Kinetics and mechanism of unimolecular heterolysis of cage-like compounds: XIX. Effect of the nucleofuge nature on the activation parameters of heterolysis of 1-halo-1-methylcyclohexanes in cyclohexane. Heterolysis rate ratio in aprotic and protic solvents

Article abstract of DOI:10.1134/S1070428007010046

Heterolysis of 1-bromo-1-methylcyclohexane in cyclohexane (E1 reaction) involves solvation of the transition state (ΔS^≠ = -81 J mol^-1K^-1), while heterolysis of 1-chloro-1- methylcyclohexane is characterized by desolvation of the transition state (ΔS^≠ = 92 J mol^-1K^-1). The probability for the formation of transition state (interaction between cationoid intermediate and solvent cavity) increases in the first case due to enhanced stability of the solvated intermediate, and in the second, due to reduction in its size. The bromide/chloride heterolysis rate ratio decreases as the ionizing power of aprotic solvent decreases and that of protic solvent increases.

Full text of DOI:10.1134/S1070428007010046

ISSN 1070-4280, Russian Journal of Organic Chemistry, 2007, Vol. 43, No. 1, pp. 50–55. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © G.F. Dvorko, I.V. Koshchii, E.A. Ponomareva, 2007, published in Zhurnal Organicheskoi Khimii, 2007, Vol. 43, No. 1, pp. 50–55.
Kinetics and Mechanism of Unimolecular Heterolysis
of Cage-Like Compounds: XIX.* Effect of the Nucleofuge
Nature on the Activation Parameters of Heterolysis of 1-Halo-
1
-methylcyclohexanes in Cyclohexane. Heterolysis Rate Ratio
in Aprotic and Protic Solvents
G. F. Dvorko, I. V. Koshchii, and E. A. Ponomareva
“
Kievskii politekhnicheskii institut” National Technical University of Ukraine, pr. Pobedy 37, Kiev, 03056 Ukraine
e-mail: m_ponomaryov@ukr.net
Received July 10, 2004
Abstract—Heterolysis of 1-bromo-1-methylcyclohexane in cyclohexane (E1 reaction) involves solvation of
≠
–1 –1
the transition state (ΔS = –81 J mol K ), while heterolysis of 1-chloro-1-methylcyclohexane is characterized
≠
–1
–1
by desolvation of the transition state (ΔS = 92 J mol K ). The probability for the formation of transition state
interaction between cationoid intermediate and solvent cavity) increases in the first case due to enhanced
(
stability of the solvated intermediate, and in the second, due to reduction in its size. The bromide/chloride
heterolysis rate ratio decreases as the ionizing power of aprotic solvent decreases and that of protic solvent
increases.
DOI: 10.1134/S1070428007010046
The rate of unimolecular heterolysis (S 1, E1,
The nucleofuge effect on the rate of heterolysis in
aprotic solvents weakens as the ionizing power of the
medium decreases [13, 14]. For example, the rate of
heterolysis of 1-chloro-1-methylcyclohexane (І) in
propylene carbonate is lower by two orders of magni-
tude than the rate of heterolysis of 1-bromo-1-methyl-
cyclohexane (ІІ), while in cyclohexane, the rates of
both reactions are similar [15, 16].
N
solvolysis) of alkyl halides in the nucleofuge series
I > Br > Cl usually decreases by 2 to 3 orders of
magnitude [2, 3] due to increase in the carbon–halogen
bond energy: 240, 270, and 325 kJ/mol, respectively.
The rate of these reactions is determined by heterolytic
dissociation of the covalent bond, which includes con-
secutive formation of three types of ion pairs: contact,
loose, and solvent-separated [4–6]. The driving force
of heterolysis in a protic medium is electrophilic assist-
ance by the solvent, which becomes stronger as the
solvent electrophilicity (acidity) and nucleofuge elec-
tronegativity rise [2, 4, 7, 8]. Increase in the acidity of
a protic solvent could level the nucleofuge effect on
the reaction rate and even invert the reactivity series.
