Electrophilic bromination of specifically deuterated cyclohexenes: A combined experimental and theoretical investigation

Article abstract of DOI:10.1021/ja971145h

The electrophilic addition of Br₂ to specifically deuterated cyclohexenes (1-5) was studied methanol (MeOH) by stopped-flow kinetics in order to determine a deuterium kinetic isotope effect (DKIE) for the various isotopomers. The DKIE for bromi

Full text of DOI:10.1021/ja971145h

2578
J. Am. Chem. Soc. 1998, 120, 2578-2585
Electrophilic Bromination of Specifically Deuterated Cyclohexenes:
A Combined Experimental and Theoretical Investigation
†
†
†
,†
‡
H. Slebocka-Tilk, A. Neverov, S. Motallebi, R. S. Brown,* O. Donini,
‡
,‡
J. L. Gainsforth, and M. Klobukowski*
Contribution from the Department of Chemistry, Queen’s UniVersity, Kingston, Ontario, Canada K7L 3N6,
and Department of Chemistry, UniVersity of Alberta, Edmonton, Alberta, Canada T6G 2G2
ReceiVed April 10, 1997
Abstract: The electrophilic addition of Br2 to specifically deuterated cyclohexenes (1-5) was studied methanol
(MeOH) by stopped-flow kinetics in order to determine a deuterium kinetic isotope effect (DKIE) for the
various isotopomers. The DKIE for bromination of the isotopomers was also determined by a mass spectrometric
method where exactly known quantities of two of the cyclohexenes were incompletely brominated in MeOH
and where the ratio of the remaining isotopomers was determined. A computational study using density
functional theory (DFT) was undertaken to examine the equilibrium isotope effect (EIE) for the equilibrium
involving the formation of the cyclohexenyl bromonium ion from cyclohexene plus Br2. The agreement between
experiment and theory is remarkably good and indicates that, for perdeuteriocyclohexene, the inverse DKIE
and EIE of ∼1.5 can be partitioned two-thirds to the two vinyl CH’s and one-third to the four homoallylic
CH’s, the four allylic CH’s contributing negligibly to the overall effect. The computational study also indicates
that there is extensive mixing of the CC and CH vibrational modes and that it is not possible to identify all the
individual modes responsible for the large inverse EIE. Analysis of the computational data indicates that the
isotopic effects may be divided into two groups; those associated with the deuteriums on the vinyl positions
and those associated with the remaining allylic and homoallylic carbons. In the former, the inverse EIE is due
to the changes in all bending modes. For the latter, the isotopically sensitive modes are those of all ten C-H
stretches with changes in bending frequencies being unimportant. The bending vibrational modes were found
to be strongly coupled.
Introduction
occurred in the rate-limiting transition state. For 1,1-diphenyl
ethylene, rate-limiting bromination proceeds to an R-bromocar-
bocation so that the nearly unit secondary DKIE comprises two
competing effects, an inverse one arising from the rehybrid-
ization and a normal one attributable to hyperconjugation of
the C-L bonds with the benzylic cationic center. However,
for bromination by tribromide, the DKIE is a complicated mix
of rehybridization effects, and those arising from nucleophilic
Some time ago we reported secondary deuterium kinetic
isotope effects (DKIE) for the bromination of H10 and D10
cyclohexene (1, L ) H, D) in acetic acid at 25 °C.1 The inverse
value obtained, kD10/kH10 ) 1.9 ( 0.15, was surprisingly large
considering that sparse previous work had indicated that
secondary DKIEs for electrophilic brominations were small. For
example, Denney and Tunkle2 reported that the secondary
R-DKIE for bromination of trans-stilbene-d2 was kD/kH ) 1.1,
while Wilkins and Regulski2b showed that the para-substituted
styrenes, when brominated in HOAc at 40 °C, produced small
inverse secondary R-DKIE’s of kD/kH ) 1.01-1.05. More
4
b
a
-
4a
attack of Br on the charge-transfer complex. Note that in
any of the above cases, the presence of the phenyl rings
introduces the possibility that the bromonium ions and the charge
distribution within them may be highly distorted.
recently,3
a,b
In our symmetrical aliphatic cases, although one must be
careful about the effect of the remote deuteriums, comparison
of the DKIE for bromination of 1, L ) H, D with that for
3,3,6,6-tetradeuteriocyclohexene (2) indicated that the allylic
deuteriums contributed negligibly to the observed effect. That
fact, along with the assumption that the more remote γ-deute-
riums could be neglected as contributors to the observed DKIE,
led to the conclusion that the two R-deuteriums in cyclohexene
contributed equally to the effect, the value per deuterium being
Bellucci and co-workers have reported inverse
-
-
DKIEs of about 1.2 for the addition of Br /Br2 (Br3 ) to each
of stilbene, 1,1-diphenylethylene, and R-(3-trifluoromethylphen-
yl)styrene, the respective values for the addition of Br2 to these
being 1.33, 1.03, and 1.42.3b Most of the above results for Br2
addition were rationalized in terms of the customary model in
which changes in the out-of-plane bending frequencies ac-
2
3
companying rehybridization of the R-carbons from sp to sp
†
Queen’s University.
University of Alberta.
‡
roughly
x
1.9 ) 1.4.
(
1) Slebocka-Tilk, H.; Zheng, C. Y.; Brown, R. S. J. Am. Chem. Soc.
993, 115, 1347.
2) (a) Denney, D. B.; Tunkle, N. Chem. Ind. (London) 1959, 1383.
Wilkins, C. L.; Regulski, T. W. J. Am. Chem. Soc. 1972, 94, 6016.
3) (a) Bellucci, G.; Chiappe, C.; Lo Moro, G. J. Org. Chem. 1997, 62,
1
(4) (a) Lowry, T. H.; Richardson, K. S. In Mechanism and Theory in
Organic Chemistry, 3rd ed.; Harper and Row: New York, 1987; pp 232-
244. (b) Maskill, H. In The Physical Basis of Organic Chemistry; Oxford
University Press: Oxford, 1985; pp 367-404. (c) Westaway, K. C. In
Isotopes in Organic Chemistry; Buncel, E., Lee, C. C., Eds.; Elsevier:
Amsterdam, 1987; Vol. 7, pp 275-392.
