Theoretical investigations on the HOMO–LUMO gap and global reactivity descriptor studies, natural bond orbital, and nucleus-independent chemical shifts analyses of 3-phenylbenzo[d]thiazole-2(3H)-imine and its para-substituted derivatives: Solvent and subs

Article abstract of DOI:10.1177/1747519820932091

Natural bond orbital analysis, salvation, and substituent effects of electron-releasing (–CH₃, –OH) and electron-withdrawing (–Cl, –NO₂, –CF₃) groups at para positions on the molecular structure of synthesized 3-phenylbenz

Full text of DOI:10.1177/1747519820932091

932091CHL0010.1177/1747519820932091Journal of Chemical ResearchMiar et al.
research-article2020
Research Paper
Journal of Chemical Research
1–12
© The Author(s) 2020
Article reuse guidelines:
sagepub.com/journals-permissions
Theoretical investigations on the HOMO–LUMO
gap and global reactivity descriptor studies,
natural bond orbital, and nucleus-independent
chemical shifts analyses of 3-phenylbenzo[d]
thiazole-2(3H)-imine and its para-substituted
derivatives: Solvent and substituent effects
https://doi.org/10.1177/1747519820932091
DOI: 10.1177/1747519820932091
journals.sagepub.com/home/chl
Marzieh Miar1, Abolfazl Shiroudi2 , Khalil Pourshamsian1,
Ahmad Reza Oliaey1 and Farhad Hatamjafari1
Abstract
Natural bond orbital analysis, salvation, and substituent effects of electron-releasing (–CH3, –OH) and electron-
withdrawing (–Cl, –NO2, –CF3) groups at para positions on the molecular structure of synthesized 3-phenylbenzo[d]
thiazole-2(3H)-imine and its derivatives in selected solvents (acetone, toluene, and ethanol) and in the gas phase by
employing the polarizable continuum method model are studied using the M06-2x method and 6-311++G(d,p) basis
set. The relative stability of the studied compounds is influenced by the possibility of intramolecular interactions between
substituents and the electron donor–acceptor centers of the thiazole ring. Furthermore, atomic charges, electron
density, chemical thermodynamics, energetic properties, dipole moments, and nucleus-independent chemical shifts of
the studied compounds and their relative stability are considered. The dipole moment values and the highest occupied
molecular orbital–lowest unoccupied molecular orbital energy gaps reveal different charge-transfer possibilities within
the considered molecules. Finally, natural bond orbital analysis is carried out to picture the charge transfer between the
localized bonds and lone pairs.
Keywords
3-phenylbenzo[d]thiazole-2(3H)-imines, density functional theory, nucleus-independent chemical shift, natural bond
orbital, polarizable continuum model, solvent effects
Date received: 16 April 2020; accepted: 15 May 2020
1Department of Chemistry, Islamic Azad University, Tonekabon, Iran
Khalil Pourshamsian, Department of Chemistry, Islamic Azad University,
2Young Researchers and Elite Club, Islamic Azad University, Tehran, Iran Tonekabon Branch, Tonekabon 46841-61167, Iran.
Email: kshams49@gmail.com
Corresponding authors:
Abolfazl Shiroudi, Young Researchers and Elite Club, Islamic Azad
University, East Tehran Branch, Tehran 18661-13118, Iran.
Email: abolfazl.shiroudi@iauet.ac.ir

2
Journal of Chemical Research 00(0)
1. How do the donor-acceptor interactions influence
the occupancies of the involved bonds?
2. Is there a relationship between the highest occupied
molecular orbital (HOMO)-lowest unoccupied
molecular orbital (LUMO) gaps in the considered
compounds?
Introduction
Heterocycles are the largest and one of the classical divi-
sions of organic chemistry. They are of immense impor-
tance not only biologically but also industrially. The
majority of pharmaceutical products that mimic natural
products with biological activity are heterocycles. Fused
heterocyclic compounds are key valuable and structural
scaffolds in a broad variety of natural products, drug mol-
ecules, and functional materials.1–3 Among them, research
on benzothiazoles, organosulfur heterocyclic compounds
has become a rapidly developing and increasingly active
topic. Such compounds are used as building blocks in
organic synthesis due to their wide range of biological
activities, and they form core in various drugs such
as anticancer, antimicrobial, anti-asthmatic, antitumor,
antibacterial, antitubercular, anticonvulsant, anti-HIV,
anti-inflammatory, antifungal, antiproliferative, antiviral,
anti-Alzheimer, antimalarial, and anti-diabetic, agents.4–13
Herein, we report a facile, environmentally friendly
method for intramolecular cyclization under solvent-free con-
ditions. The reaction occurs in two steps in the presence of
sodium tert- butoxide as a strong base. Finally, the challenges
of using organic solvents in industrial processes are discussed
from the perspective of cost, stability, and safety. We suggest
that a holistic view of solvent effects, the mechanistic elucida-
tion of these effects, and careful consideration of the chal-
lenges associated with solvent use could assist researchers in
choosing and designing improved solvent systems for tar-
geted benzothiazole biomass conversion processes.14–16
At present, density functional theory (DFT) is accepted
as a popular post-Hartree–Fock (HF) approach for the ab
initio computation of molecular structures, and the energies
of molecules.17 It has proved to be extremely useful in the
study of the electronic structures of molecules. There are
several basic approaches available for modeling molecular
systems in solution. One of them is the implicit treatment of
solvent molecules,18 Self-consistent reaction field (SCRF)
models employ this approach,19 with the polarizable con-
tinuum model (PCM) being the first proposed SCRF
method. Employing the PCM model in DFT is a good
method while investigating solvent effects.20 In this study,
we present an overview of organic solvent effects. In our
pursuit of an improved synthetic method for the preparation
of organic compounds, the M06-2x quantum method21 uti-
lizing the 6-311++G(d,p) basis set22 has been used in the
studied solvents (toluene, acetone, and ethanol), and the
obtained data has been compared with the same properties
in the gas phase in order to determine their electronic and
spectroscopic properties and to benefit from two major
types of effects: solvent effects on solubility of benzothia-
zole components and solvent effects on chemical thermo-
dynamics including those affecting the products.23,24
Moreover, an attempt is made to supply further qualitative
chemical insights using the donor-acceptor interaction
energies, nucleus-independent chemical shift (NICS) tech-
niques,25–29 and natural bond orbital (NBO) analysis.30,31
This study aims to present quantitative answers to the fol-
lowing questions32 concerning the solvent and substituent
effects on the electronic structures of 3-substituted
3-phenylbenzo[d]thiazole-2(3H)-imines:
3. How does the resonance energy relate to the donor-
acceptor interactions in the considered compounds?
As a final point, we justify the obtained results with
global reactivity descriptor studies in order to give a deeper
insight into the solvent and substituent effects.
Theory and computational details
All quantum chemical calculations were performed using
the Gaussian 09 program.33 The molecular structures were
visualized based on the output data of the DFT calculations
using the GaussView program.34 Geometry optimizations
and frequency calculations were carried out using DFT
along with the M06-2x exchange-correlation functional in
conjunction with the split-valence 6-311++G(d,p) basis
function because of its high accuracy in achieving geome-
tries, zero-point energy (ZPE)35 and frequencies36 com-
bined with computational efficiency.37,38
All the optimized structures gave no negative vibra-
tional modes showing that all structures were stationary
points in the geometry optimization procedures. The ration-
ale for choosing the M06-2x functional was based on the
fact that it is the best for studies involving main group ther-
mochemistry, kinetics, noncovalent interactions, and elec-
tronic excitation energies to the valence and Rydberg states.
The M06-2x functional and its analogs are dedicated to pre-
cise energetic considerations.39
The nature of all the optimized structures are determined
based on the harmonic vibrational frequency calculations
determined at the same level of theory to confirm that a
minimum on the potential energy surface was achieved
under the imposed constraint of the indicated symmetry.40
The NBO populations, atomic charges, frontier molecu-
lar orbital (FMO) properties, second-order perturbation sta-
bilization energies, and dipole moments are considered at
the same theoretical level using the NBO 5.0 program.41
Furthermore, the aromaticity index NICS values for all the
studied compounds are estimated within the gauge-included
atomic orbital (GIAO) method at the M06-2x/6-
311++G(d,p) level of theory. Finally, in order to estimate
the effect of the liquid environment, the geometries of the
studied compounds are re-optimized at the same level of
theory in three different solvents: non-polar toluene
(ε=2.374), polar aprotic acetone (ε=20.493), and polar
protic ethanol (ε=24.852).
Results and discussion
The synthesis of 3-phenylbenzo[d]thiazole-2(3H)-imine
and its para-substituted derivatives (3a–f) was carried out
by reaction of different synthesized N-acyl-N′-aryl thioureas
(1a–f) with diazonium salts (2). The optimized structures of
all the compounds (see Scheme 1) were then investigated by

