The rate constants of the two channels of the reaction of F atoms with HD in the temperature range 193-300 K

Article abstract of DOI:10.1016/j.cplett.2004.11.103

The rate constants for the two channels of the reaction of F atoms with HD, k_{F + HD} and k_{F + DH}, have been determined in the temperature range 193-300 K. The sum of rate constants k_{F + HD} + k_{F + DH} was determined by a competitive method and a discharge-flow-mass spectrometric technique, using the F + D₂ reaction as a reference reaction. By combining the results for this sum of rate constants with published results for the rate constant kF+D2 and for the ratio of rate constants k_{F + HD}/k_{F + DH}, values were derived for the individual rate constants k_{F + HD} and k_{F + DH}. The experimental results are compared with published results of quantum mechanical calculations and of quasiclassical calculations on the Stark-Werner potential energy surface.

Full text of DOI:10.1016/j.cplett.2004.11.103

Chemical Physics Letters 401 (2005) 455–458
www.elsevier.com/locate/cplett
The rate constants of the two channels of the reaction of F atoms
with HD in the temperature range 193–300 K
Avigdor Persky *
Department of Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
Received 14 November 2004; in final form 14 November 2004
Available online 15 December 2004
Abstract
The rate constants for the two channels of the reaction of F atoms with HD, kF + HD and kF + DH, have been determined in the
temperature range 193–300 K. The sum of rate constants kF + HD + kF + DH was determined by a competitive method and a dis-
charge-flow-mass spectrometric technique, using the F + D reaction as a reference reaction. By combining the results for this
2
sum of rate constants with published results for the rate constant kFþD2 and for the ratio of rate constants kF + HD/kF + DH, values
were derived for the individual rate constants kF + HD and kF + DH. The experimental results are compared with published results
of quantum mechanical calculations and of quasiclassical calculations on the Stark–Werner potential energy surface.
Ó 2004 Elsevier B.V. All rights reserved.
1
. Introduction
of F atoms with HD (intramolecular kinetic isotope ef-
fect kF + HD/kF + DH) [7]
The study of the F + H reaction is of central impor-
2
F þ HD ! HF þ D
F þ DH ! DF þ H
ð1aÞ
ð1bÞ
tance to the development of theories in chemical dynam-
ics [1,2]. Numerous experimental and theoretical studies
of this reaction and of its isotopic variants F + D and
2
F + HD have been carried out in recent years. Compar-
isons between theoretical predictions based on various
potential energy surfaces (PESs) and experimental mea-
surements have led to conclusions concerning the accu-
racy of these surfaces. Among the experimental
measurements carried out for this system are the deter-
minations of rate constants as a function of tempera-
ture. Quite accurate kinetic results over wide
However, no experimental results are available concern-
ing the individual rate constants kF + HD and kF + DH
.
The ab initio PES developed by Stark and Werner
(SW PES) [8] is considered to be the most accurate
PES available today [1,2,9]. Nevertheless, there are still
some discrepancies between some experimental results
and results of quantum mechanical (QM) calculations
based on this PES [9–15]. Significant discrepancies exist
with respect to the intramolecular kinetic isotope effect
kF + HD/kF + DH, especially at low temperatures (see Fig.
7 of [14] and Fig. 7 of [15]). Discrepancies also exist with
temperature ranges are available for the F + H and
2
F + D reactions [3–5] (for a critical review of available
2
kinetic data and recommended rate constants see [6]).
Quite accurate results are also available for the ratio
of rate constants for the two channels of the reaction
respect to the rate constants of the F + H reaction at
2
low temperatures [16]. In both cases the QM rate con-
stants are significantly higher than the experimental rate
constants. It was suggested [12,13] that some of the dis-
crepancies between QM calculations and experimental
data indicate that the potential energy barrier of the
*
Fax: +972 3 535 1250.
E-mail address: persky@mail.biu.ac.il.
0
009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2004.11.103

