Electrophilic bromination of ethylene and ethylene-d4. A combined experimental and theoretical study

Article abstract of DOI:10.1021/ja974151m

The deuterium kinetic isotope effect (dkie) for the electrophilic bromination of ethylene-h₄ and ethylene-d₄ in methanol and dichloroethane (DCE) at 25 °C has been determined using mass spectrometry. The dkie's are inverse, that in methanol being k(H)/k(D) = 0.664 ± 0.050 and that in DCE being k(H)/k(D) = 0.572 ± 0.048. A product study of the bromination of trans-ethylene-d₂ in dichloroethane indicates that the addition is trans. Computations of the expected equilibrium deuterium isotope effect (EIE) for the process C₂H₄ + Br⁺ ? C₂H₄-Br⁺ using density functional theory indicate that the EIE is also inverse at K(H)/K(D) = 0.63. Detailed analyses of the molar partition functions and the zero-point energies for the various vibrational modes in the ground and ion states indicate that the major contributor to the EIE is the creation of a new mode in the ion, termed the CH₂-symmetric twist, that arises from the loss of the rotational freedom about the C-C axis in ethylene. In the absence of this new mode, the computed EIE is normal, K(H)/K(D) = 1.12. The computations also indicate that the ion state undergoes very little rehybridization of the carbons, the sum of the H- C-H and H-C-C angles at each carbon being 357.3°. A discussion is presented concerning the detailed sequence of events contributing to the reaction mechanism in both solvents and how each of these might contribute to the dkie.

Full text of DOI:10.1021/ja974151m

5628
J. Am. Chem. Soc. 1998, 120, 5628-5636
Electrophilic Bromination of Ethylene and Ethylene-d4. A Combined
Experimental and Theoretical Study
Terry Koerner,† R. S. Brown,*,† J. L. Gainsforth,‡ and M. Klobukowski*,‡
Contribution from the Departments of Chemistry, Queen’s UniVersity, Kingston, Ontario K7L 3N6,
Canada, and UniVersity of Alberta, Edmonton, Alberta T6G 2G2, Canada
ReceiVed December 8, 1997
Abstract: The deuterium kinetic isotope effect (dkie) for the electrophilic bromination of ethylene-h4 and
ethylene-d4 in methanol and dichloroethane (DCE) at 25 °C has been determined using mass spectrometry.
The dkie’s are inverse, that in methanol being kH/kD ) 0.664 ( 0.050 and that in DCE being kH/kD ) 0.572
( 0.048. A product study of the bromination of trans-ethylene-d2 in dichloroethane indicates that the addition
is trans. Computations of the expected equilibrium deuterium isotope effect (EIE) for the process C2H4 +
Br+ h C2H4-Br+ using density functional theory indicate that the EIE is also inverse at KH/KD ) 0.63.
Detailed analyses of the molar partition functions and the zero-point energies for the various vibrational modes
in the ground and ion states indicate that the major contributor to the EIE is the creation of a new mode in the
ion, termed the CH2-symmetric twist, that arises from the loss of the rotational freedom about the C-C axis
in ethylene. In the absence of this new mode, the computed EIE is normal, KH/KD ) 1.12. The computations
also indicate that the ion state undergoes very little rehybridization of the carbons, the sum of the H-C-H
and H-C-C angles at each carbon being 357.3°. A discussion is presented concerning the detailed sequence
of events contributing to the reaction mechanism in both solvents and how each of these might contribute to
the dkie.
Introduction
Secondary dkie’s have been determined for a variety of
electrophilic processes5 including brominations of styrenes,6
stilbenes,7 7,7′-norbornylidenenorbornane,8 and cyclohexene.9
In general, the observed effect for R-substitution is inverse which
is commonly explained by invoking isotope-sensitive changes
in the out of plane bending frequencies of the R-C-L bonds of
the alkene in passing from an sp2 ground state to an sp3-like
transition state.10,11 Strausz and co-workers have offered another
explanation for the inverse dkie observed for thiirane formation
from addition of S atoms to ethylene, namely the creation of
new isotopically sensitive vibrations in the transition state that
were not present in the ground state.12 In fact, recent work by
Bender13a has shown that the inverse equilibrium isotope effect
of KH/KD ) 0.7 for reversible binding of C2L4 to (µ-η1,η1-C2L4)-
Considerable recent effort has been expended in detailed study
of electrophilic bromination of congested olefins which, by
virtue of their steric crowding, retard the passage of the
bromonium ion intermediates to normal products of addition.1
Particularly well-studied is the case of adamantylideneadaman-
tane, the bromination of which was first reported by Wynberg
and co-workers;2 this olefin currently stands alone in chemistry
as producing the only room-temperature stable, structurally
characterized three-membered bromonium and iodonium ions.3
Less well studied is the bromination of the simplest olefin,
ethylene, which surely must form a highly unstable bromonium
ion with almost no steric barrier to product formation. This
olefin is technically difficult to handle because it is a gas at
room temperature, so reliable kinetic data are sparse.4 Never-
theless, because of its simplicity, high degree of symmetry, and
the fact that one can substitute all four positions with deuterium,
ethylene is an ideal candidate for experimental investigation of
the secondary deuterium kinetic isotope effects (dkie) for various
reactions which are also amenable to detailed theoretical
analysis.
(5) Freeman, F. Chem. ReV. 1975, 75, 439.
(6) (a) Wilkins, C. L.; Regulski, T. W. J. Am. Chem. Soc. 1972, 94,
6016. (b) Bellucci, G.; Chiappe, C.; Lo Moro, G. J. Org. Chem., 1997, 62,
3176. (c) Bellucci, G.; Chiappe, C. J. Chem. Soc., Perkin Trans. 2 1997,
581.
(7) Denney, D. B.; Tunkle, N. Chem. Ind. (London) 1959, 1383.
(8) Slebocka-Tilk, H.; Motallebi, S.; Nagorski, R. W.; Turner, P.; Brown,
R. S.; McDonald, R. J. Am. Chem. Soc., 1995, 117, 8769.
(9) (a) Slebocka-Tilk, H.; Zheng, C. Y.; Brown, R. S. J. Am. Chem. Soc.
1993, 115, 1347. (b) Slebocka-Tilk, H.; Neverov, A.; Motallebi, S.; Brown,
R. S.; Donini, O.; Gainsforth, J. L.; Klobukowski, M. J. Am. Chem. Soc.
1998, 120, 2578.
† Queen’s University.
‡ University of Alberta.
* To whom correspondence should be sent.
(1) For a summary of recent work, see: Brown, R. S. Acc. Chem. Res.
1997, 30, 131.
(2) Strating, J.; Wieringa, J. H.; Wynberg, H. J. Chem. Soc., Chem.
Commun. 1969, 3581.
(3) (a) Bennet, A. J.; Brown, R. S.; McClung, R. E. D.; Klobukowski,
M.; Aarts, G. H. M.; Santarsiero, B. D.; Bellucci, G.; Bianchini, R. J. Am.
