Kinetics of reactions of H atoms with methane and chlorinated methanes

Article abstract of DOI:10.1021/jp0023359

The reactions of H atoms with methane, four chlorinated methanes, and isobutene have been studied experimentally using the discharge flow/resonance fluorescence technique over wide ranges of temperatures. The rate constants were obtained in direct experiments as functions of temperature. The experimentally obtained activation energies of the reactions of H atoms with chlorinated methanes demonstrate a correlation with the enthalpies of the reactions. Transition state theory reaction models were created on the basis of ab initio calculations, the Marcus expression for correlation between reaction barriers and reaction energetics, and analysis of experimental data. It is demonstrated that the formalism based on the Marcus expression adequately describes the observed temperature dependencies of the rate constants of the overall reactions. According to the models, abstraction by H atoms of hydrogen atoms from chloromethanes is an important process accounting for significant fractions of the overall rate constants. The models result in expressions for the rate constants of Cl and H atom abstraction channels and the corresponding reverse reactions over wide ranges of temperatures.

Full text of DOI:10.1021/jp0023359

J. Phys. Chem. A 2001, 105, 3107-3122
3107
Kinetics of Reactions of H Atoms With Methane and Chlorinated Methanes
Mikhail G. Bryukov,†,‡ Irene R. Slagle,† and Vadim D. Knyazev*,†,§
Department of Chemistry, The Catholic UniVersity of America, Washington, D. C. 20064, and National Institute
of Standards and Technology, Physical and Chemical Properties DiVision, Gaithersburg, Maryland 20899
ReceiVed: July 3, 2000; In Final Form: January 25, 2001
The reactions of H atoms with methane, four chlorinated methanes, and isobutene have been studied
experimentally using the discharge flow/resonance fluorescence technique over wide ranges of temperatures.
The rate constants were obtained in direct experiments as functions of temperature. The experimentally obtained
activation energies of the reactions of H atoms with chlorinated methanes demonstrate a correlation with the
enthalpies of the reactions. Transition state theory reaction models were created on the basis of ab initio
calculations, the Marcus expression for correlation between reaction barriers and reaction energetics, and
analysis of experimental data. It is demonstrated that the formalism based on the Marcus expression adequately
describes the observed temperature dependencies of the rate constants of the overall reactions. According to
the models, abstraction by H atoms of hydrogen atoms from chloromethanes is an important process accounting
for significant fractions of the overall rate constants. The models result in expressions for the rate constants
of Cl and H atom abstraction channels and the corresponding reverse reactions over wide ranges of temperatures.
I. Introduction
detection of reactants and products. Several measurements of
the rate constant of the H + CH3Cl reaction are reported in the
To make the incineration of industrial wastes more efficient
and less hazardous, it is necessary to understand all aspects of
this combustion process. Basic understanding of the incineration
mechanism is especially important in the case of chlorinated
hydrocarbons (CHCs), whose burning has the potential to
generate products such as phosgene which are more hazardous
than the CHCs themselves. Fundamental knowledge of mech-
anisms, specific pathways, and rate constants of important
elementary reactions, including those of chlorinated hydrocar-
bons, is of key importance to the success of kinetic modeling
of these systems.
In CHC/O2 and CHC/hydrocarbon/O2 flames, the major
channels of consumption of CHCs are unimolecular decomposi-
tion and the reactions of CHCs with Cl and H atoms.1-14 The
results of numerical simulations of these complex combustion
systems indicate a high sensitivity of the rates of CHC
destruction and of the concentration of active species to the rates
of Cl + CHC and H + CHC reactions.1,2,5,8,10-14 The inhibitive
effect of these reactions is associated with the binding of
hydrogen atoms into stable HCl, which then scavenges OH
radicals to form Cl atoms and water.5,10 In fuel-rich flames, the
reactions of H atoms with CHCs compete directly with the main
chain-branching reaction, H + O2 f OH + O.1,14-16
literature,17-21 including three studies where temperature de-
pendencies are reported.17-19 However, the results of these
studies are in substantial disagreement with each other, with
rate coefficients differing by more than an order of magnitude.
In refs 16 and 18-21, high initial concentrations of H atoms
were used (1013-1015 atoms cm-3), which could result in errors
in the rate measurement due to the effects of secondary reactions
(see Discussion).
To firmly establish the rate coefficients of H + CHC
reactions, experiments must be conducted with very low initial
concentrations of hydrogen atoms (<1011 atoms cm-3), thus
ensuring the absence of any complications due to fast secondary
reactions. To this end, we have constructed a heatable discharge
flow reactor with resonance fluorescence detection of H atoms.
This technique has excellent sensitivity to hydrogen atoms
(detection limit <108 atoms cm-3), allowing us to make rate
measurements with the necessary low initial concentrations.
Here we report the results of our first study, the reactions of H
atoms with the simplest members of the class of chlorinated
hydrocarbons, chlorinated methanes
H + CCl4 f HCl + CCl3 (297-904 K)
H + CHCl3 f products (455-854 K)
H + CH2Cl2 f products (498-787 K)
H + CH3Cl f products (586-839 K)
(1)
(2)
(3)
(4)
Although the importance of the H + CHC reactions has been
shown, little is known about the rates of even the chlorinated
methanes, the simplest CHC reactions. There are no direct
measurements of the rate constants of H + CCl4 or CHCl3
reported in the literature. The only experimental determination
of the rate constant of the H + CH2Cl2 reaction at elevated
temperatures (298-460K) is that of Combourieu et al.,16 who
used the discharge flow method with mass spectrometric
(Numbers in parentheses indicate the experimental ranges of
the current work.) In a series of ancillary experiments, two
reactions whose rate constants are well established22-28
H + CH4 f H2 + CH3 (748-1054 K)
H + iso-C4H8 f tert-C4H9 (299-503 K)
(5)
(6)
* Corresponding author. E-mail: knyazev@cua.edu.
† The Catholic University of America.
‡Due to different methods of transliteration from Cyrillic alphabet, this
name has also been spelled as Mikhail G. Brioukov.
§ National Institute of Standards and Technology.
were also studied in order to validate the experimental tech-
niques used.
10.1021/jp0023359 CCC: $20.00 © 2001 American Chemical Society
Published on Web 03/02/2001

3108 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
differences were 5 K at the highest temperature used and less
at lower temperatures).
Various aspects of the discharge flow technique of measuring
rate constants of gas phase chemical reactions have been
extensively discussed in the literature.30-33 These discussions
are not repeated here. Care was taken to ensure that, under all
experimental conditions used in the current work, the plug-flow
approximation was valid. The only exception to the plug flow
approximation was the minor, although non-negligible, contri-
bution of axial diffusion of H atoms. Corrections for the axial
diffusion had to be introduced into the experimentally obtained
atom decay rates (vide infra).
Three reactors were used in these experiments: a quartz
reactor with an internal diameter (i.d.) of 1.93 cm, a Pyrex29
reactor with i.d. ) 2.19 cm, and a Pyrex reactor with i.d. )
4.66 cm. The reactor surface, the surface of the movable injector,
and the inside of the discharge tube were treated to reduce
heterogeneous loss of H atoms first by soaking in a 5% aqueous
solution of ammonium bifluoride for 30 min and then by the
method of Sepehrad et al.34 The resultant values of the first-
order wall loss rate constant, kw, were always below 30 s-1
.
Typical values of kw were ∼4 s-1 for the Pyrex reactors and
12-25 s-1 for the quartz reactor. Reactors of different diameters
were used to rule out potential contributions of heterogeneous
reactions to the rate constant values obtained in the experiments
(vide infra).
H atoms were generated by a 2.45 GHz microwave discharge
(5) in a H2/He mixture. Hydrogen atoms formed in the discharge
area were carried through the reactor by a flow of helium
injected through inlet (13), and their concentration was moni-
tored by resonance fluorescence in the detection zone (4). An
additional flow of helium was introduced in the back section
of the reactor (inlet 14) to eliminate any stagnant “dead volume.”
The molecular substrate (CxHyClz) was introduced through a
quartz movable injector (7).
H atom resonance fluorescence (Lyman-R, 121.6 nm) was
induced by light from a discharge flow resonance lamp35,36 and
detected by a solar blind photomultiplier (EMR model 542-G-
0929). A molecular oxygen optical filter (11) (18.7 kPa (140
Torr) of O2, optical path length 3 cm)37 effectively cut off
radiation at all wavelengths in the range corresponding to the
peak of the photomultiplier sensitivity (115-170 nm) except
for the four narrow gaps in the spectrum of O2 (between 115
and 122 nm), one of which coincides with the Lyman-R
hydrogen atom line (121.6 nm).36
The sensitivity of the atom detection system to H atoms was
determined by titration with NO2 (rate constant of the H + NO2
reaction is 1.4 × 10-10 cm3 molecule-1 s-1).38 Typical
concentrations at which the fluorescence signal was equal to
the scattered light from the discharge flow lamp were ∼109 atom
cm-3. The sensitivity limit (defined by a signal-to-noise ratio
of unity) was <108 atom cm-3. In the titration experiments,
relatively high concentrations of H atoms had to be used (∼1012
atoms cm-3). Such concentrations caused some degree of self-
absorption of light at the Lyman-R line, which resulted in a
nonlinear dependence (saturation) of the resonance fluorescence
signal on the atom concentration. Thus, the calibration of the
H atom signal based on measuring the decrease in fluorescence
signal upon the addition of a small flow of NO2 to the reactor
yielded underestimated values of sensitivity coefficients (defined
as the ratio of signal to H concentration). Therefore, the values
of the initial concentrations of H atoms used in the experiments
to determine the rate constants of reactions 1-6 (listed in Table
1) are somewhat overestimated and should be understood as
upper limits to [H]0.
Figure 1. Schematic of the discharge flow/resonance fluorescence
apparatus. Equipment parts are the following: reactor tube (1), heater
(2), cooling coils (3), optical detection assembly (4), atom-generating
microwave discharge (5), pressure measurement outlets (6), moveable
injector (7), discharge flow lamp (8), MgF2 windows (9), light traps
(10), oxygen optical filter (11), photomultiplier tube (12), and carrier
gas inlets (13 and 14).
This article is organized as follows. Section I (current) is an
introduction. Experimental method, procedures, and results are
reported in section II. In section III, quantum chemical calcula-
tions and the transition state theory modeling of reactions 1-5
are presented. Modeling is used to separate the experimentally
determined overall rate constants into those of H and Cl atom
abstractions. The results are discussed in section IV.
II. Experimental Section
Rate constant measurements were conducted in a heatable
tubular flow reactor under pseudo-first-order conditions with a
large excess of molecular substrate. H atoms were detected by
resonance fluorescence and their decay measured as a function
of contact time over a wide range of experimental conditions.
II.1. Experimental Apparatus. A schematic of the experi-
mental apparatus is shown in Figure 1. The tubular quartz or
Pyrex29 flow reactor (1), resistively heated by a Nichrome29 wire
heater (2), was attached to a Pyrex six-way cross that served as
the base of the optical detection system. Pressure in the reactor
was monitored through outlets (6) positioned at the ends of the
heated zone.
The viscous pressure drop in the heated zone of the reactor
was obtained by measuring the difference in pressure values
obtained upstream and downstream of the heated zone and by
subsequent interpolation. A typical value of the viscous pressure
drop in the working part of the heated zone was 4-8 Pa (0.03-
0.15 Torr).
Temperature profiles along the reactor were measured with
a movable thermocouple and referenced to a readout of a fixed
thermocouple positioned in the heater. The uniformity of the
temperature profiles in the working part of the heated zone (20-
30 cm in length) was at least 5 K (maximum temperature

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3109
TABLE 1: Conditions and Results of Experiments to Measure Rate Constants of the Reactions of H Atoms with Chlorinated
Methanes, Methane, and Isobutene
[CxHyClz] range/
[H]0/1010
kie/10-15 cm3
No a
T/K
P/kPab
1012 molecules cm-3
k0/s-1 c
V/cm s-1 d
molecules cm-3
((kO′ BSD/V2))max
molecules-1 s-1
H + CCl4 f HCl + CCl3
1-1*
1-2+
1-3+
1-4+
1-5+
1-6*
1-7+
1-8*
1-9+
1-10+
1-11+
1-12
1-13
1-14
1-15
1-16
1-17
1-18
297
297
325
346
363
381
399
437
456
503
561
606
690
754
806
854
904
904
0.780-0.884
0.380-0.403
0.388-0.403
0.404-0.407
0.399-0.405
0.775-0.827
0.400-0.404
0.397-0.411
0.399-0.400
0.387-0.407
0.373-0.408
0.400-0.405
0.400-0.408
0.360-0.377
0.405-0.412
0.392-0.401
0.396-0.408
0.396-0.400
1400-3540
475-7285
779-6690
190-1351
200-2744
502-1350
180-1920
64.7-970
198-1080
329-1250
119-773
63.0-435
24.5-183.9
19.4-119.9
7.15-112.8
9.82-115.8
20.2-94.4
22.8-73.9
0.1 ( 0.9
2.0 ( 3.9
2.1 ( 6.0
-1.1 ( 3.8
0.7 ( 3.9
0.9 ( 5.2
-1.4 ( 7.5
-0.1 ( 7.8
8.7 ( 19.8
-0.6 ( 12.4
-4.3 ( 17.8
-8.3 ( 32.0
0.7 ( 11.3
1.2 ( 5.6
12 ( 22
319-353
3.8
7
2
5
7
0.066
0.082
0.165
0.045
0.141
0.144
0.195
0.262
0.025
0.198
0.142
0.204
0.198
0.171
0.092
0.255
0.137
0.107
7.04 ( 0.39
8.91 ( 0.94
15.2 ( 1.7
28.1 ( 4.8
49.2 ( 2.7
51.1 ( 5.9
102.4 ( 8.7
139 ( 12
627-656
276-654
739-779
783-809
428-452
3.6
4
850-870
658-674
3
2923-2981
1314-1383
1594-1651
1909-2131
1801-2196
2185-2253
2534-3788
2476-2565
2755-3658
3613-3633
3
176 ( 29
2
310 ( 18
647 ( 45
3
10
8
1090 ( 130
1760 ( 130
3113 ( 87
4080 ( 370
4570 ( 460
5920 ( 430
5670 ( 820
2
10
2
7-10
3
30 ( 29
-16 ( 21
5 ( 32
H + CHCl3 f products
2-1*
2-2*
2-3+
2-4*
2-5+
2-6+
2-7
417
437
455
483
503
563
629
721
807
854
854
0.743-0.825
0.781-0.843
0.396-0.403
0.377-0.431
0.401-0.404
0.391-0.401
0.391-0.397
0.379-0.405
0.385-0.399
0.395-0.404
0.384-0.393
511-2020
450-2020
602-2267
204-1790
563-2946
107-1473
167-632
63.3-290
69-284
0.5 ( 4.0
-0.7 ( 3.3
0.2 ( 4.0
0.0 ( 2.8
-14.5 ( 14.8
-17 ( 18
-5.5 ( 10.0
13 ( 18
394-436
2.4
2.5
1
0.138
0.149
0.117
0.232
0.061
0.118
0.083
0.086
0.175
0.137
0.151
23.0 ( 3.1
36.7 ( 2.7
39.8 ( 2.9
69.7 ( 2.7
91.1 ( 7.9
196 ( 22
465-505
840-1050
738-736
2267-2552
1355-2467
2157-2369
1238-2865
2488-2641
1906-2584
2521-2666
2.3
3
4
8
338 ( 27
2-8
4
1000 ( 120
1390 ( 160
1830 ( 140
2070 ( 180
2-9
2-10
2-11
8 ( 23
5
7.2-153
4 ( 13
3
24.8-148
4 ( 18
3
H + CH2Cl2 f products
3-1*
3-2
491
498
530
556
583
633
684
708
735
787
787
0.787-0.833
0.395-0.408
0.389-0.400
0.371-0.400
0.395-0.401
0.391-0.397
0.396-0.404
0.392-0.401
0.397-0.415
0.399-0.416
0.395-0.408
819-2590
887-3100
232-2030
250-1790
258-1630
136-986
126-836
197-811
92.4-804
55.6-530
89.6-731
1.8 ( 4.7
5 ( 11
488-551
4.4
4.0
3
0.151
0.162
0.143
0.220
0.196
0.190
0.190
0.118
0.219
0.198
0.130
25.8 ( 2.8
32.0 ( 5.9
42.4 ( 5.4
61.6 ( 6.6
95.4 ( 17.5
164 ( 24
315 ( 61
335 ( 22
438 ( 75
697 ( 46
626 ( 56
880-1183
857-1018
836-853
1113-1292
1218-1339
1702-1824
2242-2460
2048-2158
2117-2240
3043-3281
3-3
-4 ( 6
3-4*
3-5
2.0 ( 6.8
10 ( 17
7 ( 14
2
4
4
2.5
1.5
4
4
4
3-6
3-7
11 ( 31
-12 ( 12
-5 ( 34
11 ( 12
-17 ( 23
3-8
3-9
3-10
3-11
H + CH3Cl f products
4-1*
4-2*
4-3
4-4
4-5
4-6
4-7
4-8
4-9
586
615
633
684
708
735
787
839
839
0.753-0.824
0.371-0.425
0.381-0.428
0.407-0.408
0.391-0.415
0.396-0.400
0.401-0.407
0.403-0.405
0.392-0.420
490-2530
209-3400
715-2500
388-1420
173-1730
300-1190
279-922
143-505
95.2-951
-0.7 ( 5.1
-2.0 ( 7.0
-5.6 ( 8.9
-12.8 ( 9.6
-4.9 ( 6.7
-15 ( 14
-21 ( 13
3 ( 15
601-648
1.4
2.3
1.8
2.6
1.6
3.3
2.5
6
0.126
0.211
0.128
0.088
0.126
0.087
0.138
0.118
0.086
22.4 ( 3.3
34.7 ( 4.1
45.7 ( 5.7
86.0 ( 10.5
106.9 ( 7.3
137 ( 19
934-959
1374-1640
1585-1726
1725-1903
2009-2195
2036-2164
2148-2257
3196-3370
257 ( 23
379 ( 47
336 ( 31
-12 ( 16
3
H + CH4 f H2+CH3
5-1*
5-2
5-3
5-4
5-5
5-6
5-7
5-8
748
806
0.747-0.816
0.769-0.829
0.403-0.433
0.400-0.427
0.389-0.428
0.399-0.425
0.796-0.828
0.821-0.859
636-3290
934-3220
719-2820
469-3610
418-2470
239-1450
172-1454
216-1550
-2.1 ( 4.1
12 ( 11
20 ( 15
-29 ( 16
12 ( 16
23 ( 14
33 ( 21
19 ( 14
791-817
1.8
4.9
8.7
4.4
5.8
5.3
3.7
8.2
0.152
0.145
0.169
0.222
0.256
0.246
0.213
0.234
25.9 ( 2.0
51.3 ( 5.2
84.2 ( 9.6
103.0 ( 8.0
137 ( 11
192 ( 16
270 ( 24
380 ( 18
1231-1257
1970-2005
1914-2181
1971-2009
1839-1870
1895-1935
2205-2249
855
889
905
956
1005
1054
H + iso-C4H8 f tert-C4H9
6-1
6-2
6-3
6-4
6-5
6-6
299
301
346
399
456
503
0.133
3.15-14.6
4.49-14.7
16.4-73.6
6.87-41.7
10.9-75.9
9.18-44.3
4.6 ( 7.0
4 ( 5
576
9
3
3
2
3
1
0.23
3880 ( 460
3930 ( 700
6100 ( 360
7610 ( 1220
8800 ( 0510
10700 ( 1000
0.128
591
0.23
0.380-0.389
0.395-0.396
0.400
9.1 ( 13.7
-0.1 ( 22.9
-7.5 ( 19.1
-2.3 ( 26.6
2215-2333
2247-2553
2697
0.057
0.049
0.096
0.063
0.395-0.399
2961-2989
a Experiment number. Pyrex reactor with internal diameter with i.d. ) 4.66 cm was used in experiments marked with *, Pyrex reactor with i.d.
) 2.19 cm was used in experiments marked with +, and quartz reactor with i.d. ) 1.93 cm was used in unmarked experiments. b 1 kPa ) 7.5006
Torr. Minor variations in pressure are due to changes in flow conditions upon addition of large flows of molecular substrate (CxHyClz). c Zero-
abscissa intercept on the k′ vs [CxHyClz] dependence (see discussion of formula IV in the text). d Bulk flow velocity range. Minor variations in flow
velocity are due to changes in flow conditions upon the addition of large flows of molecular substrate (CxHyClz). Also, in some experiments, large
variations of flow velocity were introduced intentionally. e Error limits represent statistical uncertainties and are reported as 2σ. Maximum estimated
systematic uncertainties are 8% of the rate constant value (see text).

3110 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
Molecular substrates (CxHyClz) were stored undiluted in
Pyrex29 reservoirs. Flows of these reagents into the reactor were
determined by measuring the pressure drop in a calibrated
volume over time. These pressure measurements were performed
with a differential capacitance manometer (MKS Instruments
model 223BD-00010ACU).29 The independence of the measured
flows of the surface-to-volume ratio of the calibrated volume
was verified to ensure the absence of interference from
heterogeneous absorption and desorption processes on the walls
of vacuum manifold. Flows of molecular hydrogen to the atom-
producing discharge were measured in a similar way. It was
found that the typical dissociation efficiency of the discharge
was ≈20%. This resulted in the concentrations of undissociated
H2 in the reactor being approximately a factor of 2-3 higher
than the initial H atom concentrations.
II.2. Reaction Rate Measurements and Results. All experi-
ments to measure the rate constants of reactions 1-6 were
conducted under the conditions of large excess of molecular
substrate (35 e [CxHyClz]/[H]0 e 3.4 × 105). Initial concentra-
tions of H atoms in the detection zone were in the range of
(1-10) × 1010 atoms cm-3. (These values of [H]0 should be
understood as upper limits to the actual concentrations of
hydrogen atoms since the calibration procedure underestimated
the calibration coefficient values, as described in subsection II.1.)
Exact knowledge of H atom concentrations is not needed for
determination of rate constants because the experiments were
conducted under pseudo-first-order conditions. Rate constants
of heterogeneous loss of H atoms on the walls of the reactor
and the movable injector were regularly measured (in the
absence of molecular substrate). In these measurements, the time
of contact between H atoms generated in the discharge and the
walls was varied by changing the flow velocity (by means of
switching flow of helium carrier gas between inlet 14 and the
movable injector 7 (Figure 1) at various positions of the latter)
without changing the conditions in the discharge and monitoring
the resultant changes in the signal of H atoms in the detection
zone. The rate constants for H atom wall loss were typically in
Figure 2. Examples of experimentally obtained ln(SH) vs x depend-
encies. Data from experiments 1-1 and 5-5 (see Table 1). Numbers in
parentheses are flow velocities and concentrations of the CHyClz
substrate (in 1014 molecules cm-3).
reactor. Examples of experimentally obtained ln(SH) versus x
dependencies are presented in Figure 2. The observed values
of kO′ BS were corrected for the axial and radial diffusion of H
atoms via the formula30,33,39
kO′ BSD kO′ BSR2
k′ ) k′ 1 +
+
(II)
OBS
(
)
V2
48D
the range of 4-25 s-1 and always less than 30 s-1
.
The time of contact between the molecular substrate and H
atoms was varied by changing the position of the movable
injector. Under the experimental conditions used, plug flow
conditions are satisfied (except for a required correction for axial
diffusion, vide infra), and increments of contact time can be
obtained by dividing the corresponding changes in the length
of the contact zone by the bulk flow velocity, V. The tip of the
movable injector was always kept within the constant temper-
ature zone of the reactor.
where D is the diffusion coefficient of H atoms in He and R is
the reactor radius. The values of D were taken from the
D ) 1.790(T/273 K)1.77 cm2 s-1 (P ) 1.01 bar) (III)
dependence derived by Krasnoperov et al.40 based on the results
of experiments and calculations reported in refs 41-43. This
correction for diffusion never exceeded 21% of the final value
of k′.
The bimolecular rate constants of reactions 1-6 were
obtained from the slopes of the linear dependencies of k′ on
the concentration of substrate, [CxHyClz]
The total signal (counts s-1) detected by the photomultiplier
consisted of three components: the fluorescence of H atoms
(SH), the photomultiplier dark current (less than 1 count s-1),
and the scattered light originating from the resonance lamp and
reflected by the walls of the detection system (typically, ∼30
counts s-1). The contributions from the dark current and the
scattered light were measured directly in the absence of H atoms
but with the molecular substrate present (to account for possible
absorption of the scattered light) and later subtracted from the
total signal to obtain SH.
k′ ) ki[CxHyClz] + k0
(IV)
Here, ki is the bimolecular rate constant of the reaction under
study (i ) 1-6), and k0 is the zero-abscissa intercept of the k′
versus [CxHyClz] dependence. The conditions and results of
experiments to determine the values of rate constants of reactions
1-6 are presented in Table 1.
The k0 intercept appears due to the non-negligible wall losses
of H atoms on the surfaces of the reactor and the movable
injector. k0 can acquire both positive and negative values. If
the probability of H atom loss upon collision with the wall of
the movable injector is similar to or higher than that for the
collision with the reactor wall, k0 should be negative. However,
if heterogeneous loss is significantly more efficient on the
reactor wall than on the injector surface, or if this heterogeneous
The effective first-order rate constant values, k′OBS, were
obtained from least-squares-fits of the H atom fluorescence
signal SH to the equation
ln(SH) ) constant - kO′ BSxV -1
(I)
where x is the distance between the tip of the movable injector
and the detection zone and V is the bulk flow velocity in the

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3111
Figure 5. Experimental temperature dependencies of the rate constants
of reactions 1-6. Symbols are experimental data points: filled triangles,
reaction 1; open triangles, reaction 2; filled squares, reaction 3; open
squares, reaction 4; diamonds, reaction 5; filled circles, reaction 6; open
circles, data on reaction 6 from Harris and Pitts.28 Solid lines are
Arrhenius fits of data obtained in the current work (formulas 5-10).
The dotted line is the temperature dependence of k6 from ref 28.
Figure 3. Examples of experimentally obtained k′ vs [CCl4] (a) and
k′ vs [CHCl3] (b) dependencies. Experimental temperatures are indicated
on the plots.
of experimentally obtained k′ versus [CxHyClz] dependencies
are presented in Figures 3 and 4.
Heterogeneous reactions of H atoms with the CxHyClz
substrate adsorbed on the reactor wall could potentially influence
the observed rate of H atom decay, k′. If adsorption of substrate
is saturated, this effect would be manifested only by positive
values of k0, and the values of ki obtained would not be affected.
If, however, the adsorption is not saturated but increases with
the concentration of substrate, the contribution of such a
heterogeneous reaction can influence the slope of the k′ versus
[CxHyClz] dependence. Here, there are two possibilities. First,
the dependence of the surface density of substrate on its
concentration in the gas phase is nonlinear. In this case, a
hypothetical heterogeneous component to the observed H atom
decay rate would exhibit a nonlinear dependence on [CxHyClz].
The second case is encountered if the density of the adsorbed
substrate increases linearly with its gas-phase concentration. In
this case, the observed k′ versus [CxHyClz] dependencies are
expected to be linear, as in the case of a purely gas-phase
reaction.
To ensure that the measured rates of H atom decay in the
presence of CxHyClz represent the homogeneous reactions 1-5,
we conducted the experiments with reactors of different internal
diameters (1.93-4.66 cm) possessing different surface-to-
volume ratios. The experimentally obtained values of rate
constants were independent of the reactor used (Table 1). This
independence, as well as the linearity of the observed k′ versus
[CxHyClz] dependencies, indicates the absence of any significant
effects of potential heterogeneous reactions on the values of
the rate constants.
Figure 4. Examples of experimentally obtained k′ vs [CH2Cl2] (a) and
k′ vs [CH3Cl] (b) dependencies. Experimental temperatures are indicated
on the plots.
The rate constants of reactions 1-6 demonstrate no depen-
dence on pressure or initial concentration of H atoms within
the experimental ranges. The observed pressure independence
is expected since the mechanisms of reactions 1-5 are expected
to be those of atom abstraction and reaction 6 is expected to be
in its high-pressure limit under the experimental conditions
used.44 The rate constants display no dependence on the initial
loss is enhanced by the presence of molecular substrate in the
reactor (wall reaction with the adsorbed substrate), k0 can acquire
positive values. In the current study, both positive and negative
values of k0 were observed. However, these values of k0 were
minor compared with the first term in eq IV (see Table 1), and
uncertainties in k0 were comparable with the k0 values. Examples

3112 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
H atom concentration, indicating the absence of any influence
of potential secondary reactions on the kinetics of H atoms, as
can be expected due to the low values of [H]0 used ([H]0 )
(1-10) × 1010 atoms cm-3).
was purified by passing through liquid nitrogen cooled traps.
To verify that no potential impurities in methane or chlorinated
methanes could affect the measured rate constants, we analyzed
these gases for potential contaminants by gas chromatography.
A Shimadzu GC-9A gas chromatograph29 was used in these
analyses. After purification by vacuum distillation, the purity
of all chloromethanes was better than 99.98%, significantly
exceeding the specifications provided by the manufacturers.
The rate constants of reactions 1-6 exhibit positive temper-
ature dependencies (Figure 5) that can be represented with
Arrhenius expressions within their corresponding experimental
temperature ranges
k1 ) (1.36 ( 0.31) × 10-10 exp(-2937 ( 92 K/T)
cm3 molecule-1 s-1(297-904 K) (V)
III. Modeling
Rate constants of reactions 1-5 were obtained experimentally
over wide temperature ranges. Nevertheless, the temperatures
used in the experiments to determine the rates of each of these
reactions (Table 1) are still far from covering the whole
temperature range of practical interest, which extends to the
temperatures of combustion, i.e., up to 2000-2500 K. Accurate
extrapolation of rate constants to higher temperatures requires
application of theory and modeling.
k2 ) (1.33 ( 0.43) × 10-10 exp(-3640 ( 154 K/T)
cm3 molecule-1 s-1(417-854 K) (VI)
k3 ) (1.43 ( 0.50) × 10-10 exp(-4250 ( 184 K/T)
cm3 molecule-1 s-1(491-787 K) (VII)
The reactions of H atoms with partially chlorinated methanes
can proceed through the abstraction of both chlorine and
hydrogen atoms
k4 ) (2.24 ( 0.75) × 10-10 exp(-5394 ( 202 K/T)
cm3 molecule-1 s-1(586-839 K) (VIII)
H + CHCl3 f HCl + CHCl2
f H2 + CCl3
(2a)
(2b)
k5 ) (2.55 ( 0.89) × 10-10 exp(-6874 ( 267 K/T)
cm3 molecule-1 s-1(748-1054 K) (XI)
k6 ) (4.57 ( 1.32) × 10-11 exp(-729 ( 92 K/T)
cm3 molecule-1 s-1(299-503 K) (X)
H + CH2Cl2 f HCl + CH2Cl
f H2 + CHCl2
(3a)
(3b)
The error limits in expressions V-X represent uncertainties of
the fits only and are reported as 2σ. The lowest temperatures
used were determined either by ambient temperature or by the
impracticality of measuring rate constants that are significantly
lower than 10-14 cm3 molecule-1 s-1. The upper limits of the
experimental temperature ranges for reactions 1-4 were deter-
mined by the observed onsets of thermal decomposition of
chlorinated methanes. Decomposition reactions manifested
themselves by the apparent dependencies of the observed rates
of H atom decay, k′, on the flow velocity inside the movable
injector, which was interpreted as resulting from the reactions
of H atoms with the decomposition products. At the highest
temperatures used in studies of reaction 1-4, the absence of
any potential effects of thermal decomposition of chlorinated
substrate was verified by measuring the rate constants twice
with flow velocities through the movable injector differing by
at least a factor of 2.
The sources of error in the measured experimental parameters
such as temperature, pressure, flow rate, signal count, etc. were
subdivided into statistical and systematic. Statistical uncertainties
were estimated for parameters statistical in physical nature (for
example, signal count). The estimate of possible systematic
errors was based on the finite accuracy of the equipment and
on the uncertainty in the H atom diffusion coefficient.40 The
uncertainties of the measured experimental parameters were
propagated to the final values of the rate constants using different
mathematical procedures for propagating systematic and statisti-
cal uncertainties.45 The error limits of the experimentally
obtained values reported in this work (Table 1) represent 2σ
statistical uncertainty. The maximum estimated systematic
uncertainty is 8% of the rate constant value.
H + CH3Cl f HCl + CH3
f H2 + CH2Cl
(4a)
(4b)
The experimental values of the rate constants of reactions 2-4
reported in Table 1 and presented in Figure 5 reflect the sums
of Cl and H abstraction processes. On the basis of the
experimental information obtained in this work, one cannot
distinguish these different reaction channels. Therefore, model-
ing must be applied to separate the experimental rate constant
values into those of the individual elementary reactions and to
extrapolate these values to higher temperatures.
In this section, efforts on modeling of reactions 1-5 are
described. This modeling was based on application of transition
state theory, analysis of relationships between reaction barriers
and thermochemistry, and quantum chemical calculations. A
significant portion of this modeling is directed toward the
estimation of the relative importance of chlorine versus hydrogen
atom abstraction in reactions 2-4. First, ab initio calculations
of some of the properties of the transition states are performed
(subsection III.1), and the results are used to construct first
approximation models. The quantitative estimation of the
importance of H atom abstraction channels is then performed
by an extrapolation of the experimentally obtained H abstraction
rates (reaction 5, H + CH4) to the cases of reactions 2-4. This
extrapolation is performed within the framework of transition
state theory with an application of the Marcus equation (see
subsection III.2.). The rates of the Cl atom abstraction processes
in reactions 2-4 are obtained by subtracting the estimated H
abstraction rates (minor channels) from the experimental overall
rate data. Finally, models of all channels of reactions 1-5 are
created and used to predict rate constants at temperatures outside
of the experimental ranges. These reaction models, including
the reaction energetics, and computation of the rate constants
are described in subsection III.2. As with any modeling based
on statistical rate theories, the estimates of branching in reactions
Gases used the experiments were obtained from MG Indus-
tries29 (He, >99.999%), Aldrich29 (CH2Cl2, >99.9%; CHCl3,
>99.9%; CCl4, >99.9%), and Matheson29 (iso-C4H8, >99%;
CH4, >99.99%; CH3Cl, >99.5%; O2 > 99.6%). All gases except
helium were purified by vacuum distillation prior to use. Helium

