Kinetics and thermochemistry of the R + HBr ->/<- RH + Br (R = C2H5 or β-C2H4Cl) equilibrium An ab initio study of the bond energies in partly chlorinated ethanes and propanes

Article abstract of DOI:10.1039/a706440c

The kinetics of the reaction of ethyl and β-chloroethyl radicals with HBr have been investigated under pseudo-first-order conditions in a heatable tubular reactor.The pressure-independent rate constants determined were fitted to the following Arrhenius expression (error limits stated are I? + Student's t values, units in cm³ molecule^-1 s^-1): k(C2H5) = (1.87+/-0.14) x 10^-12 exp<+(3.7+/-0.2) kJ mol^-1/RT> and k(β-C2H4Cl) = (5.7+/-1.6) x 10^-13 exp<+(2.2+/-0.8) kJ mol^-1/RT>.The kinetic data were used in a second-law procedure to calculate the entropy and enthalpy of formation values for the radicals studied at 298 K (entropy in J K^-1 mol^-1 and enthalpy in kJ mol^-1): 244 +/- 6, 120.7 + 2.1 (C2H5) and 271 +/- 7, 93.0 +/- 2.4 (p-C2H4Cl).The enthalpy of formation values of chloroethyl radicals were used in group additivity calculations to obtain Δ_fH₂₉₈⁰ values for six monochlormated propyl and butyl radical isomers.Extensive ab initio molecular orbital calculations at the MP4/6-311G(d,p) level were used to determine all bond energies in monochlormated ethane and propane, and in dichlorinated ethane molecules.The global minimum structures of open- and closed-shell species needed for calculations were determined at the MP2/6-31G(d,p) level.The calculated values are in close agreement with experimentally determined bond enthalpies.The calculations show a significant effect of chlorine atom(s) on the structure of chlorinated free radicals and on the bond energies of chlorinated mol-ecules.

Full text of DOI:10.1039/a706440c

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Kinetics and thermochemistry of the R + HBr ¢ RH + Br (R =
C H or b-C H Cl) equilibrium
2 5
2 4
An ab initio study of the bond energies in partly chlorinated ethanes and propanes
Jorma A. Seetula¤
L aboratory of Physical Chemistry, P.O. Box 55 (A. I. V irtasen aukio 1) FIN-00014 University of
Helsinki, Finland
The kinetics of the reaction of ethyl and b-chloroethyl radicals with HBr have been investigated under pseudo-Ðrst-order condi-
tions in a heatable tubular reactor. The pressure-independent rate constants determined were Ðtted to the following Arrhenius
expression (error limits stated are 1p ] StudentÏs t values, units in cm3 molecule~1 s~1): k(C H ) \ (1.87 ^ 0.14) ] 10~12
2
5
exp[ ] (3.7 ^ 0.2) kJ mol~1/RT ] and k(b-C H Cl) \ (5.7 ^ 1.6) ] 10~13 exp[](2.2 ^ 0.8) kJ mol~1/RT ]. The kinetic data were
2
4
used in a second-law procedure to calculate the entropy and enthalpy of formation values for the radicals studied at 298 K
(entropy in J K~1 mol~1 and enthalpy in kJ mol~1): 244 ^ 6, 120.7 ^ 2.1 (C H ) and 271 ^ 7, 93.0 ^ 2.4 (b-C H Cl). The
2
5
2 4
enthalpy of formation values of chloroethyl radicals were used in group additivity calculations to obtain * H¡ values for six
f
298
monochlorinated propyl and butyl radical isomers. Extensive ab initio molecular orbital calculations at the MP4/6-311G(d,p)
level were used to determine all bond energies in monochlorinated ethane and propane, and in dichlorinated ethane molecules.
The global minimum structures of open- and closed-shell species needed for calculations were determined at the MP2/6-31G(d,p)
level. The calculated values are in close agreement with experimentally determined bond enthalpies. The calculations show a
signiÐcant e†ect of chlorine atom(s) on the structure of chlorinated free radicals and on the bond energies of chlorinated mol-
ecules.
The role of chlorine as an atom, molecule or a part of an
organic compound is central in combustion processes of
chlorine-bearing polymeric materials. As an atom it has very
high reactivity and a tendency to react with saturated hydro-
carbons by a hydrogen atom abstraction reaction and with
unsaturated hydrocarbons by a pressure-dependent addition
reaction which, at elevated temperatures, becomes reversible
(the abstraction channel then also becomes signiÐcant).1,2 The
abstraction reaction produces free radicals and HCl whereas
the reaction with unsaturated hydrocarbons gives only free
radicals at low temperatures. The resultant free radicals can
react with molecular chlorine in exothermic reactions to
produce molecular chlorides and Cl atoms.3 Finally, the Cl
atom attacks certain bonds preferentially. Typically, a-
chlorinated alkyl radicals are formed as the principal pro-
ducts. The stability of these and other chlorinated alkyl
radicals is largely inÑuenced by intramolecular electronic
e†ects and, hence, these free radicals will decompose
unimolecularly to alkenes at di†erent temperatures.
