A theoretical evaluation of the Michael-acceptor ability of conjugated nitroalkenes

Article abstract of DOI:10.1002/ejoc.200600505

A theoretical evaluation of the relative Michael-acceptor abilities of a variety of substituted aromatic and aliphatic nitroalkenes is reported. Several global and local reactivity indices were evaluated with the incorporation of natural charge obtained f

Full text of DOI:10.1002/ejoc.200600505

FULL PAPER
DOI: 10.1002/ejoc.200600505
A Theoretical Evaluation of the Michael-Acceptor Ability of Conjugated
Nitroalkenes
[a]
[a]
Vishal Rai and Irishi N. N. Namboothiri*
Dedicated to Prof. K. Venkatesan on the occasion of his 75th birthday
Keywords: Michael addition / Nitroalkenes / NBO / Condensed Fukui functions and local softness / Ab initio calculations /
Density functional calculations
A theoretical evaluation of the relative Michael-acceptor
abilities of a variety of substituted aromatic and aliphatic ni-
troalkenes is reported. Several global and local reactivity in-
dices were evaluated with the incorporation of natural
charge obtained from natural bond orbital (NBO) analysis.
of cases. The computational methods employed in the calcu-
lation of natural charge, the condensed Fukui function, local
softness and other reactivity parameters were chosen after
evaluation of various methods for their ability to satisfactorily
predict the NMR chemical shift of the 1H atom β and cis to
Natural charges at the carbon atom β to the NO
the condensed Fukui functions derived by this method were
quite consistent with the reactivity. The reactivity of nitroal- of various nitroalkenes, based on the β-carbon natural charge
2
group and
the NO
2
group (β-H) in nitroalkenes. Our approach appears
suitable for predicting the relative Michael-acceptor abilities
kenes was further examined by kinetic experiments that
were monitored by NMR spectroscopy. The isolated yields
and the indices derived from it.
reported in the literature were also found to have a depend- (© Wiley-VCH Verlag GmbH & Co. KGaA, 69451 Weinheim,
able correlation with these reactivity indices in the majority
Germany, 2006)
the catalytic[6] and other[7] approaches to the asymmetric
Introduction
[
8]
version of conjugate addition to nitroalkenes re-emphas-
ize the pivotal role nitroalkenes play as powerful Michael
acceptors in the synthesis of complex molecular frame-
works, including numerous functionalized ring systems, es-
pecially heterocycles.
Conjugated nitroalkenes are valuable precursors to a
wide variety of intermediates and targets in organic synthe-
sis by virtue of their ability to react as dienophiles, heterodi-
[
1]
enes, 1,3-dipoles and, above all, as Michael acceptors.
Conjugate addition of carbon and heteroatom nucleophiles
to nitroalkenes represents the initiating step not only for
introducing substituents by enolate trapping, but also for
other useful synthetic transformations including those in-
Despite their well-documented Michael-acceptor ability,
nitroalkenes sometimes behave abnormally, for instance, in
[9]
their reaction with organometallic reagents and as sub-
[10,11]
strates in the Morita–Baylis–Hillman (MBH) reaction,
[1,2]
volving the NO group.
This is primarily because of the
2
to mention a few. A multitude of reasons have been sug-
gested to explain these abnormalities such as single electron
transfer, oligomerization/polymerization, attack of the rea-
gents on the primarily formed nitronates, multiple ad-
ditions, and reversibility in the conjugate additions, some
unique umpolung reactivity of the nitroalkyl moiety and its
ability to undergo facile conversion to functionalities such
as 1,3-dipoles, alkyl radicals, carbonyl groups, and ox-
[
2]
imes. Furthermore, ring-closing reactions initiated by the
Michael addition to nitroalkenes provide functionalized
and fused rings, often with high stereoselectivity, in a single
of which are attributable to the nature of the substrate sub-
[9,11]
stituents.
Therefore, the reactivity of nitroalkenes, espe-
step. While the NO group in the 1,4-adduct is a “silent
spectator” in some ring-closing reactions, other such reac-
tions involve the NO group directly.
2
cially as Michael acceptors, is still speculative. Furthermore,
appreciable differences have been observed experimentally
in the reactivity of aliphatic and aromatic (including het-
eroaromatic) nitroalkenes and in their sensitivity to remote
substituents (e.g. substituents on the aromatic ring of β-
nitrostyrene). Kinetic studies performed by Bernasconi and
co-workers on the addition of piperidine and morpholine
to a series of β-nitrostyrenes in water and DMSO/water
suggested an energetic advantage of having the negative
[3]
[4,5]
Recent successes in
2
[
a] Department of Chemistry, Indian Institute of Technology,
Bombay,
Mumbai 400076, India
Fax: +91-22-2576-7152
E-mail: irishi@iitb.ac.in
Supporting information for this article is available on the
WWW under http://www.eurjoc.org or from the author.
Eur. J. Org. Chem. 2006, 4693–4703
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
4693

V. Rai, I. N. N. Namboothiri
FULL PAPER
charge delocalized into the NO group in the transition presented.[21] However, there are only a few reports, to the
2
[
12]
state. A radical anionic character for the transition state best of our knowledge, where these parameters have been
22]
(
vide infra) was proposed by Hoz and Gross through their applied to understand conjugate-addition chemistry.[ The
kinetic studies on the addition of cyanide to a series of 1,1- electronic distribution cannot be directly determined, but
diarylnitroethylenes in water and DMSO.[13] More recently, it reveals itself in several chemical phenomena that can be
the kinetics of the addition of thiophenol to para-substi- experimentally explored to obtain its measure. Several
tuted β-nitrostyrenes in acetonitrile/water showed an accel- methods based on magnetic properties are used to probe
eration of the reaction rate by electron-withdrawing substit- the magnetic shielding at a given point in space.[ The
23]
[
14]
uents. All three groups observed a Hammett-type corre- NMR chemical shifts of protons and other nuclei can be
lation of the reactivity with the substituents, which was also conveniently used to not only explore the extent of π-conju-
[
12–14]
influenced by the nature of the solvent.
