Isotope effects, dynamic matching, and solvent dynamics in a Wittig reaction. Betaines as bypassed intermediates

Article abstract of DOI:10.1021/ja506497b

The mechanism of the Wittig reaction of anisaldehyde with a stabilized ylide was studied by a combination of ¹³C kinetic isotope effects, conventional calculations, and molecular dynamics calculations in a cluster of 53 THF molecules. The isoto

Full text of DOI:10.1021/ja506497b

Communication
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Open Access on 09/11/2015
Isotope Effects, Dynamic Matching, and Solvent Dynamics in a Wittig
Reaction. Betaines as Bypassed Intermediates
Zhuo Chen, Yexenia Nieves-Quinones, Jack R. Waas, and Daniel A. Singleton*
Department of Chemistry, Texas A&M University, P.O. Box 30012, College Station, Texas 77842, United States
S
* Supporting Information
limitation as all such evidence: it can only show that the lifetime
ABSTRACT: The mechanism of the Wittig reaction of
anisaldehyde with a stabilized ylide was studied by a
combination of 13C kinetic isotope effects, conventional
calculations, and molecular dynamics calculations in a
cluster of 53 THF molecules. The isotope effects support a
cycloaddition mechanism involving two sequential tran-
sition states associated with separate C−C and P−O bond
formations. However, the betaine structure in between the
two transition states is bypassed as an equilibrated
intermediate in most trajectories. The role of the dynamics
of solvent equilibration in the nature of mechanistic
intermediates is discussed.
of any intermediate is insufficient for stereochemical equilibra-
tion. The computational studies are naturally subject to the
usual concerns over the accuracy of the calculated energy
surface, but they are also subject to other subtler if potentially
substantial defects. We have previously shown that statistical or
nonstatistical dynamics can complicate the understanding of
reactions that appear concerted in simplistic calculations, for
example by leading to kinetically important intermediates that
are not observable on the potential energy surface.7 Here, a
combined experimental, computational, and dynamic trajectory
study provides evidence for a betaine intermediate in the
cycloaddition, but we then see how dynamics complicates the
nature of that intermediate. Our results highlight the
inadequacy of the conventional mechanistic paradigm for
subtle mechanistic questions in complex solution reactions.
The role of dynamics in the Wittig reaction was initially of
interest because of the exceptional asynchronicity of the
putative cycloadditions, exhibiting P−O interatomic distances
of up to 4.4 Å in calculated structures.5 We have observed that
asynchronous cycloadditions can be subject to substantial
transition-state recrossing, and we had found that kinetic
isotope effects (KIEs) can be used to probe this otherwise
hidden phenomenon.7b,8 We therefore sought to examine the
Wittig reaction using KIEs and trajectory calculations.
long-standing textbook mechanism of the Wittig reaction
A
involved a two-step formation of the observable
oxaphosphetane species via a betaine intermediate. For Wittig
reactions under salt-free conditions, this “betaine mechanism”
has been largely dismissed in the recent literature. An elegant
The reaction of anisaldehyde (1) with the stabilized ylide 2
was chosen for study. The 13C KIEs for this clean homogeneous
reaction were determined at natural abundance by NMR
methodology. For reactions of 1 at 67 °C taken to 69 2% and
73 2% conversion, the reisolated unreacted 1 was analyzed by
13C NMR in comparison with samples of 1 that had not been
subjected to the reaction conditions. For the ylide carbon of 2,
stereochemical experiment by Vedejs and Marth provided key
evidence in its observation of differing oxaphosphetane
mixtures from the Wittig reaction versus independently
generated betaine.1 In place of the betaine mechanism, Vedejs
proposed that the phosphonium ylide and carbonyl compound
undergo an asynchronous [2+2] cycloaddition to afford the
oxaphosphetane. Diverse experimental observations and
computational studies have supported a concerted cyclo-
addition mechanism.2−5 The evidence against the intermediacy
of betaines has been described as overwhelming.3,4,6
The older support for the betaine mechanism had largely
consisted of rationalizations of Wittig stereoselectivity in terms
of the reversibility of adduct formation, and in retrospect these
arguments were flawed.4 However, the evidence for a concerted
cycloaddition to afford the oxaphosphetane is itself less than
conclusive. As recognized by Vedejs, the stereochemical
evidence for a concerted cycloaddition is subject to the same
the 13C KIE was measured by analysis of samples of 3 from
reactions in which 2 was taken to 20% conversion versus
samples of 3 obtained from complete conversion of 2 using
excess 1. In the analyses, the carbons meta to the aldehyde of 1
and in the ketonic methyl group of 3 were used as internal
standards with the assumption that their isotopic fractionation
is negligible. From the changes in the relative isotopic
Received: June 27, 2014
© XXXX American Chemical Society
A
dx.doi.org/10.1021/ja506497b | J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
Communication
composition in the various positions, the 13C KIEs were
calculated in standard ways.
