An experimental and theoretical high temperature kinetic study of the thermal unimolecular dissociation of fluoroethane

Article abstract of DOI:10.1039/b808168a

The thermal dissociation of fluoroethane has been studied using shock tube (ST)/time-of-flight mass spectrometry (TOF-MS) at 500 and 1200 Torr over the temperature range 1200-1550 K. The ST/TOF-MS experiments confirm that elimination of HF is the only reaction channel and rate coefficients for this reaction were extracted from concentration/time profiles derived from the mass spectra. Results from a novel diaphragmless shock tube coupled to the TOF-MS are also presented and demonstrate the unique ability of this apparatus to generate sufficiently reproducible shock waves that signal averaging can be performed over multiple experiments; something that is not possible with a conventional shock tube. The dissociation is also studied with ab initio transition state theory based master equation simulations. A modest increase in the calculated barrier height (i.e., by 1 kcal mol^-1) yields predicted high pressure rate coefficients that are in good agreement with the existing literature data. The present pressure dependent observations are accurately reproduced for a downwards energy transfer for neon at 1200 to 1500 K of ～270 cm ^-1, which is somewhat smaller than that found in previous studies on fluorinated ethanes with the same bath gases. the Owner Societies.

Full text of DOI:10.1039/b808168a

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PAPER
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An experimental and theoretical high temperature kinetic study
of the thermal unimolecular dissociation of fluoroethane
a
b
b
a
Binod R. Giri,w John. H. Kiefer, Hui Xu,z Stephen J. Klippenstein and
a
Robert S. Tranter*
Received 14th May 2008, Accepted 3rd July 2008
First published as an Advance Article on the web 10th September 2008
DOI: 10.1039/b808168a
The thermal dissociation of fluoroethane has been studied using shock tube (ST)/time-of-flight
mass spectrometry (TOF-MS) at 500 and 1200 Torr over the temperature range 1200–1550 K.
The ST/TOF-MS experiments confirm that elimination of HF is the only reaction channel and
rate coefficients for this reaction were extracted from concentration/time profiles derived from the
mass spectra. Results from a novel diaphragmless shock tube coupled to the TOF-MS are also
presented and demonstrate the unique ability of this apparatus to generate sufficiently
reproducible shock waves that signal averaging can be performed over multiple experiments;
something that is not possible with a conventional shock tube. The dissociation is also studied
with ab initio transition state theory based master equation simulations. A modest increase in the
ꢀ1
calculated barrier height (i.e., by 1 kcal mol ) yields predicted high pressure rate coefficients that
are in good agreement with the existing literature data. The present pressure dependent
observations are accurately reproduced for a downwards energy transfer for neon at 1200 to
ꢀ
1
1
500 K of B270 cm , which is somewhat smaller than that found in previous studies on
fluorinated ethanes with the same bath gases.
Introduction
Non-RRKM behavior is very rare although much antici-
pated, see ref. 1 and references therein. Consequently, inves-
tigation of other fluorinated ethanes, at conditions similar to
the ST/LS TFE studies, may yield better understanding of
vibrational relaxation and HF elimination. Additionally, a
more extensive dataset describing the fall off behavior of HF
elimination from fluoroethanes will be gained. To date we
Elimination of hydrogen fluoride from fluorinated ethanes has
been extensively studied at conditions close to the high pres-
sure limit, see ref. 1 and 2 and references therein. Generally,
good agreement with k
N
derived from theoretical calculations
is found. These studies indicate that the elimination of HF
proceeds via a four centered transition state.
1
have studied vibrational relaxation and dissociation of TFE,
1
Until recently, no experimental data concerning HF elim-
ination from fluorinated ethanes in the high temperature fall
off region were available. A high temperature shock tube/laser
schlieren (ST/LS) study of 1,1,1-trifluoroethane (TFE) gave
5
,1-difluoroethane and ethane itself in the high temperature
6
fall off region. 1-Fluoroethane, FE, concludes the series of
fluorinated alkanes where the substituents are on a single
carbon atom.
the surprising result of deep fall off from k
N
but little pressure
We have previously applied both ST/LS and ST/TOF-MS
1
dependence. Based on observations of double relaxation in
the same study and the inability of standard RRKM models to
simulate the data the authors tentatively concluded that the
dissociation of TFE at high temperatures was non-statistical in
nature. Very recently, support for the ST/LS results was
obtained from a new shock tube/time-of-flight mass spectro-
2
5
to the study of TFE and vinyl fluoride, the main decomposi-
tion product of DFE. The combination of these two techni-
ques allows coverage of a much wider experimental range for
the dissociation reaction than is possible by either method
5
alone. ST/LS appears to be uniquely suited to observation of
vibrational relaxation at high temperatures and the ST/TOF-
MS technique provides confirmation of rate and mechanism
through direct identification of reaction products.
