19412
J. Phys. Chem. 1996, 100, 19412-19416
Picosecond Dynamics of Intermolecular Proton and Deuteron Transfer between Benzophenone and N,N-Dimethylaniline Jens Dreyer and Kevin S. Peters* Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0215 ReceiVed: July 17, 1996; In Final Form: September 20, 1996X
Picosecond absorption spectroscopy is used to study the dynamics of proton and deuteron transfer in the benzophenone/N,N-dimethylaniline contact radical ion pair in the solvents benzene and tetrahydrofuran. From temperature-dependent studies of this kinetic process, the energy of activation and A factors for proton and deuteron transfer are derived. These parameters are then analyzed within the classical and semiclassical models for proton transfer, the Borgis-Hynes model for proton transfer, and the two-step model developed by Kreevoy and Kotchevar for hydride transfer. We conclude that prior to proton transfer there is a ratelimiting reorganization of the contact radical ion pair complex that allows for the transfer of the proton.
Introduction Proton-transfer reactions are among the most frequently encountered elementary chemical reactions. They form the basis of acid-base equilibria, participate in a number of basic organic reactions, and play an important role in biochemical processes.1-3 Despite extensive experimental1-9 and theoretical10-16 work on this topic, many principal questions are still open: What is the rate-limiting step of proton transfer in solution? How is nuclear motion coupled to solvent motion? How important is tunneling? In order to address these questions, the reaction dynamics of protron transfer has to be studied in detail. Particularly valuable information can be gained by determining the influence of isotopic substitution on rate constants as well as Arrhenius parameters such as energies of activation and A factors. The interpretation of kinetic isotope effects (KIE ) kH/kD), A factor ratios (AH/AD), and differences in energies of activation for proton and deuteron transfer (EAD - EAH) within the semiclassical treatment of KIEs has been shown to provide useful insight into the basic mechanism of proton transfer and, in particular, about the structure of transition states.3-5,13 The classical and semiclassical theories of KIEs do not consider dynamical solvent effects explicitly. However, solvation must play an important role in controlling the reaction dynamics of proton-transfer reactions through static as well as dynamical interactions.17 Several theories of proton transfer mediated by solvent polarization have been developed.10,11,14,15 Borgis and Hynes derived proton-transfer rate constants that account for strong coupling to the solvent and the influence of heavy particle vibration of the two nuclei between which the proton is transferred.15 Kreevoy and Kotchevar have shown that the magnitude of KIEs can be significantly reduced under the assumption of a ratelimiting solute and solvent reoganization step prior to proton transfer.18,19 In this paper we present a study of the reaction dynamics of intermolecular proton and deuteron transfer between the benzophenone (Bp) radical anion (Bp•-) and the N,N-dimethylaniline (DMA) radical cation (DMA•+) in the triplet state. Since the photoreduction of Bp by amines has been thoroughly investigated and the basic mechanism is well established,20-32 this reaction is ideally suited for studying reaction dynamics of intermolecular proton and deuteron transfer. It has been shown that Bp and DMA form radical ion pairs in acetonitrile in the X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)02169-7 CCC: $12.00