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3113
2-4 must be understood as approximate and thus treated with
caution. Potential uncertainties in the calculated rates of H atom
abstraction arise from several sources such as the undetermined
accuracy of the transition state theory, the use of the Marcus
equation to predict (extrapolate) reaction barriers, and the
method of vibrational frequencies adjustment (subsection III.2.).
Uncertainties of the modeling results are discussed in greater
detail in “Discussion” (subsection IV. 2.).
III.1. Ab Initio Study of Transition States of Reactions
1-5. Ab initio calculations are not expected, at the current state
of quantum chemical theory, to produce reaction energy barrier
values that are comparable in accuracy with the best experi-
mental determinations of activation energy. Similarly, transition
state properties, such as vibrational frequencies will most likely
require adjustment to reproduce the experimental preexponential
factors for reactions 1-5. However, ab initio calculations can
be used successfully to provide other important properties of
the reaction transition states, such as geometrical structures
(including characteristic barrier widths important for tunneling,
vide infra) and vibrational frequencies of those modes that are
not significantly coupled to the reaction coordinate. Therefore,
in this work, ab initio quantum chemical calculations were
performed in order to obtain first-approximation-level transition
state properties and reaction barrier widths.
Properties of the transition states for reactions 1, 2a, 2b, 3a,
3b, 4a, 4b, and 5 were studied. The geometry was optimized,
and vibrational frequencies were obtained at the UMP2/6-31G-
(d,p) level. The detailed results of ab initio calculations of
transition states are presented as Supporting Information.
GAUSSIAN 9429,46 was used in all ab initio calculations.
Reaction 5 has been studied before at higher levels of theory
(see, for example refs 47 and 48 and references therein). The
modeling part of this study, however, is primarily concerned
not with the prediction of the reaction 5 rate constant from first
principles but with accurate extrapolation of the experimental
data and with reactivity trends in a series of similar reactions.
Therefore, lower-level ab initio calculations are uniformly
applied here to all reactions under study.
Tunneling can be expected to play a significant role in
reactions 1-5 since they each involve a transfer of an H atom.
The treatment of tunneling in the current work follows the
approach used by Knyazev and Slagle49 and Knyazev et al.22
in their modeling of the C2H3 T H + C2H2 and C2H3 + H2 T
H + C2H4 reactions. Computation of under-barrier tunneling
and above-barrier reflection probabilities is based on knowledge
of the barrier “width.” To determine the “width” parameters of
reactions 1-5, we determined the shapes of the barriers of these
reactions using the method of reaction path following (intrinsic
reaction coordinate, IRC)50,51 in mass-weighted internal coor-
dinates. IRC calculations were done at the UMP2/6-31G(d,p)
level for all reactions. For reaction 1, IRC calculations were
also performed using the density functional B3LYP/6-31G(d,p)
method. The potential energy profile along the reaction path
was fitted with the Eckart function
Figure 6. Potential energy profiles along IRC for reaction 1 obtained
at the UMP2/6-31G(d,p) and B3LYP/6-31G(d,p) levels (squares and
circles, respectively). Lines are fits with the Eckart formula (see text).
The dotted line illustrates the poor quality of fit obtained by using all
UMP2/6-31G(d,p)-level points with energies above that of H + CCl4.
The solid lines are obtained when only the top one-third of the barrier
(relative to the energy of H + CCl4) is used for fits.
parameter A was fixed at the value obtained from ab initio
calculations, and B and l were determined from the fitting.
Figure 6 presents the results of IRC calculations for reaction
1. As can be seen from the plot, the UMP2 and B3LYP methods
with 6-31G(d,p) basis result in significantly different barrier
heights (factor of 6 difference). Attempts to reproduce the barrier
shapes with equation XI using all points with energies above
those of H + CCl4 result in a poor quality of fit, which is
illustrated in Figure 6 by the dotted line for the case of the
UMP2-level barrier. However, considering that it is the top part
of the barrier that plays the most significant role in the tunneling
effect, it is more important to describe this upper portion with
the Eckart equation than the barrier as a whole. Thus, we limited
the fitting attempts to the top one-third of the barrier, where
the quality of fits was acceptable. The results are demonstrated
in Figure 6 with solid lines. Although the UMP2 and the B3LYP
methods yield drastically different reaction barrier heights, the
values of the “width” parameter l obtained at these two levels
of calculations are very close to each other for reaction 1:
l(reaction 1,UMP2) ) 1.685 and l(reaction 1,B3LYP) ) 1.661
amu1/2Å. A weak dependence of the barrier width parameter
on the level of ab initio method used was previously demon-
strated by the authors of refs 49 and 22, who found that
improvement of the level of theory from UMP2 to UMP4 and
spin-projected PMP453,54 methods did not result in significant
changes of the “width” parameter l for the C2H3 T H + C2H2
and C2H3 + H2 T H + C2H4 reactions. This is not surprising
since l is, essentially, a geometrical parameter and, as such, can
be expected to be determined with reasonable accuracy by
relatively low-level ab initio methods, i.e., methods that cannot
provide sufficient accuracy in energies but still are suitable for
calculation of transition state geometries. Thus, only the UMP2/
6-31G(d,p)-level calculations were performed for the other
reactions under study and UMP2 values of l were used in the
models of reactions 1-5 (Table 2). The values of l obtained
display a noticeable decrease upon Cl substitution, changing
from 1.414 for reaction 5 to 1.168 for reaction 2b (H abstraction
channels) and from 2.191 for reaction 4a to 1.685 for reaction
1 (Cl abstraction channels). Since only the upper one-third of
each barrier was fitted with the Eckart formula, the l values
provide information not about the barrier as a whole but only
about the top region, where most of the tunneling occurs. Units
of l are amu1/2Å.
Aê
(1 + ê)
Bê
(1 + ê)2
2πx
l
V )
+
ê ) exp
(XI)
(
)
where x is a coordinate along the reaction path, l is the “width”
parameter, and parameters A and B are related to the barriers
for the direct and reverse reactions E1 and E-1
A ) ∆E1,-1 ) E1 - E-1
B ) ( E + E )2
(XII)
x
x
1
-1
The transition probability for such a barrier can be described
analytically, as shown by Eckart.52 In the fitting process,

3114 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
TABLE 2: Values of the Reaction “Barrier Width”
TABLE 3: Experimental Values of the Standard Enthalpies
of Formation of Species Used in the Models of Reactions
1-5
Parameter (l) Used in the Models of Reactions 1-5
reaction
la/amu1/2
Å
molecule
∆Hf°298/kJ mol-1
ref
H + CHCl3 f H2 + CCl3
H + CH2Cl2 f H2 + CHCl2
H + CH3Cl f H2 + CH2Cl
H + CH4 f H2 + CH3
H + CCl4 f HCl + CCl3
H + CHCl3 f HCl + CHCl2
H + CH2Cl2 f HCl + CH2Cl
H + CH3Cl f HCl + CH3
(2b)
(3b)
(4b)
(5)
1.168
1.276
1.371
1.414
1.685
1.789
1.936
2.191
CCl4
CHCl3
CH2Cl2
CH3Cl
CH4
-95.6 ( 1.0
-102.7 ( 1.1
-95.0 ( 0.3
-81.87 ( 0.6
-74. 87 ( 0.34
-92.31 ( 0.10
71.13 ( 2.51
89.0 ( 3.0
55
55
55
55
56
56
57
58
(1)
(2a)
(3a)
(4a)
HCl
CCl3
CHCl2
CH2Cl
CH3
a Reaction “barrier width” parameter obtained from fitting the
potential energy profile along IRC with the Eckart formula (see text
and Figure 6). For each reaction, only the upper one-third of the barrier
was fitted since it is the top part of the barrier that plays the most
significant role in the tunneling effect, and therefore, it is more important
to describe this upper portion with the Eckart equation than the barrier
as a whole.
117.3 ( 3.1
58
59,60
56
146.0 ( 1.3
217.999 ( 0.006
H
for reactions 1-4 used for this plot are those of chlorine atom
abstraction (see Table 3 for thermochemical data used in
calculations). It is not surprising that a strong correlation (the
decrease of the activation energy with increasing reaction
exothermicity) is observed for the H + chloromethanes reac-
tions.
Numerous efforts have been reported in the literature that
were directed at finding a simple relationship between the rates
of reactions and thermochemical properties of reactants and
products for a series of reactions of similar types (see, for
example, refs 61-64). In 1968, Marcus derived an equation
relating the reaction barrier ER and the 0 K energy of reaction
∆HR specifically for gas-phase reactions of atom transfer64
∆HR ln 2
2E°
1
2
E ) ∆H + E° 1 + (ln 2)-1 ln cosh
(XIII)
{
(
) }
]
R
R
[
Here, E° is the “intrinsic barrier” for a series of similar type
reactions (ER ) E° if ∆HR ) 0). Equation XIII, derived by
Marcus on the basis of the BEBO method,65 is very similar in
behavior to the Marcus equation for electron-transfer reactions62
Figure 7. Correlation between activation energies (Ea) and enthalpies
(∆H2°98) of reactions 1-5 (see text, subsection III.2). Circle, reaction
1; upward triangles, reaction 2; squares, reaction 3; downward triangles,
reaction 4; diamond, reaction 5. Filled symbols, experimental Ea values
for the overall reactions and reaction enthalpy values (Cl atom
abstraction enthalpy values are used for reactions 1-4). Open symbols
and dashed line, Ea for H abstraction computed with the Marcus formula
(XIII) using the experimental Ea value for reaction 5 and reaction
enthalpy values for H atom abstraction. As can be seen from the plot,
the H abstraction channels can be expected to be important in reactions
2-4 since the estimated activation energies for these channels (open
symbols, dashed line) are close to the experimental values of the
activation energies of the overall reactions (filled symbols).
2
∆HR
E ) E° 1 +
(XIV)
(
)
R
4E°
at |∆HR/E°| < 4 but differs from it outside this region, providing
a more realistic limiting behavior for the cases of very large
positive and negative ∆HR. Numerous successful applications
of equations XIII and XIV to a variety of series of reactions of
similar types have been reported. An update of the literature
can be found in the recent article by Blowers and Masel.66
The solid line in Figure 7 shows a fit of the experimental
III.2. Models of Reactions 1-5 and Computation of
Reaction Rate Constants. The experimental data obtained in
the current work provide no information on individual channels
(Cl or H abstraction) in reactions 2-4. Therefore, modeling of
these elementary reactions is the only means of assessing the
relative importance of the reaction channels. For each overall
reaction i (i ) 2-4), the rate constant of one of the channels
can be estimated by means of modeling and that of the other
channel can be obtained by subtracting the computed rate from
the experimentally measured value of ki. Since the abstraction
of a hydrogen atom from chloromethanes by an H atom is likely
to be less efficient than the abstraction of a chlorine atom, we
choose to apply modeling to estimation of the rates of these
minor channels (2b, 3b, 4b).
The experimental results of the current study demonstrate a
correlation between the activation energies of the reactions of
H atoms with chlorinated methanes and reaction thermochem-
istry. Figure 7 presents the dependence of the experimental
activation energies of the overall reactions 1-5 on the standard
reaction enthalpy values (filled symbols). The enthalpy values
activation energy (Ea) versus heat of reaction (∆H° ) for
298
reactions 1-4 with formula XIII. The fact that the Marcus eq
XIII approximately describes the observed correlation provides
qualitative support for its application to reactions 1-5, to both
Cl and H atom abstraction channels. One can approximately
assess the importance of the H abstraction channels by drawing
a similar Ea versus ∆H° dependence (equation XIII, dashed
298
line) through the point representing the H + CH4 reaction (filled
diamond). Using the experimental values of the heats of
reactions for the hydrogen abstraction channels of reactions 2-4
(2b, 3b, and 4b) and the computed dashed line, one obtains
estimates of the activation energies for the reaction channels
2b, 3b, and 4b (shown by the open symbols on the plot). It can
be seen from the plot that H abstraction channels are expected
to be important in reactions 2-4 since the estimated activation
energies for these channels are close to the values of the
activation energies of the overall reactions. The differences
between the corresponding filled (Ea for overall reactions) and

