Noncatalytic bromination of benzene: A combined computational and experimental study

Article abstract of DOI:10.1002/jcc.23985

The noncatalytic bromination of benzene is shown experimentally to require high 5-14 M concentrations of bromine to proceed at ambient temperatures to form predominantly bromobenzene, along with detectable (<2%) amounts of addition products such as tetra and hexabromocyclohexanes. The kinetic order in bromine at these high concentrations is 4.8 ± 0.06 at 298 K and 5.6 ± 0.11 at 273 K with a small measured inverse deuterium isotope effect using D₆-benzene of 0.97 ± 0.03 at 298 K. These results are rationalized using computed transition states models at the B3LYP+D3/6-311++G(2d,2p) level with an essential continuum solvent field for benzene applied. The model with the lowest predicted activation free energies agrees with the high experimental kinetic order in bromine and involves formation of an ionic, concerted, and asynchronous transition state with a Br₈ cluster resembling the structure of the known Br₉^-. This cluster plays three roles; as a Br⁺ donor, as a proton base, and as a stabilizing arm forming weak interactions with two adjacent benzene C-H hydrogens, these aspects together combining to overcome the lack of reactivity of benzene induced by its aromaticity. The computed inverse kinetic isotope effect of 0.95 agrees with experiment, and arises because C-Br bond formation is essentially complete, whereas C-H cleavage has not yet commenced. The computed free energy barriers for the reaction with 4Br₂ and 5Br₂ for a standard state of 14.3 M in bromine are reasonable for an ambient temperature reaction, unlike previously reported theoretical models involving only one or two bromines.

Full text of DOI:10.1002/jcc.23985

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Noncatalytic Bromination of Benzene: A Combined
Computational and Experimental Study
[
Andrey V. Shernyukov, Alexander M. Genaev,* George E. Salnikov,
a]
[a]
[a,b]
[c]
Henry S. Rzepa,*
[
a]
and Vyacheslav G. Shubin
2
The noncatalytic bromination of benzene is shown experimen-
tally to require high 5–14 M concentrations of bromine to pro-
ceed at ambient temperatures to form predominantly
bromobenzene, along with detectable (<2%) amounts of addi-
tion products such as tetra and hexabromocyclohexanes. The
kinetic order in bromine at these high concentrations is
resembling the structure of the known Br
9
. This cluster plays
1
three roles; as a Br donor, as a proton base, and as a stabiliz-
ing arm forming weak interactions with two adjacent benzene
CAH hydrogens, these aspects together combining to over-
come the lack of reactivity of benzene induced by its aroma-
ticity. The computed inverse kinetic isotope effect of 0.95
agrees with experiment, and arises because CABr bond forma-
tion is essentially complete, whereas CAH cleavage has not
yet commenced. The computed free energy barriers for the
4
.8 6 0.06 at 298 K and 5.6 6 0.11 at 273 K with a small meas-
ured inverse deuterium isotope effect using D -benzene of
6
0
.97 6 0.03 at 298 K. These results are rationalized using com-
puted transition states models at the B3LYP1D3/6-
1111G(2d,2p) level with an essential continuum solvent field
2 2
reaction with 4Br and 5Br for a standard state of 14.3 M in
bromine are reasonable for an ambient temperature reaction,
unlike previously reported theoretical models involving only
3
for benzene applied. The model with the lowest predicted
activation free energies agrees with the high experimental
kinetic order in bromine and involves formation of an ionic,
one or two bromines. V
C
2015 Wiley Periodicals, Inc.
DOI: 10.1002/jcc.23985
concerted, and asynchronous transition state with a Br cluster
8
polar acidic media and/or Lewis acid catalysis are essential to
accelerate the reaction to an observable rate. The main pur-
pose of the present report is to explore further low energy
mechanistic pathways for the uncatalyzed reaction between
benzene and bromine and to establish if the computational
models are supported by experiment.
Introduction
Electrophilic substitution of aromatic compounds, including
halogenation, is typically described by a two-stage mechanism
with formation of a Wheland (arenium cation) intermediate at
[
1]
[2]
the first stage of the reaction. However, in a recent paper,
an alternative addition–elimination (A ) mechanism for electro-
philic substitution, first proposed about a 100 years ago, has
been firmly established for the chlorination of anisole by Cl
CCl . It is of interest to reveal if such a mechanism takes place
E
[
3]
in Experimental Results for Reaction Between
2
4
Bromine and Benzene
in the case of noncatalytic bromination of benzene itself. This
reaction is unusual, as bromination of aromatic compounds
with bromine is usually performed in the presence of a cata-
The kinetics of the reaction were studied at a large excess of
bromine and/or at low benzene conversion, so that the
change in the concentration of bromine could be neglected. It
was found that under these conditions, the order of the reac-
tion in benzene was pseudo first order, but that the rate of
[4]
lyst. The apparent inability of benzene to be involved in a
noncatalytic reaction with bromine is noted in numerous text-
[5]
books (see also the Supporting Information for more exam-
ples) and is regarded as a dogma of aromaticity. To the best
of our knowledge, there is only one article in which informa-
tion on the noncatalytic bromination of benzene under mild
[
a] A. V. Shernyukov, A. M. Genaev, G. E. Salnikov, V. G. Shubin
N.N. Vorozhtsov Novosibirsk Institute of Organic Chemistry, Siberian
Branch of the Russian Academy of Sciences, 9, Acad. Lavrentiev Ave.,
Novosibirsk, 630090, Russian Federation
[
6]
[7]
(
i.e., at ambient rather than reflux ) conditions is presented.
