"Concerted" transition state, stepwise mechanism. Dynamics effects in C2-C6 enyne allene cyclizations

Article abstract of DOI:10.1021/ja0508673

The C²-C⁶ (Schmittel)/ene cyclization of enyne-allenes is studied by a combination of kinetic isotope effects, theoretical calculations, and dynamics trajectories. For the cyclization of allenol acetate 9, the isotope effect (k_C

Full text of DOI:10.1021/ja0508673

Published on Web 06/07/2005
“Concerted” Transition State, Stepwise Mechanism. Dynamics
Effects in C2-C6 Enyne Allene Cyclizations
Tefsit Bekele,‡ Chad F. Christian,† Mark A. Lipton,*,‡ and Daniel A. Singleton*,†
Contribution from the Department of Chemistry, Purdue UniVersity, West Lafayette, Indiana
47907, and Department of Chemistry, Texas A&M UniVersity, Post Office Box 30012, College
Station, Texas 77842
Received February 9, 2005; E-mail: lipton@purdue.edu; singleton@mail.chem.tamu.edu
Abstract: The C2-C6 (Schmittel)/ene cyclization of enyne-allenes is studied by a combination of kinetic
isotope effects, theoretical calculations, and dynamics trajectories. For the cyclization of allenol acetate 9,
the isotope effect (kCH /kCD ) is approximately 1.43. The isotope effect is interpreted in terms of a highly
3
3
asynchronous transition state near the concerted/stepwise boundary. This is supported by density functional
theory calculations that locate a highly asynchronous transition structure for the concerted ene reaction.
However, calculations of both the experimental system and a model reaction were unable to locate a
transition structure for formation of the diradical intermediate of a stepwise mechanism. The stepwise
mechanism and the asynchronous concerted mechanism start out geometrically similar, and the two
pathways appear to have merged as far as the initial transition structure. For the model reaction,
quasiclassical direct dynamics trajectories emanating from the initial transition structure afforded the diradical
intermediate in 29 out of 101 trajectories. A large portion of the remaining trajectories completes hydrogen
transfer before carbon-carbon bond formation, despite the advanced carbon-carbon bond formation in
the asynchronous transition structure. Overall, the single minimum-energy path from starting material to
product is inadequate to describe the reaction, and a consideration of dynamic effects is necessary to
understand the mechanism. The implications of these observations toward questions of concert in other
reactions are discussed.
The formation of reactive diradical intermediates in the
thermal cyclizations of enediynes and enyne-allenes is both
fundamentally intriguing and biologically momentous.1,2 Myers3
and Saito4 showed that enyne-allenes (1) undergo thermal C2-
C7 cyclizations to afford R,3-tolyl diradicals (2), and this is
thought to be the key step in the biological activation of
neocarzinostatin A.2b The ability of simple reactants to form
such highly reactive intermediates is usually attributed to the
aromaticity gained on cyclization. Schmittel, however, estab-
lished a second reaction motif for enyne-allenes in which C2-
C6 cyclization affords products apparently derived from fulvenyl
diradicals (3).5-7 This cyclization gains no aromaticity but is
still promoted by the formation of a strong sp2-sp2 σ bond from
sp-hybridized carbons. The Schmittel cyclization motif has
proven valuable in synthesis and has received extensive interest.8
† Texas A&M University.
Evidence for the intermediacy of a diradical in the C2-C6
cyclization of enyne-allenes has included trapping with 1,4-
‡ Purdue University.
(1) (a) Nicolaou, K. C.; Maligres, P.; Shin, J.; de Leon, E.; Rideout, D. J. Am.
Chem. Soc. 1990, 112, 7825-7826. (b) Grissom, J. W.; Slattery, B. J.
Tetrahedron Lett. 1994, 35, 5137-5140. (c) Wang, K. K.; Wang, Z.;
Sattsangi, P. D. J. Org. Chem. 1996, 61, 1516-1518. (d) Liu, B.; Wang,
K. K.; Petersen, J. L. J. Org. Chem. 1996, 61, 8503-8507. (e) Wang, K.
K. Chem. ReV. 1996, 96, 207-222.
(5) (a) Schmittel, M.; Strittmatter, M.; Vollmann, K.; Kiau, S. Tetrahedron
Lett. 1996, 37, 999-1002. (b) Schmittel, M.; Maywald, M.; Strittmatter,
M. Synlett 1997, 165-166. (c) Schmittel, M.; Strittmatter, M.; Kiau, S.
Tetrahedron Lett. 1995, 36, 4975-4978. (d) Schmittel, M.; Keller, M.;
Kiau, S.; Strittmatter, M. Chem.-Eur. J. 1997, 3, 807-816. (e) Schmittel,
M.; Steffen, J.-P.; Auer, D.; Maywald, M. Tetrahedron Lett. 1997, 38,
6177-6180.
(6) Schmittel, M.; Strittmatter, M.; Kiau, S. Angew. Chem., Int. Ed. Engl. 1996,
35, 1843-1845.
(7) Engels, B.; Lennartz, C.; Hanrath, M.; Schmittel, M.; Strittmatter, M. Angew.
Chem., Int. Ed. 1998, 37, 1960-1963.
(8) (a) Zhang, H.-R.; Wang, K. K. J. Org. Chem. 1999, 64, 7996-7999. (b)
Li, H.; Zhang, H.-R.; Petersen, J. L.; Wang, K. K. J. Org. Chem. 2001, 66,
6662-6668. (c) Li, H.; Petersen, J. L.; Wang, K. K. J. Org. Chem. 2001,
66, 7804-7810. (d) Yang, Y.; Petersen, J. L.; Wang, K. K. J. Org. Chem.
