Effect of Isotopic Substitution
J. Phys. Chem. A, Vol. 101, No. 48, 1997 8993
1,3-dioxane-4,6-dione crystals, an intrinsic potential barrier
depth estimated from the tunneling frequency is twice the size
of the activation energy of obtained from the linear high-
temperature region of the exchange rotation rate plot.
In liquids, two mechanisms of activation energy modification
have been suggested. Rakhimov et al.25 discuss the indirect
cage effect which they assume can give up to 50% reduction in
the free activation energy of intramolecular chemical exchange
due to the solvent. Additionally, the exchange rate2,25 is
inversely proportional to the friction parameter, which in liquids
has an exponential temperature dependence thus affecting the
effective overall activation energy. In the case of one-
dimensional rotation in crystals, the interpretation of this
parameter, beyond that it represents a simplified representation
of the dissipative interaction with the reservoir, is not very lucid.
We can, however, see no reason for it not to be exponentially
temperature-dependent.
It has been pointed out to us that the reason deuterium has a
lower activation energy may be related to the fact that the zero-
point vibrational amplitude is smaller, making the deuterium
atom in a molecule “smaller” than hydrogen.
An alternative theory involving the observed inertial de-
pendence is the spin-rotation interaction discussed by Gutowsky
et al.,26 Brown et al.,27 and Hubbard.28 This interaction is shown
to have a temperature-dependent effect on nuclear relaxation
in liquids28 that is also dependent on the nuclear species.26 It
may be, however, that the rotational correlation time is too short
for the coupling.
Figure 6. Calculated low-temperature spectrum (no exchange) of the
CD3C˙ (COOH)2 radical with hyperfine coupling constant a ) 4.0 G,
potential twist angle δ ) 50°, potential barrier depth V3 ) 387 K and
similar broadening as for the calculations in the 5K spectrum of Figure
4b.
analogue radical exhibits an exchange activation energy of 387
K ((21 K), considerably lower than the intrinsic potential
barrier.
The results reported in the present work are surprising in two
ways: First, that the hydrogenated and deuterated radical do
not exhibit similar activation energies in the high-temperature
region; second, that in particular the deuterated system has an
activation energy very different from the intrinsic potential
barrier depth.
As stated in the Introduction, it has previously been argued
that C˙ -CH3 radicals and methyl-deuterated analogue radicals
should exhibit the same exchange rates, both on theoretical2
and experimental3 grounds. The experimental observations of
Erickson et al.3 do indicate small discrepancies between such
systems, but they are believed to be insignificant. It should be
noted that those experiments are conducted at much higher
temperatures than the experiments reported in the present work.
The results of Erickson et al.3 indicate a higher activation energy
for the deuterated analogue radical, i.e., in contrast to our
findings.
Whatever the mechanism may be, it seems apparent that the
relationship between activation energies and hindering potentials
for the methyl rotor is rather complex and not yet fully
understood.
Acknowledgment. A.R.S. was supported by the Norwegian
Research Council, NFR, and wishes to thank Einar Sagstuen
for discussions and suggestions. N.P.B. was supported by the
Swedish TFR. A.S.M. wishes to thank SAREK and the
International Science Program, ISP, for financial support. R.E.
was supported by the Swedish Natural Science Council, NFR.
References and Notes
The hydrogenated radical spectrum shows subsidiary peaks
not reproducible by our theory which are believed to originate
from other radicals, and the ENDOR observations of Clough
et al.6 indicate the presence of a radical of 600 MHz tunneling
frequency, which is equivalent to a 230 K potential barrier depth.
An alternative hypothesis could therefore be to assume that the
deuterated spectra are influenced greatly by such a radical. This
assumption may be rejected for two reasons. First, the quality
of the fit of the single radical model to the experiments is rather
good. Second, a potential barrier depth equal to the activation
energy of 387 K would give a tunneling frequency of about 27
MHz. This may be observed from the calculations of Figure 6
to give a severely distorted low-temperature spectrum. It is
therefore definite from our results alone that the observed
activation energy cannot be interpreted as an intrinsic potential
barrier. Thus, the parameters V3 and Ea,D both correspond to
the same single radical, which is the methyl-deuterated analogue
of the CH3C˙ (COOH)2 radical discussed in the literature6-9 and
in the present work.
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Although believed to be subjected to numerous intermolecular
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(19) Sørnes, A. R.; Benetis, N. P. Accepted for publication in Chem.
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