Unexpected course of reaction between (E)-2-aryl-1-cyano-1-nitroethenes and diazafluorene: why is there no 1,3-dipolar cycloaddition?

Article abstract of DOI:10.1007/s00706-016-1893-5

Abstract: Reactions between (E)-2-aryl-1-cyano-1-nitroethenes and diazafluorene lead to acyclic 2,3-diazabuta-1,3-diene derivatives, instead of the expected pyrazoline systems. DFT calculations suggest that this is a consequence of formation of zwitterionic structure in the first stage of the reaction. It must be noted that this is a specific property of the (E)-2-aryl-1-cyano-1-nitroethenes group, in contrast to most other conjugated nitroalkenes. Graphical abstract: [Figure not available: see fulltext.]

Full text of DOI:10.1007/s00706-016-1893-5

Monatsh Chem
DOI 10.1007/s00706-016-1893-5
ORIGINAL PAPER
Unexpected course of reaction between (E)-2-aryl-1-cyano-1-
nitroethenes and diazafluorene: why is there no 1,3-dipolar
cycloaddition?
1
Radomir Jasinski Karolina Kula1 Agnieszka Ka˛cka1 Barbara Mirosław2
•
•
•
´
Received: 29 June 2016 / Accepted: 10 December 2016
Ó The Author(s) 2017. This article is an open access publication
Abstract Reactions between (E)-2-aryl-1-cyano-1-ni-
troethenes and diazafluorene lead to acyclic 2,3-diazabuta-
1,3-diene derivatives, instead of the expected pyrazoline
systems. DFT calculations suggest that this is a conse-
quence of formation of zwitterionic structure in the first
stage of the reaction. It must be noted that this is a specific
property of the (E)-2-aryl-1-cyano-1-nitroethenes group, in
contrast to most other conjugated nitroalkenes.
Introduction
Conjugated nitroalkenes (CNA) are very useful and uni-
versal synthons in organic synthesis. On their basis, many
valuable compounds may be prepared, such as nitronic acid
esters [1], amines [2], oximes [3] and others [2]. Addi-
tionally, the presence of a highly electron-withdrawing
nitro group stimulates p-deficiency of a double bond,
which activates these compounds in a stereo-controlled
reaction with nucleophilic reagents such as dienes [2, 4, 5],
1,3-dipoles [3, 6] and acetylenes [4].
Graphical abstract
(E)-2-Phenyl-1-cyano-1-nitroethene and their aryl-sub-
stituted analogs (ACNE) were prepared for the first time in
the first half of the twentieth century [7]. At present, sev-
eral compounds from this group are known [8–11].
However, their chemical properties are not well known.
Some compounds have been described very recently. In
particular, some examples of participation of ACNE in
Diels–Alder reactions as dienophiles [12–15] as well as
heterodienes [8, 16, 17] are explored. Additionally, some
examples of catalyzed 1,3-dipolar cycloadditions between
ACNE and trimethylsilyl azide are also analyzed [18, 19].
Unfortunately, this method does not yield stable adducts,
because the primary reaction products decompose partially
under reaction conditions. Actually, any examples of
thermal (non-catalyzed) 1,3-dipolar cycloadditions
involving ACNE are unknown. This work is an attempt to
fill this gap and is a continuation of our systematic study
about participation of CNA in cycloaddition reactions
[15, 20–24]. In particular, we have decided to shed light on
the reactions between the homogenous series of ACNE
(1a–1d) and diazafluorene (2), as a model allenyl-type 1,3-
dipole with [(C-)–(N?):N functional group. Theoreti-
cally, these reactions should give attractive, from a
practical point of view, nitrofunctionalized pyrazoline
Keywords Alkenes Á Cycloadditions Á Diazo compounds Á
Quantum chemical calculations Á Reaction mechanism
Electronic supplementary material The online version of this
article (doi:10.1007/s00706-016-1893-5) contains supplementary
material, which is available to authorized users.
´
& Radomir Jasinski
radomir@chemia.pk.edu.pl
1
Institute of Organic Chemistry and Technology, Cracow
University of Technology, Warszawska 24, 31-155 Cracow,
Poland
2
Department of Crystallography, Maria Curie-Skłodowska
University, Maria Curie-Skłodowska 3, 20-031 Lublin,
Poland
123

´
R. Jasinski et al.
systems (Scheme 1). In addition to experimental studies,
we also performed comprehensive quantum chemical
studies to understand better the nature and molecular
mechanism of these reactions.
