Unimolecular rate constant and threshold energy for the HF elimination from chemically activated CF3CHFCF3

Article abstract of DOI:10.1021/jp100195e

Combination of CF₃CHF and CF₃ radicals at room temperature generated chemically activated CF₃CHFCF₃ molecules with 95 ± 3 kcal/mol of internal energy that decompose by loss of HF, initially attached to adjacent carbons, with an experimental unimolecular rate constant of (4.5 ± 1.1) x 10² s^-1. Density functional theory was used to model the unimolecular rate constant for HF elimination, k_HF, to determine a threshold energy of 75 ± 2 kcal/mol.

Full text of DOI:10.1021/jp100195e

6996
J. Phys. Chem. A 2010, 114, 6996–7002
Unimolecular Rate Constant and Threshold Energy for the HF Elimination from
Chemically Activated CF3CHFCF3
Juliana R. Duncan, Michael S. Roach, Brooke Sibila Stiles, and Bert E. Holmes*
Department of Chemistry, UniVersity of North Carolina at AsheVille, One UniVersity Heights,
AsheVille, North Carolina 28804-8511
ReceiVed: January 8, 2010; ReVised Manuscript ReceiVed: May 18, 2010
Combination of CF3CHF and CF3 radicals at room temperature generated chemically activated CF3CHFCF3
molecules with 95 ( 3 kcal/mol of internal energy that decompose by loss of HF, initially attached to adjacent
carbons, with an experimental unimolecular rate constant of (4.5 ( 1.1) × 102 s-1. Density functional theory
was used to model the unimolecular rate constant for HF elimination, kHF, to determine a threshold energy of
75 ( 2 kcal/mol.
1. Introduction
A theoretical investigation at the QCISD(T) level recom-
mended28 E0 ) 79.2 kcal/mol, but five different levels of theory
predicted an E0 in the range 82.3-89.1 kcal/mol and B3LYP
with 6-31G(d) gave a barrier of 75.4 kcal/mol. The E0 is
typically two or three kcal/mol lower than Ea at high temper-
ature; thus, the theoretical work suggested an activation energy
between 75 and 90 kcal/mol. The flame profile modeling
studies1,26 agreed that unimolecular elimination of HF from
CF3CHFCF3 is an important step in the complex reaction
chemistry of inhibited flames and, because a precise threshold
energy is essential to accurately model the combustion system,
an experimental investigation of the 1,2-HF elimination reaction
from CF3CHFCF3 seems warranted.
The reactions of CF3CHFCF3 in the gas phase are of great
interest because CF3CHFCF3 is used as a fire suppressant in
place of Halon 1301, CF3Br;1–6 as a working fluid in refrigeration
and air conditioning applications;7–9 as a foam blowing agent
with fire retardant capabilities;10 and as a propellant in medical
sprays.11–13 Modeling studies of low-pressure and atmospheric
pressure combustion rely upon accurate kinetic data for the
unimolecular decomposition of CF3CHFCF3 and its bimolecular
reactions with OH radicals and other reactive species. Experi-
mental and computational studies14–26 of the product profile for
combustion of CF3CHFCF3 and of the reactions between
CF3CHFCF3 and OH radicals or atomic species (F, Cl, H, O,
etc) have appeared.
We will measure the unimolecular rate constant for HF loss
from CF3CHFCF3 chemically activated by the combination of
CF3 and CHFCF3 radicals. The average energy, 〈E〉, of the
chemically activated CF3CHFCF3 is estimated as 95 kcal/mol
from the CF3CHF-CF3 bond dissociation energy, D0(CF3CHF-
CF3), plus the average thermal energy of the combining radicals.
The RRKM theory29 will be used to calculate the rate constant
for HF elimination from CF3CHFCF3, with an energy equal to
〈E〉, and the threshold energy, E0, will be varied until the
computed unimolecular rate constant matches the experimental
result. Input parameters needed for the RRKM computation of
the rate constant (vibrational frequencies and moments of inertia)
will be calculated with density functional theory (DFT) using
the Gaussian03 suite30 of programs. A systematic study31 of DFT
and ab initio methods for the 1,2-HF (DF) elimination from
CF3CH3 (CF3CD3) determined that B3LYP or B3PW91 together
with either a 6-31G(d′,p′) or a cc-PVDZ basis set gave the best
agreement between computed and experimental rate constants
and the kinetic isotope effect. In our recent work,32–34 DFT using
the B3PW91 method with a 6-31G(d′,p′) or a 6-311+G(2d,p)
basis set was found to give close agreement between the
computed and experimental assigned E0(HF) for nine halopro-
panes and one halobutane.
