Multiparameter correlation of the rate of a [2 + 2] cycloaddition reaction versus solvophobicity parameter and normalized polarity parameter in aqueous solutions

Article abstract of DOI:10.1002/1099-1395(200008)13:8<468::AID-POC258>3.0.CO;2-E

The second-order rate constants of the [2 + 2] cycloaddition reaction between diethyl azodicarboxylate and ethyl vinyl ether were obtained spectrophotometrically in various solvents and aqueous solutions of 1,4-dioxane and methanol at 30 ± 0.1 °C. In all media except aqueous solutions, a very good linear correlation of logk₂ vs E_T^N (normalized polarity parameter) was obtained (n = 11, r = 0.991, s = 0.086). Because of the higher polarity of the activated complex relative to the reactants, the rate of the reaction increase with increasing solvent polarity parameter. Dual-parameter correlation of logk₂ vs π* (dipolarity/polarizability) and a (hydrogen bonding acidity) also gives good results in various solvents (n = 11, r = 0.985, s = 0.118). Both n* and α have approximately equal effects on the reaction rate. In aqueous solutions of 1,4-dioxane and methanol, the second-order rate constants of the reaction increase dramatically with increasing mole fraction of water. A dual-parameter correlation of logk₂ vs Sp (solvophobicity parameter) and E_T^N was found in aqueous solutions (n = 13, r = 0.988, s = 0.165), in which Sp plays an important role in determining the reaction relative to E_T^N. This model represents a significant improvement in regression coefficient with respect to the single parameter correlation vs Sp or E_T^N (r = 0.954 and 0.854, respectively). Similarly to aqueous solutions, a dual-parameter correlation of logk₂ vs Sp and E_T^N was obtained in all media (n = 21, r = 0.987, s = 0.177). Copyright

Full text of DOI:10.1002/1099-1395(200008)13:8<468::AID-POC258>3.0.CO;2-E

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2000; 13: 468–472
Multiparameter correlation of the rate of a [2 ‡ 2]
cycloaddition reaction versus solvophobicity parameter
and normalized polarity parameter in aqueous solutions
M. R. Gholami* and A. Habibi Yangjeh
Department of Chemistry, Sharif University of Technology, P.O. Box 11365-9516, Tehran, Iran
Received 25 November 1999; revised 24 February 2000; accepted 24 February 2000
ABSTRACT: The second-order rate constants of the [2 ‡ 2] cycloaddition reaction between diethyl azodicarboxylate
and ethyl vinyl ether were obtained spectrophotometrically in various solvents and aqueous solutions of 1,4-dioxane
N
and methanol at 30 Æ 0.1°C. In all media except aqueous solutions, a very good linear correlation of logk vs E
2
T
(
normalized polarity parameter) was obtained (n = 11, r = 0.991, s = 0.086). Because of the higher polarity of the
activated complex relative to the reactants, the rate of the reaction increase with increasing solvent polarity parameter.
Dual-parameter correlation of logk vs p* (dipolarity/polarizability) and a (hydrogen bonding acidity) also gives good
2
results in various solvents (n = 11, r = 0.985, s = 0.118). Both p* and a have approximately equal effects on the
reaction rate. In aqueous solutions of 1,4-dioxane and methanol, the second-order rate constants of the reaction
increase dramatically with increasing mole fraction of water. A dual-parameter correlation of logk vs Sp
2
N
(
solvophobicity parameter) and ET was found in aqueous solutions (n = 13, r = 0.988, s = 0.165), in which Sp plays
an important role in determining the reaction relative to ET . This model represents a significant improvement in
regression coefficient with respect to the single parameter correlation vs Sp or ET (r = 0.954 and 0.854, respectively).
Similarly to aqueous solutions, a dual-parameter correlation of logk vs Sp and E was obtained in all media (n = 21,
N
N
N
2
T
r = 0.987, s = 0.177). Copyright  2000 John Wiley & Sons, Ltd.
KEYWORDS: solvophobicity parameter; cycloaddition reaction; solvent effects; polarity parameter; kinetics;
multiparameter correlation; dipolarity; hydrogen bonding acidity
INTRODUCTION
has been paid to Diels–Alder cycloadditions owing to the
different solvation mechanisms involved in this pro-
12–16
Water is an unconventional solvent for organic reactions.
