Kinetics of the R + HBr ? RH + Br (R = CH2Br, CHBrCl or CCl3) equilibrium. Thermochemistry of the CH2Br and CHBrCl radicals

Article abstract of DOI:10.1039/b210787m

The kinetics of the reaction of the CH₂Br, CHBrCl or CCl₃ radicals, R, with HBr have been investigated separately in a heatable tubular reactor coupled to a photoionization mass spectrometer. The CH₂Br (or CHBrCl or CCl₃) radical was produced homogeneously in the reactor by a pulsed 248 nm exciplex laser photolysis of CH₂Br₂ (or CHBr₂Cl or CBrCl₃). The decay of R was monitored as a function of HBr concentration under pseudo-first-order conditions to determine the rate constants as a function of temperature. The reactions were studied separately over a wide ranges of temperatures and in these temperature ranges the rate constants determined were fitted to an Arrhenius expression (error limits stated are 1σ + Student's t values, units in cm³ molecule^-1 s^-1): k(CH₂Br + HBr) = (7.5 ± 0.9) × 10^-13 exp[- (2.53 ± 0.13) kJ mol^-1/RT], k(CHBrCl + HBr) = (4.9 ± 1.1) × 10^-13 exp[-(8.2 ± 0.3) kJ mol^-1/RT] and k(CCl₃ + HBr) < (6 ± 1)× 10^-15 at 787 K. The kinetics of the reverse reactions, Br + R′H → HBr + R′ (R′ = CH₂Br or CHBrCl), were taken from the literature and also calculated by ab initio methods at the MP2(fc)/6-31G(d,p)//MP2(fc)/6-31G(d,p) level of theory in conjunction with the thermodynamic transition state theory to calculate the entropy and the enthalpy of formation values of the radicals studied. The thermodynamic values were obtained at 298 K using a second-law method. The results for entropy values are as follows (units in J K^-1 mol^-1): 263 ± 7 (CH₂Br) and 294 ± 6 (CHBrCl). The results for enthalpy of formation values at 298 K are (in kJ mol^-1): 171.1 ± 2.7 (CH₂Br) and 143 ± 6 (CHBrCl). The C-H bond strength of analogous halomethanes are (in kJ mol^-1): 427.2 ± 2.4 (CH₃Br) and 406.0 ± 2.4 (CH₂BrCl). Thermodynamic properties of the CH₂Br radical were calculated by statistical thermodynamic methods over the temperature range 100-1500 K.

Full text of DOI:10.1039/b210787m

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Kinetics of the R + HBr 0 RH + Br (R ¼ CH2Br, CHBrCl or CCl3)
equilibrium. Thermochemistry of the CH2Br and CHBrCl radicals
Jorma A. Seetula
Laboratory of Physical Chemistry, P.O. Box 55, (A. I. Virtasen aukio 1), FIN-00014,
University of Helsinki, Helsinki, Finland. E-mail: seetula@csc.fi
Received 1st November 2002, Accepted 3rd January 2003
First published as an Advance Article on the web 24th January 2003
The kinetics of the reaction of the CH2Br, CHBrCl or CCl3 radicals, R, with HBr have been
investigated separately in a heatable tubular reactor coupled to a photoionization mass spectrometer. The CH2Br
(or CHBrCl or CCl3) radical was produced homogeneously in the reactor by a pulsed 248 nm exciplex laser
photolysis of CH2Br2 (or CHBr2Cl or CBrCl3). The decay of R was monitored as a function of HBr concentration
under pseudo-first-order conditions to determine the rate constants as a function of temperature. The
reactions were studied separately over a wide ranges of temperatures and in these temperature ranges the rate
constants determined were fitted to an Arrhenius expression (error limits stated are 1s + Student’s t values, units
in cm3 moleculeꢀ1
s
ꢀ1): k(CH2Br + HBr) ¼ (7.5 ꢁ 0.9) ꢂ 10ꢀ13 exp[ꢀ(2.53 ꢁ 0.13) kJ molꢀ1/RT],
k(CHBrCl + HBr) ¼ (4.9 ꢁ 1.1) ꢂ 10ꢀ13 exp[ꢀ(8.2 ꢁ 0.3) kJ molꢀ1/RT] and k(CCl3 + HBr) < (6 ꢁ 1) ꢂ 10ꢀ15 at
787 K. The kinetics of the reverse reactions, Br + R0H ! HBr + R0 (R0 ¼ CH2Br or CHBrCl), were taken
from the literature and also calculated by ab initio methods at the MP2(fc)/6-31G(d,p)//MP2(fc)/6-31G(d,p)
level of theory in conjunction with the thermodynamic transition state theory to calculate the entropy and the
enthalpy of formation values of the radicals studied. The thermodynamic values were obtained at 298 K using a
second-law method. The results for entropy values are as follows (units in J Kꢀ1 molꢀ1): 263 ꢁ 7 (CH2Br)
and 294 ꢁ 6 (CHBrCl). The results for enthalpy of formation values at 298 K are (in kJ molꢀ1): 171.1 ꢁ 2.7
(CH2Br) and 143 ꢁ 6 (CHBrCl). The C–H bond strength of analogous halomethanes are (in kJ molꢀ1):
427.2 ꢁ 2.4 (CH3Br) and 406.0 ꢁ 2.4 (CH2BrCl). Thermodynamic properties of the CH2Br radical were
calculated by statistical thermodynamic methods over the temperature range 100–1500 K.
this information establishes the magnitudes of the various C–H
bond strengths which are associated with the enthalpy change
of the following reaction: radical–H ! radical + H.
