Competition between reaction and intramolecular energy redistribution in solution: Observation and nature of nonstatistical dynamics in the ozonolysis of vinyl ethers

Article abstract of DOI:10.1021/ja2043497

Experimental product ratios in ozonolyses of alkyl vinyl ethers in solution do not fit with expectations based on statistical rate theories. The selectivity among cleavage pathways increases with the size of the alkyl group but to an extent that is far less than RRKM theory would predict. Trajectory studies account for the observed selectivities and support a mechanism involving a competition between cleavage of the primary ozonide and intramolecular vibrational energy redistribution. A statistical model is presented that assumes that RRKM theory holds for a molecular subset of the primary ozonides, allowing the rates of energy loss from the ozonides to be estimated from the observed product ratios.

Full text of DOI:10.1021/ja2043497

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pubs.acs.org/JACS
Competition between Reaction and Intramolecular Energy
Redistribution in Solution: Observation and Nature of
Nonstatistical Dynamics in the Ozonolysis of Vinyl Ethers
Larisa Mae M. Quijano and Daniel A. Singleton*
Department of Chemistry, Texas A&M University, P.O. Box 30012, College Station, Texas 77842, United States
S Supporting Information
b
product distributions betraying a lack of symmetry.9 Alter-
natively, a competition between reaction and IVR has been
inferred from pressure effects on product selectivity.10 These
experiments did not exclude the direct coupling of an
intermediate’s excess energy into its decomposition path-
ways; unusual rates and selectivities were assumed to arise
simply from uneven distributions of molecular vibrational
energy. The applicability of such experimental probes is
limited,11 and little is known about the competition between
IVR and reaction in ordinary solution reactions.
We describe here a different approach to probing the
competition between reaction and IVR, the importance of
this competition in an ozonolysis reaction in solution and the
unusual observations that result, and a simple theoretical
model for understanding those observations.
ABSTRACT: Experimental product ratios in ozonolyses of
alkyl vinyl ethers in solution do not fit with expectations
based on statistical rate theories. The selectivity among
cleavage pathways increases with the size of the alkyl group
but to an extent that is far less than RRKM theory would
predict. Trajectory studies account for the observed
selectivities and support a mechanism involving a com-
petition between cleavage of the primary ozonide and
intramolecular vibrational energy redistribution. A statis-
tical model is presented that assumes that RRKM theory
holds for a molecular subset of the primary ozonides,
allowing the rates of energy loss from the ozonides to be
estimated from the observed product ratios.
The ozonolysis of alkenes is a fundamental organic reac-
tion that is also of importance in atmospheric chemistry.
The normal mechanism for these cycloadditions involves a
1,3-dipolar cycloaddition to afford a 1,2,3-trioxolane called
the primary ozonide (PO), followed by cleavage of the PO to
afford a carbonyl compound and a carbonyl oxide, known as
the Criegee intermediate (CI). The combination of the high
exothermicity of the cycloaddition step (>50 kcal/mol) and
the low stability of the PO, initially saddled with that excess
energy, would promote nonstatistical dynamics in the cleav-
age step. In fact, Hase and co-workers performed theoretical
studies of the dynamics of the gas-phase ozonolysis of
propene and predicted aspects of its post-transition-state
dynamics to be nonstatistical.12 We envisioned that in the
right system we might be able to see substantial experimental
consequences of nonstatistical dynamics on ozonolyses in
solution and use the experimental observations to probe the
dynamics.
We chose to study the ozonolysis of vinyl ethers because it is a
well-behaved reaction that avoids some of the common compli-
cations in ozonolyses of alkenes and because the regiochemistry
of the cleavage of the PO can be readily studied. The PO derived
from a vinyl ether may cleave in two ways: cleavage A, which
affords an alkyl formate (1) and formaldehyde oxide (CI-A), or
cleavage B, which affords a formate oxide (CI-B) and formal-
dehyde. In methanol, the CIs are rapidly trapped, affording
hydroperoxides 2 and 3, and the formaldehyde is converted to
its hemiacetal 4. In ozonolysis of vinyl ethers in methanol-d4, 1H
NMR peaks attributable to products 1ꢀ4 were readily identified.