However, in addition to obvious economical and
environmental advantages, water has surprisingly bene-
ficial effects on organic reactions, which has popularized
cess.
More recently, in the 1,3-dipolar cycloaddition
reaction of C,N-diphenylnitrone with various dipolaro-
philes, hydrophobic interactions were considered to be a
major factor in increasing of the reaction rate in aqueous
1
,2
17,18
water as a reaction medium. Studies in the last decade
have revealed that a number of organic reactions proceed
more rapidly in aqueous solutions than in organic
media.
After the success of the Diels–Alder and 1,3-dipolar
cycloaddition reactions in aqueous solutions, we were
interested in a [2 ‡ 2] cycloaddition reaction in order to
investigate the effects of aqueous solutions on these class
of cycloadditions. Detailed kinetic studies of organic
reactions in this field have been restricted to [2 ‡ 4] and
3
–7
solvents.
Detailed kinetic studies and computer
simulations suggest that hydrophobic interactions have
an important role in the acceleration of organic reactions
in aqueous solutions.
kinds of approaches to hydrophobic hydration is
necessary for a better understanding of its key role in
controlling biochemical processes in water.
Modeling of solvent effects is one of the most useful
methods to obtain information about the mechanism of
organic reactions. In the last few years, special attention
8
,9
The development of various
6,7
[2 ‡ 3] cycloaddition reactions. Therefore, we studied
the [2 ‡ 2] cycloaddition reaction of diethyl azodicar-
boxylate with ethyl vinyl ether in various solvents and
aqueous solutions of 1,4-dioxane and methanol at 30°C
(Scheme 1).
1
0,11
*
Correspondence to: M. R. Gholami, Department of Chemistry, Sharif
University of Technology, P.O. Box 11365-9516, Tehran, Iran.
E-mail: gholami@ch.sharif.ac.ir
Scheme 1.
Copyright  2000 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2000; 13: 468–472

MULTIPARAMETER CORRELATION OF RATE OF A [2 ‡ 2] CYCLOADDITION REACTION
469
a
Table 1. First-order rate constants of reduction and hydrolysis reaction of diethyl azodicarboxylate in various solvents at 30°C
�
1
5
k0 (s� 1)Â105
Medium
k0 (s )Â10
Medium
MeOH
4.23 Æ 0.11
1.21 Æ 0.04
1.69 Æ 0.05
2.68 Æ 0.08
17.9 Æ 0.5
33.2 Æ 0.8
42.9 Æ 0.9
64.9 Æ 1.2
MeOH (50:50)
1,4-Dioxane (90:10)
1,4-Dioxane (80:20)
1,4-Dioxane (70:30)
1,4-Dioxane (60:40)
1,4-Dioxane (50:50)
1,4-Dioxane (40:60)
102 Æ 2
EtOH
0.272 Æ 0.006
2.02 Æ 0.05
5.06 Æ 0.11
11.3 Æ 0.2
21.3 Æ 0.5
48.3 Æ 0.9
Propan-1-ol
Propan-2-ol
MeOH (90:10)
MeOH (80:20)
MeOH (70:30)
MeOH (60:40)
a
Errors are standard deviations; at least three runs were averaged. Solutions were prepared in water (ratios are v/v).
RESULTS AND DISCUSSION
obtained in all solvents except aqueous solutions of
methanol and 1,4-dioxane:
The solvents were selected according to their Sp
N
(solvophobicity parameter) and ET (normalized polarity
N
log k ˆ � 5:305ꢀÆ0:051† ‡ 2:553ꢀÆ0:114†E
ꢀ2†
2
T
parameter) values in order to cover a broad range of
solvents. Diethyl azodicarboxylate is reduced by alco-
ꢀ
n ˆ 11; r ˆ 0:991; s ˆ 0:086; F ˆ 498:2†
1
;9
1
9
20,21
hols and is hydrolyzed in aqueous solutions
of 1,4-
N
dioxane and methanol; therefore the second-order rate
Figure 1 shows plot of logk vs E . The second-order
2 T
constants of the [2 ‡ 2] cycloaddition reaction (k ) of this
rate constants of this reaction increase with increasing
solvent polarity parameter. This increase is attributed to a
major interaction of polar solvents with the activated
complex relative to the reactants; therefore, the polarity
of the activated complex of the reaction is higher than
those of the reactants. Changes in solute–solvent
interactions during the activation process will influence
the rate constant. Reactions which are accompanied by an
increase in charge separation in their activation process
are accelerated in solvents of increasing polarity. It is
clear that solvent effects for the reaction are modest such
that k (in methanol)/k (in toluene) is approximately 46.
