Proton-coupled electron transfer in the
electrocatalysis of CO
2
reduction: prediction of
sequential vs. concerted pathways using DFT†
Adrien J. G
¨
ottle and Marc T. M. Koper
*
Herein we investigate computationally in detail the mechanism of the formation of the carboxylate adduct
during the electroreduction of CO
2
in water catalysed by cobalt porphyrin complexes. Specifically, we
address qualitatively the competition between the concerted and sequential pathways for the proton-
coupled electron transfer. We use a simple methodology for accurate computation of the pK
a
of the
neutral and anionic carboxylate intermediates, [CoP–COOH] and [CoP–COOH]
(where CoP is a cobalt
porphine complex), based on the isodesmic proton-exchange reaction scheme. The predicted values are
used as in input for a theoretical model that describes the transition between the sequential and
concerted pathways. The activation of the sequential pathway (ET–PT) that leads to the formation of the
neutral [CoP–COOH] intermediate at pH z 3.5 (pK
a
[CoP–COOH] ¼ 3.5 0.4), as predicted by the
calculations, is in good agreement with the drastic increase in the faradaic efficiency of the CO
2
reduction reaction towards CO at pH ¼ 3 compared to pH ¼ 1, as experimentally observed. This
confirms the existence of the CO
2
anionic adduct [CoP–CO
2
]
as a viable intermediate at pH ¼ 3 and its
crucial role for the pH dependence of the faradaic efficiency for the CO
2
reduction. The analysis also
shows that when the pH is significantly higher than the pK
a
of the neutral carboxylate adduct, the CO
2
reduction has to go through an alternative pathway with the formation of the anionic carboxylate
intermediate [CoP–COOH]
. It is formed through a concerted proton–electron transfer step from the
anionic CO
2
adduct [CoP–CO
2
]
when the pH is below 8.6 (pK
a
[CoP–COOH]
¼ 8.6 0.4). At pH z
8.6 and above, another decoupled ET–PT is predicted to take place, leading to the formation of
a dianionic CO
2
adduct [CoP–CO
2
]
2
.
1. Introduction
The reduction of carbon dioxide into valuable products is
a research area that currently attracts signicant attention
within the eld of environmental and energy science.
1
Successful achievements in this highly topical theme could have
a drastic impact on modern society, especially by decreasing its
dependence on fossil fuels.
2,3
Still, an efficient system is
currently far from realized and progress in this area is closely
related to the development of catalysts that are efficient, stable
and contain cheap and abundant non-noble metals.
4
The unravelling of important aspects of the electrochemical
CO
2
reduction reaction (CO
2
RR) mechanism for various type of
catalysts using rst-principle electronic-structure calculations
has provided valuable insights.
5–17
So far, these investigations
have mainly focused on the determination of overpotentials and
product selectivity by computation of the thermodynamic
energy proles along the possible reaction pathways. An
important mechanistic aspect that is typically not dealt with in
these rst-principles calculations is the possibility for proton-
coupled electron transfers (PCET) to follow pathways where the
electron and the proton are either transferred sequentially
(sequential proton–electron transfer: SPET) or concertedly
(concerted proton–electron transfer: CPET). It is typically
believed that the selection between CPET and SPET pathways is
closely related to the nature of the catalyst. For molecular
catalysts decoupled ET and PT steps are expected, whereas for
solid metallic electrocatalysts one assumes CPET steps.
However, there is growing evidence for the importance of SPET
pathways also on metallic electrocatalysts,
18–25
and therefore
a complete picture must consider both sequential and
concerted PCET steps in the whole reaction mechanism. From
the computational point of view, the heterogeneous electro-
catalysis community typically employs the so-called computa-
tional hydrogen electrode (CHE) methodology introduced by
Nørskov et al.,
26
which has been very successful in predicting
the thermodynamics of CPET steps. However, the CHE meth-
odology cannot account for SPET pathways. Up to now, there is
no simple and accurate computational methodology available
Leiden Institute of Chemistry, Leiden University, PO Box 9502, 2300 RA Leiden, The
Netherlands. E-mail: m.koper@chem.leidenuniv.nl
† Electronic supplementary information (ESI) available. See DOI:
10.1039/c6sc02984a
Cite this: Chem. Sci.,2017,8,458
Received 7th July 2016
Accepted 20th August 2016
DOI: 10.1039/c6sc02984a
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to systematically address the selection or competition between
SPET and CPET pathways in electrocatalytic mechanisms.
