Electron-transfer studies of a peroxide dianion

Article abstract of DOI:10.1021/ic500759g

A peroxide dianion (O₂^2-) can be isolated within the cavity of hexacarboxamide cryptand, [(O₂)∪mBDCA-5t-H ₆]^2-, stabilized by hydrogen bonding but otherwise free of proton or metal-ion association. This feature has allowed the electron-transfer (ET) kinetics of isolated peroxide to be examined chemically and electrochemically. The ET of [(O₂)∪mBDCA-5t-H₆] ^2- with a series of seven quinones, with reduction potentials spanning 1 V, has been examined by stopped-flow spectroscopy. The kinetics of the homogeneous ET reaction has been correlated to heterogeneous ET kinetics as measured electrochemically to provide a unified description of ET between the Butler-Volmer and Marcus models. The chemical and electrochemical oxidation kinetics together indicate that the oxidative ET of O₂^2- occurs by an outer-sphere mechanism that exhibits significant nonadiabatic character, suggesting that the highest occupied molecular orbital of O ₂^2- within the cryptand is sterically shielded from the oxidizing species. An understanding of the ET chemistry of a free peroxide dianion will be useful in studies of metal-air batteries and the use of [(O ₂)∪mBDCA-5t-H₆]^2- as a chemical reagent.

Full text of DOI:10.1021/ic500759g

Article
pubs.acs.org/IC
Electron-Transfer Studies of a Peroxide Dianion
Andrew M. Ullman,† Xianru Sun,‡ Daniel J. Graham,† Nazario Lopez,§ Matthew Nava,§
Rebecca De Las Cuevas,§ Peter Muller,§ Elena V. Rybak-Akimova,‡ Christopher C. Cummins,*,§
̈
and Daniel G. Nocera*,†
†Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, Massachusetts 02138, United
States
§Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139,
United States
‡Department of Chemistry, Tufts University, 62 Talbot Avenue, Medford, Massachusetts 02155, United States
S
* Supporting Information
ABSTRACT: A peroxide dianion (O22−) can be isolated within the cavity of hexacarboxamide cryptand, [(O2)⊂mBDCA-5t-
H6]2−, stabilized by hydrogen bonding but otherwise free of proton or metal-ion association. This feature has allowed the
electron-transfer (ET) kinetics of isolated peroxide to be examined chemically and electrochemically. The ET of
[(O2)⊂mBDCA-5t-H6]2− with a series of seven quinones, with reduction potentials spanning 1 V, has been examined by
stopped-flow spectroscopy. The kinetics of the homogeneous ET reaction has been correlated to heterogeneous ET kinetics as
measured electrochemically to provide a unified description of ET between the Butler−Volmer and Marcus models. The
2−
chemical and electrochemical oxidation kinetics together indicate that the oxidative ET of O2 occurs by an outer-sphere
mechanism that exhibits significant nonadiabatic character, suggesting that the highest occupied molecular orbital of O22− within
the cryptand is sterically shielded from the oxidizing species. An understanding of the ET chemistry of a free peroxide dianion
will be useful in studies of metal−air batteries and the use of [(O2)⊂mBDCA-5t-H6]2− as a chemical reagent.
at a gold electrode in dimethyl sulfoxide (DMSO), and in the
presence of tetraethylammonium (TEA) perchlorate, results in
deprotonation-induced decomposition of the TEA cation to
INTRODUCTION
■
Aerobic life is driven by the thermodynamic potential provided
by dioxygen (O2). In its ground state, O2 is kinetically stable
with respect to the chemical bonds found in living organisms.
The controlled activation of O2 in nature is therefore mediated
by electron transfer (ET) to produce its diatomic congeners of
superoxide (O2•−) and peroxide (O22−).1 In nonaqueous
environments, superoxide is stable in the absence of electro-
philic species such as protons or metal ions, and the anion
exhibits reversible ET behavior; accordingly, the outer-sphere
oxidation of superoxide has been comprehensively studied
using chemical and electrochemical techniques.2−4 The ET
chemistry of peroxide as an isolated species, however, remains
ill-defined because the dianion is not readily available in free
form. Peroxide is extremely unstable under nonaqueous
conditions because of its ability to act as a strong Brønsted
base.5 For example, the electrochemical reduction of superoxide
−
form protonated peroxide (HO2 ), which in turn, oxidizes
DMSO to dimethyl sulfone (DMSO2).6 Peroxide is therefore
stabilized by coordination to a metal ion, and hence the
intrinsic oxidation−reduction properties of the isolated dianion
are difficult to establish because of metal−oxygen orbital mixing
and electrostatic effects. Given the importance of peroxide as a
deleterious intermediate in the biochemical reduction of
molecular O2,7 as a valuable industrial feedstock,8 and, in
particular, as a primary discharge product in nonaqueous
lithium−air batteries,9,10 it is desirable to understand the basic
Received: April 5, 2014
Published: April 28, 2014
© 2014 American Chemical Society
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a 100 mL Schlenk flask and 30 mL of dry tetrahydrofuran (THF) was
added. This reaction mixture was stirred under N2 with the vessel
connected to the Schlenk line. The contents formed a white-yellow
slurry. A yellow solution was formed after 12 h. This reaction mixture
was stirred for 24 h with no evident color change. The contents were
subjected to three cycles of freeze−pump−thaw and brought into the
glovebox. The remaining insoluble materials were removed by
filtration, and the solid was washed with 3 × 5 mL of THF to
dissolve any peroxide adduct that might have precipitated. THF was
removed under a dynamic vacuum. The contents were redissolved in a
minimum amount of THF (10 mL). The product was induced to
precipitate by adding Et2O dropwise with stirring. Excess 18-crown-6
was removed by washing the yellow solid with 3 × 10 mL of Et2O. A
sample of the yellow solid was dissolved in DMSO-d6, and a 1H NMR
spectrum was taken. The 1H NMR spectrum indicated complete
conversion to the peroxide adduct. Single crystals were obtained after
4 days by vapor diffusion of diethyl ether into a THF solution of
[K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6]. Yield: 0.80 g (0.54 mmol,
ET properties of peroxide uncoupled from the complicating
effects of protons or metal ions.
