J. Phys. Chem. 1995,99, 5193-5191
5793
Vibrationally Enhanced Proton Transfer Sharon Hammes-Schiffer* and John C. Tully AT&T Bell Laboratories, Murray Hill,New Jersey 07974 Received: December 9, 1994; In Final Form: February 17, 1995@
We report a computational study of the effects of vibrational excitation of the hydrogen atom motion (i.e,, excitation of the hydrogen bond asymmetric stretch mode) on proton transfer in solution. We use the method “molecular dynamics with quantum transitions” (MDQT) to properly treat the quantum mechanical nature of the hydrogen motion. Previously we applied MDQT to a model for the proton transfer reaction AH-B =+ A--+HB in liquid methyl chloride, where the AH-B complex corresponds to a typical phenol-amine complex. In that application, the hydrogen motion was treated quantum mechanically, and MDQT was used to incorporate transitions among the hydrogen quantum states into the molecular dynamics. It is a simple step to extend this approach to study the effects of vibrational excitation of the hydrogen motion. We show that, for this model system, the vibrational excitation significantly enhances the proton transfer rate for both hydrogen and deuterium, although the enhancement is much greater for deuterium. Thus, the proton transfer reaction is fast enough to couple with vibrational energy redistribution. We outline pictorially the competing pathways for vibrational relaxation and vibrationally assisted tunneling that we observed in the simulations. Our demonstration of the feasibility of the application of MDQT to photoinduced and photoassisted reactions should motivate further application of MDQT to such systems. More importantly, we hope that our results will motivate experimental investigations of vibrational excitation of the hydrogen bond asymmetric stretch mode in proton transfer reactions.
I. Introduction Since proton transfer reactions involve the motion of a light atom (hydrogen), they frequently exhibit significant quantum mechanical behavior.’ As a result, several different molecular dynamics methods that incorporate quantum mechanical effects have been developed and applied to the simulation of proton transfer in This paper is concerned with one of these methods, namely, that of ref 14. In this method, the hydrogen atom being transferred is treated quantum mechanically, while the remaining degrees of freedom in the system are treated classically. Thus, the hydrogen atom can be thought of as a quantum mechanical particle moving in a potential dictated by the positions of the classical atoms, with proper feedback of the quantum particle on the classical forces. The method in ref 14 differs from previous methods in that quantum transitions among the vibrational-like quantum states of the hydrogen atom are incorporated into the dynamics using a surface hopping method called “molecular dynamics with quantum transitions” (MDQT).I5 In ref 14, MDQT was applied to a model for the intramolecular proton transfer reaction AH-B == A--+HB in liquid methyl chloride, where AH-B is a linear complex with parameters chosen to model a phenol-amine complex. This model was first introduced by Azzouz and B o r g i ~ .Both ~ the overall rate and the dynamics of this model proton transfer reaction were significantly affected by the inclusion of quantum tran~iti0ns.l~ In this paper, we study the effects of vibrational excitation of the hydrogen atom motion, Le., excitation of the hydrogen bond asymmetric stretch mode. Experimentally, this could represent excitation of the hydrogen bond asymmetric stretch mode either by infrared photoexcitation in the case of electronic ground-state proton transfer or by photoexcitation to the blue of the fundamental in the case of proton transfer in an electronic excited state.l6,l7 We demonstrate that MDQT can easily be EI Abstract
published in Advance ACS Abstracts, April 1, 1995.
applied to this type of photoassisted reaction. Moreover, our results show that vibrational excitation of the proton enhances the overall rate of proton transfer for this model system. We discuss below the mechanisms of vibrational relaxation and vibrationally assisted tunneling that we observed in the simulations. For clarification, we constrast our study with that presented in a recent paper by Staib et al.13 for a similar type of model proton transfer reaction. Staib et al. treated both the proton coordinate and the solute heavy-atom (AB) vibrational motion quantum mechanically, whereas we treat only the proton coordinate quantum mechanically. Moreover, Staib et a1 found that, for their model, the reaction was occumng in the proton adiabatic regime; Le., the proton remained in the ground hydrogen quantum state. In contrast, we have shown that, for our model, the adiabatic approximation is not valid and transitions among the hydrogen quantum states are important.l4 Staib et al. studied the effect of exciting the solute heavy-atom vibration (i.e, the hydrogen bond symmetric stretch mode) and found that this slows down the proton transfer reaction. They did not include nonadiabatic transitions among the heavy-atom vibrational states because they determined that these nonadiabatic hopping processes are slow enough that they do not disturb the barrier-top dynamics. In comparison, we are studying the effect of vibrational excitation of the hydrogen atom motion (i.e., the hydrogen bond asymmetric stretch mode), and we include nonadiabatic transitions among the hydrogen quantum states because they are crucial for the proper description of the competition between enhanced proton transfer and quenching of vibrational excitation. An outline of this paper is as follows. In the first section we briefly describe the model system and summarize our methods. In the second section we present our results and discuss the different mechanisms for vibrational relaxation and vibrationally assisted tunneling. In the final section we discuss some implications of these results.
