnson, P. M.; Albrecht, A. C. J . Chem. Phys. 1968, 48, 851. (11) Watmann-Grajcar, L. J . Chim. Phys. 1969, 66, 1023. (12) Friedrich, D. M.; Albrecht, A. C. J . Chem. Phys. 1973, 58, 4766. (13) Bromberg, A.; Friedrich, D. M.; Albrecht, A. C. Chem. Phys. 1974, 6, 353. (14) Friedrich, D. M.; Albrecht, A. C. Chem. Phys. 1974, 6, 366. (15) Okamura, T.; Obi, K.; Tanaka, I. Chem. Phys. Lett. 1974, 26, 218. (16) Laposa, J. D.; Morrison, V. Chem. Phys. Lett. 1974, 28, 270. (17) Okamura, T.; Tanaka, I. J . Phys. Chem. 1975, 79, 2728. (18) Hiratsuka, H.; Okamura, T.; Tanaka, I.; Tanizaki, Y. J . Phys. Chem. 1980, 84, 285. (19) Miller, J. H.; Andrews, L. J . Mol. Spectrosc. 1981, 90, 20. (20) Meisel, D.; Das, P. K.; Hug, G. L.; Bhattacharyya, K.; Fessenden, R. W. J . Am. Chem. SOC.1986, 108, 4706.
Present address: Chemicals Research Laboratory, Showa Denko, Ohgimachi 5-1, Kawasaki 210, Japan.
0022-3654/89 , ,/2093-0 16 lS01.50 /O 0 1989 American Chemical Societv I
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162 The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 I
.4, I
Tokumura et al.
n
L
. CH.
I 1
61
I
”
{emission
‘t
1
0 250
300
350
400 450 500 WA VELENG TH / nm
550
600
Figure 1. Transient absorption spectra at 1.4-ps (0) and 12-ps (A)delay from the 248-nm pulse excitation of p-(ch1oromethyl)anisole(0.31 mM) in hexane at room temperature. Enlarged ( X 1 7 ) visible spectrum at 1.4-ps delay is also displayed. The emission spectrum, induced by the 308-nm pulse excitation delayed by 1.4 ps from the 248-nm photolysis, is shown together with the fluorescence spectrum of benzyl in hexane at room temperature.
1 248-nm pulse
on
determined for transient p-methoxybenzyl in fluid solution by two-step laser excitation transient spectroscopy. The weakly temperature-dependent lifetime of the D1-statep-methoxybenzyl will be discussed.
Experimental Section p-(Chloromethy1)anisole (CMA, Tokyo Kasei) was purified by distillation under reduced pressure. Spectrograde hexane (Nakarai) without further purification was used as solvent at room temperature. 3-Methylpentane (Aldrich), purified by distillation after refluxing over lithium aluminum hydride, was employed as solvent at low temperature. All sample solutions were degassed by repeated freeze-pump-thaw cycles. The laser-flash apparatus consisting of two excimer lasers and a pulsed xenon arc lamp was employed in the two-pulse experiments as follows. The 248-nm pulse from an excimer laser (Lambda Physik EMG 5OE/KrF: 14-ns fwhm, 75 mJ) induced fragmentation of CMA, yielding a chlorine atom and a p-methoxybenzyl radical in the ground state (Do). The 308-nm pulse from an excimer laser (Lambda Physik EMG 53MSC/XeCl: 13-11s fwhm, 80 mJ) was selected as the second pulse to populate the radical in the fluorescence state (D1). The electromagnetic shutter, operating synchronously with the two lasers, cut the beam of the xenon arc. Ordinary and two-step laser-induced transient absorption signals were obtained by monitoring the light intensity of pulsed xenon arc after the first and the second laser pulse excitations, respectively. Laser-induced fluorescence (LIF) signals were measured by the laser-flash apparatus without turning on the xenon arc. Electric signals from the photomultiplier tubes (Hamamatsu Photonics R666/transient absorption; R928/LIF) were converted into digital signals by a storagescope (IWATSU TS-8123), and they were transferred into a microcomputer (Fujitsu Micro 11). The lifetimes of the D, D1 absorption and the D I Do fluorescence of p-methoxybenzyl radical in the lowest excited doublet state (D,) were determined by the simulation using a least-squares program. The standard deviation is within 45% for the intense and long-lived fluorescence. The delay time between the two excimer laser pulses was controlled by a digital delay generator (BNC 7010) with a resolution time of 100 ns.
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Results and Discussion Electronic Spectra of p-Methoxybenzyl Radical in Hexane at Room Temperature. Transient absorption spectra were observed in the 248-nm KrF laser photolysis of p-(chloromethy1)anisole (CMA) in hexane at room temperature, as shown in Figure 1. (21) Tokumura, K.; Udagawa, M.; Ozaki, T.; Itoh, M. Chem. Phys. Lett. 1987, 141, 558.