A shock tube pyrolysis26 of CF3CHFCF3 over the temperature
range 1200-1500 K concluded that thermal decomposition
dominated the removal processes of CF3CHFCF3 and that HF
elimination predominates over C-C bond fission. They modeled
the combustion profile using an assumed Arrhenius activation
energy, Ea, for 1,2-HF loss of 69.6 kcal/mol. The Ea was
estimated by adding 38.8 kcal/mol to the enthalpy change for
the HF elimination reaction and corresponds to a threshold
energy, E0(HF), of 67.4 kcal/mol; the A-factor was assumed to
be 7.9 × 1012 s-1. A modeling study1 using laser-induced
fluorescence detection of radical species in the CF3CHFCF3
inhibited CH4 + O2 flame agreed that unimolecular HF
decomposition was dominant, but concluded that C-C bond
rupture was increasingly important as the flame temperature
increased, and it appeared that the same Arrhenius parameters
were used as the earlier26 work. A very recent thermal
decomposition investigation19b using UV photoelectron detection
also found that 1,2-HF elimination was favored but suggested
that formation of HCF3 + CF2dCF2, rather than C-C bond
rupture, became more important at higher temperatures. A
modeling study of the product profile from the reaction between
CF3CHFCF3 and either atomic hydrogen or O(3P) used Ea )
69.5 kcal/mol23 for HF elimination, but a similar approach27
for the inhibition by CF3CHFCF3 on shock heated ethane-
oxygen-argon mixtures used Ea ) 75.6 kcal/mol.
There are three main sources of uncertainty in matching the
computed rate constant to the experimental measurement to
determine the E0 for HF elimination: (1) The enthalpy of
formation for CF3CHFCF3, the CF3CHF radical, and the CF3
radical are used to determine D0(CF3CHF-CF3). The experi-
mental uncertainty in thermochemistry for these fluorocarbon
species is often (1-2 kcal/mol leading to an uncertainty of
* To whom correspondence should be addressed. E-mail: bholmes@
unca.edu.
10.1021/jp100195e  2010 American Chemical Society
Published on Web 06/10/2010

HF Elimination from Chemically Activated CF3CHFCF3
J. Phys. Chem. A, Vol. 114, No. 26, 2010 6997
(2-4 kcal/mol for the 〈E〉. This uncertainty will be represented
as the horizontal edges of a box in Figure 2. (2) There is some
error in measuring the experimental rate constant, but this is
frequently less than the uncertainty associated with the colli-
sional deactivation mechanism. This uncertainty will be repre-
sented by the height of a box in Figure 2. (3) The electronic
structure calculations give vibrational frequencies and moments
of inertia for the molecule and the transition state that are needed
to evaluate the rate constant, kE, at a specific energy E according
to the RRKM formulation. In Section 3.3 we will demonstrate
that different DFT methods and basis sets, for a common E0,
give nearly identical dependence of kE versus E. However, the
two CF3 torsional frequencies can be treated as a vibration,
hindered internal rotor or as a free rotor. The sums and densities
of states can be sensitive to the specific model used to describe
the torsional motion, and we will test different models for the
CF3 torsional motion for the effect on kE. The best calculated
rate constants are subject to the assumption inherent in transition
state theory with harmonic counting of states. Any kE curve in
Figure 2 that touches the box illustrating the uncertainty in 〈E〉
and in the experimental rate constant will be criteria for an
acceptable E0. Agreement between the computed and the
experimental rate constants should reduce the wide variation
in the currently published E0 value (67-89 kcal/mol)23,26–28 to
(2 kcal/mol.
which is of the form y ) mx + b (y ) [CF2dCFCF3]/[CF3-
CHFCF3], m ) k1,2-HF/kM, x ) 1/[M], and b ) 0). The
concentration of the collision partner, [M], equals the pressure,
P; thus, a plot of [CF2dCFCF3]/[CF3CHFCF3] versus 1/P would
be linear with a slope of k1,2-HF/kM and an intercept of zero.