Miar et al.
3
of the considered compounds (Table 1). The polar solvents
(ethanol and acetone) stabilized the studied compounds
through hydrogen bonding and dipole-dipole interactions
more than the non-polar solvent (toluene).
S
R
NH
O
S
Cl-
N+
N
N
1) tert-BuONa,tert-BuOH
N
N
+
H
H
2) reflux
Br
R
1a-f
2
3a-f
Dipole moments
R: H (a), CH3 (b), OH (c), Cl (d), CF3 (e), NO2 (f)
The dipole moment (μ) prediction is an important issue
which is associated with the molecular stability in polar envi-
ronments.42 In this work, the experimental dipole moment is
not known. The calculated dipole moments in different envi-
ronments (i.e. toluene, acetone, and ethanol) are shown in
Table 2. The influence of the polar environment (i.e. acetone
and ethanol) is notable in comparison to the dipole moment
values in both phases. The order of the calculated dipole
moment values are NO2 >CF3 >Cl>CH3 >H>OH.
Among the considered compounds 1–6, compound 6
(X=NO2 substituent) has the highest dipole moment in the
studied solvents and gas phases because it has a higher dipole
interaction. The order of the calculated dipole moment val-
ues for the studied molecules in solvents with different polar-
ity (ethanol>acetone>toluene) the arising results related to
the increase of the dielectric constant which corresponds to
the dielectric constant value orders that it will be increased
with increasing dielectric constant (Table 2).
Scheme 1. The synthetic route of 3-phenylbenzo[d]thiazole-
2(3H)-imine and its derivatives.
The highest dipole moment for all the compounds was
observed in ethanol. As can be seen in Table 2, the dipole
moment increases from the gas phase to a more polar sol-
vent, with the highest dipole moment occurring for com-
pound 6 with a NO2 substituent in ethanol solution with a
value of ~5.94, while compound 1 has the lowest dipole
moment in the gas phase (~1.91). It is noticeable that dipole
moments are related to the influence of the nature of the
substituents at the N7 position. In this work, higher dipole
moment values were observed in the compounds possess-
ing in electron acceptors (i.e. NO2, Cl, CF3) compared to
those with electron-donor groups (i.e. H, CH3, OH) in the
studied solvents and gas phase. This is explained by consid-
eration of the charge values on the atoms of the THREE-
substituted six-membered ring. It is well known that in the
studied compounds, the nitrogen N7 atom carries the most
negative charge (Table 3).
Scheme 2. The synthesis of the studied compounds.
comprehensive computational studies and are presented in
Supplemental Figure S1.
Energy and thermodynamic parameters
The structures and numbering of the three-substituted
3-phenylbenzo[d]thiazole-2(3H)-imines are shown in Scheme
2. The computed corrected total energy (Ecorr) and Gibbs free
energies (G), relative energies (ΔE) as well as the relative
Gibbs free energies (ΔG) using the M06-2x method in differ-
ent solvents and gas phases at T=298 K are listed in Table 1.
The relative energies and Gibbs free energies in acetone
are more stable by about 0.46–18.31 and 0.63–18.77kcal/
mol, respectively, than those determined in the solvents.
The major difference between the obtained energies and
Gibbs free energies were found in the gas phase (18.31 and
18.77kcal/mol, respectively, for the OH substituent). The
order of stability in the considered solvent and gas phases is
Cl>CF3 >NO2 >OH>CH3 >H. The obtained results
show that the stability increases with increasing electron-
withdrawing substituents.
On other hand, all the species were stabilized more or
less by the solvent dielectric constant, where the corrected
total energy (Ecorr) decrease in polar solvents (ethanol and
acetone) was more than in the non-polar solvent (toluene).
The solute-solvent interactions further stabilized the struc-
tures compared to either the non-polar solvent (toluene) or
in the gas phase. It is noted that the values of solvation
energies (Esolv) are higher in the case of ethanol and acetone
compared to toluene, which agrees with the polar character
Solvent effects
Solvent effects are significant in stability phenomena
because polarity differences between tautomers can induce
important changes in their relative energies in solution.43
PCM calculations were used to evaluate the solvent effects
on the 3-phenylbenzo[d]thiazole-2(3H)-imine and its para-
substituted derivatives. It is noted that the PCM model does
not consider the presence of explicit solvent molecules;
therefore, specific solute-solvent interactions are not
defined and the studied solvation effects arise only from
mutual solute-solvent electrostatic polarization.43 The low-
est energy values of compounds 1–6 are obtained from
aqueous solution calculations. The dipole moments are
increased by increasing the solvent polarity and changing