456
A. Persky / Chemical Physics Letters 401 (2005) 455–458
SW PES is too narrow, causing excessive tunneling. The
potential energy curve of the SW PES along the entrance
channel was calculated in [16] and was presented in Fig.
5 of [16]. This figure shows that the barrier is rather thin,
thus permitting significant tunneling.
2. Experimental
Experiments to determine the ratio of rate constants
ðkFþHD þ kFþDHÞ=kFþD2 were carried out in the tempera-
ture range 193–300 K. The experimental setup and pro-
cedure used in this study were similar to those used by us
in our earlier studies of the reactions of F atoms with
HBr [18], DBr [19], CH [20,21], H S [21], CH F and
Quantum mechanical tunneling is of prime impor-
tance for the F + H system at low temperatures. How-
2
ever, the extent of the tunneling contribution to reaction
depends on the isotopic variant. As was discussed by
Castillo and Manolopoulos [9], out of the four isotopic
variants F + H , F + D , F + HD and F + DH, the QM
4
2
3
CH F [22] and C H [23]. Therefore they will be de-
2
2
2
6
scribed here only briefly.
Experiments were carried out in a fast-flow system
with mass spectrometric analysis of the reaction mix-
ture. In the experiments below room temperature the
reaction cell was cooled by a stream of cold nitrogen
gas. The temperature in the cell was measured by cop-
per-constantan thermocouples at three locations along
the axis of the cell. The temperature in the cell was uni-
form to within ±2 °C in all the experiments.
2
2
tunneling effect is expected to be least important for
F + DH and most important for F + HD, due to the fact
that the skewing angle in the potential energy surface is
the largest for F + DH and the smallest for F + HD (see
Fig. 1 of [9]). Thus, the two channels of the F + HD
reaction constitute two extremes with respect to the sig-
nificance of the tunneling contribution to reaction. This
fact finds its expression in the differences between the
excitation functions for these two reactions at low colli-
sion energies. A combined experimental and QM study
of integral cross-sections as a function of collision en-
ergy at 50 K for the reaction of F atoms with HD was
carried out by Skodje et al. [12,13]. For the F + DH
channel, the behavior was found to be essentially classi-
cal, with a direct over-the-barrier mechanism. On the
other hand, it was found that the F + HD channel, at
very low collision energies, is dominated by tunneling
through the barrier. Whereas the cross-section increases
monotonically with collision energy for the F + DH
channel, for the F + HD channel, a resonance peak is
observed, both experimentally and theoretically, near a
Fluorine atoms were produced by a microwave dis-
charge in a dilute mixture of CF in Ar and flowed into
4
the reaction cell through one of its inlets. The F atoms
reacted with a mixture of HD and D , also diluted by
2
Ar, which flowed into the reaction cell through a second
inlet. The reaction mixture was continuously sampled
through a small orifice and analyzed by a quadrupole
mass spectrometer (Balzers Model QMG 511). As in
our earlier studies of reactions of F atoms, the walls of
the discharge tube and reaction cell, both made of
quartz, were treated by a 10% HF solution to minimize
the heterogeneous recombination of F atoms. The flow
rates of the reagents into the reaction cell were con-
trolled by calibrated capillaries and were of the order
ꢀ1
ꢀ
1
collision energy of 0.5 kcal mol . No such peak was ob-
served in quasiclassical calculations on the same PES
of 0.005–0.012 lmol s for HD and D , 0.002–0.008
2
ꢀ
1
ꢀ1
for Ar.
lmol s
for CF4 and around 100 lmol s
(
the SW PES) [17]. In view of these significant differ-
The total pressure in the reaction cell was 1–1.5 Torr.
The concentrations of the reagents were followed, by
measuring the appropriate mass spectrometric signals
(mass to charge ratios m/e = 3 and 4, due to HD and
ences in the behavior for the two channels of the reac-
tion of F atoms with HD, it seems rather interesting
and important to determine experimentally the individ-
ual rate constants kF + HD and kF + DH and to compare
the results with available results of QM calculations
D , respectively). The ratio of rate constants for the
2
competing reactions is given by the expression
[
[
14] and of quasiclassical trajectory calculations (QCT)
17] on the SW PES. This was the purpose of the present
ðkFþHD þ kFþDHÞ=kFþD2 ¼ lnð½HDꢁ =½HDꢁÞ= lnð½D
2
ꢁ0=½D
2
ꢁÞ
0
ðIÞ
where [HD] and [D ] are the concentrations of these
study.
In this study the sum of rate constants
2
kF + HD + kF + DH was determined experimentally over a
wide temperature range by a competitive method, using
reagents at the end of the reaction cell when the reac-
tions with F atoms take place (microwave discharge
turned on) and [HD] and [D ] are their concentrations
as a reference reaction the reaction of F atoms with D2
0
2 0
when no F atoms are present (microwave discharge
turned off).
F þ D ! DF þ D
ð2Þ
2
From the ratios of rate constants ðkFþHD
þ
k
FþDHÞ=kFþD2 and available data for kFþD2 [6] and for
the ratios of rate constants kF + HD/kF + DH [7], absolute
values were calculated for the individual rate constants
kF + HD and kF + DH. The experimental results are com-
pared with results of QM [14] and of QCT [17]
calculations.
3. Results and discussion
The ratio of rate constants ðk
FþHD
was determined at four temperatures in the temperature
þ k
FþDH
Þ=k
FþD2
range 193–300 K. At each temperature, a set of experi-