We have discovered that a soluble source of discrete O2
2−
units can be isolated by using hexacarboxamide cryptand
(mBDCA-5t-H6) as a sequestering agent (Figure 1).11 The
1
91%). ATR-FTIR on solid: (N−H) 3272 cm−1. H NMR (300 MHz,
DMSO-d6, δ): 14.63 (s, 6 H), 10.10 (s, 3 H), 8.16 (s, 6 H), 3.53 (s, 48
H), 3.39 (br, 6 H), 2.60 (br d, 6 H), 2.33 (br d, 12 H), 1.32 (s, 27 H).
NMR (100 MHz, DMSO-d6, δ): 165.56, 148.90, 134.99, 126.70,
124.23, 69.39, 59.97, 40.79, 34.40, 31.19. Anal. Calcd (found) for
C72H114N8O20K2: C, 58.04 (57.90); H, 7.71 (7.72); N, 7.52 (7.44).
Stopped-Flow Kinetic Measurements. THF solutions of the
reagents were prepared in an MBraun glovebox filled with ultrahigh-
purity argon (Airgas) and placed in Hamilton gastight syringes
equipped with three-way valves. Time-resolved spectra (380−800 nm)
were acquired over a range of temperatures using a Hi-Tech Scientific
KinetAsyst SF-61DX2 Multi-Mixing CryoStopped-Flow system (TgK
Scientific Ltd.) equipped with a quartz tungsten halogen light source, a
J&M TIDAS diode-array detector, and a Brandenburg 4479 series
PMT monochromator. The instrument was equipped with poly(ether
ether ketone) tubing fitted inside stainless steel plumbing, a 1.00 cm3
quartz mixing cell submerged in an ethanol cooling bath, and an
anaerobic kit purged with argon. The temperature in the mixing cell
was maintained to 0.1 °C, and the mixing time was 2−3 ms. All flow
lines of the instrument were extensively washed with degassed,
anhydrous THF before charging the driving syringes with reactant
solutions. The reactions were studied by rapid-scanning spectropho-
tometry under second-order conditions with a 1:1 molar ratio of the
two reactants. All of the experiments were performed in a single-
mixing mode of the instrument, with a 1:1 (v/v) mixing ratio. A series
of three or four measurements gave an acceptable standard deviation
(within 10%). Data analysis was performed with Kinetic Studio (TgK
Scientific Ltd.) and IGOR Pro 5.0 (Wavemetrics, Inc.).
Electrochemical Methods. Cyclic voltammograms (CVs) were
collected using a CH Intstruments (Austin, TX) 730C potentiostat.
Solutions of 0.5 mM [TBA]2[(O2)⊂mBDCA-5t-H6] in N,N-
dimethylformamide (DMF; 0.1 M [TBA][PF6]) were prepared in a
nitrogen glovebox. The cell was covered with a Teflon cap containing
the electrodes and sealed with parafilm. It was then removed from the
glovebox and immediately placed under a blanket of argon. The
temperature was controlled by placing the cell in an ethylene glycol
bath kept at 298 K. The working electrode was freshly polished glassy
carbon (area = 0.07 cm2), the counter electrode was a platinum wire,
and a fresh silver wire in DMF (0.1 M [TBA][PF6]) separated from
the working solution by a vycor frit was used as a pseudoreference
electrode. Prior to use, DMF had been dried by passage through an
alumina column followed by exposure to activated 4 Å sieves
overnight. At the conclusion of the experiments, ferrocene was
added and all potentials were referenced to the ferrocenium/ferrocene
(Fc+/0) couple.
Figure 1. View of the crystal structure of [K(18-crown-
6)]2[(O2)⊂mBDCA-5t-H6] depicting the 1D coordination polymer
formed in the solid state. Solvents of crystallization, tert-butyl groups,
and hydrogen atoms are omitted for clarity. Color code: C, gray; N,
blue; O, red; K, pink.
dianion does not interact with surrounding cations, and O2 is
released upon chemical oxidation of the sequestered dianion.