singlet29 as well as in the triplet state.27,29 The mechanism leading to their formation is shown in Scheme 1: SCHEME 1 1(BP •
–
• • • DMA• + )
1BP * +
ET
DMA
IS
hν (355 nm)
BET
(BP • • • DMA)
hν (355 nm)
BP + DMA
C
1(BP •
–
3BP * +
• • • DMA• + ) DMA
ET 3(BP •
–
• • • DMA• + )
Bp and DMA form a ground-state charge-transfer complex.29 The equilibrium constant for complex formation is estimated to be 0.1-0.5 M-1 in acetonitrile. Irradiating the sample with 355 nm light therefore excites Bp as well as the charge-transfer complex leading to uncomplexed 1Bp* (λmax ≈ 575 nm) and a singlet contact radical ion pair (λmax ≈ 740 nm). In acetonitrile this contact radical ion pair decays exclusively via back electron transfer (BET) within 85 ps to the ground state, regenerating the reactants. 1Bp* can undergo intersystem crossing (ISC) to 3Bp* (λ max ≈ 525 nm) within 9 ( 2 ps in acetonitrile. Both excited-state species, 1Bp* and 3Bp*, can be quenched by electron transfer (ET) from DMA, forming radical ion pairs. The emerging Bp•- and DMA•+ absorb at about 700 and 475 nm, respectively. In contrast to the radical ion pair formed by exciting the ground-state complex, the two radical ion pairs formed upon excitation of the uncomplexed Bp can undergo proton transfer, leading to the ketyl radical (BpH•, λmax ≈ 545 nm) and the DMA radical (no visible absorption), or dissociate to free radical ions (Scheme 2). SCHEME 2 BP • – + DMA• +
kesc
1, 3[BP •
–
• • • DMA• + ]
kH or kD
1, 3[BPH •
• • • DMA• ]
For the singlet radical ion pair back electron transfer is a competitive decay channel, whereas this process requires spin conversion in the case of the triplet radical ion pair and therefore is not observed on the picosecond time scale. Based upon a study of Mataga and co-workers, proton transfer is found to be 1 order of magnitude faster in the triplet state (5.4 × 109 s-1) than in the singlet state (6.6 × 108 s-1).29 Dissociation to free radical ions is about 4 times slower than proton transfer in the triplet state (1.4 × 109 s-1) but faster in the singlet state (9.5 × 108 s-1). Back electron transfer in the singlet state (5.8 × 108 © 1996 American Chemical Society
Proton and Deuteron Transfer between Bp and DMA
J. Phys. Chem., Vol. 100, No. 50, 1996 19413 TABLE 1: Observed Rate Constants and Kinetic Isotope Effects (at 298 K) solvent
kH (109 s-1)a
kD (109 s-1)a
kH/kD
benzene THF
6.2 5.6
2.6 2.8
2.4 2.0
a
Uncertainties in fits are estimated to (10%.
Figure 2. Arrhenius plots for proton (top curves) and deuteron transfer (bottom curves) for the temperature range 5.5-58.2 °C in benzene (0) and THF ((). A factors and activation energies are given in Table 2.
Figure 1. (A, top) Proton transfer. Transient absorption of Bp•monitored at 680 nm in benzene at 6.5 °C, fit to the model shown in Scheme 2. Laser excitation at 355 nm, kH ) 4.9 × 109 s-1, kesc ) 1.9 × 108 s-1, σ ) 20.8 ps, and t0 ) 135 ps. (B, bottom) Deuteron transfer. Transient absorption of Bp•- monitored at 680 nm in benzene at 5.5 °C, fit to the model shown in Scheme 2. Laser excitation at 355 nm, kD ) 1.7 × 109 s-1, kesc ) 2.0 × 108 s-1, σ ) 28.9 ps, and t0 ) 159 ps.