For example, the ratio of the rates of solvolysis of
We performed correlation analysis of solvation
effects and found that the rate of heterolysis of com-
pounds І and ІІ depends on the solvent polarity (which
is a function of its dielectric constant ε), electrophil-
2
icity (E), and cohesion energy density (δ ).
logk
I
= –(11.0±0.2) + (2.07±0.72)(ε – 1)/(2ε + 1)
2
+ (0.0345±0.0100)E + (0.00210±0.00100)δ ;
R = 0.954, S = 0.20, N = 20;
(1)
(2)
1
(
-adamantyl iodide (1-AdI) and 1-adamantyl bromide
1-AdBr) in EtOH at 25°C is equal to 4, in 2,2,2-tri-
fluoroethanol, to 1, and in (CF ) CHOH, to 0.4 [9, 10].
logkIІ = –(12.1±0.3) + (8.08±1.21)(ε – 1)/(2ε + 1)
3
2
2
+
(0.0541±0.0170)E + (0.00215±0.00100)δ ;
R = 0.969, S = 0.34, N = 20.
Analogous inversion of the reactivity was observed in
the solvolysis of various secondary (Ph CHX, i-PrX)
2
and primary alkyl halides (RCH X, 1-halomethylnaph-
thalenes, allyl halides) [11, 12].
2
The polarity and electrophilicity of aprotic solvents
affect the rate of heterolysis of bromide II more
strongly (by factors of 3.9 and 1.6, respectively) than
*
For communication XVIII, see [1].
50

KINETICS AND MECHANISM OF UNIMOLECULAR HETEROLYSIS ... XIX.
51
the rate of heterolysis of chloride I. The reason is
likely to be higher polarizability of the C–Br bond,
which facilitates electrostatic solvation of bromide.
creases; the reason is that the effects of the solvent
polarity and electrophilicity on the rate of heterolysis
of the bromide are stronger by factors of 1.6 and
1
.3, respectively, as compared to the corresponding
chloride.
Heterolysis of five-membered halogen-containing
In cyclohexane (E = 0), the difference between
compounds І and ІІ is determined only by the solvent
polarity (ε = 2.02), while the effects of cohesion
2
–1 –1
energy density (δ = 281 kJ mol l ) are almost sim-
substrates is likely to involve a linear transition state,
for formation of a six-membered cyclic activated com-
plex is impossible for steric reasons, and the prob-
ability for formation of a four-membered complex is
low [18]. In fact, gas-phase heterolysis of t-BuCl and
t-BuBr occurs through a linear transition state like B
[2, 5], though the formation of four-membered cyclic
transition state C is often postulated without any sub-
stantiation [19, 20]. The formation of a linear activated
complex is supported by the fact that the entropy of
activation in the dehydrohalogenation of tert-butyl
ilar. Calculation using Eqs. (1) and (2) gives logk =
I
–
9.99 and logk = –9.87; these values satisfactorily
IІ
coincide with those found experimentally [14–16]:
logk = –9.88, logk = –9.56. The fact that the free
I
IІ
term in Eq. (3) is considerably smaller than in Eq. (2)
is also responsible for the close rates of heterolysis of
chloride I and bromide II in cyclohexane. Substituting
2
the parameters for vacuum (ε = 1, E = 0, δ = 0) into
Eqs. (2) and (3) leads to logk = –11.0, logk = –12.1,
I
IІ
i.e., compound I appears to be more reactive than II by
an order of magnitude.
≠
halides in the gas phase is close to zero (ΔS ≈ 0) [2].
The formation of a four-membered cyclic transition
state could be accompanied by reduction in the entropy
by 100–150 J mol K [21, 22].
Presumably, the rate-determining stage in the gas
phase is the formation of contact ion pair. The most
stable conformation of 1-halo-1-methylcyclohexanes is
chair with the halogen atom occupying axial position
–
1
–1
X
[
17]. The higher reactivity of chloride I compared to
Me
C
H
Me C Cl–
+
Me
CH2
H
bromide II may be rationalized in terms of the greater
electronegativity of the nucleofuge: the formation of
cyclic transition state like A via interaction between
the axial halogen atom and axial hydrogen atom in the
Me
3
Cl
A
B
C
3
-position is more energetically favorable for X = Cl.
Decrease in the solvent ionizing power also makes
the rates of heterolysis of t-BuCl and t-BuBr in aprotic
media closer, for the effects of the solvent polarity and
electrophilicity on the heterolysis of t-BuBr are
stronger by factors of 1.5 and 1.1, respectively, than on
the heterolysis of t-BuCl [5, 23].
