Elucidating Proton-Coupled Electron Transfer Mechanisms of Metal Hydrides with Free Energy- And Pressure-Dependent Kinetics

Article abstract of DOI:10.1021/jacs.9b08189

Proton-coupled electron transfer (PCET) was studied in a series of tungsten hydride complexes with pendant pyridyl arms ([(PyCH₂Cp)WH(CO)₃], PyCH₂Cp = pyridylmethylcyclopentadienyl), triggered by laser flash-generated Ru^III-tris-bipyridine oxidants, in acetonitrile solution. The free energy dependence of the rate constant and the kinetic isotope effects (KIEs) showed that the PCET mechanism could be switched between concerted and the two stepwise PCET mechanisms (electron-first or proton-first) in a predictable fashion. Straightforward and general guidelines for how the relative rates of the different mechanisms depend on oxidant and base are presented. The rate of the concerted reaction should depend symmetrically on changes in oxidant and base strength, that is on the overall ?G⁰ _PCET, and we argue that an "asynchronous" behavior would not be consistent with a model where the electron and proton tunnel from a common transition state. The observed rate constants and KIEs were examined as a function of hydrostatic pressure (1-2000 bar) and were found to exhibit qualitatively different dependence on pressure for different PCET mechanisms. This is discussed in terms of different volume profiles of the PCET mechanisms as well as enhanced proton tunneling for the concerted mechanism. The results allowed for assignment of the main mechanism operating in the different cases, which is one of the critical questions in PCET research. They also show how the rate of a PCET reaction will be affected very differently by changes of oxidant and base strength, depending on which mechanism dominates. This is of fundamental interest as well as of practical importance for rational design of, for example, catalysts for fuel cells and solar fuel formation, which operate in steps of PCET reactions. The mechanistic richness shown by this system illustrates that the specific mechanism is not intrinsic to a specific synthetic catalyst or enzyme active site but depends on the reaction conditions.

Full text of DOI:10.1021/jacs.9b08189

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Article
Elucidating Proton-Coupled Electron Transfer Mechanisms of
Metal Hydrides with Free-energy and Pressure Dependent Kinetics
Tianfei Liu, Robin Tyburski, Shihuai Wang, Ricardo J.
Fernández-Terán, Sascha Ott, and Leif Hammarström
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.9b08189 • Publication Date (Web): 06 Oct 2019
Downloaded from pubs.acs.org on October 7, 2019
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Elucidating Proton-Coupled Electron Transfer Mechanisms of Metal
Hydrides with Free-energy and Pressure Dependent Kinetics
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†
,§
†,§
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†
Authors: Tianfei Liu , Robin Tyburski , Shihuai Wang , Ricardo Fernández-Terán ,
†
*,†
Sascha Ott , Leif Hammarström
Affiliations:
†Department of Chemistry, Ångström Laboratory, Uppsala University, Box 532, SE-
51 20 Uppsala, Sweden.
7
*Corresponding author. e-mail: Leif.Hammarstrom@kemi.uu.se
§Author Contributions. T.L. and R.T. contributed equally to this work.
Abstract
Proton-coupled electron transfer (PCET) was studied in a series of tungsten hydride
complexes with pendant pyridyl arms ([(PyCH Cp)WH(CO) ], PyCH Cp =
2
3
2
III
pyridylmethylcyclopentadienyl), triggered by laser flash-generated Ru -tris-
bipyridine oxidants, in acetonitrile solution. The free energy dependence of the rate
constant and the kinetic isotope effects (KIEs) showed that the PCET mechanism could
be switched between concerted and the two stepwise PCET mechanisms (electron-first
or proton-first) in a predictable fashion. Straightforward and general guidelines for how
the relative rates of the different mechanisms depend on oxidant and base are presented.
The rate of the concerted reaction should depend symmetrically on changes in oxidant
and base strength, i.e. on the overall G0PCET, and we argue that an “asynchronous”
behavior would not be consistent with a model where the electron and proton tunnel
from a common transition state. The observed rate constants and KIEs were examined
as a function of hydrostatic pressure (1-2000 bar) and were found to exhibit
qualitatively different dependence on pressure for different PCET mechanisms. This is
discussed in terms of different volume profiles of the PCET mechanisms as well as
enhanced proton tunneling for the concerted mechanism. The results allowed for
assignment of the main mechanism operating in the different cases, which is one of the
critical questions in PCET research. They also show how the rate of a PCET reaction
will be affected very differently by changes of oxidant and base strength, depending on
which mechanism dominates. This is of fundamental interest as well as of practical
importance for rational design of e.g. catalysts for fuel cells and solar fuels formation,
which operate in steps of PCET reactions. The mechanistic richness shown by this
system illustrates that the specific mechanism is not intrinsic to a specific synthetic
catalyst or enzyme active site, but depends on the reaction conditions.
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Introduction
Proton-coupled electron transfer (PCET) is a ubiquitous elementary process in
chemistry and biology.1-3 It is at the heart of biological energy conversion processes
4-7
8-12
and nitrogen fixation13-15 in nature and in the
such as photosynthesis , respiration
corresponding artificial catalytic transformations.16-24 In the last decades, high
resolution structures of many of the enzymes involved in these processes have been
reported, such as hydrogenases25, 26, carbon dioxide reductase27, 28 and dioxygen
reductases29, 30. Their structures indicated that proton relays in the second coordination
sphere of the cofactors of many enzymes might have an effect on PCET reactions at the
active site. Inspired by this, the use of acid/base groups as putative proton relays in the
second coordination sphere of catalysts has become an increasingly popular motif,
intended to accelerate protonation and deprotonation of metal-bound hydrido (M-H)22,
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1-33, carboxylates (M-CO2)34-37, dioxygen (M-O ) or aqua species (M-OH/M-OH )
38
39-
2
2
41.
However, the exact mechanism by which these acid/base groups accelerate catalytic
reactions is often not clarified, and is often not even related to proton transfer42, 43
.
Understanding these fundamental processes is important towards the rational design of
faster and more efficient catalysts for the production of solar fuels or for fuel cells.
Moreover, an important but often challenging task when studying PCET is to elucidate
whether the reaction occurs sequentially, through electron transfer followed by proton
transfer (ETPT), proton transfer followed by electron transfer (PTET); or in a single,
concerted electron-proton transfer step (CEPT). CEPT avoids the high energy barriers
often associated with the initial steps in stepwise reactions. However, this requires
tunneling of both electron and proton in the transition state, which may lower the
probability compared to tunneling of a single electron or proton. The rate of PCET of a
catalyst will respond very differently to modifications of the catalyst or reaction
conditions, depending on the mechanism of its PCET steps. Determining and steering
the operative PCET mechanism in catalysis is a promising strategy for catalyst
improvement, as avoiding the high energy barriers associated with stepwise
mechanisms can lower the overpotential of the reaction of interest. Therefore, methods
for elucidating the PCET mechanism for the reaction in question are highly desirable.
Only in a few cases of interest is it possible to directly monitor the intermediates of the
4
4
stepwise reactions , because of an unusually slow second step, which then provides
conclusive mechanistic evidence for or against a reaction intermediate. Instead,
4
5
thermodynamic arguments are frequently employed to exclude the stepwise reactions .
The argument is that the first step is sufficiently uphill, as estimated from relative pKa
0
or E values, that the predicted rate is at least one order of magnitude slower than the
observed overall rate constant. However, relative pK values in hydrogen-bonded
a
systems are often different from those of the isolated components. A significant kinetic
isotope effect (KIE) upon proton/deuteron substitution is commonly used to argue that
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proton transfer is involved in the rate-determining step, and thus signify CEPT instead
of ETPT. However, a KIE  1.0 does not generally exclude proton involvement in the
1, 46-48
rate-determining step
. Free energy relationships, where the rate is studied as a
0
function of driving force, show characteristic dependencies on the E and pK for
the different mechanisms.
a
4
5, 49
In cases where both these parameters can be varied
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independently over a sufficient range, a clear mechanistic assignment can often be made,
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but often the E and pK values of a PCET reactant show strong co-variation upon
a
synthetic substitutions.
Our group has reported several systems with tyrosine or tryptophan residues covalently
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linked to a Ru -polypyridine photosensitizer, with water as primary proton acceptor,
for which the PCET mechanism could be switched between CEPT and ETPT by
III
44, 50, 51
varying the strength of the photogenerated Ru oxidant.
In one study, the
mechanism shifted between all three mechanisms (ETPT, CEPT and PTET) depending
52
on the pH of the solution. In a later paper, the proton-coupled oxidation of a tungsten
III
III
hydride complex [(Cp)WH(CO) ] by a series of Fe - and Ru -trisbipyridine oxidants
3
49
and pyridine bases was studied in acetonitrile . This allowed for well-defined
variations of the PCET driving force by varying both the oxidant and the base. By using
weak oxidants and weak bases, the reaction was steered to follow a CEPT mechanism.
This was the first demonstration that a metal hydride could undergo a CEPT reaction,
with the electron and proton transferred to different acceptors. In a recent study,
inspired by proton relays in natural catalysts, the pyridine bases were linked to the Cp
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ring ([(PyCH Cp)WH(CO) ]) . This resulted in a strong increase of the PCET rate. In
2
3
contrast to the previous study, a PTET dominated at low oxidant strengths, whereas a
CEPT reaction only arose when the oxidant strength was increased. The difference in
mechanistic preferences between the systems with intra- and intermolecular pyridine
bases is interesting, and suggests that the hydrogen bond geometry between the W-H
and pyridine units is somewhat different in the respective transition states, resulting in
differences in proton vibrational wavefunction overlap. It seems that the intramolecular
base then favors proton tunneling, making both CEPT and PTET more competitive than
in the system with external bases. Despite its importance, the concerted pathway
remains elusive in many systems. The very similar [(Cp)WH(CO) (PMe )] system
2
3
5
4
studied by Dempsey and co-workers differs from our motif only in the substitution of
one CO ligand by PMe . Interestingly, CEPT was shown to give only a minor
3
0
contribution to the rate, in a very similar range of E and pK values between the
a
tungsten complex, oxidants and bases, as that in ref. 49, which was attributed to a larger
54
reorganization energy associated with deprotonation of [(Cp)WH(CO) (PMe )].
2
3
The present study uses stronger oxidants than previously employed to measure the
PCET rate constants of [(PyCH Cp)WH(CO) ] derivatives with covalently attached
2
3
bases of different strength. The variation in electron transfer driving force tunes the
system to display additional mechanistic regions, from PTET, via CEPT to ETPT even
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in a single compound. The mechanistic assignments are based on free energy
relationships and KIEs within the framework of electron-proton tunneling theories for
PCET. We point out that within a tunneling theory for CEPT, the rate constant must
respond symmetrically to changes in driving force from changes in the oxidant and base
strength (G0 and G , respectively), as opposed to a so-called asynchronous CEPT.
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Moreover, hydrostatic pressure is used for the first time as a tool to distinguish the
stepwise and concerted PCET reactions. The pressure dependence of the rate constants
reveals information about the volume profile of the PCET reaction, i.e. volume changes
between reactants, transition states and products. PTET and ETPT shows distinctly
different experimental activation volumes, such that the rate of the former increases
with pressure while that of the latter decreases. For some combinations of oxidant and
base the PCET mechanism is mixed, but increasing pressure resulted in an increasing
contribution from CEPT, which could not be identified by only varying oxidant and
base strength or determining the KIE. The acceleration of CEPT with increasing
pressure may be attributed to a shorter proton tunneling distance due to compression of
the W-H complex. Our study shows an unprecedented mechanistic richness for a single
PCET system. Compared to our previous studies49, 53 all three mechanisms are
displayed by a single WH-pyridine compound by just varying the oxidant, and also the
pre-equilibrium kinetic limit of ETPT is shown. Moreover, with the combined use of
free-energy and pressure dependence, our study shows methods to distinguish
experimentally which mechanism is dominating under the given conditions. This also
suggests the possibility to analyze and steer the PCET mechanism of catalysts with
metal-hydride intermediates.
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Results and discussion
0
E and pKa values. The tungsten hydride complexes 1a-e with internal pyridine
bases (Scheme 2, labeled 1a-e in order of increasing base strength) and the reference
complex [(MeCp)WH(CO) ] that does not contain an internal base were prepared as
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reported earlier . The thermodynamic data for the latter compound in acetonitrile from
our previous report is given in Scheme 1, together with data for [(Cp)WH(CO) ] from
the groups of Tilset and Norton.55-59 The methylene substituent on the Cp ring shifts the
potentials cathodically by 30-50 mV, and increases the pK value by about 0.4 units.
The first oxidation of [(Cp)WH(CO) ] is irreversible with a peak potential at +0.76 V,
and this was used to estimate the E value. An exact value of E is not critical to the
present study as it is based on free-energy correlations, i.e. relative values of E in the
3
a
3
0
57
0
0
reactions with different oxidants. Oxidation of the deprotonated complex
-
[
(Cp)W(CO) ] occurs at ca. 1.10 V more negative values, showing that the
3
thermodynamic coupling of the transferred electron and proton is strong. The pK value
a
of [(Cp)WH(CO) ] (pKa = 16.1) shows a corresponding downshift by ca. 19 units upon
3