2. Experimental Section
Pyrex vessels with volumes ranging from 552 to 4900 mL
containing normally 0.182 µmol of 1-iodo-1,2,2,2-tetrafluoro-
ethane and 0.547 µmol trifluoromethyl iodide, and small
amounts of mercury(I) iodide, were photolyzed with a high-
pressure Oriel 68811 arc lamp operating with a 500 W mercury
lamp. The reaction vessel was placed at least 25 cm from the
Hg lamp to reduce local heating during the photolysis. The
presence of mercury(I) iodide in the vessels during photolysis
aids in formation of the trifluoromethyl and 1,2,2,2-tetrafluo-
roethyl radicals.35 Photolysis times were between 10 and 20 min,
at room temperature, resulting in the conversion of 12-22%
of the reactants. For sample preparation, a pressure of either
1.00 or 3.00 Torr of an iodide was measured in a small,
calibrated vessel with a MKS 270 electronic manometer and
then transferred to the much larger reaction vessel. The total
pressure in the reaction vessel was determined by adding
together the residual pressure prior to addition of the iodides,
typically between (2 and 4) × 10-4 Torr, and the pressure due
to the iodides that had been transferred from the calibrated
vessel. Following addition of the CF3CHFI and CF3I samples
to the reaction vessel the total pressure was between (0.22 and
3.0) × 10-2 Torr.
The chemically activated CF3CHFCF3, denoted with an
asterisk (*), was formed by the combination of CF3CHF and
CF3 radicals, eq 1 and the other radical combination reactions
are 2 and 3.
Product identification was based on comparison of mass
spectral fragmentation patterns and retention times with au-
thentic samples. A Shimadzu QP 5000 GC/MS with a 0.25 mm
by 105 m Rtx-200 column was used for mass analysis, a GC/
MS trace is in Supporting Information. Analytical data were
collected using a 0.53 mm by 210 m Rtx-200 combination
column in a Shimadzu GC-14A with flame ionization detector
and a Shimadzu CR501 Chromatopac Integrator for integration
of peak areas. For an isothermal GC analysis at 35 °C the typical
retention times were as follows: C2F6, 19.4 min; CF2dCFCF3,
20.4 min.; CF3CHFCF3, 21.2 min.; CF3I, 22.1 min, meso- and
d,l-CF3CHFCHFCF3, 26 min and 29 min.; and CF3CHFI, 33
min. Kinetic data were collected using a 210 m GC column to
ensure baseline separation of C2F6, CF2dCFCF3, CF3CHFCF3,
and CF3I. Authentic samples of all products were available
except CF3CHFCHFCF3. The flame ionization detector calibra-
tion factor was [CF2dCFCF3]/[CF3CHFCF3] ) 0.685 ( 0.007
based on four replicates from five different mixtures of authentic
samples.
kc
CF3CHF + CF3
98 CF3CHFCF3*
(1)
kc
2CF3CHF 98 meso- and d, l-CF3CHFCHFCF3* (2)
kc
2CF3
9
8 CF3CF3*
(3)
Photolysis of CF3CHFI and CF3I in pyrex vessels containing
small amounts of mercury(I) iodide (to scavenge atomic
iodine)35 produced the radicals shown in eqs 1-3. Equation 5
shows that chemically activated CF3CHFCF3* may be stabilized
by collision with bath gas molecules, M, mainly the iodide
precursors, or at sufficiently low pressures it may decompose
via 1,2-HF elimination, eq 4. The hexafluoroethane, reaction 3,
and meso- and d,l-CF3CHFCHFCF3, reaction 2, are stabilized
at the pressures of these experiments.
3. Results and Discussions
3.1. Experimental Chemical Activation Rate Constant.
This chemical activation study using CF3CHFI and CF3I to
produce the CF3CHF and CF3 radicals is a clean chemical
activation system with no evidence for secondary unimolecular
reactions and no evidence for disproportionation reactions of
the radicals. A typical GC/MS trace of a photolyzed sample
used to identify products, which is presented in Supporting
Information, shows only products from eq 1-5 were observed.
A plot of [CF2dCFCF3]/[CF3CHFCF3] versus inverse pres-
sure, see eq 6, is in Figure 1 for 29 data points. The pressure
range is smaller than desirable, but we wanted the pressure in
the reaction vessels to be an order of magnitude larger than the
residual pressure; thus, our vacuum system restrictioned the low
pressure limit to 2 × 10-3 Torr which is 1/P ) 500 Torr-1. As
k1,2-HF
CF3CHFCF3*
8 CF2dCFCF3 + HF
(4)
(5)
k [M]8 CF3CHFCF3
M
The rate ratio for eqs 4 and 5 equals the product ratio so we
can write eq 6.
[CF2dCFCF3]/[CF3CHFCF3] ) k1,2-HF/kM[M]
(6)

6998 J. Phys. Chem. A, Vol. 114, No. 26, 2010
Duncan et al.
-371.2 kcal/mol and corrected to 0 K to give ∆H° (CF3-
f,0
CHFCF3) ) -368.0 kcal/mol. The ∆H° for reaction 1 is
rxn,0
-91.3 kcal/mol with a combined uncertainty of (3 kcal/mol.