Chem. Soc. 1991, 113, 8532. (b) Brown, R. S.; Nagorski, R. W.; Bennet,
A. J.; McClung, R. E. D.; Aarts, G. H. M.; Klobukowski, M.; McDonald,
R.; Santarsiero, B. D. J. Am. Chem. Soc. 1994, 116, 2448.
(4) (a) Bienvenue-Goetz, E.; Dubois, J. E. Tetrahedron 1968, 24, 6777.
(b) Atkinson, J. R.; Bell, R. J. P. J. Chem. Soc. 1963, 3260. (c) Dubois, J.
E.; Mouvier, G. Bull. Soc. Cheim. Fr. 1968, 1426.
(10) Streitwieser, A., Jr.; Jagow, R. H.; Fahey, R. C.; Suzuki, S. J. Am.
Chem. Soc. 1958, 80, 2326.
(11) (a) Isotope Effects in Chemical Reactions; Collins, C. J., Bowman,
N. S., Eds.; ACS Monograph 167; Van Nostrand Reinhold Co.: New York,
1970. (b) Westaway, K. C. In Isotopes in Organic Chemistry; Buncel, E.,
Lee, C. C., Eds.; Elsevier: Amsterdam, Vol. 7, 1987; pp 275-392. (c)
Lowry, T. H.; Richardson, T. H. In Mechanism and Theory in Organic
Chemistry, 3rd ed.; Harper and Row: New York, 1987; pp 232-234.
(12) (a) Strausz, O. P.; Safarik, I.; O’Callaghan, W. B.; Gunning, H. E.
J. Am. Chem. Soc. 1972, 94, 1828. (b) Safarik, I.; Strausz, O. P. J. Phys.
Chem. 1972, 76, 3613.
S0002-7863(97)04151-6 CCC: $15.00 © 1998 American Chemical Society
Published on Web 05/30/1998

Electrophilic Bromination of Ethylene
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5629
using liquid nitrogen. After evacuation of the line a small amount of
trans-ethylene-d2 was frozen over the bromine solution. The flask was
allowed to warm to room temperature and the contents stirred (15 min).
If the bromine color persisted an additional amount of trans-ethylene-
d2 was added to the reaction vessel in a similar manner (vide supra).
When no bromine color could be detected, the reaction vessel was
removed from the vacuum line and the excess 1,2-dichloroethane was
removed by fractional distillation (bp 83 °C at 760 mmHg, lit. 83.5 °C
at 760 mmHg).16 The remaining solution was treated with an excess
of a KOH (0.063 mol) dissolved in ethanol.17 The excess ethanol/
KOH solution was used to ensure that all of the 1,2-dibromoethane
and any residual 1,2-dichloroethane reacted. After sufficient time (2
h) the expected products, vinyl bromide (bp 15.8 °C)16 and vinyl
chloride (bp -13.4 °C),16 were distilled at room temperature by flushing
the flask with an argon stream and collecting the effluent in a vessel
containing CD2Cl2 (0.5 mL) which was cooled in a dry ice/2-propanol
bath. This solution was then analyzed by 1H NMR. The products were
then distilled (0 °C) into CH2Cl2 (0.5 mL, vide supra), and the 2H NMR
was obtained. The instrument used for the analyses of the reaction
mixtures was a Bruker 400-MHz NMR.
Os2(CO)8 is mostly due to a zero-point energy factor from a
vibrational mode (termed a b2-symmetry twist) for the com-
plexed ethylene which is not present in free ethylene. Herein
we report the results of an experimental study of the electrophilic
addition of Br2 to ethylene and ethylene-d4 in methanol and
dichloroethane which show that (a) there is a large inverse dkie
of kH/kD ∼ 0.6 for bromination in both methanol and dichlo-
roethane and (b) the addition process in dichloro-
ethane gives trans-1,2-dibromoethane. We also give a detailed
theoretical analysis of the origin of the dkie based on density
functional theory (DFT) computations of the equilibrium isotope
effect (KH/KD) for the process
which is best interpreted in terms of the Strausz model.
Experimental Section
Computational Methods
(a) Materials. Methanol (Sigma-Aldrich, 99.9% ACS HPLC grade)
was purified as previously described.14 Ethanol (Sigma-Aldrich,
absolute grade) and 1,2-dichloroethane (Sigma-Aldrich, 99.8% HPLC
grade) were both used without purification; however, fresh bottles of
each were used and precautions were taken to minimize moisture
contamination. Ethylene (Matheson of Canada Ltd., CP grade),
ethylene-d4 (Merck Sharp & Dohme), and trans-ethylene-d2 (Merck
Sharp & Dohme) were also used as supplied.
(b) Dkie. The secondary R-deuterium kie’s were determined using
a competitive technique15 in which approximately equal amounts of
ethylene and ethylene-d4 were incompletely brominated (20-30%). The
fraction of reaction, initial isotopic ratio, and final isotopic ratios were
determined by gas chromatography-mass spectrometric analysis (GC-
MS). In a typical experiment a stock solution was prepared by adding
ethylene (1.0 mmol), ethylene-d4 (1.0 mmol) and methane (2.5 mmol)
to a specially designed vessel containing degassed purified methanol
(40.0 mL) affixed to a vacuum line. The gas additions were
accomplished by monitoring the pressure in a vacuum line of known
volume (74.77 mL) and then freezing the sample over the solvent using
liquid nitrogen.
Using a 2-mL gas-tight syringe a sample of the stock solution (1.80
mL) was withdrawn and injected into a 2-mL amber vial fitted with a
Teflon-coated septum. This sample was immediately analyzed using
GC-MS to determine the initial ethylene/ethylene-d4 ratio and the ratio
of methane to total ethylene. To this same vial was introduced 100
µL of a 0.11 M bromine in purified methanol solution via syringe.
After mixing and allowing sufficient time for the reaction to be
completed (10 min), the ethylene/ethylene-d4 and total ethylene/methane
ratios were determined by GC-MS. The analyses were performed on
a Fisons Quattro mass spectrometer coupled to a Fisons GC 8000 gas
chromatograph [Plot GS-Q column, Chromatographic Specialties Inc.
(30 m, 0.53 mm i.d.), T ) 40 °C, He carrier (2.0 psi)]. Each sample
was subject to three or four (0.2-mL) independent analytical runs.
Quantitative analysis was done by integration of the mass peaks (15
for methane, 27 for ethylene, 30 for ethylene-d4). Each isotope effect
was confirmed by three or four independent experiments.