Introduction
The natural source of bromomethane has been found to be a
marine phytoplankton.1 Bromomethane is considered to be
the most abundant atmospheric source of bromine atoms,
which recently have been considered to take a part in the cat-
alytic dectruction of ozone in the Earth’s atmosphere. Bromo-
methane is a very toxic compound and it is generally prepared
from a reaction of hydrogen bromide with methanol. It is used
for methylation in organic synthesis and as a fumigant. The
concentration of bromomethane in atmosphere is largely lim-
ited by its reactions with atoms and OH radical where CH2Br
radical is the product of these reactions. Of these, the reaction
with OH has a principal loss process for atmospheric bromo-
methane. The CH2Br radical may react further in exothermic
reactions with other open shell species at atmospheric condi-
tions to release Br atoms for secondary reactions with ozone.
The other product from this reaction is BrO which self-
reaction produces molecular bromine and oxygen. A similar
set of elementary reactions may be considered to occur for bro-
mochloromethane. It has also considered as an effective fire
suppressant. Both bromomethane as well as bromochloro-
methane have been detected at lower stratosphere among other
brominated compounds.2
The current study presents a time-resolved experimental
kinetic investigation of the CH2Br, the CHBrCl and the CCl3
radicals with HBr. The reactions have not previously been
studied. Two of the reactions were studied over a wide tem-
perature range and CCl3 + HBr reaction only at temperature
of 787 K. The approach for all three reactions is similar as
that used for the study of chlorinated radicals with HBr.3
The current study was carried out to investigate the enthalpy
of formation of the CH2Br and of the CHBrCl radicals using
a second-law method. The kinetics of the reverse reaction
direction Br + RH ! HBr + R was taken form the literature
and also studied theoretically. Different reaction channels of
the Br + CH3Br/CH2BrCl reactions were studied by ab initio
methods. The enthalpy of reactions were later used to calculate
C–H bond energies of analogous halogenated methanes. These
values were compared with other C–H bond energies of hydro-
carbons and halogenated hydrocarbons.
Kinetics and computational
Another function of the current study is on fundamental
understanding of free radical kinetics and reactivity with
hydrogen halides. These include both alkyl and halogenated
alkyl free radicals. Accurate kinetic information of the both
reaction directions provide enthalpy and free energy changes
for the overall reaction under study from which the enthalpy
of formation of the free radical can be determined. Moreover,
Description of kinetic experiments
The rate constants of the reaction of CH2Br or CHBrCl with
HBr were measured as a function of the temperature range.
The experimental apparatus used has been previously
described.4,5 Pulsed, unfocused 248 nm radiation from a
Lambda Physik EMG 201 MSC exciplex laser operated at
DOI: 10.1039/b210787m
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Table 1 Measurements of the rate constant of the R + HBr ! RH + Br (R ¼ CH2Br, CHBrCl or CCl3) reaction
Ta /K
[He]/1016 cmꢀ3
[HBr]/1014 cmꢀ3
k4/sꢀ1
Wall
kib /10ꢀ13 cm3 sꢀ1
CH2Br + HBr ! CH3Br (k1)
299
300
348
348
409
510
510
677
5.81
17.7
2.71–7.51
1.24–9.52
1.62–5.31
1.77–5.20
2.11–9.68
0.99–3.97
1.74–4.79
1.96–3.92
3.4
3.6
3.9
10
HW
HW
2.76 ꢁ 0.15
2.80 ꢁ 0.16
3.06 ꢁ 0.18
3.07 ꢁ 0.22
3.46 ꢁ 0.17
4.11 ꢁ 0.26
4.15 ꢁ 0.14
5.3 ꢁ 0.6
5.83
5.90
5.85
5.86
5.86
5.89
HW
PDMS
PDMS
PDMS
B2O3
B2O3
7.7
19
5.5
6.9
k1 ¼ (7.5 ꢁ 0.9) ꢂ 10ꢀ13exp[ꢀ(2.53 ꢁ 0.13) kJ molꢀ1/RT] cm3 moleculeꢀ1 sꢀ1
CHBrCl + HBr ! Br + CH2BrCl (k2)
414
457
511
579
667
722
787
11.9
11.9
5.47–22.2
2.90–15.2
3.69–11.0
5.48–10.3
5.32–12.1
2.84–9.28
3.72–8.47
3.2
1.9
0.0
0.7
1.5
0.0
0.1
B2O3
B2O3
B2O3
B2O3
B2O3
B2O3
B2O3
0.48 ꢁ 0.02
0.57 ꢁ 0.02
0.69 ꢁ 0.03
0.84 ꢁ 0.03
1.06 ꢁ 0.03
1.25 ꢁ 0.03
1.58 ꢁ 0.08
5.85
5.88
5.90
5.91
5.92
k2 ¼ (4.9 ꢁ 1.2) ꢂ 10ꢀ13 exp[ꢀ(8.2 ꢁ 0.3) kJ molꢀ1/RT] cm3 moleculeꢀ1 sꢀ1
CCl3 + HBr ! Br + CHCl3 (k3)
787
5.92
10.0–14.8
0.0
B2O3
0.06 ꢁ 0.01
a
b
Temperature uncertainty: ꢁ1 for 299–348 K, ꢁ2 for 409–510 K and ꢁ3 for 667–787 K. Errors are 1s + Student’s t and based on statistical
uncertainties.
5 Hz was collimated and then directed along the axis of a hea-
table Pyrex reactor. The 10.5 mm id reactor was coated with
halocarbon wax,y poly(dimethylsiloxane)z or boric oxide to
reduce heterogeneous reactions on the reactor wall. Gas flow-
ing through the tube at 5 m sꢀ1 was completely replaced
between laser pulses. The flowing gas contained the radical
precursor (typically below 0.05%), HBr in varying concentra-
tions and the carrier gas, He, in large excess ( > 98%). Gas
was sampled through a 0.44 mm id hole located at the end
of a nozzle in the wall of the reactor and was formed into a
beam by a conical skimmer before it entered the vacuum cham-
ber containing the quadrupole mass filter. As the gas beam tra-
versed the ion source, a portion was photoionized by VUV
light and then mass selected. Temporal ion signal profiles were
recorded from 10–30 ms before each laser pulse and 16–25 ms
after the laser pulse with a multichannel scalar. Data from
1000 to 11 000 repetitions of the experiments were accumulated
before the data were analyzed by a non-linear least-squares
analysis program. At the photolysis wavelengths used to gen-
erate CH2Br or CHBrCl radicals, it is practically impossible to
photodissociate the reactant, HBr, to a measurable extent.6
Photogeneration of CH2Br, CHBrCl and CCl3 radicals
Up to four quartz plates were used to diminish laser fluence to
a very low level. A typical radical concentration was below
1011 radical cmꢀ3. The CH2Br radical was photogenerated
by photodissociating CH2Br2 at 248 nm. The CH2Br radical
was formed from the precursor by C–Br bond rupture.The
CHBrCl radical was photogenerated by photolysis of CHBr2Cl
at 248 nm. The CCl3 radical was photogenerated by photo-
lysis of CBrCl3 at 248 nm. The primary products are
CCl3 + Br. A minor channel is the formation of CCl2 .