otion along a reaction coordinate is faster than either loss of
M
energy to the medium or intramolecular vibrational energy
redistribution (IVR). As a result, mechanistic intermediates
are formed with excess energy, and that excess energy is to
varying degrees not initially statistically distributed.1 The
governing theory for understanding the rates and selectiv-
ities of further conversions of the intermediate then depends
on the time scale of those conversions. If they are slow,
thermal equilibration will occur, and the rate and selectivity
are predictable from transition state theory (TST). Riceꢀ
RamspergerꢀKasselꢀMarcus (RRKM) theory governs well
the realm in which the steps following formation of an
intermediate are slower than IVR but faster than or compe-
titive with thermal equilibration, as is common in gas-phase
reactions. In the fastest realm, the kinetic energy acquired
during the formation of the intermediate is strongly coupled
into modes that bring about its subsequent reaction faster
than IVR. In such cases, experimental results (e.g., product
formation selectivity) can be demonstrably inconsistent with
statistical expectations,2 but the selectivity can often be
understood (at least qualitatively) by the idea of “dynamic
matching.” Such nonstatistical dynamic effects have been
proposed to be important in many reactions.3ꢀ7
A middle realm in which the reaction of a mechanistic
intermediate competes with IVR of the excess energy in that
intermediate has long been considered.8 Classic experiments
by Doering and Rabinovitch sought to probe this competi-
tion by generating a formally symmetrical intermediate with
an unsymmetrical energy distribution and then looking for
Received: May 12, 2011
Published: August 03, 2011
r
2011 American Chemical Society
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|

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Table 1. Experimental and Statistically Predicted A/B Ratios
predicted A/Bd,e
alkyl group
exptl A/Ba,b,c (n)
TST
RRKM
methyl
ethyl
25.9 ( 1.2 (12)
36.3 ( 1.0 (33)
47.2 ( 2.0 (14)
54.8 ( 1.8 (16)
63.2 ( 2.0 (7)
43 ꢁ 105
9.8 ꢁ 105
8.5 ꢁ 105
9.6 ꢁ 105
5.7 ꢁ 105
9.6 ꢁ 105
2.4 ꢁ 105
10.0
10.9
18.5
47.8
61
butyl
octyl
3,7-dimethyloctyl
3,7,11,15-tetramethylhexadecyl 74.5 ( 1.9 (9)
343
ethyl (ꢀ31 °C)
ethyl (8 °C)
ethyl (23 °C)
octyl (ꢀ31 °C)
octyl (8 °C)
33.7 ( 1.3 (10)
10.9
10.9
10.8
47.9
48.0
48.1
24.7 ( 1.4 (10) 0.45 ꢁ 105
23.6 ( 2.1 (14) 0.26 ꢁ 105
Figure 1. Approximate energy profile for the reaction of the various
vinyl ethers with ozone based on G4 calculations.
51.5 ( 1.0 (5)
43.1 ( 0.6 (7)
40.0 ( 0.7 (8)
2.5 ꢁ 105
0.44 ꢁ 105
0.26 ꢁ 105
octyl (23 °C)
between the two is 10 bonds away from a reactive center. The
effect of the alkyl groups is not attributable to a medium effect;
addition of pentane to the reaction mixture had no effect on the
selectivity.
a The ratios given are based on the 1H NMR integration for the methine
peak of 3 vs the formyl peak of 1. b Uncertainties are 95% confidence
ranges; the number of measurements is given in parentheses. c The
reactions were conducted at ꢀ55 °C unless otherwise noted. d Gaussian-
4 (G4) energetics were used for R = methyl, ethyl, and butyl. For the
larger alkyl groups, the R = butyl G4 relative energies were used, and
small correction factors for differences in the relative energies seen in
B3LYP/GTBas3 calculations were included. e The two lowest-energy
cleavage-A TSs and the two lowest-energy cleavage-B TSs were used in
all of the calculations.
Another observation is that the changes in selectivity with
temperature are relatively small. The observed selectivities with
R = ethyl and R = octyl from ꢀ55 to 23 °C correspond to ΔΔHq
values of 0.8 and 0.5 kcal/mol, with ΔΔSq values of ꢀ4 and ꢀ6 e.u.,
respectively. If ΔΔSq were ∼0 e.u., as might be expected intuitively
for the similar A and B cleavages (in the G4 calculations, it is +0.6 e.u.
at ꢀ55 °C), then the selectivity would change by a factor of 2.6ꢀ2.9
instead of only 1.4ꢀ1.5 over the temperature range.