If the dehydrohalogenation according to the E1
mechanism does not involve cyclic transition state like
A, bromides in the gas phase react at a higher rate than
chlorides; however, the bromide/chloride heterolysis
rate ratio strongly falls down as the ionizing power of
aprotic solvent decreases [5, 15, 16]. For example,
In order to get mechanistic explanations of the fact
that the rate of heterolysis of 1-halo-1-methylcyclo-
hexanes in cyclohexane almost does not depend on the
nucleofuge nature, we compared the corresponding en-
tropies and enthalpies of activation. For this purpose,
we examined temperature effect on the rates of
heterolysis of 1-halo-1-methylcyclohexanes I and II in
cyclohexane. These reactions are very slow: the half-
conversion period for chloride I at 25°C is about
1
-chloro-1-methylcyclopentane (ІІІ) in propylene car-
bonate reacts more slowly than does 1-bromo-1-
methylcyclopentane (IV) by 3 orders of magnitude
(
logkIII = –6.57, logkIV = –3.51), whereas the corre-
sponding difference in going to cyclohexane is only one
order of magnitude (logk = –9.87, logk = –8.60).
III
IV
We obtained the following correlations for the
heterolysis of chloride III and bromide IV in aprotic
solvents [15]:
2
00 years. Therefore, we used the verdazyl technique
[
6, 24] which makes it possible to determine within
logkIII = –11.8 + 7.30(ε – 1)/(2ε + 1) + 0.0718E; (3)
R = 0.957, S = 0.30, N = 21;
several hours the rate of a reaction with a half-con-
version period of about 1000 years.
logkIV = –11.2 + 11.5(ε – 1)/(2ε + 1) + 0.0912E; (4)
R = 0.971, S = 0.26, N = 20.
Kinetic experiments were carried out in the pres-
–
4
ence of a small amount (~10 M) of 3,5-bis(4-meth-
oxyphenyl)-1-phenylverdazyl (Vd ) which quickly and
quantitatively reacted with the solvent-separated ion
·
Thus the reactivities of five-membered substrates
become close as the ionizing power of solvent de-
RUSSIAN JOURNAL OF ORGANIC CHEMISTRY Vol. 43 No. 1 2007

5
2
DVORKO et al.
Scheme 1.
C H OMe-p
Me
C H OMe-p
C H OMe-p
6
4
6
4
6
4
Me
X
·
X–
C H OMe-p
+
2
N
N
N
N
+
N
N
N
N
+
N
N
NH
N
Ph
C H OMe-p
Ph
Ph
C H OMe-p
6 4
6
4
6
4
·
+
Vd X–
Vd
VdH
X = Cl, Br.
pair derived from the substrate to give the correspond-
ing olefin, verdazylium salt Vd X , and leucoverdazyl
VdH (Scheme 1). The reaction rate was measured by
methylcyclohexanes I and II in cyclohexane were
+
–
≠
≠
thus estimated as follows: ΔH = 157±2 kJ/mol, ΔS =
I
I
–
1
–1
≠
I
≠
92 ± 6 J mol K , ΔG = 129 ± 4 kJ/mol; ΔH =
II
≠
–1
–1
≠
spectrophotometry, following decrease in the concen-
103±4 kJ/mol, ΔS = –81±11 J mol K , ΔG =
II II
·
tration of Vd (λ = 740 nm, ε = 3500); it satisfac-
128±7 kJ/mol. Bromide ІІ at 25°C is more reactive
than chloride I by a factor of 2.2; at 35°C, the rates
of their heterolysis become similar (k = k = 9.96×
max
torily fits first-order kinetic equation (5):
I
II
·
–10 –1
υ = –∂[Vd ]/2∂τ = k[RX].
(5)
10 s ); and at 49.5°C chloride I is more reactive
than bromide II by a factor of 1.6.
The results of experiments carried out at 25°C
Although the nature of nucleofuge in 1-methyl-
cyclohexyl halides I and II weakly affects the rate of
their heterolysis in cyclohexane, the enthalpies and en-
tropies of activation of these reactions differ consider-
ably. This may be rationalized in terms of solvation
effects. In the heterolysis of bromide II solvation of
–
10
demonstrated their reliability: k = (1.22±0.15)×10 ,
I
–
10 –1
kII = (2.72±0.16)×10 s ; these values agree satis-
factorily with those determined previously: k = 1.32×
I
–10
–10 –1
1
0 , k = 2.74×10 s [15, 16].