0022-3654/95/2099-5793$09.Q~I0 0 1995 American Chemical Society
Hammes-Schiffer and Tully
5794 J. Phys. Chem., Vol. 99, No. 16, 1995
B
A
Figure 2. Two possible starting configurations for excited proton transfer. The curve represents the potential in which the proton moves,
and the horizontal lines indicate the energies and localizations of the hydrogen quantum states, where the solid line denotes the occupied state.
0.60 0.80 1.0 1.2 1.4 1.6 1.8 2.0
r (Angstroms)
Figure 1. Classical potential of mean force as a function of the proton coordinate at R = 2.7 A. This curve was obtained using the following approximate expression for the classical potential of mean force W(R,r): W(R,r) VHB(R,r)- (&Ro,r))(R - Ro)- Shdr‘ (Ro,r’ )) - 2kT ln(R/Ro),for Ro = 2.7 A, where (C(R’,r’)) indicates an
(e
average of the solvent forces (Le., all forces except for those due to Vm(R,r))on x = r, R performed with the constraints r = r’ and R = R’. (This approximation was originally used by Azzouz and Borgis in ref 3.) We obtained the average forces by performing classical molecular dynamics simulations with r and R constrained to select values, calculating the forces on r and R using a finite-difference method, and averaging these forces over a period of 40 ps.
11. Methods A. Model System. We use the model system fist introduced by Azzouz and B ~ r g i s .The ~ parameters we used are given in detail in ref 14. The model system consists of a linear complex AH-B in a dipolar solvent. The position of the hydrogen atom is represented by a one-dimensional variable r, which is the distance between A and H in the complex, and the distance between A and B in the complex is denoted R. The interactions within the AH-B complex (VHB(R,I)) consist of a hydrogenbonding potential and a repulsion between A and B where the parameters for these interactions are chosen to model a phenolamine complex. The dipolar solvent is represented by rigid diatomic molecules, and the solvent-solvent interaction consists of Lennard-Jones and Coulomb interactions, where the parameters are chosen to model methyl chloride. The interaction of the solvent with the complex also consists of Lennard-Jones and Coulomb interactions. The charges on A, H, and B in the complex are functions of the hydrogen atom coordinate r. The simulations described in this paper were performed using periodic boundary conditions for a system of 255 solvent molecules and one AH-B complex in a cube with sides of length 28 8, at a temperature of 247 K. For more details about the simulations, the reader is referred to ref 14. Figure 1 depicts the classical potential of mean force as a function of r for R = 2.7 A. The potential well at r % 1.0 represents the reactant, covalent state AH-B, and the potential well at r 1.6 represents the product, ionic state A--+HB. In a molecular dynamics simulation, fluctuations of the solvent alter the relative depths of the two potential wells, and fluctuations of R alter primarily the barrier height. Thus, the potential in which the proton moves is constantly changing with time. B. MDQT Method. As discussed above, in proton transfer the hydrogen atom exhibits quantum mechanical behavior. Thus, we apply the MDQT method in which the hydrogen coordinate r is treated quantum mechanically, while all other degrees of freedom in the system are treated classically. In MDQT, the hydrogen remains in a single quantum state except for the possibility of sudden switches from one state to another that occur in infinitesimal time. The algorithm is outlined as follows.
