7972 J. Am. Chem. Soc., Vol. 122, No. 33, 2000
Slaughter et al.
than compensate for inverse factors arising from replacement
of one substrate CH stretch with a higher frequency NH stretch.
Similarly, in the CH activation event, transition-state bending
modes involving the transferred hydrogen acquire some het-
eroatom character, and would be expected to have lower
frequencies than the free substrate bending modes with which
they correlate. If these bending frequencies drop substantially
in the transition state, they can provide the necessary augmenta-
tion to afford KIEaddn and KIEelim values beyond the organic
semiclassical limit. In summary, activation of CH bonds by
heteroatom-containing functionalities, especially those whose
transition states are symmetricsnot particularly “early” or
“late”sare attractive candidates for the observation of extra-
ordinarily large KIEs.
up making substantial contributions. Furthermore, the greater
variation and scope of vibrational frequencies encountered in
transition metal systems, especially when different heteroatom-
H/D bonds are exchanged, leads to isotope effects of greater
magnitudes, and additional mechanistic hypothesesssuch as
light atom tunnelingsneed to be scrutinized with the utmost
care before they are applied. In summary, it is safe to interpret
EIEs, and presumably KIEs, through an understanding of zero-
point energy differences, as long as the importance of bending
vibrations is emphasized, but individual cases may manifest
unexpected complications.
Experimental Section
General Considerations. All manipulations were performed using
glovebox or high-vacuum techniques. Hydrocarbon and ethereal
solvents were dried over and vacuum-transferred from sodium ben-
zophenone ketyl. Benzene-d6 was dried sequentially over sodium and
4-Å molecular sieves, and stored over and vacuum-transferred from
sodium benzophenone ketyl. Cyclohexane-d12 was dried over sodium
and then stored over and vacuum-transferred from Na/K alloy. All
glassware was base-washed and oven-dried. NMR tubes for sealed tube
experiments were flame-dried under active vacuum immediately prior
to setup.
Conclusions
On the basis of this combined experimental and computational
assessment of equilibrium isotope effects (EIEs) pertaining to
isotopologues of (silox)2(tBu3SiNH)TiR (1-R), several conclu-
sions can be reached. It is evident that modern ab initio methods,
when applied to reasonable model complexes, are adequate for
the calculation of EIEs. As a cautionary note, recognize that it
is the special nature of equilibria of this type, and the generally
appropriate application of the Born-Oppenheimer approxima-
tion, that renders each EIE subject to the calculation of only a
single metal complex. Calculations of “normal” equilibria, i.e.,
1′-R + R′H a 1′-R′ + RH (R, R′ are different hydrocarbyls),
which require the calculation of two independent model
complexes, are not nearly as energetically accurate.
Perhaps the most interesting consequence of this study
concerns the importance of the MMI and EXC terms in the
statistical mechanics formalism of the EIE (eq 4). Recall that
in organic systems, both terms are typically neglected because
of insignificant changes in mass and moment of inertia upon
deuteration of large molecules, and because vibrational frequen-
cies of organics are usually >500 cm-1, rendering EXC
contributions to EIE minimal. Generalizing from this work, it
appears that the EXC and MMI terms can continue to be
ignored, but for reasons that are significantly different. Both
the MMI and EXC terms are substantial, but the latterswith
help from components of the EXP[-(∆∆ZPE/kBT)] terms
derived from low-frequency vibrationssattenuates the former
to the extent that both can be neglected. It is the mass-dependent
properties of the relatively small organic substrates in this study
that constitute the MMI term, yet it is the low-energy vibrations
of the metal complex that compensate for it via the EXC and
EXP[-(∆∆ZPE)/kBT] terms. In a sense, it is the arbitrary way
that the formalism in eq 4 partitions components of free energy
that has led to some confusion regarding interpretation of EIEs.
For example, if eq 4 had a rotational/vibrational partition
function ratio instead of terms for rotation and vibration, the
MMI component would not be distinct, etc.
1H NMR spectra were obtained using a Varian Unity 500 spectrom-
2
eter; H spectra were obtained on a Varian VXR-400S spectrometer
equipped with a broad-band probe.
