Experimental evidence for heavy-atom tunneling in the ring-opening of cyclopropylcarbinyl radical from intramolecular 12C/13C kinetic isotope effects

Article abstract of DOI:10.1021/ja1055593

The intramolecular ¹³C kinetic isotope effects for the ring-opening of cyclopropylcarbinyl radical were determined over a broad temperature range. The observed isotope effects are unprecedentedly large, ranging from 1.062 at 80 °C to 1.163 at -100 °C. Semiclassical calculations employing canonical variational transition-state theory drastically underpredict the observed isotope effects, but the predicted isotope effects including tunneling by a small-curvature tunneling model match well with experiment. These results and a curvature in the Arrhenius plot of the isotope effects support the recently predicted importance of heavy-atom tunneling in cyclopropylcarbinyl ring-opening.

Full text of DOI:10.1021/ja1055593

Published on Web 08/19/2010
Experimental Evidence for Heavy-Atom Tunneling in the Ring-Opening of
12
13
Cyclopropylcarbinyl Radical from Intramolecular C/ C Kinetic Isotope Effects
†
‡
‡
‡
,‡
Ollie M. Gonzalez-James, Xue Zhang, Ayan Datta, David A. Hrovat, Weston Thatcher Borden,*
,
†
and Daniel A. Singleton*
Department of Chemistry, Texas A&M UniVersity, College Station, Texas 77842, and Department of Chemistry and
Center for AdVanced Scientific Computing and Modeling, UniVersity of North Texas, 1155 Union Circle #305070,
Denton, Texas 76203-5017
Received June 24, 2010; E-mail: singleton@mail.chem.tamu.edu
barrier is calculated to allow tunneling to occur rapidly, without
any thermal activation, from the molecule’s vibrational ground state.
We sought to determine if tunneling in the ring-opening of 3 would
be apparent in experimental observations made at higher and more
Abstract: The intramolecular 13C kinetic isotope effects for the
ring-opening of cyclopropylcarbinyl radical were determined over
a broad temperature range. The observed isotope effects are
unprecedentedly large, ranging from 1.062 at 80 °C to 1.163 at
routinely accessible temperatures in solution.
-
100 °C. Semiclassical calculations employing canonical varia-
7
1
3
Toward that end, we studied the intramolecular C KIE for
the ring-opening of 3. As probes for tunneling, intramolecular KIEs
have significant advantages over absolute rate measurements;
intramolecular KIEs reflect only the first irreversibly desymme-
trizing step in a mechanism, and they can be readily determined
precisely at a broad range of temperatures. To measure the
intramolecular KIEs in the ring-opening of 3, samples of bromom-
ethylcyclopropane (1) at natural abundance were reduced at
temperatures ranging from -100 to 80 °C under free-radical chain
conditions, employing tributyltin hydride as the reductant and
tional transition-state theory drastically underpredict the observed
isotope effects, but the predicted isotope effects including tun-
neling by a small-curvature tunneling model match well with
experiment. These results and a curvature in the Arrhenius plot
of the isotope effects support the recently predicted importance
of heavy-atom tunneling in cyclopropylcarbinyl ring-opening.
Tunneling is a fundamental physical phenomenon that affects
the rates of barrier crossings in all chemical reactions. In most
reactions, the effects of tunneling are subtle, and the impact of
tunneling on experimental observations is not readily recognizable.
This is particularly true of reactions involving heavy-atom tunneling,
since the probability of tunneling decreases rapidly with increasing
mass. The theoretical support for heavy-atom tunneling is unques-
tioned, but its experimental manifestations are less obvious.
The most common evidence for heavy-atom tunneling has been
the observation of reactions that occur at cryogenic temperatures,
where there is little thermal energy to allow passage over a reaction
triethylborane/O
2
as the initiator. This reduction affords 1-butene
(
2) as the major product, arising from the ring-opening of 3, along
with small amounts of methylcyclopropane (5), formed by the
reduction of 3 before ring-opening. Under the conditions employed,
the ring-opening of 3 should be irreversible (see the Supporting
Information for a discussion).
1
-4
barrier.
Without tunneling, calculations show that passage over
the barrier is much too slow to account for the measured reaction
rates, but the inclusion of tunneling provides calculated rate
constants that are in good agreement with those that have been
measured.
Accurate theoretical calculations can be used to predict the
contribution of tunneling to a reaction at any temperature. However,
for reactions that are carried out at noncryogenic temperatures, the
question of what experimental observations, by themselVes, reliably
implicate heavy-atom tunneling remains open.
The relative 13C content in the C-3 versus C-4 positions of 2 was
7
13
analyzed by NMR. In all cases, less C was observed at the C-4
position of the 1-butene than at C-3, reflecting a preference for 12C to
undergo the bond-breaking process that places it in C-4 of the ring-
opened radical 4. The intramolecular KIEs that are defined by the ratios
We describe here an experimental study of the intramolecular
1
3
C kinetic isotope effect (KIE) for the ring-opening of the
13
of C at C-3 and C-4 are summarized in Table 1.
5
cyclopropylcarbinyl radical (3). The results reveal an unprecedent-
edly large 13C KIE and confirm recent predictions of an important
role for tunneling in this reaction. A careful scrutiny of the
temperature dependence of the KIE reveals an experimental
diagnostic of heavy-atom tunneling in the ring-opening of 3 that
does not depend on a comparison between predicted and measured
rate constants.
The KIEs in Table 1 are strikingly large. Even at 80 °C, the 13C
1
3
isotope effect is over 6%, and the C KIE ultimately increases to
1
3
1
6% at -100 °C. Larger C magnetic isotope effects have been
8
13
observed, but among conventional C KIEs, those in Table 1 are
the largest known at each temperature.
In order to investigate the role that tunneling plays in the 13C
KIEs in Table 1, the KIEs were computed both with and without
Datta, Hrovat, and Borden have recently predicted that tunneling
6
inclusion of tunneling. Canonical variational transition-state theory
should make the ring-opening of 3 fast at 20 K. A narrow reaction
9
(
CVT) was used to calculate the semiclassical rate constants,
†
without tunneling, and the effect of multidimensional tunneling on
the reaction dynamics was computed using the small-curvature
Texas A&M University.
University of North Texas.
‡
1
2548 9 J. AM. CHEM. SOC. 2010, 132, 12548–12549
10.1021/ja1055593  2010 American Chemical Society

