Determining Proton-Coupled Standard Potentials and X-H Bond Dissociation Free Energies in Nonaqueous Solvents Using Open-Circuit Potential Measurements

Article abstract of DOI:10.1021/jacs.0c01032

Proton-coupled electron transfer (PCET) reactions are increasingly being studied in nonaqueous conditions, where the thermochemistry of PCET substrates is largely unknown. Herein, we report a method to obtain electrochemical standard potentials and calculate the corresponding bond dissociation free energies (BDFEs) of stable PCET reagents in nonaqueous solvents, using open-circuit potential (OCP) measurements. With this method, we measure PCET thermochemistry in acetonitrile and tetrahydrofuran for substrates with O-H and N-H bonds that undergo 1e^-/1H⁺ and 2e^-/2H⁺ redox processes. We also report corrected thermochemical values for the ¹/₂H₂(g)/H^?_1M and H⁺/H^? (C_G) couples in several organic solvents. For 2e^-/2H⁺ couples, OCP measurements provide the multielectron/multiproton standard potential and the average of the two X-H BDFEs. In contrast to traditional approaches for calculating BDFEs from electrochemical measurements, the OCP method directly measures the overall PCET reaction thermodynamics and avoids the need for a pK_a scale in the solvent of interest. Consequently, the OCP approach yields more accurate thermochemical values and should be general to any solvent mixture compatible with electrochemical measurements. The longer time scale of OCP measurements enables accurate thermochemical measurements for redox couples with irreversible or distorted electrochemical responses by cyclic voltammetry, provided the PCET reaction is chemically reversible. Recommendations for successful OCP measurements and limitations of the approach are discussed, including the current inability to measure processes involving C-H bonds. As a straightforward and robust technique to determine nonaqueous PCET thermochemistry, these OCP measurements will be broadly valuable, with applications ranging from fundamental reactivity studies to device development.

Full text of DOI:10.1021/jacs.0c01032

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Article
Determining Proton-Coupled Standard Potentials and
X–H Bond Dissociation Free Energies in Nonaqueous
Solvents using Open-Circuit Potential Measurements
Catherine F. Wise, Rishi Gupta Agarwal, and James M. Mayer
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.0c01032 • Publication Date (Web): 20 May 2020
Downloaded from pubs.acs.org on May 20, 2020
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Determining Proton-Coupled Standard Potentials and X–H Bond Dissociation Free
Energies in Nonaqueous Solvents using Open-Circuit Potential Measurements
Catherine F. Wise, Rishi G. Agarwal, and James M. Mayer*
Department of Chemistry, Yale University, New Haven, CT 06520-8107, USA
*Corresponding author, james.mayer@yale.edu
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Abstract. Proton-coupled electron transfer (PCET) reactions are increasingly being studied in nonaqueous
conditions, where the thermochemistry of PCET substrates is largely unknown. Herein, we report a method to
obtain electrochemical standard potentials and calculate the corresponding bond dissociation free energies
(BDFEs) of stable PCET reagents in nonaqueous solvents, using open-circuit potential (OCP) measurements.
With this method, we measure PCET thermochemistry in acetonitrile and tetrahydrofuran for substrates with O-
–
+
–
+
H and N-H bonds that undergo 1e /1H and 2e /2H redox processes. We also report corrected thermochemical
(g)/H•1M and H /H (C
) couples in several organic solvents. For 2e /2H couples, OCP
+
•
–
+
values for the ½H
2
G
measurements provide the multi-electron/multi-proton standard potential and the average of the two X-H BDFEs.
In contrast to traditional approaches for calculating BDFEs from electrochemical measurements, the OCP method
directly measures the overall PCET reaction thermodynamics and avoids the need for a pK scale in the solvent
a
of interest. Consequently, the OCP approach yields more accurate thermochemical values and should be general
to any solvent mixture compatible with electrochemical measurements. The longer timescale of OCP
measurements enables accurate thermochemical measurements for redox couples with irreversible or distorted
electrochemical responses by cyclic voltammetry, provided the PCET reaction is chemically reversible.
Recommendations for successful OCP measurements and limitations of the approach are discussed, including the
current inability to measure processes involving C-H bonds. As a straightforward and robust technique to
determine nonaqueous PCET thermochemistry, these OCP measurements will be broadly valuable, with
applications ranging from fundamental reactivity studies to device development.
Introduction
Proton-coupled electron transfer (PCET) reactions are pervasive in biological systems, energy conversion,
and catalysis. As a result, the PCET reactivity of organic small molecules, such as quinones, phenols, and
hydroxylamines, is the subject of wide-ranging studies. For example, organic PCET reagents are increasingly
being utilized as redox mediators in flow batteries,1-6 electrocatalysis,7-8 and aerobic oxidations.9-11 Studies of N
2
1
2
oxidation13-16 are beginning to use organic PCET reagents to add or remove hydrogen atom
reduction and NH
3
equivalents from M–N
x
H species, and their mechanisms are increasingly being discussed as PCET.
y
Understanding and optimizing the reactivity of PCET substrates and intermediates requires knowledge of their
underlying thermochemistry. However, the standard potentials and corresponding bond dissociation free energies
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(BDFEs) of PCET reagents are often unavailable, particularly in nonaqueous solvents where many studies of
PCET reactivity are performed.
The lack of thermochemical data for PCET reagents in organic solvents stems in part from the challenge
of measuring these values directly. Nonaqueous X–H BDFEs can be obtained through several different methods
since Gibbs free energy is a state function and therefore path-independent. Most commonly, these values are
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–
of the substrate (i.e. the ‘Bordwell’ analysis).17-19
obtained by summing a 1e reduction potential and pK
a
However, this method is limited by its reliance on measurements of the thermodynamics of individual electron
transfer (ET) and proton transfer (PT) steps for high-energy and often unstable intermediates, and by its
requirement of a pK scale in the solvent of interest. Alternatively, in cases where the aqueous PCET standard
a
potential of a reaction is known, the corresponding nonaqueous potential can be derived.20-21 These conversions
require the free energy to transfer the oxidized and reduced substrate between water and the organic solvent,
which is generally not known and can be challenging to measure for PCET reagents with low solubility and/or
solvents with high miscibility. Finally, the relative nonaqueous thermochemistry of two PCET reagents can be
obtained by measuring the equilibrium constant for the reaction between the oxidized form of one substrate and
1
7
the reduced form of the other. However, this method does not provide absolute thermodynamic values and is
feasible only for substrates that are relatively close in potential, as a difference of 0.059V/n (where n = number
–
+
of e /H equivalents) corresponds to an order of magnitude difference in equilibrium constant.
Given the limitations of these approaches, a direct method for measuring the standard potential and
BDFE(s) of a PCET substrate in nonaqueous conditions would be valuable. In aqueous solutions, direct
measurements of PCET potentials are possible using electrochemical methods such as cyclic voltammetry (CV).
