**Deuterium Isotope Effects for Probing
Aspects of the Interaction of H–H and C–H Bonds with Transition
Metals
**

**Introduction**

It is well known that the measurement of kinetic
deuterium isotope effects (*i.e.* *k*_{H}/*k*_{D}) provides a useful means to ascertain details of the
nature of the transition state for the rate determining step of a reaction that
involves cleavage of an X–H bond. However, since many reactions are multistep, the observed
kinetic isotope effect often represents a composite of the individual isotope
effects for all steps (both forward and reverse) up to, and including, the rate
determining step. Therefore, an
understanding of equilibrium deuterium isotope effects is of importance for the
interpretation of kinetic deuterium isotope effects. Deuterium isotope effects are often rationalized by using
two guidelines, namely:

(i) Primary kinetic isotope effects (KIEs) are typically
normal (*k*_{H}/*k*_{D} > 1).

(ii)* *Primary
equilibrium isotope effects (EIEs) may be either normal (*K*_{H}/*K*_{D} > 1) or inverse (*K*_{H}/*K*_{D}
< 1), with a value that is dictated by deuterium preferring to be located in
the highest frequency oscillator.

We are interested in investigating the generality of these rules as they apply to the various interaction of H–H and C–H bonds with transition metal centers.

**Equilibrium Isotope Effects for Oxidative Addition of
Dihydrogen**

*1. An
Inverse Equilibrium Isotope Effect for Oxidative Addition of H _{2} to
W(PMe_{3})_{4}X_{2}*

Rather surprisingly, prior to 1993, there had been no
detailed discussion in the literature pertaining to the equilibrium isotope
effect for the oxidative addition of H_{2 }to a metal center. For this reason, we directed effort
towards establishing the EIE for oxidative addition of H_{2} and D_{2}
to a metal center, and specifically W(PMe_{3})_{4}I_{2}.

Interestingly, the equilibrium isotope effect for
oxidative addition of H_{2} and D_{2} to W(PMe_{3})_{4}I_{2}
is characterized by a substantial *inverse*
equilibrium deuterium isotope effect, with *K*_{H}/*K*_{D} = 0.63(5) at 60ûC.
In particular, the inverse nature of the equilibrium isotope effect is
counter to that which would have been predicted on the basis of the simple
notion concerning primary isotope effects, namely that deuterium prefers to
reside in the higher frequency oscillator.

Analysis of the temperature dependence of *K* reveals that the origin of the inverse equilibrium
deuterium isotope effect is enthalpic, with oxidative addition of D_{2}
being more exothermic than oxidative addition of H_{2}. The entropic contribution to the
equilibrium isotope effect is small, but actually attempts to counter the
inverse nature.

A more complete analysis of isotope effects, however,
focuses on factors other than the ZPE term. Specifically, equilibrium isotope effects are conventionally
determined by the expression EIE = SYM ¥
MMI ¥ EXC ¥
ZPE where SYM is the symmetry factor, MMI is the mass-moment of inertia term,
EXC is the excitation term, and ZPE is the zero point energy term, an approach
that has been applied by others in organometallic
chemistry.

It is convenient to recognize that the combined [SYM¥MMI¥EXC]
term corresponds closely to the entropy component, while the ZPE term
corresponds closely to the enthalpy component. Most commonly, the ZPE term dominates the EIE, which is the
reason why the direction of the EIE can be predicted on the basis of
vibrational frequencies alone.
Specifically, since the difference in X–H and X–D zero point
energies scales with n_{X–H},
the zero point energy stabilization for a system is greatest when deuterium
resides in the highest frequency oscillator. Thus, a normal EIE is predicted if n_{Y–H} in the product is less than n_{X–H} in the reactant, while
an inverse EIE is predicted if n_{Y–H}
in the product is greater than n_{X–H}
in the reactant.

On this basis, a normal EIE would have been expected for
oxidative addition of H_{2} and D_{2} to W(PMe_{3})_{4}I_{2}
because the H–H stretch is of much higher energy that the W–H
stretch and one customarily focuses on ** stretching** vibrations when evaluating
primary isotope effects. Since
this prediction is counter to the experimental result, it was evident that this
simple appraisal did not provide an accurate evaluation of the EIE for
oxidative addition of H

The inverse EIE may, however, be rationalized if** bending**

Inclusion of the bending modes results in a significant
lowering of the zero point energy for W(PMe_{3})_{4}D_{2}I_{2}
with respect to W(PMe_{3})_{4}H_{2}I_{2}, to
the extent that an inverse equilibrium isotope effect is obtained. The occurrence of an inverse deuterium
equilibrium isotope effect is, therefore, a consequence of there being a *single* isotope sensitive vibrational mode in the reactant
(H_{2}), yet *six* (albeit
lower energy) isotope sensitive modes in the product.