2003, 68, 5832-5837. (e) Yang, Y.; Petersen, J. L.; Wang, K. K. J. Org.
Chem. 2003, 68, 8545-8549.
(2) (a) Myers, A. G.; Proteau, P. J. J. Am. Chem. Soc. 1989, 111, 1146-1147.
(b) Myers, A. G. Tetrahedron Lett. 1987, 28, 4493-4496. (c) Myers, A.
G.; Proteau, P. J.; Handel, T. M. J. Am. Chem. Soc. 1988, 110, 7212-
7214. (d) Ishida, N.; Miyazaki, K.; Kumagai, K.; Rikimaru, M. J. Antibiot.
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8057-8059. (b) Myers, A. G.; Dragovich, P. S. J. Am. Chem. Soc. 1989,
111, 9130-9132. (c) Myers, A. G.; Dragovich, P. S.; Kuo, E. Y. J. Am.
Chem. Soc. 1992, 114, 9369-9386.
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30, 4995-4998. (b) Nagata, R.; Yamanaka, H.; Murahashi, E.; Saito, I.
Tetrahedron Lett. 1990, 31, 2907-2910.
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J. AM. CHEM. SOC. 2005, 127, 9216-9223
10.1021/ja0508673 CCC: $30.25 © 2005 American Chemical Society

Dynamics Effects in C2-C6 Enyne Allene Cyclizations
A R T I C L E S
Scheme 1
Scheme 2
two-step mechanism involving a diradical intermediate is
imminently credible based on the chemistry in Scheme 1. In a
theoretical study by Engels, the two-step and concerted mech-
anisms were predicted to have nearly equal free energies of
activation.17 Engels suggested that the two mechanisms could
be distinguished using kinetic isotope effects, as have been
applied to many ene reactions.
The energetic similarity of concerted and two-step mecha-
nisms in these reactions raises fundamental issues. By the
Thornton hypothesis,18 when the intermediate for a potential
two-step mechanism is low in energy, the transition state for
the corresponding concerted process should geometrically
approach the stepwise process. As the intermediate goes
lower in energy, the concerted mechanism ultimately transi-
tions into the stepwise pathway. However, the nature of
mechanisms at the concerted/stepwise boundary is not well
understood. Should such reactions involve a mixture of mech-
anisms?19 What is the effect of intrinsic entropic differences
between a two-step mechanism and a more organized concerted
process?
cyclohexadiene7 (Scheme 1) as well as the observation of
double-stranded DNA cleavage by structures known to undergo
the Schmittel-type cyclization. Schmittel found that changing
solvent polarity did not affect the rate of reaction or product
ratios, leading him to rule out zwitterionic intermediates.
Theoretical studies on the cyclization of the parent (Z)-1,2,4-
heptatrien-6-yne have supported a diradical mechanism for the
C2-C6 cyclization.9 In this system, the C2-C7 cyclization is
predicted to be favored over C2-C6 by approximately 10 kcal/
mol, consistent with the experimental observation of exclusive
C2-C7 cyclization.10 The C2-C6 cyclization is predicted to be
relatively favored by benzannulation,11 and it is also favored
by bulky terminal substituents and radical stabilizing groups at
C7. Studies in one of our laboratories have demonstrated an
interesting acceleration of the C2-C6 cyclization by oxyanion
substituents.12
We describe here a combined experimental and theoretical
study of the C2-C6/ene cyclization of enyne-allenes, a reaction
with a mechanism at the concerted/stepwise boundary. We find
that this reaction is not well-described by either concerted
or two-step labels and that the consideration of dynamic effects
is necessary to understand the nature of these intriguing
reactions.
Results
When the enyne-allene is substituted by an alkyl group at
C1, the ultimate product of the C2-C6 cyclization has undergone
hydrogen transfer from the alkyl substituent to C7 and the overall
conversion is formally an ene reaction (Scheme 2). The ene
reaction is allowed as a concerted pericyclic process, but, as a
whole, ene reactions have been notably mechanistically diverse.
Concerted mechanisms have been experimentally supported
often,13,14 yet many ene reactions have been found to involve
more complex mechanisms.14-16 The mechanism of any given
ene reaction may be considered uncertain in the absence of
evidence, but the mechanistic ambiguity of these reactions of
enyne-allenes seems particularly interesting. In this case, the
Kinetic Isotope Effect. The allenol acetate 9 was chosen for
study because of its clean conversion to the cyclized product
10 at a moderate temperature and rate. Both the unlabeled
substrate 9a and the deuterium labeled 9b were prepared by
the addition of the appropriate Gilman reagent to the acetylenic
ketone 8 by a previously reported procedure.12 The deuterium
incorporation in 9b prepared in this way is >98% based on 1H
NMR analysis.
(15) (a) Seymour, C. A.; Greene, F. D. J. Org. Chem. 1982, 47, 5226-5227.
(b) Leach, A. G.; Houk, K. N. Org. Biomol. Chem. 2003, 1, 1389-1403.
(c) Stephenson, L. M.; Speth, D. R. J. Org. Chem. 1979, 44, 4683-4689.
(d) Singleton, D. A.; Hang, C. J. Org. Chem. 2000, 65, 7554-7560. (e)
Snider, B. B.; Ron, E. J. Am. Chem. Soc. 1985, 107, 8160-8164. (f)
Singleton, D. A.; Hang, C. J. Org. Chem. 2000, 65, 895-899. (g) Cheng,
C.-C.; Seymour, C. A.; Petti, M. A.; Greene, F. D.; Blount, J. F. J. Org.
Chem. 1984, 49, 2910-2916. (h) Singleton, D. A.; Hang, C. J. Am. Chem.
