# Studies of the Chemical Reactivity of a Series of Rhodanine Derivatives by Approaches to Quantum Chemistry

Wacothon Karime Coulibaly, Jean Stéphane N'dri, Mamadou Guy-Richard

Koné, Camille Déliko Dago, Christelle N'ta Ambeu, Jean-Pierre Bazureau,
Nahossé Ziao

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Wacothon Karime Coulibaly, Jean Stéphane N'dri, Mamadou Guy-Richard Koné, Camille Déliko Dago, Christelle N'ta Ambeu, et al. Studies of the Chemical Reactivity of a Series of Rhodanine Derivatives by Approaches to Quantum Chemistry. Computational Molecular Bioscience, 2019, 09 (03), pp.49-62. 10.4236/cmb.2019.93005. hal-02572308

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# Studies of the Chemical Reactivity of a Series of Rhodanine Derivatives by Approaches to Quantum Chemistry

Wacothon Karime Coulibaly<fnref n="1" />,<fnref n="2" />*, Jean Stéphane N'dri<fnref n="3" />, Mamadou Guy-Richard Koné<fnref n="3" />, Camille Déliko Dago<fnref n="2" />, Christelle N'ta Ambeu<fnref n="2" />, Jean-Pierre Bazureau<fnref n="2" />, Nahossé Ziao<fnref n="3" />

**How to cite this paper:** Coulibaly, W.K., N'dri, J.S., Koné, M.G.-R., Dago, C.D., Ambeu, C.N., Bazureau, J.-P. and Ziao, N. (2019) Studies of the Chemical Reactivity of a Series of Rhodanine Derivatives by Approaches to Quantum Chemistry. *Computational Molecular Bioscience*, *9*, 49-62.

https://doi.org/10.4236/cmb.2019.93005

Received: June 22, 2019

Accepted: August 6, 2019

Published: August 9, 2019

Copyright © 2019 by author(s) and
Scientific Research Publishing Inc.
This work is licensed under the Creative
Commons Attribution International
License (CC BY 4.0).

http://creativecommons.org/licenses/by/4.0/

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Open Access

## Abstract

This theoretical chemical reactivity study was conducted using the Density Functional Theory (DFT) method, at computational level B3LYP/6-31G (d). It involved a series of six (06) 5-arylidene rhodanines and allowed to predict the chemical reactivity of these compounds. DFT global chemical reactivity descriptors (HOMO and LUMO energies, chemical hardness, softness, electronegativity) were examined to predict the relative stability and reactivity of rhodanin derivatives. Thus, the compound 6 which has an energy gap between the orbitals of ΔEgap = 3.004 eV is the most polarizable, the most reactive, the least stable, the best electron donor and the softest molecule. Calculation of the local indices of reactivity as well as dual descriptors revealed that the sulfur heteroatom of the Rhodanine ring is the privileged site of electrophilic attack in a state of sp3 hybridization and privileged site of nucleophilic attack in a state of sp2 hybridization.

## Keywords

Rhodanine Derivatives, Global Descriptors, Local Descriptors, Dual Descriptors

## 1. Introduction

The tumor is an abnormal structure that appears in the body. It comes from multiplication of cells. It is insensitive to the controls of the body and more or

<footnote n="1">¹UFR des Sciences Biologiques, Université de Péléforo Gon Coulibaly, Korhogo, Cote d'Ivoire</footnote>

<footnote n="2">²Université de Rennes 1, Institut des Sciences Chimiques de Rennes (ISCR), UMR CNRS 6226, Groupe ICMV, Bât. 10A, Campus de Beaulieu, Rennes Cedex, France</footnote>

<footnote n="3">³Laboratoire de Thermodynamique et de Physico-Chimie du Milieu, UFR SFA, Université Nangui Abrogoua, Abidjan, Côte-d'Ivoire</footnote>

