Kinetics of the R + HBr → RH + Br (R = CH2I or CH3) reaction. An ab initio study of the enthalpy of formation of the CH2I, CHI2 and CI3 radicals

Article abstract of DOI:10.1039/b107407p

The kinetics of the reaction of the CH₂I and CH₃ radicals, R, with HBr have been investigated separately in a heatable tubular reactor coupled to a photoionization mass spectrometer. The CH₂I (or CH₃) radical was produced homogeneously in the reactor by a pulsed 248 or 351 nm exciplex laser photolysis of CH₂I₂ (or CH₃I). 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 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(CH₂I + HBr) = (3.8 ± 0.7) × 10^-13 exp[+ (1.4 ± 0.6) kJ mol^-1/RT] and k(CH₃ + HBr) = (2.3 ± 0.5) × 10^-12 exp[+ (0.60 ± 0.17) kJ mol^-1/RT]. The threshold energies of the reverse reactions, Br + R′H → R′ + HBr (R′ = CH₂I, CHI₂ or CI₃), were calculated by ab initio methods at the MP2(fc)/6-311G(df)//MP2(fc)/6-311G(df) level of theory. These were combined with the experimentally determined activation energies of the forward reactions in a second-law method to determine the enthalpies of the reactions. The enthalpy of formation values at 298 K are (in kJ mol^-1): 228.0 ± 2.8 (CH₂I), 314.4 ± 3.3 (CHI₂) and 424.9 ± 2.8 (CI₃). The C-H bond strengths of analogous iodomethanes are (in kJ mol^-1): 431.6 ± 2.8 (CH₃I), 412.9 ± 3.3 (CH₂I₂) and 391.9 ± 3.1 (CHI₃). The Arrhenius expression of the reverse reactions as determined by the thermodynamic transition state theory. The entropies of activation of the reactions were obtained by ab initio calculations.

Full text of DOI:10.1039/b107407p

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Kinetics of the R+HBr ! RH+Br (R ¼ CH2I or CH3) reaction.
An ab initio study of the enthalpy of formation of the CH2I,
CHI2 and CI3 radicals
Jorma A. Seetula
Laboratory of Physical Chemistry, P.O. Box 55 (A.I. Virtasen aukio 1), FIN-00014
University of Helsinki, Helsinki, Finland
Received 15th August 2001, Accepted 7th November 2001
First published as an Advance Article on the web 15th January 2002
The kinetics of the reaction of the CH2I and CH3 radicals, R, with HBr have been investigated separately in a
heatable tubular reactor coupled to a photoionization mass spectrometer. The CH2I (or CH3) radical was
produced homogeneously in the reactor by a pulsed 248 or 351 nm exciplex laser photolysis of CH2I2 (or CH3I).
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 the rate constants determined were fitted to an Arrhenius expression (error limits
stated are 1s + Student’s t values, units in cm3 moleculeÀ1
s
À1): k(CH2I + HBr) ¼ (3.8 0.7) Â 10À13
exp[+ (1.4 0.6) kJ molÀ1=RT ] and k(CH3 + HBr) ¼ (2.3 0.5) Â 10À12 exp[+ (0.60 0.17) kJ molÀ1=RT ].
The threshold energies of the reverse reactions, Br + R0H ! R0 + HBr (R0 ¼ CH2I, CHI2 or CI3), were
calculated by ab initio methods at the MP2(fc)=6-311G(df)== MP2(fc)=6-311G(df) level of theory. These were
combined with the experimentally determined activation energies of the forward reactions in a second-law
method to determine the enthalpies of the reactions. The enthalpy of formation values at 298 K are
(in kJ molÀ1): 228.0 2.8 (CH2I), 314.4 3.3 (CHI2) and 424.9 2.8 (CI3). The C–H bond strengths of
analogous iodomethanes are (in kJ molÀ1): 431.6 2.8 (CH3I), 412.9 3.3 (CH2I2) and 391.9 3.1 (CHI3).
The Arrhenius expression of the reverse reactions as determined by the thermodynamic transition
state theory. The entropies of activation of the reactions were obtained by ab initio calculations.