2
meter (ST/TOF-MS) study. The laser schlieren studies also
3
,4
prompted theoretical investigations, the results of which
question the source of the apparent non-RRKM behavior in
the ST/LS experiments.
The LS technique effectively measures density gradients, dr/
dx, and these are proportional to the rate, r, through the heat
of reaction, DH, with a usually small reduction from expan-
sion through any increase in mole number, DN, as in eqn (1).
a
Chemical Sciences and Engineering Division, Argonne National
Laboratory, 9700 South Cass Avenue, Argonne, IL 60439-4831,
USA. E-mail: tranter@anl.gov
Department of Chemical Engineering, University of Illinois at
Chicago, Chicago, IL-60607, USA
w Current address: Department of Chemistry, Acadia University,
Wolfville, Nova Scotia, Canada.
P
dr
r
rðDH ꢀ CpTDNÞ
¼
ð1Þ
b
2
dx r uðCpT=M ꢀ Cvv =RÞ
0
Here, the remaining quantities are just molecular heat capa-
cities or incident shock parameters, which are easily obtained
7
from measurements or calculations. The value of the
z Current address: Cummins Inc., Cummins Technical Center, 1900
McKinley Ave, Columbus, IN-47201, USA.
6
266 | Phys. Chem. Chem. Phys., 2008, 10, 6266–6273
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ꢀ
1
expression C
The literature values of DHf,298 for FE are ꢀ65.8 kcal mol
ꢀ111
p
TDN is typically of the order 10–15 kcal mol
.
To produce the very weak shocks necessary for observation
of the fast relaxation found in these fluorides, a slow flow of
driver gas was achieved by introducing various converging/
diverging nozzles of different throat diameters at the dia-
phragm. The experiments all used Mylar diaphragms of
0.001–0.005 in thickness, burst spontaneously with helium.
Molar refractivities used in the calculation of the density
gradient from the measured angular deflection were 11.38
ꢀ
1 8
,
ꢀ
1 9
ꢀ110
ꢀ
66.5 kcal mol , ꢀ65.1 kcal mol
and ꢀ62.9 kcal mol
and so the dissociation of FE is endothermic by, at most, just
ꢀ
1
3.7 kcal mol . Thus, for the dissociation of FE, very small to
1
vanishing density gradients will be produced, effectively ren-
dering the technique blind to this reaction. Hence, here we
present only ST/TOF-MS measurements of HF elimination
and confine ST/LS to measurements of vibrational relaxation.
The majority of the literature data for dissociation of FE
2
3
24
for fluoroethane and 6.367 for Kr. These were taken as
constant throughout the decomposition; an excellent approx-
imation for such species.
1
2
are below 1000 K. Day and Trotman-Dickenson studied
the reaction in a static reactor over the temperature range
ST/TOF-MS and DFST/TOF-MS
6
virtually no pressure dependence and obtained Arrhenius
84–739 K and pressures of 0.7–216 Torr. They observed
The ST/TOF-MS and differentially pumped molecular beam
sampling system that couples the shock tube and TOF-MS
ꢀ
1
parameters, log A = 13.31 and E = 58.2 kcal mol . In
a
1
3
2,25
subsequent work, Kerr and Timlin employed a similar tech-
nique using identical conditions to that of Day and Trotman-
Dickenson, and obtained excellent agreement with the earlier
have been extensively described elsewhere.
The shock tube
consists of a 23 in long, 7.7 in id driver section and 23 ft. long
driven section that reduces from 2.8 in id to 2.5 in id as it
25
enters the sampling system. Pressure transducers are located
1
4
results. Sianesi et al. observed pyrolysis in a conventional
flow system (T = 843–923 K, P = 1 atm) and reported a rate
coefficient expression for FE dissociation that had a pre-
exponential factor which was a factor of 13 greater than that
of Kerr and Timlin and an activation energy which was
close to the end wall of the driven section and the shock
velocities and hence post shock conditions are obtained in a
similar manner to the ST/LS experiments with similar
uncertainties.