Peterson and Francisco28 calculated D0(CF3CHF-CF3) ) 92.3,
in good agreement with our 91.3 ( 3 kcal/mol. Inserting these
values into eq 7 gives 95.2 ( 3 kcal/mol, and we will use 〈E〉
) 95 ( 3 kcal/mol. An alternative method to compute 〈E〉 will
be given in Section 3.4.
3.3. Computed Chemical Activation Rate Constant. The
vibrational frequencies and moments of inertia for the molecule
and the transition state, used in the statistical rate constant
calculations, were determined by DFT using Gaussian 03,30 see
Table 1. The two CF3 torsional motions were treated as either
torsion vibrations (TOR), hindered-internal rotors (HIR) or as
free rotors for calculations42 of the harmonic density or sum of
vibrational states. The reaction path degenercies were 4 for the
TOR and 6 for the HIR or free-rotor models. Pitzer’s method
was used to calculate the reduced moments of inertia, shown
in Table 1, for the CF3 group for the molecule and for the
transition state structure; the torsional potential energy barrier
for rotation of a CF3 group, V(CF3), was calculated, using
B3PW91 or B3LYP with the five basis sets listed in Table 2,
to be 3 kcal/mol for the CF3CHFCF3, independent of method
and basis set, and it was assumed the V(CF3) did not change in
the transition state. At 〈E〉 ) 100 kcal/mol with an E0(HF) )
74 kcal/mol, the HIR rate constant was just 6.8% lower than
the rate constant calculated using a free-rotor model; thus, Figure
2 will only show the energy dependence of rate constants
calculated using the HIR or TOR models.
Figure 1. The ratio of [CF2dCFCF3]/[CF3CHFCF3] vs reciprocal
pressure for the 1,2-elimination of HF from chemically activated
CF3CHFCF3, see eq 6 in the text. The slope is (3.4 ( 0.2) × 10-5
Torr, the intercept is -(2.9 ( 4.8) × 10-4, and the correlation coefficient
is 0.96.
anticipated for a unimolecular reaction in an efficient bath gas,
the plot is linear and the intercept, -(2.9 ( 4.8) × 10-4, is
zero within the experimental uncertainty ((1 standard devia-
tion). The slope is (3.4 ( 0.2) × 10-5 Torr and equals k1,2-HF
/
kM. The use of the strong collision model is defended in Section
Two DFT methods (B3PW91 and B3LYP) and the five basis
sets shown in Table 2 were used to illustrate that the calculate
E0(HF) can decrease by more than 6 kcal/mol from the smallest
to the largest basis set. However, the two DFT methods give
very similar threshold energies for a common basis set. To
explore whether rate constants computed using different methods
or basis sets exhibited different magnitude and energy depen-
dence the B3LYP/6-31G(d), B3PW91/6-31G(d′,p′), and B3PW91/
6-311+G(2d, p) DFT methods were used to compute kE versus
E, see Figure 2. The HIR method was used for all calculations.
The rate constants at E0(HF) ) 74 kcal/mol with B3LYP/6-
31G(d) were indistinguishable from the rate constants calculated
using frequency and moments of inertia data computed using
B3PW91/6-31G(d′,p′), see Figure 2. The same result was found
at E0(HF) )76 kcal/mol when rate constants were compared
for the B3PW91/6-31G(d′,p′), and B3PW91/6-311+G(2d, p)
methods. Even though the E0(HF) values varied significantly
for different DFT methods, the computed rate constants for a
common threshold energy were nearly identical. Thus, we can
compute kE at specific energies, E, using just one DFT method
with confidence that other basis sets would give similar results.
The remaining calculations will use B3PW91/6-31G(d′,p′),
which has been very successful in our previous work.32–34
3.5. The rate constant in pressure units is converted to units of
s-1 by multiplication by the collision rate constant kM
)
πd2A,M(8kT/πµA,M)1/2Ω2,2(T*). Using collision theory with col-
lision diameters, d, and ꢀ/k values (in parentheses) of 5.1 Å
(288 K), 5.2 Å (300 K), and 6.1 Å (200 K) for CF3I, CF3CFHI,
and CF3CHFCF3, respectively, kM ) 1.32 × 107 (torr-s)-1. The
slope is converted to a rate constant for HF elimination from
CF3CHFCF3, k1,2-HF ) (4.5 ( 1.1) × 102 s-1. The collision
diameters and the ꢀ/k values used for CF3CHFI and CF3CHFCF3
are estimates based on values employed for the CF3CHFCH3
system.32 The 6% uncertainty in the slope of the plot Figure 1
was increased to (25% to account for the uncertainty in
converting the rate constant from pressure units to s-1 units.
