Moving protons with pendant amines: Proton mobility in a nickel catalyst for oxidation of hydrogen

Article abstract of DOI:10.1021/ja201838x

Proton transport is ubiquitous in chemical and biological processes, including the reduction of dioxygen to water, the reduction of CO₂ to formate, and the production/oxidation of hydrogen. In this work we describe intramolecular proton transfe

Full text of DOI:10.1021/ja201838x

ARTICLE
pubs.acs.org/JACS
Moving Protons with Pendant Amines: Proton Mobility in a Nickel
Catalyst for Oxidation of Hydrogen
Molly O’Hagan, Wendy J. Shaw,* Simone Raugei,* Shentan Chen, Jenny Y. Yang, Uriah J. Kilgore,
Daniel L. DuBois, and R. Morris Bullock*
Center for Molecular Electrocatalysis, Pacific Northwest National Laboratory, P.O. Box 999, K2-57, Richland, Washington 99352,
United States
S Supporting Information
b
ABSTRACT: Proton transport is ubiquitous in chemical and biological processes,
including the reduction of dioxygen to water, the reduction of CO2 to formate,
and the production/oxidation of hydrogen. In this work we describe intramole-
cular proton transfer between Ni and positioned pendant amines for the hydrogen
oxidation electrocatalyst [Ni(PCy2NBn2H)2]2þ (PCy2NBn = 1,5-dibenzyl-3,7-
2
dicyclohexyl-1,5-diaza-3,7-diphosphacyclooctane). Rate constants are deter-
mined by variable-temperature one-dimensional NMR techniques and two-
dimensional EXSY experiments. Computational studies provide insight into the
details of the proton movement and energetics of these complexes. Intramolecular
proton exchange processes are observed for two of the three experimentally
observable isomers of the doubly protonated Ni(0) complex, [Ni(PCy2NBn2H)2]2þ
,
which have NꢀH bonds but no NiꢀH bonds. For these two isomers, with pendant
amines positioned endo to the Ni, the rate constants for proton exchange range
from 104 to 105 sꢀ1 at 25 °C, depending on isomer and solvent. No exchange is observed for protons on pendant amines
positioned exo to the Ni. Analysis of the exchange as a function of temperature provides a barrier for proton exchange of ΔGq
= 11ꢀ12 kcal/mol for both isomers, with little dependence on solvent. Density functional theory calculations and molecular
dynamics simulations support the experimental observations, suggesting metal-mediated intramolecular proton transfers
between nitrogen atoms, with chair-to-boat isomerizations as the rate-limiting steps. Because of the fast rate of proton
movement, this catalyst may be considered a metal center surrounded by a cloud of exchanging protons. The high
intramolecular proton mobility provides information directly pertinent to the ability of pendant amines to accelerate proton
transfers during catalysis of hydrogen oxidation. These results may also have broader implications for proton movement in
homogeneous catalysts and enzymes in general, with specific implications for the proton channel in the NiꢀFe hydrogenase
enzyme.
’ INTRODUCTION
A significant advance in understanding proton movement in
hydrogenases was made when the crystal structure of the FeꢀFe
hydrogenase revealed a dithiolate bridge that is widely accepted
to contain an amine, positioned properly to transfer protons to
and from the distal Fe (1).13ꢀ15
The controlled movement of protons is essential in many
biological transformations. Cytochrome c-oxidase,1,2 gramici-
din A,3,4 and carbonic anhydrase II5 are well-known examples
of enzymes that move protons easily over large distances.
Hydrogenases6ꢀ10 are another example of a family of enzymes
that move protons efficiently; they have received substantial
attention in recent years due to interest in the production or
oxidation of hydrogen for energy storage and use. The bimetallic
active site and outer-coordination sphere of these enzymes6,11,12
have evolved to control the efficient formation or cleavage of the
HꢀH bond and facilitate proton transfer between the metal
center and proton relays within the protein matrix during the
catalytic cycle. However, studying proton movement at a
molecular level within these enzymes is challenging due to their
size and complexity, and the exquisite studies that are done
often require many mutations to indirectly identify the proton
channel.6
These con0siderations and others led our laboratories to develop
Ni(PR NR
)
2þ electroca0talysts containing 1,5-diaza-3,7-dipho-
2
2 2
sphacyclooctane (PR NR 2) ligands that provide positioned
2
Received: February 28, 2011
Published: May 19, 2011
r
2011 American Chemical Society
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pendant amines in the second coordination sphere to facilitate
proton movement (2).16ꢀ25 The pendant amine has been
demonstrated to be necessary for the fast rates observed for
hydrogen production23ꢀ25 (up to 1850 sꢀ1 at 22 °C),26
exceeding those of the NiꢀFe hydrogenase (700 sꢀ1 at
30 °C).27 The simplicity of these catalysts and their similarity
with the enzyme active site provide an opportunity to in-
vestigate proton movement to and from the metal at a
molecular level, with implications for both enzymatic systems
and organometallic catalysts involved in multi-proton and
multi-electron reactions.
50 °C, in 10 °C increments (20 °C increments shown in Figure 1
for clarity). Consistent with previous results,21 the spectrum for
A at ꢀ40 °C shows resonances at 21.2 and 16.0 ppm. The
observation of two 31P chemical shifts for this isomer is attributed
to two of the phosphorus atoms being adjacent to an NꢀH group
in a boat conformation, while the other two are not spatially near
an amine. Similarly, the phosphorus atoms of the exo-protonated
ligand of isomer B have chemical shifts at ꢀ5.8 and ꢀ10.2 ppm,
depending on the orientation relative to the protonated amine on
the opposite ligand. The phosphorus atoms on the endo-
protonated ligand of isomer B have equivalent chemical shifts
(15.5 ppm), as do the phosphorus atoms in isomer C (ꢀ11.0
ppm).28 The additional splitting observed on the resonances for
A, as well as for the exo portion of B, is due to the inequivalence of
the phosphorus atoms, creating AA0BB0 splitting patterns.
The multiple narrow 31P NMR resonances for complexes A
and B at ꢀ40 °C indicate that exchange processes are very slow at
this temperature. The resonances for isomers A and B begin to
broaden at about ꢀ20 °C, indicating an increased rate of
exchange. The coalescence temperature for B is ∼0 °C; at
20 °C, this resonance has begun to narrow again as it approaches
the fast exchange limit. A slightly different temperature regime is
observed for A, where coalescence occurs at ∼10 °C. At 20 °C,
this resonance is still very broad, indicating that the fast exchange
limit has not yet been reached. The downfield resonance for B
and the resonance for C remain sharp throughout the tempera-
ture range, likely indicating the absence of exchange on the NMR
time scale, although rapid exchange would look similar. The
variable-temperature spectra for [Ni(PCy2NBn2H)2]2þ in acet-
one and methylene chloride are similar to those observed in
acetonitrile (Figures S1 and S2 in the Supporting Information).
