Foot of the Wave Analysis for Mechanistic
Elucidation and Benchmarking Applications in Molecular Water Oxidation Catalysis
,which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/cssc.201601286/abstract
"This is the peer reviewed version of the following article:

This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for SelfArchiving."

Foot of the Wave Analysis for Mechanistic Elucidation and
Benchmarking Applications in Molecular Water Oxidation Catalysis
Roc Matheu,[a],[b] Sven Neudeck,[c] Franc Meyer,[c],[d] Xavier Sala*,[e] and Antoni Llobet*,[a], [e]
Abstract: The description of the foot of the wave analysis (FOWA)
applied to the electrocatalytic oxidation of water to dioxygen is
reported for cases where the rate determining step is first order and
second order with regard to catalyst concentration. This coincides
with the so called water nucleophilic attack (WNA) and interaction of
two M-O units (I2M) mechanism respectively. The newly adapted
equations are applied to a range of relevant molecular catalysts both
in homogeneous and heterogeneous phase and the kinetic
parameters, including apparent rate constants and turnover
frequencies, are determined. In this respect the application of FOWA
at different catalyst concentrations allows elucidating the reaction
mechanism that operates in each case. In addition catalytic Tafel
plots are used for assessing the performance of several molecular
water oxidation catalysts (WOCs) as a function of overpotential
under analogous conditions and thus can be used for benchmarking
purposes. While this had been earlier carried out for oxide based
WOCs, now it is the first time reported for molecular WOCs.

1. Introduction
Hydrogen generated by water splitting with sunlight is today
considered as one of the most promising energy vectors for
replacing fossil fuels. 1 , 2 , 3 This can be achieved using

[a]

[b]

[c]

[d]

[e]

Pr. A, Llobet and Mr. R, Matheu
Institute of Chemical Research of Catalonia (ICIQ), Barcelona
Institute of Science and Technology
Avinguda Països Catalans 16, 43007 Tarragona, Spain
Mr. R, Matheu
Departament de Química Física i Inorgànica
Universitat Rovira i Virgili
Marcel—lí i Domingo s/n, 43007 Tarragona, Spain
Pr. F, Meyer and Dr. S, Neudeck
Institute of Inorganic Chemistry
Georg-August-University Göttingen, D-37077 Göttingen, Germany
Pr. F, Meyer
International Center for Advanced Studies of Energy Conversion
Georg-August-University, 37077, Göttingen, Germany
Pr. A, Llobet and Dr. X, Sala
Departament de Química
Universitat Autònoma de Barcelona, Cerdanyola del Vallès, 08193,
Spain.
allobet@iciq.cat and xavier.sala@uab.cat
Supporting information for this article is given via a link at the end of
the document.

photoelectrochemical cells where water oxidation is occurring at
the anode and proton reduction at the cathode, driven by
sunlight.4 The H2 obtained in this way is generally termed solar
fuel, generated by an artificial photosynthetic device, in analogy
with the main mode of action of photosynthesis in green plants
and algae.5 The anodic water oxidation reaction is one of the key
reactions involved in these processes common to both water
splitting with sunlight and natural photosynthesis, and thus it is
essential for the construction of functional devices6,7 as well as
for the comprehension of the reactions involved in natural
photosynthesis.8 In addition, the water oxidation anodic reaction
can be potentially coupled to other interesting reactions such as
CO2 or N2 reduction reactions to build artificial photosynthetic
devices for instance for the generation of MeOH or NH3
respectively.9,10,11 The water oxidation reaction thus emerges as
the key partner for various reduction reactions for energy and
industrially relevant applications in the near future. For this
reason it is imperative to understand the main pathways
involved in the catalytic water oxidation reaction as well as the
pathways that deactivate the catalyst.12,13,14 In this respect water
oxidation catalyzed by molecular transition metal complexes
represent an ideal ground because of the ligand engineering
possibilities for modulating the electronic and steric properties of
the catalyst.15
While the capacity of transition metal oxides to carry out water
oxidation to dioxygen has been known for a long time16,17,18,19
and recently benchmarked, 20 , 21 , 22 that of molecular transition
metal complexes is more recent and has boomed only over the
last 10 years.12,23,24,25,26,27,28,29,30 There is nowadays a variety of
transition metal complexes that have been reported to very
efficiently oxidize water to dioxygen. However the conditions
under which the catalysis is carried out differ from one another
and hamper a meaningful comparison. In addition precise
electrochemical methods are not available when S-shape
catalytic response is not obtained.31,32,33,34
Thus there is a need to develop techniques to benchmark water
oxidation catalysis with molecular systems in order to be able to
identify the best catalyst for a given application. For this purpose
we have adapted the so called “Foot of the Wave Analysis”
(FOWA) for water oxidation catalysts that can be applied even
when an ideal S-shape response is not obtained in Cyclic
Voltammetry. The methodology is based on the analysis of the
first points of the catalysis, where the catalytic response is

unperturbed by side phenomena that usually prevents the
extraction of the kinetic information. The methodology was first
reported by Costentin, Robert, Saveant et al.35 and was applied
to the electrocatalytic reduction of protons and carbon
dioxide.36,37,38,3940,41 Recently, Mayer et al.42 have also shown a
very nice agreement between apparent rate constants derived
spectroscopically by UV-vis and based on FOWA for the
catalytic oxygen reduction, which further validates this
methodology.
Herein we extend the concept of FOWA to catalytic water
oxidation by molecular transition metal complexes. We thus
report the FOWA mathematical equations adapted for
electrocatalytic water oxidation reactions and their applications
to some of the most relevant examples reported so far in the
literature.43,44,45,46,47 Chart 1 shows drawn structures and general
nomenclature of the water oxidation catalysts discussed in the
present work. In addition, the FOWA methodology is used as a
tool for the elucidation of reaction mechanisms for these
molecular water oxidation catalysts (WOCs), in particular with
respect to the O-O bond formation. Finally, based on the FOWA
results catalytic Tafel plots are reported for all these WOCs
under similar conditions, allowing for a fair comparison among
them.

Chart 1. Drawn structure of the complexes discussed in this work.