In this work, we focus on a concrete example in CO
2
RR
catalysis where it has been experimentally supported that the
selectivity between CPET and SPET pathways matters: the
formation of the carboxylate adduct (*–COOH) and its further
reduction (at low pH) and decomposition (at higher pH) to CO
during CO
2
RR in water catalysed by a cobalt protoporphyrin IX
complex immobilized on an inert pyrolytic graphite electrode.
27
The neutral *COOH intermediate is assumed to be formed aer
the addition of the rst proton–electron pair and its subsequent
reduction leads to the formation of CO or further reduced
species (formaldehyde, methanol or methane). We have found
that the faradaic efficiency of CO
2
RR on this immobilized
molecular catalyst features a drastic change from pH ¼ 1topH
¼ 3, with CO production becoming competitive at pH ¼ 3 with
the concomitant but undesirable hydrogen evolution reaction
(HER). This observation made us postulate the existence of an
anionic CO
2
adduct, capable of subtracting a proton from
a nearby water molecule, thereby allowing a high turnover to be
maintained for the CO
2
RR in a proton-poorer environment
compared to the HER reaction (which is proton diffusion
limited at pH ¼ 3). The existence of this intermediate implies
a decoupling between ET and PT of the initial PCET.
As mentioned, rst-principles studies of the CO
2
RR mecha-
nism on metallic catalysts in water assume that the formation of
the neutral carboxylate adduct follows a CPET pathway,
* +CO
2
+H
+
+e
/ *–COOH
whereas studies dealing with molecular catalysts typically
assume a SPET (ET–PT) pathway. Such a SPET mechanism was
also suggested from a recent theoretical study from our group
on CO
2
RR catalysed by cobalt porphyrin complexes:
15
* +CO
2
+e
/ *–CO
2
*–CO
2
+H
+
/ *–COOH
In our recent DFT study,
15
we showed with the CHE method-
ology that the potential limiting step of the CORR to CO is the
formation of the neutral carboxylate intermediate (subsequent
reduction is predicted to be exothermic). The computed onset
potential of 0.43 V (vs. a reversible hydrogen electrode) agrees
well with the experimental onset potential. It is noteworthy that
in both mechanisms (concerted and sequential), in addition to
the transfer of the proton–electron pair, there is the association
of the CO
2
with the catalyst. Here, * stands for the active site of
the molecular catalyst (metal centre) and e
for the electron of
the initially reduced catalyst responsible for the actual reduc-
tion of CO
2
. This notation follows more closely the notation
used for PCET steps in heterogeneous electrocatalysis but one
has to keep in mind that from the molecular electrocatalysis
point-of-view, the electron actually “ows” to the substrate in
two steps with the initial reduction of the catalyst, followed by
subsequent ligation by the adduct with a corresponding charge
redistribution. Aer the formation of the CO
2
anionic adduct,
different scenarios are possible depending on the catalyst and
on the experimental conditions (applied potential, pH). In
particular, from the work of Leung et al., a PCET pathway is
predicted to take place at neutral pH from the CO
2
anionic
adduct to form an anionic carboxylate intermediate, which can
readily decompose to form CO.
6
Our specic aim in this work is to introduce a simple and
general methodology to elucidate the mechanism of the
formation of the carboxylate adduct for a simple porphyrin
catalyst (cobalt porphine complex: CoP) taking into account the
active role of the pH in the selectivity between the CPET and
SPET pathways, and also in the selectivity between the possible
charged states of the carboxylate adduct (neutral or anionic).
The key ingredient of this methodology is the calculation of the
acid–base equilibrium constant, which is a necessary quantity
to compare the thermodynamics of the CPET and SPET path-
ways and to rationalize the transition between sequential and
concerted PCET. To this end, we base ourselves on the accurate
computation of pK
a
values of the neutral [CoP–COOH] and
anionic [CoP–COOH]
species using a simple method known as
the isodesmic proton exchange reaction scheme (IPER).
28
We
predict that at pH z 3.5 and higher, the formation of the
neutral [CoP–COOH] intermediate follows preferentially the
sequential pathway with the formation of the anionic CO
2
adduct [CoP–CO
2
]
as a viable intermediate. At much higher
pH, another pathway takes place that results in the formation of
the anionic [CoP–COOH]
intermediate, followed by another
SPET at pH z 8.3 and higher. Beyond the specic example
investigated in this work, the simple methodology introduced
in this paper can be applied to any molecular or metallic elec-
trocatalyst for the systematic prediction of the selectivity
between SPET and CPET, and thereby allows the calculation of
reaction schemes beyond the CHE methodology.