The NMR data were modeled using a two-site exchange
process, shown schematically in Figure 2; representative fits are
shown in Figure S3.29 The rate constants for exchange as
functions of temperature and solvent are shown in Table 1,
ranging from about 104 to 105 sꢀ1 at room temperature for both
isomers A and B. Activation parameters were determined by
fitting the variable-temperature data covering the temperature
range of ꢀ40 to 50 °C (Figures 3 and S4). The resulting
activation parameters as a function of solvent are shown in
Table 2. The free energies of activation show little dependence
on isomer or solvent. Only a moderate dependence on the
activation enthalpy is observed as a function of isomer (∼2ꢀ4
kcal/mol higher for B than for A) and solvent, but the activation
entropy for the two isomers shows a clear trend (Table 2). We
observe low or negative entropies of activation for isomer A
We have chosen [Ni(PCy2NBn2)2]2þ, a catalyst for the oxida-
tion of hydrogen (Cy = cyclohexyl, Bn = benzyl),20 to investigate
intramolecular proton transfer. This catalyst was chosen because
it allows the direct observation of many of the proposed reaction
intermediates using experimental NMR techniques. Addition of
H2 to [Ni(PCy2NBn2)2]2þ has been shown to produce
[Ni(PCy2NBn2H)2]2þ, a Ni0 complex with two protonated
amines.21 Characterization of [Ni(PCy2NBn2H)2]2þ by 1H, 31P,
and 15N NMR revealed that this complex exists as three isomers,
A, B, and C, that differ in the orientation of the NꢀH bonds.
Isomer A has both NꢀH bonds endo to the nickel, while isomer
C has both NꢀH bonds exo to the nickel, in a “pinched”
(NꢀHꢀN) configuration. Isomer B has a mixed endo-exo
(ꢀ7.5 to 1.4 cal molꢀ1
K
K
ꢀ1) and larger, positive values for B
geometry. Based on the structure and the proposed mechanism
(7.4 to 11.4 cal molꢀ1
ꢀ1), which suggests a more organized
0
for H2 production and oxidation for [Ni(PR NR 2)2]2þ
2
catalysts,23ꢀ26,34 only pendant amines having an endo geometry
are properly positioned to function efficiently as proton relays
during catalysis, as demonstrated by complexes 1 and 2. In order
to provide detailed mechanistic insight on how these intramole-
cular proton transfer reactions occur, we report combined experi-
transition state for the proton exchange in A compared to B.
[Ni(PCy2NMe2H)2]2þ Isomers: Relative Free Energy. The
NMR measurements along with previous experimental evidence20,21
suggest that the intramolecular proton exchange is mediated by
the metal center (Figure 2). To verify this mechanism and to
address the potential impact of the overall molecular dynamics
on the kinetics of the proton exchange, a series of ab initio
calculations were performed. To reduce the computational cost,
density functional theory (DFT) calculations were carried out on
[Ni(PCy2NMe2)2]2þ, where the benzyl substituents of the N
atoms were replaced by methyl groups.30
mental and computational studies for [Ni(PCy2NBnH)2]2þ
a catalytic intermediate for the oxidation of hydrogen.
,
’ RESULTS AND ANALYSIS
Proton Exchange Rates for [Ni(PCy2NBn2H)2]2þ. To gain
a better understanding of the nature of the exchange processes
occurring for isomers AꢀC, 31P{1H} NMR spectra of
[Ni(PCy2NBn2H)2]2þ in CD3CN were recorded from ꢀ40 to
Ab initio geometry optimizations support the assignment of
the geometries shown in AꢀC as the lowest-energy doubly
protonated isomers (Figure 4). The relative free energies in
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Figure 1. 31P{1H} NMR spectra of [Ni(PCy2NBn2H)2]2þ in CD3CN as a function of temperature.
Table 1. Exchange Rate Constants (sꢀ1) for Intramolecular
Proton Transfer for the A (Endo-Endo) and B (Endo-Exo)
Isomers of [Ni(PCy2NBn2H)2]2þ as a Function of
Temperaturea
isomer A
isomer B
temp (K) CD3CN acetone CH2Cl2 CD3CN acetone CH2Cl2
233
243
253
263
273
283
293
298
303
313
323
46
99
39
110
34
70
31
78
17
87
95
360
320
270
220
560
1 300
2 800
5 700
8 600
ꢀ
240
170
1 550
3 500
8 600
Figure 2. Simplified schematic representation of the proton exchange
mechanism for the endo-endo isomer A based on the NMR data. Red
arrows indicate the metal-mediated proton movement between two
nitrogens. Figure 6 shows the complete mechanism for proton exchange.
740
640
720
640
1 700
3 900
9 300
12 000
20 000
41 000
85 000
1 400
2 500
5 300
6 600
ꢀ
2 600
5 400
15 000
27 000
39 000
100 000
1 800
4 600 25 000
14 000 51 000
16 000 84 000
N
HN hydrogen bonds results in species AꢀC having similar
3 3 3
ꢀ
ꢀ
ꢀ
ꢀ
ꢀ
energies, consistent with the experimentally observed equilibri-
um between these three species. The six-membered rings con-
taining non-protonated amines are all in chair conformations
based on the computational analysis. Double protonation of a
ligand is higly unfavorable. The lowest-energy isomer with a doubly
protonated ligand lies 7 kcal/mol above A. This is consistent with
experimental results, where double protonation of the same ligand
is not observed for these complexes (see below).
ꢀ
24 000
ꢀ
ꢀ
280 000 100 000
a Determined by line shape analysis of the 31P{1H} NMR spectra. Rate
constants at 298 K are calculated from the resulting activation
parameters.
acetonitrile are 1.6, 0.0, and 0.4 kcal/mol for isomers A, B, and C,
respectively (Figure 4; a more complete ranking of the free
energies of the different conformations of these three isomers is
reported in Figure S5).
The six-membered rings containing endo protonated amines
are found computationally to be in a boat conformation. Calcula-
tions indicate a significant hydrogen-bond-like d(Ni)fσ*-
(NꢀH) interaction,31 with a hydrogen bond strength of approxi-
mately 7 kcal/mol between the Ni0 and the NH proton for
isomers A and B. The six-membered rings for the exo (pinched)
moiety of isomers B and C are in chair conformations. In both
Assessment of the Proton Exchange Pathways. To assess
the possible paths for intramolecular exchange of the endo
protons in isomers A and B, the free energy map for the proton
movement in the all-boat conformer A00 (Figure 4) was calcu-
lated via gas-phase ab initio molecular dynamics. In this method,
Newton’s equations of motion are propagated in time according
to forces obtained in the density functional theory electronic
structure framework. In the following we will refer to free
energies obtained via molecular dynamics as “classical” nuclei
free energies. Although conformer A00 is not the lowest-energy
endo-endo conformer (ΔG = 5.2 kcal/mol, Figure 4), it repre-
sents the best choice for studying the proton movement because
of the symmetry introduced by all of the six-membered rings
isomers, the pinched moiety features a NH N hydrogen bond
3 3 3
with an estimated free energy of about 9ꢀ10 kcal/mol. The
similarity of the hydrogen bond energies for the Ni0 HN and
3 3 3
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being in the boat conformation. Indeed, each non-protonated
pendant amine is in an optimal position for receiving the proton
from a protonated amine. In addition, the use of conformer A00
avoids any complication due to the chair/boat conformational
dynamics. The latter will be considered in a second stage (see
below), where nuclear quantum (zero point energy, ZPE) effects
will also be included.