However, CV measurements of PCET substrates in nonaqueous conditions often show electrochemically
+
–
22-28
irreversible responses for the nH /ne process.
This electrochemical irreversibility typically results from
complex hydrogen bonding interactions and/or slow kinetics of proton and electron transfers that prevent the
substrate from equilibrating with the electrode on the CV timescale. Consequently, the measured CV midpoint
potential does not necessarily indicate a thermodynamic potential. Circumventing these complications requires
an electrochemical method that reaches equilibrium on longer timescales.
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WE
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HA
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A– HA
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XH
A
X
HA
X
A–
n
–
XHn
A–
–
Figure 1. Schematic of open-circuit potential measurement for substrate (X/XH ) in a buffered (HA/A ) solution.
The substrate equilibrates at the working electrode (WE), and the potential is measured relative to a reference
electrode (RE).
n
To that end, we hypothesized that open-circuit potential (OCP) measurements could be used to obtain
thermodynamic information about PCET substrates in nonaqueous conditions. The open-circuit potential of a
solution is defined as the potential at which no current flows, or the equilibrium potential. In an OCP
measurement, all electroactive solution species equilibrate at a working electrode, and the resulting potential is
measured against a reference electrode; in essence, the potentiostat acts as a voltmeter (Figure 1). Therefore, the
OCP is a purely thermodynamic measure of the solution potential, without complications from kinetic or
+
couple in acetonitrile by Roberts and Bullock29
mechanistic factors. This has been demonstrated for the H /H
2
3
0
and for electrochemically irreversible (but chemically reversible) redox processes of biological molecules and
3
1
metal complexes in water.
Herein, we demonstrate that open-circuit potential measurements are a straightforward, robust, accurate
–
+
and accessible method for directly measuring ne /nH standard potentials of PCET reagents in organic solvents.
OCP measurements of 2,6-dimethyl-1,4-benzoquinone in acetonitrile serve as a case study to describe the
theoretical and experimental aspects of the method and to provide strategies for obtaining accurate and
reproducible results. We demonstrate the applicability of the method for various types of PCET substrates, and
we report their standard potentials and corresponding BDFEs in acetonitrile and tetrahydrofuran. Comparisons of
the OCP method to other approaches for determining standard potentials and BDFEs highlight its scope,
advantages, and limitations. The method is only applicable to X/XH couples whose interconversions are
n
chemically reversible and give some sort of electrochemical response. Particularly valuable is its compatibility
with any solvent or solvent mixture amenable to electrochemical measurements. These results and analyses
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further an understanding of PCET reaction thermochemistry in nonaqueous solvents and provide a tool that will
be valuable for applications in catalysis, energy science, and beyond.
Results
I. General Experimental Considerations for Open-Circuit Potential Measurements
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All OCP measurements were performed in an N -filled glovebox using a standard three-electrode set-up,
2
with a glassy carbon working electrode, Pt auxiliary electrode, and Ag wire pseudoreference electrode separated
from the solution by a glass frit. The OCP was collected on solutions containing both the oxidized (X) and reduced
(
XH
n
) form of the substrate of interest, in X:XH ratios ranging from 0.4:1 to 2.5:1. All solutions also contained
n
0
.1 M [Bu
4
N][PF ] electrolyte and a 1:1 acid:conjugate base buffer. Use of a 1:1 ratio of acid:conjugate base
6
minimizes the effects of homoconjugation on the proton activity of the solution29, 32 (for substrates that undergo
–
+
ne /nH redox changes, see below). The buffer was present in at least 20-fold excess to the concentrations of X
and XH , and the solutions were stirred during OCP measurements to promote faster equilibration of substrate.
n
In general, the OCP was recorded every second for 5-10 minutes, or until the potential had stabilized such that it
was changing less than ~1.5 mV over 5 minutes (~0.005 mV/s). The reported OCP values are averages of data
collected in this plateau region. Measurements performed in acetonitrile and tetrahydrofuran with a range of
substrates, and we note that the magnitude of drift can vary with solvent and substrate. Significant drift results in
larger experimental uncertainties but does not preclude obtaining valuable results, unless it prevents observation
of a Nernstian dependence on substrate ratio (vide infra). More experimental details are provided in the
Supporting Information (SI).
II. Case Study: Open-Circuit Potential Measurements and Validation using 2,6-dimethyl-1,4-benzo-
quinone (DMQ)
In this section, we use 2,6-dimethyl-1,4-benzoquinone (DMQ) as a case substrate to describe how to
perform OCP measurements and to validate the method. Following the above procedure, the OCP was measured
for a solution of equimolar DMQ and 2,6-dimethyl-1,4-hydroquinone (H
2
DMQ) in acetonitrile (MeCN)
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+
containing an excess of 1:1 pyridinium tetrafluoroborate:pyridine (pyrH /pyr) buffer. In this case, the OCP reports
on the equilibrium potential for the reaction in eq 1. As shown in Figure 2A, the OCP decreased by several mV
in the first ~30 seconds of measurement and then reached a plateau, staying constant within <1 mV over 10
minutes. The stability of these measurements is indicated by the highly magnified y-axis scale, which spans only
a 6 mV range. The small upward drift in potential is negligible, approximately 0.03 mV/min, making the total
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change over 10 minutes 0.3 mV, or less than 0.01 kcal mol .
–
+
DMQ + 2e + 2pyrH
2
H DMQ + 2pyr
(1)
-0.210
-0.211
-0.212
-0.213
-0.214
-0.215
-0.216
-0.200
-0.205
A
B
-0.210
-0.215
-0.220
-0.225
-0.230
-0.235
y-int: –0.216 V
slope: 0.031 V/dec
-0.4 -0.2 0.0 0.2 0.4
0
100 200 300 400 500 600
Time (s)
log([H DMQ]/[DMQ])
2
+
Figure 2. All measurements were performed in MeCN containing 0.05 M 1:1 pyrH /pyr buffer and 0.1 M
[Bu
DMQ and 1.0 mM H
ratios of DMQ:H DMQ and plotted against log([H
4
N][PF
6
] supporting electrolyte. (A) The open-circuit potential measured over 600 s for a solution of 1.0 mM
DMQ. Data was collected every second. (B) Open-circuit potentials measured at different
DMQ]:[DMQ]), showing Nernstian dependence. Error bars
2
2
2
represent one standard deviation in the measured potential over 600 s. The intersection of the dashed lines is the
formal potential, E°¢OCP = –0.216 V vs Fc+ (vide infra).
/0
Several experimental considerations were developed to facilitate the OCP measurements and minimize
potential sources of error. First, the DMQ:H DMQ ratio was kept close to 1:1, since we have found that large
2
excesses in one direction or the other result in slow equilibrations and, as a result, less reliable data. As shown by
Figure 2A, the equilibrated potential changes slowly over time, likely due to electroactive impurities or drift in
the reference electrode over the long timescales of these experiments. The direction of the drift is consistent, so
the DMQ:H
2
DMQ ratio was varied in both directions to offset any error introduced by this effect. We have found
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that this strategy is particularly useful for cases where the magnitude of the drift is larger, and we recommend
employing it for all substrates.