2. Results
2.1 Main mechanistic scenarios described for molecular water
oxidation catalysts
Scheme 1 shows the reaction mechanism proposed for complex
12+
(damp
is
2,6[RuII(damp)(bpy)(H2O)]2+,
bis(dimethylaminomethyl)-pyridine and bpy is 2,2’-bipyridine;
see Chart 1)43 and the seven coordinated complex
[RuIV(O)(bda)(4-Me-py)2], 2 (pKa (RuIV-OH/RuIV-O) = 5.9; bda2-

is 2,2'-bipyridine-6,6'-dicarboxylate and py is pyridine).45 These
two complexes follow two different O-O bond formation
pathways that are representative of the main mechanisms that
have been reported in recent years25, 48 , 49 , 50 For the sake of
simplicity and easy follow up of electron counting, we will refer
only to formal oxidation states at the Ru metal center. This does
not neglect the obvious total or partial contribution from the Ru
bonded terminal oxido or hydroxido ligands on the removal of
electron density especially at high oxidation states. Complex 12+
follows the so-called water nucleophilic attack (WNA)
mechanism where the O-O bond formation occurs via a
nucleophilic attack of solvent water to an electrophilic RuV-O
group and is the rate determining step (rds), as is also proposed
for a number of so called single site catalysts. 51 The rate
constants for the WNA step and the last ET step are also
indicated in Scheme 1 and presented as equations 1 and 2
below,

IV

2+

[(damp)(bpy)Ru -O]

V

3+

- 1e- -> [(damp)(bpy)Ru -O]

[(damp)(bpy)RuV-O]3+ + H2O -> [(damp)(bpy)RuIII-OOH]2+ + H+

(1)
(2)

Scheme 1. Main O-O bond formation mechanism described for molecular
water oxidation catalysis. Top, WNA mechanism proposed for
[RuII(damp)(bpy)(H2O)]2+, 12+. The 3N and 2N linked by arcs represents the
damp and bpy ligands respectively. Bottom, I2M mechanism proposed for
IV
2[Ru (O)(bda)(4-Me-py)2], 2. The O and N linked by arcs represent the bda
ligand whereas the picoline ligand is represented by a single N.

kO2
IV

IV

2+

[(bda)(py)2Ru -OO-Ru (bda)(py)2]

+ 2 H2 O

------------>
III

+

2 [(bda)(py)2Ru (OH2)]

[(bda)(py)2RuIV-OO-RuIV(bda)(py)2]2+

On the other hand the Ru-bda complex 2H+, at low pH, follows
the so-called interaction of two M-O units (I2M) mechanism
where the O-O bond formation is proposed to occur via
dimerization of two M-O groups.45 For a mononuclear complex
this is an intermolecular reaction but for a dinuclear complex this

-1 e-

+ O2

----------->

[(bda)(py)2RuIV-OO--RuIV(bda)(py)2]3+

[(bda)(py)2RuIV-OO--RuIV(bda)(py)2]3+ + 2 H2O --------->

(3c)

(4a)

(4b)

[(bda)(py)2RuIII(OH2)]+ + [(bda)(py)2RuIV(OH)]+ + H+ + O2

Table 1. Summary of reactions and key equations obtained for the WNA, I2M and hetero-WNA mechanisms including TOF-η relationships and TOFMAX
formulas.

WNA

I2M

(k1—[H2O]=kWNA)

(5)

Hetero-WNA
(6)

(8)

(11)

(15)

˩
=
˝

˫
˘{˗ " − ˗{
1+˥
F
˞ˠ

(12)

(14)

TOF3- = ˫

(9)

(7)

(10)

(13)

TOF3- = ˫

(16)

Abbreviations used: C0cat or [Ru], initial bulk concentration of catalyst; Eo, standard potential for the P and Q Couple; EH2O/O2, standard potential of oxidation of
water at the working pH; F, Faradaic constant; η, overpotential; i, CV current intensity; ip, peak current intensity of one-electron redox process of the catalyst; k1,
apparent WNA rate constant; kWNA, apparent WNA pseudo-rate constant (k1—[H2O]); kD, apparent dimerization constant; QRu, moles of electrons associated with
a 1 electron transfer process of the immobilized catalyst; R, gas constant; T, temperature; TOF, turn over frequency; x, distance from the electrode surface.

could potentially occur in an intramolecular manner. 52 In the
former case the dimerization is produced upon reaching the
Ru(V) state and under stoichiometric conditions the slowest
steps are associated with the dimerization process (kD = 1.1 x
105 M-1s-1) and the subsequent oxygen ejection (kO2 = 5.8 s-1)
displayed in equations 3a and 3b respectively and in Scheme 1.
In both cases the kinetic processes are independent of the
[Ce(IV)] used as chemical oxidant. Given the second and first
order nature of kD and kO2 respectively, the rds of the process
depends on the initial concentration of Ru. For low [Ru] (below
the 5 µM range) the dimerization process (3b) is the rds and
above the 0.5 mM range the oxygen ejection (3c) is the rds.
Further under excess of Ce(IV) the peroxo is proposed to be
further oxidized to superoxo (4a) that in turn evolves oxygen (4b).
Both processes are described to be very fast under these
conditions and thus the kinetics again are independent of
[Ce(IV)] and the rds is governed by kD at the Ru µM
concentration range.
IV

+

-

V

+

[(bda)(py)2Ru -OH] - 1e -> [(bda)(py)2Ru -O] + H

+

kD
2 [(bda)(py)2RuV-O]+ -----------> [(bda)(py)2RuIV-OO-RuIV(bda)(py)2]2+

(3a)
(3b)

2.2. The FOWA equations for water oxidation catalysis.
We have adapted the FOWA methodology35-39 using the
equations 5 and 6 (see Table 1) for the WNA and I2M
mechanisms respectively in homogeneous phase. Therefore, we
used the generic “P” and “Q” labels that correspond to equations
1-2 and 3a-3b respectively just described above for catalyst 12+
and 2. In both cases, we are assuming that the O-O bond
formation is the rds. Other scenarios for water oxidation
catalysis with different rds steps are not considered in the
present work; however systems where the rds is first order with
regard to [Ru] will also be comprised within the equations of the
WNA mechanisms49 as will be the intramolecular O-O bond
formation in dinuclear complexes.47,53,54

