Kinetics of elementary reactions in the chain chlorination of cyclopropane

Article abstract of DOI:10.1021/jp022121m

The kinetics of elementary reactions involved in the chain chlorination of cyclopropane were studied using a combination of absolute and relative rate constant measurements and first principles electronic structure calculations. Absolute rate coefficients for the reaction of Cl with cyclopropane were measured between 293 and 623 K by a laser-photolysis/CW infrared absorption method. To support the experimental investigations, first principles electronic structure calculations were performed. Vibrational spectra of c-C₃H₅Cl, c-C₃H₄Cl₂, and c-C₃H₃Cl₃ were calculated. Gem-C₃H₄Cl₂ is calculated to be the kinetically and thermodynamically most favored dichlorocyclopropane. The computational results were consistent with a model in which gem-C₃H₄Cl₂ is the predominant product of chlorination of C₃H₅Cl, and gem-C₃H₃Cl₃ is the only product of chlorination of gem-C₃H₄Cl₂. Chlorocyclopropane was ～ a factor of 10 times more reactive than cyclopropane toward chlorine atoms at 296 K and is converted into dichlorocyclopropane.

Full text of DOI:10.1021/jp022121m

J. Phys. Chem. A 2003, 107, 2003-2010
2003
Kinetics of Elementary Reactions in the Chain Chlorination of Cyclopropane
Michael D. Hurley,* William F. Schneider, Timothy J. Wallington, and David J. Mann†
Ford Research Laboratory, Mail Drop 3083/SRL, Dearborn, Michigan 48121-2053
John D. DeSain‡ and Craig A. Taatjes*
Combustion Research Facility, Mail Stop 9055, Sandia National Laboratories,
LiVermore, California 94551-0969
ReceiVed: September 23, 2002; In Final Form: December 31, 2002
The kinetics of elementary reactions involved in the chain chlorination of cyclopropane are examined using
a combination of absolute and relative rate constant measurements and first principles electronic structure
calculations. Relative rate methods are used in a smog chamber FTIR apparatus to determine k(Cl + c-C3H6)
) (1.15 ( 0.17) × 10-13 and k(Cl + c-C3H5Cl) ) (1.06 ( 0.18) × 10-12 cm3 molecule-1 s-1 in 10-700 Torr
of air, or N2, diluent at 296 K. Absolute rate coefficients for the reaction of Cl with cyclopropane are measured
between 293 and 623 K by a laser-photolysis/CW infrared absorption method. The data can be represented
in Arrhenius form as k(Cl + c-C3H6) ) ((1.8 ( 0.3) × 10-10 cm3 molecule-1 s-1)e-(2150(100)/T. To support the
experimental investigations, first principles electronic structure calculations are performed. Vibrational spectra
of c-C3H5Cl, c-C3H4Cl2, and c-C3H3Cl3 are calculated and are presented. gem-C3H4Cl2 is calculated to be the
kinetically and thermodynamically most favored dichlorocyclopropane. The experimental observations are
consistent with the computational findings.
1. Introduction
interfaced to a Mattson Sirus 100 FTIR spectrometer described
elsewhere.4 The reactor is surrounded by 22 fluorescent black
Optimization of the performance of modern internal combus-
tion engines relies on computational models incorporating
detailed descriptions of combustion chemistry.1 Chemical
models of combustion processes require accurate data concern-
ing the formation and fate of alkyl radicals in such systems.2
Reactions of chlorine atoms with suitable hydrocarbon precur-
sors are often used as convenient sources of alkyl radicals for
laboratory study. Prior to such studies it is advisable to
understand the kinetics and mechanism of the Cl + hydrocarbon
reaction. The cyclopropyl radical, as the smallest cyclic alkyl
radical, is an interesting species for investigating the effects of
ring strain energy on chemical reaction. In conjunction with a
collaborative study3 of the reaction of cyclopropyl radicals with
O2, we have studied the kinetics of the chain chlorination of
cyclopropane.
In the present work a combination of absolute rate, relative
rate, and first principles electronic structure calculations is
employed to investigate elementary reactions in the chain
chlorination of cyclopropane. Fundamental data concerning the
kinetics, mechanisms, and thermochemistry of reactions 1 and
2 and the infrared spectra of c-C3H5Cl, c-C3H4Cl2, and c-C3H3-
Cl3 are reported herein.
lamps (GE F15T8-BL) that are used to photochemically initiate
the experiments. Cl atoms are generated by photolysis of
molecular chlorine in 700 Torr total pressure of N2 diluent at
295 ( 2 K. c-C3H5Cl is produced by reaction 4.
Cl2 + hν f 2Cl
(3)
(4)
c-C3H5 + Cl2 f c-C3H5Cl + Cl
Loss of c-C3H6 and formation of products are monitored by
Fourier transform infrared spectroscopy using an infrared path
length of 27.5 m and a spectral resolution of 0.25 cm-1. Infrared
spectra are derived from 32 coadded interferograms. Reagents
are obtained from commercial sources at the following stated
purities (cyclopropane (>99.9%); chlorine (>99.99%); N2
(UHP); O2 (UHP)) and are used as received. In smog chamber
experiments, unwanted loss of reactants and products via
photolysis, dark chemistry, and wall reaction has to be consid-
ered. Control experiments are performed to check for these
losses. Mixtures of c-C3H6 and air are subjected to UV
irradiation for 5 min and then left in the dark for 30 min. There
is no observable loss (<2%) of c-C3H6, c-C3H5Cl, or c-C3H4-
Cl2 when mixtures containing these compounds are left in the
chamber in the dark for 45 min. Heterogeneous reactions are
not a significant complication in the present work.