(
(
3
5
176. (b) Bellucci, G.; Chiappe, C. J. Chem. Soc., Perkin Trans. 2 1997,
81.
S0002-7863(97)01145-1 CCC: $15.00 © 1998 American Chemical Society
Published on Web 03/07/1998

Bromination of Deuterated Cyclohexenes
J. Am. Chem. Soc., Vol. 120, No. 11, 1998 2579
Scheme 1
Although the reported DKIE is within the realm of possible
values for two olefinic C-L bonds undergoing maximum
changes in rehybridization, it is suspiciously large enough that
we undertook a more detailed experimental and theoretical study
of this process. In particular we were interested in whether
neglect of the effect of the γ-deuteriums is warranted. Herein
we report our findings for the bromination of specifically
deuterated cyclohexenes 1-5 in methanol. As well, we report
mass spectrometric determination of the DKIE where mixtures
of two unreacted alkenes were recovered from the reaction after
incomplete competitive bromination in MeOH and analyzed for
their isotopic composition. Finally, we report a detailed
computational study using density functional theory (DFT) to
model the equilibrium deuterium isotope effect (EIE) for the
equilibrium involving formation of the cyclohexenyl bromonium
ion from cyclohexene and Br2.
CHCl
room temperature after which a mild exothermic reaction takes place
cooling not required). After standing for 15 h, the contents of the
tube were transferred to another flask, and 30 mL of D O was carefully
added. The mixture was then heated to 95 °C for 15 min at which
point an exothermic reaction occurred and the dicarboxylic acid
3
. The tube was sealed and the contents were allowed to reach
(
2
precipitated as a white solid. The excess D
residue washed with a small portion of toluene and then CH
2
O was removed and the
Cl . After
2
2
drying under vacuum, 13.5 g (95%) of a white solid was obtained:
mp 170-172 °C. This was carried on to the next step.
The above unsaturated dicarboxylic acid (13.0 g, 0.073 mol) was
dissolved in 100 mL of dioxane, and 2.0 g of Pd/C was added. This
2
mixture was deuterated under a D atmosphere until no more deuterium
Experimental Section
was consumed. The suspension was filtered through a pad of Celite,
and the solvent removed to give 9.5 g of a white powder: mp 170-
a. Materials. Acetic acid (Fisher, reagent grade, 99.7%) was
5
purified as described. LiBr (General Intermediates) and LiClO
4
1
72 °C, yield ∼72%. The final octadeuteriocyclohexene (3) was
(
(
2 5
Alpha) were dried in a vacuum at 120 °C over P O for 48 h. Br
2
prepared from the total of the preceding material in 36% yield, (1.6
g), using the procedure of Wolfe and Campbell: H NMR (400 MHz,
Aldrich) was used as supplied. Methanol (2 L, Sigma-Aldrich, 99.9%
and allowed to
7
1
ACS HPLC grade) was treated with 2 drops of Br
2
2
CDCl
922, 2207 (st), 2112 (st), 1644 cm ; GC MS, m/z ) 90. H NMR
analysis indicated that the above material contained 4.5-5% residual
H at C3,6 and 8-8.5% at C4,5
b. Kinetics. The rate constants of Br
deuterated cyclohexenes were measured at 25 °C under pseudo-first-
order conditions of excess olefin in HOAc (µ ) 0.1 (LiClO )), methanol
no salt) using an Applied Photophysics SX-17MX stopped-flow
3
) δ 5.70 (s); H NMR (CHCl
3
) 1.64 (s), 2.03 (s); GC ir 3031,
stand in the dark for 24 h after which it was distilled through a 70 cm
Vigreux column with the middle fraction only being collected.
-
1
1
2
Cyclohexene-d10 (1, L ) H) was made in ∼50% yield by dehydration
6
.
of cyclohexanol-d12 according to a published procedure. Cyclohexene-
2
addition to selectively
3
4
,3,6,6-d (2) was prepared in 22% yield according to the published
7
procedure of Wolfe and Campbell. Mass analysis indicated a 98%
4
incorporation of deuterium in 2.
(
Cyclohexene-1,2-d
2
(4) was also prepared by the procedure of Wolfe
and Campbell in 33% yield starting from cyclohexane-1,2-dicarboxylic
anhydride which was exchanged at the 1,2-positions using D SO and
-3
7
instrument. The olefin concentration was varied (2-7) × 10 M (after
-
4
mixing) and the [Br
2
] was varied (0.5-5) × 10 M. Solutions were
2
4
8
1
prepared and stored with protection from moisture and light. The
pseudo-first-order rate constants were evaluated by nonlinear least-
squares fitting of the absorbance vs time traces for the disappearance
2
D O. H NMR analysis indicated the product had 93% deuterium at
(5) was prepared by dehydration9
the vinyl positions. Cyclohexene-d
of d
hexanone with LiAlD
tion of deuterium at C
Cyclohexene-3,3,4,4,5,5,6,6-d
1
1
-cyclohexanol, this being prepared from the reduction of cyclo-
10
1
of Br
of 10-16 runs. The second-order rate constants were evaluated as k
obs/[alkene].
c. Mass Spectrometry. A mass spectrometric method was used
2
to an exponential model. The kobs values used were the averages
4
.
H NMR analysis indicated a 98% incorpora-
2
1
.
)
k
8
(3) was prepared as outlined in the
process shown in Scheme 1. Zn dust (98 g, 1.51 mol) and 90 mL of
anhydrous dioxane were placed in a 500 mL round-bottom flask
equipped with a gas inlet tube, a gas exit tube leading into a thick-
walled tube cooled to -78 °C, and a solid addition tube. This was
then flushed with Ar and 1.0 g of NaI, 6.0 g of anhydrous CuCl, and
wherein mixtures of known quantities of various selectively deuterated
cyclohexenes were incompletely brominated in methanol and the
unreacted alkenes subjected to GC MS analysis.12
In the standard experiment, equimolar amounts (0.04 mmol) of
deuturated (d
n
) and protonated (H10) cyclohexenes were added to about
3
2
0 mL D O were added, and the mixture heated to 80 °C with stirring.
