Isotope effects and heavy-atom tunneling in the Roush allylboration of aldehydes

Article abstract of DOI:10.1021/ol300789a

Intermolecular ¹³C kinetic isotope effects (KIEs) for the Roush allylboration of p-anisaldehyde were determined using a novel approach. The experimental ¹³C KIEs fit qualitatively with the expected rate-limiting cyclic transition sta

Full text of DOI:10.1021/ol300789a

ORGANIC
LETTERS
2012
Vol. 14, No. 9
2370–2373
Isotope Effects and Heavy-Atom Tunneling
in the Roush Allylboration of Aldehydes
Mathew J. Vetticatt† and Daniel A. Singleton*
Department of Chemistry, Texas A&M University, P.O. Box 30012, College Station,
Texas 77842, United States
singleton@mail.chem.tamu.edu
Received March 27, 2012
ABSTRACT
Intermolecular 13C kinetic isotope effects (KIEs) for the Roush allylboration of p-anisaldehyde were determined using a novel approach. The
experimental 13C KIEs fit qualitatively with the expected rate-limiting cyclic transition state, but they are far higher than theoretical predictions
based on conventional transition state theory. This discrepancy is attributed to a substantial contribution of heavy-atom tunneling to the reaction,
and this is supported by multidimensional tunneling calculations that reproduce the observed KIEs.
Tunneling allows reactive trajectories that do not adhere
to the classical limitation of the transition state energy, so
that conventional transition state theory (TST) under-
estimates the reaction rate. Large kinetic isotope effects
(KIEs) in hydrogen transfer reactions have often been
interpreted as a diagnostic for tunneling through the
reaction barrier.1,2 The extent of tunneling is mass depen-
dent and decreases with increasing mass of the atom. The
much larger mass of carbon decreases its tunneling prob-
ability, and consequently the effect of carbon tunneling on
reaction rates is often ignored. As a result, carbon tunnel-
ing is much less understood and has been addressed for
only a handful of chemical reactions.2 It has been observed
that allowance for tunneling improves the prediction of
heavy-atom isotope effects, but tunneling corrections in
most reactions not involving hydrogen transfer are very
small. As a result, heavy-atom KIE predictions based
solely on TST, not allowing for tunneling, are still usually
reasonably accurate3 and sufficient for mechanistic inter-
pretation.
We describe here a 13C isotope effect study of the Roush
allylboration reaction. The experimental KIEs in this
reaction are much larger than expected from TST, and
theoretical analysis suggests that the large KIEs result
from a surprisingly large contribution of tunneling to the
reaction. The results provide several insights into the role
of heavy-atom tunneling in ordinary organic reactions.
The allylboration ofaldehydes(eq1inScheme 1) affords
homoallylic alcohols and formally accomplishes an aldol
reaction when coupled with oxidative cleavage of the
alkene. Enantioselective versions of this reaction have
proven to be particularly useful because the stereochemical
and regiochemical outcome is readily predictable and is
† Current address: Department of Chemistry, Michigan State University,
East Lansing, Michigan 48824.
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r
10.1021/ol300789a
Published on Web 04/16/2012
2012 American Chemical Society

