Kinetics and mechanism of the reaction of fluorine atoms with trifluoroacetic acid

Article abstract of DOI:10.1016/j.cplett.2011.07.023

The kinetics of the reaction between fluorine atoms and trifluoroacetic acid has been studied experimentally at T = 258-343 K. The overall reaction rate constant decreases with temperature: k₁(T) = 1.09 × 10 ^-12 exp((+1034 K)/T) cm³ molecule^-1 s ^-1. The potential energy surface of the reaction has been studied using quantum chemistry. The results were used in transition state theory calculations of the temperature dependences of the rate constants of the two channels of the reaction. The abstraction channel ultimately producing HF is dominant at the experimental temperatures; the addition-elimination channel producing CF₃ and CF(O)OH becomes important above 1000 K.

Full text of DOI:10.1016/j.cplett.2011.07.023

Chemical Physics Letters 512 (2011) 172–177
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Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
Kinetics and mechanism of the reaction of fluorine atoms with trifluoroacetic acid
a
a,
E.S. Vasiliev a, V.D. Knyazev b, , E.S. Savelieva , I.I. Morozov
⇑
⇑
a Semenov Institute of Chemical Physics RAS, 4 Kosygin St., 119991 Moscow, Russia
b Department of Chemistry, The Catholic University of America, Washington, DC 20064, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
The kinetics of the reaction between fluorine atoms and trifluoroacetic acid has been studied experimen-
tally at T = 258–343 K. The overall reaction rate constant decreases with temperature: k1(T) = 1.09 ꢀ 10ꢁ12
exp((+1034 K)/T) cm3 moleculeꢁ1 sꢁ1. The potential energy surface of the reaction has been studied using
quantum chemistry. The results were used in transition state theory calculations of the temperature
dependences of the rate constants of the two channels of the reaction. The abstraction channel ultimately
producing HF is dominant at the experimental temperatures; the addition–elimination channel producing
CF3 and CF(O)OH becomes important above 1000 K.
Received 28 June 2011
In final form 6 July 2011
Available online 13 July 2011
Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction
the reaction channel 1a to temperatures outside the experimental
range and to predict the rate constants of channel 1b as a function
Trifluoroacetic acid (CF3C(O)OH, TFA) is a molecule of signifi-
cant environmental interest and concern (e.g., [1,2]). It has been
found in substantial amounts in aqueous environments and in
the Earth’s atmosphere, with a fraction of its abundance attributed
to anthropogenic origins [3,4]. Very little is known about the reac-
tivity of TFA in the gas phase, with only a few reactions studied
experimentally [5–8]. In the current study, we report the results
of our experimental and computational study of the kinetics and
mechanism of the reaction of TFA with fluorine atoms:
of temperature.
2. Experimental study and results
The experimental setup and methodology of relative rates
kinetic experiments have been described in detail before [9]; thus,
only a brief description is given here. The experiments were
performed in a discharge flow reactor, 5 cm long and 2.3 cm i.d.,
coupled to a molecular beam electron impact quadrupole mass
spectrometer. Fluorine atoms were produced in a microwave
discharge in a F2/He mixture in a side arm of the reactor located
40 cm upstream from the mass spectrometer sampling inlet. The
discharge zone contained an alumina insert to minimize produc-
tion of oxygen atoms (due to the reaction of fluorine with the wall)
in the discharge. The central inlet of the reactor (1.7 cm i.d., 20 cm
upstream from the mass spectrometer sampling inlet) was used to
supply flows of the reactants, CF3C(O)OH and the reference com-
pound, diluted in the carrier gas, helium, in varying concentrations.
A typical flow velocity inside the reactor was 1.6 m sꢁ1 and the
reactor pressure was 0.80 Torr.
The concentrations of the reactants and products in the reactor
detection zone were monitored using a molecular beam mass spec-
trometer. The molecular beam was formed by the nozzle and a
skimmer; a modulating chopper was located between the skimmer
and the electron impact ion source. Electron impact energy of
70 eV was used. The following gases were used: helium
(99.996%), trifluoroacetic acid (99.5%, Fluka), chloroform (99.9%,
Sigma–Aldrich), 1,1,1-trichloroethane (99%, Sigma–Aldrich), fluo-
rine (99.9%, 5% mixture in helium, Merck AG).
