Analysis of Hydrogen-Bonding Effects on Excited-State Proton

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Analysis of Hydrogen Bonding Effects on Excited State Proton-Coupled Electron Transfer from a Series of Phenols to a Re(I) Polypyridyl Complex Prateek Dongare, Annabell G. Bonn, Somnath Maji, and Leif Hammarström J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 01 May 2017 Downloaded from http://pubs.acs.org on May 4, 2017

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The Journal of Physical Chemistry

Analysis of Hydrogen Bonding Effects on Excited State ProtonCoupled Electron Transfer from a Series of Phenols to a Re(I) Polypyridyl Complex Prateek Dongare†, Annabell G. Bonn†, Somnath Maji‖ and Leif Hammarström*

Department of Chemistry-Ångström Laboratory, Uppsala University, Box 523, SE-751 20 Uppsala, Sweden.

Supporting Information Placeholder

ABSTRACT: In the present study of proton coupled electron transfer (PCET) reactions, the excited state of a fac-[(CO)3ReI(bpy)(4,4’-bpy)] + (bpy = 2,2’-bipyridine and 4,4’-bpy = 4,4’bipyridine) complex was reductively quenched by a series of phenols. Variation of substituents on the phenols substantially alters their pKa and E0 values and provides an opportunity to study photoinduced PCET as a function of their redox properties. Analysis of absorption spectral changes indicate that the phenols form a weak hydrogen bond with the pyridinic nitrogen of the 4,4’-bpy ligand in the ground state, and ground state association constants (KA) were determined. This H-bonded adduct quenches the excited Re-complex by PCET from the phenol, to form the reduced and protonated Re-complex. The KA values obtained aid quantitative evaluation of the rate constant for the PCET reaction in the H-bonded adduct. Thus, photophysical studies and mechanistic analysis indicate that the reaction occurs via a concerted mechanistic pathway, for unsubstituted phenol and phenols with electron-withdrawing substituents. Furthermore, the magnitude of the quenching varies systematically with the protoncoupled potentials of the phenols and not their hydrogen bonding strength (as reflected in KA). This study is one of the first detailed analyses of intermolecular H-bonding between selfassembling metal complex and substituted phenols in an effort to study their relationship with the kinetic parameters in a PCET reaction. INTRODUCTION Proton-coupled electron transfer (PCET) reactions are at the heart of many chemical and biological processes such as respiration, water oxidation, and photosynthesis.1-11 Studies on PCET reactions appear in the literature in rapidly increasing numbers. Of particular interest are

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mechanistic investigations aiming towards the ultimate goal of catalysis and artificial photosynthesis.12-14 PCET reactions may follow a concerted electron-proton transfer (CEPT) or a step-wise mechanism, with either electron transfer (ET-PT) or proton transfer (PT-ET) as the first step. The CEPT mechanism, with tunneling of both electron and proton from the same transition state, is of particular interest. It avoids formation of the ET and PT intermediates that often are high in energy,13 and CEPT may therefore lead to a more energy-efficient catalysis.14 Earlier reports have suggested that hydrogen bonding of the proton to be transferred can facilitate a concerted mechanism. Therefore, the effect of hydrogen bonding remains one of the pivotal factors in the mechanistic analysis of a PCET reaction. PCET in covalently linked phenol-base systems have been studied, but only rarely in a series (i.e. more than two) of homologous compounds.15-20 For synthetic convenience, self-association of phenols and bases has been used instead for systematic studies. However, the phenol-base adduct formation constant (KA) is typically small, so that quenching occurs via a transient formation of the hydrogen-bonded encounter complex (the adduct). Thus, the observed reaction rate constant is a function of both KA and the rate constant for PCET (kPCET) of the phenol-base adduct. Therefore, in order to analyze the effect of hydrogen bonding on kPCET in a series of compounds, KA must be determined. In an early example, Linschitz and co-workers demonstrated quenching of triplet C60 by phenol via hydrogen-bonded phenol-pyridine pairs.21-22 While qualitative effects of the added base were clear in this pioneering work, KA could not be consistently determined, which hampered quantitative analysis.23 More recently, the effects of Hbonding were investigated in a number of studies on excited state PCET involving Re as well as Ru polypyridyl-based complexes with phenolic quenchers.8,