(c) Product Study. The products for the bromination of trans-
ethylene-d2 in 1,2-dichloroethane were determined by 1H and 2H NMR
analysis of the products obtained from the elimination of the bromi-
nation products. In a typical experiment 5.0 mL of a 0.1 M Br2 in
1,2-dichloroethane solution and a stirring bar were added to a 25-mL
round-bottom flask which was wrapped in foil to prevent exposure to
light. The flask was attached to a vacuum line and the contents frozen
(a) Methodological Details. A computational study was undertaken
to examine the equilibrium deuterium isotope effect (EIE) for the
equilibrium involving the formation of the ethylene bromonium ion
from ethylene plus Br+. The isotope effects were modeled using results
obtained with the density functional theory (DFT) as found in the
Gaussian 9418 program. Gradient-corrected (nonlocal) functionals are
very successful in kinetic isotope effect studies,19 and previous work
with the cyclohexene system9b has shown that various functionals
produce quite similar results. Therefore only one set of gradient-
corrected functionals was used in this work: Becke’s 3-parameter
exchange20 functional was combined with the Lee, Yang, and Parr21
correlation functional, denoted as B3LYP. To minimize the compu-
tational effort, the compact effective core potentials of Stevens et al.22
were used. The basis set for carbon was used in the original double-ú
contraction (31/31) while that for bromine was modified to give a
quadruple-ú contraction (2111/2111). A single d-type polarization
function was added to carbon (Rd ) 0.80) and bromine (Rd ) 0.389).
The (31) basis set from Huzinaga’s (4s)23 expansion was used for the
hydrogens with a single p-type polarization function (Rp ) 1.1) added.
As the present study focuses on the effect of hydrogens on the
vibrational structure and on the proximity and interactions of hydrogens
with the reaction site, the addition of polarization functions on
hydrogens is necessary to get a better description of these atoms.
(b) System Studied. The ethylene bromonium ion is not a transition
state in the bromination reaction, but rather a minimum. In solution,
as expected, the transition state is calculated to be an ion pair with
bromide having either C2 or C2V symmetry depending on the solvent.24
(16) CRC Handbook of Chemistry and Physics, 50th ed.; The Chemical
Rubber Co.: Clevland, OH. 1962.
(17) Bernoulli, A. L.; Kambli, W. HelV. Chem. Acta. 1933, 16, 1187.
(18) GAUSSIAN 94, Revision D.3: Frisch, M. J.; Trucks, G. W.;
Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman,
J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.;
Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.;
Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng,
C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Repolgle, E.
S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.;
Baker, J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A.
Gaussian, Inc., Pittsburgh, PA, 1995.
(19) Wiest, O.; Black, K. A.; Houk, K. N. J. Am. Chem. Soc. 1994, 116,
10336.
(20) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
(21) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
(22) (a) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81,
6026. (b) Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem.
1992, 70, 612.
(13) (a) Bender, R. B. J. Am. Chem. Soc. 1995, 117, 11239. (b) Bender,
R. B.; Kubas, G. J. Jones, L. H.; Swanson, J. E.; Capps, K. B.; Hoff, C. D.
J. Am. Chem. Soc. 1997, 119, 9179.
(14) Brown, R. S.; Slebocka-Tilk, H.; Bennett, A. J.; Bellucci, G.;
Bianchini, R. J. J. Am. Chem. Soc. 1990, 112, 6310.
(15) Bigeleisen, J.; Wolfsberg, M. AdV. Chem. Phys. 1958, 1, 15.
(23) Huzinaga, S. J. Chem Phys. 1965, 42, 1293.
(24) Strnad, M.; Martins-Costa, M. T. C.; Millot, C.; Tun˜o´n, I.; Ruiz-
Lo´pez, M. F.; Rivail, J. L. J. Chem. Phys. 1997, 106, 3643.

5630 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Koerner et al.
Table 1. Secondary R-Deuterium kie’s for the Bromination of
Ethylene in Methanol and 1,2-Dichloroethane at 25 °C
bromination which was accomplished by monitoring the intensi-
ties of the mass ions relative to an internal standard of CH4 (15
for methane, 27 for ethylene, 30 for ethylene-d4).28 These mass
ions were chosen for analysis rather than the M+ peaks (16 for
methane, 28 for ethylene, 32 for ethylene-d4) for three reasons:
(i) since both ethylene and ethylene-d4 contain a mass 28 ion
and these two compounds could not be separated by the gas
chromatography column, it is important to choose mass ions
that are exclusive to each compound, i.e., 27 for ethylene and
30 for ethylene-d4; (ii) due to the fluctuations in O2 and N2
(masses 32 and 28) entering the mass spectrometer, accurate
determination of the isotopic ratio of the ethylenes could only
be obtained by choosing different mass ions; and (iii) the mass
fragments chosen all have significant intensities (80% (15 in
methane), 65% (27 in ethylene), 65% (30 in ethylene-d4)). In
addition to the ethylene/ethylene-d4 ratios, the extent of bro-
mination is also required for this competitive technique and was
determined from the ratio of total ethylene to an internal standard
(methane). The kie can then be calculated using eq 3:
(kH/kD) methanol
(kH/kD) 1,2-dichloroethane
0.686 ( 0.052a
0.603 ( 0.053
0.703 ( 0.029
0.518 ( 0.19a
0.635 ( 0.21
0.507 ( 0.09
0.566 ( 0.18
av 0.572 ( 0.048b
av 0.664 ( 0.05b
a The error calculated using eq 4. b The standard deviation of the
mean.
In the gas phase, a transition state has been reported,25 but at the RHF/
3-21G level, its imaginary frequency does not correspond to Br-
dissociation; reoptimized at the RHF/6-311G(d) level, it is a minimum.
Since the transition state in solution comprises the developing ions,
the likelihood of finding a gas-phase transition state is small due to
the lack of charge separation in this environment. Indeed, it is well-
known that electrophilic bromination does not occur in the gas phase
for this same reason.26
Rivail and co-workers looked at the first step of ethylene bromination
in water in a recent molecular dynamics study using the novel QC/
MM MD method.24 Their results confirm that the reaction has a late
transition state, with the ions already formed. According to the
Hammond principle,27 one can make the assumption that the transition
state resembles the ethylene bromonium ion more than it does the
ethylene and bromine reactants, as clearly shown in Figure 6 of ref 24.
The structure of the ethylene bromonium ion can then be used as an
adequate representation of the genuine transition state. In the present
work, the calculations were done for the equilibrium isotope effect (EIE)
for the equilibrium involving the formation of the reaction intermediate
[C2H4Br]+
k
Rf
(1 + R0)
(1 + Rf)
kie ) H ) 1+ log
log (1 - f)
(3)
(
)
]
[ ]
[
kD
R0
/
where Ro and Rf are the ethylene/ethylene-d4 ratios initially and
after some fraction, f, of bromination, respectively. The errors
for the individual kie’s were calculated by propagation of error
using eq 4:
Rf
log
( )
R0
∆kie )
×
(1 + R0)
(1 + Rf)
log (1 - f)
[
]
[
]
)
For the equilibrium
2
2 1/2 2
X h Y
∆Rf
∆R0
(0.434)
+
(
(
)
[
]
Rf
R0
the EIE is calculated in the gas phase, rigid rotor, harmonic oscillator
approximation according to27
+
Rf
(
[
)
log
( )
R0
QY/QX
KH/KD )
exp[-(δEY0 - δEX0 )]/RT
(2)
QY′/QX′
2
2
2 1/2
2
∆Rf
∆R0
∆f
f
(0.434)
+
+
(
[
)
(
)
( )
]
where δEX0 is the difference between the total molar vibrational zero-
point energies for the light and heavy reactant compounds X and X′,
δEY0 is the difference between the total molar vibrational zero-point
energies for the light and heavy product compounds Y and Y′, and Q
is the total molar partition function. The Br+ contribution to the
partition coefficient is canceled out in the term (QY/QX)/(QY′/QX′) and
will not be addressed further.