4
Journal of Chemical Research 00(0)
Table 1. Total energies and Gibbs free energies (in Hartree), relative energies and Gibbs free energy, ΔG (in kcal/mol) and
solvation energies (ΔESolv) for three-substituted 3-phenylbenzo[d] thiazole-2(3H)-imines 1–6 (P=1atm, T=298K).
Substituent
–H (1)
Parameter
Gas (ε=1.0)
Toluene (ε=2.374)
Acetone (ε=20.493)
Ethanol (ε=24.852)
Ecorr
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
Ecorr
−1008.800
−1008.840
15.662
15.949
0.000
−1048.080
−1048.121
16.241
16.692
0.000
−1468.410
−1468.452
15.959
16.433
0.000
−1084.021
−1084.062
18.306
18.766
0.000
−1345.847
−1345.893
15.447
15.632
0.000
−1213.287
−1213.330
17.342
−1008.819
−1008.859
3.666
−1008.825
−1008.866
0.000
−1008.822
−1008.863
1.837
4.084
0.000
1.731
−11.996
−1048.100
−1048.142
3.731
−15.662
−1048.105
−1048.148
0.000
−13.825
−1048.102
−1048.145
1.856
–Me (2)
–Cl (3)
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
Ecorr
3.797
0.000
1.884
−12.510
−1468.431
−1468.473
3.272
−16.241
−1468.436
−1468.478
0.000
−14.384
−1468.433
−1468.476
1.775
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
Ecorr
3.343
0.000
1.616
−12.686
−1084.042
−1084.084
5.077
−15.959
−1084.050
−1084.092
0.000
−14.184
−1084.049
−1084.091
0.462
–OH (4)
–CF3 (5)
–NO2 (6)
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
Ecorr
5.041
0.000
0.626
−13.229
−1345.866
−1345.912
3.792
−18.306
−1345.872
−1345.918
0.000
−17.844
−1345.869
−1345.915
1.674
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
Ecorr
3.881
0.000
1.728
−11.655
−1213.308
−1213.352
3.912
3.902
−13.430
−15.447
−1213.314
−1213.358
0.000
0.000
−17.342
−13.774
−1213.310
−1213.353
2.874
2.920
−14.468
Gcorr
ΔEcorr
ΔGcorr
ΔESolv
17.449
0.000
ΔEsolv =(Ecorr in solvent−Ecorr in gas).
Table 2. Calculated dipole moment of the optimized compounds 1–6 (in Debyes) in the studied solvent and gas phases.
Substituent
Gas (ε=1.00)
Toluene (ε=2.374)
Acetone (ε=20.493)
Ethanol (ε=24.852)
X=H [1]
X=Cl [2]
X=CH3 [3]
X=OH [4]
X=CF3 [5]
X=NO2 [6]
1.9064
2.6144
2.0122
1.7086
3.7871
5.7918
1.9685
2.6481
2.1487
2.0246
3.8093
5.8150
2.0949
2.6672
2.2518
2.3897
3.8620
5.8889
2.1042
2.6940
2.2748
2.4145
3.8774
5.9361
Table 3. The calculated natural atomic charges of compounds 1–6.
Atom
H (1)
0.17376
CH3 (2)
Cl (3)
0.17195
OH (4)
CF3 (5)
NO2 (6)
C4
C5
N7
C8
S9
N10
C11
H
0.17432
−0.20499
−0.51206
0.34003
0.30570
−0.72200
0.14786
0.35237
0.17411
−0.20493
−0.51070
0.33997
0.30587
−0.72398
0.12327
0.35246
0.16989
−0.20340
−0.51524
0.33725
0.31535
−0.72088
0.17962
0.35600
0.16800
−0.20311
−0.51537
0.33565
0.32064
−0.71983
0.19328
0.35771
−0.20438
−0.51340
0.33961
0.30698
−0.72158
0.15776
0.35294
−0.20450
−0.51398
0.33817
0.31156
−0.72168
0.15530
0.35456

Miar et al.
5
Figure 2. Optimized structure of 3-phenylbenzo[d]thiazole-
2(3H)-imine (compound 1).
Figure 1. Dielectric constant dependence of the dipole
moments for the considered compounds.
from gas to solution phases. Hence, increased stability with material). The result suggests that the atoms bonded to
an electron-donating group in polar solvents could be asso- nitrogen atoms (H21 and C11) are electron acceptors and
ciated with an increase of dipole moments (Table 2). Plots also indicates the charge transfer from them (H21 and
of the dipole moment of the considered compounds versus C11) to the nitrogen atom (N10). The relationship between
dielectric constants are shown in Figure 1.
the C–H wavenumber shifts and calculated Mulliken
The charge distributions of dipolar compounds are often charges of C16 (−0.1833e) and N10 (−0.7216e) also indi-
altered considerably in the presence of the solvent field.44 cates that they take part in intramolecular hydrogen bond-
We have studied the charge distribution for compounds 1–6 ing. The influence of electronic effect resulting from the
in solvents and in the gas phase using the NBO technique. hyperconjugation and induction of the substituent group
The charge distribution with increasing polarity varies dif- (X: H, Me, Cl, OH, CF3, NO2) in the aromatic six-mem-
ferently for any atoms in solvents, for example, a regular bered ring causes a large negatively charged value on the
increase of the negative charge was found for the N7 atom carbon atom C14.
derivatives when passing from the gas phase to a more
These calculations showed the electronegative nature of
polar solvent (Table 2). The charge distribution on the N7 the O, S, and N atoms. In compound 6, the hydrogen atom
atom is affected by the nature of the substituent and the H21 was the most electropositive atom among all the
polarity of the solvents.
hydrogen atoms (see Figure 2). The proton of the triazole
NH group possesses the highest value of 0.35771e. In com-
pounds 1–6, the charges at this H-site (H21 atom) were cal-
culated to be 0.35294e, 0.35237e, 0.35456e, 0.35246e,
Mulliken atomic charges
The Mulliken45,46 population analysis is probably the best 0.35600e, and 0.35771e, respectively. The order of the
known of all models for predicting individual atomic charge density at the NH hydrogen of the triazole ring is
charges which is computationally very popular due to its 6>5>3>1>4>2. This order agrees with the chemical
simplicity. Mulliken charges were shown to be highly sense where the electron-releasing substituent, namely the
basis set dependent and unpredictable with marked fluc- CH3 group (compound 2), decreases the positive charge at
tuations in partial charges.47 We have studied the charge this H-site, while the NO2 substituted derivative (com-
distribution using NBO techniques in different media. The pound 6) has the highest positive NH proton, which agrees
Mulliken population analysis in compounds 1–6 calcu- with its high electron-withdrawing character (−0.71983e),
lated using the NBO method at the M06-2x/6- although the substituent is not directly attached to the tria-
311++G(d,p) level of theory, and the obtained results are zole ring. It should be pointed out that the nitrogen atom
illustrated in detail in Table S1 of the Supplemental mate- corresponding to the NH group in the studied compounds
rial. In the case of benzene rings, all the carbon atoms are has high negative values. The charge on this nitrogen atom
expected to be negative, but carbon atoms C4 and C11 are (N10) is in the range of −0.71983e to −0.72398e for the
found to be positively charged, which may be due to the considered compounds. Instead, the charge on the nitrogen
attachment of the nitrogen atom N7 in the five-membered atom of the ring (N3) of compounds 1–6 is calculated to be
ring at these carbon atoms. All the hydrogen atoms in the less (−0.51340e, −0.51206e, −0.51398e, −0.51070e,
studied molecules are found to be equally slightly positive −0.51524e, and −0.51537e, respectively) negative than that
as expected, as with other hydrogen atoms in the consid- on the NH one (N6 atom). Compound 6 showed a high
ered molecules.
positive value for the hydrogen atom (H21) associated with
As can be seen in Figure 2, the nitrogen atom (N10) has the NO2 group, 0.35771e, resulting from its bonding to the
more negative charges whereas all the hydrogen atoms six-membered ring which is connected to the triazole ring
have positive charges (see Table S1 in the Supplemental (see Table S1 in the Supplemental material).