ꢀ1
4
.4 kcal mol larger. Rate coefficients calculated from Sinaesi
et al.’s expression are however in good agreement with the
Recently, the driver section of the shock tube has been
modified to create a diaphragmless shock tube, DFST which is
2
6
extrapolated lower temperature data from Kerr and Timlin. A
fully described elsewhere. Essentially, the diaphragm has
been replaced by a novel, fast acting valve mounted inside
the driver section and this is shown schematically in Fig. 1.
Initially the interior of the bellows is pressurized causing the
bellows to expand and push the seal plate into the throat of the
driven section thereby separating the driver and driven
sections. This is the configuration shown in Fig. 1. The two
sections of the shock tube can now be filled to the desired
pressures and then fired by rapidly venting the bellows causing
them to collapse and draw the seal plate out of the driven
section. The DFST has several advantages that are discussed
1
5
similar flow reactor study by Dastoor and Emovon, how-
ever, reported rate coefficients for T = 793–873 K that were
more than an order of magnitude slower than the earlier
1
3
studies. However, as noted by Kerr and Timlin, the pre-
exponential factor (log A = 12.16) appears to be too low to
account for a reasonable change in the entropy of activation
for such HF elimination.
Above 1000 K, the only literature data are two single-pulse
16,17
shock tube studies.
16
Okada et al. studied FE dissociation at
P = 2500–8700 Torr and T = 996–1137 K using the relative rate
method and deduced a high pressure limiting rate expression:
2
6
elsewhere. Of particular relevance to the current study is that
26
very reproducible reaction conditions can be achieved for
1
3.65ꢂ0.20
7
ꢀ1
ꢀ1
kN(T) = 10
exp(ꢀ59.5 ꢂ 1.0 kcal mol /RT) s
.
1
Cadman et al. also used the single pulse shock tube method
and their results for T = 1275–1659 K and P E 800 Torr
indicate a small fall off from the likely high pressure limit of
Okada et al. However, the reliability of Cadman et al.’s data for
separate experiments with identical loading conditions. This
reproducibility gives rise to the possibility of signal averaging
over multiple experiments to improve signal quality. In the
current work, both the diaphragmed shock tube and the
diaphragmless apparatus were used and from hereon DST
16,18
HF eliminations has been seriously questioned
likely that agreement with other datasets may be fortuitous.
and it appears
Experimental
ST/LS
The shock tube used in the LS experiments has a 4 ft long
driver section of 4 in id connected to a 10 ft driven section of
1
.5 in id, whose detailed layout has been fully described. The
9
2
ST/LS diagnostics and software have also been described
7
,20–22
19
As before, velocities were set by interpola-
previously.
tion of four intervals calculated from measured times centered
about the LS beam. On the basis of extensive experience, the
uncertainty in velocity is estimated as ꢂ0.2%, corresponding
to a temperature error of less than ꢂ0.5%, here amounting to
the order of ꢂ10 K.
Fig. 1 Schematic of the diaphragmless driver section of the DFST.
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2
(B3LYP) functional and the 6-31G* and 6-311++G(d,p)
7
will be used to refer to the shock tube operated with
diaphragms and ST to refer to both DST and DFST.
2
8
basis sets. The properties of the saddle point and products
were further explored with second order perturbation theory
Unlike the ST/LS experiments, which are conducted behind
the incident shock waves, the ST/TOF-MS experiments are
performed behind the reflected shock. Following reflection of
the shock wave from the endwall, a thermal boundary layer
grows into the shock heated zone. Sampling from this layer is
avoided by the use of a differentially pumped molecular beam
system; the first stage of which is a 0.4 mm diameter orifice in
2
9
(PT2) employing a 4-electron 4-orbital complete active space
(CAS). The active space consisted of the orbitals correlating
with the HF bonding and antibonding orbitals and the C H p
2
4
3
0
and p* orbitals. Dunning’s correlation consistent basis sets
up to cc-pvqz were employed in these CASPT2 calculations.
Finally, the properties of the stationary points were examined
with quadratic configuration interaction calculations with
2
5
the driven section endwall. Gases flow continuously from the
shock tube into the ion source of the reflectron mass spectro-
meter where ion packets are generated by electron impact
ionization (30 eV). To produce well defined ion packets the
electron beam is pulsed in and out of the ion source and this is
synchronized with the draw out pulse used to gate ion packets
3
1
perturbative inclusion of triple excitations (QCISD(T)).
