Elevated reaction order of 1,3,5-tri-tert-butylbenzene bromination as evidence of a clustered polybromide transition state: a combined kinetic and computational study

Article abstract of DOI:10.1039/C9OB00607A

The kinetics and mechanism of concurrent bromo-de-protonation and bromo-de-tert-butylation of 1,3,5-tri-tert-butylbenzene at different bromine concentrations were studied experimentally and theoretically. Both reactions have high order in bromine (experimental kinetic orders ～5 and ～7, respectively). According to quantum chemical DFT calculations, such high reaction orders are caused by participation of clustered polybromide anions Br_2n?1^- in transition states. Bromo-de-tert-butylation has a higher order due to its bigger reaction center demanding clusters of extended size. A significant primary deuterium kinetic isotope effect (KIE) for bromo-de-protonation is measured indicating proton removal is rate limiting, as confirmed by computed DFT models. The latter predict a larger value for the KIE than measured and possible explanations for this are discussed.

Full text of DOI:10.1039/C9OB00607A

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Page 1 of 14
Organic & Biomolecular Chemistry
1
Elevated Reaction Order of 1,3,5-tri-tert-butylbenzene Bromination as Evidence of a
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Clustered Polybromide Transition State: a Combined Kinetic and CompuDtaOtI:i1o0n.10a3l9/SCt9uOBd0y0607A
Andrey V. Shernyukov[a,b], Alexander M. Genaev*[a], George E. Salnikov[a,b,c], Vyacheslav G.
Shubin[a], and Henry S. Rzepa*[d]
[a] N.N. Vorozhtsov Novosibirsk Institute of Organic Chemistry, Siberian Branch of the
Russian Academy of Sciences, 630090, Novosibirsk, Acad. Lavrentiev Ave., 9, Russian
Federation
[b] Novosibirsk State University, 630090, Novosibirsk, Pirogova, 2, Russian Federation
[c] International Tomography Center, 630090, Novosibirsk, Institutskaya, 3a, Russian
Federation
[d] Department of Chemistry, Imperial College London, MSRH, 80 Wood Lane, London, W12
0BZ, UK.United Kingdom
E-mail: genaev@nioch.nsc.ru, rzepa@imperial.ac.uk
Abstract
Kinetics and mechanism of concurrent bromo-de-protonation and bromo-de-tert-butylation of
1,3,5-tri-tert-butylbenzene at different bromine concentrations were studied experimentally and
theoretically. Both reactions have high order in bromine (experimental kinetic orders ~5 and ~7,
respectively). According to quantum chemical DFT calculations, such high reaction orders are
caused by participation of clustered polybromide anions Br2n-1– in transition states. Bromo-de-tert-
butylation has a higher order due to its bigger reaction center demanding clusters of extended size.
A significant primary deuterium kinetic isotope effect (KIE) for bromo-de-protonation is measured
indicating proton removal is rate limiting, as confirmed by computed DFT models. The latter
predict a larger value for the KIE than measured and possible explanations for this are discussed.
Introduction
The classical electrophilic halogenation of aromatics is still a popular subject of research in
theoretical organic chemistry.1 It has been shown in our previous paper2 that the noncatalytic
bromination of benzene requires high (5–14 M) concentrations of bromine to proceed at ambient
temperature. An intriguing feature of the reaction is a very high (~5) kinetic order in bromine.
Such a high order3 was explained by the specific structure of transition states through which the
bromination proceeds. According to DFT calculations, the reaction is concerted (SEAr), with
transition states resembling ionic pairs composed of arenium ions C6H6Br+ and cluster
polybromide anions4 Br2n-1–. The calculated free energy barrier decreases sharply as the number
of bromine molecules forming a transition state cluster increases: the predicted rate ratio is
1:106:1014:1017 for one, two, three and four molecules, respectively. A big cluster simultaneously
plays three different roles in the reaction pathway: as a Br+ donor, as a proton acceptor, and as a
stabilizing arm forming weak dispersion interactions with the arenium ion (Figure 1). To assemble
such a transition state for a reaction which incorporates a further increase in volume via e.g. a
sterically hindered reaction center, a bromine cluster of even larger size may be required.
Bromination of 1,3,5-tri-tert-butylbenzene (I, Scheme 1) provides a suitable model for verification
of this hypothesis. The compound is known to undergo two reactions with bromine at comparable
rates: electrophilic substitution of a hydrogen atom (bromo-de-protonation) or of a tert-butyl
substituent (bromo-de-tert-butylation).5,6 The relevant reaction centers (H–C–Br and t-Bu–C–Br,
respectively) are very different in volume. If the cluster hypothesis is correct, bromo-de-tert-
butylation transition state must demand clusters of a larger size which will lead to increased order
in bromine compared to that of bromo-de-protonation.