6
Journal of Chemical Research 00(0)
Furthermore, carbon atoms C4, C8, and C11 are nega- from the donor (HOMO) to the acceptor (LUMO) in mole-
tively charged except for those attached to the strong elec- cules. It also plays an important role in determining the
tronegative N atom (see Table S1 in the Supplemental chemical reactivity of a system and is defined as follows
material). The charge on the carbon atom in the six-mem-
bered ring of compounds 1–6 are calculated as −0.19844e
(X=H), −0.02914e (X=CH3), −0.04327e (X=Cl),
2
µ
ω =
(1)
2η
0.32693e (X=OH), −0.14892e (X=CF3), and 0.06419e where η denotes the global chemical hardness and μ repre-
(X=NO2), respectively. The carbon atom of the C–Cl bond sents the electronic chemical potential which describes the
in compound 3 has a less negative charge of −0.04327e charge transfer within a system in the ground state as
than that of the C–CF3 bond of compound 5 (−0.14892e) follows55
that is in agreement with the higher electronegative nature
E
− E
2
LUMO
HOMO
of the chlorine atom (0.01100e) compared to the carbon
atom in the CF3 group (1.08796e). The phenolic oxygen
atom of compound 4 has the highest negative value of
−0.68134e. As a result, the attached carbon atom, C14
(0.32693e) in compound 4 is found to have the most posi-
tivearomaticcarbonatom(seeTableS1intheSupplemental
material).
(2)
(3)
η =
E
+ E
HOMO
LUMO
µ =
2
Compounds having greater values of chemical potential
are more reactive than those with small electronic chemical
potentials. It is clear that compound 6 is the most reactive
while compound 1 is the least reactive of all. Similarly, the
electronegativity (χ) is a measure of the attraction of an
FMO analysis
Molecular orbitals and their properties such as energy are atom for electrons in a covalent bond; thus, compound 6
useful for physicists and chemists. This is also used in fron- has higher electronegativity (χ), and it does exhibit high
tier electron density for predicting the most reactive posi- charge flow. Also, the obtained results show that compound
tion in π-electron systems and also explains several types 6 (X=NO2) is strongly electrophilic, while compound 2
of reactions in conjugated systems.48 FMO analysis is (X=CH3) is nucleophilic (see Table 4).
widely employed to explain the optical and electronic prop-
Moreover, ΔNmax represents the maximum electronic
erties of organic compounds.49 Knowledge of the HOMO charge, S is the global softness, and χ denotes the absolute
and LUMO, and their properties namely their energy, is electronegativity, which is used to calculate the electron
very useful to gauge the chemical reactivity of molecules. transfer direction and is given by
During molecular interactions, the LUMO accepts elec-
µ
η
∆N
= −
trons and its energy corresponds to the electron affinity
(EA), while the HOMO represents electron donors and its
energy is associated with the ionization potential (IP).48
The HOMO-LUMO energy gap explains the concluding
charge transfer interaction within the molecule and is useful
in determining molecular electrical transport properties. A
molecule with a high frontier orbital gap (HOMO-LUMO
energy gap) has low chemical reactivity and high kinetic sta-
bility,50–52 because it is energetically unfavorable to add an
(4)
max
χ = −µ
(5)
(6)
1
S =
η
The absolute electronegativity is a good measure of the
electron to the high-lying LUMO in order to remove elec- molecular ability to attract electrons to itself
trons from the low-lying HOMO. For instance, compounds [χ=(IP+EA)/2] where EA and IP are the electron affinity
that have a high HOMO-LUMO energy gap are stable, and and IP, respectively. It is noted that a small IP value along
hence are chemically harder than compounds having a small with a high EA is equal to high nucleophilicity and high
HOMO-LUMO energy gap.52 Thus, it is clear from Table 4 electrophilicity, respectively. As can be seen from Table 4,
that compound 1 (X=H) is hard and more stable (less reac- the para functional group will further influence the
tive), while compound 6 (X=NO2) is soft and the least stable HOMO and LUMO energy levels in the studied com-
of all (more reactive) in the studied solvents and gas phases. pounds (1–6). Electron-donating groups lead to an
The HOMO-LUMO energy gap decreases from compounds increase in the energy levels of the frontier orbitals
1 to 6. The minimum energy gap is achieved with a NO2 whereas electron-withdrawing groups have the opposite
substituent in the considered solvent and gas phases. Thus, effect. The energy levels increase in order from the most
this substituent increases the reactivity of the five-membered strongly electron-withdrawing group (–NO2) to the most
ring. The computed HOMO and LUMO energies are listed in strongly electron-donating group (–CH3). The CH3 sub-
Table 5 in all the media considered.
stituent (compound 2) has the lowest IP and therefore is
The global electrophilicity index (ω), introduced by Parr the most nucleophilic species. All the considered com-
et al.,53,54 is based on thermodynamic properties and meas- pounds in the solvents and gas phases have positive ΔNmax
ures the favorable change in energy when a chemical system values and act as electron acceptors from their environ-
attains saturation by the addition of electrons. It can be ment. The global reactivity of compounds 1–6 is discussed
defined as the decrease in energy due to the flow of electrons in terms of the HOMO and LUMO energies, the energy

