The Kinetic Effect of Internal Hydrogen Bonds on Proton-Coupled

Transient absorption data allowed direct determination of the rate constant for these intramolecular, bidirectional, and concerted PCET (CEP) reaction...
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J. Phys. Chem. B 2009, 113, 16214–16225

The Kinetic Effect of Internal Hydrogen Bonds on Proton-Coupled Electron Transfer from Phenols: A Theoretical Analysis with Modeling of Experimental Data Linus O. Johannissen,† Tania Irebo, Martin Sjo¨din, Olof Johansson, and Leif Hammarstro¨m* Department of Photochemistry and Molecular Science, Uppsala UniVersity, Box 523, SE-751 20 Uppsala, Sweden ReceiVed: May 25, 2009; ReVised Manuscript ReceiVed: October 20, 2009

Proton-coupled electron transfer (PCET) was studied in two biomimetic covalently linked Ru(bpy)3-tyrosine complexes with the phenolic proton hydrogen-bonded to an internal carboxylate group. The phenolic group is either a salicylic acid (o-hydroxybenzoic acid, SA) or an o-hydroxyphenyl-acetic acid (PA), where the former gives a resonance-assisted hydrogen bond. Transient absorption data allowed direct determination of the rate constant for these intramolecular, bidirectional, and concerted PCET (CEP) reactions, as a function of temperature and H/D isotope. We found, unexpectedly, that the hydrogen bond in SA is in fact weaker than the hydrogen bond in the complex with PA, which forced us to reassess an earlier hypothesis that the proton coupling term for CEP with SA is increased by a stronger hydrogen bond. Consequently, the kinetic data was modeled numerically using a quantum mechanical rate expression. Sufficient experimentally determined observables were available to give robust and well-determined parameter values. This analysis, coupled with DFT/B3LYP and MP2 calculations and MD simulations, gave a detailed insight into the parameters that control the CEP reactions, and the effect of internal hydrogen bonds. We observed that a model with a static proton-tunneling distance is unable to describe the reaction correctly, requiring unrealistic values for the equilibrium proton-tunneling distances. Instead, when promoting vibrations that modulate the proton donor-acceptor distance were included, satisfactory fits to the experimental data were obtained, with parameter values that agree with DFT calculations and MD simulations. According to these results, it is in fact the weaker hydrogen bond of SA which increases the proton coupling. The inner reorganization energy of the phenolic groups is a significant factor contributing to the CEP barriers, but this is reduced by the hydrogen bonds to 0.35 and 0.50 eV for the two complexes. The promoting vibrations increase the rate of CEP by over 2 orders of magnitude, and dramatically reduce the kinetic isotope effect from ca. 40 for the static case to a modest value of 2-3. Introduction Proton-coupled electron transfer (PCET) attracts rapidly increasing attention because of its fundamental importance in diverse areas of chemistry and biology.1-6 A concerted PCET (CEP) is an important mechanism for many redox enzymes, since the simultaneous coupled proton transfer allows oxidation to occur at small reaction free energies by maintaining charge neutrality. Bidirectional PCET, in which the proton and electron are transferred in opposite directions, is essential in many radical enzymes where long-range electron transfer is coupled to shortrange proton transfer.7,8 For example, TyrZ in photosystem II supplies the oxidative equivalents required for water oxidation to the manganese cluster via PCET.9-13 Understanding the mechanism of such reactions is critical for the current efforts to design molecular systems for solar fuel generation by artificial photosynthesis.14-16 Much research has focused on concerted, bidirectional PCET reactions, as observed for the intramolecular PCET oxidation of tyrosine to photogenerated [Ru(bpy)3]3+ or *[Re(CO)3(bpy)(PPh3)]+ complexes, in mimics of TyrZ oxidation.17-24 The proton transfer (PT) component in this biomimetic reaction occurs from * To whom correspondence should be addressed. E-mail: [email protected]. † Current address: School of Chemical Engineering and Analytical Science, Manchester Interdisciplinary Biocentre, The University of Manchester, 131 Princess Street, Manchester M1 7DN, U.K.