8]
E-mail: genaev@nioch.nsc.ru
[
In a more recent paper, the uncatalyzed electrophilic bromi-
nation of aromatics in supercritical CO2 has been described,
[
[
b] G. E. Salnikov
Novosibirsk State University, Pirogova, 2, Novosibirsk 630090, Russian
Federation
with the suggestion that the efficiency of the CO in this reac-
2
c] H. S. Rzepa
tion is due to its high quadruple moment, Lewis acid character
9]
Department of Chemistry, Imperial College London, Exhibition Road, South
Kensington Campus, London SW7 2AZ, United Kingdom.
E-mail: rzepa@imperial.ac.uk
[
and low basicity. A recent theoretical study of the interaction
of benzene and other aromatic compounds with bromine in
4
the nonpolar solvent CCl or in isolation concluded that the
We dedicate this article to Paul Schleyer, who was a passionate advo-
cate of the fertile interplay between computation and experiment.
energetic barriers for benzene bromination under such condi-
tions are too high for practicable mechanistic studies and that
V
2015 Wiley Periodicals, Inc.
C
2
10
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Table 1. Dependence of pseudo first order rate constant on Br
concentration (at 298 K, with 0.2 volume fraction of CD Cl ).
2
2
2
2
1
Volume fraction of Br
2
Concentration of Br
2
(M)
1
k , s
2
2
2
2
2
2
4
5
5
6
7
9
0
0
0
0
0
0
.74
.60
.43
.29
.18
.084
14.3
11.5
8.3
2.3 3 10
7.4 3 10
1.5 3 10
2.6 3 10
1.9 3 10
6.9 3 10
5.7
3.5
1.6
2
the reaction increased dramatically with increasing Br concen-
tration (Table 1, Scheme 1; full experimental details can be
found in the Supporting Information).
The order of the reaction in bromine was determined by a
[
10]
differential method
using the kinetic eqs. (1) and (2) relating
a pseudo first order reaction to a formal reaction of order
n11, respectively. From these equations, we obtained eq. (3).
Figure 1. Determination of the reaction order in bromine. [Color figure can
be viewed in the online issue, which is available at wileyonlinelibrary.com.]
2
d½PhHꢀ=dt ¼ k1½PhHꢀ
d½PhHꢀ=dt ¼ kn11½PhHꢀ½Br2ꢀ
log k1 ¼ n log½Br2ꢀ1log kn11
(1)
(2)
(3)
n
2
the bromine concentration increases this dependence
slightly (Fig. 1, Supporting Information p. S4)
3. Replacing pure benzene with a 1:5 by volume mixture of
From the kinetic data inserted into eq. (3), we infer a reac-
benzene and CCl at constant amount of bromine does not
4
tion order in bromine of 4.8 6 0.06 at 298 K and 5.6 6 0.11 at
2
73 K (Fig. 1). According to these data, the rate of benzene
significantly affect the reaction rate constant. More polar
bromination proceeding under mild conditions without any
solvent or catalyst is high enough to be measured if a large
concentration of bromine is used, the order of the reaction in
bromine being about 5. We have excluded the following fac-
tors as contributing significantly to these rates.
methylene chloride (CD
2 2
Cl ) or traces of water markedly
accelerate the reaction (Supporting Information, p. S4).
4. After keeping the reaction mixture for longer times at
high bromine concentrations, traces of p- and o-dibro-
mobenzenes are slowly formed (Supporting Information,
pp. S7, S9), the kinetics of such polybromination being
beyond the present study.
1. Catalysis by HBr produced by the reaction. (The autocata-
lytic effect of HCl formed as one of the reaction products
[
was observed experimentally for anisole chlorination and
2]
[
11]
Computational Modeling
studied theoretically for benzene chlorination:
However,
the presence of formed HBr does not influence the benzene
bromination rate during the whole time course of the reac-
tion [see e.g., Supporting Information, pp. S6–S7]).
. Catalysis by light.
Our start point involved a search of the Cambridge crystallo-
graphic database for likely structures involving aggregated ani-
onic bromine clusters, the outcomes in any initial formation of
a putative Wheland intermediate (arenium ion). Unlike iodine,
which forms linear zig–zag chains, bromine appears to favor
bromine-centered dendrimer-like clusters, with two recent
crystal structures shown in Figure 2.
2
3
. Catalysis by triplet oxygen.
Further attributes of this reaction include:
1
. The kinetic isotope effect k /k measured for a mixture
H D
1
2
6 6 6 6
of C H and C D by H and H NMR spectra was found
Computational Methodology
to be 0.97 6 0.03 (1r, Supporting Information, pp. S10–
S12).
The potential energy surface (PES) of benzene bromination
characterizing the S Ar and AdE mechanisms is potentially
E
2
. The reaction has only a weak dependence on tempera-
3
00
273
complex, even assuming only one bromine molecule is
involved in the reaction. As the number of participating bro-
mine molecules increase, the PES becomes more complex. At
the initial stage of our calculations therefore, a fast DFT code
ture: k1 /k1 5 1.3 at a concentration of 14.3 M bro-
mine (Supporting Information, pp. S7–S9). A decrease in
[
14]
as implemented in the PRIRODA program
pathfinder, using a gas-phase model (See zip-archive in Sup-
was used as a
[
15]
porting Information).