It was found that this reaction proceeds in MeNO2 solu-
tion under mild conditions and yields a dark brown solid.
HPLC analysis of the post-reaction mixture shows the
existence of one reaction product, which was isolated by
crystallization from ethanol. Its constitution was estab-
lished by means of elemental analysis as well as spectral
techniques. It was found unexpectedly that the results of
the elemental analysis were fundamentally different from
those of the expected adduct. Next, in the IR spectrum,
any bands from NO2 as well as CN groups were not
observed. On the other hand, the MS spectrum gives a
molecular ion, which suggests that the molecular weight
is less than that in the expected adduct. This suggest the
absence of the C(CN)NO2 moiety in the molecule. Thus,
we established that it is not a five-membered heterocyclic
product, but a 2,3-diazabuta-1,3-diene derivative 5a. This
was fully confirmed by the single crystal X-ray structure
determination (Fig. 1 as well as Supplementary Material).
For a full characteristic of this compound, 1H and 13C
NMR spectra were also recorded (see ‘‘Experimental’’
section).
Results and discussion
Firstly, we prepared the reaction components. For this
purpose, we applied methodologies described earlier (see
the experimental section). Next, the analysis of the inter-
action between the addends in the expected cycloaddition
course was performed. Global and local electronic prop-
erties of (E)-2-aryl-1-cyano-1-nitroethenes had been
analyzed in detail previously [17, 25]. It was discovered
that all these compounds were characterized by a high
global electrophilicity (in the case of compounds 1a–1d
and were in the range of 3.14-3.68eV). In comparison
(Table 1), diazafluorene has evidently weaker electrophilic
nature (x = 1.84 eV). Additionally, 2 is characterized by a
relatively high global nucleophilcity (more than 3.5 eV). In
consequence, the interaction between CNA 1a–1d and 2
may be considered a polar one [26]. Subsequently, the local
electronic properties of addends have been analyzed. As
established earlier, in all CNA 1a–1d, most of the elec-
trophilic center is located at the b-position of the nitrovinyl
moiety [17, 25]. On the other hand, most of the nucle-
ophilic center in the [CNN moiety of 2 is located on the
terminal nitrogen atom. In polar cycloadditions, a reaction
course is controlled by the nature of the local nucleophile–
electrophile interaction. Therefore, we have assumed that
the reaction channel A should be preferred.
Similarly, we analyzed the reactions involving ACNE
1a–1d. In all cases, respectively, 2,3-diazabuta-1,3-diene
derivatives 5b–5d were isolated instead of the expected
nitropyrazolines. Next, we tested the reactions between
diazafluorene 2 and used ACNE in other, different solvents
such as acetonitrile, DCM and chlorobenzene. In all cases,
only 2,3-diazabuta-1,3-diene derivatives were isolated,
without any cycloadducts.
This phenomenon can be explained when assuming that
the primary reaction product 3a–3d spontaneously
decomposed with: C(CN)NO2 carbene elimination
according to the retro-[4 ? 1]-cycloaddition scheme (path
C on Scheme 2). Theoretically, the highly substituted five-
member heterocycles may have decomposed with the ring
To verify the quantum chemical simulations, we per-
formed experimental tests of the reactions of interest. In
the first step, we explored reactions involving ACNE 1a.
Scheme 1
123

Unexpected course of reaction between (E)-2-aryl-1-cyano-1-nitroethenes and diazafluorene:…
Table 1 Selected global and local electronic properties for diazafluorene (2) in comparison to other diazocompounds
Diazocompound
Global properties
Local properties
x/eV
N/eV
PC-
PN-
NC/eV
NN/eV
Diazafluorene (2)
1.84
1.47
1.70
3.61
4.00
3.75
0.23
0.21
0.22
0.39
0.41
0.40
0.83
0.86
0.81
1.41
1.63
1.50
4-Methylphenyl-phenyl-diazomethane [27]
4-Chlorophenyl-phenyl-diazomethane [27]
zwitterionic structure of I is probably stabilized by a push–
pull electronic effect, which is determined by the presence
of two EWG groups (NO2 and CN) in the terminal position.
A similar effect has been recently explored [11] in detail in
the case of a molecule, which has similar structural moi-
eties. In the next step, it is converted via C(CN)NO2
carbene elimination into a 2,3-diazabuta-1,3-diene deriva-
tive (Scheme 2). It should be noted at this point that the
possibility of the existence of zwitterionic structures on the
paths of reactions involving CNA has been recently
described in the case of interactions between diarylnitrones
and 1-EWG-substituted 1-nitroethenes [33, 34] as well as
between thiocarbonylylides and nitroethene [35, 36].
