Dynamic effects on the periselectivity, rate, isotope effects, and mechanism of cycloadditions of ketenes with cyclopentadiene

Article abstract of DOI:10.1021/ja0606024

The cycloadditions of cyclopentadiene with diphenylketene and dichloroketene are studied by a combination of kinetic and product studies, kinetic isotope effects, standard theoretical calculations, and trajectory calculations. In contrast to recent reports, the reaction of cyclopentadiene with diphenylketene affords both [4 + 2] and [2 + 2] cycloadducts directly. This is surprising, since there is only one low-energy transition structure for adduct formation in mPW1K calculations, but quasiclassical trajectories started from this single transition structure afford both [4 + 2] and [2 + 2] products. The dichloroketene reaction is finely balanced between [4 + 2] and [2 + 2] cycloaddition modes in mPW1 K calculations, as the minimum-energy path (MEP) leads to different products depending on the basis set. The MEP is misleading in predicting a single product, as trajectory studies for the dichloroketene reaction predict that both [4 + 2] and [2 + 2] products should be formed. The periselectivity does not reflect transition state orbital interactions. The ¹³C isotope effects for the dichloroketene reaction are well-predicted from the mPW1K/6-31+G** transition structure. However, the isotope effects for the diphenylketene reaction are not predictable from the cycloaddition transition structure and transition state theory. The isotope effects also appear inconsistent with kinetic observations, but the trajectory studies evince that nonstatistical recrossing can reconcile the apparently contradictory observations. B3LYP calculations predict a shallow intermediate on the energy surface, but trajectory studies suggest that the differing B3LYP and mPW1K surfaces do not result in qualitatively differing mechanisms. Overall, an understanding of the products, rates, selectivities, isotope effects, and mechanism in these reactions requires the explicit consideration of dynamic trajectories.

Full text of DOI:10.1021/ja0606024

Published on Web 05/17/2006
Dynamic Effects on the Periselectivity, Rate, Isotope Effects,
and Mechanism of Cycloadditions of Ketenes with
Cyclopentadiene
Bryson R. Ussing, Chao Hang, and Daniel A. Singleton*
Contribution from the Department of Chemistry, Texas A&M UniVersity, P.O. Box 30012,
College Station, Texas 77842
Received January 26, 2006; E-mail: singleton@mail.chem.tamu.edu
Abstract: The cycloadditions of cyclopentadiene with diphenylketene and dichloroketene are studied by a
combination of kinetic and product studies, kinetic isotope effects, standard theoretical calculations, and
trajectory calculations. In contrast to recent reports, the reaction of cyclopentadiene with diphenylketene
affords both [4 + 2] and [2 + 2] cycloadducts directly. This is surprising, since there is only one low-energy
transition structure for adduct formation in mPW1K calculations, but quasiclassical trajectories started from
this single transition structure afford both [4 + 2] and [2 + 2] products. The dichloroketene reaction is
finely balanced between [4 + 2] and [2 + 2] cycloaddition modes in mPW1K calculations, as the minimum-
energy path (MEP) leads to different products depending on the basis set. The MEP is misleading in
predicting a single product, as trajectory studies for the dichloroketene reaction predict that both [4 + 2]
and [2 + 2] products should be formed. The periselectivity does not reflect transition state orbital interactions.
The 13C isotope effects for the dichloroketene reaction are well-predicted from the mPW1K/6-31+G**
transition structure. However, the isotope effects for the diphenylketene reaction are not predictable from
the cycloaddition transition structure and transition state theory. The isotope effects also appear inconsistent
with kinetic observations, but the trajectory studies evince that nonstatistical recrossing can reconcile the
apparently contradictory observations. B3LYP calculations predict a shallow intermediate on the energy
surface, but trajectory studies suggest that the differing B3LYP and mPW1K surfaces do not result in
qualitatively differing mechanisms. Overall, an understanding of the products, rates, selectivities, isotope
effects, and mechanism in these reactions requires the explicit consideration of dynamic trajectories.
Selectivity in cycloadditions may take many forms, e.g., endo/
exo stereoselectivity, regioselectivity, facial stereoselectivity, and
diene/dienophile role selectivity. When two distinct formally
allowed processes are possible, as in the [4 + 2] versus [6 +
4] cycloadditions of cyclopentadiene with tropone,1 their dif-
ferentiation is referred to as periselectivity. The underlying
framework within which chemists usually understand any of
these forms of selectivity is transition state theory (TST). The
preferred product would be that involving the lowest-energy
transition state, and the degree of selectivity would be deter-
mined by the relative energies for separate transition states. Even
when there is no enthalpic barrier, reactivity and selectivity can
be discussed in terms of free-energy barriers.2 Qualitative
theories of selectivity such as FMO theory may be thought of
as a simplified surrogate for TST, easing the task of predicting
which cycloaddition barrier is lowest in energy.
result of relatively slow IVR is “nonstatistical” transition state
recrossing, slowing reaction rates in a way that cannot be
predicted by statistical theories such as microcanonical varia-
tional TST.4 Hase in particular has extensively studied this effect
in gas-phase SN2 reactions.4,5 Another effect of relatively slow
IVR is that the selection of trajectories passing through an initial
transition state can influence selectivity among subsequent
transition states. Due to such a “dynamic matching” effect, the
selectivity among products requires consideration of dynamic
trajectories.6 Carpenter has brought to light the importance of
this phenomenon in a series of organic reactions.7 Related effects
(3) For a discussion, see: Carpenter, B. K. J. Phys. Org. Chem. 2003, 16,
858-868.
(4) Vande Linde, S. R.; Hase, W. L. J. Chem. Phys. 1990, 93, 7962-7980.
Cho, Y. J.; Vande Linde, S. R.; Zhu, L.; Hase, W. L. J. Chem. Phys. 1992,
96, 8275-8287. Hase, W. L. Science 1994, 266, 998-1002. Wang, H.;
Hase, W. L. J. Am. Chem. Soc. 1995, 117, 9347-9356. Sun, L.; Hase, W.
L.; Song, K. J. Am. Chem. Soc. 2001, 123, 5753-5756.
(5) Vande Linde, S. R.; Hase, W. L. J. Phys. Chem. 1990, 94, 6148-6150.
Li, G.; Hase, W. L. J. Am. Chem. Soc. 1999, 121, 7124-7129. Wang, Y.;
Hase, W. L.; Wang, H. J. Chem. Phys. 2003, 118, 2688-2695. Sun, L.;
Chang, E.; Song, K.; Hase, W. L. Can. J. Chem. 2004, 82, 891-899.
(6) Carpenter, B. K. Angew. Chem., Int. Ed. 1998, 37, 3340-3350.
(7) Carpenter, B. K. J. Am. Chem. Soc. 1985, 107, 5730-5732. Newman-
Evans, R. H.; Simon, R. J.; Carpenter, B. K. J. Org. Chem. 1990, 55, 695-
711. Carpenter, B. K. Acc. Chem. Res. 1992, 25, 520-528. Carpenter, B.
K. J. Am. Chem. Soc. 1995, 117, 6336-6344. Reyes, M. B.; Carpenter, B.
K. J. Am. Chem. Soc. 2000, 122, 10163-10176. Reyes, M. B.; Lobkovsky,
E. B.; Carpenter, B. K. J. Am. Chem. Soc. 2002, 124, 641-651. Nummela,
J. A.; Carpenter, B. K. J. Am. Chem. Soc. 2002, 124, 8512-8513.
This all seems so fundamental that the assumptions involved
in understanding selectivity with TST may be obscured. One
of these assumptions is that intramolecular vibrational energy
redistribution (IVR) is fast on the time scale of reaction
coordinate motion.3 This is not necessarily the case. One possible
(1) Cookson, R. C.; Drake, B. V.; Hudec, J.; Morrison, A. Chem. Commun.
1966, 15-16. Ito, S.; Fujise, Y.; Okuda, T.; Inoue, Y. Bull. Chem. Soc.
Jpn. 1966, 39, 1351.
(2) Hase, W. L. J. Chem. Phys. 1976, 64, 2442-2449.
9
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10.1021/ja0606024 CCC: $33.50 © 2006 American Chemical Society

Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
bond shifting in cyclooctatetraene,22 dimerization of cyclopen-
tadiene,23 and deazetization leading to semibullvalene.24 The
selectivity in symmetry breaking is naturally 1:1, and the
products are either indistinguishable or enantiomers, so that the
selectivity has no synthetic consequence. Lluch has proposed
that variational TST may sometimes be applied to predicting
selectivity when the otherwise symmetrical surfaces are de-
symmetrized by isotopic substitution.25
More chemically interesting, but far less understood, are
reactions on unsymmetrical bifurcating surfaces,11b,26-30 as in
Figure 1b. On such a surface, the MEP does not bifurcate, but
there may still be trajectories that lead to two, now distinguish-
able, products. In this case, the product mixture cannot currently
be predicted from any form of TST.31 No qualitative theory
presently exists for understanding selectivity in such reactions,
and trajectory calculations are required for quantitative predic-
tions. We recently found that singlet oxygen ene reactions appear
to involve a surface of this type, and trajectory calculations were
applied to understand the experimental formation of two
regioisomeric products despite having only one of the products
connected to the starting material by an MEP.28,29
Figure 1. Bifurcating surfaces in which dynamic effects would control
selectivity. (a) The surface is symmetrical, and the MEP bifurcates at a
second transition state. Real trajectories would tend to diverge from the
MEP in the area of the valley-ridge inflection (VRI). (b) The surface is
unsymmetrical, and the MEP does not bifurcate. However, some possible
trajectories afford a product not on the MEP.