tyrosine to bulk water, whereas in the PSII reaction PT is from TyrZ to a hydrogen-bonded histidine. PCET from hydrogenbonded phenols has also been studied by bimolecular or electrochemical methods, in organic solvents25-29 as well as in aqueous solution.30,31 Recently, intramolecular phenol oxidation in a phenol-imidazole unit linked to a photoexcited porphyrin in a bioinspired assembly was reported.32 In a recent report, some of us described the kinetics of intermolecular PCET between [Ru(bpy)3]3+ and two differently substituted phenols with an internal hydrogen bond to a carboxylate group, and could conclude that it occurred by a CEP mechanism.30 As the solution pH and thus the protonation state of the complexes was varied, the PCET rate constant spanned 4 orders of magnitude for the same complex (kPCET ) 102-106 s-1), depending on whether water or the carboxylate group was the primary proton acceptor. The pure electron transfer (ET) from phenolate to the RuIII unit was even more rapid (kET ) 108 s-1). These results show the large effects that the protonation state and hydrogen bond situation may have on a CEP reaction. There has been much debate over which factors contribute to the large variation in rate with different hydrogen-bonding proton acceptors, and between a CEP and a pure ET, for this type of CEP reactions. The proton vibrational wave function overlap in the reactant and product states (the proton coupling) has been emphasized as perhaps the most important factor.23,33,34

10.1021/jp9048633 CCC: $40.75  2009 American Chemical Society Published on Web 11/19/2009

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kCEP )

∑ Pµ ∑ µ

ν

q ∆Gµν



1 |V | 2 2π µν

{

q -∆Gµν 4π3 exp RΤ λRTp2

} (1)

vib (∆G0 + ∆Eµν + λ)2 ) 4λ

(2)

The rate depends on the Marcus parameters in the exponential term of eq 1 as well as the coupling Vµν for each vibrational state µ and ν of the transferring proton in the reactants and products, respectively (O-H vibration). Pµ is the Boltzmann vib is the energy factor for the µth state of the reactant, and ∆Eµν difference between states µ and ν, which are, for a quantum Morse oscillator,37 Figure 1. Structures of the complexes studied.

Evib n ) (n + 1/2)pω We have on the other hand argued that the internal reorganization energy (λi) for phenols is higher for CEP than ET18,20 but that λi may be reduced in the case of short hydrogen bonds to the phenols.18,20,30 We also argued that the small kinetic isotope effects (KIEs) typically observed experimentally (KIE ≈ 1.5 - 3) may indicate that the proton coupling is not such a strongly retarding factor in the phenolic model systems.20 Finally, an obviously important factor is the pKa of the proton accepting base, which modulates the phenol redox potential and therefore the CEP driving force. Recent experimental studies have also verified the expected variation of the CEP rate constant with base pKa,28,31 and the same trend was also shown qualitatively by Linschitz and co-workers.25 In a recent study of seven phenol derivatives, Mayer and co-workers27 showed a straightforward dependence of the phenol oxidation rate on driving force, but surprisingly, they were unable to find correlations with any of the other parameters that described, e.g., the hydrogen bond length or bond strength. This is in contrast to our results30,35 where the relative rates could not be explained by the difference in driving force alone. Instead, we suggested a stronger hydrogen bond partially offsetting a less favorable driving force; this hypothesis is revisited in the current study. To fully understand the origins of the effect on PCET of hydrogen bonding between the proton donor and acceptor, we present in this paper an in-depth analysis of the kinetics of unimolecular CEP in the two compounds Ru-SA and Ru-PA (Figure 1). We present for the first time experimental activation energies and temperature dependent kinetic isotope effects (KIEs) for a bidirectional CEP reaction in aqueous solution, from direct measurements of the rates in intramolecular model complexes with an internal hydrogen bond. The experiments yield precise rate constant data without complications and uncertainties related to bimolecular or heterogeneous reaction steps, and to simulations of electrochemical data. Furthermore, we use this data to examine, by theoretical calculation and modeling of the data, how different parameters contribute to the difference in rates for the two hydrogen-bonded systems. Specifically, we determine the relative importance of variations in reorganization energy and proton coupling, and how the latter is affected by donor-acceptor distance fluctuations (“promoting vibrations”) along the hydrogen bond that reduce the protontunneling distance. Model for Concerted PCET. The rates and isotope effects were measured over a wide range of temperatures, and then modeled using a complete rate expression:36

((n + 1/2)pω)2 4De

(3)

where n is µ or ν. The majority of the temperature dependence of the rate constantsthe observed activation energysarises from the Marcus activation free energy, ∆Gq, which depends on the driving force, ∆G0, and the reorganization energy, λ, although the Boltzmann distribution of excited states may give some additional contribution to the activation energy. For a nonadiabatic reaction, the vibronic coupling term Vµν is23