Cl + c-C3H6 f c-C3H5 + HCl
(1)
Cl + c-C3H5Cl f c-C3H4Cl + HCl
(2)
2. Experiment
2.1. FTIR Smog Chamber System at Ford Motor Com-
pany. Experiments are performed in a 140-L Pyrex reactor
2.2. Theoretical Methods. First principles electronic structure
calculations are performed using the Mulliken5 suite of pro-
grams. Heats of reaction, barrier heights, and bond energies are
computed using a combined restricted open shell Hartree-Fock
and second-order Møller-Plesset (MP2/ROHF) level of theory
with a 6-311G** basis set. All structures are optimized at the
ROHF level, and the energies at these geometries are corrected
* To whom correspondence should be addressed. E-mail: mhurley3@
ford.com and cataatj@sandia.gov.
† Present address: Zyvex Corporation, 1321 N. Plano Road, Richardson,
TX 75081.
‡ Present address: The Aerospace Corporation, 2350 E. El Segundo
Blvd., El Segundo, CA 90245-4691.
10.1021/jp022121m CCC: $25.00 © 2003 American Chemical Society
Published on Web 03/04/2003

2004 J. Phys. Chem. A, Vol. 107, No. 12, 2003
Hurley et al.
at the MP2 level. This level of theory has been applied to the
reaction of Cl with methane, and excellent agreement is found
with higher-level calculations performed by Dobbs and Dixon.6
•
The MP2 optimized geometries for CH3 and CH4 they report
are identical to those we obtained at the ROHF level, and the
ROHF optimized internal coordinates for the [CH3- -H- -Cl]•
transition state agree to within 3% of their MP2 results. In
addition, the ROHF optimized geometry of the cyclopropyl
radical is in good overall agreement with the MP2/TZ2P
optimized structure obtained elsewhere.7 Finally, we computed
and compared optimized structures for cyclopropane and
chlorocyclopropane at both the ROHF and MP2 levels, using
the same 6-311G** basis set, and the resulting internal
coordinates agree to within 1%. Similar levels of theory have
been applied successfully to other halogenated radical reactions.8
ROHF is preferred over UHF, since for open-shell systems UHF
has a tendency to produce errors that result from spin contami-
nation of the HF wave function.9 Unsuccessful attempts were
made with density functional theory, using the B3LYP func-
tional, to locate a transition state for the reaction of Cl with
cyclopropane. The inability to locate a transition state or to
underestimate barrier heights is a problem often encountered
with density functional theory.6,10,11 Vibrational spectra for the
monochloro-, dichloro-, and trichlorocyclopropanes are com-
puted at the ROHF level with harmonic frequencies scaled by
the homogeneous scaling factor 0.9054.12
2.3. Absolute Rate Coefficient Measurements at Sandia
National Laboratories. Absolute rate constants for the reaction
c-C3H6 + Cl are measured by using the laser-photolysis/CW
infrared long path absorption (LP/CWIRLPA) method as
described in previous publications.13,14 The Cl is generated by
excimer laser photolysis of CF2Cl2 at 193 nm, and the HCl
product is detected by time-resolved infrared absorption of an
F-center laser tuned to the R(8) line of the vibrational
fundamental.
Figure 1. Loss of cyclopropane versus CH4 (circles) and CH3Cl
(triangles) following exposure to Cl atoms in 700 Torr of N2 (open
symbols) or air (filled symbols) diluent. Data acquired in 10 Torr of
air are shown by filled diamonds.
detection, and also by GC/MS. The major impurity is found to
be 1,3-dichloropropane, with smaller amounts of 1,1-dichloro-
propane, 1-propanol, and propene. The contribution to the
observed HCl formation of reaction of Cl with these impurities
(at the 0.1% level) is significant at room temperature, amounting
to ∼20% of the measured rate constant, but decreases rapidly
with increasing temperature as the Cl + cyclopropane rate
coefficient increases.
3. Results and Discussion
3.1. Relative Rate Study of k(Cl + c-C3H6). The kinetics
of reaction 1 are measured relative to reactions 5 and 6 using
the relative rate technique.16
Cl + c-C3H6 f products
Cl + CH4 f products
Cl + CH3Cl f products
(1)
(5)
(6)
Cl2 hν (355 nm)8 2Cl
(3)
(1)
Cl + c-C3H6 98 c-C3H5 + HCl
The experiments are performed in a slow-flow reactor sur-
rounded by a commercial ceramic-fiber heater. The IR probe is
passed multiple times through the reactor using Herriott-type
multipass optics.15 This multipass arrangement allows the IR
probe to intercept the UV photolysis beam only in the center
of the flow cell, where the temperature is more readily
controlled. The overall effective path length is approximately
20 m. To increase the signal-to-noise ratio, a balanced detector
method is employed, with one detector (reference) monitoring
the laser prior to the reactor and a second detector (signal) after
multipassing through the flow cell. The total average dc power
on each detector is kept equal, and the signals from the two
detectors are subtracted to reduce laser amplitude noise.