consistent with a formal ene reaction proceeding by the
chairlike transition state 2.4
the 13C KIEs for both components in the allylboration
reaction were determined by NMR analysis at natural
abundance.9 The results are summarized in Figure 1.
Scheme 1. Chairlike Transition State for Allylboration Reaction
Scheme 2. Design of Allylboration KIE Experiment
Mechanistically, these are well-behaved reactions with
straightforward bimolecular kinetics.5 Gajewski observed
a significantly inverse secondary deuterium kinetic isotope
effect (KIE) in the addition ofthe Roush allylboronate4a to
benzaldehyde, consistent with rate-limiting addition to the
carbonyl and inconsistent with rate-limiting single-elec-
tron transfer.6 Theoreticalstudies have supported the basic
mechanistic picture derived initially from experimental
observations7 and have identified stereochemical control
elements in the enantioselective reactions.8 From our
perspective, the reaction provided a special opportunity
to measure a series of differing 13C KIEs at low tem-
perature.
C1, C2, and C4 all exhibit substantial 13C KIEs, and
their normal qualitative interpretation is that all three
carbons are undergoing σ-bonding changes in the rate-
limitingtransitionstate. Thisisnot anunexpected result, as
it fits with the conventional cyclic mechanism in the
qualitative transition state 2. The KIEs notably suggest
that the transition state is relatively synchronous (for
comparison the 13C KIEs in asynchronous DielsꢀAlder
reactions are more uneven10) though the larger KIEs at C1
and C2 versus C4 suggest that CꢀC bond formation is
more advanced than CꢀB bond breaking. This argument
assumes that the transition state is not late, as seems
reasonable for a one-step exothermic reaction. Although
aldehydeꢀboronate complexes are surely intermediates in
these reactions, the large KIEs show that complex forma-
tion must be reversible. Additionally, the slightly inverse
KIE for C3 is also consistent with its restricted environ-
ment at the transition state.
The reaction of the Roush (þ)-diisopropyl L-tartrate-
modified allylboronate 4 with 5 proceeds smoothly at
ꢀ78 °C and affords the homoallylic alcohol 6 in quantita-
tive yield and 52% ee based on NMR analysis using
Eu(hfc)3 after basic hydrolysis (eq 2). In principle the 13
C
KIEs in the reaction could be obtained from either analysis
of recovered starting materials or analysis of the product,
but in practice the difficulty of recovering the allylboronate
quantitatively precludes a starting material analysis. Pro-
duct analysis is also subject to a problem that is common in
KIE measurements, that is, the isotopic composition of
products from reactions taken to low conversion must be
compared to product in which no isotopic fractionation
has occurred, most commonly product taken from reac-
tions taken to “100%” conversion. This method is subject
to error because small departures from a true 100%
conversion lead to relatively large errors in the KIEs, and
100% conversion of both reactants is difficult to achieve in
a bimolecular stoichiometric reaction. To avoid this pro-
blem, multiple reactions forming isotopic standards would
be required. The experimental design used here, as shown
in Scheme 2, requires only two reactions, the key idea being
that the low-conversion reaction for one of the starting
materials serves as the 100%-reaction standard for the
other starting material, and vice versa. Using this design,
Figure 1. Experimental 13C KIEs (k12C/k13C, ꢀ78 °C) for the
reaction of 4 with 5. The two sets of KIEs represent two
independent experiments, and the standard deviations from
six measurements are indicated in parentheses. A second mea-
surement at the ortho carbon was precluded by interference
from solvent C6D6.
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Lett. 1989, 30, 6457–6460.
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As a first step in the quantitative interpretation of the
experimental KIEs, fully optimized transition structure
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Org. Lett., Vol. 14, No. 9, 2012
2371