This led us to conclude that reinvesti-
gation using a solvent model was essential, as many of the
identified stationary points so located were found to have
Scheme 1.
Journal of Computational Chemistry 2016, 37, 210–225
211

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2
9
[12]
2
[13]
˚
cluster b) Br11 cluster. Bond lengths in A. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Figure 2. a) Br
Table 2. Computed properties for transition state models for the reaction between bromine and benzene.
[a]
H D
k /k , 298 K
[b]
System
DDG298 @0.041 M
DDG298 @14.3 M
Data DOI
Separated Benzene 1 1 Br
2
0.0
0.0
21.7
42.5
189806, 189804
189804, 189806
189612, 189704
189495, 189638
189621
Benzene 1 1Br
2
1.8 (3.2)
46.0 (50.9)
44.3 (47.3)
S
S
S
S
E
Ar reaction, Cs symmetry, 2 negative force constants
E
Ar reaction, C1 symmetry, 1 negative force constants
E
Ar reaction, Cs symmetry, 2 negative force constants, biradical
E
Ar reaction, C1 symmetry, 1 negative force constants, biradical
e
40.8
36.2
0.75
0.84
0.83
39.7
38.6
35.1
39.4
189517
Ad
Ad
E
, cis-1,2-addition
, cis-1,2-addition, biradical
42.9 (47.5)
37.9
19.3
189500, 189555
191199
191202
E
34.4
15.8
cis-1,2-dibromocyclohexadiene
trans-di-axial-1,2-dibromocyclohexadiene
trans-di-equatorial-1,2-dibromocyclohexadiene
Bromobenzene 1 HBr
14.0 (12.4)
22.0
10.5
18.5
189526, 189706
189529
29.9 (211.9)
212.7 (215.0)
4.6 (5.0)
27.4 (30.2)
33.8 (37.1)
31.8
213.3
212.7
22.3
20.5
189535, 189711
189535, 189711
189501, 189612
189554, 189703
189498, 189598
189496
Separated Bromobenzene 1 HBr
Benzene 1 2Br
Benzene 1 Br
Ar reaction, C
2
4
S
E
s
symmetry, 2 negative force constants
26.9
Ad
E
Ad
E
Ad
E
Ad
E
Ad
E
, trans-1,2-addition
, cis-1,4-addition
24.9
24.5
31.4
29.3
189497
189516
, trans-1,4-addition, first CABr
, trans-1,4-addition, Wheland intermediate
, trans-1,4-addition, second CABr
22.4
16.8
23.7
30.5
189524
189515
23.6
10.3
trans-1,4-dibrobromocyclohexadiene 1 Br
cis-1,4-dibrobromocyclohexadiene 1 Br
trans-1,2-dibrobromocyclohexadiene 1 Br
Bromobenzene 1 HBr 1 1Br
Separated Bromobenzene 1 HBr 1 1Br
Benzene 1 3Br
2
17.2
19.4
189537
189544
189538
2
12.5
2
16.3
9.4
2
25.5 (27.6)
212.7 (215.0)
7.8
212.4
212.7
22.6
19.7
189539, 190787
189535, 189711
189505
2
2
S
S
E
Ar concerted substitution, C
Ar concerted substitution, C1, 1 negative FC
, trans-1,2-addition
s
, 2 negative FC
30.1
26.6
191206
191257
E
16.2
15.8
0.94
0.91
Ad
E
26.2
28.7
191204
191224
S
S
S
E
Ar stepwise substitution, CABr bond formation
E
Ar stepwise substitution, Wheland intermediate
E
Ar stepwise substitution, proton removal
18.3
7.2
17.6
21.9
191230
189581
11.5
6.8
trans-1,2-dibrobromocyclohexadiene 1 2Br
Bromobenzene 1 HBr 1 2Br
Separated bromobenzene 1 HBr 1 2Br
Benzene 1 4Br
2
20.3
21.2
212.7 (215.0)
12.2
189528
189599
2
211.6
212.7 (215.0)
21.7
22.6
2
2
189750
189722
191241
189771
S
S
E
Ar concerted substitution, C
Ar concerted substitution, C
s
, 1 negative FC
, 1 negative FC
36.5
26.5
0.93
0.95
E
s
12.6
Bromobenzene 1 HBr 1 3Br
Separated bromobenzene 1 HBr 1 3Br
Benzene 1 5Br
2
12.0
212.7 (215.0)
15.7
211.9
212.7 (215.0)
21.7
18.2
2
2
189768
189705
191237
191238
191236
189767
S
S
E
Ar concerted substitution, C
s
, 2 negative FC
35.6
32.0
E
Ar stepwise substitution, CABr formation
14.6
3.9
0.95
TS
TS
E
Ar stepwise substitution, Wheland intermediate
21.3
22.2
E
Ar stepwise substitution, proton removal
4.8
Bromobenzene1HBr 1 4Br
Separated bromobenzene 1 HBr 1 3Br
2
7.0
212.7 (215.0)
210.4
212.7 (215.0)
2
[a] B3LYP1D3/6-31111G(2d,2p)/SCRF 5 benzene (B2PLYPD3/6-31111G(2d,2p)/SCRF=benzene). Relative free energies in kcal/mol, for a standard state
of 0.041M. [b] A digital repository identifier (DOI), resolved as e.g. http://doi.org/10.14469/ch/189499.