Saveant.55 Within this framework it is important to realize that the
key features that distinguish the FOWA equations for the WNA
vs. I2M mechanisms are the different dependences of “i/ip“ on
catalyst concentration (where “i”, is the current intensity at the
CV and “ip” is the peak current intensity of the one electron redox
process of the catalyst; see equations 8 and 9 in Table 1). This
concentration dependence is an intrinsic property of each
mechanism that will be used for the subsequent discussions.
Further the turnover frequency (TOF) and its maximum value,
TOFMAX, are two key features for the proper catalyst
characterization, whose equations (11-14) are displayed in
Table 1 for both the WNA and I2M mechanisms.
We also have applied the FOWA formalisms to GC-2, which is a
homologue of catalyst 2 attached to the surface of an electrode,
under severely restricted translational mobility conditions, and
thus with basically no diffusion. We have used the chemical
equations 7 (Table 1) with the generic terminology “het-P” and
“het-Q”, to denote the heterogeneous phase nature for the
anchored catalyst, under different oxidation states and deduced
its corresponding TOF and TOFMAX equations 13 and 16.
Table 2. Kinetic, thermodynamic data and experimental conditions for the complexes studied in the present work.
.

Complex

pH

4
52
2
2
GC-2

7.0
1.0
1.0
7.0
12.0
7.0

Mec. FOWAa
(Mec. Lit)b
WNA
WNA (WNA)g
I2M (I2M)i
I2M
I2M
WNA

TOFMAX
s-1
(7.7±1.5)—103
50 ± 10
11 ± 3j
11 ± 3j
11 ± 3j
1.9l

ˠ˛˘

c

(TOF lit)d
-1

s
0.37
0.07 (0.07)h
11j (30)k
11
11
1.9l

kD—10-3
s-1M-1
----170 ± 50
160 ± 30
170 ± 40
---

Eo,ap Ve
1.43
1.71
1.39
1.08
1.08
1.08

[Ru]f
mM
0.15 - 1.5
0.08 – 0.79
0.2
0.12 – 0.84
0.14 – 0.94
0.05 - 0.4m

a) Mechanism established in this work, b) Mechanism established in the literature, c) TOFECe stands for estimated TOF obtained by FOWA at a 1.55 V applied
-

potential; that is the Ce(IV)/Ce(III) standard potential calculated with the FOWA equations based on the kinetics obtained for complex 5 using Ce(IV) as oxidant,
under the conditions used here. See text for more information and reference 67, d) Calculated TOF using Ce(IV) as a sacrificial oxidant in the literature, e)
Apparent potential of the redox couple extracted from DPV in this work, f) Concentration range used in this work, g) The mechanism was elucidated based on
47
47
isotope labeling experiments, h) Experimental conditions: [CF3SO3H] = 0.1 M, [Ce(NH4)2(NO3)6] = 0.1 M and [Ru] = 1 mM, i) Mechanism stablished thought
45
45
kinetic studies, j) Calculated TOFMAX with [2] = 0.2 mM, k) Experimental conditions: [CF3SO3H] = 0.1 M, [Ce(NH4)2(NO3)6] = 0.538 M and [Ru] = 0.2 mM, l)
2
= 0.10 and 0.06 nmol/cm ), m) Superficial concentration range
Calculated from the average of CVs from GC-2 electrodes at low superficial concentration (
(nmol/cm2).

Figure 1: Left, grey solid line shows a CV of a 3/4 mixture (3.0 mM/1.5 mM) at
pH = 7.0. The black dashed line indicates the data points used for the FOWA.
The black solid arrows indicate the one-electron processes of complexes 3
44
o,ap
and 4. Top right, i/ip vs. [1/(1+e((E -E)(F/RT)))] plot assuming a WNA
o,ap
mechanism and the used equation. Bottom right, i/ip vs. [1/(1+e((E 3/2
E)(F/RT))) ] plot assuming an I2M mechanism and its equation. The fitting
points for the extraction of rate constants at the foot of the wave are
represented as a black solid line in the three graphs.

A complete mathematical description of the FOWA equations is
presented in the SI and the most relevant are gathered at Table
1. It is worth mentioning that for the WNA mechanism, kWNA is an
apparent pseudo-rate constant defined as kWNA = k1—[H2O] (see
Table 1) that is associated with the chemical reaction (equation
2) following electron transfer. In a similar manner kD correspond
to the dimerization process (equation 3b) that occurs after
electron transfer in the I2M mechanism. A related bimolecular
mechanism had been previously considered by Costentin and

2.3 The FOWA methodology applied to [RuIV(O)(tda)(py)2], 4,
and {[RuII(OH2)(4-SO3-py)2]2(µ-Mebbp)}-, 5-, complexes.
Under neutral and basic condition the seven coordinate complex
32+,(tda2is
[2,2':6',2''-terpyridine]-6,6''[RuIV(tda)(py)2]2+,
dicarboxylate), has recently been reported to undergo hydroxide
substitution
with concomitant
proton
loss
to
form
[RuIV(O)(tda)(py)2], 4, (pKa [Ru(OH)/Ru(O)] = 5.6)44 containing a
pendant carboxylate that coexists with 32+. Complex 4 has been
shown to display a spectacular activity with regard to the
catalytic oxidation of water with maximum turnover frequencies
ranging from 8.000 to 50.000 cycles per second depending on
the pH and thanks to the pendant group that acts as an
intramolecular proton acceptor. From a mechanistic perspective,
a WNA mechanism has been proposed based on DFT upon
reaching [RuV-O] followed by O-O bond formation via a water
nucleophilic attack by a solvent water molecule in an analogous
manner as described for 12+ in equations 1-2.44

