Dynamic effects on [3,3] and [1,3] shifts of 6-methylenebicyclo[3.2.0]hept- 2-ene

Article abstract of DOI:10.1002/anie.200500027

(Figure Presented) Deuterium labeling experiments on the rearrangement of methylenebicycloalkene 1 to 3 show stereoselectivity despite the intermediacy of a stabilized diradical structure 2. A theoretical model built from computational studies explains the observed product ratios. Stereoselectivity among [3,3] (minor) products implicates an unusual bifurcation of reaction trajectories after the initial bond-breaking transition state.

Full text of DOI:10.1002/anie.200500027

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ment of 6-methylenebicyclo[3.2.0]hept-2-ene (1) to 5-meth-
ylenenorbornene (3) is more intriguing, as it yields a non-
random distribution of products despite the stabilizing effect
of the 6-methylene substituent on the intermediate 2.
Dideuterio labeling has revealed a preference for [1,3] over
[3,3] shifts,[4] and the stereochemistry observed with methyl
labels has led to the hypothesis that diradical intermediates do
not equilibrate rotationally before collapsing to form the
bicyclic products.[5] New experimental studies of monodeu-
terated species currently show modest levels of both regio-
and stereoselectivity (Table 1),[6] and DFT and ab initio
calculations provide a theoretical framework for understand-
ing these results.
Reaction Dynamics
Dynamic Effects on [3,3] and [1,3] Shifts of
6-Methylenebicyclo[3.2.0]hept-2-ene**
Christopher P. Suhrada, Cenk Selꢀuki, Maja Nendel,
Carina Cannizzaro, K. N. Houk,* Peter-Jꢁrgen Rissing,
Dirk Baumann, and Dieter Hasselmann*
Table 1: Deuterium label distribution in product 3 from the thermolysis
of 7x-, 8E-, and 8Z-1, extrapolated to t=0 min.
Educt
6x-3
6n-3
8E-3
8Z-3
Dedicated to Professor Wolfgang Kirmse on the occasion of
his 75th birthday
7x-1
8E-1
8Z-1
0.37
0.13
0.24
0.20
0.23
0.14
0.22
0.64
–
0.21
–
0.62
The controversies over concerted versus stepwise diradical
mechanisms of potentially pericyclic reactions have subsided
with improvements in the understanding of stereoselectivity
in thermal rearrangements that involve modestly stabilized
diradical intermediates. The thermal rearrangements of
vinylcyclopropanes[1] and vinylcyclobutanes,[2] including
bicyclo[3.2.0]hept-2-ene,[3] involve diradical intermediates
that lack a deep potential energy well, and their outcomes
deviate from statistical predictions. The thermal rearrange-
UB3LYP and CASSCF calculations indicate that two
ꢀ
modes of C1 C7 cleavage produce stereoisomeric diallyl
intermediates 2 from 1 (Figure 1). The favored transition
state, TS-12n, moves C7 toward C3 and places the 7x
substituent in an E configuration. In contrast, TS-12x moves
C7 away from C3 and puts the 7x substituent in the Z position.
The preference (1.8 kcalmolꢀ1; CASPT2//UB3LYP) for TS-
12n over TS-12x is analogous to torquoselectivity in electro-
[*] C. P. Suhrada, Dr. C. Selꢀuki, Dr. M. Nendel, Dr. C. Cannizzaro,
Prof. Dr. K. N. Houk
Department of Chemistry and Biochemistry
University of California, Los Angeles
Los Angeles, CA 90095-0569 (USA)
Fax: (+1)310-206-8143
E-mail: houk@chem.ucla.edu
Dr. P.-J. Rissing, Dr. D. Baumann, Prof. Dr. D. Hasselmann
Fakultꢁt fꢂr Chemie, Organische Chemie II
Ruhr-Universitꢁt Bochum
44780 Bochum (Germany)
Fax: (+49)234-32-14109
E-mail: dieter.hasselmann@ruhr-uni-bochum.de
[**] Work at UCLA was supported by the National Science Foundation
(research grant to K.N.H. and IGERT fellowship to C.P.S.) and
TUBITAK (fellowship to C.S.). The Bochum group thanks the
Deutsche Forschungsgemeinschaft and Fonds der Chemischen
Industrie.
