Experimental and theoretical studies of the rate coefficients of the reaction O(3P) + HCl at high temperatures

Article abstract of DOI:10.1021/jp020916n

Rate coefficients of the reaction O(³P) + HCl in the temperature range 1093-3197 K were determined using a diaphragmless shock tube. O atoms in the ground electronic ³P states were generated either by photolysis of SO₂ with a KrF excimer laser at 248 nm or by pyrolysis of N₂O with the shock wave. Their concentrations were monitored via atomic resonance absorption excited by emission from a microwave-discharged mixture of O₂ and He. Rate coefficients determined in this work show non-Arrhenius behavior, with values consistent with previously reported measurements for T < 1486 K; they fit well with the equation k₁(T) = (9.27 ± 0.03) × 10^-24 T^3.67±0.18 exp[-(1030 ± 160)/T] cm³ molecule^-1 s^-1; listed errors represent one standard deviation in fitting. Theoretical calculations at the CCSD(T)/6-311+G(d, p) level locate a bent ³A″ (TS1) and a linear ³A′ (TS3) transition state characterized previously. On the basis of the results computed by CCSD(T)/ 6-311+G(3df,2p)//CCSD(T)/6-311+G(d,p), the rate coefficients predicted with conventional transition-state theory, including Eckart-tunneling corrections and with variational transition-state theory including zero- and small-curvature tunneling corrections, all agree satisfactorily with experimental observations.

Full text of DOI:10.1021/jp020916n

J. Phys. Chem. A 2002, 106, 10231-10237
10231
Experimental and Theoretical Studies of the Rate Coefficients of the Reaction O(3P) + HCl
at High Temperatures
Chih-Chang Hsiao and Yuan-Pern Lee*,†
Department of Chemistry, National Tsing Hua UniVersity, 101, Section 2, Kuang Fu Road,
Hsinchu 30013, Taiwan
Niann S. Wang
Department of Applied Chemistry, National Chiao Tung UniVersity, 1001, Ta Hsueh Road,
Hsinchu 30010, Taiwan
J. H. Wang and M. C. Lin*,‡
Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322
ReceiVed: April 8, 2002; In Final Form: July 23, 2002
Rate coefficients of the reaction O(3P) + HCl in the temperature range 1093-3197 K were determined using
3
a diaphragmless shock tube. O atoms in the ground electronic P states were generated either by photolysis
of SO2 with a KrF excimer laser at 248 nm or by pyrolysis of N2O with the shock wave. Their concentrations
were monitored via atomic resonance absorption excited by emission from a microwave-discharged mixture
of O2 and He. Rate coefficients determined in this work show non-Arrhenius behavior, with values consistent
with previously reported measurements for T < 1486 K; they fit well with the equation k1(T) ) (9.27 ( 0.03)
3.67(0.18
× 10-24
T
exp[-(1030 ( 160)/T] cm3 molecule-1 s-1; listed errors represent one standard deviation
in fitting. Theoretical calculations at the CCSD(T)/6-311+G(d, p) level locate a bent 3A′′ (TS1) and a linear
3A′ (TS3) transition state characterized previously. On the basis of the results computed by CCSD(T)/
6-311+G(3df,2p)//CCSD(T)/6-311+G(d,p), the rate coefficients predicted with conventional transition-state
theory, including Eckart-tunneling corrections and with variational transition-state theory including zero- and
small-curvature tunneling corrections, all agree satisfactorily with experimental observations.
1. Introduction
reactors and reported rate coefficients with a slight positive
deviation from Arrhenius behavior at high temperature. Com-
bining the then-available data, they reported
The reaction
O(3P) + HCl f OH + Cl
(1)
k1(T) )
5.6 × 10-21T 2.87 exp[-(1766/T)] cm3 molecule-1 s-1 (2)
is important because it converts stable HCl into reactive Cl
atoms that can catalytically destroy O3 in the atmosphere.1 In
combustion systems at elevated temperature, this reaction is the
most fundamental that involves Cl atoms; it plays an important
role in the combustion of ammonium perchlorate propellants,2
incineration of toxic waste, inhibition of flames, and formation
of soot.3,4
Rate coefficients of reaction 1 were determined in the
temperature range 290-1486 K by several groups.5-11 All
measurements below 720 K show, within experimental uncer-
tainties, consistent Arrhenius behavior. Mahmud et al.11 deter-
mined the rate coefficient of reaction 1 in the temperature range
350-1486 K with two types of high-temperature photochemical
for 350 K < T < 1486 K with an error limit (2σ) of 23%.