Soc. 1999, 121, 11885-11893. (i) Frimer, A. A.; Stephenson, L. M. In
Singlet O2; Frimer, A. A., Ed.; CRC Press: Boca Raton, FL, 1985; pp
68-87. (j) Song, Z.; Chrisope, D. R.; Beak, P. J. Org. Chem. 1987, 52,
3938-3940. (k) Starflinger, W.; Kresze, G.; Huss, K. J. Org. Chem. 1986,
51, 37-40.
(16) (a) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Greenwald, E. E. J. Am.
Chem. Soc. 2003, 125, 1176-1177. (b) Singleton, D. A.; Hang, C.;
Szymanski, M. J.; Meyer, M. P.; Leach, A. G.; Kuwata, K. T.; Chen, J. S.;
Greer, A.; Foote, C. S.; Houk, K. N. J. Am. Chem. Soc. 2003, 125, 1319-
1328.
(17) Engels, B.; Musch, P. W. J. Am. Chem. Soc. 2001, 123, 5557-5562.
(18) Thornton, E. R. J. Am. Chem. Soc. 1967, 89, 2915-2927.
(19) For examples in Diels-Alder reactions, see: Bartlett, P. D.; Mallet, J. J.-
B. J. Am. Chem. Soc. 1976, 98, 143-151. Bartlett, P. D.; Jacobsen, B. M.;
Walker, L. E. J. Am. Chem. Soc. 1973, 95, 146-150.
(9) (a) Engels, B.; Hanrath, M. J. Am. Chem. Soc. 1998, 120, 6356-6361.
(b) Schreiner, P. R.; Prall, M. J. Am. Chem. Soc. 1999, 121, 8615-
8627.
(10) Myers, A. G.; Dragovich, P. S.; Kuo, E. Y. J. Am. Chem. Soc. 1992, 114,
9369-9386.
(11) Wenthold, P. G.; Lipton, M. A. J. Am. Chem. Soc. 2000, 122, 9265-
9270.
(12) Brunette, S. R.; Lipton, M. A. J. Org. Chem. 2000, 65, 5114-5119.
(13) (a) Gajewski, J. J. In Secondary and SolVent Isotope Effects; Buncel, E.,
Lee, C. C., Eds.; Isotopes in Organic Chemistry; Elsevier: New York,
1987; Vol. 7, pp 115-176. (b) Dai, S.-H.; Dolbier, W. R., Jr. J. Am. Chem.
Soc. 1972, 94, 3953-3954. (c) Achmatowicz, O., Jr.; Szymoniak, J. J.
Org. Chem. 1980, 45, 1228-1232. (d) Achmatowicz, O., Jr.; Szymoniak,
J. J. Org. Chem. 1980, 45, 4774-4776. (e) Jenner, G.; Papadopoulos, M.
J. Org. Chem. 1982, 47, 4201-4204. (f) Singleton, D. A.; Hang, C.
Tetrahedron Lett. 1999, 40, 8939-8942.
(14) (a) Song, Z.; Beak, P. J. Am. Chem. Soc. 1990, 112, 8126-8134.
(b) Stephenson, L. M.; Orfanopoulos, M. J. Org. Chem. 1981, 46, 2200-
2201.
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A R T I C L E S
Bekele et al.
structure could be located for the formation of 12 from 9. The
third possible pathway is cyclization of 9 with an “outward”
rotation of the methyl group on C1 to afford diradical 15 via
transition structure 14q. This cyclization has the effect of running
together the two trimethylsilyl groups and is rather sterically
encumbered. As a result, the predicted barrier for this cyclization
is 8.8 kcal/mol above that for the ene pathway. Based on this
result and the absence of experimental support for long-lived
diradicals in this reaction,12 this pathway is unlikely to be
experimentally relevant.
It should be noted that the predicted energies of 12 and 15
are dubious due to spin contamination ( S2 is 0.43, 0.09, 0.04,
and 0.47 for 12, 13q, 14q, and 15, respectively). The diradical
energies will be considered further for a model reaction.
Structure 11q was identical for restricted and unrestricted
calculations, and its wave function was spin-unrestricted stable.
The cyclization of 8 in toluene-d8 at 50 °C was conveniently
followed by H NMR. The conversion of 9a versus time was
1
consistent with a first-order process over the course of the
reaction with a half-life of ∼9000 s, and first-order kinetics
were assumed in rate-constant determinations. The conversion
of 9 to 10 was monitored by the intensity of characteristic
aromatic signals for each relative to the residual methyl signal
of toluene-d8 used as an internal standard. The signals corre-
sponding to the acetate and TMS groups were unsuitable due
All attempts to locate a transition structure for formation of
12 failed, using both restricted and unrestricted calculations.
Instead, the saddle-point searches invariably converged on 11.
This is in agreement with the observations of Musch and Engels,
who reported for a similar cyclization that a transition structure
for formation of a diradical could not be located when the C7
methyl group twists toward the alkyne.17 An attempt to locate
a transition structure for formation of 12 in UBPW91/6-31G-
(d,p) calculations also converged instead on a transition structure
similar to 11q (see the Supporting Information).
1
to peak overlap. H NMR spectra were collected at 30-min
intervals until no further change in relative peak heights was
observable, and the resulting data were fit directly as a first-
order process (see Supporting Information). The isotope effect
for the reaction was determined from both the disappearance
of 9 and the appearance of 10 in two reactions each for labeled
and unlabeled materials, affording a total of four measurements
with an average kCH /kCD of 1.43 and a standard deviation of
How could there be no transition structure for formation of
12? Both 11q and a hypothetical transition structure for formation
of 12 would involve formation of the C2-C6 bond, and the
difference between the two is that 11q also involves hydrogen
transfer. However, the degree to which hydrogen transfer has
progressed in 11q is very minor - the breaking C-H bond is
only slightly elongated as compared to 9. As a result, the
structure of 11q is very close to that expected for a transition
structure forming 12. Rather than involving two separate
transition structures with extremely similar geometries, it appears
that the stepwise and concerted pathways have merged in the
single transition structure 11q. The significance of this observa-
tion will be explored in more detail after the interpretation of
the experimental kinetic isotope effect is considered.
