PH-dependent reduction potentials and proton-coupled electron transfer mechanisms in hydrogen-producing nickel molecular electrocatalysts

Article abstract of DOI:10.1021/ic302056j

The nickel-based P₂Ph N₂Bⁿ electrocatalysts comprised of a nickel atom and two 1,5-dibenzyl-3,7-diphenyl-1, 5-diaza-3,7-diphosphacyclooctane ligands catalyze H₂ production in acetonitrile. Recent electrochemical experiments revealed a linear dependence of the Ni^II/I reduction potential on pH with a slope of 57 mV/pH unit, implicating a proton-coupled electron transfer (PCET) process with the same number of electrons and protons transferred. The combined theoretical and experimental studies herein provide an explanation for this pH dependence in the context of the overall proposed catalytic mechanism. In the proposed mechanisms, the catalytic cycle begins with a series of intermolecular proton transfers from an acid to the pendant amine ligand and electrochemical electron transfers to the nickel center to produce the doubly protonated Ni⁰ species, a precursor to H₂ evolution. The calculated Ni ^II/I reduction potentials of the doubly protonated species are in excellent agreement with the experimentally observed reduction potential in the presence of strong acid, suggesting that the catalytically active species leading to the peak observed in these cyclic voltammetry (CV) experiments is doubly protonated. The Ni^I/0 reduction potential was found to be slightly more positive than the Ni^II/I reduction potential, indicating that the Ni^I/0 reduction occurs spontaneously after the Ni^II/I reduction, as implied by the experimental observation of a single CV peak. These results suggest that the PCET process observed in the CV experiments is a two-electron/two-proton process corresponding to an initial double protonation followed by two reductions. On the basis of the experimental and theoretical data, the complete thermodynamic scheme and the Pourbaix diagram were generated for this catalyst. The Pourbaix diagram, which identifies the most thermodynamically stable species at each reduction potential and pH value, illustrates that this catalyst undergoes different types of PCET processes for various pH ranges. These thermodynamic insights will aid in the design of more effective molecular catalysts for H₂ production.

Full text of DOI:10.1021/ic302056j

Article
pubs.acs.org/IC
pH-Dependent Reduction Potentials and Proton-Coupled Electron
Transfer Mechanisms in Hydrogen-Producing Nickel Molecular
Electrocatalysts
Samantha Horvath,† Laura E. Fernandez,‡ Aaron M. Appel,§ and Sharon Hammes-Schiffer*,†
†Department of Chemistry, 600 South Mathews Avenue, University of Illinois at Urbana−Champaign, Urbana, Illinois 61801, United
States
‡Department of Chemistry, 104 Chemistry Building, Pennsylvania State University, University Park, Pennsylvania 16802, United
States
§Center for Molecular Electrocatalysis, Pacific Northwest National Laboratory, P.O. Box 999, K2-57, Richland, Washington 99352,
United States
S
* Supporting Information
ABSTRACT: The nickel-based PP2hNB2n electrocatalysts comprised of a nickel
atom and two 1,5-dibenzyl-3,7-diphenyl-1,5-diaza-3,7-diphosphacyclooctane
ligands catalyze H2 production in acetonitrile. Recent electrochemical
experiments revealed a linear dependence of the NiII/I reduction potential
on pH with a slope of 57 mV/pH unit, implicating a proton-coupled electron
transfer (PCET) process with the same number of electrons and protons
transferred. The combined theoretical and experimental studies herein
provide an explanation for this pH dependence in the context of the overall
proposed catalytic mechanism. In the proposed mechanisms, the catalytic
cycle begins with a series of intermolecular proton transfers from an acid to
the pendant amine ligand and electrochemical electron transfers to the nickel
center to produce the doubly protonated Ni0 species, a precursor to H2
evolution. The calculated NiII/I reduction potentials of the doubly protonated
species are in excellent agreement with the experimentally observed reduction
potential in the presence of strong acid, suggesting that the catalytically active species leading to the peak observed in these cyclic
voltammetry (CV) experiments is doubly protonated. The NiI/0 reduction potential was found to be slightly more positive than
the NiII/I reduction potential, indicating that the NiI/0 reduction occurs spontaneously after the NiII/I reduction, as implied by the
experimental observation of a single CV peak. These results suggest that the PCET process observed in the CV experiments is a
two-electron/two-proton process corresponding to an initial double protonation followed by two reductions. On the basis of the
experimental and theoretical data, the complete thermodynamic scheme and the Pourbaix diagram were generated for this
catalyst. The Pourbaix diagram, which identifies the most thermodynamically stable species at each reduction potential and pH
value, illustrates that this catalyst undergoes different types of PCET processes for various pH ranges. These thermodynamic
insights will aid in the design of more effective molecular catalysts for H2 production.
1,5-R′-diaza-3,7-R-diphosphacyclooctane ligands with substitu-
ents R and R′ covalently bound to P and N, respectively. These
molecular electrocatalysts contain phosphorus in the first
coordination sphere of the metal and nitrogen in the second
coordination sphere. The nitrogen atoms act as proton relays,
transferring protons intramolecularly to and from the Ni center
and intermolecularly to and from species in solution.
Depending on the R and R′ substituents, these complexes
can catalyze either H2 oxidation or production. These catalysts
have been studied extensively with experimental and theoretical
methods.6−24
INTRODUCTION
■
Efficient generation and subsequent storage of energy from
renewable resources continues to be an important area of
research.1,2 A promising direction is the use of H2 in fuel cells
and other energy devices.3 Such processes require cost-effective,
man-made, mass-produced catalysts directed toward H2
oxidation and evolution.2,3 Current industrial catalysts contain
costly platinum, making them impractical for large-scale
production.4 On the other hand, hydrogen oxidation and
production are catalyzed in nature by hydrogenase enzymes,5
which serve as inspiration for the design of molecular catalysts.
