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Intrinsic reactivity and driving force dependence in concerted proton–electron transfers to water illustrated by phenol oxidation Julien Bonin, Cyrille Costentin, Cyril Louault, Marc Robert, Mathilde Routier, and Jean-Michel Savéant1 Laboratoire d’Electrochimie Moléculaire, Unité Mixte de Recherche Université, Centre National de la Recherche Scientifique No 7591, Université Paris Diderot, Bâtiment Lavoisier, 15 rue Jean de Baïf, 75205 Paris Cedex 13, France

Three experimental techniques, laser flash photolysis, redox catalysis, and stopped-flow, were used to investigate the variation of the oxidation rate constant of phenol in neat water with the driving force offered by a series of electron acceptors. Taking into account a result previously obtained with a low–driving force electron acceptor thus allowed scanning more than half an electronvolt driving force range. Variation of the rate constant with pH showed the transition between a direct phenol oxidation reaction at low pH, where the rate constant does not vary with pH, and a stepwise reaction involving the prior deprotonation of phenol by OH− , characterized by a unity-slope variation. Analyses of the direct oxidation kinetics, based on its variation with the driving force and on the determination of H/D isotope effects, ruled out a stepwise mechanism in which electron transfer is followed by the deprotonation of the initial cation radical at the benefit of a pathway in which proton and electron are transferred concertedly. Derivation of the characteristics of counterdiffusion in termolecular reactions allowed showing that the concerted process is under activation control. It is characterized by a remarkably small reorganization energy, in line with the electrochemical counterpart of the reaction, underpinning the very peculiar behavior of water as proton acceptor when it is used as the solvent. photochemistry ∣ proton-coupled electron transfer ∣ water as proton acceptor

T

he mechanisms of proton-coupled electron transfers (PCETs), in which proton and electron transfers involve different molecular centers, is the object of active current attention in view of the role that such reactions play in many natural processes (1–3). Oxidation of phenols holds a major place in this area in view of its relevance to reactions occurring in natural systems. Photosystem II is the most prominent example (4–6), but evidence has been gathered that similar processes are involved in the functioning of several other biochemical systems (7). Another aspect of the oxidative PCETchemistry of phenols is related to other biological roles, notably their antioxidant properties (8–10). Oxidative dehydrodimerization of phenols is also an important class of reactions, being involved in the first stages of natural processes such as lignin formation (11, 12). The production of phenoxyl radicals, which eventually dimerize, is a PCET process that may involve stepwise and concerted pathways (Scheme 1). The former constitute a square reaction scheme that may involve electron transfer first, followed by proton transfer (EPT pathway) or, conversely, proton transfer first followed by electron transfer (PET pathway). In the CPET pathway, proton and electron transfers are concerted. The particular interest of CPET pathways is that they allow bypassing the highenergy intermediates involved in the stepwise pathways. The occurrence of concerted processes has been established in the oxidation of phenols bearing an attached amino group in an effort to mimic the role of histidine that captures the proton resulting from the oxidation of tyrosine in photosystem II (13–16). Similar investigations have been carried out with the www.pnas.org/cgi/doi/10.1073/pnas.0914693107