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3115
open (Ea for H abstraction) symbols are only 2.9 kJ mol-1 for
reaction 2 and 5.4 kJ mol-1 for reaction 3.
In all modeling calculations, rate constant values were
computed using the transition state theory formula67
q
k T
ER
κ(T)Q
B
k∞A+B(T) )
exp -
(XV)
(
)
h
QAQB
kBT
where Qq, QA, and QB are partition functions of the transition
state and the reactants A and B respectively, ER is the reaction
energy barrier, and κ(T) is the temperature-dependent tunneling
factor
∞
E
kBT
κ(T) )
P′(E) exp -
dE
(XVI)
∫
-ER
(
)
Here, P′(E) is the first derivative of the energy-dependent
tunneling transition probability P(E), which was calculated using
the analytical formula of Eckart52 (see subsection III.1).
To estimate the rate parameters of the H abstraction channels
of reactions 2-4, we first created a model of the reaction of H
atoms with methane (reaction 5) and used it to extrapolate the
experimentally obtained k5 temperature dependence to temper-
atures outside of the experimental range. Frequencies of the
transition state and barrier width parameter for H atom abstrac-
tion were obtained from the UMP2/6-31G(d,p) ab initio study
(see subsection III.1 and Table 2). Four frequencies representing
bending deformations of the H3C‚‚‚H‚‚‚H transitional structure
(doubly degenerate C‚‚‚H‚‚‚H bend and CH3 rock) and the
reaction barrier height (ER1) were adjusted to reproduce the
experimental rate constant temperature dependence. Vibrational
frequencies were adjusted by multiplying all four frequencies
by a uniform scaling factor (0.95). The experimental data set
reproduced in the calculations consisted of the rate constant
values determined in this work and the values of the rate
constant for the reverse reaction (CH3 + H2 f H + CH4,
reaction -5) reported by Knyazev et al.22 For the purpose of
data fitting, the values k-5 were converted into k5 via the known
reaction thermochemistry (Table 3). It should be noted here that
the conversion of k-5 into k5 values performed originally in ref
22 contains an error that appeared due to incorrect temperature
values used in the equilibrium constant calculations. The correct
k5 expression from the results of ref 22 is k5 (T, ref 22) ) 5.52
Figure 8. Plot of the rate constants of reactions 5 and -5. Experimental
data: open circles, k5 values obtained in the current study; open squares,
experimental k-5 values of Knyazev et al.;22 crosses, the same values22
converted into k5 via the reaction thermochemistry; filled circles, k5
from Marquaire et al.;23 heavy lines, k5 values from Roth and Just26
and Rabinowitz et al.25 and k-5 values from Baeck et al.24 and several
low-temperature measurements analyzed in ref 23. Dashed lines,
calculations of Marquaire et al.23 Solid thin lines, calculations with the
model created in the current work.
in the value of the “intrinsic barrier” for H abstraction reactions,
E° ) 55.89 kJ mol-1
.
H
The rate constants of the H atom abstraction channels in
reactions of H atoms with CH3Cl, CH2Cl2, and CHCl3 (reactions
4b, 3b, and 2b) were calculated in an analogous way using the
transition state theory formula XV and expression XVI for the
tunneling correction coefficient. Reaction energy barriers (listed
in Table 4) were obtained from the Marcus eq XIII using the
above value of the “intrinsic barrier,” E° ) 55.89 kJ mol-1
.
H
For each reaction transition state, ab initio vibrational frequen-
cies were used (UMP2/6-31G(d,p) scaled by 0.942769), and the
four frequencies of the bending deformations of the C‚‚‚H‚‚‚H
transitional structure were adjusted by the same factor of 0.95
derived from fitting the k5(T) and k-5(T) experimental data. The
reaction models resulted in the temperature dependencies of the
rate constants for the direct and the corresponding reverse
reactions that can be represented with the following modified
Arrhenius expressions within the 298-3000 K temperature
× 10-10 exp(-7504 K/T) cm3 molecule-1 s-1
.
Figure 8 presents the results of rate constant calculations in
comparison with the experimental data of the current and
previous studies22-26 (see Discussion, section IV). The calculated
k5(T) and k-5(T) dependencies (in essence, an extrapolation of
the experimental data via transition state theory) can be
represented by the following modified Arrhenius expressions
in the 298-3000 K temperature region
interval (units are cm3 molecule-1 s-1
)
k2b(T) ≡ k(H+CHCl3fH2+CCl3) )
3.25 × 10-20 T2.74 exp(-2444 K/T) (XIX)
k-2b(T) ≡ k(H2+CCl3fH+CHCl3) )
k5(T) ) 7.45 × 10-19 T2.59 exp(-5057 K/T)
6.36 × 10-24 T3.51 exp(-7280 K/T) (XX)
cm3 molecule-1 s-1 (XVII)
k3b(T) ≡ k(H+CH2Cl2fH2+CHCl2) )
k-5(T) ) 1.06 × 10-20 T2.70 exp(-4451 K/T)
1.52 × 10-19 T2.66 exp(-3065 K/T) (XXI)
cm3 molecule-1 s-1 (XVIII)
k-3b(T) ≡ k(H2+CHCl2fH+CH2Cl2) )
Properties of the transition state, reactants, and products of
reaction (5,-5) are listed in Table 4.
The value of the energy barrier of reaction 5 obtained in the
fitting of the experimental data is ER1 ) 56.00 kJ mol-1. Within
the framework of the Marcus formula, this value of ER1
combined with the 0 K reaction enthalpy (energy difference
between products and reactants; ∆HR1 ) 0.23 kJ mol-1) results
3.21 × 10-22 T3.03 exp(-6792 K/T) (XXII)
k4b(T) ≡ k(H+CH3ClfH2+CH2Cl) )
4.65 × 10-19 T2.59 exp(-3847 K/T) (XXIII)
k-4b(T) ≡ k(H2+CH2ClfH+CH3Cl) )
1.73 × 10-21 T2.78 exp(-5826 K/T) (XXIV)

