Controlling Selectivity by Controlling Energy Partitioning in a Thermal Reaction in Solution

Article abstract of DOI:10.1021/jacs.6b09052

The comparison of experimental and predicted kinetic isotope effects in the α-cleavage of alkoxy radicals is used here to judge the applicability of statistical rate theories. It is found that the governing rate theory and the statistical versus nonstatistical nature of the cleavage depend on the cleavage barrier and how much energy is imparted to the radical. The latter can then be controlled by changing the size of substituents in the system. With a large alkyl group substituent, the vibrational energy of the alkoxy radical is increased, but this energy is not statistically distributed, leading to a lower isotope effect than predicted by statistical theories. The observed isotope effect can be approximately rationalized using a semistatistical localized RRKM model.

Full text of DOI:10.1021/jacs.6b09052

Subscriber access provided by CORNELL UNIVERSITY LIBRARY
Communication
Controlling Selectivity by Controlling Energy
Partitioning in a Thermal Reaction in Solution
Hiroaki Kurouchi, Ivonne L. Andújar-de Sanctis, and Daniel A. Singleton
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.6b09052 • Publication Date (Web): 21 Oct 2016
Downloaded from http://pubs.acs.org on October 21, 2016
Just Accepted
“Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted
online prior to technical editing, formatting for publication and author proofing. The American Chemical
Society provides “Just Accepted” as a free service to the research community to expedite the
dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts
appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been
fully peer reviewed, but should not be considered the official version of record. They are accessible to all
readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered
to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published
in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just
Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor
changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers
and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors
or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Journal of the American Chemical Society is published by the American Chemical
Society. 1155 Sixteenth Street N.W., Washington, DC 20036
Published by American Chemical Society. Copyright © American Chemical Society.
However, no copyright claim is made to original U.S. Government works, or works
produced by employees of any Commonwealth realm Crown government in the course
of their duties.

Page 1 of 5
Journal of the American Chemical Society
1
2
3
4
5
6
Controlling Selectivity by Controlling Energy Partitioning
in a Thermal Reaction in Solution
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Hiroaki Kurouchi, Ivonne L. Andujar-De Sanctis, and Daniel A. Singleton*
Department of Chemistry, Texas A&M University, P.O. Box 30012, College Station, Texas 77842, United States
Supporting Information Placeholder
ABSTRACT: The comparison of experimental and predicted
cal 3 then undergoes a facile α-cleavage to afford the ring-
opened radical 4. Chlorine atom transfer to 4 from 1 affords
the product 5 and a new molecule of 3 to continue the chain.
These reactions are clean and highly exothermic (37
kcal/mol for n=2, 55 kcal/mol for n=1 (CCSD(T)/cc-
pvtz//M11L/6-311+G**)). The α-cleavage of alkoxy radi-
cals is important in diverse areas of chemistry and has been
assumed to be fully understood using statistical rate theo-
ries.6
kinetic isotope effects in the α-cleavage of alkoxy radicals is
used here to judge the applicability of statistical rate theories.
It is found that the governing rate theory and the statistical
versus nonstatistical nature of the cleavage depend on the
cleavage barrier and how much energy is imparted to the
radical. The latter can then be controlled by changing the
size of substituents in the system. With a large alkyl group
substituent, the vibrational energy of the alkoxy radical is
increased but this energy is not statistically distributed, lead-
ing to a lower isotope effect than predicted by statistical the-
ories. The observed isotope effect can be approximately ra-
tionalized using a semi-statistical localized RRKM model.
R
O Cl
a: n = 2, R = methyl
b: n = 1, R = methyl
c: n = 1, R = n-octyl
13
α
β
β
*
n
=
*
C
1
H
H
‡
ω
β
In any reaction passing over an energy barrier, the products
are initially imbued with excess energy. The partitioning of
that energy between translational, rotational, and vibrational
forms has long been a core interest of the field of gas-phase
reaction dynamics, in part due to the ambition of selectively
promoting or controlling reactions.1 Some general expecta-
tions for the energy partitioning are specified by the Polanyi
rules, which relate the position of the transition state (TS) to
vibrational versus translational energy in the reactant and
products in the simplest atom-transfer reactions.2 Energy
partitioning in larger molecules and in condensed phases is
R
O
Cl
C
*
R
•
H C
α
R
2
*
*
*
n
n
O
O
*
n
4
2‡
chlorine-atom
abstraction
O•
R
α
ω
β
β
β
R
α-cleavage
Cl
*
*
*
n
n
O
3
5
When a 13C is in the β-position of 1, the α-cleavage of 3
partitions the C between the β and ω positions of the ring-
opened radical 4. The selectivity in this cleavage can be
measured from the ratio of C in the two positions and ex-
pressed as an intramolecular kinetic isotope effect (KIE).