Figure 1. Two transition states for bond breaking lead to stereoiso-
meric diallyl intermediates 2. Structures shown are (U)B3LYP-opti-
mized with selected bond distances indicated in angstroms. Enthalpy
values (CASPT2//UB3LYP), in kcalmolꢀ1 relative to that of 1, are listed
below each structure label.
Supporting information for this article is available on the WWW
under http://www.angewandte.org or from the author.
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DOI: 10.1002/anie.200500027
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Angewandte
Chemie
cyclic ring openings;[7] the favored structure minimizes closed-
shell repulsion and maximizes hyperconjugation between the
senses (Figure 3). Both transition states involve the formation
of a bond between C3 and the proximal allyl terminus in 2.[8]
From a given intermediate 2, the two products 3 that can be
formed are thus epimers with respect to the substituents on
that carbon. TS-23n is favored slightly and places the pseudo-
E substituent in the 6x position in the product; TS-23x places
the same substituent in the 6n position.
ꢀ
ꢀ
orbitals of the breaking C1 C7 s bond and the C2 C3 p bond.
Also, TS-12x brings the 8Z hydrogen atom into close
proximity with the one in the 4-cis position.
The diradical 2 lies 4.3 kcalmolꢀ1 below TS-12n. Once
ꢀ
formed, 2 can isomerize by rotation about the C5 C6 bond
with a calculated barrier of only 2.4 kcalmolꢀ1 (TS-22,
Figure 2). This motion exchanges the positions of C7 and
Figure 3. Two cyclization routes form epimeric products from a given
intermediate 2. Structures shown are (U)B3LYP-optimized with
selected bond distances indicated in angstroms. Enthalpy values
(CASPT2//UB3LYP), in kcalmolꢀ1 relative to that of 1, are listed below
each structure label.
ꢀ
Figure 2. Rotation about C5 C6 exchanges the position of proximal
and distal allyl termini, yet the pseudo-E/Z configuration of substitu-
ents is preserved. Structures shown are (U)B3LYP-optimized with
selected bond distances indicated in angstroms. Enthalpy values
(CASPT2//UB3LYP), in kcalmolꢀ1 relative to that of 1, are listed below
each structure label.
TS-23n and TS-23x lie only 2.0 and 2.5 kcalmolꢀ1 above 2,
respectively. Compared with 2.4 kcalmolꢀ1 for TS-22, this
suggests that cyclization competes with conformational
isomerization in the intermediate, and therefore a majority
of products will come from an intermediate in the conforma-
tion in which it is initially formed.
These pathways imply the kinetic model outlined in
Scheme 1 for a single-labeled system. For comparison with
the experimental zero-time data, reversions from 2 to 1 may
C8. Allylic stabilization preserves the pseudo-E/Z configu-
ration of C7 and C8 substituents during the lifetime of the
ꢀ
ꢀ
intermediate; barriers for rotation about C6 C7 and C6 C8
are calculated to be ꢁ 12–13 kcalmolꢀ1 higher than those that
separate 2 from the product 3.
In analogy to the bond-breaking step, the formation of a
new bond at C3 can occur in two different stereochemical
Scheme 1. Stepwise kinetic model for rearrangements of 1 bearing a single deuterium label on C7 or C8.
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3549

Communications
be ignored,[9] and the relative yield of products can be
computed based on three independent parameters, related to
k12n versus k12x, and k23n versus k23x versus k22 (Supporting
Information).
With the model in Scheme 1 and the selectivity parame-
ters from CASPT2//UB3LYP transition-state energies, calcu-
lations predict the product distribution listed in Table 2,
The problem is solved by incorporating a concerted Cope
pathway into the stepwise model. The addition of a corre-
sponding fourth selectivity parameter, described below,
improves the fit from R2 = 0.628 to R2 = 0.969 (Table 2,
Column 4). The goodness of fit alone is evidence to support
the presence of such a pathway, yet how can this be reconciled
theoretically? Examination of the potential energy surface of
the reaction gives clues to what may be
happening.[10] Preliminary single-point
Table 2: Product distributions from experiment, CASPT2//UB3LYP calculations, and least-squares fits
of two theoretical models to the experimental data. Corresponding kinetic parameters and relative TS
energies are listed along with predicted product distributions.[a]
energy calculations prompted us to suspect
that
a
CASPT2//UB3LYP treatment[11]
would give the most accurate representation
of the PES shape (Figure 4a). At this level
of theory, the TS-12x saddle point lies at a
low value of R(3,8), and the transition
vector has a component in the negative
R(3,8) direction. At the same time, the
flattening of the diradical potential energy
well shifts TS-23x toward larger values of
R(3,8), positioning it almost directly in front
of TS-12x. Thus situated, one can easily
envision how TS-23x might bifurcate the
ensemble of trajectories passing over TS-
12x, sending them either to intermediate 2
or to the product 3 (Figure 4b).[12]
According to this model, TS-12x is
populated based on its relative free energy,
as before. After the transition state, that
population is divided into two portions
according to a new parameter. One portion
goes to 2 and a statistical distribution of
products from there, and the other produces
[3s,3s]-3 directly. The relative TS energies
corresponding to this fit are listed in Table 2
and agree reasonably well with CASPT2//
UB3LYP values. As for the additional
parameter, the fit suggests that 81 ꢂ 16%
of the TS-12x trajectories (16% of the total
product distribution) go directly to 3.