Introduction
Kinetics and computational
Iodomethane is largely used as a methylation agent in organic
chemistry. Its natural source has been indentified as pelagic
ocean and ocean surface waters and recently volcanic pro-
duction.1,2 The natural source of diiodomethane has been
found to be a marine phytoplankton.3
Description of kinetic experiments
The rate constants of the reaction of CH2I or CH3 with HBr
were measured as a function of temperature. The experimental
apparatus used has been described previously.6,7 Pulsed,
unfocused 351 or 248 nmradiation froma Lambda Physik
EMG 201 MSC exciplex laser operated at 5 Hz was collimated
and then directed along the axis of a heatable Pyrex reactor.
The 10.5 mm id reactor was coated with fluorinated halo-
The current study presents a time-resolved experimental
kinetic investigation of the CH2I and the CH3 radicals with
HBr. The first reaction has not previously been studied. The
approach is similar to that used for the study of chlorinated
radicals with HBr.4 The current study was carried out to
investigate the enthalpy of formation of the CH2I using a sec-
ond-law method. For this, ab initio calculations were needed to
study the different reaction channels of the Br + CH3I reaction.
Of these, the H atomabstraction reaction cannot be studied
experimentally, as the I atom abstraction reaction is the
dominant channel. The quantum chemical calculations were
further used in conjuction with a second-law method to extend
the kinetic and thermodynamic studies to include CHI2 and CI3
free radical reactions with HBr in order to obtain the other
C–H bond energies of iodinated methanes for comparison.
It was shown previously that Cl atoms significantly decrease
the Ca–H bond strength of alkyl chlorides by decreasing the
threshold barrier of the H atomabstraction reaction. 5 A similar
effect can be expected to occur with I atoms.
carbon wax or Teflon to reduce heterogeneous reactions. Gas
À1
flowing through the tube at 5 ms
was completely replaced
between laser pulses. The flowing gas contained the radical
precursor CH2I2 (< 0.1%), HBr in varying concentrations 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 chamber containing the
quadrupole mass filter. As the gas beam traversed 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 for
analysis by a non-linear least-squares analysis program.
DOI: 10.1039/b107407p
Phys. Chem. Chem. Phys., 2002, 4, 455–460
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At the photolysis wavelengths used to generate CH3 or CH2I
radicals, it is practically impossible to photodissociate the
reactant, HBr, to a measurable extent.8
Moreover, collisional deactivation of the vibrationally excited
CH2I radical occurs rapidly (< 0.5 ms) compared to the time-
scale used.9 The formation of CH2 + I2 , is energetically pos-
sible at 248 nm but forbidden by symmetry considerations.
Also the products of this channel were not detected in the
current study.
Kinetic results from experimental studies
The CH3 radical was generated by photolysis of CH3I at 248
nm. The main photolysis channel is the formation of
CH3 + I(2P1=2).9
The chemical kinetics of the following metathetical reactions
were studied separately:
The absorption spectrumof CH 2I2(g) at 308 K is shown as an
insert of Fig. 1. The wavelengths of both laser lines used are
shown in the insert to demonstrate that the photodissociation
occurred via a different electronic excitation of the precursor,
depending on the wavelength used. The spectrumwas recorded
using a dual beamCary 100 spectrophotometer. The resolution
used was 0.2 nm. The quartz absorption cell of 5 cm length used
with a thermostattable cell holder was coupled to a thermo-
statting bath to maintain a constant temperature in the cell.
CH2I þ HBr ! CH3I þ Br
CH3 þ HBr ! CH4 þ Br
ð1Þ
ð2Þ
The temperature dependence determined for reaction (1) was
combined with the quantum chemically calculated threshold
energy of the reverse reaction, (- 1), in order to calculate the
enthalpy of formation of the CH2I radical. The results
obtained from the experiments to measure reactions (1) and (2)
are given in Table 1. Reaction (2) was remeasured to calibrate
the experimental conditions used by comparing the kinetic
data obtained with the previously measured rate constants of
the same reaction.