Recently, Mondal et al. investigated the reactivity of vari- ment at an atom of interest.
ous α,β-unsaturated carbonyl compounds towards nucleo- Chemical potential (µ), electronegativity (χ), hardness
gation but also to gain insight into the electronic environ-
[
15]
[24]
philes by the local hard-soft acid-base (HSAB) approach.
(η), and softness (S) are defined as follows (E, N, and V
This study indicated the suitability of employing local reac- are energy, number of electrons, and external potential of
tivity indices such as local softness and the Fukui function the system, respectively) [Equation (1)]:
for describing the activation of the C=C bond towards nu-
2
2
χ = –µ = –δE/δN|V; 2η = 1/S = –δ E/∆N |V = –δµ/δN|V
(1)
cleophilic attack. In a related work, Domingo et al. de-
scribed the reactivity of a variety of activated alkenes, in-
These interrelated global parameters have found wide ap-
cluding some nitroalkenes, by global and local electrophilic- plicability, where a high value of µ and low value of η can
ity indices and tested the ability of their model to predict characterize a good electrophile. On the other hand, the
the reactivity of certain Michael acceptors.[ However, in maximum amount of electronic charge that an electrophilic
view of the intriguing reactivity of nitroalkenes owing to system can accept is given by, ∆Nmax (= –µ/η). Parr et al.
16]
2
strong electron delocalization, the development and experi- have also proposed the electrophilicity index as, ω (= µ /
[
25]
mental evaluation of a methodology for the prediction of 2η). In order to understand the reactivity of nitroalkenes,
the Michael-acceptor ability of nitroalkenes appeared desir- where regioselectivity is well established, these parameters
able. Therefore, we report here our results on the correlation can be utilized, preferably in a localized approach. Local
+
+
of the reactivity of nitroalkenes as Michael acceptors with softness (s
) and the Fukui function (f β-C) are mutually
β-C
[
26]
the nature of substituents through the application of ab ini- related, as in Equation (2):
tio and hybrid density functional theoretical (DFT) meth-
f+β-C = δρ/δN|V = δµ/∆V|N; s+β-C = f+β-C·S
(2)
ods, which were selected on the basis of NMR analysis. The
results are interpreted with the help of natural bond orbital
In a way, the Fukui function represents the response of
potential. There are several systems for which it has been
(
NBO) analysis, a method which has been successfully ap- the chemical potential of a system to a change in external
[
17]
plied to localized and delocalized systems in many cases.
To the best of our knowledge, the application of the NBO shown, through ab initio calculations, that a soft electro-
method of analysis for the interpretation of the substituent phile prefers the site with the maximum Fukui function.[
27]
effects on the reactivity of substrates also appears novel.
In finite difference approximation, the condensed Fukui
function for the β-C atom (with β-carbon electron density,
β-CED) within a molecule gives an expression for nucleo-
philic attack, as in Equation (3):
Theoretical Background
f+β-C = [qβ-C(N+1)–qβ-C(N)]
(3)
Electron density is sensitive to structural perturbations
and responds to changes in external conditions, and its sen-
sitivity and responsiveness were found to be more impor- further in its local form as, ω
tant than its absolute value in reflecting the chemical reac- (= ∆Nmax
tivity of a system. This also led to the development and electrophilicity patterns of carbenes,
The electrophilicity index (ω or ∆N ) may be defined
max
+
+
+
(= ωf β-C) or ∆Nmax
β-C
β-C
+
[28]
f
β-C).
These have been utilized to obtain the
[
29]
[30]
cations,
and
[
31]
application of reactivity indices derived from electron den- active sites in Diels–Alder reactions.
sity.[ Many well-known chemical concepts such as chemi-
18]
Natural atomic orbitals (NAOs) are localized one-center
cal potential (µ), electronegativity (χ), hardness (η), and effective natural orbitals of an atom in the molecular envi-
softness (S) naturally appear within the framework of ronment. The distinguishing feature of NAOs is their spa-
[
19]
DFT.
In a more localized approach, these parameters tial diffuseness, which is optimized for effective atomic
may also emerge as a useful tool for rationalizing, interpret- charge and the incorporation of important nodal features
ing and predicting the diverse aspects of chemical bonding, due to steric confinement. Thus, NAOs account for realistic
reactivity and reaction mechanism. The theoretical research local charge shifts and steric properties in the molecular
efforts in this area in the past years have made it possible environment. This clearly gives NAOs an edge over isolated
to provide more details about local applications of both ab atom natural orbitals and standard basis orbitals. Hence,
initio SCF and DFT calculations.[ The mathematical ex- NAOs are defined as eigen orbitals of the density operator
pression and application of these quantities have been well for an atom. Parallel to the one-center NAOs, the natural
20]
4694
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© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Org. Chem. 2006, 4693–4703

Theoretical Evaluation of the Michael-Acceptor Ability of Conjugated Nitroalkenes
FULL PAPER
bond orbitals (NBOs) can be described as local two-center tral resonance structure (a) [Scheme 1 (a)], whereas the con-
eigen vectors of the density operator, preserving the maxi- densed Fukui function [Equation (3)] considers both neu-
mum occupancy, orthonormality, and integrity properties tral and radicaloid structures (b) and (c) [Scheme 1 (b), (c)].
of natural orbitals. NBOs may have limited practical value Since conjugated nitroalkenes have a higher reactivity than
in highly delocalized systems, as they are strictly localized. most other activated olefins, the ground-state properties
Therefore, a semi-localized alternative [the natural localized should comparatively show more resemblance to that of the
molecular orbital (NLMO)] is used, which closely resembles transition state with the lowest energy pathway. In other
+
the parent NBO and also captures the associated delocal- words, the β-CED should be as expressive as f β-C.