To confirm this hypothesis, we have performed DFT
simulation of theoretically possible paths for a model
reaction involving CNA 1c. It was found that, in contrast to
the reaction 1c ? 2 ? I, both cycloadditions leading
finally to pyrazoline systems (3c and 4c) should be treated
as forbidden from a kinetic point of view. In particular, for
reactions 1c ? 2 ? 3c(4c), Gibbs free energy of activa-
tion is higher than 141 kJ/mol, whereas in reaction
1c ? 2 ? I about 128 kJ/mol. In consequence, our
Fig. 1 Molecular structure of 5a with atom labels
opening via carbene elimination. It should be highlighted,
however, that any cases of this type of decomposition of
nitropyrazoline systems had not been previously described.
Some of these heterocycles decomposed under mild con-
ditions, but via completely different mechanisms [28–32].
Alternatively, it may be assumed that in the first reaction
stage, a zwitterionic intermediate I is formed. The
Scheme 2
123

´
R. Jasinski et al.
calculations may support mechanism via paths D ? E,
which is illustrated in Scheme 2. The key physical
parameters of all considered transition states are presented
in Fig. 2. It should be noted that the zwitterionic nature of
I, as well as the charge distribution on its molecule, was
confirmed by a population Mulliken analysis (see the
GEDT value).
contrast to most other conjugated nitroalkenes. We found
that a similar reaction between (E)-3,3,3-trichloro-1-nitro-
prop-1-ene and diazafluorene proceeds under mild
conditions and gives 4-nitropyrazoline as the product.
Experimental
Finally, it should be noted that the described reaction
course is a specific property of the ACNE group. In com-
parison, a similar reaction between (E)-3,3,3-trichloro-1-
nitroprop-1-ene (6) (which has similar electrophilicity to
ACNE [22]) and diazafluorene proceeds in MeNO2 solu-
tion under mild conditions and gives pyrazoline 7 with
quantitative yield (Scheme 3). Interestingly, this adduct is
easily decomposed into 8 under relatively mild conditions.
This decomposition proceeded via the HCl elimination
stage.
The melting points were determined on a Boetius apparatus
and are uncorrected. Elemental analyses were performed
on a Perkin-Elmer PE-2400 CHN apparatus. IR spectra
were recorded on a Bio-Rad spectrophotometer in CCl4
solution. The 1H NMR (500 MHz) and 13C NMR
(125 MHz) spectra were recorded on a Bruker AMX 500
spectrometer. Liquid chromatography (HPLC) was done
using a Knauer apparatus equipped with a UV/Vis detector.
For monitoring of the reaction progress, LiChrospher
18-RP 5 lm column (4 9 240 mm) and 75% methanol as
the eluent at a flow rate of 1.0 cm3/min were used.
Nitroalkenes 1a–1d [9, 11] and 6 [46] and diazafluorene
(2) [45] were synthesized according to the procedures
described earlier.
Conclusion
Reactions between allenyl-type 1,3 dipoles and ethylene/
acetylene derivatives proceed generally according to the
cycloaddition scheme [27–39]. Unexpectedly, diazafluo-
rene reacts with (E)-2-aryl-1-cyano-1-nitroethenes via
another mechanism. In particular, in these processes,
acyclic 2,3-diazabuta-1,3-diene derivatives are formed
instead of heterocyclic adducts. Probably, this is a conse-
quence of the formation of the zwitterionic structure in the
first reaction stage. This hypothesis is supported by DFT
calculations. It must be noted that there is a specific
property of the (E)-2-aryl-1-cyano-1-nitroethenes group, in
X-ray crystal structure determination
The X-ray diffraction intensities for 5a were collected at
120 K on SuperNova X-ray diffractometer equipped with
Atlas S2 CCD detector using the mirror-monochromatized
˚
CuKa radiation (k = 1.54184 A). All data were collected
using the x scan technique, with an angular scan width of
1.0°. The programs CrysAlis CCD, CrysAlis Red and
CrysAlisPro [40, 41] were used for data collection, cell
Fig. 2 Views of TSs for reaction between 1c and 2
123

Unexpected course of reaction between (E)-2-aryl-1-cyano-1-nitroethenes and diazafluorene:…
Scheme 3
J = 8.5 Hz, CHAr), 7.68–7.62 (m, 2H, CHAr), 7.52–7.43
refinement and data reduction. The structures were solved
by direct methods using SHELXS-97 and refined by the
full-matrix least squares on F2 using the SHELXL-97 [42].