The gases are admitted to the cell through calibrated mass
flow controllers, and the total pressure in the cell is measured
by a capacitance manometer and is actively controlled by a
butterfly valve on the outlet. CF2Cl2 concentrations are 1.75 ×
1015 cm-3, cyclopropane concentrations are varied from 2.6 ×
1015 to 14.2 × 1015 cm-3, and and Ar buffer (99.9999%) is
added to reach a total density of 3.22 × 1017 cm-3. The
cyclopropane has a manufacturer-stated purity of 99.9% (chro-
matographic lot analysis). Measurements of the impurity
composition have been undertaken at Sandia National Labora-
tories by gas chromatographic analysis using flame ionization
Initial concentrations are 10-81 mTorr of c-C3H6, 10-15 mTorr
of CH4, 10 mTorr of CH3Cl, and 104-657 mTorr of Cl2 in 10
or 700 Torr of air or nitrogen diluent. The observed loss of
c-C3H6 versus the loss of the reference compounds in the
presence of Cl atoms is shown in Figure 1. As seen from Figure
1, there is no discernible effect of the nature or total pressure
of diluent gas. Linear least-squares analysis of the data in Figure
1 gives k1/k5 ) 1.17 ( 0.09 and k1/k6 ) 0.233 ( 0.014. We
derive k1 ) (1.17 ( 0.09) × 10-13 using k5 ) 1.0 × 10-13 17
,
and k1 ) (1.12 ( 0.07) × 10-13 using k6 ) 4.80 × 10-13 cm3
molecule-1 s-1 17
We estimate that potential systematic errors
.
associated with uncertainties in the reference rate constants add
10% to the uncertainty range for k1. Propagating this additional
uncertainty for the two relative rate measurements gives k1 )
(1.17 ( 0.15) × 10-13 and k1 ) (1.12 ( 0.13) × 10-13 cm3
molecule-1 s-1. We choose to quote a final value for k1 which
is the average with error limits which encompass the extremes
of the individual determinations; hence, k1 ) (1.15 ( 0.17) ×
10-13 cm3 molecule-1 s-1. This result is in good agreement with
the previous absolute rate measurement of k1 ) (1.21 ( 0.15)
× 10-13 by Baghal-Vayjooee and Benson18 but lower than k1
) 1.7 × 10-13 cm3 molecule-1 s-1 from the relative rate study
by Knox and Nelson19 (based upon k(Cl + C2H6) ) 5.7 × 10-11
cm3 molecule-1 s-1 at 298 K17). Knox and Nelson reported an

Kinetics of Chain Chlorination of Cyclopropane
J. Phys. Chem. A, Vol. 107, No. 12, 2003 2005
TABLE 1: Measured Absolute Rate Coefficients for Cl +
Cyclopropane
temp (K)
k
meas (cm3 molecule-1 s-1
)
kcorra (cm3 molecule-1 s-1
)
293
373
423
473
523
573
623
(1.49 ( 0.12) × 10-13
(5.67 ( 0.44) × 10-13
(1.09 ( 0.06) × 10-12
(1.92 ( 0.08) × 10-12
(2.81 ( 0.12) × 10-12
(4.13 ( 0.18) × 10-12
(5.75 ( 0.36) × 10-12
(1.12 ( 0.22) × 10-13
(5.30 ( 0.54) × 10-13
(1.04 ( 0.07) × 10-12
(1.88 ( 0.09) × 10-12
(2.77 ( 0.13) × 10-12
(4.09 ( 0.19) × 10-12
(5.71 ( 0.37) × 10-12
a Includes correction for estimated impurity contribution of 3.7 ×
10-14 cm3 molecule-1 s-1 and additional uncertainty estimate of 1 ×
10-14 cm3 molecule-1 s-1
.
Figure 2. Time-resolved absorption trace of HCl formed in the reaction
of Cl with cyclopropane at 423 K. The solid line shows a fit to the
difference of two exponentials. The cyclopropane concentration is 1.42
× 1016 cm-3
.
Figure 4. Arrhenius plot of the measured rate coefficients for the Cl
+ cyclopropane reaction. The present absolute measurements are shown
as the open circles and the solid triangles (corrected for estimated
impurity contributions). The present relative rate determination is shown
as the open square. The absolute measurement by Baghal-Vayjooee
and Benson18 is given as the solid circle, and the Arrhenius fit from
the relative measurements of Knox and Nelson19 (using kCl+ethane from
ref 13) is shown as the dashed line. The solid line is a weighted fit to
the present data, k2 ) ((1.8 ( 0.3) × 10-10 cm3 molecule-1
Figure 3. Plot of the pseudo-first-order rate coefficient for HCl
formation versus cyclopropane concentration at 423 K. The slope of
this plot yields the second-order rate coefficient for the Cl +
cyclopropane reaction.
s-1)e-(2150(100)/T
.
appreciable dark reaction between Cl2 and cyclopropane in their
system that may explain an overestimation of k1 in their work.
3.2. Absolute Rate Coefficients for Cl + c-C3H6. A typical
time-resolved absorption signal from formation of HCl in the
Cl + cyclopropane reaction is shown in Figure 2. This signal
can be fit by the difference of two exponentials,20 with the rise
time reflecting the formation of HCl by the Cl + cyclopropane
reaction and the decay reflecting loss of HCl, principally by
diffusion out of the probe region. A plot of the reciprocal of
the rise time versus cyclopropane concentration, as shown in
Figure 3, yields a linear plot, the slope of which provides an
absolute measurement of the second-order rate coefficient. The
intercept of this plot reflects other losses of Cl atom, including
diffusion and possible reactions with impurities in the photolyte
or buffer gas.20 The absolute rate coefficients for Cl +
cyclopropane measured by LP/CWIRLPA are given in Table 1
and shown in Figure 4. The error estimates are (2σ on the
basis of the statistical error of the rate coefficient determination
convolved with an estimate of the uncertainties associated with
concentration, temperature, and pressure measurements. The
absolute measurement is expected to suffer a systematic error
associated with the impurities in the cyclopropane sample. This
contribution can be estimated on the basis of the impurity
composition from the gas chromatographic analysis. The relative
peak areas for the 1,3-dichloropropane, 1,1-dichloropropane,
1-propanol, and propene impurities, using flame ionization
detection, are 71:13:10:6. The room-temperature rate coefficients
for the Cl + 1,3-dichloropropane,21 Cl + propene,22,23 and Cl
+ 1-propanol24-26 reactions have been measured. The Cl + 1,1-
dichloropropane rate coefficient is set to the value for the Cl +
1-chloropropane reaction.21,27,28 Assuming a total impurity level
of 0.1% (the upper limit based on the manufacturer’s lot
analysis), the rate coefficient from impurity reactions is
estimated to be 3.7 × 10-14 cm3 molecule-1 s-1. Comparison
of the room-temperature absolute measurement with the relative
rate measurements, which are insensitive to impurities in the
cyclopropane sample, yields a difference of 3.4 × 10-14 cm3
molecule-1 s-1
.
On the basis of measurements of similar Cl + hydrocar-
bon13,23 and Cl + alcohol20,26 reactions, the Cl + impurity
reactions are unlikely to have a significant temperature depen-
dence. The correction for impurity contributions therefore
becomes insignificant at higher temperatures, where the Cl +
cyclopropane rate coefficient is larger. Rate coefficients cor-
rected for the estimated impurity contribution (kcorr ) kobs
-
3.7 × 10-14 cm3 molecule-1 s-1) are shown as the triangles in
Figure 4. The temperature-dependent absolute rate coefficient
measurements can be fit to an Arrhenius form, shown as the
straight line in Figure 4, k1 ) ((1.8 ( 0.3) × 10-10 cm3
molecule-1 s-1)e-(2150(100)/T. A weighted fit to the uncorrected
absolute measurements and the present relative rate measurement
gives a result essentially identical to that from a fit to the
corrected absolute determinations (kcorr). The activation energy
is in excellent agreement with the 4.14 kcal mol-1 activation

2006 J. Phys. Chem. A, Vol. 107, No. 12, 2003
Hurley et al.
and 1300 cm-1. Further irradiation lead to the formation of a
new set of product features at 735, 772, 954, 1035, 1137, 1249,
and 1415 cm-1 which scaled linearly in all spectra and which
increased at the expense of the original product. It seems
reasonable to assign the first set of features to chlorocyclopro-
pane formed in reaction 4 and the second set of features to
dichloropropane formed in reaction 7. Figure 5 shows infrared
spectra acquired before (A) and after (B) a 10 s irradiation of
99.2 mTorr of c-C3H6 and 1.0 Torr of Cl2 in 700 Torr of N2.
The 10 s irradiation led to 32% consumption of c-C3H6.
Subtraction of features attributable to c-C3H6 from panel B gives
the product spectrum shown in panel C. By comparing product
spectra containing different amounts of chloro- and dichloro-
cyclopropane, we are able to provide the IR spectra of c-C3H5-
Cl and c-C3H4Cl2 shown in panels D and E. For experiments
employing cyclopropane conversions of <90%, only two
products are observed: c-C3H5Cl and c-C3H4Cl2. Absolute
calibration of the c-C3H5Cl and c-C3H4Cl2 spectra is achieved
by comparing the results from experiments with different
consumptions of cyclopropane and different relative amounts
of c-C3H5Cl and c-C3H4Cl2 and equating the sum of c-C3H5Cl
and c-C3H4Cl2 with the cyclopropane loss. This approach gave
σe(c-C3H5Cl) at 1307 cm-1 ) (1.62 ( 0.32) × 10-19 and σe-
(c-C3H4Cl2) at 1145 cm-1 ) (2.55 ( 0.51) × 10-19 cm2
molecule-1
.
There are three possible dichlorocyclopropane products: gem-
C3H4Cl2 (both Cl atoms attached to the same C atom), trans-
1,2-C3H4Cl2 (Cl atoms attached to different C atoms and directed
to opposite sides of the planar ring), and cis-1,2-C3H4Cl2 (similar
to trans-C3H4Cl2 except both Cl atoms are on the same face of
the planar ring):
Figure 5. IR spectra acquired before (A) and after (B) a 10 s UV
irradiation of a mixture of 99.2 mTorr of cyclopropane and 1 Torr of
Cl2 in 700 Torr of N2 diluent. Subtraction of cyclopropane features
from panel B gives panel C. Spectra of c-C3H5Cl and c-C3H4Cl2 are
shown in panels D and E.
energy reported in the previous measurement of the temperature
dependence by Knox and Nelson.19 However, using the most
recent measurement of the temperature dependence of the Cl
+ ethane reaction to place the Knox and Nelson relative rate
measurements on an absolute scale yields somewhat poorer
agreement, as shown by the dashed line in Figure 4.
3.3. Photochemical Chain Chlorination of c-C3H6. The
chlorination of cyclopropane is studied using the UV irradiation
of c-C3H6/Cl2/N2 mixtures. The reactions occurring in such a
chemical system are
As discussed in section 3.6, the gem-isomer is kinetically and
thermodynamically favored and we assign the spectrum in
Figure 5E to gem-C3H4Cl2. Continued irradiation of C3H4Cl2/
Cl2/N2 mixtures led to the loss of C3H4Cl2 and the formation
of another product with IR features at 700, 855, 900, 955, 1030,
1045, 1065, and 1405 cm-1 which we ascribe to C3H3Cl3. As
is the case for the possible C3H4Cl2 products, three isomers of
C3H3Cl3 are possible, and we use a similar nomenclature to
define them as gem (two Cl atoms on one C and one Cl on
another C), cis (Cl atoms on all three C atoms, all on the same
side of the C3 ring), or trans (Cl atoms on all three C atoms,
one on the opposite face of the C3 ring from the other two):
Cl2 + hν f 2Cl
(3)
(1)
(4)
(2)
(7)
(8)
(9)
c-C3H6 + Cl f c-C3H5 + HCl
c-C3H5 + Cl2 f c-C3H5Cl + Cl
c-C3H5Cl + Cl f c-C3H4Cl + HCl
c-C3H4Cl + Cl2 f c-C3H4Cl2 + Cl
c-C3H4Cl2 + Cl f c-C3H3Cl2 + HCl
c-C3H3Cl2 + Cl2 f c-C3H3Cl3 + Cl
3.4. Relative Rate Study of k(Cl + c-C3H5Cl). Irradiation
of c-C3H6/Cl2/N2 mixtures results in the conversion of c-C3H6
into c-C3H5Cl that is then converted into c-C3H4Cl2. The yield
of c-C3H5Cl is described by the following expression29
The chain is terminated by loss of Cl atoms through recombina-
tion, reaction with other radicals, or loss at the walls. Initial
concentrations are 48-207 mTorr of c-C3H6 and 100-1040
mTorr of Cl2 in 700 Torr of N2 diluent at 296 ( 3 K. Short
irradiations (1-2 s) resulted in the loss of cyclopropane and
the formation of a product with prominent IR features at 1031
[c-C3H5Cl]
[c-C3H6]0
1
2
1
)
(1 - x){(1 - x)(k /k )-1 - 1}
{
}
(1 - k2/k1)

Kinetics of Chain Chlorination of Cyclopropane
J. Phys. Chem. A, Vol. 107, No. 12, 2003 2007
Figure 6. Concentration of c-C3H5Cl normalized to the initial
concentration of c-C3H6 versus the fractional consumption of c-C3H6
following irradiation of c-C3H6/Cl2/N2 mixtures. The curve is a fit to
the data (see text for details).
where x is the conversion of cyclopropane, defined as
∆[c-C3H6]
x ≡
[c-C3H6]0
Figure 7. ROHF/6-311G** optimized structures for (a) C3H6, (b) C3H5-
Figure 6 shows a plot of ([c-C3H5Cl]t/[c-C3H5Cl]0) versus
∆[c-C3H6]/[c-C3H6]0 for the chlorination experiments described
above. The curve in Figure 6 shows the result of a least-squares
fit of the expression above to the data which gives k2/k1 ) 9.2
( 0.7. Combining this ratio with the value for k1 reported in
section 3.1 gives k2 ) (1.06 ( 0.18) × 10-12 cm3 molecule-1
Cl, (c) gem-C3H4Cl2, (d) the transition state for C3H6 + Cl• f C3H5
•
+ HCl, (e) the transition state for C3H5Cl + Cl• f gem-C3H4Cl• +
HCl, and (f) the transition state for gem-C3H4Cl2 + Cl• f gem-C3H3-
•
Cl2 + HCl.
vibrational frequencies are scaled using the homogeneous scaling
factor 0.9054.10 The prefactor and rate constant are listed in
Table 2 along with the MP2/ROHF heat of reaction, barrier
height, and zero-point energy corrected barrier height. The TST
rate constant is calculated using the zero-point corrected MP2/
ROHF barrier height, ∆EqZPE, 4.0 kcal mol-1, using the ex-
pression
s-1
.
3.5. Computational Study of Hydrogen Abstraction. The
objective of this computational study is to investigate the kinetics
and mechanism of the reaction of Cl atoms with cyclopropane
and determine which of the dichloro- and trichlorocyclopropane
isomers are predominant products using first principles elec-
tronic structure theory.
The rate-limiting step for the reaction of chlorine with
cyclopropane is the hydrogen atom abstraction step leading to
the formation of a cyclopropyl radical (reaction 1). As computed
at the ROHF level, this reaction proceeds with a barrier of 25.6
kcal mol-1 with respect to the energy of the reactants at infinite
separation. Structures for cyclopropane and the transition state
for this reaction are shown in Figure 7. The transition state
structure for Cl + cyclopropane is almost identical to that of
the reaction of Cl with methane. For the chlorination of methane
the ROHF transition state internal coordinates rCH and rH Cl
QTS
kBT
kTST ) σNA
-∆E qZPE
-∆E qZPE
exp
) A exp
(
)
(
)
h QAQB
kBT
kBT
where QA and QB are the partition functions for the reactants
and QTS is the transition state partition function. The symmetry
factor σ represents the number of identical reaction pathways
and equals 6 for the reaction of Cl with cyclopropane. The TST
calculated rate constant 5 × 10-14 cm3 molecule-1 s-1 (Table
2) underestimates the experimental value by only a factor of 2,
which is remarkable agreement for the crude computational
model applied here. This agreement gives confidence that the
calculated barriers can be used to assess the relative rates of
hydrogen abstraction from the Cl-substituted cyclopropanes.
The C-H bond dissociation energy (BDE) is one possible
indicator of the relative ease of H abstraction by Cl atoms. A
reasonable estimate of the C3H5-H BDE can be obtained from
the isodesmic32,33 reaction
a
a
have the values 1.309 and 1.517 Å, respectively, where Ha
corresponds to the abstracted H atom. Similarly, the transition
state internal coordinates rCH and rH Cl for the cyclopropane
a
a
transition state have the values 1.312 and 1.503 Å, respectively.
The C-Ha-Cl angle in the methane transition state is 180°,6
as is expected because of the 3-fold symmetry along the reaction
coordinate. This angle is slightly perturbed by 1.9° in the
cyclopropane transition state as a result of van der Waals
interactions with nearby H atoms. Since Hartree-Fock notori-
ously overestimates barrier heights,30 which will erroneously
underestimate rate constants, the energies are corrected with
MP2 using the ROHF geometries. The MP2 energy correction
•
•
c-C3H6 + CH3 f c-C3H5 + CH4
(10)
in conjunction with the experimental heat of reaction of 105.1
lowers the barrier to 8.3 kcal mol-1
.
kcal mol-1 for CH4 f CH3 + H•.34 Isodesmic reactions are
•
The prefactor, A, and transition state theory (TST)31 rate
constant, kTST, for this reaction are also computed at 300 K using
the ROHF vibrational frequencies and moments of inertia. The
those in which reactants and products contain the same type
and number of bonds.32,33 Because of this electronic similarity,
errors in the energy due to defects in the basis set and electronic

2008 J. Phys. Chem. A, Vol. 107, No. 12, 2003
Hurley et al.
TABLE 2: MP2/6-311G**//ROHF/6-311G** Barrier Heights (∆Eq), Zero-Point Energy Corrected Barrier Heights
(∆EqZPE), Transition State Theory Prefactors (A), and Transition State Theory Rate Constants (kTST
)
q
a
b,c
reaction
∆Eq a
∆EZPE
Ab,c
kTST
C3H6 + Cl• f C3H5• + HCl
8.3
6.0
9.6
12.1
12.3
9.2
12.9
5.7
4.0
1.8
5.1
7.6
7.7
4.9
8.4
1.4
5.3
10.2
3.7 × 10-11
2.0 × 10-11
4.3 × 10-11
2.7 × 10-11
1.2 × 10-11
2.8 × 10-12
4.0 × 10-12
4.6 × 10-12
3.3 × 10-12
2.3 × 10-12
4.6 × 10-14
1.0 × 10-13
8.3 × 10-15
7.6 × 10-17
2.8 × 10-17
7.6 × 10-16
2.0 × 10-16
3.3 × 10-18
4.3 × 10-16
1.7 × 10-19
C3H5Cl + Cl• f gem-C3H4Cl• + HCl
C3H5Cl + Cl• f trans-C3H4Cl• + HCl
C3H5Cl + Cl• f cis-C3H4Cl• + HCl
gem-C3H4Cl2 + Cl• f gem-C3H3Cl2• + HCl
trans-C3H4Cl2 + Cl• f gem-C3H3Cl2• + HCl
trans-C3H4Cl2 + Cl• f trans-C3H3Cl2• + HCl
cis-C3H4Cl2 + Cl• f gem-C3H3Cl2• + HCl
cis-C3H4Cl2 + Cl• f trans-C3H3Cl2• + HCl
cis-C3H4Cl2 + Cl• f cis-C3H3Cl2• + HCl
9.9
14.7
a Energies in kcal mol-1 b k in cm3 molecule-1 s-1 c Prefactors and rate constants computed at 300 K.
. .
more than 3 kcal mol-1 lower than the barrier leading to the
trans radical and almost 6 kcal mol-1 lower than that leading
to the cis radical, consistent with the BDEs. In the gem radical
unpaired electron density can be delocalized from the C center
to the Cl atom, stabilizing this radical relative to the other two
isomers. This greater delocalization is reflected in a lower
electron spin density on the C center, as shown in Table 3.
TABLE 3: MP2/6-311G**//ROHF/6-311G** C-H Bond
Energies and Carbon Radical Spin Densities
reaction
BDEa
C spin density
C3H6 f C3H5• + H•
102.1
99.7
0.9316
0.8776
0.9202
0.9314
0.9228
0.8804
0.9193
0.8695
0.9055
0.9296
C3H5Cl f gem-C3H4Cl• + H•
C3H5Cl f trans-C3H4Cl• + H•
102.2
103.3
103.3
101.0
103.4
98.4
C3H5Cl f cis-C3H4Cl• + H•
gem-C3H4Cl2 f gem-C3H3Cl2• + H•
trans-C3H4Cl2 f gem-C3H3Cl2• + H•
trans-C3H4Cl2 f trans-C3H3Cl2• + H•
cis-C3H4Cl2 f gem-C3H3Cl2• + H•
cis-C3H4Cl2 f trans-C3H3Cl2• + H•
cis-C3H4Cl2 f cis-C3H3Cl2• + H•
The structures of chlorocyclopropane and the transition state
leading to the gem radical intermediate are shown in Figure 7.
Also listed in Table 2 are prefactors and rate constants for each
of the three possible reactions computed at 300 K. A somewhat
surprising result is the order of magnitude larger prefactors for
the trans and cis reactions over the gem reaction. This is partially
a result of the statistical advantage of forming the trans and cis
intermediates over the gem intermediate. There exist two
equivalent pathways leading to each of the trans and cis radicals
as opposed to just a single pathway leading directly to the gem
radical. Since the prefactor is a measure of the encounter rate,
this suggests that the gem pathway is only energetically favored
over the remaining two pathways, even though encounters
leading to the trans and cis pathways occur more frequently.
The computed rate constant for the gem pathway is a factor of
2 greater than kTST for H abstraction from C3H6 (Table 2), in
good qualitative agreement with the factor of 9 derived from
the relative rate study above.
101.7
104.0
a Zero-point corrected bond dissociation energies calculated from
the isodesmic reaction C3H6-nCln + CH3• f C3H5-nCln• + CH4 using
the experimental bond dissociation energy of 105.1 kcal mol-1 for CH4
f CH3 + H•.34
•
correlation tend to cancel between reactants and products. The
C3H5-H BDE derived from reaction 10 using the MP2 and ZPE
corrected energies is 102.1 kcal mol-1 (Table 3), or 4.2 kcal
mol-1 less than that derived from the reaction 1 equilibrium.18
Chlorination of the cyclopropyl radical produces chloro-
cyclopropane (reaction 4), and the calculated scaled vibrational
spectrum agrees well with the experimentally observed spectrum
(Figure 5D). As described above, further chlorination can
produce up to three possible dichlorocyclopropane isomers. The
calculated vibrational spectra for each of these three were
compared with the observed spectrum of the dichlorocyclopro-
pane product (Figure 5E). The most intense peaks in the
calculated spectra for the gem, trans, and cis isomers are located
at 1145, 666, and 1330 cm-1, respectively, compared to the
most intense peak at 1140 cm-1 in the experimental spectrum.
The bands at 666 and 1330 cm-1 expected for the trans and cis
isomer spectra do not appear in the experimental spectrum.
Furthermore, an intense peak in the experimental spectrum at
725 cm-1 is consistent with the asymmetric C-Cl stretch in
the gem isomer that is not present in the trans or cis isomers.
These results provide strong evidence that chlorination of
chlorocyclopropane proceeds predominately or exclusively to
the gem-dichlorocyclopropane product. Vibrational frequencies
and relative intensities for the gem isomer are listed in Table 4
along with the experimental frequencies for dichlorocyclopro-
pane. Intensities are uniformly scaled such that the most intense
peak has a value of 100.
The above argument is based on the notion that, once formed,
the gem radical only reacts with Cl2 to produce the gem product
(reaction 7). Internal isomerization of the gem radical to the
trans by H migration is possible but the MP2/ROHF barrier of
49.0 kcal mol-1 indicates that this is a very unlikely pathway.
The barrier for a direct gem f cis radical isomerization is
expected to be even higher because of the very large strain
involved. Another possibility is ring-opening of the gem radical
to form a chlorinated allyl radical. Although ring-opening was
not explicitly investigated in this study, conclusions regarding
its occurrence can be drawn from previous studies of the ring-
opening of the cyclopropyl radical.35-38 Both experimental35,36
and high-level computational37,38 studies predict a barrier of 22
kcal/mol for ring-fission leading to the allyl radical. This is still
substantially larger than the zero-point corrected barriers for H
atom abstraction, and therefore, ring-opening is not expected
under the experimental conditions reported in this study.