II
Figure 1 shows the dependence log(k/T)—1/T. The
activation parameters for the heterolysis of 1-halo-1-
≠
the transition state (ΔS < 0) stabilizes cationoid inter-
≠
mediate, and ΔH decreases. The heterolysis of
–
log(k/T)
chloride I involves desolvation of the transition state
≠
≠
(
ΔS > 0), so that ΔH sharply increases. As a result of
≠
≠
≠
ΔH –ΔS compensation, the ΔG values become closer.
Thus the relative rates of heterolysis of compounds
differing only by the nucleofuge nature strongly
depend on the solvent. In protic solvents, increase of
the ionizing power leads to leveling and subsequent
inversion of the reactivities of such substrates, for the
effect on the less active substrate is stronger (espe-
cially, the effect of solvent electrophilicity) [9, 10].
The reason is greater electronegativity of the nucleo-
fuge in less reactive substrate and hence higher
sensitivity to electrophilic assistance by the solvent via
formation of H-complex RX···HOS. In aprotic sol-
vents, leveling of the substrate reactivities occurs when
the ionizing power of the medium decreases; here, the
effect (especially of the solvent polarity) is stronger on
the more reactive substrate due to greater polarizability
of the C–Br bond compared to C–Cl, which favors
dipolar solvation. Thus the solvation effects in protic
and aprotic solvents are different; therefore, these
effects should be analyzed separately for each group of
solvents.
1
2
1
0
T = 308 K
k = 9.96×10
–
10 –1
s
1
II
I
1
3
3
.0
3.1
3.2
3.3
1/T×10
Fig. 1. Temperature dependences of the rate constants for
heterolysis of 1-chloro-1-methylcyclohexane (I) and
Solvent effects on the heterolysis rate ratio of
substrates differing only in the nucleofuge nature may
1
-bromo-1-methylcyclohexane (II) in cyclohexane.
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KINETICS AND MECHANISM OF UNIMOLECULAR HETEROLYSIS ... XIX.
53
logk
be roughly illustrated by a rhomboid dependence in the
Aprotic
Protic
logk—E coordinates (Fig. 2). Here, the right-hand
T
–
–
–
–
–
–
4
5
6
7
8
9
part of the rhomboid refers to protic solvents, and the
left-hand part, to aprotic ones. The bottom sides reflect
the effect of solvent ionizing power on the rate of
heterolysis of substrates with more electronegative
nucleofuge (less reactive substrates), while the upper
sides show the effect on the more active substrate con-
taining less electronegative nucleofuge.
The maximal difference in the rates of heterolysis
of such substrates is observed in most polar aprotic
solvents (e.g., propylene carbonate) and least polar
–
–
10
11
110
protic solvents (tert-butyl alcohol). In these cases, E ≈
150
190
T
E , kJ/mol
230
270
T
2
2
00 kJ/mol, and the difference in the reaction rates is
to 3 orders of magnitude. When the polarity of
Fig. 2. Plots of the rate of heterolysis of substrates differing
only by the nucleofuge nature versus ionizing power of
solvent E .
T
an aprotic solvent decreases to E ≈ 130 kJ/mol (cyclo-
hexane) or the polarity of a protic solvent increases to
E ≈ 270 kJ/mol (hexafluoropropan-2-ol), the dif-
T
T
ference in the rates of heterolysis becomes smaller
since the rate of heterolysis of more reactive substrate
speak about nonequilibrium solvation [26] which is
related to orientational polarization [29]; the latter is
–16
depends to a stronger extent on E of aprotic solvent
characterized by a sufficiently high rate (~10 s), so
that it capable of affecting transition state formation.
However, orientational polarization could not affect
T
and the rate of heterolysis of less reactive substrate
depends to a stronger extent on E of protic solvent. In
T
≠
≠
the limiting cases, the rates of heterolysis of the sub-
strates under study may coincide or be inverted.
ΔS . Change of ΔS requires essential reorganization of
the initial state solvate shell. It is reasonable to pre-
sume that the initial state includes several solvates and
that only some of them could reach transition state
[30]. It follows that in the heterolysis of bromide II
only the most solvated substrate molecules reach the
transition state, while in the heterolysis of chloride I,
the least solvated. Why?