3116 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
TABLE 4: Properties of Molecules, Transition States, and Reaction Channels Used in the Models of Reactions 1-5
Vibrational Frequencies and Degeneracies (cm-1
458, 218(2), 776(3), 314(3)
3034, 680, 363, 1220(2), 774 (2), 261(2)
299, 1467, 717, 282, 1153, 3040, 898, 1268, 758
2937, 3039(2), 1452(2), 1355, 1017(2), 732
4161
)
56
CCl4
68
CHCl3
68
CH2Cl2
CH3Cl68
56,a
H2
HCl56
2885
57
CCl3
487, 898(2), 266(2), 322b
c
CHCl2
302, 534, 755, 902, 1226, 3138
401, 827, 997, 1391, 3101, 3246
3002, 580, 3184(2), 1383(2)
220[175](2), 262[209](2), 299(2), 304, 450, 779,
808(2)
244[190], 276[215], 310[241], 323[251], 344,
644, 769, 811, 1125, 1239, 3078
259[209], 284[229], 327[264], 858[692], 786,
788, 1095, 1186, 1418, 3037, 3140
286[230](2), 1038[834](2), 726, 1224, 1427(2),
3004, 3150(2)
CH2Cld
56
CH3
qe
H‚‚‚Cl‚‚‚CCl3
qe
H‚‚‚Cl‚‚‚CHCl2
H‚‚‚Cl‚‚‚CH2Clqe
qe
H‚‚‚Cl‚‚‚CH3
qe
H‚‚‚H‚‚‚CCl3
319[336](2), 1165[1226](2), 261(2), 375, 588,
818(2), 1538
qe
H‚‚‚H‚‚‚CHCl2
297[313], 336[354], 1112[1170], 1179[1241],
289, 707, 818, 932, 1262, 1587, 3066
287[302], 506[533], 1134[1194], 1148[1208],
777, 1005, 1028, 1411, 1671, 3029, 3139
510[537](2), 1075[1132](2), 1073, 1417(2), 1805,
3003, 3158(2)
H‚‚‚H‚‚‚CH2Clqe
qe
H‚‚‚H‚‚‚CH3
Rotational Constants (cm-1) and Symmetry Numbers
56
56
CCl4
0.05756 (12)
0.08670 (3)
0.2278 (2)
1.0159 (3)
59.344 (2)
10.440 (1)
0.08909 (6)g
0.26096 (1)
1.34405 (1)
CH3
7.6036 (6)
0.05406 (3)
0.08066 (1)
0.20228 (1)
0.8427 (3)
0.08670 (3)
0.19809 (1)
0.6964 (1)
2.6990 (3)
f
qf
CHCl3
H‚‚‚Cl‚‚‚CCl3
f
qf
CH2Cl2
H‚‚‚Cl‚‚‚CHCl2
CH3Clf
H‚‚‚Cl‚‚‚CH2Clqf
56,a
qf
H2
H‚‚‚Cl‚‚‚CH3
qf
HCl56
H‚‚‚H‚‚‚CCl3
57
qf
CCl3
H‚‚‚H‚‚‚CHCl2
H‚‚‚H‚‚‚CH2Clqf
f
CHCl2
CH2Clf
H‚‚‚H‚‚‚CH3
qf
h
Reaction Energy Barriers (kJ mol-1), Degeneracies, and Imaginary Frequencies (cm-1
)
E1 ) 24.35;
E2a ) 27.96;
E3a ) 31.63;
E4a ) 37.46;
E2b ) 36.04;
E3b ) 39.94;
E4b ) 45.77;
E5 ) 56.00;
E-1 ) 167.10;
E-2a ) 146.82;
E-3a ) 131.27;
E-4a ) 122.33;
E-2b ) 82.28;
E-3b ) 75.80;
E-4b ) 67.48;
E-5 ) 55.78;
g ) 4
g ) 3
g ) 2
g ) 1
g ) 1
g ) 2
g ) 3
g ) 4
νi,1 ) 1007i
νi,2a ) 971i
νi,3a ) 919i
νi,4a ) 848i
νi,2b ) 1459i
νi,3b ) 1354i
νi,4b ) 1277i
νi,5 ) 1247i
a In calculations of rate constants, partition functions of H2 were computed by direct summation. Differences between ortho- and para-H2 were
shown to be negligible. b The model of CCl3 from Hudgens et al.57 was used. The degree of freedom listed as having vibrational frequency equal
to 322 cm-1 is an inversion (double well). In calculations of rate constants, the partition function of this inversion was calculated by direct summation
over all energy levels (computed in ref 57). c Combination of UMP2/6-31G(d,p) calculations scaled69 by 0.9427 and experimental data from ref 70.
d Combination of UMP2/6-31G(d,p) calculations scaled69 by 0.9427 and experimental data from refs 71 and 72. e Vibrational frequencies of transition
states were obtained in UMP2/6-31G(d,p)-level ab initio calculations and scaled69 by 0.9427. Frequencies of four transitional modes were adjusted
via multiplication by a uniform factor (see text, subsection III.2). Numbers in square brackets are original (unadjusted) scaled ab initio values.
f From UMP2/6-31G(d,p)-level ab initio calculations. g Symmetry factor of 6 is consistent with the treatment of one vibrational mode as double-
well inversion (see ref 57 for discussion of rotational symmetry and degeneracy of vibrational levels in relevance to CCl3). h Imaginary frequencies
obtained from barrier “width” parameters and fitted values of barrier heights.
These calculated values of the rate constants of the H
abstraction channels were subtracted from the experimental
values of the rate constants of the overall reactions 2-4 to
evaluate the rates of the Cl abstraction channels. The relative
contribution of H abstraction in reactions 2-4 decreases with
chlorination changing from 42 to 55% (reaction 4) to 15-25%
(reaction 3) and 5-10% (reaction 2) in the experimental
temperature ranges. This change of the relative importance of
H abstraction is in agreement with the trend that can be derived
from the changes in ordinate differences between the filled and
the open symbols in Figure 7. A discussion of the uncertainties
associated with the calculation of H atom abstraction rates and
the use of the results for the evaluation of the rate constants of
the Cl atom abstraction channels is presented in Section IV.
The temperature-dependent values of the Cl abstraction
channels of reactions 1-4 obtained either directly from the
experiments (reaction 1) or via applying “corrections” for H
abstraction to the experimental rate constant data (reactions 2a,
3a, and 4a) were extrapolated to higher and lower temperatures.
This extrapolation was performed by the same modeling method
that was described above in relation to the H + CH4 f H2 +
CH3 reaction (reaction 5). Rate constants were calculated using
the transition state theory formula (XV). Ab initio (UMP2/6-
31G(d,p) level) vibrational frequencies of the corresponding
transition states scaled by 0.942769 were used. Reaction energy
barriers and four vibrational frequencies corresponding to the
C‚‚‚H‚‚‚H bending deformations were adjusted to reproduce the
observed rate constant temperature dependencies. The adjust-

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3117
ment of vibrational frequencies was carried out by multiplication
by a uniform factor. Optimization was performed by minimizing
the sum of squares of deviations of the rate constants. The
resultant transition state properties and energy barriers are listed
in Table 4.
temperature dependencies of the rate constants of reactions 1
and 2
H + CCl4 f HCl + CCl3
H + CHCl3 f products
(1)
(2)
The values of the frequency adjustment factor that had to be
applied to the ab initio frequencies in order to reproduce the
observed Cl abstraction rate constants were similar for all four
reactions: 1.255 (reaction 1), 1.285 (reaction 2a), 1.240 (reaction
3a), and 1.245 (reaction 4a). This similarity of the four
adjustment factors can be expected on the basis of a hypothesis
that the same ab initio method applied to four reactions of the
same type would overestimate (or underestimate) the force
constants of the transitional modes by the same factor.
Reactions 3-6 have been studied experimentally before
H + CH2Cl2 f products
(3)
(4)
(5)
(6)
H + CH3Cl f products
H + CH4 f H2 + CH3
The reaction models resulted in the temperature dependencies
of the rate constants for the direct and the corresponding reverse
reactions that can be represented with the following modified
Arrhenius expressions within the 298-3000 K temperature
H + iso-C4H8 f tert-C4H9
There is agreement between the results of several groups on
the rate constant values of reactions 5 and 6.22-28,73 The most
precise determination of k6(T) is that of Harris and Pitts28 who
used flash photolysis to generate and resonance fluorescence
to detect H atoms. A discussion of this and other studies of
reaction 6 can be found in ref 44. The values of k6 obtained in
the current work are in good agreement with the results of Harris
and Pitts over the experimental temperature interval (Figure 5).
Reactions 5 and -5 have been studied by many groups using
a variety of experimental methods. Reviews are available in
refs 74, 22-25, and 27 and references therein. Approximate
agreement has been reached between the results of different
groups, with the exception of the values of k5 at temperatures
above 1700 K, where rate constants obtained by Rabinowitz et
al.25 are lower than those of Roth and Just26 by a factor of 3.5.
An earlier controversy due to the disagreement between k5/k-5
values obtained from experimental data and those calculated
from the known thermochemistry of the reaction has been
resolved by Marquaire et al.,23 who studied reaction 5 by the
ESR/discharge flow method at temperatures 348-412 K. These
authors reproduced their experimental data and those of other
groups on reactions 5 and -5 with transition state theory
modeling to provide k5 and k-5 temperature dependencies
consistent with the thermochemistry of reaction (5,-5). Re-
cently, Knyazev et al.22 studied the reverse reaction, CH3 + H2
f H + CH4 (-5) using the laser photolysis/photoionization
mass spectrometry experimental method. Experimental data on
k5 obtained in the current study are presented in Figure 8,
together with the experimental literature data on reactions 5 and
-5 and the values calculated by Marquaire et al.23 from their
model. The experimental data of Roth and Just,26 Rabinowitz
et al.,25 Marquaire et al.,23 Baeck et al.,24 and Knyazev et al.22
are shown. Also, since the fit of Marquaire et al. provides a
near perfect representation of the results of a number of earlier
measurements of k-5 at relatively low temperatures (see ref 23
for individual data references), the corresponding segment of
the calculated curve from ref 23 is shown by a heavy solid line
to illustrate these low-temperature data. As can be seen from
the plot, the results of the current experimental study are in
good agreement with these data and predictions. The differences
in calculated curves of the extrapolated k5(T) and k-5(T)
dependencies at low temperatures between ref 23 and the current
work are primarily due to slightly different values of the CH3
enthalpy of formation used in these two studies.
interval (units are cm3 molecule-1 s-1
)
k1(T) ≡ k(H+CCl4fHCl+CCl3) )
2.85 × 10-16 T1.80 exp(-2062 K/T) (XXV)
k-1(T) ≡ k(HCl+CCl3fH+CCl4) )
2.77 × 10-25 T3.72 exp(-18686 K/T) (XXVI)
k2a(T) ≡ k(H+CHCl3fHCl+CHCl2) )
1.52 × 10-16 T1.81 exp(-2472 K/T) (XXVII)
k-2a(T) ≡ k(HCl+CHCl2fH+CHCl3) )
1.25 × 10-23 T3.20 exp(-16269 K/T) (XVIII)
k3a(T) ≡ k(H+CH2Cl2fHCl+CH2Cl) )
1.38 × 10-16 T1.79 exp(-2961 K/T) (XXIV)
k-3a(T) ≡ k(HCl+CH2ClfH+CH2Cl2) )
1.71 × 10-22 T2.85 exp(-14296 K/T) (XXX)
k4a(T) ≡ k(H+CH3ClfHCl+CH3) )
1.35 × 10-16 T1.73 exp(-3755 K/T) (XXXI)
k-4a(T) ≡ k(HCl+CH3fH+CH3Cl) )
6.41 × 10-23 T2.56 exp(-13236 K/T) (XXXII)
An attempt was made to model the rate constants of reactions
2-4 without applying any corrections for H atom abstraction,
i.e., assuming that Cl atom abstraction is the only process
responsible for the experimentally observed overall rate con-
stants. The resultant energy barrier values (ER2 ) 28.17, ER3
)
32.08, ER4 ) 38.17, units are kJ mol-1) were close to those
obtained when H abstraction is taken into account (see Table
4). However, the frequency adjustment factors obtained in this
exercise are significantly different for different reactions: 1.255
(1), 1.237 (2), 1.095 (3), and 0.895 (4) (reaction numbers are
given in parentheses).
The main motivation for studying reactions 5 and 6 in the
current work was a validation of the experimental technique.
Reactions 5 and 6 possess very different activation energies and,
therefore, different temperature dependencies (Figure 5). Good
IV. Discussion
IV.1. Experimental Values of the Rate Constants. The
current study provides the first direct determination of the