2. Theory and methodology
2.1 Theoretical background
PCET reactions are ubiquitous in chemistry.
29
The well-known
square scheme depicted in Fig. 1 illustrates the possible
scenarios for PCET reactions in general: the CPET pathway
corresponding to the “diagonal” path, and SPET pathways cor-
responding to “off-diagonal” paths. Signicant attention has
Fig. 1 Possible pathways for a proton-coupled electron transfer (ET:
electron transfer, PT: proton transfer) and the thermodynamic quan-
tities associated with the reaction steps.
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been devoted to the fundamental description and the experi-
mental implications of these pathways.
29–34
In order to address the selectivity between these pathways,
one has to take into account their relative kinetics and ther-
modynamics. A recently proposed theoretical model describes
the transition between SPET and CPET pathways by providing
analytical expressions for the activation energies of the ET, PT
and CPET steps that include as parameters both thermody-
namic quantities and reorganization energies.
35
Depending on
the relative values of these parameters, one can distinguish
when a certain pathway, CPET or SPET, is preferred over the
other due to a lower activation barrier(s). Assuming outer-
sphere charge transfer, the rate constants of the ET, PT and
CPET steps are given by the following Marcus-type expressions:
k
ET
¼ k
0
ET
exp
ðl
ET
þ DG
ET
Þ
2
4l
ET
RT
!
(1)
k
PT
¼ k
0
PT
exp
ðl
PT
þ DG
PT
Þ
2
4l
PT
RT
!
(2)
k
CPET
¼ k
0
CPET
exp
ðl
CPET
þ DG
CPET
Þ
2
4l
CPET
RT
!
(3)
In these equations, the k
0
parameters are pre-exponential
factors, the l variables are the reorganization energies and the
DG values are the free reaction energies of the separate ET, PT
and CPET reaction steps. The above expressions for outer-
sphere charge transfer may not be directly applicable to PCET
reactions involving catalysts, but they are useful in that they
clearly distinguish between the impact of activation-related
parameters (l values) and thermodynamics-related parameters
(DG values). Explicit expressions for the solvent-related part of
the reorganization energies l
ET
and l
PT
based on a continuum
representation of the solvent may be found in the literature.
36–39
The expression for l
CPET
is given by:
40
l
CPET
¼ l
ET
+ l
PT
+2
l (4)
where
l is the so-called cross reorganization energy, or solvent
overlap. This parameter describes the extent to which the
solvent reorganization for ET and PT involves the reorganiza-
tion of the same or different modes. In case there is no overlap
between ET and PT modes,
l ¼ 0. Unfortunately, simple models
for
l do not exist but computational examples have been
considered by Hammes-Schiffer et al.
41,42
However, note that if
l z 0, and if all steps are close to thermodynamic equilibrium,
i.e. all DG z 0, the activation energy for CPET is always higher
than the activation energies for ET and PT, and hence under
those circumstances SPET is more likely than CPET (Fig. S1†
illustrates this particular case).
The thermodynamics of the three reaction steps ET, PT and
CPET scale differently with pH and, thus, the pH also impacts
differently the kinetics of these steps due to the DG term in eqn
(1)–(3). This is illustrated in Fig. 2, which represents the ther-
modynamic equilibria of the various steps in a Pourbaix
diagram. When pH ¼ pK
a
(AH), all steps are equilibrated and the
competition between CPET and SPET pathways is governed by
the reorganization energies (see above). The thermodynamics of
the CPET and PT steps are sensitive to the pH and so are their
kinetics. More precisely, their rate increases (decreases) when
the pH decreases (increases). By contrast, the thermodynamics
and kinetics of the ET step are not sensitive to pH. As a result,
the pH can modify the competition between the CPET and SPET
pathways if eqn (1)–(3) apply (for a reduction reaction). The pH
dependence of the competition between the CPET and the
decoupled ET–PT pathways, which is relevant for the concrete
example studied in this work, will now be discussed in more
detail.