A trajectory is started at specified classical positions and momenta and in a specified hydrogen quantum state. At each time increment, the eigenenergies and eigenfunctions of the lowest n hydrogen quantum states are computed by solving the time-independent Schrodinger equation. (For this simulation we chose n = 4.) Then, the Hellmann-Feynman forces corresponding to the occupied quantum state are computed and are used to integrate the equations of motion for the classical degrees of freedom. Simultaneously,the time-dependent Schrodinger equation is integrated in order to determine the complex amplitudes Cj(t) corresponding to each of the n quantum states. This information is used in conjunction with a probabilistic algorithm to determine whether or not a quantum transition occurs at this time increment. The algorithm ensures that, for a large ensemble of trajectories, the fraction of trajectories assigned to any state j at any time t will equal the quantum probability of occupation I C,(t)j2.l8This procedure is continued until the simulation is terminated according to a specified criterion. In our previous application of MDQT,I4 we chose the initial classical positions and momenta of each trajectory from a random ensemble with the constraint that the hydrogen ground state was localized in the reactant region. (The localization of a particular state j is determined by (r), (YjrlYj), where Yj is the Born-Oppenheimer wave function associated with state j and the brackets denote integration over the quantum mechanical coordinate r. Note that (r), % 1.0 when state j is localized in the reactant region, (r)j % 1.6 when state j is localized in the product region, and (r), 1.4 when state j is delocalized.) We always started the trajectories in the ground state; Le., the complex coefficients were initialized such that C1 = 1 and C, = 0 for m 1. In this paper, we choose the initial classical positions and momenta in the same way as in ref 14. However, in this paper we study the effects of photoexcitation of the hydrogen motion (Le., the hydrogen bond asymmetric stretch mode). Since the oscillator strength will be substantial only when the ground and excited vibrational wave functions have large spatial overlap, we initially prepare the quantum state in the lowest excited state that is localized largely in the reactant region. Thus, we are not studying direct photoassisted tunneling from the ground state localized on the reactant side of the potential barrier to an excited state localized on the product side. To be specific, we start each trajectory in an excited state j (Le., the coefficients are initialized such that Cj= 1 and C, = 0 form j ) , where the initial state j is chosen as follows: if state 2 is localized in the reactant region, then we set j = 2, and if state 3 is localized in the reactant region, then we set j = 3. If neither states 2 nor 3 are localized in the reactant region, then we do not use this starting configuration. See Figure 2 for a depiction of the potential curves corresponding to these two possibilities. Note that these two potential curves could interchange due to fluctuations of the solvent coordinates; Le., A will be converted to B if the right well
*
*
. I . Phys. Chem., Vol. 99, No. 16, 1995 5795
Vibrationally Enhanced Proton Transfer
TABLE 1: Application of MDQT to Simulation of the Transfer of Hydrogen (H) and Deuterium (D) with Initial Vibrational Excitation for the Model System Described in the Text?' fraction
LL3
RR3
mean time (ps)
atom
quenched
reacted
H D
0.43 0.28
H D
0.72 0.46
Started in LR3 0.28 0.54
H D
0.62 0.35
Total 0.38 0.65
Started in LL2 0.57 0.72
quenched
reacted
0.32
0.41 0.63
6.0 1.6
6.0
4.7
3.0 0.79
LL2 1.o
1.3
A
1.1
Results are given for trajectories started in LL2, for those started in LR3, and for the combination of both types of trajectories.
becomes lower and a switch from state 2 to state 3 occurs, and B will be converted to A if the right well becomes higher and a switch from state 3 to state 2 occurs. The excitation energies corresponding to the initial configurations are approximately 2240 cm-l for hydrogen and 1720 cm-' for deuterium; Le., they correspond to the v = 0-1 vibrational transitions for hydrogen and deuterium. We terminate a trajectory if the proton is in the ground state and if one of two conditions are satisfied. The first condition is that ( r ) ~ 1.03, in which case we consider the trajectory to have quenched (not reacted) since the proton is still in the reactant, covalent state. This is an example of vibrational relaxation. The second condition is that (r)o > 1.62, in which case we consider the trajectory to have undergone proton transfer (reacted) since the proton is localized in the product, ionic state. This is an example of vibrationally assisted proton transfer.
