176
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: