Kinetics and thermodynamics of small molecule binding to pincer-PCP rhodium(I) complexes

Article abstract of DOI:10.1021/ic300672g

The kinetics and thermodynamics of the binding of several small molecules, L (L = N₂, H₂, D₂, and C₂H ₄), to the coordinatively unsaturated pincer-PCP rhodium(I) complexes Rh[^tBu₂PCH₂(C₆H₃)CH ₂P^tBu₂] (1) and Rh[^tBu ₂P(CH₂)₂(CH)(CH₂)₂P ^tBu₂] (2) in organic solvents (n-heptane, toluene, THF, and cyclohexane-d₁₂) have been investigated by a combination of kinetic flash photolysis methods, NMR equilibrium studies, and density functional theory (DFT) calculations. Using various gas mixtures and monitoring by NMR until equilibrium was established, the relative free energies of binding of N₂, H₂, and C₂H₄ in cyclohexane-d₁₂ were found to increase in the order C ₂H₄ < N₂ < H₂. Time-resolved infrared (TRIR) and UV-vis transient absorption spectroscopy revealed that 355 nm excitation of 1-L and 2-L results in the photoejection of ligand L. The subsequent mechanism of binding of L to 1 and 2 to regenerate 1-L and 2-L is determined by the structure of the PCP ligand framework and the nature of the solvent. In both cases, the primary transient is a long-lived, unsolvated species (τ = 50-800 ns, depending on L and its concentration in solution). For 2, this so-called less-reactive form (LRF) is in equilibrium with a more-reactive form (MRF), which reacts with L at diffusion-controlled rates to regenerate 2-L. These two intermediates are proposed to be different conformers of the three-coordinate (PCP)Rh fragment. For 1, a similar mechanism is proposed to occur, but the LRF to MRF step is irreversible. In addition, a parallel reaction pathway was observed that involves the direct reaction of the LRF of 1 with L, with second-order rate constants that vary by almost 3 orders of magnitude, depending on the nature of L (in n-heptane, k = 6.7 × 10 ⁵ M^-1 s^-1 for L = C₂H₄; 4.0 × 10⁶ M^-1 s^-1 for L = N₂; 5.5 × 10⁸ M^-1 s^-1 for L = H₂). Experiments in the more coordinating solvent, THF, revealed the binding of THF to 1 to generate 1-THF, and its subsequent reaction with L, as a competing pathway.

Full text of DOI:10.1021/ic300672g

Article
pubs.acs.org/IC
Kinetics and Thermodynamics of Small Molecule Binding to Pincer-
PCP Rhodium(I) Complexes
Mark D. Doherty,†,§ David C. Grills,*,† Kuo-Wei Huang,†,∥ James T. Muckerman,†
Dmitry E. Polyansky,*,† Rudi van Eldik,‡ and Etsuko Fujita*,†
†Chemistry Department, Brookhaven National Laboratory, P.O. Box 5000, Upton, New York 11973-5000, United States
‡Department of Chemistry and Pharmacy, University of Erlangen-Nurnberg, Egerlandstrasse 1, 91058 Erlangen, Germany
̈
S
* Supporting Information
ABSTRACT: The kinetics and thermodynamics of the binding of several small molecules,
L (L = N2, H2, D2, and C2H4), to the coordinatively unsaturated pincer-PCP rhodium(I)
complexes Rh[tBu2PCH2(C6H3)CH2PtBu2] (1) and Rh[tBu2P(CH2)2(CH)(CH2)2PtBu2]
(2) in organic solvents (n-heptane, toluene, THF, and cyclohexane-d12) have been
investigated by a combination of kinetic flash photolysis methods, NMR equilibrium studies,
and density functional theory (DFT) calculations. Using various gas mixtures and
monitoring by NMR until equilibrium was established, the relative free energies of binding
of N2, H2, and C2H4 in cyclohexane-d12 were found to increase in the order C2H4 < N2 < H2.
Time-resolved infrared (TRIR) and UV−vis transient absorption spectroscopy revealed that
355 nm excitation of 1−L and 2−L results in the photoejection of ligand L. The subsequent
mechanism of binding of L to 1 and 2 to regenerate 1−L and 2−L is determined by the
structure of the PCP ligand framework and the nature of the solvent. In both cases, the
primary transient is a long-lived, unsolvated species (τ = 50 − 800 ns, depending on L and
its concentration in solution). For 2, this so-called less-reactive form (LRF) is in equilibrium with a more-reactive form (MRF),
which reacts with L at diffusion-controlled rates to regenerate 2−L. These two intermediates are proposed to be different
conformers of the three-coordinate (PCP)Rh fragment. For 1, a similar mechanism is proposed to occur, but the LRF to MRF
step is irreversible. In addition, a parallel reaction pathway was observed that involves the direct reaction of the LRF of 1 with L,
with second-order rate constants that vary by almost 3 orders of magnitude, depending on the nature of L (in n-heptane, k = 6.7
× 105 M−1 s−1 for L = C2H4; 4.0 × 106 M−1 s−1 for L = N2; 5.5 × 108 M−1 s−1 for L = H2). Experiments in the more coordinating
solvent, THF, revealed the binding of THF to 1 to generate 1−THF, and its subsequent reaction with L, as a competing
pathway.
Scheme 1. Some of the Possible Reaction Pathways for a
Coordinatively Unsaturated Metal Complex (II) Generated
by Photoejection of a Ligand L, Showing the Formation of
Solvated (IIIa), Agostic (IIIb), and C−H Activated (IIIc)
Intermediates, and Their Reactions with L To Regenerate
the Original Complex
INTRODUCTION
■
The activation of small molecules (e.g., N2, H2, CO2, etc.) by
transition metal centers has attracted a considerable amount of
attention since these types of reactions are often relevant to
catalytic processes such as nitrogen fixation and CO2 reduction.
In many cases, an initial coordination of the small molecule to a
coordinatively unsaturated metal complex occurs. Effective
catalyst development therefore requires a thorough under-
standing of the kinetic and thermodynamic barriers associated
with such substrate or ligand binding reactions.
UV−vis transient absorption and time-resolved infrared
(TRIR) studies have shown that, in the gas phase, in the
absence of an intramolecular agostic interaction, the vacant site
of a coordinatively unsaturated transition metal complex II
(formed by photoejection of a ligand from I in Scheme 1)
remains unoccupied. The binding of small molecules to this
vacant site is thus extremely fast, with bimolecular rate
constants typically on the order of 1010 M−1 s−1 (k1 in Scheme
1).1−4 However, in solution these unsaturated complexes are
often weakly coordinated via a σ-interaction from a solvent
molecule5−14 (II to IIIa, k2 in Scheme 1), or stabilized through
an internal agostic interaction15,16 (II to IIIb, k3 in Scheme 1)
Received: March 30, 2012
© XXXX American Chemical Society
A
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
Kex
within picoseconds of their formation, either of which may or
may not lead to a C−H activated product (e.g., IIIc in Scheme
1). Most solvents will bind to the vacant site of a metal center
via these weak σ-interactions, even apparently inert solvents
such as hydrocarbons.6,8−10,17−21 Although weak when
compared to a covalent bond, the interaction is real and
measurable, with binding energies on the order of 5−15 kcal
mol−1.1,3,4,8,15,22−24 The breaking of the M−solvent (or agostic)
bond is thus an important factor, and the binding rates of small
molecules in solution decrease by several orders of magnitude,
with typical bimolecular rate constants in the 105−108 M−1 s−1
range (k5, k6, or k7 in Scheme 1).2,8,18−21
I
I
(PCP)Rh−L + L′ HooI (PCP)Rh−L′ + L
(1)
(2)
°
ΔGrel.bind = −RT ln(Kex)
The relative equilibrium binding strengths of various small
molecule ligands, L/L′ (eqs 1 and 2) to complex 2 were
determined by Milstein and co-workers using high-pressure
NMR equilibrium methods to be in the order L = H2 > N2 >
C2H4 > CO2.68
hν
I
(PCP)Rh−L → "(PCP)Rh" + L
(3)
k
I
There are, of course, exceptions to this generalized model of
ligand binding to photogenerated coordinatively unsaturated
metal complexes. For example, some species that are ground
state triplets, such as Cp′Co(CO) (Cp′ = η5-C5H5 or η5-
"(PCP)Rh" + L → (PCP)Rh−L
(4)
In an effort to further understand the differences between
complexes 1 and 2 in terms of their reactivity with small
molecules, and to gain mechanistic and kinetic insight into
these ligand binding reactions, we have used a combination of
high-pressure NMR equilibrium studies, time-resolved UV−vis
and infrared spectroscopy (eqs 3 and 4), pressure-dependent
kinetics, and DFT calculations to determine both the
equilibrium and kinetic binding affinities of L = H2, D2, N2,
and C2H4 to the coordinatively unsaturated complexes 1 and 2.
This has resulted in the discovery of long-lived unsolvated
forms of 1 and 2, with lifetimes on the order of 50−800 ns,
depending on the identity of L and its concentration in
solution. Although the precise structure of these species
remains unknown, it is proposed that they are stabilized by
the adoption of a particular conformation of the three-
coordinate (PCP)Rh fragment that exhibits diminished
reactivity (or in the case of 2, no reactivity) with L. Other
factors such as agostic stabilization, blocking of the
coordination site by solvent, and spin state changes, are also
considered. A much more reactive form of 1 and 2 is generated
from the initial long-lived form, and the mechanism of the
subsequent reactivity with L and/or solvent molecules is
dictated by the structure of the PCP ligand and the nature of
the solvent.