+
oxidation, rendering the oxidized hydride [(Cp)W H(CO) ] very acidic (pKa  -3).
3
The potentials and pK values of the tungsten hydride in 1a-e are assumed to be very
a
similar to those of [(MeCp)WH(CO) ]. The pyridine group shows a pK for the free
conjugate acid of 9.55-14.23. A new oxidation peak appeared in the cyclic
voltammograms of 1a-e, at ca. 0.8-1.0 V lower values (-0.08 to -0.33 V vs. Fc ) than
the first oxidation for [(MeCp)WH(CO) ] (+0.71 V). This peak was attributed to metal
oxidation coupled to transfer of the hydride proton to the pyridine base. Indeed, the
observed electrochemical peak shift from [(MeCp)WH(CO) ] to 1a-e agreed within
experimental error with that predicted from the relative pK values of the W H (ca. -
3
a
+
/0
5
3
3
3

+
a
2
.5) and free pyridinium, assuming 59 mV shift per unit of pK difference. Moreover,
a
the peak potential in the series 1a-e showed a near-Nernstian shift of ca. -52 mV per
pK unit of the free pyridinium. This shows that the relative driving forces for PCET in
a
0
1
a-e agree well with what is expected from the E and pK values determined for the
a
components.
In our previous study, we used Fe - and Ru -tris(bipyridine) complexes with M
potentials of 0.36-0.73 V vs. Fc+/0 to study the proton-coupled oxidation of 1a-e. These
potentials are thus low enough that an initial electron transfer step to generate W H
would be uphill or near isoenergetic. At the same time, the pyridinium pK values are
III
III
III/II

+
a
all at least two units lower than the pK of W-H, making an initial intramolecular proton
a
transfer step uphill. In contrast, the concerted PCET is downhill for all combinations of
oxidant and base. The overall stepwise ETPT and PTET processes are obviously also
downhill by the same amount as CEPT, thanks to the second step on both those

+
-
pathways being strongly exergonic: PT-b from W H and ET-a from W (cf. Scheme
2
), respectively. With these oxidants, most of the reactions with 1a-e occurred via pre-
equilibrium PTET, and some via CEPT. In the present study, we use four RuIII-
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tris(bipyridine) complexes that are stronger oxidants (E0
Table 1) in an attempt to shift the reaction in favor of CEPT and possibly also of ETPT.
= 0.82-1.03 V vs. Fc+/0;
Ru(III/II)
(A)
ET-b
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
E  +0.76 V
(+0.71 V)
R
W
PT-a
H
Py
W
W
H
Py
PT-b
pK  -3
CEPT
pK = 16.1
a
a
(16.5)
W
(-2.5)
H Py
1/2
W
W
H Py
ET-a

E = -0.38 V
-0.41 V)
(
(B)
0
0
0



G ET = -F(E Acceptor - E Donor)
0
G PT = -ln(10)RT(pKaAcceptor - pKaDonor)
0
0
0
0
0
G PCET = G ET-a + G PT-a = G ET-b + G PT-b
Scheme 1. (A) PCET square scheme showing the mechanistic pathways for 1a-1e:
stepwise PTET (pathway a, black), stepwise ETPT (pathway b, red), and concerted
electron-proton transfer (CEPT; pathway in blue). The thermodynamic data given are
0
+/0
55-59
for the previously studied [CpWH(CO) ] in CH CN (E vs. Fc and pK ),
with
3
3
a
53
data for [(MeCp)WH(CO) ] in brackets. pK values for the free pyridinium groups of
3
a
1
a-e are given in Scheme 2. (B) The free energy for the ET, PT and PCET steps of
0
panel (A) can be estimated from the E and pK values of the W-species relevant for
a
0
each step, E of the oxidants and pK of the pyridinium groups.
a
(
W
II)
R
Q
RuIIIL3]3+
H
N
[
OC
OC CO
Q2+
1