Examples of such catalysts are the Ni-based PR2N2R′ electro-
catalysts,6−8 which were designed to mimic the pendant amine
Received: September 21, 2012
Published: March 11, 2013
ligands found in hydrogenase enzymes. Here PR2N2R′ denotes
© 2013 American Chemical Society
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Figure 1. Proposed mechanisms for H2 production involving a series of electron and proton transfer steps. Pathway A (red) is characterized by an
initial reduction (2a), followed by intermolecular proton transfer (3a). Pathway B (blue) is characterized by an initial double intermolecular proton
transfer (2b), followed by a reduction (3b). The dashed arrows indicate a net transfer of one electron and one proton for Pathway A and one
electron for Pathway B. The asterisk by each dashed arrow indicates that the system is thought to undergo one or more of the following: ring
isomerization, intramolecular proton transfer, and intermolecular proton transfer. The alternative Pathway A′ is the same as Pathway A except the
first proton transfer occurs prior to the first reduction. The full substituents on P and N are not shown for clarity, and in species 2b and 3b, the
proton is thought to be shared equally between the two nitrogens.
Recently, the effect of acid strength was investigated for the
production of H2 using [Ni(PP2hN2Bn)2]2+ as a catalyst (Ph =
phenyl; Bn = benzyl).16 These electrochemical experiments
indicated that the reduction potential of the NiII/I couple
shifted to values positive of the unprotonated NiII/I couple
under acidic conditions, where the largest shifts were observed
with the strongest acids.16 Measurement of the reduction
potentials for several acids in acetonitrile (MeCN) revealed a
linear relationship between the reduction potential and pH, as
determined by the acid pKa, with a slope of 57 mV/pH unit.16
Such shifts are indicative of coupling between the protons and
electrons via proton-coupled electron transfer (PCET). The
main unanswered question from this experimental study is the
fundamental nature of this coupling in the context of the overall
mechanism for H2 evolution.
The net reaction of the catalytic cycle for hydrogen
production is 2H+ + 2e− → H2. Using the form of the Nernst
equation for PCET reactions, the slope of the pH-dependence
of the reduction potential is (m/n) 59 mV/pH unit for the
transfer of n electrons and m protons at 298 K.16,25−27 Thus, a
one-electron/one-proton coupled process would give the same
slope as a two-electron/two-proton coupled process. In the
context of electrocatalytic H2 production, both types of PCET
processes would be consistent with the experimentally
measured slope. The experimental data indicate that both
singly and doubly protonated species may form, but the
experiments do not enable the determination as to whether
these species are stable yet unproductive intermediates or
directly relevant to the catalytic cycle.16 A wide range of
mechanisms involving various electron transfer (ET) and
proton transfer (PT) steps is possible.
Two proposed mechanisms for H2 production are depicted
in Figure 1, where the pathways for the first portion of the cycle
are labeled as Pathway A (red) and Pathway B (blue). Pathway
A begins with electrochemical reduction, leading to species 2a,
followed by intermolecular PT, leading to species 3a,
comprising a net reaction of [NiIIN]2+ + e− + H+
→
[NiINH]2+. Subsequently, another electrochemical reduction
and intermolecular PT occur to produce the doubly protonated
Ni0 species 4. Pathway B begins with two intermolecular PT
steps, leading to species 2b, followed by two electrochemical
reduction steps, leading to species 3b and then to species 4,
comprising a net reaction of [NiIIN]2+ + 2e− + 2H+
→
[Ni0NH2]2+. For both pathways, the electrons are provided by
the electrode, and the protons are provided by acid molecules
in solution. Based on previous experimental and theoretical
studies, the later steps leading to species 4 are thought to
involve one or more of the following: ring isomerization,
intramolecular PT between the Ni center and the pendant
amine, and intermolecular PT between the acid/base in
solution and the pendant amine. Because of the short lifetimes
of the many possible intermediates relative to the exper-
imentally accessible time scale, these steps are represented by
dashed arrows with asterisks in Figure 1. The dashed arrows
indicate a net transfer of one electron and one proton for
Pathway A and one electron for Pathway B. Although Figure 1
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cyanoanilinium (pKaMeCN ∼ 7.0, denoted “Anl”), respectively.16,39 In
the acid−catalyst supramolecular complex, the amine substituent of
the acid or conjugate base is hydrogen bonded to the pendant amine
ligand of the Ni catalyst. For the associated acid−catalyst complexes,
we examined four species corresponding to the four different charge
transfer states with the electron and proton on their donors or
acceptors. The two proton transfer states are denoted as either
(NiN···HB), where the hydrogen bond is between the acid (HB) and
the unprotonated Ni catalyst, or (NiNH···B), where the hydrogen
bond is between the conjugate base (B) and the protonated Ni
catalyst. The two electron transfer states correspond to the NiI and NiII
oxidation states, respectively. These calculations enabled us to
investigate the thermodynamics of proton transfer from the acid to
the pendant amine of the catalyst both before and after reduction.
Computational Details. We calculated reduction potentials of the
various species directly by optimizing the geometries in solution
(MeCN). We also calculated the reduction potentials by applying the
Born−Haber cycle with structures optimized in the gas phase for
comparison.40,41 Note that the use of structures optimized in the gas
phase is not valid when large structural changes occur upon solvation.
Based on the structural differences observed for some of the species
optimized in the gas phase and in solution, we report only the
solution-optimized data. For cases exhibiting minimal structural
differences, the results of the two approaches were qualitatively similar
(see Supporting Information). Selected bond distances and angles, as
well as the Cartesian coordinates of the optimized structures, are
available in the Supporting Information.
Detailed descriptions of the methods used to calculate reduction
potentials were reported elsewhere,21 and only a brief summary will be
given here. All calculations were performed using the B3P86 density
functional42,43 in Gaussian 09.44 We used the SDD pseudopotential
and basis set of Preuss and co-workers for Ni,45 the 6-31G** basis set
for the protonated amine hydrogens of both acid and catalyst,46 and
the 6-31G* basis set for all other atoms.47,48 A comparison to other
functionals and basis sets is provided in the Supporting Information.
We used the conductor-like polarizable continuum model (C-
PCM)49,50 with Bondi atomic radii51 and included the nonelectrostatic
interactions, specifically the dispersion,52,53 repulsion,52,53 and
cavitation energies,54 to obtain the solvent-optimized geometries.