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After the OCP measurements, ferrocene (Fc) was added to the DMQ/H DMQ solution, and a cyclic
2
+
voltammogram was collected to obtain E1/2(Fc /Fc) as a reference. Ferrocene cannot be present during the OCP
+
measurements because it is electroactive and would skew the measured potential. The accuracy of E1/2(Fc /Fc) is
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critical to ensure day-to-day reproducibility in the OCP measurements, since pseudo-reference electrodes often
drift slightly between experiments. However, collecting reliable CVs of Fc can be challenging in organic solvents
that have low ion mobility and, as a result, high solution resistance. Thus, the internal resistance of the cell must
be properly compensated such that the peak-to-peak separation of the Fc+/0 couple is as close as possible to the
3
3
+/0
theoretical 57.0 mV (at 25 °C). If the Fc couple overlaps with redox features of the substrate or is incompatible
34
–
with the buffer, another 1e redox agent can be used as an internal standard and its potential measured with
respect to Fc in a separate solution under the same conditions.
The measured OCPs were validated as equilibrium potentials for the interconversion of DMQ and H DMQ
2
by showing that they followed the Nernst equation. The Nernst equation to describe the reaction shown in eq 1
+
and similar PCET reactions is given in eq 2, where the more typical [H ] in the logarithm term has been substituted
+
–
for the equilibrium expression [H ] = K [HA]/[A ]. Eq 2 predicts that an order of magnitude change in the ratio
a
of oxidized to reduced substrate should be accompanied by a shift in the OCP of (0.0592/n) V, where n is the
+
number of electrons passed. OCP measurements collected at varying ratios of H
buffer solution in MeCN trended as predicted. A plot of the measured OCP vs. log([H
0.031(2) V/dec slope (Figure 2B), which is close to the theoretical slope of –0.0296 V/dec for a 2e /2H process
such as this one (dec = decade, a 10-fold change in relative concentrations).
2
DMQ:DMQ in a 1:1 pyrH /pyr
2
DMQ]/[DMQ]) showed a
–
+
–
– ꢉ
ꢂ.ꢂꢃꢄꢅ
ꢆ
[ꢇꢈ ][ꢊ ]
°
ꢉ
ꢀ =ꢁꢀ −ꢁ
log
− 0.0592pꢋꢌ
(2)
[ꢇ][ꢈꢊ]ꢉ
To further validate the OCP method, the response of the measured potential to changes in buffer strength
and buffer identity were examined. Per the Nernst equation, the OCP should not be affected by changing the
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buffer strength (the absolute concentration of the 1:1 HA and A ). Consistent with this analysis, the OCP of an
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+
equimolar DMQ/H
2
DMQ solution was constant within 1–2 mV at pyrH /pyr buffer strengths from 2–50 mM
(Figure 3A). The Nernst equation also predicts that changing the identity of the 1:1 buffer should change the
OCP by –0.0592 V per pK unit. We probed this expected dependence by measuring the OCP of equimolar
DMQ/H DMQ solutions in MeCN with 1:1 buffers of N,N-dimethylformamidium triflate/N,N-dimethylforma-
a
2
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+
35
+
36
+
mide (H -DMF/DMF, pK
a
= 6.1), pyrH /pyr (pK
= 14.13), and triethylammonium tetrafluoroborate/triethylamine (Et
measurement, the buffer was in approximately 50-fold excess to substrate. A plot of OCP vs pK
a slope of –0.058 V/pK unit, in good agreement with the expected value. Observing the expected changes to the
a
= 12.53), lutidinium tetrafluoroborate/lutidine (lutH /lut,
3
6
+
36
pK
a
3
NH /Et
3
N, pK
a
= 18.82). For each
a
(Figure 3B) had
a
OCP with variations in buffer strength and identity indicates that the method gives accurate equilibrium
thermodynamic measurements.
-0.217
Eº´OCP = 0.506
A -
0.218
0.219
0.220
0.221
0.222
0.223
B 0.2
– 0.058pKa
0.0
-
-
-
-
-
-0.2
2 mV
+
[
H -DMF]/DMF
+
-0.4
-0.6
[
pyrH ]/pyr
+
[lutH ]/lut
+
[
Et N ]/Et N
3
3
-0.224
8
12
pKa
16
20
0
10 20 30 40 50 60
Buffer Strength (mM)
Figure 3. All measurements were performed in MeCN containing 0.1 M [Bu
4
N][PF
DMQ with 2–50 mM 1:1 pyrH /pyr
buffer. Gray dashed trace is the average OCP from all buffer strengths. Error bars represent one standard deviation
in the measured potential over 600 s. (B) Open-circuit potentials measured for solutions of 1:1 DMQ:H DMQ
N (blue). Error
6
] supporting electrolyte.
+/0
+
(
A) Open-circuit potentials (vs Fc ) for solutions of 0.56 mM DMQ and H
2
2
+
+
+
+
with buffers of 0.05 M H -DMF/DMF (black), pyrH /pyr (red), lutH /lut (green) or Et
bars (one standard deviation) are smaller than the data points.
3
NH /Et
3
The measured OCP at a 1:1 ratio of X:XH
n
, gives the formal potential vs. Fc+/0 (E°¢OCP) under the
3
7
+
experimental conditions. For the DMQ/H
2
DMQ redox couple with a pyrH /pyr buffer in MeCN, E°¢OCP is the
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+
/0
y-intercept at the center of the plot in Figure 2B: –0.216 V vs Fc . The formal potentials reported here are all
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
defined at equal concentrations of oxidized and reduced substrate ([X] = [XH ]) and in 1:1 buffers ([HA] =
n
–
[A ]). Because a proton is involved in the redox process, the formal potential of DMQ depends on the proton
activity of the solution and therefore is only comparable to potentials of other PCET substrates measured under
the same experimental conditions. We note that these formal potentials can be converted to the corresponding
standard potential vs Fc+/0 (E°OCP) using the Nernst equation (eq 2). For a redox couple involving equal numbers
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
of protons and electrons, E°OCP is the formal potential plus 0.0592pK , or in other words, the formal potential
a
extrapolated to standard state for proton activity. Measured values of the standard potential E°OCP are equal
regardless of the buffer condition in which the measurement was performed, as illustrated above by the near
Nernstian slope of the data in Figure 3B.
III. Generality of the OCP Method
After establishing the validity of the OCP method with DMQ in MeCN as a case substrate, we explored
the generality of the technique by performing measurements on a variety of substrates in MeCN and
tetrahydrofuran (THF) using the same experimental set-up and procedure as described above. All substrates
–
+
examined have stable, well-defined oxidized and reduced forms and undergo ne /nH reactions. The substrate
–
+
–
+
scope included compounds that contain O–H and N–H bonds and that undergo 1e /1H as well as 2e /2H redox
2
+
II
transformations. The metal complex iron(II) tris(2,2′-bi-imidazoline) (Fe H
multi-site PCET with electron transfer to the metal and proton transfer to the ligand, was also measured. The
substrates are shown in Figure S1, with the relevant H atom(s) highlighted in red. Table 1 reports E°¢OCP(X/XH
with the associated buffer and solvent conditions. In all cases, the OCP was measured at different ratios of X:XH
and the reported E°¢OCP is the y-intercept of the corresponding plot of OCP vs log([XH ]/[X]) (where [XH ] =
X]) (see SI).