3118 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
Figure 9. Temperature dependence of the rate constant of reaction 3
(H + CH2Cl2 f products). Open circles, experimental data obtained
in the current study. Filled circles and dashed line, experimental data
and Arrhenius fit of Combourieu et al.16 Solid line, model of reaction
3 created in the current study.
Figure 10. Temperature dependence of the rate constant of reaction 4
(H + CH3Cl f products). Experimental data: open circles, results of
the current study; filled squares, Westenberg and deHaas;18 open
triangles, Hart et al.;17 filled triangle, Jones and Ma;20 open square,
Triebert et al.;21 heavy solid line, Aders et al.19 Thin solid line, model
created in the current study.
agreement reached between the results of this work and those
of other groups on the rate constants of both reactions 5 and 6
confirms the accuracy of the method and the equipment used
in the current experiments.
The kinetics of reaction 3 has been studied by Combourieu
et al.,16 who used the discharge flow method with mass
spectrometric detection of reactants and products to determine
rate constants in the 298-460 K temperature interval. The values
of k3 reported by Combourieu et al. are higher than those
calculated via the extrapolation of the experimental data obtained
in the current work, on average, by a factor of 2 (Figure 9) and
have a somewhat lower activation energy.
the experiments were conducted under pseudo-first-order condi-
tions for H atoms). Both of these studies employed the fast flow
technique with ESR detection of H atoms19,20 and, in ref 19,
mass spectrometric detection of stable species. Although not
considered by the authors of these two works, secondary
reactions are likely to have significantly influenced the observed
values of the rate constants, as described below.
In most earlier studies of reaction 4, Cl atom abstraction was
assumed to be the only channel
H + CH3Cl f HCl + CH3
(4a)
Several groups17-21 reported experimental studies of reaction
4, including three studies where temperature dependencies have
been determined.17-19 The results of these works are in
substantial disagreement with each other, with rate coefficients
differing by more than an order of magnitude. Figure 10
compares the results of the current study on k4 with the results
of earlier investigations. The values of k4 obtained in this work
are in good agreement with the determination of Westenberg
and deHaas,18 who used the discharge flow method with mass
spectrometric detection of CH3Cl and ESR detection of H atoms.
The disagreement with the results of Hart et al.17 is not very
meaningful since these authors used an experimental method
(“point source technique” in flames) that yields only ap-
proximate rate constant values, as reflected in large uncertainties
reported by the authors (Figure 10).
However, as shown in section III of the current work, the
abstraction of an H atom is likely to be an important channel,
reaching approximately 50% of the overall rate constant
H + CH3Cl f H2 + CH2Cl
(4b)
Due to the very high concentrations of H atoms employed in
all earlier studies of reaction 4, the reaction of CH2Cl radicals
with H atoms
CH2Cl + H f CH3Cl* f Cl + CH3
(7)
must be a very fast process. In the initial step of this chemically
activated reaction, a highly vibrationally excited CH3Cl*
molecule is formed. This CH3Cl* molecule decomposes into
Cl atom and CH3 radical due to the weaker (compared with
C-H) C-Cl bond. Additional production of Cl atoms could
occur by reaction of H with HCl
The rate constants of reaction 4 reported by Aders et al.,19
Jones and Ma,20 and Triebert et al.21 are in significant disagree-
ment with those obtained in the current work from the
experiments and from extrapolation of experimental data to low
temperatures. The values of k4 from refs 19-21 are larger than
the results of this study by 1-3 orders of magnitude.
In refs 18-21, high initial concentrations of H atoms were
used (1013-1015 atoms cm-3). At the same time, in two of these
studies, relatively high concentrations of CH3Cl were employed
([CH3Cl] ) (6-84) × 1014 molecules cm-3 in ref 19; the [CH3-
Cl] range was not reported in ref 20 but must have been at least
an order of magnitude higher than [H]≈ 1014 atoms cm-3 since
H + HCl f Cl + H2
(8)
(k8 ) 2.8 × 10-11 exp(-2082 K/T) cm3 molecule-1 s-1 75).
Since high (∼1015 molecules cm-3 or higher) concentrations
of CH3Cl were used, the Cl atoms formed in reactions 7 and 8
will react with CH3Cl (rate constant k9 g 5 × 10-13 cm3
molecule-1 s-1 76) to produce HCl and CH2Cl
Cl + CH3Cl f HCl + CH2Cl
(9)

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3119
Reactions 7-9 form a chain that quickly consumes H atoms
and CH3Cl. Thus, the observed decays of H atoms20 and CH3-
Cl19 in the experiments of Aders et al.19 and Jones and Ma20
did not reflect the rate of reaction 4 but rather the rates of the
above chain reaction.
can be expected to be sufficiently fast (k11 g 3.6 × 10-13 cm3
molecule-1 s-1 76) to result in an effective stoichiometric factor
of 2 or larger. For example, at 298 K, the first-order rate of
CH2Cl2 decay due to reaction 3 in the experiments of Com-
bourieu et al. (k′ ) k3[H]0 ) 6 × 10-16 × 2.14 × 1015 ) 1.28
s-1; calculated here on the basis of k3 and [H]0 values reported
in ref 16) is comparable to the pseudo-first-order rate of reaction
11 (k11[Cl] ) 3.6 × 10-13 × 3.9 × 1012 ) 1.4 s-1). Here, the
Cl atom concentration was estimated assuming 5% conversion
of CH2Cl2 in the (slow) reaction 3 and equal efficiency of Cl
production. Exact modeling of H and CH2Cl2 kinetics under
the experimental conditions of ref 16 is not possible because
of the likelihood of Cl atom wall loss that would decrease the
stoichiometric factor.
It is impossible to conclude whether a similar process affected
the experiments of Triebert et al.21 because these authors did
not report the CH3Cl concentrations employed in their experi-
ments. In this study (discharge flow technique with mass
spectrometric detection of CH3Cl), significant wall losses of H
atoms (first-order wall loss rate constant kH,w ≈ 30-80 s-1
)
were reported by the authors who used kH,w as one of the
adjustable parameters in fitting the observed [CH3Cl] versus
time data.
The above discussion of the experimental values and tem-
perature dependencies of the rate constants of reactions 1-6
yields the following conclusions. (1) The experimentally
observed rates of reactions 5 and 6 (those of H atoms with
methane and isobutene) are in excellent agreement with the
earlier reported literature data. (2) The temperature dependence
of the rate constant of reaction 4 obtained in this work is in
agreement with the results of Westenberg and deHaas.18 (3)
Disagreement between the values of k3 and k4 obtained in this
work and in earlier studies16,19-21 can be explained by fast
secondary reactions that affected the results of the latter.
The only earlier experimental study of reaction 4 that reported
using low concentrations of CH3Cl was the discharge flow/ESR/
mass spectrometry study of Westenberg and deHaas18 ([CH3-
Cl] ≈ 1013 molecules cm-3 as estimated here from a typical
[H] ≈ (0.5-2.5) × 1015 atoms cm-3 and [H]/[CH3Cl] ratio of
100-250 reported by the authors). It is interesting to note that
these authors reported that a much faster reaction was observed
if they attempted to conduct experiments with high CH3Cl
concentrations under pseudo-first-order conditions for H atoms.
Also, in the experiments performed with an excess of H atoms,
Westenberg and deHaas, in some instances, observed a slight
decay of H atoms although, due to the high [H]/[CH3Cl] ratio,
H decay would be expected to be negligible. In these cases,
reduction of the CH3Cl concentration resulted in the disappear-
ance of the H atom decay. The authors of ref 18 interpreted
these effects as resulting from a hypothetical heterogeneous
reactions, that of a fast wall loss of H due to a reaction with
absorbed CH3Cl. However, as can be seen from the above
discussion of secondary chemistry, a more likely explanation
is the chain process formed by reactions 7-9 when large
concentrations of both H and CH3Cl are used. Since, in the
actual k4 measurements, low CH3Cl concentrations were used,
reaction 8 was not sufficiently fast to influence the CH3Cl decay,
and therefore, the resultant rate constant values were not
significantly affected by the secondary reactions. One can
estimate from the values of the concentrations used in the
experiments of Westenberg and deHaas and the rate constants
of reactions 4 and 9 that reaction 9 could account for ap-
proximately e30% of the overall CH3Cl decay. However, Cl
atom heterogeneous decay, known to be rather efficient on an
uncoated glass or quartz surface,77 could have reduced the
influence of reaction 9 on the overall kinetics. As can be seen
from the plot in Figure 10, the temperature dependence reported
by Westenberg and deHaas coincides with that obtained
experimentally in the current study.
IV.2. Models of Reactions 1-5. Subsection III.3 describes
the method and the results of extrapolation of the experimental
values of the rate constants of reactions 1-5 to temperatures
outside the experimental ranges and their separation into those
of H atom and Cl atom abstraction. The method is based on
modeling these reactions within the framework of the transition
state theory. Since no experimental information exists on the
branching ratios in reactions 2-4, the relative importance of
hydrogen and chlorine abstraction was assessed by applying ab
initio methods and the Marcus eq XIII which relates reaction
barrier to the 0 K enthalpy of reaction (see subsection III.3 and
ref 64). First, the rate constants of reaction 5 (H + CH4 f H2
+ CH3) determined in direct experiments were analyzed. The
transition state theory model of reaction 5 based on ab initio
calculations and fitting of experimental data resulted in the value
of the “intrinsic barrier” (to be used within the framework of
the Marcus equation) for the reactions of H atom abstraction
from substituted methanes by an H atom. Then, rates of H
abstraction in reactions 2-4 were calculated on the basis of
analogy with reaction 5, using the obtained “intrinsic barrier”
value, experimental thermochemistry, and ab initio vibrational
frequencies of transition states corrected by a uniform factor
derived from modeling of reaction 5. The calculated rates of
the H atom abstraction channels (reactions 2b, 3b, and 4b) were
subtracted from the experimental values of the rate constants
of the overall reactions 2-4 to obtain the rates of the Cl atom
abstraction processes. Finally, these rate constants of the
reactions of Cl atom abstraction from CHCl3, CH2Cl2, CH3Cl,
and CCl4 (CCl4 rates were obtained directly from experiments)
were reproduced by transition state theory modeling and
extrapolated to higher and lower temperatures.
The differences between the results of the current determi-
nation of the rate constant of reaction 3 (H + CH2Cl2
f
products) and those of Combourieu et al.16 can be explained by
the interference of secondary reactions similar to the kinetic
mechanism discussed above for the H + CH3Cl reaction. In ref
16, experiments to determine k3 were conducted in an excess
of H atoms ([H] ) (0.76-2.14) × 1015 atoms cm-3) with
moderately high CH2Cl2 concentrations ([CH2Cl2] ) (2.9-7.7)
× 1013 molecules cm-3). The sequence of reactions
Figure 11 shows the energy barriers obtained in modeling of
the Cl and H abstraction channels as a function of the 0 K
reaction enthalpies (∆HR, products-reactants energy differences).
The plot is similar to that in Figure 7. However, the main
distinction is that in Figure 11 the Cl and H abstraction channels
are fully separated. Also, in Figure 11, energies and barrier
heights are plotted instead of standard enthalpies and observed
activation energies. Open symbols and the dashed line represent
H + CH2Cl2 f HCl (or H2) + CHiCl3-i
i ) 1, 2 (3)
H + CHiCl3-i f CHi+1Cl3-i* f CHi+1Cl2-i + Cl
Cl + CH2Cl2 f HCl + CHCl2
(10)
(11)