To obtain the reduction potentials, standard relationships were used
to cancel systematic error resulting from the chosen method and basis
set.21 Specifically, we used the following expression to calculate the
NiII/I reduction potentials of the singly and doubly protonated species:
depicts only sequential mechanisms, some ET and PT steps
could occur via concerted mechanisms.28−38 Distinguishing
between sequential and concerted mechanisms is beyond the
scope of this work.
To assist in interpreting the electrochemical experiments, we
examined three different sequential pathways using a
thermodynamic analysis. The first part of Pathway B (species
1 to 3b) is presumed to occur via the PT−PT−ET mechanism
shown in Figure 1 for reasons that will be explained below.
While the first part of Pathway A (species 1 to 3a) is shown to
occur via an ET−PT mechanism in Figure 1, it could also occur
with the proton transferring first via a PT−ET mechanism. The
possibility of this alternative mechanism, denoted Pathway A′,
will also be considered. To investigate these three pathways, we
calculated the reduction potentials and the free energy
differences for the various species occurring in the proposed
mechanisms. An analysis of these calculations, as well as the
experimental data, provides mechanistic insight into the
experimentally observed pH dependence of the experimental
cyclic voltammograms (CVs).
METHODS
■
We used density functional theory (DFT) with a dielectric continuum
solvent model to calculate reduction potentials for comparison to
available experimental electrochemical data. We also calculated
reaction free energies to evaluate the different protonation pathways
and to determine the viability of acid association before and after
reduction of the Ni center. The reaction free energies, ΔG0, were
obtained from the differences in the free energies of the optimized
solvated reactant and product structures. For notational simplicity, the
PR2NR2′ catalyst is abbreviated (R,R′) for the remainder of the paper,
and this work focuses on the PP2hNB2n catalyst, abbreviated (Ph,Bn).
To examine the possible mechanisms, we calculated the reduction
potentials of various protonated forms of the catalyst. We considered
the singly protonated endo and exo forms, as well as the doubly
protonated endo−endo and exo−exo forms, depicted in Figure 2. Each
E0 = E0,ref − ΔΔGr0(e−)/F
(1)
In this expression, E0 is the NiII/I reduction potential for the species of
interest; E0,ref is the experimentally measured reduction potential of the
reference species, which is the unprotonated (Ph,Bn) complex;7,16
ΔΔG0r(e−) is the calculated difference in free energies of the reduction
reaction for the species of interest and the reference species; and F is
Faraday’s constant. In other words, the reduction potentials are
calculated relative to the experimentally known NiII/I reduction
potential for the unprotonated (Ph,Bn) species. All calculated and
experimental reduction potentials are given in volts (V) relative to the
ferrocenium/ferrocene (Fc+/Fc) couple in MeCN and are therefore
directly comparable without the necessity of calculating the reduction
potential for the Fc+/Fc couple. Note that the calculated reduction
potentials may be viewed as standard potentials that are relative to the
Fc+/Fc couple in acetonitrile and are calculated for various
protonation states. The calculated value for the unprotonated species
is assumed to be equal to the experimentally measured E1/2 in the
absence of acid. As discussed below, the calculated value for the doubly
protonated species is shown to be consistent with the experimentally
observed potential of the catalytic wave in the presence of the
strongest acid.
Figure 2. Relevant isomers of singly and doubly protonated forms of
the Ni catalyst with charge +Z. The full substituents on P and N are
not shown for clarity, and in exo and exo−exo species, the proton is
thought to be shared equally between the two nitrogens.
protonated cyclic ligand of the Ni complex can be either endo or exo
with respect to the metal center, corresponding to the six-membered
chelate ring of the bidentate cyclic ligands arranged in either the boat
or chair conformation, respectively. Note that for exo protonation,
both chelate rings on that bidentate ligand are in the chair
conformation, corresponding to the “pinched” configuration shown
in Figure 2.
We also investigated the association of both weak and strong acids
hydrogen bonded to the singly protonated catalyst in the endo
conformation: p-anisidinium (pKMa eCN ∼ 11.9, denoted “Asd”) and p-
The PT and association reaction free energies, ΔG0PT and ΔGa0ssoc
,
respectively, are the free energy differences between the solvent-
optimized structures. In the calculation of ΔG0assoc, we include the
thermal contributions from the vibrations and translations but not
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Table 1. Calculated NiII/I Reduction Potentials of Relevant
Catalytic Species
from the rotations for reasons discussed in ref 55 and summarized in
the Supporting Information. The association reaction free energies
calculated using various approaches are also provided in the
Supporting Information. Moreover, ΔG0assoc does not account for
basis set superposition error (BSSE). The BSSE could not be
determined for the solvent-optimized structures, but gas-phase
counterpoise-corrected calculations of these structures suggest that
these errors would be small in this case. Lastly, we examined the acid−
catalyst proton transfer reactions by calculating the one-dimensional
proton potentials, where the coordinates of all nuclei except the
transferring hydrogen were fixed. Although the three-dimensional
analogues of these proton potentials could be generated, the
qualitative trends are expected to be captured with the one-
dimensional treatment of the proton motion. The technical details
of these types of calculations were presented previously.21,56
a
species
E0(NiII/I
)
b
[NiN]2+
−0.94
−0.79
−0.86
−0.57
−0.57
c
[NiNH]3+
[NiNH]3+
[NiNH2]4+
[NiNH2]4+
endo
c
exo
c
endo−endo
exo−exo
c
a
b
V vs Fc+/Fc couple in MeCN. Reference reduction potential used in
eq 1, so it agrees with experimental E1/2 value by construction; (bbcc)
c
conformer from ref 21. Isomers of singly and doubly protonated
forms of Ni catalyst shown in Figure 2.
catalyst is used as the reference, all other reduction potentials
are calculated relative to this value, which agrees exactly with
the experimental NiII/I reduction potential by construction. In
the crystal structure of the (Ph,Bn) catalyst and in crystal
structures for similar electrocatalysts, a weakly bound MeCN
ligand is coordinated to the unprotonated NiII species
(1).6,7,13,16,57 In contrast, the Ni0 crystal structures for similar
electrocatalysts are four-coordinate without a solvent li-
gand.13,57,58 From a qualitative perspective, five-coordinate
NiII complexes with a weakly coordinating solvent ligand and
four-coordinate Ni0 complexes are expected to be stable
according to the 18-electron rule for metal complexes, whereas
five-coordinate NiI complexes with a solvent ligand are not
expected to be stable, as they would be 19-electron complexes.