Data analysis
Experiments were conducted under pseudo-first-order condi-
tions where HBr existed in great excess compared with the con-
centration of radicals. Only the following two reactions
had significant rates under these conditions:
R þ HBr ! RH þ Br
R ! heterogeneous loss on the wall
ð1), (2) or (3Þ
ð4Þ
Kinetic results from experimental studies
In all sets of experiments the initial radical concentration was
adjusted to be so low that radical–radical or radical–atom
reactions had negligible rates compared to reactions (1)–(4).
This was ensured by comparing the measured first-order wall
loss decays, k4 , of the radical with that produced (in the
absence of HBr) at different conditions where precursor con-
centration was held steady but the laser radiation was attenu-
ated by a factor of two using quartz plates (the radical
concentration was changed by the same factor). The decays
from these different experiments were equal with respect to
their statistical error limits.
The chemical kinetics of the following metathetical reactions
were studied separately:
CH2Br þ HBr ! CH3Br þ Br
CHBrCl þ HBr ! CH2BrCl þ Br
CCl3 þ HBr ! CHCl3 þ Br
ð1Þ
ð2Þ
ð3Þ
Rate constants of the forward reactions (1) and (2) were com-
bined with the rate constants of the reverse,
Br + RH ! HBr + R,7,8 in order to calculate the enthalpies
of formation and the experimental entropy values of the radi-
cals. The kinetics of the reverse reactions were also calculated
by ab initio methods. The results obtained from the experi-
ments to measure reactions (1)–(3) are given in Table 1.
Rate constants for reaction (1)–(3) were obtained from the
slopes of plots of the exponential radical decay constant k0
vs. [HBr] {from [R+]t ¼ [R+]0exp(ꢀk0t)}, where k0 ¼
k
1–3[HBr] + k4 . A representative ion signal decay profile and
a decay constant plot from one set of experiments to measure
k1 are shown in Fig. 1. The results obtained from all the
decay constant plots to measure reactions (1)–(4) are given in
Table 1.
y Halocarbon Wax is a product of the Halocarbon Wax Corp.
z Poly(dimethylsiloxane), 200 fluid was obtained from Aldrich.
850
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Fig. 2 Arrhenius plot of CH2Br + HBr, CHBrCl + HBr and
CCl3 + HBr reactions measured in the current study. The dotted line
shown is ab initio calculated threshold energy of a value of 15.3 kJ
molꢀ1. The lines are Arrhenius expressions fitted to the rate constants
k1–3 . Three other R + HBr reactions are from refs. 3 and 13.
hydrogen lamp (10.2 eV; with a MgF2 window) to detect
CCl2 and an argon lamp (11.6, 11.8 eV; with a LiF window)
to detect CH3Br, HBr, Br2 and Br.
Fig. 1 Plot of first-order decay constant k0 vs. [HBr] for one set of
experiments conducted to measure the CH2Br + HBr rate constant,
k1 , at 348 K. The inset in the lower right corner is the ion signal profile
of CH2Br+ recorded during one of the experiments shown as a solid
circle ([HBr] ¼ 4.12 ꢂ 1013 molecule cmꢀ3) in the linear regression fit.
The line through the data in the insert is an exponential function fitted
by a nonlinear least-squares procedure. The first-order decay constant
Computation details
Ab initio calculations were carried out with the Gaussian 98
package of programs.9 All calculations were carried out on
an Origin 2000 computer at the Centre for Scientific Comput-
ing (Espoo, Finland). All structures of species needed for the
transition state calculations were fully optimized at the MP2
level of theory using the 6-31G(d,p) basis set and frozen-core
approximation.10 The reactions of Br + CH3Br/CH2BrCl
were also calculated at the MP2(fc)/6-311G(df)//MP2(fc)/6-
311G(df) level of theory for comparison (for these calculations
the basis set for Br was taken from the literature).11 The transi-
tion state of the equilibrium reaction was localized at the mini-
mum energy path using a quadratic synchronous transit
method (QST3).10 In the calculations the expectation values,
S2, for free radicals were in the range of 0.7658–0.7671 and
for transition states in the range of 0.7821–0.7901. Normal
mode analyses were carried out at the same level of theory
for all species and transition states. These frequency calcula-
tions show the optimized transition state to be a first-order
saddle point with all the second derivatives of energy being
positive except for one, which has an imaginary vibrational
frequency along the reaction coordinate. The imaginary fre-
quencies were in the range of ꢀ679 to ꢀ1251 cmꢀ1. The force
constant matrix has only one eigenvalue. The corresponding
eigenvector of the Hessian matrix is associated with the broken
H–Br bond and the formed C–H bond. The relative movement
of the H atom is the largest. The C–H–Br asymmetric stretch is
the reaction coordinate. Furthermore, frequencies and zero-
point energies of species were multiplied by a value of 0.9676
for the calculations.10 Zero-point energy corrected energies
of the reactants of the reverse reactions were compared to that
of the reaction transition state for the threshold energy calcula-
tion at 0 K (see Table 2). The ab initio calculations were used in
conjunction with the thermodynamic transition state theory to
determine the kinetics of the Br + molecule reactions.
for CH2Br+ in the displayed ion signal profile is (132.9 ꢁ 2.3) sꢀ1
.