III. Results We ran 100 trajectories of this type for both hydrogen and deuterium and calculated the quantities given in Table 1. The vibrational excitation energy (averaging 6.4 kcaymol for H and 4.9 k c d m o l for D) is a significant fraction of the classical free energy barrier to proton transfer (about 10 kcdmol, as shown in Figure 1). The MDQT simulations show that this added energy can be efficiently utilized to promote proton transfer. As will be discussed below, the enhancement factor is much larger for deuterium transfer than for hydrogen transfer, even though the mean energy of excitation initially deposited in the A-D bound is less than that deposited in the A-H bond by a factor of about U f i . Even more surprisingly, for those vibrationally excited molecules that undergo proton (or deuteron) transfer rather than nonreactive vibrational relaxation, the mean time for reaction is only 0.79 ps for deuterium compared to 3.0 ps for hydrogen. In order to understand the enhancement mechanism and the origin of the inverse isotope effect, it is helpful to construct the schematic flow chart in Figure 3 as a framework for discussion. The labels of the configurations in the diagram can be interpreted as follows: the letters denote the localizations of the lowest two quantum states (where "L" represents left and "R' represents right localization), and the number indicates which state is occupied. Thus, LR2 indicates that the first quantum state is localized mainly on the left (reactant), the second quantum state is localized mainly on the right (product), and the second state is occupied. Note that no additional label is required to describe the localization of the third state. In fact, for the hydrogen isotope the energy of the third state generally
I
I
LL1
RR 1
krFigure 3. Flow chart depicting the pathways for proton transfer. The configurations (which are drawn as in Figure 2) are labeled as follows: the letters denote the localizations of the lowest two quantum states (where "L" represents left and "R' represents right localization), and the number indicates which state is occupied. The two vertical dashed lines with arrows denote the initial vibrational excitations. The solid lines with double arrows denote the significant transitions. The four configurations in the box depict proton transfer in the absence of vibrational excitation. See the text for a detailed explanation. lies near the top of the reaction barrier, and the state is so delocalized that it is not meaningful to classify it as right or left localized. Moreover, the fourth state was not included because excitation to the fourth state was found to be insignificant. We can trace out the possible reaction paths as sequences of transitions among the configurations shown in Figure 3. Transitions in the horizontal direction (e.g., LR2 to RL2) are due primarily to reorientation of solvent dipoles which alter the relative stabilities of the covalent (reactant) and ionic (product) states. Such transitions are adiabatic (i.e., they do not change the quantum state). Diagonal transitions (e.g., LR1 to RL2) are also driven by solvent dipole reorientation, but they simultaneously change the quantum state and are thus nonadiabatic. Finally, vertical transitions (e.g., RL2 to RL1) are nonadiabatic (Le., the quantum state is changed), but the ordering of the states remains the same. The arrows in Figure 3 indicate the allowed transitions between configurations. Direct transitions between quantum states 3 and 1 were found to play a minor role and are thus neglected. In addition, nonadiabatic transitions occur almost exclusively when solvent dipole reorientation brings the two quantum states into near re~0nance.l~Thus, diagonal transitions in which one of the occupied states does not participate in the near-resonance condition (e.g., LR3 to RL2 and LL1 to LR2) are unimportant. Moreover, usually the solvent reorientation proceeds further, producing a switching of the order of the states, as indicated by the horizontal and diagonal arrows in Figure 3. Thus, all vertical transitions can be neglected in this analysis. Within this approximate framework, characterization of the proton transfer reaction in the absence of initial vibrational relaxation is straightforward. The four configurations involved are depicted in the box in Figure 3. In our previous simulat i o n ~ reactants ,~~ and products were defined such that the quantum ground state is occupied and is localized in the appropriate potential well. Thus, LR1 is the reactant configuration, RL1 is the product configuration, and LR2 and RL2 are
5796 J. Phys. Chem., Vol. 99, No. 16, I995