The NMR assignments were confirmed by independent synth-
eses (ozonolyses of ethylene and trans-1,2-diethoxyethylene) as
well as a H NMR study of a reaction employing 1-deutero-1-
ethoxyethylene [see the Supporting Information (SI)]. The ratio of
the cleavage-A and -B products did not vary significantly with
ozonolysis conversions from 20 to 100% conducted within a few
minutes, though secondary reactions did occur with excess ozone or
extended reaction times. The ratios of the cleavage products observed
for a series of alkyl vinyl ethers are shown in Table 1.
The most striking observation is that the experimental selec-
tivities are 4ꢀ5 orders of magnitude lower than expected on the
basis of TST. The energy profile for the reaction of ozone with
vinyl ethers is depicted in Figure 1. Cleavage A is thermodyna-
mically favored over cleavage B by 13.0 kcal/mol, and the
calculated free-energy barriers reflect the thermodynamics, fa-
voring cleavage A by 5.9ꢀ6.6 kcal/mol in G4 calculations (see
the SI for alternative computational methods, including solvent-
model calculations). If TST were applicable in this reaction,
cleavage B would be unobservable.
2
RRKM theory comes closer to predicting the observed
selectivity but fails in an important way. RRKM rate constants
were calculated for the cleavage of the POs, assuming that the
ozone/vinyl ether cycloaddition transition states (TSs) have a
canonical energy distribution and that no energy is lost in
forming the POs. With the resulting >57 kcal/mol of extra
energy, the RRKM-predicted A/B selectivities are much lower
than the TST-predicted selectivities and fall in a range similar to
that for the experimental results. However, there is a substantial
problem with the trend in the RRKM-predicted selectivities: the
RRKM calculations predict that as the size of the alkyl group
increases, the selectivity should increase greatly. This prediction is
understandable because RRKM theory assumes that the distribu-
tion of molecular energy is equilibrated, allowing large alkyl groups
toactas“heatsinks” for thereactions. Such a heat-sinkeffect would
in essence cool the hot 1,2,3-trioxolane ring, causing the selectivity
to rise dramatically. Experimentally, this does not happen; the
increase in selectivity is much smaller than that predicted by
RRKM theory.
The experimental selectivities are surprising in a number of
ways. The selectivityincreases consistentlywiththe sizeofthe alkyl
group, and the selectivity changes in going from R = ethyl to
R = butyl or from R = butyl to R = octyl are larger than normally
attributable to electronic substituent effects. The selectivity with
R = 3,7,11,15-tetramethylhexadecyl is greater than that with R = 3,
7-dimethyloctyl, even though the first structural difference
The most economical explanation for this data is that the
selectivities reflect a competition between cleavage of the PO ring
and IVR. Larger alkyl groups can better accept the energy generated
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Table 2. Trajectory Results, Projected Cleavage-B
Percentages after 1 ps (%B), and Projected A/B Ratios
thermal deactivation to give a “cold” state thataffords only cleavage
A, but the initially formed “hot” state affords either cleavage A
or cleavage B at a rate that is assumed to match that given by the
trajectory results in the time period between 200 and 500 fs after
the cycloaddition TS. (Negligible cleavage B occurs before 200 fs
into the trajectories.) From an average lifetime of the hot state, the
A/B ratio can be calculated. This process is to some degree an
exercise in numerology, but the lifetime of the hot state is the only
adjustable parameter. When the average lifetime of the hot state is
set at the seemingly reasonable value of 1 ps, the projected A/B
ratios for the various vinyl ethers are in phenomenal agreement
with experiment.15
alkyl group
endo TS
exo TS
%Ba
A/Bb
methyl
A: 522
A: 1147
3.6
27
B: 38 (1.0%)
no rxn: 3129
A: 420
B: 36 (0.6%)
no rxn: 5423
A: 395
B: 24 (0.4%)
no rxn: 5731
A: 417
B: 27 (0.4%)
no rxn: 7136
A: 258
B: 24 (0.4%)
no rxn: 5278
A: 265
B: 12 (0.3%)
no rxn: 4163
B: 129 (2.2%)
no rxn: 4470
A: 1089
B: 131 (2.3%)
no rxn: 4445
A: 1075
B: 119 (2.1%)
no rxn: 4564
A: 560
B: 52 (1.6%)
no rxn: 2655
A: 811
B: 61 (1.3%)
no rxn: 3872
A: 561
B: 51 (1.5%)
no rxn: 2709
ethyl
2.8
2.2
1.8
1.7
1.6
35
45
55
57
62
butyl
octyl
The flow of energy from the primary ozonide ring into the
alkyl groups was examined by following the kinetic energy of the
atoms in the alkyl groups in the 100ꢀ500 fs time frame. The
average rates of increase in the alkyl group energy for R = ethyl,
R = butyl, and R = octyl (based on ∼400 trajectories in each case)
were 17, 19, and 20 kcal molꢀ1 psꢀ1, respectively. This observa-
tion suggests that the decrease in cleavage B as the alkyl group
size is increased, experimentally and in the trajectories, is
associated with the increasing rate at which the larger alkyl
groups take up energy. However, the rate at which the octyl
group absorbs energy in the trajectories within the first few
hundred femtoseconds is only moderately greater than that for
the ethyl group, and the selectivity change is lower than would be
expected from the two groups’ total ability to take up energy.
Since the trajectory results appear to reflect the experimental
observations well, it is of interest to compare some of the details
of the trajectory results with RRKM predictions. For this
comparison, we consider only the trajectories initiated from
the exo cycloaddition TS, because the endo TS leads to a PO
conformer that must undergo conformational interconversion to
access the lowest-energy cleavage TSs (see the SI for a discussion
of this conformational interconversion). For the small R = methyl
system, RRKM theory appears to work quite well in predicting
3,7-dimethyloctyl
3,7,11,15-tetramethyl-
hexadecyl
a Calculated by weighting the endo and exo results in a 74:26 ratio
(based on G4 energetics) and assuming that the average rate of cleavage
B observed between 200 and 500 fs continues for, on average, a total time
of 1 ps (see the text). b Calculated as (100% ꢀ %B)/%B.
by PO formation, but the vibrational energy that is initially localized
in the 1,2,3-trioxolane cannot be fully distributed throughout the
molecule before substantial ring cleavage occurs.
To explore this idea, quasiclassical direct-dynamics trajectory
calculations13 were used to study these reactions. The trajectories
were carried out on an ONIOM potential energy surface using
density functional theory (DFT) for the PO ring and the PDDG/
PM3 semiempirical method14 for the various alkyl chains. The
DFT part of the calculation employed a locally modified hybrid
functional (see the SI for details) that was parametrized to
approximately reproduce a known barrier for a primary ozonide
cleavage as well as G4 energetics for the initial cycloaddition
barrier and exothermicity. The lowest-energy endo and exo TSs
(Figure 1) for the various ozone/vinyl ether cycloadditions were
used as the starting point for the trajectories. Each normal mode
was given its zero-point energy (ZPE) plus a Boltzmann sam-
pling of additional energy appropriate for a temperature of
ꢀ55 °C and a random phase and sign for its initial velocity.
The trajectories were integrated in 1 fs steps until either ring
cleavage occurred or a 500 fs time limit (to minimize nonphysical
IVR of the ZPE) was reached.
The trajectory results (Table 2) provide both qualitative and
quantitative support for a competition between ring cleavage and
IVR. Qualitatively, the trajectories show a substantial proportion
of cleavage B that falls off moderately as the size of the alkyl group
increases. With R = methyl and R = ethyl, the proportion of
cleavage B observed in the trajectories is very close to that
predicted by the RRKM calculations. With larger alkyl groups,
the proportion of cleavage B decreases but by only a factor of
2ꢀ3 for the largest group as opposed to a factor of 34 in the
RRKM predictions. All of this fits with the experimental
observations.
both the rate of cleavage B (5 ꢁ 1010 sꢀ1 vs ∼6 ꢁ 1010
s
ꢀ1 in the
trajectories) and the A/B ratio (10:1 vs 9:1 in the trajectories). On
the other hand, for the R = tetramethylhexadecyl system, RRKM
theory predictions are off by 3 orders of magnitude for the rate of
cleavage B (4 ꢁ 107 sꢀ1 vs ∼4 ꢁ 1010 sꢀ1 in the trajectories) and a
factor of 31 for the A/B ratio (343:1 vs 11:1 in the trajectories).