Vµν ≈ VET〈φµ |φν〉

(4)

where VET is the electronic coupling term and the bracketed term is the overlap between the reactant and product vibrational wave functions for states µ and νsthe proton coupling term. For very similar sets of reactants, for which VET is expected to be very similar, the magnitude of Vµν informs on the relative strengths of the proton coupling. Since the wave function overlap is directly dependent on the tunneling distance, and the other terms in eqs 1-3 are largely isotope-independent, the kinetic isotope effect (KIE) depends strongly on the proton coupling. Proton wave functions are much more localized than electronic wave functions due to the greater mass of the proton, making PT very sensitive to the tunneling distance. Therefore, vibrations coupled to the transfer coordinate that decrease the proton donor-acceptor (D-A) distance and increase the probability of tunnelingsso-called promoting vibrationsscan cause the majority of CEP events to occur over distances that are lower than the average separation. Strictly speaking, the KIE therefore informs on the dominant tunneling distance. Numerical Modeling of CEP Rates. Important developments in the theoretical treatment of PCET reactions have been made by Hammes-Schiffer and co-workers,38-40 who recently incorporated donor-acceptor distance fluctuations in an enzyme as a linear modulation of the vibronic coupling.34 Here, we employ a modification of the model of Kuznetsov and Ulstrup,41 previously implemented by Knapp et al.,42 Meyer et al.,43 Johannissen et al.,44 and Hay et al.;45 in this model, the tunneling probability is proportional to the square of the overlap of the reactant and product proton wave functions, and a promoting vibration increases the rate by modulating this term. λ and VET can be obtained by fitting to eqs 1-4. A promoting vibration is here modeled as a classical harmonic oscillator that modulates the donor-acceptor (D-A) distance, and therefore the H/D tunneling distance, as illustrated in Figure

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Figure 2. The effect of a promoting vibration on the proton-tunneling distance. The large circles represent the donor and acceptor, the small filled circle the proton bound to the donor, and the dotted-line circle the proton bound to the acceptor; φ0,R and φ0,P are the ground-state reactant and product proton wave functions, respectively. At the transition state, where quantum degeneracy has been achieved, r0 is the tunneling distance corresponding to the equilibrium donor-acceptor separation. The promoting vibration decreases the tunneling distance by rX, thus achieving a new tunneling distance ∆r, which increases the overlap between the reactant and product proton wave functions.

2 (a comparison of the effect of classical and quantum harmonic oscillators is presented in section S3 of the Supporting Information; the effect was found to be minor). Starting from the tunneling distance r0 at the equilibrium D-A separation (at the transtition state, i.e., a configuration with quantum degeneracy between reactant and product), the force constant kX for the promoting vibration, which relates to its frequency ωX and effective mass mX by Hooke’s law, governs the energy EX required to deviate from r0 by a distance rX along a unitless D-H · · · A coordinate X, to achieve a given tunneling distance ∆r:42

∆r ) r0 - rX

(5)

X ) rX√mXωX /p

(6a)

1 EX ) pωXX2 2

(6b)

Note that only ∆r and kX are needed, since combining eqs 6a and 6b gives EX ) 1/2rX2kX. The nuclear wave function overlap at temperature T is the integral of the overlap terms for all possible values of ∆r, weighted by their respective population:

〈φµ |φν〉 )

r ∫r)0 0

[

〈φµ|φν〉r

exp(-EX /kBT) ∞ exp(-EX /kBT) ∫∆r)0

]

(7)