Figure 1 shows a cyclic voltammogram of a mixture of 3.0 mM
32+ and 1.5 mM 4 at pH = 7.0 with a large electrocatalytic activity
in the 1.3-1.6 V range that is associated with the generation of
the corresponding [RuV] complex whose RuV/RuIV apparent
potential occurs at Eo,ap = 1.43 V. This apparent potential is
obtained by Differential Pulse Voltammetry (DPV) although it
has its intrinsic limitation, see supporting information for more
details.
All the potentials in this work are measured vs. the
mercury/mercurous sulfate (MSE, K2SO4 saturated at 25 oC)
reference electrode although are reported vs. NHE by adding
0.65 V. We consider the peak current intensity of the wave
associated with the background corrected (i.e., blank current
subtracted) RuIII/RuII couples as the “ip“ of the RuV/RuIV couple.
Here it is important to mention that FOWA considers that the
electron transfer kinetics of the process coupled to the catalytic
reaction is infinitely fast and thus assumes a reversible
Nernstian behavior. Compelling evidence that advocates for
Nernstian behavior in our complexes is suggested by the 59 mV
anodic-cathodic peak separation in the redox waves of 3 within
the 50-500 mV—s-1 range (see Figure S1).44,45,47 We thus assume
Nernstian behavior in all the 1-5- complexes studied in this work.
While this estimation of the standard potential of the redox
couple is certainly not ideal, it is actually the only way to
calculate it for the water oxidation catalysis. Therefore it
constitutes an intrinsic limitation of FOWA applied to water
oxidation catalysis.

standard deviation of each data point is represented with vertical lines. The
solid orange line indicates the trend for the WNA mechanism.

For complex 4, the FOWA equations 8 and 9 in Table 1 were
applied for the WNA and the I2M mechanisms respectively
giving acceptable mathematical simulations in both cases as can
be seen in the right hand side of Figure 1 where a plot of “i/ip” vs.
“1/(1+e((E0,ap-E)—(F/RT)))” and vs. “1/(1+e((Eo,ap-E)—(F/RT)))3/2” is
presented. 56 To discern between the two mechanisms the
FOWA methodology was carried out at different [Ru]. A set of
CVs within the 0.15-1.50 mM concentration range was carried
out for 4 as shown in Figure 2 left, together with their ip
normalized CV on the right hand side. The latter clearly shows
that the slope (“i/ip” vs. E) at the foot of the wave zone for all the
normalized CVs is identical and thus clearly points out to a WNA
mechanism. Indeed the extraction of the apparent rate constants
kWNA and kD values (FOWA equations 8 and 9 respectively)
show that while for the former they are constant with a value of
(7.7±1.5)—103 s-1, for the latter they decrease as the [Ru]
increases. A plot of the k values vs. [Ru] (see inset Figure 2)
graphically shows this point and thus unambiguously confirms
the WNA nature of the mechanism operating in this case. It is
important to emphasize here that the dependence of the rate
constant vs. catalysts concentration is the key tool to determine
the reaction mechanism and on the other hand the consistency
of the concentration dependence results obtained further reveals
the virtue of the methodology used. The preference of this
mechanism is readily explained by the intramolecular proton
abstraction by the dangling carboxylate and by the steric
hindrance that any potential mechanism based on a dimerization
process will suffer for this particular complex. All the kinetic data
obtained for this complex and all the other complexes described
in this work are reported in Table 2.
Another interesting asset of the FOWA methodology is the fact
that since the measurement is done at the foot of the wave, at
the very beginning of the catalytic reaction, a number of
undesired reactions or effects are either suppressed or
minimized.38 In the case of Ru-tda complex 4, the water
oxidation catalysis is so fast that significant changes of the local
pH at the electrode surface are evidenced by an anodic shift of
the Ru-OH2 waves after catalysis.44 For this reason the value
obtained with the classical Shain et al. methodology33 based on
plotting “i/ip“ vs. the “ν−1/2“ even under pure kinetic control, would
not give the correct apparent rate constant.

Figure 2: Left, CV of a 3/4 mixture at pH=7 at different concentrations (3.00
mM/1.50 mM; orange solid line, 1.50 mM/0.75 mM; black solid line, 0.75
mM/0.37 mM; blue solid line and 0.30 mM/0.15 mM; red solid line respectively).
Right, ip normalized CVs. Inset, plot of calculated kD and kWNA vs. [4]. The

The same FOWA treatment was also applied for complex
{[RuII(OH2)(4-SO3-py)2]2(µ-Mebbp)}-, 5-, (Mebpp is 3,5-di([2,2'bipyridin]-6-yl)-4-methylpyrazolate) that has been recently
reported to undergo a WNA mechanism at pH = 1.0, based on
H218O labeling experiments. The FOWA at different [5-] further
confirm the proposed WNA nature of the mechanism as can be
observed in the corresponding “i/ip“ plots shown in Figure S5 in
the SI. A constant value of TOFMAX = 50 ± 10 s-1 is obtained for
this complex at different concentrations and all the related
kinetic data is also presented in Table 2.

2.4 The FOWA methodology applied to the [RuIV(O)(bda)(py)2], 2,
complex.
As shown in the previous section the WNA mechanism operates
in case of catalysts 4 and 5-. We thus focused our endeavors on
catalyst 2, that had previously been shown to undergo an I2M
type of mechanism at pH = 1.0 using Ce(IV) as a chemical
oxidant.45 We carried out the analogous FOWA analysis at pH =
7.0 and 12.0, and the results are shown in the supporting
information (Figure S8-S13), in Figure 3 and in Table 2. Figure 3
shows the cyclic voltammograms of complex 2 at pH = 7.0 at
four different concentrations of Ru (in the 0.12-0.84 mM range).
As can be observed upon reaching the wave associated with the
RuV/RuIV couple a large electrocatalytic current emerges at
approximately 1.1 V, that increases with increasing
concentration of the Ru catalyst. Figure 3 (right) shows the
normalized “i/ip“ voltammograms that now clearly show that the
slope (“i/ip” vs. E) at the foot of the catalytic current increases
with [Ru] and thus points towards an I2M type of mechanism.
Indeed using equations 8 and 9 in Table 1 the apparent kWNA
and kD were extracted and are plotted in the inset versus
catalyst concentration. In sharp contrast with complex 4 the
calculated kD = (160 ± 40)—103 M-1—s-1 is independent of the
catalyst concentration whereas the calculated kWNA is dependent.
Thus, these experiments unambiguously show that the
mechanism that operates at pH = 7.0 for Ru-bda complex 2 is
the I2M. Finally, kD was used to estimate the TOF and TOFMAX
using equation 12 and 15 in Table 1 at 0.2 mM concentration.
This concentration value was used to compare the
electrochemical TOFs at all pHs as well as with the ones
obtained using CAN as sacrificial oxidant at pH = 1.0 in
homogeneous phase. The same FOWA methodology was
applied at pH 12 for this catalyst obtaining very similar results
(see SI Figure S11-S13 and Table 2), and confirming the I2M
nature of the mechanism operating at this pH. Very similar kD
values were obtained at pH = 7.0 and 12.0 in a comparable
range of concentrations confirming once again the
independence of the rds on the concentration of OH-.