The largest basis set employed for these QCISD(T) calcula-
3
2
tions was the cc-pvtz basis set. The GAUSSIAN98 quantum
chemistry package was used for all the B3LYP calculations,
while the remaining calculations were performed with the
2
5
33
into the TOF-MS for analysis. The ionization pulse has a
duration of 0.4 ms and ion packets are injected every 9.52 ms to
obtain sufficient temporal resolution for determining the initial
rate of reaction. The pressure in the ion source increases
during the course of an experiment and the subsequent change
in ion signals is accounted for with a non-reactive internal
MOLPRO package.
There are only modest variations in the optimized structures
and vibrational frequencies with quantum chemical method.
The imaginary frequency shows the largest variation, with
predicted values of 1965, 1977, 1927, and 1711 for the
QCISD(T)/cc-pvtz, CASPT2/cc-pvtz, CASPT2/cc-pvqz, and
B3LYP/6-311++G(d,p) calculations respectively. The varia-
tions in the remaining transition state frequencies yield varia-
tions of 20% or less in the predicted rate coefficients for
temperatures in the 1000 to 2000 K regime.
2
5
standard, here argon. Both pre-shock and post-shock data
are acquired and in-house software is used to interpret the
mass spectra and create concentration/time profiles for the
species of interest.
In ST/TOF-MS experiments it is not uncommon to observe
peaks of greatly different sizes in the mass spectra which often
force the sensitivity of the detector to be reduced to avoid
Larger basis sets (up to cc-pvqz or aug-cc-pvqz) were
employed in QCISD(T) single point calculations at the
QCISD(T)/cc-pvtz, the B3LYP/6-311++G(d,p), and various
of the CASPT2 optimized geometries. These QCISD(T)/
cc-pvtz and QCISD(T)/cc-pvqz energies were extrapolated to
2
saturation of the detector. Consequently, the measurement of
species with small peaks can be impaired. With the DST/TOF-
2
,26
34
MS each experiment has to be considered unique
and
the complete basis set (CBS) limit as in our prior studies.
Due in large part to the sharp nature of the barrier, there is
little dependence of the barrier height on optimization
techniques such as signal averaging cannot be applied.
However, with the DFST/TOF-MS, experiments performed
with identical loading conditions in the shock tube produce
sufficiently similar post shock conditions that variations are
within the experimental error, and the results can be consid-
ꢀ
1
method, with variations of less than 0.2 kcal mol in the
barrier height predicted for the different geometries. The basis
set extrapolations based on the cc-pvnz and aug-cc-pvnz series
yielded essentially identical results (differing by only 0.02) kcal
2
6
ered near identical. Thus, as will be demonstrated, mass
spectra from several experiments obtained from DFST/TOF-
MS measurements can be averaged improving signal/noise,
S/N, and the shapes of small peaks and reducing the scatter in
concentration/time plots derived from the mass spectra.
ꢀ
1
mol . This modest discrepancy suggests that the basis set
extrapolation, which amounts to a lowering of the barrier
ꢀ1
height by B0.4 kcal mol from the cc-pvqz values, should be
quite accurate.
The minimum energy path (MEP) was followed at the
Regent mixtures
35
CASPT2/aug-cc-pvdz level with POLYRATE coupled to a
3
6
All reaction mixtures were prepared manometrically in 50 L
glass vessels. The mixtures were homogenized either through
stirring (ST/LS) or diffusion overnight (ST/TOF-MS) prior to
use. For both experiments fluoroethane (97+%) was obtained
from Synquest Laboratories. ST/LS mixtures contained 10 or
modified version of GAUSSRATE that allowed for the
direct use of the MOLPRO quantum chemistry software. This
procedure also produced projected vibrational frequencies
along the path. Higher level QCISD(T)/CBS energies were
also obtained along the CASPT2/aug-cc-pvdz MEP. The latter
energies, relative to the saddlepoint energy, were found to be
essentially identical to those from the CASPT2/aug-cc-pvdz
MEP. The CASPT2/aug-cc-pvdz properties along the MEP
were employed in variational transition state theory calcula-
tions, yielding a nearly temperature independent reduction in
the rate by 25% for temperatures in the 1000 to 2000 K range.
The effect of tunneling was examined with both one-
dimensional Eckart corrections and with the small curvature
2
0% FE diluted in krypton (Spectra Gases excimer grade).