This selectivity is readily determined by analysis of samples
of 5 at natural abundance by NMR methodology. In all cas-
es, the 13C content in the β position of 5 was in excess over
that in the ω position, reflecting the qualitative expectation
3
13
much less well understood. The literature provides no guid-
ance as to how one might structurally control energy parti-
tioning in an ordinary solution reaction or how this might be
used to affect product selectivity.
13
We describe here a simple structural effect on the amount
of vibrational energy that is partitioned to a reactive interme-
diate in an atom-transfer step, and how that engenders non-
7
4
statistical dynamics and changes the selectivity of a reaction.
The results show how ideas from collision dynamics can be
used to influence complex organic reactions in solution.
12
of a faster cleavage of a β- C in 3. However, there were sur-
prising variations in the magnitude of the excess.
The reaction of interest is the conversion of cycloalkyl hy-
pochlorites (1a-c) to ω-chloroalkylketones (5a-c). This
reaction involves a chain mechanism in which a chlorine at-
The results are summarized in Table 1. At 6.1%, the large
KIE observed for α-cleavage in the five-membered ring 3a is
comparable to that observed previously for the ring-opening
5
om is abstracted from 1 to afford the alkoxy radical 3. Radi-
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 2 of 5
of the cyclopropylcarbinyl radical, a high heavy-atom tunnel- However, the experimental KIEs for 3b and 3c are far below
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
ing system. The KIE is then strikingly decreased for the
methylcyclobutoxy radical 3b, at 4.4%. Most surprisingly,
the KIE is further decreased to 2.9% for the octylcyclobutoxy
radical 3c, less than half that observed for 3a.
the predicted values. The first-order interpretation of this
difference is that it is associated with the differing barriers for
α-cleavage in the systems. The cleavage barrier for 3a is rela-
tively large, at 10.8 kcal/mol, and this leads to a lifetime that
is sufficiently long for full energy equilibration to occur. As a
result, the ring opening is governed by transition state theory
and the CVT/SCT KIE prediction is accurate. With 3b and
3c, the α-cleavage barriers are much smaller. If the ring
opening is faster than thermal equilibration, transition state
theory is not applicable. This would cause the CVT/SCT
predictions to be inaccurate.
Table 1. Experimental and predicted KIEs (42 °C).
CVT / α-cleavage available
b
alkoxy
radical
exptl
SCT
barrier vibrational RRKM
KIEa
KIE (kcal/mol) energy
KIE
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
Me O•
1
.061(2) 1.063
10.8
5.8
-
3a
Me O•
A more detailed interpretation of the results requires con-
sideration of the amount of energy available to the interme-
diates 3a-c. The excess energy of ≈39 kcal/mol that is gen-
erated in the abstraction of a chlorine atom from 1 by 4 is
partitioned into the two products, 3 and 5, and within each
product that energy is partitioned into rotational, transla-
tional, and vibrational components (Figure 1). Of these, only
the vibrational energy in 3 is available to promote α-cleavage.
To assess this pivotal portion of the energy, we applied a
modified version of the classical single-trajectory approxima-
1
.044(1) 1.060
3.0
4.8
1.043
3
b
Octyl O•
1
.029(1) 1.062
2.6
7.2
1.038c
3
c
(
1.033 )
a
13
Based on the ratio of C in the β versus ω positions of 5. The 95%
confidence limit on the last digit is shown in parentheses.
b
c
UM11L/6-311+G** potential energy barrier, in kcal/mol. Predic-
tion using a localized RRKM model in which the excess energy is
limited to a molecular subset.