Thus, typically these NiII species are assumed to be five-
coordinate with a solvent ligand, whereas these NiI and Ni0
species are assumed to be four-coordinate without a solvent
ligand.
Consistent with the above discussion, we explicitly include an
MeCN ligand for the NiII species but not for the NiI species in
our calculations. Note that the free energy of solvation for the
MeCN ligand is not required in the calculation of the NiII/I
reduction potentials using eq 1 because it cancels in the
calculation of the difference in free energies of the reduction
reactions for the species of interest and the reference species.59
The calculated NiII/I reduction potentials are consistent with
the experimental data only by accounting for the change in
coordination number upon reduction. Other approaches that
treat both oxidation states the same (i.e., both the NiI and NiII
species with or without the fifth ligand) yield a qualitatively
different interpretation of the pathways leading to H2
production. The results from alternative treatments are
provided in the Supporting Information. These results suggest
that the MeCN binding strength is different for the
unprotonated, singly protonated, and doubly protonated
species. As a result, the effects of the MeCN ligand are not
additive and do not cancel when the unprotonated species is
chosen as the reference.
RESULTS AND DISCUSSION
■
We investigated the singly and doubly protonated forms of the
catalyst. While the singly protonated endo species has not been
directly observed experimentally, at least one of the four
protonated chelate rings must be in the endo orientation for H2
production to occur according to the proposed mechanisms in
Figure 1.9,23 In contrast, NMR spectroscopy data have provided
strong evidence for the presence of the doubly protonated exo−
exo species in solution.16 For the present study, the NMR
spectroscopy studies reported in ref 16 were repeated in the
presence of electrolyte and are in quantitative agreement with
the previous results. These new experimental results suggest
that the doubly protonated exo−exo species is dominant under
electrochemical conditions as well as standard NMR spectros-
copy conditions. The details of the experimental methods for
these studies are provided in the Supporting Information.
Chair−boat isomerization from the exo or exo−exo form to
the catalytically active endo or endo−endo form is thought to be
required before H2 can be produced. The chair−boat
isomerization barrier for the protonated species is on the
order of 10−15 kcal/mol and thus constitutes a possible
bottleneck in the catalytic cycle.9,17,23 This bottleneck is
presumed to result in the low concentrations of the endo−
endo form (4) that could undergo intramolecular proton
transfer to form the protonated Ni-hydride species (5) that is
thought to exergonically evolve H2.7,15,16
An explanation for the lack of experimental observation of
the singly protonated endo NiII and Ni0 species with NMR
spectroscopy was provided by previous calculations on the
related (Ph,Ph) H2 production catalyst.9,17,23 These calculations
indicated that the singly protonated Ni0 species is much less
stable than the doubly protonated Ni0 species.23 Moreover,
upon endo protonation of the NiI species to form 3a in Figure
1, the system readily undergoes PCET with intramolecular PT
to the Ni center,9 yielding a monohydride species that is
extremely stable and observed by NMR spectroscopy for both
the (Ph,Ph) and (Ph,Bn) catalysts.7 Furthermore, intermolec-
ular proton transfer to an exo protonation site is less sterically
hindered and therefore may be more favorable, although it
would require subsequent isomerization to the catalytically
active endo form. Based on these previous experimental and
theoretical studies, we considered the singly protonated endo
and exo and the doubly protonated endo−endo and exo−exo
(Ph,Bn) catalysts in this paper.
For simplicity, we considered only the high and low pH
limits in our calculations of the reduction potentials. At high
pH values, the catalyst is unprotonated, so the experimentally
measured reduction potential would be the reduction potential
of the unprotonated catalyst and represents the most negative
value for the observed potential: −0.94 V vs Fc+/Fc.7,16
Conversely, at very low pH values, the majority of the catalyst is
protonated, so the experimentally measured reduction potential
would be the reduction of the protonated species and
represents the least negative value for the observed potential.
These two regimes correspond to the plateau regions (i.e., pH-
Reduction Potentials of Singly and Doubly Proto-
nated Species. The calculated reduction potentials for the
species described in the previous subsection are presented in
Table 1. Because the NiII/I couple of the unprotonated (Ph,Bn)
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independent regimes) in the plot of reduction potential versus
pH. For intermediate pH values, a mixture of protonated and
unprotonated species is present in solution such that the
observed reduction potential changes linearly with pH. The
experimental results indicate that for the strongest acid studied
(2,5-dichloranilinium, pKMa eCN ∼ 6.2), the potential at half the
maximum current was observed to be −0.58 V vs Fc+/Fc.16
The theoretical methodology used in this study allows us to
calculate the reduction potentials of various protonated forms
of the catalyst, such as endo, exo, endo−endo, and exo−exo. As
evident from Table 1, the calculated reduction potentials of the
singly protonated species (both endo and exo) are significantly
more negative relative to the observed potential of the catalytic
wave in the presence of the strongest acid (−0.58 V vs Fc+/Fc),
while the calculated reduction potentials of the doubly
protonated species are in excellent agreement with this
experimental value.16 These results suggest that the catalytically
active species is doubly protonated rather than singly
protonated because the reduction potentials for the doubly
protonated, but not the singly protonated, species are
consistent with the cyclic voltammetry experiments. This
observation is also consistent with the NMR spectroscopy
experiments indicating the prevalence of the doubly protonated
exo−exo species in solution.16
Proton Transfer Reactions and Association Free
Energies. We examined the hydrogen-bonded associated
acid−catalyst complexes with both a weak and a strong acid.
The proton is transferring between the acid and the pendant
amine of the catalyst, and the two proton transfer states of
interest correspond to the proton on the acid or the catalyst.
For electrochemical reactions, the electron is transferring
between the complex and the electrode, so the two electron
transfer states of interest correspond to the two oxidation states
of the complex. For complexes with the weak acid, we found
four stationary points corresponding to the four combinations
of the electron and proton being on their donors and acceptors.