Accuracy of measurements
The error limits stated in Arrhenius expressions are
1s + Student’s t and they are based only on the statistical
uncertainties. The reactions were studied under pseudo-first-
order conditions when it was needed to know accurately only
the concentration of HBr. The other errors, such as measured
temperature and gas flow rates, were always <1%. All these
errors are very small and were thus ignored. The statistical
uncertainties of the decay constants were taken into account
in data analysis and their effects on the rate constants are
shown in Fig. 2. The Arrhenius expression of the reaction
was obtained by weighting the measured rate constants with
the reciprocals of their variances for the fitting procedure.
Reagent sources and purification procedures
CH2Br2 , > 99%, CHBr2Cl, 98%, CBrCl3 , > 99.5% and HBr,
99%, were obtained from Aldrich and helium, 99.995%, from
Matheson.
The carrier gas, He, was used as provided. The radical pre-
cursors were degassed by using freeze–pump–thaw cycles and
stored in darkness. HBr was collected to a flow trap kept at
77 K and was repeatedly distillated to remove any traces of
bromine. HBr was stored in a dark Pyrex bulb. The flow of
precursor/He mixture and HBr were not mixed until they
reached the reactor. The gas handling system, which was used
to set up a known HBr flow to the reactor gas inlet, was made
from Pyrex glass and Teflon tubes.
Photoionization energies used
Reactants and products of the photolysis as well as the pre-
cursors were photoionized using atomic resonance radiation.
A chlorine lamp (8.9–9.1 eV) coupled with a CaF2 salt win-
dow was used to detect CH2Br, CHBrCl or CCl3 radicals, a
Computationally calculated kinetics of the reverse reactions
The results of the ab initio calculations at the MP2(fc)/6-
31G(d,p)//MP2(fc)/6-31G(d,p) level of theory were used also
Phys. Chem. Chem. Phys., 2003, 5, 849–855
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Table 2 Symmetry point groups, total and zero-point energies. Ener-
gies at the MP2(fc)/6-31G(d,p)//MP2(fc)/6-31G(d,p) level are in Eh
using a second-law method. Because no mole change is
involved, the standard reaction enthalpy change, DrHꢃ, is the
difference between the activation energies of the forward and
the reverse reactions. The Arrhenius expressions of the reverse
reactions were either calculated from the ratios of the rate con-
stants of k(Br + CH3Br)/k(Br + C2H6) and k(Br + CH3Br)/
k(Br + CH2BrCl) and the absolute rate constant of the reac-
tion of C2H6 with Br or calculated using ab initio methods.7,14
The DrHꢃ was calculated from experimental studies at the mid-
dle of the overlapping temperature, Tm , ranges on a 1/T scale
of the forward and reverse reactions.
Zero-point
energy
Compound
Symmetry
Total energy
Br
HBr
Kh
C
ꢀ2569.955833
ꢀ2570.592802
ꢀ2609.768741
ꢀ2609.101190
ꢀ3068.781685
ꢀ3068.121445
ꢀ1417.402148
ꢀ1416.749188
ꢀ5179.693207
ꢀ5179.684408
ꢀ5638.711637
ꢀ5638.704376
ꢀ5638.677589
ꢀ3987.335633
0.0
0.006300
0.038485
0.023500
0.029865
0.015953
0.020889
0.007694
0.030888
0.034806
0.022182
0.027593
0.027167
0.013450
1v
CH3Br
CH2Br
C3v
Cs
CH2BrCl
CHBrCl
Cs
C1
C3v
C3v
C1
C1
C1
C1
C1
C1
The standard free energy change of the reaction DrGꢃ and
the standard entropy of the reaction DrSꢃ at Tm were obtained
from simple thermodynamic relations DrGꢃ ¼ ꢀRT ln K ¼
DrHꢃ ꢀ TDrSꢃ. The values of thermodynamic functions were
corrected to 298 K using the heat capacities of reactant species.
The enthalpy of formation of the radical at 298 K was calcu-
CHCl3
CCl3
Brꢄ ꢄ ꢄHꢄ ꢄ ꢄCH2Br
Brꢄ ꢄ ꢄBrꢄ ꢄ ꢄCH3
Brꢄ ꢄ ꢄHꢄ ꢄ ꢄCHBrCl
Brꢄ ꢄ ꢄBrꢄ ꢄ ꢄCH2Cl
Brꢄ ꢄ ꢄClꢄ ꢄ ꢄCH2Br
Brꢄ ꢄ ꢄHꢄ ꢄ ꢄCCl3
ꢃ
lated from the DrH298 and the tabulated heat of formation
values of the other reaction species (see Table 5). Furthermore,
the enꢃtropy of the radical at 298 K was calculated from the
DrS298 and the tabulated entropy values of Br and HBr.
The entropies of the CH3Br and CH2BrCl molecules were
calculated using ab initio method.
to determine entropies of the reactants and the transition states
of Br + RH ! HBr + R (R ¼ CH2Br or CHBrCl) reactions
(Tables 3 and 4 and ref. 12 for structural parameters, frequen-
cies and moments of inertia). The Arrhenius expressions of
the bimolecular reactions at 298.15 K were obtained using
the thermodynamic transition state theory.13 The Arrhenius
activation energies at 298.15 K were calculated from the
heat capacity corrected threshold energies. The Arrhenius
rate expressions of reactions (ꢀ1) and (ꢀ2) determined at
298.15 K are as follows:
The thermodynamic values obtained are as follows:
Df H298ꢃðCH2BrÞ ¼ 171:1 ꢁ 2:7 kJ molꢀ1
S298ꢃðCH2BrÞ ¼ 263 ꢁ 7 J Kꢀ1 molꢀ1
Df H298ꢃðCHBrClÞ ¼ 143 ꢁ 6 kJ molꢀ1
S298ꢃðCHBrClÞ ¼ 294 ꢁ 6 J Kꢀ1 molꢀ1
The C–H bond energies at 298 K were calculated directly from
kðBr þ CH3Br ! HBr þ CH2BrÞ
ꢃ
the enthalpies of the reactions: Ed,298 ¼ ꢀDrH298
¼ 4 ꢂ 10ꢀ11 expðꢀ64:8 kJ molꢀ1=RTÞ cm3 moleculeꢀ1 sꢀ1
(R + HBr 0 RH + Br) + Ed,298(HBr). The C–H bond strengths
obtained are 427.2 ꢁ 2.4 kJ molꢀ1 of CH3Br and 406.0 ꢁ 2.4 kJ
molꢀ1 of CH2BrCl.