A similar approach was used to examine the three possible
trichlorocyclopropane isomers. The most intense peaks in the
calculated vibrational spectra for the gem-, trans-, and cis-
trichlorocyclopropane isomers are located at 766, 651, and 686
cm-1, respectively, compared to the most intense peak in the
experimental spectra at 785 cm-1. The second most intense
peaks in the calculated spectra for the gem, trans, and cis isomers
are located at 1074, 1236, and 1365 cm-1, respectively,
To explain this preference, MP2/ROHF bond dissociation
energies (BDEs) and barrier heights are computed for the three
reactions leading to gem, trans, and cis-chlorocyclopropyl
radical intermediates and are listed in Tables 2 and 3. The C-H
BDE leading to the gem radical is lower than that leading to
trans and cis radicals by 2-3 kcal mol-1. The zero-point energy
corrected barrier leading to the gem radical intermediate is also

Kinetics of Chain Chlorination of Cyclopropane
J. Phys. Chem. A, Vol. 107, No. 12, 2003 2009
gem-C3H3Cl3
TABLE 4: Scaled ROHF/6-311G** Normal-Mode Frequencies and IR Intensities
gem-C3H4Cl2
mode description
freqa theory (expt)
rel intb
mode description
freqa theory (expt)
rel intb
Cl-C-Cl wag
sym Cl-C-Cl def
Cl-C-C def
270
292
297
394
1
0
0
Cl-C-C-Cl torsion
Cl-C-C-Cl torsion
Cl-C-Cl def
146
168
264
299
393
449
515
675
766 (700)
914 (855)
962 (900)
980 (955)
1074 (1030)
1104 (1045)
1135 (1065)
1233
1326
1451 (1405)
2978
3050
3067
2
2
2
1
2
Cl-C-C def
0
Cl-C-C def
sym C-Cl str
asym C-Cl str
asym CH2 rock
asym CH2 wag
asym C-C-C def
sym C-C-C def
sym CH2 rock
sym H-C-C def
sym H-C-C def
asym H-C-C def
sym CH2 def
482
25
92
28
1
Cl-C-C def
sym C-Cl str
715 (725)
763 (775)
886
4
24
37
100
17
4
933
0
CH2 rock
CH2 wag
971 (960)
1076 (1025)
1099
1145 (1140)
1160
1240 (1240)
1431
1477 (1420)
2976
21
13
1
100
0
19
9
7
9
1
0
4
9
H-C-C def
H-C-C def
H-C-C def
H-C-C def
sym CH2 def
sym C-C str
asym C-H str
asym C-H str
sym C-H str
41
11
30
14
17
14
1
asym CH2 def
sym C-C str
asym C-H str
sym C-H str
2981
3057
3067
sym C-H str
4
1
asym C-H str
a Frequencies in units of cm-1 b Relative intensities scaled to 100 for the most intense mode.
.
compared to the second most intense peak in the experimental
spectra at 1030 cm-1. The similarity between the calculated
spectra for gem-C3H3Cl3 and the experimental spectra suggests
that the gem isomer is the only observed trichlorocyclopropane
product. Calculated frequencies and assignments for gem-C3H3-
Cl3 are listed in Table 4 along with the experimental frequencies.
From the results above, the only experimentally relevant H
abstraction pathway (reaction 8) starts from gem-C3H4Cl2, and
as all the H atoms are equivalent in this molecule, only one
abstraction pathway is possible. As shown in Table 2, the
reaction barrier and rate constant for this reaction are consistent
with the cis and trans results for C3H5Cl, as are the C-H BDE
and C center spin density. H abstraction and, thus, gem-
trichlorocyclopropane formation are predicted to occur much
more slowly than mono- and dichlorocyclopropane formation.
H abstraction is predicted to be more rapid from the cis- and
trans-dichlorocyclopropane isomers (Table 2); we see that the
H abstraction barrier is predominantly determined by the
presence or absence of a Cl atom at the reacting C center and
that the reaction barrier scales with the calculated C-H BDE
and with the C center spin density in the daughter radical.
In summary, the computational results are consistent with a
model in which gem-C3H4Cl2 is the predominant product of
chlorination of C3H5Cl, and gem-C3H3Cl3 is the only product
of chlorination of gem-C3H4Cl2. Both chlorinations occur by H
abstraction and chlorine substitution with preservation of the
radical stereochemistry.
from the electronic structure calculations and comparisons with
experimental vibrational spectra show that chlorination of
chlorocyclopropane predominately leads to the gem-dichloro-
cyclopropane isomer, which inevitably leads to the gem-
trichlorocyclopropane isomer. The gem-C3H4Cl2 isomer is both
the kinetically and thermodynamically favored product. Chlo-
rination of gem-C3H4Cl2 can only lead to the gem-trichloro-
cyclopropane isomer.
Acknowledgment. The work at Sandia National Laboratories
(C.A.T. and J.D.D.) is supported by the Division of Chemical
Sciences, Geosciences, and Biosciences, the Office of Basic
Energy Sciences, the U. S. Department of Energy. Sandia is a
multiprogram laboratory operated by Sandia Corporation, a
Lockheed Martin Company, for the United States Department
of Energy under Contract DE-AC04-94-AL85000.
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