Rf
R0
(4)
(1 + R0)
(1 + Rf)
(
)
log (1 - f)
]
[
]
where ∆Ro, ∆Rf, and ∆f are the standard deviations in
determining Ro, Rf, and f, respectively.
There are two observations of note from the data in Table 1:
(i) the R-kie’s in both solvents are large and inverse and (ii)
within experimental error they are of similar magnitude. Both
dkie’s are consistent with a rate-limiting transition state for the
bromination where there is considerable rehybridization of the
olefinic carbons,10,11 but the experimental data alone do not
allow one to determine the structure of the transition state. As
will be shown later, there are more satisfying interpretations of
the dkie’s.
Results and Discussion
(a) Kinetic Isotope Effects (kie’s). Given in Table 1 are
the secondary R-deuterium kie’s for the bromination of ethylene
and ethylene-d4 in methanol and 1,2-dichloroethane at 25 °C.
These were determined by mass spectrometric analysis of a
reaction mixture following incomplete bromination of ap-
proximately equal amounts of ethylene and ethylene-d4 in the
same reaction vessel.15 This method requires that the ratio of
ethylene and ethylene-d4 be exactly determined before and after
(b) Mechanistic Possibilities. The generalized pathways for
alkene bromination are shown in Scheme 1. Across the top of
the scheme is the normal mechanism proceeding via charge
transfer complex (CTC) and bromonium ion intermediates. The
lower half of the scheme corresponds to a preassociation
mechanism occurring in the presence of a nucleophilic solvent
(25) Yamabe, S.; Minato, T.; Inagaki, S. J. Chem. Soc., Chem. Commun.
1988, 532.
(26) Ruasse, M.-F.; Motallebi, S. J. Phys. Org. Chem. 1991, 4, 527.
(27) Maskill, H. In The Physical Basis of Organic Chemistry; Oxford
University Press: New York, 1985. See also: van Hook, W. A. In Isotope
Effects in Chemical Reactions; Collins, C. J., Bowman, N. S., Eds.; Van
Nostrand: New York, 1970.
(28) Registry of Mass Spectral Data; Stenhagen, E., Abrahamsson, S.,
McLafferty, F. W., Eds.; John Wiley & Sons. Inc.: New York, 1974.

Electrophilic Bromination of Ethylene
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5631
Scheme 1
which leads to bromo-solvate products and is likely followed
when the bromonium ions are very unstable (vide infra).
In hydroxylic solvents such as methanol or acetic acid,
electrophilic bromination of alkenes is usually second-order
overall, first order in [Br2], while in chlorinated hydrocarbon
solvents such as 1,2-dichloroethane, the reaction is generally
third order, second order in [Br2].29,30 In a nucleophilic solvent
like methanol it is known that bromonium ion intermediates
such as those produced from Br2 addition to cyclohexene,
cyclopentene, stryrene, or tetramethylethylene are very unstable,
the lifetimes being ∼10-9-10-11 s.31 Due to the lack of alkyl
group stabilization, the bromonium ion of ethylene must be less
stable yet, so that there is a real question as to whether it can
be produced as a discrete intermediate during the reaction.
Ruasse et al. have commented extensively on the role of solvent
nucleophilic assistance in electrophilic brominations.32 Their
recent work supports a situation where there is a preassociation
mechanism33 for the bromination of electron-deficient stilbenes
in nucleophilic solvents including methanol. That mechanism
is shown in Scheme 1 as the lower pathway where association
of the methanol with the alkene occurs prior to the formation
of the bromonium ion and would be enforced if ion pair return
of the Br- and bromonium ion is faster than diffusional
separation followed by solvent capture of the free ion. Given
the anticipated instability of the ethylene bromonium ion, a
preassociation mechanism is likely, and if this course is
followed, the rate-limiting step for the reaction could be the
formation of the HOS:bromonium:Br- complex or its break-
down to methoxy bromide product. In either event, the
transition state would have to be close to the bromonium ion.
If the ion is sufficiently unstable that the preassociation
mechanism cannot occur, then in the limit the reaction will
involve a concerted solvent attack on the CTC analogous to
the SN2 attack in nucleophilic displacement reactions.34 In this
case one anticipates small secondary dkie’s.11
Figure 1. 1H and 2H spectra of the products obtained from the
bromination and subsequent elimination of ethylene in DCE. (A)
Bromination and elimination of ethylene. (B and C) Bromination and
elimination of trans-ethylene-d2.
does with other aliphatic alkenes. On the basis of rate data for
bromination of methylated ethylenes in methanol given by
Dubois and Mouvier35 and data in acetic acid and tetrachloro-
ethylene given by Modro, Schmid, and Yates,36 one can
construct linear free energy relationships relating the log k and
number of methyl groups attached to the double bond.37 That
ethylene lies on these lines indicates that it adheres to the same
mechanism for bromination in a given solvent as do the other
methylated ethylenes. This probably rules out an SN2 displace-
ment by methanol on the CTC but does not rule out a
preassociation mechanism since that could occur to greater or
lesser extents with the others as well, depending on the inherent
stability of their bromonium ions.
It can safely be concluded from the bromination results in
tetrachloroethylene36 that the bromination of ethylene in the
related solvent, DCE, is third-order overall, second order in
[Br2]. According to the pathway presented at the top of Scheme
1, the second Br2 assists in the ionization of the CTC to form
-
a bromonium ion/Br3 pair. Due to the instability of the
ethylene bromonium ion, the contact ion pair in DCE must be
short-lived so the question arises as to how the product is
actually formed in this solvent. To do so, the nascent contact
ion pair must translocate the Br3- or bromonium ion 180° from
their initial positions to a configuration where displacement of
the CH2-Br+ bond by Br- can occur to form the dibromide
product. On the basis of the rotational correlation times for
molecules rotating by Brownian motion,38 this process could
take 10-10-10-11 s. Even if the lifetime of the ion is
comparable to, or even 100-fold shorter than, the rotational
correlation, product formation could occur by leakage through
this pathway and rotation would then be the rate-limiting step.
There are some experimental data that indicate that the
electrophilic addition of Br2 to ethylene proceeds much as it
(29) (a) de la Mare, P. D. B.; Bolton, R. Electrophilic Additions to
Unsaturated Systems, 2nd ed.; Elsevier: New York, 1982; pp 136-197.