s-1) occurs with a slightly slower rate than proton transfer. The different reactivities of the three radical ion pairs, each having a different mode of production, are attributed to different geometrical structures. It is concluded that these structures do not change during the proton-transfer process. In contrast, we found in a previous study that, although the radical ion pair is formed as an encounter complex, the complex has to reorient to allow for proton transfer.27 Employing picosecond pumb-probe spectroscopy the protonand deuteron-transfer step in the triplet radical ion pair (Scheme 2) is investigated in benzene and tetrahydrofuran (THF). These solvents were chosen so as to minimize the rate of radical ion pair diffusional separation. By using appropriate Bp and DMA concentrations, it is possible to minimize the contributions of singlet-state chemistry and thus isolate the triplet-state protontransfer step (cf. Results section). Temperature-dependent studies are carried out to determine energies of activation and A factors. The results are discussed with respect to predictions of classical theories, the Borgis-Hynes model, and the twostep model of Kreevoy and Kotchevar. Experimental Section Benzophenone (Aldrich) was recrystallized from ethanol. N,N-Dimethylaniline (Aldrich) was distilled from calcium hydride under reduced pressure and stored under argon. Tetrahydrofuran (Mallinckrodt) was distilled, and benzene (Baker) was used without further purification. N,N-Dimethyl-d6-aniline was prepared by condensation of aniline and CD3OD with P2O5
according to a procedure described earlier.27 The purity was larger than 97% as measured by NMR and GC-MS. The picosecond absorption spectrometer, based upon a Continuum (PY61C-10) Nd:YAG laser with a pulse width of 19 ps, as well as the method for deconvoluting the kinetic data has been described previously.32 Results To minimize the contribution of benzophenone singlet-state and charge-transfer chemistry in the observed proton-transfer reaction, the concentration of Bp was set to 0.02 M, producing an optical density of about 1.6 at 355 nm, while the DMA concentration was set to 0.5 M. These concentrations yield the maximum amount of triplet-state chemistry. The kinetics for the decay of Bp•- were found to be constant over the DMA concentration range 0.3-0.5 M in both solvents. Above 0.6 M the kinetics for the Bp•- decay were dependent on the DMA concentration, reflecting the intervention of singlet-state chemistry. The solution of 0.02 M Bp and 0.5 M DMA was irradiated with 355 nm laser light. The proton- and deuteron transfer rates were examined in benzene and THF by monitoring the decay of Bp•- at 680 nm and averaging over two to four runs. A representative kinetic trace is shown in Figure 1A for proton transfer (6.5 °C) and in Figure 1B for deuteron transfer (5.5 °C) in benzene. In each of the kinetic traces there is a small long time constant absorbance, less than 3% for benzene and 6% for THF of the maximum absorbance, reflecting residual Bp•-. Whether the residual absorption reflects Bp•- that has undergone cage escape to the solvent-separated ion pair or Bp•found in an equilibrium between the contact radical ion pair and the radical pair cannot be determined. Thus, we have employed Scheme 2 for the data analysis to arrive at kH(D). The rate constants for proton (kH) and deuteron transfer (kD), measured at 25 °C, as well as the corresponding KIEs are given in Table 1. Temperature-dependent measurements were carried out in the range 5.5-58.2 °C. Arrhenius plots are shown in Figure 2, and activation parameters for kH and kD are compiled in Table 2. All rate constants show Arrhenius behavior. A factors in benzene are significantly larger than in THF. Interestingly, the
19414 J. Phys. Chem., Vol. 100, No. 50, 1996
Dreyer and Peters
TABLE 2: Arrhenius Parameters for Proton (H) and Deuteron Transfer (D) solvent benzene H D THF H D a
ln A
(s-1)a
A
(s-1)
AH/AD
EA (kcal/mol)a
EAD - EAH (kcal/mol)
26.3 ( 0.1 26.8 ( 0.5
2.6 × 1011 4.5 × 1011
0.6
2.2 ( 0.1 3.1 ( 0.3
0.9
24.9 ( 0.1 24.1 ( 0.2
6.6 × 1010 2.7 × 1010
2.4
1.5 ( 0.1 1.4 ( 0.1
- 0.1
Error represents 1σ.