izations. NLMOs adopt the characteristic bonding pattern
of a localized Lewis structure, averting symmetry imposed-
mixing that limits the transferability and interpretability of
canonical molecular orbitals.[
Applying the above facts, we analyzed nitroalkenes in
terms of localized electron pair bonding units. The program
17]
Scheme 1. Three major resonance structures (a)–(c) contributing to
the transition state.
employed carries out the determination of NAOs, natural
Electronic delocalization has been investigated by study-
ing the magnetic shielding at a localized point in space by
hybrid orbitals, NBOs and NLMOs and uses these to per-
form natural population analysis (NPA). This approach is
not based on a unitary transformation of the occupied
MOs, as in previous methods, but on a mixing of the occu-
pied and virtual spaces that localize bonds and lone pairs
as basic units of the molecular structure. We derived the β-
CED of nitroalkenes from NPA, which was further used to
[
23,33]
examining NMR chemical shifts (vide supra).
For the
calculation of the chemical shifts of the β-H atom in nitro-
alkenes 1–14 (Figure 1), β-nitrostyrene (1) was taken as the
benchmark (Table 1). Examination of Table 1 indicates that
the B3LYP level of theory with lower basis sets provides
chemical shift values for the β-H atom with considerable
deviation (ca. 5–10% error, Table 1, Entries 1–4) from the
experimental value of δ = 8.011 ppm. However, when a
larger basis set [6-311++G(3df, 3pd)] was employed at the
B3LYP level, the deviation was minimal (1% error, Table 1,
Entry 5). Later, chemical shift values were also calculated at
the MP2/6-31G(d) level, which provided comparable results
+
calculate the condensed Fukui function (f β-C) and local
+
softness (s β-C). The Fukui function may also be considered
as a normalized local softness. Therefore, the reactivity in-
+
dices, namely β-CED and f β-C, have been used in parallel
to explain the reactivity of various nitroalkenes. This ap-
proach may simplify the understanding of the reactivity of
various Michael acceptors.
(Table 1, Entry 6).
Results and Discussion
The parameters derived from basic properties of nitroal-
kenes governed by small changes away from the initial state
are of great importance. In the Michael addition to nitroal-
kenes, the transition state is not an intermediate structure
between that of the reactant and the product. It was pro-
posed and experimentally confirmed to have a partial radi-
cal character along with partial charge.[ Therefore, fur-
ther transfer of spin density from the nucleophile to a nitro-
alkene should take place on the resonating structures thus
formed (Scheme 1). The relative contribution of these struc-
tures to the transition state structure is governed by intrin-
sic parameters such as the activating group and the solvent,
but the final outcome will probably depend largely on the
relative contribution of the structure having a radicaloid
center at the benzylic carbon [Scheme 1 (b)]. This, in turn,
will depend on the activating group, the substituents, and
the coplanarity of the substrate. However, it is clear that
substituents with a positive mesomeric effect will be very
effective in stabilizing the radical center at the benzylic car-
bon atom [Scheme 1 (b)], leading to the high reactivity of
nitroalkenes with electron-donating substituents. It is obvi-
ous that the precise situation in a given case demands its
own detailed examination, but our parameters are expected
to have a significant contribution in most cases. The β-CED
32]
Figure 1. Nitroalkenes chosen for evaluation of reactivity in conju-
gate additions.
Table 1. Optimization of the level of theory and basis set for esti-
mation of the chemical shift of the proton β and cis to the NO
group in β-nitrostyrene (1).
2
Entry Level of theory
Basis set
Calculated δ[a] % Error[b]
1
2
3
4
5
6
B3LYP
B3LYP
B3LYP
B3LYP
B3LYP
MP2
6-31G(d)
6-31G(d,p)
6-311G(d,p)
7.2210
7.4903
7.5694
7.6230
7.9298
7.9291
–9.8
–6.5
–5.5
–4.8
–1.0
–1.0
6-311++G(d,p)
6-311++G(3df,3pd)
6-31G(d)
explains the reactivity of nitroalkenes on the basis of neu- [a] All δ values are in ppm. [b] Experimental δ = 8.011 ppm.
Eur. J. Org. Chem. 2006, 4693–4703
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjoc.org
4695

V. Rai, I. N. N. Namboothiri
FULL PAPER
The two levels of theory and their corresponding basis This is in terms of the difference between calculated and
sets that were found suitable for the calculation of the experimental chemical shifts as expressed in % error. It is
chemical shift of the β-H atom were subsequently employed important to note that the deviation from the experimental
for calculation of the chemical shifts in nitroethylene (14, value is Ͻ10% in all but two cases (see Table 3, Entries 8
Table 2). Besides the chemical shift of the β-H atom and 9). The chemical shifts with Method C are inferior to
(Table 2, Entry 1), the chemical shifts of the other two pro- those with Methods A and B, but the error is well within
tons in nitroethylene (14, Table 2, Entries 2 and 3) were acceptable limits. The advantage associated with this
also estimated. Overall, both Method A [B3LYP/6- method is better consideration of charges during optimiza-
3
6
11++G(3df,3pd)//B3LYP/6-31G(d)] and Method B [MP2/
-31G(d)//B3LYP/6-31G(d)] satisfactorily predicted the
1
2
3
chemical shift values for H , H (β-H) and H (α-H). How-
ever, Method B appeared marginally superior to Method A
both in terms of the extent of agreement between calculated
and experimental values, as well as the requirement of a
smaller basis set. Similar trends were found with Method C
[
MP2/6-31G(d)//B3LYP/6-31+G(d)], as well.
Having confirmed the efficacy of the level of theory used
for computing the chemical shifts of the β-H atom in β-
nitrostyrene (1) and nitroethylene (14), the corresponding
chemical shifts were calculated in the other nitroalkenes 2–
1
3 (Table 3). While Method B appeared superior to Method
Figure 2. Correlation of theoretical and experimental chemical shift
values for the proton β and cis to the NO group in nitroalkenes
–14; Series 1: exp. δ; Series 2: calcd. δ (Method A); Series 3: calcd.