C 5 ( C H 3 ) 5 ) , 2 2 , 2 5 , 2 6 a n d ( P N P ) C o ( P N P
=
(tBu2PCH2SiMe2)2N),27,28 show no evidence for solvent
coordination and exhibit low rate constants for the binding of
small molecules. Another photogenerated triplet fragment,
3Fe(CO)4, exhibits an unusually long lifetime in solution (τ =
1
12 ns) in its reaction with n-heptane to form Fe(CO)4(n-
heptane).29 There are also singlet species that show no
evidence for solvent coordination, e.g., a family of square-planar
MP4 complexes (M = Ru or Os; P4 = dmpe, depe, dfepe, dppe,
or P(CH2CH2PPh2)3), generated upon photolysis of the
dihydrides, MP4H2, which subsequently react directly with
incoming ligands, such as CO, H2, and C2H4 via second order
kinetics.30−35
For some time we have been interested in the coordination
and activation of CO2, H2, and other small molecules by late
transition metal centers with respect to the development of
effective pathways for their conversion into ultimately more
desirable species such as liquid fuels and ammonia.36−46 Late
transition metal complexes bearing PCP-type pincer ligands
have been employed in a variety of chemical transformations47
including hydrogen transfer reactions,48−56 C−X bond
activation reactions,57−60 and C−C coupling reactions61−66
due to the ease with which the PCP ligand can be modified to
control catalyst stability, reactivity, and selectivity.51,52 In
particular, the PCP-pincer rhodium dihydrogen complexes 1−
H2 and 2−H2 (L = H2 in Chart 1) have been reported to
EXPERIMENTAL SECTION
■
General. 1−N2 and 2−N2 were synthesized according to literature
procedures.68,69 All manipulations were carried out in a drybox under
dinitrogen, and solid samples were transferred to a high vacuum line
for solution preparations. Research grade N2, H2, D2, and ethylene
(from Praxair) were used without further purification. HPLC grade
hexanes and THF were purified in the published manner70 and stored
under vacuum over NaK. HPLC grade toluene and n-heptane were
distilled with NaK prior to use and stored under vacuum over NaK.
Heptane solutions for UV−vis transient absorption spectroscopy
experiments were typically prepared at concentrations of ∼5−8 × 10−5
M by adding a small amount of solid 1−N2 or 2−N2 to a high-vacuum
quartz UV−vis cuvette specially adapted with a side arm bulb and
Swagelok valve (SS-4H). The solvent was then vacuum transferred
into the side arm bulb under high-vacuum, the vapor pressure of the
solvent recorded, and then a known pressure of gas L added to the
solution to generate 1−L or 2−L. If L ≠ N2, the solution was typically
degassed again by freeze−pump−thaw degassing (to remove all traces
of N2) and then L added again to a known pressure. Concentrations of
gases in solution were calculated from literature data71−74 and the
measured partial pressure of L added (taking into account the solvent’s
vapor pressure). Throughout this Article the concentrations of
dissolved gases in solution are reported. These concentrations can
be converted back to partial gas pressures according to the following
data, which are the concentrations of dissolved gas at a partial pressure
of 1 atm at 25 °C: N2 in n-hexane (10.67 mM),72 N2 in n-heptane
(9.20 mM),72 N2 in THF (6.43 mM),73 N2 in toluene (5.37 mM),72
Chart 1. PCP-Pincer Rhodium(I) Complexes
reduce CO2 stoichiometrically at room temperature to generate
a rhodium(III) hydrido formate complex, which in the case of
1−H2 reacts further to produce CO and H2O in a reverse
water-gas shift type reaction.45,67,68 While 1−H2 and 2−H2 can
activate CO2 via insertion of CO2 into the Rh−H bond, only
the formation of 2−CO2 has been reported.68 Such a difference
in reactivity might be due to stronger σ-donor and/or π back-
bonding interactions between Rh and C (phenyl) in 1−L,
which may weaken the Rh−CO2 bond in 1−CO2.
B
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
H2 in n-heptane (4.66 mM),72 H2 in THF (3.38 mM),74 D2 in n-
heptane (4.76 mM),72 C2H4 in n-heptane (137.0 mM).71 Toluene and
THF solutions were prepared by a direct Na/Hg reduction of the RhIII
complex 1−(H)(Cl) in solution under high vacuum in specially
prepared glassware, again at concentrations of ∼5−8 × 10−5 M. The
Na/Hg amalgam was held in a separate compartment (isolated by a
frit), and the sample was gradually reduced with UV−vis spectral
monitoring. Once the reduction was complete, and after removal of
the Na/Hg compartment by flame sealing, the appropriate 1−L
complex was prepared by addition of gas L to the solution at a known
pressure. Since the reduction reaction generates NaCl as a side
product, which is not soluble in toluene, the suspended NaCl in the
toluene solutions was allowed to settle to the bottom of the vessel
before transient spectroscopic measurements were conducted. It
should be noted that solutions of 1−L and 2−L are extremely oxygen
sensitive. If there is a small leak and the solutions are exposed to air,
they immediately decompose to a pale green solution of the dioxygen
complex, 1−O2, the UV−vis spectrum of which is reported
elsewhere.75 All solutions for transient spectroscopy were prepared
with recrystallized samples and purified solvents, and no impurities
could be detected by NMR, UV−vis, and/or IR spectroscopy.
Figure 1. UV−vis absorption spectra of 1−L complexes in n-hexane,
obtained by Na/Hg reduction of 1−(H)(Cl), followed by addition of
gas L. Each complex was prepared sequentially by freeze−pump−thaw
degassing the solution followed by addition of a different gas L.
Spectra in n-heptane, toluene, and THF are very similar. The spectrum
of 1−(H)(Cl) is also shown for comparison.
NMR Equilibrium Binding Studies. Equilibrium measurements
were performed in 5 mm or 10 mm high-pressure NMR tubes
(Wilmad 522-PV-7 and 513−7PVH-7). In a typical experiment, a
solution of 1−N2 or 2−N2 in cyclohexane-d12 (3.8 × 10−4 to 6.5 ×
10−3 M) was introduced into the high-pressure NMR tubes and
degassed under high vacuum (10−5 to 10−6 Torr). Gas mixtures of
various ratios (N2:H2 = 0.17, 0.55, 0.97, 1.74, 3.20; N2:C2H4 = 1.06,
2.19) were prepared using a high pressure steel manifold at a total
pressure of 5 atm and introduced into the degassed high pressure
NMR tubes (the total pressure decrease was taken into consideration).
The ratio of [Rh]−N2 to [Rh]−H2 or [Rh]−C2H4 complexes was
spectra of a series of 1−L complexes (L = H2, N2, C2H4) and
the spectra of 2−L can be found in the SI (Figure S1). Each of
these complexes exhibits a unique and characteristic UV−vis
spectrum, apart from 1−D2 (not shown), whose spectrum is
identical to that of 1−H2. In contrast to other transition metal
complexes containing small molecules as ligands, e.g., mer,trans-
W(CO)3(PCy3)2L (Cy = cyclohexyl),15 the ligand L in 1−L
solutions cannot be removed by repeated freeze−pump−thaw
degassing cycles, despite the fact that it can easily be exchanged
by the addition of a different gas L. Band maxima and molar
absorption coefficients for the complexes under study are
presented in Table 1.
1
monitored using H NMR at 25 °C (for [Rh] = 1, monitoring Ar−
CH2−P virtual triplet resonance at ∼3.2 ppm) or 31P{1H} NMR at 25
°C (for [Rh] = 2, monitoring the 31P doublet resonance), and
equilibrium conditions were usually achieved within 1−2 h.
Transient Spectroscopy. Complete details of the instrumentation
and techniques used for nanosecond time-resolved infrared (TRIR)
spectroscopy, nanosecond (ns) and femtosecond (fs) UV−vis
transient absorption spectroscopy, and transient absorption spectros-
copy under high pressure are provided in the Supporting Information.
Computational Details. DFT calculations on 1, 2, and 1−L were
performed using the Gaussian 03 program (Revision E.01).76
Geometry optimizations were performed using the default con-
vergence criteria without any constraints. The B3LYP functional was
used together with the LANL2DZ ECP basis set77−79 for the Rh and P
atoms and the all-electron D95 V basis set80 for all other atoms in TD-
DFT calculations and “preliminary” DFT geometry optimizations.
Additional calculations to investigate possible agostic bonding were
carried out at the B3LYP and MP2 levels of theory using the MWB28
ECP basis81,82 for Rh and the 6-31G(d,p) basis83,84 for all other
elements. In order to obtain the final energies and geometries, further
DFT calculations were carried out using the B3LYP/LANL2TZ(f)
basis77,85,86 for the Rh atom and the 6-311G(d) basis87,88 for all other
atoms. Frequency calculations were employed to characterize the
stationary points as minima or transition state structures, to determine
zero-point energies (ZPEs), and for free-energy calculations.
Table 1. Band Maxima (nm) and Molar Absorption
Coefficients, ε (in parentheses, M−1 cm−1) for 1−L in n-
Hexane, and Band Maxima for 2−L Complexes in n-Heptane
a
complex
maxima (ε), nm (M−1 cm−1
)
1−(H)(Cl)
1−N2
2−N2
248 (6630), 272 (5060), 288 (5210), 422 (1680)
370 (12 100), 416 (3060), 444sh (1600), 478 (560)
334, 408, 422
1−H2
2−H2
304 (6180), 340 (8240), 394 (3550), 420 (33 400)
320, 400
1−C2H4
2−C2H4
1−THF
322 (9020), 374 (5380), 488 (1960)
292, 350, 462
b
330, 386, 486
a
ε’s for 1−L (L = N2, H2, and C2H4) were determined by assuming
b
100% conversion of 1−(H)(Cl). In THF.