The H atoms were positioned geometrically and allowed to
ride on their parent atoms, with Uiso(H) = 1.2 Ueq(C). The
molecular plot was drawn with Olex2 [43]. Compound 5a
crystallizes in an orthorhombic Pna21 space group. The
molecule is nearly planar. The two aromatic parts of the
molecule are twisted around the central linear fragment by
ca. 14.6(9)°. The bond lengths in the linear fragment were
(m, 5H, CHAr), 7.35–7.31 (m, 2H, CHAr) ppm; 13C NMR
(125 MHz, CDCl3): d = 158.2, 142.5, 137.3, 132.9, 131.6,
131.3, 131.0, 130.6, 129.8, 129.3, 128.3, 128.2, 123.0,
122.9, 120.1, 120.0, 119.9 ppm; MS: m/z = 316 (M?),
205; UV–Vis (methanol): kmax = 342, 260, 196 nm.
1-(4-Fluorophenyl)-2,3-diaza-4-(9-fluorenylidene)buta-
1,3-diene (5b, C20H13FN2)
Yield: 93%; tR = 9.5 min; yellow crystals; m.p.:
-1
ꢀ
99–101 °C; IR (KBr): m = 2160, 1957, 1549, 1103 cm
;
˚
˚
as follows: C1 = N1 1.302(6) A, N1–N2 1.392(6) A,
1H NMR (500 MHz, CDCl3): d = 8.56 (s, 1H, CH), 7.96
(dd, 2H, J = 5.5 Hz, 8.7 Hz, CHAr), 7.92 (d, 1H,
J = 7.6 Hz, CHAr), 7.66–7.62 (m, 2H, CHAr), 7.46–7.43
(m, 3H, CHAr), 7.33 (q, 2H, J = 8.7 Hz, CHAr), 7.22 (t, 2H,
J = 8.5 Hz, CHAr) ppm; 13C NMR (125 MHz, CDCl3):
d = 158.5, 142.1 (d, JC–F = 114.4 Hz), 136.8, 131.7, 131.5,
131.2, 130.7, 130.6, 130.5, 130.3, 128.2, 122.9, 120.0, 119.9,
116.3, 116.1, 116.0 ppm; MS: m/z = 300 (M?), 205; UV–
Vis (methanol): kmax = 338, 259, 201 nm.
˚
˚
N2 = C14 1.298(6) A, and C14–C15 1.442(7) A, showing
some degree of electron delocalization along this molecular
fragment in comparison to another related structure of p-
methoxybenzaldehyde 9-fluorenylidenehydrazone with the
˚
respective bond lengths: C8 = N2 1.286 (4) A, N1–N2
˚
˚
˚
1.418 (3) A, N1 = C7 1. 264 (4) A, and C7–C6 1.453 (4) A
(atom labels as in the original paper) [44].
The experimental details and final atomic parameters for
5a have been deposited with the Cambridge Crystallo-
graphic Data Centre as supplementary material (CCDC ID
1448932). Copies of the data can be obtained free of charge
on request via http://www.ccdc.cam.ac.uk/conts/retrieving.
html (or from the Cambridge Crystallographic Data Centre,
12, Union Road, Cambridge CB2 1EZ, UK; fax: ?44 1223
336033).
1-Phenyl-2,3-diaza-4-(9-fluorenylidene)buta-1,3-diene (5c,
C20H14N2)
Yield: 95%; tR = 8.5 min; orange crystals; m.p.:
-1
ꢀ
83–84 °C; IR (KBr): m = 2161, 1955, 1543, 1099 cm
;
1H NMR (500 MHz, CDCl3): d = 8.59 (s, 1H, CH), 8.49
(d, 1H, J = 7.5 Hz, CHAr), 7.97–7.93 (m, 3H, CHAr),
7.66–7.62 (m, 2H, CHAr), 7.54–7.52 (m, 3H, CHAr),
7.46–7.42 (m, 2H, CHAr), 7.36–7.31 (m, 2H, CHAr) ppm;
13C NMR (125 MHz, CDCl3): d = 160.4, 159.6, 142.5,
136.9, 134.4, 131.7, 131.5, 131.2, 130.7, 129.0, 128.7,
128.1, 127.9, 127.7, 125.5, 122.9, 120.8, 119.9 ppm; MS:
m/z = 282 (M?), 205; UV–Vis (methanol): kmax = 338,
255, 208 nm.