Cyclopropane-d6 was purchased from CDN isotopes, Pointe-Claire,
PQ, Canada. Lithium aluminum deuteride, iodoethane-2,2,2-d3, cyclo-
hexane-d12, toluene-d8, benzene-d6, benzene-1,3,5-d3, ethylene-d4, eth-
ylene-trans-1,2-d2, ethane-d6, and methane-dn (n ) 2, 3, 4) were ordered
from Cambridge Isotope Laboratories, Andover, MA. Organotitanium
compounds (silox)2(tBu3SiNH)TiR (1-R) were prepared as previously
reported.17
Preparation of Deuterated Substrates. 1. Toluene-r-d. To a flask
containing 20 mL of dry THF and 2.0 g of LiAlD4 (0.047 mmol) at 0
°C was added 6.47 g (4.5 mL, 0.038 mmol) of benzyl bromide by
syringe under Ar counterflow. The mixture was allowed to warm slowly
to room temperature and stirred for 24 h. The flask was then transferred
to a 14/20 distillation apparatus with a Vigreaux column, and THF
was removed from the product by distillation under 1 atm of Ar. A
fraction collected at 104 °C (∼4 mL, 3.3 g) was found by 1H NMR to
be 95.6 mol % toluene-R-d and 4.4 mol % THF (89.1% yield of toluene-
R-d, isotopic purity >99%). This mixture was dried over sodium and
used without further purification in preparing the toluene intramolecular
EIE samples.
2. Ethane-1,1,1-d3. An oven-dried bomb reactor charged with 1.43
g of LiAlH4 (0.038 mmol) was evacuated, and THF (20 mL) and
CD3CH2I (1.5 mL, 0.019 mmol) were vacuum-distilled in at -78 °C.
The mixture was stirred for 3 h, during which time it warmed slowly
to room temperature. The bomb reactor was then degassed at -196
°C, warmed to -78 °C, and opened to another bomb reactor held at
-196 °C, where the ethane-1,1,1-d3 condensed. Further purification
of the gaseous product was achieved by passing it through two -127
°C traps (1-propanol/liquid N2), with the aid of a Toepler pump, and
1
into a glass bomb reactor at -196 °C. H NMR confirmed that the
3
purified gas contained only CD3CH3 (septet, δ 0.77 (C6D6), JHD
)
1.3 Hz). No other isotopologues could be observed, so isotopic purity
From the perspective herein, EXP[-(∆∆ZPE)/kBT] terms,
primarily bending vibrations, are the major contributors ac-
counting for the magnitude of the EIEs and, presumably,
corresponding KIEs. Uncorrelated bending modessones that
are not common to metal complex and substrateshave proven
to be the dominant factors in the generally greater magnitudes
found for inter- vs intramolecular isotope effects. When
comparing inter- and intramolecular isotope effects for the
purpose of distinguishing mechanisms, these intrinsic differences
must be carefully analyzed in order to avoid misinterpretation.
As an additional cautionary note, cases can be deceptively
complicated, and seemingly inconsequential vibrations can end
was assumed to be >99%.
3. Cyclopropane-1,1-d2. 1,1-Dibromocyclopropane (600 mg, 3.00
mmol), prepared by literature methods,45 was introduced into an oven-
n
dried glass bomb reactor, along with 1.80 g (6.16 mmol) of Bu3SnD
and 324 mg (1.97 mmol) of AIBN. Benzene (30 mL) was added by
vacuum distillation, and the bomb reactor was heated at 60 °C for 24
h. After the reaction was done, the bomb was cooled to -196 °C and
degassed. The solution was then warmed to room temperature, and
cyclopropane-1,1-d2 was isolated by trapping the solvent at -78 °C
(45) Seyferth, D.; Burlitch, J. M.; Minasz, R. J.; Mui, J. Y.; Simmons,
H. D.; Treiber, A. J. H.; Dowd, S. R. J. Am. Chem. Soc. 1965, 87, 4259-
4270.
Slaughter, Legrande M.