II
2+/*
[
Ru L3]
Proton-coupled Electron Transfer
kPCET
(PCET)

II
2+
460 nm
[Ru L3]
(I)
R
W
H N
OC
OC CO
2
1
a, R = 3-CF3; pKa = 9.55
Dimerization
k2
1
1
1
1
b, R = 2-OMe; pKa = 9.93
c, R = H;
d, R = 2-Me; pKa = 13.32
e, R = 4-OMe; pKa = 14.23
pKa = 12.53
OC
CO
OC
N H
(I)
(I)
R
W
W
H N
CO
R
OC CO
3
Scheme 2. Reaction scheme for the photoinduced PCET reactions.
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Kinetic PCET measurements. The PCET kinetics of compounds 1a-e with the different
III
Ru -bipyridine-based oxidants were investigated with the commonly used laser flash-
quench photolysis method (Scheme 2).60-62 In our experiment, the RuIII oxidant was
prepared in-situ by laser flash excitation, followed by oxidative quenching. A typical
II
sample contained 0.5-12 mM of the tungsten hydride [WH⋯B], 50 µM of the Ru
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5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
2
+
photosensitizer (Table 1), here denoted [Ru] , and 100 mM of the diquat electron
acceptor (1,1’-butylene-2,2’-bipyridine, BDQ2+ or 1,1’-propylene-2,2’-bipyridine,
2+
2+
PDQ ) as quencher Q in deoxygenated acetonitrile. The samples were prepared in a
1
010 mm quartz cuvette and sealed in an argon glove box. For the measurements at
elevated pressure (1-2000 bar), the samples were put in 9 mm diameter round quartz
cells, filled to the brim and sealed with a plastic septum in the glove box. The septum
transmits pressure from the pressure cell, while containing the reaction solvent. In the
experiments, the sample was flashed with a 10 ns laser pulse at 460 nm (see SI), exciting
the Ru-based photosensitizer. The excited state of the sensitizer, [Ru]2+* was
2
+
oxidatively quenched by Q , on a time scale of 100 ns. The resulting products were the
3
+
●+
oxidized form of the Ru-complex, [Ru] , and the quencher monocation radical, Q .
3
+
The [Ru] generated (<10 µM in one laser shot) reacted in a pseudo-first order PCET
reaction with [WH⋯B], which is in great excess, on a time scale of a few s.
Figure 1 gives examples of transient absorption and photoluminescence traces used to
2
+
follow these reactions. The emission of [Ru] * can be followed at 600 nm. It decays
in a mono exponential fashion:
퐼(푡) = 퐼 exp ( ―
(
푘푞
[
푄2 +
]
+ 푘0
)
∙ 푡)
(1)
0
2
+
where 푘 is the second-order rate constant for excited state quenching by Q and 푘
푞
0
2
+
2+
is the rate constant for exited state decay in the absence of Q . The recovery of [Ru]
was followed at 450 nm. Note that, while both [Ru]2+* and [Ru] have small extinction
3+
2
+
3+
coefficients at 450 nm compared to the [Ru] ground state, the yield of free [Ru] in
2
+
the quenching process is only around one third (the rest returns to [Ru] ), which leads
6
2
to significant bleach recovery at 450 nm also during the quenching process. Thus, the
traces were fit to a double exponential decay model, where the first component
represents quenching of [Ru]2+* to form [Ru] , and the second component represents
3+
3
+
2+
the PCET reaction of [Ru] with [WH⋯B], regenerating [Ru] :
∆
퐴450(푡) = 퐴 exp + 퐴 ∙ exp ― 푘PCET[WH⋯B] ∙ 푡
(
―
(
푘푞[푄] + 푘0) ∙ 푡
)
( )
(2)
1
2
The pseudo-first order time constant for the second component was typically ten times
larger than for the first, which made the fits robust. Kinetic traces and residual plots
from the fits are shown in the Supporting Information. From these fits, the observed
PCET rate constant could be extracted. At 550 nm, the absorption of the reduced
quencher Q●+ was followed. Under the experimental conditions used, Q does not
●+
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2
2
2
2
2
2
2
2
2
3
3
3
3
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3
3
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2
+
decay significantly during the recovery kinetics of the [Ru] bleach (Figure 1, blue
symbols; vide infra) and does not affect the 450 nm recovery.
0
,10
,05
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
0
0,00
0,05
0,10
-
-
-0,15
0
2
4
6
8
time (µs)
Figure 1. Typical kinetic traces of the reaction between compound 1d and laser flash-
3
+
quench generated [Ru(Me bpy) (bpy)] in acetonitrile, showing the decay of
2
2
2
+*
[Ru(Me bpy) (bpy)] emission at 600 nm (black squares; the black line is a single
2
2
●+
exponential fit) and formation of BDQ , monitored at 550 nm (blue triangles; the blue
2
+
line is a single exponential fit to the rise), due to oxidative quenching by BDQ . The
2
+
recovery of [Ru(Me bpy) (bpy)] monitored at 450 nm (red dots) is fitted with a
2
2
biexponental function (red line), where the excited state quenching reaction during the
first ca. 0.1 μs is followed by the much slower PCET reaction with 1d.
●+
In the absence of [WH⋯B], the oxidized sensitizer recombines with Q in a diffusion-
controlled bimolecular reaction, with a half-life of around 20 s (SI, figure S2). With
WH⋯B] present, [Ru] reacts with [WH⋯B] by PCET before it can recombine with
3
+
[
●+
●+
●
+
Q . Charge recombination between the diquat radical Q and the [W ⋯H B] that is
●
+
formed by the PCET reaction is also possible. However, [W ⋯H B] rapidly dimerizes
upon formation; we could follow the formation of the W-W dimer by transient mid-IR
spectroscopy, giving a formation half-life of ca. 1 us for the dimeric product (see SI,
3
+
pages S24-S27). The large excess of [WH⋯B] over [Ru] , and rapid dimerization of
W ⋯H B], results in a clean PCET reaction to give [Ru] and W-W dimer, without
significant secondary oxidation of the radical. The Q generated in these studies are
not reducing enough to react with the tungsten dimer, resulting in accumulation of Q●+
when the PCET reaction is triggered (SI figure S3). Significant accumulation of Q●+
●
+
2+
[
●+
2
+
will result in accelerated recovery of the [Ru] bleach due to direct reaction between
●+
3+
Q and [Ru] . For this reason, the samples were kept in the dark during preparation
and measurement. It was found that the observed PCET kinetics did not change
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significantly within the first four laser shots (SI, figure S5), and thus maximally four
measurements per sample were conducted to avoid interference from accumulated Q●+
2+
and tungsten dimer complex. We noted that methyl viologen (MV ) was reduced to
the radical form MV already in the dark, probably by the small fraction of
deprotonated 1a-e. In contrast, PDQ2+ and BDQ2+ have a 100 and 200 mV more
negative potential for their first reduction, respectively, and did not react in the dark.
+
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
The following will first describe the qualitative trends of the kinetic data. In the next
section, theoretical predictions for the difference in free-energy dependencies of the
kPCET between the PCET mechanisms are presented, and how their rates may depend
on pressure. Thereafter, the experimental data are compared with the predictions and
mechanistic assignments are made.
The second-order rate constants of the photoinduced PCET reactions in compounds 1a-
3
+
e with all oxidants are given in Table 1. The data obtained with [Ru(Me bpy) (bpy)]
2
2
3
+
and [Ru(bpy) ] are compared to those obtained with weaker oxidants from a previous
3
study (Figure 2).53, 63 A clear increase in the PCET rate constants is observed when
stronger oxidants are used, which is, however, much greater for the compounds with
weaker bases (1a-b). As a consequence, the rate dependence on pyridine base strength
becomes weaker with stronger the oxidants. This is highlighted in Figure 2 by the linear
fits to data with the same oxidants. The kinetic isotope effects (KIE = k /k , measured
H
D
3
+
with a series of W-D analogues of 1a-1e) in the reactions with [Ru(dmb) (bpy)]
2
3+
decreased from ca. 0.90 to 0.51, going from 1a to 1d. With [Ru(bpy) ] , the KIEs of
3
compound 1a and 1b were 1.13 and 1.05, increased slightly to 1.27 for 1c, and then
dropped to 0.89 and 0.74 for 1d and 1e, respectively. In Figure 3, the rate constants are
0
instead plotted as a function of oxidant strength (E ). Here it is obvious that the rates
0
for 1a-b are much more sensitive to changes in E than are those of 1c-d. However, it
is also clear that the strength of this dependence for each compound 1a-d varies in
0
different regions of oxidant E . These results indicate that the main reaction mechanism
varies with the strength of both oxidant and base.
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1
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1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
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3
3
3
3
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2
2
2
2
6
4
2
0
0.74
1
.27 0.89
1
.13
0.91
0.28
0
1
2
3
4
5
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8
9
0
1
2
3
4
5
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7
8
9
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1
2
3
4
5
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7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
18
0.51
0
.88
0.19
16
1.21
2.4
0.14
[Fe((OMe)2bpy)3]3+
14
3
+
[
Fe(Me bpy) ]
2
3
12
Fe(bpy) ]3
+
[
3
[Ru(Me2bpy)3]3+
10
8
0
.31
3
+
[
[
Ru(Me bpy) (bpy)]
2
2
0.38
Ru(bpy) ]3
+
3
6
9