As with the DMQ/H
2
bim), which is known to undergo
38
n
)
n
,
n
n
[
2
DMQ case, collecting OCP measurements at different X:XH ratios for each
n
substrate provided a means to internally validate the accuracy of the measured potentials. Specifically, we probed
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–
+
–
+
the expected Nernstian dependences of 59.2 or 29.6 mV/dec for substrates that undergo 1e /1H or 2e /2H redox
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
processes, respectively. For the majority of the substrates, the OCP vs log([XH ]/[X]) plot showed a slope within
n
5 mV/dec of the expected value (Figures S2-S21). However, in some cases the slopes differed from the expected
values by 10-15 mV/dec. We attribute these deviations to the occurrence of side reactions that form new
electroactive species in solution (see SI Section 3). In such situations, we recommend performing OCP
measurements with several buffers to identify conditions that reduce undesired side reactivity and/or to obtain an
average potential value. Even for the substrates that displayed significantly non-Nernstian behavior, we found
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
that E°OCP(X/XH ) agrees within ~20 mV between buffer conditions, an improvement on standard literature
n
-1
17
methods for measuring PCET thermochemistry, which typically report values to ± 2 kcal mol (~ 87 mV).
Table 1. Measured formal potentials for PCET substrates in acetonitrile and tetrahydrofuran
Acetonitrile a
Tetrahydrofuran b
+
/0
E°¢OCP (V vs Fc+/0)
Substrate
E°¢OCP (V vs Fc )
buffer
+
2
1
4
,4,6-tri-tert-butylphenol
–0.15(1)
0.147(8)
–0.274(1)
–0.429(3)
–0.106(2)
–0.120(1)
–0.219(3)
–0.295(6)
0.08(1)
Et
3
NH /Et
3
N
–0.180(7)
–0.216(7)
+
,1-diphenyl-2-picrylhydrazine
-methoxy-2,6-di-tert-butylphenol
pyrH /pyr
+
Et
Et
3
3
NH /Et
3
3
N
N
–0.311(1)
II
bim]c
+
ndd
[
Fe H
2
NH /Et
+
1
,4-hydroquinone
pyrH /pyr
–0.480(8)
–0.560(8)
–0.588(7)
nd
TEMPOHe
pyrH /pyr
+
+
2
2
2
1
2
,6-dimethyl-1,4-hydroquinone
,6-di-tert-butyl-1,4-hydroquinone
,6-dimethoxy-1,4-hydroquinone
,4-dihydroxynaphthalene
pyrH /pyr
+
pyrH /pyr
+
DMF-H /DMF
nd
nd
–0.683(7)
,7-di-tert-butyl-1,4-
nd
–0.734(2)
dihydroxynaphthalene
+
1
5
1
,2-diphenylhydrazine
,10-dihydrophenazine
,8-dichloro-9,10-
–0.383(2)
–0.479(1)
pyrH /pyr
nd
nd
+
pyrH /pyr
nd
–0.998(4)
dihydroxyanthracene
a
All measurements in MeCN contained 50 mM buffer and 0.1 M [Bu
values are y-intercepts of plots of OCP vs log([XH ]/[X]). The reported uncertainty is one standard deviation of
multiple measurements (multiple y intercepts) in the same buffer condition with different stock solutions on
4
N][PF ] supporting electrolyte. Reported
6
n
b
+
different days. All measurements in THF contained 20 mM Et
supporting electrolyte. Reported values are y-intercepts of plots of OCP vs log([XH
uncertainty is one standard deviation from multiple measurements of 1:1 X:XH mixtures. Iron(II) tris(2,2′-bi-
imidazoline) . not determined (so no buffer is listed). 2,2,6,6-tetramethyl-1-hydroxypiperidine.
3
NH /Et
3
N buffer and 0.1 M [Bu
]/[X]). The reported
4
N][PF ]
6
n
c
n
2
+
d
e
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Discussion
I. PCET Standard Potentials vs Hydrogen
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
We advocate in this report that nonaqueous PCET reduction potentials be referenced to the hydrogen
potential in the solvent of interest (eq 3), similar to the use of NHE and RHE for aqueous solutions (see supporting
3
9
+/0
information of ). While ferrocene (Fc ) is the typical standard for electrochemistry in organic solvents,
(g)
has a number of advantages for ne /nH redox couples. By using hydrogen gas as a reference
state, PCET potentials are largely independent of the solvent and solution conditions. From another perspective,
potentials vs H are not electrochemical reactions at all, but simply the free energy of hydrogenation of X to XH
in the solvent of interest. We emphasize that these arguments and the thermochemical cycles developed below
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
2
H+(solvent) + 2e–
H
2
(3)
+
–
+
changing to H /H
2
2
n
are for reactions involving equal numbers of protons and electrons, X/XH
n
. Reactions with unequal numbers of
protons and electrons, such as hydride transfers, have somewhat more complex thermochemistry.40
In acetonitrile, converting the formal potential vs Fc+/0 to the standard potential vs H /H
+
is straight-
2
forward, since the standard hydrogen potential vs Fc+/0 (eq 6 in Scheme 1) has been reported. Roberts and Bullock
+
+/0
29
determined E°(H /H
2
) = –0.028(4) V vs Fc using a related OCP method. Combining E°¢OCP(X/XH
, V vs H ). These values are reported in Table 2. Each estimated
) measurements, the reported
), and the measured uncertainty in E1/2(Fc /Fc). The small overall uncertainties (<10 mV)
n
), pK
a
(HA),
+
and E°(H /H
2
) per Scheme 1 gives E°(X/XH
n
2
uncertainty includes: one standard deviation from multiple E°¢OCP(X/XH
n
+
+
uncertainty in E°(H /H
2
reflect the stability of the OCP measurements and robustness of the method. See SI Section 3 for a more detailed
discussion of error analysis.