Miar et al.
7
Table 4. Global reactivity descriptors calculated for 3-phenylbenzo[d]thiazole-2(3H)-imine and its para-substituted derivatives
(1–6) at the M06-2x/6-311++G(d,p) level of theory.
Substituent Paramater
HOMO
(a.u.)
LUMO
(a.u.)
ΔE (eV) μ (eV) η (eV)
ω (eV) S (eV)
χ (eV)
ΔNmax (eV) IP (eV) EA (eV)
Gas (ε=1.00)
H
CH3
Cl
OH
CF3
NO2
−0.25760 −0.00555 6.859
−0.25536 −0.00560 6.796
−0.26253 −0.01111 6.841
−0.25555 −0.00798 6.737
−0.26749 −0.02327 6.646
−0.27284 −0.06525 5.649
−3.580 3.429
−3.551 3.398
−3.723 3.421
−3.586 3.368
−3.956 3.323
−4.600 2.824
50.858 7.935
50.474 8.008
55.131 7.955
51.928 8.079
64.081 9.634
101.929 8.189
3.580
3.551
3.723
3.586
3.956
4.600
28.410
28.432
29.616
28.966
32.397
44.318
7.010
6.949
7.144
6.954
7.279
7.424
0.151
0.152
0.302
0.217
0.633
1.776
Toluene (ε=2.374)
H
CH3
Cl
OH
CF3
NO2
−0.25765 −0.0056
6.859
−0.25589 −0.00563 6.810
−0.26263 −0.01125 6.840
−0.25657 −0.00877 6.743
−0.26742 −0.02410 6.621
−0.27273 −0.06636 5.616
−3.582 3.429
−3.558 3.405
−3.726 3.420
−3.610 3.371
−3.966 3.311
−4.614 2.808
50.897 7.935
50.589 7.992
55.237 7.956
52.595 8.071
64.654 9.691
103.139 8.220
3.582
3.558
3.726
3.610
3.966
4.614
28.420
28.436
29.647
29.137
32.602
44.711
7.011
6.963
7.147
6.982
7.277
7.421
0.152
0.153
0.306
0.239
0.656
1.806
Acetone (ε=20.493)
H
CH3
Cl
OH
CF3
NO2
−0.25774 −0.00547 6.865
−3.581 3.432
−3.561 3.403
−3.727 3.423
−3.631 3.367
−3.973 3.296
−4.624 2.789
50.837 7.928
50.719 7.997
55.200 7.948
53.290 8.082
65.150 9.755
104.278 8.256
3.581
3.561
3.727
3.631
3.973
4.624
28.391
28.482
29.623
29.349
32.798
45.105
7.013
6.964
7.150
6.998
7.269
7.413
0.149
0.159
0.303
0.264
0.677
1.834
−0.25592 −0.00584 6.805
−0.26277 −0.01115 6.847
−0.25719 −0.00972 6.734
−0.26712 −0.02487 6.592
−0.27243 −0.06741 5.579
Ethanol (ε=24.852)
H
CH3
Cl
OH
CF3
NO2
−0.25774 −0.00549 6.864
−3.581 3.432
−3.561 3.403
−3.729 3.421
−3.630 3.368
−3.973 3.296
−4.635 2.782
50.849 7.929
50.711 7.997
55.294 7.955
53.223 8.078
65.164 9.783
105.067 8.255
3.581
3.561
3.729
3.630
3.973
4.635
28.396
28.480
29.659
29.324
32.800
45.340
7.013
6.964
7.150
6.998
7.270
7.416
0.149
0.159
0.308
0.262
0.677
1.853
−0.25591 −0.00583 6.805
−0.26274 −0.01131 6.842
−0.25719 −0.00961 6.737
−0.26716 −0.02488 6.593
−0.27254 −0.06810 5.563
HOMO: highest occupied molecular orbital; LUMO: unoccupied molecular orbital; IP: ionization potential; EA: electron affinity.
Table 5. The second-order perturbation energies E2 (in kcal/mol) for the most important charge transfer interactions in
compounds 1–6 in the gas phase.
Donor
NBO (i)
ED(i) (a.u.) Acceptor ED(j) (a.u.) Interaction type
NBO(j)
E2 (kcal/mol)
X=H X=CH3 X=Cl X=OH X=CF3 X=NO2
σN7–C8
1.97864
σ*C3–C4
σ*C4–N7
σ*N7–C11
σ*C8–N10
0.02373
0.03489
0.04266
0.00937
σ N7–C8 →σ*C3–C4
σ N7–C8 →σ*C4–N7
σ N7–C8 →σ*N7–C11
σ N7–C8 →σ*C8–N10
σ N7–C8 →σ*N10–H21
σ N7–C8 →σ*C11–C12
σ N7–C8 →π*C11–C12
σ C8–N10 →σ*N7–C8
σ C8–N10 →σ*N10–H21
πC8–N10 →π*C8–N10
σ C4–C5 →σ*C3–C4
σ C4–C5 →σ*C3–H19
σ C4–C5 →σ*C4–N7
σ C4–C5 →σ*C5–C6
σ C4–C5 →σ*C6–H20
σ C4–C5 →σ*N7–C11
σ C4–C5 →σ*C8–S9
3.12
2.62
2.52
1.65
2.64
1.03
0.89
1.62
0.71
1.77
5.64
2.24
1.56
4.83
2.55
4.60
0.71
3.13
2.61
2.52
1.66
2.64
1.01
0.90
1.64
0.71
1.77
5.61
2.24
1.55
4.84
2.55
4.60
0.71
3.11
2.61
2.52
1.62
2.66
1.04
0.93
1.59
0.72
1.76
5.68
2.24
1.54
4.83
2.54
4.62
0.71
3.13
2.61
2.53
1.65
2.63
0.96
0.98
1.64
0.71
1.78
5.62
2.24
1.55
4.84
2.56
4.58
0.71
3.08
2.60
2.51
1.60
2.67
1.11
0.92
1.55
0.72
1.74
5.73
2.25
1.54
4.83
2.52
4.62
0.70
3.07
2.57
2.50
1.56
2.69
1.19
0.93
1.50
0.72
1.71
5.76
2.27
1.52
4.84
2.49
4.64
0.70
σ*N10–H21 0.00794
σ*C11–C12 0.02670
π*C11–C12 0.36802
σC8–N10
1.99183
σ*N7–C8
0.07155
σ*N10–H21 0.00794
πC8–N10
σC4–C5
1.98974
1.96633
π*C8–N10
σ*C3–C4
σ*C3–H19
σ*C4–N7
σ*C5–C6
σ*C6–H20
σ*N7–C11
σ*C8–S9
0.30326
0.02373
0.01307
0.03489
0.02103
0.01400
0.04266
0.08416
(Continued)