This simple oxidative ET serves as a model for the desired half-
reaction needed for a rechargeable lithium−air battery, for
which a large overpotential is required. This overpotential has
been the subject of numerous studies12−14 and remains a hurdle
in the pursuit of a practical metal−air battery.15 Herein, we
report the ET kinetics of chemical and electrochemical
oxidation of [(O2)⊂mBDCA-5t-H6]2−, with the goal of
providing insight into the inherent properties germane to
peroxide oxidation. Knowledge of the ET behavior from
2−
discrete O2 is useful not only for the design of metal−air
batteries capable of recharging at lower overpotentials but also
2−
for the informed use of a cryptand-encapsulated O2 oxidant
and/or atom-transfer reagent, in chemical transformations.
EXPERIMENTAL SECTION
■
General Methods. All manipulations were performed either with
use of Schlenk techniques or in a nitrogen-atmosphere glovebox. All
reagents were purchased from Aldrich. Quinones were sublimed three
times. Solvents (EMD Chemicals) were either used as received or
purified on a Glass Contour Solvent Purification System built by SG
Water USA, LLC. IR spectra were recorded on a Bruker Tensor 37
Fourier transform infrared (FTIR) spectrometer. NMR solvents were
obtained from Cambridge Isotope Laboratories, and H and 13C{1H}
1
NMR spectra were obtained on a Varian 300 MHz or a Bruker 400
MHz spectrometer and are referenced to residual solvent signals.
Elemental analyses were performed by Midwest Microlabs, LLC.
Crystallography. Low-temperature diffraction data were collected
on a three-circle diffractometer coupled to a Bruker-AXS Smart Apex
charged-coupled-device (CCD) detector with graphite-monochro-
mated Mo Kα radiation (λ = 0.71073 Å) for the structure of [K(18-
crown-6)]2[(O2)⊂mBDCA-5t-H6], performing φ and ω scans. The
structures were solved by direct methods using SHELXS and refined
against F2 on all data by full-matrix least squares with SHELXL-97
using established methods.16 All non-hydrogen atoms were refined
anisotropically.17
Electrochemical Modeling. The diffusion coefficient (D) and
reduction potential (E0) of O2 were determined from a CV of a 4.6
mM (saturated) solution of O2 in DMF (0.1 M [TBA][PF6]). The
18
•−
1
diffusion coefficient of O2 was approximated as /3D(O2). The
literature value for the heterogeneous rate constant (ks) of 0.093 cm/s
O2 in DMSO (0.1 M [TBA][ClO4]) was used.19 All other quantities
Preparative Methods. For [K(18-crown-6)]2[(O2)⊂mBDCA-5t-
H6], mBDCA-5t-H6 (0.587 mmol, 1.00 equiv), 18-crown-6 (1.292
mmol, 2.2 equiv), and KO2 (1.292 mmol, 2.2 equiv) were loaded into
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were varied in the DigiElch software suite21 until a satisfactory fit to the
experimental data was achieved with reasonable values.
according to Butler−Volmer kinetics for α = 0.5.20 This result,
together with the broadness of the oxidation wave, indicates
that ET attendant to the cryptand peroxide oxidation process is
not an electrochemically or chemically facile process.
RESULTS
■
Synthesis. The sequestration of K+ ions of [K2(DMF)5]-
[(O2)⊂mBDCA-5t-H6] by 18-crown-6 affords the appropria-
tion of [K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6] in 73%
isolated yield and engenders good solubility of the complex
in THF.11 Alternatively, a more facile preparative route of
[K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6] was found, which
avoids the extra step of isolating [K2(DMF)5]-
[(O2)⊂mBDCA-5t-H6]. For this method, a slurry of
mBDCA-5t-H6 and 2.2 equiv of 18-crown-6 is treated with
2.2 equiv of KO2 in THF, resulting in a 91% isolated yield for
the peroxide-guest complex. The 1H NMR spectra of
compounds obtained by either of these preparative methods
are identical except for the additional resonances corresponding
to 18-crown-6 (Figure S1 in the Supporting Information, SI).
Single crystals of the complex were obtained by vapor diffusion
of Et2O into a THF solution of [K(18-crown-6)]2[mBDCA-5t-
H6]. The solid-state structure reveals two environments for the
K+ ions: one ion is coordinated to the CO of neighboring
cryptands, forming a 1D coordination polymer, and the other
one is bound terminally (Figure 1).
The broad oxidation wave may be modeled according to the
Butler−Volmer formalism using α = 0.38 for the one-electron
oxidation of [TBA]2[(O2)⊂mBDCA-5t-H6].11 The data can
also be described using the Marcus−Hush model of electrode
kinetics. Figure 2 shows that a satisfactory representation of the
data is achieved for all scan rates using electrochemical
simulation software, such as DigiElch,21 with a reorganization
energy λ = 0.79 eV, an ET rate constant of ks = 2.7 × 10−5 cm/
2−
s, and a standard reduction potential of O2•−/O2 within the
cryptand of −0.85 V versus Fc+/0 (Table S1a,b in the SI). The
poor fit at low scan rates of the reduction of free O2 is ascribed
to unwanted convection contributions to the current.