*2.
Inverse to Normal Temperature Dependent Transitions for Equilibrium
Isotope Effects Involving Oxidative Addition of Dihydrogen*

While inverse EIEs have become a commonly accepted
feature for oxidative addition of H_{2} and D_{2} to a metal
center, literature reports that coordination of alkanes to a metal center can
be characterized by both normal and inverse EIEs, the possibility that
oxidative addition of H_{2} to a single metal center could also be
characterized by a normal EIE deserved further consideration. To examine this possibility, the EIE
for oxidative addition of H_{2} and D_{2} to {[H_{2}Si(C_{5}H_{4})_{2}]W}
was calculated as a function of temperature.

Interestingly, the calculations predicted that the EIE
for oxidative addition of hydrogen to {[H_{2}Si(C_{5}H_{4})_{2}]W}
does *not* vary with temperature in the
simple monotonic manner predicted by the vanÕt Hoff relationship, for which the
EIE would be expected either to progressively increase or decrease and
exponentially approach unity at high temperature. Rather, the EIE exhibits a maximum, being *inverse* at low temperature and *normal* at high temperature.

The precise form of the temperature dependence of the EIE is determined by the values of the individual SYM, MMI, EXC and ZPE terms. Since the SYM and MMI terms are temperature independent, the occurrence of a maximum is a result of the ZPE and EXC terms opposing each other. It is, however, more convenient to analyze the temperature dependence of the EIE in terms of the combined [SYM¥MMI¥EXC] term and the ZPE term, which respectively correspond to the entropy and enthalpy terms. Thus, at all temperatures the [SYM¥MMI¥EXC] entropy component favors a normal EIE, while the ZPE enthalpy component favors an inverse EIE. At high temperatures, the [SYM¥MMI¥EXC] entropy component dominates and the EIE is normal, while at low temperatures the ZPE enthalpy component dominates and the EIE is inverse.

The notion that an inverse-to-normal transition of the
EIE could be a general phenomenon was confirmed by calculating the temperature
dependence of the EIE for oxidative addition of H_{2} and D_{2}
to Ir(PH_{3})_{2}(CO)Cl.

^{ }

Experimental verification of the prediction that the EIE
for oxidative addition of H_{2} to a transition metal center could
undergo a temperature dependent transition from an inverse to a normal value
was obtained by investigation of oxidative addition of H_{2} and D_{2}
to Ir(PMe_{2}Ph)_{2}(CO)Cl. Thus, the strongly inverse EIE of 0.41(4) observed for
oxidative addition of H_{2} and D_{2} to Ir(PMe_{2}Ph)_{2}(CO)Cl
at 25ûC becomes normal at temperatures greater than *ca.* 90ûC, and reaches a maximum value of 1.41(6) at
130ûC, thereby providing important verification for the theoretical
calculations.

Shortly after demonstrating that oxidative addition of H_{2}
and D_{2} to Ir(PMe_{2}Ph)_{2}(CO)Cl undergoes a
transition from inverse to normal at high temperatures, a system was discovered
for which the EIE for oxidative addition to a single metal center is normal at
relatively low temperature (40 ûC).
Specifically, the EIE for oxidative addition of H_{2} and D_{2}
to the anthracene complex (h^{6}–AnH)Mo(PMe_{3})_{3
}(AnH = anthracene) giving (h^{4}–AnH)Mo(PMe_{3})_{3}H_{2}
is normal over virtually the entire temperature range (30 – 90ûC)
measured.

The important issue to address is concerned with the
factors that influence the temperature of the inverse/normal EIE
transition. Calculations on a
variety of systems shows that the transition temperature is a sensitive
function of the system such that some systems may exhibit a normal EIE, whereas
others exhibit an inverse EIE. The
main factors responsible for influencing the transition temperature are the
M–H stretching frequencies such that systems for which n_{M–H} are low are more likely
to exhibit a normal EIE than systems for which n_{M–H}
are high.