6
mL of purified methanol containing 0.01 mmol of benzene as an
To this heated mixture was added, over the course of 3 h, 52 g (0.2
mol) of hexachlorobutadiene. The volatile hexadeuteriobutadiene that
was produced was trapped in the thick-walled tube to give a crude
internal standard. A portion of this mixture was set aside and the exact
ratio of its alkene components determined subsequently by GCMS
1
1
analysis. Approximately 0.04 mmol of Br
added to the reaction mixture at ambient temperature with vigorous
stirring. The remaining amounts of d and H10-cyclohexenes in reaction
2
in methanol was slowly
yield of 7.25 mL (5.3 g, 44%). To the tube was immediately added
0 mL of CHCl and fumaroyl chloride (12.2 g, 0.08 mol) in 45 mL of
1
3
n
mixture were determined by GCMS analysis using benzene as an
internal standard. The analyses were performed on a Fisons Quattro
mass spectrometer coupled to a Fisons GC 8000 gas chromatograph;
DB-5HS column, 30m, 0.25 mm id, T ) 40 °C, 4 psi, He carrier. Each
sample was subjected to three or four independent analytical runs.
Quantitative evaluation was done by determining the ion current
corresponding to the molecular ions of the alkenes materials (78 for
(
5) Brown, R. S.; Gedye, R.; Slebocka-Tilk, H.; Buschek, J.; Kopecky,
K. R. J. Am. Chem. Soc. 1984, 106, 4515.
(
(
(
6) Waldmann, H.; Petru, F. Ber. Dtsch. Chem. Ges. 1950, 287, 83.
7) Wolfe, S.; Campbell, J. R. Synthesis 1979, 117.
8) Ahlgren, G.; Akermark, B.; Dahlquist, K. I. Acta Chem. Scand. 1968,
2
2, 1124.
(
(
9) Monson, R. S. Tetrahedron Lett. 1971, 7, 567.
10) (a) Lambert, J. B.; Putz, G. J. J. Am. Chem. Soc. 1973, 95, 6313.
(
b) Wolkolf, P.; Holmes, J. L. Can. J. Chem. 1979, 57, 348.
(11) Charlton, J. L.; Agagnir, R. Can. J. Chem. 1973, 51, 1852.
(12) Bigeleisen, J.; Wolfsberg, M. AdV. Chem. Phys. 1958, 1, 15.

2580 J. Am. Chem. Soc., Vol. 120, No. 11, 1998
Slebocka-Tilk et al.
benzene, 82 for H10 cyclohexene, 83 for 5, 84 for 4, 86 for 2, 90 for 3,
2 for 1 (d10)).
Table 1. Second-Order Rate Constants for the Bromination of
Cyclohexenes 1-5 in MeOH at 25 °C. No Added Salts
9
(M- s-1) (×10 )
1
4
a
b
olefin
k
2
D H
k /k
Computational Section
1
1
2
3
4
5
, L ) H
, L ) D (D10
1.14(0.10)
1.66(0.15)
1.11(0.12)
1.25(0.14)
1.50(0.15)
1.35(0.12)
)
1.45(0.18)
0.97(0.15)
1.10(0.15)
1.31(0.17)
1.18(0.15)
A computational study was undertaken to examine the
equilibrium deuterium isotope effect (EDIE) for the equilibrium
involving the formation of the cyclohexenyl bromonium ion
from cyclohexene plus Br2. The isotope effects were modeled
using results obtained with the DFT. The gradient-corrected
8
(D )
a
Values are averages of 3 independent runs; bracketed values are
(
nonlocal) functionals were shown to be very successful in the
2
2
2 1/2
errors calculated according to δx ) [(δa) + (δb) + (δc) ] where a,
13
studies of kinetic isotope effects. Three sets of gradient-
corrected functionals were used in the present work. Becke’s
b
b, and c are the standard deviations in the individual numbers. DKIE
computed from ratio of k value of deuterated olefin to that of 1, L )
H. Propagated error in ratio where z ) x/y given as δz ) z[(δx/x) +
2
2
exchange (B) or Becke’s 3-parameter exchange15 (B3) func-
14
2
1/2
(
δy/y) ] .
tionals were combined with two correlation functionals devel-
oped by Perdew16 (P86) and by Lee et al. (LYP). The three
combinations were denoted as BP86, BLYP, and B3LYP,
respectively. For comparison, the restricted Hartree-Fock
17
be used as a qualitative substitute for the genuine transition state.
The calculations were done for the equilibrium isotope effect
(
EIE) in the equilibrium involving the formation of the reaction
(RHF) calculations were also done. To minimize the compu-
+
intermediate [C6H10Br] :
tational effort, the compact effective core potentials of Stevens
et al.18 were used. The basis sets were used with double-ú
contraction on the carbon atoms and quadruple-ú contraction
on the bromine atom, along with the (31) basis set for the
hydrogens obtained from Huzinaga’s (4s) expansion.1 Single-
polarization functions were used: d-type on all heavy atoms
and p-type on hydrogens. Polarization functions were included
in the hydrogen basis sets since it is the effect of the hydrogen
atoms on the vibrational structure and the proximity and
interactions of hydrogens with the reaction site which are
important in this study. Geometry optimization and Hessian
+
+
C H + Br h [C H Br]
6
10
6
10
For the equilibrium:
9
X h Y
the EDIE is calculated in the gas phase, rigid rotor, harmonic
2
2
oscillator approximation according to
Q /Q
Y
X
e-(δO
YE
-δE )/RT
X
O
K /K )
) FQF
ZPE
(1)
2
0
H
D
evaluation were done using the Gaussian 94 program. All
calculations were done in C1 symmetry allowing for the
maximum number of degrees of freedom in the computed
structures.
Q /Q
Y′
X′
X
O
where δE is the difference between the total molar vibra-
tional zero-point energies for the light and heavy reactant
compounds X and X′, δE 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.