proton acceptor dispersed in nonaqueous (17, 18) or aqueous (19, 20) solutions. However, the role of water in PCET reactions, when it is used as solvent, is obviously of considerable interest with reference to natural systems. It is also an important fundamental issue. Although investigated over decades, the mechanisms of proton conduction in water are still under active experimental and theoretical scrutiny (21–24). The mechanism of PCET reactions involving water should deserve the same attention. We may note in this connection the scarcity of available experimental data concerning the case where water is the proton acceptor. One exception concerns the reduction of superoxide ions (25–27). Another exception, concerning phenol oxidation, is a series of cleverly designed experiments, nicely mimicking the oxidation of tyrosine in photosystem II, in which the variation of the log of the rate constant with pH was found to exhibit a 1∕2 slope in a substantial portion of the pH range (28–30). This latter behavior was explained by means of the highly problematic notion of pH-dependent driving force. We also note that the same behavior was also reported in the reaction of photogenerated RuIII ðbpyÞ3 (where bpy is 2,2′ bipyridine) with phenol itself (31), whereas this unexpected variation was not found in the reaction with IrIV Cl6 (32). It is not the purpose of the present contribution to detail again the reasons that the notion of a pHdependent driving force is incorrect as pointed out previously (33, 34). In short, in water with no other proton acceptor present besides water itself, water and the proton produced upon oxidation are reactants in the CPET process as depicted in Scheme 1. The driving force is then governed by the standard potential of this reaction: FE0CPET ¼ μ0H3 Oþ þ μ0ArO• − μ0ArOH − μ0H2 O (where μ0 is the standard chemical potential), which, because it is defined under standard conditions, does not depend on pH. It is equal to the pH-dependent apparent standard potential (as pictured by Pourbaix diagrams) at the fixed pH ¼ 0. It also follows that the 1∕2-slope variation with pH found in some cases (29–31), for unknown reasons, may not be taken as a diagnostic criterion of the occurrence of a CPET mechanism, as sometimes done (30). Rather, noting that little is known about the essential reactivity characteristics of H2 O-triggered CPET oxidation of phenols, the present work is an attempt to fill this gap by investigating the variation of the kinetics with the driving force offered by several Author contributions: C.C., M. Robert, and J.-M.S. designed research; J.B., C.L., and M. Routier performed research; J.B., C.C., M. Robert, and J.-M.S. analyzed data; and J.-M.S. wrote the paper. The authors declare no conflict of interest. 1

To whom correspondence should be addressed. E-mail: [email protected].

This article contains supporting information online at www.pnas.org/cgi/content/full/ 0914693107/DCSupplemental.

PNAS ∣ February 23, 2010 ∣ vol. 107 ∣ no. 8 ∣ 3367–3372

CHEMISTRY

Contributed by Jean-Michel Savéant, December 24, 2009 (sent for review October 23, 2009).

EPT ArOH

P+

+Q

0 EEPT

+

+ H3 O +

+ H2O

0 ECPET

pK

+ Q + H2 O ArOH

ArO

+ P + H3O + CPET

+ H2O

+ OH -

ArOH +

2kdim

dimer

+ArO P+

pKArOH

+Q 0 EPET

-

ArO

PET Ar: phenyl or other aryl groups. Scheme 1

Stepwise and concerted pathways.

electron acceptors in neat water and estimating the intrinsic reactivity (reactivity at driving force zero) thereof. The first of these electron acceptors was RuIII ðbpyÞ3 photogenerated in the same way as in reference 31, but in the absence of buffer. The same reaction was also investigated by a totally different technique, namely redox catalysis. In order to increase the driving force, another Ru-bpy complex, which will be called RuðbpyÞ ðester-bpyÞ2 , was used in which two of the bpys are substituted in the 4,4′ position by an ethyl ester group, while the third remains unsubstituted. Going to lower driving forces, still another Ru-bpy complex, which will be called Ruðmethyl-bpyÞ3 , was used in which all the bpys are substituted in the 4,4′ position by a methyl group (SI Appendix). In the two first cases, the variation of the oxidation rate constant with pH was inspected and the experiments were repeated in D2 O for all three electron acceptors. The data obtained previously with IrCl2− 6 (32), which provides an example of a particularly low driving force, were also used in the discussion. Uncovering the way in which the kinetics varies with the driving force offered by the electron acceptors is an essential preliminary step for a comprehension of the reaction, in particular for testing the sophisticated (35–38) or less sophisticated (16) theoretical models. Results and Discussion Oxidation of Phenol by Laser Flash Photogenerated RuIII ðbpyÞ3 . The experiments were carried out in neat water, the pH being adjusted by small addition of concentrated HCl or NaOH. The principle of the method is depicted in Scheme 2. Starting from 50 μM RuðbpyÞ2þ 3 , we found, as detailed in the SI Appendix, that in the presence of a large excess (40 mM) of methylviologen •þ have been formed (MV2þ ), 4 μM of both RuðbpyÞ3þ 3 and MV 100–200 ns after the laser pulse (all characteristic rate constants