<footnote>Email: *wacothon@gmail.com</footnote>
less resembles the tissue from which it derives. The tumor is recognizable
because it is autonomous and no longer responds to the mechanisms of the body
that limit the proliferation of cells. Treatment of the tumor is done either by
surgical removal in the case of the benign tumor; or by radiotherapy and cancer
chemotherapy if it is a malignant tumor. It is in this context that medicinal
chemistry or therapeutic chemistry which is a scientific discipline at the
intersection of chemistry and pharmacy including the design of new molecules
and their development is on the lookout for new molecular entities with biological
activity or therapeutic even more powerful with a broad spectrum of action. It is
for this purpose that Rhodanine derivatives and heterocyclic compounds study as
potential pharmacochemical precursors has been initiated [1]. These compounds
are widely distributed in nature and are essential to life in various ways [2]. The
chemistry of heterocyclic compounds is one of the most complex branches of
organic chemistry. It is also interesting for its theoretical implications, for the
diversity of its synthetic processes, and for the physiological and industrial
significance of heterocyclic compounds. Studies on heterocyclic compounds have
long been an interesting area in medicinal chemistry. A number of heterocyclic
derivatives containing a sulfur or nitrogen atom serve as unique and versatile
scaffolds for the design of experimental drugs [3]. Rhodanine derivatives are
attractive compounds because of their many biological activities. The various
biological activities of rhodanines (2-thioxothiazolidin-4-ones) and their
analogues have been known since the beginning of the 20th century. The five
multi-heterocyclic rings, and in particular the synthon rhodanine, are currently
the subject of controversial debate in the medicinal chemistry community [4].
Indeed, these compounds and their derivatives have a broad spectrum of
biological effects [5]. They include anticonvulsants, antibacterial [6] antivirals
[7], antidiabetic agents [8], antimalarial [9] anti-tuberculosis [10], pesticides
[11], fungicides [12], anti-inflammatory [13] insecticides [14], antithyroid [15],
anti-tumor [16]. To date, numerous molecules derived from rhodanine have
been synthesized, characterized and tested for their properties, in particular
5-arylidene-2-thioxo-1,3-thiazolidinin-4-ones or 5-arylidene rhodanines, which
are the object of several scientific studies. Studies on heterocyclic compounds
have long been an interesting area in medicinal chemistry. A number of
heterocyclic derivatives containing heteroatoms (nitrogen, sulfur, oxygen) serve
as unique and versatile scaffolds for the design of experimental drugs [17]. The
therapeutic properties are related to the conformation of the molecules and the
interactions that they can establish with each other. The knowledge of the
molecular conformation and the interactions goes through the determination of
the physicochemical descriptors through the theoretical chemistry. With the
development of computer techniques and computational chemistry, quantum
chemistry gives insight into the electronic structures of molecules and strongly
propels the development of traditionally experimental chemistry [18]. Currently,
the method of Density Functional Theory (DFT) has been accepted as a popular
approach for the calculation of structural features and energies of molecules by
the scientific community [19] [20] [21] [22] and for the efficiency and accuracy
of the evaluation of a number of molecular properties [23]. Parr and Yang
followed the idea that well-known chemical properties such as electrone-
gativity, chemical potentials, and affinities could be accurately described and
calculated by manipulating the electron density as the fundamental quantity
[24] [25]. Moreover, from the work of Fukui and his theory of Frontier Mole-
cular Orbitals (FMO) [26], the same authors generalized the concept and
proposed Fukui's function as a tool for describing local reactivity in molecules
[27] [28]. The present study focuses on six (06) Rhodanine derivatives shown
Figure 1.

These Rhodanine derivatives studied in our work were synthesized and identified as potential inhibitors of several protein kinases by Wacothon Coulibaly *et al.* [3]. Indeed, these authors tested a series of 5-arylidene rhodanine derivatives on a panel of six representative 6 tumor cell lines, namely Huh7 D12 (differential hepatocellular carcinoma), Caco2 (differentiation of colorectal adenocarcinoma), HCT (colorectal carcinoma at active proliferation), PC3 (carcinoma of the prostate), NCI-H2 (lung carcinoma), MDA-MB 231 (breast carcinoma) and diploid skin fibroblasts as normal cell lines for control. The purpose of this work is to theoretically determine the preferred sites of electrophilic and nucleophilic attack on the aromatic carbon atoms and heteroatoms contained in the rhodanine ring by different methods of quantum chemistry.