Chemical Oxidation with Quinones. Quinones are
rapidly reduced by [(O2)⊂mBDCA-5t-H6]2−, requiring the
use of stopped-flow spectroscopy at low temperature in order
to determine the ET reaction rate. Dichlorodicyanoquinone
(DDQ) cleanly reacts with [K2(DMF)5][(O2)⊂mBDCA-5t-
H6] in DMF under stoichiometric conditions to produce free
O2 (quantified by gas chromatography), free cryptand, and the
DDQ dianion, DDQ2−.11 However, DMF could not be used as
a solvent in the stopped-flow measurements because of the
solvent’s relatively high freezing point, relatively high viscosity,
and incompatibility with some materials used to seal the flow
lines of the instrument. Thus, THF was employed instead,
necessitating the use of the more soluble [K(18-crown-
6)]2[(O2)⊂mBDCA-5t-H6] complex.
E l e c t r o c h e m i c a l O x i d a t i o n . C V s o f
[TBA]2[(O2)⊂mBDCA-5t-H6] under an atmosphere of argon
exhibit oxidation and reduction features (Figure 2). The
The kinetics of the reaction between [K(18-crown-
6)]2[(O2)⊂ mBDCA-5t-H6] and DDQ was measured over a
broad temperature range (−85 to +25 °C) under second-order
conditions with equal concentrations of reactants. Reaction
times varied when the stopped-flow experiment was performed
in the diode-array mode as opposed to reproducible reaction
times when the experiment was performed in the single-
wavelength mode. Intense illumination with white light was
used in the former case, whereas low-intensity, monochromatic
visible light was used in the latter. These effects indicate
photosensitivity of the reaction, which is circumvented in
single-wavelength-mode detection. Thus, only single-wave-
length data measured at λ = 601 nm was used for kinetic
analyses.
Figure 3a shows the time-resolved visible absorption trace of
the formation of a species at low temperature (−85 °C) with
absorption maxima at λ = 445, 561, and 601 nm. These features
are consistent with DDQ•−,22 which forms rapidly. The kinetics
for the prompt appearance of DDQ•− is in accordance with the
ET reaction
Figure 2. Experimental (black solid line) and simulated (red solid
line) CVs of 0.5 mM [TBA]2[(O2)⊂mBDCA-5t-H6] in DMF (0.1 M
[TBA][PF6]) at (a) 50, (b) 100, (c) 250, and (d) 500 mV/s. Crosses
and arrows depict the initial point and direction of the scan.
kET
2−
−
LO2 + DDQ ⎯⎯→ LO2 + DDQ•−
(1)
where L = mBDCA-5t-H6. The initial rate of formation of the
anion (inset in Figure 3a) fits pseudo-first-order reaction
kinetics,
reduction wave, which we have attributed to the chemically
irreversible reduction of O2, only appears after oxidation of
[(O2)⊂mBDCA-5t-H6]2− (Figures S2 and S3 in the SI).11 The
oxidation peak current (ip) displayed a linear variation with the
square root of the scan rate (ν; Figure S4 in the SI), indicating
well-defined Cottrell kinetics for a soluble diffusion-controlled
species. The oxidation peak potential (Ep) varied linearly with
log(ν) with a slope equal to 95 mV/decade (Figure S5 in the
SI), which is inconsistent with an electrochemically reversible
ET or an ET followed by a chemical step (30 mV/decade)
1obst
rate = ae−k
(2)
to yield the observed rate constants k1obs (Figure S6 in the SI),
from which second-order ET rate constants kET were estimated
using kET = k1obs/[DDQ] = 4 × 106 M−1 s−1. No pronounced
differences in the values of kET were found at the three
temperatures studied (Table S2 in the SI), which is likely due
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presented in Figure S9 in the SI and are summarized in Table
S2 in the SI. Monitoring the reaction for several minutes at low
temperature (see Figure S8 in the SI) revealed yet an
additional, though minor, absorption growth phase. Because
these secondary growth phases associated with reactions (3)
and (4) were slow with respect to the kinetics of reaction (1),
they posed no interference to analysis of the ET kinetics of
peroxide as described by reaction (1).
Whereas DDQ•− persists at low temperature, it dispropor-
tionates to DDQ and DDQ2− at higher temperatures, as
evidenced by growth of the dianion’s characteristic spectral
features, the most prominent of which is a band at λmax ∼ 417
nm.22 Figure 3b shows this conversion at 20 °C. Figure S10 in
the SI presents the time-dependent bleach at λ = 601 nm that
accompanies this transformation at 5 °C. Formation of DDQ2−
may occur by either the reaction of DDQ•− with the cryptand
superoxide or cryptand peroxide complex. The activation
parameters for the appearance of DDQ2− are derived from
the kinetic data in Figure S11 in the SI, and they are
summarized in Table S2 in the SI. Because conversion of
DDQ− to DDQ2− occurs over long time scales and only at
higher temperature, this process does not interfere with
examination of the ET kinetics of reaction (1).