8
Journal of Chemical Research 00(0)
Table 5. (Continued)
Donor
NBO (i)
ED(i) (a.u.) Acceptor ED(j) (a.u.) Interaction type
E2 (kcal/mol)
X=H X=CH3 X=Cl X=OH X=CF3 X=NO2
NBO(j)
πC4–C5
1.64246
1.67385
π*C1–C6
π*C2–C3
π*C2–C3
π*C4–C5
π*C8–N10
σ*C11–C12 0.02670
π*C11–C12 0.36802
σ*C11–C16 0.02649
σ*C4–C5
σ*C5–C6
σ*N7–C8
σ*C8–N10
π*C4–C5
π*C8–N10
σ*N7–C8
σ*N7–C11
σ*C8–S9
0.35810
0.35677
0.01442
0.46854
0.30326
πC4–C5 →π*C1–C6
πC4–C5 →π*C2–C3
LP(1)N7 →π*C2–C3
LP(1)N7 →π*C4–C5
LP(1)N7 →π*C8–N10
LP(1)N7 →σ*C11–C12
LP(1)N7 →π*C11–C12
LP(1)N7 →σ*C11–C16
LP(1)S9 →σ*C4–C5
LP(1)S9 →σ*C5–C6
LP(1)S9 →σ*N7–C8
LP(1)S9 →σ*C8–N10
LP(2)S9 →π*C4–C5
LP(2)S9 →π*C8–N10
LP(1)N10 →σ*N7–C8
LP(1)N10 →σ*N7–C11
LP(1)N10 →σ*C8–S9
30.29 30.39
24.20 24.20
–
–
30.41
24.18
0.51
–
–
–
–
LP(1)N7
0.51
0.51
< 0.5
45.22 44.72
59.25 60.42
< 0.5
44.40
58.29
4.73
11.06
4.53
2.15
0.52
2.06
0.55
23.23
31.46
5.29
0.66
24.20
< 0.5
43.63
57.08
4.52
13.12
4.34
2.18
0.51
2.10
0.55
23.28
31.79
5.37
0.63
24.03
44.53 44.73
60.07 60.39
4.89
8.34
4.89
2.13
0.53
2.01
0.54
4.97
7.99
4.89
2.14
0.53
2.01
0.54
5.00
8.90
4.85
2.15
0.52
2.03
0.55
23.29 19.94
31.19 30.81
5.22
0.68
5.00
6.88
5.26
2.13
0.53
2.01
0.54
LP(1)S9
1.98211
0.03264
0.02103
0.07155
0.00937
0.46854
0.30326
0.07155
0.04266
0.08416
LP(2)S9
1.77794
1.89453
19.95 19.99
30.82 30.77
LP(1)N10
5.10
0.69
5.06
0.69
5.06
0.68
24.35 24.35
24.31 24.32
ED: electron density; NBO: natural bond orbital.
gap ELUMO-HOMO, besides the chemical reactivity descrip- making the ring even more unreactive) have the HOMO
tors which are computed at the M06-2x/6-311++G(d,p) energy of −7.42eV. The nitro group in compound 6 is a very
level, and are presented in Table 4.
strong electrophile; that is, it has a strong ability to attract
The values of the LUMO-HOMO energy gap reflect the electrons. This ability can also be represented by the net
chemical activity of the molecule. The decrease in the charges of the nitro group. The higher the negative charge the
HOMO-LUMO energy gap explains the eventual charge nitro group possesses, the lower the electron attraction abil-
transfer interaction taking place within the studied com- ity and therefore the more stable the nitro compound is. An
pounds [1–6] because of the strong electron-accepting ability electron-withdrawing group removes electrons and, there-
of the electron acceptor group (Table 4). As a result, the sta- fore decreases the HOMO and LUMO energies. An electron-
bility of the studied compounds is 1>3>2>4>5>6. The donating group usually acts through an occupied nonbonding
calculated results show that compounds 1 and 6 have the orbital. This is energetically close to the HOMO. Thus, it has
highest and lowest stabilities, respectively, in the solvent and a stronger effect on the HOMO than on the LUMO (at least
gas phases. Similarly, the calculated ΔNmax values revealed in organic molecules).
the same trend (see Table 4). Moreover, because of the larger
HOMO-LUMO energy gap, the global hardness increases
NBO analysis
for compounds 1–6 as follows: 1>3>2>4>5>6, and the
chemical reactivity decreases in the opposite order:
1<3<2<4<5<6.
NBO analysis has already proved to be an effective tool for
the chemical interpretation of hyperconjugative interactions
and electron density transfer from the filled lone-pair elec-
tron.56 These changes in electron density are referred to as
“delocalization” corrections to the zeroth-order natural Lewis
structure to a stabilizing donor–acceptor interaction. In order
to consider the different second-order perturbation energies
(E2) between the filled orbitals of one subsystem and the
vacant orbitals of another subsystem, the M06-2x method has
been used, and it predicts the delocalization or hyperconjuga-
tion.57 In the NBO analysis, the charge transfer between the
lone pairs of the proton acceptor and antibonding orbitals of
the proton donor is the most important. For each donor
NBO(i) and acceptor NBO(j), the stabilization energy (E2)
associated with the delocalization i→j is given by58
The FMOs of compounds 1–6 have been investigated at
the M06-2x/6-311++G(d,p) level of theory. The corre-
sponding energy levels of the FMOs for the studied com-
pounds are given in Figure 3. Based on the investigation on
the FMOs energy levels, we find that the corresponding
electronic transfers happened between the HOMO and
LUMO.
As can be seen in Table 4, the para functional group will
further influence the HOMO and LUMO energy levels in the
studied compounds (1–6). Electron-withdrawing substitu-
ents lead to a decrease in the energy levels of the frontier
orbitals whereas electron-donating groups have the opposite
effect. In this work, the energy levels increase in order from
the most strongly electron-withdrawing group (–NO2) to the
most strongly electron-donating group (–CH3). It is noted
that 3-phenylbenzo[d]thiazole-2(3H)-imine has HOMO
energy of −7.01eV, and nitro-substituted derivatives (a nitro
group being the strong electron-withdrawing group, and
2




F
(i, j)
(7)
E = ∆E = q
i
2
ij


ε −ε
i
j



Miar et al.
9
Figure 3. (Continued)

