The model of 1,3-dipolar cycloaddition reaction of 4,5-dihydro-1H-imidazole 3-oxide derivatives with alkynes

Article abstract of DOI:10.1016/j.molstruc.2007.02.015

The influence of solvents and different structural factors on the rate of 1,3-dipolar cycloaddition reaction of the 4,5-dihydro-1H-imidazole 3-oxide derivatives with alkynes have been studied. Nitrones and alkynes have been ranged by their relative activity in this reaction. Using the DFT calculation with the triple zets basis set, the energy profile of the reaction has been plotted, and the structures and energy characteristics of the transition states have been determined. The mechanism of this reaction has been shown to be concerted and asynchronous. The validity of the used computational approach for the detailed investigation of 1,3-dipolar cycloaddition of nitrones has been demonstrated.

Full text of DOI:10.1016/j.molstruc.2007.02.015

Available online at www.sciencedirect.com
Journal of Molecular Structure 872 (2008) 30–39
www.elsevier.com/locate/molstruc
The model of 1,3-dipolar cycloaddition reaction of 4,5-dihydro-1
H-imidazole 3-oxide derivatives with alkynes
a,
b
a
Sergey A. Popov *, Galina V. Romanenko , Vladimir A. Reznikov
a
N.N. Vorozhtsov Institute of Organic Chemistry, Siberian Branch of the Russian Academy of Sciences, akad. Lavrent’ev Ave. 9, 630090 Novosibirsk, Russia
b
International Tomography Center, Siberian Branch of Russian Academy of Sciences, Institutskaya str. 3a, 630090 Novosibirsk, Russia
Received 27 March 2006; received in revised form 2 February 2007; accepted 6 February 2007
Available online 17 February 2007
Abstract
The influence of solvents and different structural factors on the rate of 1,3-dipolar cycloaddition reaction of the 4,5-dihydro-1H-imid-
azole 3-oxide derivatives with alkynes have been studied. Nitrones and alkynes have been ranged by their relative activity in this reaction.
Using the DFT calculation with the triple zets basis set, the energy profile of the reaction has been plotted, and the structures and energy
characteristics of the transition states have been determined. The mechanism of this reaction has been shown to be concerted and asyn-
chronous. The validity of the used computational approach for the detailed investigation of 1,3-dipolar cycloaddition of nitrones has
been demonstrated.
ꢀ 2007 Elsevier B.V. All rights reserved.
Keywords: 1,3-Dipolar cycloaddition; Kinetics; DFT calculation; Nitrones; Alkynes
1. Introduction
interactions for the stereo- and regioselectivity in the fore-
going reactions [13,14].
Well known 1,3-dipolar cycloaddition reactions of nitro-
nes as 1,3-dipoles are used for a long time in the organic
synthesis. Nevertheless, discussion about the mechanism
of these reactions initiated in the early sixties of the past
century [1,2] is still continuing. There are at least three sub-
stantially different variants of the 1,3-dipolar cycloaddition
pathways: concerted (but asynchronous) mechanism [1,3]
and two stepwise (biradical [2,4–6] and zwitterionic [7])
mechanisms. The number of stages and thereupon the
structure of the transition state in the case of the concerted
mechanism are fundamental questions concerning the reac-
tion path.
Lately, the series of theoretical researches was focused
on characterization of the structure and energy of the tran-
sition states in the 1,3-dipolar cycloaddition reactions [8–
12]. The experimental data and ab initio calculations
undoubtedly point out the predominant role of the orbital
One of the insufficiently explored nitrone types is 4,
5-dihydro-1H-imidazole 3-oxide derivatives [15]. The dis-
tinctive feature of these compounds is the presence of the
heteroatomic substituent at the a-carbon atom of the
nitrone group. This sp3-hybridized nitrogen atom is capa-
ble of efficient conjugation with p-system of the nitrone
group, thereby determining the peculiarity of the latter.
There are numerous literature data concerning the rate
constants of 1,3-dipolar cycloaddition reactions of nitrones
to alkenes [16,17]. In particular, the slight decrease of the
reaction rate with the enhance of the solvent polarity is
noted [16,18], which is in accordance with the conception
of the concerted mechanism of this process.
The reaction of 2-substituted 4,5-dihydro-1H-imidazole 3-
oxide derivatives with activated alkynes, as we shown earlier,
occurs with high regioselectivity [19]. The goal of our study is
to ascertain the mechanism of 1,3-dipolar cycloaddition reac-
tions of 4,5-dihydro-1H-imidazole 3-oxyde derivatives with
alkynes taking into consideration experimental data and the
quantum-mechanical model of this process.
*
Corresponding author.
E-mail address: serge@nioch.nsc.ru (S.A. Popov).
0022-2860/$ - see front matter ꢀ 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2007.02.015

S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
31
2. Results and discussion
Investigation of the influence of solvents and substitu-
ents nature on the reaction rate and selectivity is very
important when studying the reaction mechanism. We have
reported [19] that variation of R1 and R2 substituents in the
4,5-dihydro-1H-imidazole 3-oxide derivatives 1 (Table 1)
does not result in changing the regioselectivity of cycload-
dition (Scheme 1).
The literature data [20] allows assumption that 1,3-dipo-
lar cycloaddition is a reaction of first order on each reagent
and fits the Eq. (1)
rate ¼ k½nitroneꢀ½alkyneꢀ
ð1Þ
When the process is carried out under pseudo-first order
conditions (the significant excess of one of the compo-
nents), the solution of Eq. (1) is Eq. (2):
Fig. 1. First-order plot of the reaction of 1f with 10-fold excess of 2e in
chloroform at 24 ꢁC.
ln½Riꢀ ¼ ꢁkeff ꢂ t þ Const
where Ri is a minor component and keff is the effective rate
ð2Þ
Only few data concerning the constant rate values for
the reactions of nitrones with alkynes in some solvents were
obtained [18,20] when acyclic N-alkyl-C-phenylnitrones 5
were studied (Scheme 2). The rate constants for the forma-
tion of cycloadducts 7a and 7c in some solvents are pre-
sented in Table 4 [18,20].
constant.
As it follows from Eq. (2), for the reaction of first order
on component Ri a linear dependence between ln[Ri] and
reaction time t should be observed. The correlation
between ln[nitrone] and t in the reaction of derivative 1f
with 10-fold excess of alkyne 2e in chloroform is outlined
on Fig. 1. Similar correlations are obtained for some nitro-
nes and alkynes in various solvents (Tables 2 and 3,
respectively).
Thus, the reaction under consideration is described by
kinetic Eq. (1) for different derivatives 1 and 2 irrespective
of solvent nature that allows the values of rate constants k
to be obtained.
In the present work the rate constants for the cycloaddi-
tion of nitrones 1e and 1f with alkynes 2d–f were deter-
1
mined using H NMR and UV spectroscopy (Table 4). In
order to compare the literature and experimental data,
we also determined the rate constants for the formation
of 7b from 5b and 2d (Table 4).
It should be noted that cycloadduct 7b formed from 5b
by the interaction with 1,3-diphenylpropynale 2d is stable
under the reaction conditions and does not rearrange to
2,3-dihydroisoxazole derivative 8b even at 80 ꢁC (Scheme
2), as it occurs in the case of similar 4H-isoxazole deriva-
tives 7 [21]. The structure of 7b was proved by X-ray anal-
ysis (Fig. 2).
Table 1
Nitrones 1 and alkynes 2 under investigation
Nitrones
R1
R2
Alkynes
R3
R4
1a
1b
1c
1d
1e
1f
H
H
H
Me
Me
Me
Me
H
Me
Ph
Me
2a
2b
2c
2d
2e
2f
H
H
Me
Ph
MeO
MeO
MeO
EtO
H
Ph
Ph
Ph
H
Ph
CO2Me
CF3
2.1. Solvent effect
Data of Table 4 demonstrate that the rate of the reac-
tion of nitrones 1 with disubstituted alkynes 2 noticeably
increases with the enhancement of the medium polarity
(Fig. 3).
Ph
4-NO2-C6H4
4-MeO-C6H4
1g
2g
2h
O
R4
R3
O
R4
O
O
56
N
N
7
N
R3
7a
4
3
2
+
R2
R4
1
N
R2
R2
N
N
O
R1
3
R1
R1
O
R3
1a-g
not observed
2a-h
Scheme 1. Regioselectivity in the 1,3-cycloaddition reaction of the 4,5-dihydro-1H-imidazole 3-oxide derivatives 1 with alkynes.