Reactions between CNA and diazafluorene: general
procedure
A mixture of appropriate nitroalkene (1a–1d or 6,
0.012 mol) and diazafluorene (0.010 mol) in 5 cm3 of the
appropriate solvent was stirred at room temperature for
12 h. The solvent was evaporated in vacuo to dryness and
the semisolid residue was recrystallized firstly from ethanol
and then from cyclohexane.
1-(4-Methoxylphenyl)-2,3-diaza-4-(9-fluorenylidene)buta-
1,3-diene (5d, C21H16N2O)
Yield: 95%; tR = 9.2 min; yellow crystals; m.p.:
127–130 °C; IR (KBr): mꢀ = 2160, 2038, 1599,
1099 cm-1; 1H NMR (500 MHz, CDCl3): d = 8.58 (s, 1H,
CH), 8.57 (d, 1H, J = 7.8 Hz, CHAr), 7.94 (d, 1H,
J = 9.5 Hz, CHAr), 7.91 (d, 2H, J = 8.6 Hz, CHAr), 7.65
(dd, 2H, J = 8.2 Hz, 5.2 Hz, CHAr), 7.43 (t, 2H,
J = 6.7 Hz, CHAr), 7.35–7.31 (m, 2H, CHAr), 7.05–7.03
1-(4-Chlorophenyl)-2,3-diaza-4-(9-fluorenylidene)buta-
1,3-diene (5a, C20H13ClN2)
Yield: 95%; tR = 10.6 min; yellow crystals; m.p.:
ꢀ
103–105 °C; IR (KBr): m = 2160, 1954, 1539,
1083 cm-1 1H NMR (500 MHz, CDCl3): d = 8.54 (s,
1H, CH), 7.92 (d, 1H, J = 7.6 Hz, CHAr), 7.88 (d, 2H,
;
123

´
R. Jasinski et al.
(m, 2H, CHAr), 3.90 (s, 3H, CH3) ppm; 13C NMR (125 MHz,
CDCl3): d = 162.3, 160.3, 160.0, 142.4, 137.0, 131.8, 131.3,
131.0, 130.8, 130.7, 130.5, 128.2, 128.1, 127.3, 122.8, 119.9,
119.8, 114.5, 55.5 ppm; MS: m/z = 312 (M?), 205; UV–Vis
(methanol): kmax = 358, 225, 197 nm.
N ¼ EHOMOðdiazafluoreneÞ À EHOMOðtetracyanoetheneÞ
:
The local nucleophilicity (Nk) [51] condensed to atom k
was calculated using global nucleophilicity N and Parr
function P-k [52] according to the formula:
Nk ¼ PÀk N:
40,50-Dihydro-40-nitro-50-(trichloromethyl)spiro[9H-fluo-
rene-9,30-[3H]pyrazole] (7, C16H10Cl3N3O2)
Yield: 93%; tR = 14.8 min; white crystals; m.p.:
For the simulation of the reaction paths, hybrid
functional B3LYP with the 6-31 ??G(d), basis set
included in the GAUSSIAN 09 package [53] was used. It
was found previously that calculations using B3LYP
functional illustrate well the structure of transition states
in polar 1,3-dipolar cycloadditions involving conjugated
nitroalkenes [22, 23, 30]. The critical points on the reaction
paths were localized in an analogous manner as in the case
of the previously analyzed cycloadditions of
diaryldiazomethanes with nitroacetylene [54]. In
particular, for structure optimization of the reactants and
the reaction products, the Berny algorithm was applied.
First-order saddle points were localized using the QST2
procedure. The transition states were verified by
diagonalization of the Hessian matrix and by an analysis
of the intrinsic reaction coordinates (IRC).
ꢀ
138–140 °C; IR (KBr): m = 2993, 2950, 1557, 1359,
748 cm-1 1H NMR (500 MHz, CDCl3): d = 7.83 (d,
;
1H, J = 8.5 Hz, CHAr), 7.79 (d, 1H, J = 6.9 Hz, CHAr),
7.61–7.58 (m, 1H, CHAr), 7.52 (t, 1H, J = 7.6 Hz, CHAr),
7.46–7.42 (m, 2H, CHAr), 7.33–7.29 (m, 1H, CHAr), 7.03
(d, 1H, J = 7.0 Hz, CHAr), 6.82 (d, 1H, J = 7.6 Hz,
CHAr), 5.70 (d, 1H, J = 7.9 Hz, CHAr) ppm; 13C NMR
(125 MHz, CDCl3): d = 142.0, 134.7, 131.5, 131.1, 129.0,
128.4, 125.2, 124.1, 121.0, 120.9, 104.5, 103.8, 94.8,
88.6 ppm.