intermediate configurations. There are three possible dynamical pathways. The first and simplest is direct adiabatic passage from LR1 to RL1, leading to proton transfer. The second, indirect proton transfer, involves nonadiabatic passage from LR1 to RL2, followed by an odd number of adiabatic transitions between RL2 and LR2, and ending with a nonadiabatic transition to products, LR2 to RL1. The third, nonreactive pathway also starts with nonadiabatic passage from LR1 to RL2, followed by an even number of adiabatic transitions between RL2 and LR2, and ends with a nonadiabatic transition back to reactants, RL2 to LR1. The following three pieces of information from ref 14 provide some of the relative probabilities and time scales for these pathways. First, the mean time for proton transfer with the system constrained to the quantum ground state (i.e., for a transition from LR1 to RL1) is about 6 ps for both proton and deuteron transfer. Second, the probability that a transition is adiabatic, Le., that a transition from LR1 will produce RL1 rather than RL2, is 0.26 for H and 0.05 for D. Third, the mean times for proton and deuteron transfer, including nonadiabatic transitions, are 13 and 50 ps, respectively. These numbers indicate that the mean time for adiabatically switching configurations is considerably faster in state 2 than in state 1 (Le., the transition from LR2 to RL2 is faster than that from LR1 to RL1). The physical explanation for this phenomenon is that, in the ground state, the solvent tends to stabilize the localized hydrogen atom wave function, generating an energy barrier to solvent reorientation. In the excited state, however, the solvent is destabilizing to the hydrogen wave function, removing the energy barrier. This accelerated rate in the excited state is essential to the vibrational enhancement of proton transfer discussed below. Any theory which treats the solvent as a fluctuating bath with no feedback from the hydrogen bond configuration to the solvent motion cannot properly describe this effect. In comparison, we now discuss vibrationally enhanced proton tunneling, which requires the entire flow chart in Figure 3. The reaction is initiated by a vertical photoexcitation from groundstate reactants, LL1 or LR1, to excited configurations LL2 or LR3, respectively. This corresponds to vibrational excitation of the hydrogen bond asymmetric stretch mode, i.e., of the A-H bond. LR2 is bypassed because this configuration corresponds to direct photoinduced proton transfer, not vibrational excitation. LR2 is localized on the product side, so it will have a low oscillator strength and typically a much lower excitation energy than the A-H vibration. After excitation, the system evolves until it reaches the ground state, either to LR1, corresponding to nonreactive vibrational relaxation (quenching), or to RL1, corresponding to proton transfer (reacting). Since vertical transitions were found to be unimportant, as discussed above, vibrational relaxation does not occur by a direct mechanism but rather occurs by a sequence of near-resonant proton transfer steps. The time scale for vibrational relaxation is fast, on the order of a few picoseconds, as shown in Table 1. By constrast, we estimate that, for a conventional A-H vibration in a single well potential, vibrational relaxation would occur on roughly the 100-ps time scale. The dominance of indirect proton transfer-mediated vibrational relaxation over direct relaxation is essential to producing the observed vibrational enhancement of proton transfer. If the direct mechanisms were much faster than the indirect one, the vibrational energy would be largely quenched nonreactively. Since this indirect relaxation mechanism dominates, however, there is a relatively large probability that a vibrationally excited species will produce the proton
Hammes-Schiffer and Tully transfer product rather than undergo nonreactive vibrational relaxation: 38 and 65% respectively for hydrogen and deuterium. Referring to Figure 3, we now discuss the fundamental transitions involved in the mechanism of vibrationally enhanced proton tunneling. As stated above, the initial excitation produces either LL2 or LR3, depending on whether, prior to excitation, the ground-state configuration was LL1 or LR1. We found that the probability of starting in LL2 rather than LR3 is 35% for hydrogen and 61% for deuterium. This difference is simply a result of the fact that, for deuterium, a quantum of vibrational energy is smaller than for hydrogen. Those trajectories that begin in LL2 can make either of two initial transitions, to LR2 or LR3. We have already established that adiabatic transitions among configurations in state 2 are faster than in state 1. We also make the physically reasonable assumption that nonadiabatic transitions involving states 2 and 3 will generally be of lower probability than those involving states 1 and 2 since the 2-3 avoided crossings occur higher up