32
S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
Table 2
Pseudo-first order equations for the reactions of nitrones 1e and 1f with the excess of alkynes 2d–f in different solvents
Nitrone
alkyne
Excess of alkyne
Solvent
Equation
R
Method
1e
1f
2f
2d
9.0
7.0
CCl4
CCl4
Y = ꢁ2.732 · 10ꢁ4 · X ꢁ 3.901
Y = ꢁ1.843 · 10ꢁ4 · X ꢁ 6.866
Y = ꢁ1.350 · 10ꢁ3 · X ꢁ6.546
Y = ꢁ1.310 · 10ꢁ3 · X ꢁ 7.352
Y = ꢁ3.515 · 10ꢁ4 · X ꢁ5.823
Y = ꢁ8.879 · 10ꢁ5 · X ꢁ 8.084
Y = ꢁ8.368 · 10ꢁ4 · X ꢁ 6.112
0.9996
NMR
UV
UV
UV
UV
UV
UV
0.99997
0.99993
0.99996
0.99999
0.9997
10.4
10.1
10.0
10.0
10.0
Acetone
DMSO
CHCl3
Acetone
DMSO
2e
0.99994
Table 3
Pseudo-first order equations for the reactions of alkynes 2e and 2f with the excess of nitrone 1e
Alkyne
Nitrone
Excess of nitrone
Solvent
Equation
R
Method
2e
2f
1e
1e
4.5
9.0
CHCl3
CCl4
Y = ꢁ0.0012 · X ꢁ 4.713
0.998
0.9995
NMR
NMR
Y = ꢁ3.186 · 10ꢁ4 · X ꢁ3.805
R2
R3
R3
R2
R3
O
O
k
R1
N
R1
N
R1
N
+
O
80 oC
Ph
R2
Ph
Ph
2d
6(a,b)
7(a-c)
5(a,b)
8b
R1
Me 5a
t-Bu 5b
R2
R3
R1
Me
R2
R3
CN
H
6a
CN
H
7a
C[W(CO)5]OMe
Ph 6b
t-Bu COPh
t-Bu C[W(CO)5]OMe
Ph 7b
Ph 7c
Scheme 2. Constant rates for the reactions of acyclic N-alkyl-C-phenylnitrones 5 with alkynes.
This effect is atypical for C-substituted nitrones 5 (cf. Table
4) and observed for nitrones 1 may testify the higher polarity
of the transition states in comparison with the polarity of the
reagents. At the same time, the relatively low influence of the
solvent polarity on the reaction rate does not allow one to con-
clude that the zwitterionic intermediate is formed. Thus, the
replacement of carbon tetrachloride by acetonitrile accelerates
[2+2] cycloaddition of the tetracyanoethylene to 3,4-dihydro-
2H-pyran proceeding with the formation of the zwitterionic
intermediate by a factor of 17,000 [22].
The absence of the mentioned tendency for the terminal
alkynes is obviously the result of the formation of hydro-
gen bond C–Hꢃ ꢃ ꢃO between the dipolarophile and the sol-
vent or nitrone [23,24].
Table 4
The rate constants of cycloaddition reaction of nitrones 1e and 1f and 5 with alkynes 2d–f and 6
Nitrone
Alkyne
k · 10ꢁ4 (Mꢁ1 sꢁ1) at 24 ꢁC
MeOH
CHCl3
C6H6
CCl4
THF
Acetone
CH3CN
DMSO
1e
1f
2fa
2db
2eb
<0.4
–
7.25
1.8
61
123
–
–
–
18
274
425
–
620
–
35
950
287
–
1390
–
80
2110
396
5a
5b
6ac
2da
6bc
34
–
–
–
–
–
190
–
–
–
–
–
2270
140
0.007
3510
–
–
3080
150
0.036
–
0.028
–
a
According to 1H NMR.
According to UV spectroscopy.
At 25 ꢁC.
b
c

S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
33
Table 5
Relative rate constants for the reactions of alkynes 2 with nitrones 1(d–g)
and 5a in chloroform at 24 ꢁC obtained from 1H NMR and UV data
Alkynes
krel
1d
1e
1f
1g
5aa
2f
2c
2d
2e
2b
2g
2a
2h
a
–
–
–
1
16.5
–
–
5.2 · 10ꢁ3
1.26 · 10ꢁ1
3.94 · 10ꢁ1
1
18.7
370
–
–
–
–
–
1
18.1
–
–
–
–
–
1
–
75
–
4.95 · 10ꢁ1
1
13.7
–
–
–
810
>8 · 104
–
–
–
At 25 ꢁC in CDCl3 [27].
order: 2f < 2c < 2d < 2b. This tendency, however, has dis-
tinctive features. For example, the replacement of terminal
alkynes 2a and 2e by their phenyl-substituted analogs 2d
and 2f, respectively, leads to the diminution of the reaction
rate by two orders of magnitude, on average (cf. Table 5).
Taking into account regioselectivity of the reaction, this
effect cannot be explained by steric hindrance. Another
example is more than the 100-fold increase of the reaction
rate of 4,4,4-trifluorobut-2-ynoate 2h as compared to that
of dimethylacetylenedicarboxylate (DMAD) 2g, i.e. when
the ester group is replaced by the trifluoromethyl residue,
which has no p-withdrawing effect (Table 5). The ester
group, however, remains to be the substituent determining
the regioselectivity of the reaction.
Fig. 2. Crystal structure of (2-tert-butyl-3,5-diphenyl-2,3-dihydroisoxa-
zol-4-yl)phenyl-methanone 7b, CCDC 293549.