Data analysis
Experiments were conducted under pseudo-first-order condi-
tions where HBr existed in great excess compared with the
concentration of radicals. Only the following two reactions
had significant rates under these conditions:
Photogeneration of CH2I and CH3 radicals
The CH2I radical was photogenerated by photodissociating
CH2I2 at 248 or 351 nm. Up to 9 meshes or a thick vycor plate
were used to diminish laser fluence to a very low level. This
ensured that the photon flux did not generate Br atoms from
HBr to any measurable extent or that any CH2I radical
recombination reaction was too slow to interfere with the
kinetics observed because the initial CH2I radical concentra-
tion was below 1011 radical cmÀ3. The CH2I radical was
formed from the precursor by C–I bond rupture. The main
photodissociation process is to generate CH2I + I(2P1=2 or
2P3/2) at 248 and 351 nm.9 The quantumyield of I( 2P1=2) is 0.46
R þ HBr ! RH þ Br
R ! heterogeneous loss on the wall
ð1Þ or ð2Þ
ð3Þ
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)–(3).
This was ensured by comparing the measured first-order wall
loss decays, k3 , of the radical with that produced (in the
absence of HBr) at different conditions where precursor
9,10
at 248 nmand decreases to nonexistence at 355 nm.
Table 1 Measurents of the rate constant of the R + HBr ! Br + RH
(R ¼ CH2I or CH3) reaction
[He]=
[HBr]=
kib=
T a=K
1016 cmÀ3
1013 cmÀ3
k3=sÀ1
10À13 cm3 sÀ1
CH2I + HBr ! Br + CH3I (k1)
297
298
299
328
363
408
465
2.83
5.79
5.81
5.81
5.83
5.84
5.85
8.74 – 39.2
5.70 – 34.7
9.66 – 47.5
11.6 – 46.5
11.1 – 53.1
11.8 – 43.7
9.31 – 58.2
16
19
25
15
15
15
18
6.5 0.4c
6.6 0.6c
6.9 0.7d
6.0 0.5c
6.2 0.4c
5.7 0.4d
5.3 0.4d
k1 ¼ (3.8 0.7) Â 10À13 exp[+ (1.4 0.6) kJ molÀ1=RT ]cm3 mole-
culeÀ1 sÀ1
CH3 + HBr ! Br + CH4 (k2)
299
300
348
348
409
510
510
677
5.82
2.32 – 11.4
3.05 – 8.54
5.83 – 11.1
2.07 – 7.21
3.28 – 8.59
2.02 – 6.58
2.14 – 8.70
1.91 – 9.80
8.7
15
9.5
7.2
13
17
1.5
5.7
29.3 2.1d
29.2 0.9d
29.3 0.5d
31.5 1.2d
25.9 0.8d
25.3 1.0d
26.0 1.0d
27.4 0.8d
17.8
5.89
5.89
5.85
5.86
5.87
5.88
Fig. 1 Plot of first-order decay constant k0 vs. [HBr] for one set of
experiments conducted to measure the CH2I + HBr rate constant, k1 ,
at 363 K. The insert in the upper left corner is the ion signal profile of
CH2I+ recorded during one of the experiments shown as a solid circle
([HBr] ¼ 3.37 Â 1014 molecule cmÀ3) 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 for
CH2I+ in the displayed ion signal profile is (224.7 3.9) sÀ1. The
insert in the lower right corner is the gas phase absorption spectrumof
CH2I2 at 308 K. The resolution of the spectrumis 0.2 nm. The two
maxima shown are at 248.4 nm and 288.4 nm. The CH2I radical was
photogenerated fromCH 2I2 by a Xe=F2* emission wavelength of the
exciplex laser to study the data set shown.
k2 ¼ (2.3 0.5) Â 10À12 exp[+ (0.60 0.17) kJ molÀ1=RT ]cm3 mole-
culeÀ1 sÀ1
a
Temperature uncertainty:
1 for 299–328 K and
3 for 348–
b
677 K. Fluorinated halocarbon wax used for wall coating at 297–
363 K, Teflon at 408–510 K and B2O3 at 510–677 K, errors are
1s + Student’s t and are based on statistical uncertainties. 351 nm
photolysis. 248 nmphotolysis.
c
d
456
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concentration was held steady but the laser radiation was
attenuated by the use of 2 meshes and a Vycor plate (the
radical concentration was changed by the same factor). The
decays fromthese different experiments were equal with
respect to their statistical error limits.
MgF2 window) to detect CH3 , I, CH3I and I2 and an argon
lamp (11.6, 11.8 eV; with a LiF window) to detect HBr, Br2
and Br.