The ST/TOF-MS reaction mixtures were, 1–4% FE, 1.5–6%
argon (Linde 99.999%) diluted in neon (Linde 99.999%).
Theoretical calculations
The geometric structures and rovibrational properties of the
reactants, products, and transition state for the dissociation of
C H F into C H + HF were studied with a variety of
3
7,38
tunneling formalism of Truhlar and coworkers.
These two
2
5
2
4
methods. Initial explorations were performed with density
functional theory employing the Becke-3 Lee-Yang Parr
methods were found to yield quantitatively similar tunneling
corrections for temperatures in the 600 to 2000 K range. At
6
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1
000 K, tunneling increases the rate by a factor of 1.4, this
factor reduces to 1.1 by 2000 K. For computational reasons,
the one-dimensional Eckart tunneling correction was em-
ployed in the final temperature and pressure dependent
calculations.
Master equation simulations of the temperature and pres-
sure dependent kinetics were performed as described
3
9,40
elsewhere.
The collision rate for collisions with neon was
calculated from Lennard-Jones potentials. A single exponential-
down model was employed for the energy transfer function.
The average downwards energy transfer, hDEidown, was taken
to increase with temperature according to the form: 150
n
ꢀ1
(
T/298) cm . This form was chosen in analogy with our
4
0
findings for a number of other reactions and the specific
values employed are based on a fit to experiment as discussed
below. The internal rotor in ethyl fluoride was treated as a
4
1
hindered rotor employing a Pitzer–Gwinn approximation.
Fig. 2 Raw data obtained at an ionization cycle of 105 kHz from a
5 5
ST/TOF-MS experiment, P = 1262 Torr, T = 1425 K. The down-
ward spikes represent the mass spectra and show pre-shock as well as
the post-shock data. The increase in signal intensity at 350 ms is
discussed in the text. The upward spikes show the timing signals used
to gate deflect the electron beam and gate the ion packets in the
TOF-MS.
Results and discussion
Relaxation
1
In previous work on 1,1,1-trifluoroethane, 1,1-diflurorethane
5
6
and ethane vibrational relaxation could be resolved in ST/LS
experiments. For TFE and ethane double relaxation was
observed with a fast initial process being followed by a slower
secondary one that preceded dissociation. For completeness
we attempted to study vibrational relaxation in fluoroethane.
Unfortunately, although indications of vibrational relaxation
were observed, the process was simply too fast to be clearly
resolved preventing reliable data from being obtained. Conse-
quently, no results from the vibrational relaxation experiments
will be presented.
Dissociation
An example of the raw mass spectra and timing signals used to
control the injections of ion–ion packets into the TOF-MS are
shown in Fig. 2 with the regions corresponding to before and
after reflection of the incident shock wave indicated. The
increase in signal at approximately 350 ms is due to the
increasing pressure in the ion source following reflection of
the shock wave and in conjunction with concentration profiles
Fig. 3 A 20 ms time segment from Fig. 2 180 ms after formation of the
reflected shock wave which defines the start of reaction. Ions are
generated while the timing pulses are high and injected when the pulse
goes low. The labeled peaks are associated with the pulse labeled, A,
and the flight times are measured from the falling edge of this pulse.
The unlabelled peaks belong to a prior pulse.
2
5
is used to locate the onset of reaction, t
0
.
The mass spectra
for unreacted FE show a dominant peak at m/z = 47 and a
minor peak at m/z = 48, the parent ion, which is about 10%
the height of the m/z = 47 peak. Additionally, peaks at m/z =
3
found along with several minor peaks. These observations are
3 (25% of m/z = 47) and m/z = 28 (10% of m/z = 47) are
4
2
in good agreement with the literature MS for FE. Fig. 3
shows a segment, from Fig. 2, 180 ms after the occurrence of
the reflected shock wave, and a number of additional peaks
that correspond to the reaction product ethylene and its
fragments (m/z = 28, 27, 26). An additional peak at m/z =
with the appearance of m/z = 28 and by comparison with
experiments where the temperature is too low to dissociate FE.