For complexes with the strong acid, however, we were unable
to determine stationary points with the proton on its donor
(i.e., on the acid) but were able to identify two stationary points
with the proton on its acceptor (i.e., on the catalyst pendant
amine).
For the weak acid-associated complexes, we calculated the
reaction free energies for the proton transfer steps in the ET−
PT and PT−ET mechanisms associated with Pathways A and
A′, respectively. The reaction free energies for these two PT
steps are −0.03 and −0.09 eV, respectively. We also calculated
the one-dimensional proton potentials for the proton transfer
steps of the weak acid-associated complexes. These results are
provided in the Supporting Information. These proton
potentials were generated by moving the proton along a one-
dimensional axis with all other atoms fixed and thus provide
only a qualitative indication of the proton potential for these
specific equilibrium structures. For the weak acid, the proton
potentials corresponding to the equilibrium structures with the
proton bonded to the acid exhibit relatively low barriers,
suggesting relatively facile PT without significant hydrogen
tunneling effects. As mentioned above, for the strong acid, we
were unable to find equilibrium structures with the proton on
the acid, also suggesting facile PT from the acid to the catalyst.
Thus, proton transfer is likely to be facile after the acid−catalyst
complex is formed.
association, ΔG0assoc, before and after reduction for the endo
isomer. The results are reported in Table 2. In all cases, the
Table 2. Calculated Reaction Free Energies for Acid
a
Association to Ni Catalyst
base (B)
b
b
association reaction
p-anisidine
p-cyanoaniline
[NiIIN]2+ + [HB]+ → [NiIIN···HB]3+
[NiIIN]2+ + [HB]+ → [NiIINH···B]3+
[NiIN]+ + [HB]+ → [NiIN···HB]2+
[NiIN]+ + [HB]+ → [NiINH···B]2+
0.75
0.65
0.26
0.24
n/a
0.44
n/a
0.06
a
b
Reaction free energies in units of eV. Reaction free energy, ΔGa0ssoc
,
obtained from free energies of optimized solvated reactant and product
structures in the endo form. ΔG0assoc does not account for basis set
superposition error (BSSE) and does not include rotational
contributions to the partition function.
effect of bringing two positively charged species in close
proximity to one another is thermodynamically unfavorable,
yielding small association constants. Although still somewhat
unfavorable, the reaction free energies are smaller for the strong
acid than for the weak acid and decrease significantly after
reduction. Both of these observations are consistent with basic
electrostatic arguments. As mentioned above, ΔG0assoc includes
the translational contributions but excludes the rotational
contributions to the partition functions and does not account
for BSSE. As a result of these approximations, these values are
expected to provide only a qualitative evaluation of the relative
favorability of association. In other words, the trends are
meaningful, but the absolute magnitudes are not quantitatively
reliable.
In addition to the thermodynamic penalty of acid association,
steric hindrance could be a key factor, especially for less
accessible protonation sites within the catalyst.9,17,23 Note that
acid−catalyst association may be more favorable for the exo
isomer than for the endo isomer due to less steric hindrance. In
this case, however, the complex must surmount a substantial
free energy barrier for isomerization from the exo to the endo
form. Moreover, while the acids examined here are typical of
those studied experimentally,16 as the size of the acid or the R
and R′ substituents on the catalyst increases, the acid−catalyst
association constants may become prohibitively small, partic-
ularly for endo protonation. To overcome these problems, a
catalytic amount of water could be added to act as a Grotthus-
̈
type proton shuttle. Experimental evidence has shown that
addition of water significantly increases the observed catalytic
turnover frequency.16,60,61
Thermodynamic Scheme. Previously a thermodynamic
scheme for the (Ph,Bn) catalyst was reported on the basis of
experimentally determined values.16 Within this thermody-
namic scheme, however, relations between some species were
omitted because these species were not directly observable.
Moreover, for some of these processes (shown as dashed
arrows in Scheme 3 of ref 16), only average values associated
with two consecutive ET or PT steps were determined.
Utilizing the data presented herein, we report a completed
thermodynamic scheme for the (Ph,Bn) catalyst in Figure 3.
These species are still depicted in gray to illustrate that their
relative thermodynamic stabilities are determined from an
analysis of the calculations presented herein rather than from
direct experimental measurement.
To investigate the free energy associated with the formation
of the acid−catalyst complex, we calculated the free energies of
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Figure 3. Experimental and calculated thermodynamic data for the (Ph,Bn) catalyst, where the P2N2 ligand is denoted by L. The thermodynamic
scheme shows the relationships among the species in terms of E1/2, pKa, homolytic solution bond dissociation free energy (BDFE), ΔG0 , and ΔG0
H−
H2
values. Formulas are intended to indicate only composition and not structure (i.e., notation does not distinguish between nickel hydrides and
protonated pendant amines). The species in gray have not been directly observed experimentally, and their relative stabilities are therefore
determined from the calculations presented herein. A version of this scheme was reported in ref 16; however, since all thermodynamic relationships
have been determined, the scheme is presented here in its entirety. Details of the quantities required to complete this scheme are provided in the
Supporting Information.
In ref 16 average values were reported for the double
deprotonation of [NiIINH2]4+ to [NiIIN]2+ (left diagonal red
arrows in Figure 3) and for the double reduction of
[NiIINH2]4+ to [Ni0NH2]2+ (lowest horizontal black arrows
in Figure 3). Since these values are discussed herein, a summary
of the methods used to obtain these average values is given.
On the basis of the agreement between our calculated value
for the NiII/I reduction potential of the doubly protonated
species and the experimental reduction potential at the lowest
pH buffered solution studied, we deduce that the NiII/I couple
of [NiIINH2]4+ occurs at a potential of −0.57 V vs Fc+/Fc
(lower left black arrows in Figure 3). To obtain the average
value of −0.54 V vs Fc+/Fc discussed above, the NiI/0 couple of
[NiINH2]3+ must occur at a potential of −0.51 V vs Fc+/Fc
(lower right black arrows in Figure 3). Note that the second
reduction (i.e., the NiI/0 couple) occurs at a potential positive of
the first reduction (i.e., the NiII/I couple) and as a result should
occur spontaneously, most likely resulting from loss of the
solvent ligand during the NiII/I reduction. However, these
values are considered to be virtually identical within the
accuracy of the calculations. As given in Table 1, the NiII/I
reduction potentials of the singly protonated endo and exo
[NiIINH]3+ species are −0.79 and −0.86 V vs Fc+/Fc,
respectively. The difference between the reduction potentials
of the endo and exo isomers for the singly protonated species is
within the error of our calculations, and for this reason we
utilize the average of these two potentials, −0.83 V vs Fc+/Fc,
for the NiII/I reduction potential of [NiIINH]3+ in Figure 3
(middle left black arrows) and the associated analysis.