Computation details
Rate constants for reactions (1) and (2) were obtained from
the slopes of plots of the exponential radical decay constant k0
vs. [HBr] {from[R +]t ¼ [R+]0 exp(Àk0t)}, where k0 ¼ k1 or 2
[HBr] + k3 . 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 fromall the experi-
ments to measure reactions (1)–(3) are given in Table 1.
Ab initio calculations were carried out with the Gaussian 98
package of programs.11 All calculations were carried out on an
Origin 2000 computer at the Centre for Scientific Computing
(Espoo, Finland). All structures of species needed for the
transition state calculations were fully optimized at the MP2
level of theory using 6-311G basis set with supplementary
functions for d and f shells [labelled as 6-311G(df)], and fro-
zen-core approximation.12 The basis sets for I and Br are taken
Accuracy of measurements
13,14
fromthe literature.
The transition state of the equilibrium
The error limits stated in the 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 reci-
procals of their variances for the fitting procedure.
reaction was localized at the minimum energy path using a
quadratic synchronous transit method.12 In the calculations
the expectation values, S2, for free radicals were in the range
0.7579–0.7918 and for transition states in the range 0.7920–
0.8062. Normal mode analyses were carried out at the same
level of theory for all species and transition states. These
frequency calculations 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 ima-
ginary vibrational frequency along the reaction coordinate.
The imaginary frequencies were in the range À 746 cmÀ1 to
À 1180 cmÀ1. The internal coordinates of the transition state,
which according to the calculated normal modes experience
the largest changes during the reaction, are the C–H and H–Br
bond lengths. The relative movement of the H atom is the
largest. The C–H–Br asymmetric stretch is the reaction coor-
dinate. Unscaled harmonic frequencies were used in the cal-
culations. 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 calculation at 0 K (see
Table 2). The ab initio calculations were needed to determine
the kinetics of the Br + molecule reactions.
Reagent sources and purification procedures
CH2I2 , 99%, CH3I, 99.5%, and HBr, 99%, were obtained
fromAldrich and helium, 99.995%, fromMatheson.
The carrier gas, He, was used as provided. CH2I2 and CH3I
were degassed by using freeze–pump–thaw cycles, stabilized
with copper and stored in darkness. The vaporized precursor
gas was mixed with the carrier gas flow before it entered the
reactor inlet. HBr was collected to a flow trap kept at 77 K and
was repeatedly distilled 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 reac-
tor. 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.
Computationally calculated kinetics of the reverse reactions
Ab initio calculations were also used to determine the entropies
of the reactants and the transition states of Br + RH !
HBr + R (R ¼ CH2I, CHI2 or CI3) reactions (see Tables 3 and
4 for structural parameters, frequencies and moments of
inertia). The Arrhenius expressions of the bimolecular reac-
tions at 298.15 K were obtained using thermodynamic transi-
tion state theory.
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 window
was used to detect CH2I, a hydrogen lamp (10.2 eV; with a
The canonical rate constant used is
ꢀ
ꢁ
ꢀ
ꢁ
kLze2kBT
hco
DrSoz À 371:26
Ea
kðTÞ ¼
exp
exp À
R
RT
where k ¼ transmission coefficient,15 Lz ¼ reaction path degen-
eracy, kB ¼ Boltzmann constant, h ¼ Planck’s constant,
Table 2 Symmetry point groups, total and zero-point energies. Ener-
gies at the MP2(fc)=6-311G(df)== MP2(fc)=6-311G(df) level are in Eh
Compound
Symmetry
Total energy
Zero-point energy
Br
HBr
CH3I
CH2I
CH2I2
CHI2
CHI3
Kh
C
C3v
Cs
C2v
Cs
C3v
C3v
C1
À 2572.639864
À 2573.271159
À 6956.834592
À 6956.174294
À 13873.317448
À 13872.664184
À 20789.798621
À 20789.153875
À 9529.443493
À 16445.932381
À 23362.419833
0.0
0.006172
0.037418
0.022203
0.027787
0.014140
0.017211
0.004797
0.030083
0.020610
0.010161
1v
CI3
Br–H–CH2I
Br–H–CHI2
Br–H–CI3
Fig. 2 Arrhenius plot of CH2I + HBr and CH3 + HBr reactions
measured in the current study. The lines are Arrhenius expressions
fitted to the rate constants k1 and k2 .