2−
To further elucidate the ET chemistry of the LO2 adduct,
the ET reactions of six additional quinones (Br4Q, Cl4Q, F4Q,
Cl2Q, ClQ, and H4Q; see Table 1) were examined by the
stopped-flow method. The overall driving force of the reaction
Figure 3. (a) Time-resolved spectral changes obtained upon mixing
THF solutions of [K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6] (0.05
mM) and DDQ (0.05 mM) at −85 °C, showing rapid formation of
the DDQ•− radical anion. (b) Time-resolved spectral changes obtained
upon mixing THF solutions of [K(18-crown-6)]2[(O2)⊂mBDCA-5t-
H6] (0.1 mM) and DDQ (0.1 mM) at 20 °C. The insets are the
kinetic traces at λ = 601 nm. All concentrations are reported after
mixing in the stopped-flow cell.
kET
2−
−
Q + LO2 ⎯⎯→ Q•− + LO2
(5)
Table 1. Driving-Force and ET Rate Constants of Quinone/
2−
LO2 at −80 °C for Reaction (5)
to our inability to accurately observe a difference in the rate
with sufficient fidelity over this small temperature range.
Accordingly, accurate activation parameters could not be
obtained.
After the initial absorption rapidly increased because of the
formation of DDQ•−, more quinone anion appeared in two
slower steps (Figures S7 and S8 in the SI). The formation of
the quinone monoanion on slower time scales is consistent
with the bimolecular reaction of the superoxide cryptand
complex produced from reaction (1)
k2
−
LO2 + DDQ → L + DDQ•− + O2
(3)
or from the disproportionation reaction of the superoxide
adduct
−
2−
2LO2 → LO2 + L + O2
(4)
followed by the reaction of LO22− with DDQ per reaction (1).
Superoxide in the presence of free cryptand rapidly produces
LO22− and O2. Hence, we believe that superoxide disproportio-
nation is facile and that one of the slower events that leads to
DDQ•− is most likely due to reaction (4), followed by reaction
(1). This slower growth of DDQ•− appeared to be complete
within tens of seconds (Figure S7 in the SI). Because the time
scale for this event was well separated from the initial kinetic
phase, the slow process could be examined independently from
reaction (1) over a broad temperature range (−85 to −59 °C).
Activation parameters for this event are extracted from the data
a
Reduction potentials of quinones are referenced versus Fc+/0
Measured in DMF at −80 °C. The rate constant for the H4Q/
.
b
c
peroxide reaction at −80 °C was obtained by extrapolation from
measurements at +25 to −50 °C using the activation parameters (Ea)
obtained from the higher temperature data (see Table S2 in the SI).
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spans 1 V with this set of quinone reactants. The free-energy
change (ΔG°) of ET from [K(18-crown-6)]2[(O2)⊂mBDCA-
5t-H6] to members of the quinone series is obtained from
orders of magnitude, from the mildly endergonic H4Q system
to the most exergonic DDQ system. The driving-force
dependence of the ET rate constants is shown in Figure 5,
ΔG° = −e(Ered − E1)
(6)
where E1 = −0.85 V versus Fc+/0 (in DMF) is the reduction
potential of [(O2)⊂mBDCA-5t-H6]2− and Ered is the first
reduction potential of the quinones listed in Table 1.23,24 The
reactions were performed under second-order conditions with
identical concentrations of reactants in all cases. The time-
resolved diode-array spectra of reactions of the seven quinones
and [K(18-crown-6)]2[(O2)-⊂mBDCA-5t-H6] in THF were
acquired at −80 °C, except for H4Q, which required higher
temperatures for the reaction to proceed readily (−50 to +25
°C). The spectral changes accompanying the ET reaction are
shown in Figures 4 and S12−S16 in the SI. To avoid
Figure 5. Dependence of RT ln kET on ΔG° for the first one-electron
oxidation of [K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6] with seven
different quinones in THF at −80 °C. (black solid line) Marcus
curve, eq 11, with kmix = 3.8 × 106 M−1 s−1, λ(LO /Q) = 1.2 eV, and Z =
2−
2
9 × 108 M−1 s−1. The linear regions denoted by α = 0.38 (red) and α =
0.5 (green) are the tangents of the Marcus curve at the points directly
above the midpoints of the lines. Their slopes are −0.38 and −0.5,
respectively.