A similar process can be used to obtain the pKa values for the
singly and doubly protonated NiII species. As discussed above,
the experimental value of 6.7 is the average pKa for the two
protonation steps to form the exo−exo [NiIINH2]4+ species
from the unprotonated NiII species. On the basis of the
theoretical data, the reduction potential of the doubly
protonated NiII species is −0.57 V vs Fc+/Fc, and the
experimentally obtained relation in eq 2 indicates that the
pKa of the doubly protonated species is 5.9 at this potential
(lower left red arrows in Figure 3). To obtain an average pKa of
6.7, the pKa of the singly protonated NiII species must be 7.5
(upper left red arrows in Figure 3). In previous NMR
spectroscopy experiments, the singly protonated NiII species
1
From previous H and 31P NMR spectroscopy studies, the
relative ratios of acid/base and doubly protonated/unproto-
nated NiII (Ph,Bn) complex, respectively, were determined.16
The equilibrium constant for the double deprotonation of
[NiIINH2]4+ was calculated using the relative concentrations of
the four species: [NiIINH2]4+ + 2[B] ⇌ [NiIIN]2+ + 2[HB]+.16
The equilibrium constant for this reaction (Keq) was converted
to an average pKa value using the following expression:
pKaMeCN,avg = pKraef − 0.5 log(Keq), where pKaref is the pKa of the
reference acid in acetonitrile (p-cyanoanilinium, pKaMeCN
∼
7.0).16,39 As mentioned above, these results were reproduced in
the presence of electrolyte, yielding an average pKa of 6.8 0.5,
which is quantitatively similar to the previously measured value
of 6.7 0.4.16 Note that the singly protonated complex was
never observed in either set of experiments.
Using a combination of the experimentally determined
average pKa for [NiIINH2]4+ and the free energy for addition of
H2 to (Ph,Bn) of 2.7 kcal/mol,7 the average potential for the
double reduction of [NiIINH2]4+ to [Ni0NH2]2+ can be
determined using a thermodynamic cycle. As given in ref 16,
this procedure leads to an average reduction potential of −0.54
V vs Fc+/Fc. For complete details of the thermochemical
reactions and relationships used to obtain this value, see the
Supporting Information of ref 16. In addition to these average
values, the shift in the reduction potential with acid strength
was measured experimentally, and the following relationship
was obtained from a linear fit of the pH-dependent reduction
potential data:16
E = −0.057 V × pH − 0.230 V
(2)
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was not observed in equilibrium experiments using two
different acids with pKa values of 5.1 and 7.0,16 suggesting
that the pKa of the singly protonated species is less than or
equal to that of the doubly protonated species. While the
experimental results suggest that the singly protonated species
is less stable than the doubly protonated and unprotonated
species in this pH range, the precise difference in energy is not
indicated experimentally. Our calculations suggest that there
may be a region of pH between 5.9 and 7.5 in which the singly
protonated species is stable, but the pKa values of 7.5 and 5.9
for the singly and doubly protonated NiII species are considered
to be virtually identical within the accuracy of our calculations.
Thus, this region may be narrower than calculated and
therefore not experimentally observed, or it may not exist,
given the limitations of the calculations. This issue does not
impact the overall conclusions of the present work. For
comparison, we generated a thermodynamic scheme using the
average reduction potentials and average pKa values for these
steps and provide this alternative scheme in Figure S1 of the
Supporting Information. The thermodynamic values in this
alternative scheme are the same as those in Figure 3 to within
the accuracy of the calculations and experiments.
Pourbaix Diagram. The linear fit of the experimental
data16 has a slope of 57 mV/pH unit (eq 2), which is similar to
the slope of 59 mV/pH unit expected for a PCET process
involving the same number of electrons and protons, as
indicated by the standard form of the Nernst equation for
PCET reactions.25,27 Based on the agreement between the
calculated and experimental reduction potentials, we deduced
that the observed shift of the reduction potential in the
presence of the strongest acid arises from the NiII/I reduction of
the doubly protonated species. Given the experimentally
observed slope of ∼59 mV/pH unit, as well as the lack of
experimental observation of the singly protonated species, this
PCET process is presumed to involve the transfer of two
electrons, along with the transfer of two protons, on the time
scale accessible in the CV experiments. According to this
analysis, this PCET process connects species 1 and 4 through
Pathway B in Figure 1. In other words, the PCET process
observed in the CV experiments under catalytic conditions is
the PT−PT−ET−ET process in Pathway B.
On the basis of the calculated data given in Table 1 and
Figure 3, in conjunction with the experimental data reported in
Figure 6 of ref 16, we generated the Pourbaix diagram for the
(Ph,Bn) catalyst in MeCN. The resulting Pourbaix diagram,62
which depicts the most thermodynamically stable species for a
given reduction potential and pH value, is presented in Figure
4. In this figure, the horizontal and vertical black lines
correspond to the reduction potentials and pKa’s, respectively,
of various protonated and unprotonated forms of the (Ph,Bn)
catalyst. The portions of the Pourbaix diagram at pH < 5 and
pH > 20 are independent of acid concentration (horizontal
black lines) and represent the reduction of the doubly
protonated species (2e− process) and reduction of the
unprotonated species (two 1e− processes), respectively. In
between these two limits of pH, various protonated forms of
the catalyst are thermodynamically stable. The blue line
between pH ≈ 8 and pH ≈ 12 has a slope consistent with
the two-electron/two-proton (2e−−2H+) process shown in
Pathway B of Figure 1 and corresponds to the experimentally
measured slope reported in eq 2 from ref 16.