10
tion of Hase. Series of trajectories were started from TSs
‡
6
a-c for chlorine-atom abstraction from 1a-c by an ethyl
radical, providing no zero-point energy for the real normal
modes and a Boltzmann-random energy in the transition
vector. The trajectories were then integrated forward in time
and the components of the energy were evaluated as the
products 3 and chloroethane separated. Average energy par-
titionings were then calculated for each series.
To interpret these results, we turned to computational and
dynamic trajectory studies. Diverse DFT methods were ex-
plored in comparison with CCSD(T)/jun-cc-pvtz single-
point energies for the 1a,b-5a,b energy surface. In this com-
parison, UM11L/6-311+G** calculations provided a highly
accurate description of the α-cleavage (barriers within 0.1
kcal/mol, see the Supporting Information (SI)) but the chlo-
rine-atom abstraction was more accurately modeled in
UM11/6-31+G** calculations.
‡
‡
CH3
H
1
O
.80
Cl
H
1.80
O
H
Cl 2.36
2
.38
H
CH3
We first explored how the observations compared with
predictions from transition state theory. Rate constants for
C
CH3
H
H
R
13
6a‡
‡
the α-cleavage of β- C-substituted 3a-c were calculated us-
6b : R = H
c : R = n-C H
‡
6
7
15
ing canonical variational transition state theory (CVT) in-
cluding small-curvature tunneling (SCT) 8 using the
‡
The exothermic atom abstractions 6a-c have early TSs, so
the Polanyi rules would predict that the largest proportion of
the excess energy ends up as vibrational energy in 5. This
prediction is correct; the chloroethane receives two-thirds of
the energy, 26 kcal/mol, with 21 kcal/mol ending up as vi-
brational energy. The incipient alkoxy radical 3 receives 13
kcal/mol of excess energy. For 3a, 5.8 kcal/mol is put into
,9
GAUSSRATE / POLYRATE set of programs. The KIE
predictions are subject to a series of complicating issues. For
3
a, there are two competitive low-energy TSs. For 3b, the
two C -C bonds are not equivalent (differing by 0.04 Å),
α
β
with bond-length isomers separated by a 0.4 kcal/mol barri-
er. This required allowance for the isotopically perturbed
equilibrium between the isomers. For 3c, the octyl-group
conformation desymmetrizes the ring opening, and it was
assumed that conformational interconversion in the octyl
group was slower than the very rapid ring opening. The tun-
neling contribution to the KIEs was in all cases substantial, at
vibrational energy but this is not enough to overcome the α-
cleavage barrier so the intermediate radical must await ordi-
nary thermal activation. For 3b and 3c, however, their initial
excess vibrational energy exceeds the cleavage barrier. This
by itself would not guarantee that the α-cleavage would oc-
cur before thermal equilibration, but it signals the possibility.
1
.0 – 1.2%. After allowing for each complication (see the SI
for details), the predicted KIEs are shown in Table 1.
For 3a, the CVT/SCT-predicted KIE matches closely with
the experimental value, within the error of the measurement.
ACS Paragon Plus Environment

Page 3 of 5
Journal of the American Chemical Society
tunneling corrections of 1.002-1.004 (see the SI). As shown
2‡
1
2
3
4
5
6
7
8
9
in Table 1, the RRKM KIE matches well that observed for
the α-cleavage of 3b. The RRKM-predicted KIE for 3c is
however far too high versus experiment. Why?
5trans+rot
1 + 4
5vib
3
9
Some insight into this question comes from trajectory
kcal/mol
1
2
studies. Quasiclassical direct-dynamics trajectories were
E
‡
‡
3
btrans+rot
bvib
3ctrans+rot
3cvib
initiated from the area of TSs 6b and 6c . Each normal
‡
‡
mode in 6b and 6c was given its zero-point energy (ZPE)
plus a randomized excitation energy based on a Boltzmann
distribution at 42 °C, with a random phase and sign for its
initial velocity. The trajectories were then propagated for-
3
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
3
+ 5
ward and backward in time until either α-cleavage occurred
to afford 4 or until 1 and ethyl radical were reformed. For
both sets of trajectories, the ring-opening α-cleavage ensues
within a few hundred fs after 3b / 3c has separated from the
4
Figure 1. Energy partitioning in the chlorine-atom abstraction.