The calculated classical nuclei free energy as a function of
nitrogen/hydrogen coordination numbers (n1 and n2, see Com-
putational Details) is shown in Figure 5. The map is symmetric
with respect to the y = x diagonal and features four distinct
minima: the diproton species with a doubly protonated P2N2
ligand (n1 = 2, n2 = 0 or n1 = 0, n2 = 2), the diproton species with
both the P2N2 ligands singly protonated (n1 = 1, n2 = 1), the
proton-hydride species (n1 = 1, n2 = 0 or n1 = 0, n2 = 1), and the
dihydride species (n1 = 0, n2 = 0).
the A00 species, consistent with the B3P86 calculations. (3) The
free energy surface is rather flat, which implies a very facile proton
transfer from the pendant amine to the metal center. The overall
classical nuclei activation free energy for moving a proton from
N to Ni is about 7.0 kcal/mol. (4) Analysis of the metadynamics
trajectory suggests that the hydride ligand easily moves from one
face to another of the tetrahedron defined by the four phos-
phorus atoms. The activation barrier for this process is less than
3 kcal/mol (Figure S6). (5) Finally, the different proton-hydride
species can also, in principle, be connected via a high-energy
dihydride intermediate (ΔG = 11.0 kcal/mol). No other proton
exchange pathways within 25 kcal/mol from the lowest-energy
minima were found.
High-Energy Pathways of Proton Exchange. Our computa-
tional studies suggested that intermediates involving either
the Ni(IV) dihydride, [(H)2Ni(PCy2NBn2)2]2þ, or the Ni(0)
doubly protonated ligand, [Ni(PCy2NBn2H2)(PCy2NBn2)]2þ
,
Several important conclusions can be drawn from this map:
(1) The proton exchange between the N atoms is mediated by
the Ni atom. Indeed, the analysis of the molecular dynamics
trajectory (Figure 5) shows that all of the possible diproton
species are connected by a proton-hydride intermediate. (2)
Double protonation of one ligand is disfavored by 4 kcal/mol for
were unlikely due to the high relative energies. To provide
experimental confirmation, we prepared the HꢀD complex
[Ni(PCy2NBn2H)(PCy2NBn2D)]2þ, because it results in unique
31P resonances due to the proximity of the 31P to an NꢀH or an
NꢀD (see Figure S7 and Figure 5 of ref 21). If there is exchange
of the H and D between ligands, the mechanism would involve
one of two intermediates: a doubly protonated ligand,
[Ni(PCy2NBn2HD)(PCy2NBn2)]2þ, or the hydride-deuteride,
[(H)(D)Ni(PCy2NBn2)2]2þ. Due to the unique resonances,
Figure 4. Ranking of the lowest free energy isomers of [Ni(PCy
-
2
Figure 3. Eyring plots in CD3CN (O), acetone (4), and dichloro-
methane ([) for proton exchange in [Ni(PCy2NBn2H)2]2þ, isomers
A (top) and B (bottom).
NMe2H)2]2þ calculated in acetonitrile at the B3P86/{Ni(SDD);P,N,C,
H(6-31G*);(N-)H(6-31G**)} level of theory. For clarity, cyclohexyl
groups on the P atoms are not shown.
Table 2. Activation Parameters for Proton Transfer in A (Endo-Endo) and B (Endo-Exo) Isomers of [Ni(PCy2NBn2H)2]2þa
isomer A
isomer B
CD3CN
acetone
CH2Cl2
CD3CN
acetone
CH2Cl2
ΔHq (kcal molꢀ1
ΔSq (cal molꢀ1 Kꢀ1
ΔGq (kcal molꢀ1
)
12.3 ( 0.3
1.4 ( 1.0
11.9 ( 0.3
10.0 ( 0.2
ꢀ7.5 ( 0.6
12.2 ( 0.2
11.5 ( 0.4
ꢀ1.9 ( 1.3
12.0 ( 0.4
14.8 ( 0.3
11.4 ( 0.9
11.4 ( 0.3
13.9 ( 0.2
7.4 ( 0.9
11.7 ( 0.2
13.7 ( 0.3
10.0 ( 1.1
10.7 ( 0.3
)
)
a Determined from the rate constants shown in Table 1 and Figure 3.
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This confirms that each proton remains on the same ligand,
providing strong evidence that neither the dihydride nor the
diprotonated ligand species are intermediates in the proton
transfer process (Figure 5, top). This is consistent with the inter-
pretation that both the dihydride and the doubly protonated
ligand species are significantly higher in energy than species with
two singly protonated ligands.
Proton Exchange and Conformational Dynamics. The anal-
ysis reported above is strongly suggestive of a metal-mediated
proton exchange mechanism. However, the pictureemergingfrom
the study of the all-boat endo-endo isomer is not complete.
Indeed, all of the lowest-energy isomers feature the non-
protonated pendant amine in a chair conformation. This finding
suggests that, in the exchange pathway, a chair-to-boat conforma-
tional change should follow or precede the proton migration to the
metal. We now analyze the effect of this conformational change as
well as the proton movement in the overall transfer of the proton
from one amine to the other.
To this end, we will not rely on ab initio simulations. Although
they represent a powerful tool to carry out exhaustive searches for
reaction channels, they are time-consuming, and it is impractical
to use them to investigate all of the relevant isomers and conformers
involved. In addition, they do not take nuclear quantum effects into
account. In particular, inclusion of the vibrational ZPE is crucial to
properly describe the relative energetics of the species involved in
the proton movement, which are essential to properly describe the
energetics of proton transfer. This contribution is missing in the
Newtonian dynamics on which molecular dynamics is based. For
these reasons, the structures of a series of species involved in the
proton exchange dynamics as suggested by the ab intio simulations
described above was refined by less time-demanding standard
quantum chemistry geometry optimizations.
On the basis of the local minima and transition states located
with the metadynamics simulation of the all-boat endo-endo A00
isomer (Figure 5), we have characterized the structure and
energetics of all of the diproton species and hydride species
involved in the hydrogen movement for all of the relevant endo-
endo (A) and endo-exo (B) conformers at the DFT/B3P86 level
of theory (Figures 6 and S8). Our computations indicate that the
intramolecular proton exchange observed for isomers A and B
involves three distinct processes: the transfer of a proton from N
to Ni, migration of the resulting hydride ligand from one face to
another of the tetrahedron defined by the four phosphorus
atoms, and chair-to-boat conformational changes of the non-
protonated rings.
Figure 5. (Top) Schematic representation of the intramolecular proton
exchange in the all-boat [Ni(PCy2NMe2H)2]2þ (conformer A00, Figure 4),
where each species maps to the corresponding lowest-energy isomer
found in the ab initio meta-dynamics (lower panel). Equilibria leading to
high-energy species whose presence is ruled out by NMR measurements
are crossed out with an X. (Bottom) Corresponding free energy land-
scape projected onto the nitrogen/hydrogen coordination number of
the two ligands. Local minima and transition states between them are
marked with blue and red dots, respectively. Free energies at minima and
transition states are also reported using the same colors. The dotted lines
indicate lowest free energy pathways. Calculations were performed using
PBE/{Ni(DZV2P);P,C,N,H(TZV2P)} gas-phase ab initio meta-dynamics
simulations. For clarity, the 2þ charge on the Ni complex is not shown.