can impact reactions in which trajectories pass through a flat,
typically diradicaloid, area of a potential energy surface.8-10
Alternatively, trajectories can effectively bypass minima on the
reaction coordinate.11,12
Another assumption in understanding selectivity, perhaps
more subtle, is that the separate products arise from separate
transition states. The intertwined idea that a transition state may
only connect a reactant set with a single product set was once
considered a rule, usable to exclude certain symmetries in
transition states.13 However, this pervasive implicit assumption
is not reliable.14-16 On a bifurcating energy surface, such as
those shown in Figure 1, the rate-limiting transition state is
adjacent to a transition state interconverting products, and
reactants that pass through the rate-limiting transition state can
proceed to two product wells without a barrier. If the surface is
symmetrical, as in Figure 1a, the minimum-energy path (MEP)
bifurcates to afford equally two equivalent products. Such
bifurcating surfaces associated with symmetry breaking have
been analyzed theoretically for many simple reactions.16,17
Examples include the ring opening of cyclopropylidene to form
allene,18 pseudorotations in SiH4F- and PH4F,19 1,2-hydrogen
migration in H3CO•,20 photodissociation of thioformaldehyde,21
The reaction of interest here is the cycloaddition of ketenes
with 1,3-dienes. Early workers were surprised to find that these
reactions afforded cyclobutanones from a formal [2 + 2]
cycloaddition instead of the expected [4 + 2] Diels-Alder
products.32
The [2 + 2] cycloadditions of ketenes played a
significant role in the elaboration of the Woodward-Hoffmann
rules,33 and their particularly facile reactions with 1,3-dienes
have found substantial synthetic utility. It was therefore quite
momentous when Machiguchi and Yamabe reported that [4 +
2] cycloadducts (e.g., 3) are the initial product in reactions of
diphenylketene (2) with cyclic dienes such as cyclopentadiene
(1).34 The ultimate cyclobutanones (e.g., 4) were concluded to
arise by a [3,3]-sigmatropic (Claisen) rearrangement of the initial
product.
(20) Yanai, T.; Taketsugu, T.; Hirao, K. J. Chem. Phys. 1997, 107, 1137-
1146. Kumeda, Y.; Taketsugu, T. J. Chem. Phys. 2000, 113, 477-484.
Taketsugu, T.; Kumeda, Y. J. Chem. Phys. 2001, 114, 6973-6982.
(21) Tachibana, A.; Okazaki, I.; Koizumi, M.; Hori, K.; Yamabe, T. J. Am.
Chem. Soc. 1985, 107, 1190-1196.
(8) (a) Doubleday, C., Jr.; Bolton, K.; Hase, W. L. J. Am. Chem. Soc. 1997,
119, 5251-5252. (b) Doubleday, C., Jr.; Bolton, K.; Hase, W. L. J. Phys.
Chem. A 1998, 102, 3648-3658. (c) Doubleday, C.; Nendel, M.; Houk,
K. N.; Thweatt, D.; Page, M. J. Am. Chem. Soc. 1999, 121, 4720-4721.
(d) Doubleday, C. J. Phys. Chem. A 2001, 105, 6333-6341. (e) Doubleday,
C.; Li, G.; Hase, W. L. Phys. Chem. Chem. Phys. 2002, 4, 304-312.
(9) Hrovat, D. A.; Fang, S.; Borden, W. T.; Carpenter, B. K. J. Am. Chem.
Soc. 1997, 119, 5253-5254.
(22) Castan˜o, O.; Palmeiro, R.; Frutos, L. M.; Luisandre´s, J. J. Comput. Chem.
2002, 23, 732-736.
(23) Caramella, P.; Quadrelli, P.; Toma, L. J. Am. Chem. Soc. 2002, 124, 1130-
1131.
(24) Zhou, C.; Birney, D. M. Org. Lett. 2002, 4, 3279-3282.
(25) Gonzalez-Lafont, A.; Moreno, M.; Lluch, J. M. J. Am. Chem. Soc. 2004,
126, 13089-13094.
(10) Jarzecki, A. A.; Gajewski, J.; Davidson, E. R. J. Am. Chem. Soc. 1999,
121, 6928-6935. Kless, A.; Nendel, M.; Wilsey, S.; Houk, K. N. J. Am.
Chem. Soc. 1999, 121, 4524-4525.
(26) Yamataka, H.; Aida, M.; Dupuis, M. Chem. Phys. Lett. 1999, 300, 583-
587. Bakken, V.; Danovich, D.; Shaik, S.; Schlegel, H. B. J. Am. Chem.
Soc. 2001, 123, 130-134. Yamataka, H.; Aida, M. Bull. Chem. Soc. Jpn.
2002, 75, 2555-2569.
(11) (a) Carpenter, B. K. J. Am. Chem. Soc. 1996, 118, 10329-10330. (b) Sun,
L.; Song, K.; Hase, W. L. Science 2002, 296, 875-878.
(12) Debbert, S. L.; Carpenter, B. K.; Hrovat, D. A.; Borden, W. T. J. Am.
Chem. Soc. 2002, 124, 7896-7897.
(27) Mann, D. J.; Hase, W. L. J. Am. Chem. Soc. 2002, 124, 3208-3209.
(28) 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.
(13) Murrell, J. N.; Laidler, K. J. Trans. Faraday Soc. 1968, 64, 371-377.
(14) Metiu, H.; Ross, J.; Silbey, R.; George, T. F. J. Chem. Phys. 1974, 61,
3200-3209.
(29) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Greenwald, E. E. J. Am.
Chem. Soc. 2003, 125, 1176-1177.
(15) Bosch, E.; Moreno, M.; Lluch, J. M.; Bertran, J. Chem. Phys. Lett. 1989,
160, 543-548. Quapp, W.; Hirsch, M.; Heidrich, D. Theor. Chem. Acc.
1998, 100, 285-299. Ramquet, M.-N.; Dive, G.; Dehareng, D. J. Chem.
Phys. 2000, 112, 4923-4934. Quapp, W. J. Mol. Struct. 2004, 695-696,
95-101. Quapp, W.; Hirsch, M.; Heidrich, D. Theor. Chem. Acc. 2004,
112, 40-51.
(30) Bekele, T.; Lipton, M. A.; Singleton, D. A.; Christian, C. F. J. Am. Chem.
Soc. 2005, 127, 9216-9223.
(31) It should be noted that the variational transition state theory procedure in
ref 25 is not applicable to an unsymmetrical surface.
(32) (a) Smith, L. I.; Agre, C. L.; Leekley, R. M.; Prichard, W. W. J. Am. Chem.
Soc. 1939, 61, 7-11. (b) Brooks, B. T.; Wilbert, G. J. Am. Chem. Soc.
1941, 63, 870-871. (c) Staudinger had in fact observed these reactions
prior to the discovery of the Diels-Alder reaction: Staudinger, H. Liebigs
Ann. Chem. 1907, 40, 51-123.
(16) Valtazanos, P.; Ruedenberg, K. Theor. Chim. Acta 1986, 69, 281-307.
(17) Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 1992, 114, 5879-5881.
Wenthold, P. G.; Hrovat, D. A.; Borden, W. T.; Lineberger, W. C. Science
1996, 272, 1456-1459.
(18) Valtazanos, P.; Elbert, S. T.; Ruedenberg, K. J. Am. Chem. Soc. 1986,
108, 3147-3149. Kraus, W. A.; DePristo, A. E. Theor. Chem. Acta 1986,
69, 309-322.
(33) Woodward, R. B.; Hoffmann, R. Angew. Chem., Int. Ed. Engl. 1969, 8,
781-853.
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Chem. Soc. 1996, 118, 6518-6519. (b) Machiguchi, T.; Hasegawa, T.;
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1991, 113, 4356-4357.
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A R T I C L E S
Ussing et al.
In the mechanism of Machiguchi and Yamabe, 4 is formed
exclusively via 3. In fact, their theoretical calculations place
the transition structure for the direct formation of 4 over 14
kcal/mol higher in energy than the transition structure for for-
mation of 3, so that any formation of 4 without the intermediacy
of 3 would be inconsistent. Despite this, we report here that
some 4 is formed directly.
This seemingly minor difference in experimental observations
gains significance from the inability of the standard35 theoretical
analysis via TST to explain the periselectivity observation.
Additional experimental observationsskinetic isotope effects
(KIEs) seemingly inconsistent with other kinetic observationss
are equally perplexing within the standard framework. While
our results cannot be understood within current TST, we find
that a consistent and explanatory picture of the mechanism arises
with the detailed consideration of dynamic trajectories. The
results challenge some standard ideas used to understand the
reactivity, selectivity, and mechanism of cycloadditions.
Figure 2. Composition versus time for the diphenylketene reaction at -20
°C, based on NMR observations. Solid lines are predicted, based on a kinetic
model in which both 3 and 4 are formed concurrently, with 3 rearranging
directly to 4. The inset shows an expansion of the early points.
cyclobutanone 7 is formed cleanly, except for a small amount
of dicyclopentadiene.
Results
The two reactions studied here are the cycloadditions of
cyclopentadiene with diphenylketene and with dichloroketene
(5). Diphenylketene is isolable and is readily reacted with
cyclopentadiene in quantitative yield under diverse conditions.
However, dichloroketene is highly reactive and unisolable. This
high reactivity increases its utility in cycloadditions,36,37 and
dichloroketene has seen common use in complex synthesis.38
Dichloroketene is conveniently generated in situ by treatment
of a solution of cyclopentadiene and trichloroacetyl chloride
(6) with powdered zinc at 0 °C in ether. Under these conditions,
Product Composition and Kinetics. Due to unusual isotope
effect observations (vide infra), we began to suspect that the
reaction of cyclopentadiene with diphenylketene was not as
simple as had been reported. Machiguchi and Yamabe had
previously examined this reaction at low temperatures by NMR,
but we could not determine from their data whether 3 was the
exclusive initial product in the reaction. We therefore reexam-
ined this reaction. Figure 2 shows the composition of 3 and 4
versus time in a reaction in CD2Cl2 at -20 °C. At this
temperature, the concentration of 3 reached a maximum at ∼2
h and then fell off slowly due to the isomerization of 3 to 4. A
key observation was that the concentration of 4 increased
steadily, even within the first half hour while the concentration
of 3 was relatively low. This was not consistent with 4 arising
solely by isomerization of 3. A best-fit simulation of the reaction
composition versus time at -20 °C had rate constants of 4.1 ×
10-4 M-1 s-1 for formation of 3, 0.9 × 10-4 M-1 s-1 for
formation of 4, and 2.9 × 10-5 s-1 for rearrangement of 3 to 4.