(22) Claridge, R.
F. C.; Fischer, H. J . Phys. Chem. 1983, 87, 1960.
(23) According to the spectrum (Figure 7 of ref 22), the maximum wavelength of the strongest UV band should not be 263 nm (listed in Table 111) but 283 nm. (24) Langhals, H.; Fischer, H. Chem. Ber. 1978, 111, 543. (25) Laufer, M.; Dreeskamp, H. J . Magn. Reson. 1984, 60, 357.
The Journal of Physical Chemistry, Vol. 93, No. 1, 1989 163
p-Methoxybenzyl Radical
.15 @
Q.05-
c
3
1
0
0.4 0.8 1.2 Probe Delay / u s
0
e"
0. 0
t
-*05 -. 101 250
O :
3w
1
350
4dO
450
500
350
4w
450
500
1.6
Figure 3. Oscillogram traces for the two-step laser excitation transient absorption spectroscopy of p-(chloromethy1)anisole (0.30 mM) in hexane at room temperature. Pair of 248-nm pulse-induced transient absorption signals (280 and 340 nm) with and without the subsequent 308-nm pulse excitation at 420-11s delay are shown.
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absorption and the TS LIF to the D, Doabsorption and the D, Do fluorescence of pmethoxybenzyl. The oscillogram traces (c) for the transient absorption at 330 nm, detected upon the 248-nm excitation of CMA followed by the 308-nm excitation with various delay times, are shown in the lower part of Figure 2. These two-step laser-induced absorption (TS LIA) exhibit the exponential decay with a lifetime of 112 A10 ns, which is nearly equal to the fluorescence lifetime (1 20 ns) of p-methoxybenzyl. As seen in Figure 2, the decreases in the intensity of both TS LIA and TS LIF with increasing probe delay time are almost identical with each other, and they parallel the decay of the 308-nm transient absorption due to the ground-state p-methoxybenzyl. The TS LIA may be therefore assigned to the D, +D, absorption of p-methoxybenzyl. Figure 3 shows the 248-nm pulse-induced transient absorption signals monitored with and without the delayed 308-nm pulse excitation. The long-lived transient absorption at 280 nm is ascribed to the ground-state p-methoxybenzyl, though the signal immediately after the 248-nm pulse excitation is considerably deformed by the bleaching of the CMA absorption. As already shown in Figure 2, short-lived (1 12 ns) absorptions (a and b) due to the excited-state p-methoxybenzyl were observed at 340 nm upon both the 248-nm excitation and the following 308-nm exD,absorption (a) is ascribed citation, respectively. The D, to the 248-nm biphotonic process, which was suggested to be responsible for the brilliant green emission (D, Dofluorescence) upon the 248-nm excitation. On the other hand, the 308-nm pulse induces the depletion followed by a recovery (c) at 280 nm contrary to the positive TS LIA (b). The estimated recovery time is D,absorption and consistent with the decay times of the D, the D, Dofluorescence. Such features can be clearly demonstrated by the time-resolved spectra upon the 248-nm pulse excitation of CMA. As shown in Figure 4b, the broad band D,absorption rapidly fades out in (330-400 nm) of the D, contrast to the slow decay of the UV band (285 nm) of the D, Do absorption. Upon the 308-nm pulse excitation of the long-lived D, Doabsorption, the D, D,absorption spectrum was obtained as the positive difference spectrum (3 10-400 nm), D, absorption as shown in Figure 4a. This is the first D, spectrum of benzyl radical,26 though the D, D, absorption spectra have been reported for benzylic radicals such as diphenylmethy12' and l-naphthylrnethylz8 in solution at room tem-
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-
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-
-
-
-
-
--
(26) For the short-lived ( T 5 1 ns) fluorescent-state benzyl in solution at room temperature, the D, D,absorption spectrum cannot be detected by nanosecond two-step laser excitation spectroscopy.
n
250
3w
WAVELENGTH / nm
Figure 4. Two-step and ordinary laser-induced-absorption (LIA) spectra of p-(chloromethy1)anisole (0.32 mM) in oxygen-free hexane at room temperature. The ordinary LIA spectra (b) were recorded at 80- ( O ) , 160- ( O ) , and 325-11s (A) delay from the KrF laser photolysis of p (chloromethy1)anisole. At 430-11s delay, the transient LIA was further exposed to XeCl laser pulse yielding the T S LIA, the spectrum (a) of which was observed at 100 ns after the pulse excitation of the XeCl pulse.