kðBr þ CH2BrCl ! HBr þ CHBrClÞ
¼ 2 ꢂ 10ꢀ11 expðꢀ49:7 kJ molꢀ1=RTÞ cm3 moleculeꢀ1 sꢀ1
Error limits for the A factors are not considered, for the activa-
tion energies they are typically ꢁ2.4 kJ molꢀ1 in comparison of
the experimentally determined activation energies with the
quantum chemically calculated threshold energies.12 The tun-
neling effect may increase the rate constant of reaction (ꢀ1)
at 298.15 K by 45% and of reaction (ꢀ2) by 85% if Wigner cor-
rection is used. However, the tunneling effect was not used in
the thermochemical calculations.
Discussion
Kinetics of the forward reactions
The kinetics of the CH2Br, CHBrCl and CCl3 radicals with
HBr are shown in Fig. 2. The kinetics of the three other
R + HBr reactions are also given for comparison. As it is
shown, halogen atom substitution at the radical site lowers
the reactivity and increases the Arrhenius activation energy
of the reaction. These phenomena become more obvious as
the number of halogen atoms in substitution at the radical site
increases. Furthermore, in series of monohalogenated methyl
radicals, an I atom substituent has smallest and a Cl atom
Thermochemical calculations
Both the enthalpy and entropy changes of the R + HBr 0
RH + Br (R ¼ CH2Br or CHBrCl) equilibria were obtained
Table 3 Structural parameters of the species optimized in ab initio calculations at the MP2(fc)/6-31G(d,p)//MP2(fc)/6-31G(d,p) level of theory.
˚
Bond lengths in A and angles in degrees
c
d
ad
e
ao
Species
rCH
rCBr
rCCl
rC–H
rH–Br
aBrCH
aHCH
aBrCCl
aC–H–Br
CH2Br
CH3Br
CHBrCl
1.075
1.083
1.078
1.083
—
1.865
1.949
1.873
1.946
—
—
—
—
—
—
—
—
—
—
—
116.6
107.8
115.6
106.8
—
122.5
111.1
—
—
—
—
—
—
—
21.3
—
1.702
1.761
1.713
1.766
—
—
—
118.9
113.1
116.8a
111.3a
—
—
—
—
—
30.2
—
CH2BrCl
CCl3
CHCl3
111.6
—
107.5b
118.5
—
—
—
—
—
—
—
30.2
—
1.083
1.081
1.084
—
—
—
Br–H–CH2Br
Br–H–CHBrCl
Br–H–CCl3
1.869
1.886
—
1.537
1.471
1.411
1.513
1.533
1.559
114.3
112.8
—
180
159.4
180
173.1
184.6
180
36.0
40.0
39.0
1.710
1.727
117.5
114.7a
—
a
b
c
d
˚
Valence angle of atoms Cl–C–Cl. Valence angle of atoms Cl–C–H. The bond length of HBr is 1.406 A. The dihedral angle ad is given as
a3126 (see Fig. 3). e The out-of-plane angle ao at the radical center of transition state or free radical is an angle between a plane (consists of a C and
two H or two halogen atoms) and a remaining bond.
852
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Table 4 Moments of inertia and unscaled vibrational frequencies as wavenumbers of the species calculated at the MP2(fc)/6-31G(d,p)//MP2(fc)/
6-31G(d,p) level of theory. The numbers in parenthesis refer to two similar wavenumbers if given as integers
Compound
Wavenumber/cmꢀ1
Moment of inertia/10ꢀ47 kg m2
CH2Br
CH3Br
445, 711, 978, 1462, 3280, 3439
3.073, 74.85, 77.73
5.351, 88.40, 88.40
45.95, 1096, 1136
19.93, 392.7, 411.9
28.43, 399.5, 422.6
381.9, 1073, 1430
249.3, 249.3, 495.3
256.3, 256.3, 494.4
492.2, 1119, 1119
3.270
631, 1003(2), 1394, 1540(2), 3174, 3303(2)
57, 315, 493, 725, 822, 888, 1010, 1187, 1460, 3230, 3371, 679i
256, 548, 699, 896, 1282, 3322
Br–H–CH2Br
CHBrCl
CH2BrCl
Br–H–CHBrCl
CCl3
238, 629, 797, 886, 1208, 1314, 1516, 3214, 3306
52, 108, 250, 400, 707, 822, 874, 912, 1076, 1275, 3260, 938i
289(2), 368, 526, 952(2)
CHCl3
Br–H–CCl3
HBr
277(2), 387, 704, 825(2), 1310(2), 3255
80(2), 180, 289(2), 458, 849, 881(2), 959(2), 1251i
2766
substituent has the largest effect to diminish reactivity of the
radical. Clearly intramolecular electrostatic effects are present.