An alternative kinetic model in which the conversion of 3 to
4 occurs indirectly, via reversion to cyclopentadiene + diphen-
ylketene, did not reasonably fit the composition data (see the
(35) The word “standard” is used in this paper to refer to theoretical or
mechanistic analyses of reactions in which the selectivity is determined by
transition state barriers, and the reaction path is decided by the MEP
connection of stationary points. The “standard” analysis ignores dynamic
trajectories, except to the degree that they are implicitly assumed to
approximately follow the MEP. The “standard” analysis is not limited to
conventional TST.
(36) Initial reports on the observation and stability of dichloroketene in solution
(Brady, W. T.; Liddell, H. G.; Vaughn, L. L. J. Org. Chem. 1966, 31,
626-628) appear inconsistent with later observations: Colbourne, D.; Frost,
D. C.; McDowell, C. A.; Westwood, N. P. C. Chem. Commun. 1980, 250-
251. Gerry, M. C. L.; Lewis-Bevan, W.; Westwood, N. P. C. Can. J. Chem.
1985, 63, 676-677. Davidovics, G.; Monier, M.; Allouche, A. Chem. Phys.
1991, 150, 395-403.
(37) Stevens, H. C.; Reich, D. A.; Brandt, D. R.; Fountain, K. R.; Gaughan, E.
J. J. Am. Chem. Soc. 1965, 87, 5257-5259. Ghosez, L.; Montaigne, R.;
Mollet, P. Tetrahedron Lett. 1966, 135-139. Brady, W. T.; Waters, O. H.
J. Org. Chem. 1967, 32, 3703-3705. Greene, A. E.; Depre´s, J.-P. J. Am.
Chem. Soc. 1979, 101, 4003-4005.
(38) (a) Grieco, P. A.; Oguri, T.; Gilman, S. J. Am. Chem. Soc. 1980, 102,
5886-5891. (b) Greenlee, M. L. J. Am. Chem. Soc. 1981, 103, 2425-
2426. (c) Greene, A. E.; Luche, M.-J.; Depre´s, J.-P. J. Am. Chem. Soc.
1983, 105, 2435-2439. (d) Greene, A. E.; Charbonnier, F.; Luche, M.-J.;
Moyano, A. J. Am. Chem. Soc. 1987, 109, 4752-4753. (e) Resende, P.;
Almeida, W. P.; Coelho, F. Tetrahedron: Asymmetry 1999, 10, 2113-2118.
(f) Baldwin, J. E.; Shukla, R. Org. Lett. 1999, 1, 1081-1082. (g) Chen,
X.-T.; Bhattacharya, S. K.; Zhou, B.; Gutteridge, C. E.; Pettus, T. R. R.;
Danishefsky, S. J. J. Am. Chem. Soc. 1999, 121, 6563-6579.
9
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Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
Supporting Information). A mixed kinetic model, in which some
conversion of 3 to 4 occurs directly and some via starting
materials, was also explored. The fit of the mixed model with
the experimental data became poor if less than 75% of the
conversion of 3 to 4 was direct, but it was not possible to
exclude that some portion of the conversion of 3 to 4 occurs
via reversion to the starting materials. The predominantly direct
nature of the conversion of 3 to 4, important later, is supported
by Machiguchi and Yamabe’s observation of a maximum of
8% addends in the rearrangement of isolated 3 at -10 °C.
For the reaction of cyclopentadiene with dichloroketene,
repeated attempts to observe an initial [4 + 2] adduct 8, as would
be analogous to 3, were unsuccessful.
Kinetic Isotope Effects. Because of the complicating [1,5]-
sigmatropic rearrangement in cyclopentadiene and the instability
of ketenes, these reactions are not readily amenable to a standard
study of their intermolecular KIEs. However, the 12C/13C
isotopic composition at C1 versus C4 and C2 versus C3 of the
product 4 should reflect an intramolecular isotope effect.
Intramolecular isotope effects in general reflect the transition
state for product-determining steps, but as long as a reaction’s
regiochemistry or stereochemistry is settled in the rate-limiting
step, as would be expected here, the intramolecular isotope effect
should reflect the rate-limiting step. If the mechanistic pathways
affording 3 and 4 result from competing rate-limiting transition
states, the isotope effects will reflect a weighted average of the
pathways, but if the 3/4 kinetic selectivity is determined after a
single rate-limiting step, the isotope effects will reflect the single
initial transition state. The subsequent rearrangement of 3 to 4
is irrelevant as long as cycloreversion to starting materials is
minimal.
Figure 3. (a) Relative 13C integrations in samples of 4 and the derived
intramolecular 13C KIEs (25 °C), defined as (k12C/k13C at C1)/(k12C/k13C at
C4) or (k12C/k13C at C2)/(k12C/k13C at C3). (b) Relative 13C integrations in
samples of 7 and the derived intramolecular 13C KIEs (0 °C), defined as
above. The numbers in parentheses refer to 95% confidence limits on the
last digit.
change in that step. The low relative isotope effect at C1 of 4
thus qualitatively indicates that this carbon is not changing
bonding in the rate-limiting step. Since both the major formation
of 3 and the minor formation of 4 require C1-CR bond
formation, the C1-CR bond must already be fully formed when
the isotope effects are decided.41
This conclusion fits well with intramolecular 2H isotope
effects previously obtained by Holder and co-workers for the
reaction of diphenylketene with 5,5-dimethylcyclopentadiene.42
The inverse H1/H4 isotope effect of 0.84 ( 0.02 observed in
the Holder reaction is so large that it does not fit with rate-
limiting C1-CR bond formation. For comparison, isotope
effects of ∼0.91 are seen in highly asynchronous Lewis acid
catalyzed Diels-Alder reactions.43 Holder’s KIE is quite
consistent with a fully formed C1-CR bond.
The intramolecular 13C KIEs in the formation of 4 were
determined at natural abundance by our previously reported
NMR methodology.28,39 Samples of 4 were analyzed by 13C
NMR under the demanding requirements for accurate relative
integrations within spectra. This includes high digital resolution,
long delays, centering of the peaks of interest within the spectral
window, and integration ranges that are a constant multiple of
the peak width at half-height. A complication in the numerical
interpretation of these integrations is that C1 and C2 are subject
1
to three J 13C-13C couplings with satellites not included in
the integration range, while C3 and C4 are only subject to two
such satellite couplings. To allow for this, the integrations at
C3 and C4 were adjusted by the 0.0107(8) natural abundance
of 13C.40 After this correction, the integration of the 13C peak
for C4 of 4 was consistently less than for C1, and integration
of the 13C peak for C3 of 4 was consistently greater than that
of C2 (Figure 3a). The ratios of abundances represent the inverse
of the relative isotope effects at C1 versus C4 and at C2 versus
C3, and these intramolecular isotope effects are also shown in
Figure 3a.
To interpret these results qualitatively, their relative nature
must be kept in mind. If the σ bonding to a carbon is changing
in the rate-limiting step (either making or breaking a σ bond),
that carbon should exhibit a higher relative isotope effect than
a corresponding center that is not undergoing a σ bonding
2
One possible explanation for the observed 13C and H KIEs
would be a stepwise cycloaddition in which reversible bond
(41) The results could also in principle be consistent with an asynchronous
cycloaddition involving leading bond formation at C4, but this is not
supported by either theoretical calculations or qualitative expectations from
frontier orbital theory.
(42) Holder, R. W.; Graf, N. A.; Duesler, E.; Moss, J. C. J. Am. Chem. Soc.
1983, 105, 2929-2931.
(43) Singleton, D. A.; Merrigan, S. R.; Beno, B. R.; Houk, K. N. Tetrahedron
Lett. 1999, 40, 5817-5821.
(39) (a) Singleton, D. A.; Szymanski, M. J. J. Am. Chem. Soc. 1999, 121, 9455-
9456. (b) Singleton, D. A.; Schulmeier, B. E. J. Am. Chem. Soc. 1999,
121, 9313-9317.
(40) De Laeter, J. R.; Bo¨hlke, J. K.; De Bie´vre, P.; Hidaka, H.; Peiser, H. S.;
Rosman, K. J. R.; Taylor, P. D. P. Pure Appl. Chem. 2000, 75, 683-800.
9
J. AM. CHEM. SOC. VOL. 128, NO. 23, 2006 7597

A R T I C L E S
Ussing et al.
Figure 4. Diphenylketene cycloaddition pathway in mPW1K/6-31+G** [mPW1K/6-31G*] calculations. Energies (see ref 47) are in kcal/mol, relative to
the separate starting materials.
formation at C1 is followed by rate-limiting bond formation at
C4 to form 3 or C2 to form 4. However, it will be seen that
this is inconsistent with the kinetic observations. An alternative
explanation involving dynamic trajectories is presented below.
The intramolecular 13C KIEs in the formation of 7 were
determined in an analogous fashion to those of 4 (Figure 3b).
Unlike the formation of 4, the rate-limiting step for the formation
of 7 appears to involve substantial σ bonding change at C1 but
little or no bonding change at C2. Because the absolute KIE at
C4 is unknown, the intramolecular KIE for C1 versus C4 cannot
qualitatively distinguish an asynchronous [4 + 2] transition state
from one in which there is solely bond formation at C1.