24-28

However, the KA and kPCET


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values were calculated based on the incorrect assumption that association constants could be determined independently from luminescence intensity quenching data (see below and the Supplementary Information for a full discussion). Therefore, the reported rate constants were instead the product of KA and kPCET, rather than kPCET itself. For example, Bronner et al. used a range of phenols to quench a [Ru(2,2’-bipyrazine)3]2+ complex, where the bipyrazine ligands act as internal bases.24 Interestingly, they reported that the kinetic isotope effect (KIE) of the observed PCET rate constant, kobs(H)/kobs(D), increased with increasing driving force. This behavior contrasts the theoretical prediction that the KIE of kPCET reaches a maximum at ∆G0 = 0 and is therefore unexpected.29 Bronner et al. reported a large variation of KA (5 – 1400 M-1) within the series of phenols, while the intrinsic kPCET would (surprisingly) be essentially constant. However, this was based on an incorrect model to separate kPCET and KA, which casts doubts on their conclusions. To summarize, there are several interesting studies on the correlation of kPCET with the properties of self-associated phenol-base systems that have suffered from the inability to separate kPCET and KA from the observed reaction rate constants.25, 30-31 Thus, we decided to investigate the quenching of photo-excited fac-[(CO)3ReI(bpy)(4,4’bpy)]+ (Re-N) by a series of phenol derivatives that form a hydrogen bond with the 4,4’-bpy ligand (Scheme 1). The aim was to determine KA from independent measurements and thus extract reliable values of kPCET in self-associated hydrogen-bonded systems. Oxidation of the phenol shifts its pKa value, from 10 to -2 for unsubstituted phenol,32 and reduction of the 4,4’bpy ligand makes this more basic; these changes provide the energetic basis for coupling of electron and proton transfer in this system. For comparison, a reference compound (Re-ref), fac[(CO)3ReI(bpy)(4-phenpy)]+ (4-phenpy = 4-phenylpyridine) with no basic proton acceptor site was prepared (Scheme 1). The use of Re-ref is particularly illustrative for extracting the pure ET


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rate constants (kET) and comparing the relative effect of phenol addition where no basic proton acceptor site is present.

+ N

N Re

OC OC

N

N

CO

OH

Re-N

R +

N OC OC

R= 4-OMe 4-Me H 4-Br 2,6-F2

N Re

N CO

Re-ref

Scheme 1. Structure of the fac-[(CO)3ReI(bpy)(4,4’-bpy)]+ (Re-N) and fac-[(CO)3ReI(bpy)(4phenpy)]+ (Re-ref) complexes and studied phenols.

The present study contributes to revealing the mechanistic implications of excited-state PCET in self-associated, hydrogen-bonded complexes. Herein, the KA values are directly extracted from ground state spectroscopic data showing saturation behavior of absorption (KA), as well as from the curvature of luminescence lifetime and intensity quenching data (τ0/τ and I0/I, respectively) as a function of phenol concentration (KA’). The obtained data allows separation of the observed quenching rate constants into KA and kPCET values. The study also addresses the possible variation of KIE with driving force for kPCET of hydrogen-bonded, phenol-base-Re systems.


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I

KA

+

[(CO)3Re (bpy)(4,4’-bpy)] + PhOH

I

[(CO)3Re (bpy)(4,4’-bpy)---HOPh] hv

hv II

KA’

+

−•

*[(CO)3Re (bpy )(4,4’-bpy)] + PhOH

II

*[(CO)3Re (bpy −• )(4,4’-bpy)---HOPh]

kET I

+

+

kPCET +

•

+

[(CO)3Re (bpy −• )(4,4’-bpy)] + PhO H

I

•

[(CO)3Re (bpy)(4,4’-bpy • H)--- OPh]