The title reaction has been subjected to extensive theoretical
investigation by many research groups. It is an example of a
heavy-light-heavy reaction with a small skew angle and is
therefore expected to manifest important quantum effects. The
system, with only one H, one O, and one Cl atom, is simple
enough to allow accurate theoretical calculations. Characteriza-
tion of the potential energy surface (PES) of this system12-20
and, on the basis of this PES, predictions of thermal and state-
specific rate coefficients21-31 using various methods have
improved significantly and show satisfactory agreement with
experiments. Excellent reviews of previous theoretical work can
be found in several articles.16,26,30
* Corresponding authors. Y.-P. Lee: E-mail: yplee@mx.nthu.edu.tw;
Fax: 886-3-5722892. M.C. Lin: E-mail: chemmcl@emory.edu; Fax:
1-404-727-6586.
Because of the importance of this reaction in combustion,
kinetic data at higher temperatures are needed. We have
constructed a diaphragmless shock tube and determined rate
coefficients of the title reaction up to 3197 K. Because previous
theoretical predictions of k1 are limited to 1000 K, we also
† Jointly appointed by the Institute of the Atomic and Molecular Sciences,
Academia Sinica, Taipei, Taiwan.
‡ National Science Council Distinguished Visiting Professor in the
Department of Applied Chemistry, Chiao Tung University, Taiwan.
10.1021/jp020916n CCC: $22.00 © 2002 American Chemical Society
Published on Web 09/28/2002

10232 J. Phys. Chem. A, Vol. 106, No. 43, 2002
Hsiao et al.
performed theoretical calculations and found excellent agreement
between theory and experiments throughout the temperature
range of study.
(in units of mhartree) corrected with the zero-point energy (ZPE)
is calculated as follows:39
E[(G2M, CC2)] ) Ebas + ∆E(+) + ∆E(2df) + ∆E(CC) +
∆′ + ∆E(HLC, CC2) + ZPE (3)
2. Experiments
Details of the diaphragmless shock tube apparatus can be
found in ref 32. The shock tube, of length 5.9 m and i.d. 7.6
cm, is coupled to a detection system using atomic resonance
absorption. Four pressure sensors were installed at 3, 18, 28,
and 38 cm from the end of the tube to monitor the shock wave.
Three time-frequency counters (Tabor Electronics, model 6010)
were employed to determine the time intervals for arrival of
the shock wave between each sensor; the speed of the shock
wave is thus determined. A microwave-discharged lamp with a
flowing gas mixture of ∼10% O2 in He served as a lamp for
the atomic absorption of O atoms. Emission of the lamp at
130.23, 130.49, and 130.60 nm, corresponding to atomic
transitions of O(3S) f O (3P2, 1, 0), passes perpendicularly near
the end of the shock tube and a vacuum UV monochromator
(ARC, VM502, focal length 20 cm, reciprocal linear dispersion
4.0 nm mm-1, slit width 500 µm) before being detected with a
solar-blind photomultiplier tube (Hamamatsu, R972). Variation
of the signal from the photomultiplier was monitored with a
digital storage oscilloscope and transferred to a computer for
further processing.
When needed, a KrF excimer laser (248 nm) was employed
for photolysis. Light from the laser enters the shock tube from
the quartz end-plate and passes along the tube. A delayed pulse
generator (Stanford Research Systems, DG535) was employed
to trigger the laser about 200 µs after the arrival of the incident
shock wave at the last pressure sensor.
Before each experiment, the system was pumped below 5.0
× 10-7 Torr. The temperature (T5), density (F5), and pressure
(P5) in the reflected shock regime were calculated from the
measured velocity of the incident shock, the composition of the
test gas, the initial pressure, and the temperature using the ideal
shock-wave theory33 with Mirels’ boundary-layer correc-
tions.34,35
with
Ebas ) E[PMP4/6-311G(d,p)]
∆E(+) ) E[PMP4/6-311+G(d,p)] - Ebas
∆E(2df) ) E[PMP4/6-311G(2df,p)] - Ebas
∆E(CC) ) E[CCSD(T)/6-311G(d,p)] - Ebas
∆′ ) [UMP2/6-311+G(3df,2p)] - E[UMP2/6-311+G(2df,p)] -
E[UMP2/6-311+G(d,p)] + E[UMP2/6-311(d,p)]
∆E(HLC, CC2) ) -5.78nâ - 0.19nR
in which nR and nâ are the number of valence electrons, nR g
nâ.
Because the present system is relatively small, we have
also calculated the energies of all species at the CCSD(T)/
6-311++G(3df,2p) level of theory using the B3LYP/6-311+G-
(3df,2p) optimized geometries. For comparison, we have also
carried out similar calculations using the geometries optimized
at the CCSD(T)/6-311+G(d,p) of theory. All calculations were
carried out with the Gaussian 9840 and MOLPRO 9641 programs.
Rate coefficients for various reaction channels were calculated
with conventional transition-state theory (TST) with Eckart-
tunneling corrections using the program previously employed
for the reaction C6H5 + CH4.42 We employed also the Polyrate
program of Truhlar et al.43 based on variational TST including
zero- or small-curvature tunneling corrections.