C1
C1
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Table 3 Structural parameters of the species optimized in ab initio calculations at the MP2(fc)=6-311G(df)== MP2(fc)=6-311Gdf) level of theory.
+
Bond lengths in A and angles in degreesa
Species
rCH
rCI
rC–H
rH–Br
aICH
aHCH
aICI
ad
aC–H–Br
ao
CH3I
CH2I
CH2I2
CHI2
CHI3
CI3
Br–H–CH2I
Br–H–CHI2
Br–H–CI3
1.087
1.079
1.086
1.083
1.087
—
1.085
1.088
—
2.137
2.044
2.135
2.052
2.143
2.068
2.061
2.078
2.104
—
—
—
—
—
—
1.523
1.467
1.403
—
—
—
—
—
—
1.529
1.549
1.580
108.1
118.5
107.7
116.7
106.4
—
114.9
112.6
—
110.8
122.4
111.3
—
—
—
117.2
—
—
—
—
—
—
—
—
—
—
180
180
180
—
—
—
—
—
—
170.4
185.1
180
—
8.5
—
23.3
—
19.3
36.5
40.5
38.0
114.8
122.6
112.4
118.8
—
119.5
115.0
+
a
The bond length of HBr is 1.416 A. The dihedral angle ad is given as a3126 (see Fig. 3) and the out-of-plane angle ao at the radical center of the
transition state or free radical is an angle between a plane (consists of a C and two H or I) and a remaining bond.
Table 4 Moments of inertia and unscaled vibrational frequencies as wavenumbers of the species calculated at the MP2(fc)=
6-311G(df)== MP2(fc)=6-311G(df) level of theory. The numbers in parentheses refer to two similar wavenumbers if given as integers
Compound
Wavenumber=cmÀ1
Moment of inertia=10À47 kg m2
CH2I
CH3I
Br–H–CH2I
CHI2
CH2I2
Br–H–CHI2
CI3
CHI3
Br–H–CI3
HBr
170, 659, 898, 1421, 3222, 3376
3.011, 94.95, 97.93
5.365, 111.8, 111.8
49.47, 1478, 1522
25.12, 1368, 1393
37.63, 1368, 1400
1374, 1405, 2752
1338, 1338, 2673
1349, 1349, 2675
2635, 2635, 2659
3.320
574, 933(2), 1343, 1513(2), 3125, 3246(2)
60, 305, 436, 670, 834, 886, 951, 1171, 1419, 3171, 3302, 746i
132, 326, 548, 760, 1189, 3253
121, 515, 630, 756, 1106, 1188, 1462, 3165, 3254
45, 91, 135, 324, 615, 687, 788, 944, 1056, 1164, 3197, 950i
112(2), 154, 219, 754(2)
105(2), 160, 453, 626(2), 1141(2), 3194
48(2), 110(2), 123, 196, 669(2), 726, 880(2) 1180i
2709
kðBr þ CH2I2 ! HBr þ CHI2Þ ¼ 1:5 Â 10À11
T ¼ absolute temperature, R ¼ universal gas constant,
DrSoz ¼ standard entropy of activation of the reaction and
Ea ¼ Arrhenius activation energy. The DrSoz ¼ Soz À SSo
(reactants) refers to a standard state of co (molecule cmÀ3).
À1
À1
 expðÀ 48:0 kJ m ol =RTÞ cm3 molecule sÀ1
kðBr þ CHI3 ! HBr þ CI3Þ ¼ 5:0 Â 10À12
The value of 371.26 (in J KÀ1 molÀ1) changes the standard
À3 16
Arrhenius activation
 expðÀ 29:9 kJ m oÀl 1=RTÞ cm3 moleculeÀ1 sÀ1
state from1 atmto molecule cm
.
energies at 298.15 K were calculated fromthe heat capacity
corrected threshold energies. The Arrhenius rate expressions
determined at 298.15 K are as follows:
Error limits for the A factors are not considered, for the
2.4 kJ molÀ1 in com-
activation energies they are typically
parison with experimentally determined activation energies
kðBr þ CH3I ! HBr þ CH2IÞ ¼ 3:3 Â 10À11
 expðÀ 63:9 kJ m oÀl 1=RTÞ cm3 moleculeÀ1 sÀ1
5
with quantumchemically calculated threshold energies.