A. Persky / Chemical Physics Letters 401 (2005) 455–458
Table 1
457
ments was carried out in which the extent of reaction
was varied over a wide range, by varying the concentra-
Ratios of rate constants ðkFþHD þ kFþDHÞ=kFþD2 and rate constants
k
F + HD and kF + DH as a function of temperature
tion of the F atoms. Plots of ln ([HD] /[HD]) vs
0
a
12
a,b
F + HD
12
a,b
T (K)
193
ðkFþHD þ kFþDHÞ=kFþD
10
k
10
k
F + DH
ln ([D ] /[D ]) for the two extreme temperatures, 193
2
2
0
2
and 300 K, are presented in Fig. 1. The straight lines in
this figure were calculated by the least-squares method.
As can be seen, no significant scatter of the points around
the lines is observed, and the lines have near-zero inter-
cepts. This behavior indicates that the calculated ratios
of rate constants are independent of the extent of reac-
tion and proves that secondary reactions are not impor-
tant under the conditions of our experiments. Plots for
the two other temperatures, 219 and 249 K, not shown
in Fig. 1, also gave results independent of the extent of
reaction.
1.53 ± 0.06
1.48 ± 0.04
1.39 ± 0.03
1.31 ± 0.03
3.65 ± 0.35
5.15 ± 0.45
6.80 ± 0.60
9.80 ± 0.90
2.40 ± 0.23
3.50 ± 0.30
4.70 ± 0.42
6.90 ± 0.65
2
2
3
19
49
00
a
Quated errors are 2r.
Units: cm molecule s .
b
3
ꢀ1 ꢀ1
respectively, and are plotted, on a logarithmic scale, as
a function of 1000/T, in Fig. 2. The Arrhenius expres-
sions corresponding to the experimental straight lines are
FþHD ¼ ð5:80 ꢂ 0:80Þ ꢃ 10ꢀ11
k
Ratios of rate constants ðk
þ k
Þ=k
, cal-
FþHD
FþDH
FþD2
3
ꢀ1 ꢀ1
ꢃ exp½ꢀð530 ꢂ 70Þ=Tꢁ cm molecule
s
culated from the straight lines shown in Fig. 1, and from
similar lines, not shown in this figure, for two other tem-
peratures, are presented in Table 1. These ratios of rate
constants were combined with available data for kFþD2
ðIVÞ
ðVÞ
¼ ð4:60 ꢂ 0:60Þ ꢃ 10ꢀ
11
k
FþDH
[
6] and for the ratio of rate constants kF + HD/kF + DH
3
ꢀ1 ꢀ1
ꢃ exp½ꢀð565 ꢂ 70Þ=Tꢁ cm molecule
s
[7] to calculate the individual rate constants kF + HD
and kF + DH. The Arrhenius expressions used for this
purpose are ([6,7], respectively)
(
a)
F +HD --> HF+D
10
k
FþD2 ¼ ð1:06 ꢂ 0:12Þ ꢃ 10ꢀ
3
ꢀ1 ꢀ1
0-11
1
ꢃ exp½ꢀð635 ꢂ 55Þ=T ꢁ cm molecule
s
ðIIÞ
QM
and
k
FþHD=kFþDH ¼ ð1:26 ꢂ 0:02Þ ꢃ exp½ð35 ꢂ 3Þ=T ꢁ
ðIIIÞ
The calculated values of kF + HD and kF + DH are pre-
EXP
sented in the third and fourth columns of Table 1,
QCT
1
0
0
0
0
0
.0
.8
.6
.4
.2
.0
1
0-12
(
b)
F+DH --> DF +H
1
0-11
QM
EXP
QCT
0-12
1
3
.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
3
1
00 K
93 K
-
1
1000/T (K )
Fig. 2. Semi-logarithmic plots of the rate constants for the two
channels of the reaction of F atoms with HD, kF + HD and kF + DH, as a
function of 1000/T. A comparison between the present experimental
results (solid lines) and results of quantum mechanical calculations
(dashed lines) [14] and of quasiclassical trajectory calculations (dot-
dashed lines) [17] on the SW PES.
0
.0
0.2
0.4
0.6
ln([D ] /[D ])
2
0
2
Fig. 1. Plots of ln([HD]
0
/[HD]) vs ln ([D
2 0 2
] /[D ] for the reaction of F
atoms with a mixture of HD and D
2
at 193 and 300 K.