ratio of A factors AH/AD is smaller than unity for benzene (0.6) but larger than one for THF (2.4). Activation barriers are again considerably larger in benzene than in THF. In benzene the barrier for deuteron transfer is 0.9 kcal/mol higher than for proton transfer, whereas both processes show the same activation barrier in THF within the error of the experiment. Discussion Classical and Semiclassical Theories.1-5 The classical theory for the interpretation of KIEs attributes the KIE to the difference in hydrogen isotope zero-point energies of the reactant and the transition state. A more complete treatment is based upon transition-state theory, usually referred to as the semiclassical approach, where the effect of isotopic substitution for translational, rotational, and all vibrational levels is taken into account. Within this treatment four cases concerning the structure of the transition state can be distinguished.3-5,13 If the transition state is assumed to be linear and symmetrical, a maximum KIE with values between 6 and 8 is expected at 25 °C. The difference in activation energies (EAD - EAH) corresponds approximately to the difference in zero-point energies (ED0 - EH0 ) of the reactant, which is about 1.15 kcal/mol for a C-H bond. The ratio of A factors (AH/AD) may vary between 0.7 and 21/2, but usually it is close to unity. However, if the transition state is linear but unsymmetrical, the KIE is reduced to about 2-5. The difference in activation energies is reduced as well to about 0.3-1 kcal/mol, whereas the A factor ratio is not affected. The inclusion of quantum mechanical tunneling effects increases the KIE to larger values than the maximum values of 6-8 without tunneling. The difference in activation energies becomes larger than the difference in zero-point energies, typically 1.5-6 kcal/mol. The ratio of A factors is decreased to values lower than 0.7. The appearance of tunneling is manifested in Arrhenius plots that become curved at low temperatures. However, sufficiently low temperatures are not easily accessible experimentally. Finally, the H transfer can be nonlinear, resulting in a bent transition state. In this case the KIE is even smaller than the KIE for the linear unsymmetrical H transfer. Zero-point energies of the reactant and the transition state tend to be equal, and the difference in activation energies approaches zero. Therefore, the KIE becomes temperature independent, and its magnitude is determined only by the ratio of A factors, which is typically larger than 21/2. Interpreting our results (Table 2) in terms of classical and semiclassical theories, it appears that the H transfer in benzene is a linear process with an unsymmetrical transition state since the KIE is 2.4 and the difference in activation energies of 0.9 kcal/mol falls in the appropriate range. However, the ratio of A factors (0.6) is smaller than expected for this type of H transfer, but taking the error of the experiment into account, this value is consistent with a linear process. On the other hand, one might take this value as indication of tunneling contributions, but the small KIE clearly contradicts this interpretation.
Nevertheless, a tunneling contribution cannot be excluded. For a reaction in THF the structure of the transition state is clearly different. The ratio of A factors (2.4) is significantly larger than 21/2, the difference in activation energies (-0.1 kcal/mol) is essentially zero, and the KIE (2.0) is even smaller than for benzene. Therefore, the H transfer in THF seems to be a nonlinear process occurring through a bent transition state. From the magnitudes of the KIE, the ratio of A factors, and the differences in the energy of activation, the semiclassical model predicts different geometries for the radical ion pair in THF and benzene. However, upon closer examination of the energies of activation and magnitude of the A factor, the applicability of the semiclassical model is called into question. First, it is anticipated that the activation barrier for proton transfer should be larger in THF than in benzene since the polar solvent should stabilize the ionic reactant more than the less ionic transition state. In fact, the energy of activation for proton transfer in benzene, 2.2 ( 0.1 kcal/mol, is greater than the energy of activation in THF, 1.5 ( 0.1 