2
compound with ethyl vinyl ethyl (EVE) in these media
were obtained from the equation
kobs � k ˆ k ‰EVEŠ
ꢀ1†
0
2
where k is the first-order rate constant of hydrolysis and
0
reduction reaction of diethyl azodicarboxylate and kobs is
observed pseudo-first-order rate constant of the overall
reaction of diethyl azodicarboxylate. The values of k0
were obtained in aqueous solutions and alcoholic media
in separate experiments (Table 1).
2
2
The second-order rate constants of [2 ‡ 2] cycloaddi-
tion were obtained in various solvents and aqueous
solutions of 1,4-dioxane and methanol at 30°C (Tables 2
and 3).
In contrast to strongly solvent-dependent [2 ‡ 2] cy-
cloaddition reactions (which proceed through a 1,4-
dipolar zwitterionic intermediate by a two-step mechan-
ism or through a dipolar activated complex by a one-step
mechanism), [2 ‡ 2] cycloadditions are also known
which exhibit one-step, nearly synchronous bond forma-
tion without significant charge separation in the activated
N
A very good linear correlation of logk vs E was
2
T
Table 2. Rate constants of [2 ‡ 2] cycloaddition reaction of diethyl azodicarboxylate with ethyl vinyl ether in various solvents at
a
3
0°C
N
� 1 � 1
5
Solvent
ET
Sp
p*
a
k2 (l mol
s
)Â10
logk2
Toluene
Benzene
0.099
0.111
0.164
0.207
0.228
0.404
0.444
0.546
0.617
0.654
0.762
0.000
0.000
0.079
—
0.064
0.138
0.227
0.100
0.108
0.144
0.200
0.49
0.59
0.55
0.58
0.55
0.88
1.00
0.49
0.52
0.51
0.58
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.76
0.84
0.98
1.14
0.807 Æ 0.026
1.19 Æ 0.05
1.33 Æ 0.05
1.36 Æ 0.06
1.94 Æ 0.06
3.72 Æ 0.13
8.38 Æ 0.18
14.6 Æ 0.3
20.4 Æ 0.4
24.6 Æ 0.5
36.8 Æ 0.5
� 5.093
� 4.924
� 4.876
� 4.866
� 4.712
� 4.429
� 4.077
� 3.836
� 3.690
� 3.609
� 3.434
1
,4-Dioxane
THF
Ethyl acetate
DMF
DMSO
Propan-2-ol
Propan-1-ol
Ethanol
Methanol
a
Errors are standard deviations; at least three runs were averaged.
Copyright  2000 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2000; 13: 468–472

4
70
M. R. GHOLAMI AND A. H. YANGJEH
Table 3. Rate constants of [2 ‡ 2] cycloaddition reaction of diethyl azodicarboxylate with ethyl vinyl ether in various pure
a
solvents and aqueous solutions at 30°C
N
� 1 � 1
5
Medium
ET
Sp
k2 (l mol
s
)Â10
logk2
1
1
1
1
1
1
1
,4-Dioxane
0.164
0.494
0.565
0.624
0.667
0.707
0.750
0.762
0.784
0.799
0.818
0.836
0.852
0.079
0.062
0.139
0.245
0.390
0.521
0.646
0.200
0.273
0.354
0.446
0.531
0.631
1.33 Æ 0.05
5.54 Æ 0.05
16.4 Æ 0.6
51.6 Æ 1.7
120 Æ 1.9
419 Æ 14
� 4.876
� 4.256
� 3.785
� 3.287
� 2.921
� 2.378
� 2.066
� 3.434
� 3.237
� 2.815
� 2.188
� 1.940
� 1.439
,4-Dioxane (90:10)
,4-Dioxane (80:20)
,4-Dioxane (70:30)
,4-Dioxane (60:40)
,4-Dioxane (50:50)
,4-Dioxane (40:60)
858 Æ 22
MeOH
36.8 Æ 0.5
58.0 Æ 2.1
153 Æ 8
MeOH (90:10)
MeOH (80:20)
MeOH (70:30)
MeOH (60:40)
MeOH (50:50)
649 Æ 16
1148 Æ 26
3636 Æ 74
a
Errors are standard deviations; at least three runs were averaged. Solutions were prepared in water (ratios are v/v).