Rate coefficients were computed on the basis of results using
the G2M and the CCSD(T)/6-311+G(3df,2p)//CCSD(T)/
6-311+G(d,p) methods. In the calculation using the latter
method, we performed the IRCMax calculation44 to stimulate
the IRC curves at the level IRCMax{energy[CCSD(T)/
6-311+G(d,p)]}//IRC{geometry[B3LYP/6-311+G(d,p)]}. The
first and second derivatives of the points on the IRC curves for
zero- or small-curvature tunneling treatments were calculated
at the CCSD(T)/6-311+G(d,p) level.
We calibrated the concentration of O atoms in the shock tube
with N2O, assuming a 100% yield of O atoms from the pyrolysis
of N2O. For kinetic measurements, O atoms were generated from
the laser photolysis of SO2 at 248 nm. In some experiments, O
atoms were generated from the pyrolysis of N2O for comparison.
At 248 nm, the absorption cross section of SO2 is 7.7 × 10-20
cm2 at 1100 K and 5.3 × 10-19 cm2 at 2000 K.36
4. Results and Discussion
He (99.9995%, AGA Specialty Gases), O2 (99.999%, Scott
Specialty Gases), SO2 (99.98%, Matheson), and HCl (99.999%,
AGA Specialty Gases) were used without further purification.
Mixtures of HCl in Ar (23.4-202 ppm), SO2 in Ar (292-971
ppm), and N2O in Ar (11.6 ppm) were used.
4.1. Calibration of [O]. Figure 1A shows a typical temporal
profile of the signal intensity of the photomultiplier observed
for the thermal decomposition of N2O in the reflected shock
regime. The calibration of [O] using the thermal decomposition
of N2O has become a standard procedure to account for
deviation from the Beer-Lambert law.45 The calibration curve
of [O] for our system is shown in Figure 2. Absorbance A is
calculated with the equation
3. Computational Methods
The geometry of reactants, intermediates, transition states,
and products of the O-H-Cl system were optimized at the
B3LYP/6-311G(d,p) level of theory with Becke’s three-
parameter nonlocal exchange functional37 and the nonlocal
correlation functional of Lee et al.38 Energies of all species were
calculated by the G2M39 method, which makes a series of
calculations with geometries optimized with the B3LYP method
to approximate the CCSD(T)/6-311+G(3df,2p) level of theory,
including a “higher-level correction” (HLC) based on the
number of paired and unpaired electrons. The total G2M energy
A ) ln(I0/I)
(4)
in which the light intensity before and after the production of
O atoms is denoted as I0 and I, respectively. The concentration
of O atoms is fitted with the equation
[O]/1013 molecule cm-3 ) 4.4233A - 0.0336A2 +
2.5741A3 (5)

Rate Coefficients of O(3P) + HCl at High T
J. Phys. Chem. A, Vol. 106, No. 43, 2002 10233
fitted to a first-order decay curve to yield a pseudo-first-order
rate coefficient kI. The apparent bimolecular rate coefficient,
k1′, is thus derived from
k1′ ) kI/[HCl]
(6)
At high temperatures, interference from reactions of O atoms
with precursor SO2 and with reaction products SO and OH
should be considered,
O + SO2 f SO3
f SO + O2
(7a)
(7b)
(8)
O + SO f SO2
O + OH f H + O2
(9)
with these reported temperature dependences of the rate coef-
ficients:
k7a(T) ) 1.21 × 10-33 exp(3163/T) cm6 molecule-2 s-1
(ref 47) (10)
Figure 1. Temporal profiles of photomultiplier signals observed for
the (A) thermal decomposition of N2O (30 ppm in Ar), (B) laser-
irradiated Ar sample containing SO2 (697 ppm), and (C) laser-irradiated
Ar sample containing SO2 (697 ppm) and HCl (150 ppm).
k7b(T) ) 8.3 × 10-12 exp(-9800/T) cm3 molecule-1 s-1
(ref 48) (11)
k8(T) ) 3.3 × 10-26T -1.84 cm6 molecule-2 s-1
(ref 49) (12)
k9(T) ) 2.41 × 10-11 exp(-350/T) cm3 molecule-1 s-1
(ref 50) (13)
Although recent experimental data51 show a nearly constant rate
coefficient of (1.54 ( 0.14) × 10-11 cm3 molecule-1 s-1 for
reaction 9 in the temperature range 1850-3550 K, we used a
previously recommended value (eq 13) that is about 40% greater
at 3000 K for the worst-case scenario. We modeled an observed
temporal profile of [O] with reactions 1, 7-9 with the
commercial kinetic modeling program FACSIMILE;52 literature
values of rate coefficients of reactions 7-9 were held constant,
and the bimolecular rate coefficient of the title reaction, k1, was
varied to yield the best fit. Experimental conditions and values
of k1 for 50 measurements in the temperature range 1093-2525
K using mixtures with various concentrations of HCl and SO2
are summarized in Table 1. Values of k1′ obtained with eq 6
from pseudo-first-order decays are slightly greater than k1,
indicating that interference reactions play a minor role; we list
k1/k1′ in Table 1 for comparison. For experiments with large
concentrations, [HCl] > 1 × 1015 molecule cm-3 and [SO2] >
6 × 1015 molecule cm-3, the deviation is as much as 65%.