2
12
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Figure 3. IRC computed for the synchronous asymmetric S Ar reaction between benzene and 1Br on a closed-shell pathway, showing a) the energy profile
and b) the energy gradient norm. The red arrow indicates the region of a hidden intermediate approximately corresponding to an arenium cation. [Color
figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
E
2
calculated dipole moments >10D. Accordingly, these were
then reinvestigated at a higher level with inclusion of a solva-
tion correction as described below. Transition state models
similar and that mixed-solvent models are not readily sup-
ported. Selected models for n 5 1 and 2 Br2 units were then
checked by reoptimization at the B2PLYP1D3 double-hybrid
[
19]
based on n 5 1–5 Br
2
units were constructed in this manner,
method
using the same basis set and solvation model
informed by the observed reaction order in bromine of ꢁ5 at
(such a calculation is too expensive for larger clusters, and
especially so for characterization using an intrinsic reaction
coordinate [IRC]) The B2PLYP1D3 barriers obtained were only
ꢁ3 kcal/mol higher than the B3LYP method. IRCs leading
from the transition states at the B3LYP-level established the
nonstochastic trajectories, leading to reactant and product for
all transition states. The relative total energies along the reac-
tion paths are presented in Table 2 for standard states of 1
atm (0.041 M) and 350 atm (14.3 M).
high concentrations and the structural motifs shown in Figure
2
. Our chosen computational model used the B3LYP density
[
16]
functional as implemented in the Gaussian program,
which
is a thoroughly explored method for a wide variety of reac-
tions, and combined with the 6–31111G(2d,2p) basis set
[
used in the earlier study of this system. We have also added
9]
[
17]
Grimme’s D3 dispersion correction
plus and York smoothed-cavity self-consistent reaction field
together with the Kar-
(
SCRF) continuum solvation model with benzene specified as
We next discuss individually the results obtained for each of
[18]
the solvent.
We retained the benzene continuum solvation
noting that the dielec-
tric constants of liquid bromine (ꢁ3) and benzene (2.3) are
the five models of (Br
2 n
) . Full interactive 3D models of all the
model for higher mole fractions of Br
2
stationary points, along with animations of the IRCs are avail-
[
able in the interactive version of Table 2.
20]
Journal of Computational Chemistry 2016, 37, 210–225
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Figure 4. IRC computed for the synchronous asymmetric S
E
2
Ar reaction between benzene and 1Br on an open-shell pathway, showing a) the energy profile
˚
with the computed structure (lengths, in A) shown as an inset, b) the energy gradient norm. The red arrow indicates the region of a hidden intermediate
approximately corresponding to a biradical comprising a bromine atom and bromocyclohexadienyl radical. [Color figure can be viewed in the online issue,
which is available at wileyonlinelibrary.com.]
intermediate, although there is a clear sign of the arenium cat-
Benzene 1 1Br
2
[21]
ion participating as a so-called hidden intermediate (Fig. 3b).
Another characteristic is the relatively flat potential in the region
The stationary point for the S Ar mechanism located when a
E
plane of symmetry is imposed shows as a second-order saddle
point. If an IRC is computed based on the most negative force
constant, an entirely concerted single-stage profile emerges
rather than the classical two stage one involving the Wheland
of the transition state with v having the relatively low value of
I
2
64i cm . The second negative force constant (8i cm ) corre-
[1]
21
sponds to deviation from C symmetry, and the reason for this
s
emerges most clearly with the product, a hydrogen-bonded
2
14
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Figure 5. IRC computed for the synchronous asymmetric Ad
˚
E
reaction between benzene and 1Br
2
on an open shell biradical pathway, showing a) the
energy profile with the computed structures (lengths, in A) shown as insets, b) the energy gradient norm. The red arrows indicate the region of hidden
intermediates. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
complex between bromobenzene and HBr. The proton of the
latter is directed away from the plane of symmetry toward the
ortho-position of the bromobenzene, induced by the o/p-direct-
ing nature of the bromine substituent. (The positioning of
hydrogen bonds to the aryl ring as determined from crystal
structures can also be used to demonstrate the directing influ-
ence of electron donating and withdrawing groups; H. S. Rzepa,
J. Chem. Ed., submitted. See also http://www.ch.imperial.ac.uk/
rzepa/blog/?p =13962. Accessed 5th May, 2015). A true transi-
tion state with just one imaginary transition mode reveals a
fully concerted, albeit asynchronous reaction with an arenium
for the central region close to the transition state, but closed
shell behavior closer to reactant or product. Although the bar-
rier decreases by about 4.6 kcal/mol compared with a spin-
restricted closed shell calculation, the essential features remain
very similar. These are of an asynchronous S Ar substitution
E
reaction, with the transition state being defined by largely
completed CABr bond formation and CAH bond cleavage
occurring only well after the transition state. Both are on the
same concerted reaction path with again evidence of a hidden
rather than an explicit intermediate, now with biradical rather
than ion-pair character (Fig. 4). The overall energetics corre-
sponds to an exo-energic reaction of 212 to 215 kcal/mol.
[
21]
cation making an appearance only as a hidden intermediate
Fig. 3). The very high barrier to reaction with 1-2Br has already
(
2
E
Ad cis-addition across a double bond was found to corre-
[
2,9]
been remarked upon.
spond to a separate reaction profile. As with the S Ar route, the
E
Such high barriers tend also to be associated with multire-
[
wavefunction manifests biradical character close the transition
21
22]
ference character for the wavefunction.