+

Follow-up proton transfer reactions with solvent Scheme 2. Mechanism of reductive quenching of fac-[(CO)3ReI(bpy)(4,4’-bpy)]+ by phenols, analogous to the one with 1,4-dihydroxybenzene as quencher reported by Meyer and coworkers.33 RESULTS AND DISCUSSION Prior to this report, Meyer and co-workers have delineated two competing pathways33 in a photochemical

reaction

between

a

fac-[(CO)3ReI(bpy)(4,4’-bpy)]+

complex

and

1,4-

dihydroxybenzene (H2Q). Their work suggested as one pathway an outer-sphere, sequential ETPT to the excited Re complex and in a second one, pre-association in the ground state at higher phenol concentrations, followed by photoexcitation and CEPT. Our study extends this systematic investigation to a range of phenols (Scheme 1) with varying pKa’s and redox potentials. Timeresolved and steady-state luminescence quenching experiments were employed to investigate the PCET reactions. The key observation of our study is an excited-state PCET reaction in the *Rephenol adduct, where reductive quenching of excited *ReII by a phenol is accompanied by PT from the hydrogen-bonded phenol to the pyridinic nitrogen, resulting in a noticeable H/D KIE (Scheme 2).


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As reported earlier,34 the absorption spectrum of [(CO)3ReI(bpy)(4,4’-bpy)]+ in CH3CN comprises intense (bpy)π→(bpy)π* transitions in the UV region and a broad, convoluted Re(dπ)→(bpy)π* MLCT band in the visible region. After excitation at 355 nm, the structureless emission band, typical for an MLCT transition in such Re complexes, can be observed at 580 nm. Irradiation of [(CO)3ReI(bpy)(4,4’-bpy)]+ in a deoxygenated CH3CN/H2O 3:1 (v/v) mixture at room temperature induces an MLCT transition from ReI to 2,2’-bpy, forming [(CO)3(bpy •− )*ReII(4,4’-bpy)]+, and this excited state decays within τ = 262± 5 ns.33 The MLCT excited state *ReII exhibits an increased Lewis acidity and has the potential to oxidize a series of phenol molecules. Upon variation of pKa and E0 of phenols with systematic substitutions, one can predict a change in ΔG0ET of PhOH → *ReII. Also ΔG0PT for proton transfer from the oxidized PhO•H+ to 4,4’-bpy the reduced complex will vary with substitution of the phenol.35 Considering that ΔG0PCET = ΔG0ET + ΔG0PT, systematic studies of a series of substituted phenols aids in the overall mechanistic analysis of such a PCET reaction. The convenient thermodynamics make [(CO)3ReI(bpy)(4,4’-bpy)]+ and a series of phenols a suitable platform to study the PCET reactions in the context of H-bonding effects. Ground-state association constant: In order to determine the association constant KA in the rhenium ground-state, absorption spectra as a function of increasing phenol concentrations were acquired. A representative data set illustrating the change in absorption with increasing phenol = 4-Br concentration is shown in Fig. 1. Additional data is shown in Fig S1-S2. From this, KA was calculated by employing non-linear regression analysis to the resulting plots according to Eq. 1.36 2

[𝑀]0 + [𝑃ℎ𝑂𝐻] + 𝐾𝐴−1 [𝑀]0 + [𝑃ℎ𝑂𝐻] + 𝐾𝐴−1 [𝑀𝑄] = ± �� − [𝑀]0 [𝑃ℎ𝑂𝐻] 2 2

[1]


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Here, [MQ] is the adduct concentration, [M]0 the initial Re complex concentration, and [PhOH] the concentration of added phenol. All obtained parameters are listed in Table 1. The data shows only little variation in KA values between the phenols, ranging from 4.8 to 7.1 M-1 and no clear trend is observable. Specifically, KA = 6.0 M-1 was extracted for the phenol with the most electron-donating group, R = 4-OMe, as compared to 5.2 M-1 for the phenol with the most electron-withdrawing one, R = 2,6-F2.