3.2. Thermochemistry. Calculation of nonequilibrium rate
constants for comparison with the experimental chemical
activation results requires the average energy, 〈E〉, deposited in
the CF3CHFCF3 from eq 1. The mean energy of the chemically
activated CF3CHFCF3 is given by eq 7, where D0(CF3CHF-
CF3) is the bond dissociation energy for the C-C bond formed
by radical combination, and it equals -∆H° for eq 1. The
rxn,0
mean vibrational energy of the radicals is determined from their
vibrational frequencies 〈Evib(CF3)〉 ) 0.4 kcal/mol and 〈Evib
-
(CHFCF3)〉 ) 1.7 kcal/mol, and 3RT is the rotational energy of
the radicals.
By contrast, use of TOR versus HIR models gave calculated
rate constants differing by about a factor of 2, depending on
the specific 〈E〉, see Figure 2. The two CF3 torsional motions
appear to be strongly coupled because the frequencies are
significantly different: one in the 10-25 cm-1 range and the
other near 85 cm-1, see Table 1. Thus, the HIR model is
preferred and just the HIR model based on B3PW91/6-
31G(d′,p′) will be consided. Rate constant calculations were
done for a range of E0(HF) values for the HIR model to
determine which threshold energies produced computed rate
constants that encompassed the uncertainties in both the
experimental rate constant and the 〈E〉 shown as the box in
〈 〉
E ) D (CF CHF-CF ) + 3RT + E (CF ) +
〈
〉
0
3
3
vib
3
E (CHFCF ) (7)
〈
〉
vib
3
The ∆H° (CF3) ) -111.7 kcal/mol is established.36 We adopt
f,0
∆H°f,298(CF3CHF) ) -166.7 kcal/mol, which is an average of
four recent values (-168,37 -167.4,38 -166.7,39 and -164.5
kcal/mol26) and correction to 0 K gives ∆H° (CF3CHF) ) -165
f,0
kcal/mol. Five reports (-371.1,40 -374.2,41 - 374.5,38 -370.6,2
and -365.626b) for ∆H°f,298(CF3CHFCF3) were averaged to give

HF Elimination from Chemically Activated CF3CHFCF3
J. Phys. Chem. A, Vol. 114, No. 26, 2010 6999
TABLE 1: Calculated Frequencies, Moments of Inertia, and Reduced Moments of Inertia for CF3CHFCF3 and the HF
Elimination Transition State at B3PW91/6-31G(d′,p′), B3LYP/6-31G(d), and B3PW91/6-311+G(2d, p)
CF3CHFCF3
transition
6-31G(d)
6-31G(d′,p′)
6-31G(d)
6-311+G(2d,p)
6-31G(d′,p′)
6-311+G(2d,p)
frequencies (cm-1
)
9.389a
83.56a
149.6
213.5
234.5
288.8
322.3
342.1
454.9
519.3
537.4
552.8
608.1
688.0
743.4
868.7
917.0
1145.2
1156.8
1212.3
1246.0
1273.6
1297.1
1330.0
1394.5
1407.9
3106.4
242.1
16.66a
87.52a
153.6
215.3
233.6
288.5
322.1
341.1
450.5
512.0
530.1
546.3
606.9
683.7
742.3
875.9
923.4
1158.5
1166.8
1224.1
1257.8
1286.3
1310.1
1341.1
1410.8
1426.6
3121.2
242.4
478.5
543.0
24.06a
85.12a
149.7
214.9
239.2
288.4
319.7
341.2
449.9
512.4
531.6
547.5
602.5
684.9
739.8
859.6
910.1
1114.8
1141.7
1168.9
1212.5
1225.0
1273.0
1305.1
1377.3
1394.3
3097.6
241.5
481.8
545.9
52.44a
77.56
156.2
200.9
240.7
268.9
287.1
346.0
374.7
420.5
504.0
547.9
599.4
621.7
716.1
777.0
812.0
1029.9
1146.1
1207.9
1226.6
1245.4
1363.0
1455.6
1575.2
1736.3
263.8
510.9
558.2
54.13a
79.12
159.1
199.7
238.3
263.9
279.6
344.6
371.9
419.3
498.5
544.6
596.7
618.7
718.1
775.8
813.4
1033.2
1142.3
1217.1
1232.8
1257.3
1368.9
1468.7
1580.8
1733.2
265.0
510.8
556.9
51.09a
80.38
153.1
204.9
235.7
260.4
271.1
344.7
368.9
403.0
499.6
532.7
595.2
612.3
694.7
763.5
787.7
1025.0
1141.7
1181.0
1198.7
1237.5
1347.3
1446.9
1554.5
1738.7
265.8
513.6
556.5
amu (Å2)
Ix
Iy
Iz
479.5
544.1
Reduced Moment of Inertia of the CF3 Group (Ired
)
Ired (amu Å2)
60.9
61.1 60.6 62.1
62.3
62.1
a Frequency replaced with Ired in hindered internal rotor and free rotor rate calculations.