3
3
0.12. This standard deviation may underestimate the uncertainty
in kH/kD because only two completely independent reactions are
involved.
This isotope effect will be discussed in more detail below,
but we note here that the kH/kD is smaller than normally observed
in concerted ene reactions.13d,14a,15g,20 However, the kH/kD is
qualitatively too large to support a stepwise ene process. This
is in line with the idea that the mechanism is near the concerted/
stepwise boundary.
Theoretical Pathways from 9. Engels has previously
reported extensive careful calculations on the C2-C6 cyclization
of a series of enyne-allenes capable of undergoing the overall
ene conversion.17 The focus here is in two areas - the reaction
of the experimental system 9 and a more detailed study of a
model system. The results of these studies suggested a more
complex picture of the reaction mechanism than would con-
ventionally be considered.
Three possible pathways for the C2-C6 cyclization of 9 were
explored in restricted and unrestricted B3LYP calculations
employing a 6-31G(d,p) basis set (Figure 1). The first is direct
formation of 10 by a concerted process. Transition structure
11q was located for this conversion, and the predicted barrier
of 23.8 kcal/mol is well consistent with a reaction that proceeds
in a few hours at 50 °C. (The predicted half-life at 50 °C after
inclusion of an entropy estimate based on the unscaled harmonic
frequencies is a fortuitous 8900 s.) The second possible pathway
is cyclization of 9 with an “inward” rotation of the methyl group
on C1 to afford diradical 12. Intramolecular hydrogen transfer
in 12 could then afford product 10 via transition structure 13q.
As will be considered in greater detail below, no transition
Predicted Isotope Effects. To aid in interpreting the experi-
mental H/D isotope effect, predicted isotope effects based on
transition structures 11q and 14q were calculated. These predic-
tions used the scaled theoretical vibrational frequencies21 in
conventional transition state theory by the method of Bigeleisen
and Mayer.22 For the secondary H/D isotope effect associated
with transition structure 14q, a tunneling correction was applied
using a one-dimensional infinite parabolic barrier model.23 No
tunneling correction was applied for the prediction of the
primary H/D isotope effect associated with transition structure
11q, and the resulting prediction is likely a lower bound as
compared to a complete treatment of tunneling and variational
transition state effects (impractical in this case).
(21) The calculations used the program QUIVER (Saunders, M.; Laidig, K. E.;
Wolfsberg, M. J. Am. Chem. Soc. 1989, 111, 8989-8994). Frequencies
were scaled by 0.9614 (Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100,
16502-16513).
(22) (a) Bigeleisen, J.; Mayer, M. G. J. Chem. Phys. 1947, 15, 261-267. (b)
Wolfsberg, M. Acc. Chem. Res. 1972, 5, 225-233. (c) Bigeleisen, J. J.
Chem. Phys. 1949, 17, 675-678.
(23) Bell, R. P. The Tunnel Effect in Chemistry; Chapman & Hall: London,
1980; pp 60-63.
(20) Singleton, D. A.; Hang, C. J. Org. Chem. 2000, 65, 7554-7560.
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Dynamics Effects in C2-C6 Enyne Allene Cyclizations
A R T I C L E S
Figure 1. Predicted pathways for the cyclization of 9 in (U)B3LYP/6-31G(d,p) calculations. Structures 12, 13q, 14q, and 15 were obtained using unrestricted
calculations, while the remaining structures were identical in restricted and unrestricted calculations. Relative energies are in kcal/mol and include zpe.
The idea behind the prediction of an isotope effect for
transition structure 14q is that 14q may serve as a surrogate for
a transition structure that would lead to diradical 12. The
predicted kCH /kCD at 50 °C for 14q is 1.06. This is slightly
greater than unity because the adjacent radical character in 14q
has the effect of weakening the C-H bonds in the methyl group
on C1, but this prediction is much smaller than the experimental
isotope effect. This appears to exclude rate-limiting formation
of the diradical, but for reasons that will soon be clear, we opt
for a more careful wording: the experimental isotope effect is
inconsistent with a predominant rate-limiting transition state
involving C2-C6 ring closure without partial C-H bond
breakage.
a perturbative estimate of triple excitations (BD(T)),24 employing
a 6-31+G(d,p) basis set. An unrestricted wave function was
employed for diradical structures; for other structures, the
difference between unrestricted and restricted BD(T) results was
negligible. The applicability and accuracy of this calculational
approach was supported by studies of the thermodynamics of
cyclizations of cis-hex-3-en-1,5-diyne to p-benzyne (eq 1) and
hepta-1,2,4-trien-6-yne to R,3-didehydrotoluene (eq 2), which
can be compared with reported experimental data.25,26 In both
cases, the predicted cyclization energies [(U)BD(T)//6-31+G-
(d,p)//(U)B3LYP/6-311+G(d,p) + thermal correction for 25 °C]
are within the uncertainty of the experimental values.