kcal/mol, contrary to expectation. Also, the A factor for benzene, 2.6 × 1011 s-1, is significantly greater than the A factor for THF, 6.6 × 1010 s-1. This pronounced solvent effect upon the A factor cannot be accommodated within the semiclassical model. In the final analysis, the semiclassical model for proton transfer appears not to be applicable to the proton-transfer process within the Bp/DMA contact radical ion pair, and thus we turn our discussion to theoretical formulations that explicitly account for solvent effects upon the dynamics of proton transfer. Borgis and Hynes.15 Borgis and Hynes developed a dynamic theory of unimolecular proton transfer in solution along a linear hydrogen bond. The proton potential is considered as double well with localized vibrational wave functions in the reactant and product well. These diabatic proton wave functions are coupled due to their overlap leading to two split adiabatic vibrational levels. The model is restricted to reactions from the ground vibrational state. Strong electrostatic coupling to the surrounding solvent and vibrational motion of the nuclei between which the proton is transferred are taken in account. The influence of the latter is to decrease the intrinsic barrier for proton transfer by lowering the distance between the two nuclei. To distinguish between different coupling regimes, the strength of the hydrogen bond is used. For proton transfer along weak hydrogen bonds the intrinsic barrier is high, leading to small proton coupling. The actual proton transfer then occurs via tunneling. Initially, the solvent is equilibrated to the reactant, introducing an asymmetry to the W-shaped proton potential and thus prohibiting tunneling. According to a golden rule perspective, tunneling can occur only when the vibrational levels in the reactant and product well become degenerate. Therefore, the solvent has to fluctuate to restore the symmetry of the potential and to allow for tunneling. In this regime the activation barrier of the reaction arises from solvent reorganization, whereas the actual proton transfer occurs barrierless nonadiabatically via tunneling. These ideas are similar to Marcus interpretation of charge transfer in solution.10 For proton transfers along strong hydrogen bonds the proton potential is broad and flat with a small intrinsic barrier, leading to large proton coupling. In fact, the intrinsic barrier can be lower than the proton vibrational levels, which are then delocalized over the whole potential. Proton transfer now occurs adiabatically by going over the barrier. If the charge redistribution accompanying proton transfer is small, the solvent can easily adjust to reactant and product configurations, and thus the proton transfer occurs on this solvent time scale. Therefore,
Proton and Deuteron Transfer between Bp and DMA
J. Phys. Chem., Vol. 100, No. 50, 1996 19415
no activation barrier is expected. On the other hand, if the proton transfer includes a considerable charge redistribution, solvent reorganization becomes an activated process and is ratelimiting. In summary, this theory assumes that, in the weak as well as in the strong hydrogen bond regimes, experimentally observable activation barriers can only be attributed to solvent reorganization and not to the actual proton-transfer process. Invoking golden rule expressions and a Landau-Zener curve crossing formulation, Borgis and Hynes derived analytical rate constants for the full coupling range of proton transfer.15 The weak coupling rate constant for nonadiabatic tunneling in the high-temperature classical vibration regime is given by
( ) [
π β k ) 〈C2〉 p βEtot
1/2
(
β exp ∆E + Etot + 4Etot 4 (E E )1/2 βpωQ Q R
)] 2
(1)
The rate constant for the adiabatic, strong coupling limit is
k)
(
)
ωS2ES + ωQ2EQ 1 2π E + E - 2E E C2 S Q S Q
1/2
exp[-β∆Gq]
(2)