To address this pH dependence more quantitatively, it is
important to pay attention to the numerical values of the reor-
ganization energies (l
ET
and l
CPET
)(l
PT
for the decoupled PT–
ET pathways). We nd that the position of the pH domains with
qualitatively different competition, namely the two pH domains
where either the CPET or the SPET takes place exclusively, and
the transition region where both pathways compete at compa-
rable rates, is very sensitive to the values of the reorganization
energies. When l
CPET
z l
ET
, the transition region is always
centred around pH z pK
a
(AH) and spans approximately the pH
range pK
a
¼2topK
a
¼ +2 (see Fig. S2a in the ESI†). As a result,
in this case, the pH dependence of the CPET–SPET competition
can be qualitatively addressed based on the sole knowledge of
the pK
a
of the AH species formed following a PCET. This is
depicted in Fig. 2 where we illustrate the three relevant pH
domains. The transition region is dened by pH z pK
a
(AH) for
the sake of simplicity but one has to keep in mind that it spans
1–2 pH units around the pK
a
(AH) (see above). When the
difference between l
CPET
and l
ET
increases, specically when
l
CPET
> l
ET
as predicted by eqn (4), the position of the transition
region can be substantially shied to lower pH compared to the
case where l
CPET
z l
ET
(see Fig. S2b in the ESI†). As a result, in
general, evaluating the pH dependence of the competition
between the CPET and SPET pathways requires the computa-
tion of reorganization energies. To full the condition l
CPET
z
l
ET
, strong overlap is required between the ET and PT reaction
coordinates (the solvent overlap
l should have a substantially
Fig. 2 Pourbaix diagram showing the thermodynamic equilibria of the
CPET (green, A + H
+
+e
/ AH), ET (red, A + e
/ A
) and PT (blue,
A
+H
+
/ AH) steps.
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negative value) and it has been argued that this is typically the
case when the directionality for PT and ET is similar.
37,41,42
Interestingly, strong solvent overlap could in principle lead to
a situation for which l
CPET
< l
ET
and consequently CPET would
be favoured over SPET even if on purely thermodynamic
grounds one would expect that SPET is to be the most likely
pathway.
2.2 Isodesmic proton-exchange reaction scheme
With the isodesmic proton-exchange reaction scheme (IPER),
the pK
a
of an acid AH is calculated with respect to the known
pK
a
of a reference acid “refH”.
28
AH
sol
m
+ ref
sol
n1
/ A
sol
m1
+ refH
sol
n
; DG
sol
(5)
pK
a
AH
¼
DG
sol
2:303RT
þ pK
a
refH
(6)
The main purpose of this method is to improve the accuracy of
the predictions using continuum solvation models (CSM) by
taking advantage of error cancelation, especially regarding
solvation energies of ionic species, which has been shown to be
the main source of errors with CSM (5 kcal mol
1
).
43–47
The key
point for achieving good predictions is the choice of the refer-
ence acid. In practice, references with similar charge distribu-
tion and chemical environment in the vicinity of the acid group
are considered to perform well and the total charges m and n in
eqn (5) can actually be different without loss of accuracy (the
solute–continuum electrostatic interaction is computed based
on the local charge distribution).
28,48
The remainder of the
molecule has little impact on the quality of the prediction. Note
that attention must be paid to the microsolvation e ffect on the
acid group, in our case the addition of two water molecules was
necessary to produce an accurate pK
a
prediction for the anionic
carboxylate intermediate, as we will show below. The specicity
of the IPER method is that the reaction energy in solution,
DG
sol
, is obtained directly from the computed free energies of
the individual species in solution. In other words, all calcula-
tions (geometry optimization and nite temperature correc-
tions for these geometries) have been performed with the
continuum solvation model. It thus differs from the thermo-
dynamic cycles which requires the computation of gas phase
free energies and the solvation free energies. In our case, the
calculation of pK
a
[CoP–COOH] using thermodynamics cycles
methods is compromised by the fact that the neutral CO
2
adduct is not stable in the gas phase.
15
Recent studies per-
formed on extensive sets of acids have shown that the IPER
method provides pK
a
values with accuracies comparable to the
one obtained with thermodynamic cycles and can even
outperform them in some cases.