Figure 4. Pourbaix diagram62 for the (Ph,Bn) catalyst calculated from
the thermodynamic scheme in Figure 3. The horizontal and vertical
lines are the reduction potentials and pKa’s, respectively, of various
protonated and unprotonated forms of the catalyst in MeCN. The red
lines have slopes of ∼29.5 mV/pH unit and correspond to 2e−−1H+
processes. The blue line has a slope of ∼59 mV/pH unit and
corresponds to a 2e−−2H+ process. The green line has a slope of ∼59
mV/pH unit and corresponds to a 1e−−1H+ process. The analogous
Pourbaix diagram that does not include the [NiIINH]3+ region is
provided as Figure S2 in the Supporting Information. Note that
[Ni0NH]+ corresponds to the NiII-hydride species.
studied experimentally. The green line between pH ≈ 15 and
pH ≈ 20 has a slope consistent with a 1e−−1H+ process and
corresponds to conversion between the [Ni0NH]+ species and
the unprotonated NiI species. Because the same number of
electrons and protons are being transferred, the green line
(1e−−1H+ process) has the same slope of ∼59 mV/pH unit as
the blue line (2e−−2H+ process). The red line between pH ≈
12 and pH ≈ 15 has a slope consistent with a 2e−−1H+ process
and corresponds to conversion between the [Ni0NH]+ species
and the unprotonated NiII species. Note that [Ni0NH]+
corresponds to the NiII-hydride species rather than the singly
protonated amine Ni0 species. Thus, the red line is bounded on
the left by the pKa of 11.8 for the doubly protonated Ni0 species
(i.e., removal of a proton from the pendant amine as well as
intramolecular proton transfer from the other pendant amine to
the Ni center), and the green line is bounded on the right by
the pKa of 19.4 for the NiII-hydride species (i.e., removal of a
proton from the metal center), as reported in Figure 3.
In addition to the 2e−−1H+ process between pH ≈ 12 and
pH ≈ 15, a second red line between pH ≈ 6 and pH ≈ 8 also
has a slope consistent with a 2e−−1H+ process, corresponding
to conversion between the doubly protonated Ni0 species and
the singly protonated NiII species. This red line is bounded by
the two pKa values of the doubly and singly protonated NiII
species, 5.9 and 7.5, respectively, as reported in Figure 3. As
discussed above, the singly protonated species is not observed
in the experiments. Moreover, the differences in these pKa
values (5.9 and 7.5) are within the errors of our calculations,
and this region may be narrower than calculated or may not
exist. For this reason, we also present an alternative version of
Figure 4 in Figure S2 of the Supporting Information using the
average pKa value for these steps, as well as the average
reduction potential for the doubly protonated NiII and NiI
species. The only difference between Figure 4 and Figure S2 is
that the area associated with the singly protonated species
disappears, and only the doubly protonated NiII species is
For other ranges of pH, the Pourbaix diagram has regions
that correspond to different PCET processes that were not
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shown for pH values lower than ∼7 in Figure S2. This
difference does not affect the overall conclusions of this paper.
A description of the approach used to generate these Pourbaix
diagrams, as well as the specific reduction potentials and pKa’s,
are also provided in the Supporting Information.
Pathway B for p-anisidinium due to the higher population of
the unprotonated form of the catalyst. Pathway A may require
fewer isomerizations, which are thought to be rate determining
in the overall catalytic cycle. Another possible explanation for
this behavior is that the difference in pKa values between the p-
anisidinium (pKMa eCN ∼ 11.9) and the doubly protonated Ni0
catalyst (pKMa eCN = 11.8)7,16 is smallest for p-anisidinium,
resulting in more facile deprotonation and reprotonation of the
amine groups on the catalyst. As a result of this pKa matching,
the isomerization reactions are expected to be faster, and
therefore would be less of a hindrance if they are required
during the catalytic cycle. Both factors may contribute to the
higher rate observed using p-anisidinium.
The net reaction for H2 production requires two reduction
steps, as illustrated in Figure 1. In this paper, we calculated the
reduction potential for only the first reduction step, but we also
consider these results in the context of the overall catalytic cycle
by analyzing the thermodynamic scheme. For Pathway A (ET−
PT mechanism), the NiII/I reduction potential of the
unprotonated species is −0.94 V vs Fc+/Fc,7,16 whereas for
Pathway A′ (PT−ET mechanism), the NiII/I reduction
potential of the singly protonated species (average of the two
isomers) is −0.83 V vs Fc+/Fc. For Pathway B, the NiII/I
reduction potential for the doubly protonated species is −0.57
V vs Fc+/Fc. If Pathways A and A′ follow a PT−ET mechanism
for the later part of the cycle (dashed arrows in Figure 1), all
three pathways contain some combination of two PT reactions
and an ET reaction prior to the second ET reaction. For the
resulting doubly protonated NiI species, the subsequent NiI/0
reduction occurs at a more positive potential of −0.51 V vs
Fc+/Fc and should occur spontaneously, most likely due to the
solvent ligand release occurring during the NiII/I reduction. If
Pathways A and A′ follow an ET−PT mechanism for the later
part of the cycle instead, the subsequent NiI/0 reduction of the
singly protonated NiI species still occurs at a more positive
potential of −0.60 V vs Fc+/Fc and should also occur
spontaneously, as it is positive of the NiII/I couple for the
singly protonated species.
H2 Production Mechanism: Effects of Acid Strength.
Our calculated reduction potential for the doubly protonated
species is consistent with the experimentally observed potential
for the catalytic wave in the presence of the strongest acid,
suggesting that the doubly protonated species is being reduced
in these CV experiments.16 The linear fit of the experimental
pH dependence follows the standard form of the Nernst
equation for PCET reactions.25,27 Thus, the combination of
theoretical and experimental data implies that the pH
dependence can be explained in the context of this Nernst
equation, where the catalyst is present in a mixture of
unprotonated and doubly protonated forms. For the strongest
acids studied (pKa’s less than ∼7), the doubly protonated form
dominates, and H2 production occurs mainly through Pathway
B with a reduction potential near −0.58 V vs Fc+/Fc. For very
weak acids (pKa’s greater than ∼12), the unprotonated form
dominates, and H2 production occurs mainly through Pathway
A with a reduction potential near −0.94 V vs Fc+/Fc, the value
for the unprotonated catalyst. For intermediate strength acids
(blue lines in Figures 4 and S2), a mixture of unprotonated and
doubly protonated forms is present, and H2 production occurs
through both Pathways A and B, where the reduction potential
is controlled by the relative populations of the unprotonated
and doubly protonated forms.