The free energy barrier for the chair-to-boat isomerization of
the non-protonated rings ranges from 7.7 to 10.7 kcal/mol,
depending on the species. However, the corresponding barrier
for the chair-to-boat isomerization of the pinched ring, which
involves the loss of the NꢀH N hydrogen bond, is about
3 3 3
16 kcal/mol. This result is consistent with the failure to observe
intramolecular exchange of the pinched proton in isomer B
with the endo proton. The chair-to-boat barriers for the
unprotonated ligands of the proton-hydride species corre-
sponding to A and B are 7.7 and 8.3 kcal/mol, respectively,
about 2.4 kcal/mol smaller than the corresponding barriers
for the protonated ligands of the diproton species. DFT/
B3P86 calculations also confirm that the dihydride species,
which has not been observed experimentally, is considerably
higher in energy than the proton-hydride species.
scrambling of the proton and deuteron between ligands could be
31
observed using 31Pꢀ P NMR exchange spectroscopy (EXSY).32,33
While intraligand exchange was observed (Figure S7, solid lines), no
interligand exchange was observed over the temperature range where
the individual ligand resonances are resolved (ꢀ65 to ꢀ10 °C).
In acetonitrile, the computed harmonic reaction free energy
barrier for the N-to-Ni proton transfer is 5.1 and 5.3 kcal/mol for
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Figure 6. (Top) Free energy diagram for the exchange pathway indicated by numbers in the bottom scheme; reactant, product, and intermediates
are indicated with blue lines placed on top of the corresponding species as reported in the bottom scheme, whereas transition states between them are
reported as red lines (free energies are given with respect to the initial state). (Bottom) Full reaction mechanism of the intramolecular proton exchange
for the endo-endo [Ni(PCy2NMe2H)2]2þ isomer. Circled numbers indicate one of the eight possible shortest (five-step) exchange pathways.
Blue numbers indicate the free energy of the species involved with respect to the initial isomer; red numbers indicate the activation free energy (in
the direction of the arrow) of a given step. In both panels the numbers in parentheses indicate the free energy for the deuterated species. Calculations
were carried out for acetonitrile solution at the B3P86/{Ni(SDD); P,N,C,H(6-31G*);(N-)H(6-31G**)} level of theory with harmonic estimates of
thermal effects and entropy contributions using the CPCM solvation model. For clarity, the 2þ charge on the Ni complexes is not shown.
A and B, respectively. The barrier for the N-to-Ni proton transfer
calculated for the all-boat conformer, A00, is 5.6 kcal/mol. This
value is lower than the 7.0 kcal/mol obtained from the classical
nuclei molecular dynamics in the gas phase (Figure 5). ZPE and
different exchange and correlation functionals account for this
difference.35 The free energy barriers for hydride migration
between faces of the tetrahedron range from 2.4 to 4.3 kcal/
mol, depending on the chair/boat conformation of the non-
protonated six-membered rings. Overall, the calculated activa-
tion free energy barriers for the N-to-Ni proton transfer and
migration from one face to another are lower than the barrier for
the chair-to-boat conformational change of the ring.
Kinetics of Proton Exchange. The intermediates involved in
the proton exchange can be connected to each other in several
ways, yielding the complete exchange mechanism shown in
Figure 6 for isomer A and in Figure S8 for isomer B. From
Figure 6 it is easy to see that the shortest exchange pathways
involve five steps. There are a total of eight such pathways, which
are the lowest-energy pathways; they differ only in the sequence
of events.
(step 1). The hydride then migrates from one face to another
of the tetrahedron defined by the four phosphorus atoms
(step 2). These two processes are very fast. The third step is
slower and involves a chair-to-boat transition of the ring contain-
ing the Nb atom (step 3). Finally, the proton transfers from Ni to
Nb (step 4), and the ring containing Na undergoes a boat-to-chair
isomerization (step 5).
The other possible pathways can be derived starting from the
pathway discussed above. For instance, the chair-to-boat isomer-
ization (step 3) can take place before the hydride migration
(step 2), or the boat-to-chair isomerization (step 5) can take
place before the hydride-to-proton transformation (step 4). A
chair-to-boat transition before the N-to-Ni proton transfer is
equally possible.
The overall effective activation free energy, ΔGqeff, can be
derived from the (steady-state) effective kinetic constant ob-
tained by solving the master equation of the network of reactions
illustrated in Figures 6 and S8. Our calculations give a ΔGqeff at
room temperature of about 10.7 and 10.3 kcal/mol for isomers
A and B, respectively. Considering the slightly different chemi-
cal nature between the [Ni(PCy2NMe2)2]2þ complex and
[Ni(PCy2NBn2)2]2þ, the agreement with the activation barrier
determined from the NMR data in acetonitrile (11.9 and
11.4 kcal/mol respectively) is remarkable. The activation free
As an example, consider the top pathway in the reaction
diagram reported in Figure 6, whose steps are indicated by
circled numbers. The first step consists of a proton transfer
from Na to Ni that leads to a proton-hydride intermediate
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exchange is (see Experimental Section, eq 11)
k1k2k3k4k5
ðfÞ
k
ꢁ
k
eff
ꢀ1kꢀ2ðkꢀ3kꢀ4 þ k4k5Þ
k3k4k5
ð1Þ ð2Þ
¼ K
K
ð1Þ
eq eq
k
ꢀ3kꢀ4 þ k4k5
where k(efff) is the overall forward rate constant, kn and kꢀn are the
(2)
forward and reverse rate constants of step n, and K(e1q) and K are
eq
the equilibrium constants of steps 1 and 2 of Figures 6 and S8.
From these figures it is evident that deuterium substitution
predominantly affects the steps involving proton transfers
between N and Ni (e.g., steps 1 and 4) and has little effect on
the other steps (chair/boat interconversion and proton migra-
tion around the metal center). In particular, the first equilibrium
constant K(e1q) of the deuterated species is about 3.8 times smaller
than the one for the non-deuterated species. This is a conse-
quence of the different ZPE content associated with NꢀH and
NiꢀH bonds in the deuterated and non-deuterated species. A
similar argument holds for the other possible pathways, but with
a different magnitude. Therefore, the experimentally observed
kinetic isotope effect is interpreted as being due to equilibrium
isotopic effects on the steps involving proton transfers between
Ni and N.
Figure 7. (Top) 31P{1H} NMR spectra of [H-Ni(PCy2NBz 2)2]þ as a
function of temperature. (Bottom) The Eyring plot of the chair-to-boat
interconversion over the temperature range of ꢀ50 to ꢀ80 °C.
energies calculated in methylene chloride and acetone are very
similar to those in acetonitrile, also in agreement with the
corresponding experimental results. We note that the free energy
barriers for proton exchange derived from each single five-step
pathway are similar (about 11 kcal/mol, where differences
among pathways are within 1.0 kcal/mol), and therefore all of
them are potentially operative.
’ DISCUSSION
Mechanism of Proton Tr0ansfer. The pendant amines incor-
porated into the [Ni(PR NR 2)2]2þ complexes23ꢀ25 function as
2
proton relays that facilitate intramolecular proton transfers in the
catalytic oxidation and production of H2. Catalytic activity for
complexes containing positioned pendant amines occurs at much
higher rates and/or lower overpotentials compared to catalysts
that have no pendant amines, indicating their ability to lower
barriers for these catalytic reactions.16ꢀ26 An important aspect of
many catalytic processes is the transfer of the proton between a
metal center and an amine, and the results presented here
provide detailed insight into this movement. Specifically, protons
are transferred from the pendant amines to the metal center and
out to the opposite pendant amine within the same ligand. The
rate-limiting step in this process is the chair-to-boat conforma-
tional change of the non-protonated pendant amine. Our results
show that several different pathways with comparable activation
barriers connect the various species described above, as shown in
Figure 6.