Indeed, a broken-
I
state (Fig. 5) and v has the rather higher value of 230i cm .
symmetry unrestricted calculation reveals biradical character
The product is cis-1,2-dibromobenzene in which one bromine is
Journal of Computational Chemistry 2016, 37, 210–225
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Figure 6. IRC computed for the synchronous asymmetric S
showing a) the energy profile with the computed transition state structure (lengths, in A) shown as an inset, b) the energy gradient norm and starting from a geometry
with C symmetry and two negative force constants. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
E 2 2
Ar reaction between benzene and 2Br on the closed-shell pathway forming bromobenzene 1 HBr 1 Br ,
˚
s
Benzene 1 2Br
2
axial and the other is equatorial. Remarkably, the axial CABr
˚
bond is significantly lengthened (2.06 A) compared with the
The significant difference for this potential is that the transition
state regions now have closed shell character only. The station-
ary point located when a plane of symmetry is imposed is again
˚
equatorial one (1.98 A), because of hyperconjugation of the
axial CABr bond with the diene leads to partial rearomatization
of the ring. The free energy barrier for this alternative addition
route is only 3 kcal/mol lower than the substitution mechanism;
the height of the barriers means that neither is a feasible ther-
mal reaction.
2
1
a second-order saddle point (v 42 and 17i cm ). The IRC follow-
I
0
ing the more negative force constant vectors (of A symmetry)
E
corresponds to a concerted but asynchronous S Ar mode, in
which CABr bond formation is largely completed prior to any
2
16
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Figure 7. IRC computed for the synchronous asymmetric Ad
2
ent norm. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
E
reaction between benzene and 2Br
-dibromocyclohexadiene showing a) the energy profile with the computed-transition state structure (lengths, in A) shown as an inset, b) the energy gradi-
2
on closed-shell pathway forming trans21,
˚
CAH bond removal, but with no evidence of hidden (ionic)
intermediates (Fig. 6). The free energy barrier (Table 2) is notably
benzene and HBr, which is an exo-energic thermodynamic
sink, the products of this path are endo-energic by ꢁ13 kcal/
mol, with the implication that the reverse free energy barrier
(ꢁ15 kcal/mol) corresponds to a rapid thermal reaction at
ambient temperatures.
reduced compared with the 1Br reaction, but is still too large to
2
be a facile thermal reaction at around room temperatures.
If the symmetry restriction is removed by optimization fol-
0
0
lowing the second negative root vectors of A symmetry, no
Ar path was located. Instead, only the Ad path was identi-
The addition of a second active Br to the system also signifi-
2
S
E
E
cantly increases the complexity of the potential surface. Thus,
fied but with the subtle difference that the product corre-
sponds to trans rather than cis-1,2-addition (Fig. 7), in which
the formation of one CABr bond is again largely complete
and the second is still very incomplete. The transition state
free energy is lowered by ꢁ2 kcal/mol compared with the
two further alternative Ad
E
paths can also be located corre-
sponding to 1,4 addition. The first follows a concerted route (v
2
I
1
64 cm ) but requires an unusual high-energy allotrope of bro-
mine, Br (Fig. 8a) and the product is the cis-1,4-adduct (Fig. 8c).
4
2
The second stepwise alternative mechanism (v 48 cm ) fea-
1
I
S
E
Ar second-order stationary point, with a value that is starting
tures the first appearance of an intermediate arenium cation
(Wheland intermediate) on the path to forming the trans-1,4-
adduct and overall is the lowest energy route (Table 2).
to correspond to a slow thermal reaction at reflux tempera-
tures (for benzene). Compared with the formation of bromo-
Journal of Computational Chemistry 2016, 37, 210–225
217

Figure 8. Geometries of key stationary points for Ad
E
paths for benzene 1 2Br
starting from the high energy allotrope Br a). A stepwise route d–h) starting from the low energy form 2Br
2
, showing a–c), a concerted addition to form cis21,4-dibromocyclohexadiene
d) to trans21,4-dibromocyclohexadiene
4
2
involves a Wheland intermediate ion-pair f) and involving two transition states e) and g) either side of f). [Color figure can be viewed in the online issue,
which is available at wileyonlinelibrary.com.]
Figure 9. IRC computed for the asynchronous asymmetric S
E
Ar reaction between benzene and 3Br
˚
, showing a) the energy profile with the computed geometries (lengths, in A) shown as insets, b) the energy gradient norm, with the red arrow,
2
on the closed-shell pathway forming bromobenze-
ne 1 HBr 1 2Br
2
indicating the position of a hidden Wheland intermediate. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

WWW.C-CHEM.ORG
FULL PAPER
region of the transition state. When the solvent model is
applied, the dipole moment increases by ꢁ4D, and the large
value persists for longer along the reaction path.
An equally interesting solvent response can be seen in the
computed CAH and CABr bond lengths participating in the
transition state (Fig. 11). The more dramatic difference is
induced for the former bond, with its removal being signifi-
cantly postponed until well after the transition state is passed
when solvation is included. The response on the CABr bond is
much smaller.
The increasing complexity of the potential surface is further
illustrated by the location of an isomeric S Ar reaction pathway,
E
which is stepwise in nature involving a true rather than a hidden
Wheland intermediate (Fig. 12). The rate determining step of this
alternative mode is 2.1 kcal/mol above the concerted S Ar alter-
E
21
native and corresponds to CABr bond forming (v 30 cm ).