F þ CF3CðOÞOH ! HF þ CF3CðOÞOÅ
ð1aÞ
ð1bÞ
! CF3CFðOÅÞOH ! CF3 þ CFðOÞOH
Å
Reaction (1) has been studied before at room temperature by
Wallington and Hurley [5]. These authors used the relative rates
technique with methane and deuterated methane as the reference
compounds to determine the overall rate constant of reaction (1) at
the temperature of 295 K: k1(295 K) = (5.6 1.8) ꢀ 10ꢁ11 cm3
moleculeꢁ1 sꢁ1, where error limits include experimental and
relative-rate uncertainties. The current study focused on the
temperature dependence of the rate constant of reaction (1) in
the 258–343 K temperature range. The relative rates technique
based on mass spectrometric detection of the reactants was used.
The potential energy surface of reaction (1) was studied using
quantum chemical methods and the competition between the
two possible channels (1a and 1b) was analyzed. Transition state
theory modeling was used to extrapolate the rate constants of
⇑
Corresponding authors. Fax: +7 495 137 83 18 (I.I. Morozov).
E-mail addresses: knyazev@cua.edu (V.D. Knyazev), morozov@chph.ras.ru (I.I.
Standard relative rate procedures were employed. Mixtures of
TFA and reference compounds in varying concentrations diluted
Morozov).
0009-2614/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2011.07.023

E.S. Vasiliev et al. / Chemical Physics Letters 512 (2011) 172–177
173
in the excess of helium carrier gas were supplied through the
central injector. The extent of depletion of TFA relative to that of
the reference compound (REF) was monitored and rate constant
ratios, k1/kREF, were determined using the following equation:
k1
lnð½TFAꢂ0=½TFAꢂÞ
¼
ðIÞ
kREF lnð½REFꢂ0=½REFꢂÞ
The mass spectrum of TFA has the base peak at m/z = 45 (attrib-
uted to the C(O)OH+ ion). The molecular ion peak is very weak, only
2.7% relative to the base peak. The spectrum is in qualitative, if not
quantitative agreement with the two database spectra obtained
from the NIST Mass Spectral database [10] and from [11]. A com-
parison between these mass spectra is provided in the Supplemen-
tary material, where mass spectra of other compounds used are
also given. Because of the weakness of the molecular ion peak, it
was not possible to use it for monitoring the concentration of
TFA. Instead, the m/z = 45 base peak was used for this purpose.
The products of the reaction channel 1a (HF + CF3C(O)O) cannot
provide any contribution to this mass. The products of the other
possible channel of reaction (1), channel 1b, potentially, can con-
tribute to the m/z = 45 peak. However, as is shown below, the
branching fraction of channel 1b is negligible under the conditions
of the experiments performed in the current study. Therefore, the
observed mass peak at m/z = 45 can be fully attributed to TFA only.
The choice of the reference compounds to be used in kinetics
measurements is guided by three considerations. First, both the
reference compound and the products of its reaction with atomic
fluorine should have mass spectra that do not interfere with the
mass peak used for the detection of TFA. Second, rate constant of
the reaction between F atoms and the reference compound should
be reasonably close in value to that of the reaction under study,
reaction (1). If the second requirement is not satisfied, then the
accuracy of the relative rate measurement suffers. Ideally, the most
favorable signal-to-noise ratio is obtained under the conditions
where both the [TFA]0/[TFA] and the [REF]0/[REF] ratios signifi-
cantly differ from unity but are not too large, roughly in the 1.2–
10 range. If the rate constants of the reference reaction and that
of the reaction under study differ by an order of magnitude or
more, it becomes difficult to find the optimal experimental condi-
tions and even more difficult to vary the extent of reaction ratios
while still staying in the good signal-to-noise ratio range. And
finally, the third requirement is that the rate constant of the refer-
ence reaction has to be known at the temperature of interest.