Up to 10 species can be involved in the intramolecular transfer
of a proton from Na to Nb. The numbered pathway in Figure 6 is
representative of one of the shortest pathways for the endo-endo
isomer A, which includes two proton transfers between N and Ni,
one proton migration around the Ni face, and two chair-to-boat
interconversions. Independent of which pathway is chosen, the
chair-to-boat interconversion is the rate-limiting step in all cases,
a result that was not obvious or anticipated. Particularly, the
observed KIE would suggest that the rate-determining step
involves the proton transfer. Because only the starting material
and final products can be detected by NMR, and in this case
multiple unobservable intermediate processes are encompassed
in between, the computational analysis provides additional in-
sight into the mechanism. While the rate-determining step does
not involve the proton movement, the calculations show that the
equilibration steps prior to the chair/boat interconversions (for
Chair/Boat Interconversion. Our computational results
strongly suggest that the chair-to-boat interconversion is the
rate-limiting step for intramolecular proton exchange, prompting
additional experimental measurements. While we are unable to
uniquely observe this interconversion for [Ni(PCy2NBn2H)2]2þ
,
this process is observed for both [Ni(PCy2NBn2)2]0 and
[H-Ni(PCy2NBn2)2]þ by 31P{1H} NMR (Figures S9 and 7,
respectively). The free energies of activation for interconversion
were found to be 7.7 kcal/mol for [Ni(PCy2NBn2)2]0 and
9.3 kcal/mol for [H-Ni(PCy2NBn2)2]þ, in good agreement with
computational predictions of 9.8 kcal/mol for [Ni(PCy2NMe2)2]0
and 8.7 kcal/mol for [H-Ni(PCy2NMe2)2]þ. Additionally, the
similarity in barriers for both hydride and non-hydride species
provides indirect experimental evidence that the migration of the
hydride about the Ni is facile.
Kinetic Isotope Effect (KIE). Deuterium exchange rates for
[Ni(PCy2NBn2D)2]2þ were investigated experimentally, follow-
ing the same procedure used in the proton exchange studies. The
KIE was measured in CD3CN and methylene chloride. For both
solvents, kH/kD for A and B at 20 °C are 2.9 and 1.9, respectively.
Our calculations on [Ni(PCy2NMe2D)2]2þ are consistent with
the experimentally determined isotope effect, with theoretical
KIEs of 2.4 and 1.8 for isomers A and B, respectively. Since the
barriers for proton transfer are smaller than the barriers for the
chair-to-boat conversion, it is of interest to analyze the origin of
the observed isotope effect. To this end, it is useful to focus on
just one of the possible exchange pathways, for instance the one
marked with numbers from 1 to 5 in Figures 6 and S8. Since the
chair/boat conversion steps (step 3 and 5) are slower than the
proton transfer steps, the effective rate constant for the proton
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Journal of the American Chemical Society
ARTICLE
instance, step 1, Figure 6) are sensitive to deuteration, providing
a reduction in rate (kH/kD = 2ꢀ3) similar to that observed
experimentally. Additionally, direct measurement of the chair-to-
boat interconversion in both [Ni(PCy2NBn2)2] and [H-Ni-
(PCy2NBn2)2]þ provides barriers similar to those observed
computationally for [Ni(PCy2NBn2H)2]2þ, providing experimen-
tal corroboration for the height of this barrier (8ꢀ11 kcal/mol).
Notably, neither the dihydride [(H)2Ni(PCy2NBn2)2]2þ nor
species (Figures 6 and S8) provides the largest contribution to
the observed increase in rate for isomer B. The observed free
energy barriers to intramolecular exchange also depend very little
on solvent for both isomers, as shown in Table 2. The lack of
significant solvent dependence for ΔGq suggests that the rate-
limiting step does not involve significant charge redistribution,
consistent with a chair-to-boat transition as the rate-limiting step.
The rate constants of intramolecular proton transfer observed
here are 100ꢀ1000 times larger than the rates of catalytic
hydrogen production or oxidation, so proton transfer is clearly
not the rate-limiting step in catalysis. Because the movement of
protons to or from the metal is a necessary step in the catalytic
cycle for both hydrogen production and oxidation, this work
highlights the benefits of a carefully positioned proton relay in
systems that have been thermodynamically matched to minimize
the barrier to proton transfer. It is precisely because of the correct
positioning that amine-to-metal proton transfer is not a rate-
determining step; consequently, enhancing catalytic activity will
require improvement of other proton transfers or electron
transfers in the catalytic cycle.
It is interesting to compare the rates observed here to those for
nitrogen-to-nitrogen proton transfers between organic amines
and protonated amines, which typically occur at diffusion-
controlled rates unless there is a significant steric influence.
Because it is an intramole0cular process, the rate of proton
exchange in the [Ni(PCy2NR 2H)2]2þ system can be comparable
to the bimolecular self-exchange rate constants observed for
amines, depending on the concentrations being considered (for
example, 0.1 to 0.01 M amine would give first-order rate
constants of 105 to 107 sꢀ1). While the mechanism for proton
exchange for isomers A and B occurs in a multi-step pathway
involving two proton transfers between the pendant amines and
the metal, in addition to chair-to-boat conformational changes,
these results highlight that the Ni-to-N proton transfer is not
rate-limiting when amines are positioned correctly. In contrast,
barriers to proton transfers between metal hydrides and metal
anions38ꢀ40 involve significantly higher barriers (and hence
the doubly protonated ligand, [Ni(PCy2NBn2H2)(PCy2NBn2)]2þ
,
are observed experimentally or participate as intermediates, as
determined from EXSY NMR experiments (Figure S7). This is
consistent with the high energies predicted computationally.
Thus, the proton moves between N atoms on the same ligand,
mediated by proton transfer to the metal, but not between
ligands. This conclusion is consistent with the observation of
an intramolecular exchange process in isomer B as well as for
isomer A. It is interesting to note that both the Ni(IV) dihydride
species and a doubly protonated PPh2NBn ligand (3) were
2
observed for a related complex, [Ni(PPh2NBn2)(dppp)]2þ (dppp
= 1,2-bis(diphenylphosphino)propane), suggesting that the en-
ergetic landscape is relatively flat and highly tunable by modest
changes in substituents.22
The present results also provide insight for the interpreta-
tion of previous studies. For instance, the addition of H2 to
[Ni(PNP)2]2þ (PNP = Et2PCH2N(Me)CH2PEt2), which con-
tains pendant but unpositioned amines, gives the proton-hydride
complex [H-Ni(PNP)(PNHP)]2þ (4).36 Facile intramolecular
proton exchange, with rate constants on the order of 104 sꢀ1, was
observed between the NꢀH and the NiꢀH in this complex. A
dihydride or dihydrogen intermediate was proposed for this
intramolecular proton exchange.36 The current results shown in
Figure 5 place the dihydride complex 7 kcal/mol higher in energy
than the proton-hydride, with a barrier of 12 kcal/mol. By
extension, this suggests that, in the [Ni(PNP)2]2þ catalyst, the
fast intramolecular proton transfer was from the NiꢀH to the
unprotonated amine, probably never going through a nickel
dihydride species.