I
Benzene 1 4Br
2
Whereas all the previous stationary points located for S Ar
E
mechanisms with an imposed plane of symmetry had an anti-
symmetric imaginary vibration that forces an out of plane distor-
tion, the incorporation of four Br molecules now reveals (Table
2
21
2
) a symmetric-concerted pathway for substitution (v 25i cm ),
I
Figure 10. IRC computed for the asynchronous symmetric S
between benzene and 3Br on the closed-shell pathway forming bromo-
benzene 1 HBr 1 2Br , showing a) the energy profile computed for the gas
E
Ar reaction
2
2
phase, b) computed with a continuum solvent model for benzene, c) the
dipole moment computed for the gas phase, and d) computed with a con-
tinuum solvent model. [Color figure can be viewed in the online issue,
which is available at wileyonlinelibrary.com.]
Benzene 1 3Br
2
As with 2Br , the C symmetric for S Ar transition state has
2
s
E
2
two negative computed force constants (v 58, 8 cm ) the
1
I
0
00
vectors again having, respectively, A and antisymmetric A
symmetry. A true asymmetric transition stationary point 3.5
kcal/mol lower in energy can be located which reveals a con-
certed asynchronous nature for the path (Fig. 9a).
The S Ar route is adjacent to an Ad reaction path for trans-
E
E
2
1
1
I
,2-addition (v 52 cm ) which is 0.4 kcal/mol lower in free
energy (Table 2).
As noted previously, the previous reaction paths are all com-
puted with inclusion of a continuum solvation model. It is
instructive at this stage to illustrate the effect solvation has on
the reaction. This is illustrated by comparing the energies of
the reaction paths with and without inclusion of solvation for
the symmetric SEAr mechanism (Fig. 10). The solvent-
stabilization for reactant and product is modest (ꢁ3–5 kcal/
mol), but substantial (ꢁ11 kcal/mol) in the region of the transi-
tion state. The dipole moments increase dramatically in the
Figure 11. IRC computed for the asynchronous symmetric S
between benzene and 3Br2 on the closed-shell pathway forming bromo-
benzene 1 HBr 1 2Br , showing a) the CAH bond length computed for the
gas phase, b) computed with a continuum solvent model for benzene, c)
the CABr bond length computed for the gas phase, and d) computed with
a continuum solvent model. [Color figure can be viewed in the online
issue, which is available at wileyonlinelibrary.com.]
E
Ar reaction
2
Journal of Computational Chemistry 2016, 37, 210–225
219

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WWW.C-CHEM.ORG
2
Figure 12. IRC computed for the reaction between benzene and 3Br on the closed-shell pathway forming an arenium cation (Wheland) intermediate
showing a) the energy profile with the computed geometries (lengths, in A) shown as insets, b) the energy gradient norm. [Color figure can be viewed in
the online issue, which is available at wileyonlinelibrary.com.]
which then follows a valley ridge down from the transition state
to a desymmetrization point where the forming HBr bifurcates
to one of the two ortho-positions in the product bromobenzene
to establish a hydrogen bond. More importantly, a second-
concerted transition state can be located which is lower in free
energy than the first by 10 kcal/mol (Table 2) and which reveals
a new asymmetrical structural motif (Fig. 13). The key feature is
An IRC for this lower energy transition state is shown in Fig-
ure 14, along with various computed properties along the
path. As with the smaller bromine clusters, the concerted tran-
sition state involves almost complete CABr bond formation
and almost no CAH cleavage. After the transition state is
passed, a hidden Wheland intermediate precedes the proton
removal. The dipole moment reaches its maximum value of
almost 16D at the transition state, but this ionic character lasts
until the proton is fully transferred.
2
the incorporation of a Br7 like cluster with a central Br atom
from which radiate three dendritic bromine arms. One serves to
1
deliver a Br electrophile to the benzene, the second serves
later on the pathway after the transition state as a base to
remove the proton from the ring and the final arm anchors the
bromine cluster to the benzene via weak noncovalent interac-
Benzene 1 5Br
2
As with 3Br
has two computed negative force constants (v 45i, 12i cm ) but
I
, the C symmetric geometry for S Ar substitution again
2
s
E
[23]
2
21
tions (NCI) (Fig. 13b). The structure of the key Br7 unit is sim-
2
ilar to the crystallographic structure for a Br9 system (Fig. 2a).
a lower energy asymmetric true transition state can also be
2
20
Journal of Computational Chemistry 2016, 37, 210–225
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Figure 13. Geometry of the lower energy transition state for the S
˚
E
Ar path for benzene 1 4Br
2
, for concerted reaction to form bromobenzene 1 HBr 1 3Br2
showing a) key lengths, in A and b) the NCI analysis (color code; blue 5 strongly stabilizing, green 5 weakly stabilizing, yellow, red 5 destabilizing).
E 2
Figure 14. Computed properties along the S Ar IRC path for benzene 1 4Br , for concerted reaction to form bromobenzene 1 HBr 1 3Br2 showing a) the rela-
tive total energy, b) the gradient norm, with the feature indicated by the arrow corresponding to a hidden Wheland intermediate, c) the dipole moment, d) the
forming CABr length, and e) the cleaving CAH length. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
Journal of Computational Chemistry 2016, 37, 210–225
221

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WWW.C-CHEM.ORG
E
Figure 15. Geometry of the lower energy transition state for the S Ar path for concerted reaction to form bromobenzene 1 HBr 1 4Br2 showing a) key
˚
lengths, in A and b) the NCI analysis (color code; blue 5 strongly stabilizing, green 5 weakly stabilizing, yellow, red 5 destabilizing).