The UV−vis absorption spectrum of the RhI species
generated after Na/Hg reduction of the RhIII complex 1−
(H)(Cl) in freeze−pump−thaw degassed THF is assigned to
the THF complex, 1−THF (Figure S2). This is because the RhI
species formed after two-electron reduction of 1−(H)(Cl) will
be very unstable, and is unlikely to exist as a three-coordinate
species in the presence of a coordinating solvent. The reactive
nature of this RhI species was confirmed by similar experiments
in n-heptane. While the spectrum is very sensitive to the
presence of a small amount of H2 formed by the Na/Hg
reduction, upon addition of N2 to any of the n-heptane
solutions after Na/Hg reduction, 1−N2 was always formed
RESULTS
■
UV−Vis Spectroscopy. Dissolution of 1−N2 or 2−N2 in
N2-saturated n-hexane, n-heptane, toluene, or THF results in
pale yellow solutions that exhibit similar UV−vis spectra. Since
the N2 ligand in 1−N2 or 2−N2 is easily displaced, the other 1−
L or 2−L complexes under study (L = H2, D2, and C2H4) are
readily generated by the addition of an appropriate pressure of
gas L to a freeze−pump−thaw degassed solution of 1−N2 or
2−N2, and subsequently repeating this procedure to obtain the
other complexes. Figure 1 shows the UV−vis absorption
C
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
quantitatively. To further explore the nature of the RhI species
in THF under these conditions, the Na/Hg reduction was
repeated in THF-d8 in a custom-built apparatus that allows
NMR spectra of the solution to be recorded after the reduction
reactions involving 1 are smaller than for the corresponding
reactions with 2.
Ligand Dissociation from the Photoexcited States of
1−L and 2−L. Ligand dissociation from the photoexcited
states of 1−L and 2−L was studied by time-resolved IR and
UV−vis spectroscopies. Of all the complexes under study, only
1−N2 and 2−N2 were appropriate for investigation by TRIR
spectroscopy, due to the strong νNN stretching band of the end-
on bound N2 ligand (2134 and 2118 cm−1, respectively, in
alkane solvent). The only transient feature observed after 355
nm laser flash photolysis of 1−N2 in n-hexane in the presence
of 21 mM N2 was an instantaneous bleach of the νNN band at
2134 cm−1, indicative of Rh−N2 bond cleavage (Figure S3).
The bleach band recovered completely with single exponential
kinetics as the photoproduct reacted with N2, with an observed
rate constant (kobs) of 1.3 × 106 s−1. Very similar results were
obtained for 2−N2, which exhibits a νNN band at 2118 cm−1 in
n-heptane, with the observed rate constant of recovery of 2−N2
being 1.8 × 107 s−1. The TRIR experiments thus confirmed that
photoexcitation of a solution of 1−N2 or 2−N2 results in the
photoejection of N2, which then rebinds to 1 or 2 under
pseudo-first-order conditions of excess N2 to reform 1−N2 or
2−N2. While no transient intermediates were identified from
TRIR experiments, most likely due to their lack of IR activity,
short-lived transient species were identified by laser flash
photolysis using UV−vis detection.
1
reaction (see SI for details). H NMR spectra taken between
room temperature and −90 °C were consistent with a C2
symmetric (PCP)Rh complex and showed no Rh−H peaks out
to δ = −50 ppm. 31P{1H} NMR spectra taken over the same
temperature range revealed a 103Rh−31P coupling constant
ranging from 151 to 158 Hz, consistent with a rhodium(I)
species.89 Although 13C NMR showed no strong evidence for a
bound THF molecule, this is to be expected for a weakly bound
solvent complex in which the solvent ligand is likely to be
rapidly exchanging with other solvent molecules. A comparison
with the NMR spectra of the separately prepared 1−N2, 1−H2,
1−O2, 1−CO, and 1−CH3CN complexes (see SI) confirmed
that no such species were formed in the Na/Hg reduction
reaction in THF-d8.
NMR Equilibrium Studies. In order to measure the relative
binding free energies of ligands L to 1 (eqs 1 and 2), and also
to compare with the relative binding free energies of L to the
analogous complex 2, reported by Milstein,68 we performed a
series of NMR equilibrium studies in cyclohexane-d12 (eq 5).
Upon 355 nm laser flash photolysis of 1−N2 or 2−N2 in n-
heptane in the presence of N2, the transient absorption (TA)
spectra shown in Figure 2 were recorded. An instantaneous
formation of a strong transient absorption band in the visible
After pressurizing a degassed solution of 1−N2 with various
mixtures of N2/H2 or N2/C2H4 at a total pressure of 5 atm, and
monitoring the approach to equilibrium by NMR (see
Experimental Section), the equilibrium constant, Kex, for eq 5
was calculated from eq 6. This allowed the free energy change
of the reaction to be calculated, which is equivalent to the
difference in the free energies of binding of the incoming ligand
L and the N2 ligand to 1 (eq 2). The results are summarized in
Table 2.
[Rh−L][N2]
[Rh−N2][L]
Kex
=
(6)
Table 2. Equilibrium Parameters Determined by NMR
Spectroscopy in Cyclohexane-d12 at 25 °C for Equation 5
PCP complex incoming ligand, L
Kex (298 K)
ΔG°298, kcal mol−1
1−N2
1−N2
2−N2
2−N2
H2
3.33 ( 0.18)
0.16 ( 0.01)
−0.71 ( 0.03)
+1.08 ( 0.01)
C2H4
H2
a
a
a
a
8.08 ( 0.48)
0.07 ( 0.001)
−1.24 ( 0.04)
a
a
C2H4
+1.57 ( 0.01)
These data were reported by Milstein and co-workers.68
a
Our experimental method was first validated by repeating
Milstein’s reaction of 2−N2 with H2 under H2/N2. The ΔG°298
we obtained for that reaction (−1.12 ( 0.06) kcal mol−1) was
almost identical to that obtained by Milstein (−1.24 ( 0.04)
kcal mol−1).68 For complexes 1−L, the trend in stability is the
same as that previously observed for complexes 2−L. Thus,
formation of the 1−H2 complex is slightly more favorable
(−0.71 kcal mol−1) than formation of the 1−N2 complex,
whereas C2H4 binding is less favorable than N2 binding (+1.08
kcal mol−1). However, the magnitudes of ΔG°298 for the
Figure 2. UV−vis TA spectra recorded at several time intervals (Δt)
after 355 nm laser flash photolysis of (a) 1−N2 in n-heptane ([N2] =
8.8 mM), and (b) 2−N2 in n-heptane ([N2] = 8.8 mM). All data at 25
°C.
D
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
(between ca. 400 and 550 nm) and a much broader and weaker
band in the NIR region (around 800 nm) were observed,
together with an intense absorption in the UV region (<320
nm) and a bleach of the parent complex absorption at 370 nm
(1−N2) or 340 nm (2−N2). The TA spectra for the 2−N2
complex were qualitatively similar to those for the 1−N2
complex. The visible and NIR transient absorption bands
decayed together with single exponential kinetics, and the
bleach recovered at the same rate. Kinetic traces recorded at the
ground state absorption maxima revealed the complete
recovery of 1−N2 and 2−N2, and UV−vis absorption spectra
recorded before and after the experiment were identical, thus
confirming that the photoreaction is fully reversible under these
conditions (see Figure S4). Even when the experiment was
performed under 400 Torr argon, in the absence of any
additional N2, the recovery of the 1−N2 transient bleach was
100% complete within 30 ms of excitation (see Figure S4).
The transient absorption spectra measured after 355 nm flash
photolysis of 1−L and 2−L in n-heptane (L = H2 and C2H4)
are shown in Figures S5−S8 and are essentially identical to
those measured for the nitrogen complexes. The transient
absorption spectra of 1−N2 in toluene and THF are shown in
Figures S9−S10. While the early time spectra in THF solution
are similar to those in other solvents, the spectra recorded at
longer time delays (ca. > 1 μs) show the appearance of a new
band around 395 nm (i.e., the formation of 1−THF, see the
Discussion section below) that grows concomitantly with the
decay of the 470 nm band, with an observed rate constant of
1.7 × 106 s−1 in the presence of 5.4 mM N2. The decay of the
395 nm band has the same rate as the recovery of the ground
state absorption at 370 nm. The photolysis of 1−L in THF
under conditions of excess L was found to be reversible on the
experimental time scale and was confirmed by comparing UV−
vis spectra of the solution before and after transient
experiments.
In the case of 1−L a plot of kobs versus [L] yielded a straight
line with a slope, equal to the second-order rate constant for
reaction of the photogenerated “(PCP)Rh” fragment with L
(k470‑slope), and an intercept (k470‑int) (Figure 3).
Figure 3. Plots of observed rate of decay (kobs) versus concentration of
L ([L]) for the 470 nm transient absorption band generated after 355
nm laser flash photolysis of 1−L (L = N2, H2, D2 or C2H4) in n-
heptane (black), toluene (red) and THF (blue) at 25 °C. C2H4 data
are shown inset due to the much higher solubility of C2H4 than the
■
▲
(n-heptane, L = H2), (n-
●
other gases.
(n-heptane, L = N2),
heptane, L = D2), ⬟ (n-heptane, L = C2H4), red triangle (toluene, L =
N2), blue diamond (THF, L = N2), blue hexagon (THF, L = H2).