Only the vibrational energy in 3 can promote the second step.
chloroethane. However, the 3c α-cleavage occurs much
For the 13 kcal/mol of excess energy in 3a-c, the partition-
ing depends strikingly on the structure. In particular, the
presence of the octyl chain in 3c leads to a much higher pro-
portion of the energy partitioned into vibrational energy
(Table 1).
‡
more quickly; the average trajectory times starting from 6b
‡
was 377 fs, while for 6c the time is reduced to 259 fs. After
formation of 3b and 3c, approximately 80 fs after 6b and
c , their decay was approximately exponential (see the SI)
‡
‡
6
with half-lives of 200 fs and 125 fs, respectively. For compar-
ison, the RRKM half-lives would be 340 and 300 fs, respec-
tively. Both radicals are decaying faster than expected from
their energies, but with 3c the α-cleavage is more accelerat-
ed.
To explain this novel observation, we consider a limiting
11
pure impulsive model for 3 in which the impulse from the
repulsion between the oxygen and chlorine atoms after TS 2‡
acts only on these atoms, imparting a size-independent ener-
gy of E
alkoxy fragment at rest. The initial momentum of the oxygen
atom p would be defined by eq 1, where m is the oxygen-
atom mass. Ignoring rotations for now, the E would some-
time later be partitioned into translational energy Etrans and
vibrational energy Evib Assuming that the molecular mo-
mentum pmol is conserved over short times in solution, so that
, the Etrans would be defined by eq 2, where malkyl is
O
to the oxygen atom, with all other atoms in the
Our hypothesis is that the energy in 3c is not statistically
distributed and that little energy has been distributed to the
octyl chain at the time of α-cleavage. The effect of the non-
statistical distribution of the energy is that the cyclobutyl
ring moiety is much “hotter” than would be expected from
the available vibrational energy. In the single-trajectory
O
O
O
.
‡
study starting from 6c , about 1 kcal/mol of the 7.2 kcal/mol
p
mol = p
O
of vibrational energy is passed down the octyl chain rapidly,
within 100 fs, by ballistic energy transfer.13 Over the course
of the next 300 fs, about 1 kcal/mol of additional energy
makes its way into the chain. At equilibrium ≈ 4.8 kcal/mol
of the vibrational energy, over half of the excess vibrational
energy, would be in the alkyl chain, but 3c never lasts long
enough for either the chain or the solvent to take up much
energy. Instead, the non-statistically localized excess energy
promotes the rapid α-cleavage of 3c before equilibration can
proceed.
the mass of the alkyl group in 3. In going from 3b to 3c, malkyl
increases from 69 amu to 167, and Etrans would fall by more
than a factor of 2. This model shows clearly why the transla-
tional energy should decrease as the alkyl group size increas-
es from 3b to 3c, leaving more energy in Evib (eq 3). A paral-
lel but more complex analysis can be made for rotational
energy (see the SI). Overall, the effect in Table 1 is dramatic
and has experimental consequences.
)1/2
|
p
O
| = (2m
O
E
O
(1)
(2)
(3)
E
trans = p 2
O
/2(m + malkyl)
O
We have previously applied a “localized RRKM” model,14
E
vib = E
O
– Etrans
15
adapted from Rabinovitch, that assumes that the excess
The effect of the differing excess energies in 3b and 3c was
analyzed in two ways, statistically and with dynamic trajecto-
ries. If the excess energy in 3b and 3c is distributed statisti-
cally and if it is temporarily assumed that no energy is lost
from 3 to the solvent on the time scale of the α-cleavage,
then RRKM theory would apply. RRKM KIEs were predict-
ed for 3b and 3c based on an energy distribution in each that
is the sum of the canonical distribution and the excess vibra-
tional energies derived above, including approximate SCT
energy is localized within a “molecular subset ” of the mol-
ecule. This process allows an approximate statistical pre-
diction of the rate or selectivity when only a portion of a
larger molecule is vibrationally excited. In the current
case, our molecule subset replaces the n-heptyl chain of 3c
with a hydrogen atom (making it 3b). The model is then
applied simply in an RRKM calculation by replacing the fre-
quencies of 3c and its cleavage TS by those of 3b and its
cleavage TS. When this is done, the predicted RRKM KIE is
decreased to 1.033. While this is still higher than the exper-
ACS Paragon Plus Environment

Journal of the American Chemical Society
imental value, the model prediction is close enough to sup-
Page 4 of 5
1
2
3
4
5
6
7
8
9
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
4
4
4
4
4
4
4
4
4
4
5
5
5
5
5
5
5
5
5
5
6
port the general idea that the low KIE with 3c is the result of
a combination of greater excess energy in 3c relative to 3b
and a nonstatistical distribution of that energy.