Comparison of the relative reaction rates of nitrones 1 and
‘‘isolated’’ nitrone 5a (Table 5) reveals significantly lower sub-
strate selectivity of the latter in the reactions with alkynes; in
other words, compounds 1 are more sensitive to the substitu-
ent nature in alkyne molecule than compound 5a.
2.3. Effect of substituents in nitrone
In order to reveal the influence of substituents R1 and
R2 in nitrones 1 on the reaction rate, a several experiments
were carried out using the method of competitive reactions.
Relative rate constants for the reactions of nitrones 1 with
alkynes 2 are represented in Table 6.
Fig. 3. Dependence of the rate constants k on solvent polarity (e) in the
reaction of nitrones 1f and 1e with alkynes 2d and 2f, respectively.
Solvents such as chloroform and, especially, methanol
are capable of forming strong H bonds with the oxygen
atom of nitrone [25,26] thereby hindering the reaction
(Table 4).
The nature of R2 directly bound to nitrone appreciably
influences the reaction rate. Thus, the replacement of
Table 6
Relative rate constants for the reactions of nitrones 1 with alkynes 2 in
chloroform at 24 ꢁC obtained from 1H NMR data
2.2. Effect of substituents in alkyne
a
Nitrones
krel
rpþ
2a
2b
2e
2.2b
0.29
1
2.8
6.1
17.1
2g
2h
The nature of the substituent in alkyne is shown to be
the important factor influencing the reaction rate. Using
the method of competitive reactions and comparing the
rate constants, the relative activities of alkynes 2 with
respect to nitrones 1 were determined (Table 5).
The data of Table 5 demonstrate that the reaction rate
increases, as a rule, with the enhance of the p-withdrawing
effect of the substituent in alkyne; rate constants rises in
1b
1c
1f
1e
1g
1d
a
–
–
1
–
2.9
–
–
–
1
2.7
6.2
–
–
1
–
4.7
–
–
–
1
–
6.9
–
–
–
0.79
0
ꢁ0.78
18.9
Ref. [28].
At 21 ꢁC.
b

34
S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
methyl group (compounds 1b and 1d) by phenyl group
(compounds 1c and 1e) leads to slow down the reaction
by factors of 6–7 (Table 6), probably, due to increasing
the steric hindrances. This assumption is in accordance
with the fact that the (2,4-dimethyl)phenyl substituent con-
siderably reduces the reactivity of the studied nitrone, while
4,5-dihydro-1H-imidazole 3-oxyde, bearing (2,4,6-tri-
methyl)phenyl substituent, is practically inactive with
respect to dipolarophiles [19].
N-tert-alkyl nitrone 1e and C-phenyl nitrone 5b (cf. Tables
4 and 6). These compounds differ from each other by the
nitrogen atom attached to nitrone group (1e). Nitrone 1e
reacts with alkyne 2d faster than 5b by a factor of
2.7 · 104 in CCl4 and of 4 · 105 in acetone [30]. Similar
but not so significant activating effect of the a-heteroatomic
substituent was demonstrated earlier for oxazoline-N-oxi-
des 9 (Scheme 3 and Table 7) [31,32].
Thus, the influence of a-heteroatomic substituent on the
nitrone activity can be also evaluated by comparison of the
relative rate constants krel for the reactions of nitrones 1e
and 9a and 9b with DMAD in chloroform as represented
in Table 7.
The p-nitrophenyl (1f), phenyl (1e) and p-methoxyphe-
nyl (1g) substituents at position 2 of the imidazoline cycle
have the same steric characteristics, while their p-withdraw-
ing effects are noticeably different. The reactivity of
nitrones is shown to increase with the enhancement of
p-donor effect of the substituents (Table 6). This observa-
tion is consistent with the conclusion, based on Frontier
Molecular Orbital Theory (FMO) [29]. Actually, the reac-
tions are found to be controlled by the interaction of the
HOMO of dipole with the LUMO of dipolarophile; [19]
the nitrone, therefore, plays a part of donor. Moreover, a
good linear correlation between the reactivity (log(kX/
kH)) of para-aryl substituted nitrones 1(e–g) and rpþ
constants is revealed (Table 6 and Fig. 4) that allows
estimation of the sensitivity coefficient of the reaction (q).
The q value of the reaction of nitrones 1f and 1g with
alkyne 2b is ꢁ0.51 (for 2e q = ꢁ0.50) and it is in compliance
with the presence of insignificant positive charge on the car-
bon atom C-2 of imidazoline ring in the transition state. It
is unlike the q value for solvolysis of (1-chloro-1-methyl-
ethyl)-benzene in 90% aqueous acetone is equal to ꢁ4.52 [28].