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perature. The negative difference spectrum (270-3 10 nm) is Doabsorption spectrum approximately the inversion of the D, with,,,A of 285 nm. The fact implies that the bleaching of the Do absorption predominates over the D, D1 intense D, absorption. The fluorescent state (D,) was estimated to be at 2.58 eV above the ground state (Do), based on the onset (-480 nm) of the D1 Dofluorescence spectrum. Taking account of this energy, the of 340 nm (3.65 eV) in the D, D,absorption band with A, Doabsorption spectrum should appear around 200 nm in the D, Dotransitions are strongly forbidden. spectrum, unless the D, Significant absorbance of solvents prevents us from observing such a short-wavelength band with the energy of 6.23 eV, which is close to the gas-phase ionization potential (6.82 eV)?9 Unfortunately, the electronic spectrum of p-methoxybenzyl vapor has not been reported. For the D, Dotransition of benzyl, the LCI-SCF M O calculation predicted the short-wavelength band (229.2 nm) with a high oscillator strength of 0.309.30 Such a UV band was actually detected by the flash photolysis of benzyl chloride (bromide) in the vapor phase3, and by the 193-nm A r F laser photolysis of gaseous benzyl chloride,32 and it was suggested as a longest wavelength member of a Rydberg series converging to the ionization potential (7.73 eV).29 It is known that sharply peaked Rydberg bands of benzene vapor are largely blue-shifted and blur in solution.33 At the present stage, however, it is difficult D,absorption spectrum (Figure to assign the newly observed D, 4a) of p-methoxybenzyl in hexane at room temperature. The Rydberg transitions as well as high-energy TIT-T*and ~ - n * transitions might be responsible for the D, D,absorption bands.
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--
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(27) Bromberg, A,; Schmidt, K. H.; Meisel, D. J . Am. Chem. SOC.1984, 106, 3056; 1985, 107, 83.
(28) Johnston, L. J.; Scaiano, J. C. J. Am. Chem. SOC.1985, 107,6368. (29) Harrison, A. G.;Kebarle, P.; Lossing, F. P. J . Am. Chem. SOC.1961, 83,111.(30) Cirsky, P.; Zahradnik, R. J . Phys. Chem. 1970, 74, 1249. (31) Bayrakpeken, F. Chem. Phys. L e f f .1980, 74, 298. (32) Ikeda, N.; Nakashima, N.; Yoshihara, K. J . Phys. Chem. 1984.88, 5803. (33) Nakashima, N.; Sumitani, M.; Ohmine, I.; Yoshihara, K. J . Chem. Phys. 1980, 72, 2226.
J . Phys. Chem. 1989, 93, 164-170
164
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The D, state, exhibiting a strong transient D, Do(lBZ)absorption with,,,A of 285 nm (4.35 eV), has been assigned to the D1(1A2) absorption could 4B2 state.22 However, the D,(4B2) not be detected in the near-IR region. Temperature Dependence of the Fluorescence Lifetime of p-Methoxybenzyl Radical. The fluorescence lifetimes of higher benzylic radicals such as 9-anthrylmethyl and 1-naphthylmethyl were found to be actually independent of the temperature (157-300 K).34335The fluorescence lifetime of benzyl with close-lying Dl and D2 states in solution, on the contrary, exhibits the elongation of 3 orders of magnitude with lowering temperature from 300 to 100 K.20,21 Meisel et aL20 have demonstrated that the activation energy (3.83 kcal mol-]) of the nonradiative relaxation corresponds to a set of vibrational energies of 1A2(D1) vibronic levels that are strongly mixed with the vibronic levels of 2B2(D2). Tokumura et a1.21have also reported the extensively temperature-dependent fluorescence lifetimes with the activation barriers of 6.2 and 5.3 kcal mol-' for benzyls with p-methyl and p-chloro substituents, respectively. Only minor perturbation to the electronic levels of the benzyl system was demonstrated for the p-chloro22 and p-methyl group.36 Such a high activation barrier may be therefore ascribed to the vibronic interaction between close-lying D1 and D2 states, as demonstrated for benzyl. The decay signals of p-methoxybenzyl fluorescence were observed in the TS LIF measurements for p-(chloromethy1)anisole in 3-methylpentane at 100-300 K. The fluorescence lifetime ( T , ~ ) of 120 ns at room temperature was slightly elongated to a constant ) 200 ns below 140 K. A linear relationship was value ( T ~ of obtained in the Arrhenius plot of T , ~ [ ~ - T ~ - ~which was taken as +-
(34) Tokumura, K.; Mizukami, N.; Udagawa, M.; Itoh, M. J. Phys. Chem. 1986, 90, 3873.
(35) We confirmed almost the same fluorescence lifetime of 32-34 ns for I-naphthylmethyl in hexane at 180-300 K. Johnston and Scaiano also reported a poor temperature dependence with the activation ener of 300 & 200 cal mol-' for I-naphthylmethyl in methanol at 21 1-297 K. (36) Charlton, T. R.; Thrush, B. A. Chem. Phys. Lett. 1986, 125, 547.