We also considered an alternative explanation of the pH
dependence. In a sequential PCET process, protonation could
occur either before or after electron transfer. Protonation prior
to reduction could result in a very large shift in potential
because the electron is transferred to chemically distinct
species, as in Pathway A′ and Pathway B. The above analysis of
the pH dependence is based on this effect. However,
protonation after reduction can also significantly affect the
observed reduction potential if the PT reaction is fast and
exergonic. This scenario could be relevant to Pathway A. To
estimate the magnitude of the shift in potential that may occur
due to a subsequent PT reaction, digital simulations of this
process were performed, as described in detail in the
Supporting Information. For a diffusion-controlled, second-
order reaction (catalyst plus one substrate) that is exergonic,
the maximum shift in potential is estimated to be ∼270 mV
under conditions similar to those reported for the currently
discussed catalytic process. For processes that are slower than
diffusion controlled, the shift in potential will be even smaller,
and similarly, for processes with a higher reaction order, the
shift in potential is also expected to be smaller. Therefore, a fast
subsequent PT reaction does not appear to provide a suitable
explanation for the entirety of the previously observed shift in
potential of up to 440 mV.16 This type of kinetic potential shift
could explain the pH dependence of the reduction potential for
weak acids but not the observed shifts for the strongest acids,
although this effect may contribute at some level to the overall
observed pH dependence.
Thus, regardless of the pathway, the experimentally observed
reduction potential arises from the NiII/I couple, and the
subsequent NiI/0 reduction occurs spontaneously. These results
are consistent with the experimental observation of only a
single peak in the CV.16 This analysis illustrates that a
combination of pathways is possible, and the branching among
these pathways is likely pH-dependent.16 For all pathways, a
series of isomerizations and deprotonations/protonations most
likely occur prior to and/or subsequent to the second reduction
step, and the barriers to these processes may be prohibitively
large and rate-determining.9,17,23 We emphasize that this type
of thermodynamic analysis can be used to rule out certain
mechanisms and can be found to be consistent with proposed
mechanisms but cannot unequivocally prove a particular
mechanism.
CONCLUSIONS
■
In this paper, we investigated three proposed mechanisms for
H2 evolution catalyzed by the [Ni(PP2hN2Bn)2]2+ molecular
electrocatalyst. The net reaction of the catalytic cycle for
hydrogen production is 2H+ + 2e− → H2. The electrons are
provided by the electrode, and the protons are provided by acid
molecules in solution. Pathway A is characterized by an initial
reduction, followed by intermolecular proton transfer (ET−
PT), whereas Pathway A′ occurs in the reverse order (PT−
The experimentally measured catalytic rate in the regime
independent of acid concentration was observed to increase
with increasing pH.16 In particular, the rate with p-anisidinium,
the weakest acid studied, is much larger than the rates for the
stronger acids. One possible explanation for this behavior is that
the mechanism is predominantly Pathway A rather than
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ET). Both of these pathways are followed by an additional
reduction and proton transfer in an unspecified order. Pathway
B is characterized by an initial double intermolecular proton
transfer, followed by two reductions (PT−PT−ET−ET). All
three pathways converge at the doubly protonated Ni0 species,
a precursor to H2 evolution. The reduction potentials and
relative free energies of the singly and doubly protonated
species along these reaction pathways were calculated to
identify the pathway that is most consistent with the
experimental data.
ASSOCIATED CONTENT
■
S
* Supporting Information
Description of computational methods; selected geometric
parameters and Cartesian coordinates of solution-phase
optimized structures; NiII/I reduction potentials calculated
using different approaches; association reaction free energies
calculated using different approaches; relative energies of
protonated species using alternate approaches; one-dimensional
proton potentials for acid−catalyst complexes with weak acid;
description of experimental methods and results; alternative
thermodynamic scheme and Pourbaix diagram; table of related
hydrogen reaction free energies in MeCN. This material is
available free of charge via the Internet at http://pubs.acs.org.
The experimentally observed slope of the pH-dependence of
the NiII/I reduction potential is consistent with the slope of 59
mV/pH unit predicted by the Nernst equation for PCET
reactions with the same number of electrons and protons
transferred.25,27 The calculated NiII/I reduction potentials of the
doubly protonated species are in excellent agreement with the
experimentally observed reduction potential in the presence of
strong acid, suggesting that the catalytically active species
leading to the peak observed in these CV experiments is doubly
protonated. This observation is also consistent with the NMR
spectroscopy experiments implicating the prevalence of the
doubly protonated exo−exo species in solution.16 The second
NiI/0 reduction potential was found to be slightly more positive
than the initial NiII/I reduction potential, indicating that the
NiI/0 reduction occurs spontaneously, as implied by the
experimental observation of a single CV peak. The more
positive reduction potential for the NiI/0 reduction could arise
from the solvent ligand release occurring during the NiII/I
reduction. On the basis of the experimentally observed slope of
the pH-dependence of the reduction potential, in conjunction
with the calculated reduction potentials, the PCET process
observed in the CV experiments with strong acid was deduced
to be consistent with the two-electron/two-proton process
corresponding to an initial double protonation followed by two
reductions.
AUTHOR INFORMATION
■
Corresponding Author
*E-mail: shs3@illinois.edu.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We thank Brian Solis, Alexander Soudackov, Monte Helm,
Shentan Chen, and Simone Raugei for their helpful scientific
discussions and insights. We would especially like to thank
Wendy Shaw, Ming-Hsun Ho, and Roger Rousseau for their
assistance with the Pourbaix diagrams. This research was
supported as part of the Center for Molecular Electrocatalysis,
an Energy Frontier Research Center funded by the U.S.
Department of Energy, Office of Science, Office of Basic Energy
Sciences.
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