Ru(bpy)32+

hv

*Ru(bpy)32+

Ru(bpy)32+ + MV2+ ArO -

- MV2+ dimer

Ru(bpy)33+ +ArO-

[ Ru(bpy)33+ … MV+• ]

MV +• + Ru(bpy)33+ k-1 ArO • + H +

k1 + ArOH

+ ArO • Ru(bpy) 2+ 3 2kd ArOH at equilibrium ArO- + H2 O at equilibrium

ArOH + OH-

3368 ∣

kb

kb +MV •+

ArO -+ H +

Scheme 2

+ MV 2+

k2

Ru(bpy)32+ + ArO •

Laser flash-triggered CPET reaction.

www.pnas.org/cgi/doi/10.1073/pnas.0914693107

for this part of Scheme 2 were found to be in agreement with literature data as detailed in the SI Appendix). In the absence of phenol and oxygen, the only follow-up reaction is the back electron transfer with a rate constant kb ≃ 5 × 109 M−1 s−1 . Analysis of the kinetics in the presence of phenol, leading to the rate constant of interest, may thus be derived from the RuðbpyÞ3þ 3 bleaching traces recorded after 200 ns, taking into consideration only the reactions contained in the dashed rectangle portion of Scheme 2. Particular care was exerted to remove oxygen and carbon dioxide from the reaction medium. Trace oxygen reacts with MV•þ , thus perturbing the analysis of the kinetics in the presence of phenol. Adventitious carbonates resulting from small concentrations of CO2 may distort the analysis of the reaction where water is the proton acceptor, which is the objective of this work. In all cases, phenol is introduced in excess (at least 5 mM). The sum of the concentrations of phenol and phenoxide ions may thus be considered as constant. We start the analysis with the case where the oxidation of ArOH would follow a CPET and/or an EPT pathway. The contribution of the PET pathway is also taken into account and becomes more and more important as the pH increases. The multistep kinetics may be simplified as follows, leading to the following closed-form equations (see SI Appendix): 1 1 ¼ þ kb t ½MV•þ  ½MV•þ t¼0

[1]

and ½RuIII  ¼

½RuIII t¼0 expð−kþ ½ArOHtotal × tÞ; 1 þ kb ½MV•þ t¼0 t

[2]

½ArOH ½ArO−  k1 þ k ; ½ArOHtotal ½ArOHtotal 2

[3]

with kþ ¼

which avoid multiparameter fitting of the kinetic traces at 605 and 450 nm representing MV•þ decay and the bleaching of the Ru complex, respectively. The second term in Eq. 3 corresponds to the PET pathway, whereas the first relates to the CPET and/or EPT pathways. The applicability of these equations hinges upon the validity of the following approximations. Dimerization of ArO• radicals is neglected, the CPET reaction is irreversible, and fractions of phenol and phenoxide ions remain constant in spite of the absence of buffer. A first justification of these assumptions is provided by the quality of the fitting. An example is given in Fig. 1, where it can be seen that the fit of Ru complex bleaching is excellent at all times, leading to the determination of kþ , whereas this is not the case for the MV•þ decay at long times (traces and fittings at all pHs are available in SI Appendix). It was also checked that the pseudo first-order rate constant for phenol oxidation is indeed proportional to phenol concentration. Self-consistency tests were also applied: Deriving the rate constant from the experimental data under the above assumptions, it was then checked, by a multiparameter numerical calculation, that they are indeed valid (SI Appendix). In all cases, the fractions of phenol, ½ArOH∕½ArOHtotal , and phenoxide ions, ½ArO− ∕½ArOHtotal ¼ 1 − ½ArOH∕½ArOHtotal , remain constant in the course of the reaction over the whole pH range of interest (SI Appendix). An example is given in Fig. 1D. It is their constancy, rather than that of the pH (the pH variations are computed and discussed in SI Appendix), which justifies the applicability of Eq. 3. The resulting variations of the rate constant with pH are shown in Fig. 2A together with the data likewise obtained in D2 O. Bonin et al.