Attachment of the methyl group to the nitrogen atom of
imidazoline ring (R1) results in the increase of the reaction
rate of nitrone 1 by a factor of 7–10 (Table 6), that could be
rationalized by enhance of the donor ability of the nitrogen
atom bound to the nitrone group. The influence of this
nitrogen atom in itself on the nitrone activity can be eval-
uated by comparison of the reaction rate constants for
2.4. Quantum-mechanical model of the reaction
In order to rationalize the peculiarities of the behavior
of the 4,5-dihydro-1H-imidazole 3-oxide derivatives in the
1,3-dipolar cycloaddition reaction with alkynes and to
consider its mechanism in detail, we constructed the quan-
tum-mechanical model for the reaction of nitrones 1 with
alkynes 2.
As it was mentioned above, there are three possible vari-
ants of the cycloaddition mechanism: biradical stepwise,
zwitterionic stepwise, and concerted pathways. The forego-
ing experimental data such as the increase of the rate con-
stant with the enhance of the medium polarity (Table 4 and
Fig. 3) and with the increase of the p-electron-donating
effect of R2 (Table 6 and Fig. 4) as well as the higher activ-
ity of 2b as compared to 2c and 2d testify against the birad-
ical mechanism. Thereupon, the calculation was performed
with the conservation of the system multiplicity.
The energy surface for the cycloaddition reaction of 1a
with 2a was plotted on coordinates of the lengths of the
R
X
N
X
CO2Me
CO2Me
k
R
DMAD
N
O
O
9a,b
10a,b
X = CH2
X = O
a
b
Scheme 3. The influence of a-heteroatomic substituent on the nitrone
activity.
Table 7
Rate constants k and relative rate constants krel for the reactions of
nitrones 1e and 9a and 9b with DMAD in chloroform
Compound
R = Me krel
R = Ph
k · 10ꢁ4 (Mꢁ1 sꢁ1
)
krel
9aa
9ba
1eb
a
1
160
–
1.62
1
70
8 · 104
1.12 · 102
1.28 · 105
Fig. 4. Linear dependence of the reactivity (log(kX/kH)) of para-aryl
substituted nitrones 1 (e–g) on rþp constants.
Ref. [32] for 9a at 19 ꢁC, for 9b at 17 ꢁC.
At 24 ꢁC.
b

S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
35
formed bonds C–C (r1) and C–I (r2) using DFT calculation
with triple zets basis set (Fig. 5a). The lengths of C–C and
C–O bonds in the product were taken as a datum.
influence of substituents R1 and R2 on the nitrone reactiv-
ity. Thus, the sensitivity coefficient q, for the reaction of
1e–g with 2e, calculated from the data of Table 8 is
ꢁ0.55 and it is consistent with the experimental value
ꢁ0.50. The EA values for the reactions of N-unsubstituted
nitrone 1c exceed those for N-methylated analogue 1e that
corresponds to the higher reactivity of the latter deter-
mined experimentally (Table 6).
According to the calculated data (Table 8), distinction
between the energy barriers for the reactions of 1e and 5b
with 2d is 6.1 kcal/mol; this value corresponds to k1e/
k5b = 3 · 104 that coincides with the experimentally evalu-
ated value (2.7 · 104) in CCl4 solution. Good agreement
between the DFT computation results and experimental
data demonstrates the validity of the approach and allows
its use for the interpretation of the studied process.
The habitus of the plotted surface and, in particular, the
absence of the local minimum (exclude the minimum of the
reactants and products) demonstrates that the energy-opti-
mal path is the concerted one. The ‘‘oblongness’’ of the
forming C–C ðDr#1 Þ and C–O ðDr#2 Þ bonds is appreciably
different (Dr#1 noticeably more than Dr#2 ), that implies sub-
stantial skewness of the transition state (Fig. 5a). Further-
more, the value of q obtained from the Hammett plot
(q = ꢁ0.51, Fig. 4), which is quite different from those
observed for typical ionic processes, [28] as well as not very
significant influence of solvent polarity on the reaction rate
(Fig. 3) testify against the zwitterionic mechanism but to
the concerted one.
The structures of the series of the transition states for
cycloaddition reaction of alkynes 2 with nitrones 1 and 5
were determined by the DFT computation method with tri-
ple zets basis set (for example, Fig. 5b). The values of acti-
vation (EA) and formation (DEf) energies and the alteration
of dipole moments (Dl#) and bond lengths ðDr1#; Dr#2 Þ of
the transition states are presented in Table 8.
The comparison of the calculated values – EA and exper-
imental values ln(kexp) for the reactions of 1e with 2 dem-
onstrates good agreement in the case of the internal alkynes
(Fig. 6). The noticeable deviation of – EA observed for ter-
minal alkynes 2a and 2e can be explained by the specific
interaction between the dipolarophile and a dipole or a sol-
vent, [23,24] (see above), which cannot be taking into
account upon computation in the gas phase.