3
3
The predicted kCH /kCD based on 11q is 1.54. Qualitatively,
3
3
both this predicted isotope effect and the experimental isotope
effect of ∼1.43 are in the realm of very small primary isotope
effects. The difference is perhaps small enough to ignore - the
experimental isotope effect is consistent with the qualitative
nature of 11q in which C-H bond breakage has progressed to
a minimal extent. However, it is enlightening for the discussion
later to consider possible origins for the difference between the
experimental and predicted isotope effects. Aside from experi-
mental error, the simplest explanation is inaccuracy in 11q. In
this regard, the smaller observed isotope effect suggests that
the progress of C-H bond breaking in the experimental
transition state is less than in 11q. An alternative, more complex,
explanation is that the observed isotope effect represents a
mixture of concerted and two-step mechanisms. These two
possibilities are distinct in classical physical organic terms, but
the difference will be less well defined when dynamics are
considered below.
The results for the cyclization of 16 are summarized in Figure
2. Transition structure 17q was located for the concerted
formation of product 18 from 16. This structure is similar to
11q, with substantial C2-C6 bond formation but little progress
in the hydrogen transfer from the methyl group on C1 to C7. As
(24) Handy, N.; Pople, J. A.; Head-Gordon, M.; Raghavachari, K.; Trucks, G.
W. Chem. Phys. Lett. 1989, 154, 185-192.
Theoretical Pathways in a Model Reaction. To explore the
C2-C6/ene cyclization in more detail and with higher-level
calculations, the model cyclization of 16 was studied. Stationary-
point geometries for the reaction path were optimized in
restricted or unrestricted B3LYP calculations employing a
6-311+G(d,p) basis set. Single-point energies were then com-
puted using Brueckner orbitals including double excitations and
(25) (a) Roth, W. R.; Hopf, H.; Horn, C. Chem. Ber. 1994, 127, 1765-1779.
(b) Wenthold, P.; Squires, R. R. J. Am. Chem. Soc. 1994, 116, 6401-
6412. (c) Cramer, C. J.; Squires, R. R. Org. Lett. 1999, 1, 215-218.
(26) (a) Wenthold, P. G.; Wierschke, S. G.; Nash, J. J.; Squires, R. R. J. Am.
Chem. Soc. 1994, 116, 7378-7392. (b) In ref 11, it was suggested by one
of the coauthors of ref 25a that the experimental heat of formation of R,3-
didehydrotoluene may be too low. An error in the direction suggested would
bring the energetics of eq 2 into even closer agreement with the (U)BD-
(T)/6-31+G(d,p)-predicted energetics.
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J. AM. CHEM. SOC. VOL. 127, NO. 25, 2005 9219

A R T I C L E S
Bekele et al.
Figure 2. Predicted pathways for the cyclization of 16. Structures 19 and
20q were obtained using unrestricted calculations. The relative energies (kcal/
mol) shown are (U)BD(T)/6-31+G(d,p)//B3LYP/6-311+G(d,p) + zpe.
Relative (U)B3LYP/6-31G(d,p) energies are shown in parentheses for
comparison.
Figure 3. Qualitative energy surface for the cyclizations of 9 and 16.
the qualitative features shown in Figure 3. From the rate-limiting
transition structures 11q or 17q, the steepest-descent path in mass-
weighted coordinates (the “minimum energy path”) affords the
ene product. A standard theoretical analysis would thus conclude
that the ene reaction occurs in a concerted fashion. However,
continued formation of the new C2-C6 bond from 11q or 17q
without concomitant hydrogen transfer could lead in a downhill
process to 12 or 19. It was thus possible that trajectories passing
through the “concerted” ene transition state could lead to the
diradical intermediate. In such a situation, whether a significant
proportion of the reaction involves a stepwise process, and the
competition between concerted and stepwise mechanisms,
becomes a question of dynamics.
To study this issue, 17q was used as the starting point for
quasiclassical direct dynamics trajectories on the UB3LYP/6-
31G(d,p) surface. With all atomic motions freely variable, the
trajectories were initialized by giving each vibrational mode a
random sign for its initial velocity, along with an initial energy
based on a random Boltzmann sampling of vibrational levels
appropriate for 323.15 K, including zero point energy. The mode
associated with the imaginary frequency was treated as a
translation and given a Boltzmann sampling of translational
energy “forward” over the col. Two processes were explored
for assigning the starting atomic positions. In the first, the
geometry of 17q was used as the starting point, forcing all
trajectories to go through 17q exactly. In the second, the starting
atomic positions on the potential energy ridge in the area of
17q were randomized using a linear sampling of possible
harmonic classical displacements for each normal mode, adjust-
ing the kinetic energy for each mode accordingly. The two
processes ultimately gave similar results. Forces were calculated
directly at the UB3LYP/6-31G(d,p) level at each point, and,
employing a Verlet algorithm, 1-fs steps were taken until either
the ene product 18 was formed (defined by a C2-C6 distance
< 1.5 Å with a C7-H distance < 1.1 Å) or diradical 19 was
formed (defined by a C2-C6 distance < 1.5 Å with the C7-H
distance increased to > 2.1 Å). The median time for product
formation was 30 fs, and all trajectories were complete within
85 fs. With such short simulation times, the effect of intramo-
lecular vibrational energy redistribution30 should be minimal.
was the case for 9, no transition structure could be located for
formation of diradical 19 from 16. Our search for such a
transition structure included imposing constraints to preclude
hydrogen transfer in the transition structure. Invariably, when
the constraints were removed, the transition structure converged
to 17q. An attempt to locate a transition structure for formation
of 19 in MP2/6-31G(d,p) calculations also converged instead
on a transition structure similar to 17q (see the Supporting
Information). Two transition structures for the formation of E-Z
isomers of 19 were located, and these are shown in the
Supporting Information. Because our focus is on the energy
surface in the area of 17q, 19, and 20q as a model for the
experimental reaction of 9 and the energy surface in the area
of 11q, 12, and 13q, we did not explore the likely favored C2-
C7 cyclization of 16.