Figure 4. Time-resolved spectral changes obtained upon mixing THF
solutions of [K(18-crown-6)]2[(O2)⊂mBDCA-5t-H6] (0.1 mM) and
Cl2Q (0.1 mM) at −80 °C, showing rapid formation of the Cl2Q•−
radical anion. Inset: Kinetic trace at 452 nm acquired in a single-
wavelength registration mode. All concentrations are reported after
mixing in the stopped-flow cell.
where the values of RT ln kET are plotted against the driving
force (ΔG°). An increase of the RT ln kET values as a function
of ΔG° is observed over more than 5 orders of magnitude of
kET in the less exergonic region (−0.48 eV < ΔG° < 0.04 eV).
For the strongest oxidant, DDQ (at ΔG° = −0.98 eV), the ET
rate appears to level off. However, the ET rate for reaction (1)
could not be measured accurately because the mixing time of
the stopped-flow instrument has a limiting value, kmix, which we
have approximated with 3.8 × 106 M−1 s−1.
contributions from photochemistry, single-wavelength kinetic
traces were acquired at λ = 610 nm for DDQ, λ = 448 nm for
Cl4Q and Br4Q, λ = 432 nm for F4Q, λ = 452 nm for Cl2Q, λ =
451 nm for ClQ, and λ = 449 nm for H4Q. The kinetic traces in
Figures S17−S23 in the SI were analyzed with the bimolecular
expression
The activation free energy, ΔG⧧, for outer-sphere ET,25−27
(ΔG° + λ)2
ΔG⧧ =
(8)
4λ
1obst
2obst
rate = ae−k + be−k
is related in the Marcus formalism to the free energy of the
reaction, ΔG°, and the reorganization energy, λ. In its simplest
elaboration, Marcus theory provides the ET rate constant via
the Eyring equation
(7)
We note that the kinetic traces for the fastest reactions, Q =
Cl4Q and F4Q, were not fit well by eq 7. In this case, the traces
were better fit by eq 2 to yield k1obs, from which the second-
order rate constant was then estimated from kET = k1obs/[Q].
For consistency, kinetic traces from the other four reactions, Q
= Br4Q, Cl2Q, ClQ, and H4Q, were treated in a similar manner.
The rate constant obtained from eq 7 and those estimated from
the first-order fitting of the initial segment of the kinetic traces
with eq 2 were in accordance with each other.
ΔG⧧
RT
⎛
kact = Z exp⎜−
⎝
⎞
⎟
⎠
(9)
where Z is the bimolecular collision frequency, often taken as
∼1011 M−1 s−1. In semiclassical expressions of Marcus theory, Z
is replaced by nuclear and electronic tunneling terms. In either
classical or semiclassical formalisms, by utilizing a series of
structurally related quinones, we assume with good confidence
that the values for Z and λ are the same for all reactions in the
present study. Under this supposition, only changes in ΔG° will
influence the magnitude of the measured rate constants.
λ was estimated using the activation energy measured for
reaction between ClQ and [(O2)⊂mBDCA-5t-H6]2− (Figure
S26 in the SI). Assuming that the activation entropy is minimal,
DISCUSSION
■
The ability to encapsulate a peroxide dianion within the cage of
hexacarboxamide cryptand (mBDCA-5t-H6) permits the ET
chemistry of an isolated peroxide ion to be investigated. The
homologous quinone series listed in Table 1 allows ET reaction
(5) to be analyzed by Marcus theory over a larger driving force.
The second-order rate constants listed in Table 1 vary over 6
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ΔG⧧ = ΔH⧧ = 24.0 kJ/mol (0.249 eV), and the reorganization
linchpin between the Butler−Volmer model and the Marcus
ET formalism.31,32 Formally, the transfer coefficient is defined
2−/Q)
energy for reaction (5) is calculated to be λ(LO
= 1.2 eV.
2
as
Furthermore, because λ for a cross-reaction is an average of the
λ values of the relevant self-exchange reactions,28 the
component contributions from the reactant partners
[(O2)⊂mBDCA-5t-H6]2− and the quinone are furnished from
∂ΔG⧧
α =
(13)
°
∂ΔG
Within the context of Butler−Volmer kinetics, it is assumed,
without any theoretical basis, that a linear relationship exists
between ΔG⧧ and ΔG°. In Marcus theory, ΔG⧧ has a quadratic
dependence on ΔG°, according to eq 8, leading to
(LO22−/LO2
)
)
−
•−
λ
+ λ(Q/Q
2−
λ(LO
=
/Q)
2
(10)
2
•−
Values for the self-exchange λ(Q/Q are known to depend on
)
the nature of the countercation due to ion-pairing effects.29
⎛
⎜
⎞
⎟
Though λ(Q/Q has not been measured with K(18-crown-6)+
1
2
ΔG°
λ
•−
)
α =
1 +
⎝
⎠
(14)
as the cation, it has been measured for quinones with
countercations of K([2,2,2]cryptand)+, λ(Q/Q = 0.42 eV,
•−
)
and K(THF)4 , λ(Q/Q ) = 0.99 eV.29 Taking an average of these
+
Excursions in the potential around the standard reduction
potential involving small molecules are typically small, in the
range of 30−200 mV, and thus λ ≫ |ΔG°|. Therefore, in most
electrochemical experiments, the transfer coefficient is in the
linear Marcus regime where α = 0.5 (green region of Figure 5)
and a Butler−Volmer approximation with α = 0.5 is often
appropriate. However, when the electrode kinetics is sluggish
owing to poor coupling to the electrode, large driving-force
overpotentials are required to produce a peak current response
in a CV, despite moderate or low values of λ. Therefore,
according to eq 14, as the absolute magnitude of ΔG°
approaches λ, the value of the transfer coefficient will decrease
from α = 0.5 to a lower value, depending precisely on the ratio
of ΔG°/λ. In a graphical sense, the measured current response
is then occurring in a region of the Marcus curve that is closer
to the curve’s apex, for example, in the red region of Figure 5.