ES and EQ are the solvent and vibrational reorganization energy with ωS and ωQ being the corresponding frequencies. Etot is the sum of ES, EQ, and ER, the latter being the quantum energy associated with the coupling Q vibration. ∆E is the sum of ∆ES and ∆EQ, the energy differences between the reactant and the product states in the solvent and the vibrational coordinate, respectively, and β equals 1/kBT. ∆Gq is the Gibbs free energy of activation and C the proton coupling constant. In eq 1, the rate constant depends quadratically on the proton coupling C, which is the main source for KIEs within this model. The coupling constant shows up only in the preexponential factor, and therefore the A factor ratio contains the dominant KIE information. The exponential factor is isotopically less sensitive, because the solvent and vibrational reorganization energies ES and EQ vary only slightly upon isotopic substitution. The coupling is larger for a proton than for a deuteron since the proton wave function falls of less rapidly. Consequently, the overlap and thus the tunneling probability are larger for the proton. Therefore, large KIEs are expected for the weak coupling regime of nonadiabatic tunneling, and small KIEs are expected for the strong coupling regime of adiabatic transitions. The rate constant expressions are simplified when a solvent like benzene is employed as the reorganization energy ES vanishes. The tunneling rate constant, eq 1, is only slightly modified, since the total energy Etot reduces to the sum of EQ and ER, but the adiabatic rate constant is simplified considerably to
k ) (1/2π)ωQ exp[-β∆Gq]
In the view of these two models, our observed KIEs would appear to fall in the regime of strong hydrogen bonds and are clearly inconsistent with the model formulated in eq 1. For the solvent benzene, where ES is approximately zero, the appropriate rate expression is given by eq 3. The A factor for benzene should then correspond to the quantity (1/2π)ωQ. In this model for intermolecular proton transfer, the vibrational frequency, ωQ, is associated with the vibration of the radical ion pair. Assuming the frequency associated with this motion is of the order of 100 cm-1, then the magnitude of the preexponential term should be greater than 1013 s-1, which is significantly larger than the observed A factor for benzene, 2.6 × 1011 s-1. Also, there should be almost no isotope effect on the A factor, again contrary to our experimental observation. Thus, neither the adiabatic model, eqs 2 and 3, nor the tunneling model, eq 1, can be used to rationalize the observed kinetic data. Because neither the semiclassical model nor the BorgisHynes models for proton transfer can account for the observed isotope effects found in the proton-transfer reaction within the Bp/DMA contact radical ion pair, we are then lead to consider the two-step kinetic model developed by Kreevoy and Kotchevar in their study of hydride transfer.18,19 Two-Step Mechanism. Studying intermolecular proton transfer, one must consider possible diffusional control of the reaction. However, we are investigating proton transfer subsequent to electron transfer, guaranteeing that the two reacting molecules are already organized in an encounter complex resulting from electron transfer. In our previous study on proton transfer between Bp and various amines, we found that even in an encounter complex, prior reorganization (kr) of the complex and solvent structure must take place before a proton is transferred (Scheme 3).27 SCHEME 3 3[BP
• – • • • DMA• + ]e
kr k–r
3[BP
• – • • • DMA• + ]p
kH or kD k–H or k–D 3[BP •
• • • DMA• ]
This can be rationalized, because the equilibrium geometry of the complex for electron transfer (subscript e) must not be the same for proton transfer (subscript p). A kinetic analysis according to Scheme 3 including consequences for the KIE has been given by Kreevoy and Kotchevar for hydride transfers.18,19 Applying the steady-state approximation for the pre-protontransfer configuration the overall observable rate constant is given by
k)
krkH k-r + kH
(4)
(3)
In this case the preexponential factor is much less sensitive to isotopic substitution, and only a very small KIE is expected. In their quantum molecular dynamics simulation for a model proton transfer along OH-N bonds, Borgis and Hynes find KIEs of about 150 for weak H bonds and about 10 for strong H bonds. Interestingly, this change in KIEs is mediated by a change of only 0.1 Å in the O-N distance. Therefore, the KIEs are highly distance dependent. Borgis and Hynes conclude that the usually observed small KIEs all belong to the strong coupling regime. Large KIEs are expected for weakly H-bonded intermolecular complexes or, in particular, for intramolecular proton transfer over long distances imposed by a rigid molecular geometry.