28
In general, good linear correlations between experimental
and computed pK
a
values with proton exchange methods have
been observed
28
for various families of acids and thus, reliable
predictions can be derived from them. It is worth noting that
the quality of the correlation depends little on the calculation
level used for the electronic energies as there is no signicant
difference between density functional and high-level ab initio
calculations. Instead, the accuracy of the pK
a
calculation
primarily depends on the performance of the implicit solvation
model used. However, the parameters of the linear t obtained
are usually far from the ideal behaviour (slope ¼ unity and
offset ¼ 0) and, as a consequence, the absolute errors increase
with the pK
a
difference with respect to the reference. Small
regular absolute errors can be obtained over the pK
a
range
investigated by applying a correction that shis all the
computed values so that a new linear t based on the corrected
values matches the ideal behaviour (the mathematical details
for the case treated in this study are provided in Fig. S3†).
2.3 Computational details
All density functional theory electronic structure calculations
were performed with the Gaussian 09 package.
49
The hybrid
functional Perdew, Burke and Ernzerhof (PBE0) was used.
50
A
triple-z quality basis set that includes one polarization function
and augmented with one diffuse function (6-311+G*)
51–53
was
used for non-metallic atoms, and the Stuttgart–Dresden effec-
tive core potential MDF10
54
together with its corresponding
basis set
55
have been used for the cobalt. The solvent e ffects are
modelled by the universal continuum solvent model based on
density commonly called SMD.
43
3. Results and discussion
SincewewanttocomputethepK
a
of carboxylic acids ([Co P–
COOH] and [Co P–COOH]
), we have considered a series of
acids of the same family in order to derive the parameters of
the linear t that corresponds to the calculation level used. We
have chosen a set of acids with pK
a
spanning the range 0.5
(triuoroacetic acid) to 4.8(butyricacid)andformicacidwas
arbitrarily chosen as the reference species. A very good linear
correlation is found (r ¼ 0.983), which demonstrates that
formic acid, despite being the simplest carboxylic acid, is
a reliable reference. As expected, the parameters are far from
their ideal values (slope ¼ 2.03 and offset ¼3.52, see
Fig. S3a†). Aer correction, the mean absolute error obtained
is 0.4 pK
a
unit (Fig. S 3b†) which is consistent with the values
that have been typically obtained in previous works with other
functionals.
28
One can expect the same accuracy for the pK
a
values predicted for [CoP–COOH] and [CoP – C OOH ]
.ThepK
a
values obtained for the series of acids considered together
with the values obtained for [CoP–COOH] and [CoP–COOH]
are displayed Fig. 3.
WepredictthatpK
a
[CoP–COOH] z 3.5 0.4 and pK
a
[CoP–
COOH]
z 8.6 0.4. It is worth noting that the pK
a
value of
the anionic [CoP–CO OH]
intermediate is signicantly far
from the values usually observed for carboxylic acids
(expla ined in detail late r). The la ck of experimental pK
a
values
above 5 makes the estimation of the accuracy derived from
the chosen seri es of acids (0.4 pK
a
units) less reliable for t he
extrapolated pK
a
[CoP–COOH]
. Still, the pK
a
values obtained
are in very good agreement with values that have been previ-
ously obtained by Leung et al. with ab initio molecular
dynamics (AIMD) simulations (3.8 and 9.0 respectively for
[CoP–COOH] and [C oP–COOH]
).
6
Attention must be paid to
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the structures considered for both inte rmedi ates. In particular
for the anionic species, the addition of explicit water mole-
cules was necessary to predict a pK
a
value in agreement with
the AIMD value. For both [CoP–COOH ] and [CoP–COOH]
,two
isomers are possible depending on the position of the
hydrogen of the carboxylic group (H can point towards or away
from the porphyrin ring, see Fig. S4†). For the neutral [CoP–
COOH], they are almost degener ate and have very similar pK
a
values (3.42 and 3.60). We c onsider the average of these two
values as the pK
a
of this intermediate (pK
a
z 3.5) . For the
anionic intermediate these two isomers are also relatively
close in energy with pK
a
¼ 5.02 and 5.79, but they are far from
the value p redicte d from AIMD (p K
a
¼ 9.0). The reason for
such a di fference is related to a drastic difference in the charge
distribution within the complex with and without explicit
solvation. According to a natural charg e analysis (Table S1†),
the charge born e by th e carboxylic group for the isomer with
the hydrogen pointing towards the por phyri n ring is negligible
without any explicit solvent molecules whereas it is 0.5
with the addition of two explicit water molecules (Fig. S5†).