458
A. Persky / Chemical Physics Letters 401 (2005) 455–458
Fig. 2 includes also the results of QM [14] and of QCT
17] calculations, based on the SW PES. As can be seen
correctly the rate constants reported here for the two
channels of the reaction of F atoms with HD.
[
from Fig. 2, the experimental results are between the
QCT and the QM results. The QCT results are some-
what lower than the experimental results, since they do
not include any tunneling contributions. On the other
hand, the QM results are higher than the experimental
results, probably because of excessive tunneling contri-
butions. The differences in the tunneling contributions
for the two channels of the reaction of F atoms with
HD are clearly observed by comparing the correspond-
ing figures (Fig. 1a,b). While for the F + DH channel,
the QM and QCT results are rather close and do not dif-
fer significantly from the experimental results, in the
temperature range of this study, significant differences
are observed for the F + HD channel and they increase
as the temperature is lowered. As pointed up in Section
References
[
[
1] D.E. Manolopoulos, J. Chem. Soc., Faraday Trans. 93 (1997) 673.
2] S.C. Althorpe, D.C. Clary, Ann. Rev. Phys. Chem. 54 (2003) 493.
[3] E. Wurzberg, P.L. Houston, J. Chem. Phys. 72 (1980) 4811.
[4] M.A.A. Clyne, A. Hodgson, J. Chem. Soc., Faraday Trans., 2 81
(
1985) 443.
5] P.S. Stevens, W.H. Brune, J.G. Anderson, J. Phys. Chem. 93
1989) 4068.
6] A. Persky, H. Kornweitz, Int. J. Chem. Kinet. 29 (1997) 67.
[
(
[
[7] A. Persky, J. Chem. Phys. 59 (1973) 5578.
[8] K. Stark, H.-J. Werner, J. Chem. Phys. 104 (1996) 6515.
[9] J.F. Castillo, D.E. Manolopoulos, Faraday Discuss., Chem. Soc.
1
10] J.F. Castillo, D.E. Manolopoulos, K. Stark, H.-J. Werner, J.
10 (1998) 119.
[
1
, following the discussion in [9], the large differences in
Chem. Phys. 104 (1996) 6531.
[11] F.J. Aoiz, L. Banares, B. Martinez-Haya, J.F. Castillo, D.E.
Manolopoulos, K. Stark, H.-J. Werner, J. Phys. Chem. A 101
the tunneling contributions for the two competing chan-
nels F + HD and F + DH are rather expected.
(
1997) 6403.
This study clearly indicates that the SW PES predicts
too much tunneling for the F + HD channel of the reac-
tion of F atoms with HD. This is consistent with earlier
conclusions based on the comparison between QM and
experimental cross-sections for this reaction [12,13] and
on the comparison between QM and experimental re-
sults for the ratios of rate constants kF + HD/kF + DH
[
[
12] R.T. Skodje, D. Skouteris, D.E. Manolopoulos, S.-H. Lee, F.
Dong, K. Liu, J. Chem. Phys. 112 (2000) 4536.
13] R.T. Skodje, D. Skouteris, D.E. Manolopoulos, S.-H. Lee, F.
Dong, K. Liu, Phys. Rev. Lett. 85 (2000) 1206.
[14] D.H. Zhang, S.-Y. Lee, M. Baer, J. Chem. Phys. 112 (2000) 9802.
[
[
15] H. Kornweitz, A. Persky, J. Phys. Chem. A 108 (2004) 8599.
16] E. Rosenman, S. Hochman-Kowal, A. Persky, M. Baer, Chem.
Phys. Lett. 257 (1996) 421.
[14,15]. It seems that some modifications in the SW
PES are needed in order to close the gaps between the-
[17] F.J. Aoiz, L. Banares, V.J. Herrero, V.S. Rabanos, K. Stark, I.
Tanarro, H.-J. Werner, Chem. Phys. Lett. 262 (1996) 175.
[18] R. Edrei, A. Persky, Chem. Phys. Lett. 157 (1989) 265.
oretical and experimental results for the F + H system.
2
[
[
19] E. Schwartz, A. Persky, Chem. Phys. Lett. 196 (1992) 133.
20] A. Persky, J. Phys. Chem. 100 (1996) 689, An updated Arrhenius
equation and a value at 298 K for kFþCH4 based on updated
recommended values for kFþH2 are given in [21].
Recently, Aquilanti et al. [24,25] carried out QM calcu-
lations for the F + H reaction using the SW PES, after
2
it was modified in the entrance channel. The barrier for
the modified PES is broader than the barrier of the ori-
ginal SW PES, thus reducing the amount of tunneling,
while the barrier height is preserved. The QM rate con-
stants obtained by them were found to be in good agree-
[21] A. Persky, Chem. Phys. Lett. 298 (1998) 390, Erratum: Chem.
Phys. Lett. 306 (1999) 416.
22] A. Persky, Chem. Phys. Lett. 376 (2003) 181.
[
[
[
23] A. Persky, Chem. Phys. Lett. 380 (2003) 286.
24] V. Aquilanti, S. Cavalli, D. De Fazio, A. Volpi, A. Aguilar, X.
Gimenez, J.M. Lucas, Chem. Phys. Lett. 371 (2003) 504.
ment with the experimental data for the F + H reaction
2
[3–6]. It would be very interesting to find out whether
this PES, or any other modified SW PES, reproduces
[25] V. Aquilanti, S. Cavalli, D. De Fazio, A. Volpi, A. Aguilar, J.M.
Lucas, Chem. Phys. 308 (2005) 237.