Detailed modeling shows that reaction 9 is more important than
reaction 7 at low temperatures but vice versa at high temper-
atures.
Figure 2. Calibration curve of [O] versus absorbance of O atoms.
4.2. Rate Coefficient k1 of the Reaction O + HCl. Figure
1B shows a typical temporal profile of the signal intensity of
the photomultiplier observed when the gas mixture contained
only SO2 and Ar. The first stepwise decrease in intensity
(upward direction in Figure 1B) corresponds to variation in the
absorbance of SO2 upon arrival of the incident wave; SO2 has
a nonnegligible absorption cross section of ∼1.1 × 10-17 cm2
near 130 nm at 300 K.46 The second stepwise change is
associated with the arrival of the reflected shock wave, and the
third step is due to the production of O atoms upon laser
irradiation at 248 nm. Figure 1C shows a typical temporal profile
recorded similarly except that the mixture contains SO2 and HCl.
Because O atoms reacted with HCl, the light intensity detected
by the photomultiplier increased with time as [O] reacted. The
concentration of O atoms at reaction period t, [O]t, is derived
according to eqs 4 and 5, with the light intensity before
photolysis taken as I0. Experiments were carried out under
pseudo-first-order conditions with [HCl] . [O]. If there were
no interference reaction, the temporal profile of [O]t could be
Complementary experiments at high temperatures were
carried out with O atoms produced from the thermal decomposi-
tion of N2O. Under such conditions, reaction 14 replaces
reactions 7 and 8 in the kinetic model
O + N2O f NO + NO
f N2 + O2
(14a)
(14b)
with a temperature-dependent rate coefficient of53,54
k
14a(T) ) 1.52 × 10-10 exp(-13930/T) cm3 molecule-1 s-1
(15)
k
14b(T) ) 6.13 × 10-12 exp(-8020/T) cm3 molecule-1 s-1
(16)

10234 J. Phys. Chem. A, Vol. 106, No. 43, 2002
Hsiao et al.
TABLE 1: Experimental Conditions and Rate Coefficient k1
for the Reaction O + HCla
P1
P4
T5 [SO2] [O] [HCl]
k1
k1
/k1′
/Torr /Torr Ms
/K /1015 /1013 /1014
/10-12
707 ppm SO2, 202 ppm HCl
80.31 2000 2.06 1093 8.30 3.06 23.7 0.422 ( 0.031 0.53
70.49 2000 2.15 1176 7.69 3.34 22.0 0.496 ( 0.026 0.55
60.23 2000 2.25 1281 6.69 2.86 19.9 0.844 ( 0.030 0.72
50.85 2000 2.29 1319 5.99 2.74 17.1
50.45 2000 2.39 1429 6.24 3.87 17.8
1.33 ( 0.04 0.83
1.37 ( 0.03 0.81
697 ppm SO2, 150 ppm HCl
60.55 2000 2.30 1334 7.05 2.63 15.2
50.80 2000 2.42 1457 6.23 3.24 13.4
40.27 2000 2.55 1594 5.20 3.57 11.2
35.21 2000 2.63 1700 4.71 3.46 10.1
1.14 ( 0.06 0.75
1.30 ( 0.04 0.78
2.11 ( 0.04 0.85
2.53 ( 0.04 0.85
30.19 2000 2.67 1726 4.12 3.34 8.87 3.23 ( 0.05 0.84
699 ppm SO2, 99.7 ppm HCl
30.21 2000 2.66 1729 4.09 3.04 5.83 3.44 ( 0.08 0.86
30.16 2000 2.75 1860 4.21 3.67 6.00 3.72 ( 0.06 0.83
30.05 2150 2.78 1895 4.24 4.64 6.04 3.72 ( 0.07 0.81
30.13 2250 2.82 1945 4.10 4.77 6.13 5.13 ( 0.08 0.87
30.22 2375 2.92 2069 4.43 5.57 4.77 7.03 ( 0.14 0.83
30.11 2500 2.97 2167 4.48 4.72 3.26 7.91 ( 0.14 0.77
Figure 3. Arrhenius plots of k1 in the temperature range 1000-3197
K; Mahmud et al.11 (b); this work (other symbols); our fitted equation
(solid line); equation of Mahmud et al. (dashed line).