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+
Scheme 1. Thermochemical Cycle for Converting OCP to Standard Potential vs H /H
2
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
E°′OCP (V vs Fc+/0
)
–
X + nHA + ne–
(4)
(5)
XH + nA
n
0
.059[pK (HA)]
a
+
–
nHA
nH + nA
E°(H /H , V vs Fc+/0)
+
−
2
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
(n/ )H (g)
+
–
(6)
2
2
nH + ne
E°(X/XH , V vs H )
n
2
n
XHn
(7)
X + ( / )H (g)
2
2
Scheme 1 requires a standard hydrogen potential vs Fc+/0 and therefore cannot be applied to THF or any
solvent mixture without an established pK scale. However, the net reaction at the bottom of Scheme 1 (eq 7) can
be attained by an alternative thermochemical cycle that does not require either the pK of the buffer or the standard
hydrogen potential in the solvent of interest. Scheme 2 also starts from the OCP measurement of the X/XH
a
a
n
–
+
couple in an HA/A buffer but uses the H
2
potential in the same buffer (E°¢(H /H
2
), eq 8) to obtain the standard
+
reduction potential of the substrate (E°(X/XH
n
)). Measurements of E°¢(H /H
2
) can be performed following the
29
literature procedure and involve a similar OCP approach to that described above (see SI Section 4 for details).
Scheme 2. Thermochemical Cycle to Directly Convert OCP to Standard Potential vs H
2
E°′OCP (V vs Fc+/0
)
XH + nA–
X + nHA + ne–
(4)
(8)
n
–E°′(H /H , V vs Fc+/0)
+
2
nHA + ne–
(n/ )H (g) + nA
–
2
2
E°(X/XH , V vs H )
n
2
n
XHn
(7)
X + ( / )H (g)
2
2
This H couple inherently contains thermochemical information about both the proton and the electron; thus, by
2
n
following the cycle in Scheme 2, the buffer properties cancel, and E°(X/XH ) is simply the sum of E°¢OCP(X/XH )
n
+
and E°¢(H /H
2
). Values of E°(X/XH ) for substrates measured in THF are reported in Table 2, and the uncertainty
n
reflects one standard deviation from multiple E°¢OCP(X/XH
n
) measurements as well as the measured uncertainty
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+
in E°¢(H /H
electrochemical measurements, and use of this cycle removes any error or uncertainty associated with reported
pK values. These features of the OCP method are potentially very valuable because accurate pK scales and
extensive tables of pK values exist only for a few organic solvents.
2
). Scheme 2 can be applied to any solvent, mixed solvent, or electrolyte condition amenable to
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
a
a
a
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Table 2. Standard potentials and BDFEs for PCET substrates in acetonitrile and tetrahydrofuran
Acetonitrile Tetrahydrofuran
BDFE BDFE
)a
E°(V vs H
)c
Substrate
,4,6-tri-tert-butylphenol
1,1-diphenyl-2-picrylhydrazine
E° (V vs H
2
2
-1 b
-1
b
(
kcal mol )
74.8
73.1
72.0
68.4
67.3
66
(kcal mol )
74.4
73.5
71.3
nd
2
0.99(1)
0.97(1)
0.93(1)
0.917(9)
0.868(4)
0.713(5)
0.664(4)
0.60(6)
0.550(7)
0.475(8)
0.469(7)
nd
4
-methoxy-2,6-di-tert-butylphenol
0.837(7)
nde
II
bim]d
[Fe H
2
1
,4-hydroquinone
TEMPOHf
,6-dimethyl-1,4-hydroquinone
2,6-di-tert-butyl-1,4-hydroquinone
,6-dimethoxy-1,4-hydroquinone
1,4-dihydroxynaphthalene
,7-di-tert-butyl-1,4-
0.66(1)
0.58(1)
0.56(1)
nd
67.4
65.5
64.9
nd
2
64.6
62.9
62.8
nd
2
nd
nd
0.46(1)
62.7
2
nd
nd
0.414(7)
61.5
dihydroxynaphthalene
1,2-diphenylhydrazine
0.387(4)
0.291(4)
60.9
58.7
nd
nd
nd
nd
5
,10-dihydrophenazine
1,8-dichloro-9,10-
dihydroxyanthracene
nd
nd
0.150(8)
55.4
a
+
) = –0.028(4) V vs Fc+/0 and the appropriate buffer pK
Calculated following Scheme 1, using E°(H /H
2
a
. The
reported uncertainty is one standard deviation from multiple measurements (in the same or different buffer
+
+/
b
conditions) propagated with the uncertainties in E°(H /H
3.06E°(X/XH ) + DG°(½H
(g)/H•1M) (eq 13), where DG°(½H
THF Table 3). Relative uncertainties can be converted from the uncertainties in E°(X/XH
2
) and E1/2(Fc Fc).
(g)/H•1 M) = 52.0 kcal mol for both MeCN and
) and are
0.3 kcal mol for most substrates. Absolute uncertainties are about ± 1 kcal mol taking into account the
Calculated as BDFE(X–H) =
-1
2
n
2
2
n
-
1
-1
<
•
uncertainty in approximating the solvation of H as H , which is discussed in more detail in SI Section 3.1.5 and
2
4
1
c
+
) = –1.148(7) V vs Fc+/0 in a Et
+
ref. . Calculated using E°¢(H /H
Scheme 2. The reported uncertainty is one standard deviation from multiple measurements of 1:1 mixtures of
2
3
NH /Et N buffer (SI Section 4.1), following
3
+
d
2+
e
f
X:XH
n
propagated with the uncertainty in E°¢(H /H
2
). Iron(II) tris(2,2′-bi-imidazoline) . not determined.
2
,2,6,6-tetramethyl-1-hydroxypiperidine.
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II. BDFEs from PCET Standard Potentials vs H
2
1
2
3
4
The standard potential vs H
2
for a PCET reagent is closely related to its average X–H BDFE, as shown in
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
Scheme 3. Equation 9 converts the standard potential to the free energy to remove H
BDFE is the free energy for the homolysis of a single X–H bond to form solvated X and H . Thus, the sum of
the X–H BDFEs in XH , for example, is the sum of: (i) the energy to remove H (eq 9), (ii) the free energy of
homolysis of H gas into 2H (eq 10), and (iii) the free energy to transfer the two H from the gas phase to solution
eq 11).
2
(g). By definition, a solution
•
•
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
2
2
•
•
2
(
Scheme 3. Thermochemical Cycle for Converting Standard Potential to BDFE
ΔG° = nFE°(X/XHn)
n
XH (solv)
(9)
(10)
(11)
n
X (solv) + ( / )H (g)
2
2
1
nΔG°( / H /H )
2
2
(n/ )H (g)
nH (g, 1 atm)
2
2
nΔG°(H (g)/H (solv))
ΔG° = n(BDFE)
nH (g, 1 atm)
nH (solv, 1M)
XH (solv)
X (solv) + nH (solv, 1M) (12)
n
Equations (10) and (11) in Scheme 3 involve only hydrogen and not the PCET reagent of interest. The
•
-1
gas-phase BDFE of ½H to H (eq 10) is solvent-independent and is very accurately known to be 48.6 kcal mol
2
4
2
from literature enthalpies and entropies of formation. Eq 11 is a solvent-dependent term for the free energy of
•
solvation for H , from the gas-phase standard state of 1 atm to the solution-phase standard state of 1 M. This term
has been much discussed, with the consensus that it is well approximated as being the same as that of H
number of organic solvents.37,43,44 The derivation of ΔG°(½ H (g)/H•1M) from these data is discussed in Section
of the SI, and the values are reported in Table 3 below.