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Figure 1. Transition state of SEAr synchronous substitution7 (benzene + 4Br2 system, B3LYP+D3/6-
311++G(2d,2p)/SCRF=benzene)
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DOI: 10.1039/C9OB00607A
Results and Discussion
As the kinetics were studied at a large excess of bromine, all involved bromination reactions can
be considered as pseudo first order ones. It was explicitly verified that carrying out the reactions
in the dark and in the presence of a bromine radical trap, t-BuONO, does not influence the reaction
rates.8 In agreement with previous studies,5,6 the intermediate bromination products II and III also
react with Br2 forming the same final product, dibromide IV (Scheme 1). The observed
concentration decay of the initial compound I is not mono-exponential (Figure 2) which clearly
points to the reversibility of the first stage. An explicit experiment has shown that equimolar
mixture of II and t-BuBr does not transform back into I, therefore by exclusion the reversible
process must be I + Br2 = III + HBr. Accounting for its reversibility allowed improved
approximation accuracy for the whole kinetics scheme by more than an order of magnitude.
Neither reaction of the second stage is reversible: after keeping the mixture for a long time, the
NMR signals of all the compounds I, II, and III disappear. Thus, the kinetic system shown in
Scheme 1 is inferred as complete.
Scheme 1. Bromination of 1,3,5-tri-tert-butylbenzene
Br
Br2, t-BuBr
Br2, HBr
t-Bu
t-Bu
k24
II
k12
Br
t-Bu
Br
HBr, Br2
t-Bu
t-Bu
t-Bu
t-Bu
k31
t-Bu
IV
I
k34
k13
Br
Br2, t-BuBr
Br2, HBr
t-Bu
t-Bu
III
first stage
second stage

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Figure 2. Experimental graph ln [I]0/[I] vs. time (Table 1, run 2)
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DOI: 10.1039/C9OB00607A
Accounting for HBr concentration changes in the numeric solution of the kinetics equations system
was problematic, as it takes part in the reactions involved in the scheme in non-stoichiometric
quantities. Additional HBr is formed due to the subsequent bromination of tert-butyl bromide
(Scheme 2) 9 in the process of bromo-de-tert-butylation of I and III. Moreover, up to 20% of HBr
is evaporated from the solution and produces an excess pressure in the ~1.5 mL gas volume
between the liquid phase and the sealed NMR tube cap. Knowing the exact HBr concentration is
important for the evaluation of the bimolecular reaction III + HBr  I + Br2. HBr was therefore
treated as an external agent, with the actual concentration directly determined from NMR spectra
and used in the kinetics equations system as a predefined value.
Scheme 2. Bromination of tert-butyl bromide
Br
Br
Br
kBu
+
C Br
Br
C Br
Br
C Br
+
C Br
+Br2, -HBr
Br
The experimental kinetic data were evaluated by numerical integration of the differential equations
followed by a nonlinear least square fitting of the involved rate constants. The complete processing
algorithm was implemented in the form of SciLab10 script. Representative kinetics are shown in
Figure 3, while the fitted values of rate constants are given in Table 1. From the data of Table 1 it
follows that tert-butyl groups exert a significant steric effect on the rates of reaction. Thus,
substitution of a tert-butyl group with a bromine atom does not cause a strong deceleration of the
bromo-de protonation reaction (k13/k24≈2). Usually the deactivating effect of bromine is much
greater (for example, kPhH/kPhBr=11).11 Surprisingly, the rate of bromo-de-tert-butylation reaction
IIIIV is higher than that of III (k12/k34≈0.1) in spite of the deactivating effect of bromine in
compound III.

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Figure 3. Representative kinetics of bromination of 1,3,5-tri-tert-butylbenzene (Table 1, run 2, experimental points
are denoted by circles, fitted curves by solid lines). For other kinetics, see the supporting information.
View Article Online
DOI: 10.1039/C9OB00607A
Table 1. Experimental conditions and fitted parameters (pseudo first order rate constants and
equilibrium constants) for reactions of Scheme 1.
[I]0
mol/L
k13,
k34,
k12,
k24,
K,a
a
[Br2]
mol/L K
T
ΔG0
Run
10–5 s–1 10–5 s–1 10–5 s–1 10–5 s–1 10–3
kcal/mol
1
2
3
4
5
0.16 3.9 296 5.16±0.06 4.34±0.09 0.30±0.01 2.1±0.3 2.4±0.3 3.55±0.08
0.17 5.8 298 27.2± 0.7 49± 2
4.1± 0.2
36± 2
650±110 500± 20
15± 2 2.2±0.3 3.61±0.08
69± 4 2.7±0.4 3.53±0.10
0.17 7.8 301 111± 6
380±30
b
b
0.065 11.6 298
-
-
2.4 c
0.17 5.8 273 9.2±0.4
28± 2 1.55±0.06 6.2±0.4 1.1±0.2 3.72±0.08
a K (see considerations below) is the equilibrium constant for reaction I + Br2 = III + HBr, ΔG0 is corresponding free
Gibbs energy. b Undefined, as the parameter deviation is too large (above 100%). c At fitting this value was fixed.
Deviations in the fitted values of rate constant were estimated by the two methods: bootstrap Monte
Carlo12 and parameter variation to constant chi-square13 (confidence limit 3σ). Both methods give
similar results, while the parameter variation method seems to be more robust for large deviations.
The error probability distribution analysis indicates considerable mutual correlation (Figure 4a)
between the variable parameters k13 and k31 corresponding to the reversible reaction I+Br2 =
III+HBr. This would prevent accurate determination of the equilibrium constant K = k13/k31.
Therefore, K and k13 were used as actual fitted parameters while k31 was derived from them. This
simple change of variables allowed compensation for the correlation influence (Fig. 4b), reducing
the deviation in K by a factor of almost two.
Figure 4. Correlation of the optimized parameters by bootstrap method (Table 1, run 2, 200 synthetic data sets).
a.
b.

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In the case of high concentrations of bromine (Table 1, run 4), the initial compound I is exhausted
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too rapidly (96% in 5 min.) and hence hiding from NMR observation the most informative region
of the reaction for least squares fitting. To obtain numerically stable results inDtOhIi:s10s.1p03e9c/Cia9lOBc0a0s6e07aA
fixed value of the equilibrium constant K was used, as this parameter was found to have very
similar values in all other experiments. Nevertheless, the rate constants k13 and k34 could still be
determined only with a huge uncertainty and their values are not included in Table 1 as deviations
exceed 100%.
The order of the reaction in bromine was determined by a differential method14 using the kinetic
eqs. (1) and (2) relating a pseudo first order reaction to a formal reaction of order n+1. [Ar] stands
for the concentration of any of compounds I, II, or III, and k stands for any of constants k12, k13,
k24, or k34.
-d[Ar]/dt = k [Ar]
(1)
(2)
(3)
-d[Ar]/dt = kn+1 [Ar] [Br2]n
log k = n log [Br2] + log kn+1
After feeding the kinetic data into the eq. (3), the following orders in bromine have been derived
(Figure 5); for reaction I  III 4.4±0.3, for II  IV 5.0±0.1, for I  II 7.0±0.2 and for III  IV
6.4±0.4.
Figure 5. Determination of the reaction orders in bromine.
Kinetic Isotope Effect
The presence of bulky tert-butyl groups in compound I may retard proton removal from the
arenium intermediate, inducing a primary H/D kinetic isotope effect (KIE).15 To determine the
KIE for the reaction I  III, compounds I and I-d3 were used.
t-Bu
t-Bu
t-Bu
H
H
D
D
D
D
t-Bu
t-Bu
t-Bu
t-Bu
t-Bu
t-Bu
H
D
H
I
I-d3
I-d2

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Unfortunately, KIE determination by the common method of carrying out competitive reactions
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in a mixture of natural abundance and enriched reagents was not viable. The source of the problem
DOI: 10.1039/C9OB00607A
is proton exchange with HBr, observed in broadening of NMR signals of aromatic protons of
compound I as well as in the corresponding exchange cross peaks in 2D EXSY spectra.
1
Comparison of H NMR signal broadening of I in bromine and in mixtures of CF3COOH and
TfOH16 allowed estimating the rather high HBr acidity (Figure 6). The proton exchange rate
increases sharply with increase in bromine concentration (the reaction order about 5, nearly the
same as for bromo-de-protonation). This behavior can be explained by the Lewis acidity of
bromine.17
Figure 6. 1H NMR signal of compound I in the presence of acids. [I] = [HBr] = [CF3COOH+TfOH] = 0.1 mol/L,
CD2Cl2: 0.1 mL. (Br2 + CCl4), mL: (0.1+0.28) (a), (0.15+0.23) (b), (0.2+0.18) (c), (0+0.38) (d,e); wt% TfOH in
CF3COOH: 35 (d), 21 (e).
As proton exchange between I and HBr proceeds much faster than bromination, any H/D
distribution (possibly distorted due to KIE) between I and I-d3 in their mixture would be
immediately averaged. Therefore, the reaction rates I  III and I-d3  III-d2 were measured in
separate experiments (SI, p. 2, runs 6, 7). The relevant concentrations were determined from
integral intensities of 1H NMR signals of t-butyl groups not involved in isotope exchange. As III
participates in further processes (transformation back to I and bromo-de-tert-butylation), the rate
constants k13(H) and k13(D) were determined at the very beginning of the reaction. The incomplete
enrichment in I-d3 sample (β = 91.4±0.3%) makes some contribution to the value of the measured
rate constant: k13(D+H) = (1-β)k13(H) + βk13(D), assuming equality of proton substitution rates in
compounds I and I-d2 and to deuterium substitution rates in compounds I-d3 and I-d2. The
measured values k13(H) = (5.38±0.08)10–5 and k13(D+H) = (1.665±0.007)10–5 s–1 for I and I-d3,
respectively, give KIE: k13(H)/k13(D) = 4.1±0.2. This value is close to that observed earlier for
Br2/Ag+ system.5,6
Quantum Chemical Computations
It follows from the experiments that the energy barriers for bromo-de-protonation and bromo-de-
tert-butylation are drastically lowered with increasing bromine concentration, in particular for
the latter reaction. To confirm the hypothesis of polybromide clusters participation it was
necessary to find transition states I-Br+Br2n-1– for both reactions and compare their energies at
different values of n, using a “pathfinder” DFT/PBE/Λ01 method with calculated
thermochemical free energies and Grimme’s D3+BJ18 dispersion corrections. The system under
consideration has a variety of possible stationary points on the potential energy surface (scheme
1, first stage). Nevertheless, in all cases for n ≥ 3, the most stable transition states (Figure 7, see
SI for others) have “chelate” geometries where the reaction centers H–C–Br and t-Bu–C–Br are
surrounded by the anionic fragment Br2n-1–. For the reaction III (TS3, reaction center t-Bu–C–