The results are summarized in Figure 1. The carbonyl carbon
of 1 exhibits a substantial 13C KIE, while the ylide carbon of 2
Figure 1. 13C KIEs (k12/k13, 67 °C) for the reaction of 1 with 2.
exhibits a modest but still significant KIE. These KIEs indicate
that carbon−carbon bond formation is either fully or at least
partially rate limiting. Qualitatively, this does not distinguish
between stepwise and concerted formation of the expected
oxaphosphetane intermediate.
Computations were used for a quantitative interpretation.
Diverse DFT methods were explored versus G3B3 calculations
for the model reaction of Me3PCHCHO with formaldehyde
[see the Supporting Information (SI)]. Previously employed
B3LYP calculations fared poorly, having average absolute errors
versus G3B3 of 4.2−6.2 kcal/mol. The lowest average errors,
only 1.0−1.3 kcal/mol, were seen in M06-2X, B3P86, and lc-
wPBE calculations with large basis sets (e.g., aug-cc-pvtz), but
these were impractical for full-system optimizations. Calcu-
lations with 6-31G* and 6-31+G** basis sets showed average
errors of 1.3− 2.6 kcal/mol and had relative energies for the key
transition states and intermediate (see below) that matched
closely with the large-basis results. We opted to use these basis
sets for geometry optimizations and dynamics, augmented by 6-
31+G(2df,p) single-point energies (average error 1.1 kcal/mol).
These calculations in combination with a PCM implicit solvent
model for THF were applied to the complete mechanism for
the full experimental system. An alternative solvent model
(SMD) and alternative solvation parameters were also explored,
with no qualitative difference in the results (see the SI).
The three “benchmarked” DFT methods each predict a
different mechanism. The M06-2X calculations nominally
predict a stepwise mechanism with competitive rate-limiting
steps (Figure 2). In this mechanism, 1 and 2 react via the
potential-energy saddle point 4⧧ to afford the potential-energy
minimum betaine 5. The formation of the oxaphosphetane 7 is
completed by P−O bond formation via saddle point 6⧧. The lc-
wPBE mechanism is concerted, with an asynchronous
transition state resembling 4⧧ (see the SI). The B3P86
mechanism is stepwise but with the second step, P−O bond
formation, being rate limiting.
Figure 2. Calculated pathway for the reaction of 1 with 2. Relative
potential energies are given in kcal/mol, with harmonic free energies in
parentheses.
Table 1. Predicted versus Experimental 13C KIEs
a
13C KIE
mechanism/method
ArCHO
1.043
Ph3PCHCOMe
concerted (lc-wPBE)
2nd step RLS (B3P86)
4⧧ (M06-2X)
1.024
0.998
1.022
0.994
1.008
1.012
1.017
1.043
1.015
1.028
1.033
6⧧ (M06-2X)
b
4⧧/6⧧ weighted
c
4⧧/6⧧ weighted
experimental
b
1.032−1.033
1.011
a
12
13C
k
C/k at 67 °C Weighted by the difference in harmonic free
energies at 67 °C in M06-2X/6-31+G(2df,p)//M06-2X/6-31+G**
c
calculations. Weighted from recrossings in trajectories.
So the KIEs strongly support a stepwise mechanism through
a betaine intermediate, but what does that mean? The
complexity of this question can be recognized by noting that
the betaine is predicted to be >1 kcal/mol higher in free energy
than either of the flanking transition states. (For the purpose of
comparison with classical trajectories below, it should be noted
that the same unusual order of relative free energies is obtained
using fully classical enthalpy/entropy calculations.) The energy
surface is extraordinarily flat over the broad range encompass-
ing 4⧧, 5, and 6⧧, varying by only 1.4 kcal/mol in potential
energy. Frequency calculations along the minimum-energy path
between 4⧧ and 6⧧ (projecting out the transition vector)
suggest that there is a minimum in the free energy within the
harmonic approximation, but the limitations of frequency
calculations and the harmonic approximation with a large
system on a small energy scale would make a detailed
interpretation dubious. A more subtle concern was that
continuum solvent models implicitly assume equilibrium
solvation. The dipole moment increases rapidly with C−C
bond formation, reaches a maximum of 10 D at 5, and then falls
to <5 D at 7. The time scale of trajectories was expected to be
faster than solvent can reorganize to maintain equilibrium
To distinguish these mechanisms, 13C KIEs were predicted
for each by conventional transition-state theory including a
one-dimensional tunneling correction.9 Such predictions have
been found to be highly accurate for diverse reactions, provided
that the mechanisms and calculated transition states are
accurate.10 Table 1 summarizes the results. Whether stepwise
or concerted, C−C bond formation entails large motions of the
carbonyl and ylide carbons in the transition vector and larger
KIEs than observed. With rate-limiting P−O bond formation,
the 13C KIE would be smaller for the carbonyl carbon and
inverse for the ylide carbon. Only the M06-2X mechanism with
competitively rate-limiting 4⧧ and 6⧧ agrees reasonably with
experiment.11
B
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Journal of the American Chemical Society
Communication
solvation. The same problem would apply to approaches
mapping the potential of mean force.