A similar trend of decreasing radical reactivity has been
demonstrated previously by R + HI reactions.18 The intramo-
lecular electrostatic effects are explained successfully by the
inductive effects of the substituents to either increase (alkyl
groups) or to decrease (halogen atoms) the partial charge
and the spin density at the radical site. The algebraic sum of
Pauling’s atomic electronegativities19 attached to the radical
carbon is used as the measure of the inductive effect.18
reaction channel can take over. During the rotation period
also a bent adduct complex could be formed but threshold
energy of such reaction is even higher than to form a linear
adduct complex.12 After the rotation, the Rꢄ ꢄ ꢄH–Br van der
Waals complex proceeds to a transition state, which structure
is tighter than that of the adduct complex. The transition state
is affected by electrostatic effects. These effects seem to affect
the structure and the density of energy levels more for an alkyl-
ated transition state than for a halogenated transition state.12
With high density of energy levels, the transition state can
more easily be thermally activated as temperature of the reac-
tion increases. Moreover, a thermally excited transition state
should have a feature to fall apart to reactants more easily
and the overall rate constant should decrease with increasing
temperature. This has been observed with radical + HBr reac-
tions in time-resolved experimental studies by various mass
spectrometric and spectroscopic techniques.20,21
As it is shown in Fig. 2, also a trend of the energy barriers of
the R + HBr ! RH + Br reactions seem to be affected by elec-
z
trostatic effects. This is because k / exp(ꢀDrGꢃ /RT ). The
more positive the standard free energy of activation is, the
lower is the rate conzstant. For bimolecular reactions with no
mole change ꢀDrGꢃ ¼ TDrSꢃz + 2RT ꢀ Ea . Thus the lower
the rate constant, the more positive the Arrhenius activation
energy because the entropy factor is always negative. The
DrSꢃz is typically ꢀ120 J Kꢀ1 molꢀ1. The standard free energy
of activation is related to electrostatic ezffects of the radical.
This is shown in Fig. 4 by plotting DrGꢃ values at 298.15 K
vs. Delectronegativity values of the radicals. The plot is linear.
The more positive DrGꢃz value, the slower is the reaction. This
is in perfect agreement with Fig. 2.
Kinetics of the reverse reactions
The ab initio calculated Arrhenius rate expressions for the
Br + CH3Br and Br + CH2BrCl reactions are relative accurate
compared to the experimental values available.7,8,14 The differ-
ence between the Arrhenius activation energies is only 0.4 kJ
molꢀ1 for the reaction (ꢀ1) and 0.7 kJ molꢀ1 for the reaction
(ꢀ2). The largest disagreement can be found between the A
factors. For reaction (ꢀ1) the ab initio calculated A factor is
by a factor of four smaller than that of the experimental value.
For reaction (ꢀ2) a similar factor is 1.6, respectively. The tun-
neling is not considered here. However, if one takes into
Complex reaction system
Generally metathetical R + HBr reactions are considered to
occur via two transition states. The radical may initially be
attracted loosely to the Br end of HBr to form an adduct com-
plex. This seems to be reasonable because Br is more electrone-
gative than H, and has stronger tendency and larger size to
form a bond with the radical carbon. This bond formation
should become more obvious with bulky alkyl radicals because
large electronegativity difference between the radical carbon
and the Br end of HBr compared to the H end of HBr should
favour a strong bond formation. However, this channel is
strongly endothermic and thus may finally not proceed any
further. The HBr molecule has to rotate before the exothermic
Table 5 Heats of formation and entropies used in the thermochemical
calculations
Species
DfHꢃ298/kJ molꢀ1
Sꢃ298/J Kꢀ1 molꢀ1
HBra
ꢀ36.44 ꢁ 0.17
111.86 ꢁ 0.06
ꢀ38.1 ꢁ 1.3
ꢀ45.0 ꢁ 5.0
198.70
175.02
245.29
286.49
Bra
CH3Brb c
CH2BrCld c
Fig. 3 Optimized transition state of the Br + CH3Br ! CH2Br + HBr
reaction at 0 K. The parameters are calculated at the MP2(fc)/6-
31G(d,p)//MP2(fc)/6-31G(d,p) level of theory. The dihedral angle
ad ¼ a3126 ¼ 180ꢃ.
a
b
c
Data taken from ref. 15. Data taken from ref. 16. This work.
Data taken from ref. 17.
d
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853

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MP2(full)/6-31G(d,p) level of theory (also Gaussian G2 the-
ory) to calculate DfH298 (CHBrCl) to be 147 ꢁ 6 kJ molꢀ1 26
ꢃ
.
The C–H bond strength of halogenated methanes
The C–H bond strength of CH3Br is 427.2 ꢁ 2.4 kJ molꢀ1 and
of CH2BrCl is 406.0 ꢁ 2.4 kJ molꢀ1. These values are in very
good accord with the values of the other halogenated
methanes. The C–H bond strength decreases from methane
to chloroform in the following order (values in kJ molꢀ1
and determined experimentally): methane (437.9)3 > iodo-
methane (431.6)13 > bromomethane (427.2) > chloromethane
(419.0)3 > bromochloromethane (406.0) > dichloromethane
(402.5)3 > chloroform (393.9)3. Experimentally determined
Arrhenius activation energies of an H atom abstraction reac-
tion by the Br atom on a substituted methane are as follows
(in kJ molꢀ1): methane (76.1) > iodomethane (63.9)13
ꢅ
bromomethane (64.4) > chloromethane (57.7) > bromochlor-
omethane (49.0) > dichloromethane (47.0) > chloroform
(38.9).12 Clearly, the energy barrier of Br + substituted
methane reaction becomes smaller parallel to the trend of
decreasing C–H bond strength from methane to chloroform.
These trends are most likely caused by intramolecular electro-
static effects where electronegative halogen atoms make the C–
H bond weak in a similar manner as they affect to the reactivity
of halogenated methyl radicals.
Fig. 4 Plot of the standard free-energy of activation at 298.15 K of
some R + HBr reactions vs. Delectronegativity of R.
account the error limits of the experimental A factors given,
which are from 55 to 60%, the disagreement is relative small.