geometries for the reaction of 4 with 5 were obtained in
M06-2X/6-31þG** calculations,11 both in the gas phase
and using a PCM solvent model12 for dichloromethane.
The lowest-energy PCM transition structure 7 (Figure 2)
involves attack of the allyl moiety on the si face of the
aldehyde (given the L-tartrate-derived 4). An alternative
structure for the re addition (see the Supporting Information)
was found to be 0.5 kcal/mol higher in energy (M06-2X/
6-31þG**/PCM þ zpe), fitting well with the experimental
enantioselectivity (with a ΔΔG‡ of 0.45 kcal/mol).
conventional TST predictions have no allowance for either
tunneling or recrossing, we have also generated KIE pre-
dictions based on canonical variational transition state
theory15 (CVT) with the effect of multidimensional tunnel-
ing on the reaction dynamics computed using the small-
curvature tunneling16 (SCT) approximation.
Table 1. Predicted versus Experimental 13CKIEs(k12/k13, ꢀ78 °C)
from Conventional TST and from CVT/SCT
method
C1
C2
C3
C4
conventional TST KIEsa
gas phase
PCM
1.038
1.041
1.026
1.025
0.997
0.998
1.018
1.016
CVT/SCT corrections
1.010
gas phase
PCM
1.008
1.010
1.001
1.001
1.003
1.002
1.013
CVT/SCT KIEsb
1.036
gas phase
PCM
1.047
1.052
0.998
0.999
1.020
1.019
1.038
experimental KIEs
1.052(5)
1.051(4)
1.036(5)
1.034(3)
0.997(5)
0.997(3)
1.019(8)
1.023(5)
a The conventional TST KIEs shown are based on 7. The corre-
sponding KIEs for the lowest-energy transition structure leading to the
minor enantiomer, 24% of the reaction, are within 0.0012 of those
shown in each case. b The CVT/SCT KIEs were obtained by multiplying
the conventional TST KIEs by corrections obtained from model-system
CVT/SCT calculations.
The prediction of small KIEs by the CVT/SCT method
has the problem that tight convergence criteria and small
step sizes are required for sufficient numerical conver-
gence. This made a CVT/SCT study of the full system with
the best calculational level and solvent model impractical.
Instead, the CVT/SCT study was carried out for a simpli-
fiedmodelof4 inwhich the ester groupswerereplaced with
hydrogen atoms. These calculations were performed using
GAUSSRATE17 as the interface between POLYRATE18
and Gaussian 09.19 The semiclassical rate constants were
computed using the PageꢀMcIver method20 to follow the
minimum energy path (MEP) with a step size of 0.001
bohr. The Hessian matrix was recalculated, and a mode
analysis was performed every 0.01 bohr. The predicted
TST and CVT/SCT KIEs for each carbon atom were
computed from the rate constants obtained from the
parent calculation (all carbon atoms being 12C) and cal-
culations with a 13C label at each carbon atom of interest.
Figure 2. Lowest-energy transition structures for the reaction of
4 with p-anisaldehyde (5). The distances in italics are M06-2X/
6-31þG** (gas phase) while nonitalicized distances are M06-2X/
6-31þG**/PCM. Some hydrogens have been removed for clarity.
The 13C KIEs predicted from conventional TST for
transition structure 7 were calculated from the scaled
theoretical vibrational frequencies13 by the method of
Bigeleisen and Mayer (Table1).14 The first key observation
from Table 1 is that irrespective of the calculational
method, the predicted KIEs based on TST are significantly
lower than the experimental values. This discrepancy is
most pronounced for C1 and C2, the two carbon atoms
that are most intimately associated with motion along
the reaction coordinate at the transition state. Since
(11) A very similar complete set of results was obtained in B3LYP
calculations, and more limited explorations were carried out in MP2,
M05, and MPW1K calculations; see the Supporting Information for
details. The M06-2X calculations are expected to perform better than
B3LYP here due to the weakness of B3LYP calculations in handling the
dative bonds to boron, but the two methods predict very similar
transition structures and isotope effects.
(15) Truhlar, D. G.; Garrett, B. C. Acc. Chem. Res. 1980, 13, 440–
448.
(16) Lu, D. H.; Truong, T. N.; Melissas, V. S.; Lynch, G. C.; Liu, Y.-P.;
Garrett, B. C.; Steckler, R.; Isaacson, A. D.; Rai, S. N.; Hancock, G. C.;
Lauderdale, J. G.; Joseph, T.; Truhlar, D. G. Comput. Phys. Commun.
1992, 71, 235–262.
(17) Zheng, J.; Zhang, S.; Corchado, J. C.; Chuang, Y.-Y.; Coitino,
E. L.; Ellingson, B. A.; Truhlar, D. G. GAUSSRATE, version 2009-A;
University of Minnesota: Minneapolis, MN, 2010.
(18) Zheng, J.; et al. POLYRATEꢀversion 2010; University of
Minnesota: Minneapolis, MN, 2010.
(12) Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027–2094.
(13) The calculations used the program QUIVER (Saunders, M.;
Laidig, K. E.; Wolfsberg, M. J. Am. Chem. Soc. 1989, 111, 8989–8994).
All frequencies were scaled by 0.9614; small changes in the scaling factor
have a negligible effect on the predicted isotope effects.
(19) Frisch, M. J.; et al. Gaussian 09, revision A.02; Gaussian, Inc.:
Wallingford, CT, 2009.
(20) Page, M.; McIver, J. W., Jr. J. Chem. Phys. 1988, 88, 922–935.
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267. (b) Wolfsberg, M. Acc. Chem. Res. 1972, 5, 225–233. (c) Bigeleisen,
J. J. Chem. Phys. 1949, 17, 675–678.
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Org. Lett., Vol. 14, No. 9, 2012