the potential barrier, resulting in larger wave function overlap and larger adiabatic energy splitting. This information, together with the branching ratio for proton transfer in the absence of vibrational excitation, suggests that there is a significant probability of a transition from LL2 to LR2 and of a subsequent transition from LR2 to RL1, resulting in a reaction. In contrast, those trajectories that begin in LR3 are more likely to experience adiabatic transitions (indicated by horizontal arrows) that remove the initial leftright asymmetry, thus decreasing the probability of reaction. Moreover, the substantial amount of time spent making these adiabatic transitions also increases the mean time of reaction for those trajectories starting in LR3. Thus, trajectories that start in LL2 are expected to have a higher probability of reaction and a smaller mean time of reaction than those that start in LR3. These trends are verified in Table 1. Furthermore, recall that the probability of starting in LL2 rather than LR3 is greater for deuterium than for hydrogen. As a result, deuteron transfer is expected to have a higher probability of reaction and a smaller mean time of reaction than proton transfer. In addition, recall that the probability of a nonadiabatic transition is greater for deuteron transfer than for proton transfer. This also leads us to expect the probability of reaction to be greater (and the mean time of reaction to be smaller) for deuteron transfer than for proton transfer. Note that this effect is expected to be especially important for trajectories starting in LR3, which must undergo at least two nonadiabatic transitions. All of these trends can also be seen in Table 1. Now we discuss the enhancement of the overall proton transfer rate due to the vibrational excitation. In order to calculate the mean time z for a proton transfer reaction with vibrational excitation, we use the following equation:
+
z = FRzR FQ(z,
+ zN)
where FR and FQ are the fractions that reacted and quenched, respectively, and ZR and ZQ are the mean times for reaction and quenching, respectively, for trajectories with initial vibrational excitation. The remaining quantity, ZN, is the mean time for reaction with no initial vibrational excitation. Note that the trajectories that quench (described by the second term in eq 1) are assumed to be delayed by ZQ relative to those reacting in the absence of initial excitation. Thus, it would be possible for the initial excitation to slow down the overall reaction. For this model, however, the overall reaction rate is enhanced: the mean times for reaction with vibrational excitation are 12 and 18 ps for proton and deuteron transfer, respectively, as opposed to 13 and 50 ps for proton and deuteron transfer, respectively,
Vibrationally Enhanced Proton Transfer in the absence of vibrational excitation. Thus, vibrational excitation leads to an enhancement of 1.1 and 2.8 for proton and deuteron transfer, respectively. We also point out that although our simulations model relatively broad band vibrational excitation of the asymmetric hydrogen bond (with excitation energies ranging from 1830 to 2770 cm-' for H and 1360 to 1980 cm-' for D), it would be feasible to simulate the frequency dependence of vibrationally enhanced proton transfer using the same methods. Moreover, we expect that excitation in the lower energy (red) edge of the vibrational transition would lead to a greater probability of producing the faster reacting and more selective initial LL2 configuration. Thus, we expect greater enhancement of proton (or deuteron) transfer when photoexciting on the red side of the hydrogen bond asymmetric stretching band. Although statistical uncertainties were too large for us to be able to verify this effect for our model system, it might be experimentally observable.
J. Phys. Chem., Vol. 99, No. 16, 1995 5797 before a sufficient number of quanta can be deposited in the selected mode. Significant vibrational enhancement is predicted to occur in this proton transfer situation for two reasons. First, tunneling rates are greatly increased through excitation by a single vibrational quantum. Second, as discussed above, direct vibrational relaxation is slower than sequential proton transfermediated relaxation. To our knowledge, there has been no experimental study of the possible enhancement of proton transfer rates by excitation of the hydrogen bond asymmetric stretching mode. This is presumably due, at least in part, to the congestion of the spectra coupled with the relatively weak oscillator strength for this mode. The results in this paper suggest, however, that the measurement of this enhancement with its isotope effect might reveal considerable information about the mechanisms of proton transfer and vibrational relaxation.