The rate constants derived from the slope and intercept of
the decay of the 470 nm band are summarized in Table 3 for
Table 3. Rate Constants Derived from the Slopes and
a
Kinetics of the Formation of Transient Species:
Ultrafast Transient Absorption Spectroscopy. In an effort
to identify the transient intermediate that absorbs at 470 and
800 nm, we performed a transient absorption experiment with
1−N2 in n-heptane in the presence of ∼9 mM N2 on the
femtosecond time scale with an apparatus that has an
instrument response time of ∼400 fs. Since it has previously
been shown that solvent molecules can take as long as a few
picoseconds to bind to photogenerated coordinatively unsatu-
rated metal centers,14 we should observe the initial formation of
a “naked” (PCP)Rh fragment followed by its solvation by a
heptane molecule, if such a solvated species forms during the
reaction. Interestingly, we found that the 470 and 800 nm
transient bands are formed instantaneously (within the
instrument response time), together with a much weaker,
broad absorption band centered at 680 nm (Figure S12−S14).
The 680 nm band then rapidly decays to 15% of its initial
intensity with a lifetime of τdecay = 1.04 ps (Figure S14), while
the 470 and 800 nm bands remain stable for the 3 ns duration
of the ultrafast experiment, with no other transient absorption
features being observed. These data suggest that the 470 and
800 nm transient bands may be due to a long-lived
coordinatively unsaturated (PCP)RhI fragment 1 rather than
a solvent complex 1−solvent. The 680 nm band may be due to
a vibrationally “hot” state that cools on the 1 ps time scale.
Kinetics of Ligand Binding. After photoexcitation of 1−L
or 2−L, the observed rate of decay of the 470 nm transient
band was monitored as a function of dissolved L concentration.
Intercepts of Plots of the Observed Rate of Decay
L
solvent
TA band (nm) slope (M−1 s−1
)
intercept (s−1
)
N2
n-heptane
n-heptane
n-heptane
n-heptane
toluene
THF
470
470
470
470
470
470
470
395
395
4.0 × 106
5.5 × 108
2.9 × 108
6.7 × 105
9.7 × 106
1.1 × 107
3.5 × 108
4.7 × 106
1.1 × 107
1.3 × 106
1.3 × 106
1.3 × 106
1.3 × 106
1.5 × 106
1.6 × 106
1.6 × 106
0
H2
D2
C2H4
N2
N2
H2
THF
N2
THF
H2
THF
0
a
kobs versus [L] for the 470 and 395 nm transient absorption bands
that are generated after 355 nm laser flash photolysis of 1−L (L = N2,
H2, D2, and C2H4) in n-heptane, toluene, and THF at 25 °C. All data
have a 10% instrumental error.
different incoming L and solvents. The second-order rate
constant derived from the slope is dependent on both the
incoming ligand and solvent, while the intercept depends only
weakly on the solvent used. The rate constant derived from the
slope indicates a normal KIE of 1.9 for the H2/D2 binding
process.90,91 The plots for the decay of the 395 nm transient
band observed in THF as a function of L (Figure 4) had zero
intercept, and the slopes are reported in Table 3.
The observed rate of decay of the 470 nm transient band
after photoexcitation of 2−L is different from that of 1−L. The
decay of the transient absorption bands occurs on a shorter
E
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
were likely observing the same limiting value of kobs with L =
C2H4 that we observed for L = H2 and N2 at [L] ≥ 10 and 20
mM, respectively. Double-reciprocal plots of 1/kobs versus 1/
[L] for L = N2 and H2 were linear (Figure S11), indicating
saturation kinetics. A linear fit of the reciprocal plots of 1/kobs
versus 1/[L] resulted in 1.5 × 10−10 M s as a slope and 4.0 ×
10−8 s as an intercept for 2−N2, and 7.5 × 10−11 M s as a slope
and 4.0 × 10−8 s as an intercept for 2−H2.
The observation of nonlinear saturation kinetics and linear
plots of 1/kobs versus 1/[L] (Figures 5 and S11, respectively)
for 2−L suggests a two-step scheme for the reaction of the
photofragment generated in eq 7 with L to regenerate 2−L,
where the first step is reversible (eqs 8 and 9).
2−L ⎯h→⎯ν 2′
(7)
−L
k1
2′ HooI 2
Figure 4. Plots of observed rate of decay (kobs) versus concentration of
L ([L]) for the 395 nm transient absorption band that is generated
after 355 nm laser flash photolysis of 1−L (L = N2 or H2) in THF at
k−1
(8)
(9)
k2
2 + L → 2−L
■
●
25 °C. (L = N2), (L = H2).
Applying the steady-state approximation to species 2, it can
be shown that a plot of 1/kobs vs 1/[L] should be linear, with an
intercept equal to 1/k1 and a slope equal to k−1/k1k2 (Figure
S11). In order to extract the k−1 rate term from the slope, an
estimation of k2 must be made. In this case we estimate that k2
is close or equal to the diffusion-controlled rate constant in n-
heptane (k2 = kdiff = 1.7 × 1010 M−1 s−1 for H2 and 1.2 × 1010
M−1 s−1 for N2).92 This assumption is supported by fitting the
initial slopes of the kobs versus [L] plots in Figure 5, which
reveals extremely high initial rate constants for the reaction of
N2 and H2 with 2 (4.5 × 109 M−1 s−1 for N2 and 8.3 × 109 M−1
s−1 for H2).93 A summary of the kinetic analysis for N2 and H2
binding to 2 is shown in Table 4.
time scale than for 1−L (ca. 5 times faster for L = N2 and H2,
and ca. 14 times faster for L = C2H4). The observed rate
constant of decay of the high-energy transient absorption band
was plotted as a function of [L] (Figure 5). For L = N2 and H2
Kinetics of the Ligand Binding at High Pressures:
Activation Volume Studies. Measuring rate constants as a
function of externally applied pressure (up to 2000 bar) can
assist the formulation of a mechanism by allowing the volume
of activation, ΔV⧧, for a process to be determined (eq 10).94
d ln k
dP
−ΔV‡
RT
⎛
⎜
⎞
⎟
T
=
⎝
⎠
(10)
In general, for ligand substitution processes a positive ΔV⧧
indicates a dissociative transition state, and a negative ΔV⧧
implies an associative step, whereas a ΔV⧧ close to zero
indicates an interchange mechanism, which has little or no
pressure dependence. We have therefore monitored the rate of
decay of the 470 nm transient absorption band as a function of
external pressure for H2 binding to 1 in n-heptane at 25 °C.
A series of pressure-dependent plots of kobs versus [H2] for
the decay of the 470 nm transient absorption band after
photoejection of H2 from 1−H2 in n-heptane (Figure S15)
were constructed by transposing the data from several kobs
versus pressure plots at different H2 concentrations. The slopes
Figure 5. Plots of kobs vs [L] for the decay of the visible transient
absorption band generated after photoexcitation of 2−L, L = N2
(black) and H2 (red) in n-heptane at 25 °C. C2H4 data are shown in
the inset.
these plots are nonlinear, displaying saturation kinetics
behavior, with kobs increasing with [L], and then reaching a
limiting value at [N2] = 20 mM and [H2] = 10 mM. It should
be noted that the intercepts of these plots are essentially zero.
Over the range of [C2H4] measured, the plot is approximately
linear. However, it is difficult to operate below ca. 10 mM of
C2H4 due to its high solubility in n-heptane, and therefore we
a
Table 4. Kinetic Parameters for the Decay of the 430-nm Band Following Photoexcitation of 2−L in n-Heptane
L
slope (M s)
intercept (s)
k1 (s‑1)
k‑1 (s‑1)
Keq (k1/k‑1)
N2
H2
1.5 × 10−10
7.5 × 10−11
4.0 × 10−8
4.0 × 10−8
2.5 × 107
2.5 × 107
4.5 × 107
3.2 × 107
0.6 0.1
0.8 0.1
a
Obtained from linear plots of 1/kobs vs 1/[L] (k2 ≡ kdiff = 1.7 × 1010 M−1 s−1 and 1.2 × 1010 M−1 s−1 for H2 and N2, respectively). The initial error
of 10% for both the slope and intercept will propagate to 17% in Keq due to the calculations involved.
F
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
and intercepts from the plots in Figure S15 were then used to
construct ln(kslope) and ln(kintercept) versus pressure plots
(Figure 6). As can be seen in Figure 6, the intercept rate
for N2 and C2H4 binding were not undertaken since the
changes in observed rate constant, kobs, as a function of [N2]
and [C2H4] are much smaller than for H2, making the high-
pressure experiments less informative.
Theoretical Calculations. The gas-phase calculated 1−N2
complex was found to share similar geometrical parameters
with those in analogous (PCP)Rh complexes (Figure S16),45,69
suggesting that the structure of the common (PCP)Rh
framework is not sensitive to ligands such as N2, H2, and
C2H4 in the ground state. Although the four tBu groups provide
a certain amount of steric bulk, it is clear that the Rh
coordination cavity is sufficiently open that ligands at least as
large as C2H4 can bind with ease (Figure S16). The square
planar Rh center is also open to attack from above and below
the (PCP)Rh coordination plane.95
We have also calculated the structures of the 3-coordinate
14-electron “naked” (PCP)Rh species, 1 (Figure 7a), and the 4-
coordinate n-hexane and THF solvated complexes, 1−hexane
and 1−THF. For 1, we were unable to locate a structure with
strong internal agostic interactions from the four tert-butyl
groups, even after repeating the calculation at the higher
MP2(FC) level of theory, with the closest Rh···H interactions
being 3.095 Å (Figure 7a). When we performed a DFT
calculation on the saturated version of the complex, 2, a
significant agostic interaction was located between the Rh
center and the C−H bond of the central C atom in the PCP
ligand backbone (Figure 7b, Rh−H 2.545 Å, Rh−C 2.068 Å). A
similar agostic interaction was previously reported by Milstein
in the 2−CO2 complex.68
In order to further probe the nature of the intermediate
species observed by transient absorption spectroscopy, we
performed gas-phase TD-DFT calculations on three-coordinate
1 and four-coordinate 1−L complexes (L = n-hexane, THF, N2,
H2, and C2H4) for comparison with the experimentally
observed UV−vis and TA spectra. Although the calculated
spectra are slightly blue-shifted, good agreement between the
spectral features of the calculated and experimentally acquired
UV−vis spectra of 1−N2, 1−H2, and 1−C2H4 was observed
Figure 6. Plots of ln(kslope) and ln(kintercept) versus externally applied
pressure, where kslope and kintercept are the rate constants obtained from
the slopes and intercepts of the graphs shown in Figure S15.
constant essentially has a zero pressure dependence, implying
that the process associated with the intercept in our kinetic
plots could have an interchange nature. However, the rate
constant from the slope exhibits significant pressure depend-
ence. The curvature of this plot is caused by the compressibility
of the solvent, and the data were fitted to a polynomial
expression to account for this.94 Extracting the linear slope
from the fit revealed an activation volume, ΔV⧧ of −31 cm3
mol−1, which is strongly negative and indicative of an
associative mechanism for the binding of H2 (and presumably
the other incoming ligands under study) to the 470 nm
absorbing transient species. Similar investigations of the
pressure dependence of the slope and intercept rate constants
Figure 7. (a) MP2(FC)-calculated structure of 1, and (b) DFT-calculated structure of agostically stabilized 2.