Figure 3. Left, CV of a 2 at 0.84 mM (orange solid line), 0.47 mM (black solid
line), 0.25 mM (blue solid line) and 0.12 mM (red solid line) at pH = 7.0. The
black solid arrows indicate the one-electron processes of 2.45 Right, ip
normalized CVs. Inset, plot of calculated kD and kWNA vs. [2]. The standard
deviation of each data point is represented with vertical lines. The solid purple
line indicates the trend for the I2M mechanism.

At pH = 1.0 the solubility of the catalyst precursor, 2, is very low
preventing a complete kinetic analysis using FOWA within a
reasonable range of concentrations. For this reason we carried
out the FOWA analysis for a single catalyst concentration, 0.2
mM, and we run the CV at a scan rate of 10 mV/s (all the
previous examples described were carried out at 100 mV/s).
This gave practically the same kD values as the ones obtained at
higher pH (see SI Figure S19-S21 and Table 2) and thus
confirms that for 2 the I2M mechanism operates over the pH
range 1.0-12.0.
Finally, we proceeded to evaluate catalyst 2 under restricted
translational mobility conditions by anchoring it on a glassy
carbon electrode. Under these conditions complex 2 cannot
undergo a bimolecular dimerization and thus needs to change
the reaction mechanism for water oxidation catalysis. We
anchored
a
related
Ru-NO
catalyst
precursor,
{[Ru(NO)(bda)(PyPh-N2+)2][PF6]3}, 6, (PyPh-N2+ is 4-(pyridin-4yl)benzenediazonium), on the surface of the electrode following
the reduction of its diazonium salt as has been recently
described.46 In this way we generate a Ru-NO species at the
surface of the electrode that is converted to GC-2 after one CV
cycling in the range 0.2 V – 1.5 V as described in our previous
work and in the SI.46 The amount of GC-2 catalyst generated in
this by this protocol ranges from 0.06 to 0.34 nmols/cm2, and
nicely correlates with the initial concentration of 6 used (See
Figure S14 in the SI).

Figure 4. CV of 0.5 mM 2 that generates an ip= 1.9 µA (red) and GC-2 with
o
2
Γ cat = 0.34 nmol/cm that generates a ip= 2.6 µA (blue) both at pH = 7.0. Inset,
plot of TOFMAX for 2 (red squares) and GC-2 (blue squares) vs. different Ru
concentrations (red squares) and the Ru superficial concentrations (blue
squares). The relative position of the two horizontal axis in the inset is set so
that the ip values for 2 and GC-2 are coincident (see figure S18 for the plot of
TOFmax vs. ip values).

Application of the FOWA methodology at different surface
coverage (0.06-0.39 nmol/cm2 range, see SI Figure S15-S17) in
this case using equation 10 in Table 1 gave a kWNA value of 1.9
s-1 (see inset Figure 4 and SI, Figure S17). The catalyst
concentration independency with regard to the rate constant is a
clear evidence for the mechanistic change, from I2M to WNA,
due to the lack of translation mobility of the active species in
GC-2. For higher surface coverages of 0.19 and 0.39 nmol/cm2
the apparent rate decreases to 0.6 s-1, a fact that might be
attributed to surface effects associated with the electrode
roughness.57 Further, the TOFMAX of GC-2 obtained by FOWA is
similar to the TOF obtained in a previous work under
heterogeneous conditions (0.03-0.84 s-1 within overpotentials in
the 0.3-0.8 V window). They were calculated dividing the
electrical charge associated to the O2 evolution (QO2) in a bulk
electrolysis by the charge associated to the catalyst (QRu): TOF
= QO2/(4—QRu).46,58
In addition to the different mechanistic scenarios for 2 and GC-2,
the physical meaning of ip in the voltammogram for dissolved
species and ip in the voltammogram for the surface-confined
systems is also different and therefore a direct comparison of
apparent rate constants for 2 and GC-2 is meaningless.
However it is very instructive to see the behavior of these two
catalysts when their corresponding ip values are very similar.
This can be observed in Figure 4 for [2] = 0.5 mM and for GC-2
with a surface coverage of 0.34 nmol/cm2, both at pH = 7.0.
Under these conditions the catalytic current density for 2 is more
than one order of magnitude higher than for GC-2 at E = 1.2 V
(2.3 mA/cm2 vs. 0.2 mA/cm2).

-

Figure 5: Catalytic Tafel plot of 5 and 2 at pH = 1.0 (pink solid line and red
dashed line respectively) and 2, 4 and GC-2 at pH = 7.0 (red, black and blue
solid lines respectively). The green dashed line represents the potential of Eo’
(CeIV/CeIII) at pH = 1.0. For catalyst 2, a concentration of 0.2 mM was used for
the plot.

2.5 Catalytic Tafel plots based on FOWA equations.
The catalytic Tafel plots used in this work are different from the
commonly
used
“electrochemical
Tafel
plots”.
The
electrochemical Tafel plots define a relationship between the
current density and the overpotential with respect to the
equilibrium potential.59,60 On the other hand catalytic Tafel plots
establish a relationship between the Turn Over Frequency of the
catalyst and the applied potential with respect to the standard
potential of the reaction.35,38
Catalytic Tafel graphs were drawn by plotting TOF as a function
of overpotential (η) following equations 11, 12 and 13 in Table 1
for the WNA, I2M and hetero-WNA mechanisms respectively.35
Figure 5 illustrates the catalytic Tafel plots for the complexes
discussed in this work, allowing an easy and quick comparison
among them. There are three key features that define the shape
of the Tafel plot and thus reflects the activity and nature of the
catalyst: a) the TOFMAX which is the apparent rate at which the
curve reaches a Plateau and that is described by equations 14,
15 and 16 in Table 1 for the WNA, I2M and hetero-WNA

mechanisms respectively, b) the lowest value of potential where
TOF = TOFMAX and c) the slope that defines the relationship
between TOF and overpotential which is a distinctive feature of
each mechanism.