The
effect of rotational symmetry of the molecule in its rotational
entropy is included in the Lz and excluded fromthe value of
DrSoz. Furthermore, the tunnelling effect is ignored because
activation energies of the forward reactions are in the range
(À 0.2–4.3) kJ molÀ1 and either Wigner or unsymmetrical
Eckart barrier correction overestimates the tunnelling effect
for the reverse reactions. The calculated Arrhenius A factors
per H atomare 11.0 Â 10À12 and 7.6 Â 10À12 and 5.0 Â 10À12
cm3 moleculeÀ1 À1. The trend of decreasing A factors per
s
H atomas a function of increasing iodination substitution on
methane is similar to that of the reactions of Br atom with
CH3Cl and CH2Cl2 .4
Thermochemical calculations
(
In the reactions of the R + HBr RH + Br (R ¼ CH2I, CHI2
+
or CI3) equilibriumno mole change is involved. Consequently,
the standard reaction enthalpy change, DrHo, is simply the
difference between the activation energies of the reaction
directions. The kinetics of CH2I + HBr reaction was deter-
mined experimentally whereas the temperature dependences
of CHI2=CI3 + HBr reactions were estimated using a linear
Fig. 3 Optimized transition state of the Br + CH3I ! CH2I + HBr
reaction at 0 K. The parameters are calculated at the MP2(fc)=
6-311G(df)==MP2(fc)=6-311G(df) level of theory. The dihedral angle
ad ¼ a3126 ¼ 180ꢀ.
458
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was remeasured, and found to be (2.9 0.2) Â 10À12 cm3
moleculeÀ1 sÀ1 at 299 1 K at pressures of a few torr. These
results are a clear indication that the observed kinetics of free
radical reactions with hydrogen halides4,21,22 in the gas phase
are not affected by the reactions of any vibrationally excited
states of the radical. The photogenerated free radicals are
indeed collisionally deactivated in less than 0.5 ms by the
buffer gas at the experimental conditions used. Thus an
attempt to explain the kinetics measured in flow reactors22
simply by heterogeneous wall reactions (caused by inadequate
collisional relaxation of the radical with the buffer gas) is
unreasonable and misleading.23
Table 5 Heats of formation used in the thermochemical calculations
Species
DfHo298=kJ molÀ1
HBra
Bra
À 36.44 0.17
111.86 0.06
14.4 1.4
119.5 2.2
251.0 1.4
CH3Ib
b
CH2I2
b
CHI3
a
b
Data taken fromref. 18.
Data taken fromref. 19.
relationship between the experimental activation energies of
free radical (R) reactions with HBr and the algebraic sumof
Pauling’s electronegativities of the atoms attached to the
radical carbon in R.5,17
Threshold energies
The kinetics of the CH2I + HBr reaction is shown in Fig. 2. The
product of reaction (1) was detected to be CH3I. The transition
states of the two reaction channels of the reverse reaction
direction were characterized. In general, the energy barrier
for abstracting a H atomby the Br atomon CH 3I, CH2I2 or
CHI3 is about 8–10 kJ molÀ1 larger than the competing
channel for abstracting an I atom. This implies for instance that
the reverse reaction (-1) cannot be studied experimentally. Solid
evidence for this is provided in a crossed-molecular-beam
experiment of the reaction Br + CH3I. The product IBr was
concluded to be formed as the product of the reaction.24
The zero-point energy corrected threshold energy of reaction
(À1) was determined by ab initio calculations at the
MP2(fc)=6-311G(df)== MP2(fc)=6-311G(df) level of theory to
be 62.0 kJ molÀ1 at 0 K. More accurate calculations at the
MP4(SDTQ)=6-311G(df)==MP2(fc)=6-311G(df) level yielded a
similar value. On the other hand, the 3-21G basis set (the
largest basis set available for iodine in Gaussian 98) is inade-
quate to calculate the threshold energy of reaction (À1)
accurately. The other two quantumchemically calculated
threshold energies for abstracting H atomat 0 K are 48.0 kJ
molÀ1 for Br + CH2I2 and 29.9 kJ molÀ1 for Br + CHI3 .