The rate-limiting step is therefore determined by competition between the actual proton-transfer step (kH or kD) and the reversion of the reorientation step (k-r), which corresponds to solvent relaxation. Both the reorientation step and the protontransfer step are considered to be sensitive to isotopic substitution. This leads to the following expression for the KIE:
kH krHkH(k-r + kD) ) kD krDkD(k-r + kH)
(5)
If complex-solvent relaxation is fast (k-r >> kH or kD), the observed rate constant and the KIE are given by
19416 J. Phys. Chem., Vol. 100, No. 50, 1996
Dreyer and Peters
kr k ) KrkH k-r H
(6)
kH krHkH ) kD krDkD
(7)
k)
The proton-transfer step is now rate-limiting, and the KIE is determined by the effect of isotopic substitution on the reorientation step as well as the proton-transfer step. The KIE has its maximum value within this model. For slow complex-solvent relaxation (k-r , kH or kD) the reorientation step is rate-limiting, and the KIE, determined only by the influence on this step, is reduced to its minimum value:
k ) kr
(8)
kH/kD ) krH/krD
(9)
Applying this model to hydride-transfer reactions in different solvents, Kreevoy and Kotchevar find groups of KIE values of about 5.2 and 2.9, corresponding to the two limiting regimes of fast and slowly relaxing solvents. However, no correlation of KIEs to solvent relaxation times is found in this study. The solvent dependence of the KIE is instead attributed to the property of the solvents being protic or aprotic. Comparing our observed KIEs of 2.4 and 2.0 to this model, it appears that the reorientation step within the encounter complex of the radical ion pair is important and rate-limiting. The actual mechanism for proton transfer can be either tunneling or an adiabatic transition over the barrier. Consequently, the observed rate constants and Arrhenius parameters do not contain any information about the proton-transfer event. Conclusion On the basis of the above considerations, we conclude that the rate-limiting step in the transfer of a proton within the Bp/ DMA contact radical ion pair is not just the actual proton transfer itself but that the reorganization of the reaction complex is also involved in the rate-determining steps. Whether the proton transfer occurs through a thermally accessible transition state (classical model) or through tunneling is not revealed in these studies due to the involvement of complex reorganization. If the actual mechanism of the proton-transfer step is to be investigated, it will be necessary to minimize the involvement of complex reorganization by studying intramolecular protontransfer processes.8,33-36 Such experiments are currently in progress. Acknowledgment. This work is supported by a grant from the National Science Foundation, CHE 9408354. J.D. is grateful to the Deutsche Forschungsgemeinschaft for a postdoctoral fellowship. References and Notes (1) (a) Bell, R. P. The Proton in Chemistry, 2nd ed.; Chapman and Hall: London, 1973. (b) Bell, R. P. The Tunnel Effect in Chemistry; Chapman and Hall: London, 1980.