Experiment
CASPT2//UB3LYP
(fully stepwise)
Least-squares fit
(fully stepwise)
Least-squares fit
(stepwise plus
concerted [3s,3s])
7x-1!6x-3
0.37
0.20
0.22
0.21
0.63
0.23
0.14
0.39
0.25
0.26
0.10
0.64
0.13
0.23
0.33
0.28
0.20
0.19
0.62
0.17
0.21
0.39
0.22
0.20
0.19
0.61
0.24
0.15
7x-1!6n-3
7x-1!8E-3
7x-1!8Z-3
8E-1!8E-3[b]
8E-1!6n-3[b]
8E-1!6x-3[b]
R2[c]
(1.000)
(0.251)
0.628
0.969
k12n/(k12n+ k12x
)
–
–
–
–
0.861
0.308
0.634
–
0.744
0.265
0.556
–
0.797
0.252
0.643
0.808
k22/(2k22+ k23n + k23x
k23n/(k23n+ k23x
Fraction direct
)
)
TS-12x to [3s,3s]-3
DDG°ðTS-12xꢀTS-12nÞ
DDG°ðTS-22ꢀTS-23nÞ
DDG°ðTS-23xꢀTS-23nÞ
–
–
–
+1.8
+0.4
+0.5
+1.0
+0.7
+0.2
+1.3
+0.9
+0.6
[a] For CASPT2//UB3LYP, relative TS energies (DDH°) give parameters that produce the product
distribution. Least-squares fits produce both kinetic parameters and expected values for the product
distribution; relative TS energies are calculated from the kinetic parameters thus obtained. [b] The 8E-1
and 8Z-1 experiments are redundant under all models considered, excluding isotope effects. For this
reason, they have been averaged for comparison and fit to theory to simplify the analysis and not to
assign the two 8-d-1 experiments undue weight in comparison with the single 7-d-1 experiment. For
example, the entry for 8E-1!6n-3 is actually the average of experimental proportion in which 8E-1 forms
6n-3, and 8Z-1 forms 6x-3. [c] R2 =ꢀ(ypredictedꢀyexpt)2/ꢀ(yexptꢀyrandom
)
in which yrandom represents the
2
hypothetical nonselective product distribution: yrandom =0.25 for each product except the [1,3] product in
the 8-d-1 experiment, for which yrandom =0.50. Although the CASPT2//UB3LYP prediction does not
involve a fit to experiment, the R2 analysis is applied for comparison with the least-squares results.
Having obtained an adequate quantita-
tive fit between theory and experiment, we
consider the fact that the experimental
[1,3]/[3,3] ratio is subject to a large posi-
Column 2. The major products of both experiments are
correctly identified, although the minor product ratios deviate
from experiment markedly.
tional secondary isotope effect, outside of probable error
limits: [1,3]/[3,3] = 58:42 from 7x-1 but 63:37 from 8E-1 or
8Z-1 (see also Reference [4]). This remains puzzling:
although our calculations predict reasonable isotope effects
for the various rate constants in Scheme 1, their combined
effect (60:40 from 7x-1 versus 61:39 from 8-d-1) is much
smaller than what is experimentally observed.