The electrode kinetics of [TBA]2[(O2)-⊂mBDCA-5t-H6] is
consistent with this latter case. Simulation of the CVs of
[(O2)⊂mBDCA-5t-H6]2− yields a heterogeneous ET rate
constant of ks = 2.7 × 10−5 cm/s, which places ET on the
border of what is commonly accepted as an electrochemically
quasi-irreversible or irreversible ET.33 The broadness of the
wave is in accordance with the attenuated transfer coefficient of
α = 0.38, as determined from the Butler−Volmer model.11 By
modeling the CV features using the Marcus−Hush model of
electrokinetics, λ may be obtained, where α is treated as a
variable according to eq 14.34 We find a heterogeneous
reorganization energy of λel = 0.79 eV from the electrochemical
simulations (vide supra). This electrochemical-derived reor-
ganization energy can be compared to the homogeneous
reorganization energy derived from the fit of the Marcus curve
•−
•−
two values to approximate λ(Q/Q = 0.71 eV for K(18-crown-
)
6)+, then the estimate of λ(LO
= 1.7 eV is determined
−
2−/LO2
)
2
from eq 10.
For the stopped-flow experiment, the observed ET rate
constant is convoluted with the mixing time of the reactants.
The equation that governs the observable ET kinetics is
1
kET
1
1
kact
1
kmix
1
=
+
=
+
2
⎡
⎤
−(ΔG ° + λ)
4λRT
kmix
Z exp
⎢
⎣
⎥
⎦
(11)
This equation is a double-reciprocal model for the observable
kinetics in a stopped-flow instrument, which has an inherent
30
2−
mixing time defined by kmix
.
Using λ(LO
= 1.2 eV, which
/Q)
2
was deduced from the temperature dependence of the reaction
with ClQ and the driving force for the ET reactions, the
observed measurements are approximated by eq 11 for Z = 9 ×
108 M−1 s−1 (Figure 5). Figure S26 in the SI shows a
comparison of the plots derived from eq 11 for a range of Z
values.
The differentiated Marcus expression yields
⎡
⎢
⎣
⎤
⎥
⎦
⎛
⎞
∂RT ln kET
∂ΔG°
∂
λ
4
ΔG°
2
ΔG°2
4λ
=
RT ln Z −
+
+
⎜
⎝
⎟
⎠
∂ΔG°
⎛
⎞
⎟
1
2
ΔG°
λ
⎜
= − 1 +
⎝
⎠
(12)
This equation defines the local slope in the activation
controlled regime of the curve in Figure 5 at any driving-
force value. For the driving-force range of λ ≫ |ΔG°|, as
depicted in the green region in Figure 5, a linear free-energy
relationship (LFER) is obtained with a slope −0.5. For a regime
in Figure 5, though not directly. The homogeneous
−
2−/LO2
reorganization energy, λ(LO
), is defined for a bimolecular
2
self-exchange reaction, which includes contributions from two
reactant molecules, whereas the electrochemical reorganization
energy involves only a single-molecule reactant (there is no
contribution from the electrode surface). Therefore, the correct
comparison is between the electrochemical reorganization
1
in which the average driving force is /4 the magnitude of λ, as
depicted by the red region of Figure 5, then a LFER is obtained
with a slope of −0.38. In this study, the specific quinones were
chosen such that a large range of driving force was explored
and, therefore, we prefer to model the Marcus kinetics with the
quadratic Marcus equation (eq 11), as shown by the black solid
line in Figure 5. The data in the activation control region fit this
expected curve, with a limiting region eventually achieved
because of the mixing time of the stopped-flow spectrometer.
The homogeneous ET kinetics of LO22−, as explained by
Figure 5, is related to its heterogeneous ET reaction at an
electrode surface, as defined by the CVs of Figure 2. The
Butler−Volmer model of electrode kinetics accounts for a rate-
limiting ET and is characterized by the symmetry factor, α, also
known as the transfer coefficient. This transfer coefficient is the
35
1
−
2−/LO2
)
energy, λel, and /2λ(LO
,
2
1
2
2−/LO2
)
−
λ(LO
= 0.85 eV
2
(15)
The agreement between the two reorganization energies is
quite good considering that the assumption of an intermediate
reorganization energy for quinones in the presence of the
cation, K(18-crown-6)+, was needed to arrive at the
homogeneous reorganization energy for [(O2)⊂mBDCA-5t-
H6]2− oxidation (vide supra).