(b) Schmid, G. H. In The Chemistry of Double-Bonded Functional Groups;
Patai, S., Ed.; Wiley: New York, 1989; Suppl. A, Vol. 3, Part 1, p 699.
(30) (a) Ruasse, M.-F.; Motallebi, S.; Galland, B. J. Am. Chem. Soc.
1991, 113, 3340. (b) Ruasse, M.-F.; Motallebi, S. J. Phys. Org. Chem. 1991,
4, 526.
(31) Nagorski, R. W.; Brown, R. S. J. Am. Chem. Soc. 1992, 114, 7773.
(32) Ruasse, M.-F.; Lo Moro, G.; Galland, B.; Bianchini, R.; Chiappe,
C.; Bellucci, G. J. Am. Chem. Soc., in press.
(33) (a) Jencks, W. P. Chem. Soc. ReV. 1981, 10, 345. (b) Eldin, S.;
Jencks, W. P. J. Am. Chem. Soc. 1995, 117, 4851 and references therein.
(34) It is generally considered30 that this is an unlikely event since it
has never been documented. The lack of evidence, however, is not as
compelling an argument as one would like.
(35) Dubois, J. E.; Mouvier, G. Tetrahedron Lett.1963, 20, 1325.
(36) Modro, A.; Schmid, G. H.; Yates, K. J. Org. Chem. 1977, 42, 3673.
(37) The slopes and intercepts for these log k vs number of methyl groups
are as follows: methanol, 1.64, 0.95, r2 ) 0.9831; acetic acid, 1.86, -0.64,
r2 ) 0.998; tetrachloroethane, 2.19, 1.34, r2 ) 0.987. This form of the
linear free energy relationship is equivalent to the form used by Dubois
and Mouvier, who plotted log k vs ∑σ*, where the latter term refers to the
sum of the Taft σ* terms for the methyl groups, regardless of their position
on the double bond.

5632 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Koerner et al.
2
Table 2. 1H and H NMR Results Obtained for Bromination of
Scheme 2
trans-Ethylene-d2 and Subsequent Elimination from the
1,2-Dibromo-1,2-dideuterioethane in 1,2-Dichloroethane along with
1
the H NMR for the Same Process Using Ethylene
a The numbers in the parentheses represent the literature values for
the chemical shifts and the coupling constants (see ref 41). b These are
the chemical shifts and coupling constants from the deuterium NMR
(Figure 1C).
Finally, if the bromonium ion has lifetime in DCE too short
to allow its existence, product formation must proceed by an
alternative mechanism. A possible process could involve two
Br2 molecules and one ethylene (or the CTC and one Br2),
leading to cis-1,2-dibromoethane plus Br2, by either a concerted
pathway or a two-step pathway involving an open â-bromo
cation. We have two pieces of data that support a bromination
Table 3. Geometry of Ethylene and the Ethylene Bromonium Ion
ethylene
bromonium ion
ethylene
parametera
DFTb
exptlc
DFTb
-
process in DCE that proceeds by bromonium ion/Br3 inter-
C-C
1.364
1.107
1.339
1.087
1.472
1.104
2.062
108.0
119.7
118.5
mediates leading to trans dibromide products. The first is the
fact that ethylene fits the linear free energy relationship described
for bromination of substituted ethylenes in tetrachloroethane,36,37
so that if these are considered to proceed via bromonium ions,
then so too does ethylene. Second, we have determined that
the product of the addition of Br2 to ethylene in DCE is trans-
1,2-dibromoethane. These experiments are described below.
C-H
C-Br
H-C-H
C-C-H
H-C-Br
117.4
121.3
117.3
121.3
a Bond lengths in Å, bond angles in deg. b This work. c Experimental
rz and θz from microwave studies.44
1
2
(c) Product Study. Given in Figure 1 are the H and H
NMR spectra obtained from a product study for the bromination
and subsequent elimination of trans-ethylene-d2 along with the
1H NMR results obtained for a similar experiment using
ethylene-h4 in 1,2-dichloroethane. This study was undertaken
to ascertain if the bromination of ethylene proceeded by a trans-
addition through a bromonium ion intermediate (a or b, Scheme
2) or by some cyclic process leading to cis-addition (f, Scheme
2). One-to-one intermediates leading to cis addition products
have been computed39 for chlorination and bromination of
ethylene and found experimentally40 for the fluorination of
olefins.
Two bromination products are possible from the bromination
of trans-ethylene-d2. The first, meso-1,2-dibromoethane-d2 (c,
Scheme 2), is a result of trans addition, (a or b, Scheme 2). Cis
addition of bromine to trans-ethylene-d2 through either a cyclic,
concerted, or stepwise transition state (f, Scheme 2) forms only
d,l-1,2-dibromoethane-d2. Elimination of meso-1,2-dibromo-
ethane-d2 and d,l-1,2-dibromoethane-d2 could result in four
possible vinyl bromides, d or e and h or i (Scheme 2),
respectively. It is assumed that these products are obtained from
trans eliminations, which, in the absence of special effects, are
greatly favored over cis eliminations in these systems.42 The
NMR results (Figure 1B) clearly indicate that the only products
present are those from HBr and DBr elimination from
meso-1,2-dibromoethane-d2: this finding is confirmed by
deuterium NMR (Figure 1C). Thus, the bromination of ethylene
in DCE gives exclusive trans addition, probably via a two-step
mechanism involving the bromonium ion. The relative areas
In a control experiment a small amount of ethylene was
subjected to the bromination and elimination process, the results
1
of which are presented in Figure 1A and Table 2.41 The H
NMR indicated the only products to be vinyl chloride, which
is expected because all of the DCE solvent could not be removed
prior to the elimination step, and vinyl bromide, which is the
expected product from the elimination of 1,2-dibromoethane,
the bromination product of ethylene.
1
2
of the H and H NMR peaks were used to obtain a primary
isotope effect of 3.3 ( 0.5 for the elimination which is consistent
with results found for similar processes.43
(38) According to the following: Abragam, A. In Principles of Nuclear
Magnetism; Clarendon Press: Oxford, U.K., 1961; p 300. The rotational
correlation time for a molecule of radius a, rotating by Brownian motion
in a solvent of viscosity η, is τ1 ) 4πηa3/kT, where k is Boltzmann’s
constant and T is the temperature in Kelvin. If the radius of the bromonium
(d) Computations. The structural parameters for ethylene
and the ethylene bromonium ion are collected in Table 3 and
compared with available experimental data.44 For ethylene, the
DFT bond lengths are larger than experimental ones by about
0.02 Å, possibly due to the use of either ECPs and their
associated basis sets or the B3LYP combination of functionals.
ion is 3 Å and the viscosity is that of methylene chloride (0.45 × 10-3
N
m2 s), the time for reorientation of one axis of the molecule through an
angle of 1 rad (57°), or τ1, is 38 × 10-12 s. The time for rotation by 180°
would be larger.