As noted above, primary isotope effects are often
rationalized in terms of ZPE arguments using the concept that deuterium prefers
to be located in the highest frequency oscillator. On this basis, the observation of a normal isotope effect
for oxidative addition of H_{2} to (h^{6}–AnH)Mo(PH_{3})_{3}
could have simply been interpreted in terms of the two Mo–H stretching
frequencies of (h^{4}–AnH)Mo(PH_{3})_{3}H_{2}
being lower than that of the H–H stretching frequency. However, such an analysis would be
incorrect because the ZPE term actually favors an inverse EIE at *all* temperatures and the occurrence of a normal EIE is
purely a consequence of the [SYM¥MMI¥EXC] (entropy) term. The important feature of (h^{4}–AnH)Mo(PH_{3})_{3}H_{2}
which results in a normal EIE at relatively low temperatures is that the
M–H vibrational modes are of low energy and cause the ZPE term to
approach unity rapidly. Thus, the
[SYM¥MMI¥EXC]
entropy term is able to dominate the EIE at a relatively low temperature,
thereby resulting in a normal EIE for oxidative addition of H_{2} to (h^{6}–AnH)Mo(PH_{3})_{3}.

*3. Equilibrium Isotope Effects for Coordination of
Dihydrogen *

In addition to the majority of EIEs for oxidative
addition of H_{2} and D_{2} being inverse at ambient
temperature, the EIEs for formation of dihydrogen complexes are also inverse. However, on the basis of the above
studies, we considered the possibility that the EIE for coordination of
dihydrogen could also exhibit a similar behavior. Indeed, calculations on the pentacarbonyl complex **W(CO) _{5}(**

**Isotope Effects Pertaining to the Interaction of
Transition Metals with C–H Bonds **

*1.
Experimental Measurement of Isotope Effects for Reductive Elimination of
Methane from [Me _{2}Si(C_{5}Me_{4})_{2}]W(Me)H*

The kinetic isotope effect for reductive elimination of
methane from [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{3})H
and [Me_{2}Si(C_{5}Me_{4})_{2}]W(CD_{3})D
is characterized by a substantial inverse KIE of 0.45(3) in benzene at 100ûC.

Although a normal KIE may have been expected since this
has a substantial primary component, the inverse value may be readily
rationalized by recognizing that the reductive elimination reaction is not a
single step, but is rather a two step sequence involving formation of a s–complex intermediate [Me_{2}Si(C_{5}Me_{4})_{2}]W(s–MeH) prior to rate-determining
elimination of methane.

Specifically, for a situation involving a s–complex intermediate, the rate
constant for irreversible reductive elimination is a composite of the rate
constants for reductive coupling (*k*_{rc}),
oxidative cleavage (*k*_{oc}),
and dissociation (*k*_{d}),
namely *k*_{obs} = *k*_{rc}*k*_{d}/(*k*_{oc}
+ *k*_{d}). The latter expression simplifies to *k*_{obs} = *k*_{rc}*k*_{d}/*k*_{oc}
= *K*_{s}*k*_{d}, where *K*_{s} is the
equilibrium constant for the conversion of [M](R)H to [M](s–RH) if methane dissociation is rate
determining, *i.e.* *k*_{d} << *k*_{oc}.
If the isotope effect for dissociation of RH (*i.e. *[*k*_{d(H)}/*k*_{d(D)}]) is close to unity (since the
C–H bond is close to being fully formed), the isotope effect on reductive
elimination would then be dominated by the *equilibrium* isotope effect *K*_{s}_{(H)}/*K*_{s}_{(D)}
for formation of the s–complex
[M](s–RH). The latter would be predicted to be
inverse on the basis of the simple notion that deuterium prefers to be located
in the higher frequency oscillator, *i.e *C–D
*versus* M–D. As such, an inverse KIE may result for
the overall reductive elimination, without requiring an inverse effect for a
single step. Indeed, this
explanation has been invoked in the literature to rationalize inverse KIEs for
a variety of systems.

However, while the preequilibrium mechanism provides a
commonly accepted rationalization of inverse kinetic isotope effects for
reductive elimination of RH, consideration must be given to the possibility
that it could also correspond to the isotope effect for the reductive coupling
step if that were to be rate determining.
Since there is relatively little information pertaining to the
individual isotope effects for the reductive elimination step, we considered it
worthwhile to investigate this system in more detail. Although it is not possible to address this issue by
studying the kinetics of reductive elimination of [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{3})H
and [Me_{2}Si(C_{5}Me_{4})_{2}]W(CD_{3})D,
it is possible to address the issue by studying the elimination of CH_{3}D
from [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{3})D
and [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{2}D)H.
Specifically, [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{3})D
is observed to isomerize to [Me_{2}Si(C_{5}Me_{4})_{2}]W(CH_{2}D)H
*via* the s–complex intermediate [Me_{2}Si(C_{5}Me_{4})_{2}]W(s–CH_{3}D) on a time-scale that
is comparable to the overall reductive elimination of CH_{3}D, and a
kinetics analysis of the transformations permits the KIE for reductive coupling
to be determined.