## 2. Material and Methods

### 2.1. Level of Calculation Theory

The theoretical study of chemical reactivity was conducted based on three
theoretical approaches. The first concerns the analysis of molecular electrostatic
potential surfaces. The second approach relates to boundary molecular
orbitals. The last approach focuses on local indices of responsiveness as well as
dual descriptors. The geometries of the molecules were optimized at the DFT
calculation level with the functional B3LYP [29] [30] in the base 6-31 G (d)
using the Gaussian 09 software [31]. This Hybrid functional gives better
energies and is in line with the ab initio methods of high level [32] [33]. As for
the split-valence and double-dzeta base (6-31G (d)), it is sufficiently extended
and the taking into account of the polarization functions are important for the
explanation of the free doublets of the heteroatoms. Geometries are kept
constant for cationic and anionic systems. Global indices of reactivity were
obtained from the conceptual DFT model [19]. The hierarchical ascending
classification analysis was conducted using the XLSTAT software [34]. As for
the indices of local chemical reactivity, they were determined using the
electronic populations calculated with the Mulliken population analysis (MPA)
[35].
<figure><img src="image_4.png" /><figcaption>Figure 1. Molecular structures of the Rhodanines derivatives studied.</figcaption></figure>

## 2.2. Reactivity Descriptors

### 2.2.1. Global Descriptors

To predict chemical reactivity, some theoretical descriptors related to conceptual DFT have been determined. In particular, the Lowest Unoccupied (vacant) Molecular Orbital (LUMO) energy ($E_{LUMO}$), the Highest Occupied Molecular Orbital (HOMO) energy ($E_{HOMO}$), the electronegativity ($\chi$), the global softness ($\sigma$) and the overall electrophilicity index ($\omega$). These descriptors are all determined from the optimized molecules. It should be noted that the descriptors related to frontier molecular orbitals have been calculated in a very simple way in the context of the Koopmans approximation [36]. LUMO energy characterizes the sensitivity of the molecule to a nucleophilic attack, and as for the HOMO energy, it characterizes the susceptibility of a molecule to an electrophilic attack. Electronegativity ($\chi$) is the parameter that reflects the ability of a molecule not to let out its electrons. Global softness ($\sigma$) expresses the resistance of a system to the change in its number of electrons. The overall electrophilicity index characterizes the electrophilic power of the molecule. These different parameters are calculated from the Equations (1):
$$
\begin{align}
I &= -E_{\text{HOMO}} \\
A &= -E_{\text{LUMO}} \\
\chi &= -\mu = -1/2(E_{\text{LUMO}} + E_{\text{HOMO}}) \\
\eta &= (E_{\text{LUMO}} - E_{\text{HOMO}})/2 \tag{1} \\
\omega &= \frac{\chi^2}{2\eta} \\
\sigma &= 1/\eta
\end{align}
$$

2.2.2. Local Descriptors and Dual Descriptors

In order to differentiate the reactive behaviors of atoms forming a molecule,
different indices have been used. These are precisely local indices and dual
descriptors of responsiveness.Local responsivity descriptors, in this case Fukui
function [37] ($f_k^+$, $f_k^-$), local softness ($\sigma_k^+$, $\sigma_k^-$), local electrophilic power ($\omega_k^+$, $\omega_k^-$), and dual descriptors have been proposed to explain the electrophilic
and nucleophilic selectivity of the molecule.It should be remembered that
Fukui's function $f_k^+$ expresses reactivity when the molecule is attacked by a
nucleophilic reagent, whereas Fukui's function $f_k^-$ provides information on
electrophilic attack on a given site. The value of the highest Fukui function is
assigned to the most active site. The condensed indices $\sigma_k^+$ and $\omega_k^+$ express
the ability of a site to receive electron density by nucleophilic attack, whereas the
indices $\sigma_k^-$ and $\omega_k^-$ express the ability of a site to yield electron density by
electrophilic attack. With regard to the dual descriptor, it is a good tool for
predicting responsiveness and identifying the problem of regioselectivity. Indeed, a
positive dual descriptor corresponds to a site likely to receive electron density, so
more electrophilic. Conversely, a negative dual descriptor corresponds to a site
capable of yielding electronic density, and therefore more nucleophilic. A site with
a value of the dual descriptor near zero corresponds to a site whose capacity to
receive and that to yield of the electronic density are equivalent. The different
values of the local descriptors are calculated from the Equations (2) [38] [39]
[40] [41]:

$$
\begin{align*}
f_k^+ &= q_k(N+1) - q_k(N) \\
f_k^- &= q_k(N) - q_k(N-1) \\
\sigma_k^+ &= \sigma f_k^+ \\
\sigma_k^- &= \sigma f_k^- \\
\omega_k^+ &= \omega f_k^+ \\
\omega_k^- &= \omega f_k^- \tag{2}
\end{align*}
$$