The first reference compound used in the experiments was
chloroform, CHCl3. The kinetics of the reaction between fluorine
atoms and chloroform
Figure 1. Dependences of the extents of depletion of TFA relative on those of the
reference compounds (REF) obtained in room-temperature experiments. The ratios
of the rate constants k1/kREF were obtained from the slopes of the fitted straight
lines (reaction (1)).
to 6.19 ꢀ 10ꢁ12 cm3 moleculeꢁ1 sꢁ1. Using the latest direct determi-
nation of Louis and Sawerysyn [14], k2 = (2.67 0.20) ꢀ 10ꢁ12 cm3
moleculeꢁ1 sꢁ1, one obtains the value of k1 = (3.90 0.83)ꢀ10ꢁ11
cm3 moleculeꢁ1 sꢁ1. On the other hand, combining the above k1/k2
value with that of k2 = (5.4 1.5) ꢀ 10ꢁ12 cm3 moleculeꢁ1 sꢁ1 deter-
mined by Catoire et al. [17] in relative rate measurements results in
k1 = (7.9 3.3) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1. These two values of k1
bracket the room-temperature determination of Hurley and Wal-
lington ((5.6 1.8) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1), and uncertainties
overlap (see inset in Figure 2).
F þ CHCl3 ! HF þ CCl3
ð2Þ
has been studied by several groups, using both direct [12–14] and
relative rate [15–17] methods. The mass spectra of chloroform
and CCl3 do not have any peaks at m/z = 45 and thus do not interfere
with the signal of TFA. Due to the weakness of the molecular ion
peak, the base peak at m/z = 83 (CHCl2+) was used to monitor the
concentration of CHCl3.
During the experiments, the ratio of the flows of TFA and the
reference compound was varied and the resulting changes in the
[TFA]0/[TFA] and [REF]0/[REF] ratios were recorded. The results
obtained at the room temperature (295 K) are presented in Figure
1a. The slope of the fitted straight line yields the k1/k2 ratio of
The uncertainty in the value of the reference reaction (2) rate
constant and the large, far from optimum value of k1/k2 motivated
a search for more suitable reference reactions. The second reference
reaction used was that of fluorine atom with 1,1,1-trichloroethane:
F þ CH3CCl3 ! HF þ CH2CCl3
ð3Þ
14.6 2.0 (2
r
). This relatively large ratio results in significant differ-
The rate constant of this reaction at 295 K has been determined
by Platz et al. [18] as k3 = (6.79 1.49) ꢀ 10ꢁ12 cm3 moleculeꢁ1 sꢁ1
in relative rates experiments. The mass spectrum of 1,1,1-trichlo-
roethane has the base peak at m/z = 97 (CH3CCl2+) and the intensity
of the molecular ion peak is less that 0.1% of that of the base peak.
No peaks at m/z = 45 (used to detect TFA) are present in the mass
ences between the measured extents of reactions, as can be seen
from the plot in Figure 1a, thus putting many of the measurements
outside the optimal range of conditions (see above). The room-
temperature rate constant of the reference reaction has been re-
ported by five groups, with the values ranging from 1.69 ꢀ 10ꢁ12

174
E.S. Vasiliev et al. / Chemical Physics Letters 512 (2011) 172–177
experiments performed in the current work, the concentration of
HNO3 was monitored using the molecular ion at m/z = 63, where
neither TFA nor products of reaction (1) provide any contribution.
The results of the room-temperature relative rates experiment
performed using reaction (4) as reference are presented in Figure
1c. The obtained value of k1/k4 = 1.57 0.30, combined with the va-
lue of k4(295 K) = (2.33 0.35) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1 ob-
tained from the Arrhenius expression and quoted 15% absolute
uncertainty of [21], results in the room temperature rate constant
of reaction (1) k1(295 K) = (3.66 0.91) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1
.
Reaction (4) was used as the reference reaction in experiments
performed at temperatures below and above ambient, T = 258–
343 K. The results are presented in Figure 2 and in Table 1. Two
sets of error bars are given for the data points on the Arrhenius
plot. The smaller, wider-cap error bars represent the uncertainties
of the current experimental relative-rates study (2r). The larger,
narrow-cap error bars show the overall uncertainties of k1 deter-
minations, which include the 15% uncertainties for the rate con-
stants of the reference reaction (4) reported by Wine et al. [21].