Page 7 of 14
Organic & Biomolecular Chemistry
7
Br), the chelate chain of most favorable transition states comprises 7 bromine atoms (n = 4), with
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a possible auxiliary side chain (for n > 4). A similar feature exists for the reactiDoOnI: I10.10I3I9I/C(9TOSB020,607A
the more compact reaction center H–C–Br), but no transition states with a 7-membered chelating
chain were found. 5-membered chains always appeared to be more energetically favorable, with
the extra bromine atoms displaced into side chains. Notably, similar V-shaped, pyramidal and
tetragonal Br2n-1– structures (n = 3, 4 and 5) were observed experimentally in the crystal phase4,19
in the forms of polybromide salts. For the reaction III at n = 4,5 an additional energy minimum
was found in the PES, corresponding to the II + t-Bu+Br2n-1– system.
Figure 7. Transition states of the bromination reactions (DFT/PBE/Λ01).

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Figure 8. a) Dependence of the energy barriers of bromination reactions (DFT/PBE/Λ01 with thermochemical free
energy + D3/BJ18 corrections) on the number of bromine molecules. Zero energy corresponds to separated arene and
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#
DOI: 10.1039/C9OB00607A
bromine molecules. b) Dependence of free activation energy of bromination reactions on bromine concentration. ΔG
was derived from the pseudo monomolecular rate constants given in Table 1 according to the Eyring equation. The
value of the rate constant for reaction I→III at [Br2]=11.6 mol/L was extrapolated according to equation (3).
a)
b)
Relative energies of the transition states identified using this method are shown in Fig. 7 and as a
function of the number of bromine molecules in Figure 8a. The n = 1 case presents a model of low
bromine concentration ([Br2] ~ 1 mol/L) where cluster formation is unlikely. Non-catalytic
bromination of benzene and other unactivated aromatics is known not to proceed under these
conditions,20 in line with very high calculated energy barriers (> 40 kcal/mol, see also refs.2,21).
As n increases, the energy barriers decrease and at n>2 can be overcome at ambient temperature.
The bromo-de-tert-butylation barrier (III) decreases more rapidly than that for bromo-de-
protonation (IIII,) which reflects qualitatively the experimental tendencies of the relative
reaction rates (Fig. 8b). Thus, quantum chemical modeling supports the assumption of the
formation of bromine clusters in the transition states.
A previous quantum chemical study of benzene bromination concluded that this reaction proceeds
via a concerted SEAr mechanism with the transition state in the form of ion-pair of the cation
[C6H6Br]+ and polybromide anion4 [Br2n-1]– (Fig. 1). The key difference for the bromination
mechanism of the tert-butyl derivative I is a two-step mechanism with facile formation of a
Wheland intermediate (WI-I, Scheme 3) as stabilized by the three electron donating substituents.
It is also well known that Wheland intermediates (arenium ions) can easily undergo a further 1,2-
shift of a hydrogen atom.22 In our case (Scheme 3) this latter process as followed by tert-butyl
group elimination must lead to 1-bromo-2,4-di-tert-butylbenzene V. Indeed, the signals of product
V are observed in NMR spectra of the reaction mixtures, although in very low concentrations
(0.5%). Thus, the presence of product V serves as an additional argument for the participation of
Wheland intermediates such as WI-III (scheme 3) in the bromination process of I.

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Organic & Biomolecular Chemistry
9
t-Bu
t-Bu
t-Bu
H
H
H
H
H
H
H
TS1
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DOI: 10.1039/C9OB00607A
-
-
[Br2n-1
]
[Br2n-1]
+ nBr2
t-Bu
t-Bu
t-Bu
t-Bu
t-Bu
t-Bu
H
Br
H
Br
I
WI-I
- H+
WI-III
- t-Bu+
TS2
t-Bu
t-Bu
Br
t-Bu
H
H
H
H
H
H
H
-
[Br2n-1
]
t-Bu
t-Bu
t-Bu
t-Bu
t-Bu
Br
Br
H
WI-II
III
V
TS3 - t-Bu+
t-Bu
H
H
+ t-BuBr + Br2n-2
t-Bu
Br
H
II
Scheme 3. Mechanistic scheme for bromination.
We then proceeded to a higher-level computational model which includes continuum solvation
corrections (B3LYP+GD3BJ/Def2-TZVPP/SCRF=CCl4) with the focus on two models for the
bromine clusters selected from the ones shown in Figure 7, n=3 and n=5. Location of three
transition states was attempted at this level. TS1 (Scheme 3) corresponds to the formation of a
Wheland intermediate (WI-I) and corresponds to a very lower barrier process compared to TS2,
the subsequent proton loss from WI-I. TS3 involves loss of one tert-butyl group from an isomeric
Wheland intermediate WI-II. The latter is itself higher in energy than WI-I because the cationic
Centre’s are less stabilized by electron donation. WI-III is more stable than WI-II because of
cationic stabilization by an adjacent bromine. The computational results are collected in Table 2.

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Table 2. Calculated properties for the reaction between 1,3,5-tri-tert-butylbenzene and
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DOI: 10.1039/C9OB00607A
brominea
Speciesb
3Br2
5Br2
0.0 [5.4]
3.1 [15.3]
-2.7 [16.2]
14.2 [12.5]
4.3 [4.8]
I
0.0c [4.4]d
e
TS1
WI-I
TS2
-
3.9 [12.9]
18.0 [12.6]
6.1 [4.7]
III
WI-II
WI-III
TS3
II (ion pair)
II
15.1 [14.6]
12.4 [12.3]
23.8 [23.4]
-1.7 [14.4]
-9.8 [7.1]
9.2 [18.1]
6.2 [13.8]
12.8 [20.0]
-10.8 [10.1]
-12.4 [6.7]
aThe overall data collection is available at DOI: 10.14469/hpc/4748. A FAIR data version of this table has DOI: 10.14469/hpc/4948. bSpecies shown in
Scheme 3. cRelative free energy, ΔΔG298 in kcal/mol. dDipole moment, Debye. eNot located.
As follows from Table 1, the bromination reaction I + Br2 = III + HBr is thermodynamically
unfavorable, with experimental free energy of the reaction being 3.53.7 kcal/mol. The calculated
value for the reaction I + 5Br2 = III + HBr + 4Br2 of G298 is +4.3 kcal/mol (Table 2) in good
agreement with experiment. This can be compared with the similar bromination reaction of
benzene C6H6 + 4Br2 = C6H5Br + HBr + 3Br2 which is thermodynamically favorable, ΔG298 = -
11.0 kcal/mol.2 The reason for the equilibrium shift is the reduced stability of the product III due
to a bulky bromine atom situated in a close vicinity of two tert-butyl groups. The synthetically
suitable preparation of III from I seems to be practically possible only in the presence of reagents
sequestering HBr (Ag+23, trimethyl phosphate24). The stability of the Wheland intermediate WI-I
depends on the bromine cluster size, with G298 for its formation being favourable only with the
5Br2 cluster, for which a discrete transition state TS1 indicates a very lower barrier to its formation.
No equivalent transition state could be found for the 3Br2 cluster, in probability because of a more
sensitive requirement to rearrange the bromine cluster during the reaction path. The ring-bound Br
in WI-I occupies a hyperconjugated pseudo-axial position, with the adjacent proton being pseudo-
equatorial (Figure 9). This intermediate, which is the kinetic resting state, then reacts by proton
abstraction via TS2 to give product III, TS2 rather than TS1 being rate limiting. As previously
noted, (Figure 7), ΔG# for TS3 (loss of the tert-butyl group) becomes lower than TS2 for the larger
5Br2 cluster compared to the smaller 3Br2 one, again confirmed by experiment. The overall
reaction profile is shown in Figure 10.