A first item of note is that the trajectories predict that the
cycloaddition is subject to two dynamical bottlenecks, one
involving C−C bond formation and resembling 4⧧, and a
second involving P−O bond formation and resembling 6⧧. The
presence of such bottlenecks is most readily recognized by the
paths of long trajectories such as D, I, and K in Figure 3 that
traverse the area between bottlenecks many times before
crossing one threshold or the other and proceeding to 7 or 1 +
2. A second item of note is the agreement of the trajectories
with experimental observations. That is, the proportion of
trajectories that fully form the C−C bond and then recross (i.e.,
with reversible betaine formation) versus those that form 7
(76:128) can be used to weight the expected contributions of
6⧧ versus 4⧧, respectively, to the overall observed KIE. (This
assumes that the KIEs predicted for the PCM structures are
reasonably representative of those for the solution bottlenecks.)
When this is done, the overall KIEs (Table 1) are in striking
agreement with experiment.
The trajectories themselves then tell an even more
interesting story. Many of the productive trajectories pass
directly through the area of 5 in the manner of B and G in
Figure 3. Such trajectories are indistinguishable from those of
many asynchronous concerted cycloadditions.7b,12 Nearly 30%
traverse the area between 4⧧ and 6⧧ within 100 fs and 50%
within 150 fs. Put another way, once the betaine is formed
(defined by a C−C distance <1.65 Å), its half-life is 90 fs, less
than two vibrations of the weak C−C bond. But the trajectories
are bimodal: At longer times, the betaine persists longer than
would be expected from the earlier decay (see the SI), and 5%
last 1−2 ps. On a shorter time scale, bimodal decay can arise
simply from the confounding effect of orthogonal vibrational
motions on bond formation,12b but the times here are more
suggestive of a competition between concerted and stepwise
pathways.
To learn about the nature of this “stepwise” mechanism and
the betaine with minimal assumptions, we carried out molecular
trajectory calculations in a cluster of 53 THF molecules in a
20.4 Å cubic box (density 0.84). In a series of independent
trajectories, the carbonyl atoms of 1 and the ylide carbon and
phosphorus atoms of 2 were constrained in the area of 4⧧ while
the full system was subjected first to an extended equilibration
in PM3 calculations and then to a 1.25 ps equilibration at 67 °C
in ONIOM calculations, using M06-2X/6-31G* for all atoms of
4⧧ and using PM3 for the THF molecules. The series of
constrained ONIOM equilibrations was then continued for 10
ps each. At 250 fs intervals, structures and velocities were
extracted, and the constrained atoms were given independent
Boltzmann-random velocities. The resulting unconstrained
trajectories were integrated forward and backward in time
using direct dynamics until either 7 was formed or 1 + 2 were
re-formed.
To gain insight into the bimodal behavior, we carried out a
series of trajectories in which the system was now equilibrated
in the area of 5, instead of 4⧧. The productive trajectories
resulting from this initialization in explicit THF now require a
median of 600 fs to traverse the area between 4⧧ and 6⧧, and
they bear no resemblance to concerted cycloadditions. The
half-life of the equilibrated betaine is now 260 fs.
Our interpretation of these results is that, in trajectories
started from 4⧧, the “full intermediacy” of a betaine is
bypassed.13 Trajectories certainly pass through the area of 5,
but few linger. They either rapidly pass through 6⧧ or are
rapidly reflected by the bottleneck of 6⧧. Why? The equilibrium
stability of an intermediate by definition reflects the complete
ensemble of accessible molecular and solvent structures, but
most trajectories here do not have time to representatively
explore this ensemble. When 5 is formed from 4⧧, neither the
atomic motions nor the solvation is initially equilibrated. The
effect of the former can be discerned in the shortest 10−20% of
trajectories through the area of 5; they lead to product or
starting-material channels by a direct continuation or reflection
of atomic motions along the path taken from 4⧧ (see
trajectories F and G in Figure 3, and see the SI for additional
trajectory plots). This is a form of dynamic matching,12c,14 in
which the path taken through an initial transition state dictates
the subsequent outcome of trajectories. Most trajectories,
however, lack discernible dynamic matching but still finish
much faster than those from equilibrated 5. Our hypothesis is
that this is an effect of the time required for solvent
reorganization. Optimal solvent stabilization of 5 simply takes
Figure 3. Stacked plot of the paths for C−C and P−O bond formation
in representative trajectories. See the SI for a movie and additional
plots.