full quantum mechanical expression, with only one λ term for all vibrational levels and ∆r values. There are therefore only three variable parameters in the model which are modified during the fitting, while there are four independent experimental observables to which the model is fitted. These observables are kCEP, Ea, ∆Ea (the difference in activation energy between the two isotopes), and the kinetic isotope effect (KIE) at 298 Kssee results belowswhile the independent model parameters are VET, λ, and kX; the parameters that define the wave function for the transferring proton/deuteron and the equilibrium tunneling distance r0 are determined a priori from molecular models (using DFT/B3LYP and MP2) and are not modified to fit the data. Vibrational modes which cause compression along the donor-acceptor axis have previously been shown to enhance the tunneling probability across a hydrogen bond in internal PT; for example, the tunneling splitting for the extensively studied PT across the internal hydrogen bond of tropolone is enhanced by excitation of specific vibrational modes (e.g., see ref 46 and refs 1-15 therein). More recently, donor-acceptor distance fluctuations have been invoked to explain the temperature-dependent KIEs observed for certain enzymatic PT reactions,41,42,47,48 and were attributed to large-scale motions involving multiple amino acid residues.49-52 Furthermore, if the KIEs are only very weakly temperature-dependent, such promoting vibrations were not expected to contribute significantly to the rate.42 It has recently been shown, however, that smallscale vibrations can act as promoting vibrations34,44 while not necessarily causing strongly temperature dependent KIEs.44 Costentin et al.29 studied hydrogen-bonded phenols including a distribution of tunneling distances in their model. They were, however, unable to fit their electrochemical data with realistic parameters, so a possible effect of promoting vibrations could not be demonstrated. Donor-acceptor distance fluctuations have also recently been summoned by Presse´, Nocera, and co-workers to explain an inverse KIE (kH/kD < 1) in an ET across a hydrogen bond, where the D-A vibration modulates VET.53 This differs from the bidirectional CEP reactions studied here where the electron and proton are transferred in opposite directions, and thus the promoting vibration is not expected to have an effect on VET. Nevertheless, their study provides another important illustration of the impact dynamics can have on PCET reactions, and the potential risks associated with ignoring such contributions. Results and Discussion 1. Experimental Results. 1.1. Kinetic Data. The PCET rate constants were obtained using a flash-quenched method with transient absorption detection described previously.17,35 The Ru compound was excited by a 0, while eq 1 gives KIEs that are nearly temperature independent and a very small ∆Ea value that lies significantly below experimental error (95% confidence level); the small temperature dependence of the KIEs in this model arises from excited state contributions. In conclusion, attempts to model the kinetic data with a fixed proton-tunneling distance give significant deviation from the data, and results in parameter values that appear unrealistic: too small ∆r and too large λ. 3.3. Incorporating Promoting Vibrations in the Model. The kinetic data sets for Ru-SA and Ru-PA at 298 K were modeled using an r0 value of 0.6 Å (see section 2.4). Figure 6 shows how the KIE and ∆Ea vary with the promoting vibration force constant, kX. The KIE increases with kX as the dominant tunneling distance increases. As kX increases, a small increase in temperatureswhich increases the available range of tunneling distancesshas a larger effect on the tunneling probability of D than H, causing also ∆Ea to increase. Note that, at very large kX values (not shown), ∆Ea decreases again because D-A compression becomes less significant at thermal energies around room temperature. The general procedure for reproducing the experimental kinetics using eq 8 is as follows: (i) r0, ∆G0, and the parameters that describe the H/D wave functions are fixed; (ii) kX is modified until the experimental value of KIE at 298 K is reproduced Figure 6a; (iii) λ is modified until the activation energy Ea (from a fit to eq 10a) matches the experimental value in Table 1 (note that λ has almost no effect on the KIE); (iv) VET is modified until kCEP(H) at 298 K agrees with the experimental value. Note that the parameters are not varied to obtain the correct ∆Ea, but the value of ∆Ea obtained corresponds within experimental uncertainty to the experimental value for both compounds. The resulting parameter values are as follows (see also Table 4). To reproduce the experimentally determined KIE for Ru-PA of 2.8 at 298 K, kX ) 21.2 J m-2 was used. This value gives a ∆Ea of 2.7 kJ mol-1, very similar to the experimental value of 2.9 ( 1.4, showing consistency of the parameters. For Ru-SA, the experimentally observed KIE of 1.9 at 298 K requires a softer promoting vibration, with kX ) 11.9 J m-2, since a smaller KIE requires a shorter dominant tunneling distance. A lower

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TABLE 4: Best-Fit Parameters for Modeling the Experimental Data to eq 8a model

r0b (Å)

VET (kJ mol-1)

fixed tunneling distance promoting vibration

0.23 0.6c

2.64 4.90

fixed tunneling distance promoting vibration

0.29 0.6c

2.56 3.82

kX (J m-2)

λ (kJ mol-1)

Ea(H) (kJ mol-1)

Ea(D) (kJ mol-1)

∆Ea (kJ mol-1)

11.9d

Ru-SA 148 132

41.0 40.9

41.3 42.5

0.33 1.54

21.2d

Ru-PA 173 153

35.2 35.2

35.9 37.9

0.66 2.73

a The rightmost three columns show activation parameters from a fit of the simulated data to eq 10a. kCEP(H) and KIE at 298 K are not shown but have the same values as in Table 1. b For the fixed tunneling distance model, ∆r ) r0. c Fixed according to DFT calculations. d Fitted to match experimental values for KIE.