Ru(bpy)32+ + MV2+ kb +MV•+

ArO-

-

MV2+

kb

k-1 k1 ArOH•++ + ArOH

k-p

ArO• + H+

kp + ArO • 2kd

kb Ru(bpy) 2+ 3 MV•+ + - MV2+

dimer

ArOH at equilibrium

ArO-+ H+ ArOH +

MV+• + Ru(bpy)33+

ArOH

ArO- + H2O at equilibrium

OHk2

Ru(bpy)33++ArOScheme 3

Ru(bpy)32+ + ArO •

Laser flash-triggered EPT reaction.

reaching the pseudo first-order rate constant. Phenol remains nevertheless in large excess (1 mM vs. 0.9 μM). Details on procedures and kinetic analyses are in SI Appendix.

Fig. 1. Oxidation of phenol by laser flash photogenerated RuIII ðbpyÞ3 (see text) at pH 3.2. (A and B) Kinetic traces at 450 and 605 nm and fitting (full lines) with Eqs. 1 and 2 and Eq. 1, respectively. (C) Variation of the pseudo first-order rate constant with phenol concentration. (D) Constancy of the phenol relative concentration; pH ¼ 2.4; 3.2; 4.0; 5.1; 6.0; 6.2; 6.3 (full line), 6.7 (dashed-dotted), 7.1 (dotted), 7.9 (dashed).

In the case where the reaction would rather follow an EPT pathway (Scheme 3), the multistep kinetics may be simplified in the same way (SI Appendix) thanks to the same assumptions (irreversibility of the oxidation reaction involves the electron transfer step in this case). The results shown in Figs. 1 and 2 may thus be a priori interpreted by a CPET or an EPT mechanism. Oxidation of Phenol by Laser Flash Photogenerated RuIII ðbpyÞðester-bpyÞ2 . The same method as for RuðbpyÞ2þ 3 was em-

ployed. The competition between the exit from the solvent cage of RuIII and MV•þ and back electron transfer is more in favor of the latter, resulting in a smaller concentration of these two reactants (0.88 instead of 4 μM) at the initial time of the reaction of RuIII with phenol. The latter is faster than in the preceding case, as expected from the more favorable driving force, requiring the use of smaller phenol concentrations (1 mM at maximum) for 10 -1 -1

log k + (M s )

9

-1 -1

5

-1 -1

log k + (M s )

log k + (M s ) 9

A

8

10

4

8

7

B

6

7

2

6

1

5

5

0

pH (pD)

pH (pD)

pH (pD)

3

C

4

4 0

2

4

6

8 10 0

2

4

6

8 10 12

-1 0

2

4

6

8

Fig. 2. Variation with pH (or pD, see ref 44) of the overall forward rate constant of phenol þ phenoxide oxidation by the various electron acceptors. (A) RuIII ðbpyÞ3 . (B) RuIII ðbpyÞðester-bpyÞ2 . (C) IrIV Cl6 . Black dots: results obtained in H2 O by the laser flash technique in A and B and by the stoppedflow method in C (from ref. 32). Gray dots: results obtained in the same way in D2 O. Black and gray lines: application of Eq. 2 to the H2 O and D2 O data, respectively (parameter values in Table 1).

Bonin et al.

generated electrochemically instead of photochemically, and the rate constant of interest derived from the redox catalytic (39) enhancement of the cyclic voltammetric reversible response of P ¼ RuðbpyÞ2þ 3 as shown in Fig. 3. We used the clever implementation of the method proposed in ref. 41, which uses an indium-tin-oxide electrode, prepared as described in SI Appendix, that slows down the direct oxidation of phenol at the electrode and makes the catalytic enhancement of the current more apparent. The value found for the rate constant, kþ ¼ 3 × 105 M−1 s−1 , confirms the photochemical result, which may, however, be considered as more accurate in view of the remaining overlap between catalytic current and direct oxidation current in the redox catalytic technique. Stopped-Flow

Oxidation

of

Phenol

RuIII ðmethyl-bpyÞ3.