292 ppm SO2, 97.5 ppm HCl
60.06 2000 2.22 1256 2.83 1.27 9.45 0.965 ( 0.06 0.82
50.26 2000 2.36 1398 2.53 1.29 8.45 1.59 ( 0.05 0.81
50.24 2000 2.41 1445 2.58 1.22 8.62 1.39 ( 0.04 0.83
40.24 2000 2.51 1556 2.16 1.37 7.20 2.02 ( 0.06 0.89
35.13 2000 2.57 1625 1.93 1.35 6.43 2.15 ( 0.05 0.84
30.11 2000 2.64 1725 1.84 1.19 5.73 2.24 ( 0.09 0.84
25.12 2000 2.69 1787 1.58 1.06 4.82 3.91 ( 0.13 0.87
25.10 2000 2.85 1989 1.51 1.58 5.03 4.75 ( 0.11 0.88
20.16 2000 2.95 2149 1.24 1.26 4.15 9.84 ( 0.26 0.91
20.06 2000 2.98 2177 1.25 1.17 4.15 10.1 ( 0.30 0.94
At low concentrations of [N2O] and [HCl], reactions 9 and 14
have negligible effects on k1, as shown in Table 1.
Values of k1 at various temperatures are plotted in Figure 3;
data by Mahmud et al.11 (b) are included for comparison; our
data agree well with theirs in the region of overlapping
temperature, 1093-1486 K. We extended the temperature range
from 1486 to 3197 K and show clearly the non-Arrhenius
behavior of k1.
971 ppm SO2, 97.4 ppm HCl
60.13 2000 2.19 1212 9.22 2.55 9.25 0.645 ( 0.05 0.35
40.28 2000 2.48 1519 7.08 2.58 7.11 1.61 ( 0.06 0.65
40.20 2000 2.52 1576 7.19 3.75 7.22 2.02 ( 0.08 0.68
35.11 2000 2.58 1644 6.43 3.27 6.45 2.64 ( 0.07 0.70
30.19 2000 2.68 1754 5.72 3.23 5.73 3.49 ( 0.09 0.79
25.10 2000 2.79 1909 4.92 3.18 4.94 4.03 ( 0.11 0.73
25.08 2000 2.84 1985 4.99 2.95 5.01 5.17 ( 0.15 0.84
20.07 2000 2.91 2079 4.07 2.57 4.09 8.64 ( 0.03 0.83
Fitting our results combined with previous data yields the
expression
k1 ) (9.27 ( 0.03)10-24
3.67(0.18 exp[-(1030 ( 160)/T] cm3 molecule-1 s-1 (17)
×
T
in which the listed errors represent one standard deviation of
the fit. By comparing with the equation reported by Mahmud
et al.11
702 ppm SO2, 70.0 ppm HCl
30.16 1750 2.61 1672 4.03 1.60 4.02 3.45 ( 0.11 0.84
30.33 2000 2.74 1830 4.22 2.50 4.21 4.50 ( 0.11 0.83
30.19 2000 2.79 1887 4.28 2.73 4.27 4.38 ( 0.20 0.85
20.12 1750 2.85 1980 2.90 2.22 2.89 8.46 ( 0.20 0.90
k1 ) 5.6 × 10-21T 2.87 exp [-(1766/T)] cm3 molecule-1 s-1
20.61 2250 2.92 2076 3.00 1.79 2.99 10.6 ( 0.4
20.11 2375 2.99 2171 3.00 2.83 3.00 11.2 ( 0.3
20.25 2375 3.02 2205 3.05 2.68 3.06 12.4 ( 0.3
20.27 2375 3.05 2242 3.06 3.67 3.84 15.1 ( 0.4
20.35 2500 3.17 2420 3.17 2.21 3.14 17.8 ( 0.7
20.11 2500 3.20 2468 3.19 2.30 3.16 20.7 ( 1.0
0.92
0.89
0.88
0.89
0.90
0.88
(2)
we find that eq 17 describes the rate coefficients at high
temperature better.
4.3. Potential Energy Surfaces and Reaction Mechanism.
The reaction O + HCl may proceed via the following two paths,
producing OH and ClO, respectively:
700 ppm SO2, 50.9 ppm HCl
30.80 2500 2.93 2065 4.53 3.81 3.29 6.92 ( 0.30 0.80
30.23 2500 2.97 2123 4.49 5.62 3.27 10.3 ( 0.4
27.62 2500 3.00 2184 4.14 3.95 3.01 10.3 ( 0.5
25.16 2500 3.08 2294 3.84 4.71 2.79 10.8 ( 0.6
22.63 2500 3.16 2410 3.52 3.16 2.56 16.6 ( 0.6
20.25 2500 3.24 2525 3.20 2.67 2.33 26.8 ( 2.1
0.82
0.82
0.77
0.85
0.90
O(3P) + HCl(1Σ+) f OH(2Π) + Cl(2P)
f ClO(2Π) + H(2S)
(1a)
(1b)
11.6 ppm N2O, 23.4 ppm HCl
However, as will be shown later, reaction 1b plays an
insignificant role even at a temperature as high as 3000 K
because it has a large barrier and is significantly more
endothermic.