The peak areas in the mass spectrum are directly proportional
to concentration and by integrating the peak areas for each
m/z of interest in every mass spectrum and scaling by the
2
,25
2
0 is observed which could correspond to HF. However, the
argon peak area concentration/time plots for each species
are obtained, Fig. 4. Fragmentation of FE in the ion source
generates small amounts of m/z = 28, 27 and 26 and this is
mass resolution of the current instrument HF is not sufficient
to distinguish between HF and the bath gas neon. The
formation of neon ions is minimized by using an ionization
energy of 30 eV and the presence of HF is inferred through the
increase in the m/z = 20 signal that occurs simultaneously
2 4
accounted for in determining the C H concentration. Initial
estimates of the HF elimination rate coefficient for each
experiment are obtained directly from the concentration/time
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Fig. 4 Concentration/time plot for the dissociation of FE. Points are
experimental data and the solid lines represent the results of simula-
tions used to extract the initial rate coefficients and account for
non-isothermal effects.
profiles assuming first order kinetics. To account for tempera-
ture changes during reaction, which are small due to the low
endothermicity of the 1,2-HF elimination from FE, the esti-
2
mated rate coefficients are refined through simulation. The
mass spectra show no evidence of reaction paths other than
HF elimination and thus the model consists solely of a single
reaction for 1,2 elimination.
In the current work the portion of the concentration/time
profiles that correspond to gases sampled from behind the
reflected shock wave, e.g. Fig. 4, are quite well defined.
However, prior to formation of the reflected shock wave the
pressure in the driven section of the shock tube is low, which
results in a low density in the TOF-MS ion source and the
production of few ions. Consequently, at early times the peaks
in the mass spectra are poorly formed and susceptible to
random fluctuations in area. This results in an increased
scatter in the early portions of the concentration/time profiles
as is evident in Fig. 5a. These sections of the concentration/
Fig. 5 Concentration/time plots for the dissociation of fluoroethane
in DFST/TOF-MS. Solid points represent experimental data and lines
represent the results of simulations to extract initial rate coefficients
and account for non-isothermal effects. (a) Concentration time profiles
for an individual experiment at T
b) Concentration profile derived from averaged mass spectra from
experiments T = 579 ꢂ 6 Torr.
= 1393 ꢂ 11 K, P
5 5
= 1397 K, P = 582 Torr;
(
2
5
time profiles are used to locate the onset of reaction and the
scatter may affect the accuracy with which this is determined.
However, averaging the mass spectra from several identical
experiments may reduce the scatter in the data. Such experi-
ments are possible with the DFST and three sets of experi-
ments each consisting of five experiments with identical
loading conditions were performed. The loading conditions
were chosen to produce conditions corresponding to the low,
mid and high temperature points of the DST\TOF-MS experi-
ments. The resulting mass spectra from each set were averaged
and the concentration/time profiles extracted from the aver-
aged spectra. Fig. 5a shows the result from a single experiment
from the set near the mid point of the temperature range.
Fig. 5b shows the concentration/time profile obtained from the
average of the five mass spectra from this set. Clearly, the
scatter is now much reduced particularly at early times, and
this is simply due to the increased S/N and improved peak
shapes.
5
5
5
points are shown in Fig. 6 where they are compared with the
results from the DST/TOF-MS experiments (Table 1), single
1
6,17
pulse shock tube experiments
and the results of the current
theoretical calculations. As is evident in Fig. 6, the ST/
TOF-MS data show strong fall off from kN and a small
pressure dependency over the experimental range similar to
5
that observed with DFE. Furthermore, there is excellent
agreement between the DFST/TOF-MS results obtained from
averaging the mass spectra of several, near identical experi-
ments and the DST/TOF-MS results.
The present QCISD(T)/CBS//QCISD(T)/cc-pvtz predic-
tions for the classical dissociation barrier and dissociation
ꢀ
1
energy are 63.1 and 15.8 kcal mol , respectively. With
QCISD(T)/cc-pvtz zero point corrections, these values are
ꢀ1
revised to 58.4 and 10.8 kcal mol , respectively. The Q1
4
3
The rate coefficients derived from Fig. 5a and b and the
results from averaged spectra at the low and high temperature
diagnostic is 0.022 or lower for each of the stationary points
considered here. The low value of this diagnostic suggests that
6
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Table 1 Experimental conditions and the corresponding rate coeffi-
cients for the thermal unimolecular dissociation of fluoroethane
ꢀ
k/s
1
P
5
/Torr
T
5
/K
1
1
1
1
1
1
1
1
5
5
6
6
6
6
5
4
5
5
5
6
3
5
6
6
6
4
448
543
273
110
153
326
262
176
94
15
14
04
09
40
39
47
70
78
63
78
96
08
08
01
47
83
1551
1409
1269
1514
1207
1377
1435
1491
1381
1282
1248
1330
1495
1491
1490
1254
1435
1370
1278
1556
1354
1496
1410
1303
1560
1288
14 400
6599
1005
13 520
511
6399
9183
9993
3633
862
776
1791
10 540
11 100
8764
514
6326
2980
722
12 760
1331
11 870
3057
1606
14 106
1230
Fig. 6 Arrhenius plot of the ST/TOF-MS results and comparison
with the shock tube literature data and the results of the master
equation calculations. (a) shows the complete range and (b) is an
17
expanded view of the current work. n Cadman et al.; & Okada
16
et al.; DST experiments: m 500 Torr; K 1200 Torr. DFST experi-
ments, 500 Torr: c single experiment; % average of five mass spectra;
Master Equation results: dashed line 500 Torr; dotted line 1200 Torr;
N
solid line k .