by

RuIII ðmethyl-bpyÞ3 offers a driving force in between that of RuIII ðbpyÞ3 and IrIII Cl6 . The expected rate constant k1 is, however, too slow to be conveniently measured by the laser flash photolysis technique. We therefore switched to the stoppedflow technique (SI Appendix). First, a premix is realized with RuII ðmethyl-bpyÞ3 and CeIV ðSO4 Þ2 in sulphuric acid medium, thus generating RuIII ðmethyl-bpyÞ3 very rapidly by oxidation with Ce(IV) thanks to the large redox potential difference between the two couples. Then, the latter is mixed with ArOH in an absorption cell in which kinetics of the RuII -complex recovery is followed at 438 nm on a timescale of 1 s (SI Appendix). Ce (IV) being unstable in basic media, we limited the investigation 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6

i (µ A)

i (µ A)

Experimental

Simulated

E (V vs. NHE)

E (V vs. NHE) 0.6

0.8

1

1.2

1.4

0.6

0.8

1

1.2

1.4

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 -0.2 -0.4 -0.6

1.6

Fig. 3. Redox catalysis determination of the rate constant of phenol (pH ¼ 3.4) oxidation by RuðbpyÞ2þ 3 . Cyclic voltammetry of 0.01 mM RuðbpyÞ2þ 3 , alone (gray line) and in the presence of 0.02 mM phenol (black line). Phenol alone: dotted line. Parameter values for simulation (40): diffu−6 and diffusion coefficient of phenol sion coefficient of RuðbpyÞ2þ 3 is 3.6 × 10 −3 is 3.65 × 10−5 cm2 ∕s. Standard rate constant (cm∕s) for RuðbpyÞ2þ 3 is 3 × 10 and standard rate constant for phenol is 7 × 10−4 . Transfer coefficients: 0.5 · kþ ¼ 3 × 105 M−1 s−1 . Other parameter values are listed in Table 1. PNAS ∣

February 23, 2010 ∣

vol. 107 ∣

no. 8 ∣

3369

CHEMISTRY

Oxidation of Phenol by Electrochemically Generated RuIII ðbpyÞ3 (Redox Catalysis). The electron acceptor Q in Scheme 1 may be

to a single pH (¼1.3). The results obtained in H2 O and D2 O this way are reported in Fig. 4. Discussion In all three cases where it was investigated, the variation of the observed forward rate constant, kþ , with pH obeys Eq. 3, with pK ArOH ¼ 10. In no case did we find the 1∕2 slope previously reported for the oxidation of phenol by RuIII ðbpyÞ3 in the presence of 0.1 M buffer (31) or in similar experiments, in buffered and unbuffered media, where the phenol, tyrosine in that case, was attached to the RuðbpyÞ3 structure (28–30). Such a pH dependence, explained by a variation of the driving force of the H2 O-CPET reaction with pH, is actually not expected because, as mentioned earlier, there is no reason for the driving force of this reaction to vary with pH. We do not know the reasons behind these unexpected behaviors, but the fact that they are not observed here in all four cases allows proceeding further in the analysis of the reactivity characteristics. In this connection, Fig. 4A represents the values of the forward rate constant of phenol oxidation, derived from the horizontal asymptotes in Fig. 2, as a function of the driving force of the reaction. In this representation, the driving force scale is that of the CPET pathway:−ΔG0CPET ¼ FðE0Q∕P − E0CPET Þ, where E0Q∕P is the standard potential of the electron acceptor. As discussed in the following, other driving force scales may be used instead, provided they include, as here, the oxidizing power of the electron acceptor, through its standard potential, E0Q∕P . Over the four data points in Fig. 4, the three points relative to uphill processes approximately fall on a 1∕60 mV straight line, suggesting a counterdiffusion control of the reaction rather than an activation control. However the occurrence of counterdiffusion control CPET reaction may be ruled out for the following reasons. For reactions that are bimolecular in both directions, the Debye–Smoluchowsky model (42, 43) leads to the following three-term expression of the rate constant (kdif , kact , and k−act being the diffusion, the forward, and the backward activationcontrolled rate constants, respectively): 1 1 1 1 þ þ ; ¼ k kcdif kact kdif