The geometries of all of the transition states (TS) and local
minima (van der Waals complexes) identified by searching with
the intrinsic reaction coordinate (IRC)55 at the B3LYP/6-311+G-
(3df,2p) level of theory are presented in Figure 4; potential
energy diagrams for reaction paths 1a and 1b are shown in
Figure 5. Three local minima, LM1, LM2, and LM3, were
found. The linear LM1, OHCl (3A′′), formed by the association
30.48 2500 2.97 2115
25.12 2500 3.10 2323
20.14 2500 3.26 2549
20.02 2500 3.29 2574
15.14 2500 3.36 2683
10.22 2500 3.56 3062
10.63 2600 3.65 3197
7.51 6.59 7.18 ( 0.04 0.89
6.39 5.61 20.0 ( 0.1
5.30 4.65 27.7 ( 0.2
5.29 4.64 28.2 ( 0.1
4.06 3.56 44.8 ( 0.3
2.84 2.49 59.5 ( 0.9
2.99 2.62 61.4 ( 1.5
0.93
0.94
0.94
0.95
0.97
0.97
a P1: pressure of reactant gas mixture; P4: pressure of driver gas;
Ms: Mach number; T5: temperature of reaction. Concentrations are in
units of molecule cm-3; k1 values in cm3 molecule-1 s-1 are fitted with
kinetic modeling, and k1′ values are derived from pseudo-first-order
decays; see text.

Rate Coefficients of O(3P) + HCl at High T
J. Phys. Chem. A, Vol. 106, No. 43, 2002 10235
TABLE 2: Predicted Enthalpies of Reaction for Two Reaction Paths and ZPE-Corrected Energies of Transition States and
Intermediates Relative to the Energy of the Reaction O + HCla
B3LYP/
6-311+G(3df,2p)//
B3LYP/
MP2/
MP4(SDTQ)/
CCSD(T)/
CCSD(T)/
6-311++G(3df,2p)// 6-311++G(3df,2p)// 6-311G++(3df,2p)// 6-311+G(3df,2p)//
B3LYP/
6-311+G(3df,2p)
B3LYP/
6-311+G(3df,2p)
B3LYP/
6-311+G(3df,2p)
CCSD(T)/
6-311+G(d,p)
6-311+G(3df,2p)
G2 G2Mb
JANAFc
path 1a
path 1b
TS1
TS2
TS3
-1.82
35.99
0.56
1.26
2.81
43.59
-1.23
-15.10
36.16
2.21 -0.17
38.07 46.95
9.19
1.28
41.82
11.91
15.01
14.10
60.15
-1.48
-10.23
42.45
1.28
43.15
11.51
15.42
12.76
60.15
-1.50
-9.46
43.53
1.20
41.46
8.96
10.45
11.05
53.03
-1.35
-7.31
41.76
1.01
0.48
38.98
9.63
11.66
11.23
53.45
11.54
TS4
LM1
LM2
LM3
-1.22
-7.04
-7.80
42.04
a Total energies in hartrees for O + HCl are B3LYP/6-311+G(3df,2p), -535.9188519; G2, -535.3222061; G2M, -535.3348626; MP2/
6-311++G(3df,2p), -535.2511837; MP4(SDTQ)/6-311++G(3df,2p), -535.2976216; CCSD(T), -535.2993457; and CCSD(T)/6-311++G(3df,2p),
-535.2993457 based on the geometry and frequencies computed at B3LYP/6-311+G(3df,2p); CCSD(T)/6-311+G(3df,2p)//CCSD(T)/6-311+G.(d,p),
-535.2991418. b G2M results were calculated according to the G2M(RCC2) model. c Using enthalpies of formation listed in the JANAF table57
and the revised value of OH58.
TS2 with a nearly linear structure of 3A′′ symmetry and energy
between TS1 and TS3 (see Table 2 and Figure 5); it was not
confirmed by the CCSD(T)/6-311+G(d,p) calculation. Similarly,
Ramachandran et al.16 also failed to identify such a transition
state at the MR-CI+Q/cc-pVTZ level of theory. Koizumi et al.13
identified a stationary point (with two imaginary frequencies)
with an energy ∼0.08 kcal mol-1 above their TS1; this stationary
point may be compared with our TS2. The disappearance of
TS2 at higher levels of theory may result from differences in
dynamic correlations at varied levels of theory.
Predicted enthalpies of reaction for two reaction paths and
enthalpies of formation of various species at various levels of
theory are tabulated in Table 2. For reaction path 1a leading to
products OH + Cl, barriers of 8.96, 10.45, and 11.05 kcal mol-1
,
Figure 4. Optimized geometries of four transition states and three local
minima of the O-H-Cl system. Listed bond lengths are in Å, and
bond angles are in degrees.
respectively, for TS1, TS2, and TS3 were predicted at the
CCSD(T)/6-311++G(3df,2p) level of theory on the basis of
geometries optimized with the B3LYP/6-311+G(3df,2p) method.