(3) (a) Crim, F. F. Faraday Discuss. 2012, 157, 9-26. (b) Ebrahimi, M.;
Guo, S. Y.; McNab, I. R.; Polanyi, J. C. J. Phys. Chem. Lett. 2010, 1, 2600-
605. (c) Liu, J. Song, K.; Hase, W. L.; Anderson, S. L. J. Am. Chem. Soc.
004, 126, 8602-8603. (d) Kroes, G.-J.; Gross, A.; Baerends, E.-J.;
Scheffler, M.; McCormack, D. A. Acc. Chem. Res. 2002, 35, 193-200. (e)
Halstead, D.; Holloway, S. J. Chem. Phys. 1990, 93, 2859-2870. (f) Voth, G.
A.; Hochstrasser, R. M. J. Phys. Chem. 1996, 100, 13034-13049. (g) Camp-
bell, V. L.; Chen, N.; Guo, H.; Jackson, B. Utz, A. L. J. Phys. Chem. A 2015,
119, 12434-12441. (h) Xu, L.; Doubleday, C. E.; Houk, K. M. J. Am. Chem.
Soc. 2010, 132, 3029-3037. (i) Guo, H.; Jiang, B. Acc. Chem. Res. 2014 47,
2
2
Overall, the governance of statistical rate theories in the α-
cleavage of alkoxy radicals depends on the barrier for the
cleavage, the amount of vibrational energy available from
their formation, and the size of the system. With 3a, the bar-
rier is larger than vibrational energy engendered by its for-
mation, and TST governs the α-cleavage. With 3b, the avail-
able vibrational energy is greater than the barrier, but the
system is small and RRKM theory provides a reasonable pre-
diction of the selectivity. By increasing the size of the alkyl
chain, the vibrational energy in 3c is increased and the α-
cleavage occurs faster than equilibration of the vibrational
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
3
679-3685.
4) (a) Carpenter, B. K. Accounts Chem. Res. 1992, 25, 520-528. (b)
(
Debbert, S. L.; Carpenter, B. K.; Hrovat, D. A.; Borden, W. T. J. Am. Chem.
Soc. 2002, 124, 7896-7897. (c) Carpenter, B. K.; Harvey, J. N.; Orr-Ewing,
A. J. J. Am. Chem. Soc. 2016, 138, 4695-4705. (d) Doubleday, C., Jr.; Bol-
ton, K.; Hase, W. L. J. Am. Chem. Soc. 1997, 119, 5251-5252. (e) Double-
day, C.; Suhrada, C. P.; Houk, K. N. J. Am. Chem. Soc. 2006, 128, 90-94. (f)
Biswas, B.; Collins, S. C.; Singleton, D. A. J. Am. Chem. Soc. 2014, 136,
energy. The α-cleavage selectivity becomes non-statistical,
but it can be approximately rationalized using a localized
statistical model.
3
740-3743. (g) Chen, Z.; Nieves-Quinones, Y.; Waas, J. R.; Singleton, D. A.
J. Am. Chem. Soc. 2014, 136, 13122-13125. (h) Oyola, Y.; Singleton, D. J.
Am. Chem. Soc. 2009, 131, 3130-3131. (i) Thomas, J. R.; Waas, J. R.; Har-
mata, M.; Singleton, D. A. J. Am. Chem. Soc. 2008, 130, 14544-14555. (j)
Ussing, B. R.; Hang, C.; Singleton, D. A. J. Am. Chem. Soc. 2006, 128, 7594-
The results here illustrate one new rule with respect to en-
ergy partitioning in reactions and how control of that parti-
tioning can lead to nonstatistical effects in experimental ob-
servations. We expect that other rules await discovery. On a
more general level, our results show how the behavior of a
reactive intermediate can depend on how it is formed, and we
are pursuing reactions that will make use of this history-
dependence to affect selectivity.