X
O
The bridged bromonium complex is not a transition state in
the reaction, but rather a minimum. Presumably the transition
state resembles an ion pair with bromide in solution, perhaps
stabilized by counterion(s). However, computation of the true
transition state structure for the process Br2 + alkene bromonium
-
ion + Br in the gas phase is not possible due to the prohibitive
Results and Discussion
endothermicity associated with charge separation. Indeed, it is
well-known that electrophilic bromination does not occur in the
i. Kinetics. Precise stopped-flow kinetic data in HOAc
proved difficult to obtain because of slight nonfirst-order
behavior of the kinetic plots, so further stopped-flow studies in
this solvent were discontinued. Given in Table 1 are the
stopped-flow data for the bromination of olefins 1-5 in
methanol containing no salt at 25 °C. None of the data is
corrected for the incomplete deuteration, although such correc-
tion would not change the numbers appreciably. The data given
in Table 1, while being the result of numerous runs, contain
relatively large errors on the order of (10%. Also, the methanol
21
gas phase for the same reason. According to the Hammond
22
principle, it may be assumed that the transition state resembles
the bromonium ion more than it does the cyclohexene and
bromine reactants. The structure of the bromonium ion can then
(
13) Wiest, O.; Black, K. A.; Houk, K. N. J. Am. Chem. Soc. 1994, 116,
1
0336.
(
(
(
(
(
14) Becke, A. D. Phys. ReV. A. 1988, 38, 3098.
15) Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
16) Perdew, J. P. Phys. ReV. B 1986, 33, 8822.
17) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785.
DKIE of 1.45 ( 0.18 reported in Table 1 for 1, L ) H, D, are
18) Stevens, W. J.; Basch, H.; Krauss, M. J. Chem. Phys. 1984, 81,
lower than those given in our earlier work in acetic acid.1
6
1
026. Stevens, W. J.; Krauss, M.; Basch, H.; Jasien, P. G. Can. J. Chem.
992, 70, 612.
In fact, inspection of the stopped-flow data in Table 1
indicates that many of these experimental numbers are indis-
tinguishable. Since the accumulated errors in the above numbers
severely limits mechanistic conclusions, we turned to a competi-
tive technique involving mass spectrometry where exactly
known amounts of two of the cyclohexenes were incompletely
brominated and the unreacted olefins analyzed by GCMS. The
method requires that the ratio of the intensities of the mass ions
of the olefins be determined before reaction and at some
precisely known time during the reaction. The time-zero ratio
incorporates the detector response factors, and importantly, since
the mass detector “sees” only the mass ion of the desired
isotopomer, the DKIE determined in this manner is corrected
(
19) Huzinaga, S. J. Chem. Phys. 1965, 42, 1293.
(20) 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.; Replogle, 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 94, Revision D.3;
Gaussian, Inc.: Pittsburgh, PA, 1995.
(
(
21) Ruasse, M.-F.; Motallebi, S. J. Phys. Org. Chem. 1991, 4, 527.
22) Maskill, H. The Physical Basis of Organic Chemistry; Oxford
University Press: New York, 1985. Also see: van Hook, W. A. In Isotope
Effects in Chemical Reactions; Collins, C. J., Bowman, N. S., Eds.; Van
Nostrand: New York, 1970.

Bromination of Deuterated Cyclohexenes
J. Am. Chem. Soc., Vol. 120, No. 11, 1998 2581
Table 2. DKIEs Determined for Bromination of Specifically
Deuterated Cyclohexenes in MeOH Using GC MS Analysisa
b
olefin
k
D
/k
H
(MeOH)
1
2
3
4
5
, L ) D
1.31(0.06)
1.07(0.07)
1.14(0.07)
1.23(0.01)
1.06(0.09)
a
Determined by MS analysis of the intensities of the mass ions of
the deuterated and nondeuterated olefins as described in text. b KIE
errors were computed by using the formula δKIE) ulog (Raf/Rao)/
2
2
Figure 2. Structure of the cyclohexene boat conformation.
[
log(1 - f)(1 + Rao)/(1 + Raf)]u(((δRao/Rao) + (δRaf/Raf) )/(ln[Raf
/
2
2
2 0.5
R
-
ao]) + (((δRao/(1 + Rao)) + (δRaf/(1 + Raf)) ) + δf/(1 - f))/ln [(1
2
0.5
f)(1 + Rao)/(1 + Raf)]) ) where Rao is the experimental ratio of the
isotopomers at time zero, Raf is the ratio of the isotopomers at final
incomplete bromination, and f denotes the fraction of reaction at the
time of incomplete bromination.
Figure 3. Structure of the cyclohexenyl bromonium ion twist
conformation.
Figure 1. Structure of the cyclohexene twist conformation.
for incomplete deuteration of the olefin. The data are then
analyzed as
[
(k/k′) - 1] ) log(R /R )/[log(1 -f)(1 + R )/(1 + R )]
af ao ao af
(2)
where Rao and Raf are the isotopic ratios of the substrate olefins
before reaction, and after a stoichiometrically measured fraction,
1
2
f, has reacted, and k and k′ are the rate constants for the light
and heavy cyclohexenes, respectively. Given in Table 2 are
the DKIEs determined for bromination of olefins 1-5 in MeOH
using this technique. Values in HOAc could not be determined
this way because direct injections of the solution caused
deterioration of the Gc column, and attempted isolation of the
products by exhaustive extraction gave irreproducible results.
Comparison of the MeOH data in Tables 1 and 2 indicate a
consistent trend of kD/kH 1 > 4 > 5 ≈ 3 > 2 ≈ 1 (5 out of
order in the two tables), but differing absolute numbers.
Despite the large errors, the kinetic and mass spectrometric
data suggest that two-thirds of the DKIE arises from the vinyl
hydrogens, one-third from the remote homoallylic hydrogens,
and the allylic hydrogens contribute almost nothing. The
suggestion that the homoallylic H’s contribute so significantly
to the DKIE is intriguing, but cannot be verified in our hands
by further experimental determinations because of limitations
imposed by the cumulative errors in the techniques available
to us. Therefore we resorted to high level calculations to provide
confirmation of the numbers and insight into the origins of the
DKIEs.
ii. Computations. Calculations were carried out with the
three density functionals for the two conformers of cyclohexene
reactant, twist (TR) and boat (BR), and for the three conformers
of the cyclohexenyl bromonium ion product, twist (TP), boat
down (BD), and boat up (BU). The five conformers are shown
in Figures 1-5. The relative energies for all conformers are
shown in Table 3. All methods predict that the twist conformers
are most stable. However, the energy differences between the
conformers are not large: for cyclohexene, the BR conformer
Figure 4. Structure of the cyclohexenyl bromonium ion boat-down
conformation.