10
11
12
13
14
15
16
pKa
Figure 2: Dependence of the observed second-order PCET rate constant on the pK value of
a
the pyridinium derivative residue (Scheme 2). The standard deviation of kPCET is smaller than
the size of the data points. The lines are linear fits to the data with the same oxidant (fits for
3
+
3+
[
Fe(dmb) ] and [Fe(bpy) ] are omitted for clarity. Kinetic isotope effect (KIE) values are
3 3
given where measured. All rate constants are given in Table 1.
2
6
24
2
2
20
1
1
1
1
8
6
4
2
1
1
a
b
1c
1
d
3+
3+
[
[
[
Fe((OMe) bpy) ]
Fe(bpy)3]3+
[Fe(Me bpy) ]
2
3
2
3
10
8
3+
[Ru(Me bpy) ]
2
3
3+
3+
Ru(Me bpy) (bpy)]
[Ru(Me bpy)(bpy) ]
2 2
2
2
[Ru(bpy)3]3+
[Ru(bpy) ((EtO C) bpp)]
2 2 2
3+
6
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
0
+
E of the Oxidant (V, vs Fc/Fc )
Figure 3. Dependence of the observed second-order PCET rate constant on the oxidant
0
strength (E ). The standard deviation of k
is smaller than the size of the data points. The
PCET
0
lines are linear fits to the data: for 1c-d the data with E = 0.35-0.73 V were used, while for
0
1
a-b linear fits are made in two different regions: E = 0.50-0.73 and 0.73-0.90 V,
respectively. All rate constants are given in Table 1.
1
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-
1 -1 a)
Table 1. Second-order rate constants (M s ) , kinetic isotope effects (KIEs, shown in
b)
0
brackets) and G
(eV) for the reactions of complexes 1a-e with different oxidants
in CH CN at 25 °C. Data for the first four oxidants are from ref. 53.
PCET
3
Complex
(
pKa)d)
1a
1b
1c
1d
1e
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Oxidant
(9.55)
(9.93)
(12.53)
(13.32)
(14.23)
( Eo) c)
.1×104
4.8×104
2.3×107
1.1×108
5.4×108
1
3
+
[
Fe((OMe) bpy) ]
(0.38)
(0.31)
(0.14)
(0.19)
2
3
(0.36V)
-0.36 eV
-0.38 eV
-0.54 eV -0.58 eV -0.64 eV
3
.0×104
6.9×104
6.9×107
3.4×108
NDe)
NDe)
NDe)
3
+
[
Fe(Me bpy) ]
2
3
(0.51V)
-0.51 eV
.6×105
-0.53 eV
-0.69 eV -0.73 eV
5
6.7×105
(0.99)
5.4×107
(0.19)
3.4×108
[Fe(bpy)3]3+
0.66V)
(0.88)
(
-0.66 eV
-0.68 eV
-0.84 eV -0.88 eV
1.6×106
(2.4)
2.7×106
(1.2)
7.2×107
(0.28)
3.7×108
3+
[
Ru(Me bpy) ]
2
3
(0.73V)
- 0.73 eV
-0.75 eV
-0.91 eV -0.95 eV
1
.2×108
1.6×108
(0.88)
3.3×108
(0.91)
6.0×108
(0.51)
NDe)
3
3
+
+
[
Ru(Me bpy) (bpy)]
(0.90)
-0.82 eV
NDe)
2
2
(0.82 V)
-0.84 eV
6.0×108
-1.00 eV -1.04 eV
5.9×108
9.8×108
NDe)
[Ru(Me bpy)(bpy) ]
2
2
(0.85 V)
-0.87 eV
-1.03 eV -1.07 eV
5
.8×108
(1.1)
6.4×108
(1.1)
1.3×109
(1.3)
1.3×109
(0.89)
1.6×109
(0.74)
[
Ru(bpy)3]3+
(0.89 V)
-0.89 eV
.2×108
-0.91 eV
-1.07 eV -1.11 eV -1.17 eV
7
1.2×109
4.9×109
2.0×109
NDe)
3
+
[Ru(bpy) ((EtO C) bpy)]
2
2
2
(1.03 V)
-1.03 eV
-1.05 eV
-1.21
-1.25
a) Standard deviations of rate constants were 5-10%, from an average of fits to single traces
for three independent samples, and are given in Table S1.
b) For combinations when KIE was not determined the field is left blank.
c) M3+/2+ reduction potentials in CH CN versus Fc /Fc
+
49, 64, 65
. bpy = 2,2’-bipyridine, (OMe) bpy
2
3
=
4,4’-dimetoxy-2,2’-bipyridine, Me bpy = 4,4’-dimethyl-2,2’-bipyridine; (EtO C) bpy = 4,4’-
2 2 2
diethylester-2,2’-bipyridine.
5
3
d) pK of the conjugate acid of the corresponding pyridine derivative residue in CH CN .
a
3
e) Not determined.
1
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3
In our previous study, we assigned the PCET mechanism for 1a-e and the weakest
3
+
oxidants to pre-equilibrium PTET (Figure 2: grey line for [Fe((OMe) bpy) ] ). With
2
3
intermediate oxidants, the mechanism was assigned to CEPT for 1a-b, and a mix of
3
+
CEPT and PTET for 1c-e (blue line for [Ru(Me bpy) ] ). With the stronger oxidants
2
3
used here, we assign the mechanism for 1a-b to ETPT, while there is evidence for both
CEPT and ETPT for 1c-e, depending on the strength of oxidant and base. These
assignments, and their theoretical background, are described in the following sections.
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Further indication that the mechanism changes was obtained from the pressure
dependence of kPCET (Table 2). We found a linear variation of ln kPCET with pressure,
‡
‡
and the slope of that line equals ―Δ푉 푅푇, where Δ푉 is the activation volume (i.e.
the difference in volume between the transition state and the reactants). While the
compounds with weaker bases showed rates that decreased with increasing pressure,
the rates for compounds with stronger bases the rate increased instead (Figure 4). This
can be related to the different signs of the activation volume that are predicted for the
different mechanisms, based on the changes in charge density and solvation of the
different intermediates and transition states, as explained below. Interestingly, for some
3+
3+
combinations of compounds, (1c with [Ru(Me bpy) ] , and 1d with [Ru(bpy) ] ) the
2
3
3
protonated and deuterated compounds showed different dependences on pressure,
giving rise to strongly pressure dependent KIEs. This may be related to changes in
proton tunneling probability as the W-H complex is compressed.1, 48
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Table 2. Apparent activation volumes for the W-H and W-D complexes 1a-e from
analysis of pressure dependent rate constants (eq. 12), and kinetic isotope effects
(KIE) at 1 bar.
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
3
+
[Ru(bpy)3]3+
[
Ru(Me bpy) (bpy)]
2
2
‡
3
a)
‡
3
a)
Compound
ΔV (cm /mol)
ΔV (cm /mol)
KIE
1 bar)
KIE
(
(1 bar)
W-H
W-D
2.6
5.1
-4.2
-7.7
-
W-H
3.6
W-D
4.0
1a
2.2
3.8
-1.2
-7.7
-
0.9
0.89
0.91
0.51
-
1.1
1.1
1
b
5.2
4.1
1
c
3.0
2.1
1.3
1
d
-4.8
-0.54
0.65
-0.44
0.87
0.76
1
e
3
-1
66
a) For comparison, the volume of acetonitrile is 52,9 cm mol at 25 C and 1 bar.
Figure 4: The observed pseudo-first order rate constants for the W-H (black symbols) and W-
D (red symbols) compounds at different applied pressure from the samples containing (left) 67
2+
2+
2+
μM [Ru(bpy) ] , 50 mM [BDQ] and 1 mM Compound 1a; (right) 40 μM [Ru(dmb) (bpy)] ,
3
2
2
+
5
0 mM [BDQ] and 6 mM compound 1d. The lines are linear fits to the data (cf. eq. 12). Data
for the other pressure dependent experiments are shown in the SI.
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5
6
Predicted free energy dependence of concerted and stepwise PCET mechanisms
In this section, we describe theoretical predictions for the free-energy dependence of
PCET reactions. PCET can occur in a single elementary step or in two sequential steps
(see Scheme 1). The observed rate constant is the sum of the contributions from these
three mechanisms:
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
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9
0
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0
1
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8
9
0
푘PCET = 푘ETPT + 푘PTET + 푘CEPT
(3)
The stepwise PCET reaction may be rate-limited by the initial ET or PT step:
푘ETPT = 푘ET ― b (rate limiting first step) (4)
푘PTET = 푘PT ― a (rate limiting first step) (5)
They can also occur in the kinetic pre-equilibrium limit, where their rate constants are
given by the equilibrium constant for the initial reaction multiplied by the rate constant
for the following step:
푘ETPT = 퐾 ∙ 푘
(pre-equilibrium)
(pre-equilibrium)
(6)
(7)
ET
PT ― b
푘PTET = 퐾 ∙ 푘
PT
ET ― a
The CEPT pathway is always thermodynamically favored because it uses all the
available PCET free energy in a single reaction step; therefore, it may have a lower
reaction barrier. In contrast, the initial steps of the ETPT and PTET have lower driving
force and are often even uphill reactions. On the other hand, the tunneling probability
of CEPT can be smaller because it involves both electron and proton. A balance
between these two factors can often explain the competition between the mechanisms.
A strong oxidant favors ETPT while a strong base favors PTET, if both oxidant and
base are weak, however, CEPT can be favorable. The energetic part of this argument,
and how this can be used to switch the preferred mechanism, are clarified in this section.
Eq. 8 gives the general rate expression for non-adiabatic ET, PT or CEPT:
Δ퐺푖‡
푘 = 퐴 ·exp ―
(8a)
푖
푖
(
)
푅푇
2
0
(
∆퐺 + 휆푖)
푖
‡
Δ퐺 =
(8b)
푖
4
휆푖
where the index i indicates ET, PT or CEPT.1, 67, 68 This expression is also valid for the
cases of rate-limiting ET or PT in the stepwise PCET mechanisms (eq. 4-5). For
simplicity and clarity, eq. 8 does not explicitly include variations in contributions from
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different vibronic states. The relative contribution from different vibronic states to the
CEPT reaction may also vary with driving force; see Concluding Remarks. The free-
energy dependence can also be expressed by the derivative form of eq. 8:
∂
ln 푘푖
1
∆퐺0푖
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
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5
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5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
(9)
=
(1 +
0
)
2
푅푇
휆푖
∂( ― ∆퐺 )
푖
0
At moderate driving force, and sufficiently small range of G values, eq. 9 shows an
0
-1
approximately linear behavior (Scheme 3). At G = 0 the slope equals (2 RT) , which
-1
-1
at room temperature is (50 meV) , or 20 eV . For a plot of log(k
) vs. pK , where
CEPT
a
0
-1