10
Journal of Chemical Research 00(0)
Figure 3. The shapes of the HOMO and LUMO orbitals of compounds 1–6 at the M06-2x/6-311++G(d,p) level.
where qi is the ith donor orbital occupancy, εi and εj are diag-
onal elements (orbital energies), and F(i, j) is the off-diagonal
NBO Fock matrix elements. The strong intramolecular
hyperconjugative interactions of the σ and π electrons of
C–C, C–H, N–H, and C–N to the antibonding C–C, C–H,
N–H, and C–N bonds lead to stabilization of some part of
the ring.59 As can be seen in Table 5, the σ→σ* interactions
have minimum delocalization energy compared to the
π→π* interactions. Therefore, the σ bonds have higher
electron density than the π bonds.
The strong intramolecular hyperconjugative interaction
of the C4–C5 bond is formed by orbital overlap between
the bonding orbital πC4–C5 to the corresponding antibonding
orbital π*
with increasing electron density of 0.3581
C1–C6
leading to stabilization energy of 30.29kcal/mol, which
results in intramolecular charge transfer causing stabiliza-
tion of the molecule. Similarly, π→π* interactions take
place between the bonding πC4–C5 and antibonding orbitals
π*
as well as the bonding πC8–N10 and antibonding
C2–C3
orbitals π*C8–N10, with an increase in electron density of
0.3568 and 0.30326, respectively, such that the respective
bonds are stabilized by 24.20 (strong) and 1.77 kcal/mol
(weak), respectively.
The NBO analysis also describes the bonding in terms of
the natural hybrid orbital which emphasizes that the lone
pair of the nitrogen N7 has an exclusive p-character
(>99.9%) and a low occupation number (1.67385a.u.) in
compounds 1–6, leading to stronger stabilization interac-
tions. Therefore, a very close to pure p-type lone-pair
Figure 4. Overall aromaticity of the studied compounds
estimated as a function of NICS versus the considered solvents.
NICS values at maximum diatropic current are tabulated [up:
NICS(+0.5); down: NICS(−0.5)].
orbital participates in the electron donation to the π*
interactions from the nonbonding S9 atom, LP(2)S9 to
π*C8–N10 and π*C4–C5 occur, leading to the stabilization ener-
gies of 30.82 and 19.95kcal/mol, respectively. While the
LP(n)→σ* interaction takes place between the nonbonding
N10 atom, LP(1)N10 to the σ*C8–S9 antibonding orbital with
the highest stabilization energy of 24.35kcal/mol which
results in intramolecular charge transfer causing stabiliza-
tion of the molecular system.
C4–C5
interaction,
antibonding orbital for the LP(1)N7 →π*
C4–C5
and π*C8–N10 antibonding orbital for the LP(1)N7 →π*
C8–N10
interaction in the considered compounds. The results are
given in Table 5.
It is noted that the lone-pair LP(1)N10 nitrogen atom
occupies a higher energy orbital (1.89453a.u.) with p-char-
acter of ~34.4%. Also, the other lone-pair LP(1)S9 sulfur
atom has a high occupation number (1.98211a.u.) with
p-character (~63%). The lone-pair electrons are readily
available for interactions with the excited electrons of the
acceptor antibonding orbital. The LP(n)→π* interaction
from nonbonding N7, LP(1)N7 donates an electron to the
antibonding π*C8–N10 and π*C4–C5 orbitals with considerably
higher stabilization energies of 60.07 and 44.53 kcal/mol,
respectively. Similarly, intramolecular hyperconjugative
NICS analysis
Aromaticity is a significant parameter related to cyclic arrays
of mobile electrons and is a useful tool in organic chemis-
try.60 Theoretical criteria of aromaticity allow information on
the physico-chemical properties of aromatic rings, namely
structural chemical reactivity and stability. Schleyer et al.61

Miar et al.
11
developed a simple and effective criterion for determining The lowest HOMO-LUMO band gap is calculated for com-
the aromaticity of different systems based on the diatropic pound 6, which results in it having interesting electronic
current induced on placing the aromatic system in an exter- properties. The obtained HOMO-LUMO energy gap corre-
nal magnetic field. The NICS parameter was calculated as sponds to intramolecular hyperconjugative interactions
the negative shielding constant of a ghost atom (Bq) located π→π*. The results were confirmed by FMO analysis with
at the ring center. Negative NICS values indicate a diatropic energy gaps of 6.859, 6.796, 6.841, 6.737, 5.649, and
ring current in the presence of an applied magnetic field (aro- 6.649eV, respectively, being determined for molecules 1–6.
matic molecule), while a low negative or positive NICS The calculated results show that molecules 1 and 6 have the
value indicates a paratropic ring current (non-aromatic or highest and lowest stabilities, respectively, in the solvent
anti-aromatic molecule).62,63 NICS values were taken at a and gas phases. NBO analysis showed intramolecular
location near the geometrical center of the ring.
charge transfer causing stabilization of the molecule.
In this study, for 3-phenylbenzo[d]thiazole-2(3H)-
imines 1–6, the sets of points (Bq ghost atoms) lying above
and below, geometric center of rings were used at 2 Å.
Their locations correspond with distances from −2 to 2Å
with 0.5Å steps. The NICS(0) values are calculated at the
center of the ring that is influenced by σ-bonds, while the
NICS(+2) and NICS(−2) values determined at 2Å above
and below the plane, respectively, were more affected by
the π-electron system. The maximum total diatropic current
is observed at 0.5Å above/below the geometric center of
molecule in compounds 1–6 (Figure 4).
Acknowledgements
The authors would like to thank the referees for their valuable
comments which helped to improve the manuscript.
Declaration of conflicting interests
The author(s) declared no potential conflicts of interest with respect
to the research, authorship, and/or publication of this article.
Funding
Interestingly, the NICS values at the minimum point of The author(s) received no financial support for the research,
authorship, and/or publication of this article.
the six-membered rings are more negative (i.e. indicating
greater aromaticity) than those of the five-membered rings
for all the considered compounds (see Table S2 of the
Supplemental material). As can be seen from Table S2, the
NICS values of compound 2 in the studied solvent and gas
phases were calculated to be in ranges of −22.7965 to
−23.2507ppm, while the NICS values of compound 6 were
slightly higher ranging from −24.4163 to −24.7124ppm.
For points located at the center of the six- and five-mem-
ORCID iD
Abolfazl Shiroudi
https://orcid.org/0000-0002-0765-6315
Supplemental material
Supplemental material for this article is available online.
bered rings and points located at ±2Å, the ring centers References
confirm that the aromaticity of compounds 1–6 changes
1. Asif M. Int J Bioorg Chem 2017; 2: 146.
2. Marzi M, Shiroudi A, Pourshamsian K, et al. J Sulfur Chem
with the varying dielectric constant of the media (see Table
S2 in the Supplemental material).
2019; 40: 166.
3. Saini MS, Kumar A, Dwivedi J, et al. Int J Pharma Sci Res
2013; 4: 66.
Conclusion
4. Chhabra M, Sinha S, Banerjee S, et al. Bioorganic Med
Chem Lett 2016; 26: 213.
5. Jiang J, Li G, Zhang F, et al. Adv Synth Catal 2018; 360:
In this work, the solvation and substituent effects of the
electron-releasing/withdrawing derivatives (i.e. at the para
position on the three-substituted molecular structure of the
synthesized compounds) 1–6 [1 (X=H), 2 (X=CH3), 3
(X=Cl), 4 (X=OH), 5 (X=CF3), and 6 (X=NO2)] were
investigated using at the DFT/M06-2x/6-311++G(d,p)
level of theory in selected solvents (toluene, acetone, and
ethanol) and in the gas phase by employing the polarizable
continuum method model. In addition, the Fukui function,
dipole moment, and distribution of electric charges on the
atoms of the considered compounds were also studied with
the same method and basis set.
FMO analysis showed that compound 6 in the selected
solvents and gas phase has very low HOMO-LUMO energy
gaps and thus is kinetically less stable. Chemical reactivity
indices (dipole moment, μ) predict the highest activity for
compound 6 in different solvents as well as in the gas phase,
whereas the lowest activity was decreased for compounds 4
and 1 in the gas phase and the studied solvents, respectively.
1622.
6. Haroun M, Tratrat C, Kositzi K, et al. Curr Top Med Chem
2018; 18: 75.
7. Rabbani MG, Islamoglu T and El-Kaderi HM. J Mater Chem
A 2017; 5: 258.
8. Gill RK, Rawal RK and Bariwal J. Arch Pharm 2015; 348:
155.
9. Diao P-C, Lin W-Y, Jian X-E, et al. Eur J Med Chem 2019;
179: 196.
10. Abdelgawad MA, Bakr RB and Omar HA. Bioorg Chem
2017; 74: 82.
11. Ali R and Siddiqui N. J Chem 2013; 345198.
12. Das D, Sikdar P and Bairagi M. Eur J Med Chem 2016; 109:
89.
13. Aitken L, Benek O, McKelvie BE, et al. Molecules 2019; 24:
2757.
14. Shuai L and Luterbacher J. ChemSusChem 2016; 9: 133.
15. Noviandri I, Brown KN, Fleming DS, et al. J Phys Chem B
1999; 103: 6713.