The ratios of the CVT/SCT and TST KIEs for the model
system at ꢀ78 °C are listed in Table 1. These ratios were
then applied as corrections to the TST KIEs for the full
systems.21 Upon inclusion of the contributions from tun-
neling and statistically predictable recrossing,22 the pre-
dicted KIEs are in excellent agreement with the
experimental KIEs (Table 1). This agreement with the
inclusion of heavy-atom tunneling versus the disagreement
when not including it strongly supports the role of heavy-
atom tunneling in the reaction.
CVT/SCT versus CVT rate constants, the acceleration due
to tunneling is a factor of 1.36.
It is understood that tunneling contributes to the rates of
all reactions passing though a barrier. Except for reactions
at exceedingly low temperatures,2 however, the role of
heavy-atom tunneling in organic reactions has been gen-
erally been assumed to be trivial. In the case of the ring
opening of a cyclopropylcarbinyl radical, we recently
demonstrated that there were relatively large effects of
heavy-atom tunneling at ꢀ100 °C,2h but the cyclopropyl-
carbinyl radical system has been postulated to be an
exceptional case owing to an unusually narrow barrier in
the reaction.23 The allylboration reaction here is a perfectly
ordinary organic reaction, and the temperature, while low,
is one that is commonly used in organic chemistry. The
effect of tunneling on the 13C KIEs is not as large as it was
with the cyclopropylcarbinyl radical case, but it is large
enough that the experimental observations cannot be
understood without allowing for heavy-atom tunneling.
The rate acceleration due to tunneling by a factor of 1.36
is not directly recognizable in the rate of the reaction; an
Arrhenius plot of the rate versus temperature between ꢀ78
and 0 °C would not be detectably nonlinear, and there is
never a theory-independent way of knowing what the
rate would be in the absence of tunneling. In this
respect, the heavy-atom tunneling is hidden from che-
mists, and we only know about it from its effect on the
KIEs. Despite the hidden character of this acceleration,
it has a substantial effect on how long the reaction
takes. Heavy-atom tunneling plays a role in simple
everyday organic reactions.
A number of observations in the results provide notable
new insights. First, tunneling increases all of the 13C KIEs,
even the inverse KIE at C3. The effect at C3 is obviously
small, only 0.1%, but C3 is moving as the reaction
coordinate progresses; this leads to a tunneling effect on
the KIE. Second, the contribution of tunneling to the KIEs
is a large part of their observed values. The KIEs consist of
three parts:14b,c a part due to changes in the reduced
isotopic partition function between the starting material
and transition state (which tends to be dominated by zero-
point energy effects), a part due to the ratio of imaginary
frequencies for parent versus substituted isotopologs
(which is largely the entropic part of the KIE), and a part
due to tunneling. For the KIE at C2, the parts are 18%,
48%, and 34% of the isotope effect, respectively. Heavy-
atom tunneling is more important to the KIE at C2 than is
zero-point energy! A third observation is that the largest
impact of tunneling on the KIEs does not occur at the
position with the largest KIE. C2 is the atom moving the
greatestamount inthe transition vector, and theCVT/SCT
correction at C2 is larger than that at C1 despite the KIE at
C1 being larger. This shows that the magnitude of the KIE
by itself is not a good indicator of the impact of tunneling.
A final observation is that heavy-atom tunneling is having
a substantial and, to our view, surprisingly large effect on
the absolute rate of the reaction. Based on the ratio of
Acknowledgment. We thank NIH Grant No. GM-
45617 for financial support.
Supporting Information Available. Experimental and
calculational procedures, additional calculations, ener-
gies and geometries of all calculated structures, and
complete refs 18 and 19. This material is available free
of charge via the Internet at http://pubs.acs.org.
(21) The process here of using the Bigeleisen and Mayer method (see
ref 14) to calculate the TST isotope effects and using GAUSSRATE/
POLYRATE to calculate CVT/SCT corrections was found to minimize
numerical error, as is important in the calculation of very small isotope
effects. For discussions of the advantages of the Bigeleisen and Mayer
method, see: (a) Schaad, L. J.; Bytautas, L.; Houk, K. N. Can. J. Chem.
1999, 77, 875–878. (b) Hirschi, J. S.; Takeya, T.; Hang, C.; Singleton,
D. A. J. Am. Chem. Soc. 2009, 131, 2397–2403.
(23) Datta, A.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2008,
130, 6684–6685.
(22) CVT repositions the transition state hypersurface to minimize
recrossing.
The authors declare no competing financial interest.
Org. Lett., Vol. 14, No. 9, 2012
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