The product of reaction (1) was detected to be CH3Br. The
transition states of the two reaction channels of Br + CH3Br
reaction and the three reaction channels of Br + CHBrCl reac-
tion were characterized (see Table 2 for energies). In general,
the energy barrier for abstracting an H atoms by the Br atom
on CH3Br is about 33 kJ molꢀ1 smaller than the competing
channel for abstracting a Br atom. On the other hand, the
Br atom can abstract an H atom, a Br atom or a Cl atom
on CH2BrCl. For these the energy barriers at 0 K are 48.4,
81.2 and 150.5 kJ molꢀ1. Clearly the Br + CH2BrCl ! HBr
+ CHBrCl channel dominates.
The threshold energies of reactions (ꢀ1 and ꢀ2) at 0 K were
also calculated at the MP2(fc)/6-311G(df)//MP2(fc)/6-
311G(df) level of theory for comparisons. The zero-point energy
corrected threshold energy of reaction (ꢀ1) is 62.3 kJ molꢀ1
and of reaction (ꢀ2) is 50.3 kJ molꢀ1 (zero-point energies
were scaled by a factor of 0.95). On the other hand the previously
used MP4/6-311++G(3d,2p)//MP2(fc)/6-31G(d,p) level of
theory does not apply here.22 This level of theory used for
the QST3 calculations yielded a value of 51.0 kJ molꢀ1 for
abstraction an H atom on bromomethane by the Br atom at
0 K (reaction (ꢀ1)). This is clearly too low value and implies
that this level of theory is not suitable for threshold energy
calculations of the reactions studied.
Frequencies for CH2Br. The ground state electronic config-
uration of the pyramidal CH2Br radical could be:
2
. . .(5a00)2(14a0)2(15a0)2(6a00)2(16a0)2 A0 (Cs). The calculated
vibrational frequencies given as wavenumbers of the CH2Br
are shown in Table 4. As expected, the radical has six normal
modes, which span the representation G ¼ 4a0 + 2a00. The
values are compared to the experimental values, which are
measured in an argon matrix.27 Of these 368 cmꢀ1 umbrella
mode is very strong, 693 cmꢀ1 CBr stretch and 1356 cmꢀ1
CH2 scissors are strong modes, and 953 cmꢀ1 CH2 rock mode
is weak. The equivalent ab initio calculated scaled values (by
0.9676) for an anharmonic correction are 430, 688, 1414, 947
cmꢀ1 (two other 3174 cmꢀ1 CH2 symmetric stretch and 3328
cmꢀ1 CH2 asymmetric stretch are weak). All wavenumbers cal-
culated except the umbrella mode have similar values and simi-
lar relative intensities as the experimental ones. This was
expected. The ab initio program calculates a harmonic fre-
quency which does not apply to the umbrella mode. Because
the CH2Br radical is pyramidal, the umbrella (or OPLA) mode
of the radical is not harmonic. This mode should possess two
potential energy minima along the umbrella coordinate. As the
barrier of inversion becomes smaller, the increased interaction
of the two wave functions on the potential energy minima
causes the degeneracy of the energy levels to be split. The
degree of splitting is largest at higher vibrational levels near
the top of the inversion barrier, where the energy levels can
not be taken to be harmonic. A similar phenomenon has been
calculated for the CHCl2 radical.28
Enthalpy of formation values determined
The enthalpy of formation of the CH2Br radical was found to
be 171.1 ꢁ 2.7 kJ molꢀ1 at 298 K. This value is in very good
agreement with the value of 170.3 ꢁ 8.4 kJ molꢀ1 from the
appearance energy measurement of Holmes and Lossing.23
Thermochemical functions of the CH2Br. Ideal gas thermody-
namic parameters Cpꢃ, Sꢃ, ꢀ(Gꢃ ꢀ H0 )/T and (Hꢃ ꢀ H0 )
were calculated by the statistical thermodynamic method
based on a rigid rotor harmonic oscillator model. The values
were tabulated in a JANAF manner. For this also DfHꢃ, DfGꢃ
and log10Kf were calculated as a function of temperature. The
heat of formation values were fitted to give a kineticallyꢃdeter-
mined value at 298.15 K. For the calculations (Hꢃ ꢀ H0 ) and
Sꢃ values for elements were taken from the literature. For these
calculations the ab initio calculated umbrella mode wavenum-
ber was replaced by the more reliable experimental value of
368 cmꢀ1. This is because low frequency modes have the stron-
gest effect to the calculated thermodynamic parameters. All the
other calculated wavenumbers were multiplied by 0.9676 for
ꢃ
ꢃ
The other determination by them gave 168.2 ꢁ 8.4 kJ molꢀ1 24
.
Tschuikow-Roux and Paddison determined the heat of forma-
tion of the CH2Br radical to be 169.0 ꢁ 4.1 kJ molꢀ1 25
.
value is based on the analysis of thermochemical and kinetic
The
data on the bromination of bromomethane.
The DfH298 (CHBrCl) was found to be 143 ꢁ 6 kJ molꢀ1
ꢃ
.