These values agree within ∼1 kcal mol-1 with those predicted
by the G2M method that employs a series of corrections to
expand the basis set from 6-311G(d,p) to 6-311++G(3df,2p)
as previously mentioned. Although TS2 was not confirmed at
the CCSD(T)/6-311+G(d,p) level of theory, the energies
computed for TS1 and TS3 with CCSD(T)/6-311+G(3df,2p)
using the geometry obtained at CCSD(T)/6-311+G(d,p) are
in good accord with those predicted with the G2M and the
CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311+G(3df,2p) methods,
as shown in Table 2.
TS1 has been studied the most extensively; our predicted
structure agrees with those predicted by Koizumi et al.13 and
Ramachandran et al.,16 except that our value of OHCl )
139.5° is greater than these earlier predictions by about 6 and
8°, respectively. Our predicted barrier of 9.63 kcal mol-1 for
TS1 by CCSD(T)/6-311+G(3df,2p)//CCSD(T)/6-311+G(d,p) is
about 1.1 kcal mol-1 greater than a barrier (KSG) fitted by
Koizumi et al. on the basis of MP2/6-31G(d,p) calculations
but is about 0.2 kcal mol-1 smaller than the scaled (S4) barrier
of Ramachandran et al. that is based on calculations with
MR-CI+Q/cc-pVTZ. Significant tunneling effects preclude
direct comparison of the predicted barrier at 0 K with the
Figure 5. Potential energy diagram for reaction paths 1a and 1b
based on energies calculated with CCSD(T)/6-311+G(3df,2p)//
B3LYP/6-311+G(3df,2p) and CCSD(T)/6-311+G(3df,2p)//CCSD(T)/
6-311+G(d,p) (listed in parentheses). Listed energies are in kcal mol-1
.
of reactants is not connected with any TS according to IRC
analysis. A nonlinear LM2 with OHCl ) 63.3°, a complex
of products OH and Cl, connects with the reactants O + HCl
via TS1 and TS2. In contrast, TS3 connects directly with
products OH + Cl according to IRC and IRCMax analyses.
experimental activation energy, ∼8.7 kcal mol-1
.
3
Both TS1 and TS2 belong to A′′ symmetry, whereas TS3
TS3 is predicted to be linear with 3A′ symmetry, lying 11.54
kcal mol-1 above the reactants and 1.91 kcal mol-1 above TS1
at the CCSD(T)/6-311+G(3df,2p)//CCSD(T)/6-311+G(d,p) level.
Koizumi et al.13 also reported the existence of a similar linear
belongs to 3A′ symmetry. For reaction path 1b, LM3 is a linear
complex of products H and ClO; it connects with the reactants
via a linear transition state TS4.
Our search for transition states at the B3LYP/6-311+G-
(3df,2p) level of theory located an additional transition state
3
TS with A′ symmetry, which lies 11.9 kcal mol-1above their

10236 J. Phys. Chem. A, Vol. 106, No. 43, 2002
Hsiao et al.
ground state. Calculated rate coefficients indicate that, at tem-
peratures below 3000 K, contributions from the reaction channel
via TS3 are small, as is discussed in the next section.
The transition state TS4 for reaction path 1b producing H +
3
ClO is predicted to have a linear structure and A′′ symmetry
(Figure 4); both the G2M(CC2) and CCSD(T)/6-311++G-
(3df,2p) calculations predict a barrier height of ∼53 kcal mol-1
for this path. This reaction path is therefore unimportant
kinetically, as mentioned previously.
4.4. Calculation of Rate Coefficients. Rate coefficients of
the reaction O + HCl, calculated for the lowest two reaction
channels producing OH + Cl via TS1 and TS3 on the basis
of the energies predicted at the CCSD(T)/6-311+G(3df,2p)
level using the molecular parameters computed by CCSD(T)/
6-311+G(d,p), are illustrated in Figure 7. Fitting results of
calculated rate coefficients from 200 to 3200 K to an analytical
form similar to eq 17 yield
Figure 6. Imaginary vibrational wavenumbers and associated displace-
ment vectors of transition states based on B3LYP/6-311+G(3df,2p)
and CCSD(T)/6-311+G(d,p) (in parentheses).
kTST(Eckart) ) (3.60 ( 0.08)10-23
3.48(0.14 exp[-(1390 ( 90)/T] cm3 molecule-1 s-1 (18)
kTST(ZCT) ) (3.56 ( 0.04)10-19
2.35(0.06 exp[-(2430 ( 40)/T] cm3 molecule-1 s-1 (19)
kTST(SCT) ) (1.66 ( 0.02)10-21
2.99(0.08 exp[-(1550 ( 50)/T] cm3 molecule-1 s-1 (20)
kTST ) (2.36 ( 0.01)10-15
1.30(0.01 exp[-(4160 ( 50)/T] cm3 molecule-1 s-1 (21)
×
T
×
T
×
T
×
T
in which ZCT and SCT represent zero- and small-curvature
tunneling corrections, respectively. In Figure 7A, we compare
the total rate coefficients for the formation of OH + Cl
calculated by conventional TST, TST with Eckart-tunneling
corrections,42 and variational TST including corrections for zero-
and small-curvature tunnelings43 with the existing experimental
data of Ravishankara et al.,1 Brown and Smith,6 Mahmud et
al.11 and the present work. Results from these three model
calculations, although different to some extent at lower tem-
peratures, all agree satisfactorily with experimental values.