Significantly, assuming that secondary effects do not
play a dominant role, the primary KIE for reductive coupling of [Me_{2}Si(C_{5}Me_{4})_{2}]W(Me)X
(X = H, D) to form the s–complex
intermediate [Me_{2}Si(C_{5}Me_{4})_{2}]W(s–XMe) is *normal*, with a value of 1.4(2). As such, the observation of an inverse kinetic isotope
effect for the overall reductive elimination can only be rationalized in terms
of an inverse *equilibrium* isotope
effect for the formation of the s–complex. In this regard,**
Jones** has also demonstrated that the EIE for the interconversion of
[Tp^{Me2}]Rh(L)(Me)X and [Tp^{Me2}]Rh(L)(s–XMe) is *inverse*
(0.5), even though the individual KIEs for oxidative cleavage (4.3) and
reductive coupling (2.1) are *normal*.
Therefore, at present, there is no
experimental evidence which supports the notion that the inverse KIEs for
reductive elimination of methane may be attributed to an inverse primary KIE
for a single step.

^{ }

*2.
Equilibrium Isotope Effect for Coordination of Methane to {[H _{2}Si(C_{5}H_{4})_{2}]W}*

In addition to coordination of dihydrogen exhibiting a
temperature dependent transition between inverse and normal EIEs, coordination
of methane exhibits a similar behavior.
Specifically, the EIE for coordination of CH_{4} and CD_{4}
to {[H_{2}Si(C_{5}H_{4})_{2}]W} exhibits a
maximum: the EIE is 0 at 0 K, increases to a maximum value of 1.57, and then
decreases to unity at infinite temperature.

Although there are no experimental reports of the EIEs
for coordination and oxidative addition of methane to a metal center for
comparison with that for {[H_{2}Si(C_{5}H_{4})_{2}]W},
there are several conflicting reports of EIEÕs for coordination of other
alkanes. Specifically, Geftakis
and **Ball** reported a normal EIE (1.33
at –93ûC) for coordination of cyclopentane to [CpRe(CO)_{2}],
whereas **Bergman** and **Moore **reported inverse EIEs for the
coordination of cyclohexane (Å 0.1 at –100ûC) and neopentane (Å 0.07 at
–108ûC) to [Cp*Rh(CO)].
While the observation of both normal and inverse equilibrium isotope
effects for coordination of alkanes to metal centers is counterintuitive, a
simple rationalization is provided by the above calculations on {[H_{2}Si(C_{5}H_{4})_{2}]W}.

*3.
Equilibrium Isotope Effect for Oxidative Addition of Methane to [H _{2}Si(C_{5}H_{4})_{2}]W(Me)H*

In marked contrast to the EIE for coordination of
methane which approaches zero at low temperature, the corresponding EIE for
oxidative addition of methane to {[H_{2}Si(C_{5}H_{4})_{2}]W}
is normal at all temperatures and actually approaches infinity at low
temperature.

This dramatic difference between coordination and oxidative addition of methane is associated with the ZPE terms. Specifically, the ZPE term for coordination of methane is inverse at all temperatures (and zero at 0 K), while that for oxidative addition is normal at all temperatures (and infinity at 0 K).

While the total number of isotope sensitive vibrations
are the same for both [H_{2}Si(C_{5}H_{4})_{2}]W(s–HMe) and [H_{2}Si(C_{5}H_{4})_{2}]W(Me)H,
the principal difference in the ZPE term is a consequence of the fact that the
isotopically sensitive vibrations associated with the W–H bond of the
methyl hydride complex [H_{2}Si(C_{5}H_{4})_{2}]W(Me)H,*
*namely a W–H stretch and two bends, are
of sufficiently low energy that they do not counter those associated with the
C–H bond that has that has been broken. As a result, the ZPE term for oxidative addition of the
C–H bond is normal

**Selected References**

ÒApplications of Deuterium Isotope Effects for Probing
Aspects of Reactions Involving Oxidative Addition and Reductive Elimination of
H–H and C–H Bonds.Ó Gerard
Parkin *J. Labelled Compounds and Radiopharmaceuticals* **2007**, *50*, 1088-1114.