2
in a
2
5
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Table 3. Free Energy to Convert ½ H
(g) to H•1M in Organic Solvents a
2
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
(½ H (g)/H•1M)
Solvent
ΔG
°
2
acetonitrile
N,N-dimethylformamide
52.0
52.3
52.2
51.9
52.0
52.0
51.7
1
,4-dioxane
acetone
tetrahydrofuran
toluene
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
n-hexane
a
Calculated using data from references 42 and , values in kcal mol at 298 K, see SI Section 5 for details. The
43
-1
•
uncertainty in these values is dominated by the uncertainty in the assumption that the solvation of H can be
approximated with that of H
2
. The validity of this assumption has been rigorously examined in water with a
-1
reported uncertainty of ± 0.03 V, or ~0.7 kcal mol . We therefore conservatively apply an uncertainty of ± 1 kcal
-1
mol to these free energies.
The E°(X/XH ) values in Table 2 can be combined with the appropriate ΔG°(½ H
to yield BDFEavg(XH ), also reported in Table 2 (eq 13). As discussed in Section III below, BDFEs should be
(g)/H•1M) from Table
n
2
3
n
relatively solvent independent. Consistent with this analysis, the calculated BDFEs for the six substrates measured
-1
in both MeCN and THF differed by less than 0.6 kcal mol . External validation of the OCP method by comparing
our results to literature BDFEs was more challenging, since most of the BDFE values presented in Table 3 have
never previously been measured. However, the few reports of BDFEs in MeCN agree well with our OCP
-1
measurements (all values in kcal mol ): BDFE(TEMPOH) = 66 ± 1 (here) and 64.2 ± 2 (adjusted lit.);
t
II
BDFE(2,4,6- Bu
and 69.4 ± 2 (adjusted lit.) (the adjusted literature values have been recalculated from the prior report17, 45 using
the corrected C for MeCN reported in Section IV below). As the OCP method directly measures the PCET
potential of the substrate, it should yield more accurate BDFE values than other methods.
BDFEavg(X–H) = 23.06E°(X/XH ) + ΔG°(½ H
III. Solvent Dependence of Standard Potentials vs. H and BDFEs
3
PhOH) = 74.7 ± 0.3 (here) and 74.8 ± 2 (adjusted lit.), and BDFE(Fe H
2
bim) = 68.3 ± 0.1 (here)
G
(g)/H•1M
)
(13)
n
2
2
+
The standard potential for X to XH
n
referenced to H /H
2
is simply the free energy of hydrogenation in that
solvent (E° = –∆G°/nF), as noted in Discussion Section I above. This implies that the value of E° in different
solvents should differ only by the changes in the free energies of solvation for X and XH
n
between solvents.
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Neutral organic molecules of similar size tend to have similar solvation free energies in organic solvents, and
these ∆G°solv typically have small magnitudes. The primary difference in solvation of XH and X is the formation
of XH -solvent hydrogen bonds, but the strength of those hydrogen bonds vary only slightly between H-bond
accepting solvents like MeCN and THF.17, 46-47 Therefore, OCP measurements of E° values vs. H
can be directly
compared and should vary only a small amount between solvents. The average BDFEs should also be similar in
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
n
n
2
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
different solvents, since the free energy to convert ½H
(g) to H•solv differs only slightly between solvents (± 0.5
2
-1
kcal mol , Table 3). For comparisons of both E° and BDFE values, the largest differences will be observed
between solvents with very different hydrogen bonding properties, as discussed elsewhere.17, 48-50
As an example, Table 4 compares E° and BDFE values for the DMQ/H
2
DMQ couple in in acetonitrile,
THF, DMF, isopropanol, and water. The values in organic solvents are from OCP measurements (Table 2 and SI
5
1
Sections 2.3 and 2.4); the aqueous experimental value is from cyclic voltammetry studies in reference . All E°
values are the same within 30 mV, despite the very large differences in polarity and hydrogen bonding over this
-1
series of solvents. Similarly, the BDFEs vary by only 1.3 kcal mol . Table 4 also includes a computed aqueous
51
E° value for this quinone, from DFT calculations, which is in excellent agreement as well. Similar comparisons
between solvents and with computations for other substrates are presented in Table S3 of the SI. The close
agreement between these various values provides further validation of the OCP method presented here. The
conclusion that E° values vs. H and BDFEs vary little with solvent should be of broad value and reinforces our
2
encouragement to report E° for PCET couples versus the hydrogen reference electrode.
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Table 4. Solvent dependence of standard potentials and BDFEs for 2,6-dimethyl-1,4-hydroquinone
and comparison with computation.
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
)a
Solvent
E
°
(V vs H
2
BDFE (kcal mol-1)b
MeCN
THF
0.550(7)
0.56(1)
0.578(2)
0.566(5)
0.5475
64.6
64.9
65.6
ndc
DMF
IPA
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
H
2
2
O (expt.)
O (DFT)
65.9
66.1
H
0.553
a
Experimental E° in organic solvents from OCP measurements (Table 2 and SI Table S3). Experimental
5
1 b
and computational E° in H
ΔG°(½ H
c
2
O taken from reference . BDFE values from Table 2 or eq 13, where
•
-1
-1
39
2
(g)/H 1M) = 52.3 kcal mol for DMF from Table 3 and 53.3 kcal mol for H
2
O from ref. .
not determined.
IV. Comparing the OCP Method to Standard Methods for Determining Solution BDFEs
+
+/0 17
Solution BDFEs are most commonly determined using eq 14 or its variant with pK
a
(XH ) and E°(XH ).
This approach, developed by Bordwell,18-19 requires thermodynamic parameters for high-energy intermediates
and having a pK scale in the solvent of interest. In addition, accurate BDFE calculations require that the
thermodynamic measurements be performed under identical conditions, while literature pK values are rarely
measured in the presence of the electrolyte used for E° measurements. pK values and electrochemical potentials
a
a
a
often vary substantially with solvent because the solvation of ions is exoergic and strongly dependent on the
properties of the solvent. In some solvents, such as THF, ion pairing effects must also be taken into account, both
5
2
when deriving a pK
a
scale (as done in ref ) and when determining the proton activity of THF solutions. For
instance, the proton activity will typically depend on the absolute concentrations of acid/base and on the nature
+
–
–
+
of the counter ion in the [BH ][Y ]/B or AH/[A ][Z ] buffer. The OCP method avoids many of these
complications by providing direct measurements of the proton-coupled potential and the hydrogen potential under
the exact conditions of interest. Using the same solution conditions to collect thermodynamic data for the substrate
–
+
and the e /H equivalents (eqs 4 and 8 in Scheme 2) minimizes the effects of ion pairing and solvation on the
accuracy of the data.