As can be seen from the plot, k1 shows noticeable negative temper-
ature dependence, which can be expressed with the following
equation:
Figure 2. Main plot: the experimental (circles, rate constants obtained using
reaction (4) as the reference reaction) and the calculated (lines) k1(T) dependences.
Dashed line – Model 1 (fitted energy barrier); dotted line – Model 2 (fitted energy
barrier and four lowest vibrational frequencies of transition state TS1). Inset: room
temperature values of k1 obtained from the results of [5] (open symbols) and those
of the current study (filled symbols) using different reference reactions. Axes of the
plot have the same meanings as in the main plot. Open square, k1 from [5], as
reported; open circle, k1 recalculated using data from [5] and k6 from [38]; filled
squares, two values of k1 obtained using reaction (2) as reference, with different k2
values (see text); filled diamond, reaction (3) used as reference; filled circle,
reaction (4) used as reference. The data points corresponding to T = 295 K are
shifted relative to each other along the 1000 K/T axis to avoid overlap.
k1ðTÞ ¼ ð1:09 ꢃ 0:38Þ ꢀ 10ꢁ12 expðþð1034
ꢃ 101 KÞ=TÞcm3moleculeꢁ1sꢁ1
ðIIÞ
Table 1
Conditions and results of the experiments to determine k1.
spectra of either CH3CCl3 or CH2CCl3. However, a small peak (2.8%
of the base m/z = 45 peak) at m/z = 97 is present in the mass spec-
trum of TFA. Thus, the results of measurements of the concentra-
tions of CH3CCl3 had to be corrected for this minor interference
from TFA.
The results of the relative rate measurements using reaction (3)
as the reference reaction are presented in Figure 1b. The value of
k1/k3 obtained is 8.40 0.60 (2r). Combining this value with the
rate constant of the reference reaction, one obtains
k1 = (5.70 1.66) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1, in agreement with
the value of [5]. The value of k1/kREF is still not optimal for the best
signal-to-noise ration, and the temperature dependence of k3 is un-
known. Therefore, a third reference reaction had to be selected for
the study of the kinetics of reaction (1) at temperatures other than
ambient.
c
d
e
T/K [TFA]a
[REF]b
k1/kREF
kREF
k1
Reaction (2) used as referencef
295 35–80
295 35–80
12.4–
19.9
12.4–
19.9
14.6 2.0
14.6 2.0
0.267 0.020g 3.90 0.53
( 0.83)
0.540 0.150h 7.88 1.08
( 3.27)
Reaction (3) used as referencef
295 4.0–18 6.2–9.7
8.40 0.60 0.679 0.149i
5.70 0.41
( 1.66)
Reaction (4) used as referencej
258 0.11–
0.9
268 0.22–
1.0
273 0.56–
3.0
296 0.56–
1.7
313 0.67–
3.8
333 0.34–
1.6
343 0.78–
4.4
3.5–5.2
3.4–4.7
4.9–14.6
19.6–48
4.1–5.8
2.19 0.97
1.97 0.25
1.75 0.56
1.57 0.16
1.29 0.17
1.25 0.35
1.14 0.37
2.83 0.42k
2.67 0.40
2.59 0.39
2.33 0.35
2.15 0.32
2.00 0.30
2.00 0.30
6.19 2.73
( 3.66)
5.26 0.67
( 1.46)
4.54 1.45
( 2.13)
3.66 0.36
( 0.91)
2.77 0.37
( 0.79)
2.49 0.69
( 1.07)
2.27 0.74
( 1.08)
The third reference reaction used in the current work is that of
fluorine atoms with gaseous nitric acid:
10.9–
19.6
12–16.3
F þ HNO3 ! Products
ð4Þ
The room temperature kinetics of this reaction has been studied
experimentally by four groups [19–22], with reasonable agreement
on the value of the rate constant (2.1–2.7) ꢀ 10ꢁ11 cm3 mole-
culeꢁ1 sꢁ1. The temperature dependence of the k4 has been deter-
mined by Wine et al. [21] in the temperature range of 260–
373 K. The values of the rate constant decrease with increasing
temperature in the 260–320 K range but stay independent of tem-
perature above 330 K. The authors of [21] attributed this complex
temperature dependence to changing relative importance of two
channels of reaction (4), with abstraction of an H atom dominating
at low temperatures and substitution channel(s) being more
important at higher temperatures. The expected products of all
possible channels of reaction (4) include HF, NO3, OH, FNO2, FNO,
and HO2. None of these compounds interfere with mass spectro-
metric monitoring of the concentration of TFA at m/z = 45. In the
Concentrations of CF3C(O)OH in units of 1012 molecule cmꢁ3
.
