errors on these two parameters. This is attributable entirely to
the high-end limit of the experimental pressure range, which is
too low to allow reliable extrapolation to the high-pressure
regime. We then used the method proposed by Troe33,34 to
predict the broadening factor FC, and used this FC as a fixed
value in two-parameter Troe fits of our experimental data.
Since an accurate prediction of FC requires the a priori knowl-
edge of some parameters, e.g. the collisional efficiency factor
A good MVIPF fit of the experimental data points reported
in this work can be obtained using an adjustable parameter cadj
of 0.24 to 0.5 Aꢂ2, with values for bcoll ꢁ ZLJ of 1.6 ꢁ 10ꢂ11 to
1.4 ꢁ 10ꢂ11 cm3
s
ꢂ1, respectively. Fig. 6 shows the MVIPF
recombination rate coefficients for the experimental pressure
range, computed using cadj and bcoll ꢁ ZLJ of 0.31 Aꢂ2 and 1.42 ꢁ
10ꢂ11 cm3 ꢂ1, respectively, showing a good agreement with
s
our experimental data. Similar to the Troe fits described ear-
lier, a more precise estimate of cadj and hence kN is not possible
due to the low experimental pressures, with kN varying from
1 ꢁ 10ꢂ10 to 2 ꢁ 10ꢂ10 cm3 sꢂ1 over the parameter range
mentioned. The low-pressure rate coefficient k0 is much less
sensitive to the value of the adjustable parameters, changing
only from 1.58 ꢁ 10ꢂ28 to 1.67 ꢁ 10ꢂ28 cm3 sꢂ1 between the
extreme fitting parameter values; such results are in very good
agreement with those from the Troe fits. The efficiency-cor-
rected collision numbers bcoll ꢁ ZLJ of (1.4–1.6) ꢁ 10ꢂ11 cm3
sꢂ1 correspond to a weak-collision efficiency bcoll of 0.06 to
0.07, assuming a reasonable collision number ZLJ of 2.3 ꢁ
10ꢂ10 cm3 sꢂ1 (M ¼ He); this translates to an average down-
ward collisional energy transfer hDEdowni of about 65 to 72
cmꢂ1 when assuming an exponential energy-down model. The
value of the parameter cadj is directly comparable to values
found for similar recombination reactions,35 while the energy
transfer parameter hDEdowni for M ¼ He is in good agreement
with commonly accepted energy transfer parameters.37
b
coll, we varied the FC value used in these 2-parameter fits
between 0.40 to 0.60, to account for any uncertainties in the
derivation of our predicted FC; this range includes the FC
¼
0.54 adopted by Plumb and Ryan, and agrees with typical
results for strongly bonded, tight product molecules. The Troe
fit with FC ¼ 0.50 is displayed in Fig. 6. The value for kN
remains strongly correlated with the adopted value of FC and
the statistical weighting of the data points, varying from 8 ꢁ
10ꢂ11 to 3 ꢁ 10ꢂ10 cm3 sꢂ1 for the range of FC values
mentioned higher. As such, a reliable estimate for this para-
meter is not possible, though our results seem to indicate
N
N
a somewhat higher k2 than Plumb and Ryan’s19 k2 of
2.0 ꢁ 10ꢂ11 cm3 sꢂ1. On the other hand, k0 was found to be
nearly independent of the value of FC used, ranging from 1.51
to 1.44 ꢁ 10ꢂ28 cm6 sꢂ1 and with statistical errors of about
15%, and furthermore remained very close to the results of the
three-parameter fits; k0 can therefore be reliably estimated
from our experimental data, with:
Reproducing the high-pressure and low-pressure limits as
reported by Plumb and Ryan19 proved less straightforward.
Their high-pressure limit of kN(290 K) of 2 ꢁ 10ꢂ11 cm3 sꢂ1
could only be reproduced using a cadj of 0.152 Aꢂ2; this latter
value is well outside the range of values found for similar
reactions35 and corresponds to an unlikely tight transition
state. Furthermore, using this cadj, we could only reproduce
0
k2 ¼ (1.47 ꢀ 0.24) ꢁ 10ꢂ28 cm6 sꢂ1
This value of k0 is significantly different from the value
obtained by Plumb and Ryan, k2 ¼ 3.80 ꢁ 10ꢂ27 cm6 sꢂ1
0
.