Figure 2 also shows how the BD(T)/6-31+G(d,p)//(U)-
B3LYP/6-311+G(d,p) energies compare with those obtained
for 16-20 in (U)B3LYP/6-31G(d,p) calculations (the calcula-
tions used for 9-15, and for dynamics below). The DFT
approach performs well in predicting the reaction barrier, as
previously suggested by the comparison with experiment, but
slightly overestimates the stability of diradical 19. This is
unsurprising as 19 is subject to spin contamination ( S2 ) 0.28).
The barrier for product formation from 19 is estimated reason-
ably. Overall, the DFT calculations appear to reproduce the key
features of the energy surface.
Dynamics. The fascinating common feature in the C2-C6
cyclization of 9 and the model 16 is the absence of a separate
transition state for formation of diradicals 12 and 19. This
observation is reminiscent of recent discussions in the literature,
by one of us and by others, of reactions in which a single initial
transition state can lead to two separate products.16,27-29 We
hypothesized that the energy surface in these cyclizations has
(27) (a) Yamataka, H.; Aida, M.; Dupuis, M. Chem. Phys. Lett. 1999, 300, 583-
587. (b) Bakken, V.; Danovich, D.; Shaik, S.; Schlegel, H. B. J. Am. Chem.
Soc. 2001, 123, 130-134.
(28) Debbert, S. L.; Carpenter, B. K.; Hrovat, D. A.; Borden, W. T. J. Am.
Chem. Soc. 2002, 124, 7896-7897.
(29) For other discussions of one transition state giving rise to two products,
see: (a) Valtazanos, P.; Ruedenberg, K. Theor. Chim. Acta 1986, 69, 281-
307. (b) Kraus, W. A.; DePristo, A. E. Theor. Chim. Acta 1986, 69, 309-
322. (c) Yanai, T.; Taketsugu, T.; Hirao, K. J. Chem. Phys. 1997, 107,
1137-1146. (d) Windus, T. L.; Gordon, M. S.; Burggraf, L. W.; Davis, L.
P. J. Am. Chem. Soc. 1991, 113, 4356.
(30) Ben-Nun, M.; Levine, R. D. J. Chem. Phys. 1994, 101, 8768-8783.
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Dynamics Effects in C2-C6 Enyne Allene Cyclizations
A R T I C L E S
Discussion
Within conventional physical organic chemistry, much has
been made of the distinction between concerted and stepwise
mechanisms for reactions with multiple bonding changes. This
is seemingly a well-defined problem - concerted mechanisms
occur by a pathway involving a single transition state and no
intermediate, while a stepwise mechanism passes through at least
two transition states with an intervening intermediate. The steps
of a stepwise mechanism are always conceivably kinetically
distinguishable, that is, separately influenceable. A concerted
mechanism, in contrast, has a single kinetic barrier, and any
factor that influences product formation or selectivity must
equivalently influence starting material disappearance. A suf-
ficiently detailed characterization of a reaction’s transition state,
whether it be experimental (substituent effects, isotope effects,
entropy of activation, volume of activation, spectroscopic
observation, etc.) or theoretical, is considered adequate to
distinguish between stepwise and concerted mechanisms, at least
in principle. The possibility that a mixture of separate stepwise
and concerted mechanisms can be operative is well recognized,
but this adds no essential complication. The borderline between
stepwise and concerted mechanisms is classically straightforward
- does the mechanistic pathway involve an intermediate, or
does it not?
Figure 4. Graph of C2-C6 versus C7-H distances for selected dynamics
trajectories starting from 17q; along with the steepest-descent pathway
through 17 is mass-weighted coordinates (the minimum energy path).
Dynamic effects complicate the situation. Carpenter and
others have discussed extensively the situation in which dynamic
trajectories pass through the area of an intermediate without
equilibration of vibrational energy.31-33 As a result, the product
selectivity does not reflect the presence of an intermediate or
the presence of a second kinetically distinguishable step. In
effect, the mechanistic pathway follows the energy surface of a
stepwise mechanism but the reaction “acts” concerted in
observables, for example, in stereochemistry.
Recent work by Yamataka, Aida, and Dupuis has further
complicated the distinction between stepwise and concerted
mechanisms.34 In theoretical calculations on the ionization of
22, the minimum-energy path on the potential energy surface
passes through transition structure 23 to afford the tertiary cation
24. In this conversion, loss of the water leaving group and
methyl-group rearrangement occur in a concerted fashion.
However, dynamics simulations found that most trajectories at
400 K afforded initially the secondary cation 25. This cation is
not “connected” to the starting material by a minimum-energy
path, but can be formed readily by a process that simply breaks
the C-O bond without concurrent methyl rearrangement. In
effect, the reaction proceeds by a stepwise process, while a
classical analysis would predict a concerted process. A ther-
modynamic interpretation of this observation is that, in contrast
to the potential energy surface, the canonical variational
transition state on the free-energy surface leads to the secondary
cation.
A graph of C2-C6 versus C7-H distances for some typical
dynamics trajectories is shown in Figure 4.
The results were striking. Although the minimum energy path
from 17q smoothly affords 18, 29 out of 101 trajectories afforded
diradical 19. Five of the 29 trajectories entering the area of 19
were followed for an additional 100 fs, but none of these went
on to 18. It thus appears that an intermediate is formed in a
substantial portion of trajectories proceeding via the transition
structure for the concerted ene reaction. These intermediate
diradicals would ultimately go on to 18, but because the barrier
(via 20q) is substantial, the time scale for the simulation is
insufficient to observe this transformation.