0/–
BDFEsol(X–H) = 1.37pK
a
(XH) + 23.06E°(X ) + CG,sol
(14)
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1
Journal of the American Chemical Society
There are cases, however, where the OCP method cannot be used to directly obtain a BDFE. In an overall
2
–
+
•
2
e /2H redox process, for instance, it does not provide the individual BDFEs (for HX–H and X–H). These
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
individual BDFEs often differ substantially from the average BDFE calculated from OCP measurements, with
the first BDFE usually being much stronger. While average BDFEs are often better thermodynamic predictors of
1
7
overall reactivity, knowledge of individual BDFEs can be valuable for kinetic studies. Calculation of the
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
•
component BDFEs of HX–H and X–H can sometimes be accomplished using a Bordwell analysis (eq 14), barring
any of the aforementioned limitations of this approach. However, due to the instability of the various
17
intermediates, calculation of both component BDFEs in this manner is rarely possible. As a result, we propose
the complementary use of the Bordwell analysis and OCP measurements as an alternative strategy for the
experimental determination of thermochemical values across the various sections of a square scheme. Knowing
the average BDFE from OCP measurements and one component BDFE from the Bordwell approach allows facile
calculation of the second component BDFE.
As another example, when the proton and electron come from different sources, eq 14 is used to calculate
1
7
the effective BDFE of the hydrogen atom equivalent. In these situations, OCP measurements can provide a
+
/•
measurement of the C
G
term, defined as –FE°(H ), though we note that this approach is only feasible for solvents
in THF. To our knowledge, the only reported C (THF)
term, which gives a value of 61 kcal mol . Using our measured
with a pK scale. As an example, we derive here the C
a
G
G
-1 53
comes from converting the corresponding C
H
+
OCP for E°¢(H /H
2
) with 1:1 [Et
3
NH][BF
4
]/Et
3
N buffer and 0.1 M [NBu
4
][PF
6
] electrolyte in THF and
+
52
+
+/0
+
pK
a
(Et
3
NH ) = 13.66 ± 0.05 (from ref. ) yields E°(H /H
2
) = –0.339(8) V vs Fc . Addition of this E°(H /H
2
) to
-1
ΔG°(½ H
2
(g)/H•1M) for THF gives C
G
(THF) = 59.8 kcal mol . However, these thermochemical values appear to
have a significant dependence on solution conditions, likely due to the strong ion-pairing effects mentioned above.
+
For instance, a reported E°¢(H /H
2
) in THF measured with the same OCP method and buffer but with
5
4
+
) = –0.361 V vs Fc+/0
in THF containing
[NBu
and C
NBu
4
][B(C
6
F
5
)
4
] electrolyte differs from our measurement by 20 mV and yields E°(H /H
2
-1
G
(THF) = 60.3 kcal mol . Additionally, using the CV midpoint potential of HClO
4
+
+/0 55
[
4
][ClO
4
] electrolyte, another report determined E°(H /H
2
) = –0.44 V vs Fc , which would give C
G
(THF)
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Page 18 of 26
-1
56
=
62.1 kcal mol , although this value carries a greater uncertainty as has been discussed elsewhere. We
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
-
1
recommend that investigators use C
G
(THF) = 60.4 ± 2 kcal mol , an average of the value derived from C and
H
those determined using an OCP approach, with a conservative uncertainty to account for the potentially large
effects of ion pairing under different electrolyte/buffer conditions. These results also highlight the value in
studying PCET reactions under the same solution conditions as those used for thermochemical measurements, a
stipulation that is more easily met when using the OCP method to directly measure PCET thermodynamics.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
We note that previously reported C
G
terms for MeCN and DMF17, 38 should be corrected for a sign error
(g)/H•1 M) values from Table 3 and literature values of E°(H /H
+
)20, 29
in their derivations. Summing DG°(½H
2
2
-1
-1
gives the C terms for MeCN and DMF as 52.6 kcal mol and 67.6 kcal mol , respectively. See SI Section 6 for
G
details.
V. Scope, Advantages, and Limitations of OCP Measurements
The above discussion demonstrates that OCP measurements are a powerful method for obtaining accurate
standard potentials and BDFEs for a wide variety of PCET reagents in a number of solvents. In this section, we
summarize the scope of the method and its requirements, and we discuss some advantages and limitations in the
context of alternative approaches to measuring nonaqueous PCET thermodynamics.
To obtain accurate measurements with the OCP method, a few simple requirements must be met. The
solvent should be able to solubilize ³ 0.1 M electrolyte and ³ 0.02 M acid/base buffer to achieve sufficient ionic
conductivity and facilitate proton transfer. Both the oxidized (X) and reduced (XH ) forms of the substrate should
n
have appreciable solubility (≥ ~1 mM concentrations) in the solvent and electrolyte of interest, must be stable
over the course of the experiment, and their interconversion must be quantitative and chemically reversible. If
these conditions are not met, the redox potential of interest may not be the dominant one in solution, and the
measured OCP may be skewed by the occurrence of side reactions and/or the presence of redox-active impurities.
Additionally, an inherent limitation of the OCP method is its inability to provide thermochemical information for
reactions involving transient species; other methods are needed for such cases.49, 57-59 We have observed faster
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equilibration times when the concentrations of X and XH are within a factor of 2 of each other, and we generally
n
1
2
avoided measurements with concentrations that differed by more than a factor of 5. All of our successful
measurements involved substrates that are electroactive within the solvent window, as determined experimentally
by cyclic voltammetry (CV). Overall, the observation of PCET redox features in a CV, regardless of
electrochemical reversibility, is a good indication that the substrate and system will be amenable to OCP
measurements. Nonetheless, we encourage readers to use experimental checks – such as probing the dependence
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
of the OCP on log[XH
n
]/[X] and buffer pK – to determine whether their measurements are thermodynamically
a
relevant.
However, some substrates that appeared to meet these requirements showed inconsistent behavior. One
example is 2,4,6-tri-tert-butylphenol in MeCN, which showed noticeable day-to-day deviations in the measured
potential at a given substrate ratio. To compensate for these errors, we varied the substrate ratio in both directions
and averaged data collected under multiple buffer conditions. See Section 2.5 of the SI for details. Another
example is the phenazine/dihydrophenazine couple, which was measurable in MeCN but showed a large drift in
the OCP when measured in THF. A plot of OCP vs log([XH ]/[X]) had a slope that exceeded 120 mV/dec, a large
n
–
+
deviation from the expected 29.6 mV/dec for a 2e /2H redox processes. The source of this instability could not
be identified or remedied, and as a result, we chose not to report values for phenazine/dihydrophenazine in THF.
In general, we caution against extracting standard potentials or BDFEs from data that severely deviates from
Nernstian behavior.