This seems to be the first experimental enthalpy of formation
´
determination for the CHBrCl radical. Espinosa-Garcıa and
Dobe used hydrogenation and isodesmic reactions with an
´ ´
ab initio method at the MP4(SDTQ)(fc)/6-311++G(3d,2p)//
854
Phys. Chem. Chem. Phys., 2003, 5, 849–855

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Table 6 Ideal gas thermochemical functions for the CH2Br radical at a standard state of 1 bar
T/K
Cꢃp/J Kꢀ1 molꢀ1 Sꢃ/J Kꢀ1 molꢀ1 [ꢀ(Gꢃ ꢀ Hꢃ0)/T]/J Kꢀ1 molꢀ1 Hꢃ ꢀ H0ꢃ/kJ molꢀ1 DfHꢃ/kJ molꢀ1 DfGꢃ/kJ molꢀ1 log10 Kf
100
200
34.482
39.961
217.953
243.453
260.465
260.747
274.544
286.199
296.335
305.328
313.434
320.830
327.647
333.977
339.890
345.442
350.674
355.623
184.469
208.158
222.702
222.936
234.168
243.438
251.427
258.497
264.866
270.679
276.039
281.022
285.684
290.069
294.213
298.144
3.348
7.059
180.5
178.8
171.1a
171.0
154.7
153.8
153.0
152.3
151.6
151.0
150.4
149.9
149.5
149.1
148.8
148.5
171.6
163.3
156.8
156.7
155.2
155.5
155.9
156.4
157.1
157.8
158.6
159.4
160.3
161.2
162.2
163.2
ꢀ89.61
ꢀ42.65
ꢀ27.47
ꢀ27.28
ꢀ20.27
ꢀ16.24
ꢀ13.57
ꢀ11.67
ꢀ10.26
ꢀ9.16
298.15 45.518
11.259
11.343
16.151
21.381
26.945
32.782
38.854
45.136
51.607
58.250
65.047
71.984
79.046
86.219
300
400
45.616
50.357
54.093
57.084
59.599
61.809
63.796
65.596
67.226
68.696
70.016
71.197
72.251
500
600
700
800
900
1000
1100
1200
1300
1400
1500
ꢀ8.28
ꢀ7.57
ꢀ6.98
ꢀ6.48
ꢀ6.05
ꢀ5.68
a
Current study.
7
G. C. Fettis and J. H. Knox, in Progress in Reaction Kinetics,
ed. G. Porter, Pergamon, New York, 1964, vol 2, p. 1.
the anharmonic correction as has been suggested in the litera-
ture.10 The standard state for the calculated values is 1 bar.
The JANAF tabulated parameters for a temperature range
of 100–1500 K are shown in Table 6.
´
´
8
9
A private discussion with Dr S. Dobe.
M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A.
Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery,
Jr., R. E. Stratmann, J. C. Burant, S. Dapprich, J. M. Millam,
A. D. Daniels, K. N. Kudin, M. C. Strain, O. Farkas, J. Tomasi,
V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C.
Adamo, S. Clifford, J. Ochterski, G. A. Petersson, P. Y. Ayala,
Q. Cui, K. Morokuma, D. K. Malick, A. D. Rabuck, K.
Raghavachari, J. B. Foresman, J. Cioslowski, J. V. Ortiz, B. B.
Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi,
R. Gomperts, R. L. Martin, D. J. Fox, T. Keith, M. A.
Al-Laham, C. Y. Peng, A. Nanayakkara, M. Challacombe,
P. M. W. Gill, B. Johnson, W. Chen, M. W. Wong, J. L. Andres,
C. Gonzalez, M. Head-Gordon, E. S. Replogle and J. A. Pople,
Gaussian 98, Revision A.3, Gaussian Inc., Pittsburgh PA, 1998.
Summary
The kinetics of CH2Br, CHBrCl and CCl3 radical reaction with
HBr have been characterized. The temperature dependence
measured was combined with the temperature dependence of
the reverse reaction to obtain the enthalpy of formation of
CH2Br radical to be 171.1 ꢁ 2.7 kJ molꢀ1 and of CHBrCl radi-
cal to be 143 ꢁ 6 at 298 K. The different reaction channels of
reverse reactions were studied by the ab initio methods. The
C–H bond strength of bromomethane was calculated to be
427.2 ꢁ 2.4 kJ molꢀ1 and of bromochloromethane was calcu-
lated to be 406.0 ꢁ 2.4 kJ molꢀ1. The thermochemical func-
tions for the CH2Br radical are calculated and given in a
JANAF manner.
10 J. B. Foresman and Æ. Frisch, Exploring Chemistry with Electro-
nic Structure Methods, Gaussian Inc., Pittsburgh, 2nd edn., 1996.
11 M. N. Glukhovtsev, A. Pross, M. P. McGrath and L. Radom,
J. Chem. Phys., 1995, 103, 1878.
12 J. A. Seetula, Phys. Chem. Chem. Phys., 2000, 2, 3807.
13 J. A. Seetula, Phys. Chem. Chem. Phys., 2002, 4, 415.
14 P. W. Seakins, M. J. Pilling, J. T. Niiranen, D. Gutman and L. N.
Krasnoperov, J. Phys. Chem., 1992, 96, 9847.
15 M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip,
R. A. McDonald and A. N. Syverud, J. Phys. Chem. Ref. Data,
1985, 14, Suppl. No.1.
Acknowledgements
This research was supported by the University of Helsinki, the
Center for Scientific Computing at Espoo (both in Finland)
and the National Science Foundation, Chemistry Division
16 J. Bickerton, M. E. M. da Piedade and G. Pilcher, J. Chem.
Thermodyn., 1984, 16, 661.
17 L. V. Gurvich, V. S. Iorish, D. V. Chekhovskoi and V. S.
Yungman, IVTANTHERMO, NIST Database 5, National
Institute of Standards and Technology, Gaithersburg, MD, 1993.
18 J. A. Seetula and D. Gutman, J. Phys. Chem., 1991, 95, 3626.
19 L. Pauling, Nature of the Chemical Bond, Cornell University
Press, Ithaca, NY, 3rd edn., 1960.
20 J. A. Seetula and I. R. Slagle, J. Chem. Soc., Faraday Trans., 1997,
93, 1709.
21 P. D. Richards, R. J. Ryther and E. Weitz, J. Phys. Chem., 1990,
94, 3663.
´ ´
(USA). I thank Dr Dobe for showing me the preliminary
kinetic results of his and K. Imrik’s investigations concerning
the reaction of CH2BrCl with Br atom. I also wish to thank
Prof. Irene R. Slagle for kindly lending me the experimental
apparatus for this study. The kinetic experiments were carried
out at the Catholic University of America (Washington DC,
USA).
´
22 J. Espinosa-Garcıa, Mol. Phys., 1999, 97, 629.
23 J. L. Holmes and F. P. Lossing, Int. J. Mass Spectrom. Ion Proc.,
1984, 58, 113.
24 J. L. Holmes and F. P. Lossing, J. Am. Chem. Soc., 1988,
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