3. Discussion

The equations reported in this work that are summarized in
Table 1 provide a valuable tool for the integral treatment of
molecular water oxidation electrocatalysis. The data analysis
allows to progress one step forward by unravelling the
mechanisms operating for a given catalyst and in addition the
detailed kinetic information also allows comparing catalysts
under similar conditions. The latter is very important since so far
the kinetic values reported were obtained in drastically different
conditions and therefore difficult to compare. Furthermore, the
variation of the apparent rate constant as a function of
overpotential graphically shown by the catalytic Tafel plots, offer
a comprehensive view of the catalyst performance as a function
of the applied potential. Benchmarking conditions had been
recently proposed to compare WOCs based on solid metal
oxides.20, 21 On the other hand catalytic Tafel plots have been
used to benchmark molecular proton reduction catalysts. 61 ,
62
Here for the first time a comparison under the same conditions
over a large span of overpotentials is carried out based on
catalytic Tafel plots for molecular water oxidation catalysts.
Figure 5 shows Tafel plots for complexes 2, 4, 5- and GC-2, and
a number of conclusions can be drawn from the careful
examination of this graph. At high overpotentials (η > 0.6 V)
complex 4 is the best catalyst with a TOFMAX value of
(7.7±1.5)—103 s-1 that is almost two orders of magnitude higher
than that of the naturally occurring reaction in the OEC of
Photosystem II and three orders of magnitude higher than that of
complex 2, which is one of the best catalysts described so far.
Furthermore the WNA mechanism obtained here is consistent
with the molecular structure of the catalyst as the dangling
carboxylate at the [RuV=O] oxidation state favors the
intramolecular proton transfer of an approaching water molecule
for the critical O-O bond formation step, and thus favors the
WNA mechanism. For these reasons catalyst 4 would be an
ideal catalyst to anchor at the surface of a semiconductor that
generated light induced high energy holes. For instance
semiconductors such as BiVO4 or WO3 that have very oxidizing
valence bands of approximately 2.5 and 3 V respectively,6 and
thus are ideal to be integrated in such a photoanode for a water
splitting electrochemical cells.63,64
On the other hand, at high overpotentials catalyst 4 has a
TOFMAX that is 2 orders of magnitude higher than the
dinucleating Ru-Mebbp complex 5-. However at lower
overpotentials the TOF of the two complexes differ in less than
an order of magnitude and thus would be equally valuable for
potential water splitting applications. In addition, the catalytic

experiments are carried out at pH = 7.0 for 4 and at pH =1.0 for
5-. Therefore this leaves us with a couple of excellent WNA type
of catalyst at low overpotentials within the pH range 1-7.
At η = 0.45 V the plots of catalyst 2 and 4 cross and thus
indicates that under this conditions they have identical behavior.
Please note that while for the WNA cases the plot is
independent of the catalyst concentration for the I2M it depends
on the initial catalysts concentration. Here we use [2] = 0.2 mM
which is close to saturation but is a value reasonably achievable
for other molecular WOCs. At lower overpotentials, 2 clearly
outperforms 4 in homogeneous phase and is the best catalyst
studied in this work. In addition higher TOFs can be obtained for
complexes analogous to 2, by fine tuning the axial ligand
reaching TOFs up to 1000 s-1 at pH = 1.0 with a huge excess of
Ce(IV) as chemical oxidant.65, 66
It is also interesting to stress the mechanistic O-O bond
formation change of catalyst 2 in homogenous phase and
anchored on the GC electrode, GC-2, from I2M to WNA
respectively due to the restricted translation mobility of the latter.
This mechanistic change has been proposed earlier but has
been demonstrated here for the first time based on the FOWA
analysis with different catalyst surface concentrations for GC-2
and different concentrations for 2. The absence of a bimolecular
path at the anchored GC-2 catalyst involves access to a path
that is obviously higher in energy and produces a decrease of
the activity that in addition enables deactivation pathways,
ultimately leading to the formation of RuO2 dispersed at the
surface of the electrode as has been shown recently.46
Finally, using Ce(IV) at pH = 1.0 an apparent rate constant of
0.07 s-1 is obtained for 5- which implies an overpotential of 0.38
V according to equation 11 and assuming that the TOF for 5- in
homogeneous phase depends on electron transfer.47 This would
be associated with a Eo’ for the Ce(IV)/Ce(III) couple of 1.55 V
which falls within the 1.46-1.63 V range reported.67,68,69,70,71 For
complex 2 the TOF obtained at pH = 1.0 with Ce(IV) is 30 s-1,45
which compares well with the TOFMAX = 11 s-1 value obtained by
FOWA assuming also η = 0.38 V at [2] = 0.2 mM. However a
direct comparison can’t be made since in homogeneous phase
at this concentration range the rds depends on both the kD and
kO2, but is independent on Ce(IV).
It is also worth realizing that TOF values are highly dependent
on the η and thus the goodness of a catalyst can’t be judged
with a single chemical oxidant. For instance in the case of
catalysts 2 and 5-, the former is better at low η and the latter at
high η.

4. Conclusions
In conclusion, we have adapted the electrochemical
methodology of the foot of the wave analysis (FOWA) to
electrochemical water oxidation. That allows calculating catalytic
water oxidation apparent rate constants in a very simple and

reliable manner. These equations also allow elucidating the first
or second order catalyst dependence on the electrocatalytic
peak current at the foot of the wave that is directly related to the
O-O bond formation step in the case where this step is the rds.
In these cases this allows distinguishing between WNA and I2M
type of mechanisms. Finally, the catalytic Tafel plots are used
for easily and graphically comparing WOCs under identical
conditions and thus are valuable for choosing the right catalyst
for a specific application.