Figure 6. Effect of the promoting vibration force constant kX on (A) the KIE and (B) ∆Ea at 298 K, for rate constants calculated with Ru-SA input parameters (Table 4). Force constant values that reproduce the experimental KIE and ∆Ea values for Ru-SA and Ru-PA at r0 ) 0.6 are shown using black dotted lines.

kX value is in agreement with the results from the MD simulations and the relative hydrogen bond strengths for the two systems. Also, the kX value obtained for Ru-SA gives a significantly larger value for ∆Ea than the fixed tunneling distance model, agreeing within experimental error with the experimental value. With these force constants, the frequencies obtained from the MD simulations above suggest a reduced mass of ca. 3-4 au, somewhat smaller than the 8 au for two oxygen atoms. The frequencies obtained from the PM3 MD simulations are somewhat qualitative, however, and the hydrogen bonds for SA and PA calculated using PM3 are stronger than the more accurate B3LYP/6-31G(d)/PCM values (Table 2), leading to a potential overestimate of the vibrational frequenciessif smaller frequencies were used, then a larger mass would be obtained for the same force constants (kX ) mX × ωX2). The ratio of force constants kX(PA):kX(SA) ) 1.78 is larger than the squared ratio of the vibrational frequencies (3002/2602 ) 1.33) estimated from the spectral densities, although it is likely that the vibration of PA will have a somewhat larger effective mass, which will increase the ratio. Note that the promoting vibrations are treated as harmonic oscillators, even though the frequencies obtained from the MD simulations are of the same order as kBT (∼220 cm-1), which suggests that quantum effects could be important. The difference between classical and quantum harmonic oscillators is discussed in the Supporting Information (section S3), but this only leads to a slight underestimation of kX, and the main concern of this study is the relative magnitudes of kX between the two systems, i.e., kX(Ru-PA) > kX(Ru-SA). Crucially, the force constants used to model the experimental data, which correctly reproduce the experimental KIEs and ∆Ea values, are qualitatively corroborated by the MD simulations and the DFT calculations of the relative hydrogen bond strengths. With the above parameter values, the temperature-dependent data was modeled according to eq 8 by varying λ and VET, giving very close agreement with the experimental data (Figure 7). The

inset shows the temperature dependence of KIEs for this model as well as for the model with a fixed tunneling distance. While the latter fails to reproduce the temperature dependence of the KIE, the promoting vibration model gives good agreement with experiments; values of Ea, ∆Ea, and KIE agree well and the r0 values agree with DFT estimates. Parameter values for the simulations are given in Table 4. These fits give lower λ values than with a fixed tunneling distance and a slightly smaller difference in λ between the two systems, more in line with the λi difference from DFT calculations, since part of the observed activation energy is due to the promoting vibration, i.e., the temperature dependent distribution of tunneling distances according to the square-bracketed term of eq 8. Contributions to the rate from vibrationally excited reactants (µ * 0 in eq 8) also increase the observed activation energy, but they were found to be quite small for Ru-SA and Ru-PA under our conditions. Since the driving forces are weak, the contribution of transfers into excited product states (ν * 0) is also small, although it would become more significant at longer equilibrium tunneling distances. If we assume a reaction entropy of ∆S0 ) 0.05 kJ mol-1 K-1, then the values for electronic coupling (VET) and reorganization energy (λ) are affected, while the other parameters remain nearly the same (Table S3 in the Supporting Information): VET decreases 5-fold and λ decreases by ca. 30 kJ mol-1. The difference in these parameter values between Ru-SA and Ru-PA remains essentially unchanged, however. A reaction entropy of ∆S0 ) -0.05 kJ mol-1K-1 gives similar effects on VET and λ but in the opposite direction. Crucially, however, it is clear that, within the framework of eq 8, promoting vibrations are needed to explain the ∆Ea and KIEs of the two compounds with physically reasonable equilibrium PT distances, and that a larger kX is required to obtain the larger KIE of Ru-PA. Figure 8 shows the effect of the promoting vibration on the reaction. Very little PCET takes place at the equilibrium tunneling distances, r0; instead, the majority of PCET for Ru-PA occur at around 0.30 Å for H and 0.24 Å for D, and

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Figure 7. CEP rate constants for (A) Ru-SA and (B) Ru-PA, with solid lines corresponding to rates modeled with promoting vibrations. Insets: ln(KIE) from linear fits to experimental data (open circles), ln(KIE) from rates modeled with fixed tunneling distances (dotted lines), and ln(KIE) from rates modeled with promoting vibrations (solid lines). The insets are for qualitative comparison onlysfor a quantitative comparison of KIEs, see Tables 3 and 4.

Figure 8. Rate constant contributions at different tunneling distances ∆r binned at 0.02 Å intervals for H (solid lines) and D (dotted lines) for Ru-PA (black lines) and Ru-SA (gray lines).

for Ru-SA at around 0.22 Å for H and 0.18 Å for D. The figure highlights the importance of promoting vibrations, without which the PCET rate would be orders of magnitude slower. Figure 8 also illustrates the need for more barrier compression for the heavier isotope because of its more localized wave function. If there were no promoting vibration and proton tunneling occurred at the r0 values, then this model gives kCEP(H)(298 K) ) 1.6 × 103 s-1 for Ru-SA and 1.0 × 104 s-1 for Ru-PA, much smaller than the observed rates of 1.6 × 105 s-1 and 4.8 × 105 s-1, respectively, and the KIEs would be 37 for Ru-SA and 41 for Ru-PA. The presence of promoting vibrations explains how the KIEs of many PCET reactions are modest, around 2-3, in spite of the large difference in proton and deuteron tunneling probabilities from typical equilibrium reactant structures. 4. Final Remarks and General Implications. Although many principles of PCET have gradually been unraveled in recent years, important information is still lacking, e.g., the effects of internal hydrogen bonds on the transferring proton. In some previous bimolecular studies of PCET from phenols, the rate was correlated only with the driving force, which is determined mainly by the pKa of the base.27,31 In another comparison of three amine- or pyridylphenols, it was instead concluded that conjugation between the base and phenol increases the rate over that of nonconjugated systems, but that the pKa of the base was not important.28 For bimolecular PCET reactions of the present SA and PA units, we concluded that the difference in rate constant could not be explained by only the difference in pKa value (redox potential) but suggested additional effects due to the different hydrogen bonds.30 Ishikita et al.24 reported a computational study of a phenol with H2O or

HPO42- as the hydrogen-bonded proton acceptor, concluding that the latter gives a faster PCET reaction mainly because of an ca. 0.2 Å shorter hydrogen bond. There is in the case with H2O as a proton acceptor, however, an uncertainty in the driving force;21,24,29,31 moreover, donor-acceptor distance fluctuations were not included in the model and the available experimental data was for only one temperature giving but two experimental observables to fit. Costentin et al.29 attempted to model PCET rates in a hydrogen-bonded phenol using a distribution of tunneling distances but were unable to fit their electrochemical data with a reasonable value of the transmission coefficient, so that a possible effect of donor-acceptor distance fluctuations could not be demonstrated. Clearly, a coherent and experimentally verified picture of the parameters governing the PCET reactions of phenols is lacking. In the present study, modeling of accurate experimental data covering the temperature dependence of both rate constants and KIEs for two related systems has given clearer and deeper insight. Our results show that modeling the experimental data with a fixed proton-tunneling distance leads to less satisfactory fits and parameter values. The reorganization energy (λ) is significantly larger than expected from DFT calculations and previous calculated and experimental values,18,23 and the proton-tunneling distances for both systems are less than one-half of the estimated equilibrium tunneling distance. At the same time, the difference in activation energy in D2O and H2O (∆Ea) is much lower than the experimental values. When instead a promoting vibration is included, corresponding to a vibration along the hydrogen bond between the proton donor and acceptor groups (the phenol and carboxylate), λ for both systems is decreased because part of the overall activation energy arises from this vibration. Crucially, both the equilibrium tunneling distance r0 and the λ values Ru-SA and Ru-PA agree with the DFT calculations and estimates (see above). We thus show the importance of promoting vibrations for PCET in small molecular systems that are not embedded in a protein. Promoting vibrations are not a particular property of enzyme reactions, as is often discussed, though enzymes may facilitate such vibrations by coupling to vibrational modes of specific amino acid residues51,71 or binding to the substrate in the necessary conformation.72 The effect of promoting vibrations is significant:49,73,74 in the present molecules, they increase the PCET rate 100-fold for Ru-SA and 50-fold for Ru-PA as compared to the rate at the equilibrium tunneling distance (Figure 8), and drastically reduce the KIE by 1 order of magnitude, to a modest value of 2-3. Nevertheless, if the equilibrium tunneling distance r0 is larger, higher