Standard Theoretical Results for the Diphenylketene
Reaction. The reactions of diphenylketene and dichloroketene
with cyclopentadiene were examined using mPW1K44 and
B3LYP45 methods as the primary calculational models ex-
plored.46 (See the Supporting Information for RHF/6-311+G**
and BPW91/6-311+G** results, along with some MP2/
6-311+G** single-point energies.) It will ultimately be con-
cluded that one of these methods provides an inaccurate energy
surface, but we discuss both because they predict differing
mechanisms to consider versus experimental observations.
In RHF calculations employing a 3-21G basis set, Machiguchi
and Yamabe had located two transition structures for the
transition structure was 9. Structure 9 would be described as a
[4 + 2] transition structure, based on its MEP connection with
3, though it will be seen that this description is simplistic. The
alternative [2 + 2] transition structure 10 is predicted to be 12.0
kcal/mol47 above 9. It is unlikely that the predicted energies of
9 versus 10 could err so greatly, so, by a standard analysis,
these results again appear inconsistent with the experimental
direct formation of 4. Instead, it would be expected that 4 would
be formed from 3 via the [3,3]-sigmatropic rearrangement
transition structure 11.
B3LYP calculations predict a quite different mechanism
(Figure 5). On the B3LYP/6-311+G** surface, the MEP
through initial transition structure 12 leads to intermediate 13.
Structure 13 is diradicaloid in connectivity, but interestingly,
its restricted wave function is stable. The potential energy
well associated with intermediate 13 is very small, only 0.2
kcal/mol at B3LYP/6-311+G**. From 13, the transition struc-
tures 14 and 15 lead to 3 and 4, respectively. On this surface,
then, the concurrent formation of both 3 and 4 can be viewed
in a standard sense as resulting from the formation of an
intermediate that may then react by two separate transition states
to afford the two products. However, the B3LYP/6-311+G**
surface is inconsistent with our experiments in a different way.
Including zpe and thermal and entropy estimates at -20 °C from
the harmonic frequencies, the free-energy barriers associated
with 12, 14, and 15 are 30.9, 32.2, and 33.4 kcal/mol,
respectively. From this, 15 should be the rate-limiting transition
structure, and the path from 3 to 4 would primarily be indirect,
via 1 + 2, in contrast with experiment.
cycloaddition of cyclopentadiene with diphenylketene.34b
A
“[4 + 2]” transition structure, appearing to lead to the [4 + 2]
product 3, was 13.7 to 14.3 kcal/mol (MP2/6-31G*//RHF/
3-21G including thermal and entropy corrections) below a “[2
+ 2]” transition structure leading directly to the final product
4. These results supported the described initial formation of 3.
They appear inconsistent with the direct formation of 4 found
here, as 4 could only arise from 3 via a Claisen-rearrangement
transition structure that was 0.6 to 1.0 kcal/mol below the [4 +
2] transition structure.
It would thus seem that neither the mPW1K nor the B3LYP
surfaces are consistent with experimental observations. It will
be seen later that this is incorrect.
(45) Becke, A. D. J. Chem. Phys. 1993, 98, 5648-5652.
Superficially, our results in mPW1K/6-31+G** calculations
are quite similar (Figure 4). The only locatable low-energy
(46) See the Supporting Information for full details on the calculational methods
employed. Most standard calculations employed Gaussian 03, revision
C.02: Frisch, M. J. et al. Gaussian, Inc., Wallingford CT, 2004.
(47) The energies given here are not ZPE-corrected, for relevance to trajectories
on the potential-energy surface. See the Supporting Information for a
complete table of energies.
(44) Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000,
104, 4811-4815.
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Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
Figure 5. Diphenylketene cycloaddition pathway in B3LYP/6-311+G** [B3LYP/6-31G*] calculations.
Standard Theoretical Results for the Dichloroketene
Reaction. The high reactivity of dichloroketene is in part the
result of the relative instability of having chlorine as a substituent
on an sp2 carbon. From this, the formation of 7 should be more
exothermic than the formation of 4, and the energetic preference
for the [2 + 2] product 7 over [4 + 2] 8 should be greater than
the energetic preference for [2 + 2] 4 over [4 + 2] 3. Predicted
energies agree with these qualitative expectations; at the
mPW1K/6-31+G** level, formation of 7 is exothermic by 45.7
kcal/mol and favored by 14.6 kcal/mol over formation of 8,
while formation of 4 is exothermic by only 25.8 kcal/mol and
favored over 3 by only 8.1 kcal/mol.48 The overall energy
surface for the dichloroketene reaction is affected by this
relatively greater thermodynamic preference for the [2 + 2]
product.
In mPW1K/6-31+G** calculations (Figure 6), the only
locatable low-energy transition structure was 16. (A transition
structure analogous to 10 was 12.7 kcal/mol higher in energy.)
Two startling observations were associated with 16. First, since
16 seems to closely resemble 9, it might be anticipated that 16
is a transition structure for the [4 + 2] cycloaddition. This is
not correct. Rather, the MEP emanating from 16 leads to 7, not
8. Second, in the smaller 6-31G* basis set, 16 changes little,
but the MEP emanating from 16 at mPW1K/6-31G* affords 8,
not 7!
In both cases, the MEPs pass near another transition structure
17, which is the transition structure for the [3,3]-sigmatropic
rearrangement converting 8 to 7. With the larger basis set, the
MEP from 16 passes slightly to the “7-side” of 17, while, with
the smaller basis set, the MEP passes slightly to the “8-side”
Figure 6. Dichloroketene cycloaddition pathway in mPW1K/6-31+G**
[mPW1K/6-31G*] calculations.
of 17. It is notable that a standard theoretical analysis of this
reaction performed only with a 6-31G* basis set would have
predicted that only 8 is formed, but not 7, while an analysis
performed only with a 6-31+G** basis set would have predicted
that only 7 is formed, but not 8. Obviously, this points to a
substantial weakness in predicting the products of reactions from
MEPs. It will be seen below that dynamic trajectories provide
more realistic predictions.
As with the diphenylketene reaction, the B3LYP/6-311+G**
energy surface for the reaction of cyclopentadiene with dichlo-
roketene contains a very shallow dip for the diradicaloid/
zwitterionic structure 19 (Figure 7).49 From 19, the favored
pathway would be formation of the [2 + 2] product 7 via
(48) A recent paper found that DFT calculations performed relatively poorly in
predicting the overall energetics of [2 + 2] cycloadditions, but mPW1K
showed the best performance versus G3MP2 results for the methods tested.
See: Check, C. E.; Gilbert, T. M. J. Org. Chem. 2005, 70, 9828-9834.
MP2 single-point calculations show identical trends; at MP2/6-311+G**//
B3LYP/6-311+G**, formation of 7 is exothermic by 46.5 kcal/mol and
favored by 18.2 kcal/mol over formation of 8, while formation of 4 is
exothermic by only 29.0 kcal/mol and favored over 3 by only 11.3 kcal/
mol.
(49) Unlike 13, 19’s restricted wave function is not completely stable, but the
energy is lowered by only 0.02 kcal/mol at UB3LYP/6-311+G**, with
<S2> ) 0.0004.
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J. AM. CHEM. SOC. VOL. 128, NO. 23, 2006 7599

A R T I C L E S
Ussing et al.
Figure 7. Dichloroketene cycloaddition pathway in B3LYP/6-311+G** [B3LYP/6-31G*] calculations.
transition structure 21, while transition structure 20 leading to
8 is only modestly higher in energy and would be expected to
be competitive. The initial transition structure 18 is predicted
to be rate limiting. (See the Supporting Information for similar
BPW91/6-311+G** results.)
Overall, the mPW1K and B3LYP calculations predict mech-
anisms that are descriptively quite different. The experimental
Figure 8. Predicted absolute 13C KIE at 0 °C for the dichloroketene
reaction, based on the mPW1K/6-31+G** transition structure 16 and the
B3LYP/6-311+G** transition structure 18.
isotope effects will provide some measure of which method is
more accurate for the current reaction. Trajectory studies will
then show that the apparent difference in mechanisms on the
mPW1K and B3LYP surfaces is largely fallacious.
is strikingly quantitatively accurate, while the C1 KIE predicted
for the B3LYP structure 18 is less accurate. This favors the
accuracy of the mPW1K/6-31+G** surface over the B3LYP/
6-311+G** surface. The results also support the general inter-
pretation of the isotope effects in terms of a rate-limiting transi-
tion state in which there is substantial bond formation to C1
and little or no bond formation to C2 or C4. Notably, the rela-
tively tight delimitation of the transition state by the combination
of isotope effects and calculations still does not confidently
define whether the [4 + 2] or [2 +2] product should be major.
For the transition structures 9 and 12 for initial attack of the
diphenylketene on the cyclopentadiene, substantial 13C KIEs
are predicted for C1 and small KIEs are predicted for C2, C3,
and C4 (Figure 9a), in analogy with the predictions for 16 and
18 in Figure 8. These predictions are clearly inconsistent with
the experimental observations in Figure 3a. In addition, the
relative 2H KIEs predicted for H1 versus H4 are not as inverse
as experimentally observed by Holder,42 in line with the
qualitative argument presented earlier. This again weighs against
rate-limiting C1-CR bond formation.