a
b
c
Concentrations of reference compounds in units of 1012 molecule cmꢁ3
The error limits are given as twice the standard error of the fit.
.
In units of 10ꢁ11 cm3 moleculeꢁ1 sꢁ1
.
d
e
In units of 10ꢁ11 cm3 moleculeꢁ1 sꢁ1. Error limits given without parentheses are
derived from the uncertainties in k1kREF. Error limits given in parentheses include
the uncertainties in the rate constant of the reference reaction as a systematic
contribution [40].
Concentrations of fluorine atoms were in the (4–6) ꢀ 1013 atom cmꢁ3 range, as
f
determined from the measured molecular fluorine flows and the percentage of
dissociation of F2 in the microwave discharge.
g
[14].
[17].
[18].
h
i
Concentrations of fluorine atoms were in the (2–11) ꢀ 1012 atom cmꢁ3 range.
j
k
[21].

E.S. Vasiliev et al. / Chemical Physics Letters 512 (2011) 172–177
175
Here, the quoted uncertainties of the preexponential factor and
the activation energy are given as twice the standard error if the fit
and bear no physical meaning. The inset in Figure 2 shows the
room-temperature determinations of the rate constant, including
the two values resulting from the study of Wallington and Hurley
[5] (see below, in the Section 4). The data points corresponding to
T = 295 K are shifted relative to each other along the 1000 K/T axis
to avoid overlap.
3. Potential energy surface andtransition state theory model of
reaction (1)
The potential energy surface (PES) of reaction (1) was studied
using quantum chemical methods. Optimization of molecular
structures and calculation of vibrational frequencies were per-
formed using the density functional BH&HLYP [23,24] method
and single-point CCSD(T) [25,26] energies were calculated for PES
stationary points. The aug-cc-pVDZ [27] basis set was used in all
calculations. The GAUSSIAN 03 program [28] was used in all potential
energy surface (PES) calculations. The version of the BH&HLYP
functional implemented in GAUSSIAN 03 was used which, as de-
scribed in the GAUSSIAN manual, is different from that of [23]. Energy
values quoted in the text henceforth are given as X/Y, where the
first value is obtained in CCSD(T) and the second – in BH&HLYP cal-
culations and include vibrational zero point energies unless stated
otherwise. The results of the PES study are summarized in Table 2
and Figure 3 and the detailed information is given in the Supple-
mentary material.
The mechanism of reaction (1) involves two different reaction
paths, those of H atom abstraction (1a) and addition to the car-
bon atom of the carbonyl followed by a decomposition of the
vibrationally excited CF3CF(O)OH adduct into CF3 and CF(O)
OH (1b). The reaction path of channel 1a has a weakly bound
CF3C(O)OHꢄꢄꢄF complex on the reactants side (ꢁ17.6/ꢁ21.5
kJ molꢁ1, denoted vdW1 in Figure 3), followed by an energy bar-
rier. Both the BH&HLYP and the CCSD(T) calculations give ener-
gies of the barrier that are below the energy of the reactants.