The threshold energies of the Br + molecule ! HBr + radical
reactions studied will be increased by 1 kJ molÀ1 if the cal-
culated zero-point energies are multiplied by 0.95 for the
energy calculations. However, the scaling factor for unharmo-
nic corrections is not used in the current study because no
accurate value is known for it.
For a second-law calculation the mean temperature on a 1=T
scale of the studied reaction directions is always near 0 K if the
other activation energy is determined at absolute zero of
temperature. In the current study the threshold energies of
Br + molecule reactions, which at 0 K exactly equals the
activation energies, are calculated using the ab initio method.
Furthermore, the enthalpies of the reactions near 0 K are
corrected to 298 K using a heat capacity correction. For these
calculations the heat capacity values at constant pressure of Br
and HBr were taken fromthe literature. For the other com-
pounds studied, the ab initio calculated heat capacity values at
constant volume were used instead. However, for an ideal gas
reaction with no mole change these two heat capacities are
similar. The mean standard heat capacity of the reaction over
the temperature range 0–298 K is about half of the value at
298 K.5 Finally, the enthalpies of formation of the radicals
studied were calculated using the enthalpies of reaction and the
enthalpy of formation, DfHo298 , values of Br, HBr and iodi-
nated methane (see Table 5). The values obtained are as
follows:
DfHo ðCH2IÞ ¼ 228:0 ꢁ 2:8 kJ m oÀl 1
298
DfHo ðCHI2Þ ¼ 314:4 ꢁ 3:3 kJ m oÀl 1
298
DfHo ðCI3Þ ¼ 424:9 ꢁ 2:8 kJ m oÀl 1
298
The enthalpy of formation of CH2I can be obtained fromthe
C–H bond energy of CH3I at 298 K to be a value of
431.6 2.8 kJ molÀ1. Similarly the other C–H bond energies
obtained are 412.9 3.3 kJ molÀ1 of CH2I2 and 391.9 3.1 kJ
molÀ1 of CHI3 at 298 K.
Enthalpy of formation values determined
The enthalpy of formation of the CH2I radical was found to be
228.0 2.8 kJ molÀ1 at 298 K. This value is in very good
agreement with the value of 228.4 8.4 kJ molÀ1 fromthe
appearance energy measurement of Holmes and Lossing.25
Furuyama et al. have used an iodination technique to deter-
mine the enthalpy of formation of CH2I to be 230 7 kJ
Discussion
molÀ1 26
However, they assumed that the kinetics of the
.
Collisionally relaxed radicals
CH2I + I2 reaction has no temperature dependence. More
recent experiments on the free radical reactions with HBr and
Br2 indicate that the activation energy could be 2–3 kJ molÀ1
negative.21,27 This would raise the enthalpy of formation value
A great advantage of using 351 nmphotolysis instead of
193 nm photolysis (commonly used to generate free radicals in
the gas phase for kinetic purposes) is that one can generate the
radical of interest with less excess internal energy. Further-
more, the vibrational deactivation of a small polyatomic free
radical is very fast already at a few torr pressure. This
phenomenon is concluded from the CH3 + HBr studies of
Krasnoperov et al. over the pressure range from1 to 100 bar. 20
The authors used 193 nmphotolysis of acetone to generate the
CH3 radical and studied the kinetics of this radical reaction by
using time-resolved transient UV spectroscopy. A weighted
rate constant value of (3.2 1.0) Â 10À12 cm3 moleculeÀ1 sÀ1
can be calculated fromthe set of rate contants measured by the
authors at 297 3 K over a wide pressure range. The closeness
of the values of the rate constants implies that the CH3 + HBr
reaction has no pressure dependence. Here the rate constant
determined by Furuyama et al. to 232–233 kJ molÀ1
.
DeCorpo et al. determined DfHo298 of the CH2I radical to be
219.2 10 kJ molÀ1 28
appearance potential measurement of diiodomethane. How-
.
The value was obtained froman
ever, a more recent DfHo value19 for CH2I2 if used in their
calculations would raise the enthalpy of formation of CH2I to
298
225.4 10 kJ molÀ1 at 298 K.