A for all the aromatic nitroalkenes 1–7 and aliphatic nitro-
alkenes [nitrocyclohexene (13) and nitroethylene (14)], the
converse was true for heteroaromatic nitroalkenes 8–12. δ (Method B); Series 4: calcd. δ (Method C).
2
1
1
Table 2. Calculation of H NMR chemical shifts in nitroethylene (14).
[
3
a] Method A: B3LYP/6-311++G(3df,3pd)//B3LYP/6-31G(d). [b] Method B: MP2/6-31G(d)//B3LYP/6-31G(d). [c] Method C: MP2/6-
1G(d)//B3LYP/6-31+G(d). Method C was employed to take into account the delocalization of an additional electron during the calcula-
tion of the condensed Fukui function. The extra diffuse function will lead to small geometry differences, but there are considerable
differences in chemical shifts, which is evident in the results. This further emphasizes the importance of NMR validation prior to selection
of the analysis method.
1
group in nitroalkenes 1–14.[a]
Table 3. Calculated H NMR chemical shifts of the proton β and cis to the NO
2
Theoretical δ[b], % Error
Theoretical δ[b], %[d] Error
Theoretical δ[b], % Error
Entry
Nitroalkene (β, α)
1 (Ph, H)
Exp. δ[b]
Method A[
c]
Method B
Method C
[e]
1
2
3
4
5
6
7
8
9
8.0110
7.9770
7.9298, –1.0
7.7811, –2.4
7.6119, –4.0
7.8561, –1.4
7.6748, –3.9
7.8589, –7.9
7.9627, –3.8
6.7808, –12.9
8.7920, 11.9
7.3001, –6.0
7.8415, –1.3
7.5876, –5.4
7.9895, 9.0
7.9291, –1.0
7.8085, –2.1
7.8223, –1.4
7.8781, –1.1
7.8600, –1.6
8.1113, –5.0
8.0230, –3.1
6.5612, –15.7
8.7834, 11.7
7.2585, –6.6
7.7319, –2.6
7.4393, –7.2
8.0295, 8.8
8.5832, 7.1
8.5496, 7.2
8.4811, 6.9
8.5062, 6.8
8.5615, 7.2
9.3593, 9.6
8.5549, 3.3
8.5336, 9.7
8.7656, 11.5
8.3903, 7.9
8.5409, 7.6
8.6394, 7.8
8.0120, 9.4
7.3865, 11
2 (4-MeOC
3 [3,4-(OCH O)C
4 (4-ClC , H)
5 (4-FC , H)
6 4
H , H)
2
6
H
3
, H] 7.9310
7.9675
6
H
4
6
H
4
7.9880
6 (2-O
7 (4-O
2
NC
NC
6
H
H
4
, H)
, H)
8.5410
8.2810
7.7815
7.8600
7.7700
7.9410
8.0165
7.3250
6.6475
2
6
4
8 (2-furyl, H)
9 (2-furyl, Me)
10 (2-thienyl, H)
11 (3-furyl, H)
12 (3-thienyl, H)
10
11
12
13
14
13 [-(CH
2 4
) -]
14 (H, H)
7.0906, 6.2
6.7700, 1.8
[
a] SCF GIAO (self consistent field guage including atomic orbital) magnetic shielding tensors have been taken for predicting NMR
values in all cases, as SCF magnetic shielding tensors were found to be more realistic in comparison to MP2 magnetic shielding tensors.
SCF density was taken for NBO analysis. [b] All chemical shift (δ) values are in ppm. [c] Method A: B3LYP/6-311++G(3df,3pd)//B3LYP/
6-31G(d). [d] Method B: MP2/6-31G(d)//B3LYP/6-31G(d). [e] Method C: MP2/6-31G(d)//B3LYP/6-31+G(d).
4
696 Eur. J. Org. Chem. 2006, 4693–4703
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© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Theoretical Evaluation of the Michael-Acceptor Ability of Conjugated Nitroalkenes
FULL PAPER
tion of nitroalkenes with N + 1 electrons. The extent of
agreement between the calculated and the experimental
chemical shifts is delineated in Figure 2.
NBO Analysis of Charge Density Distribution
The β-CED and the corresponding electron density at
the α-carbon atom (α-CED) of nitroalkenes 1–14 were cal-
culated at the MP2/6-31G(d) level of theory (Table 4). From
comparison of the β-CED and α-CED in nitroalkenes 1–
1
4, it is obvious that nitroalkenes 7, 8, 9, 13, and 14 have a
Figure 3. Distribution of charge at the β- and α-C atoms in nitroal-
higher electron density at the β-C atom than at the α-C kenes 1–14. Series 1 and 2: electron density at the β- and α-C atoms,
respectively, with Method B: MP2/6-31G(d)//B3LYP/6-31G(d);
atom. While this result can be attributed to the negative
mesomeric (–M) and negative inductive (–I) effects of the
NO group for 7, to the –I effect of the furyl oxygen atom
Series 3 and 4: electron density at the β- and α-C atoms, respec-
tively, with Method C: MP2/6-31G(d)//B3LYP/6-31+G(d); overlap-
ping of Series 1 & 3 and Series 2 & 4 shows the reliability of the
2
for 8, and to the –I effect of the furyl oxygen atom in con- β-CED and α-CED as calculated by the applied methods.
junction with the positive inductive (+I) and hyperconjuga-
tive effects of the α-Me group for 9,[ the scenario appears
34]
The β-CED was calculated at various higher levels of
fundamentally different for 13 and 14. In aromatic nitroal-
theory to verify the accuracy and consistency of this param-
kenes 1–6 and heteroaromatic nitroalkenes 10–12, β-CED
eter (Table S2, Supporting Information). The magnitude of
parameter varies when the density is taken from different
methods but the consistency is maintained throughout the
method used as is obvious from Figure S1 (Supporting In-
formation), which ensures the adequacy of the method.