Acknowledgements
R.M. thanks “La Caixa” foundation for a PhD grant. A.L. thanks
MINECO (CTQ-2013-49075-R, SEV-2013-0319; CTQ-201452974-REDC; ENE2014-52280-REDT) and “La Caixa”
foundation for financial support. X.S. thanks MINECO/FEDER
for financial support (CTQ2015-64261-R). F.M. thanks the DFG
(Me 1313/9-1 in the ERA Chemistry framework and SFB 1073,
project C01) for financial support, and S.N. thanks the
international PhD program CaSuS (Catalysis for Sustainable
Synthesis) for a PhD fellowship. FEDER and European COST
actions, CM1202 and CM1205 are also gratefully acknowledged.
Keywords: water oxidation • water splitting • reaction
mechanisms • catalysis • electrocatalysis • foot of the wave
analysis • benchmarking

References
1

N. S. Lewis and D. G. Nocera, Proc. Natl. Acad. Sci. USA, 2006, 103, 1572915735.
2
C.-J. Zhong, J. Luo, P. N. Njoki, D. Mott, B. Wanjala, R. Loukrakpam, S. Lim,
L. Wang, B. Fang and Z. Xu, Energy Environ. Sci. 2008, 1, 454-466.
3
N. S. Lewis, Science 2016, 351, 353.
4
J. Marshall, Nature, 2014, 510, 22-24.
5
F. Rappaport, M. Guergova-Kuras, P. J. Nixon, B. A. Diner and J. Lavergne,
Biochemistry, 2002, 41, 8518-8527.
6
J. R. McKone, N. S. Lewis and H. B. Gray, Chem. Mater. 2014, 26, 407-414.
7
J. Luo, J.-H. Im, M. T. Mayer, M. Schreier, M. K. Nazeeruddin, N.-G. Park, S.
D. Tilley, H. J. Fan and M. Grätzel, Science, 2014, 345, 1593-1596.
8
M. Suga, F. Akita, K. Hirata, G. Ueno, H. Murakami, Y. Nakajima, T. Shimizu,
K. Yamashita, M. Yamamoto, H. Ago and J.-R. Shen, Nature, 2015,
517, 99-103.
9
J. J. Concepcion, R. L. House, J. M. Papanikolas and T. J. Meyer, Proc. Natl.
Acad. Sci. USA, 2012, 109, 15560-15564.
10
B. Kumar, M. Llorente, J. Froehlich, T. Dang, A. Sathrum and C. P. Kubiak,
Annu. Rev. Phys. Chem. 2012, 63, 541-569.
11
F.-F. Li and S. Licht, Inorg. Chem. 2014, 53, 10042–10044.
12
Molecular Water Oxidation Catalysis: A Key Topic for New Sustainable
Energy Conversion Schemes. 2014 Edited by A. Llobet. John Wiley
and Sons Ltd.
13 L. Francas, X. Sala, E. Escudero-Adan, J. Benet-Buchholz, L. Escriche and
A. Llobet, Inorg. Chem. 2011, 50, 2271-2781.
14 D. Hong, S. Mandal, Y. Yamada, Y.-M. Lee, W. Nam, A. Llobet and S.
Fukuzumi, Inorg. Chem. 2013, 52, 9522-9531.
15 A. Singh and L. Spiccia, Coord. Chem. Rev. 2013, 257, 2607-2622.

16

A. Coehn, M. Gläser, Z. Anorg. Chem. 1902, 33, 9-24.
A.C.C. Tseung and S. Jasem, Electrochim. Acta, 1977, 22, 31-34.
18
Y. Matsumoto, E. Sato, Electrochim. Acta, 1979, 24, 421-423.
19
A. Harriman, I. J. Pickering, J. M. Thomas and P. A. Christensen, J. Chem.
Soc. Faraday Trans. 1988, 84, 2795-2806.
20
C. C. L. McCrory, S. Jung, J. C. Peters and T. F. Jaramillo, J. Am. Chem.
Soc. 2013, 135, 16977-16987.
21
C. C. L. McCrory, S. Jung, I. M. Ferrer, S. M. Chatman, J. C. Peters and T.
F. Jaramillo, J. Am. Chem. Soc. 2015, 137, 4347-4357.
22
S. Jung, C. C. L. McCrory, I. M. Ferrer, J. C. Peters, T. F. Jaramillo, J. Mater.
Chem. A, 2016, 4, 3068-3076.
23
C. Sens, I. Romero, M. Rodriguez, A. Llobet, T. Parella and J. BenetBuchholz, J. Am. Chem. Soc, 2004, 126, 7798-7799.
24
R. Zong and R. P. Thummel, J. Am. Chem. Soc. 2005, 127, 12802-12803.
25
J. J. Concepcion, J. W. Jurss, J. L. Templeton and T. J. Meyer, J. Am. Chem.
Soc. 2008, 130, 16462-16463.
26
H. Lv, J. Song, Y. V. Geletii, J. W. Vickers, J. M. Sumliner, D. G. Musaev, P.
Kögerler, P. F. Zhuk, J. Bacsa, G. Zhu and C. L. Hill, J. Am. Chem. Soc.
2014, 136, 9268-9271.
27
L. Duan, A. Fischer, Y. Xu and L. Sun, J. Am. Chem. Soc. 2009, 131,
10397-10399.
28
P. Garrido-Barros, I. Funes-Ardoiz, S. Drouet, J. Benet-Buchholz, F.
Maseras and A. Llobet, J. Am. Chem. Soc. 2015, 137, 6758-6761.
29
S. M. Barnett, K. I. Goldberg and J. M. Mayer, Nat. Chem. 2012, 4, 498-502.
30
D. E. Polyansky, J. T. Muckerman, J. Rochford, R. Zong, R. P. Thummel
and E. Fujita, J. Am. Chem. Soc. 2011, 133, 14649-14665.
31
E. S. Rountree, B. D. McCarthy, T. T. Eisenhart and J. L. Dempsey, Inorg.
Chem. 2014, 53, 9983-10002.
32
N. Song, J. J. Concepcion, R. A. Binstead, J. A. Rudd, A. K. Vannucci, C. J.
Dares, M. K. Coggins and T. J. Meyer, Proc. Natl. Acad. Sci. USA,
2015, 112, 4935-4940.
33
R. S. Nicholson, I. Shain, Anal. Chem. 1964, 36, 706-723.
34
Electrochemical Methods, Fundamentals and Applications. Allen J. Bard
and Larry R. Faulkner, John. Wiley & Sons, Inc. 2nd Ed, New York, NY,
2001. See Chapter 12, section 3.5.
35
C. Costentin, S. Drouet, M. Robert and J.-M. Savéant, J. Am. Chem. Soc.
2012, 134, 11235-11242.
36
C. Costentin, S. Drouet, M. Robert and J.-M. Savéant, Science, 2012, 338,
90-94.
37
V. Artero and J.-M. Saveant, Energy Environ. Sci. 2014, 7, 3808-3814.
38
C. Costentin and J.-M. Savéant, ChemElectroChem, 2014, 1, 1226-1236.
39 C. Costentin, H. Dridi, J.-M. Savéant, J. Am. Chem. Soc. 2014, 136, 1372713734.
40
C. Costentin, G. Passard and J.-M. Savéant, J. Am. Chem. Soc. 2015, 137,
5461-5467.
41
Elements of Molecular and Biomolecular Electrochemistry: An
Electrochemical Approach to Electron Transfer Chemistry, J.-M.
Savéant, John. John Wiley & Sons, Inc. Hoboken, New Jersey, 2006.
42
D. J. Wasylenko, C. Rodríguez, M. L. Pegis and J. M. Mayer, J. Am. Chem.
Soc. 2014, 136, 12544-12547.
43
L. Vigara, M. Z. Ertem, N. Planas, F. Bozoglian, N. Leidel, H. Dau, M.
Haumann, L. Gagliardi, C. J. Cramer and A. Llobet, Chem. Sci. 2012, 3,
2576-2586.
44
R. Matheu, M. Z. Ertem, J. Benet-Buchholz, E. Coronado, V. S. Batista, X.
Sala and A. Llobet, J. Am. Chem. Soc. 2015, 137, 10786-10795.
45
L. Duan, F. Bozoglian, S. Mandal, B. Stewart, T. Privalov, A. Llobet and L.
Sun, Nat. Chem. 2012, 4, 418-423.
46
R. Matheu, L. Francàs, P. Chernev, M. Z. Ertem, V. Batista, M. Haumann, X.
Sala and A. Llobet, ACS Catal. 2015, 5, 3422-3429.
47
S. Neudeck, S. Maji, I. Lopez, S. Meyer, F. Meyer and A. Llobet, J. Am.
Chem. Soc. 2014, 136, 24-27.
48
X. Sala, S. Maji, R. Bofill, J. Garcia-Anton, L. Escriche and A. Llobet, Acc.
Chem. Res. 2014, 47, 504-516.
17