Figure 5. Structure of the cyclohexenyl bromonium ion boat-up
conformation.
is less stable than TR by about 5 kcal/mol; for the ion, the BU
conformer is less stable than TP by about the same amount,
while the energy of the BD conformer is higher than that of TP
by less than 2 kcal/mol. Furthermore, DFT calculations predict
+
that the C6H10Br ion is thermochemically more stable (by about
+
130 kcal/mol) than its constituents, Br and C6H10. It is
satisfying to observe that the three DFT methods give essentially
identical results, while the RHF method predicts energy spacings
that are only about 1 kcal/mol larger than the ones obtained
with the DFT methods.
The B3LYP-calculated structural parameters for all systems
studied are collected in Table 4. Results obtained with RHF
method and with the other functionals are available as Sup-
porting Information. As expected, the RHF bond lengths are

2582 J. Am. Chem. Soc., Vol. 120, No. 11, 1998
Slebocka-Tilk et al.
Table 3. Relative Energies and Total Energiesa
systemb
Br+
RHF
BP86
BLYP
B3LYP
(-12.737 15)
(-12.929 97)
(-12.878 81)
(-12.909 74)
Cyclohexene
TR
BR
0.0
6.2
(-38.726 02)
0.0
5.1
(-40.001 12)
0.0
5.0
(-39.671 38)
0.0
5.3
(-39.879 77)
Cyclohexenyl bromonium ion
0.0
TP
0.0
-93.8
2.8
(-51.612 59)
0.0
-131.9
1.4
(-53.141 32)
(-52.748 83)
0.0
-123.3
1.8
(-52.986 06)
c
∆
TP
-124.6
BD
BU
1.6
5.7
4.5
4.5
4.8
a
b
Relative energies in kcal/mol. Total energies in atomic units. Total energies are given in parentheses. See text for the meaning of abbreviations.
c
+
+
Calculated exothermicity of the reaction C
6
H10 + Br h [C
6
H10Br] , in kcal/mol.
Table 4. Structural Parameters of Conformers of Cyclohexene and
Its Bromonium Ion (distances in Å, Bond Angles in Degrees) as
Calculated with B3LYP Functional
Table 5. Experimental and Calculated Structural Parameters of the
Twist Conformer of Cyclohexene (Distances in Å, Bond Angles in
Degrees)
a
twist
boat
twist
boat down
boat up
parametera
MWb
EDc
EDd
GVBe
B3LYPf
parameterb (C
H
10
)
+
+
+
6
6 6 6 6
(C H10) (C H10Br ) (C H10Br ) (C H10Br )
C1-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-C1
C1-H
1.34
1.51
1.53
1.53
1.53
1.51
1.09
1.1
1.335
1.504
1.515
1.550
1.515
1.504
1.093
1.093
1.334
1.502
1.515
1.537
1.515
1.502
1.1
1.1
123.4
111.9
110.9
118.3
110.3
118.3
1.343
1.526
1.544
1.542
1.544
1.526
1.364
1.525
1.548
1.547
1.548
1.525
1.108
1.112
123.3
111.9
110.9
117.5
109.5
119.2
C1-C2
C2-C3
C3-C4
C4-C5
C5-C6
C6-C1
C1-H
1.364
1.525
1.548
1.547
1.548
1.525
1.108
1.112
1.363
1.522
1.560
1.568
1.560
1.522
1.107
1.115
1.447
1.523
1.556
1.546
1.545
1.511
1.104
1.108
120.73
113.78
110.61
118.40
109.99
2.127
1.473
1.507
1.552
1.567
1.552
1.507
1.104
1.120
118.51
115.61
115.64
118.86
110.20
2.129
1.475
1.514
1.573
1.569
1.572
1.515
1.104
1.105
116.21
105.74
113.30
120.13
110.91
2.120
C6-H
C6-H
C2-C1-C6 123.3
C1-C6-C5 111.6
C6-C5-C4 110.3
C6-C1-H
123.5
123.4
111.8
110.7
C2-C1-C6 123.27 118.37
C1-C6-C5 111.93 110.97
C6-C5-C4 110.91 113.44
C6-C1-H 117.54 120.28
C1-C6-H 109.51 109.07
C1-Br
112.1
111.0
114.0
109.5
122.5
C1-C6-H
C1-C2-H
109.9
119.5
a
b
For the definition of structural parameters, see Figure 1. Micro-
C6-C1-Br
C2-C1-Br
114.55
70.18
116.29
69.78
117.29
69.61
c
d
wave, ref 23. Electron diffraction, ref 24. Electron diffraction, ref
e
f
2
5. GVB calculations, ref 26. This work, B3LYP results.
a
Distances in angstroms, angles in degrees. Results for RHF, BP86,
and BLYP are available as Supporting Information. b For the definition
of structural parameters, see Figures 1-5.
Å. The longer computed bonds are probably due to an
insufficiently flexible set of polarization functions. Of note is
the rather surprising good agreement between both the experi-
mental and DFT values and the ones calculated using the GVB
method with very small basis set; this agreement is most likely
due to the cancellation of errors, the limited electron correlation
effects via GVB leading to distances that are too short and the
unpolarized basis set giving ones too long.
shorter that the ones obtained using methods that include
electron correlation effects; the three DFT methods give very
similar geometrical structures. The B3LYP exchange functional,
which contains a contribution from the Hartree-Fock exchange,
gives distances shorter than those obtained with the other two
functionals. The largest deviation is only about 0.04 Å for the
computed bond lengths and less than 0.6° for the angles. Table
illustrates the lengthening of the C1-C2 bond upon bromi-
nation, from 1.36 Å, characteristic of the double C-C bond to
.47 Å, shorter than the typical single C-C bond of about 1.55
Å. Compared with their values in the lowest-energy twist
conformation, the bond lengths of C-C bonds increase in the
distorted boat structures.