A second remarkable observation was that many trajectories
underwent rapid hydrogen transfer to C7 without simultaneous
C2-C6 bond formation. Out of 101 trajectories, 29 saw the
C7-H distance decrease to <1.1 Å, while the C2-C6 distance
was still >1.8 Å. Seven trajectories had the C7-H distance
decrease to <1.1 Å, while the C2-C6 distance increased to >2.0
Å. Such trajectories pass through a geometry resembling
structure 21. No potential-energy minimum associated with this
structure could be located, and all of the trajectories go on
rapidly to 18. The intervention of structures resembling 21 thus
has no outward consequence. Nonetheless, the surprising
prevalence of trajectories through the area of 21 would seem to
impact the conception of asynchronicity in pericyclic reactions.
Structure 17q would be described as highly asynchronous, with
the C2-C6 bond formation preceding hydrogen transition, but,
despite this, many trajectories complete the hydrogen transfer
first.
(31) Carpenter, B. K. Angew. Chem., Int. Ed. 1998, 37, 3340-3350.
(32) (a) Carpenter, B. K. J. Am. Chem. Soc. 1995, 117, 6336-6344. (b) Reyes,
M. B.; Carpenter, B. K. J. Am. Chem. Soc. 2000, 122, 10163-10176. (c)
Reyes, M. B.; Lobkovsky, E. B.; Carpenter, B. K. J. Am. Chem. Soc. 2002,
124, 641-651. (d) Carpenter, B. K. J. Am. Chem. Soc. 1996, 118, 10329-
10330.
(33) (a) Doubleday, C., Jr.; Bolton, K.; Hase, W. L. J. Am. Chem. Soc. 1997,
119, 5251-5252. (b) Doubleday, C.; Nendel, M.; Houk, K. N.; Thweatt,
D.; Page, M. J. Am. Chem. Soc. 1999, 121, 4720-4721. (c) Doubleday, C.
J. Phys. Chem. A 2001, 105, 6333-6341. (d) Doubleday, C., Jr.; Bolton,
K.; Hase, W. L. J. Phys. Chem. A 1998, 102, 3648-3658.
(34) Ammal, S. C.; Yamataka, H.; Aida, M.; Dupuis, M. Science 2003, 299,
1555-1557.
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A R T I C L E S
Bekele et al.
The results here suggest a new wrinkle on the impact of
dynamics on the idea of stepwise versus concerted mechanisms,
a wrinkle that is potentially widespread. The observed kinetic
isotope effect and the calculational results both support the idea
that the C2-C6/ene cyclization of 9 is near the stepwise/
concerted boundary. It might be envisioned that, in such cases,
separate stepwise and concerted mechanisms could be competi-
tive. Here, such a competition cannot be ruled out from the
experimental isotope effect alone, but the calculations support
a merging of the stepwise and concerted pathways as far as the
rate-limiting transition state. Under these circumstances, ex-
perimental mechanistic probes of this transition state would
appear to implicate an exclusively concerted reaction. Going
on from this transition state, however, an intermediate may or
may not be formed, depending on the dynamics of individual
trajectories. The intermediate could in principle be trapped or
detected, implicating the stepwise mechanism. Kinetic observa-
tions and trapping experiments would appear contradictory.
Figure 5. More O’Ferrall-Jencks diagram for ene reactions. The ap-
proximate minimum-energy path expected for reaction of 9 or 16 is shown
as a solid bold line. Possible qualitative trajectories are shown as dotted
lines.
existence of a path that is chemically representative of the
ensemble of trajectories connecting starting material and product.
The technical justification for this view is that trajectories should
tend to regress toward a minimum-energy path. However, such
regression will not necessarily overcome the thermal divergence
of trajectories, outside of the bottleneck area of a transition state.
When trajectories vary sufficiently, no single reaction path can
adequately describe the mechanism. This appears to be the case
for the current reaction.
It is fascinating to consider the possible applicability of the
ideas here in other pericyclic reactions. Many cycloadditions,
for example, have been predicted to occur by concerted
processes through highly asynchronous transition states. In many
such cases, both the cycloaddition product and the intermediate
for a stepwise cycloaddition may be downhill from the rate-
limiting transition state.36 If so, trajectories passing through the
“concerted transition state” could conceivably lead to intermedi-
ates in substantial amounts. A theoretical study that merely
characterized the stationary points and minimum-energy paths
in a mechanism could not resolve whether intermediates were
formed, no matter how accurate the calculation. Notably, kinetic
mechanistic probes of such reactions would be completely
incapable of deciding whether intermediates were formed.
Stereochemical and trapping probes could still be applied,
although the conventional limitations of such probes have been
discussed extensively37 and, as described above, dynamic effects
can make stepwise mechanisms appear stereochemically
concerted.31,32a-c,38 It should be of considerable interest to
explore the degree to which such dynamic effects complicate
diverse pericyclic mechanisms.
It is enlightening to qualitatively consider the ene reactions
of 9 or 16 within the context of a More O’Ferrall-Jencks
diagram (Figure 5).35 Ene reaction mechanisms can be very
complicated, but here we restrict our consideration to having
carbon-carbon bond formation and hydrogen transfer as the
dominant dimensions for the More O’Ferrall-Jencks diagram.13a
Because the overall reaction is exothermic, it would be expected
that the transition state would be relatively early, and because
the diradical intermediate after carbon-carbon bond formation
is relatively stable (as evidenced by the chemistry of Scheme
1), the transition state should be shifted toward the edge of the
diagram, as shown. This is consistent with the predicted
transition structures 11q and 17q, as well as the experimental
isotope effect with 9. The normal qualitative understanding of
these reactions would then be based on a smooth reaction path
passing through the transition state. However, a broad range of
structures are energetically downhill from the transition state,
and it is possible for trajectories to depart drastically from the
qualitative reaction path. This can include reaching an inter-
mediate in the corner of the More O’Ferrall-Jencks diagram
that is not on the reaction path.