To further investigate this discrepancy, the pressure-depen-
dent rate coefficient for recombination of CF3 þ F was also
calculated by applying the microcanonical variational (micro-
canonical variational theory of radical recombination by in-
version of interpolated partition function, MVIPF) method
described by Forst35 to the CF4 - CF3 þ F dissociation
reaction, and multiplying this dissociation rate coefficient35 by
the CF4 2 CF3 þ F equilibrium constant Keq (290 K) of 6 ꢁ
1069 cm3 as derived from thermochemical data available from
JANAF.36 The MVIPF method essentially describes the tran-
sition state for barrierless dissociation as an activated complex
with properties—and hence a partition function—intermediate
between the reactant CF4 and the products CF3 þ F. The
energy-dependent sum of states for the TS is derived from an
inverse Laplace transform of that intermediate’s partition
function; the rate-limiting minimal sum of states along the
reaction coordinate is located microcanonically as a function
of E and J. Rotational effects as a function of J are incorpo-
rated by describing the dissociating molecule as a quasi-diatom
2D molecular rotor, while rotation along the third molecular
axis is considered as an active 1D internal rotor with no
J-dependent restrictions on quantum number K. The MVIPF
method requires input of the molecular properties of CF4, CF3
and F to calculate the partition functions for products and
reactant; we used the same vibrational wave numbers and
rotational constants for CF4 and CF3 as used by Plumb and
Ryan in their RRKM analysis.19 The rate of change from
reactant-like to product-like properties and partition functions
along the reaction coordinate is controlled by a switching
function exp[ꢂcadj ꢁ (r ꢂ re)2] as a function of the length r
of the dissociating CꢂF bond compared to the equilibrium
bond length re in CF4. The constant cadj is an adjustable
parameter controlling the ‘looseness’ of the transition state
and is derived by fitting the predicted rate coefficients to
experimental rate data. In addition, the efficiency-corrected
collision number bcoll ꢁ ZLJ can be used as an adjustable
parameter to control the fall-off behavior of the rate coeffi-
cients to obtain an optimal fit to the available data. The high-
Plumb and Ryan’s19 low-pressure k2 (290 K) of 3.8 ꢁ 10ꢂ27
0
cm3 sꢂ1 by adopting an efficiency-corrected collision number
bcoll ꢁ ZLJ of 6.2 ꢁ 10ꢂ10 cm3
s
ꢂ1; even when assuming a
strong-collision system with bcoll ¼ 1 this implies an unphysi-
cally high collision number ZLJ
.
The cause of the marked difference between our experimen-
tal results and Plumb and Ryan’s is an open question, espe-
cially since our k(CF3 þ O2) measurements,38 using the same
method, are in good agreement with their and other literature
data. However, the reproduction of Plumb and Ryan’s data
requires the adoption of unlikely parameters in the MVIPF
formalism. The parameters for our results, on the other hand,
are in the ranges reported in the literature. Although this
strongly suggests that our data provide a more accurate
description of the chemical kinetics, independent third-party
measurements of this important reaction are certainly wel-
come. In particular, measurements at higher pressures would
significantly improve the Troe fits and MVIPF treatment to
determine kN, and concomitantly the fall-off parameter FC
and/or bcoll ꢁ ZLJ
.
Conclusions
We have determined the rate constants of the combination
reactions of CF3 with CF3 and F over an extended pressure
range. Our results clearly show that k(CF3 þ CF3) is in the high
pressure limit at pressures above 1 Torr He while the rate
constant of CF3 þ F is in the fall-off region at pressures of 0.5
to 6 Torr He. Our k(CF3 þ CF3) value of (1.8 ꢀ 0.6) ꢁ10ꢂ12
cm3 sꢂ1 is in close accord with the lowest literature value and is
also compatible with several other determinations, but clearly
diverges from the high k values ( Z 1.0 ꢁ 10ꢂ11 cm3 sꢂ1
)
reported by some other groups. Our CF3 þ CF3 data are fully
in line with the sharp decrease in the rates of the mutual
reactions of methyl radicals upon increasing F-substitution
(CH3; CH2F; CHF2). Our rate data on the CF3 þ F reaction,
backed by variational transition state MVIPF calculations,
pressure limit rate coefficient kN is not sensitive to bcoll ꢁ ZLJ
,
but is controlled solely by the value of cadj
.
1192
P h y s . C h e m . C h e m . P h y s . , 2 0 0 5 , 7 , 1 1 8 7 – 1 1 9 3
T h i s j o u r n a l i s & T h e O w n e r S o c i e t i e s 2 0 0 5