As it was mentioned above, the cycloaddition reaction
proceeds non-synchronously, and the ‘‘oblongness’’ of the
formed bonds Dr#1 and Dr2# differs noticeably (Table 8).
All transition states agree with asynchronous concerted
processes where the shorter distance corresponds to that
at the beta-conjugated position of propiolic derivatives
ðDr#2 Þ. Consequently, a substantial charge separation and
a high polarity should be observed in the transition states
of the studied nitrones. The positive charge is localized at
C-7a atom (Fig. 5b), while the negative charge is localized
at the interactive p-orbital of a dipolarophile. The polarity
of such structure can be characterized by the difference
between dipole moments (Dl#) of the transition state (l#)
and the corresponding reaction product (lproduct) (Table 8).
The comparison of Dr#1 , Dr2#, and Dl# showed in Table
8 demonstrates the higher polarity of the transition states
for nitrones 1 in comparison with that for nitrones 5; in
It should be noted, that the calculated values EA are also
in the agreement with the experimental data concerning the
Fig. 5. The energy surface of the 1,3-dipolar cycloaddition reaction of 1a with 2a; coordinates are the lengths of the formed bonds C–C (r1) and C–I (r2)
(a). The structure of the transition state for the reaction of 1a with 2b; atom numbering corresponds to that in the product (b).

36
S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
Table 8
Activation energy (EA
=
E# ꢁ Ereagents), formation energy ðDEr ¼ Epf roduct ꢁ ErfeagentsÞ, alteration of the dipole moment (Dl# = l#
ꢁ
l
product), and
interatomic distances ðDr#i ¼ r#i ꢁ rproductÞ of the transition states for the reactions of nitrones 1 and 5 with alkynes 2
#
#
DEf (kcal/mol)
Dr1 ðAÞ
Dr2 ðAÞ
Dl# (D)
˚
˚
Nitrone
Alkyne
EA (kcal/mol)
1a
2e
1.65
ꢁ2.83
ꢁ1.14
11.95
10.99
9.62
8.52
3.53
10.71
9.44
8.17
5.83
6.65
5.82
0.61
0.53
6.63
6.98
4.64
ꢁ46.06
ꢁ48.31
ꢁ43.12
ꢁ25.79
ꢁ25.05
ꢁ30.40
ꢁ30.31
ꢁ37.01
ꢁ27.82
ꢁ25.85
ꢁ24.13
ꢁ36.01
ꢁ32.20
ꢁ30.51
ꢁ38.73
ꢁ32.53
ꢁ36.35
ꢁ30.80
ꢁ36.41
ꢁ30.93
ꢁ37.13
ꢁ44.28
ꢁ38.79
ꢁ46.67
ꢁ31.83
ꢁ45.56
1.09
0.462
0.39
2.03
1.52
2.85
1.54
2.20
1.39
3.88
2.29
2.11
2.84
3.32
2.12
2.88
3.52
3.39
4.89
0.73
ꢁ0.64
1.92
3.47
1.29
0.60
0.11
1.38
ꢁ0.86
1.17
2a [33]
2a [33]
2c
1.191
1.248
1.213
1.264
1.232
1.228
1.312
1.288
1.37
1.421
1.398
1.378
1.362
1.47
1.458
1.365
1.291
1.411
1.392
0.727
0.932
0.602
1.046
0.781
1.038
1b
1c
0.318
0.361
0.341
0.353
0.416
0.327
0.458
0.395
0.361
0.428
0.384
0.468
0.364
0.437
0.442
0.466
0.423
0.463
0.791
0.537
0.915
0.45
2d
2b
2g
2a
1e
2f
2c
2d
2e
2b
2g
2a
2h
1f
2e
2g
1g
5a
2e
2g
4.49
2f
2e
13.74
10.11
9.30
7.35
14.27
8.31
2g
2a
5b
2d
2a
0.589
0.406
to N-1 atom (cf. Table 6). Besides, high sensitivity of 1 to
the nature of the alkyne substituents can also be explained
by the substantial charge separation in the transition state.
The common approach to the consideration of activity
and regioselectivity in the concerted processes is the use
of the FMO theory. In accordance with this approach,
the more active alkynes should possess lower HOMO
energy and, consequently, they should have substituents
with more powerful p-withdrawing effect. This approach,
however, is not always valid. Thus, the replacement of
hydrogen atom in terminal alkynes 2a and 2e by phenyl
group (alkynes 2d and 2f, respectively), as mentioned
above, leads to the diminution of the reaction rate on aver-
age by two orders of magnitude (Table 5). Another exam-
ple is more than the 100-fold increase of the reaction rate of
4,4,4-trifluorobut-2-ynoate 2h as compared to that of
DMAD 2g (Table 5).