[4]

with kcdif ¼ kdif kact ∕k−act ¼ kdif exp½ðF∕RTÞðE0Q∕P − E0CPET Þ. Because the proton acceptor, water, is the solvent, the forward reaction may be considered as being a pseudo-bimolecular reaction, whereas the reverse reaction is a termolecular re12

12

log k1 (M-1s-1 )

10

10

8

8

6

6 4

A

4 2

2

0

0

-2

0 (eV) −∆GCPET

-4 -1

-0.5

0

log k1 (M -1s-1 )

0.5

B

kCPET ¼ exp½ðF∕RTÞðE0Q∕P − E0ap Þkdif ; cdif where E0ap is the pH-dependent apparent standard potential deriving from the Pourbaix diagram of the system (see figure 1C in ref. 44):   1 þ 10ðpH−pK ArOH Þ E0ap ¼ E0CPET þ ðln 10RT∕FÞ log 10−pH : 1 þ 10ð−pHþpK ArOH•þ Þ Thus, if the counterdiffusion control was operating, the rate constant should vary as the oblique dashed straight lines in Fig. 4A (using the values in Table 1). The fact that the acid side rate constants do not vary with pH and are much lower than the predicted counterdiffusion rate constants clearly excludes a counterdiffusion control of the reaction. We may therefore conclude that the reaction would be under activation control if a CPET pathway were to be followed. Before discussing the ensuing reactivity characteristics, the possible occurrence of an EPT mechanism should be examined. The experimental data points are recast in Fig. 4B with, in abscissa, a driving force scale relative to the EPT mechanism, −ΔG0EPT ¼ FðE0Q∕P − E0EPT Þ (Table 1). In this case, the data gathered in H2 O for the three uphill cases fall exactly on the 1∕60 mV straight line, suggesting counterdiffusion control as defined from 0 0 Eq. 4 with kEPT cdif ¼ exp½ðF∕RTÞðEQ∕P − EEPT Þkdif (using the value of E0EPT in Table 1). Only the fourth data point, which involves a driving force close to zero, is under activation control. Discrimination between the counterdiffusion-controlled EPT pathway and the activation-controlled CPET pathway evoked earlier derives from the observation of a significant H/D kinetic isotope effect, i.e., a factor of 2.5–3 for all four reactions. Such an effect is not expected in the EPT case. Indeed, as shown in SI Appendix, if the EPT pathway were to be followed, it would be kinetically controlled by the electron transfer step and, in this framework, neither E0EPT , and therefore kEPT cdif [kdif decreases by a factor of only 0.8 from H2 O to D2 O (see Table 1)], nor kEPT act are anticipated to vary significantly from H2 O to D2 O. The contribution of the PET pathway, which increases with pH, is represented by the second term in the right-hand side of Eq. 3, which was shown earlier to be practically timeindependent. We may consider that OH− is the most likely proton acceptor in this PET pathway, much more likely than H2 O itself. Table 1. Parameter values pK

F

-2

0 −∆GEPT (eV)

-4 -1

-0.5

0

www.pnas.org/cgi/doi/10.1073/pnas.0914693107

Potentials (in volts vs. normal hydrogen electrode)

0.5

Fig. 4. Forward rate constant of phenol oxidation (acid limit in Fig. 1) by the various electron acceptors. Black and gray symbols for H2 O and D2 O, respectively. Square: RuIII ðbpyÞðester-bpyÞ2 ; triangle: RuIII ðbpyÞ3 ; circle: RuIII ðmethyl-bpyÞ3 ; diamond: IrIV Cl6 (from ref. 32). The dashed horizontal straight line is the diffusion rate constant. In A, the abscissa is the CPET driving force and the dashed oblique straight lines represent the counterdiffusion control expected at, from right to left, pH ¼ 2; 4; 6; 8. The solid line is the activation-controlled rate constant predicted for a preexponential factor of 2.5 × 109 M−1 s−1 and a reorganization energy of 0.45 eV (see text). In B, the abscissa is the EPT driving force. 3370 ∣

action involving proton as one of the reactants. Adapting the Debye–Smoluchowsky to this termolecular situation leads (SI Appendix) to the following expression of the counterdiffusion rate constant in Eq 4:

Diffusion-limited rate constants

pK ArOH ¼ 10.0 pK ArOD ¼ 10.7 (44) pK ArOH•þ ¼ −2 (45) E0RuðbpyÞ ¼ 1.27 3

E 0Ruðmethyl-bpyÞ ¼ 1.09 (SI Appendix) 3 E0RuðbpyÞðester-bpyÞ ¼ 1.47 (SI Appendix) 2 0 EIrCl6 ¼ 0.89 (32) E 0CPET ðH2 OÞ ¼ 1.400 (44) E 0CPET ðD2 OÞ ¼ 1.422 (44) E 0PET ¼ 0.803 (44) E 0EPT ¼ 1.519 (44) H2 O kdif ðM−1 s−1 Þ ¼ 1010 −1 s−1 Þ ¼ 8 × 109 * 2O kD dif ðM

*From the viscosities of H2 O and D2 O, 1.005 and 1.25 mPa s, respectively (46). Bonin et al.

kact ¼

P k ; ∑ μ ∑ μν μ ν  Pμ ¼ exp −μℏωR ∕RTÞ∕



 expð−μℏωR ∕RT ;

μ

where μ ¼ 0; 1; …∞ and ωR is the frequency of the O-H phenol vibration mode. Several expressions of the individual transition rate constants, kμν , have been derived for the nonadiabatic limit (48, 49), leading to an exponential quadratic dependence toward the driving force. To take into account adiabatic transitions as well as nonadiabatic ones, we consider a general formulation of the preexponential term as the product of the bimolecular collision frequency Zbi and a transmission coefficient χ μν (16): kμν ¼ Zbi χ μν exp½−ðΔG0μν þ λμν Þ2 ∕4λμν RT; with ΔG0μν ¼ ΔG000 − ℏðμωR − νωP Þ and ΔG000 ¼ ΔG0CPET ; λμν is the individual reorganization energy. The transmission coefficient χ μν takes into account the transition probability between diabatic mixed electron-proton vibronic states and also modulation of this probability by proton donor/acceptor fluctuation. The reorganization energies, which involve heavy atoms including solvent, are likely to be about the same for all pairs. The transmission coefficients are expected to increase as more and more and higher and higher excited states are involved, tending to compensate the scarceness of the corresponding Boltzmann population. This is the reason that no inverted region is anticipated upon increasing the driving force for CPET reactions (50, 51) as for proton transfer reactions for the same reasons (52). In these conditions, the reaction tends to be adiabatic and entails a small H/D isotope effect (about 1.4). For the same reason, the contribution of excited states is expected to be maximal on the opposite side of the driving force scale, implying again an H/D isotope effect that decreases with the driving force down to 1.4. Because this is not observed experimentally, we are led to conclude that the contribution of excited states is not significant within the investigated range of driving forces and therefore to apply herein the simple equation kact ¼ Zbi χ exp½−ðΔG0 þ λÞ2 ∕4λRT:

[5]

Experimental data are thus fitted with Eq. 5, leading to λ ¼ 0.45 eV and Zbi χ ¼ 2.5 × 109 M−1 s−1 (Fig. 4A). The reorganization energy λ ¼ 0.45 eV, implying most likely about 0.45 eV for the electron acceptor and about 0.45 eV for the CPET reaction, may be compared to the corresponding electrochemical reorganization energy derived from the previously measured electrochemical standard rate constant, kCPET ¼ 25 cm s−1 , for S phenol oxidation in unbuffered water via a CPET pathway (44). Taking for the preexponential factor of the electrochemical standard rate constant a value close to the limit provided by the collision frequency, Zel ¼ 6500 cm s−1 , the electrochemical reorganization energy is found to be λel ≃ 0.4 eV, showing the consistency between the homogeneous and electrochemical kinetics. Finally, taking for the preexponential collision frequency, Zbi ¼ 3 × 1011 M−1 s−1 , the transmission coefficient may be estimated as χ ¼ 0.0083. This value is well below unity, leading to the conclusion that the CPET is nonadiabatic. Such a small value has already been found in the case of an amino-phenol system in aceBonin et al.