The success of RRKM theory for the R = methyl system
suggests that cleavage B does not arise by a strong coupling of the
PO’s initial excess energy into the cleavage pathway, as in the
dynamic matching phenomenon. This idea is supported by the
observation that in the trajectories there is a significant time lag
between the formation of the PO (median time 71 fs) and the
rise of cleavage-B events (>200 fs). This contrasts with the
nonstatistical behavior seen in the cleavage of the acetone cation
radical, where the reaction reaches a maximum rate within 50 fs
and many trajectories bypass the area of the formal intermedi-
ate.3e The onset of cleavage within the PO appears to require
some IVR within the ring, which takes some time, and the
cleavage then proceeds nonstatistically simply by virtue of the
localization of the energy within the area of the ring.
If RRKM theory may be viewed as applicable for each system
within a “molecular subset” equal to the size of the R = methyl
system (or, more precisely, a subset of the normal modes
localized in that portion of the molecule), then an approximate
statistical model can be developed to interpret our experimental
observations. Following an extension of a process used pre-
viously by Rabinovitch,10a our model assumes that the ensemble
The energy generated from formation of the PO should
undergo both IVR and loss to solvent as time goes on, and a
quantitative analysis of the trajectory results requires some allow-
ance for this cooling. As the simplest possibility, we considered a
two-state model. In this model, most PO molecules undergo
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Journal of the American Chemical Society
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of energies Et within the molecular subset decays exponentially
from the initial ensemble of energies E0 (eq 1) and that the rate
constants kA(Et) for cleavage A and kB(Et) for cleavage B are
those calculated from RRKM theory for the R = methyl system.
The amount of cleavage B observed is then calculated using eq 2,
in which PO*(t) is the amount of energetic PO that survives to
time t [decreased by kA(Et) and kB(Et) processes]. The decay
constant λ is then set for each reaction to the value that affords
the experimental product ratio.
’ ACKNOWLEDGMENT
This work is dedicated to an inspiring scholar and gentleman,
the late Professor William von Eggers Doering. We thank the
NIH (Grant GM-45617) for financial support.
’ REFERENCES
(1) (a) Hase, W. L.; Buckowski, D. G.; Swamy, K. N. J. Phys. Chem.
1983, 87, 2754. (b) Hase, W. L. Science 1994, 266, 998.
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Lourderaj, U.; Hase, W. L. J. Phys. Chem. A 2009, 113, 2236. (c)
Carpenter, B. K. J. Phys. Org. Chem. 2003, 16, 858.
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2008, 130, 12085. (b) Carpenter, B. K. J. Am. Chem. Soc. 1996,
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(f) Doubleday, C.; Suhrada, C. P.; Houk, K. N. J. Am. Chem. Soc. 2006,
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2009, 131, 13896.
(8) (a) Bunker, D. L.; Hase, W. L. J. Chem. Phys. 1973, 59, 4621.
(b) Oref, I.; Rabinovitch, B. S. Acc. Chem. Res. 1979, 12, 166.
(9) (a) Doering, W. V. E.; Gilbert, J. C.; Leermakers, P. A. Tetra-
hedron 1968, 24, 6863. (b) Rynbrandt, J. D.; Rabinovitch, B. S. J. Phys.
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(10) (a) Meagher, J. F.; Chao, K. J.; Barker, J. R.; Rabinovitch, B. S.
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(11) Their interpretation has also been questioned. See: Doering,
W. v. E.; Ehlhardt, W. J. J. Am. Chem. Soc. 1987, 109, 2697. Also see:
Carpenter, B. K.; Pittner, J.; Veis, L. J. Phys. Chem. A 2009, 113, 10557.