0.02

0.01

A0- A

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0.00 0.00

0.04 0.08 Br-PhOH/M

0.12

Figure 1. Absorption spectra of [(CO)3ReI(bpy)(4,4’-bpy)]+ in CH3CN acquired after sequential addition of R = 4-Br at 298±3 K (left) and the plot of A0-A vs. concentration of R = 4-Br at 340 nm (right). The arrow in the left panel indicates the trend in absorption change. The red line in the right panel is the fit according to Eq. 1.

Excited state quenching by phenol: The photoluminescence intensity and lifetime of the rhenium complexes were monitored after sequential addition of increasing concentrations of phenol. Fig. 2 depicts a representative dataset of intensity (I0/I) and lifetime (τ0/τ) ratios after addition of R = 4-Br to [(CO)3ReI(bpy)(4,4’bpy)]+, where I0 and τ0 are the values without quencher; additional data is provided in the Supporting Information. For all phenols, both the luminescence intensity and lifetime were attenuated to the same extent, within experimental error. Higher concentrations where needed to


7


observe significant quenching for the phenols with electron-withdrawing substituents. In comparison, the reference complex Re-ref, which cannot form a hydrogen-bonded complex with

1

(a)

Intensity

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(b)

0.1

0.01

0.0

(c)

0.2

0.4 0.6 time (µs)

0.8

(d)

Figure 2. Photoluminescence data of [(CO)3ReI(bpy)(4,4’-bpy)]+ acquired after sequential addition of R = 4-Br at 298±3 K (1 atm N2) (a) luminescence spectra in 3:1 CH3CN/H2O (λexc = 400 nm) (b) luminescence decay traces in 3:1 CH3CN/H2O (λexc = 355 nm) (c) Stern-Volmer plots constructed from steady state luminescence titration data in CH3CN/H2O (black squares) and CH3CN/D2O (blue squares) (d) Stern-Volmer plots constructed from luminescence lifetime titration data in CH3CN/H2O (black squares) and CH3CN/D2O (blue squares). phenol, is quenched to a smaller extent. For R = 4-MeO, that is relatively easy to oxidize the difference compared to Re-N is smaller, but for the phenols with more electron-withdrawing substituents (thus higher PhO•H+/PhOH potential) the quenching of Re-ref is much slower in


8

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comparison. We attribute this to electron transfer from phenol to the excited Re-ref, as discussed below. The much more efficient quenching of Re-N is instead attributed to the PCET reaction of the hydrogen-bonded Re-N/phenol adduct. Transient absorption data shows the formation of the reduced and protonated complex [(CO)3ReII(bpy)(4,4’-bpy•H)] (Figures S7 and S9). We see no evidence for quenching by pure proton transfer, as the protonated Re-NH+ complex is luminescent (λmax ≈ 720 nm, Figure S8) and no such luminescence is detected in our quenching data.

The data can be analyzed by the following model: the observed rate constant for excited state decay, kobs, is given by Eq. 2a.25 k0 is the inverse of the emission lifetime in the absence of phenol, and kET is the second-order quenching rate constant that is independent of hydrogenbond formation or proton transfer to the Re complex, as observed for Re-ref. kPCET is the firstorder rate constant for PCET in the hydrogen-bonded adduct between Re-N and phenol, and KA’ is the adduct formation constant in the excited state. Phenol is in large excess, so that [PhOH] ≈ [PhOH]Total. The complex formation equilibrium is fast compared to the quenching, as [Phenol] ≥ 0.01 M and the formation can be assumed to be diffusion-controlled. The luminescence intensity and lifetime are then quenched to an equal extent, and the corresponding Stern-Volmer plots (Eq. 2b) will show downward curvature, reaching saturation at sufficiently high phenol concentrations. Note that this model is very different from the classic Stern-Volmer model of combined dynamic and static quenching, in which case there is negligible emission from the dyequencher complex, so that the intensity plot shows upward curvature but the lifetime plot is a straight line.37


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For Re-N the experimentally obtained Stern-Volmer plots of both