Proton-Coupled Electron Transfer from Phenols KIEs can be obtained; we note, for example, that HammesSchiffer and co-workers reproduced the high KIEs (ca. 50) of lipoxygenase with a similar force constant for promoting vibrations as we use here, and an ca. 0.3 Å longer r0.34 In the following paragraphs, we comment on the relative influence of the different parameters governing the PCET reactions. The proton coupling factor is a very important difference from pure electron transfer reactions, but the promoting vibrations reduce the importance of this “retardation factor”. In the current study, switching off the promoting vibration in the simulation while keeping all other parameters the same decreases the rate 50- and 100-fold; therefore, since kPCET ∝ Vµν2, the promoting vibration increases the proton coupling by about 1 order of magnitude. More precisely, the promoting vibration increases the effective proton wave function overlap (the bracketed term in eq 8) for SA from 1.7 × 10-2 to 1.7 × 10-1, and for PA from 1.4 × 10-2 to 9.8 × 10-2 (compared to unity for total overlap, analogous to pure ET without changes in the proton equilibrium position). The promoting vibrations give an additional contribution to the observed activation energy that is important to take into account in the analysis of data, and they especially affect evaluation of the reorganization energy. The pKa value of the proton-accepting base is obviously of importance, as it to a large extent determines the phenol redox potential by the free energy of proton transfer from the phenol/ phenoxyl radical. Note, however, that the hydrogen bond itself does not lower the potential, as is clear from a thermodynamic cycle. The hydrogen bond in the phenoxyl radical state is typically weak, and a strong hydrogen bond in the phenol state stabilizes the reduced state, leading instead to a higher redox potential than for a non-hydrogen-bonded system with the same proton acceptor. The reorganization energy for the present CEP reactions of 1.3-1.5 eV, from our modeling of experimental data, is indeed higher than that for a typical outer-sphere electron transfer in polar solvents. The inner reorganization energy is about 0.35-0.5 eV according to our DFT calculations, which agrees with earlier predictions20 and more recent DFT calculations on related phenols.28,29 The experimental data for the resonanceassisted hydrogen bond in Ru-SA gives a lower reorganization energy than Ru-PA, which is in qualitative agreement with DFT results on pyridinephenols.28 The previous suggestion that the stronger hydrogen bond offsets the more unfavorable driving force was based on the assumption that for very similar compounds the resonanceassisted hydrogen bond will also be the stronger hydrogen bond.30,56 It has also been proposed that the rate of PCET across a resonance-assisted hydrogen bond is enhanced due to strong hydrogen bonding which leads to a flatter proton transfer potential.28 While this argument is true for a fixed tunneling distance or where the stronger hydrogen bond leads to a shorter tunneling distance, we instead propose that the weaker hydrogen bond in Ru-SA leads to a rate enhancement because of a softer promoting vibration, which causes a shorter average protontunneling distance and therefore a stronger proton coupling (note, however, that this leads to a flatter donor-acceptor compression potential and therefore also gives rise to a flatter proton transfer potential). We therefore point out the importance of distinguishing short, strong, and stiff hydrogen bonds, which are often used synonymously. Proton tunneling is facilitated by a short hydrogen bond (with a lower r0), while a stronger hydrogen bond is in general also stiffer, which reduces the effect of promoting vibrations and leads to slower rates. This distinction is illustrated clearly by the present results: according to

J. Phys. Chem. B, Vol. 113, No. 50, 2009 16223 DFT calculations, the internal hydrogen bond in SA has somewhat shorter O-O and O-H distances than the hydrogen bond in PA, while also being weaker due to the unfavorable O-H · · · O angle. The observed PCET rate constant is higher in Ru-PA only because the higher carboxylic acid pKa value makes the driving force larger. The softer promoting vibration in Ru-SA compensates to a large extent for the lower driving force, making the difference in rate between the two compounds rather small. Conclusions In conclusion, we have obtained new data for bidirectional PCET in Ru(bpy)3-phenol complexes with two different internal hydrogen bonds. From direct kinetic measurements of an intramolecular reaction, free of the complications associated with diffusion-influenced reactions, we acquired accurate data for both the temperature and the H/D-isotope dependence of the concerted PCET (CEP) rate constant. We numerically modeled the experimental kinetics and found that, when a fixed proton-tunneling distance is employed, the fit is not quite satisfactory, and, more importantly, some of the parameter values obtained are physically unreasonable. By incorporating promoting vibrations that modulate the proton-tunneling distance, the fit to the data is quite satisfactory, and the parameter values obtained agree with estimates from DFT/B3LYP and MP2 calculations. Our data gives four independent experimental parameters for each complex, which is sufficient to determine the three fit parameters according to the rate equation. Additional input parameters which were not modified during the modeling procedure were determined from DFT calculations. In addition, DFT calculations and MD simulations give independent support for these three parameters: the proton-tunneling distance, the promoting vibration force constant, and the reorganization energy for the two complexes. Thus, the fit results are robust and reliable. We could thus elucidate in detail the factors that govern the rate of a PCET reaction with hydrogen-bonded phenols. For Ru-SA and Ru-PA, the promoting vibrations increase the PCET reaction rate by over 2 orders of magnitude compared with the rate at the equilibrium tunneling distances, and reduce the KIE from 30-40 to 1.9-2.8. This shows that promoting vibrations can strongly affect PCET reactions also in small model complexes, without involvement of a protein environment. The inner reorganization energy (λi) for proton-coupled phenol oxidation is large, ca. 0.35-0.40 eV according to DFT calculations, which contributes significantly to the activation energy and decreases the rate relative to a typical outer-sphere electron transfer reaction. In contrast to the common notion that a stronger hydrogen bond is also shorter, we found that, while the resonance-assisted hydrogen bond in Ru-SA is shorter than the hydrogen-bond in Ru-PA, it is significantly less linear and therefore somewhat weaker. Ru-SA shows the lower λi value of the two complexes, presumably due to the resonance structure, and the lower total λ obtained from modeling the experimental data. The hydrogen bond in Ru-PA is stronger and stiffer, which leads to a smaller proton coupling term and therefore the larger observed KIE. Our results give general insight into the effect of hydrogen bonds on bidirectional PCET reactions. This is important for interpreting similar reactions in proteins and model systems. They will also be useful for further design of model systems and functional molecular devices involving PCET.