TABLE 2: Computed Threshold Energies using DFT for
HF Elimination from CF3CHFCF3
radicals, four bending frequencies (two at 50 cm-1 and two at
100 cm-1), and one free rotation. The torsional motion about
the C-C bond for the CF3CHF radical was treated as a free
rotor. The calculated energy distribution function is shown in
the Supporting Information. Using the f(E) and the kE values
for HIR at E0 ) 74 kcal/mol the 〈kE〉 ) 1470 s-1. This is a
factor of 2.2 larger than k〈E〉 ) 660 s-1 for 〈E〉 ) 95 kcal/mol.
The E0 for the 〈kE〉 calculation would need to be raised by about
1 kcal/mol to give agreement with the k〈E〉.
threshold energy (kcal/mol)
basis Set
6-31G(d)
6-31G(d′,p′)
cc-PVDZ
6-311+G(2df, 2p)
6-311+G(2d, p)
B3PW91
B3LYP
75.2
71.7
69.7
69.7
69.0
75.4
71.7
69.7
69.7
69.0
3.5. Strong Collision Assumption. The experimental rate
constant was evaluated with the assumption that each collision
between the bath gas and CF3CHFCF3* (see eq 5) removed
sufficient energy such that further reaction was negligible
relative to deactivation by subsequent collisions. However, in
cases where the difference between 〈E〉 and E0 is large and/or
the collision partner is inefficient, a multistep deactivation
scheme could be more appropriate. In order to calculate a rate
constant for multistep deactivation the average energy removed
per collision and the model (stepladder, exponential, or some
other model) for the energy removal mechanism must be known
or assumed. None of this information is available for
CF3CHFCF3* colliding with a bath gas that is a mixture of CF3I
and CF3CHFI. Experimental evidence of multistep deactivation
would be the upward curvature of a D/S vs 1/P plot at lower
pressures where D/S > 1.0. Our data, see Figure 1, does not
extend beyond D/S ) 0.02, and no evidence for multistep
deactivation is observed. In addition, we have studied32,33 several
chemically activated hydrohalocarbons with CF3I and other
Figure 2. At 〈E〉 ) 95 kcal/mol, the k〈E〉 ) 170 s-1 for an E0 )
76 kcal/mol and k〈E〉 ) 660 s-1 for an E0 ) 74 kcal/mol. The
experimental value is in the range 340-560 s-1. Using the HIR
model an E0(HF) from 73 to 77 kcal/mol would just touch the
box, see Figure 2; thus, we are confident in assigning E0(HF)
) 75 ( 2 kcal/mol.
3.4. Comparing the Specific Rate Constant, k〈E〉, at an
Average Energy 〈E〉 to the Average Rate Constant, 〈kE〉. The
previous section used the specific rate constant, k〈E〉 at 〈E〉 to
determine acceptable values for the threshold energy for the
HF elimination reaction. This is an approximation because the
radical combination reaction, eq 1, produces CF3CHFCF3 with
a distribution of energies, f(E), and the average rate constant,
〈kE〉 can be calculated once f(E) is determined. Given the large
uncertainty in 〈E〉, it is not reasonable to attempt a further
refinement of E0, but it would be of interest to know how k〈E〉
compares to 〈kE〉. The f(E) can be calculated29 once a model for
the association complex for eq 1 is constructed. The association
complex consists of the vibrational frequencies for the two

7000 J. Phys. Chem. A, Vol. 114, No. 26, 2010
Duncan et al.
times larger than kE in these experiments. On the basis of this
analysis, the strong collision assumption does not introduce any
significant additional error in the assignment of the threshold
energy.