G changes by 59 meV per pK unit, this will give a slope of 0.51 pK , very close to
a
a
what is observed for the CEPT reactions of 1, and (Cp)WH(CO) with external
3
pyridines and the weaker oxidants.49
The cases of ETPT and PTET with a rate-limiting first step (eq. 4-5) will also follow
eqs. 8-9, but as the driving force is smaller than for CEPT, the slope according to eq. 7
will be larger (assuming that the reorganization energies are similar). Therefore, rate-
limiting ETPT or PTET will be more sensitive to changes in oxidant and base strengths,
4
9
respectively, than a CEPT reaction. Indeed, we showed in our previous work that k
ET
0
∂(ln 푘)
0
-1
-1
depends on G more strongly than does kCEPT:
( ― ∆퐺 ) = 23 eV vs. 15 eV ,
respectively. Therefore, if both the oxidant and base are weak, this tends to favor CEPT.
In the pre-equilibrium limit instead (eq. 6), kETPT will decrease by a factor of ten for
0
∂(ln 푘)
0
each 59 mV decrease in oxidant strength (E ). This gives
( ― ∆퐺 ) = 39
ox
-1
-1
eV (i.e. (25.6 meV) ), which is a much stronger driving force dependence than for the
single step reactions; see Scheme 3. Analogously, in the case of pre-equilibrium for
PTET (eq. 7), kPTET will decrease by a factor of ten for each pK unit decrease of the
a
pyridinium group. The latter behavior is seen when comparing the rates as a function
of base strength for 1a-e with a weak oxidant (Figure 2). This makes pre-equilibrium
PTET even more sensitive to changes in base pK than a CEPT mechanism (Scheme
a
3
). However, if the oxidant strength is increased, the PTET is less strongly affected
-
because oxidation of the basic form of 1a-e (W ) already has a large driving force. Thus,
0
the value of -G is close to  and the reaction lies close to the top of a Marcus parabola
6
7
(
cf. blue curve of Scheme 3). This behavior is seen when comparing the rates as a
function of oxidant strength for 1c or 1d with the four weaker oxidants used (Figure 3).
Thus, by changing oxidant and base, we may have the possibility to make the same
species react via either ETPT, PTET or CEPT. This was shown for the first time in our
previous studies,49,53 by combining data from inter- and intramolecular pyridine bases.
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0
pre-eq PTET (vs. G )
PT
0
pre-eq ETPT (vs. G )
ET
Marcus-type
CEPT
0
1
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9
0
1
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9
0
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9
0
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9
0
1
2
3
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5
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8
9
0
0
pre-eq ETPT (vs. G )
PT
0
ET
pre-eq PTET (vs. G )
0
0
0
ET
G or G
PT
Scheme 3. Illustration of the differences in free energy dependence for the different
PCET mechanisms (eq. 3-9). The x-axis shows differences in either G0 (orange
PT
background) or G0 (yellow background).
ET
Predicted pressure dependence of kPCET The pressure dependence of rate constants
of chemical reactions has previously been shown to be a powerful mechanistic
indicator.69, 70 Traditionally, pressure dependence has been used to construct volume
profiles for chemical reactions with great advances by the groups of le Noble, van Eldik,
Swaddle and many others.69-71 Theoretical approaches to analyzing the pressure
dependencies are well described in multiple reviews and will thus not be discussed in
detail here.69-76
Briefly, the pressure dependence of a reaction equilibrium constant can be related to
the molar volume change of the reaction (reaction volume) through the Maxwell
relation:
훿ln 퐾
Δ푉
푅푇
=
―
(10)
훿푃
where for the reaction:
퐴 + 퐵⇋퐶

V is given by:
Δ푉 = 푉 ―(푉 + 푉 )
(11)
퐶
퐴
퐵
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In a transition state theory picture, where the reactants are in thermal quasi-equilibrium
with the transition state, the pressure dependence of the rate constant reports on the
molar volume difference between the transition state and the reactants (activation
volume):
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
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5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
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8
9
0
1
2
3
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5
6
7
8
9
0
1
2
3
4
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8
9
0
1
2
3
4
5
6
7
8
9
0
Δ푉 ‡
= ― 푅푇
훿ln 푘
(12)
훿푃
where for the reaction:
‡
퐴 + 퐵⇋[퐴퐵] ⟶퐶

푉 ‡ is given by:
Δ푉 = 푉[
‡
퐴퐵] ‡
―(푉 + 푉 )
(13)
퐴
퐵
For a pre-equilibrium mechanism, the experimentally observed activation volume will
equal the sum of V for the first reaction step and Δ푉 ‡ for the second.
Many activation and reaction volumes for electron transfer reactions have been
reported.69-71 It has been found that not only intrinsic volume changes of the reactants,
but also solvent electrostriction effects due to a change in charge, affect the volume
profiles of electron transfer reactions. Thus, highly charged species will be more
2
solvated, with degree of solvation proportional to (ze) /r (ze = ionic charge, r = ionic
radius), which decreases the volume of the solvent.74, 76, 77 For an ETPT reaction in the
present case, the encounter complex has Ru3+ and WH, going to Ru2+ and W H .