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Et ¼ E0eꢀλt
ð1Þ
ð2Þ
Z
t
ꢂ
kBðE Þ PO ðtÞ dt
amount of cleavage B ¼
E0, t
The λ values obtained in this way are 1.6 ꢁ 1011, 2.5 ꢁ 1011,
3.5 ꢁ 1011, 4.2 ꢁ 1011, 4.9 ꢁ 1011, and 5.5 ꢁ 1011
s
ꢀ1 for R =
methyl, ethyl, butyl, octyl, dimethyloctyl, and tetramethylhex-
adecyl, respectively. These values are notably slower than
IVR rate constants of 1012ꢀ1013
s
ꢀ1 inferred by Rabinovitch but
quite consistent with directly measured IVR rate constants
observed by Schwarzer.16 These λ values also fit well with the
rates of energy loss to the alkyl groups found in the trajectories
studies (λ = 4 ꢁ 1011 sꢀ1 corresponds to an energy loss of ∼20
kcal/mol in 1 ps). The particular values of λ depend on both the
applicability of the model and the accuracy of the calculated
barriers,17 so there is some danger of overinterpretation, but it is
interesting that λ values for the larger alkyl groups are more than
a factor of 2 greater than that for the methyl system. This suggests
that most of the PO cooling in the larger systems is intramole-
cular, as would be consistent with direct observations of vibra-
tional relaxation by Crim.18
When an experimental product ratio does not fit with a
calculated selectivity based on theoretically calculated barriers
and statistical theory, it would normally be assumed that the
calculated barriers are simply inaccurate, not that statistical
theory is inapplicable to a reaction. In this way, outside of the
special cases of formally symmetrical intermediates, any single
selectivity observation may be shoehorned into statistical rate
theories. This is normally perfectly correct, but the present
results show that it need not be so, even for simple reactions in
solution. Our process of examining the selectivity in a homo-
logous series of reactions should be of broader value in recogniz-
ing reactions involving nonstatistical dynamics. The physical
ideas here are not new; for example, the idea that large molecules
might behave like smaller molecules was suggested by Rice in
1930.19 However, the results herein support and provide con-
siderable insight into the impact of a fundamental physical
phenomenon, the redistribution of vibrational energy in mol-
ecules, on the experimentally observed products in an ordinary
organic reaction in solution.
(13) Hase,W.L.;Song,K.H.;Gordon,M.S.Comput. Sci. Eng. 2003,5,36.
(14) Repasky, M. P.; Chandrasekhar, J.; Jorgensen, W. L. J. Comput.
Chem. 2002, 23, 1601.
(15) Recentwork(see:Zheng, J.;Papajak, E.;Truhlar, D. G.J. Am. Chem.
Soc. 2009, 131, 15754) has proposed a “canonical competitive nonstatistical
model” (CCNM) to predict product branching ratios after dynamical
bottlenecks of the type seen in the current reaction. The CCNM model
divides the branching into “indirect” and “direct” components, the former
being predicted using TST and the latter using phase-space theory. The large
barriers for the reaction of the primary ozonide in the present work cause the
CCNM model to allocate 100% of the reaction to the indirect component, so
the CCNM model fails qualitatively to the extent that TST itself fails.
(16) (a) Schwarzer, D.; Hanisch, C.; Kutne, P.; Troe, J. J. Phys. Chem.
A 2002, 106, 8019. (b) Schwarzer, D.; Kutne, P.; Schr€oder, C.; Troe, J.
J. Chem. Phys. 2004, 121, 1754.
(17) The λ values are relatively insensitive to errors in the barriers. A
2 kcal/mol decrease in the barriers for both cleavage A and cleavage B
would lead to an increase in λ by a factor of ∼2.2. A 2 kcal/mol decrease
in the barrier for cleavage B by itself would increase λ by a factor of ∼2.6.
(18) (a) Cox, M. J.; Crim, F. F. J. Phys. Chem. A 2005, 109, 11673.
Also see: (b) Bradford, S. Science 2011, 331, 1398.
’ ASSOCIATED CONTENT
S
Supporting Information. Complete descriptions of ex-
b
perimental procedures and additional observations, calculations,
and structures. This material is available free of charge via the
Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION
Corresponding Author
singleton@mail.chem.tamu.edu
(19) Rice, O. K. Z. Phys. Chem., Abt. B 1930, 7, 226.
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