tonitrile (16), in which a modeling of the transition probability has shown that such a value is consistent with the observation of a H/D kinetic isotope effect of the order of 2.5–3. Moreover, as in the case of the amino-phenol system just mentioned above, we observe that the electrochemical CPET seems to be adiabatic whereas the homogeneous CPET is nonadiabatic. This feature has been interpreted as an electric field effect boosting electrochemical reaction. The other important result of the present study is the smallness of the reorganization energy (about 0.45 eV), smaller than is the case of amino-phenol system studied in acetonitrile where it was found to be about 0.8 eV (16). The reasons behind this larger intrinsic reactivity of water clearly call for further theoretical and experimental investigations. Concluding Remarks Three experimental techniques, namely, laser flash photolysis, redox catalysis, and stopped-flow, were used to investigate the variation of the oxidation rate constant of phenol with the driving force offered by a series of electron acceptors. Adding to these results those previously obtained with IrCl2− 6 (32) allowed scanning more than half an electron-volt driving force range. The variation of the phenol oxidation rate constant with pH showed the expected transition from a CPET or EPT mechanism at low pH, which rate constant does not vary with pH, to a PET mechanism upon increasing the pH, with a unity-slope variation of the log of the rate constant with pH. In no case was a 1∕2-slope variation observed. Because in these experiments no buffer was added to the solution, water and OH− are the only proton acceptors possibly involved in these reaction pathways. There is consequently little doubt that OH− plays the role of proton acceptor in the PET pathway. Determination of the mechanism of the direct oxidation of phenol at low pH, namely, discrimination between the CPET and EPT pathways, was based on the variation of the rate constant with the driving force and on the H/D isotope effect. Examination of the role that counterdiffusion may play at the lower end of the driving force range led to the conclusion that counterdiffusion may well be rate-controlling in the framework of an EPT mechanism but not with a CPET mechanism. In the latter case indeed, adaptation of the Debye–Smoluchowsky model to a termolecular reaction allowed the prediction that the rate-constant should vary with pH, unlike what is observed, and should have values much larger than those actually determined. It follows that if a CPET pathway were to be followed, activation control would prevail. If, conversely, an EPT pathway were to be followed, control could be by activation or by counterdiffusion as well. Because no H/D isotope effect is predicted for the EPT pathway, the 2O ¼ 2.5–3 in the whole series of elecobservation that k1H2 O ∕kD 1 tron acceptors rules out the EPT pathway at the benefit of the CPET pathway. Closer analysis of the latter showed that the reorganization energy is remarkably small (0.45 eV), in line with what was found earlier for the electrochemical reaction, underpinning the very peculiar behavior of water as proton acceptor when it is used as the solvent. Materials and Methods The photochemical kinetics were obtained from nanosecond laser flash or stopped-flow experiments. Electrochemical kinetics were obtained from redox catalysis experiments. Full details on the methods and materials used are given in SI Appendix. ACKNOWLEDGMENTS. Partial financial support from the Agence Nationale de la Recherche (Programme blanc PROTOCOLE) is acknowledged. We are grateful to Jean-Michel El Hage Chahine and his coworkers (Université Paris Diderot) for the permission to use their stopped-flow apparatus and for helpful advice about the technique. Ally Aukauloo (Université Paris-Sud Orsay) is thanked for the gracious supply of a sample of Ruð4; 40 -EtCO2 -bpyÞ2 ; Cl2 . PNAS ∣

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We may thus pursue the analysis of the reactivity in the framework of a water-triggered activation-controlled CPET reaction. The activation-controlled rate constant may be described in terms of transitions between pairs of reactant and product mixed electron-proton vibronic states; each contribution being weighted by the Boltzmann probability of the reactant system being in the corresponding vibronic state (36, 47). The overall rate constant thus appears as a sum of individual rate constants:

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