+
Although the ruthenium complex has a larger radius, the main effect will be due to a
3
+
2+
decrease in charge, and a loss of solvation as Ru goes to Ru . Thus, this ETPT
reaction can be expected to have a positive reaction volume (V), as the follow-up PT
reaction is just shifting the proton in the oxidized 1a-e. For the PTET reaction, the
-
+
neutral [WH…py] complex becomes zwitterionic ([W …H py]) in the first step, which
is expected to become more strongly solvated and show a negative reaction volume.
The follow-up ET reaction of PTET has a large enough driving force to be nearly
activationless, and thus the effects on the overall PTET rate from that step will be small.
Thus, one may expect to observe an overall negative activation volume.
There are fewer pressure dependence studies of PCET reactions in small molecular
systems76, 78 or proteins79-82 but it can be expected that CEPT would have a different
3
+
2+
volume profile. In the present case, the different solvation of Ru and Ru should
dominate V, similar to ETPT, but CEPT is a single step reaction, and volume changes
‡
for the transition state (Δ푉 ) should be smaller than V. In addition to volume changes
related to solvation, an increased pressure may accelerate a CEPT reaction by
increasing the proton tunneling probability. Pressure-dependent KIEs of PT and PCET
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reactions have previously been assigned to be the result of the involvement of proton
tunneling.70, 79, 80, 83, 84 As an increased pressure favors more compressed configurations
of molecules, where the proton donor-acceptor distance may be shorter, the pressure
dependence in such systems may provide information about the distance dependence
of the CEPT rate constants without the need to synthetically vary the molecular
structure.
0
1
2
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9
0
1
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9
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0
1
2
3
4
5
6
7
8
9
0
In conclusion, the observed PCET rate constants can be expected to have fundamentally
different pressure dependencies, depending on which reaction mechanism is followed.
In the present case, the PTET reaction rate should increase with pressure, while that of
ETPT should decrease. For the CEPT reaction, the effects of solvation and proton
tunneling distance will work in opposite direction, and the net effect cannot be predicted
at the present point.
Mechanistic assignment of the PCET reactions
The mechanistic assignment will
begin from the rate vs. driving force correlations. First, trends with the protonic part of
0
the driving force (-G ) will be discussed, i.e. the variation in rate with pK of the
PT
a
pyridiniums, together with KIEs. Then the electronic part of the driving force (-G0ET)
0
will be discussed, i.e. the variation in rate with E of the oxidant. Finally, the pressure
dependence will be discussed, and how this may help in assignment of the PCET
mechanism. It is important to note that, when a mechanism is assigned, this refers to
the main mechanism. The observed PCET rate constant is always a sum of the different
contributions (eq. 1). In most cases, one mechanism clearly dominates the reaction, i.e.
it is at least ten times faster than the others are. In other cases, there are clearly
simultaneous contributions from more than one mechanism.
As noted above, the variation in rate with the base strength of the pyridine group is very
different for the different oxidants (Figure 2). With the two weakest oxidants, the
mechanism can clearly be assigned to pre-equilibrium PTET (eq 7), as discussed
5
3
before. This is because the rate increases by a factor of ca. 10 per pK unit of the
a
3
+ 53
pyridinium group ((log k)/pK = 1.03 with [Fe((OMe) bpy) ] ) , which is a far too
a
2
3
strong dependence to agree with any of the other mechanisms. Noting that one pK unit
a
corresponds to 59.2 meV of driving force (and that ln k  2.30log k), the slope
0
-1
corresponds to (ln k)/(-G ) = 40 eV (see linear fit in Figure 2), in excellent
-1
agreement with the predicted value from eq. 6 of 39 eV . Additional support for the
mechanistic assignment comes from the inverted KIE values (0.14-0.38), which can be
explained by an equilibrium isotope effect on the initial PT step. Based on differences
+
in vibrational zero point energy from spectroscopic data for W-H and H -pyridine
53
vibrations, these were predicted to be ca. 0.25. For CEPT reactions, different rate
contributions from higher vibronic states for protonated and deuterated compounds, and
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compression of the proton donor-acceptor distance, can result in inverse KIE values,85-
8
8
but it is unlikely that they would be as small as observed here. We note that Norton
and coworkers have reported normal KIEs (3-4) for proton and hydrogen atom transfer
from various metal hydrides to carbon radicals as well as in in self-exchange
reactions.59, 89 Chen and Bullock reported normal KIEs (1.7) for hydride transfer from
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
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3
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3
3
3
3
3
3
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1
2
3
4
5
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9
0
1
2
3
4
5
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9
0
1
2
3
4
5
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7
8
9
0
1
2
3
4
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7
8
9
0
1
2
3
4
5
6
7
8
9
0
+
tungsten and molybdenum complexes to Ph C , but in one case a clear invested value
3
9
0
of KIE = 0.47 was found. They discussed this result in terms of either a single-step
reaction with a high zero-point energy of the transition state, or a step-wise reaction
with a hydrogen atom transfer equilibrium followed by electron transfer, as observed
for several hydrogenation reaction involving metal hydrides (see ref. 90 and references
therein). In the latter case, the intermediate C-H bond has a higher frequency than the
reactant W-H bond in analogy to the present study, giving rise to an equilibrium isotope
effect <1.
When changing to the medium strength oxidants, the rate increased substantially for
3
+
1
a-b, but more moderately for 1c-e. A linear fit to the data with [Ru(Me bpy) ]
2 3
3
+
showed only about half the slope compared to that with [Fe((OMe) bpy) ] . Moreover,
2
3
3
+
the KIEs where larger with [Ru(Me bpy) ] and even larger than unity for 1a-b (KIE
2
3
=
2.4 and 1.2, respectively). This is not consistent with pre-equilibrium PTET. Rate
limiting PT can also be excluded for these reactions, because of the large observed rate
constants for what would then have to be strongly uphill reactions: pK > 6 for 1a-b
a
and >3.5 for 1c. Thus, the second order rate constant for reverse PT from the pyridinium
-
group to W in 1a-b would have to be at least six orders of magnitude faster than the
12
-1 -1
11
-1 -1
observed rate constants (Table 1), i.e. 110 M s (110 M s for 1c with
3
+
[
Ru(Me bpy) ] ). This would be significantly faster than the diffusion limit of ca.
2 3
10
-1 -1
1
10 M s , and rate-limiting PT can therefore be ruled out. Instead, the dependence
0
of kPCET on pK , as well as on E for 1a-b (see below), is in good agreement with a
a
5
3
CEPT mechanism, as discussed before. The KIE >1 for 1a-b also agrees with a CEPT
91
reaction, caused by different tunneling probabilities for proton and deuteron. For 1c-
e, however, we noted that the reaction proceeds probably through a mixed mechanism,
where also PTET contributes significantly. This is seen from the relatively small
3
+
3+
difference in kPCET for 1c-e with [Fe((OMe) bpy) ] vs. [Ru(Me bpy) ] , and the small
2
3
2
3
KIEs also with the latter oxidant. Thus, the slope of the fitted blue line in Figure 2 ((ln
0
-1
k)/(-G ) = 22 eV ) is somewhat larger than expected for just the CEPT contribution,
-1
which is predicted to be 20 eV or smaller.
With the four strongest oxidants, as measured in the present study, kPCET for 1a-b
increases even more, by a few orders of magnitude. Across the series 1a-e, kPCET shows
just a modest increase with increasing pK when the same oxidant is used (red lines in
a
Figure 2). The reaction is still not diffusion-limited, except possibly for 1c with the
3
+
9
-1 -1
9
-1 -1
strongest oxidant [Ru((EtO C) bpy) ] (k
= 5×10 M s ), as k
PCET
 2×10 M s
2
2
3
PCET
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in all other cases and still varies with e.g. oxidant strength and isotopic substitution.
The very weak dependence on base strength for the same oxidant is therefore not
consistent with either PTET or CEPT. Instead, we can safely assign the main
mechanism to ETPT. The KIE = 1.00.1 for 1a-b agrees with that assignment. The
weak increase in rate for 1c-e might be explained by a small acceleration of the second
PT step of a pre-equilibrium ETPT mechanism (kPT-b in Scheme 1). However, based on
the KIE values, and the dependence of the rate on oxidant strength and pressure
discussed below, we propose that contributions from CEPT and PTET are the reason
why kPCET is larger in 1c-e than in 1a-b also with the strongest oxidants. Interestingly,
0
1
2
3
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9
0
1
2
3
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9
0
1
2
3
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7
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9
0
1
2
3
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8
9
0
1
2
3
4
5
6
7
8
9
0
3
+
with [Ru(bpy) ] , KIE=1.1 for 1a, then slightly larger for 1c (KIE=1.3) and finally less
3
than 1 for 1d-e (KIE=0.9 and =0.7, respectively). This behavior agrees with
participation of more than one mechanism, as is further supported below.
In this paragraph, we discuss the dependence of the rate on oxidant strength. In Figure
we see that for 1c-d, the rate is only little affected by E : (ln k)/(-G )  3 eV-1
0
0
3
ET
0
0
(
where -G0 = eE ) for the weaker oxidants (E  0.73 V), which is consistent with
ET
0
pre-equilibrium PTET. The initial PT equilibrium is independent on E , and the
-
subsequent ET from W (k
in Scheme 1) is sufficiently exergonic to already be close
ET-a
0
to barrierless (close to the top of the Marcus parabola, where -G = ; eq. 8). With
0
0
stronger oxidants (E > 0.73), the dependence on E is stronger: the slope of a linear fit
0
-1
to the data for 1c with the four oxidants in the range E = 0.73-0.89 V is 19 eV , close
to slope expected for a CEPT a reaction, and the KIE changes from 0.28 to 1.27 for 1c
(to 0.89 for 1d). This is clear evidence that another mechanism different from PTET
0
gradually becomes dominating, and both the dependence on E and the KIE suggest
that this is CEPT. Further support for this assignment is given by the pressure
dependence, as discussed below. Turning to 1a-b, these show a very weak dependence
0
0
on E in the region E = 0.35-0.50 V, consistent with a pre-equilibrium, PTET with the
0
two weakest oxidants, as was discussed above. For E = 0.50-0.73 V, the dependence
-1
is much stronger, and a linear fit to the data in Figure 3 gives a slope of 16 eV . This
slope is consistent with a CEPT reaction with a small driving force, and is consistent
with our assignment above based on the KIE values and dependence on pKa.
0
0
Interestingly, when E is further increased, the dependence on E becomes even
0
-1
stronger. The fitted line in the region E = 0.73-0.90 V has a slope of 40 eV , which is
in within experimental error of the slope predicted for a pre-equilibrium ETPT (39 eV-
1)
. No other PCET mechanism is consistent with such a strong dependence on E . This
0