49

D. J. Wasylenko, C. Ganesamoorthy, M. A. Henderson, B. D. Koivisto, H. D.
Osthoff and C. P. Berlinguette, J. Am. Chem. Soc. 2010, 132, 16094–
16106.
50
S. Maji, L. Vigara, F. Cottone, F. Bozoglian, J. Benet-Buchholz and A. Llobet,
Angew. Chem. Int. Ed. 2012, 51, 5967-5970.
51
S. Roeser, P. Farras, F. Bozoglian,M. Martinez-Belmonte, J. BenetBuchholz and A. Llobet, Chem.Sus. Chem. 2011, 4, 197-197.
52
S. Romain, F. Bozoglian, X. Sala, A. Llobet, J. Am. Chem. Soc. 2009, 131,
2768-2769.
53
Neudeck, S.; Maji, S.; Lopez, I.; Dechert, S.; Benet-Buchholz, J.; Llobet, A.;
Meyer, F. Inorg. Chem. 2016, 55, 2508-2521.
54
Berardi, S.; Francas, L.; Neudeck, S.; Maji, S.; Benet-Buchholz, J.; Meyer,
F.; Llobet, A. ChemSusChem 2015, 8, 3688-3696.
55
See page 23 in the supporting information of C. Costentin and J. M. Saveant,
Chem.ElectroChem, 2014, 1, 1226-1236.
56
For the mathematical simulations between 50 and 100 points are
systematically used with R factors higher than 0.97.
57
D. Belanger and J. Pinson, Chem. Soc. Rev. 2011, 40, 3995-4048.
58
F. Li, B. Zhang, X. Li, Y. Jiang, L. Chen, Y. Li and L. Sun, Angew. Chem. Int.
Ed. 2011, 123, 12484-12487.
59
The Tafel equation celebrated the 100th anniversary in 2005. See Ref. 59

60

J. Tafel, K. Schmitz, K. Naremann and B. Emmert: Z. Phys. Chem. 1905, 50,
713–752.
61
C. Costentin, G. Passard, J.-M. Savéant, J. Am. Chem. Soc. 2015, 137,
5461-5467.
62
V. Artero, J.-M. Saveant, Energy Environ. Sci. 2014, 7, 3808-3814.
63
N. Guijarro, M. S. Prevot and K. Sivula, Phys. Chem. Chem. Phys. 2015, 17,
15655-15674.
64
Y. Ma, S. R. Pendlebury, A. Reynal, F. Le Formal and J. R. Durrant, Chem.
Sci. 2014, 5, 2964-2973.
65
C. J. Richmond, R. Matheu, A. Poater, L. Falivene, J. Benet-Buchholz, X.
Sala, L. Cavallo and A. Llobet, Chem. Eur. J. 2014, 20, 17282-17286.
66
L. Wang, L. Duan, Y. Wang, M. S. G. Ahlquist and L. Sun, Chem. Commun.
2014, 50, 12947-12950.
67
The standard potential of the Ce(IV/III) couple is highly sensitive to pH, ionic
strength, anion nature etc. See references: 59-62.
68
V. Nair, A. Deepthi, Chem. Rev. 2007, 107, 1862-1891.
69
S. A. Hayes, P. Yu, T. J. O’Keefe, M. J. O’Keefe and J. O. Stoffer J.
Electrochem. Soc. 2002, 149, 623-630.
70
P. Yu, T. J. O’Keefe, J. Electrochem. Soc. 2006, 153, 80-85.
71
T. N. Bondareva, A. G. Stromberg, Zh. Obsh. Khim. 1955, 25, 639-642.

FULL PAPER
Text for Table of Contents

Roc Matheu, Sven Neudeck, Franc
Meyer, Xavier Sala* and Antoni Llobet*
Page No. – Page No.
Title