(39) Yamabe, S.; Minato, T.; Inagaki, S. J. Chem. Soc. Chem. Comm.
1988, 532.
(42) (a) Skell, P. S.; Hall W. L. J. Am. Chem. Soc. 1963, 85, 2851. (b)
March, J. AdVanced Organic Chemistry, 4th ed.; Wiley-Interscience: New
York, 1992; pp 982-1006.
(43) Smith, P. J. In Isotopes in Organic Chemistry; Buncel, E., Lee, C.
C., Eds.; Elsevier: Amsterdam, Vol. 2, 1974; pp 230-269.
(44) Hirota, E.; Endo, Y.; Saito, S.; Yoshida, K.; Yamaguchi, I.; Machida,
K. J. Mol. Spectrosc. 1981, 89, 223.
(40) Rozen, S.; Brand, M. J. Am. Chem. Soc. 1986, 51, 3607.
(41) (a) Banwell, C. N.; Sheppard, N. Mol. Phys. 1960, 3, 351. (b) Bishop,
E. O.; Richards, R. E. Mol. Phys. 1960, 3, 114. (c) Mayo, R. E.; Goldstein,
J. H. J. Mol. Spectr. 1964, 14, 173. (d) Schaefer, T.; Schneider, W. G.
Can. J. Chem. 1960, 38, 2066. (e) Whipple, E. B.; Stewart, W. E.; Reddy,
G. S.; Goldstein, J. H. J. Chem. Phys. 1961, 34, 2136.

Electrophilic Bromination of Ethylene
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5633
Table 4. Assignment of Vibrational Modes for Ethylenea
vibrational factor ηvib and through the change in the zero-point
energies, contained in úpot. As Table 5 shows, ηvib contributes
almost a unity to the overall effect making úpot responsible for
the inverse isotope effect η. The overall vibrational contribution,
mode
symmetryb
DFT
exptl
assignment
CH2 sym rock
CH2 sym wag
CH2 as wag
CH2 as twist
CH2 as rock
CH2 sym scissors
CH2 as scissors
1
2
3
4
5
6
7
8
9
b2u
b2g
b3u
au
b3g
ag
b1u
ag
b1u
ag
793
900
939
843
959
969
ηvibúpot, decreases by 50% from d1 to d4 and brings about a
1021
1167
1342
1413
1692
3122
3134
3202
3229
1044
1245
1370
1473
1655
3147
3153
3232
3234
significant inverse isotope effect. Considering that no scaling
of the harmonic vibrational frequencies was done, the η value
for the perdeuterated system d4, η ) 0.630, is nicely bracketed
by the experimentally determined values of the kinetic isotope
effect kH/kD ) 0.664 ( 0.05 in methanol and 0.572 ( 0.048 in
dichloroethane. As mentioned in the discussion of experimental
results, changing the nucleophilicity of the solvent does not
affect the kinetic isotope effect in a major way. Extending this
to the gas-phase limit, the isotope effect again should not change
that much either, thus leading to good agreement between the
calculated and experimental values.
The ethylene-bromine system is simple enough to allow for
a detailed study of the origin of the inverse isotope effects, and
such a study was carried out for the d4 system. Since the modes
of all four species involved could be assigned and no vibrations
were degenerate, modes could be easily correlated between the
species. As Table 6 shows, deuteration of ethylene and the
ethylene bromonium ion results in only minor changes of the
mode ordering. (Given as Table 6S, Supporting Information,
are pictorial representations of the modes corresponding to these
frequencies.)
CC stretch
CH stretch as (CH2 sym)
CH stretch sym (CH2 sym)
CH stretch as (CH2 as)
CH stretch sym (CH2 as)
10
11
12
b3g
b2u
a Harmonic vibrational frequencies in cm-1 b Ethylene is located in
.
the yz plane, with CC bond along the z axis.
The structure of the ethylene bromonium ion has not been
characterized experimentally.
The harmonic vibrational modes calculated for ethylene and
ethylene bromonium ion were visualized using the programs
MOLDEN45a and MacMolPlt,45b and mode assignments were
done for both the hydrogenated and deuterated species. Table
4 lists the assignment for ethylene comparing the unscaled
calculated frequencies to experimental ones.46 With the excep-
tion of the CC stretch, all the modes are underestimated with
DFT by an average of ca. 40 cm-1
.
For the analysis of the origins of the isotope effects it is
convenient to factor eq 2. Setting the tunneling transmission
coefficient κ equal to unity, eq 2 may be written as follows:
Both the ηvib and úvib factors contain multiplicative contribu-
tions from each of the vibrational modes listed in Table 6; as a
result, the vibrational contribution to the overall isotope effect
úvib
ηvib may be easily factored into contributions corresponding
KH/KD ) η(σH/σD)
(5)
to individual vibrational modes:
where σX ) (sRX/sPX), X ) H or D, is the ratio of symmetry
numbers for products (sP) and reactants (sR) and η is the per-
site isotope effect. Assuming the separation of rotations and
vibrations, the isotope effect η may be factored as47
úvibηvib ) Πi)1,15ηvib,iúvib,i
where the contribution of the ith mode to úvib,i may be written
as
η ) ηtransηrotηvibúpot
(6)
úvib,i ) exp{-[∆∆νi]/2RT}
(9)
where ηX denotes the ratio of the X partition functions (X )
translational, rotational, or vibrational) for light (H) and
deuterated (D) products (P) and reactants (R)
with ∆∆νi ) ∆νi(R) - ∆νi(P) denoting the overall change in
the zero-point energies (in kJ/mol) due to the mode i in the
reactant and product. The contributions from the individual
vibrational modes are collected in Table 7. The effects due to
the vibrational partition function ratio are negligible (close to
unity) for all modes except the new modes 13-15 created by
the addition of bromine to ethylene. For a vibrational mode to
contribute significantly to the total isotope effect via úvib, the
change in the harmonic frequency upon isotopic substitution in
the reactant and products ought to be different: ∆ν(R) * ∆ν(P).
There are two such modes in the ethylene portion of the ethylene
bromonium ion system: CH2 symmetric scissors (mode 6)
contributing to a normal isotope effect and the CC stretch (mode
8) contributing to the inVerse effect. (There is a significant
motion of the substituents on the carbon atoms during the CC
stretch.) Despite large isotopic changes in all remaining modes
(see, e.g., the CH stretches, modes 9-12), their contribution to
the overall isotopic effect is negligible because ∆ν(R) ≈ ∆ν(P).
The largest contribution from an individual mode is due to the
CH2 symmetric twist (mode 15 in Tables 6 and 7), and it adds
to the magnitude of the inVerse effect. However, Table 7 clearly
shows that the CH2 symmetric twist (mode 15), while dominant,
is not the only contributor to the effect. Nevertheless, it plays
a very important role: when the isotope effect is calculated in
the absence of mode 15, the inverse isotope effect of η ) 0.630
is replaced by a normal one of η ) 1.12 (see Figure 2).
RD
ηX ) (QXPH/QXRH)/(QXPD/QX
)
(7)
and úpot represents the effect of the isotopic change on the
separation of the zero-point energies:
úpot ) exp[ -(∆ZPEP - ∆ZPER)/RT]
(8)
Several deuterated ethylenes and their associated bromine
adducts were studied. The contributions of various factors to
the overall values of the isotope effects, calculated in the gas
phase at 298.15 K and 1 atm, are shown in Table 5. The
rotational contribution increases by 30% from d1 to d4 and,
multiplied by the slowly varying translational factor, works
toward a normal isotope effect. The effect of isotopic substitu-
tion on the vibrational energy levels appears in two ways:
through the ratio of the vibrational partition functions in the
(45) (a) Schaftenaar, G. QCPE Bull. 1992, 12, 3 (available from http:/
/www.caos.kun.nl/∼schaft/molden). (b) MacMol Plt is available from http:
//www.msg.ameslab.gov/GAMESS/Graphics/MacMolPlt.html.
(46) Duncan, D. L.; McKean, D. C.; Makkison, P. D. J. Mol. Spectrosc.
1973, 45, 221.
(47) (a) Lu, D.-h.; Maurice, D.; Truhlar, D. G. J. Am. Chem. Soc. 1990,
112, 6206. (b) Zhao, X. G.; Tucker, S. C.; Truhlar, D. G. J. Am. Chem.
Soc. 1991, 113, 826.

5634 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Koerner et al.
Table 5. Contributions to Per-Site Secondary Isotope Effectsa
system
ηtrans
ηrot
ηtransηrot
ηvib
úpot
ηvibúpot
η
d1 ) H2C-CDH
1.040
1.079
1.079
1.079
1.118
1.157
1.111
1.206
1.223
1.232
1.328
1.435
1.155
1.301
1.320
1.329
1.485
1.660
0.980
0.965
0.963
0.962
0.948
0.935
0.784
0.631
0.622
0.617
0.500
0.406
0.768
0.609
0.598
0.594
0.475
0.380
0.888
0.792
0.790
0.789
0.705
0.630
d2 - trans ) DHC-CDH
d2 - cis ) DHC-CDH
d2 ) D2C-CH2
d3 ) D2C-CDH
d4 ) D2C-CD2
a The contributions ηtrans, ηrot, ηvib, and ηpot to the per-site secondary isotope effect η are defined in eqs 5-8.
Table 6. Correlations of Calculated Harmonic Frequencies for C2H4, C2D4, C2H4Br+, and C2D4Br+ a
C2L4
L ) H
C2L4Br+
mode
symmetryb
L ) D
symmetryc
L ) H
L ) D
assignment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
b2u
b2g
b3u
au
b3g
ag
b1u
ag
b1u
ag
793
900
939
570
743
711
723
950
b1
b2
a1
a2
a2
a1
b2
a1
b2
a1
a2
b1
b2
a1
b1
808
1063
1071
883
1169
1481
1414
1176
3120
3120
3234
3247
434
573
817
803
630
929
1264
1045
945
2255
2278
2424
2423
412
CH2 sym rock
CH2 sym wag
CH2 as wag
CH2 as twist
CH2 as rock
CH2 sym scissors
CH2 as scissors
1021
1167
1342
1413
1692
3122
3134
3202
3229
971
1047
1580
2243
2321
2389
2405
CC stretch
CH stretch as (CH2 sym)
CH stretch sym (CH2 sym)
CH stretch as (CH2 as)
CH stretch sym (CH2 as)
CBr stretch as
CBr stretch sym
CH2 sym twist
b3g
b2u
450
844
432
619
a Harmonic vibrational frequencies in cm-1 b Ethylene is located in the yz plane, with CC bond along the z axis. c In ethylene bromonium ion
.
the CC bond is oriented along the y axis, while the plane of L4 is parallel to the xy plane.
a
Table 7. Contributions of Various Modes to úpot and ηvib
modea
ηvib,i
∆νi(R)b ∆νi(P)b ∆∆νib
úpot,i
ηvib,iúpot,i
1
2
3
4
5
6
7
8
9
1.000
1.001
1.007
0.989
0.999
1.006
1.000
0.993
1.000
1.000
1.000
1.000
0.984
0.988
0.966
0.935c
223
157
229
299
218
371
365
112
868
813
813
824
234
247
268
254
240
217
369
230
865
842
810
824
22
11 0.973
90 0.805
39 0.909
-44 1.116
22 0.948
0.973
0.806
0.915
1.103
0.947
1.458
0.991
0.746
1.007
0.933
1.008
0.999
0.933
0.947
0.561
0.380f
-153 1.449
4
0.991
118 0.751
-2 1.007
29 0.933
-2 1.008
10
11
12
13
14
15
total
0
0.999
22 0.948
18 0.958
18
225
225 0.581
373d 0.406e
Figure 2. Displacements of atoms in mode 15 (symmetric twist of
CH2).
a Assignment of modes is shown in Table 6. b See eq 9 for the
definition of symbols. c Πi)1,15(ηvib,i). d Πi)1,15(∆∆νi). e Πi)1,15(úpot,i).
f Πi)1,15(ηvib,i
úpot,i).
al., namely that the inVerse isotope effect arises from the
creation of the CH2 symmetric twist mode rather than it being
due to a rehybridization of the carbons from sp2 to sp3. It must
be added here that there is little rehybridization at the carbon
atoms upon the addition of bromine: the sum of the three angles
C-C-H, H-C-H, and C-C-H is about 357.3°, very close
to the sum of 360°, characteristic of the sp2 hybrid.