The enthalpy of the CHI2 radical was determined to be
314.4 3.3 kJ molÀ1 at 298 K. According to this the C–H
bond strength of the CH2I2 molecule has a value of 412.9 3.3
kJ molÀ1. This value is clearly below the value of 430 11 kJ
molÀ1 determined in the studies of the reaction of CH2I2 +
HI CH I + I using an iodination technique.29 However,
(
+
3
2
Phys. Chem. Chem. Phys., 2002, 4, 455–460
459

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5
6
7
8
9
J. A. Seetula, Phys. Chem. Chem. Phys., 2000, 2, 3807.
I. R. Slagle and D. Gutman, J. Am. Chem. Soc., 1985, 107, 5342.
J. A. Seetula, Ann. Acad. Sci. Fenn., Ser. A2, 1991, 234.
B. J. Huebert and R.M. Martin, J. Phys. Chem., 1968, 72, 3046.
S. L. Baughcumand S. R. Leone, J. Chem. Phys., 1980, 72, 6531.
this method includes inaccurately estimated activation energies
for free radical reactions as mentioned above, a factor which
typically leads to the calculated C–H bond energy being too
large.30 Moreover, it seems to be unrealistic to expect that the
C–H bond energy of CH3I and CH2I2 will be similar.29 The
threshold energy calculation is strong evidence that different
energy barriers for the Br atomabstracting H atomfromCH 3I
or CH2I2 do exist. A similar trend of energy barriers as found
in the current study is obtained for the other Br atom
abstracting reactions with halogenated methanes.4
10 J. Zhang and D. G. Imre, J. Chem. Phys., 1988, 89, 309.
11 M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A.
Robb, J. R. Cheeseman, V. G. Zakrzewski, J. A. Montgomery,
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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, C. Gonzalez, M. Challacombe,
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13 M. P. McGrath and L. Radom, J. Chem. Phys., 1991, 94, 511.
14 M. N. Glukhovtsev, A. Pross, M. P. McGrath and L. Radom,
J. Chem. Phys., 1995, 103, 1878.
15 J. A. Seetula, J. Chem. Soc., Faraday T rans., 1998, 94, 3561.
16 P. J. Robinson, J. Chem. Educ., 1978, 55, 509.
17 L. Pauling, Nature of the Chemical Bond, Cornell University Press,
Ithaca, New York, 3rd edn., 1960.
18 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, Supplement No. 1.
The DfHo298(CI3) was found to be 424.9 2.8 kJ molÀ1. This
seems to be the first enthalpy of formation determination for
the CI3 radical.
Summary
The kinetics of the CH2I radical reaction with HBr has been
characterized. The temperature dependence measured was
combined with the ab initio calculated threshold energy of the
reverse reaction to obtain the enthalpy of formation of CH2I
radical to be 228.0 2.8 kJ molÀ1 at 298 K. The C–H bond
strength of iodomethane was calculated to be 431.6 2.8 kJ
molÀ1. The trend of empirically determined activation energies
of the forward free radical + HBr reactions was used with the
ab initio calculated threshold energies of the reverse reactions
to obtain DfHo value for CHI2 to be 314.4 3.3 kJ molÀ1
298
and for CI3 to be 424.9 2.8 kJ molÀ1
.
19 A. S. Carson, P. G. Laye, J. B. Pedley and A. M. Welsby, J. Chem.
T hermodyn., 1993, 25, 261.
20 L. N. Krasnoperov and K. Mehta, J. Phys. Chem. A, 1999, 103,
8008.
Acknowledgements
21 J. A. Seetula and I. R. Slagle, J. Chem. Soc., Faraday T rans., 1997,
93, 1709.
22 J. A. Seetula, J. J. Russell and D. Gutman, J. Am. Chem. Soc.,
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23 O. Dobis and S.W. Benson, J. Am. Chem. Soc., 1995, 117, 8171.
24 T he effects of reagent translational and vibrational energy on the
dynamics of endothermic reactions, D. Krajnovich, Z. Zhang, F.
Huisken, Y. R. Shen and Y. T. Lee, Phys. Electron. At. Collisions,
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26 S. Furuyama, D. M. Golden and S. W. Benson, Int. J. Chem.
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27 R. S. Timonen, J. A. Seetula, J. Niiranen and D. Gutman, J. Phys.
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28 J. J. DeCorpo, D. A. Bafus and J. L. Franklin, J. Chem.
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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
(USA). 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).
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