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DOI: 10.1039/C9OB00607A
Figure 9. Calculated structure for the Wheland intermediate for the reaction 2,6-di-tert-
butylbenzene +5Br2 at the B3LYP+GD3BJ/Def2-TZVPP/SCRF=CCl4 level. Interactive models
of all structures can be obtained from DOI: 10.14469/hpc/4948
Figure 10. Overall energy profile for (a) 3Br2 reagent and (b) 5Br2 reagent. Dashed lines
correspond to fast intermolecular rearrangements for which a true transition state could not be
located.
The computed hydrogen KIE derived from the vibrational wavenumbers computed for TS2
(Scheme 3) is 7.2 at 298K.This is larger than the measured value for the process I→III (4.1±0.2),
which itself had confirmed that TS2 is rate limiting. The discrepancy between the measured and

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calculated values might originate in the geometry of WI-I. If the pseudo-axial C-Br bond in WI-I
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were to be transposed with the C-H bond, the latter will become significantly weakened by
hyperconjugation, thus reducing the expected isotope effect. Attempts to locateDsOuIc: h10.a10n39a/lCt9eOrBn0a0t6i0v7eA
conformation for WI-I showed that for a 5Br2 cluster it is at best merely a higher energy inflexion
point in the potential surface. Nonetheless an approximate normal coordinate analysis at this
geometry suggests a lower value for the KIE of 4.9 at 298K. It remains possible that for
significantly larger bromine clusters (beyond the scope of the currently methodology employed
here), the C-H axial conformation of WI-I might be preferred. It might be also that the complexity
of the required kinetic analysis and the necessary approximations for its solution means that the
measured KIE might be subject to a larger than normal experimental error.
Conclusion
A variety of cluster bromide anions Br2n-1– discovered by X-ray of their crystal salts were actively
studied over the past decade. According to our data, similar clusters can be formed in the transition
states of chemical reactions. In case of electrophilic bromination of aromatics, bromine clusters
coordinate with the reaction center, drastically speeding up the reaction. Participation of several
bromine molecules in the transition state is manifested by unusually high reaction order in
bromine. For the example reported here, a threefold increase in bromine concentration accelerates
the substitution of a hydrogen atom and tert-butyl group in 1,3,5-tri-tert-butylbenzene by bromine
by 150 and 2000 times respectively, via a stepwise reaction involving rapid initial formation of a
Wheland intermediate. Apparently, enlarged clusters of bromine are needed to cover the bulky Br-
C-t-Bu fragments. The highest bromine concentration achieved with liquid bromine as a solvent
promotes the fast bromination of non-activated aromatics without the need for any catalyst.
Bromine, the simplest brominating agent, is thus far from being simple. Its tendency for the
formation of cluster structures should not be ignored when studying its chemical reactions.
Experimental
General methods and materials: NMR spectra were obtained at the Multi-Access Chemical
Service Centre of Siberian Branch of the Russian Academy of Sciences on Bruker AV-600, AV-
400 and DRX-500 spectrometers, using the residual proton and carbon signals of deuterated
methylene chloride as internal references (CHDCl2, δH 5.33 ppm; CD2Cl2, δC 53.6 ppm). For NMR
signal assignment 2D correlation spectra 1H-1H (NOESY) and 13C-1H (HETCOR) were used.
Bromine was boiled and distilled over KBr and then over P2O5. CCl4 was distilled over P2O5,
CD2Cl2 was drained by molecular sieves 4Å. A sample of 1,3,5-tri-tert-butylbenzene (I) prepared
according to25 was purified by crystallization from methanol followed by sublimation in vacuum.
By analogy, compound I-d3 (91 atom % D) was prepared from benzene-d6. 1-Bromo-3,5-di-tert-
butylbenzene (II) was kindly provided by Dr. T. F. Mikhailovskaya.
Preparation of samples: To bromine introduced into the NMR tube were added CCl4, 0.1 mL of
CD2Cl2 and 5-20 mg of solid aromatics (or solution of the aromatics in 0.1 mL CD2Cl2) as the three
distinct layers. Total reaction mixture volume was 0.5 mL. The volumes of Br2 and CCl4 were
chosen so as to ensure the desired bromine concentration (SI, p. S2). The tube was sealed by PTFE
cup and heat shrink tubing. The reaction was launched by stirring the layered content immediately
before recording NMR spectra. Representative 1H NMR spectrum is shown in SI (p. S3).
1
Kinetics: The composition of the reaction mixtures was determined by integration of H NMR
spectra. For kinetic data processing a dedicated SciLab script was developed.26 The following
built-in SciLab functions were used: ode (automatically selecting between nonstiff predictor-
corrector Adams method and stiff Backward Differentiation Formula method) – for the solution