Rates of Intramolecular Proton Exchange and Implica-
tions for Catalysis. The rates of proton movement from one
amine to another for isomers A and B are 104ꢀ105 sꢀ1 at 25 °C,
depending on the isomer and the solvent. The rates are con-
sistently faster for B than for A in all solvents, by a factor of
approximately 2 in acetone and acetonitrile and a factor of
approximately 10 in methylene chloride. There is no clear
dependence on solvent polarity, since rates are fastest in aceto-
nitrile and slowest in acetone (the dielectric constants are 9.1,
21, and 37.5 for dichloromethane, acetone, and acetonitrile,
respectively). The exchange rates for B are also not directly
correlated to the dielectric constant, where rate constants are 5
times faster in methylene chloride than in acetone, and the rate in
acetonitrile is 2 times faster than in acetone. The computational
analysis suggests that the reduction in the barrier height for the
chair-to-boat conformational change for the proton-hydride
lower rates) compared to proton transfers between nitrogen
0
atoms. While the proton transfers for the Ni(PR NR 2)2 catalysts
2
between the pendant amines and the Ni are accompanied by a
formal change in oxidation state of two units at Ni, these changes
in electronic states do not limit fast proton transfer from amine to
amine.
The mobility of the proton between the tetrahedral faces of the
Ni atom in these small molecular catalysts may also point to
flexibility of the location (or multiple locations) for the proton
and hydrogen channels in the NiꢀFe hydrogenase enzyme.9,12,41ꢀ43
If protons have a similar low barrier to mobility within the
enzyme, a fluxional Ni hydride could enable the facile move-
ment of the proton from one face of a four-coordinate Ni
species to the other.44 Several proton channels have been
suggested on the basis of experimental9,41 and computational
studies,42,43 all originating with the Ni, and the proposed
hydrogen channel ends near a vacant coordination site on the
Ni atom.12 For the oxidation of hydrogen, the proton channel
likely involves residue Glu-25 (Desulfovibrio fructosovorans),
since hydrogen oxidation shuts down in its absence.41 How-
ever, for proton reduction, one computational study found
similar energies for two different proton transfer pathways,
suggesting that different pathways may be used for proton
reduction and hydrogen oxidation.42 Multiple proton chan-
nels may imply that multiple proton positions on the metal
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Journal of the American Chemical Society
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are easily accessible and may all function with similar rates
due to fast intramolecular proton transfer.
methyl)cyclohexyl phosphine). The spectral properties are consistent
with those previously reported.21
Preparation of [Ni(PCy2NBn2H)2][BF4]2. [Ni(PCy2NBn2H)2]-
[BF4]2 was prepared for NMR studies following a previously reported
synthesis.21 About 10ꢀ12 mg of [Ni(PCy2NBn2)2][BF4]2 was dissolved
into ∼1 mL of solvent, either methylene chloride, acetone, or acetoni-
trile-d3, in an NMR tube under N2 at room temperature. The samples
were then purged for 3ꢀ5 min with hydrogen (ultrahigh purity,
99.999%) with an in-line drier (OxypurgeN) in series with an AT
indicating cartridge (Alltech).
In summary, the current studies demonstrate that proton
0
transfers within [Ni(PCy2NR 2H)2]2þ are significantly faster than
catalysis and do not pose a barrier to catalytic activity. Impor-
tantly, they show how easily the proton can be moved from the
Ni to the nitrogen (or vice versa) with the correct positioning of
the amine, an essential step in the catalytic cycle for these catalysts,
and more broadly to the dynamics of organometallic complexes
with hydrogen bonds and enzymatic systems.1,2,4,45ꢀ48 Investiga-
tions are ongoing to understand the mechanism of the pendant
amines in the next step of catalysis: moving the proton into
solution for catalyst regeneration.
Preparation of [Ni(PCy2NBn2D)2][BF4]2. [Ni(PCy2NBn2D)2]-
[BF4]2 was prepared as for [Ni(PCy2NBn2H)2][BF4]2, in either CD3CN
or methylene chloride, with the modification of purging with D2 (99.8%,
Cambridge Isotopes), used as received, for 3ꢀ5 min.
Preparation of [Ni(PCy2NBn2D)(PCy2NBn2H)][BF4]2. [Ni(PCy
-
2
NBn2D)(PCy2NBn2H)][BF4]2 was prepared by the addition of HD gas
(97%, Cambridge Isotopes) to the evacuated head space of a J. Young
NMR tube (to minimize the amount of HD needed) containing
a butyronitrile solution of [Ni(PCy2NBn2)][BF4]2 cooled to ꢀ78 °C.
Preparation of Ni(PCy2NBn2). [Ni(PCy2NBn2)2][BF4]2 (0.250 g,
0.020 mmol) was dissolved in 15 mL of acetonitrile. Hydrogen was
purged through the solution for 10 min, followed by addition of 1,8-
diazabicycloundec-7-ene (DBU, 0.07 mL, 0.45 mmol). After standing
for 10 min, the solution was filtered, and the yellow precipitate was
washed two times with 5 mL of acetonitrile to give the product as a
’ CONCLUSIONS
Experimental and computational studies provide a detailed
understanding of how the mobility of protons is accelerated by
pendant amines in nickel catalysts for oxidation of H2 and
production of H2. Protons are transferred intramolecularly very
rapidly (104ꢀ105 sꢀ1) from one endo-positioned amine to
another in the hydrogen oxidation catalyst, [Ni(PCy2NBn
-
2
H)2]2þ, while exchange is not observed for protons positioned
exo to the nickel. Computational models suggest a metal-
mediated pathway involving proton transfers between the amine
nitrogen and the nickel, rather than a direct nitrogen-to-nitrogen
proton transfer. The major contributor to the barriers arises from
chair/boat conformational interconversions of the six-membered
rings of the diphosphine ligands, while migration around the Ni
tetrahedron is facile. The fast rate of exchange is consistent with
the low free energy for proton transfer, about 11ꢀ12 kcal/mol
for both the endo-endo and the endo-exo isomers, essentially
independent of solvent and supported by computational models.
Due to the rapid intramolecular proton exchange, this family of
catalysts for oxidation and production of H2 may be considered
as a metal center “immersed” in a cloud of protons, allowing
multiple pathways for subsequent catalytic steps. More generally,
the facile transfer of protons between the metal center and
positioned bases/acids in the second coordination sphere of these
1
yellow solid (200 mg, 94% yield). H NMR (d6-benzene): 1.09ꢀ1.80
(m, 46H), 2.48 (d, 8H) 2.82 (d, 8H), 3.73 (s, 8H) 7.13ꢀ7.26 (m, 24H).
31P {1H} NMR (d6-benzene): 6.81 (s). NMR samples of Ni(PCy2NBn
)
2 2
were prepared by dissolving 10 mg of complex in 0.75 mL of butyroni-
trile. NMR data were collected from ꢀ103 to ꢀ81 °C.