(2) Proton-Transfer Reactions; Caldin, E. F., Gold, V., Eds.; Chapman and Hall: London, 1975. (3) Melander, R. C.; Saunders, W. H. Reaction Rates of Isotopic Molecules; Wiley: New York, 1980. (4) Westheimer, F. H. Chem. ReV. 1961, 61, 265. (5) Kwart, H. Acc. Chem. Res. 1982, 15, 401. (6) Koch, H. F. Acc. Chem. Res. 1984, 17, 137. (7) Kosower, E. M.; Huppert, D. Annu. ReV. Phys. Chem. 1986, 37, 127. (8) Special issue in Chem. Phys. 1989, 136. (9) (a) Arnaut, L. G.; Formosinho, S. J. J. Photochem. Photobiol. A: Chem. 1993, 1. (b) Arnaut, L. G.; Formosinho, S. J. J. Photochem. Photobiol. A: Chem. 1993, 21. (10) (a) Marcus, R. A. J. Phys. Chem. 1968, 72, 891. (b) Cohen, A. O.; Marcus, R. A. J. Phys. Chem. 1968, 72, 4249. (c) Marcus, R. A. J. Am. Chem. Soc. 1969, 91, 7224. (d) Marcus, R. A. Faraday Symp. Chem. Soc. 1975, 10, 60. See also: Albery, J. W. Annu ReV. Phys. Chem. 1980, 31, 227. (11) German, E. D.; Kuznetsov, A. M.; Dogonadze, R. R. J. Chem. Soc., Faraday Trans. 2 1980, 76, 1128. (12) Scheiner, S. Acc. Chem. Res. 1985, 18, 174. (13) Duan, X.; Scheiner, S. J. Am. Chem. Soc. 1992, 114, 5849. (14) (a) Morillo, M.; Cukier, R. I. J. Chem. Phys. 1989, 91, 857. (b) Morillo, M.; Cukier, R. I. J. Chem. Phys. 1990, 92, 4833. (15) (a) Borgis, D.; Lee, S.; Hynes, J. T. Chem. Phys. Lett. 1989, 162, 19. (b) Borgis, D.; Hynes, J. T. In The Enzyme Catalysis Process; Cooper, A., Ed.; NATO ASI Series; Plenum Press: New York, 1989; p 293. (c) Borgis, D.; Hynes, J. T. J. Chim. Phys. Phys.-Chim. Biol. 1990, 87, 819. (d) Borgis, D.; Hynes, J. T. J. Chem. Phys. 1991, 94, 3619. (e) Borgis, D.; Hynes, J. T. Chem. Phys. 1993, 170, 315. (e) Ando, K.; Hynes, J. T. In Structure and ReactiVity in Aqueous Solution: Characterization of Chemical and Biological Systems; Cramer, C. J., Truhlar, D. G., Eds.; ACS Symposium Series, American Chemical Society: Washington, DC, 1994; p 143. (f) Borgis, D.; Hynes, J. T. J. Chem. Phys. 1996, 100, 1118. (16) Simkin, B. Y.; Sheikhet, I. I. Quantum Chemical and Statistical Theory of Solutions: A Computational Approach; Ellis Horwood: London, 1995; Chapter 10. (17) Bernasconi, C. F. Pure Appl. Chem. 1982, 54, 2335. (18) Kreevoy, M. M.; Kotchevar, A. T. J. Am. Chem. Soc. 1990, 112, 3579. (19) Kotchevar, A. T.; Kreevoy, M. M. J. Phys. Chem. 1991, 95, 10345. (20) Hochstrasser, R. M.; Lutz, H.; Scott, G. W. Chem. Phys. Lett. 1974, 24, 162. (21) Peters, K. S.; Freilich, S. C.; Schaeffer, C. G. J. Am. Chem. Soc. 1980, 102, 5701. (22) Schaeffer, C. G.; Peters, K. S. J. Am. Chem. Soc. 1980, 102, 7566. (23) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1981, 103, 6403. (24) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1982, 104, 6542. (25) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1982, 104, 6142. (26) Simon, J. D.; Peters, K. S. J. Am. Chem. Soc. 1983, 105, 4875. (27) Manring, L. E.; Peters, K. S. J. Am. Chem. Soc. 1985, 107, 6452. (28) Devadoss, C.; Fessenden, R. W. J. Phys. Chem. 1990, 94, 4540. (29) Miyasaka, H.; Morita, K.; Kamada, K.; Mataga, N. Bull. Chem. Soc. Jpn. 1990, 63, 3385. (30) Miyasaka, H.; Morita, K.; Kamada, K.; Mataga, N. Chem. Phys. Lett. 1991, 178, 504. (31) Hasselbach, E.; Jacques, P.; Pilloud, D.; Suppan P.; Vauthey E. J. Phys. Chem. 1991, 95, 7115. (32) Peters, K. S.; Lee, J. J. Phys. Chem. 1993, 97, 3761. (33) (a) Strandjord, A. J. G.; Barbara, P. F. J. Phys. Chem. 1985, 89, 2355. (b) Strandjord, A. J. G.; Smith, D. E.; Barbara, P. F. J. Phys. Chem. 1985, 89, 2362. (34) Kim, Y. R.; Yardley, J. T.; Hochstrasser, R. M. Chem. Phys. 1989, 136, 311. (35) Heldt, J.; Gormin, D.; Kasha, M. Chem. Phys. 1989, 136, 321. (36) (a) Brucker, G. A.; Swinney, T. C.; Kelley, D. F. J. Phys. Chem. 1991, 95, 3190. (b) Swinney, T. C.; Kelley, D. F. J. Chem. Phys. 1993, 99, 211.
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