Page 13 of 14
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of the kinetic equations, lsqrsolve (Levenberg-Marquardt nonlinear least squares fitting) – for
View Article Online
numeric determination of the rate constants by fitting kinetics to the experimental curves, and
lsq_splin (least squares cubic spline fitting) – for interpolation of HBr concenDtrOaI:ti1o0.n10s3.9/TC9hOeB0i0n6p0u7At
data and output results for all the kinetics experiments are given in SI, p. S5-S11; an example of
graphical output is shown on p. S4.
Computational details: Pathfinder calculations involving optimization of geometries of nonrigid
systems I-Br2n with a many possible stationary points on the PES used a fast DFT code
implemented in the PRIRODA program27 and employing a PBE functional28 with full-electron
basis Λ0129 similar to the cc-pVDZ basis, as a gas-phase model. Since the considered transition
states are in fact ion-pairs with a possible high solvation contribution, more realistic computations
with solvation model support were then undertaken. Our chosen computational model used the
B3LYP density functional as implemented in the Gaussian 16 program (Rev A.03 and B.01),30
which is a thoroughly explored method for a wide variety of reactions, combined with the Def2-
TZVPP basis set, an improvement on the earlier study of a similar system.2,21 We have also added
Grimme’s D3 dispersion correction18 with BJ weighting, together with the Karplus and York
smoothed-cavity SCRF continuum solvation model with CCl4 specified as the solvent.31 We
retained this continuum solvation model for higher mole fractions of Br2 noting that the dielectric
constants of liquid bromine (3.1) and CCl4 (2.2) are similar. Computational data for this method
are available via a FAIR data repository.32
Acknowledgments
A.V. Shernyukov, A.M. Genaev and G.E. Salnikov gratefully acknowledge the support of the
RFBR, under Grant No. 17-03-00564. We also acknowledge the Cluster of the Information
Computation Center, Novosibirsk State University (http://www.nusc.ru/) for computing resources.
References
1 (a) B. Galabov, D. Nalbantova, P. v. R. Schleyer, H. F. Schaefer, III, Acc. Chem. Res. 2016, 49, 1191-1199; (b) M.
Liljenberg, J. H. Stenlid, T. Brinck, J. Phys. Chem. A, 2018, 122, 3270-3279.
2 A. V. Shernyukov, A. M. Genaev, G. E. Salnikov, H. S. Rzepa, V. G. Shubin. J. Comput. Chem. 2015, 37, 210-
225.
3 In physical organic chemistry such high reaction orders are unusual. But in biochemistry very high reaction orders
(up to some tens) are available, see, e.g. Z. Cao, F. A. Ferrone, J. Mol. Biol., 1996, 256, 219-222.
4 (a) H. Haller, S. Riedel, Z. Anorg. Allg. Chem. 2014, 640, (7), 1281–1291; (b) L. Mann, G. Senges, K. Sonnenberg,
H. Haller, S. Riedel, Eur. J. Inorg. Chem. 2018, 3330–3337; (c) I. D. Gorokh, S. A. Adonin, M. N. Sokolov, P. A.
Abramov, I. V. Korolkov, E. Yu. Semitut, V. P. Fedin, Inorg. Chim. Acta 2018, 469, 583-587
5 E. Baciocchi, G. Illuminati, G. Sleiter, F. Stegel, J. Am. Chem. Soc., 1967, 89, 125-129.
6 P. C. Myhre, G. S. Owen, L. L. James, J. Am. Chem. Soc., 1968, 90, 2115-2123.
7 H. S. Rzepa, Computed properties for transition state models for the reaction between bromine and benzene, DOI:
10.14469/ch/191241
8 Usually, i-AmONO is used as a free radical trap: (a) R. Bianchini, C. Chiappe, G. Lo Moro, D. Lenoir, P.
Lemmen, N. Goldberg, Chem. Eur. J. 1999, 5, 1570-1580; (b) G. H. Schmid, A. Modro, K. Yates, J. Org. Chem.
1980, 45, 665-667; (c) D. E. Applequist, R. Searle, J. Am. Chem. Soc. 1964, 86, 1389-1391; (d) M. S. Kharasch, P.
C. White, F. R. Mayo, J. Org. Chem., 1938, 3, 33-47. We used t-BuONO because it is stable in concentrated
bromine solutions.
9 G. A. Russell, H. C. Brown, J. Am. Chem. Soc., 1955, 77, 4025-4030.
10 Scilab Enterprises. Scilab: Free and Open Source software for numerical computation (Version 5.5.0), 2012.
11 Ref 2, SI, p. 9.
12 W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling. Numerical Recipes in C. Cambridge University
Press, Cambridge: 1988, p. 548.
13 Previous reference, p. 551.
14 S.W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill Book Company, New York 1960, p. 82.
15 B. C. Challis and H. S. Rzepa, The Mechanism of Diazo-coupling to Indoles and the Effect of Steric Hindrance on
the Rate-limiting Step., J. Chem. Soc., Perkin Trans 2. , 1975, 1209-1217.