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With the heterogeneous rate constant, ks, and reorganization
energy, a heterogeneous preexponential factor, Zel, can also be
derived using eq 9 with ΔG⧧ = λel/4. We find Zel = 0.059 cm/s,
which is 5 orders of magnitude lower than the collision
frequency Zel = (RT/2πM)1/2 = 2000 cm/s, where M is the
molar mass of [(O2)⊂mBDCA-5t-H6]2−. This disparity is
consistent with the results of homogeneous ET, in which a
preexponential factor of Z = 9 × 108 M−1 s−1 was found to be 2
orders of magnitude lower than the classical value. The
diminished preexponential factor, whether ET by LO22− occurs
to a molecule or electrode, is attributed to poor electronic
ASSOCIATED CONTENT
* Supporting Information
X-ray crystallographic data in CIF format, CVs, parameters
used for simulation of CVs, stopped-flow kinetic traces, decay
kinetics and summary of stopped-flow data, H NMR spectra,
■
S
1
electrochemical plots of the potential and current versus scan
rate, kinetic traces for the formation of quinone anions, time-
resolved stopped-flow spectral changes accompanying ET
2−
between LO2 and quinones, Cl4Q, F4Q, Br4Q, ClQ, and
H4Q, Arrhenius and Eyring plots, and Marcus curve plots with
different Z factors. This material is available free of charge via
the Internet at http://pubs.acs.org. Complete crystallographic
data were deposited in the Cambridge Crystallographic
Database Centre (CCDC 983504).
coupling36 because of steric shielding of O2 within the
2−
hexacarboxamide cryptand. Because the electron acceptor in
the homogeneous reaction, the quinone, is small and may have
partial access to the cavities presented by the cryptand
molecule, whereas the heterogeneous electron acceptor, the
electrode, does not, it is not surprising that the heterogeneous
ET event exhibits even greater nonadiabatic character than the
homogeneous ET.
AUTHOR INFORMATION
Corresponding Authors
*E-mail: ccummins@mit.edu.
*E-mail: dnocera@fas.harvard.edu.
■
Funding
D.G.N. acknowledges support of the Department of Energy
(DOE; Grant DE-SC0009758). C.C.C. acknowledges support
of the NSF-CCI (Grant CHE-0802907). E.V.R.-A. acknowl-
edges support of the DOE (Grant DE-FG02-06ER15799).
Grants from the NSF also provided instrument support to the
DCIF at MIT (Grants CHE-9808061 and DBI-9729592) and
to E.V.R.-A. at Tufts (Grants CRIF CHE-0639138 and MRI
CHE-1229426). D.J.G. acknowledges the support of the NSF's
Graduate Research Fellowship Program. The authors also
acknowledge the Robert Bosch Company for partial financial
support.
CONCLUSIONS
■
A free peroxide ion may be isolated within the cage of a
hexacarboxamide cryptand, thus allowing for the ET reactivity
of this dianion of oxygen to be examined. Enhanced solubility
of [(O2)⊂mBDCA-5t-H6]2− in THF is enabled by sequestra-
tion of the K+ counterions by 18-crown-6, thus allowing for the
study of homogeneous ET via the stopped-flow method. The
ET reaction of the encapsulated peroxide with quinones is
consistent with a highly nonadiabatic outer-sphere transfer
owing to steric shielding of peroxide from its reacting partner
by the hexacarboxamide cryptand. These results correlate well
with the heterogeneous ET rate measurements, which exhibit
an apparent transfer coefficient of α < 0.5. Modeling the
[(O2)⊂mBDCA-5t-H6]2− electrochemical response within a
Marcus theory framework yields a consistent set of results for
the homogeneous and heterogeneous ET reactions. We have
emphasized in this study the direct relationship between the
local slope of the Marcus curve and α. For nonadiabatic ET, α
can be treated as a variable that depends on the driving force.
The λ value thus obtained is consistent with that obtained in
homogeneous Marcus analysis. This is one of the few cases37,38
where a direct comparison between homogeneous and
heterogeneous ET reactions for a given species has been
made. Understanding the intrinsic parameters that govern the
kinetics of ET from this unique species will facilitate its
development as a reagent for oxidations, reductions, and/or
atom-transfer chemistries.
The most fundamental reaction of all molecular oxygen
species is ET. Owing to our success in using a macro-bicyclic
anion receptor39 to furnish an isolated peroxide dianion species
that is soluble in aprotic organic media, the kinetics of the
transfer of an electron from the peroxide dianion in the absence
of an intimately bound proton or metal ion has now been
established. Considering the importance of peroxide as an
intermediate in biochemical redox processes, as a valuable
industrial feedstock, and as a primary discharge product in
nonaqueous lithium−air batteries, the results reported herein
provide a basis for elucidating the chemistry of peroxide in a
range of subjects pertaining to oxygen and ET.
Notes
The authors declare no competing financial interest.
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