+
II
kinetic limit requires that the reverse ET from W H to Ru (k-ET-b) in the

+
encounter/successor complex is faster than PT from W H to the pyridine base (kPT-b).
For an Eigen acid, i.e. a common oxygen or nitrogen acid with small intrinsic barriers,
that would seem unlikely, as they become diffusion controlled already at moderate
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driving force (pK > 2). However, proton transfer in these WH complexes is
a
intrinsically much slower than that, in both the neutral and oxidized forms; see
0
Concluding Remarks. In Figure 3, the rate levels off at abut E = 0.90 V, which would
be consistent with an equilibrium constant K =1 at around that value. This seems to
ET
0
be in some disagreement with the value of E for [(Cp)W(CO) H] that was estimated
3
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
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0
to +0.76 V (+0.71 V for [(MeCp)W(CO) H]; Scheme 1). However, the potential for
3
[
(Cp)W(CO) H] was estimated from an irreversible peak potential in ref. 55, and we
3
assumed that the 50 mV cathodic shift in Epeak for [(MeCp)W(CO) H] equals the shift
3
0
in E . Moreover, the columbic work term in the encounter/successor complex disfavors
ET, as the ET products are both cationic, while the 1a-e reactant is charge neutral. This
means that G0 is slightly less favorable than estimated from just the difference in E0
values. Thus, pre-equilibrium ETPT seems reasonable for 1a-b with oxidants with E0
ET
>
0.73 V, and it explains both the larger slope in Figure 3 and the fact that kPCET levels
off with the strongest oxidant (which is still slower than diffusion control). We note
that this pre-eq ETPT mechanism must be operative with at least similar rates in 1c-e,
but the observed rates for these compounds is higher, and the KIEs different, consistent
with our assignment above that other mechanisms come into play for 1c-e. As noted
0