As a representation of the first step toward charge separation
in the bromination of ethylene, the charge-transfer complex
equilibrium
Two models were proposed to explain the origin of the
secondary R-deuterium isotope effect. The older interpretation
suggested by Streitwieser et al.10 stipulates the change of some
CH vibrational modes due to rehybridization: in a reaction that
involves sp2 to sp3 rehybridization at the R-carbons, an inverse
secondary isotope effect should be observed. A more recent,
alternative explanation of the secondary kinetic isotope effects
was offered by Strausz et al.,12 who attributed the effect to the
creation of new, isotopically sensitive, vibration(s) in the
transition state. Bender and co-workers have recently shown
13a
C2H4 + Br2 h C2H4:Br2
that, for equilibrium binding of ethylene to Os2(CO)8 and
equilibrium H2/D2 binding in a M(η2-H2) complex,13b the zero
point energy components associated with the creation of new
vibrational modes in the complexes contribute most to the
inverse EIE’s. In the case of bromination of ethylene, there is
strong eVidence in support of the model put forth by Strausz et
was studied and the isotope effects were evaluated. Table 8
compares the DFT geometry with the one calculated at the MP2
level.48 Assignments of the vibrational modes in the CTC are
listed in Table 9. The absence of imaginary frequencies

Electrophilic Bromination of Ethylene
J. Am. Chem. Soc., Vol. 120, No. 23, 1998 5635
Table 8. Geometry of the CTC (bond lengths in angstroms)
Scheme 3
bond
DFTa
MP2b
Br-Br
Br-C
C-C
2.389
2.868
1.370
2.354
3.021
1.343
a This work. b Br(16s11p5d/5s4p2d), C(10s6p1d/4s3p1d), and H(5s1p/
2s1p).48
Table 9. Assignment of Modes for the CTCa
mode
symmetryb
DFTc
assignment
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
b1
b2
a1
b2
a1
b1
b1
b2
a1
a2
a2
a1
b2
a1
b2
a1
a2
b1
74
74
112
155
262
293
800
928
972
1005
1180
1336
1420
1649
3132
3141
3219
3245
Br-Br-C2H4 def. (front to back)
Br-Br-C2H4 def. (right to left)
Br2-C2H4 stretch
C2H4 twist of Br-C as stretch
Br-Br stretch
prominent than solvent capture, kf/kr becomes a true equilibrium
constant, Keq, so the expression reduces to
d[BrOS]
CH2 sym twist
) k1KeqKCTC[Br2][olefin]
(11)
CH2 sym rock
CH2 as wag
CH2 sym wag
CH2 as twist
CH2 as rock
CH2 sym scissors
CH2 as scissors
CC stretch
CH stretch sym (CH2 as)
CH stretch sym (CH2 sym)
CH stretch as (CH2 as)
CH stretch as (CH2 sym)
dt
In this case, the R-dkie comprises the kinetic and equilibrium
terms, k1, KCTC, and Keq. Since the transition state for the solvent
capture is very early, and since the contribution of the CTC to
the R-dkie is small (vide supra), the largest contributor to the
dkie is Keq.
In another limit where each time the bromonium ion is formed
it proceeds to products, the expression reduces to
d[BrOS]
a Harmonic vibrational frequencies in cm-1 b CTC was assumed to
.
) kfKCTC[Br2][olefin]
(12)
have C2V symmetry, with Br2 was aligned along the z axis and CC
dt
bond parallel to the y axis. c This work.
and the dkie must arise largely from the kf term. Note here
that since this transition state will be relatively late it will
strongly resemble the bromonium ion with its associated
equilibrium isotope effect.
indicates that the CTC is a minimum on the potential energy
surface. A substantial inverse isotope effect of η ) 0.89 is
found; however, it is small when compared with the effect found
in the bromonium ion. In contrast to the ethylene bromonium
ion, there is no single mode responsible for the isotopic effect
in the charge-transfer complex.
In DCE, the mechanism for bromination of ethylene (Scheme
3) proceeds through a CTC that evolves to an ion pair complex
with the assistance of a second Br2. In this case, product
formation can only occur if the ions rotate to bring the CH2-
Br+ moiety into a configuration where it can be displaced by
Br3-. This step, with its associated rotational rate constant, krot,
from the calculations presented above38 is surprisingly slow and
could limit the rate of the reaction. A set of kinetic expressions
for the formation of dibromide that strongly resemble those
above describing the situation in methanol can be written.
Assuming a steady state in the nascent bromonium ion complex,
we can write
Conclusions and Mechanistic Implications
From the product study of the bromination of ethylene, the
reaction proceeds exclusively by a two-step trans addition
process. Kinetic measurements using the method of incomplete
bromination indicate that the dkie’s in both methanol and
dichloroethane are large (kH/kD ) 0.61) and inverse, and the
experimental values are in remarkably good agreement with
what is computed for the equilibrium EIE for Br+ + CH2dCH2
h bromonium ion by the methods described above.
Given the experimental and computed dkie’s, kinetic data,
the anticipated instability of the ethylene bromonium ion, and
due consideration of the constraints placed upon the ion lifetime
and the time required for ion reorganization to produce products,
the most likely mechanism(s) for bromination of ethylene are
given in Scheme 3. In methanol, the presently available
evidence supports a process involving a preassociation mech-
anism leading through a CTC which evolves to a reversibly
formed bromonium ion with an associated solvent. A general-
ized kinetic expression based in Scheme 3 and assuming a steady
state in the bromonium ion can be given as
krotkf[Br2]KCTC[Br2][olefin]
krot + kr
d[DB]
dt
)
(13)
In the limit where the ion rotation is slow relative to the reversal
to reform the CTC, the expression reduces to
d[DB]
dt
) krotKeqKCTC[Br2]2[olefin]
(14)
Once again, the R-dkie comprises two equilibrium terms and
one kinetic term, but the isotopic sensitivity of the rotational
term must be nil and, for reasons presented above, that
associated with KCTC is small. This leaves the primary
contributor to the dkie as being the equilibrium isotope effect
associated with bromonium ion formation.
In another limit, if the rate-limiting step is really bromonium
ion formation and rotation followed by ion pair collapse to form
product is fast, then eq 13 reduces to
k1kfKCTC[Br2][olefin]
kr + k1
d[BrOS]
)
(10)
dt
In one limit, where reversal of the ion to the CTC is more
(48) Assfeld, X.; Garapon, J.; Rinaldi, D.; Ruiz-Lo´pez, M. F.; Rivail,
J.-L. THEOCHEM 1996, 371, 107.

5636 J. Am. Chem. Soc., Vol. 120, No. 23, 1998
Koerner et al.
the nature of secondary isotope effects which cannot be resolved
experimentally.
d[DB]
dt
) kfKCTC[Br2]2[olefin]
(15)
Acknowledgment. The authors gratefully acknowledge the
financial contributions of the Natural and Engineering Research
Council of Canada, the University of Alberta, and Queen’s
University. In addition, they acknowledge stimulating discus-
sions with Prof. R. J. C. Brown, correspondence with Professor
Bruce R. Bender (Scripps Research Institute) informing us of
his ethylene work, and the very helpful comments of the
reviewers.
and the dkie resides primarily in the kf term. As was the case
for bromination in methanol, this transition state must be late,
resembling the bromonium ion, so the dkie can be well
approximated by the equilibrium isotope effect.
Finally, we conclude that DFT calculations of the EIE for
the equilibrium Br+ + C2H4 h [C2H4Br]+ confirm the validity
of Strausz’s model12 where the creation of a new isotopically
sensitive mode is responsible for the dkie. The ethylene system
is small enough to allow for unambiguous identification of
vibrational modes in all the species involved leading to the
identification of a single modesCH2 symmetric twiststhat is
undoubtedly responsible for the inverse EIE.13
Supporting Information Available: Table 6S, Assignment
of Modes and Frequency Comparison for the Ethylene Bromo-
nium Ion (4 pages, print/PDF). See any current masthead page
for ordering information and Web access instructions.
The good agreement between the experimental and calculated
isotope effects indicates that DFT is a useful tool for studying
JA974151M