Fig. 6. Correlation plot of the DFT calculated values
experimental values ln(kexp) for the reactions of nitrone 1e with alkynes 2.
– EA and
The consideration of the structures of the transition
states allows one to solve the observed discrepancies taking
into account their zwitterionic character. The structures of
the reaction centers in the transition state essentially differ
from those in the reactants: the s-character of C-6 atom is
substantially reduced in comparison with the initial sp-
hybridization, that prevents the conjugation of the substitu-
ent at the C-6 center with the interactive p-orbital of a dipol-
arophile. Besides, the dihedral angle between the p-system
of the substituent on the C-6 carbon in the transition state
and interactive p-orbital of dipolarophyl is near 90ꢁ. As a
result, this substituent is capable of stabilizing the negative
other words, the process of the latter compounds proceeds
more synchronously. This assertion is confirmed by the
influence of solvents polarity on the reaction rate for 1
(Fig. 3) that is not observed for 5. The reason of this fact
is, probably, a high p-donor ability of nitrogen atom
N-1. Its lone electron pair is capable of stabilizing the posi-
tive charge emergent on the C-7a atom in the course of the
reaction. This effect becomes stronger with the increase of
the electron-donating ability of the heteroatomic substitu-
ent, for example, upon attaching of the methyl group R1

S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
37
charge only as r-acceptor but not as p-acceptor. Moreover,
the violation of the conjugation in the transition state addi-
tionally increases the activation barrier EA, that causes the
diminution of the reaction rate by two orders of magnitude
in the case of 2d and 2f. At the same time, the substituent
attached to C-7 atom being conjugated with interactive p-
orbital is capable of efficient stabilizing its negative charge.
Therefore, the reaction rate should increase heavily in the
case of the location of the r-acceptor function at the C-6
atom and the p-acceptor function, at the C-7 atom. The
expressive example of such ‘‘combining’’ influence is a very
high reactivity of ethyl 4,4,4-trifluorobut-2-ynoate 2h,
which is much more active than DMAD.
cam.ac.uk/conts/retrieving.html [or from the Cambridge
Crystallographic Data Centre, 12 Union Road, Cambridge
CB2 1EZ, UK. Fax: (Internat.) + 44 1223/336 033; e-mail:
deposit@ccdc.cam.ac.uk].
All calculations were carried out by DFT method using
the original program PRIRODA developed by D.N. Lai-
kov [34] The generalized gradient approximation (GGA)
for the exchange-correlation functional by Perdew, Burke,
and Ernzerhof [35] was employed. The orbital basis sets of
contracted Gaussian-type functions of size (5s1p)/[3s1p] for
H and (11s6p2d)/[6s3p2d] for C, N, O were used. Full
geometry optimization of all the structures studied in this
work was performed using analytical gradients and was fol-
lowed by analytical calculations of the second derivatives
of energy with respect to coordinates in order to character-
ize the nature of the resulting stationary points (minima or
saddle points) on the potential energy surface (PES).
1,2-Disubstituted and 2-substituted 4,4,5,5-tetramethyl-
4,5-dihydro-1H-imidazole 3-oxide derivatives 1a–1g were
synthesized according to Ref. [26] Spectral characteristics
of the cycloadducts 2 are identical to that obtained earlier
[19].
3. Conclusions
Thus, the influence of the solvents on the rate of the 1,3-
dipolar cycloaddition reaction of 4,5-dihydro-1H-imida-
zole 3-oxide derivatives 1 with alkynes 2 has been studied.
The series of relative activities of nitrones 1 and alkynes 2
in the reaction under investigation have been established.
The structural factors influencing the rate constants have
been revealed. Using the DFT calculation with the triple
zets basis set, the energy profile of the reaction has been
plotted and the structures and energy characteristics of
the transition states have been determined. On the basis
of calculated and experimental data, the mechanism of
the reaction has been shown to be asymmetric but con-
certed one. Good correlation between the DFT computa-
tion results and experimental data demonstrates the
validity of the approach and allows its use for the interpre-
tation of the studied process.
4.1. Determination of the rate constants of the reactions of 1f
and 2 by UV detection
The UV-spectra of the appropriate solvent (for compen-
sation) and the solution of 1f (1 · 10ꢁ3–3 · 10ꢁ3 M) in the
same solvent were measured in order to determine the long-
wave maximum of adsorption (the range was from 385 nm
in MeOH to 468 nm in DMSO). Then, a solution (5 ml)
containing the 5- to 20-fold excess of alkyne 2 was added
to the solution of nitrone 1f (5 ml). UV-spectra of the reac-
tion mixture were registered automatically every 100 s at
24 1 ꢁC. The depth of the reaction in most cases was
more than 50%. The values of ki were calculated in all
points in the accordance with Eq. (1). Resultant value of
k was obtained by ki averaging.