Preparation of [H-Ni(PCy2NBn2)2]þ. The reaction of Ni-
(PCy2NBn
) (50 mg, 50 μmol) in 2 mL of THF with [HDMF]-
2 2
[OTf]64 (12 mg, 50 μmol) in 0.5 mL of acetonitrile, followed by vapor
diffusion of Et2O, gave [H-Ni(PCy2NBn2)2][OTf] as orange crystals
1
(45.6 mg, 80% yield). H NMR (CD3CN): ꢀ10.73 (pentet, JPH
=
19.9 Hz, 0.79H), 1.23ꢀ1.84 (br, 58H), 2.65 (d, 8H), 2.84 (d, 8H), 3.79
(s, 8H) 7.17ꢀ7.39 (br, 59H). 31P{1H} NMR (CD3CN): 9.95 (s). The
complex decomposes in solution to a paramagnetic species, presumably
[Ni(PCy2NBn2)2]þ. The impurity influences the integration of these
peaks due to overlap. NMR samples of [H-Ni(PCy2NBn2)2][OTf] were
prepared by dissolving 10 mg of complex in 0.75 mL of butyronitrile.
NMR data were collected from ꢀ81 to ꢀ50 °C.
0
Ni(PR NR
)
2 2
complexes provides strong support for similar
2þ
2
mechanisms proposed, but not directly observed, in enzymes.
NMR Experiments. NMR experiments were run on Varian NMR
systems at 300 or 500 MHz 1H frequency, operated with a VNMRS console.
Direct detect dual-band or OneNMR probes were used. Typical 31P 90°
pulses were ∼8μs, and 31P NMR spectra were collected with 1H decoupling.
Variable-temperature NMR data were collected from ꢀ103 to 50 °C, using
either liquid nitrogen (lower than ꢀ60 °C) or an XRII852 sample cooler
(FTS Systems, Stone Ridge, NY) (ꢀ60 to 20 °C) to achieve reduced
temperature. 2D-EXSY32,33 experiments were recorded at ꢀ65 to ꢀ10 °C
using a standard phase-sensitive VNMRJ 2D NOESY pulse program with
128ꢀ256 increments, 16 scans per increment, and 200 ms mixing times.50
NMR Peak Fitting. The gNMR program was used for variable-
temperature 31P line shape analysis using a two-site exchange model.51
Experimental spectra were processed within gNMR using a Lorentzian
function with up to 6 Hz line broadening. Rates were determined by
iteration of the simulated line widths, using both manual and gNMR
algorithm methods. Visual inspection of the overlaid experimental and
simulated spectrum was used to determine the best fit.
’ EXPERIMENTAL SECTION
General. All samples were prepared under an N2 atmosphere.
Reaction solvents were dried using an Innovative Technologies Pure
Solv solvent purification system. Acetone was not purified, but a fresh
bottle was used for each sample preparation. CD3CN was vacuum
transferred from P2O5. All other chemicals were used as received.
Synthesis of [Ni(PCy2NBn2)2][BF4]2. A procedure slightly mod-
ified from the previously reported synthesis was used.21 Bis(hydroxy-
methyl)cyclohexylphosphine20 (2.877 g, 0.016 mol) was dissolved in
50 mL of absolute ethanol in a Schlenk flask and heated to 70 °C. Neat
benzylamine (1.78 mL, 0.016 mol) was added dropwise over 30 min, and
the reaction was stirred for 12 h at 70 °C. The solvent was removed
under reduced pressure to leave a sticky white solid, characterized by 31P
NMR as PCy2NBn2 (>95% pure). All of the crude ligand was added to
[Ni(CH3CN)6][BF4]249 (2.04 g, 4.1 mmol) with 24 mL of acetonitrile;
the reaction was stirred for 8 days at room temperature. The dark red
solution was filtered and concentrated to 16 mL under reduced pre-
ssure. Vapor diffusion of Et2O gave a dark purple crystalline product,
[Ni(PCy2NBn2)2][BF4]2 (1.92 g, 39% yield based on bis(hydroxy-
Eyring parameters were determined by fitting the rates as a function
of temperature using eq 2:
kBT
h
q
q
k ¼
eꢀΔH =RT eΔS =R
ð2Þ
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The data were fit using Profit, which allowed the application of individual
error bars determined for each data point. Error bars were estimated to
be 7ꢀ15% on the basis of visual inspection of the gNMR fits.
to study the proton exchange along with the distance with the two ex-
changing hydrogens. A coordination coordinate53 was introduced for
each ligand, which assumes the value 0, 1, or 2, if none, one, or both
nitrogens of a ligand are protonated, respectively. Gaussian functions of
0.1 kcal/mol height and 0.05 kcal/mol width were employed to bias this
coordination number space.
Computational Details. DFT calculations were carried out on
[Ni(PCy2NMe2)2]2þ, where the benzyl substituents of the N atoms were
replaced by methyl groups. This choice is validated by the very similar H2
chemistry shared by [Ni(PCy2NMe2)2]2þ and [Ni(PCy2NBn2)2]2þ
(unpublished observations). To study the complexity of the intramole-
cular proton reorganization, a strategy based on two sets of ab initio
calculations was adopted. Possible proton transfer pathways were
explored on a chosen isomer via ab initio BornꢀOppenheimer classical
nuclei molecular dynamics simulations52 along with enhanced sampling
techniques53,54 (see below). The structure of a series of species involved
in the proton exchange dynamics as suggested by the ab initio simula-
tions was refined for all of the possible isomers/conformers by less
time-demanding standard quantum chemistry geometry optimizations.
These include the diproton species, different possible proton-hydride
intermediates, and transition states connecting them (Figures 6 and S8).
For each isomer the chair/boat conformational change of the six-
membered rings that incorporate the pendant amines was also characte-
rized (Figures 6 and S8). All structures were optimized using all-electron
DFT calculations with the B3P86 hybrid functional55,56 along with the
Stuttgart-Dresden relativistic ECP basis set (SDD) for Ni, 6-31G** for
the acidic protons (i.e., the NꢀH protons), and 6-31G* for all of the
other atoms. Harmonic vibrational frequencies were calculated at the
optimized structures using the same level of theory to estimate the ZPE
and thermal contributions (298 K and 1 atm) to the gas-phase free
energy. Solvation free energies were then computed using a self-
consistent reaction field model at the same level of theory as for the
other steps. The Continuum Polarizable Conductor Model (CPCM)
was used with Bondi radii.57 All the calculations were carried out with
Gaussian 09.58
As discussed in the text, the solvent has only a modest influence on
the kinetics of proton exchange. Therefore, all of the molecular dynamics
simulations have been performed in the gas phase starting from a relaxed
structure of the all-boat A00 species (see Figure 4). The molecule was left
free to evolve at 25 °C for 2 ps, and then a metadynamics simulation was
run for 30 ps, adding Gaussians every 25 fs. The equations of motion
were propagated using a time step of 0.25 fs, controlling the temperature
using a NosꢀeꢀHoover chain of thermostats.62
This computational procedure has been shown to describe the Ni-
based H2 chemistry as well as coupled cluster CCSD[T] calculations.35
In particular, B3P86, PBE, and CCSD[T] yield energy barriers for the
proton transfer from the pendant amine to the metal center within about
1 kcal/mol.35
Kinetic Modeling. The time evolution of the population, pi, of each
of the 10 species involved in the exchange process (Figure 6) can be
obtained from the following set of phenomenological first-order differ-
ential equations (master equation):63
X
dpiðtÞ
¼
½kijpjðtÞ ꢀ kjipiðtÞꢂ
ð3Þ
dt
j
where kij is the rate constant for the jfi reaction, and the summation
runs over the 10 states. The master equation can be rewritten in the
following compact matrix form:
dPðtÞ
¼ WP
ð4Þ
dt
The ab initio molecular dynamics simulations were carried out within
the DFT framework using the hybrid Gaussian and plane waves method
implemented in the CP2K code.52 A double-ζ basis augmented with two
sets of f-type, d-type, and p-type polarization functions was used for the
3s, 3p, 3d, and 4s orbitals of Ni (DZV2P), whereas a triple-ζ basis set
augmented with two sets of d-type and p-type polarization functions was
employed for the valence electrons of all of the other atoms (TZV2P
basis set).59 Norm-conserving pseudopotentials were used to treat core
electrons of all of the atoms.60 The electrostatic energy was calculated
using an auxiliary plane wave basis set with a cutoff of 300 Ry in a 25 Å
periodic cubic box.52 The DFT calculations were carried out using the
PerdewꢀBurkeꢀErnzerhof (PBE) functional.61 The use of the PBE
functional was dictated by computational cost of hybrid functionals,
which make them unsuitable for long time scale ab initio simulations.