there is little multireference character to the wavefunction at
any of the stationary points in this dissociation. Thus, these
QCISDT(T)/CBS predictions should be quite accurate, i.e.,
Fig. 7 Comparison of the experimental literature data for FE dis-
17
ꢀ1
with uncertainties of 1–2 kcal mol
HF elimination from FE has been the subject of a few prior
.
sociation and the VTST calculation of k . n Cadman et al.;
N
15
,
14
Sianesi et al.; m Dastoor and Emovoon; . Day and Trotman-
9
,44–49
1
2
13
Dickenson; J Kerr and Timlin; & Okada et al. Solid line
16
theoretical studies,
although by current standards, none
ꢀ1
ꢀ1
have been at a particularly high level. The highest level previous
calculations are the CCSD(T)/6-311++G(d,p) calculations of
E = 59.4 kcal mol ; dashed line E = 58.4 kcal mol .
0
0
4
Hase and coworkers. Their prediction of a zero point cor-
9
ꢀ1
Raising the barrier by 1 kcal mol yields predictions that are
in quantitative agreement with almost all of the experimental
ꢀ
1
rected reverse reaction barrier of 51.62 kcal mol is substan-
ꢀ
1
.
15
results. The data of Dastoor et al. are clearly discordant with
tially larger than the present prediction of 47.6 kcal mol
The present ab initio VTST predictions for the high pressure
1
7
the other experimental data, while the data of Cadman et al.
limit of the dissociation rate constant are illustrated in Fig. 7
1
are likely not in the high pressure limit. Such a revision of the
barrier height is well within the uncertainties of the quantum
chemical predictions, although we should note that the dis-
crepancies may also be indicative of other errors in the
calculations such as the limited treatments of anharmonic
and tunneling effects. The above considerations are also in
2–16
together with the available experimental data.
The pre-
dicted rate exceeds the experimental results for all tempera-
tures, but especially at the lowest temperatures where the
discrepancy is about a factor of 2. This suggests that there
may be some modest error in the calculated barrier height.
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ꢀ
1 9
accord with a slightly higher DHf,298 = ꢀ66.5 kcal mol
TFE displays apparent non-RRKM behavior and no further
conclusions regarding the source of this can be drawn from the
current work Vibrational relaxation is very fast in DFE and
FE and using ST/LS double relaxation and incubation can be
observed in TFE and ethane, although the incubation periods
are much shorter in ethane than TFE.
ꢀ1 8
than the literature values of ꢀ65.8 kcal mol
and ꢀ65.1 kcal
ꢀ
1
10
mol for FE. The small change in DH
has negligible
effect on the extracted rate coefficients and calculated reaction
f,298
conditions.
The theoretical predictions for the pressure dependent rate
coefficients illustrated in Fig. 6 were obtained from master
equation simulations. The illustrated results employed an
average energy transfer per downward collision, hDEidown, of
Acknowledgements
n
ꢀ1
1
50 (T/298) cm , with n = 0.4. This value for n, which
This work was supported by the Office of Basic Energy
Sciences, Division of Chemical Sciences, Geosciences, and
Biosciences, US Department of Energy, under contract DE-
AC02-06CH11357 (Argonne) and DE-FE85ER13384 (UIC).
ꢀ1
correlates with a hDEidown of 280 cm at 1400 K, yields good
agreement with experiment. A value of 0.9 for n, or hDEidown
ꢀ1
40
at 1400 K, is more typical, but yields an
of 600 cm
overprediction of the experimental data by about 70%. The
somewhat smaller than normal value for hDEi
is necessary
down
to capture the curvature of the data.
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