G
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
(see Figures S17−S19). Assignments of the calculated UV−vis
transitions for 1−N2 are provided in the SI (Figure S20
together with a list of assignments and discussion immediately
following that figure). The computed UV−vis spectra of 1, 1−
hexane, and O-coordinated 1−THF are shown in Figure 8.
pointing directly at the incoming ligand along the x-axis, the
situation is more complicated. Indeed, the donation of the lone
pair on N2 in an end-on (η1) attack, or by H2 in a sideways (η2)
attack almost perpendicular to the P−Rh−P plane and parallel
to the z-axis, stabilizes the bonding σ orbital to HOMO − 12
(Figures S21 and S22). The corresponding anitbonding orbital
(HOMO − 7) is also doubly occupied. In the case of N2, the
pair of electrons in the dxy orbital is donated into the vacant in-
plane N2 πy* orbital (HOMO − 3) and the pair in the dxz
orbital is donated into the out-of-plane N2 πz* orbital, forming
π bonds between the Rh and near N atom. The N−N bond in
these two orbitals is π-antibonding in character (Figure S21). In
the case of H2, the pair of electrons in the dyz orbital (a π orbital
with nodes in the xy and xz planes) is donated (HOMO − 5)
to the unoccupied σ* orbital between two H atoms (with a
node in the xy plane) to form symmetry-breaking “wrap-
around” σ-like bonds between the Rh atom and the two H
atoms (in which the xz nodal plane of the orbital rotates into
the xy plane in going from the Rh center to the two H atoms).
Participation of oppositely phased orbitals on the two P atoms
is also involved. HOMO − 1 also forms σ bonds between Rh
and the two H atoms through the interaction of the Rh dxz and
H2 σ* orbitals, while decreasing the strength of the σ bond
between the two H atoms (Figure S22). In both cases, the
2
HOMO is the lone pair in the dz orbital. The bonding in the
ethylene complex is similar to that in the H2 complex except it
involves the π and π* orbitals between the two C atoms of the
adduct (that lie roughly parallel to the z axis but slightly rotated
2
2
about the y axis) interacting with the Rh dx −y and dxz orbitals
(Figure S23).
Figure 8. Gas-phase TD-DFT calculated UV−vis spectra of O-
coordinated 1−THF, 1−hexane, and 1. Vertical lines show the
transitions, and the curves were generated by a multi-Gaussian
function with bandwidths of 0.25 eV.
DISCUSSION
■
Thermodynamics of Small Molecule and Solvent
Binding. The relative binding affinities of L = H2, N2, and
C2H4 to 1 were measured by high-pressure equilibrium NMR
methods. We found that H2 binding to 1 is more favorable than
N2 binding (ΔG°298 = −0.71 kcal mol−1 for L = H2 in eq 5),
while C2H4 binding is less favorable than dinitrogen binding
(ΔG°298 = +1.08 kcal mol−1), Table 2. This may be partially
due to the different sizes of the incoming ligands, although
differences in the electronic bonding properties of the ligands
will also play a role. Milstein and co-workers found a similar
trend in binding free energies for 2.68 These trends differ from
those of the related mer,trans-W(CO)3(PCy3)2(N2) system, in
which the binding of H2 and C2H4 are both less favorable than
N2 binding by ΔG°298 = +0.2 and +2.3 kcal mol−1,
respectively.15 However, this is not surprising given that the
tungsten complex fundamentally differs from the current
rhodium system in that it possesses an octahedral configuration
of ligands and thus a very different bonding environment and
molecular orbital configuration.
Kinetics of Small Molecule Binding and Mechanistic
Interpretation. Photoexcitation of 1−L or 2−L leads to
dissociation of L, yielding the coordinatively unsaturated
species 1 or 2 and a free ligand L. In the TA spectra of 1−L
and 2−L in n-heptane and toluene (1−L only), the transient
intermediate observed immediately after photoejection of L
possesses bands at 470 and 800 nm for 1, and at 300−500 and
750 nm for 2. Despite the relatively long observed lifetime of
this species (τ = 50−800 ns, depending on which gas, L, was
used and its concentration), there is convincing evidence from
our experiments to suggest that it does not possess any
significant Rh−solvent interaction, as follows. (i) Apart from a
The hexane complex is predicted to have a weak absorption
band at 660 nm, with much more intense overlapping bands at
shorter wavelengths (below 400 nm), while the THF complex
is calculated to exhibit a weak band at 509 nm, again with more
intense overlapping bands below 400 nm. The calculated 1−
THF spectrum is similar to the UV−vis spectrum of the RhI
species formed after Na/Hg reduction of 1−(H)(Cl) in THF
under vacuum (see Figure S2). In contrast, the coordinatively
unsaturated, 3-coordinate (PCP)Rh fragment is predicted to
have a reasonably intense band at 445 nm, a much broader,
weak absorption at 813 nm, and more intense overlapping
bands below 400 nm. It is noteworthy that no bands were
predicted for the hexane or THF complexes at wavelengths
longer than 660 nm. Despite the fact that they are slightly
shifted, the 445 and 813 nm calculated bands of 3-coordinate
(PCP)Rh are remarkably similar to the 470 and 800 nm bands
that were observed by transient absorption spectroscopy
immediately upon photoejection of L from the 1−L complexes.
The bonding in the (PCP)RhI complexes is more
complicated than might be expected. The d8 Rh(I) center in
pseudo-square-planar complexes (with the z-axis perpendicular
to the P−Rh−P plane) has pairs of electrons in the lowest
2
(degenerate) dyz and dxz (dπ) orbitals, another pair in the dz
orbital, and still another pair in the dxy orbital, with the highest
2
2
lying dx −y orbital unoccupied. While one might imagine a
ligand L on the x-axis to donate a lone pair of electrons in a σ
2
2
orbital to the unoccupied dx −y orbital, which has a lobe
H
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
Scheme 2. Proposed Mechanism for the Binding of L to the Photofragment Generated upon Photoejection of L from 1−L (L =
a
N2, H2, D2, or C2H4) or 2−L (L = N2, H2 or C2H4) in n-Heptane, Toluene, and THF
a
The PCP ligand backbone is shown in gray/black for 1 and in black only for 2. The values of k1−k5 and the predominant reaction pathways depend
on the nature of the PCP ligand, solvent, and L, as shown in the scheme and in Tables 3 and 4. kdiff = diffusion-controlled rate constant.
slight blue shifting of the bands, our TD-DFT calculated UV−
vis spectrum of three-coordinate 1 (Figure 8) is a good match
to the experimentally observed femtosecond and nanosecond
TA spectra of 1. In contrast, the calculated spectra of the 1−
hexane and 1−THF solvent complexes are a poor match,
particularly due to the complete absence of any calculated
bands near 800 nm. (ii) The position of the 470 nm band
observed in the ns-TA spectra of 1 was independent of the
nature of the solvent. If this band were due to a solvent
complex, we would expect the band to shift, especially in the
more coordinating solvent, THF (cf. Figures 2 and S10, and
Table 1; 1−THF at 386, 486 nm vs 1 at 470, 800 nm TA
bands). Shifts of >100 nm for the visible absorption bands of
coordinatively unsaturated transition metal complexes that are
weakly bound to σ-donor ligands of different donating ability
have previously been observed in cryogenic matrices96 and in
room temperature solutions.97 Our TD-DFT calculations also
predicted a +151 nm shift of the visible band from 509 nm for
1−THF to 660 nm for 1−hexane (Figure 8), in which the
hexane binding enthalpy is computed to be 6.8 kcal mol−1
weaker than that of THF. (iii) The second-order rate constants
for N2 and H2 binding derived from the slopes of the kobs vs [L]
plots for the decay of the 470 nm band of 1 are much greater
(up to a factor of 625) than those for analogous reactions of N2
and H2 with solvated species such as CpMn(CO)2(n-
heptane)98 and W(CO)5(n-heptane),99 which require a
bound solvent molecule to be replaced by N2 or H2. Similarly,
the binding of N2 and H2 to 1 is 13 and 183 times faster,
respectively, than for binding to mer,trans-W(CO)3(PCy3)2,15
which possesses a strong internal agostic interaction that must
be broken for binding to occur. (iv) The large negative value of
ΔV⧧ (−31 cm3 mol−1) for the second-order process associated
with the decay of the 470 nm transient band for H2 binding to
1 in n-heptane indicates a strongly associative transition state
for the addition of L, which would be expected for binding to a
nonsolvated species. During this process, H2 almost completely
disappears from the bulk solution as it binds to the vacant
coordination site on 1, causing a large volume collapse on going
to the transition state. It should be noted however, that binding
to an essentially square-planar (PCP)Rh(solvent) species could
also be associative, but typically with a less negative value of
ΔV⧧ ∼ −10 cm3 mol−1.100(v) Femtosecond TA spectroscopy
in n-heptane showed that the 470 and 800 nm absorption
bands of 1 are formed within the ∼400 fs response time of the
instrument. If these bands were due to a solvent complex, their
formation may be expected to take longer (e.g., a few
picoseconds).14
The preceding arguments suggest that the transient species
observed immediately after photoejection of L from 1−L, and
presumably also from 2−L, does not possess a significant Rh−
solvent bond, and that if any Rh···solvent interaction exists it
must be extremely weak. Certainly, the very strong Rh−C bond
trans to the vacant coordination site in 1 and 2 will serve to
weaken any interaction with the solvent in this position.