+
above, a constant shift of E (W -H /W-H) is no concern as our analysis is based on
0
relative G values for the different combinations of oxidants and pyridines.
Finally, in this paragraph we use the pressure dependence of the rate constants and KIEs
to discuss the PCET mechanism (Table 2). Complexes 1a-d show a clear trend in
activation volumes: a positive experimental activation volume ∆푉 ‡ with the weakest
bases turning gradually into a negative ∆푉 ‡ for the strongest bases. This is fully
consistent with ETPT for the weaker bases and PTET for the stronger bases, due to the
different charge density and solvation changes of their intermediates, as explained in
the background on pressure dependence above. We note that the data for 1e shows a
less negative ∆푉 ‡ than 1d. We speculate that this might be because pK is already
small at 1 bar, and that K increases with pressure to become close to 1. Interestingly,
a
PT
3+
‡
for 1d and [Ru(bpy) ] , ∆푉 is distinctly different for WH and WD leading to a
3
change from KIE=0.89 at ambient pressure to KIE=1.30 at 2 kbar (Figure 5). We
already assigned the mechanism at 1 bar to PTET, with significant contribution from
pre-equilibrium ETPT. Because PTET has a negative ∆푉 ‡ (rate increases with
pressure) and ETPT has a positive ∆푉 ‡ (rate decreases with pressure), a higher P
should favor PTET and lead to even lower KIEs, which is opposite to our observations.
This suggest that a different mechanism starts contributing more at higher pressure, and
because KIE increases above KIE = 1.0, we suggest that this mechanism is CEPT.
CEPT should also have a slightly positive ∆푉 ‡ based on solvation changes (see
above), but compression of the complex may lead to a shorter proton tunneling distance
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and increased CEPT rates, and the KIE > 1.0 would reflect a better vibrational overlap
for WH than for WD. The data thus suggests that we have an interesting situation for
3
+
1
d and [Ru(bpy) ] where all three mechanisms give rather similar contributions to the
3
rate, and their relative rates are sensitive to small changes in conditions. For 1c with the
same oxidant, CEPT could compete with PTET already at ambient pressure, because
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3
+
the base is slightly weaker in 1c. Also, for 1c with [Ru(dmb) (bpy)] as oxidant, Table
2
2
shows a clear difference in activation volumes between the protonated and deuterated
compounds. Increasing the pressure from 1 bar to 2 kbar decreases the KIE from 0.9 to
.7. ETPT is slowed down with pressure, whereas the PTET contribution is accelerated,
0
and therefore the KIE decreases with pressure. It appears that the rates of both
mechanisms are matched well enough with this combination of base and oxidant to
significantly alter their respective contributions with an increase in pressure.
1.3
1.2
1.1
1.0
0.9
0.8
0.7
R
N
0.6
0.5
H
W
OC
0
500
1000
1500
2000
CO
OC
Pressure (bar)
Figure 5: (left) Cartoon representing the effect of pressure on the compression of the
W-H – pyridine distance; (right) Pressure dependence of the KIEs for PCET oxidation
3
+
3+
of 1d by [Ru(dmb) (bpy)] (black dots), 1b by [Ru(bpy) ] (red squares) and 1d by
2
3
3
+
[
Ru(bpy) ] (blue triangles).
3
Concluding remarks
Understanding and elucidating the mechanisms, and to steer and control them, is of key
importance in PCET research. The present system showed an unprecedented richness
in mechanistic variation, where all three PCET mechanisms were displayed by varying
the strength of oxidant and base. Straightforward and general guidelines for how the
relative rates of the different mechanisms depend on oxidant and base, expected
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theoretically and from our earlier studies, have been presented and they seem to hold in
practice. This has not been experimentally shown before as clearly as is done in the
present study. The results should be of great and general relevance for a range of PCET
reactions, including synthetic catalysts or enzymes operating with PCET reaction steps.
The results illustrate that the mechanism for a reactant undergoing PCET is not intrinsic
to that species. Instead, it depends strongly on the reaction conditions, such as the
strength of the reductant/oxidant and the acid/base used. Moreover, the different
responses to changes in oxidant and base strengths for the different mechanisms
1
1
1
1
1
1
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0
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2
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9
0
underscore the importance of knowing the mechanism of the rate determining steps
0
when e.g. designing a catalyst that should be optimized with respect to E and pK
a
values, or when data for enzyme mutants should be interpreted.
It is intriguing that all three mechanisms showed closely similar rate constants for some
combinations of oxidants and pyridines. It is often a great challenge, both for theoretical
and experimental methods, to distinguish and determine the dominating mechanism.
Free energy correlations, using both variations in the strengths of oxidant and base,
were important in this study to assign the mechanisms, and were supported by KIEs.
Pressure dependence was used for the first time to distinguish PCET mechanisms of
small molecules. It was rewarding that mechanistic predictions based on changes in
charge density and solvation were useful to distinguish the mechanisms. The effect of
pressure on proton tunneling for the CEPT reaction is very complicated to analyze in
quantitative detail, both because of contributions from multiple vibronic transitions,
and because of a likely pressure dependence of other parameters such as driving force,
reorganization energy and the diffusional reaction steps. A theory describing the
dependence of the CEPT rate constant on pressure, that consider these parameters, is
lacking. Instead, in one approach, the pressure dependence of KIEs has been analyzed
to assess proton tunneling, assuming that most pressure effects are independent on H/D
isotope and thus cancel out.79, 80, 93 In this study, we would similarly argue that the
pressure dependence of many parameters in the homologous series 1a-e should be the
same, so that differences in the relative rates and how they depend on pressure can be
attributed to changes in mechanism. Indeed, clear systematic changes were found in
how the activation volume varied with base strength, and thus with PCET mechanism.
Data on the variation in KIE with pressure could be obtained, which indicated an
enhanced proton tunneling for a CEPT reaction as the pressure increased. This can
tentatively be attributed to compression of the W-H complex along the H···B
coordinate to give a shorter proton tunneling distance.86, 87, 93 The compression
presumably involves a combination of several normal modes of predominantly low
94
frequency. Identification of these modes would require a computational effort that is
beyond the scope of the present study. Development of a theory to describe the pressure
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dependence of CEPT reactions, combined with a wider range of experimental data
where CEPT is the main reaction, would be a complement to the temperature
1
dependence that is included in current theories, and be valuable to make progress in
our understanding and interpretation of PCET reactions.
0
1
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0
Regarding the pressure dependence, it is not only an analytical tool for reactions that
normally occur at one bar. Instead, we note that energy transformations in deep-sea
creatures occur under substantial hydrostatic pressure and it is of fundamental interest
to understand the pressure effects on these PCET reactions.95-97 Methane production in
certain methanogens has been reported to be enhanced at high pressure, up to 20 MPa
9
8
99
(
200 bar) or 76 MPa (760 bar). We are not aware of any in vitro mechanistic studies
of the pressure dependence of the proteins involved in these reactions. Human
exploration of the deep sea in the future may rely on fuel cell powered submarine
vehicles, which depend on catalytic PCET reactions at high pressure.100-102
4
9
It is interesting to compare our data for [(Cp)WH(CO) ] with similar data from
3
5
4
Dempsey and coworkers on [(Cp)WH(CO) (PMe )]. The electron donating PMe
3
2
3
0
ligand decreased E and increased pK of the complex. Nevertheless, by using weaker
a
oxidants and stronger bases than in ref 49, they obtained very similar G0PCET values,
but found that CEPT was exclusively a minor pathway. Dempsey and coworkers
suggested that the difference between the two W-H complexes is related to the rate of
proton transfer. In contrast, the present study shows cases where CEPT is the major
pathway. Proton transfer to and from metal hydrides is in general slow, compared to
that of Eigen acids, which has been attributed to large electronic and nuclear
rearrangements.59,
103-106
Bourrez et al. showed that proton transfer from
[
(Cp)W(CO) H] to aniline (pK = 2) was much slower than diffusion controlled: k
= 1×10 M s . Dempsey and coworkers estimated that proton transfer from both
3
a
PT-
5
-1 -1 49
a
the neutral [(Cp)WH(CO) (PMe )] and the oxidized complex to nitrogen bases had
2
3
5
4
large reorganization energies. They also found that the self-exchange proton transfer
was three orders of magnitude slower for the [(Cp)WH(CO) (PMe )]/
2
3
-
-
[(Cp)W(CO) (PMe )] couple than for the [(Cp)WH(CO) ]/[(Cp)W(CO) ] couple. This
2
3
3
3
led them to suggest that a larger reorganization energy for proton transfer in the PMe3
complex is related to a more sluggish CEPT. We propose instead that the more sterically
demanding PMe ligand makes the distance between the hydride and the pyridine
3
nitrogen in the encounter complex longer, which would decrease the proton
wavefunction overlap between the reactant and product states, and thus slow down
CEPT. With a smaller proton tunneling probability, it is less likely that CEPT can
compete with the stepwise pathways. For designing PCET systems, such as catalysts
with acid/base groups in their second coordination sphere, it is interesting to understand
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exactly how large the proton wavefunction overlap needs to be in order to make CEPT
competitive, and if hydrogen bonds are required to achieve sufficient overlap.
The predicted free-energy relationships in this study assume that a CEPT reaction
responds equally to changes in G0 and G . This was also shown to be the case in
0
ET
PT
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0
49
our previous study of [(Cp)WH(CO) ], as well as in several other studies of PCET
3
reactions with small organic compounds.107-111 Dempsey and coworkers instead found
0
that kCEPT for [(Cp)WH(CO) (PMe )] showed very different dependence on G
2
3
CEPT
for two different oxidants, one giving a Brønsted slope (in a plot of log kPCET vs log
54
KPCET) of  = 0.49 and the other  = 0.29. For a CEPT reaction at modest driving
-1
force, one expects   0.4-0.5, which corresponds to 16-20 eV in eq. 9. Therefore,
they suggested that CEPT in the case of one of the oxidants is asynchronous, i.e. that
the rate constant would respond differently to equal changes in G0 and G . Mayer
0
ET
PT
and coworkers showed a first example of C-H activation by CEPT, where the electron
and proton were transferred to different acceptors.112 They also found a small Brønsted
slope of  = 0.23, and suggested an asynchronous reaction. A similarly small -value
was reported by Knowles and co-workers for the PCET reduction of ketones.113
However, “asynchronous” has no meaning in the electron-proton tunneling theory for
PCET.1, 114 The concept is reminiscent from (semi-)classical theories of proton transfer
where proton-base bond elongation is an important part of the reaction coordinate. In
the tunneling theory for CEPT, however, the reaction coordinate that defines the
transition state is exclusively composed of the reorganization of solvent and the other
nuclei (except the tunneling proton). Both electron and proton tunnel from the same
transition state, and any “asynchronicity” in the tunneling process has no meaning.
Even if the electron and proton transfer parts of the CEPT reaction would contribute
different amounts to the reorganization energy, a variation in G0ET andG0PT will give
the same change in G0PCET, and consequently move the transition state up or down by
the same amount. If a Brønsted coefficient much smaller than 0.5 is found
experimentally, a different explanation should be considered. For example, the reaction
could proceed in a step-wise fashion (ETPT or PTET). Alternatively, it has been shown
that variations in the participation of excited vibronic states can reproduce a Brønsted
coefficient <0.5.115 Both G0 and G0 should be varied separately over a
ET
PT
sufficiently large range, to verify any asymmetry in the dependence of the rate on those
two parameters. Reports of an asymmetric dependence of the rate on changes in G0ET
and G0 has recently reported by several groups,116-119 which appears to be at odds
PT
with the tunneling model. However, other effects such as hydrogen bond lengths can
also vary when the relative pKa values are changed, which could be investigated by
computational methods. It is an interesting topic for further theoretical and
experimental investigation, whether CEPT reactions more generally can show an
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asymmetric dependence of G0 and G , and whether that can be described by the
0
ET
PT
tunneling model, or if a different description is more appropriate.
To conclude, the present study shows an unprecedented richness and variation of PCET
mechanisms. The systematic variation of oxidant and base strengths, as well as
hydrostatic pressure, offered correlations of rate vs. free energy and pressure that,
together with KIEs, allowed for clear distinction between mechanisms in most cases.
The study provides rational guidelines for elucidating and controlling the mechanism
that are important for understanding and designing enzymes and synthetic catalysts that
operate with PCET reaction steps.
0
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Supporting Information
Synthesis of photosensitizers and electron acceptors, experimental details, additional
characterization, spectroscopic and kinetic data.
Acknowledgements
The authors thank Dr. Starla Glover for drawing the TOC figure. This work was
supported by the Swedish Research Council (grant 2016-04271) and the Foundation
Olle Engkvist Byggmästare (granted 2016/3). S.W. gratefully acknowledges a grant
from the Chinese Scholarship Council.
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