C O M M U N I C A T I O N S
Table 1. Experimental and Predicted Intramolecular 13C KIEs for
is recognizable in the curvature in the Arrhenius plot of ln KIE
versus 1/T, shown in Figure 1.
A least-squares fit to the three high-temperature points gives
the Ring-Opening of Cyclopropylcarbinyl Radical
b
predicted KIE
1
3
12
12
13
a
E
a
( C) - E
a
( C) ) 52 cal/mol and A( C)/A( C) ) 0.987. For
temp (°C)
experimental KIE
without tunneling
with tunneling
13
12
comparison, the two low-temperature points give E
a
( C) - E
85 cal/mol and A( C)/A( C) ) 0.908. Thermally activated
tunneling by the lighter isotope increases the difference in the E
a
( C)
8
2
0
2
0
1.062 ( 0.003
1.079 ( 0.002
1.085 ( 0.003
1.131 ( 0.002
1.163 ( 0.004
1.048
1.058
1.064
1.093
1.106
1.057
1.073
1.082
1.138
1.169
1
2
13
)
a
13
12
-
78
100
values between C and C, and the effect of tunneling on lowering
A values makes A( C)/A( C) , 1.0 as the importance of tunneling
for the lighter isotope increases.
-
12
13
1
6
a
Defined as [k12C/k13C(for C-4)]/[k12C/k13C(for C-3)]. Uncertainties are 95%
The extraordinarily large 13C KIEs and curvature in the Arrhenius
plot of them are observable but subtle experimental indicators of
heavy-atom tunneling. However, tunneling has a larger, if less
directly measurable effect on the outcome of the reaction. For
example, under our conditions at -100 °C, this reaction produces
confidence ranges, based on 12 measurements at 80, 22, and 0 °C, 18
measurements at -78 °C, and 6 measurements at -100 °C. The reactions
at 80, 22, and 0 °C were conducted in o-dichlorobenzene and those at -78
b
and -100 °C in methylcyclohexane. KIE predictions without and with
tunneling are based on CVT and CVT/SCT rate constants, respectively,
calculated on the UB3LYP/6-31G* potential energy surface.
6
2% of 2 plus 38% of non-ring-opened 5. Without the rate
1
0
tunneling (SCT) approximation. These calculations were carried
out on the UB3LYP/6-31G* potential energy surface using GAUSS-
acceleration provided by heavy-atom tunneling, 2 would only be
28% of the product. This example shows that a full understanding
of ordinary observations can require allowance for the role of heavy-
atom tunneling.
11
12
13
RATE as the interface between POLYRATE and Gaussian03.
As shown in Table 1, the theoretical KIEs without allowance
for tunneling drastically underpredict the size of the observed values.
The error in these predictions grows larger as the temperature
decreases, rising to as large as 6%, but the error is still substantial
at the high end of the temperature range. In contrast, the predicted
KIEs that include tunneling match well with experiment throughout
the broad temperature range, with the error never exceeding 0.7%.
The effect of tunneling on the absolute rate of the ring-opening
of unlabeled 3, calculated from the ratio of CVT versus CVT/SCT
rate constants, is a factor of 1.3, 1.5, 1.6, 2.9, and 4.1 at 80, 22, 0,
Acknowledgment. This research was supported by NIH grant
GM-45617 at Texas A&M and by NSF grant CHE-0910527 at
UNT. W.T.B. also thanks the Robert A. Welch Foundation for
financial support.
Supporting Information Available: Complete descriptions and data
for experiments and calculations and complete refs 12 and 13. This
material is available free of charge via the Internet at http://pubs.acs.org.
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78, and -100 °C, respectively. With these modest calculated rate
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(
(
(
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(
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(
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(
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tunneling by the lighter isotope makes A( C)/A( C) > 1.0.
7
a
a
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JA1055593
J. AM. CHEM. SOC. 9 VOL. 132, NO. 36, 2010 12549