Overall, the variational TST calculation with zero- or small-
curvature tunneling corrections appears to account for experi-
mental data above room temperature slightly better. In the inset
of Figure 7A, contributions from the two low-energy channels
are compared. The major contribution stems from the channel
involving TS1 with the smallest barrier, 9.63 kcal mol-1. It
should be mentioned that similar calculations with the energies
predicted by the G2M method based on the molecular param-
eters computed at the B3LYP/6-311+G(3df,2p) level under-
estimated the rate constant at lower temperatures (by about
40% at room temperature) primarily because of the much lower
imaginary frequency (946 cm-1) and thus the effect of tunneling
corrections (see Figure 6).
In Figure 7B, we compare our predicted results with those
from previous theoretical calculations by Koizumi et al.,13
Thompson and Miller,21,22 Aoiz et al.,26 Skokov et al.,17 Allison
et al.,15 and Poirier.25 Koizumi et al.13 derived the KSG PES
by fitting the MP2/6-31G(d,p) results; they obtained the thermal
rate constant from quantum scattering calculations. On the basis
of this PES, Thompson and Miller21,22 calculated the thermal
rate constant from the time integral of the flux-flux auto-
correlation function. Aoiz et al.26 calculated the quantum
mechanical (QM) and quasi-classical trajectory(QCT) rate
constants, and Poirier25 applied the helicity-conserving and
Figure 7. (A) Comparison of predicted rate coefficient k1 (solid line:
conventional TST calculations including Eckart-tunneling corrections;
dashed line: Polyrate program of Truhlar with zero-curvature tunneling
corrections; gray line: Polyrate program with small-curvature tunneling
corrections; dotted line: conventional TST calculations) with experi-
mental data (0: Ravishankara et al.,5 9: Brown and Smith,6,7 O:
Mahmud et al.,11 +: this work); results from two different reaction
channels are shown in the inset. (B) Comparison of theoretical results
in this work with those reported previously by Koizumi et al.,13
Thompson and Miller,21,22 Aoiz et al.,26 Skokov et al.,17 Allison et al.,15
and Poirier.25
J-shifting approximations to carry out the thermal rate calcula-
tions. Furthermore, Ramachandran et al.25 constructed the S1,
S1A, S2, and S4 potential energy surfaces, which were a series
of fits to scaled ab inito data, and Allison et al.15 applied these
potential energy surfaces to calculate the thermal rate constant
by variational TST. Recently, Skokov et al.17 employed the S4
potential energy surface and calculated the thermal rate constants
by QCT, TST, and variational TST with the improved canonical

Rate Coefficients of O(3P) + HCl at High T
J. Phys. Chem. A, Vol. 106, No. 43, 2002 10237
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mechanical calculations17,21,26 with the J-shifting approximation
(QM/JS)56 based on either the KSG or the S4 PES appear to
agree with experimental data better than quasi-classical trajectory
results.17,26 A similar observation was reported by Aoiz et al.26
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5. Conclusions
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Rate coefficients of the reaction O(3P) + HCl in the
temperature range 1093-3197 K were determined using a
diaphragmless shock tube with atomic resonance absorption
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measurements with T < 1486 K but show a steep increase in
the rate coefficients for T > 2000 K. Rate coefficients fit
well with the equation k1(T) ) (9.27 ( 0.03) × 10-24T 3.67(0.18
exp[-(1030 ( 160)/T] cm3 molecule-1 s-1, in which the listed
errors represent one standard deviation. Theoretical calculations
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ClO is unimportant and that two channels lead to the formation
of OH + Cl; the major contribution stems from the channel
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.
Calculated rate coefficients fit well with experimental observa-
tions throughout the temperature range of investigation.
Acknowledgment. We thank Professors H. Matsui and A.
Tezaki for providing the driver of the shock tube and for helping
us to set up the shock-tube system and Professor D. Truhlar for
the use of the Polyrate program. Y.-P.L. thanks the National
Science Council of Taiwan (grant nos. NSC89-2119-M-007-
001 and NSC89-2113-M-009-010) for support. M.C.L. thanks
the Office of Naval Research, US Navy (contract no. N00014-
89-J1949) for support and the National Science Council of
Taiwan for the distinguished visiting professorship.
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