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𝐼0 𝐼

and

𝜏0 𝜏

indeed show

noticeable downward curvature at higher concentrations; Figure 2 shows example data with 4BrPhOH while the rest of the data is given in the Supporting Information (Figure S3-S5). In contrast, the plots for Re-ref are linear (Figure S6). Fitting the Re-ref data was done according to Eq. 2b, omitting the last term, to obtain a value for kET. For the Re-N data, the full Eq. 2b was used, with kET locked to the value determined for Re-ref. This gave values for the kPCET and the excited state association constants (KA'). For the three phenols with R = Br-, H- and 2,6-F2-, KA' was obtained as 1.0-1.5, while the curvature for the other two phenols was too small to give a reliable value. When the same value was used as obtained from the ground state absorption spectra (KA) was used it resulted in poor fits. Therefore, we assumed KA' = 1 for all five phenols; as KA did not vary significantly in the series it is reasonable to assume that also KA' does not vary significantly.. The fact that KA' < KA can be explained by the fact that the excited state is a Re-to2,2’-bipyridine charge-transfer state, so that electron density is drawn from the 4,4’-bipyridine ligand that is the hydrogen-bond acceptor. When the experiments were performed in 3:1 CH3CN/D2O instead the rates were found to be slower than those obtained in 3:1 CH3CN/H2O (see Figure 2 and the Supporting Information). Thus the kinetic isotope effect, KIE, defined as KIE = kPCET(H)/kPCET(D), is greater than unity.

𝑘𝑜𝑏𝑠 = 𝑘0 + 𝑘𝐸𝑇 [𝑃ℎ𝑂𝐻] + 𝑘𝑃𝐶𝐸𝑇

𝐾𝐴 , [𝑃ℎ𝑂𝐻] 1 + 𝐾𝐴 , [𝑃ℎ𝑂𝐻]

𝐼0 𝜏0 𝑘𝐸𝑇 𝑘𝑃𝐶𝐸𝑇 𝐾𝐴 , [𝑃ℎ𝑂𝐻] [𝑃ℎ𝑂𝐻] + = = 1+ 𝐼 𝜏 𝑘0 𝑘0 1 + 𝐾𝐴 , [𝑃ℎ𝑂𝐻]

[2a] [2b]


10

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In case of R = 4-Br a value of kET = (5.6 ± 0.01)×106 M-1s-1 as observed with Re-Ref and with

Re-N the extracted value from two independent measurement series is kPCET = 3.8 × 107 s-1 (ln(kPCET) = 17.28±0.28; see Table 1) with a KIE = 2.1. The extracted rate constants and KIEs

with all phenols are summarized in Table 1. Clearly observable from the Stern-Volmer analysis is the faster rates for phenols with electron donating groups (OMe, Me), as compared to those with electron withdrawing groups (Br, 2,6-F2; Figure S3-S5. Furthermore, the primary KIE was found to be smaller in R = 4-OMe (1.2) and 4-Me (1.1) as compared to the other studied phenols (≈2). Together with the fact that quenching of Re-N is faster than of Re-ref, these observations allow the conclusion that quenching of the excited *Re species occurs predominantly via PCET in a weakly hydrogen-bonded adduct formed between the pendent pyridine and a phenol. Furthermore, because the KA values do not vary significantly within the series, the observed variation in kPCET and KIE depend mainly on the pKa and redox potentials of the phenols, rather than variation in hydrogen-bond strength (KA’). This has important implications also for previous studies, as discussed below.


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Table 1. Kinetic and thermodynamic parameters of the studied systems (reported errors are ±S.D. from a least square fit, except for kPCET where it is the max error of the ln-average value for two independent series). Phenol

4-OMe

4-Me

4-Br

H

2,6-F2

pKa(a)

0 𝐸𝑃ℎ𝑂 • ⁄𝑃ℎ𝑂 − /V vs NHE(a)

K A’ /M-1

1.05

6.0±0.01

1e

0.71

1.15

7.1±0.01

1e

9.40

0.84

1.26

4.8±0.05

1f

2.3

9.98

0.86

1.31

6.8±0.02

1f

1.8

9.29

0.95(b)

1.36

5.2±0.04

1f

ln(kET /M-1s-1)

kH/kD

20.67 (±0.23)

20.63 (±0.01)

1.2

10.22

0.58

1.1

10.28

17.42 (±0.28)