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Experimental Section Preparation and characterization of Ru-SA or Ru-PA has been described elsewhere.35 Solutions were prepared in Milli-Q water (17 MΩ) or deuterium oxide (99.9% atom, Aldrich) using a 50:50 mixture of disodium hydrogen phosphate and boric acid as buffer, either 5 or 0.5 mM each. The rate constant showed no difference between the buffer concentrations used. Samples contained 15-40 mM methyl viologen dichloride (Aldrich, 98%) and ca. 30 µM Ru-SA or Ru-PA. The pH was adjusted to ca. pH 7 with NaOH(aq) or HCl(aq). All samples were purged with Ar(g) for at least 10 min before measurement and kept under an Ar(g) atmosphere during measurement. The temperature was controlled with a water thermostat and measured directly in the sample with a Templec thermometer. For more experimental details and control experiments, see ref 35. The electron transfer reaction was investigated using a laser flash photolysis with transient absorption detection described previously.35 A Q-switched Nd:YAG laser (Quantel Brilliant B) is used to produce the excitation light that via an OPO (Opotek) gives output pulses of ca. 7 ns at 460 nm with ca. 20 mJ/pulse. The transient absorption was detected using an Applied Photophysics LKS.60 setup with the analyzing light, produced by a pulsed xenon lamp that was directed through the sample perpendicular to the excitation light, and passed through a monochromator before hitting the photomultiplier tube (Hamamatsu 1P28 or R928). The PMT signal was digitized using a HP Infinitum digital oscilloscope (2 Gsamples/s). The PCET rate constant was obtained by fitting the 450 nm signal to a single-exponential function. Each data point is an average of analysis results from at least four traces which in turn is an average of at least eight shots. The standard deviation of the reported rate constants is within 10% of the reported value. Acknowledgment. This work was supported by The Swedish Research Council, The Swedish Energy Agency, The Swedish Foundation for Strategic Research, the Knut and Alice Wallenberg Foundation, and the EU FP7/Energy project 212508 “SOLAR-H2”. Supporting Information Available: Additional figures, tables, equations, and textual explanations. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Cukier, R. I.; Nocera, D. G. Annu. ReV. Phys. Chem. 1998, 49, 337. (2) Chang, C. J.; Chang, M. C. Y.; Damrauer, N. H.; Nocera, D. G. Biochim. Biophys. Acta 2004, 1655, 13. (3) Mayer, J. M. Annu. ReV. Phys. Chem. 2004, 55, 363. (4) Hammes-Schiffer, S. Acc. Chem. Res. 2006, 39, 93. (5) Huynh, M. H. V.; Meyer, T. J. Chem. ReV. 2007, 107, 5004. (6) Hammarstrom, L.; Styring, S. Philos. Trans. R. Soc. London, Ser. B 2008, 363, 1283. (7) Stubbe, J.; van Der Donk, W. A. Chem. ReV. 1998, 98, 705. (8) Stubbe, J.; Nocera, D. G.; Yee, C. S.; Chang, M. C. Y. Chem. ReV. 2003, 103, 2167. (9) Hoganson, C. W.; Babcock, G. T. Science 1997, 277, 1953. (10) Tommos, C.; Babcock, G. T. Biochim. Biophys. Acta 2000, 1458, 199. (11) Rappaport, F.; Lavergne, J. Biochim. Biophys. Acta 2001, 1503, 246. (12) Renger, G. Biochim. Biophys. Acta 2004, 1655, 195. (13) Haumann, M.; Liebisch, P.; Muller, C.; Barra, M.; Grabolle, M.; Dau, H. Science 2005, 310, 1019. (14) Sun, L.; Hammarstrom, L.; Akermark, B.; Styring, S. Chem. Soc. ReV. 2001, 30, 36. (15) Alstrum-Acevedo, J. H.; Brennaman, M. K.; Meyer, T. J. Inorg. Chem. 2005, 44, 6802. (16) Lewis, N. S.; Nocera, D. G. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 15729.

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