While the structure of the ion has not been determined
experimentally, there were several studies of the geometry of
The calculated (for the twist conformer) and experimental
infrared spectra of cyclohexene are compared in Figure 6. The
agreement is remarkable and allows for unambiguous assign-
ment of all the major peaks in the spectrum. In the analysis,
the harmonic vibrational modes, as calculated using the Gaussian
94 program, were visualized with the help of programs
4
1
2
7
28
MOLDEN and MacMolPlt. The assignment of the more
prominent peaks is shown in Table 6. It must be stressed here,
as it will prove important in the analysis of the isotope effects,
that apart from the 10 modes corresponding to the CH stretches,
all other vibrations present a complex mixture of CH2 bends
and CC stretches leading to the ring puckering motion.
For the twist conformers, the effects of isotopic substitution
on the equilibrium constant in the gas phase, K /K , computed
23
cyclohexene, using both microwave and electron diffrac-
tion2
cyclohexene are compared with the experimental values in Table
. The table also shows the results obtained in GVB calculations
4,25
techniques. The calculated structural parameters for
5
26
that employed the minimal basis set STO-3G. The B3LYP
results agree reasonably well with the experimental data. While
the bond angles are very close to the ones determined
experimentally, the bond lengths are longer by as much as 0.02
D
H
at 298.15 K and 1 atm pressure, are compared in Table 7 with
the experimental values of k /k as obtained in the bromination
of cyclohexene in MeOH at 25 °C (298.15 K). There is
considerable agreement between the calculated and experimental
magnitudes of the isotope effects. As was the case in the
D
H
(
23) Scharpen, L. H.; Wollrab, J. W.; Ames, D. P. J. Chem. Phys. 1968,
4
9, 2368.
(
(
24) Chiang, J. F.; Bauer, S. H. J. Am. Chem. Soc. 1969, 91, 1898.
25) Geise, H. J.; Buys, H. R. Recl. TraV. Chim. Pays-Bas 1970, 89,
(27) Schaftenaar, G. QCPE Bulletin 1992, 12, 3 (available from http://
www.caos.kun.nl/∼schaft/molden).
1
147.
26) Verbeek, J.; Van Lenthe, J. H.; Timmermans, P. J. J. A.; Mackor,
A.; Budzelaar, P. H. M. J. Org. Chem. 1987, 52, 2955.
(
(28) MacMolPlt is available from http://www.msg.ameslab.gov/GAMESS/
Graphics/MacMolPlt.html.

Bromination of Deuterated Cyclohexenes
J. Am. Chem. Soc., Vol. 120, No. 11, 1998 2583
10. The intensity units are D Da-1Å-2 for the calculated
2
Figure 6. Calculated (unscaled BP86) and experimental (neat film) IR spectra of C
6
H
spectrum, arbitrary units for the experimental spectrum.
Table 6. Assignment of the IR Spectrum of the Twist Conformer
Table 7. Calculated EDIE (K
Br T Cyclohexenyl bromonium ion at 298.15 K and 1 atm
D
/K
H
) for the Process Cyclohexene +
a
+
of C
6 10
H
experimentalb calculatedc
assignmentd
K
/K
D H
BP86 BLYP B3LYP k /k
experimentalb
D
H
olefin
RHFa
6
7
8
42
20
75
614
689
865
out-of-plane CH bending at C
out-of-plane CH bending at C
1
1
,C
,C
2
2
D
D
D
D
D
D
D
10 (1) 2.78 (3.28) 1.41
1.41
1.15
1.01
1.23
1.11
1.05
1.07
1.48
1.18
1.04
1.25
1.12
1.05
1.07
1.45(0.18)
1.10(0.15)
0.97(0.15)
1.31(0.17)
1.18(0.15)
ring deformation: C
and C shorten
rocking CH at C ,C , twisting CH
at C ,C
ring deformation: C
and C shorten
1 6 5 6
C and C C stretch,
8
4
2
1
2
2
(3) 1.96 (2.19) 1.14
(2) 1.37 (1.47) 1.02
(4) 1.37 (1.50) 1.23
(5) 1.15 (1.23) 1.11
syn 1.15 (1.21) 1.05
anti 1.15 (1.22) 1.07
C
2
C
3
3 4
C
9
18
878
2
3
6
2
4
5
1
036
1012
1 6 3 4
C and C C stretch,
C
2
C
3
5 6
C
1137
1267
1322
1439
1095
1227
1310
1389
twisting CH
twisting CH
twisting CH
2
2
2
at C
at C
at C
3
3
3
-C
-C
6
6
a
Scaling factor of 0.89 used for calculated harmonic vibrational
frequencies. (Unscaled results given in parentheses.) Experimental
results, kinetic deuterium isotope effect, k /k , this work, see Table 3.
-C6
b
out-of-phase scissoring CH
2
at C
at C
, C
3
, C
, C
6
D
H
1
1
405
418
out-of-phase scissoring
s
CH
2
4
5
in-phase scissoring
s
CH
2
at C
4
5
in agreement with the experiment, the largest contribution to
the EIE is due to the substitution of the two hydrogens at the
vinyl R-carbon atoms (4), with KD/KH ) 1.28. The next largest
contribution comes from the substitution of eight hydrogens in
D8, KD/KH ) 1.19. Substitution of four hydrogens at positions
1654
2841
2859
1664
2904
2930
CdC stretch
out-of-phase stretching
in-phase stretching CH
out-of-phase stretching
s
CH
2
at C
, C
at C
3
, C
6
5
s
2
at C
4
5
2
931
s
CH
2
4
, C
2
2
889
928
2959
2987
stretching asCH
stretching asCH
stretching asCH
2
2
2
at C
at C
at C
3
4
4
, C
, C
, C
6
5
5
3
and 6 (2) is calculated to give a modest inverse isotope effect,
2
993
3049
073
3
025
out-of-phase stretching CH at C
in-phase stretching CH at C , C
2
1
, C
2
KD/KH ) 1.06, while experimentally a negligible normal isotope
effect is found. However, both the experimental and calculated
values are very close to unity. Given that the effect at â-carbons
in D4 is so small, we calculated (using the BP86 data) the EIE
for only the γ-carbons 4 and 5 (see Figure 1). We found a
rather large KD/KH ) 1.12, comparable to that in the D8
isotopomer, where the isotopic substitution was done at both
â- and γ-carbons. Given that the Hessian matrixes were
available, it was worthwhile to investigate the nature of this
3
1
a
Frequencies are in cm-1. b The small peaks at 2659, 2986, and 3064
cm-1 are not due to the fundamental transitions. Calculated BP86
c
d
harmonic vibrational frequencies were not scaled. See Figure 1 for
the numbering of atoms. The subscripted “s” and “as” refer to symmetric
and antisymmetric modes of vibration.
molecular geometries, the various functionals predict essentially
the same isotope effects. The results of calculations show that,

2584 J. Am. Chem. Soc., Vol. 120, No. 11, 1998
Slebocka-Tilk et al.