Predicted Isotope Effects. Prediction of isotope effects for
the dichloroketene reaction is relatively straightforward, as the
B3LYP and mPW1K methods both predict that the initial attack
via transition structures 16 or 18 is rate limiting. The 13C KIEs
associated with these transition structures were predicted from
the scaled theoretical vibrational frequencies50 using TST by
the method of Bigeleisen and Mayer.51 Tunneling corrections
were applied using the one-dimensional infinite parabolic barrier
model.52 Such KIE predictions have proven highly accurate in
reactions not involving hydrogen transfer, so long as the
calculation accurately depicts the mechanism and transition state
geometry.53
The results are summarized in Figure 8. Both 16 and 18 are
predicted to afford a substantial 13C KIE at C1 and near unity
KIEs at C2, C3, and C4, in qualitative agreement with experi-
ment. However, the C1 KIE based on the mPW1K structure 16
(50) The calculations used the program QUIVER (Saunders, M.; Laidig, K. E.;
Wolfsberg, M. J. Am. Chem. Soc. 1989, 111, 8989-8994). B3LYP
frequencies were scaled by 0.9614 (Scott, A. P.; Radom, L. J. Phys. Chem.
1996, 100, 16502-16513). An mPW1K scaling factor of 0.934 was based
on a least-squares fit with the scaled B3LYP frequencies for the starting
cyclopentadiene. The exact choice of scaling factor makes little difference
in the calculated KIE; varying the scaling factor from 0.93 to 0.97 changes
the 13C KIEs by less than 0.001.
(51) (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.
(52) Bell, R. P. The Tunnel Effect in Chemistry; Chapman & Hall: London,
1980; pp 60-63.
(53) (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, D. A. J.
Am. Chem. Soc. 1999, 121, 10865-10874. (c) DelMonte, A. J.; Haller, J.;
Houk, K. N.; Sharpless, K. B.; Singleton, D. A.; Strassner, T.; Thomas, A.
A. J. Am. Chem. Soc. 1997, 119, 9907-9908. (d) Singleton, D. A.;
Merrigan, S. R.; Liu, J.; Houk, K. N. J. Am. Chem. Soc. 1997, 119, 3385-
3386.
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7600 J. AM. CHEM. SOC. VOL. 128, NO. 23, 2006

Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
Figure 9. Predicted absolute 13C and 2H KIEs at 25 °C for the diphenylketene reaction, treating the various transition structures as rate-limiting. For
comparison with the experimental KIEs, relative KIEs at competitive positions (C1/C4, C2/C3, H1/H4, H2/H3) should be considered.
Table 1. Results from Quasiclassical Trajectories Starting from 9,
12, 16, and 18
The predicted isotope effects based on later transition
structures in the diphenylketene mechanisms are enlightening
[4
+
2]
[2
+
2]
trajectories
(Figure 9b), ignoring for now apparent experimental inconsis-
tencies. The KIEs for transition structure 11 are notably close
to the experimental values; the relative KIEs at C1 and C2 would
be 0.997 and 1.009, respectively. For 14, the relative isotope
effect at C1 would be 0.978, much lower than the experimental
value. Transition structure 15, rate limiting in the B3LYP/
6-311+G** calculations, leads to relative KIEs at C1 and C2
of 0.995 and 1.012, respectively. While the latter is larger than
the observed relative KIE of about 1.007, the pattern of inverse
KIE at C1 and normal KIE at C2 resembles that of the
experimental KIEs. All of the structures 11, 14, and 15 have
relative 2H KIEs predicted for H1 versus H4 that are consistent
with Holder’s observations.42 Overall, the comparison of
experimental and predicted KIEs suggests that the molec-
ular geometry when the KIEs are decided has a fully formed
C1-CR bond and little bond formation to C2 or C4, roughly
resembling 11.
Trajectory Studies of the Reaction of Cyclopentadiene
with Ketenes. As will be discussed below, the kinetic observa-
tions and isotope effects for the diphenylketene reaction are
inconsistent when viewed in a standard way, so that no orthodox
mechanism can be reconciled with the experimental observa-
tions. From the apparent contradictions, it was suspected that
the reaction’s energy surface is of the type in Figure 1b. To
explore this issue, we turned to trajectory studies.
starting
transition structure
total
trajectories
trajectories trajectories recrossing exceeding
(3 or 8)
(4 or 7)
trajectories time limit
diphenylketene
130
24
81
9 (mPW1K/6-31G*)
9 (mPW1K/6-31+G**)
12 (B3LYP/6-31G*)
67
8
18
4
1
3
56
15
54
3
0
6
dichloroketene
130
37
121
16 (mPW1K/6-31G*)
16 (mPW1K/6-31+G**)
18 (B3LYP/6-31G*)
70
8
15
47
24
75
13
5
20
0
0
11
16 (as their 6-31+G** variants) at the mPW1K/6-31+G** level
were also studied. With all atomic motions freely variable, the
trajectories were initialized8b by giving each mode a random
sign for its initial velocity, along with an initial energy based
on a random Boltzmann sampling of vibrational levels appropri-
ate for 273.15 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. The starting atomic positions
on the potential energy ridge in the area of the transition
structures were randomized using a linear sampling of possible
harmonic classical displacements for each normal mode, adjust-
ing the kinetic energy for each mode accordingly. Employing
a Verlet algorithm, 1-fs steps were taken until either the [4 +
2] or [2 + 2] products were formed or recrossing occurred to
afford the starting materials (defined by a C1-CR distance >
2.4 Å) up to a maximum of 500 fs. The results are shown in
Table 1.
Transition structures 9, 12, 16, and 18 (as their 6-31G*
variants) were used as the starting point for quasiclassical direct
dynamics trajectories4,5,8,9,11,12,54 on the mPW1K/6-31G* (for
9 and 16) and B3LYP/6-31G* (for 12 and 18) potential energy
surfaces, using Gaussian 0346 to calculate forces at each point
and using previously described code29 to initiate and propagate
trajectories (see the Supporting Information for complete code
and details). Limited sets of trajectories emanating from 9 and
Among several striking observations, the most conspicuous
is that trajectories passing through transition structures 9 and
16 afford both the [4 + 2] and [2 + 2] products. The MEPs
passing through either lead to a single product, as must be true
in the absence of symmetry, but the trajectories show that these
transition structures may lead to two products.
The MEPs do retain value here in predicting the major product
from trajectories. Despite quite similar geometries for 16
predicted with 6-31G* versus 6-31+G** basis sets, a modest
majority of the 6-31G* trajectories afford the [4 + 2] product
(54) Bunker, D. L. Methods Comput. Phys. 1971, 10, 287-325. Bunker, D. L.
Acc. Chem. Res. 1974, 7, 195-201. Chapman, S.; Bunker, D. L. J. Chem.
Phys. 1975, 62, 2890-2899. Suzukawa, H. H., Jr.; Wolfsberg, M.;
Thompson, D. L. J. Chem. Phys. 1978, 68, 455-472. Hase, W. L. J. Phys.
Chem. 1986, 90, 365-374.
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A R T I C L E S
Ussing et al.
8 while three-quarters of the productive 6-31+G** trajectories
afforded the [2 + 2] product 7. (The majority product is in each
case statistically significant at 95% confidence.) This fits with
the surprising MEP results described in a previous section.
On the B3LYP surface, transition structures 12 and 18 lead
to intermediates that can in a standard manner partition to the
two products, so it is perhaps not surprising that trajectories
afford both [4 + 2] and [2 + 2] products in these cases.
However, an examination of the trajectories suggests that the
intermediates 13 and 19 have little impact. The standard view
is that the mechanism passes through 13 on its way to 3 and 4,
but in fact 9 out of the 18 trajectories affording 3 exhibited a
monotonic decrease of the incipient C4-O bond distance with
time. Such trajectories bypass 13, and in such cases the standard
“stepwise” mechanism seems best understood as a concerted
[4 + 2] cycloaddition. Similar results were seen for the for-
mation of 8 from 18; 9 out of 15 trajectories showed a mono-
tonic decrease in the incipient C4-O distance, effectively by-
passing 19. Intriguingly, the [2 + 2] process acts more in accord
with the involvement of an intermediate; 71 out of 75 trajectories
forming 7 from 18 involve a significant oscillation of the
incipient C2-Câ bond distance before forming 7, and these
trajectories take longer than those forming 8 (median of 342 fs
versus 178 fs for forming 7). Still, few trajectories are caught
in the area of the intermediate to the time limit of 500 fs.
A final remarkable observation is the large number of trajec-
tories recrossing to afford the reactants on both the mPW1K
and B3LYP surfaces, particularly for the diphenylketene reac-
tion. These trajectories typically form the C1-CR bond
completely, passing through the area of 11 or 13, then run into
a potential energy “wall” associated with a short C1-CR
internuclear distance and bounce back to starting materials. The
recrossing may be understood in statistical terms on the B3LYP
surface, viewing 13 as an intermediate that may partition in
three ways, including going back to starting materials. However,
the extensive recrossing from the area of 11 on the mPW1K
surfaces is problematical to rationalize statistically. Of 23
trajectories started statistically in the area of 11 on the mPW1K/
6-31G* surface, 12 afforded 3, 10 afforded 4, and only 1
afforded cyclopentadiene plus diphenylketene. This supports the
idea that the recrossing seen above in trajectories starting from
11 is nonstatistical. The congruence of these results with
experimental observations will be discussed below.
Figure 10. Limiting kinetic mechanisms for the reaction of cyclopentadiene
with diphenylketene. Single arrows imply that a step is effectively irre-
versible under the reaction conditions, while paired arrows imply revers-
ibility.
Discussion
The discussion here starts by considering the difficulty of
reconciling the experimental results with any standard mecha-
nistic scheme, largely ignoring the theoretical results. It then
considers which of the calculational methods is more coherent
with experiment, and discusses how a consistent mechanism
can be described once dynamic trajectories are taken into
account. Finally, we discuss how these results complicate the
understanding of the selectivity, rate, isotope effects, and
mechanism of cycloadditions.
Possible Mechanisms and an Experimental Paradox.
Figure 10 shows a series of possible kinetic mechanisms for
the cycloaddition of cyclopentadiene with diphenylketene. In
Figure 10a, 3 and 4 are formed concurrently and irreversibly
(or effectively so) via separate transition states, and 3 is
converted to 4 directly without reverting to the starting materials.