References and Notes
IV. Conclusions We have shown that MDQT can be used to study the effects of vibrational excitation of the hydrogen atom motion (i.e., the hydrogen bond asymmetric stretch mode) on proton transfer in solution. For the particular model system described in this paper, the initial excitation enhanced both proton and deuteron transfer, although the enhancement was larger for deuteron transfer. In addition, MDQT allowed us to study the interesting dynamics resulting from the initial excitation, including the mechanisms that control the competition between vibrational relaxation and vibrationally assisted tunneling. In particular, nonreactive vibrational relaxation was shown to be dominated by sequential proton transfer transitions between the reactant AH-B and product A--+HB configurations, rather than by direct transitions in the reactant AH-B configuration. As discussed above, the simulations reported here represent relatively broad band excitation of the hydrogen bond asymmetric stretch mode. A more rigorous treatment would involve calculating this rate enhancement as a function of the frequency v of the incident infrared radiation. This is a straightforward extension of our method. A trajectory would be started in the ground state and continued until one of the excited quantum states was exactly resonant with the specified frequency v. At this point, a probabilistic algorithm involving the oscillator strength of the transition would be used to determine if a quantum transition should occur. From this procedure, the rate enhancement could be calculated as a function of frequency v, and direct comparison with experimental data should be possible. For reasons discussed above, we predict that, for some systems, there may be a greater enhancement of proton (or deuteron) transfer when photoexciting on the red side of the hydrogen bond asymmetric stretching band. The enhancement of a reaction rate by selective excitation of a particular vibrational mode is an elusive goal that has been achieved only in special situations.20 Usually in large molecules or condensed phase situations, energy randomization occurs
(1) Bell, R. P. The Proron in Chemistry, 2nd ed.; Come11 University: Ithaca, NY, 1973. (2) Warshel, A. J . Phys. Chem. 1982,86,2218. Warshel, A,; Chu, Z. T. J . Chem. Phys. 1990, 93, 4003. (3) Azzouz, H.; Borgis, D. J. Chem. Phys. 1993, 98, 7361. (4) Borgis, D.; Tarjus, G.; Azzouz, H. J. Phys. Chem. 1992,96,3188. Borgis, D.; Ta~jus,G.; Azzouz, H. J. Chem. Phys. 1992, 97, 1390. 75) Laria, D.; Ciccotti, G.; Ferrario, M.; Kapral, R. J. Chem. Phys. 1992, 97, 378. (6) Borgis, D. C.; Lee, S.; Hynes, J. T. Chem. Phys. Left. 1989, 162, 19. Borgis, D.; Hynes, J. T. J . Chem. Phys. 1991, 94, 3619. Borgis, D.; Hynes, J. T.; Chem. Phys. 1993, 170, 3 15. (7) Morillo, M.; Cukier, R. I. J . Chem. Phys. 1990, 92, 4833. ( 8 ) Suhez, A.; Silbey, R. J . Chem. Phys. 1991, 94, 4809. (9) Berendsen, H. J. C.; Mavri, J. J. Phys. Chem. 1993, 97, 13464. Mavri, J.; Berendsen, H. J. C.; van Gunsteren, W. F. J . Phys. Chem. 1993, 97, 13469. (10) Lobaugh, J.; Voth, G. A. J . Chem. Phys. 1994, 100, 3039. Voth, G. A,; Chandler, D.; Miller, W. H. J. Chem. Phys. 1989, 91, 7749. (11) Warshel, A.; Chu, Z. T. J. Chem. Phys. 1990, 93, 4003. Hwang, J. K.; Chu, Z. T.; Yadar, A.; Warshel, A. J . Phys. Chem. 1991, 95, 8445. (12) Bala, P.; Lesyng, B.; McCammon, J. A. Chem. Phys. 1994, 180, 271. (13) Staib, A.; Borgis, D.; Hynes, J. T. in press. (14) Hammes-Schiffer, S.; Tully, J. C. J. Chem. Phys. 1994, 101,4657. (15) For an application of a different surface hopping method to
vibrational relaxation, see the following: Herman, M. F.; Arce, J. C. Chem. Phys. 1994, 183, 335. Arce, J. C.; Herman, M. F. J. Chem. Phys. 1994, 101, 7520. (16) Barbara, P. F.; Walsh, P. K.; Brus, L. E. J . Phys. Chem. 1989, 93, 29. (17) For an experimental example of vibrational excitation enhancing
the rate of an excited-state proton transfer reaction, see: Hineman, M. F.; Brucker, G. A.; Kelley, D. F.; Bernstein, E. R. J. Chem. Phys. 1992, 97, 3341. (18) Tully, J. C. J . Chem. Phys. 1990, 93, 1061. (19) This dominance of the near-resonant process has also been observed
in semiclassical and quantum mechanical calculations of excited-state-toexcited-state hydrogen atom transfer in the gas phase, as discussed in: Garrett, B. C.; Abusalbi, N.; Kouri, D. J.; Truhlar, D. G . J. Chem. Phys. 1985, 83, 2252. (20) Guettler, R. D.; Jones, G. C., Jr.; Posey, L. A,; Zare, R. N. Science 1994, 266, 259.
Jp943282W