4. Experimental
NMR 1H and 13C spectra were recorded on Bruker AC-
200, AM-400 (1H,13C) spectrometers; solvents were used as
internal standards: DMSO (d 2.54 ppm, d 39.5 ppm),
CHCl3 (d 7.24 ppm, d 76.9 ppm), MeOH (d 3.34 ppm, d
49.86 ppm). UV spectra were measured with Specord M-
40 spectrophotometer. An IR spectrum was recorded with
a Bruker IFS 66 spectrometer for KBr pellet (concentration
0.25%, pellet thickness 1 mm). Thin layer chromatography
monitoring was carried out on alumina plates (Fluka, Swit-
zerland) with chloroform and chloroform/MeOH mixture
(from 50:1 to 20:1) as eluents.
X-ray data were measured on Smart Apex diffractome-
ter with graphite monochromated Mo-Ka radiation. The
structure was solved by statistical methods (BRUKER-
SHELXS) and refined by the full-matrix least-squares
method on F2 (BRUKER-SHELXL). The positions of
the hydrogen atoms were calculated geometrically and
refined isotropically. Atomic coordinates, thermal parame-
ters, bond lengths and bond angles have been deposited at
the Cambridge Crystallographic Data Center; CCDCs con-
tain the supplementary crystallographic data for this paper.
These data can be obtained free of charge at www.ccdc.
4.2. Determination of the rate constants of the reactions of
1
nitrones 1,5 and alkynes 2 by the H NMR detection
A solution of alkyne 2 in 1 ml of appropriate deuterated
solvent was added to a solution of nitrone 1 or 5 in the
same solvent. The ratio of reagents was varied from 10:1
to 1:10, while the concentration of minor component was
1
approximately 1 · 10ꢁ2 M. H NMR spectra of the reac-
tion mixture were registered with the time domain from
1 min to 5 days at the 24 1 ꢁC. The depth of the reaction
in most cases was more than 50%. The values of ki were
calculated in all points in the accordance with Eq. (1).
The resultant value of k was obtained by ki averaging.
4.3. Competitive reactions of nitrones 1
A cooled solution of alkyne 2 (1 · 10ꢁ2 M) was added to
a cooled solution of equimolar amount of two nitrones 1

38
S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
(1 · 10ꢁ2 M each). The nitrone:alkyne ratio was from 1:0.5
to 1:0.9. The depth of the reaction was monitored by thin
layer chromatography. After completion of the reaction
the solvent was removed, and 1H NMR spectra of the reac-
tion mixture was registered. The ratio k1/k2 for the compet-
itive reactions A + X fi N (k1), B + X fi M (k2) was
calculated in accordance with the equation k1/k2 = ln(A/
A0)/ln(B/B0), where A0, B0 and A, B are the initial and final
concentrations of the corresponding nitrones.
2191, Rint = 0.1435, 363 parameters, Goof = 1.286, R indi-
ces (I > 2rI): R1 = 0.0816, wR2 = 0.1926, R indices (all
data): R1 = 0.0947, wR2 = 0.2008.
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1
After completion of the reaction H NMR spectra of the
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(dt, J = 160.5 Hz, J = 7.5 Hz, 3,5-Ph, CO-Ph, C-20, C-30),
130.1 (dt, J = 160.5 Hz, J = 7.5 Hz, 5-Ph, C-40), 131.0
(dt, J = 160.5 Hz, J = 7.5 Hz, CO-Ph, C-40), 138.7 (t,
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Found:
C 81.40, H 6.61, N 3.67. Calculated for
C24H28N2O3: C 81.43, H 6.57, N 3.65.
Crystallographic data (CCDC 293549): C26H25NO2,
FW = 383.47, monoclinic, P21/n, a = 5.9027(14), b =
˚
10.500(3),
c = 33.907(8)
A,
b = 90.816(5)ꢁ,
V =
given in Tables 4 and 6. According to data from Table 6: k1e
:
3
3
ꢁ1
˚
2101.2(9) A , Z = 4, Dc = 1.212 g/cm , l = 0.076 mm
,
k1f ꢄ 2.7, on average. Consequently, k1e + 2d ꢄ k1f + 2d · 2.7 in
2.03 < h < 20.81ꢁ, reflections collected/unique = 12,260/
various solvents, while the values of k1f + 2d are presented in Table 4.

S.A. Popov et al. / Journal of Molecular Structure 872 (2008) 30–39
39
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As is well known, in case of gas phase processes, the precoordination
is preceding the reaction. In the course of this process the overall
energy of system decreases (this energy decrease is EPrecoordination). If
the value of true EA less than absolute value of EPrecoordination, then
formal EA should be negative.
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