This is the simplest mechanism that is consistent with the kinetic
observations from the low-temperature NMR reaction. However,
this mechanism is not consistent with the intramolecular KIEs
of Figure 3a, as a substantial relative KIE at C1 would be
expected (as actually observed in the dichloroketene reaction
in Figure 3b). The same problem would apply to any more
complicated variation of this mechanism in which initial attack
of the ketene on the diene is rate limiting. This mechanism also
receives no theoretical support.
Figure 10b and 10c depict limiting mechanisms in which an
intermediate is formed followed by partitioning to the two
products, and the rearrangement of 3 to 4 passes through the
intermediate. In Figure 10b, formation of both 3 and 4 from
the intermediate would be slow, and the intermediate would
predominantly fragment to starting materials. In Figure 10c,
intermediate formation from starting material is irreversible. A
mechanism in between those in Figure 10b and 10c, involving
competitively rate-limiting steps, could also be envisioned. The
pathway in Figure 10b is essentially that predicted by B3LYP
calculations, when viewed in a standard way ignoring trajec-
Should solvent collisions impact the nonstatistical recrossing?
The efficiency of the recrossing should depend on the rate at
which energy is lost from a normal mode associated with the
C1-CR stretch, either due to IVR or solvent collisions. In 11,
this mode has a frequency of 634 cm-1. The loss of energy
from such modes in solution should be dominated by IVR and
occur at a time scale on the order of picoseconds.55 The median
time for recrossing trajectories at the mPW1K/6-31+G** level,
from their start at 9 to a C1-CR separation > 2.4 Å, was 112
fs, and the time available for energy loss is so short that the
recrossing in gas-phase trajectories should be negligibly affected
in solution.
(55) (a) Davis, A. V.; Zanni, M. T.; Frischkorn, C.; Elhanine, M.; Neumark, D.
M. J. Electron Spectrosc. Relat. Phenom. 2000, 112, 221-230. (b) Stratt,
R. M.; Maroncelli, M. J. Phys. Chem. 1996, 100, 12981-12996. (c) Dahl,
K.; Sando, G. M.; Fox, D. M.; Sutto, T. E.; Owrutsky, J. C. J. Chem. Phys.
2005, 123, 084504. (d) Yoo, H. S.; DeWitt, M. J.; Pate, B. H. J. Phys.
Chem. A 2004, 108, 1348-1364. (e) Yoo, H. S.; DeWitt, M. J.; Pate, B.
H. J. Phys. Chem. A 2004, 108, 1365-1379.
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Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
tories. Our NMR kinetic observations, showing that rearrange-
ment of 3 to 4 occurs principally or exclusively by a direct
process, rule out a majority contribution from the mechanism
in Figure 10b. The mechanism in Figure 10c is consistent with
the NMR results, as the rearrangement of 3 to 4 would occur
without involving reversion to starting materials. However, if
Figure 10c was the majority mechanism, the intramolecular KIEs
for 4 would reflect the C1-CR bond forming step and should
not so drastically differ from those for 7.
Many more complicated kinetic mechanisms can be consid-
ered; Figure 10d and 10e show two examples. To account for
the experimental results, these mechanisms have the key feature
that the rearrangement of 3 to 4 occurs without crossing the
path of the intermediates involved in the cycloaddition. In Figure
10d, two transition states lead to two distinct intermediates, with
each intermediate forming a single product, either 3 or 4. In
Figure 10e, reversible formation of a single intermediate is
followed by irreversible formation of 3 and 4. We cannot
exclude kinetic mechanisms such as these; they are clearly
consistent with experiment. However, a difficulty arises when
filling in the details of such mechanisms, as they invariably
must involve three geometrically similar but distinguishable
transition states: one for the formation of 3, the second for
formation of 4, and the third for the [3,3]-sigmatropic rear-
rangement. We have been unable to concretely envision such
mechanisms involving three similar but distinct transition states,
and calculations provide no support for such a possibility. For
example, in the B3LYP calculations the rearrangement passes
through the same intermediate as formed initially in the
cycloaddition process, and we were unable to locate an alter-
native rearrangement mechanism.
Overall, the experimental results present a paradox, irresolv-
able by a standard view of the reaction mechanism. The paradox
will be resolvable once trajectories are taken into account.
Evaluation of the Calculational Methods. The B3LYP and
mPW1K methods make descriptively distinct predictions for
the cycloadditions of cyclopentadiene with ketenes. Which is
more accurate? A variety of experimental observations aid this
evaluation.
The KIEs observed in the reaction of dichloroketene with
cyclopentadiene support the mPW1K calculations over the
B3LYP, as the former lead to much more accurate predictions
of the experimental KIEs. The mPW1K calculations predict a
lower barrier to the cycloaddition and an earlier transition
structure (cf. 16 versus 18), resulting in a lower 13C KIE at C1
that is more consistent with the observed value. The barrier for
the dichloroketene reaction is not known, so it is unclear which
method is more accurately predicting the barrier in this case,
but in the diphenylketene reaction the rate constant of ∼5 ×
10-4 M-1s-1 at 253 K corresponds to a ∆Hq barrier of ∼8.4
kcal/mol, assuming a ∆Sq of ∼ -40 eu.56 The mPW1K/
6-31+G** barrier is closer than the B3LYP/6-311+G** barrier
by 4.8 kcal/mol, though it still overestimates the phenomeno-
logical enthalpy barrier.
mol above cyclopentadiene + diphenylketene at standard state.
This conflicts with the manifest experimental observation that
4 is formed and is stable. This error is in line with recent
observations.48 The mPW1K/6-31+G** calculations predict that
the formation of 4 is exergonic by 8.3 kcal/mol.
One critical issue to consider is the mechanism of the [3,3]-
sigmatropic (Claisen) rearrangement of 3 to 4 or 8 to 7. The
B3LYP calculations predict that this rearrangement proceeds
by a loose stepwise mechanism, while the mPW1K calculations
predict a tighter concerted process. In this regard, it should be
noted that, for the parent Claisen rearrangement of allyl vinyl
ether, B3LYP calculations predict a transition structure that is
too loose versus KIEs or higher-level calculations.53b The
mPW1K/6-31+G** transition structure for the parent Claisen
(see Supporting Information) closely resembles the KIE-
supported MP2, MP4, and QCISD transition structures.
Overall, from these considerations, it would be expected that
the mPW1K energy surfaces more accurately represent the
experimental reactions. The critical question then is whether
the mPW1K surfaces can account for three key observations
here: the KIEs, the direct formation of 4, and the direct
rearrangement of 3 to 4.
A Consistent Picture of the Mechanism from Trajectories.
The observed formation of 4 without the intermediacy of 3
appeared inconsistent with the mPW1K surfaces, on which the
only low-energy transition structure (9) leads by an MEP to 3.
However, the trajectory studies show that both 3 and 4 can be
formed from 9. Thus, the trajectories resolve the contradiction
between experiment and theory.
The formation of 4 from 9 can be understood by consideration
of the qualitative potential energy surface in Figure 11a. The
MEP emanating from 9 passes near 11, and trajectories
occasionally end up on the “[2 + 2] side” of saddle point 11.
Both 3 and 4 are downhill from 9, so it should not be surprising
that trajectories can afford either. The proportion of trajectories
through 9 forming 4 is low (4:3 is 4:67 at 6-31G*, 1:8 at
6-31+G**) versus experiment (4:3 is approximately 1:4.5), but
from the necessarily limited trajectories, the statistical uncer-
tainty in the predicted product ratio is high. The critical
observation is that some trajectories afford 4.
The mPW1K/6-31G* and mPW1K/6-31+G** surfaces pre-
dict that the barrier for rearrangement of 3 to 4 via 11 is lower
than the barrier for cycloreversion to starting materials via 9,
so the mPW1K calculations appear to naturally account for the
experimental direct conversion of 3 to 4. However, the picture
is complicated by entropy, from a thermodynamic perspective,
or by the possible trajectories, from a dynamical perspective.
After taking into account an entropy estimate at 253 K (based
on the harmonic frequencies), the direct rearrangement is favored
by only 0.2-0.5 kcal/mol (60-74% direct rearrangement at 253
K). The observation that a trajectory started statistically in the
area of 11 can occasionally eschew downhill product formation
in favor of cycloreversion suggests that the exit channel to
starting materials is dynamically broad. From either perspective,
then, the expectation is that some minor portion of 3 would
revert to starting material before forming 4. The experimental
observations are consistent with this, though most of the
conversion of 3 to 4 is direct.
For the overall thermodynamics of the reaction, the B3LYP
calculations perform very poorly. After allowance for an entropy
estimate (25 °C, unscaled harmonic frequencies), the B3LYP/
6-311+G** calculations place the [2 + 2] product 4 at 4.1 kcal/
2
The intramolecular 13C and H KIEs for the diphenylketene
(56) (a) Huisgen, R.; Feiler, L. A.; Otto, P. Tetrahedron Lett. 1968, 4485-
4490. (b) Brady, W. T.; O’Neal, H. R. J. Org. Chem. 1967, 32, 612-614.
reaction seem impossible to reconcile in a standard way with
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A R T I C L E S
Ussing et al.
intermediate in a standard way, then invoke a dynamic effect
to explain the predominantly direct rearrangement of 3 to 4.
That is, the mechanism of Figure 10b could perhaps act like
that of Figure 10e due to Carpenter-like dynamic matching6 in
the rearrangement process. This would be reasonably consistent
with experimental observations, though it is not supported by
the mPW1K calculations.
Implications Regarding the Understanding of Periselec-
tivity. FMO theory provides predictions for the rates and
selectivity of cycloadditions based on HOMO-LUMO interac-
tions. Many specific reactions provide exceptions to the predic-
tions of FMO theory,57 as might be expected for any model
using starting-material orbitals to explain transition state ener-
gies. The complication added here is that even transition state
orbital interactions do not necessarily define the product of a
cycloaddition.