Despite the absence of apparent interaction with solvent, the
kinetic evolution of 1 and 2 appears to be complex. For
example, the conversion of 2 to 2−L proceeds via a precursor,
2′, which exists in equilibrium with 2 (see eqs 8 and 9). The
results of a kinetic analysis of N2 and H2 binding to 2 (Table 4)
indicate that, within experimental error, the equilibrium
constant between 2′ and 2 is independent of the nature of L.
The difference in observed kinetic behavior for the binding of
N2 and H2 to 2 is thus solely due to the different binding rate
constants, k2 for N2 and H2. Therefore, we propose the
following general reaction scheme to explain the reactivity of 2
with H2 and N2 ligands in n-heptane (Scheme 2, except for the
k4 and k5 pathways).101
In the TA experiments, the less-reactive form (LRF), 2′, is
observed immediately upon photoejection of L from 2−L, with
absorption bands at 300−550 and 750 nm. This is in
equilibrium with another species, the more-reactive form
(MRF), 2, which reacts with the incoming ligand, L, to
regenerate 2−L with a diffusion-controlled rate constant. We
assign the LRF and MRF as different conformers of three-
coordinate 2, exhibiting different reactivity toward L. Although
we calculated an agostic structure for 2 (Figure 7b), and a
similar agostic interaction with the central C−H bond of the
PCP ligand has previously been reported by Milstein and co-
workers in the CO2 complex, 2−CO2,68 we do not have any
direct evidence that the LRF is an agostically stabilized species
and therefore cannot make a definitive conclusion about its
precise structural form. The equilibrium between the LRF and
MRF slightly favors the LRF, which is consistent with the LRF
being more stable and its lack of reactivity toward incoming
I
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
ligands. However, once it is converted into the MRF, which
must have a more open molecular configuration, it is subject to
attack by incoming ligands at a rate constant, k2 that is
diffusion-controlled. Kinetic simulations for both the N2 and H2
binding using the IBM Chemical Kinetics Simulator,102 in
which k2 was set to the diffusion-controlled rate constants
stated in the caption to Table 4, and k1 and k−1 were set to the
rate constants shown in Table 4, provide an excellent fit to the
experimental data (see Figure S24). Attempts to set k2 to lower
than a diffusion-controlled rate constant did not provide a
satisfactory fit to the data.
In contrast to the binding of L to 2, nonlinear saturation
kinetics were not observed (Figure 3) for the decay of the 470
nm band of 1′ (which corresponds to the LRF of 1 in Scheme
2), even at very low N2 concentrations (down to 0.20 mM).103
This implies that for 1′, the first step involving conversion of 1′
to 1 (LRF → MRF), is irreversible, or an equilibrium that is
heavily shifted toward the MRF. Therefore, our proposed
mechanism for the binding of L to 1 is similar to that for
In addition to the L-independent pathway described above,
the LRF, 1′, reacts directly with L with second-order rate
constants corresponding to the slopes in Figure 3 (see also eq
11). For this pathway, a large negative activation volume was
found (L = H2) indicating an associative transition state. This
pathway is not significant in the binding of L to 2, presumably
due to the more flexible nature of the saturated PCP ligand
framework allowing 2′ to adopt a more stable conformation
that is less reactive compared to 1′. The rate constants for the
binding of L to 1′ vary by almost 3 orders of magnitude,
depending on the nature of L and the solvent, increasing in the
order L = C2H4 < N2 < D2 < H2 (Table 3). Such a large
variation in rate constant suggests that steric hindrance at the
Rh center influences the binding kinetics, although differences
in the electronic bonding properties of the ligands, together
with solvent viscosity, dielectric constant, and differences in the
solvation energies of the small ligands, L, will also likely play a
role. We have performed kinetic simulations based on the
proposed mechanism, and these provide an excellent fit to the
experimental data (Figure S25). We note that rate constants
ranging from 108 to 1010 M−1 s−1 for the reaction of the MRF,
1, with N2 allowed us to accurately simulate the experimental
data.
binding to 2, but irreversible in the first step (Scheme 2, k−1
≈
0). Again, since we do not have direct evidence for the
identities of the LRF and MRF, we conclude that they are
different conformers of 1 that exhibit different reactivity toward
incoming ligands, L, without speculating further about their
specific structures. Since the LRF → MRF reaction is
irreversible, this implies that 1′ is a higher-energy, metastable
species that must overcome an energy barrier to generate the
more reactive 1. Such a high-energy configuration of 1′ may be
accessible due to the excess vibrational energy left over after
photocleavage of the 1−L bond. Our DFT and MP2(FC)
calculations failed to locate any significant agostic interactions
for 1, so it is unlikely that agostic stabilization is involved.
However, there are other possibilities for the identity of 1′ (and
2′) including (i) a species in which a solvent molecule is
partially blocking the coordination cavity, thus hindering access
by L, (ii) a different spin state (e.g., a triplet) that is less reactive
toward L, and (iii) a species resulting from reaction with a
weakly binding impurity, although this is unlikely under the
described experimental conditions (see below).
k3
(11)
1′ + L → 1−L
In the case of strongly coordinating solvents, such as THF, it
was found that the MRF, 1, will also react with a solvent
molecule to form a solvent-bound species, 1−Solv (Scheme 2).
In the TA spectra of 1−L in THF, a transient band at 395 nm
grows in from the 470/800 nm bands (see inset in Figure S10).
This is very similar to the 386 nm band of 1−THF prepared by
Na/Hg reduction of 1−(H)(Cl), see Figure S2. The intercept
of the plot of kobs versus [L] for the decay of the 470 nm band
(1.6 × 106 s−1) still represents the observed rate constant for
the rearrangement of the LRF, 1′, to the MRF, 1. The direct
reaction of L with 1′ is also still operative, with a rate constant
of k470‑slope (see Table 3). While the direct measurement of the
rate of reaction between 1 and THF was not possible due to the
LRF → MRF transformation being the rate-determining step,
this rate can be estimated from kinetic simulations based on the
proposed mechanism and experimental data. Kinetic simu-
lations for N2 binding to 1 in THF according to the proposed
mechanism provide an excellent fit to the experimental data,
reproducing the kobs versus [L] plots (Figures S26−27) and the
experimental kinetic decay traces. In these simulations, a lower
limit for the second-order rate constant for the reaction of 1
with THF was found to be ∼107 M−1 s−1. This rate constant is
significantly lower than the rate constant for the reaction
between 1 and gas molecules, which was estimated to be close
to the diffusion-controlled limit. This is consistent with the
significant difference in the size of the incoming solvent
molecule compared to a gas molecule (N2, H2, etc). After the
formation of the solvent bound species 1−THF, it slowly reacts
with L to yield 1−L and a free solvent molecule with a rate
constant of k395 (see Table 3).
Arguably, the intercepts of kobs versus [L] plots may contain
contributions from one or more competing side reactions, such
as reaction with impurities. However, we note that the
magnitudes of the intercepts in Figure 3 are significant (on
the order of 106 s−1) when compared to similar experiments
previously performed in our laboratory in the same solvents
purified by the same techniques (in which intercepts on the
order of 102 to 103 s−1 were obtained).15 Furthermore, we
reproducibly observed very similar intercepts (∼106 s−1) in the
three different solvents investigated (Figure 3), using different
batches of each solvent and different samples of 1−L, and we
always observed complete photoreversibiltiy of the solutions,
based on UV−vis spectra recorded before and after laser
excitation (see Figure S4). Therefore, we believe that reaction
with impurities is not an important factor in the current
experiments. The intercepts in Figure 3 show a very weak trend
of solvent dependence, while being independent of L in a given
solvent. It is therefore likely that these intercepts represent the
observed rate constant for the transformation of the LRF, 1′
into the MRF, 1 (Scheme 2). This assignment agrees with the
zero activation volume that we found for the k470‑int intercept
rate constant for H2 binding to 1 in n-heptane, since the
transformation is not expected to involve significant volume
changes.
The overall proposed mechanism for the binding of L (L =
N2, H2, D2, and C2H4) to the photofragment generated upon
photoejection of L from 1−L and 2−L in n-heptane, toluene,
and THF is shown in Scheme 2. The values of the rate
constants, k1−k5, and the predominant reaction pathways
depend on the nature of the complex (1−L or 2−L), and on
the identity of the solvent and ligand, L as discussed above (see
J
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
inset in Scheme 2, and Tables 3 and 4). In both cases, the two
unsolvated intermediate species that are observed, 1′ (2′) and 1
(2), are assumed to be different conformers that exhibit
different reactivity toward L. While the identities of these
intermediate species cannot be conclusively determined at this
time, the proposed mechanism is the only one of many that
were considered that fits the experimentally observed kinetic
data well. More detailed experiments would be required in
order to make a more definitive assignment of the
intermediates.