Organic & Biomolecular Chemistry
Page 14 of 14
14
16 S. Saito, S.-i. Saito, T. Ohwada, K. Shudo, Chem. Pharm. Bull., 1991, 39, 2718-2120.
View Article Online
DOI: 10.1039/C9OB00607A
17 P. Atkins, T. Overton, J. Rourke, M. Weller, F. Armstrong, Shriver and Atkins' Inorganic Chemistry, 5th Edition;
W. H. Freeman, 2009, p. 135.
18 (a) L. Goerigk. S. Grimme, Phys. Chem. Chem. Phys. 2011, 13, 6670; (b) S. Grimme, J. Antony, S. Ehrlich, H.
Krieg, J. Chem. Phys. 2010, 132, 154104; (c) S. Grimme, S. Ehrlich, L. Goerigk, J. Comput. Chem. 2011, 32, 1456-
1465.
19 X. Chen, M. A. Rickard, J. W. Hull, C. Zheng, A. Leugers, P. Simoncic, Inorg. Chem., 2010, 49, 8684–8689.
20 (a) C. B. Fryhle, S. A. Snyder, Organic Chemistry, 11th ed.; Wiley: Hoboken, NJ, 2013, p. 631; (b) J. Clayden, N.
Greeves, S. Warren, Organic Chemistry, 2nd ed.; Oxford University Press, 2012, p. 474.
21 J. J. Kong, B. Galabov, G. Koleva, J.-J. Zou, H. F. Schaefer, III, P. v. R. Schleyer, Angew. Chem. Int. Ed. 2011,
50, 6809.
22 V. A. Koptyug. Arenium Ions — Structure and Reactivity. Topics in Current Chemistry, vol. 122. Contemporary
Problems in Carbonium Ion Chemistry III. 1984.
23 (a) E.E. Betts, L.R.C. Barclay, Canad. J. Chem., 1955, 33. 1768-1774; (b) H.E. Zimmermann, J.R. Dodd, J. Am.
Chem. Soc., 1970, 92, 6507-6515; (c) S.R. Ditto, R.J. Card, P.D. Davis, D.C. Neckers, J. Org. Chem., 1979, 44, 894-
896.
24 (a) D.E. Pearson, M.G. Frazer, V.S. Frazer, L.C. Washburn, Synthesis, 1976, 621-623; (b) K. Look, R.K. Norris,
Aust. J. Chem., 1999, 52, 1077-1083; (c) R. Knorr, C. Pires, C. Behringer, T. Menke, J. Freudenreich, E.C.
Rossmann, P. Böhrer, J. Am. Chem. Soc., 2006, 128, 14845-14853.
25 J. J. Dressler, S. A. Miller, B. T. Meeuwsen, A. M. S. Riel, B. J. Dahl, Tetrahedron 2015, 71, 283-292
(Supplementary Data, p. S22).
26 A. M. Genaev, SciLab script for kinetic data processing, DOI: 10.14469/hpc/4873
27 (a) D. N. Laikov Chem. Phys. Lett. 1997, 281, 151; (b) D. N. Laikov, Y. A. Ustynyuk, Russ. Chem. Bull., 2005, 54,
820-826.
28 Perdew J.P., Burke K., Ernzerhof M., Phys. Rev. Lett. 1996, 77, 3865.
29 (a) D. N. Laikov, Chem. Phys. Lett. 2005, 416, 116; (b) D. N. Laikov, arXiv:1808.05454 [physics.chem-ph] (2018).
30 Gaussian 16, Revision B.01, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R.
Cheeseman, G. Scalmani, V. Barone, G. A. Petersson, H. Nakatsuji, X. Li, M. Caricato, A. V. Marenich, J. Bloino,
B. G. Janesko, R. Gomperts, B. Mennucci, H. P. Hratchian, J. V. Ortiz, A. F. Izmaylov, J. L. Sonnenberg, D.
Williams-Young, F. Ding, F. Lipparini, F. Egidi, J. Goings, B. Peng, A. Petrone, T. Henderson, D. Ranasinghe, V.
G. Zakrzewski, J. Gao, N. Rega, G. Zheng, W. Liang, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M.
Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, K. Throssell, J. A. Montgomery, Jr., J. E. Peralta, F.
Ogliaro, M. J. Bearpark, J. J. Heyd, E. N. Brothers, K. N. Kudin, V. N. Staroverov, T. A. Keith, R. Kobayashi, J.
Normand, K. Raghavachari, A. P. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, J. M. Millam, M. Klene,
C. Adamo, R. Cammi, J. W. Ochterski, R. L. Martin, K. Morokuma, O. Farkas, J. B. Foresman, and D. J. Fox,
Gaussian, Inc., Wallingford CT, 2016.
31 (a) G. Scalmani, M. J. Frisch, J. Chem. Phys. 2010, 132, 114110; (b) D. M. York, M. J. Karplus, Phys. Chem. A
1999, 103, 11060.
32 A. V. Shernyukov, A. M. Genaev, H. S. Rzepa, G. E. Salnikov and V. G. Shubin, FAIR data archive, Imperial
College Research Data Repository, 2018, DOI: 10.14469/hpc/4748