2
located involving a four-armed Br
9
cluster (Fig. 15, cf. the crys-
est energy routes correspond to (reversible) addition. Despite
the entropic penalty, 4Br has the lowest barrier for S Ar sub-
tal structure shown in Fig. 2a). The geometry is very similar to
the 4Br transition state, but the additional fourth bromine chain
radiating from the central atom now plays no active role and
the gradual decrease in activation barriers from 1Br to 4Br is
2
E
2
stitution, whereas for 5Br entropy now starts to impact nega-
2
tively. For the standard state of 14.3 M, the entropic penalty is
2
2
lessened. For our 4Br2 model, we estimate the overall free
energy barrier as 12.6 kcal/mol (relative to separated reactants,
Table 2), 11.7 (correction relative to the resting state of the
reactants) together with an estimated correction of ꢁ13 kcal/
mol derived from the probably more accurate B2PLYP1D3 bar-
riers for the smaller clusters, giving a final value of ꢁ17.3 kcal/
mol.
now reversed (Table 2) because of the effects of the entropic
organization required.
An IRC reveals the system to be again finely balanced
between an asynchronous process in which CABr bond forma-
tion and CAH cleavage are on a concerted path and a step-
wise process involving a discrete Wheland/arenium cation
intermediate. While the latter can be located as a species with
only real vibrational modes (Table 2), it sits in such a shallow
energy minimum that the computed IRC path appears to treat
it merely as a hidden intermediate (Fig. 16). It has become
apparent that with such shallow potentials, a variety of trajec-
tories of similar energy are probable. It is not currently feasible
to compute the quantum molecular dynamics trajectory distri-
bution for such systems, but would clearly be desirable when
this does become possible.
As the energetics reveal the viability of reversible addition
reactions, we next review what is known about such path-
ways. The ability of bromine to react with polybenzenoid
[
25]
hydrocarbons forming addition products was known
but for
benzene itself this reaction has not hitherto been reported (As
far as we know, addition of bromine to benzene in darkness is
[
26]
unknown. a Hexabromocyclohexane is formed with light).
However, we have found that even for benzene, addition prod-
ucts are formed provided that the bromine concentration is
high enough (>5 M). The detected addition products include
three stereoisomers of 3,4,5,6-tetrabromocyclohexene as well
as a- and b-hexabromocyclohexanes, their total amount being
about 0.5–2% of the quantity of the reacted benzene (see
Supporting Information, pp. S7–S10). The structures of the
addition products were determined by 2D NMR (Scheme 2;
Supporting Information, pp. S13–S21).
Energies and Kinetic Isotope Effects
The standard free energy of activation, involving thermal cor-
rections derived from classical vibrational partition functions,
has a standard state of 1 atm (0.041 M at 298 K). The proce-
[
24]
dures for other standard states are explained here
and
involve a correction to 14.3 M (350 atm) by subtracting 3.467
kcal/mol from the bimolecular free energies and appropriate
multiples of these values for higher order complexes or transi-
tion states.
We tried to detect intermediate dibromocyclohexadienes
but none were ever observed. The 1,4-addition product, 3,6-
[
27]
dibromocyclohexa-1,4-diene was noted
reaction of cyclohexa-1,4-diene with N-bromosuccinimide
Scheme 3). However, in our hands, the reaction with N-
as a product of the
The first two aspects to note are that the models con-
(
structed with 1-2 Br
.041 M that are too large to explain a reaction occurring at
ambient temperatures, and that slightly lower free energy
pathways corresponding instead to cis-1,2 addition (1Br ) or
trans-1,2 and 1,4 addition (2-3 Br ) also exist. The addition
2
units have free energy barriers at
bromosuccinimide does not yield cyclohexadienes and results
instead in formation of a mixture of products containing tri-
bromocyclohexene isomers. Their structures have again been
determined by 2D NMR (Supporting Information, pp. S23–S26).
We believe that dibromocyclohexadienes are kinetically unsta-
ble intermediates that can either add a second molecule of
bromine, eliminate HBr or reverse back to Br2 immediately
after formation.
0
2
2
products, however, are endo-energic by ꢁ15 kcal/mol, imply-
ing the reverse barriers would be easily accessible at these
temperatures and that the substitution product bromobenze-
ne 1 HBr is the thermodynamic sink for the reaction. With
We infer that a key intermediate of the addition reaction of
bromine to benzene should be 1,2-trans-dibromocyclohexa-
diene according to the following considerations:
3
Br , the barriers are lowered by ꢁ6 kcal/mol, revealing the
2
first signs of thermally accessible reactivity, and again the low-
2
22
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E 2 E
Figure 16. The S Ar path for benzene 1 5Br , for concerted S Ar addition to form bromobenzene 1 HBr 1 4Br2, showing a) the energy profile with the
computed stationary point structures structure (lengths, in A) shown as an inset, b) the energy gradient norm with arrow indicating a Wheland-like hidden
intermediate preceding the proton removal. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]
1
. Among all possible products of the first stage of addition
1,2-cis, 1,2-trans, 1,4-syn, 1,4-anti-dibromocyclohexa-
dienes) 1,2-trans is predicted to be the most stable
additions from a single intermediate, such an intermedi-
(
ate can be only the 1,2-trans-dibromocyclohexadiene.