Où: $q_k(N)$: electron population of the atom k in the neutral molecule.

$q_k(N+1)$: electron population of the atom k in the anionic molecule.

$q_k(N-1)$: electron population of the atom k in the cationic molecule.

The values of the dual descriptors [42] [43] [44] are obtained from the
Equations (3):

$$
\Delta f = f_k^+ - f_k^-
$$
$$ \Delta\sigma = \sigma_k^+ - \sigma_k^- \qquad (3) $$

$$ \Delta\omega = \omega_k^+ - \omega_k^- $$

# 3. Results and Discussions

## 3.1. Molecular Electrostatic Potentials (MEP)

The different values of the electrostatic surface potential are represented by different colors. The potential increases in this order from red < orange < yellow < green < blue. The color code of these cards is between -8.026e-2 a.u. (bright red) and 8.026e-2 a.u. (dark blue) in compounds 1 to 6, where red indicates the most negative potentials and blue the most positive potentials [45] by successively passing through orange, yellow and green [46]. The surfaces of the electrostatic potentials of the studied molecules were represented after optimization at the B3LYP/6-31 G (d) level. They are shown in Figure 2.

These maps indicate that oxygen and sulfur heteroatoms in a hybridization state (sp3) of the rhodanine nucleus, have a negative neighborhood of negative potential with a high electronic concentration around the oxygen representing an electrophilic attack site on the rhodanine core. This zone is more concentrated for compounds 1 and 2. As for the other atoms of this nucleus, their light blue neighborhood indicates that they constitute electro-positive weakening zones.

## 3.2. Analysis of Frontier Molecular Orbitals

The highest occupied (HOMO) and lowest vacant (LUMO) orbitals play a fundamental role in the qualitative interpretation of chemical reactivity [47]. The highest occupied molecular orbital (HOMO), which can be thought of as the outer electron-containing orbital, tends to give these electrons as an electron donor. On the other hand, the lowest vacant molecular orbital (LUMO) is perceived as the lowest orbital containing free places to accept electrons [48]. Therefore, while the energy of the HOMO is directly related to the ionization potential, that of the LUMO is directly related to the electronic affinity. The difference in energy between the HOMO and the LUMO, called the energy gap, is an important stability factor for the structures [49]. The HOMO-LUMO energy gap helps characterize the chemical reactivity and kinetic stability of the molecule [50]. A molecule with a high energy gap (ΔE) is less polarizable and is generally associated with low chemical reactivity and high kinetic stability [51]. The energy parameters of the boundary orbitals are summarized in Table 1.

These results show that **compound 6** has the smallest energy gap (ΔEgap = 3.004 eV) so it is the most polarizable. It has the highest chemical reactivity and the lowest kinetic stability with respect to all the molecules studied. In contrast, **compound 3** has the largest value of the energy gap of 3.443 eV. Compound 3 is therefore the least polarizable, with low chemical reactivity and high kinetic stability on all six molecules studied.
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Molecular electrostatic potential surfaces of rhodanines derivatives studied.</figcaption></figure>