Table 8. Factorization of the Calculated EDIE into Bending and Stretching Contributions (BP86 Functional)
bend
stretch
δE a
bond
ZPE
stretch
ZPE
b
/K c
olefin
F
Q
δE0
δE0
0
F
F
F
ZPE
K
H
D
H D
K /K
D10 (1)
D8 (3)
D4 (2)
D2 (4)
D1 (5)
1.13
1.03
1.02
1.10
1.05
1.00
1.01
0.67
-0.02
-0.10
0.70
0.35
0.01
0.48
1.15
0.41
0.10
0.75
0.37
0.12
0.18
0.76
1.01
1.04
0.75
0.87
1.00
0.97
0.82
0.84
0.92
0.98
0.99
0.95
0.96
0.63
0.85
0.96
0.74
0.86
0.95
0.93
0.71
0.87
0.98
0.81
0.90
0.96
0.94
1.41
1.14
1.02
1.23
1.11
1.05
1.07
0.43
0.21
0.05
0.02
0.12
0.11
D
D
2
syn
anti
2
0.07
a
Y
O
X
O
) δEO + δEO . b FZPE ) e-(δOYE - δOXE)/RT see eq 1, note that FZPE ) FZPE . c
bend
stretch
bend stretch
δE
ZPE
O
≡ δE - δE see eq 1; note that δE
O
F
K
H
/K
D
)
ZPE
F
Q
F
.
Table 9. Analysis of the Stretching Modes in the D
8
Isotopomer (Calculated Using the BP86 Functional)a
product
reactant
ν(C
6
H
10
)
ν(D
8
-C
6
H
10
)
∆
ν
(R)b
ν(C
6
H
10Br+)
ν(D
8
-C
6
H
10Br+)
∆
ν
(P)b
∆(∆
ν
)c
2903
2904
2929
2931
2959
2959
2987
2993
3049
3073
2117
2117
2139
2134
2189
2190
2214
2220
3049
3073
786
787
790
797
770
769
773
773
0
2894
2948
2960
2968
2995
3011
3033
3039
3066
3077
2115
2150
2162
2164
2216
2224
2248
2253
3066
3077
779
798
798
804
779
787
785
786
0
-7
11
8
7
9
18
12
13
0
0
0
0
a
All values in cm-1. b
ν ν ν
) ν - ν(D ) ) ∆ (P) - ∆ (R).
). c ∆(∆
∆
ν
8
unusually large isotope effect at the γ-carbons in order to answer
the question if the effect could be of steric origin. To this end,
the EIEs were calculated for two deuteriums at the syn positions
are shown in Table 8. In the Table, the values of FZPE < 1
lead to inverse isotope effects, while FZPE > 1 gives normal
isotope effects; FZPE = 1 implies no effect in the equilibrium
constant upon deuteration. In other words, FZPE < 1 indicates
that in the deuterated product the vibrating atoms experience a
(with respect to bromine), D2-syn, and for two deuteriums at
anti positions, D2-anti (Table 7). The EIEs arising from both
of these arrangements are essentially equal at all levels of theory,
ruling out steric origins of the remote γ isotope effect.
It must be added that while different experimental environ-
ments produce slightly different values for the KIE (see Tables
steeper potential energy function than in the deuterated reactant.
Y
Note that the value of FZPE is tied to the magnitude of δE -
O
X
O
δE , as in eq 1. The results in Table 7 show that there are
almost no bending contributions to the EIE for both D8 and D4
isotopomers; all EIEs arise from the changes in the vibrational
frequencies of the stretching vibrations. The situation is
reversed for the bis- and mono-deuterated species, D2 and D1,
where the stretching vibrations virtually do not affect the
computed EIE. With only eight modes to compare, the D8
system afforded data for a more detailed analysis of the origins
of the EIEs in that system. The results are collected in Table
1
and 2), both experiment and theory predict very similar
ranking of the magnitude of the isotope effects: from experi-
ment, D10 > D2 > D1 ≈ D8 > D4; according to computations,
D10 > D2 > D8 > D1 > D4.
The most anticipated benefit of the computational part of the
present work was to identify the modes that are responsible for
the large inverse EIE. Given that the cyclohexene system gives
rise to numerous soft vibrational modes in which the ring
puckering vibrations are mixed with the rocking, twisting, and
wagging vibrations of the methylene units, this task proved
impossible. It was difficult to establish a unique one-to-one
correspondence between the reactant and product vibrations.