Conclusions
The KIE (kCH /kCD ) for the C2-C6/ene cyclization of 9 is
3
3
The concept of a reaction path between starting material and
product is fundamental in the chemistry paradigm. In the absence
of bifurcations, such paths can be mathematically well-defined,
the common definition as the steepest-descent path in mass-
weighted coordinates being only one example out of many
possibilities. It is of course well understood that real trajectories
do not follow exactly the reaction path. However, qualitative
discussions of reaction mechanisms implicitly assume the
approximately 1.43. This appears qualitatively too large to be
a secondary isotope effect for formation of a diradical, and the
theoretically predicted KIE based on diradical-forming 14q
supports this conclusion. The 1.43 value is very small for a
(36) For an example of a diradical intermediate that is lower in energy than the
transition structure for a concerted cycloaddition, see: Li, Y.; Houk, K. N.
J. Am. Chem. Soc. 1993, 115, 7478-7485.
(37) (a) Firestone, R. A. Heterocycles 1987, 25, 61-64. (b) Firestone, R. A.
Tetrahedron 1977, 33, 3009-3039.
(38) (a) Carpenter, B. K. J. Am. Chem. Soc. 1985, 107, 5730-5732. (b) Newman-
Evans, R. H.; Simon, R. J.; Carpenter, B. K. J. Org. Chem. 1990, 55, 695-
711.
(35) (a) More O’Ferrall, R. A. J. Chem. Soc. B 1970, 274-277. (b) Jencks, W.
P. Chem. ReV. 1972, 72, 705-718.
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Dynamics Effects in C2-C6 Enyne Allene Cyclizations
A R T I C L E S
primary H/D KIE, but it appears roughly consistent with the
predicted isotope effect of 1.54 based on 11q. From the observed
isotope effect alone, we cannot rule out a mixture of standard
concerted and two-step mechanisms. However, the theoretical
calculations do not support a conventional mixture of mecha-
nisms, and the simplest interpretation of the isotope effect is
that the ene reaction involves a highly asynchronous transition
state, near the concerted/stepwise boundary, in which hydrogen
transfer has progressed to a minimal extent.
No transition structure could be located for formation of
diradical 12 from 9 or diradical 19 from 16. The initial geometry
changes associated with these stepwise processes would be
expected to be very similar to those for the highly asynchronous
concerted mechanism, and the stepwise and concerted pathways
have apparently merged as far as the rate-limiting transition
structures. From these structures, the minimum-energy path leads
to the ene product, but it is also downhill to the diradical
intermediates.
Quasiclassical direct dynamics trajectories emanating from
17q vary greatly. Although 17q would normally be considered
the transition state for a concerted reaction, many trajectories
lead to an intermediate. A large alternative portion of the
trajectories complete hydrogen transfer before full carbon-
carbon bond formation, in contrast to what would be expected
from the asynchronicity of the transition structure. The single
minimum-energy path from starting material to product does
not adequately describe the mechanism.
The ideas of transition state theory and reaction paths are so
entwined in the mechanistic understanding of chemistry that
they limit the questions that may be asked regarding a
mechanism and the answers that may arise from mechanistic
studies. When a reaction involves multiple bonding changes, a
standard question has been whether the bonding changes occur
by a stepwise or concerted pathway. When the question is asked
this way, the only possible answers are that the reaction proceeds
by a concerted pathway, or by a stepwise pathway, or by a
mixture of the two separate pathways. Advances in the
understanding of dynamic effects in mechanisms16,27,31-34 have
shown that the question of concerted versus stepwise is too
simple and that the answer to the question may be very
complicated indeed. The consideration of a possible role for
dynamic effects, even for complex reactions in solution, should
be incorporated into the mechanistic chemistry paradigm.
Experimental Section
Kinetic Studies. The unlabeled allenol acetate 9a12 (10 mg, 0.028
mmol) was dissolved in toluene-d8 (0.075 mL) and transferred to an
NMR tube and immediately placed into the probe of a Varian Inova
300 MHz NMR spectrometer to minimize spontaneous cyclization of
9a. Prior to the experiment, the variable temperature thermostat of the
NMR was calibrated using an ethylene glycol standard by measuring
its chemical shift at 50 °C. The heights of selected aromatic protons of
9a and the cyclization product 10a were monitored by 1H NMR at 50
°C over 6 h until no further change in the heights of the aromatic protons
was observed. Data were collected every 30 min and normalized to
the height of the residual methyl signal of toluene-d8. The same
procedure was carried out for the deuterated allenol acetate 9b, and
both experiments were repeated. In each case, no side products were
observable and the formation of product appeared essentially quantita-
tive. Kinetic isotope effect values were computed by plotting the
1
selected H NMR peak heights against time and fitting the data to a
first-order simulation to obtain rate constants for the cyclization of both
9a and 9b. The two replications were used to obtain averaged values
and standard deviations for the observed kinetic isotope effects.
Acknowledgment. D.A.S. thanks NIH grant # GM-45617 and
The Robert A. Welch Foundation, and M.A.L. wishes to
acknowledge the donors of the Petroleum Research Fund,
administered by the American Chemical Society, for support
of this research. T.B. gratefully acknowledges the Sloan
Foundation and the NIH for fellowship support. We thank John
Grutzner for helpful conversations.
Supporting Information Available: Energies and full geom-
etries of all calculated structures, and kinetic data and simula-
tions. This material is available free of charge via the Internet
at http://pubs.acs.org.
JA0508673
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