After Parr’s contribution in the past decade, various
quantities representing the response of a system’s energy to
perturbation in its number of electrons and external poten-
tial were revealed. The chemical hardness (η), proposed by
Parr and Pearson, represents the resistance of a system to
Ͻ α-CED, indicating the predominance of the powerful
electron-withdrawing nature of the NO2 group. Alterna-
tively, the aromatic ring, in the absence of a suitably placed
strongly electron-withdrawing group, donates electrons to
the nitroethylenic moiety, causing polarization of the
double bond towards the NO group. In the absence of such
2
an aromatic ring β to the NO group, β-CED Ͼ α-CED, as
2
[
35]
in 13 and 14.
Table 4. β-CED and α-CED for nitroalkenes 1–14, as calculated by
NPA.
[
36]
changes in its number of electrons. The chemical softness
S) is naturally defined as the inverse of η. In other words,
(
Entry
Nitroalkene (β, α)
Natural charge Natural charge
hardness is a measure of stability and softness is a measure
of reactivity. While the global properties may explain the
reactivity of nitroalkenes, for understanding the conjugate
addition to nitroalkenes, we focused more on local param-
[
a]
[b]
Method B
β-C α-C
Method C
β-C α-C
1
2
3
4
5
6
7
8
9
1 (Ph, H)
–0.1013 0.1389 –0.0997 0.1391
–0.0904 0.1548 –0.0883 0.1553
2 (4-MeOC
3 [3,4-(OCH O)C
4 (4-ClC , H)
5 (4-FC , H)
6 4
H , H)
+
+
2
6
H
3
, H] –0.0983 0.1441 –0.0965 0.1443 eters. ∆Nmax β-C and ω β-C were found to be in low to mod-
–0.1077 0.1323 –0.1060 0.1326 erate accordance with expected behavior (Table S2 and Fig-
6 4
H
6
H
4
–0.1018 0.1405 –0.1005 0.1403
ure S1, Supporting Information).
The most important local quantity in the case of nitroal-
kenes is the electron density itself (β-CED). Chemical reac-
6 (2-O
7 (4-O
2
NC
NC
6
H
H
4
, H)
, H)
–0.1136 0.1240 –0.1121 0.1241
–0.1283 0.1072 –0.1273 0.1072
–0.1485 0.1352 –0.1469 0.1354
2
6
4
8 (2-furyl, H)
9 (2-furyl, Me)
10 (2-thienyl, H)
11 (3-furyl, H)
12 (3-thienyl, H)
–0.1679 0.0749 –0.1670 0.0749 tions are mainly the adjustment of valence electrons among
10
11
12
13
14
–0.1264 0.1330 –0.1242 0.1337
–0.1008 0.1460 –0.0990 0.1465
–0.1003 0.1418 –0.0988 0.1423
–0.1053 0.0475 –0.1046 0.0477
the reactant orbitals. Fukui proposed his frontier molecular
orbital theory (FMO), which allows a chemical reaction to
be understood in terms of the HOMO and LUMO.[ Fu-
37]
13 [-(CH
2
)
4
-]
14 (H, H)
–0.3111 0.1343 –0.3109 0.1341 kui functions are based on this concept, whereas condensed
Fukui functions at the β-C atom in a molecule can be de-
[
a] Method B: MP2/6-31G(d)//B3LYP/6-31G(d). [b] Method C:
fined in terms of associated electron populations. The
MP2/6-31G(d)//B3LYP/6-31+G(d); method A also showed a sim-
+
ilar trend. Smaller differences of charges in a few cases made it largest value of f
at the reaction site will be preferable,
β-C
necessary to further evaluate these systems with other parameters.
as it implies a large difference in chemical potentials. Since
the soft species are large in size with a small charge, it is
The β-CED, apart from being much more consistent expected that in soft–soft reactions covalent bonding will
than charge densities derived from other methods, was predominate. The nuclear charge is adequately screened by
found to have less dependence on a basis set with an ad- the core electrons, and the two soft species mainly interact
ditional diffuse function used during optimization (Fig- through frontier orbitals. Energy changes due to covalent
ure 3). This suggests that the β-CED is a dependable elec- interactions (∆Ecov) dominate electrostatic and polarization
trophilicity index.
factors in the case of soft–soft interactions, where minimi-
Eur. J. Org. Chem. 2006, 4693–4703
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjoc.org
4697

V. Rai, I. N. N. Namboothiri
FULL PAPER
[
27]
Table 5. Local reactivity indices.
zation of ∆Ecov leads to the HSAB principle. A local ver-
sion of the HSAB principle (s+β-C) has also been derived
with this approach. The amount of electronic charge trans-
ferred between the reactants during soft–soft interactions
(which are covalent, and hence, controlled by frontier orbit-
als during the small displacement along the reaction coordi-
nate) is large for small values of η with maximum overlap
+
of the Fukui functions and larger values of f
(or equiva-
β-C
+
lently, local softness, s β-C). Michael addition to nitroal-
kenes mainly involves interaction of the nitroalkene LUMO
with the nucleophile HOMO. The character of the LUMO
is an important controller of reactivity, as it is the virtual
orbital that captures an external electron to form an anion.
The LUMOs of nitroalkenes are given in Table 5, which
shows the delocalization of orbitals due to the presence of
highly conjugated π-systems. Also, we can see that the pre-
dominant contribution to the LUMO is from the β-C atom.