A total of 302 trajectories were obtained, and Figure 3
illustrates representative examples. Descriptively, the trajecto-
ries that result may be grouped into four categories:
(1) “productive trajectories” proceeding from 1 + 2 to 7 (B,
D, G, I, and M in Figure 3, observed in 128 cases)
(2) “deep recrossings” that fully form the C−C bond but
subsequently re-form 1 + 2 (A, F, K, and N in Figure 3,
76 cases)
(3) “immediate recrossings” that re-form 1 + 2 (C, H, and L
in Figure 3, 82 cases)
(4) trajectories passing from 7 to the area of 4⧧ and then re-
forming 7 (E and J in Figure 3, 16 cases)
By the nature of the simulation, it can only observe trajectories
traversing the area of 4⧧.
C
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Journal of the American Chemical Society
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(8) Ussing, B. R.; Hang, C.; Singleton, D. A. J. Am. Chem. Soc. 2006,
128, 7594−7607.
longer than its lifetime without such stabilization. The solvent
dynamics must compete with the molecular reaction dynamics,
and the latter are faster. For a portion of trajectories started
from 4⧧, however, the solvation either is better by chance to
start with or catches up when the completion of the trajectory is
delayed, leading to the bimodal behavior reflecting the longer
lifetime of an equilibrium-solvated intermediate.
(9) (a) Bigeleisen, J. J. Chem. Phys. 1949, 17, 675−678. (b) Bell, R. P.
The Tunnel Effect in Chemistry; Chapman & Hall: London, 1980; pp
60−63.
(10) (a) Beno, B. R.; Houk, K. N.; Singleton, D. A. J. Am. Chem. Soc.
1996, 118, 9984−9985. (b) Meyer, M. P.; DelMonte, A. J.; Singleton,
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2397−2403.
(11) The first step should become more rate limiting with more
reactive ylides or aldehydes and less rate limiting with less reactive
addends. This leads to the testable prediction that 13C KIEs will
increase in the former case and decrease in the latter case.
(12) (a) Thomas, J. R.; Waas, J. R.; Harmata, M.; Singleton, D. A. J.
Am. Chem. Soc. 2008, 130, 14544−14555. (b) Xu, L.; Doubleday, C.
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Z.; Hirschi, J. S.; Singleton, D. A. Angew. Chem., Int. Ed. 2009, 48,
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(13) For related phenomena, see: (a) Hu, X.; Hase, W. L. J. Phys.
Chem. 1992, 96, 7535−7546. (b) Nummela, J. A.; Carpenter, B. K. J.
Am. Chem. Soc. 2002, 124, 8512−8513. (c) Debbert, S. L.; Carpenter,
B. K.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 2002, 124,
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U.; Addepalli, S. V.; Kato, S.; DeJong, W. A.; Windus, T. L.; Hase, W.
L. J. Am. Chem. Soc. 2007, 129, 9976−9985. (f) Sun, L.; Song, K.;
Hase, W. L. Science 2002, 296, 875−878. (g) Ammal, S. C.; Yamataka,
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(14) Carpenter, B. K. J. Am. Chem. Soc. 1995, 117, 6336−6344.
The failure of the conventional paradigm dividing reactions
into concerted versus two-step processes should no longer be
surprising.7 Here, the experimental observations would
characterize a two-step mechanism with an intermediate,
while many of the productive trajectories are indistinguishable
from those of an ordinary concerted cycloaddition. The most
disconcerting aspect of our results, in our view, is the suggested
role of solvent dynamics in the nature of mechanistic
intermediates. That is, a putative intermediate may only
become an intermediate in a clear sense when the solvent
fully stabilizes it, and this takes time. Because of the role of
dynamics in this process, even energetically perfect calculations
employing any of the standard equilibrium methods cannot
unambiguously assign mechanisms.
ASSOCIATED CONTENT
* Supporting Information
■
S
Complete descriptions of experimental procedures, calcula-
tions, and structures, additional trajectory plots, and a movie of
Figure 3. This material is available free of charge via the
Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
singleton@mail.chem.tamu.edu
■
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
We thank the NIH (Grant GM-45617) for financial support.
■
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D
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