Within FMO theory, the regiochemistry and periselectivity
of a cycloaddition are decided by the interaction of the largest
coefficient of the HOMO of one addend with the largest
coefficient of the LUMO of the other addend.58 Transition states
derived from the reaction of unsymmetrical addends tend to be
asynchronous, with leading bond formation between the centers
that had the largest HOMO or LUMO coefficients and a weaker
bonding interaction at the opposite end of the transition state.
This disparity in interactions in an asynchronous cycloaddition
extends to atomic motions; the predominant motions in the
transition vector for an asynchronous cycloaddition involves the
centers leading in the bond formation, with often very little
approaching motion for the centers at the other end.59 On the
end of an asynchronous cycloaddition for which bonding is less
advanced, the centers involved are not necessarily dynamically
committed to bond formation.
Figure 11. Qualitative potential energy surfaces for reaction of cyclopen-
tadiene with diphenylketene (1 + 2). Solid lines are the MEP, and dashed
lines are possible trajectories. (a) On the mPW1K surface, there is no
intermediate and no transition state leading directly from starting materials
to 4. However, 4 can be formed from trajectories passing through 9. (b)
On the B3LYP surface, the MEP passes into shallow intermediate 13.
Trajectories may bypass this intermediate to afford 3 directly.
the mPW1K absence of an intermediate, but the trajectory
studies suggest a solution to this riddle. A starting point is the
differing amounts of recrossing with diphenylketene versus
dichloroketene. With dichloroketene, only 10-14% of the
trajectories started forward from the area of 16 revert to starting
materials. From this, it would be expected that the trajectories
should have little to no impact on the KIEs for the formation
of 7. This is apparently observed, as there is a good correlation
between the experimental and predicted KIEs for the formation
of 7.
With diphenylketene, however, a large portion of the trajec-
tories started forward from 9 recross to starting materials (44%
at 6-31G*, 63% at 6-31+G**). In this case, the experimental
KIEs should not match with those predicted from transition
structure 9, as observed. No rules let us predict the KIEs in
these circumstances; TST cannot be applied as there are no
transition states that serve as barriers passing from 9 to products.
However, the trajectories suggest that the “decision” to form
product versus revert to starting material is made in the area
around transition structure 11. The experimental KIEs, allowing
for their relative nature, are quite close to those predicted KIEs
for 11, supporting the idea that reactive versus nonreactive
trajectories are decided in this area.
This idea allows a complication to arise in the periselectivity
of cycloadditions. When an asynchronous transition state has
available an alternative bonding interaction, two product
structures may be downhill from the cycloaddition transition
state. If there is no barrier to cross in the formation of either
product, the periselectivity may be determined by the vagaries
of dynamical motion. A steepest-descent path is likely to lead
to the major product, but there is no simple way to predict the
product ratio or relate it to the transition state orbital interactions.
(57) (a) Kahn, S. D.; Pau, C. F.; Overman, L. E.; Hehre, W. J. J. Am. Chem.
Soc. 1986, 108, 7381-7396. (b) Takasu, K.; Mizutani, S.; Ihara, M. J.
Org. Chem. 2002, 67, 2881-2884. (c) Alston, P. V.; Gordon, M. D.;
Ottenbrite, R. M.; Cohen, T. J. Org. Chem. 1983, 48, 5051-5054.
(58) (a) Houk, K. N. Acc. Chem. Res. 1975, 8, 361-369. (b) Fleming, I. Frontier
Orbitals and Organic Chemical Reactions; Wiley: New York, 1976;
Chapter 4.
(59) This issue has been rarely discussed but appears generally true for the
cycloadditions that we have studied. Because the motion of carbon centers
at the transition state is related to observed 13C KIEs, the differences in
atomic motion at opposite ends of a cycloaddition are supported experi-
mentally by KIE observations. See ref 53a and (a) Birney, D. M.; Houk,
K. N. J. Am. Chem. Soc. 1990, 112, 4127-4133. (b) Singleton, D. A.;
Schulmeier, B. E.; Hang, C.; Thomas, A. A.; Leung, S.-W.; Merrigan, S.
R. Tetrahedron 2001, 57, 5149-5160.
An alternative mechanism deserves mention. In this section
we have rationalized observations by invoking dynamic effects
in the initial cycloaddition process, treating the rearrangement
of 3 to 4 as a standard reaction. An alternative would be to
have the cycloaddition process occur stepwise through an
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Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
These concepts provide insight into the cycloaddition of
ketenes with cyclopentadiene. The low-energy π*CdO of the
ketene has its largest coefficient at CR, and the asynchronous
cycloaddition transition state may be viewed as resulting from
the interaction of CR with the HOMO of the diene at its large
C1 coefficient. At the transition state, the interaction between
the carbonyl oxygen and C4 of the diene is weak, and an
alternative interaction can lead to the [2 + 2] product. If the
“strength” of these interactions is judged by the dynamical
outcome, then in the dichloroketene case the interactions are
closely balanced, and either product may be formed. In the
diphenylketene reaction, the C4-O interaction appears “stron-
ger”, as the [4 + 2] product is major.
The results here suggest that nonstatistical recrossing can also
have a substantial effect on experimental observations. When
recrossing is low, as in the dichloroketene trajectories, the
observed KIEs reflect the conventional transition state. In the
diphenylketene reaction, many of the mPW1K trajectories
recross, and the experimental KIEs differ greatly from those
predicted from conventional TST for 9. In perspective, the effect
of nonstatistical recrossing on the absolute rate of the reaction
is small; even if 90% of trajectories recrossed, the rate effect is
small compared to the exponential effect of barrier energy, so
no readily recognizable effect of recrossing would be seen in
the experimental rate. However, the recrossing is potentially
much more easily recognized from the KIEs, or conversely, it
appears that nonstatistical recrossing must sometimes be taken
into account to interpret KIEs. In this regard, it is perhaps
notable that the prediction of KIEs for simple SN2 reactions
has proven surprisingly difficult,64 since Hase has found that
SN2 reactions are subject to nonstatistical recrossing.4,5
The most fundamental idea in TST is that there exists a
hypersurface, the transition state, dividing starting materials from
products for defining reactive trajectories. In generalized TST,
the hypersurface can be placed anywhere along the reaction
coordinate, but a transition state is only useful for understanding
rates or KIEs or selectivity if the transmission coefficient does
not depart too drastically from unity. Useful transition states
may be pursued in various ways; in variational TST, the position
of a coordinate-space hypersurface transverse to the MEP is
adjusted to minimize crossing, while microcanonical variational
TST makes use of an energy-dependent continuum of hyper-
surfaces, but the ability to delineate a useful dividing hyper-
surface is a critical component of TST.
Because trajectories entering the area of 11 from starting
materials tend to revert to starting materials, while statistical
trajectories in the area of 11 tend to form 3 or 4, we cannot
envision how a useful and tractable dividing hypersurface can
be delineated in coordinate space for the reaction of cyclopen-
tadiene with diphenylketene. It is perhaps possible that by
allowing for the momenta of atoms, a dividing surface could
be manageably defined in phase space, but this is not within
the realm of current versions of TST. Within current theory,
there is no experimentally or dynamically consistent transition
state for the cycloaddition of cyclopentadiene with diphen-
ylketene.
Structurally, the presence of a bifurcating surface as in Figure
11a would not seem to be required for nonstatistical recrossing.
Rather, the key feature seems to be that the reaction involves
two bond-forming processes, one of which is not “set up” at
the transition state. In such circumstances, a reaction may fail
to dynamically consummate an asynchronous pericyclic process
after successfully completing the first bonding change. This
could make nonstatistical recrossing more common in complex
reactions than in the simple reactions typically studied dynami-
cally.
However, neither the dynamical outcome nor the MEP is a
direct measure of transition state orbital interactions. This is
highlighted by an atoms-in-molecules analysis60 of 9 and 16
(as their 6-31+G** variants). In each case, there was no bond
path between Câ and C2, and most interestingly, a C4-O bond
path was found for 16 but not 9. It should be recalled that the
MEP and a majority of trajectories from 16 with this basis set
affords [2 + 2] product 7, effectively ignoring the C4-O bond.
On the other hand, within the atoms-in-molecules formalism
there is no C4-O bonding in 9, but the experimental product
ratio reflects a significant dynamical preference for formation
of this bond. Both observations support the idea that the
periselectivity does not necessarily reflect transition state orbital
interactions.
Nonstatistical Recrossing and Isotope Effects. No Transi-
tion State! With the exception of hydrogen transfer reactions,
the combination of conventional TST and a one-dimensional
tunneling correction affords excellent predictions of heavy-atom
KIEs (provided that the underlying theoretical mechanism is
accurate).43,53,61,62 When a reaction is enthalpically barrierless
or involves a potential-energy saddle point in a nearly flat region
of the energy surface, the effect of recrossing is often substantial
and conventional TST is inadequate. In such cases, variational
TST, which effectively allows for statistical recrossing, has
provided good predictions of heavy-atom KIEs.63
(60) (a) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Clarendon
Press: Oxford, 1990. (b) Biegler,-Ko¨nig, F.; Scho¨nbohn, J.; Bayles, D. J.
Comput. Chem. 2001, 22, 545-559.
(61) (a) Singleton, D. A.; Hang, C. J. Org. Chem. 2000, 65, 7554-7560. (b)
Merrigan, S. R.; Singleton, D. A. Org. Lett. 1999, 1, 327-330. (c) Singleton,
D. A.; Merrigan, S. R.; Kim, B. J.; Beak, P.; Phillips, L. M.; Lee, J. K. J.
Am. Chem. Soc. 2000, 122, 3296-3300. (d) Singleton, D. A.; Nowlan, D.