Thislargenegativechargeonthecarboxylic group explains its
much higher basicity. The inclusion of microsolvation for the
[CoP–COOH]
intermediate c hanges the shape of the cavity
around the acid/base group, and thus the local electrostatic
interaction with the continuum is not computed in the same
way as the reference which may result in poorer error cancel-
ationorevenunexpectedartefacts.Toaddressthatpoint,we
have computed the pK
a
of the neutral [CoP–COOH] again
including microsolvation and compared the value with the
one without microsolvation. The difference is negligible
(pK
a
values are both z3.5) , so we can expect that the value
obtained for [ CoP –COOH]
is reasonable.
The formation of the neutral carboxylate adduct implies
a reorganization of the reactant conguration since it requires
the association of the catalyst with CO
2
. This may introduce an
additional energetic contribution that may signicantly
impact the thermodynamics and kinetics of the ET and CPET
steps compared to a simple PCET wit hout such adduct
formation. However, as far as the cobalt porp hine complex
used in this work is concerned, we have shown in a previous
theoretical DFT study t hat the association with the reduced
catalyst [CoP]
is almost barrierless and thermoneutral.
15
Therefore, this contribution can reasonably be neglected in
our case and the pH is the determinant f actor that governs the
competition between CPET and SPET (cf. 2.1). Still, one should
in general pay attention to this effect for other catalysts. The
pK
a
value comput ed for th e neutral [Co P–COOH] intermediate
allows the pH domains to be determined for which the SPET
and/or CPET pathways take p lace (Fig. 4). In the rest of the
discussion, we will use the same denition as in Fig. 2 to
denethesepHdomains(pH<pK
a
,pHz pK
a
and pH > pK
a
).
At a pH b elow 3.5, the formation of [CoP–COOH ] is expecte d to
follow exclusively the CPET pathway. When CO
2
RR is per-
formed at a pH close to 3.5, the SPET and CPET pathways are
predicted to co-exist. At this stage of the discussion, it is
interesting to use these theoretical predictions to address
which mechanism is likely to take place for the pH range
investigated in the experimental study.
27
At pH ¼ 1, the
formation of [Co P–COOH] is pre dicted to follow a p urely CPET
mechanism (pH < p K
a
[CoP–COOH]) whereas at pH ¼ 3it
follows a mixed SPET–CPET mechanism. If we compare the pH
dependence predicted for the mechanism of the formation of
the neutral [CoP–COOH] and fo r the experimentally observed
faradaic efficiencies of the COR and HER reactions, the simi-
larity is striking. Therefore, this theoretical study supports the
assumption that the signicant formation of the anionic [CoP–
CO
2
]
adduct is a key ingredient for understanding the drastic
change in faradaic efficiency of the CO
2
RR to CO, compared to
the HER reac tion, when the pH chang es from 1 to 3. It is also
interesting to point out that, using the value of the onset
potential value computed with the CHE methodology for the
concerted pathway (i.e., 0.43 V vs. reversible hydrogen elec-
trode),
15
the equilibrium potenti al extrapolate d at pH ¼ 3.5,
0.63 (0.059 mV shi per pH unit) is very close to the average
experimental redox potential of the catalyst 0.67 (between
0.5 to 0.84 depending on substituent and solvent).
56
It has been experimentally demonstrated that CO
2
RR on Co-
porphyrins can proceed at pH ¼ 7.
57,58
Under such a condition,
the formation of the neutral [CoP–COOH] intermediate is
unlikely (pK
a
[CoP–COOH] 7) and an alternative mechanism
must take place. Taking into account the large pK
a
value pre-
dicted for the anionic [CoP–COOH]
(pK
a
¼ 8.6), a logical
alternative is a pathway with the formation of this intermediate.
This latter species is formed aer a PCET from the anionic
[CoP–CO
2
]
adduct and, like the formation of [CoP–COOH] at
lower pH, it can follow either the SPET or CPET pathways. One
can predict that [CoP–CO
2
]
2
will only be formed when the pH
is close to or above pK
a
[CoP–COOH] ¼ 8.6, i.e. the region where
the SPET pathway is predicted to be active (Fig. 4). It results in
the following ET–PT sequence for pH > pK
a
[CoP–COOH]
z 8.6:
*–CO
2
+e
/ *–CO
2
2
Fig. 3 Plot of pK
a
predicted against experimental values for the
benchmark series of acids and pK
a
of the carboxylic intermediates
[CoP–COOH] and [CoP–COOH]
.
462
| Chem. Sci.,2017,8,458–465 This journal is © The Royal Society of Chemistry 2017
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