However, the barrier is substantial at the BH&HLYP level
(13.3 kJ molꢁ1 relative to the complex and ꢁ4.3 kJ molꢁ1 relative
to the reactants, TS1 in Figure 3) but practically disappears at
Figure 3. Potential energy surface of reaction (1) obtained in quantum chemical
calculations (see text and Table 2). Solid lines – CCSD(T)/aug-cc-pdz//BH&HLYP/
aug-cc-pdz energies, dashed lines – BH&HLYP/aug-cc-pdz energies. The dotted line
indicates the recommended fitted value of the TS1 energy barrier obtained in
modeling of the experimental data.
the CCSD(T) level (8.8 kJ molꢁ1 relative to the complex without
ZPE but ꢁ2.5 kJ molꢁ1 when ZPE is included). The products of
channel 1a, HF + CF3C(O)O, also form a weakly bound complex,
ꢁ15.4/ꢁ16.1 kJ molꢁ1 relative to the separated products (vdW2
in Figure 3). Reaction channel 1a can be expected to be followed
by a rapid decomposition of the CF3C(O)O radical to CF3 + CO2;
the energy barrier to this decomposition is only 3.5/21.7 kJ
molꢁ1
:
CF3CðOÞOÅ ! CFÅ þ CO2
ð5Þ
3
Addition to the carbon atoms of the carbonyl bond channel has
a barrier of 21.8/8.7 kJ molꢁ1 (TS2 in Figure 3). Addition to the oxy-
gen atom of the carbonyl bond does not occur: any attempt to opti-
mize the structure of the expected adduct results in convergence to
the CF3C(O)OHꢄꢄꢄF complex. The CF3CF(O)OH adduct formed in the
initial step of channel 1b is highly vibrationally excited (95/
109 kJ molꢁ1) and is expected to decompose to CF3 + CF(O)OH via
a 36.1/52.1 kJ molꢁ1 barrier (TS4 in Figure 3).
In an attempt to provide means for an extrapolation of the
experimental k1(T) dependence to temperatures outside the
experimental range, and to estimate the contribution of the reac-
tion channel 1b to the overall reaction, an RRKM / transition state
theory model of reaction (1) was created in the current work.
Molecular structure and vibrational frequencies of the saddle
point obtained in the BH&HLYP/aug-cc-pvdz calculations were
used. Energy and frequencies of the transition state for the reac-
tion channel 1a were adjusted to reproduce the experimental
k1(T) dependence in a procedure described below. For channel
1b, transition state theory [29] calculations using the CCSD(T)-
level barrier energy were performed. Contribution of this channel
to the overall reaction is negligible at the temperatures of the
experiments but becomes important at higher temperatures.
Modeling of channel 1a was performed under the assumption
that most of the trajectories sampling the coordinate space of the
CF3C(O)OHꢄꢄꢄF complex and having energies above that of the reac-
tants proceed back to F + CF3C(O)OH and only a small fraction
passes through the PES saddle point and leads to the HF + CF3C(O)O
products. Thus, the saddle point was assumed to represent the dy-
namic bottleneck of the reaction. This is a reasonable assumption
given the fact that the decomposition of the CF3C(O)OHꢄꢄꢄF complex
back to the reactants is expected to have a transition state that is
significantly ‘looser’ and thus has larger density of states than that
of the CF3CðOÞOH ꢄ ꢄ ꢄ F ! HF þ CF3CðOÞO route.
Table 2
Energies of reactants, products, and stationary points on the PES of reaction (1)
obtained in quantum chemical calculations.a
Species
Method
b
BH&HLYP
CCSD(T)c
Modelingd
Channel 1a
CF3C(O)OHꢄꢄꢄF complex (vdW1)
CF3C(O)OꢄꢄꢄHꢄꢄꢄF (TS1)
CF3C(O)OꢄꢄꢄHF complex (vdW2)
HF + CF3C(O)O
ꢁ17.6
ꢁ4.3
ꢁ21.5
ꢁ24.0
ꢁ94.4
ꢁ79.0
ꢁ75.5
ꢁ169.4
–
ꢁ11.6 (ꢁ18.8)
ꢁ82.6
ꢁ66.5
ꢁ44.8
ꢁ152.1
–
–
–
–
HF + CF3ꢄꢄꢄC(O)O (TS3)
HF + CF3 + C(O)O
Channel 1b
CF3C(ꢄꢄꢄF)(O)OH (TS2)
21.8
ꢁ87.0
8.7
ꢁ86.0
–
–
–
–
CF3CF(O)OH
CF3ꢄꢄꢄCF(O)OH (TS4)
CF3 + CF(O)OH
ꢁ34.9
ꢁ49.0
ꢁ106.3
ꢁ102.7
a
Energy values are given in kJ molꢁ1 relative to F + CF3C(O)OH and include zero-
point vibrational energy (ZPE).
b
Optimized in BH&HLYP/aug-cc-pvdz calculations.