AUTHOR INFORMATION
Corresponding Author
*E-mail: dcgrills@bnl.gov (D.C.G.), dmitriyp@bnl.gov
(D.E.P.), fujita@bnl.gov (E.F.).
■
Present Addresses
§General Electric Global Research, One Research Circle,
Niskayuna, New York 12309, United States.
∥Division of Chemical and Life Sciences and Engineering and
KAUST Catalysis Center, King Abdullah University of Science
and Technology (KAUST), Thuwal, 23955−6900, Saudi
Arabia.
CONCLUSION
Notes
■
The authors declare no competing financial interest.
In summary, we have conducted equilibrium and kinetic studies
for the binding of N2, H2, D2, and C2H4 to the (PCP)RhI
complexes, 1 and 2, by NMR spectroscopy and transient
spectroscopic techniques, including TRIR and UV−vis
transient absorption under both ambient and high-pressure
conditions. The equilibrium studies revealed that the relative
free energies of binding increase in the order C2H4 < N2 < H2.
On the basis of our kinetic measurements and kinetic modeling,
we have proposed mechanistic pathways for the binding of L to
the intermediates generated upon photoejection of L from 1−L
and 2−L. In both cases, the initial species formed after
photoejection of L is unsolvated 1′ or 2′, which is the so-called
less-reactive form. 2′ is in equilibrium with a more-reactive
form, 2, which reacts with L to regenerate 2−L at diffusion-
controlled rates. These different forms are assumed to be
different conformers of the (PCP)Rh fragment that exhibit
different reactivity toward L. For 1, we propose a similar
mechanism but with the transformation of 1′ to 1 proceeding
irreversibly. However, a parallel reaction pathway is also in
operation for 1′, involving its direct reaction with L with a
second-order rate constant that is strongly influenced by the
size of the incoming ligand, L, varying by almost 3 orders of
magnitude. Solvent binding to 1 could only be observed in
THF by the formation of a second transient band at 395 nm.
The large variation in binding rate constants, and the fact that
long-lived unsolvated species (τ = 50−800 ns, depending on L
and its concentration in solution) are the primary transients
observed in the binding of L to 1 and 2, suggests that steric
hindrance at the Rh center influences the binding kinetics in
this family of (PCP)Rh complexes. The nature of the solvent
also plays a significant role in determining the mechanism of
binding, as does the structure of the PCP ligand, and this may
have implications for the control of mechanisms of small
molecule activation with these and related complexes. Future
investigations will focus on the use of different solvents of
varying donating ability and steric bulk to more fully determine
the effect of solvent on reactivity. A more detailed investigation
of 2−L, including pressure dependence studies, will also be
conducted in different solvents.
ACKNOWLEDGMENTS
■
We thank Dr. Norman Sutin for fruitful discussions, Dr.
Andrew Cook for his help with fs transient measurements, and
Dr. Yukiko Hayashi for her preliminary work on this project.
K.-W.H. is grateful for a Goldhaber Distinguished Fellowship
awarded during his stay at BNL as a postdoctoral research
associate. This research was carried out at Brookhaven National
Laboratory under Contract DE-AC02-98CH10886 with the
U.S. Department of Energy and supported by its Division of
Chemical Sciences, Geosciences & Biosciences, Office of Basic
Energy Sciences. R.v.E. kindly acknowledges financial support
from the Deutsche Forschungsgemeinschaft within SFB 583 on
Redox-active Metal Complexes.
REFERENCES
■
(1) Brown, C. E.; Ishikawa, Y.; Hackett, P. A.; Rayner, D. M. J. Am.
Chem. Soc. 1990, 112, 2530.
(2) Grills, D. C.; Huang, K.-W.; Muckerman, J. T.; Fujita, E. Coord.
Chem. Rev. 2006, 250, 1681.
(3) Ishikawa, Y.; Brown, C. E.; Hackett, P. A.; Rayner, D. M. Chem.
Phys. Lett. 1988, 150, 506.
(4) Wells, J. R.; Weitz, E. J. Am. Chem. Soc. 1992, 114, 2783.
(5) Anfinrud, P. A.; Han, C.-H.; Lian, T.; Hochstrasser, R. M. J. Phys.
Chem. 1991, 95, 574.
(6) Dobson, G. R.; Hodges, P. M.; Healy, M. A.; Poliakoff, M.;
Turner, J. J.; Firth, S.; Asali, K. J. J. Am. Chem. Soc. 1987, 109, 4218.
(7) Joly, A. G.; Nelson, K. A. J. Phys. Chem. 1989, 93, 2876.
(8) Klassen, J. K.; Selke, M.; Sorensen, A. A.; Yang, G. K. J. Am.
Chem. Soc. 1990, 112, 1267.
(9) Lee, M.; Harris, C. B. J. Am. Chem. Soc. 1989, 111, 8963.
(10) Simon, J. D.; Xie, X. J. Phys. Chem. 1986, 90, 6751.
(11) Simpson, M. B.; Poliakoff, M.; Turner, J. J.; Maier, W. B., II;
McLaughlin, J. G. J. Chem. Soc., Chem. Commun. 1983, 1355.
(12) Wang, L.; Zhu, X.; Spears, K. G. J. Phys. Chem. 1989, 93, 2.
(13) Xie, X. L.; Simon, J. D. J. Am. Chem. Soc. 1990, 112, 1130.
(14) Joly, A. G.; Nelson, K. A. Chem. Phys. 1991, 152, 69.
(15) Grills, D. C.; van Eldik, R.; Muckerman, J. T.; Fujita, E. J. Am.
Chem. Soc. 2006, 128, 15728.
(16) Wasserman, H. J.; Kubas, G. J.; Ryan, R. R. J. Am. Chem. Soc.
1986, 108, 2294.
(17) Hall, C.; Perutz, R. N. Chem. Rev. 1996, 96, 3125.
(18) Bengali, A. A.; Schultz, R. H.; Moore, C. B.; Bergman, R. G. J.
Am. Chem. Soc. 1994, 116, 9585.
(19) Grills, D. C.; Sun, X. Z.; Childs, G. I.; George, M. W. J. Phys.
Chem. A 2000, 104, 4300.
(20) Schultz, R. H.; Bengali, A. A.; Tauber, M. J.; Weiller, B. H.;
Wasserman, E. P.; Kyle, K. R.; Moore, C. B.; Bergman, R. G. J. Am.
Chem. Soc. 1994, 116, 7369.
ASSOCIATED CONTENT
■
S
* Supporting Information
Full ref 76, additional experimental details, UV−vis, TRIR, and
TA spectra, TD-DFT calculated UV−vis spectra, DFT-
calculated geometrical parameters, Cartesian coordinates and
energies of all species calculated by DFT, kinetic simulation
results. This material is available free of charge via the Internet
at http://pubs.acs.org.
(21) Simon, J. D.; Peters, K. S. Chem. Phys. Lett. 1983, 98, 53.
(22) Bengali, A. A.; Bergman, R. G.; Moore, C. B. J. Am. Chem. Soc.
1995, 117, 3879.
K
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
(23) Muckerman, J. T.; Fujita, E.; Hoff, C. D.; Kubas, G. J. J. Phys.
Chem. B 2007, 111, 6815.
(58) Liou, S.-Y.; van der Boom, M. E.; Milstein, D. J. Chem. Soc.,
Chem. Commun. 1998, 687.
(59) Steenwinkel, P.; Gossage, R. A.; van Koten, G. Chem.Eur. J.
(24) Montag, M.; Efremenko, I.; Cohen, R.; Leitus, G.; Shimon, L. J.
W.; Posner-Diskin, Y.; Ben-David, Y.; Martin, J. M. L.; Milstein, D.
Chem.Eur. J. 2008, 14, 8183.
1998, 4, 759.
(60) van der Boom, M. E.; Liou, S.-Y.; Ben-David, Y.; Shimon, L. J.
W.; Milstein, D. J. Am. Chem. Soc. 1998, 120, 6531.
(61) Bedford, R. B.; Draper, S. M.; Scully, P. N.; Welch, S. L. New J.
Chem. 2000, 24, 745.
(25) Siegbahn, P. E. M. J. Am. Chem. Soc. 1996, 118, 1487.
(26) Siegbahn, P. E. M.; Svensson, M. J. Am. Chem. Soc. 1994, 116,
10124.
(62) Beletskaya, I. P.; Chuchurjukin, A. V.; Dijkstra, H. P.; van Klink,
G. P. M.; van Koten, G. Tetrahedron Lett. 2000, 41, 1075.
(63) Gorla, F.; Togni, A.; Venanzi, L. M.; Albinati, A.; Lianza, F.
Organometallics 1994, 13, 1607.
(64) Longmire, J. M.; Zhang, X. Tetrahedron Lett. 1997, 38, 1725.
(65) Miyazaki, F.; Yamaguchi, K.; Shibasaki, M. Tetrahedron Lett.
1999, 40, 7379.
(27) Ingleson, M.; Fan, H.; Pink, M.; Tomaszewski, J.; Caulton, K. G.
J. Am. Chem. Soc. 2006, 128, 1804.
(28) Rimmer, R. D.; Grills, D. C.; Fan, H.; Ford, P. C.; Caulton, K. G.
J. Am. Chem. Soc. 2007, 129, 15430.
(29) Portius, P.; Yang, J. X.; Sun, X. Z.; Grills, D. C.; Matousek, P.;
Parker, A. W.; Towrie, M.; George, M. W. J. Am. Chem. Soc. 2004, 126,
10713.
(30) Macgregor, S. A.; Eisenstein, O.; Whittlesey, M. K.; Perutz, R.
N. J. Chem. Soc., Dalton Trans. 1998, 291.
(31) Osman, R.; Perutz, R. N.; Rooney, A. D.; Langley, A. J. J. Phys.