17.90 (±0.02) 15.54 (±0.02)

2.1

15.43 (±0.03) 13.36 (±0.03)

19.43 (±0.79)

17.13 (±0.41) 15.65 (±0.04)

(c) 0 𝐸𝑃𝐶𝐸𝑇

KA /M-1(d)

ln(kPCET /s-1)

/V vs NHE

(a) Data in neat water from Li, C.; Hoffman, M. Z. J. Phys. Chem. B 1999, 103, 6653. (b) Data in neat water 0 from Soetbeer J., Dongare P., Hammarström L. Chem. Sci. 2016, 7, 4607. (c) Calculated as E𝑃𝐶𝐸𝑇 = 30 (d) 0 𝐼 EPhO•⁄PhO− + 𝑝𝐾𝑎 (𝑃ℎ𝑂𝐻) − 𝑝𝐾𝑎 (𝑅𝑒 ) where the latter value is 2.2. No significant difference in KA when H is replaced by D. (e) Assumed to be the same as for the lower three phenols. (f) Experimental value (1.0-1.5) rounded off to 1 and locked in the fit.

Suggested Mechanism: PCET reactions occur in either a step-wise (ET-PT or PT-ET) or concerted (CEPT) pathway.8,

38

In the former, ET from phenol to *ReII followed by PT from

phenol to the pyridinic nitrogen of 4,4’-bpy can be proposed. Hereby, reductive quenching of *

ReII occurs as a prelude to PT from phenol to 4,4’-bpy. Alternatively, PT from phenol to 4,4’-

bpy followed by reductive quenching of *ReII can occur, resulting in a PT-ET event. A PT-ET mechanism for the studied phenols can be excluded on thermodynamic grounds. For instance, the pKa of Me-PhOH in H2O is 10.28 and the pKa of the pyridinic nitrogen in [(CO)3ReI(bpy)(4,4’-bpy)]+ is ≈ 2.2.30 Therefore, the initial PT equilibrium of a PT-ET


12

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mechanism is significantly uphill and an unphysically large rate constant of the subsequent ET step (kET > 1015 s-1) would be required to match the observed rate constant (kPTET = 10-∆pKa×kET). On the other hand, ReI polypyridyl complexes are known for their significantly higher oxidative strength in the excited state, allowing for a possible stepwise ET-PT mechanism at least for R=OMe and R=Me.39-40 We note that the KIE for those two phenols is ∼ 1. For the other phenols, we attribute the PCET reaction to a CEPT, for the following reasons. First, kPCET is much greater than kET, and the ratio of kPCET/kET is not constant but increases from ∼1 M to ∼100 M within the series of phenols. This clearly suggests that the mechanisms are different for the two reactions. Also, if the reaction would have been ET-PT with pre-equilibrium kinetics, kPCET would have changed by a factor of 10 per 59 mV change in phenol potential. Instead kPCET changes only by a factor of 100 even though the phenol potentials change as much as 0.37 V. Thus, CEPT seems to be the mechanism of PCET for at least three of the phenols (R = H, Br and 2,6-F2). We note also that the KIE for these phenols is significant (KIE∼2). Driving Force Dependence: The driving force for the PCET reaction (−∆𝐺 0 PCET ) can be estimated using the potentials and the pKa’s of the phenols as listed in Table 1. We believe that

selective solvation and hydrogen bonding of the phenols by water, and the small polarity differences, will make the potentials and pKa values similar to those in neat water, and most importantly the relative values for the series of phenols should be essentially the same. Also, given the inconsistencies in the published values for phenols32, 41-43, with some added uncertainty in the 3MLCT excited state energy and relevant potentials of ReI complexes, one can only make an estimate of ∆𝐺 0 PCET using Eq. 3, to serve as orientation. However, for the trends and

correlations that are the focus of this paper, it is the relative values that are of importance.