The earlier reports utilized Mulliken population analysis
MPA) for deriving various reactivity parameters.[
20,22]
(
Comparative analysis of β-CED and MPA-derived local pa-
rameters show that the β-CED from both methods are
broadly consistent with each other, but MPA provides erro-
neous results in a few cases. Further comparison of con-
densed Fukui functions shows large differences, as ex-
pected, due to the involvement of radical anions, thus dis-
playing the shortcomings of MPA. The abnormal values in
+
the case of the β-CED of nitroalkenes 6 and 10 and f
β-C
[
a] Contours have been plotted with a contour value of 0.08, de-
rived from FMO calculations with Method C: MP2/6-31G(d)//
Figure 4. Comparison of the trends of the β-CED and f+ derived
B3LYP/6-31+G(d). [b] Parameters calculated with Method B:
β-C
MP2/6-31G(d)//B3LYP/6-31G(d); all values of f β-C and s+β-C are by natural and Mulliken charges. Series 1: natural charge derived
+
+
negative. [c] Parameters calculated with Method C: MP2/6-31G(d)//
β-CED and f β-C, respectively; Series 2: MPA derived β-CED and
+
+
+
B3LYP/6-31+G(d); all values of f β-C and s β-C are negative.
f β-C, respectively.
4698 www.eurjoc.org © 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Org. Chem. 2006, 4693–4703

Theoretical Evaluation of the Michael-Acceptor Ability of Conjugated Nitroalkenes
FULL PAPER
Table 6. Local reactivity indices (NBO vs. MPA).
En-
Nitroalkene (β, α)
|f+β-C|[a]
|f+β-C|[b]
|s+β-C|[a]
|s+β-C|[b]
β-CED[a]
β-CED[b]
try
1
2
3
4
5
6
7
8
9
1 (Ph, H)
0.1587
0.1700
0.1634
0.1535
0.1591
0.0536
0.0852
0.1545
0.1275
0.1508
0.1662
0.1610
0.1543
0.1670
0.9918
0.1056
0.1015
0.0974
0.1005
0.1182
0.0658
0.1010
0.0935
0.0941
0.1072
0.1023
0.0856
0.8270
0.4270
0.4772
0.4678
0.4205
0.4285
0.1389
0.2332
0.4385
0.3619
0.4270
0.4387
0.4292
0.3409
0.3446
2.6683
0.2968
0.2907
0.2667
0.2705
0.3064
0.1801
0.2866
0.2654
0.2666
0.2829
0.2729
0.1891
1.7065
–0.0997
–0.0883
–0.0965
–0.1060
–0.1005
–0.1121
–0.1273
–0.1469
–0.1670
–0.1242
–0.0990
–0.0988
–0.1046
–0.3109
–0.1379
–0.1302
–0.1359
–0.1389
–0.1356
–0.0937
–0.1494
–0.1732
–0.2157
–0.1171
–0.1203
–0.1252
–0.1581
–0.3507
2 (4-MeOC
3 [3,4-(OCH O)C
4 (4-ClC , H)
5 (4-FC , H)
6
H
4
, H)
6 3
H , H]
2
6
H
4
6
H
4
6 (2-O
7 (4-O
2
NC
NC
6
H
H
4
, H)
, H)
2
6
4
8 (2-furyl, H)
9 (2-furyl, Me)
10 (2-thienyl, H)
11 (3-furyl, H)
12 (3-thienyl, H)
10
11
12
13
14
13 [-(CH
2 4
) -]
14 (H, H)
a] NBO-derived parameters with Method C: MP2/6-31G(d)//B3LYP/6-31+G(d); all values of f β-C and s+β-C are negative. [b] MPA-
+
[
derived parameters with Method C: MP2/6-31G(d)//B3LYP/6-31+G(d); all values of f β-C and s+β-C are negative.
+
for several nitroalkenes such as 1, 6, 9, and 14 show the more reactive than 1, under the conditions employed, an
inconsistent behavior of MPA-derived charge densities independent verification was sought to confirm this obser-
(
Table 6, Figure 4).
vation. Therefore, in a separate experiment, the reaction
was performed at a lower temperature (18.6 °C) and with a
nitroalkene/2-propene-1-thiol ratio of 1:1 (Table 7, Exp. 2).
Analysis of the reaction mixture after 4 min showed that
while nitroalkene 2 underwent 71% conversion, 1 under-
went only 69% conversion, and 7 was much less reactive
Substituent Effect on the Reactivity of Nitroalkenes as
Michael Acceptors – Correlation of Experimental Results
with Electrophilicity Indices
(
57% conversion), as in the previous experiment (Table 7,
Prior to making any attempt to correlate the experimen-
tal results available in the literature (Supporting Infor-
mation) on the Michael addition of various nucleophiles to
nitroalkenes with our electrophilicity indices, we performed
model experiments to compare reactivity parameters with
the reaction kinetics. This is because the reaction time and
Entries 1–3, Exp. 2). These studies confirmed the reactivity
order in p-substituted nitrostyrenes 1, 2 and 7 as p-meth-
oxy-β-nitrostyrene Ͼ β-nitrostyrene Ͼ p,β-dinitrostyrene
and is consistent with the reactivity indices derived from
high-level theoretical calculations.
the conditions of the reported reactions might vary con- Table 7. Kinetics of Michael addition of 2-propene-1-thiol (15) to
nitroalkenes 1, 2 and 7.
siderably in many cases, making a meaningful correlation
of the electrophilicity indices with the reactivity of nitroal-
kenes (expressed in isolated yields of the Michael adducts)
extremely challenging. Secondly, the kinetic data available
in the literature for the conjugate addition of amines, cya-
nide and thiophenol to nitroalkenes, were based on reac-
tions carried out in water, water/DMSO or water/acetoni-
Entry Nitroalkene (β, α) β-CED[a] |f+ |[a]
Exp. 1
Exp. 2
[
12–14]
trile mixtures.