Previous calculations showed that PBE yields only a slightly worse
where the elements of the matrix W are given by
X
Wij ¼ kij ꢀ δijð
kkiÞ
ð5Þ
k
The solution of eq 4 can be expressed in terms of the eigenvectors, Oi =
(φi(1),φi(2), ..., φi(10)), and eigenvalues, λi, of the matrix W:
X
k
piðtÞ ¼
ckφiðkÞ eꢀλ t
ð6Þ
k
where the coefficients ck are obtained under the detailed balance
conditions
WijpðjeÞ ¼ Wjipði eÞ
ð7Þ
pi(e) being the equilibrium (Boltzmann) population of the species i. It
can be shown that there is an eigenvalue λ1 = 0, whereas the others are all
non-negative.63
0
description of the energy of Ni[PR NR
]
2 2
catalysts than the hybrid
2þ
2
B3P86 functional.35 To reconstruct the free energy landscape for the
proton exchange at room temperature, an adaptive biasing force
technique53 based on a coarse-grained history-dependent dynamics
(metadynamics) was employed. This approach is able to explore the free
energy landscape in the space defined by a chosen set of degrees of
freedom (collective coordinates), which describes the chemical pro-
cess of interest. The evolution of the system at every step of the meta-
dynamics is driven by the combined action of the thermodynamic force
and a history-dependent force, which penalizes configurations in the
collective variables space that have already been visited. The history-
dependent potential is constructed as a sum of Gaussians centered on
each value of the collective variable previously explored. The potential
fills the minima of the free energy surface in time, and as the simulation
proceeds, its sum converges to the free energy landscape as a function of
the collective variables. In the present study, the number of hydrogen
atoms coordinated to the nitrogen atoms of each ligand was employed
The overall rate constant inferredfrom the NMR measurements can be
obtained in the steady state regime, i.e., t > 1/λ2, since λ2 is the smallest
nonzero eigenvalue, where the following effective rate law holds:
dp ðtÞ
Nb
¼ keðfffÞpN ðtÞ ꢀ kðbÞpN ðtÞ
ð8Þ
a
b
eff
dt
(b)
eff
Here k(efff) and k are the forward and backward effective rate constants,
and pN (t) and pN (t) are the populations of the “initial” state (proton on
a
nitrogen Na) andb“final” state (proton on nitrogen Nb, see Figure 6) at
time t. Since the initial and final states are chemically identical, i.e., the
(b)
population of the two states is equal, k(efff) and k are the same.
eff
Finally, we briefly discuss the steady-state analytical solution of the
master equation for a single five-step pathway (for instance, the one
indicated by the circled numbers in Figure 6) employed for the analysis
of the isotope effect. In this case the kinetic equations in the steady-state
14310
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Journal of the American Chemical Society
ARTICLE
regime are
Molecular Science Laboratory (EMSL), a national scientific user
facility sponsored by the Department of Energy's Office of Bio-
logical and Environmental Research located at Pacific Northwest
National Laboratory and the National Energy Research Scientific
Computing Center (NERSC) at Lawrence Berkeley National
Laboratory. Pacific Northwest National Laboratory is operated by
Battelle for the U.S. Department of Energy. The authors thank Jeff
London for assistance in designing the cover artwork.
dp2
¼ k1p1 ꢀ ðkꢀ1 þ k2Þp2 þ kꢀ2p3 ¼ 0
dt
dp3
¼ k2p2 ꢀ ðkꢀ2 þ k3Þp3 þ kꢀ3p4 ¼ 0
dt
dp4
¼ k3p3 ꢀ ðkꢀ3 þ k4Þp4 þ kꢀ4p5 ¼ 0
ð9Þ
dt
dp5
¼ k4p4 ꢀ ðkꢀ4 þ k5Þp5 þ kꢀ5p6 ¼ 0
dt
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¼ kðfÞp1 ꢀ kðbÞp6
ð10Þ
eff
eff
dt
with effective (composite) rate constants
k1k2k3k4k5
ꢀ1kꢀ2kꢀ3kꢀ4 þ kꢀ1kꢀ2kꢀ3k5 þ kꢀ1kꢀ2k4k5 þ kꢀ1k3k4k5 þ k2k3k4k5
ð11Þ
ðfÞ
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¼
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and
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ꢀ1kꢀ2kꢀ3kꢀ4k
ꢀ5
ðbÞ
k
¼
eff
k2k3k4k5 þ kꢀ1k3k4k5 þ kꢀ1kꢀ2k4k5 þ kꢀ1kꢀ2kꢀ3k5 þ kꢀ1kꢀ2kꢀ3k
ꢀ4
ð12Þ
’ ASSOCIATED CONTENT
S
Supporting Information. (1) NMR spectra as a function
b
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ranking of [Ni(PCy2NMe2H)2]2þ isomers; (5) free energy for the
hydride migration around the Ni atom in isomer A00 as inferred
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energetic analysis for endo-exo isomer B; (7) 2D EXSY for
HD exchange; (8) NMR spectra and Eyring plot for
[Ni(PCy2NBn2)2] as a function of temperature; (9) complete
ref 58; and (10) Cartesian coordinates of the optimized structure
of all of the relevant species involved in the proton exchange
process. This material is available free of charge via the Internet at
http://pubs.acs.org.
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’ AUTHOR INFORMATION
Corresponding Author
wendy.shaw@pnnl.gov; simone.raugei@pnnl.gov; morris.bullock@
pnnl.gov.
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’ ACKNOWLEDGMENT
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We thank Dr. Don Camaioni and Dr. Roger J. Rousseau for
useful discussions. 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. W.J.S. was
funded by the DOE Office of Science Early Career Research
Program through the Office of Basic Energy Sciences. Computa-
tional resources were provided at W. R. Wiley Environmental
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Journal of the American Chemical Society
ARTICLE
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31
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