Chem. 1994, 98, 3562.
(32) Nicasio, M. C.; Perutz, R. N.; Tekkaya, A. Organometallics 1998,
́
(66) Morales-Morales, D.; Grause, C.; Kasaoka, K.; Redon, R.;
Cramer, R. E.; Jensen, C. Inorg. Chim. Acta 2000, 300−302, 958.
(67) Kaska, W. C.; Nemeh, S.; Shirazi, A.; Potuznik, S. Organo-
metallics 1988, 7, 13.
(68) Vigalok, A.; Ben-David, Y.; Milstein, D. Organometallics 1996,
15, 1839.
17, 5557.
(69) Nemeh, S.; Jensen, C.; Binamirasoriaga, E.; Kaska, W. C.
Organometallics 1983, 2, 1442.
(70) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic Solvents,
Physical Properties and Methods of Purification, 4th ed.; Wiley: New
York, 1986.
(71) Ethene; Hayduk, W., Ed.; Solubility Data Series; Oxford
University Press: Oxford, 1994; Vol. 57.
(72) Wilhelm, E.; Battino, R. Chem. Rev. 1973, 73, 1.
(73) Nitrogen and Air; Battino, R., Ed.; Solubility Data Series;
Pergamon: Oxford, 1982; Vol. 10.
(74) Hydrogen and Deuterium; Young, C. L., Ed.; Solubility Data
Series; Pergamon: Oxford, 1981; Vol. 5/6.
(75) Hayashi, Y.; Szalda, D. J.; Grills, D. C.; Hanson, J. C.; Huang, K.-
W.; Muckerman, J. T.; Fujita, E. Polyhedron, in press, http://dx.doi.
org/10.1016/j.poly.2012.10.006.
(33) Osman, R.; Pattison, D. I.; Perutz, R. N.; Bianchini, C.; Casares,
J. A.; Peruzzini, M. J. Am. Chem. Soc. 1997, 119, 8459.
(34) Cronin, L.; Nicasio, M. C.; Perutz, R. N.; Peters, R. G.; Roddick,
D. M.; Whittlesey, M. K. J. Am. Chem. Soc. 1995, 117, 10047.
(35) Hall, C.; Jones, W. D.; Mawby, R. J.; Osman, R.; Perutz, R. N.;
Whittlesey, M. K. J. Am. Chem. Soc. 1992, 114, 7425.
(36) Fujita, E.; Creutz, C.; Sutin, N.; Szalda, D. J. J. Am. Chem. Soc.
1991, 113, 343.
(37) Fujita, E.; Creutz, C.; Sutin, N.; Brunschwig, B. S. Inorg. Chem.
1993, 32, 2657.
(38) Ogata, T.; Yanagida, S.; Brunschwig, B. S.; Fujita, E. J. Am.
Chem. Soc. 1995, 117, 6708.
(39) Fujita, E.; Furenlid, L. R.; Renner, M. W. J. Am. Chem. Soc. 1997,
119, 4549.
(40) Fujita, E.; van Eldik, R. Inorg. Chem. 1998, 37, 360.
(41) Fujita, E.; Wishart, J. F.; van Eldik, R. Inorg. Chem. 2002, 41,
1579.
(42) Yan, S. G.; Brunschwig, B. S.; Creutz, C.; Fujita, E.; Sutin, N. J.
Am. Chem. Soc. 1998, 120, 10553.
(43) Fujita, E.; Brunschwig, B. S.; Creutz, C.; Muckerman, J. T.;
Sutin, N.; Szalda, D.; van Eldik, R. Inorg. Chem. 2006, 45, 1595.
(44) Hayashi, Y.; Kita, S.; Brunschwig, B. S.; Fujita, E. J. Am. Chem.
Soc. 2003, 125, 11976.
(45) Huang, K.-W.; Han, J. H.; Musgrave, C. B.; Fujita, E.
Organometallics 2007, 26, 508.
(46) Polyansky, D. E.; Cabelli, D.; Muckerman, J. T.; Fukushima, T.;
Tanaka, K.; Fujita, E. Inorg. Chem. 2008, 47, 3958.
(47) van der Boom, M. E.; Milstein, D. Chem. Rev. 2003, 103, 1759.
(48) Bernskoetter, W. H.; Brookhart, M. Organometallics 2008, 27,
2036.
(49) Dani, P.; Karlen, T.; Gossage, R. A.; Gladiali, S.; van Koten, G.
Angew. Chem., Int. Ed. 2000, 39, 743.
(76) Frisch, M. J.; et al. Gaussian 03, Revision E.01; Wallingford, CT,
2004.
(77) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299.
(78) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270.
(79) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284.
(80) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry;
Schaefer, H. F., III, Ed.; Plenum: New York, 1976; Vol. 3, pp 1.
(81) Martin, J. M. L.; Sundermann, A. J. Chem. Phys. 2001, 114, 3408.
(82) Andrae, D.; Haussermann, U.; Dolg, M.; Stoll, H.; Preuss, H.
̈
Theor. Chim. Acta 1990, 77, 123.
(83) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon,
M. S.; DeFrees, D. J.; Pople, J. A. J. Chem. Phys. 1982, 77, 3654.
(84) Harihara, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213.
(85) Ehlers, A. W.; Bohme, M.; Dapprich, S.; Gobbi, A.; Hollwarth,
̈
̈
A.; Jonas, V.; Kohler, K. F.; Stegmann, R.; Veldkamp, A.; Frenking, G.
̈
Chem. Phys. Lett. 1993, 208, 111.
(86) Roy, L. E.; Hay, P. J.; Martin, R. L. J. Chem. Theory Comput.
2008, 4, 1029.
(87) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639.
(88) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys.
1980, 72, 650.
(89) Frech, C. M.; Shimon, L. J. W.; Milstein, D. Helv. Chim. Acta
2006, 89, 1730.
(90) Bullock, R. M.; Bender, B. R. Isotope Methods in Homogeneous
(50) Gottker-Schnetmann, I.; Brookhart, M. J. Am. Chem. Soc. 2004,
̈
126, 9330.
(51) Gottker-Schnetmann, I.; White, P.; Brookhart, M. J. Am. Chem.
̈
Soc. 2004, 126, 1804.
(52) Gottker-Schnetmann, I.; White, P. S.; Brookhart, M. Organo-
̈
metallics 2004, 23, 1766.
(53) Gupta, M.; Hagen, C.; Flesher, R. J.; Kaska, W. C.; Jensen, C. M.
J. Chem. Soc., Chem. Commun. 1996, 2083.
Catalysis. In The Encyclopedia of Catalysis; Horvat
& Sons: New York, 2002.
́
h, I., Ed.; John Wiley
(54) Jensen, C. M. J. Chem. Soc., Chem. Commun. 1999, 2443.
(55) Krogh-Jespersen, K.; Czerw, M.; Summa, N.; Renkema, K. B.;
Achord, P. D.; Goldman, A. S. J. Am. Chem. Soc. 2002, 124, 11404.
(56) Zhu, K.; Achord, P. D.; Zhang, X.; Krogh-Jespersen, K.;
Goldman, A. S. J. Am. Chem. Soc. 2004, 126, 13044.
(57) Gandelman, M.; Milstein, D. J. Chem. Soc., Chem. Commun.
2000, 1603.
(91) Kubas, G. J. Metal Dihydrogen and σ-Bond Complexes: Structure,
Theory, and Reactivity; Kluwer Academic/Plenum Publishers: New
York, 2001; pp 222.
(92) Diffusion-controlled rate constants, kd’s, were estimated from
the following equation, kd = 4πr*DNA (where r* is the sum of the radii
of the reactants, D is the sum of the diffusion constants, D of each
reactant, and NA is the Avogadro constant). Values of D were obtained
L
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry
Article
from the Stokes−Einstein Equation, D = kBT/6πηr (where η is the
viscosity of the solvent and r is the radius of the reactant).
(93) Although setting k2 equal to the diffusion-controlled rate
constant is an assumption, we believe that it is a reasonable one based
on the initial slope fits, and also the fact that it involves the reaction of
small incoming molecules with a nonsolvated, coordinatively
unsaturated intermediate.
(94) van Eldik, R. High Pressure Kinetics: Fundamental and
Experimental Aspects. In Inorganic High Pressure Chemistry: Kinetics
and Mechanisms; van Eldik, R., Ed.; Elsevier: Amsterdam, 1986; Vol. 7,
pp 8.
(95) Huang, K.-W.; Grills, D. C.; Han, J. H.; Szalda, D. J.; Fujita, E.
Inorg. Chim. Acta 2008, 361, 3327.
(96) Perutz, R. N.; Turner, J. J. J. Am. Chem. Soc. 1975, 97, 4791.
(97) Kelly, J. M.; Long, C.; Bonneau, R. J. Phys. Chem. 1983, 87,
3344.
(98) Johnson, F. P. A.; George, M. W.; Bagratashvili, V. N.;
Vereshchagina, L. N.; Poliakoff, M. Mendeleev Commun. 1991, 26.
(99) Hodges, P. M.; Jackson, S. A.; Jacke, J.; Poliakoff, M.; Turner, J.
J.; Grevels, F. W. J. Am. Chem. Soc. 1990, 112, 1234.
(100) van Eldik, R.; Meyerstein, D. Acc. Chem. Res. 2000, 33, 207.
(101) The same scheme will also be used to explain the reactivity of
1. See details below.
(102) http://www.almaden.ibm.com/st/computational_science/ck/
?cks
(103) Very low concentrations of N2 were achieved through the use
of specially prepared gas mixtures of Ar/N2.
M
dx.doi.org/10.1021/ic300672g | Inorg. Chem. XXXX, XXX, XXX−XXX