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The excited state Re*+/0 potential is E0Re*+/0 ≈ +1.14 V vs. NHE, as estimated from the ground state E0 for the first reduction, that is based on 2,2’-bpy (-1.56 V vs NHE), plus the excitation energy (E00 ≈ 2.7 eV).44 After PCET, the excess electron is instead localized on the 4,4’-bpy ligand that is now protonated. Meyer and co-workers estimated the free energy change for interligand electron transfer from reduced 2,2-bpy to protonated 4,4’-bpy to ∆G0ILET = -0.49 eV.45 To 0 complete the calculation, we need to add 𝐸PhO • H+ ⁄PhO− = +0.86 V (Table 2) and the free energy

cost of moving a proton from PhOH (R = H; pKa = 10.2, table 2) to the 4,4’-bpy ligand (pKa = 2.2).30 Insertion of these values in Eq. 3 below gives:

0 0 0 0 = −𝑒(𝐸𝑅𝑒 Δ𝐺𝑃𝐶𝐸𝑇 ∗+⁄0 − 𝐸PhO• ⁄PhO− ) + Δ𝐺𝐼𝐿𝐸𝑇 − 2.30𝑅𝑇(𝑝𝐾𝑎𝑅𝑒(4,4′ −𝑏𝑝𝑦) − 𝑝𝐾𝑎𝑃ℎ𝑂𝐻 ) ≈

≈ -0.3 eV

[3]

For the other phenols, the corresponding values range from ∆G0PCET = -0.5 to -0.2. For the electron transfer quenching without adduct formation, as determined with Re-ref, the free energy can be estimated as: 0 0 0 Δ𝐺𝐸𝑇 = −𝑒(𝐸𝑅𝑒 ∗+⁄0 − 𝐸PhO• H+ ⁄PhOH ) ≈ +0.4 𝑒𝑉

[4]

0 0 where the value of 𝐸PhO • H+ ⁄PhOH is calculated from 𝐸PhO• ⁄PhO− by adding 12×59 mV for the 12

units difference in pKa value between the reduced and oxidized forms. For the other phenols, the corresponding values range from ∆G0ET = +0.1 to +0.5. Thus, while CEPT is expected to be a downhill reaction for a phenols, ET is uphill, which supports our assignment of the PCET reaction to CEPT, except maybe for the most easily oxidized phenols.


14

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R = OMe

(a)

R = OMe

(b) Me

Me Br Br

H

H 2,6-F2

2,6-F2

-1 0 0 • ⁄PhO− (slope = 20 eV ) and (b) lnkPCET vs 𝐸PCET Figure 3. Correlation plots of (a) lnkET vs 𝐸PhO (slope 16 eV-1). The solid line is a linear least-squares fit to the data. In (a) the error bars aresmller than the point size.

0 Figure 3a shows a Marcus-type free energy correlation between ln kET and 𝐸PhO • ⁄PhO− ,

according to Eq. 5:46

2

�∆𝐺 0 + 𝜆 � � 𝑘 = 𝐴 ∙ exp �− 4𝜆 RT

[5]

For non-adiabatic electron transfer the pre-exponential factor A is proportional to the square of the electronic coupling and λ is the reorganization energy. The derivative of ln k with respect to ∆G0 is: 𝜕𝑙𝑛𝑘 1 Δ𝐺 0 = �1 + � 𝜕(Δ𝐺 0 ) 2𝑅𝑇 𝜆

[6]

For small driving forces, in the limit of |Δ𝐺 0 | ≪ 𝜆, this is a straight line with a slope of 20 eV-1

0 0 • ⁄PhO− is equal to the variation in ∆G . (1/(50 meV)) at room temperature. The variation in 𝐸PhO


15


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A linear regression analysis of the data in Figure 3a shows good agreement with a straight line, with a slope of 20 eV-1, which is very close to the predicted value. Also CEPT reactions are expected to follow the relationship of Eqs. 5-6,47 with values of A, ∆G0 and λ that are relevant 0 for the CEPT reaction. The plot of ln kPCET vs. 𝐸PCET in Figure 3b shows good linearity, and the

fitted line exhibits a slope of 16 eV-1, as expected for a Marcus-type behavior at moderate driving force (0 < ΔG0

Analysis of Hydrogen-Bonding Effects on Excited-State Proton

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