3.6. Arrhenius Rate Constants. Studies modeling the
product profile for combustion of CF3CHFCF3 use Arrhenius
rate constant parameters. We computed k(T) for the HIR model
with V(CF3) ) 3 kcal/mol and Ired ) 61 amu Å2. The Arrhenius
parameters at 1000 K for the full reaction path degeneracy are
14.2 × 1013 s-1 and Ea ) 77.2 kcal/mol. The pre-exponential
factor for V(CF3) ) 6 kcal/mol is 20.4 × 1013 s-1. This change
arises because the HIR in the transition state is canceled by
one in the molecule, and the partition function is smaller for
the remaining HIR in the molecule with the higher barrier. If
one removes a factor of 6 for reaction path degeneracy the pre-
exponential factor is “normal” for a tight transition state.31–34 If
the pre-exponential factor for dissociation of the C-C bond is
1016 s-1, then HF elimination is dominant at 1000 K but
dissociation would become competitive with HF elimination at
higher temperatures, consistent with the experimental findings.1,26
3.7. Computed Structures for the Reactant, Transition
State, and Product. Figure 3 has the bond distance and bond
angles for the structures computed using B3PW91/6-31G(d′,p′)
for CF3CHFCF3, the transition state structure for HF loss and
the CF2dCFCF3 product. For the following discussion the
carbon losing the hydrogen is designated CH, and CF represents
the carbon losing the F. The degree of sp2 character of the
carbons in the four-centered ring of the transition state is
illustrated by the 14.7° angle at CF (the angle defined by the
triangular plane between the CF2 and an imaginary line
extending along the CdC) and the corresponding angle at CH
is 37.8°, see Figure 3. For reference, the angle is 55° for a sp3
carbon and 0° for a sp2 carbon. The degree of planarity differs
at the two carbons in the transition state ring with the carbon
losing the F being significantly more planar that the carbon
losing the hydrogen. A similar trend34g has been observed for
other transition states involving elimination of HF. It is
interesting to note that the out-of-ring C-F bond distance at
CF is shorter in the transition state (1.29 Å) than in either the
reactant (1.34 Å) or the CF2dCFCF3 product (1.31 Å), sug-
gesting that the fluorine substituents are donating electron
density to CF. By contrast, the out-of-ring C-F bond distance
(1.36 Å) at CH is nearly the same as in the CF3CHFCF3 molecule
(1.37 Å). The C-C bond distance in the ring (1.43 Å) is exactly
half way between the bond distance of the reactant (1.53 Å)
and product (1.33 Å).
3.8. Comparison with Previous Studies Involving HF
Elimination. Unimolecular rate constants for HF elimination
from other chemically activated fluoropropanes32 (CF3CH2CF3,
CF3CHFCH3, and CF3CH2CH3) have been reported. We have
previously noted32 the good agreement between threshold energy
values for these hydrofluoropropanes. A comparison would be
useful between CF3CHFCF3 and CF3CH2CF3 because for both
fluoropropanes an H on the central carbon is eliminated together
with an F atom from either end CF3 group. For CF3CH2CF3 the
〈E〉 ) 104 kcal/mol, kHF ) 1.2 × 105 s-1, and E0 ) 73 kcal/
mol compared to 〈E〉 ) 95 kcal/mol, kHF ) 4.5 × 102 s-1, and
E0 ) 75 kcal/mol for CF3CHFCF3.33 The experimental rate
constant is a factor of 270 smaller for CF3CHFCF3 compared
to CF3CH2CF3. A difference of 9 kcal/mol in 〈E〉 accounts for
a factor of 30 in the rate constant, for example, for 〈E〉 ) 95
kcal/mol the calculated kHF ) 8.8 × 102 s-1 for CF3CHFCF3
and at 〈E〉 ) 104 kcal/mol the kHF ) 2.90 × 104 s-1, which is
a difference of 33. A reaction path degeneracy of 6 for
Figure 2. Plots of log kE vs E for hindered internal rotor (HIR) and
torsional (TOR) models for various E0 using results from the B3PW91/
6-31G(d′,p′) calculations unless specified as G(d) or G(2d,p) for the
B3LYP/6-31G(d) or the B3PW91/6-311+G(2d,p) calculations, respec-
tively. [HIR, E0 ) 74 kcal/mol with two different basis sets: O -
B3PW91/6-31G(d′,p′) and b - B3LYP/6-31G(d)]; [0 - TOR, E0 ) 74
kcal/mol using B3PW91/6-31G(d′,p′)]; [HIR, E0 ) 76 kcal/mol using
two different methods and basis sets: [[ - B3PW91/6-31G(d′,p′) and
4 - B3LYP/6-31G(d)] and [2 - HIR, E0 ) 77 kcal/mol using B3PW91/
6-31G(d′, p′)].
hydrofluoroalkyl iodides as bath gases and have not found
evidence for inefficient behavior in the D/S plots. Nonetheless,
the use of the strong collision assumption for CF3CHFCF3*
colliding with a bath gas comparable to our mixture of CF3I
and CF3CHFI can be examined. The question of multistep
deactivation has been investigated for two chemically activated
molecules, CF3CH343 and 1,1,2,2-tetrafluorocyclopropane,44 with
a structure analogous to CF3CHFCF3. For cyclo-CF2CF2CH2*
colliding with CF2dCF2 the average energy removed per
collision was 9 kcal/mol.44 The more exhaustive study43 of
CF3CH3* with numerous collision partners showed that for
molecules similar to our bath gas the average energy removed
per collision would be 6-10 kcal/mol.