β-C
%
Conversion % Conversion
at 25 °C[b]
min 5 min
In view of the concerns outlined above, we examined the
reactivity of representative nitroalkenes 1, 2, and 7 with the
[c]
at 18.6 °C
4 min
2
nucleophile 2-propene-1-thiol (15) in a non-interacting sol-
1
2
3
1 (Ph, H)
2 (4-MeOC
–0.0997
, H) –0.0883
0.1587
0.1700
0.0851
98
100
91
100
100
94
69
71
57
1
vent (CDCl ) by performing kinetic experiments using H
3
H
6 4
NMR spectroscopy (Table 7).[ When the reaction was
carried out at 25 °C with a nitroalkene/2-propene-1-thiol
ratio of 2:1 and analyzed after 2 min, 100% conversion was
38]
7 (4-O NC H , H) –0.1273
2
6
4
[
3
a] Reactivity indices were derived by MP2/6-31G(d)//B3LYP/6-
1+G(d), see Tables 4 and 5. [b] A nitroalkene/2-propene-1-thiol
observed for p-methoxy-β-nitrostyrene (2), but only 98% ratio of 2:1 was used; % conversions with respect to 2-propene-1-
1
thiol were determined by H NMR spectroscopy. [c] A nitroalkene/
and 91% conversion were observed for β-nitrostyrene (1)
and p,β-dinitrostyrene (7), respectively (Table 7, Entries 1–
2
-propene-1-thiol ratio of 1:1 was used; % conversions with respect
to 2-propene-1-thiol were determined by H NMR spectroscopy.
1
3, Exp. 1). When the reaction mixture was analyzed after
5
min, the conversion of β-nitrostyrene (1) was also com-
The above observation confirmed the fact that the elec-
plete. However, p,β-dinitrostyrene (7) was the least reactive, trophilicity indices, the β-CED and condensed Fukui func-
with only 94% conversion observed after 5 min. Although tion, explain the reactivity of nitroalkenes in non-inter-
this experiment suggested that nitroalkene 7 is the least re- acting solvents with good reliability. The self-consistent re-
active among the three, and nitroalkene 2 is marginally action field polarized continuum model was used to exam-
Eur. J. Org. Chem. 2006, 4693–4703
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjoc.org
4699

V. Rai, I. N. N. Namboothiri
FULL PAPER
ine the nature of nitroalkenes in the solvent (chloroform) in analysis, but FMO condensed parameters such as local soft-
which the kinetic experiments were carried out (Table S8, ness (S) and electrophilicity indices ω and ∆Nmax were not
Supporting Information). The results were found to be con- general with either MPA or NBO analysis derived charge
sistent with those obtained from gas-phase calculations. densities. Calculations of the condensed Fukui function and
Interestingly, we found that the β-CED for p-methoxy-β- softness have encountered difficulties earlier, because these
nitrostyrene (2) is less than that of p,β-dinitrostyrene (7) in required atomic electron population in a molecule which
the ground state [Scheme 1 (a)], but the trend reverses after was not unambiguously defined irrespective of the method
the addition of an electron to the system. Thus, the relative used. We found that natural charge derived β-CED is a
contribution of the ground-state structure [Scheme 1 (a)] good reactivity index, explaining the reactivity of various
should be more than that of the radical anions nitroalkenes towards conjugate addition on par with the
[
Scheme 1 (b)–(c)]. This fact again supports the consistency Fukui function. While the electron densities and condensed
+
of the β-CED with |f β-C|, which considers the contributions Fukui functions calculated by the NBO method correlated
from all three structures [Scheme 1 (a)–(c)]. However, if rad- well with the Michael-acceptor ability of nitroalkenes, the
ical anions are stabilized by an interacting solvent or other MPA was not suitable. Our studies show that the relative
medium, leading to a higher contribution towards the tran- reactivities of conjugated nitroalkenes towards various nu-
sition state, the reactivity trend will be defined by their β- cleophiles can be quantified with reasonable accuracy using
CED.
our table of β-CED and condensed Fukui function values
Our kinetic studies confirmed the suitability of our calcu- calculated by NBO with the MP2/6-31G(d)//B3LYP/6-
lation results on the extent of polarizability of the double 31+G(d) method. Extension of the NBO analysis to esti-
bond in conjugation with the aryl ring and the NO group mate the behavior of nitroalkenes in reactions other than
2
+
in the form of local softness (s
) and, more importantly, conjugate additions and to evaluate the reactivity of other
the β-CED and condensed Fukui function (f β-C). activated alkenes appear to be an attractive prospect.
Additionally, our calculation methods reliably predicted the
β-C
+
Michael-acceptor ability of conjugated nitroalkenes. We
then decided to evaluate some of the experimental results
available in the literature on the Michael-type addition of
Experimental Section
Computational Methods: All computations were performed with
various carbon- and heteroatom-centered nucleophiles the GAUSSIAN 98, revision A.11.4 program suite[ with the DFT
to conjugated nitroalkenes. The representative examples method of Becke’s three-parameter hybrid Hartree–Fock procedure
chosen from the literature involve reactions of nitroalkenes with the Lee–Yang–Parr correlation function (B3LYP) and Møller–
43]
[
39]
Plesset perturbation theory (MP2). The geometries of all the nitro-
alkenes and their anions in this study were fully optimized by the
DFT/B3LYP method with the 6-31G(d) and 6-31+G(d) basis sets.
No symmetry constraints were imposed in the optimizations, ex-
cept for tetramethylsilane (TMS). Split-valence basis sets, polarized
basis sets, diffuse functions, and high-angular-momentum basis sets
were used to consider highly delocalized molecules. The chemical
shifts for the β-H atom in nitroalkenes were calculated by determin-
with heteroatom nucleophiles (2-aminobenzaldehyde), C-
centered nucleophiles (indole and malonate),[
organometallic reagent (Fischer aminocarbene complex).