Q
the rate constant of the nonradiative relaxation. From the slope of the Arrhenius plot, the activation energy was estimated to be ca. 1.1 kcal mol-]. It is significantly less than activation barriers (5.3 and 6.2 kcal mol-') for the extensively temperature-dependent nonraditive relaxation of p-chlorobenzyl and p-methylbenzyl in the Dl state. As shown in Figure 1, the fluorescence spectrum of p-methoxybenzyl is red-shifted by ca. 1500 cm-' compared to that of benzyl, and the spectral shape of p-methoxybenzyl fluorescence is much simpler than the vibrational structure of benzyl fluorescence consisting of allowed and vibronic bands. These facts strongly indicate that the introduction of the methoxy group to benzyl causes increasing spacing between Dland D2 states. Hence, the extensively temperature-dependent nonradiative relaxation due to the Dl-D2 proximity should not be expected for p-methoxybenzyl. In addition to the considerably high activation barriers (5.3 and 6.2 kcal mol-'), lower activation barriers have been reported to be 0.83 and 2.0 kcal mol-' by the double-exponential analysis of - ~ for p-chlorobenzyl the curved Arrhenius plots of T , ~ - ~ - T ~only and p-methylbenzyl.zl It has been demonstrated9 that the LIF signal of a jet-cooled p-methylbenzyl, in which the rotation of the methyl group was restricted, is very intense compared to the poor signal from noncooled p-methylbenzyl vapor.36 The lower activation barriers for the nonradiative relaxation of p-chlorobenzyl and p-methylbenzyl may be thus ascribable to the vibration and/or rotation of chlorine or the methyl group. The activation barrier (1.1 kcal mol-') estimated for the weakly temperature-dependent fluorescence lifetime of p-methoxybenzyl is comparable with these activation barriers (0.83 and 2.0 kcal mol-') for the nonradiative relaxation of p-chlorobenzyl and p-methylbenzyl. It is thus reasonable to assume for p-methoxybenzyl that the nonradiative Do internal conversion), in which the relaxation process (Dl rotation and/or vibration of the p-methoxy group play an important role, competes with fluorescent relaxation.
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Registry No. CMA, 824-94-2; p-methoxybenzyl, 3494-45-9.
Ultrafast Dynamlcs of a Quasi-Dissoclative Diatomic Molecule in Solution S.-B. Zhu and G . W. Robinson* Picosecond and Quantum Radiation Laboratory, Texas Tech University, P.O. Box 4260, Lubbock, Texas 79409 (Received: June 7, 1988; In Final Form: October 14, 1988)
When the role of nonlinear dynamics on reaction processes becomes appreciable, many complications, such as the change along the reaction coordinate of the memory kernel, appear. If, in addition, condensed-phasebarrier crossing reactions take place rapidly in comparison with the solvent motion, local nonequilibrium may exist. These features, observed previously for cis-trans isomerization reactions, can also be observed in much simpler, quasi-dissociation-recombination reactions of a diatomic molecule in solution. In these cases, application of the conventional Brownian motion theory and other purely hydrodynamic concepts to chemical reaction dynamics breaks down.
Introduction It is surprising that very little is known about chemical reactions in liquid-state solutions from the microscopic perspective. For example, theoretical studies1-I0 of barrier crossing have used the ( 1 ) Kramers, H. A. Physica 1940, 7 , 284. (2) Zwanzig, R. J . Chem. Phys. 1960, 32, 1172. (3) Mori, H. Prog Theor. Phys. 1965, 33, 423. (4) Kubo, R. Rep. Prog. Theor. Phys. 1965, 33, 425. (5) Adelman, S . A. Adu. Chem. Phys. 1980, LXIV, 143. (6) Larson, R. S.; Kostin, M . D. J . Chem. Phys. 1980, 72, 1392.
0022-3654/89/2093-0164$01.50/0
linear Langevin (or Fokker-Planck) approach, a model that treats the reactants and products as perturbed Brownian particles moving in phase space under the influence of thermal noise from the surrounding medium. However, modern ultrafast experimental methods can measure barrier crossing reactions on 10-13-10-10-s time scales." Such events depend on local molecular dynamics ( 7 ) Grote, R. F.; Hynes, J. T. J. Chem. Phys. 1980, 73, 2715.
(8) Marchesoni, F.; Grigolini, P.; Martin, P. Chem. Phys. Lett. 1982, 87, 451. (9) Carmeli, B.; Nitzan, A. Phys. Rev. Lett. 1982, 49, 423. (10) Hanggi, P. Phys. Rev. 1982, A26, 2996.
0 1989 American Chemical Society