40,50-Dihydro-40-nitro-50-(dichloromethylene)spiro[9H-flu-
orene-9,30-[3H]pyrazole] (8, C16H9Cl2N3O2)
Yield: 96%; white crystals; m.p.: 175–177.5 °C; IR (KBr):
1
m = 3014, 2975, 2910, 1629, 1560, 1353, 742 cm-1; H
ꢀ
All calculations were carried out for the simulated
presence of nitromethane as the reaction medium. For this
purpose, PCM [55] was used. For optimized structures, the
thermochemical data for the temperature T = 298 K and
pressure p = 1 atm were computed using vibrational
analysis data. Global electron density transfer (GEDT) [56]
was calculated according to the formula:
NMR (500 MHz, CDCl3): d = 7.83–7.81 (m, 2H, CHAr),
7.58–7.52 (m, 2H, CHAr), 7.36–7.31 (m, 2H, CHAr), 7.11
(d, 1H, J = 7.9 Hz, CHAr), 6.86 (d, 1H, J = 8.6 Hz,
CHAr), 5.73 (s, 1H, CHAr) ppm; 13C NMR (125 MHz,
CDCl3): d = 142.2, 140.5 136.4, 134.5, 131.3, 131.0,
129.0, 128.8, 124.9, 122.6, 121.1, 120.9, 101.2, 87.9 ppm;
MS: m/z = 345 (M?).
GEDT ¼ ÀRqA;
where qA is the net Mulliken charge and the sum is taken
Quantum chemical calculations
over all the atoms of the dipolarophile. Indexes of r-bonds
development (l) were calculated according to the formula
All calculations reported in this paper were performed on
‘‘Zeus’’ supercomputer in the ‘‘Cyfronet’’ computational
center in Cracow. Global and local electronic properties
were estimated on the basis of structures obtained—ac-
cording to Domingo suggestions [47, 48]—on the basis of
B3LYP/6-31G(d) calculations. For this purpose, we have
used structures created by the standard procedure [49]. In
particular, the electronic chemical potentials (l) and
chemical hardness (g) were evaluated in terms of one-
electron energies of FMO (EHOMO and ELUMO) using the
equations:
[30]:
TS
AÀB
r
À rAPÀB
lAÀB ¼ 1 À
;
rAPÀB
TS
A–B
where r
is the distance between the reaction centers A
and B at the TS and rPA–B is the same distance at the cor-
responding product.
Acknowledgements The research was carried out with the equip-
ment purchased thanks to the financial support of the European
Regional Development Fund in the framework of the Operational
Program Development of Eastern Poland 2007–2013 (Contract No.
POPW.01.03.00-06-009/11-00, equipping the laboratories of the
Faculties of Biology and Biotechnology, Mathematics, Physics and
Informatics, and Chemistry for studies of biologically active sub-
stances and environmental samples). The authors thank also the
Polish Ministry of Science and Education for financial support (Pro-
ject No. C-2/259/2015/DS) as well as for Cracov Computing Centre
‘‘Cyfronet’’ for permission to use high-performance computers (Grant
No. MNiSW/Zeus_lokalnie/PK/009/2013).
l ꢀ ðEHOMO þ ELUMOÞ=2 g ꢀ ELUMO À EHOMO
:
Next, the values of l and g were then used for the
calculation of global electrophilicity (x) [47, 48] according
to the formula:
x ¼ l2=2g;
and the global nucleophilicity (N) [50] can be expressed in
terms of the equation:
123

Unexpected course of reaction between (E)-2-aryl-1-cyano-1-nitroethenes and diazafluorene:…
´
25. Jasinski R, Baranski A (2010) J Mol Struct (TheoChem) 949:8
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´
Open Access This article is distributed under the terms of the
Creative Commons Attribution 4.0 International License (http://
creativecommons.org/licenses/by/4.0/), which permits unrestricted
use, distribution, and reproduction in any medium, provided you give
appropriate credit to the original author(s) and the source, provide a
link to the Creative Commons license, and indicate if changes were
made.
´
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