CCSD(T)/aug-cc-pvdz single point energies using BH&HLYP/aug-cc-pvdz
c
optimization.
d
Results of fitting the experimental data with Models 1 and 2 (the latter in
parenthesis).

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E.S. Vasiliev et al. / Chemical Physics Letters 512 (2011) 172–177
k1b ¼4:54 ꢀ 10ꢁ18T1:74 expðꢁ663 K=TÞcm3 moleculeꢁ1 sꢁ1
ð200—2000 KÞ
Rate constant values were calculated using the equation:
ꢀ
ꢁ
Z
QztransðTÞQzinactðTÞ
E ꢁ E0
1
ðVIÞ
kðTÞ ¼
WzðE ꢁ E1Þ exp
ꢁ
dE
ðIIIÞ
QFðTÞQCF CðOÞOHðTÞ
kBT
E0
The contribution of channel 1b becomes comparable to that of
channel 1a only at temperatures above 1000 K.
3
where QztransðTÞ and QiznactðTÞ are the partition functions of the trans-
lational and the overall 2-dimensional (inactive) rotational degrees
of freedom of the transition state, QF(T) and Q CðOÞOHðTÞ are the
CF3
4. Discussion
partition functions of the F and CF3C(O)OH reactants, Wà(E ꢁ E1)
is the sum-of-states function of the active [30–32] degrees of
freedom of the transition state, E0 and E1 are the energies of the
reactants and the transition state, respectively (E0 > E1), and kB is
the Boltzmann constant. Eq. (III) was obtained in [33] by simplifica-
tion of a formula derived by Mozurkewich and Benson [34] (Eq. (12)
of [34]) for reactions proceeding over shallow potential energy
wells. The simplification resulted from the above mentioned
assumption of predominant dissociation of the CF3C(O)OHꢄꢄꢄF
complexes to F + CF3C(O)OH and from an approximate treatment
of the effects of angular momentum (J) conservation where the rate
constant value obtained for J = 0 is multiplied by the ratio of the
partition functions of the 2-dimensional rotational (inactive) de-
grees of freedom of the transition state and the active molecule.
The latter ratio is close to unity (0.94), which justifies the use of
the approximation. The effective width of the energy barrier
[35,36] (0.931 amu1/2 Å) was obtained by fitting the potential
energy profile resulting from intrinsic reaction coordinate calcula-
tions. However, tunneling has no influence on the calculated rate
constants because k(E) dependences with and without tunneling
differ very little above the energy barrier [36,37] and energies of
the reactive trajectories passing from the CF3C(O)OHꢄꢄꢄF complex
to the products part of the PES are higher than that of the reactants
and thus are always above the energy barrier.
As the divergence of the BH&HLYP and the CCSD(T) results dem-
onstrates, the location of the barrier for channel 1a on the energy
scale is uncertain; thus the optimum value was obtained in fitting
the properties of the model to the experimental k1(T) dependence.
This fitting exercise can be performed in two possible ways: by fix-
ing the vibrational frequencies of the reactants and the transition
state at the BH&HLYP values and optimizing the energy barrier
only, or by optimizing both the energy barrier and the frequencies.
The first approach results in the energy of the transition state equal
to ꢁ11.6 kJ molꢁ1 and the calculated temperature dependence
shown by the dashed line in Figure 2 (denoted as Model 1). The
resultant temperature dependence of the rate constant of reaction
channel 1a can be represented with the following modified Arrhe-
nius expression:
The current study represents the first determination of the tem-
perature dependence of the rate constant of reaction (1). The neg-
ative temperature dependence is consistent with the barrierless
potential energy surface of the initial approach of the fluorine atom
to TFA and the reaction bottleneck located below the energy of the
reactants on the energy scale, as inferred from the quantum chem-
ical part of the study.