7
607. (k) Singleton, D. A.; Hang, C.; Szymanski, M. J.; Greenwald, E. E. J.
Am. Chem. Soc. 2003, 125, 1176-1177. (l) Yang, Z.; Yu, P.; Houk, K. N. J.
Am. Chem. Soc. 2016, 138, 4237-4242.
(5) Walling, C.; Padwa, A. J. Am. Chem. Soc. 1963, 85, 1593-1597.
(
6) (a) Orlando, J. J.; Tyndall, G. S. Chem. Rev. 2003, 103, 4657-4689.
b) Hayes, C. J.; Merle, J. K.; Haddad, C. M. Adv. Phys. Org. Chem. 2009,
3, 79-134. (c) Inoue, S.; Kumagai, T.; Tamezawa, H.; Aota, H.; Matsumo-
to, A.; Yokoyama, K.; Matoba, Y.; Shibano, M. Polymer J. 2010, 42, 716-
21. (d) Dean, R. T.; Fu, S.; Stocker, R.; Davies, M. J. Biochem. J. 1997,
(
4
7
ASSOCIATED CONTENT
324, 1-18. (e) Hartung, J.; Gottwald, T.; Spehar, K. Synthesis 2002, 1469-
1498.
Supporting Information.
(
7)(a) Singleton, D. A.; Szymanski, M. J. J. Am. Chem. Soc. 1999, 121,
Complete descriptions of experimental procedures, calculations,
and structures. The Supporting Information is available free of
charge on the ACS Publications website.
9455-9456. (b) Singleton, D. A.; Schulmeier, B. E. J. Am. Chem. Soc. 1999,
121, 9313-9317. (c) Gonzalez,-James, O. M.; Zhang, X.; Datta, A.; Hrovat,
D. A.; Borden, W. T.; Singleton, D. A. J. Am. Chem. Soc. 2010, 132, 12548-
1
2549.
8) Zheng, J.; Zhang, S.; Corchado, J. C.; Chuang, Y.-Y.; Coitino, E. L.;
(
AUTHOR INFORMATION
Ellingson, B. A.; Zheng, J.; Truhlar, D. G. GAUSSRATE, version 2009-A
Corresponding Author
singleton@mail.chem.tamu.edu
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENT
We thank the NIH (Grant GM-45617) for financial support. H.
K. thanks the Japan Society for the Promotion of Science for a
Postdoctoral Fellowships for Research Abroad.
2
621.
(12) Hase, W. L.; Song, K. H.; Gordon, M. S. Comp. Sci. Eng. 2003, 5,
3
6-44.
(13) Schwarzer, D.; Kutne, P.; Schröder, C.; Troe, J. J. Chem. Phys.
2004, 121, 1754-1764.
14) Quijano, L. M. M.; Singleton, D. A. J. Am. Chem. Soc. 2011, 133,
3824-13827.
15) Meagher, J. F.; Chao, K. J.; Barker, J. R.; Rabinovitch, B. S. J. Phys.
Chem. 1974, 78, 2535-2543. See also: Rice, O. K. Z. Phys. Chem. B 1930, 7,
26-233.
REFERENCES
(
(
1) (a) Zare, R. N. Science 1998, 279, 1875-1879. (b) Crim, F. F. Acc.
Chem. Res. 1999, 32, 877-884.
2) (a) Polanyi, J. C.; Wong, W. H. J. Chem. Phys. 1969, 51, 1439-1450.
(b) Polanyi, J. C. Acc. Chem. Res. 1972, 5, 161-168.
1
(
(
2
ACS Paragon Plus Environment

Page 5 of 5
Journal of the American Chemical Society
1
2
3
4
5
6
7
8
9
R'Cltrans+rot
ROCl
+ R'•
R'Clvib
E
RO•trans+rot
RO•vib
energy
partitioning
depends
on R
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
R'Cl + RO•
ACS Paragon Plus Environment