The HIR kE vs E curve with E0 ) 74 kcal/mol in Figure 2
will be used to examine whether the strong collision assumption
is valid for our system, and we will assume that our bath gas
mixture removes an average of 6 kcal/mol from CF3CHFCF3*
per collision. We believe this is the worst-case scenario because
the studies with CF3CH3* and cyclo-CF2CF2CH2* suggest that
each collision will likely remove more than 6 kcal/mol of
energy. At 〈E〉 ) 95 kcal/mol the kE ) 660 s-1, and if 6 kcal/
mol is removed by one collision the rate constant declines to
34 s-1 at 〈E〉 ) 89 kcal/mol. Following just one collision that
removes 6 kcal/mol of energy, the rate constant is only 5% of
the value at 〈E〉 ) 95 kcal/mol. This relatively large decline in
kE is a consequence of the steep slope of the kE versus E curve
in Figure 2. It is important to note that for the lowest pressures
in Figure 1 the D/S < 0.02; thus, the collision rate is at least 50

HF Elimination from Chemically Activated CF3CHFCF3
J. Phys. Chem. A, Vol. 114, No. 26, 2010 7001
found E0 > 95 kcal/mol for the 2,2-HF elimination reaction
forming the CF3CCF3 carbene. We found no evidence for
carbene formation consistent with their predictions. For the 1,2-
HF elimination reaction Peterson and Francisco predicted an
E0 ranging from 75.4 [B3LYP/6-31G(d)] to 89.1 kcal/mol
[QCISD(T)/6-31G(d)] and recommended 79.5 kcal/mol based
upon QCISD(T)/6-311G(d,p). Our results using 〈E〉 ) 95 kcal/
mol are consistent only with the smallest E0 calculated by
Peterson and Francisco.
A comparison of the various E0 values can also be useful to
examine the effect of different substituents. Assuming that
CF3CH3 with E0 ) 69 kcal/mol is the selected for comparison32
then E0 ) 73 kcal/mol33 for CF3CH2CF3 suggests that replace-
ment of one H of CF3CH3 with a CF3 group raises E0 by 4
kcal/mol. The present work with E0 ) 75 kcal/mol for
CF3CHFCF3 suggested that replacement of a second H with
atomic F may increase E0 by an additional 2 kcal/mol.
3.9. Conclusions
The unimolecular rate constant for HF elimination from
CF3CHFCF3 chemically activated at 95 kcal/mol was kHF ) 4.5
× 102 s-1. Matching computed rate constants to the experimental
measurement for HF elimination from chemically activated
CF3CHFCF3 at 〈E〉 ) 95 kcal/mol gives E0(HF) ) 75 ( 2 kcal/
mol. Threshold energies for 1,2-HF elimination from fluoro-
propanes span 20 kcal/mol from the simplest member of the
seriesCH3CHFCH345,46 (E0 )55kcal/mol)33a andCH3CH2CH2F46,47
(E0 ) 57 kcal/mol)33a to CF3CHFCF3, the most highly fluori-
nated propane for which HF loss is possible. In general,32,33a
replacement of H by F on a carbon increases the E0 by 2-4
kcal/mol. Elimination of F from the central carbon has a lower
E0 than loss of F from the end carbon if the total number of F
substituents is constant. Methyl substituents generally decrease32,33a
the E0, but the effect is more pronounced at CF than when
attached to CH.
Acknowledgment. Financial support from the National
Science Foundation (CHE-0647582) is acknowledged. We are
grateful to Professors George L. Heard and D. W. Setser for
helpful discussions. Professor Setser kindly assisted in comput-
ing the Arrhenius A-factor and the energy distribution for the
chemically activated CF3CHFCF3.
Supporting Information Available: The energy distribution
computed from an association complex for the chemically
activated CF3CHFCF3 and a GC/MS trace of a photolyzed
sample are included. This information is available free of charge
via the Internet at http://pubs.acs.org.
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