12
Journal of Chemical Research 00(0)
16. Pirbasti FG and Mahmoodi NO. J Chin Chem Soc Taip 2016; 40. Zahedi E, Shaabani S and Shiroudi A. J Phys Chem A 2017;
64: 80.
121: 8504.
17. Kurt M, Sertbakan TR and Ozduran M. Spectrochim Acta A 41. Glendening ED, Badenhoop JK, Reed AE, et al. NBO 5.0.
Mol Biomol Spectrosc 2008; 70: 664.
Madison, WI: Theoretical Chemistry Institute, University of
Wisconsin, 2001.
42. Shiroudi A, Safaei A, Kazeminejad Z, et al. J Mol Model
2020; 26: 57.
43. Demir S, Tinmaz F, Dege N, et al. J Mol Struct 2016; 1108: 637.
44. Mottishaw JD, Erck AR, Kramer JH, et al. J Chem Educ
2015; 92: 1846.
18. Onsager L. J Am Chem Soc 1936; 58: 1486.
19. Rivail L and Rinaldi D. Theor Chim Acta 1973; 32: 57.
20. Hall RJ, Davidson MM, Burton NA, et al. J Phys Chem
1995; 99: 921.
21. Zhao Y and Truhlar DG. Theor Chem Acc 2008; 120: 215.
22. Dunning TH. J Chem Phys 1989; 90: 1007.
23. Sastre S, Casasnovas R, Muñoz F, et al. Theor Chem Acc 45. Mulliken R. J Chem Phys 1955; 23, 1841.
2013; 132: 1310.
46. Mulliken R. J Chem Phys 1962; 36, 3428.
24. Junqueira GMA and Dos Santos HF. J Mol Model 2014; 20: 47. Rigby J and Izgorodina EI. Phys Chem Chem Phys 2013; 15,
2152.
1632.
25. Cysewski P. J Mol Struct (Theochem) 2005; 714: 29.
26. Nigam S, Majumder C and Kulshreshtha SK. J Chem Sci
2006; 118: 575.
27. Schleyer PVR, Manoharan M, Wang Z-X, et al. Org Lett
2001; 3: 2465.
48. Fukui K, Yonezawa T and Shingu H. J Chem Phys 1952; 20:
722.
49. Padmaja L, Ravikumar C, Sajan D, et al. J Raman Spectrosc
2009; 40: 419.
50. Aihara J. J Phys Chem A 1999; 103: 7487.
28. Schleyer PVR, Jiao H, Goldfuss B, et al. Angew Chem Int Ed 51. Manolopoulos ED, May JC and Down SE. Chem Phys Lett
Engl 1995; 34: 337.
1991; 181: 105.
29. Schleyer PVR, Maerker C, Dransfeld A, et al. J Am Chem 52. Ruiz-Morales Y. J Phys Chem A 2002; 106: 11283.
Soc 1996; 118: 6317.
30. Reed AE, Weinstock RB and Weinhold F. J Chem Phys
1985; 83: 735.
31. Badenhoop JK and Weinhold F. Int J Quantum Chem 1999;
72: 269.
32. Nori-Shargh D, Shiroudi A, Oliaey AR, et al. J Mol Struct
(Theochem) 2007; 824: 1.
33. Frisch MJ, Trucks GW, Schlegel HB, et al. Gaussian 09.
Wallingford, CT: Gaussian Inc, 2009.
34. Dennington R, Keith T and Millam J. Gauss View 5.0.
Shawnee, KS: Semichem Inc, 2009.
35. Baboul AG, Curtiss LA and Redfern PC. J Chem Phys 1999;
110: 7650.
36. Halls MD, Velkovski J and Schlegel HB. Theor Chem Acc
2001; 105: 413.
53. Parr RG, Szentpaly L and Liu S. J Am Chem Soc 1999; 121:
1922.
54. Parr RG and Pearson RG. J Am Chem Soc 1983; 105:
7512.
55. Parr RG, Donnelly RA, Levy M, et al. J Chem Phys 1978;
68: 3801.
56. Yang Y, Zhang W and Gao X. Int J Quantum Chem 2006;
106: 1199.
57. Carpenter JE and Weinhold F. J Mol Struct (Theochem)
1988; 169: 41.
58. Oliaey AR, Shiroudi A, Zahedi E, et al. React Kinet Mech
Cat 2018; 124: 27.
59. Durga Devi D, Manivarman S and Subashchandrabose S.
Karbala Int J Mod Sci 2017; 3: 18.
60. Gangadharana RP and Krishnanb SS. Acta Phys Pol A 2014;
125: 18.
37. Senosiain JP, Klippenstein SJ and Miller JA. J Phys Chem A
2005; 109: 6045.
61. Schleyer PVR and Jiao H. Pure Appl Chem 1996; 68: 209.
38. Greenwald EE, North SW, Georgievskii Y, et al. J Phys 62. Krygowski TM, Cyranski M, Ciesielski A, et al. J Chem Inf
Chem A 2005; 109: 6031.
Comput Sci 1996; 36: 1135.
39. Zhao Y and Truhlar DG. Acc Chem Res 2008; 41: 157.
63. Badoglu S and Yurdakul S. Struct Chem 2010; 21: 1103.