Until now bond energies of chlorinated saturated hydrocar-
bons have been determined experimentally using di†erent
spectroscopic or kinetic methods.4h6 The halogen atom e†ect
on the CwH bonds of molecules has been a subject for many
studies of Ñuorocompounds7h9 and some chlorocompounds.10
However, in the case of chlorinated species such studies are
restricted to the smallest compounds, where free radicals or
cations formed during bond rupture processes are the most
stable species containing only a few atoms. The present study
combines experimental and computational techniques. A time-
resolved kinetic technique being used to study the free radical
kinetics with HBr and quantum chemical molecular orbital
methods to determine the structures and energies of labile and
stable species.
sured previously. The approach used was the same as that
used for the study of chlorinated methyl and ethyl radical
reactions with HBr.5 The study was carried out to investigate
the Cl atom e†ect on the radical reactivity and to obtain ther-
mochemical properties of the free radicals for use in bond
energy determinations. The ab initio calculations were then
used to extend the bond enthalpy determinations to include
monochlorinated propanes and dichlorinated ethanes, in
order to investigate the inÑuence of the Cl atom on the other
bonds of the molecule. This information is useful in attempts
to model large-scale combustion processes of chlorine-
containing materials in which both oxidation and pyrolysis
reactions of molecules and free radicals occur. All thermal
molecular oxygen-free reactions will proceed through the most
energetically favourable channels, which can be identiÐed by
studying the bond energies of the species involved.
Experimental study
Kinetic measurements
The rate constants for the reactions of ethyl and b-chloroethyl
radical with HBr were studied as a function of temperature
and pressure. The reactions were studied separately under
pseudo-Ðrst-order conditions. The free radicals were photoge-
nerated from suitable precursors inside a tubular Ñow reactor
(see next section) and the kinetics of the reactions were fol-
lowed by monitoring the decay of the radical as a function of
time. Details of the experimental apparatus and conditions
used have been described previously.5,11h13 BrieÑy, pulsed
unfocused 248 nm radiation from a Lambda Physik EMG 201
MSC exciplex laser, operated at 5 Hz, was collimated and
then directed along the axis of a Pyrex or quartz reactor. The
10.5 mm id reactor was coated with di†erent materials (see
Table 1). Gas Ñowing through the reactor at 5 m s~1 was
completely replaced between laser pulses. The Ñowing gas
contained the free radical precursor (typically \0.03%), HBr
in varying concentrations and the carrier gas, He, in large
The chemical kinetics of ethyl and b-chloroethyl radicals
with HBr have been studied, the latter having not been mea-
¤ E-mail: jorma.seetula=csc.Ð
J. Chem. Soc., Faraday T rans., 1998, 94(7), 891È898
891

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Table 1 Measurement of the rate constants of the reaction R ] HBr ] RH ] Br (R \ C H or b-C H Cl)
2
5
2 4
T a/K
[He]/1016 cm~3
[HBr]/1013 cm~3
k /s~1
wall coatingb
k c/10~12 cm3 s~1
3
i
C H ] HBr ] C H ] Br (k )
2
5
2
6
1
296
297
348
409
409
510
677
5.79
17.8
5.90
5.81
5.82
5.87
5.88
0.70È4.27
0.68È4.04
0.63È5.20
1.05È4.12
1.22È5.21
1.40È5.18
1.84È5.87
21
29
19
15
15
17
12
B O
8.47 ^ 0.29
8.59 ^ 0.38
6.80 ^ 0.15
5.71 ^ 0.19
5.52 ^ 0.14
4.41 ^ 0.16
3.70 ^ 0.14
2
B O
2
3
3
3
B O
2
PDMS
B O
2
B O
2
3
3
3
B O
2
k \ (1.87 ^ 0.14) ] 10~12 exp[ ] (3.7 ^ 0.2) kJ mol~1/RT ] cm3 molecule~1 s~1
1
b-C H Cl ] HBr ] C H Cl ] Br (k )
2
4
2
5
2
300
300
300
348
378
378
409
409
17.7
5.79
17.7
5.84
5.83
5.84
5.80
5.85
7.58È22.7
5.07È18.6
8.71È21.3
2.77È20.6
8.16È24.5
5.23È25.0
8.24È35.9
4.87È28.0
50
37
31
38
64
71
84
68
HW
HW
HW
1.39 ^ 0.22
1.31 ^ 0.08
1.39 ^ 0.06d
1.25 ^ 0.12
1.04 ^ 0.30
1.12 ^ 0.16
1.13 ^ 0.12
1.04 ^ 0.10
HW
PDMS
PDMS
PDMS
PDMS
k \ (5.7 ^ 1.6) ] 10~13 exp[](2.2 ^ 0.8) kJ mol~1/RT ] cm3 molecule~1 s~1
2
a Temperature uncertainty: ^2 K (296È378 K) and ^ 3 K (409È677 K). b HW (halocarbon wax), PDMS [poly(dimethylsiloxane)] and B O .
2
3
c Errors are 1p ] StudentÏs t and based on statistical uncertainties. d CH BrCH Cl was used as a precursor.
2
2
excess ([99.5%). A portion of the gas mixture was sampled
continuously through a 0.44 mm id hole located at the end of
a nozzle in the wall of the reactor. A portion of the gas beam
was photoionized by VUV light and the mass selected by a
quadrupole mass Ðlter in the vacuum chamber. Temporal ion
signal proÐles were recorded before and after the laser pulse
with a multichannel scaler. Data were accumulated from 1000
to 20 000 repetitions of the experiments before being analysed
by a non-linear least-squares analysis program.
tion kinetics. The main photolysis channel from both mol-
ecules is production of the b-chloroethyl radical and Br/I. The
minor channel is the production of ethylene and halogen
atoms.
The b-C H Cl radical starts to decompose above 409 K at
2
4
the pressures used in the current study. At 510 K its half-life is
\0.5 ms, whereas the half-life of its more stable isomer,
a-C H Cl, is [60 ms.5 At this temperature the ion signal of
2
4
the b-isomer showed a clear Ðrst-order exponential decay
without any displacement from the baseline, indicating isom-
erization to the a-C H Cl form. It was concluded that mea-
The kinetics of the following metathetical reactions were
studied:
2
4
surements at \410
K
were not inÑuenced by the
C H ] HBr ] C H ] Br
(1)
(2)
isomerization process during the timescale of the study.
2
5
2 6
b-C H Cl ] HBr ] C H Cl ] Br
Rate constant data analysis
2
4
2 5
The Arrhenius expressions of the forward reactions were com-
bined with the Arrhenius expressions of the reverse, Br ] RH,
reactions6,14 for the thermochemical calculations of the free
radicals studied. Reaction (2) was studied over a narrower
temperature range than reaction (1) since above 409 K the
b-C H Cl radical starts to decompose unimolecularly. As
expected the reactions did not show any pressure dependence
at the gas densities used to study reactions (1) and (2). The
results are listed in Table 1.
Experiments were conducted under pseudo-Ðrst-order condi-
tions.5 Only two radical reactions had signiÐcant rates under
the conditions used for this study:
R ] HBr ] RH ] Br
(1) or (2)
(3)
2
4
R ] heterogeneous loss on the wall
The initial radical concentrations were so low that radicalÈ
radical reactions had negligible rates compared with reactions
(1)È(3). This was ensured by similar methods to those used
previously.5
Photogeneration of radicals
Bimolecular rate constants for reactions (1) and (2) were
obtained from plots of the exponential radical decay constant
k@ vs. [HBr] Mfrom [R`] \ [R`] exp[([k@t), where k@ \
The ethyl radical was generated by photolysis of ethyl iodide
with radiation at 248 nm giving 3È4% photodissociation. The
main photolysis channel is the rupture of the CwI bond. A
minor channel is the production of C H ] H ] I. This
t
0
k
k
[HBr] ] k N. An example of an experiment to determine
1 or 2
2
3
2
4
at one temperature is shown in Fig. 1. The temperature
dependence of the rate constants is shown in Fig. 2.
channel has also been observed by Brum et al. after photolysis
of deuterium labelled iodoethanes at 248 nm in a time-of-Ñight
mass spectrometer.15 H atoms were monitored via two-
photon ionization processes. It was concluded that H atoms
were photogenerated almost exclusively by b-CwH bond
scission.15
Heterogeneous wall reactions
There exists a possibility that side reactions such as heter-
ogeneous bimolecular reactions can occur in Ñow reactor
experiments. This is especially true for experiments with HBr.
The heterogeneous unimolecular reaction is taken into
account in the data analysis (see above), but there is a possi-
bility of a heterogeneous bimolecular reaction occurring
between the reactants.5 To minimize any inÑuence of heter-
ogeneous wall reactions, di†erent coating materials were used
(see Table 1). These coatings did not a†ect the value of the
bimolecular R ] HBr rate constant.
The b-chloroethyl radical was photogenerated either from
CH BrCH Cl or CH ICH Cl. The latter being mainly used
2
2
2
2
since it was easily photodissociated at 248 nm, giving a higher
photolysis yield (4È6% cf. 1% for the bromocompound).
However, the kinetic results with either precursor used under
the same experimental conditions were identical (see Table 1),
indicating that the excess internal energy formed during the
photolysis did not have any measurable inÑuence on the reac-
892
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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and 1-iodo-2-chloroethane (97%) from Lancaster. The radical
precursors were degassed by using freezeÈpumpÈthaw cycles.
HBr was collected in a Ñow trap kept at 77 K and was dis-
tilled several times under vacuum.5
Photoionization
Reactants, free radicals and precursors were photoionized
using atomic resonance radiation. An argon lamp (11.6, 11.8
eV) was used to ionize HBr, Br , Br, C H and all the precur-
2
2 4
sors. A hydrogen lamp (10.2 eV) was used to ionize CH CHCl
2
and a chlorine lamp (8.9È9.1 eV) to ionize the free radicals.
Thermochemical calculations
Thermochemical functions for reactions (1) and (2) were
obtained by a second-law method. The procedure is the same
as that used previously.5 BrieÑy, reaction enthalpy, entropy
and free energy were calculated at the mean temperature, T ,
m
of both reaction directions. The reaction enthalpy change and
entropy were then recalculated at room temperature using the
heat capacities of the reaction species. Finally, the enthalpy of
formation and the entropy of the free radical of interest were
obtained using the *H¡ and *S¡ functions at 298 K and the
tabulated * H¡ and S¡ values of the other reaction species.
Fig. 1 First-order decay constant k@ vs. [HBr] for one set of experi-
ments conducted to measure the b-C H Cl ] HBr rate constant, k ,
2
4
2
at 409 K. Insert is the ion signal proÐle of b-C H Cl` recorded
2
4
during one of the experiments, shown as a solid circle in the linear
regression Ðt. The line through the data in the insert is an exponential
function Ðtted by a non-linear least-squares procedure. The Ðrst-order
decay constant for b-C H Cl` in the displayed ion signal proÐle is
f
298
298
C H . The enthalpy of formation of the ethyl radical was
2
5
determined to be 120.7 ^ 2.1 kJ mol~1 using the second-law
method. For comparison, the third-law method yielded
* H¡ (C H ) \ 122.7 ^ 2.4 kJ mol~1. The reverse reaction
2
4
(192.9 ^ 4.0) s~1 ([HBr] \ 8.24 ] 1013 molecule cm~3).
f
298 2 5
kinetics and thermochemical functions were taken from ref. 14
and Table 2. The results are shown in Table 3.
Accuracy of measurements
The error limits in the Arrhenius expressions are
1p ] StudentÏs t and are based only on the statistical uncer-
tainties. The reactions were studied under pseudo-Ðrst-order
conditions and thus only the concentration of HBr needed to
be known accurately. This was measured before and after the
kinetic experiment and the mean value was used for the rate
constant calculation (see more details in ref. 5). The other
errors, including temperature and Ñow rate, were always
\1% and were thus ignored.
b-C H Cl. The Arrhenius expression for the reaction Br
2
4
] C H Cl ] HBr ] b-C H Cl was determined to be k
\
2
5
2
4
~2
(6.7 ^ 3.5) ] 10~12 exp[[(55.3 ^ 2.3) kJ mol~1/RT ] cm3
molecule~1 s~1 from 343 to 423 K. The kinetics of reaction
([2) were calculated from the ratio of rate constants:
Table 2 Enthalpies of formation and entropies used in thermochemi-
cal calculations
Reagents
* H¡
S¡
Helium (Matheson, 99.995%) was used without further puriÐ-
cation. Hydrogen bromide (99%) and iodoethane (99%) were
obtained from Aldrich, and 1-bromo-2-chloroethane (97%)
f
298
298
species
/kJ mol~1
/J K~1 mol~1
HBra
Bra
[36.44
111.86
198.70
175.02
228.98
276.0
C H
b
[83.85
2
6
C H Clc
[112.1
2
C H
2
5
5
d
246.8
a Data taken from ref. 16. b Enthalpy is taken from ref. 18 and
entropy from ref. 17. c Enthalpy is taken from ref. 20 and entropy
from ref. 21. d Entropy from ref. 19.
Table 3 Second-law determinations of * H¡ (R) and E
298 d 298
based on the R ] HBr ¢ RH ] Br equilibrium (R \ C H or b-
(RwH)
f
2
5
C H Cl)
2
4
R
C H
2
b-C H Cl
5
2 4
373
T
537
m
*G¡
Tm
*H¡
Tm
*S¡
Tm
*H¡
298
*S¡
298
[(35.4 ^ 1.8)
[(57.0 ^ 2.1)
[(40.2 ^ 5.1)
[(56.3 ^ 2.1)
[(38.4 ^ 5.1)
120.7 ^ 2.1
244 ^ 6
[(49.8 ^ 1.4)
[(57.5 ^ 2.4)
[(20.6 ^ 7.5)
[(56.8 ^ 2.4)
[(18.6 ^ 7.5)
93.0 ^ 2.4
* H¡ (R)
f
298
(RwH)
S¡ (R)
271 ^ 7
298
E
422.6 ^ 2.1
423.1 ^ 2.4
d 298
Fig. 2 Arrhenius plot of the radical ] HBr reactions measured in
the current study and in ref. 5 (a-C H Cl). The lines are Arrhenius
expressions of the rate constants.
Energies and entropies in units kJ mol~1 and J K~1 mol~1, and tem-
2
4
perature in K.
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
893

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Table 4 Calculated * H¡
(in kJ mol~1) of partly chlorinated
* H¡
butyl free radicals from the following principle:
f
298
propyl and butyl radical isomers
* H¡(b-C H Cl) ] * H¡(isoC H )
f
2
4
f
3 7
radical
f
298
\ * H¡(C H ) ] * H¡(b, isoC H Cl)
f
2
5
f
3 6
Æ
CH CH CHCl (propyl, 1-chloro)
56.6 ^ 3.4
58.9 ^ 3.8
36.7 ^ 3.4
28.5 ^ 3.4
39.0 ^ 3.8
24.1 ^ 3.4
3
2
The experimental * H¡ values were taken from ref. 5 and 11
Æ
CH CHCH Cl (ethyl, 2-chloro-1-methyl)
CH CH CH CHCl (butyl, 1-chloro)
f
298
3
2
Æ
and from the current study. Calculated values are shown in
Table 4. These values were needed to determine the experi-
mental bond energies of some bulky chlorinated hydrocar-
bons, the results are shown in Table 5.
3
3 2
2
2
Æ
[CH ] CHCHCl (propyl, 1-chloro-2-methyl)
Æ
CH CH CHCH Cl (propyl, 1-[chloromethyl])
3
2
2
Æ
[CH ] CCH Cl (ethyl, 2-chloro-1,1-dimethyl)
3 2
2
Computational study
Computation details
k(CH CH Cl ] Br)/k(C H ] Br) as
a
function of tem-
Ab initio molecular orbital calculations were carried out with
the GAUSSIAN 94 package of programs.25 All calculations
were carried out on an SGI Power Challenge computer at the
Centre for ScientiÐc Computing (Espoo, Finland). All geome-
tries were fully optimized at the second-order MÔllerÈPlesset
perturbation theory using 6-31G(d,p) basis set and analytical
gradient methods.26 The optimized geometries of the species
are the time independent, BornÈOpperheimer structures and
thus a possible internal rotor, such as the methyl group of the
compound, may have di†erent bond lengths and valence
angles. For free radicals of interest, expectation values, S2,
were in the range 0.7500È0.7672, suggesting that there was
only minor spin contamination. In principle, the frequency
calculations were needed only to prove that the structure of
the optimized compound was at the global minimum and to
obtain the zero-point energy of the compound for calcu-
lations.
All energies of compounds were calculated at the
MP4(SDTQ)/6-311G(d,p) level of theory. All zero-point ener-
gies were scaled by a factor of 0.9676 as suggested in ref. 24.
The calculated bond dissociation energies were temperature
corrected by 4RT where only translational and rotational
contributions have been considered.26 The bond energies were
calculated directly from a homolytic bond dissociation reac-
tion:
3
2
2 6
perature. Rate constants for the calculation were taken from
ref. 14 and 6. The calculated thermochemical functions are
shown in Table 3. Tabulated functions of the other reaction
species were taken from ref. 16, 22, 23 and from Table 2.
The third-law procedure gives the heat of formation of b-
C H Cl to be 97.5 ^ 3 kJ mol~1 at 298 K. The entropy of the
2
4
radical was found, using ab initio calculations, to be 282.9 kJ
mol~1 at the MP2/6-31G(d,p) level of theory using a harmo-
nic oscillator model (calculated frequencies were scaled by
0.9676 for the entropy calculation).24 The third-law determi-
nation is in close agreement with the value of 93.0 ^ 2.4 kJ
mol~1 obtained by the second-law method.
Experimental CwH bond energies and group additivity
The CwH bond strengths in ethane and chloroethane were
calculated directly from the reaction enthalpy changes accord-
ing to:
(HBr). See Table 3 for results.
E
\ [*H¡ (R ] HBr ¢ RH ] Br) ] E
d, 298
298
d, 298
However, a group additivity method22 was used to estimate
the enthalpy of formation of monochlorinated propyl and
Table 5 Theoretically determined bond energies (in kJ mol~1) of
partly chlorinated ethanes and propanes
RX ] R ] X
E
where X \ H, Cl or free radical.
d 298
molecule
calculated
experimental
reference
Optimized geometries
CH CH wH
416.6
370.7
419.4
405.2
340.3
375.4
424.6
397.8
324.5
378.0
407.3
338.9
375.8
419.4
407.8
371.5
418.7
406.5
407.0
345.3
376.5
378.2
420.0
401.5
347.8
376.3
422.6 ^ 2.1
375.9 ^ 1.4
423.1 ^ 2.4
406.6 ^ 1.5
354.1 ^ 2.2
375.4 ^ 3.3
n.a.
390.6 ^ 1.5
327.9 ^ 1.8
365.1 ^ 3.3
n.a.
345.1 ^ 5.0
365.4 ^ 6.2
423.3 ^ 2.1
409.1 ^ 2.0
371.2 ^ 2.3
n.a.
409.3 ^ 3.9
407.0 ^ 3.5
354.5 ^ 2.3
371.4 ^ 2.8
370.4 ^ 3.9
n.a.
this study
Geometries of open- and closed-shell molecules needed in the
bond energy calculations represent the most stable conformer
of each structural isomer. Frequency analyses were carried out
at the MP2 level for all compounds.
3
2
CH wCH
a
3
3
CH ClCH wH
this study
2
2
CH CHClwH
b
a
a
3
CH CH wCl
3
2
CH wCH Cl
3
2
Free radicals. The most stable rotameric structure for some
CHCl CH wH
2
2
free radicals was found to have no symmetry (C point group,
CH CCl wH
b
a
a
1
3
2
as a SchoenÑies symbol) even though the isomeric structure of
CH CHClwCl
3
CH wCHCl
these species allows them to have one symmetry plane. Exam-
3
2
t-CH ClCHClwH
ples of this are the a-C H Cl, b,b-C H Cl and a,n-C H Cl
2
2
4
2
3
2
3 6
CH ClCH wCl
a
a
c
c
a
radicals.
The global minimum of the n-C H radical has a di†erent
2
2
CH ClwCH Cl
2
2
CH CH CH wH
3
7
3
2
2
conformeric structure at the MP2 and HF levels. The HF
optimized structure suggests that the H atoms at the radical
site are in the same plane as the backbone, carbon skeleton,
but in the MÔllerÈPlesset optimized structure these H atoms
are at an angle of ^81.3¡ to the backbone. However, the
energy di†erence between these conformers is only 30 J mol~1
at the MP2 level.
(CH ) CHwH
3 2
CH CH wCH
3
2
3
CH ClCH CH wH
2
2
2
CH Cl(CH )CHwH
a
a
a
a
a
2
3
CH CH CHClwH
3
2
CH CH CH wCl
3
2
2
CH wCH CH Cl
3
2
2
CH CH wCH Cl
3
2
2
The most stable conformer of a,b-C H Cl is gauche. It is
CH CHClCH wH
3
2
2 3 2
(CH ) CClwH
n.a.
more stable than the trans-conformer by 6.41 kJ mol~1 at the
3 2
(CH ) CHwCl
352.9 ^ 2.1
a
a
MP2 level. Both rotamers belong to the C point group, thus
3 2
1
CH wCHClCH
367.5 ^ 2.0
they have only an identity element. On the other hand for the
3
3
molecule 1,2-dichloroethane, the trans-conformer (the chlorine
atoms are antiperiplanar to each other) was found to be more
stable than the gauche-conformer.
n.a. not available. a Enthalpy of formation values of species to calcu-
late E (experimental) are from the current study, ref. 5, 11, 16 and
d 298
20. b Ref. 5. c Ref. 11.
894
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

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Table 6 Symmetry point groups, total and zero-point energies
total
energya
zero-point
energyb
* H¡
298
exp
c
f
compound
symmetry
ref.
H
Cl
CH
CH Cl
K
h
[0.499 81
[459.602 63
[39.730 68
[498.796 20
[957.860 17
[78.944 43
[538.009 79
[538.015 35
[997.082 15
[997.078 81
[997.070 63
[118.156 36
[577.228 40
[577.227 86
[577.222 93
[118.160 72
[577.235 44
[577.228 20
[79.614 33
[538.680 07
[997.743 07
[997.743 85
[118.827 01
[577.893 35
[577.898 32
0.0
0.0
218.0
121.3
146.0
117.3
89.0
120.7
93.0
16
16
27, 28
5
K
h
D
3h
C
s
0.030 70
0.023 99
0.016 60
0.061 75
0.054 16
0.054 30
0.045 91
0.046 14
0.044 53
0.091 74
0.084 20
0.083 19
0.083 17
0.091 67
0.083 74
0.083 80
0.077 46
0.069 14
0.059 73
0.060 49
0.107 09
0.098 58
0.098 14
3
2
CHCl
C
s
5
2
C H
C
this study
this study
2
5
s
b-C H Cl
C
2
4
s
a-C H Cl
a,a-C H Cl
a,b-C H Cl
C
1
76.5
42.5
5
5
2
4
C
s
2
3
2
2
2
C
2
3
1
b,b-C H Cl
C
2
n-C H
3
3
1
C
s
100.8
86.6
11
11
7
a,n-C H Cl
C
1
3
6
b,n-C H Cl
C
3
6
1
c,n-C H Cl
C
2
isoC H
3
6
s
C
s
7
a,isoC H Cl
C
s
3
6
b,isoC H Cl
C
3
CH CH
3
6
1
D
3d
C
s
3
CH ClCH
2
3
3
CHCl CH
t-CH ClCH Cl
CH CH CH
CH ClCH CH
CH CHClCH
C
s
2
C
2h
C
2v
C
s
2
2
3
2
3
2
2
3
C
s
3
3
a In E , calculated at MP4/6-311G(d,p)//MP2/6-31G(d,p) level. b In E , unscaled value calculated at MP2/6-31G(d,p) level. c In kJ mol~1.
h
h
Typically, the radical site of ethyl and n-propyl is at a small
out-of-plane angle with the C wC bond leading to a pyrami-
n-propyl. Generally, a similar trend can also be observed for
chlorinated radicals but the Cl atom seems to confuse this
trend by having a tendency to shrink the CwH bond con-
nected at the same carbon atom. Furthermore, the CwC
bonds seem to follow the same trend in that the C wC is the
shortest bond. Generally speaking, the Cl atom has a ten-
dency to make the ClwCwH angle smaller than the
HwCwH angle for methylene carbons and for radical
centres. Tables listing the structural parameters of the free
radicals have been deposited with the British library.”
a
b
dal structure. The out-of-plane angle of all n-radicals
(including a-radicals) increases as a function of Cl substitut-
ion, suggesting that an inductive e†ect controls the degree of
non-planarity (see Table 7). However, the structure of the b,n-
C H Cl radical is quite di†erent from the other mono-
a
b
3
6
chlorinated n-propyl radicals. In the b,n-C H Cl radical the
3
6
dihedral angles of the H atoms at the radical site to the
C wC wC skeleton are at [160.1¡ and 37.3¡. The proximity
a
b
c
of a large Cl atom at C and the presence of C forces the H
b
c
a
Molecules. The point groups of molecules are given in Table
6. A table listing the geometric parameters of the molecules
has been deposited with the British Library.”
atoms to become almost parallel to the backbone of the
radical (a similar structural form was also calculated for b,n-
C H Cl). In the b-C H Cl radical the H atoms are also
4
8
2
4
a
In general, the CwCl bond is shorter in a CH Cl group
located on both sides of the Cl atom when observed along the
2
than in a CHCl group. As for the radicals, the Cl atom makes
C wC bond but the radical site is not twisted because the Cl
a
b
the nearest CwC bond the shortest of the CwC bonds in the
molecules and the HwCwCl bond angle is smaller than the
HwCwH bond angle.
atom is at the symmetry plane of the radical. For the b,n-
C H Cl (or b,n-C H Cl) radical a similar kind of symmetry
3
6
4 8
operator cannot be placed.
For isopropyl radicals the out-of-plane angle is largest for
those isomers where the Cl atom is at the radical centre. This
observed non-planarity parallels that for the n-type radicals.
For all chlorinated radicals the CwCl bond length is short-
est when the Cl atom is at C and longest when it is at C .
Discussion
Kinetics of R + HBr
The measured rate constants for the reactions of ethyl and
b-chloroethyl radical with HBr are displayed in Fig. 2 on an
Arrhenius plot together, for comparison, with the rate con-
stants of the a-chloroethyl ] HBr reaction (taken from ref. 5).
The kinetics of the ethyl ] HBr reaction measured in the
current study agree well with those found previously.14 It can
be seen from Fig. 2 that both chlorinated ethyl radicals are
less reactive than the ethyl radical with HBr. Furthermore,
b-C H Cl reacts faster than its more stable isomer.
a
b
The same trend can be found for the CwH bonds in ethyl and
Table 7 Out-of-plane angles (in degrees) of the radicals at MP2/6-
31G(d,p) level
C H
12.8
22.8
14.6
29.8
19.2
14.5
14.7
23.4
345.0
10.3
19.2
28.8
18.7
2
5
a-C H Cl
2
4
2
4
b-C H Cl
A possible reason for the decreasing reactivity on chlorine
atom substitution may be the di†erence in atom electronega-
tivities between Cl and H atoms. The Cl atom is more electro-
negative than the H atom and thus has a stronger tendency to
draw electrons from the radical centre. This phenomenon is
strongest at the a-position and weaker at the b-position
2
4
a,a-C H Cl
2
3
2
2
2
a,b-C H Cl
2
3
b,b-C H Cl
2
n-C H
3
3
7
a,n-C H Cl
3
6
b,n-C H Cl
3
6
c,n-C H Cl
3
isoC H
3
6
7
” Available as supplementary material (SUP 57342; 5 pp.) depos-
ited with the British Library. Details are available from the Editorial
Office.
a-isoC H Cl
3
6
b-isoC H Cl
3
6
J. Chem. Soc., Faraday T rans., 1998, V ol. 94
895

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because of the distance from the radical centre. Thus it is
obvious that the electron-withdrawing tendency of Cl atom(s)
from the radical centre becomes weaker in the following
order: a,a-C H Cl [ a-C H Cl [ b-C H Cl [ C H .5 The
Thermodynamic properties of the b-chloroethyl radical
Miyokawa and Tschuikow-Roux determined the enthalpy of
formation of the b-C H Cl radical to be 91.2 ^ 4.1 kJ mol~1,6
2
4
2
3
2
2
4
2
4
2 5
close to the value determined in the current study. However,
the agreement is misleading. Miyokawa and Tschuikow-Roux
used a gas-phase photobromination of ethyl chloride in the
range 343È423 K, where the abstraction of a-H atom is in
competition with the b-H atom abstraction reaction. They cal-
culated the individual Arrhenius expression for reaction ( [ 2)
using the ratio of rate constants determined by them and the
rate constant of the C H ] Br reaction obtained from very
reverse trend is found for the reactivities of these radicals.
Similarly, the reactivity increases from chlorinated to non-
chlorinated radicals for methyl radicals: CHCl \ CH Cl \
2
2
CH .5,14 Both trends can also be seen after comparing the
3
calculated atomic spin densities of the free radicals. For every
free radical studied the calculated spin density is highest at the
C
atom, a clear indication that the unpaired electron is
a
located at the radical site.
2
6
complex ratios of rate constant measurement.31 The kinetics
of this reaction have recently been remeasured by a time-
resolved resonance-Ñuorescence technique and the activation
energy of the reaction was found to be ca. 4 kJ mol~1
smaller.14 In addition Miyokawa and Tschuikow-Roux esti-
mated the activation energy of the C H ] HBr reaction from
Stability of chlorinated free radicals
The chlorine atom, as a substituent on the radical skeleton,
also has an interesting tendency to either increase or decrease
the thermal stability of the radical. The e†ect is mediated by
the position of the Cl atom on the radical skeleton. At the
a-position the Cl atom increases the thermal stability. This is
demonstrated for the ethyl and a-chlorinated ethyl radicals
where the a,a-dichloroethyl radical is the most stable.5 At the
b-position the Cl atom reduces the thermal stability of the
radical. A possible explanation is the negative inductive e†ect
of the Cl atom. The e†ect is stronger for the a-isomer than for
the b-isomer because the electron-withdrawing e†ect of the Cl
atom from the radical centre changes as a function of distance.
For chloroethyl radicals the b-isomer starts to decompose at
410 K (see Fig. 2). For the same reason the thermal stability of
CCl CH is low. It starts to decompose unimolecularly by
2
5
thermochemical calculations. This value has also been mea-
sured directly by time-resolved techniques earlier and in the
current study, and was shown to be ca. 5 kJ mol~1 smaller
than the estimated value used in ref. 6. The errors in the acti-
vation energies fortuitously cancel each other.
An electron impact method has been used to determine
* H¡ (b-C H Cl) to be 95.4 ^ 8.4 kJ mol~1, an average
f
298
2 4
value from two di†erent determinations.32
Trends in bond energies
Chlorinated compounds have been little studied by ab initio
MO calculations. A reason for this might be the presence of
Cl atom(s) which make higher level calculations time consum-
3
2
CwCl bond rupture at ca. 450 K at a few torr of pressure.
Free radical stabilities can also be considered theoretically
by comparing the calculated energies of the most stable con-
formers from ab initio calculations. However, the comparisons
are then limited to compounds containing equal numbers of
the same atoms. As a result the calculations show that the
a-chloroethyl radical is ca. 14.2 kJ mol~1 more stable than the
b-chloroethyl radical at 0 K at the MP4/6-311G(d,p) level of
theory (zero-point energy corrected values considered). The
calculations suggest the following stability order for dichloro-
ethyl radicals: a,a-C H Cl [ a,b-C H Cl [ b,b-C H Cl ,
ing. Some chlorinated C compounds33 have been optimized
1
at the MP2 level but larger molecules34 and free radicals23
have been studied only at the Hartree-Fock level.
The main reason for carrying out numerous ab initio calcu-
lations at the MP2 and MP4 levels was to investigate the
inÑuence of di†erent substituents on the CwH bond energies
in partly chlorinated saturated hydrocarbons. These have not
been studied previously by quantum chemical calculation.
Particular consideration was given to the e†ect of the Cl atom
on its neighbouring CwH bond strengths. All the calculations
were carried out at the same level of theory and thus the rela-
tive calculated energies of the compounds are accurate and,
furthermore direct and reliable bond energy determinations
can be performed. The calculated bond strengths are shown in
Fig. 3 and comparisons with experimental values are given in
Table 5.
2
3
2
2
3
2
2 3 2
the same trend as for the monochloroethyl radicals (see Table
5). The comparisons can also be extended to include the
propyl radicals studied here. The results from the calculations
suggest the following stability trend a [ b [ c and
secondary [ primary (the zero-point energy corrected MP4
energies are compared). The only exception to these trends is
found for a- and b-chloro-n-propyl radicals. According to cal-
culations the b-form is more stable by ca. 1.1 kJ mol~1 at 0 K.
The a-form has a larger zero-point energy correction, causing
it to be less stable than the b-form. Traditionally, the thermal
stabilities (or stabilities in general) of carbon centred r free
radicals have been explained by comparing CwH bond
strengths of analogous hydrocarbons. This type of consider-
ation is misleading and should not be used, as explained in ref.
11.
In general, the weakest bond in the chlorinated molecules
studied is found always to be a CwCl bond. The strongest
Thermodynamic properties of the C H radical
2
5
The enthalpy of formation of the ethyl radical was found to be
120.7 ^ 2.1 kJ mol~1, in excellent agreement with the most
recent experimental time-resolved study29 and with the theo-
retically determined value of Bauschlicher Jr. and Partridge.30
They determined the CwH bond energy in ethane directly by
using coupled cluster and perturbation theory calculations
with large basis sets. The authors concluded that the CwH
bond energy is 417.5 kJ mol~1 at 0 K, which can be temper-
ature corrected to 422.9(^2.1) kJ mol~1 using an integrated
heat capacity correction. The bond energy can be translated
to *H¡ (C H ), giving a value of 121.1 ^ 2.1 kJ mol~1.
Fig. 3 Ab initio calculated bond strengths (in kJ mol~1) of partly
chlorinated hydrocarbons
298
2 5
896
J. Chem. Soc., Faraday T rans., 1998, V ol. 94

View Article Online
bond is the CwH bond. The same can be concluded from
The di†erence between calculated and experimental CwC
bond energies are typically 1È5 kJ mol~1 for non-chlorinated
hydrocarbons and 4È14 kJ mol~1 for chlorinated hydrocar-
bons. However, comparisons with chlorinated molecules is dif-
Ðcult because of the absence of experimentally determined
enthalpy of formation values for chlorinated polyatomic free
radicals.
experimental investigations (see Table 5 and ref. 11).
CwH bonds. The inÑuence of the Cl atom on the CwH
bonds of chlorinated molecules is surprisingly obvious. The
experimental studies have already proved the a-CwH bond to
be much weaker than the b-CwH bond in chloroethane and
1,1-dichloroethane,5 a fact which was conÐrmed by ab initio
calculations here. Typically, a primary CwH bond has a
strength of 420 kJ mol~1 when the carbon atom of this bond
is not bonded to a Cl atom. However, this bond strength is
decreased by 13 kJ mol~1 if the Cl atom is also connected to
the primary carbon. On the other hand a secondary CwH is
weakened only by 6 kJ mol~1 by the presence of a Cl atom.
The clear inÑuence of the Cl atom seems to extend only to the
For CwCl bond energies the di†erence between calculated
and experimental values is ^ 13 kJ mol~1. However, in some
cases tabulated * H¡ values of chlorinated molecules have
f
298
error limits as large as ^ 8 kJ mol~1.
All calculated bond energies shown in the current study are
determined such that the most stable conformeric species of
the dissociation reaction are considered. This is not the case
for the experimental determination. Typically, the enthalpy of
formation has been determined for a molecule consisting of
a mixture of di†erent stereoisomers in accordance to the
Boltzmann distribution. The enthalpy of formation of di†er-
ent conformers of the molecule can di†er signiÐcantly. For
example, di†erent CwH bond energies of 1,2-dichloroethane
can be calculated by the ab initio method if the molecule is
considered to be either the trans- or gauche-isomer. The latter
is the less stable isomer and leads to a 6.1 kJ mol~1 weaker
CwH bond strength than the former.
neighbouring bonds (C wH).° On the other hand, if the
b
C wH bond is the primary bond, as in ethanes, Cl atom(s)
b
makes it stronger.
CwC bonds. The inÑuence of the Cl atom on the other
bonds of the molecule seems to be most marked for CwH
bonds. Calculations do not show any similar phenomenon for
CwC bonds of chlorinated compounds, in fact the CwC
bond strengths seem to decrease slightly when they are
removed further from the inÑuence of the Cl substituent.° The
weaker inÑuence of the Cl atom on the CwC bond than on
the CwH bond may be explained by considering the atom
electronegativities of these elements. The Cl atom is the most
negative and the H atom is the least negative, thus one may
expect the Cl atom to have a stronger inÑuence on the partly
ionic CwH bond than on the covalent CwC bond. As a con-
sequence of this negative inductive e†ect the electron density
above and below the nodal plane of the bond is polarized
toward the Cl atom.
Conclusion
The chlorine atom e†ect on the structures and bond energies
of partly chlorinated ethanes and propanes has been demon-
strated by experimental and theoretical investigations. Rather
straightforward ab initio calculations at MP2/6-31G(d,p)
//MP4 (SDTQ) /6-311G(d,p) level seem to be adequate to
show the importance of the electronic e†ects of a chlorine
atom on the structure of the molecule. There is good agree-
ment between the calculated and the experimental bond ener-
gies of the compounds studied. The e†ect of the chlorine atom
on the reactivity and the thermal stability of the radical is also
shown by experimental kinetic studies.
CwCl bonds. The calculated CwCl bond strengths of
monochloro compounds seem to be in the range 339È350 kJ
mol~1, where the CwCl bond strength increases with the size
of the molecule.° Only the CwCl bond in 1,1-dichloroethane
is clearly below these values. The neighbouring Cl atom most
likely causes this. The same can be concluded from a compari-
son of the CwCl bond in chlorinated methanes. The CwCl
bond becomes weaker in the following order (in kJ mol~1):
351.0 (CH Cl) [ 334.1 (CH Cl ) [ 315.1 (CHCl ) [ 288.3
This research was supported by the University of Helsinki, the
Center for ScientiÐc Computing at Espoo and by the National
Science Foundation, Chemistry Division. I wish to thank
Prof. Irene R. Slagle for kindly lending me the apparatus used
for the experimental part of this study. The kinetic experi-
ments were carried out at the Catholic University of America
(Washington DC, USA).
3
2
2
3
(CCl ).5,35
4
Accuracy of calculated bond energies
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The accuracy of the calculated bond energies can be com-
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cally, the calculated CwH bond energies are 2È6 kJ mol~1
lower than the experimentally determined values.5,11 The dif-
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and 4È6 kJ mol~1 for primary CwH bonds of non-
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