T., III; Jahed, N.; Matyjaszewski, K. Macromolecules 2003, 36, 8609-
8616. (e) Singleton, D. A.; Hang, C. J. Am. Chem. Soc. 1999, 121, 11885-
11893. (f) Singleton, D. A.; Wang, Z. J. Am. Chem. Soc. 2005, 127, 6679-
6685.
(62) The theoretical justification for this observation fails in detail, and it may
be expected that exceptions will arise. See: Truhlar, D. G.; Lu, D. H.;
Tucker, S. C.; Zhao, X. G.; Gonzalez-Lafont, A.; Truong, T. N.; Maurice,
D.; Liu, Y. P.; Lynch, G. C. In Isotope Effects in Chemical Reactions and
Photodissociation Processes; Kaye, J. A., Ed.; ACS Symposium Series
502; American Chemical Society: Washington, DC, 1992.
(63) (a) Keeting, A. E.; Merrigan, S. R.; Singleton, D. A.; Houk, K. N. J. Am.
Chem. Soc. 1999, 121, 3933-3938. (b) Nowlan, D. T., III; Singleton, D.
A. J. Am. Chem. Soc. 2005, 127, 6190-6191.
Bypassing Intermediates and the Mechanism of Cycload-
ditions. Although the B3LYP surface appears to be inaccurate
(64) (a) Hu, W.-P.; Truhlar, D. G. J. Am. Chem. Soc. 1995, 117, 10726-10734.
(b) Fang, Y.-r.; Gao, Y.; Ryberg, P.; Eriksson, J.; Kolodziejska-Huben,
M.; Dybala-Defratyka, A.; Madhavan, S.; Danielsson, R.; Paneth, P.;
Matsson, O.; Westaway, K. C. Chem.sEur. J. 2003, 9, 2696-2709. (c)
Truhlar, D. G.; Garrett, B. C.; Klippenstein, S. J. J. Phys. Chem. 1996,
100, 12771-12800. (d) Villano, S. M.; Kato, S.; Bierbaum, V. M. J. Am.
Chem. Soc. 2006, 128, 736-737.
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A R T I C L E S
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in these reactions, the intriguing observation that many trajec-
tories on this surface bypass the intermediates 13 and 19 requires
some further comment. The outcome of these trajectories may
be understood with reference to the qualitative potential energy
diagram in Figure 11b. The intermediate 13 is a shallow dip in
the potential energy surface, forward from the transition structure
12 on the MEP. However, the product 3 is also downhill from
12, so a portion of the trajectories proceed directly from 12 to
3. The great majority (about 72 out of 81) of the trajectories do
indeed pass through the area of 13, but most end up recrossing
12 to starting materials. The formation of 3 on this surface
depends substantially on trajectories being able to occasionally
bypass 13.
We have recently reported that, for an ene reaction, trajec-
tories emanating from a formally “concerted” transition structure
(a transition structure in which the MEP leads directly to the
final product) often lead to the intermediate for a stepwise
mechanism.30 In the ene-reaction case, a stepwise mechanism
can occur even though an arbitrarily accurate standard analysis
would conclude it to be concerted. The opposite is observed
here for the B3LYP trajectories; that is, a standard theoretical
analysis would describe the mechanism as stepwise, but around
half of the reactive trajectories act concerted.65 The lesson from
these observations, as well as other studies,6-8,12,28,66,67 is that
the classical division of multibond reactions into stepwise versus
concerted mechanisms is often an oversimplification. A majority
of cycloadditions and related reactions are likely to be mecha-
nistically simple, but for reactions approaching a stepwise/
concerted boundary, just those cases where the question of
concert is most interesting, the consideration of trajectories will
often be essential to understanding the mechanism.
A second mystery is presented by the KIEs. The rate-limiting
step for the dichloroketene reaction involves C1-CR bond
formation, and TST performs well in accounting for the 13C
KIEs. However, the 13C KIEs for the diphenylketene reaction
are quite different. Supported by Holder’s 2H KIEs,42 they
appear to require a rate-limiting step that follows reversible
formation of an intermediate. Yet the conversion of 3 to 4 must
somehow eschew this intermediate, or else pass through starting
materials. We can define no standard mechanism that fits both
sets of results, and standard calculational analyses provide no
helpful suggestions.
Once again, however, trajectories account for the observa-
tions. The predicted extensive recrossing to starting materials
would effectively delay the cycloaddition’s isotopic discrimina-
tion toward an area of the surface where the C1-CR bond is
fully formed, accounting for the KIEs. Because the recrossing
is nonstatistical, it can be independent of the rearrangement,
even though the two involve similar areas of the energy surface.
The trajectory-predicted failure of transition state theory regard-
ing the rate of the reaction is too small to be experimentally
gauged, but the observable impact on KIEs is potentially of
great importance to their interpretation.
The role of trajectories in deciding the products, selectivities,
rates, isotope effects, and mechanism of these reactions is all
perhaps intellectually unsatisfying. The simple model of transi-
tion state theory has tremendous predictive value and provides
insight. Chemists tend to equate the rates and selectivities and
isotope effects for reactions with the properties of transition
states and implicitly assume that the product formed is fully
defined by the transition state geometry and its orbital interac-
tions. When instead, product selectivity depends on the details
of trajectories on a dimensionally broad energy surface, the
complexity of chemistry seems daunting. For example, it is
disconcerting that after both experimentally and calculationally
characterizing the transition state for the dichloroketene reaction,
we still do not know the major initial reaction product. However,
fully understanding the role of trajectories in complex reactions
should prove an intriguing intellectual challenge for the future.
Conclusions
Mechanistic understanding starts with qualitatively accounting
for the products. It is easy to understand the [4 +2] products 3
and 8 from the cycloaddition of ketenes with cyclopentadiene.
The CdO π* is the lowest energy LUMO, the CdO is
unhindered, and [4 + 2] cycloadditions are of course allowed
pericyclic reactions with thousands of examples. It is much more
difficult to understand the direct formation of the [2 + 2]
cycloadduct 4; the CdC of the ketene is not electron poor, and
it is sterically hindered. A standard calculational analysis
provides no help in understanding the formation of 4, as there
is no low energy transition structure that leads by an MEP to 4.
Nonetheless, it has been shown here that 4 is formed directly,
at a rate that is amazingly competitive with the formation of 3.
How? One might try to explain this with a stepwise
mechanism, but contradictions arise when one tries to propose
a standard mechanism that also reconciles the direct conversion
of 3 to 4 and the KIEs. The formation of 4 becomes understand-
able only once it is recognized that a single transition state can
afford dynamically both [4 + 2] and [2 + 2] products. The
most dramatic result here is that the mPW1K trajectories can
account for a product in an ordinary cycloaddition that would
otherwise be inexplicable.
Experimental Section
NMR Study of the Cycloaddition of 1 with 2. A 0.038 M solution
of 2 in CD2Cl2 was prepared, and 0.7887 g of this solution was placed
in the 5 mm NMR tube to fill it to 4.5 cm. The tube was placed in a
400 MHz NMR, and the probe was brought to -20 °C, then tuned,
and shimmed. The system was left for 1 h at -20 °C, and the instrument
was reshimmed. The reaction was started by a series of operations
involving rapidly ejecting the NMR tube, adding 100 µL of cyclopen-
tadiene (precooled at -78 °C), shaking the tube, reinserting the tube
in the NMR, and immediately acquiring a spectrum, taking a total time
of 90 s. After the initial spectrum and periodically throughout the
experiment the NMR was shimmed. Additional spectra were acquired
after 8, 10, 15, 20, 27, 30, 45, 60, 75, 90, 105, 120, 165, 720, 965,
1200, and 1440 min. The observed compositions were fit to possible
kinetic schemes as described in the Supporting Information.
NMR Measurements. The preparation of samples of the known
compounds 4 and 7 for NMR analysis is described in the Supporting
Information. NMR samples were prepared using 223.5 mg of 4 or 300
mg of 7 in a 5-mm NMR tube filled to a 5-cm sample height with
CDCl3. The 13C spectra of 4 were recorded at 125.7 MHz using inverse
gated decoupling, 60 s delays between calibrated π/2 pulses, and a 6.4
s acquisition time to collect 512 000 points. Spectra of 7 were recorded
at 100.577 MHz using 200 s delays and a 5 s acquisition time to collect
(65) As a related example, it was recently proposed that the thermal dimerization
of styrene involves some concerted trajectories despite a stepwise transition
state, albeit without the support of trajectory studies. See: Khuong, K. S.;
Jones, W. H.; Pryor, W. A.; Houk, K. N. J. Am. Chem. Soc. 2005, 127,
1265-1277.
(66) Ussing, B. R.; Singleton, D. A. J. Am. Chem. Soc. 2005, 127, 2888-2889.
(67) Ammal, S. C.; Yamataka, H.; Aida, M.; Dupuis, M. Science 2003, 299,
1555-1557.
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Cycloadditions of Ketenes with Cyclopentadiene
A R T I C L E S
290 000 points. Integrations were determined numerically using a
constant equal integration region for peaks compared. A zeroth-order
baseline correction is generally applied, but in no case was a first-
order (tilt) correction applied. 6 spectra were obtained for each of two
independent samples of 4, and 6 and 12 spectra were obtained for two
independent samples of 7. The results in Figure 3 were obtained from
the ratios of compared peaks in each spectrum, with the 95% confidence
limits calculated in a standard way.
The Laboratory for Molecular Simulation at Texas A&M
University is acknowledged for providing the software for
atoms-in-molecules calculations.
Supporting Information Available: Energies and full geom-
etries of all calculated structures, NMR integration results for
all reactions, the code of the programs used for quasiclassical
trajectories, and complete ref 46. This material is available free
of charge via the Internet at http://pubs.acs.org.
Acknowledgment. We thank NIH Grant No. GM-45617 and
The Robert A. Welch Foundation for support of this research.
JA0606024
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