Formation of an ion pair in the course of heterolysis
is accompanied by structuring of the solvent around
≠
that intermediate (electrostriction); as a result, ΔS falls
down. Electrostriction in protic solvents leads to
≠
destructurization thus raising ΔS . The entropy of
activation in aprotic solvents is always less than zero,
and its value characterizes difference in the solvation
of the initial and transition states. Taking into account
that coordination of one unidentate ligand is accom-
Transition state in the heterolysis is formed via
interaction between the substrate contact ion pair and
solvent cavity. Cavities continuously appear and dis-
appear in solution as a result of density fluctuations,
and they move as “waves through the medium” [6, 31].
The probability for transition state formation depends
on the lifetime of cationoid intermediate and the size
of its solvate shell, for the ion separation process in
a contact ion pair requires a small energy [4, 5]. Ingold
estimated that energy at 17 kJ/mol in benzene [32].
According to the Coulomb law, extension of interionic
distance from 0.25 nm (the distance assumed for
a contact ion pair) to 1 nm (the distance assumed for
a solvent-separated ion pair) in a vacuum requires
an energy of ~20 kJ/mol. However, in going to polar
solvents (ε ≥ 30) this value decreases to <1 kJ/mol.
More advanced calculations [33] and experimental
methods [34, 35] give a value of 3–8 kJ/mol for the
energy of ion separation in a contact ion pair. From the
–
1
–1
panied by loss of ~45 J mol K [25], we presume
that two solvent molecules are additionally involved in
the formation of transition state in the heterolysis of
bromide II. By contrast, the formation of transition
state from chloride I involves desolvation of two sol-
vent molecules.
According to the transition state theory [6, 26],
solvation of transition state is an equilibrium process,
i.e., solvate shells of the initial and transition states
should have similar structures. In this case, the entropy
≠
of activation should not change, ΔS = 0. This assump-
tion is based on the postulate implying that the time
–
13
necessary for transition state formation (~10 s [27])
is insufficient for reorganization of solvate shell, which
–10
–11
≠
requires 10 –10 s [28]. In our case, ΔS values are
considerably different from zero. Therefore, we should
RUSSIAN JOURNAL OF ORGANIC CHEMISTRY Vol. 43 No. 1 2007

5
4
DVORKO et al.
above stated it follows that the energy of ion separa-
tion is not the main factor determining the limiting
stage and that the latter is determined by the frequency
of encounters of a contact ion pair with solvent
cavities having a required size. The heterolysis of
bromide II is favored by increase of the contact ion
pair lifetime due to additional solvation, while the
heterolysis of less solvated chloride I is favored by
reduction of the size of solvated contact ion pair.
0.19 to 0.74 M, the concentration of verdazyl indicator
–
4
was (1–2)×10 M, and the substrate conversion was
–
4
(1.4–28)×10 %. The error in the determination of the
rate constants was ±10%. Given below are temperature
9
–1
(°C) and k×10 (s ): 1-chloro-1-methylcyclohexane
(I): 25.0, 0.122; 41.5, 3.84; 45.0, 7.97; 49.5, 11.2;
1-bromo-1-methylcyclohexane (II): 25.0, 0.272; 32.5,
0.742; 39.5, 1.70; 44.5, 3.98; 49.5, 6.80.
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2
0
(
8
(
7
14 mm), n = 1.4866; published data [36]: bp 83–
D
2
0
4°C (100 mm), n = 1.4868. Compound II: bp 42°C
D
20
D
15 mm), n = 1.4578; published data [36, 37]: bp 78–
2
0
9°C (38 mm), n = 1.4578. Compounds I and II were
D
1
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Chem., 1995, vol. 65, p. 111.
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2. Tablitsy konstant skorosti i ravnovesiya geterolitiche-
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carbonate, dried in succession over sodium sulfate and
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1
1
1
1
1
1
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Kinetic measurements were performed using an SF-
2
6 spectrophotometer in cells maintained at a constant
temperature. Some experimental data obtained at 25°C
were characterized by a relatively large dispersion, and
it was difficult to define the linear dependence
·
[
Vd ]—τ with a required accuracy. Therefore, after
measuring the reaction rate, the reaction solution was
left to stand overnight at 25°C, and the concentration
·
of Vd was determined over a period of several hours.
In such a way, a required accuracy was attained. The
substrate concentration in kinetic experiments was
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KINETICS AND MECHANISM OF UNIMOLECULAR HETEROLYSIS ... XIX.
55
2
2
0. Abraham, M.H., Doherty, R.M., Kamlet, M.J.,
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