The only previous study of reaction (1) is that of Wallington and
Hurley, who used the reaction between the fluorine atom and
methane
F þ CH4 ! HF þ CH3
ð6Þ
as well as the reaction of fluorine atoms with deuterated methane
(with the rate constant derived from that of reaction (6)) as reference
reactions in their room-temperature study. The authors of [5] re-
ported k1(295 K) = (5.6 0.7) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1
,
with
additional 20% uncertainty resulting from that of the values of the
rate constants of the reference reactions. The rate constant of reaction
(6) has been studied by many groups; reviews can be found in [38,39]
and references cited therein. Using the data of [5] and the most recent
recommendation of the IUPAC Subcommittee on Gas Kinetic Data
Evaluation for Atmospheric Chemistry for reaction (6), k6(295 K) =
(6.3 2.2) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1 [38], one obtains a somewhat
lower value of k1 = (5.2 2.5) ꢀ 10ꢁ11 cm3 moleculeꢁ1 sꢁ1, where
large uncertainties reflect those of the rate of reaction (6). Both values
resulting from the relative rates study of Wallington and Hurley are
shown on the inset in Figure 2 with open symbols. The results of
the current study obtained at room temperature using three different
reference reactions ((2)–(4)) are shown on the same plot with filled
symbols. Two data points are entered for the results obtained using
reaction (2) as reference, with different values resulting from using
different values for k2, as described above. As one can see from the
plot, the results of the current study obtained using different refer-
ence reactions are in general agreement with each other and with
those of [5], with difference largely attributable to the uncertainties
in the rates of the reference reactions used. We recommend the data
obtained with reaction (6) used as the reference reaction as it seems
to have the lowest uncertainty associated with its rate constant: the
temperature dependence used here was obtained in direct experi-
mental study of [21] and is in a very good agreement with two other
room-temperature determinations ([19,20]).
k1a ¼6:83 ꢀ 10ꢁ10Tꢁ0:83 expð508 K=TÞcm3 moleculeꢁ1 sꢁ1
ð200—1000 KÞ
ðIVÞ
The calculated dependence lies askew relative to the experi-
mental one but still well within the envelope of uncertainties of
the individual rate constant determinations. The second approach
was implemented by applying a variable multiplier to the original
four lowest vibrational frequencies of the transition state. The
resultant optimized value of the multiplier is 2.5 and the fitted en-
ergy of the transition state is ꢁ18.8 kJ molꢁ1. The corresponding
temperature dependence of the calculated rate constants is shown
in Figure 2 by the dotted line. The resultant 200–1000 K tempera-
ture dependence can be represented with the following modified
Arrhenius expression:
The computational study of reaction (1) was performed in this
work to assess possible reaction pathways and to provide means
for the extrapolation of the k1(T) temperature dependence to out-
side the experimental temperature range. As described above,
two methods of fitting the experimental data with the model result
in the energy barrier values for the reaction channel 1a that differ
by 7.2 kJ molꢁ1. Although Model 1 results in the calculated k1(T)
dependence that lies askew relative to the experimental data on
the Arrhenius plot (Figure 2) and Model 2 was fitted to reproduce
the experimental temperature dependence exactly, the uncertain-
ties of the experimental individual data points do not allow to
meaningfully distinguish the qualities of fit of the two models.
Model 2 involved changing the four lowest vibrational frequencies
of the transition state TS1 by a factor of 2.5; the resultant fre-
quency values are probably less realistic than the original
BH&HLYP based frequencies. Thus, we recommend using the
k1a ¼4:58 ꢀ 10ꢁ3Tꢁ3:32 expðꢁ52 K=TÞcm3 moleculeꢁ1 sꢁ1
ð200—1000 KÞ
ðVÞ
The transition state theory calculations of the rate constant of
reaction channel 1b (addition–decomposition) result in the follow-
ing modified Arrhenius expression:

E.S. Vasiliev et al. / Chemical Physics Letters 512 (2011) 172–177
177
[11] A. Cornu, B. Massot, Compilation of Mass Spectral Data (Heyden 1975).
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In the absence of any experimental data on the rate of the addi-
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the quantum chemistry study performed in this work and transi-
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Acknowledgment
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