ÒA Normal Equilibrium Isotope Effect For Oxidative Addition
of H_{2} to (h^{6}–Anthracene)Mo(PMe_{3})_{3}.Ó Guang Zhu, Kevin E. Janak and Gerard
Parkin *Chem. Commun.* **2006**,
2501-2503.

ÒIntramolecular N–H¥¥¥S
Hydrogen Bonding in the Zinc Thiolate Complex [Tm^{Ph}]ZnSCH_{2}C(O)NHPh: A Mechanistic Investigation of Thiolate
Alkylation as Probed by Kinetics Studies and by Kinetic Isotope Effects.Ó Melissa M. Morlok, Kevin E. Janak,
Guang Zhu, Duncan A. Quarless, and Gerard Parkin *J. Am. Chem. Soc.* **2005**, *127*, 14039-14050.

ÒMolybdenocene Trihydride Complexes: Influence of a [Me_{2}Si] Ansa
Bridge on Classical versus Nonclassical Nature, Stability with Respect to
Elimination of Dihydrogen, and Acidity.Ó
Kevin E. Janak, Jun Ho Shin, and Gerard Parkin *J. Am. Chem. Soc.* **2004**, *126*, 13054-13070.

ÒKinetic and Equilibrium Deuterium Isotope Effects for
C–H Bond Reductive Elimination and Oxidative Addition Reactions Involving
the *Ansa*–Tungstenocene
Methyl–Hydride Complex [Me_{2}Si(C_{5}Me_{4})_{2}]W(Me)H.Ó Kevin E. Janak, David G. Churchill, and
Gerard Parkin in *Activation and Functionalization of C–H Bonds,* *ACS* *Symposium
Series* **2004**, *885*, 86-104.

ÒExperimental Evidence for a Temperature Dependent
Transition between Normal and Inverse Equilibrium Isotope Effects For Oxidative
Addition of H_{2} to Ir(PMe_{2}Ph)_{2}(CO)Cl.Ó Kevin E. Janak and Gerard Parkin *J.
Am. Chem. Soc.* **2003**, *125*, 13219-13224.

ÒDeuterium and Tritium Equilibrium Isotope Effects for
Coordination and Oxidative Addition of Dihydrogen to [W(CO)_{5}] and
for the Interconversion of W(CO)_{5}(h^{2}–H_{2})
and W(CO)_{5}H_{2}.Ó
Kevin E. Janak and Gerard Parkin *Organometallics* **2003**, *22*, 4378-4380.

ÒTemperature Dependent Transitions between Normal and
Inverse Equilibrium Isotope Effects For Coordination and Oxidative Addition of
C–H and H–H Bonds to a Transition Metal Center.Ó Kevin E. Janak and Gerard Parkin *J.
Am. Chem. Soc.* **2003**, *125*, 6889-6891.

ÒNormal and Inverse Primary Kinetic Deuterium Isotope
Effects for C–H Bond Reductive Elimination and Oxidative Addition
Reactions of Molybdenocene and Tungstenocene
Complexes: Evidence for Benzene s–Complex
Intermediates.Ó David G.
Churchill, Kevin E. Janak, Joshua S. Wittenberg and Gerard Parkin *J. Am.
Chem. Soc.* **2003**, *125*, 1403-1420.

ÒComputational Evidence that the Inverse Kinetic Isotope
Effect for Reductive Elimination of Methane from a Tungstenocene
Methyl–Hydride Complex is associated with the Inverse Equilibrium Isotope
Effect for formation of a s–Complex
Intermediate.Ó Kevin E. Janak,
David G. Churchill, and Gerard Parkin *Chem. Commun.* **2003**, 22-23.

ÒA Mechanistic and Theoretical Analysis of the Oxidative
Addition of H_{2} to the Six-Coordinate Molybdenum and Tungsten
Complexes, M(PMe_{3})_{4}X_{2} (M = Mo, W; X = F, Cl,
Br, I): An Inverse Equilibrium
Isotope Effect and an Unprecedented Halide Dependence.Ó Tony Hascall, Daniel Rabinovich,
Vincent J. Murphy, Michael D. Beachy, Richard A. Friesner, and Gerard Parkin *J.
Am. Chem. Soc.* **1999**, *121*, 11402-11417.

ÒA Mechanistic Study of the Oxidative‑Addition of
H_{2} to W(PMe_{3})_{4}I_{2}: Observation of an Inverse Equilibrium
Isotope Effect.Ó Daniel Rabinovich
and Gerard Parkin *J. Am. Chem.
Soc.* **1993**, *115*, 353-354.