40,41]
and an
[
42]
Our analysis has shown that the parameters discussed above
+
[
local softness (s β-C), the β-CED and Fukui function
+
(f
β-C)] correlate well with the isolated yields in a majority
of the cases and moderately well with the reaction time (see
Supporting Information for further discussion). Thus, these ing the difference of SCF magnetic shielding tensors for TMS and
1
parameters might serve as a useful tool for analyzing the the nitroalkenes (experimental H NMR chemical shifts were re-
reactivity of nitroalkenes with other Michael donors. The corded with TMS as an internal standard). For the purpose of iden-
tifying a theoretical method and a basis set suitable for the calcula-
tion of the charge density, especially at the β-C atom of conjugated
nitroalkenes 1–14 (Figure 1), NMR chemical shifts of the β-H atom
methodology may find further applications towards better
understanding the reactivity of other Michael acceptors.
were calculated at various levels of theory and compared with the
1
experimental chemical shifts (vide infra). H was chosen for calcu-
1
3
Conclusions
lation of the chemical shifts due to its greater sensitivity over C,
even though its spectral range is modest.[ The chemical shielding
tensors were calculated by the DFT-hybrid GIAO method with
44]
The Michael-acceptor ability of a variety of substituted
aromatic and aliphatic conjugated nitroalkenes was ana- TMS as reference. MP2/6-31G(d) and B3LYP/6-311++G(3df,3pd)
lyzed by correlating the condensed Fukui function and the were found to be practical methods for B3LYP/6-31G(d) as well
β-CED with the rate of reaction of the nitroalkenes and the as B3LYP/6-31+G(d) optimized geometries. Charge densities were
calculated by NPA with the NBO 3.1 program, which is included
%
conversion or isolated yields of the 1,4-adducts. Kinetic
in GAUSSIAN 98, with the strongly delocalized NBO set. MO cal-
culations were performed to give HOMO and LUMO energies with
the MP2/6-31G(d)//B3LYP/6-31G(d) method. Contour plots were
generated by MOLDEN 4.1. Further calculations were also carried
out over B3LYP/6-31+G(d) geometries for proper diffusion and ac-
curacy in Fukui functions. NPA was carried out with the MP2/6-
studies carried out in a non-interacting solvent showed that
the reactivity indices are indeed reliable. Further correlation
with the experimental results available in the literature on
the conjugate addition of a variety of carbon and hetero-
atom nucleophiles to nitroalkenes has shown the efficacy of
these parameters in explaining the observed reactivity. The
31G(d) and B3LYP/6-311++G(3df,3pd) methods for analyzing the
isolated yields showed excellent agreement with the con- MP2 and SCF density, respectively, with geometries optimized at
densed Fukui function and β-CED derived from NBO B3LYP/6-31+G(d), which shows the unchangeability of parameters
4700
www.eurjoc.org
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Eur. J. Org. Chem. 2006, 4693–4703

Theoretical Evaluation of the Michael-Acceptor Ability of Conjugated Nitroalkenes
FULL PAPER
derived from earlier methods. The electronic chemical potential (µ)
and chemical hardness (η) were approximated in terms of the one-
ter, 1996; i) J. P. Adams, J. Chem. Soc., Perkin Trans. 1 2002,
586; j) G. Rosini, Comprehensive Organic Synthesis (Ed.: B. M.
2
Trost), Pergamon, Oxford, 1991, vol. 2, p. 321; k) R. Ballini,
electron energies of the FMOs, HOMO and LUMO, ε
respectively, according to µ = (ε +ε )/2 and η = (ε –ε
the valence state parabola model.[ The ground-state parabola
model approximates µ and η as follows: µ = (ε +ε )/2 and η = (ε
). Global reactivity indices χ, ∆Nmax, ω, and S were calculated
according to equations mentioned earlier. Local reactivity indices
H
and ε
L
,
G. Bosica, D. Fiorini, A. Palmieri, M. Petrini, Chem. Rev. 2005,
H
L
45]
L
H
)/2, from
105, 933.
[
3] Selected articles: a) T. A. Johnson, D. O. Jang, B. W. Slafer,
M. D. Curtis, P. Beak, J. Am. Chem. Soc. 2002, 124, 11689; b)
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J. Org. Chem. 2005, 70, 2235.
H
L
L
–
[
25]
ε
H
+
+
+
+
ω
β-C, ∆Nmax β-C, f β-C, s β-C, and the β-CED were calculated with
charge densities from MPA and NBO analysis (condensed with
+
+
+
FMO parameters for ω β-C, ∆Nmax β-C, and s β-C). The self-consis-
tent reaction field polarized continuum model was used to examine
the nature of nitroalkenes in a non-interacting solvent system.
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[1c–1e]
Hetrocycl. Chem. 1994, 31, 687; c) see refs.
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3
(3 mL) were added 2-propene-
N (0.01 mL, 0.1 mmol). The
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3
1
reaction mixture was stirred at 25 °C. H NMR spectra were re-
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quots (0.5 mL each) after 2 and 5 min. The spectra recorded after
2
min showed complete conversion (100%) of 2, 98% conversion
of 1, and 91% conversion of 7. After 5 min, the reaction was com-
plete (100% conversion) for nitroalkenes 1 and 2, but only 94%
conversion was observed for 7. Experiment 2: In a separate experi-
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3 3
(2 mL), Et N
(
0.01 mL, 0.1 mmol) was added, and the reaction mixture was
1
stirred at 18.6 °C. H NMR spectra were recorded at the same
probe temperature (18.4 °C) by withdrawing aliquots (0.5 mL) after
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4
min, which showed 69% conversion for 1, 71% conversion for 2,
and 57% conversion for 7.
Supporting Information (see footnote on the first page of this arti-
cle): Details of the optimization of the level of theory and basis set,
coordinates of optimized geometries, contour plots, table of NHO
directionality and bond bending, correlations, and solvent model
calculation results.
Acknowledgments
The authors thank DST, India, for financial assistance and the edi-
tor and the referees for their valuable comments. V. R. thanks Mr.
Dipankar Roy for helpful discussions and CSIR, India, for a re-
search fellowship.
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Received: June 11, 2006
Published Online: August 22, 2006
Eur. J. Org. Chem. 2006, 4693–4703
© 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.eurjoc.org
4703