2
2,23
complex.
Since this reaction shows modest solvent
hydrogen bonding acidity of the medium have approxi-
mately equal effects on the reaction rate. A plot of
effects, we therefore suggest that the polarity of the
activated complex of the reaction cannot be very different
from those of the reactants. The unequal (non-synchro-
nous) bond formation in the activated complex creates
partial charges which are stabilized by polar solvents. As
experimental values of logk vs values calculated using
2
Eqn. (3) shows that the interpretations are accurate (Fig.
2). The single-parameter correlation of logk vs p* and a
2
gives bad results (r = 0.030 and 0.897, respectively).
Because of solubility problems and strong hydrolysis
of diethyl azodicarboxylate in water, the second-order
rate constant of the reaction in this solvent was not
obtained. In order to study effect of water on this
reaction, rate constants of the reaction were obtained in
aqueous solutions of 1,4-dioxane and methanol (Table 3).
Figure 3 shows a plot of second-order rate constants of
N
a result, the correlation of logk vs E is very good. The
2
T
N
normalized polarity parameter (ET ) is a blend of pure
polarity (dipolarity/polarizability) and hydrogen bonding
interactions. In order to show the magnitude of these
interactions in the reaction rate, a dual-parameter
correlation of logk vs p* and a was obtained:
2
Ã
the reaction vs mole fraction of water (X ). It is clear that
log k ˆ � 5:767ꢀÆ0:165† ‡ 1:606ꢀÆ0:241†ꢀ
w
2
the rate constants of the reaction increase dramatically on
addition of water. The increase in the reaction rate in
aqueous solutions of methanol is higher than that in 1,4-
dioxane. These observations are similar to those for
Diels–Alder and 1,3-dipolar cycloaddition reactions in
‡
1:361ꢀÆ0:084†ꢁ ꢀ3†
ꢀ
n ˆ 11; r ˆ 0:985; s ˆ 0:118; F2 ˆ 129:7†
;8
As can be seen, the coefficients of p* and a are not very
different. As a result, the dipolarity/polarizability and
Figure 2. Plot of the experimental values of logk2 vs
calculated values from Eqn. (2) (dual-parameter model of
N
Figure 1. Plot of logk vs ET for the [2 ‡ 2] cycloaddition
2
reaction in various solvents at 30°C
Copyright  2000 John Wiley & Sons, Ltd.
logk
2
vs p* and a) for the reaction in various solvents at 30°C
J. Phys. Org. Chem. 2000; 13: 468–472

MULTIPARAMETER CORRELATION OF RATE OF A [2 ‡ 2] CYCLOADDITION REACTION
471
�
1 � 1
Figure 4. Plot of the experimental values of logk
calculated values from Eqn. (4) (dual-parameter model of
2
vs
Figure 3. Plot of k2 (l mol
cycloaddition reaction in aqueous solutions of 1,4-dioxane
‡ symbols and right-hand scale) and methanol (* symbols
and left-hand scale) at 30°C
s
) vs Xw for the [2 ‡ 2]
N
logk vs Sp and E ) for the reaction in aqueous solutions of
2
T
(
1,4-dioxane and methanol at 30°C
1
7,18
aqueous solutions.
This increase in the reaction rate
reactants and hence the reaction rate increases. Also, the
solvent would destabilize the reactants through its
solvophobicity factor, because in the reaction of two
is not due to the polarity of the medium, because a good
linear correlation of logk vs ET was not obtained in
N
24
2
aqueous solutions of methanol and 1,4-dioxane (n = 13,
r = 0.854). In order to analyze the effects of the medium
on the reaction rate, a dual-parameter correlation of logk2
vs ET and Sp in aqueous solutions of 1,4-dioxane and
methanol was found:
apolar reactants, the unfavorable water contacts with
reactants are reduced and then the apolar reactants have a
13
tendency to stick together in aqueous solutions. These
factors increase the reaction rate dramatically so that the
ratio of k (in 50% aqueous methanol) to k (in toluene) is
N
2
2
approximately 4505. The second-order rate constant of
the reaction in water calculated from Eqn. (4) is 0.75
l mol s , but the expected value from correlation of
N
log k ˆ � 5:441ꢀÆ0:184† ‡ 1:882ꢀÆ0:354†E
2
T
�
1
� 1
‡
3:432ꢀÆ0:334†Sp ꢀ4†
n ˆ 13; r ˆ 0:988; s ˆ 0:165; F2 ˆ 207:9†
N
� 3
� 1 � 1
logk vs E [Eqn. (2)] is 1.77 Â 10 l mol s . The
2
T
ꢀ
;10
ratio of the calculated second-order rate constant of the
reaction from Eqn. (4) to the expected value from Eqn.