In summary, experiments and calculations reported herein
establish how [1,3] versus [3,3] and [1i,3s] versus [1r,3s]
preferences may arise in a strictly stepwise reaction as a result
of stereoelectronic effects on the breakage and formation of
bonds, along with incomplete conformational equilibration
among intermediate diradicals. Whereas much of the
observed selectivity can be explained by a fully stepwise,
statistical model, we find that there is also a role for a formally
concerted Cope pathway in the form of a nonstatistical post-
We have also worked backward from the experimental
result by means of a least-squares fit, to determine what
combination of relative rates would lead to the observed
outcome. Such a fit produces selectivity parameters and a
corresponding expected product distribution, shown in
Column 3 of Table 2. The fit parameters match the exper-
imental outcome more closely, despite the fact that they differ
only slightly from the CASPT2//UB3LYP predictions. How-
ever, closer inspection shows that the fit still does not
reproduce the experimental result satisfactorily in all cases.
For instance, the ratio among [3,3] products from 8-d-1 (i.e.,
8E-1 and 8Z-1) is reversed, whereas the proportion of [1r,3s]
products in the 7x-1 experiment is higher than it should be.
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isomers by vapor-phase gas chromatography. Isotopomeric ratios
were extrapolated to a thermolysis time t = 0 (Table 1).
Structures of 1 and 3, as well as that of the intervening diradical 2
and associated transition species were optimized with both UB3LYP/
6-31G(d)
and
(6,6)CASSCF/6-31G(d)
in
Gaussian98.[13]
(6,6)CASPT2/6-31G(d) single-point energies were calculated for
both sets of stationary points in MOLCAS.[14] Kinetic isotope effects
were calculated in the program Quiver[15] based on UB3LYP/6-
31G(d) frequency data.
Received: January 4, 2005
Published online: April 28, 2005
Keywords: ab initio calculations · density functional
.
calculations · diastereoselectivity · reaction mechanisms ·
sigmatropic rearrangement
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[8] It is immediately evident that TS-23n forms a bond from C3 to
the proximal allyl terminus. Although it appears feasible that TS-
23x might involve rotation of the distal allyl carbon past C4 and
into bonding distance with C3, IRC calculations show that this is
not the case: the bond is formed to the proximal carbon in TS-
23x as well as TS-23n.
[9] Although isotopomers of the educt 1 begin to accumulate with
time, their effect on the distribution of labels in the product 3
vanishes upon extrapolation to t = 0. Examination of 1 at high
levels of conversion shows a preponderance of the starting
isotopomer, indicating that educt isomerization is slow in
comparison with product formation. Regardless of its magni-
tude, the rate k21 is the same for all intermediates 2, and
therefore may be ignored in the computation of label distribu-
tion in product 3.
Figure 4. a) Two-dimensional projection of the potential energy surface
for the rearrangement of 1 to 3. The plot was mapped with CASPT2
single-point energy calculations on UB3LYP constrained-optimized
structures at intervals of 0.05 ꢃ in the coordinates R(1,7) and R(3,8),
the bond-breakage and formation distances, respectively, for a [3,3]
shift. Energy contours are marked in kcalmolꢀ1, relative to 1. b) Three-
dimensional representation of plot in part a) that schematically
illustrates the concept of bifurcation of TS-12x reaction trajectories by
TS-23x.
transition-state bifurcation. Dynamic simulations may yield
additional insight into this process.
[10] A transition state for a concerted [3s,3s] reaction, as well as one
for a concerted [1i,3s] process, can be located with RB3LYP/6-
31G(d) (Supporting Information), but these saddle points are
only artifacts of the restricted formalism, and they disappear at
the UB3LYP level.
[11] A CASPT2 single-point energy calculation was performed on
each of the UB3LYP constrained-optimized structures used to
construct the UB3LYP surface.
Experimental Section
The preparation of 7x-, 8E-, and 8Z-1 is described in the Supporting
Information. Thermolyses were carried out in the gas phase at 2208C
in a 20-L reaction flask at 1 to 3 mbar. n-Nonane served as an internal
standard and n-hexane as collision partner. Samples were taken after
approximately 20%, 40%, 60%, and 80% structural isomerization of
starting material. Besides 3, the only products observed were
isotopomers of 1. Ratios of individual isotopomers were determined
[12] A PES involving a post-TS bifurcation between a Cope pathway
and formation of an allylic-stabilized diradical intermediate has
been discussed in the case of an acyclic allenic triene: S. L.
2
by H NMR spectroscopy (61.4 MHz) after separation of structural
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Communications
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