[
29]
3. It is reported
that for the 1,3-cyclohexadiene system,
addition path-
[
19]
(
Table 2 and Fig. 17 ).
the 1,2-trans (major), and 1,4-syn (minor) Br
2
2
. Only three tetrabromocyclohexene isomers are observed
experimentally (gray-outlined structures on Fig. 17).
Assuming that they all have to be formed by 1,2 and 1,4
ways are realized. These data are in a good accordance
with our supposition: the expected intermediate 1,2-trans-
dibromocyclohexadiene gives the major products RSRS
Scheme 2.
Journal of Computational Chemistry 2016, 37, 210–225
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The bromine isotope effect for the concerted substitution is
81
7
9
Br/ Br 5 1.0053, which suggests that the product bromoben-
79
81
zene should have a slightly higher ratio of Br/ Br than the nat-
ural abundance. Again, this may be too small an effect to be
measured. The Ad alternative for trans-1,2-addition gave the
E
1
2
larger inverse value of H/ H 5 0.86. The calculated isotope
effects for the larger 4Br and 5Br models converge to a value
Scheme 3.
2
2
of 0.95, which is in good agreement with measurement.
and RSSR by 1,2-trans addition, and the minor product
RRRS by 1,4-syn addition (solid paths on Fig. 17, see Sup-
porting Information, p. S15 for kinetic data).
Conclusions
Computational exploration of the reaction between bromine
and benzene shows a highly complex energy surface emerging
leading to a variety of addition products in addition to the
standard substitution products as the reaction sink. As the num-
ber of bromine atoms participating in the transition state
increases, thermally accessible reaction pathways emerge, espe-
cially at higher concentrations such as 14.3 M. The structure of
Kinetic Isotope Effects
For an S Ar reaction in which the rate-limiting step is formation
E
of the carbon-electrophile bond, the change in hybridization at
2 [3]
the carbon center from sp to sp would induce an inverse iso-
tope effect, whereas if the rate-limiting step is CAH cleavage
the transition states resembles the crystal structures of the Br
9
[
30,31]
than a large primary effect would be expected.
As these
and Br11 anions, which are unique to bromine as a halogen.
These dendritic-like clusters facilitate the bromination of ben-
zene by delivering in a single unit both the electrophile and
base needed for substitution, as well as anchoring the unit to
the benzene via CHꢂ ꢂ ꢂBr interactions. Both experiment and com-
putation are consistent in revealing an associated high order in
bromine concentration, an unusual and possibly unique feature
of this mechanism. Pathways for both 1,2- and 1,4-addition
emerge as competitive with substitution energies, but as the
endo-energic products of these pathways have very low reverse
barriers, they only represent kinetically accessible routes and
not the thermodynamically stable outcomes. The textbook
dogma that under mild conditions (ambient temperatures, no
catalyst) bromine and benzene do not react is, therefore, shown
to be true only for dilute solutions of bromine. The partial loss
provide a good indication of the nature of the rate-limiting tran-
[32]
1
2
sition state,
for selected transition states using C
measured value of 0.97 6 0.03. For the S
Br at 298 K, inverse values of 0.75 and 0.84 for the closed shell
and biradical procedures, respectively, were obtained and 0.83
for the biradical Ad addition. The latter in particular is typical of
we have computed H/ H kinetic isotope effects
for comparison with our
Ar reaction involving
6 6
D
E
1
2
E
2
[33]
addition to an sp center.
ever, that the 1Br reaction is not a good model on the basis of
the activation barrier alone and the predicted isotope effect
confirms this. For the (closed shell) concerted S Ar reaction
at 298 K, H/ H 5 0.94, whereas a value of
H/ H 5 0.91 is obtained for the related stepwise route leading
We have already established, how-
2
E
1
2
involving 3Br
2
1
2
to a Wheland intermediate (Table 2). This difference between
the fully concerted and the stepwise pathways is probably too
small to confidently distinguish between the two alternatives.
E
of aromaticity required of a Wheland-like species on the S A
reaction pathway is more than offset by the energy gains, result-
ing from formation of these bromine anion clusters.
Acknowledgment
Financial support from the Chemistry and Material Science Depart-
ment of the Russian Academy of Sciences (project 5.1.4) and Russian
Foundation for Basic Research (grant No. 13-03-00427) is gratefully
acknowledged.
Keywords: bromination
ꢂ
benzene polybromide anions
ꢂ
How to cite this article: A. V. Shernyukov, A. M. Genaev, G. E.
Salnikov, H. S. Rzepa, V. G. Shubin. J. Comput. Chem. 2016, 37,
210–225. DOI: 10.1002/jcc.23985
]
Additional Supporting Information may be found in the
online version of this article.
Figure 17. Addition reaction paths of bromine with dibromocyclohexa-
[28]
dienes. The geometries have been optimized using the riMP2/L1
method without any corrections, the total energy of noninteracting C
and 2Br is assigned to zero. [Color figure can be viewed in the online
6
H
6
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Received: 7 May 2015
Accepted: 28 May 2015
Published online on 14 July 2015
€
Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V.
Journal of Computational Chemistry 2016, 37, 210–225
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