(2) is approximately 420. In fact, this ratio shows a
contribution of hydrophobic interactions with increase in
the reaction rate. In order to show the applicability of
It is obvious that Sp plays a more important role in
determining the reaction rate relative to the normalized
polarity parameter in aqueous solutions of 1,4-dioxane
and methanol. This dual-parameter model represents a
significant improvement in regression coefficient with
respect to the single-parameter models (r = 0.854 only
N
dual-parameter correlation of logk vs E and Sp in the
2
T
all solvents (various solvents and aqueous solutions), a
similar equation was obtained in the all solvents (except
for THF, the Sp value of which was not found in the
literature):
N
with ET and r = 0.954 only with Sp) and the calculated
results from Eqn. (4) are in good agreement with the
experimental results. The values of logk from experi-
2
N
mental data were plotted against the values of logk2
calculated by Eqn. (4) (Fig. 4). Similar studies on Diels–
Alder reactions showed lower regression coefficients
log k ˆ � 5:359ꢀÆ0:106† ‡ 1:892ꢀÆ0:255†E
2
T
‡
3:206ꢀÆ0:304†Sp ꢀ5†
ꢀ
n ˆ 21; r ˆ 0:987; s ˆ 0:177; F
ˆ 349:7†
(
r = 0.961 for the reaction of cyclopentadiene with
2;18
1
2
acrylonitrile and r = 0.942 for the reaction of cyclo-
1
6
pentadiene with methyl acrylate ). In fact, Eqn. (4)
implies that the activated complex of the reaction which
has higher polarity relative to the reactants would be
stabilized by the polarity of medium (dipolarity/polariz-
ability and hydrogen bonding ineraction). Hydrogen
bonding between water molecules and hydrogen-bond
acceptor groups in the more polarizable activated
complex stabilize the activated complex relative to the
In this case also Sp plays a more important role in
N
determining the reaction rate relative to E . Single-
T
N
parameter correlations of logk vs Sp and E do not give
good results (r = 0.948 only with Sp and r = 0.906 with
ET ). Figure 5 shows a plot of experimental values of
logk vs expected values calculated by Eqn. (5).
In 1,3-dipolar cycloaddition reactions of C,N-diphe-
nylnitrone with various dipolarophiles, the polarity of the
2
T
N
2
Copyright  2000 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2000; 13: 468–472

4
72
M. R. GHOLAMI AND A. H. YANGJEH
decrease in the diethyl azodicarboxylate absorbance at
05 nm. Thermostated water was circulated around the
4
cell of the spectrophotometer and the temperature was
maintained at 30 Æ 0.1°C.
The concentrations of ethyl vinyl ether varied from
0
.059 M (in aqueous solutions of methanol) to 0.562 M (in
toluene) and those of diethyl azodicarboxylate from
.005 M (in aqueous solutions of methanol) to 0.0368 M
0
(in toluene).
In all cases pseudo-first-order kinetics were observed.
Pseudo-first-order rate constants of the reaction rates
were obtained by the initial rate method or from slopes of
plots of ln(A � A ) vs time t. At least three runs were
t
?
averaged for each rate constant.
Figure 5. Plot of the experimental values of logk2 vs
calculated values from Eqn. (5) (dual-parameter correlation
N
of logk vs Sp and E ) for the reaction in various solvents
2
T
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2
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1
7
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8
(
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N
5
6
7
8
9
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3
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ethyl vinyl ether, Sp and ET have similar effects on in
1
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a greater interaction of polar solvents with it, and a
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1
1
EXPERIMENTAL
1
1
1
Materials. Diethyl azodicarboxylate was synthesized
2
5
according to the literature. Ethyl vinyl ether was
purchased from Merck and distilled before use. All
solvents of high purity were distilled before use. Water
was redistilled in a quartz distillation unit.
2
2
(
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Copyright  2000 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2000; 13: 468–472