The tables above demonstrate that the OCP method can be used to determine valuable thermodynamic
parameters for many classes of PCET substrates. Potentials are reported for substrates that contain O–H or N–H
–
+
–
+
bonds, substrates that undergo single (1e /1H ) or multiple (2e /2H ) PCET events, and substrates that involve
PCET to a single site (i.e. hydrogen atom transfer) or multiple sites (in our example, ET to a metal center and PT
to a ligand). All of the cases examined here involve PCET reactions with equal numbers of electrons and protons,
–
+
ne /nH couples. As laid out in the thermochemical cycles in Schemes 1–3, it is straightforward to convert OCP
–
+
measurements on such ne /nH couples to standard potentials and BDFEs. While beyond the scope of the current
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study, we expect that OCP measurements could also be useful for PCET couples with unequal proton/electron
stoichiometries, especially when the buffer pK is well known. Hydride transfers are the best studied examples,
and their thermochemistry has been developed in a recent review. A recent paper on standard potentials for N
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
a
4
0
2
reduction to NH
3
or NH +
in organic solvents examines some of the issues of uneven proton/electron
4
stoichiometry (these potentials were determined from aqueous values, not from OCP measurements).21
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
In our hands, a primary constraint on the scope of this method is that only substrates undergoing PCET at
polar X–H bonds are amenable to OCP measurements (O–H or N–H bonds). Several attempts to measure PCET
potentials for reactions of C–H bonds were unsuccessful. The OCP of MeCN or THF solutions containing varying
concentrations of anthracene and dihydroanthracene took ~40 minutes to equilibrate and did not trend with the
X:XH ratio according to the Nernst equation, suggesting that the measured potential was not the thermodynamic
n
value for this substrate. No equilibration of the OCP was observed over >1 hour for other
C–H bond-containing substrates, such as isopropanol/acetone. Similarly, THF is an inert solvent for OCP
measurements despite its ability to be oxidized to dihydrofuran and furan. We hypothesize that the inability to
measure redox processes involving C–H bonds using the OCP method can be attributed to slow PCET kinetics at
the glassy carbon working electrode. The much slower PCET reactivity of C–H vs O–H and N–H bonds has been
6
0
documented elsewhere. The very slow PCET (H-atom) self-exchange rate constants for C–H substrates are
-5
-1 -1
evident in the reported value of 8 ´ 10 M s for benzyl radical/toluene, dramatically slower than those for
6
-1 -1 47
substrates with polar X–H bonds (5 to >10 M s ). For such substrates, alternative methods for obtaining
nonaqueous PCET thermodynamics could be more viable, including spectroscopic equilibrations, reduction
measurements, or conversions from aqueous potentials.17, 38, 61-63
potential-pK
a
Finally, we emphasize that cyclic voltammetry (CV) is generally not an appropriate technique for directly
obtaining standard potentials of PCET reagents in nonaqueous conditions. While CV is a very common method
for measuring PCET thermodynamics in water and ET thermodynamics in organic solvents, proton-coupled
electrochemical reactions are almost always electrochemically irreversible in organic solutions (likely due to the
slower PT kinetics than in water). Several experimental results indicated that such electrochemically irreversible
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CVs cannot be used to estimate standard potentials. For example, the midpoint potentials of CVs collected in
buffered MeCN suggested that 2,6-di-tert-butyl-1,4-benzoquinone (DTQ) is 15 mV more oxidizing than 2,6-
dimethyl-1,4-benzoquinone (DMQ) (Figure S27A). However, OCP measurements of the same solutions
demonstrated that DTQ is more reducing than DMQ by 95 mV (Figure S27B), consistent with experimental and
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
computed aqueous potentials of the two substrates51 and with the equilibrium between DMQ and H
DTQ
2
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
measured by H NMR spectroscopy in MeCN (Figure S28). In another experiment, the midpoint potentials of
CVs of a buffered DMQ/H DMQ solution collected at glassy carbon, gold, and boron-doped diamond working
2
electrodes spanned a 50 mV range. In contrast, OCP measurements of the same solution at the same three
electrodes agreed within 6 mV (Figure S29, Table S4). While in principle the electrode material and pre-treatment
can influence potential measurements, these results indicate that the nature of the electrode material does not
significantly influence the measured OCP potential thermodynamic equilibrium between the substrate and
electrode in experiments of this kind. Overall, these data show that the slow electrochemical kinetics complicating
CV measurements of PCET processes have much less effect on OCP measurements, likely due to the longer
experimental timescale of the OCP method.
Conclusions
The results and analyses reported here show that open-circuit potential (OCP) measurements are a
straightforward and accessible method for obtaining standard potentials and bond dissociation free energies for
PCET reagents in nonaqueous solvents. The procedures for performing these measurements are described,
including experimental considerations for collecting accurate and reproducible data. Formal potentials, standard
+
potentials vs. the H /H
2
reference, and BDFEs are reported for a variety of PCET reagents in acetonitrile and
tetrahydrofuran. Comparisons to additional measurements in N,N-dimethylformamide and isopropyl alcohol and
+
literature values in water show that E° values vs. H /H
2
and BDFEs are remarkably constant across different
+
solvents for X/XH
n
PCET couples. For this and other reasons, we recommend that the H /H
2
reference scale be
used for PCET reduction potentials.
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This report also gives a C
G
term for THF, corrects our previously reported C values for MeCN and DMF,
G
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
and provides corrected thermochemical data for converting ½H
2
(g) to H•1M in seven organic solvents. Our
analysis suggests that the OCP method provides the most accurate values available for determining such
-1
thermochemical properties, for instance providing BDFEs accurate to better than ± 1 kcal mol . Relative BDFEs
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
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and standard potentials are determined significantly more accurately. For comparison, most literature values for
-1
PCET thermodynamics are reported to ± 2 kcal mol . Furthermore, many of the potentials and BDFEs reported
herein are inaccessible by conventional methods for measuring nonaqueous PCET thermodynamics due to slow
electrode kinetics, solvent incompatibilities, or the lack of a pK scale. The OCP approach appears to be accessible
a
to essentially any solvent / electrolyte / acid-base buffer system in which typical electrochemical measurements
can be made. It does, however, require that the substrate be stable in both its oxidized and reduced form over the
course of the measurement and is currently limited to reactions involving O–H and N–H bonds; no OCP response
has yet been observed for PCET at C–H bonds. Overall, this work provides the most general method available for
evaluating the thermochemistry of nonaqueous PCET processes. We anticipate that the values and method
presented herein will advance investigations of fundamental PCET reactivity and provide thermochemical data
necessary for the development of new devices and processes in energy conversion and (electro)catalysis research.
Associated Content
Supporting Information
Complete experimental details, procedures and analysis, and data from OCP measurements (PDF).
Author Information
*Corresponding Author: james.mayer@yale.edu
ORCID: James M. Mayer: 0000-0002-3943-5250
Catherine F. Wise: 0000-0002-9947-7700
Rishi G. Agarwal: 0000-0002-5133-0136
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The authors declare no competing financial interest.
Acknowledgements
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We gratefully acknowledge very helpful discussions with Dr. Eric Wiedner, Dr. Aaron Appel, and Dr. Morris
Bullock. This research was supported as part of the Center for Molecular Electrocatalysis, an Energy Frontier
Research Center funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences.
R.G.A. acknowledges support from a National Science Foundation Graduate Research Fellowship.
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