Analysis of the individual contributions to the values of KH/KD
indicates that the factor due to the partition function, FQ, deviates
only slightly from unity; the bulk of the EIE is carried by the
factor FZPE, which reflects the differential changes in the
vibrational zero-point-energy for the reactant and product upon
deuteration. To gain some insight into the origin of the isotope
effects, we partitioned all vibrations according to their stretching
and bending characteristics, and decomposed δE0 and FZPE
accordingly. Only the C-H stretches could be unambiguously
identified. Consequently, two groups of modes were defined;
in the first group all ten C-H stretches were included; the
second group contained all the remaining modes, predominantly
bending modes that were, however, coupled with some stretches
of the C-C bonds in the cyclohexane ring. The contributions
from the two groups of vibrations, the C-H stretches on one
side and all the remaining modes on the other, to the overall
EIE were then evaluated separately. The results of the analysis
9
in the form of matching stretches in both the product and
reactant systems, together with the differences ∆ν(R) and ∆ν(P),
showing the reduction of fundamental frequencies upon deu-
teration in each of them. In addition, the table shows the
difference between the reductions of frequencies for products
and reactants. Each of the eight CH stretches that dominate
the EIE in the D8 isotopomer is reduced upon deuteration more
+
in C6H10Br than in C6H10. The average extra reduction of the
frequencies in the ion as compared with cyclohexene is small,
-
1
less than 9 cm , leading to the overall contribution to FZPE of
1
-1
-1
(
/2)(8)(9) cm ) 36 cm ) 0.43 kJ/mol (to be compared
with the value of 0.41 kJ/mol from the direct calculation, see
Table 8). Most importantly, it may be seen from the table that,
even though it is the CH stretching vibrations that generate the
EIE, no single CH stretching vibration is exclusively responsible
for the EIE in the D8 system. In conclusion, it must be stressed
that the isotope effects in the cyclohexene system result from
complex interactions between all vibrational modes, in contrast
with the simplified picture often presented in textbooks.22
Two models were proposed in the past to explain the origin
of the secondary R-deuterium isotope effect. The older

Bromination of Deuterated Cyclohexenes
J. Am. Chem. Soc., Vol. 120, No. 11, 1998 2585
interpretation suggested by Streitwieser et al.29 considers the
change of some CH vibrational modes due to rehybridization:
effect is associated with the two vinyl hydrogens. One-third
of the effect is associated with the four homoallylic hydrogens
while the allylic hydrogens contribute almost nothing. An
alternative mass spectroscopic method of determining the DKIE
provides data consistent with that obtained from the kinetic
experiments. Unfortunately, the inherent experimental errors
associated with each of the above techniques for measuring the
DKIEs limit the certainty of the results and hence the ability to
make conclusions concerning the positional origins of the
experimental DKIE. Extensive density functional computations
of the equilibrium isotope effect (EIE) for the cyclohexene +
2
3
in a reaction that involves sp to sp rehybridization at the
R-carbons an inverse secondary isotope effect should be
observed. A more recent, alternative explanation of the second-
ary isotope effects was offered by Strausz et al.30 who attributed
the effect to the creation of new, isotopically sensitive, vibrations
in the transition state. The case of bromination of cyclohexene
does not seem to fall into either category. While there is no
2
doubt that the R-carbons in cyclohexene are sp hybridized as
the sum of relevant angles around each R-carbon is 360°, the
sum of the angles is 356° in the cyclohexenyl bromonium ion,
+
Br h cyclohexenebromonium ion equilibrium confirm the
3
quite far from the value of 330° expected for an ideally sp -
relative magnitude of the DKIE’s obtained from the solution
studies. From an experimental standpoint the cyclohexene
system cannot be considered large or complex. Nevertheless,
from a computational standpoint, due to the extensive mixing
of ring deformations and CH stretching and bending, it proved
impossible to identify all the unique vibrational modes in the
reactants and products that are responsible for the EIE. The
computations indicate that for the D8 and D4 isotopomers the
effect is almost entirely associated with the changes in all C-H
stretching (but not bending) frequencies which are larger upon
deuteration in the ion relative to the starting material. Impor-
tantly, due to the heavy mixing of these modes, no single C-H
stretch can be identified as the major contributor. Conversely,
the large effects noticed for the vinyl hydrogens, in D1 and D2,
show almost no isotopic sensitivity to changes in the C-H
stretching frequencies, but are instead largely associated with
the changes in all the remaining vibrations different from the
+
hybridized carbon atom. The new modes in C6H10Br that may
be associated with the three-membered ring BrCC appear in
-
1
the lowest frequency region, 90-400 cm . They are always
inseparable from the motion of the cyclohexene ring, perhaps
due to the accidental matching of the atomic mass of bromine
(80 Da) and the molecular mass of C6H10 (82 Da). Of the six
modes that display large contributions from the bromine
displacement, the bending modes (toward the cyclohexene ring)
are almost insensitive to isotopic substitution at the carbon atoms
C1 and C2. Of the BrC stretching modes, the deformation of
the BrCC ring remains essentially unchanged while the ring
-
1
breathing mode is reduced by 7 cm . Given the complexity
of the cyclohexene bromonium ion, as compared with the
systems studied by Strausz et al.,30 it is perhaps not surprising
that no simple picture emerged. A clearer picture could perhaps
3
1
be obtained in the studies of the bromination of ethylene.
1
0 C-H stretches.
Conclusions
The above study was undertaken to identify more clearly the
origins of the DKIE’s associated with electrophilic bromination
of cyclohexene and its various isotopomers and shows a nice
complementarity of experiment and theory. Kinetic measure-
ments based on the rate of disappearance of Br2 indicated that
there is a large inverse DKIE of about 1.4-1.5 for the
bromination of perdeuteriocyclohexene relative to cyclohexene
in MeOH. Attempts to sort out the positional substitution effects
by looking at the DKIEs for Br2 addition to various selectively
deuterated isotopomers suggested that roughly two-thirds of the
Acknowledgment. The calculations were done on the RS/
000 workstations and on the SP2 installation at the University
6
of Alberta. This work was financed partly by research grants
from NSERC to M.K. and R.S.B., and partly by the University
of Alberta and Queen’s University. Assistance of Mr. J. Hoyle
from the Spectral Services Laboratory at the Department of
Chemistry, University of Alberta, is gratefully acknowledged.
We are also grateful for the helpful suggestions of the referrees.
Supporting Information Available: Structural parameters
and atomic coordinates for conformers of cyclohexene and
cyclohexenyl bromonium ion (10 pages). See any current
masthead page for ordering information and Web access
instructions.
(
29) Streitwieser, A., Jr.; Jagow, R. H.; Fahey, R. C.; Suzuki, S. J. Am.
Chem. Soc. 1958, 80, 2326.
30) Strausz, O. P.; Safarik, I.; O’Callaghan, W. B.; Gunning, H. E. J.
Am. Chem. Soc. 1972, 94, 1828. Safarik, I.; Strausz, O. P. J. Phys. Chem.
972, 76, 3613.
31) Klobukowski, M.; Gainsforth, J. L.; Koerner, T.; Brown, R. S. To
be published.
(
1
(
JA971145H