3120 J. Phys. Chem. A, Vol. 105, No. 13, 2001
Bryukov et al.
TABLE 5: Activation Energies (Ea), Preexponential Factors (A), Reaction Degeneracies (g), and Per-Atom Preexponential
Factors (A′)A/g) Obtained from Reaction Models at 1000 K
reaction
Ea/kJ mol-1
Aa
g
A′ a
H + CCl4 f HCl + CCl3
H + CHCl3 f HCl + CHCl2
H + CH2Cl2 f HCl + CH2Cl
H + CH3Cl f HCl + CH3
H + CHCl3 f H2 + CCl3
H + CH2Cl2 f H2 + CHCl2
H + CH3Cl f H2 + CH2Cl
H + CH4 f H2 + CH3
(1)
32.39
35.88
39.79
45.87
43.88
48.31
54.23
64.32
4.749 × 10-10
2.705 × 10-10
2.078 × 10-10
1.255 × 10-10
9.798 × 10-11
2.390 × 10-10
4.274 × 10-10
6.724 × 10-10
4
3
2
1
1
2
3
4
1.187 × 10-10
9.017 × 10-11
1.039 × 10-10
1.255 × 10-10
9.798 × 10-11
1.195 × 10-10
1.425 × 10-10
1.681 × 10-10
(2a)
(3a)
(4a)
(2b)
(3b)
(4b)
(5)
a Units are cm3 molecule-1 s-1
.
to compute force constants of transitional modes in a series of
reactions of the same type. The similarity of the obtained
adjustment factors and the good representation of the ER versus
∆HR dependence with the Marcus equation demonstrate the
internal coherence of the model. On the other hand, if no
correction for the H atom abstraction channels is introduced
and the experimental rate constants of reactions 2-4 are
reproduced with transition state theory models assuming that
Cl abstraction is the only existing channel, the frequency
adjustment factors obtained in the process of tuning the models’
parameters demonstrate rather inconsistent behavior. These
factors differ significantly for reactions 1-4, changing from
1.255 (reaction 1) to 0.895 (reaction 4), demonstrating the lesser
plausibility of such models.
Although the models of both the H and the Cl abstraction
channels created in this work appear to be internally coherent
and agree with the experimental data (upon which they are
based), one should emphasize the approximate nature of the
calculated H atom abstraction rates in reactions 2-4. The
uncertainties in these rate constant values originate in the use
of the Marcus equation to predict (extrapolate) reaction barriers
and in the frequency adjustment factor derived from the data
on the H + CH4 reaction. Since the Cl atom abstraction rates
in reactions 2-4 are obtained by subtracting the calculated rates
of H abstraction from the experimental values for the overall
reactions, the uncertainties of calculations propagate into the
values of rate constants of the Cl abstraction channels. These
uncertainties are the highest for reaction 4, where the H and
the Cl abstraction channels have comparable importance.
Reactions 2a and 3a are affected to a lesser extent. Of course,
models of reactions 1 and 5 are not affected by any of these
sources of uncertainties. Extrapolation to temperatures outside
of the experimental ranges was performed with the use of
transition state theory with a tunneling contribution calculated
using a rather simple one-dimensional model. Any application
of these results should be performed with the awareness of the
uncertainties inherent to the models and theories used.
Figure 11. Correlation between the energy barriers (ER) and the 0 K
enthalpies (∆HR) of the Cl abstraction channels of reactions 1-5 and
the calculated ER vs ∆HR dependence for the H abstraction channels
(see text, subsection III.2). Curve on the left represents the Cl atom
abstraction channels. Curve on the right represents the H atom
abstraction channels. Circle, reaction 1; upward triangles, reaction 2;
squares, reaction 3; downward triangles, reaction 4; diamond, reaction
5. Filled symbols, ER values derived from the experimental rate constant
data (corrected for H atom abstraction contributions in the cases of
reaction 2-4). Open symbols and dashed line, ER for H abstraction
computed with the Marcus formula (XIII) using the “intrinsic barrier”
value derived from the model of reaction 5. Solid line, fit of the data
on ER,Cl vs ∆HR,Cl dependence for Cl abstraction with the Marcus
formula (XIII).
the values for the H abstraction channels obtained from the
calculations via the Marcus equation (eq XIII). Filled symbols
indicate ER (energy barrier) values obtained from modeling
experimental data on reactions 1, 2a, 3a, 4a, and 5 (corrected
for H abstraction contributions in the cases of reactions 2a, 3a,
and 4a). Error limits represent the uncertainties of the experi-
mental activation energies and the standard reaction thermo-
chemistry values. They are shown here to provide an illustration
of experimental uncertainties and their influence on the model
energetics. The solid line in the left part of the plot represents
a Marcus equation (eq XIII) fit of the ER,Cl versus ∆HR,Cl
dependence for Cl abstraction reactions obtained in the model-
ing. The resultant value of the “intrinsic barrier” is 71.9 kJ
mol-1. As can be seen from the quality of the fit, the Marcus
equation (eq XIII) provides a good description of the correlation
between reaction energy barriers (ER,Cl) and 0 K reaction
enthalpy (∆HR,Cl) for Cl abstraction.
In the modeling of the Cl abstraction reactions, the values of
the frequency adjustment factor that had to be applied to ab
initio frequencies of the transitional modes in order to reproduce
the observed rate constants were very similar for all four
reactions considered. As was discussed in subsection III.3, one
can expect such similarity if one assumes that a particular ab
initio method results in approximately similar errors when used
The models of reactions 1-5 developed in the current study
on the basis of experimental data and ab initio calculations
indicate important roles of abstraction of H atoms in the H +
chloromethanes reactions. This conclusion is in agreement with
Tsang,15 who argued that H abstraction in H + chloromethanes
can be of significant importance. Tsang based his analysis on
the results of Clark and Tedder,78 who studied reactions of H
atoms with a series of halogenomethanes by end product
analysis.
Table 5 presents the activation energies (Ea) and preexpo-
nential factors (A) for H and Cl atom abstraction channels
obtained from the models of reactions 1-5 developed in this
study. These Arrhenius parameters were computed at a fixed
temperature of 1000 K. Due to the curvature in Arrhenius
coordinates exhibited by the rate constants, the values of Ea

H Atoms With Methane and Chlorinated Methanes
J. Phys. Chem. A, Vol. 105, No. 13, 2001 3121
and A in Table 5 are noticeably different from those derived
from the temperature dependencies of the experimental rate
constants (expressions V-IX). Also present in Table 5 are the
reaction degeneracy factors (calculated following the method
of refs 79-81 and coinciding, for the reactions considered here,
with the numbers of atoms subject to abstraction) and the “per-
atom” preexponential factors A′ obtained by dividing A by the
reaction degeneracy. As can be seen from the data, A′ values
for Cl abstraction are approximately the same for all chlo-
romethanes while those for H atom abstraction decrease with
increasing chlorination (e.g., A′ for chloroform is lower than
that for methane by a factor of 1.7).
of the overall rate constants under the experimental conditions.
The models result in the expressions for the rate constants of
the Cl abstraction (reactions 1, 2a, 3a, and 4a) and the H
abstraction (reactions 2b, 3b, 4b, and 5) channels and the
corresponding reverse reactions over wide range of temperatures
(298-3000 K)
k1(T) ≡ k(H+CCl4fHCl+CCl3) )
2.85 × 10-16 T1.80 exp(-2062 K/T) (XXV)
k-1(T) ≡ k(HCl+CCl3fH+CCl4) )
2.77 × 10-25 T3.72 exp(-18686 K/T) (XXVI)
k2a(T) ≡ k(H+CHCl3fHCl+CHCl2) )
1.52 × 10-16 T1.81 exp(-2472 K/T) (XXVII)
k-2a(T) ≡ k(HCl+CHCl2fH+CHCl3) )
1.25 × 10-23 T3.20 exp(-16269 K/T) (XXVIII)
k3a(T) ≡ k(H+CH2Cl2fHCl+CH2Cl) )
1.38 × 10-16 T1.79 exp(-2961 K/T) (XXIX)
k-3a(T) ≡ k(HCl+CH2ClfH+CH2Cl2) )
1.71 × 10-22 T2.85 exp(-14296 K/T) (XXX)
k4a(T) ≡ k(H+CH3ClfHCl+CH3) )
V. Summary
Reactions of H atoms with methane, four chlorinated meth-
anes, and isobutene have been studied experimentally with the
discharge flow/resonance fluorescence technique over wide
ranges of temperatures and at low pressures.
H + CCl4 f HCl + CCl3
H + CHCl3 f products
H + CH2Cl2 f products
H + CH3Cl f products
H + CH4 f H2 + CH3
(1)
(2)
(3)
(4)
(5)
(6)
1.35 × 10-16 T1.73 exp(-3755 K/T) (XXXI)
k-4a(T) ≡ k(HCl+CH3fH+CH3Cl) )
6.41 × 10-23 T2.56 exp(-13236 K/T) (XXXII)
k2b(T) ≡ k(H+CHCl3fH2+CCl3) )
H + iso-C4H8 f tert-C4H9
The resultant rate constants can be represented with the
Arrhenius expressions (experimental temperature ranges are
given in parentheses)
3.25 × 10-20 T2.74 exp(-2444 K/T) (XIX)
k-2b(T) ≡ k(H2+CCl3fH+CHCl3) )
6.36 × 10-24 T3.51 exp(-7280 K/T) (XX)
k3b(T) ≡ k(H+CH2Cl2fH2+CHCl2) )
1.52 × 10-19 T2.66 exp(-3065 K/T) (XXI)
k-3b(T) ≡ k(H2+CHCl2fH+CH2Cl2) )
3.21 × 10-22 T3.03 exp(-6792 K/T) (XXII)
k4b(T) ≡ k(H+CH3ClfH2+CH2Cl) )
4.65 × 10-19 T2.59 exp(-3847 K/T) (XXIII)
k-4b(T) ≡ k(H2+CH2ClfH+CH3Cl) )
1.73 × 10-21 T2.78 exp(-5826 K/T) (XXIV)
k5(T) ≡ k(H+CH4fH2+CH3) )
k1 ) (1.36 ( 0.31) × 10-10 exp(-2937 ( 92 K/T)
cm3 molecule-1 s-1 (297-904K) (V)
k2 ) (1.33 ( 0.43) × 10-10 exp(-3640 ( 154 K/T)
cm3 molecule-1 s-1 (417-854K) (VI)
k3 ) (1.43 ( 0.50) × 10-10 exp(-4250 ( 184 K/T)
cm3 molecule-1 s-1 (491-787K) (VII)
k4 ) (2.24 ( 0.75) × 10-10 exp(-5394 ( 202 K/T)
cm3 molecule-1 s-1 (586-839K) (VIII)
k5 ) (2.55 ( 0.89) × 10-10 exp(-6874 ( 267 K/T)
cm3 molecule-1 s-1 (748-1054K) (IX)
7.45 × 10-19 T2.59 exp(-5057 K/T) (XVII)
k-5(T) ≡ k(H2+CH3fH+CH4) )
k6 ) (4.57 ( 1.32) × 10-11 exp(-729 ( 92 K/T)
cm3 molecule-1 s-1 (299-503K) (X)
1.06 × 10-20 T2.70 exp(-4451 K/T) (XVIII)
Error limits in expressions V-X represent uncertainties of the
fits only and are reported as 2σ.
Acknowledgment. This research was supported by the
National Science Foundation, Combustion and Thermal Plasmas
Program under Grant CTS-9807136. The authors would like to
thank Dr. L. J. Stief for helpful advice and the loan of equipment
and Dr. V. L. Orkin for advice and help with the analyses of
chloromethane samples.
Transition state theory models of reactions 1-5 were created
on the basis of ab initio calculations, the Marcus expression
for correlation between reaction barriers and energetics, and
analysis of experimental data. It is demonstrated that the Marcus-
expression-based formalism adequately describes the observed
temperature dependencies of the rate constants of the overall
reactions. According to the models, abstraction of H atoms in
reactions 2-4 is an important process accounting for 5-55%
Supporting Information Available: Results of the ab initio
calculations of the transition states, reactants, and products of

3122 J. Phys. Chem. A, Vol. 105, No. 13, 2001
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