<table><caption>**Table 1.** Energy descriptors of the compounds studied.</caption><thead><tr><th>Compounds</th><th>E<sub>HOMO</sub> (eV)</th><th>E<sub>LUMO</sub> (eV)</th><th>ΔE<sub>gap</sub> (eV)</th><th>I (eV)</th><th>A (eV)</th></tr></thead><tbody><tr><td>1</td><td>-5.923</td><td>-2.493</td><td>3.431</td><td>5.923</td><td>2.493</td></tr><tr><td>2</td><td>-5.867</td><td>-2.564</td><td>3.303</td><td>5.867</td><td>2.564</td></tr><tr><td>3</td><td>-5.897</td><td>-2.454</td><td><strong>3.443</strong></td><td>5.897</td><td>2.454</td></tr><tr><td>4</td><td>-5.909</td><td>-2.471</td><td>3.438</td><td>5.909</td><td>2.471</td></tr><tr><td>5</td><td>-5.667</td><td>-2.361</td><td>3.306</td><td>5.667</td><td>2.361</td></tr><tr><td>6</td><td>-5.432</td><td>-2.428</td><td><strong>3.004</strong></td><td>5.432</td><td>2.428</td></tr></tbody></table>

### 3.3. Hierarchical Cluster Analysis (HCA)

Figure 3 shows the hierarchical ascending classification analysis of the studied molecules. The horizontal lines represent the compounds. The vertical lines represent the similarity values between the pairs of compounds, a compound and a group of compounds and among the groups of compounds.

We can note from the results of this analysis that the compounds studied were grouped into three categories: the most active which are compounds 2 and 6. Compound 5 is moderately active and compounds 1, 3 and 4 are the least active.

### 3.4. Reactivity Descriptors

#### 3.4.1. Global Reactivity Descriptors

The study of the global reactivity of molecules is based on the calculation of global indices deduced from electronic properties. The global indices of the reactivity of the studied molecules were calculated from the Equation (1) and recorded in Table 2.
<figure><img src="image_6.png" /><figcaption>Figure 3. Dendrogram obtained from the studied compounds.</figcaption></figure>

<table><caption>Table 2. Global descriptors of chemical reactivity of rhodanine derivatives 1-6.</caption><thead><tr><th>Compounds</th><th>μ (eV)</th><th>χ (eV)</th><th>η (eV)</th><th>σ (eV)</th><th>ω (eV)</th></tr></thead><tbody><tr><td>1</td><td>-4.208</td><td>4.208</td><td>1.715</td><td>0.583</td><td>5.162</td></tr><tr><td>2</td><td>-4.216</td><td>4.216</td><td>1.652</td><td>0.605</td><td>5.380</td></tr><tr><td>3</td><td>-4.175</td><td>4.175</td><td>1.722</td><td>0.581</td><td>5.064</td></tr><tr><td>4</td><td>-4.190</td><td>4.190</td><td>1.719</td><td>0.582</td><td>5.107</td></tr><tr><td>5</td><td>-4.014</td><td>4.014</td><td>1.653</td><td>0.605</td><td>4.873</td></tr><tr><td>6</td><td>-3.930</td><td><strong>3.930</strong></td><td><strong>1.502</strong></td><td><strong>0.666</strong></td><td>5.140</td></tr></tbody></table>

Chemical reactivity varies with the structure of the molecules. Chemical hardness ($\eta$) and global softness ($\sigma$) express the resistance of a system to the change in its number of electrons. In a given series of molecules, when $\eta$ is weak, the molecule is called soft and when it is high, the molecule is called hard. This is quite the opposite of softness that evolves in the opposite direction of hardness [52]. The value of the chemical hardness of **compound 6** is the lowest ($\eta$ = 1.502 eV) among all the molecules. Also, we note that **compound 6** has a lower electronegativity value ($\chi$ = 3.930 eV) than other compounds; he is therefore the best electron donor and the softest molecule.

### 3.4.2. Local Descriptors and Dual Reactivity

Local indices and dual descriptors of reactivity were also determined for molecules 2, 6 and 5 according to Equations (2). The sites concerned are the atoms of the rhodanine ring of each molecule **Figure 4**.

These various indices and descriptors of the reactivity are grouped together in **Tables 3-5**.

The values of the local descriptors and dual descriptors of compound 2 calculated at the B3LYP/6-31G(d) level, show that the sulfur atom S1 in a sp3 hybridization state with the value $\Delta\omega$ = -0.172, is the preferred site of electrophile attack. According to this same level of calculation, a nucleophilic attack will have preferentially take place on the C4 atom with the value $\Delta\omega$ = 0.229.
<figure><img src="image_7.png" /><figcaption>Figure 4. Numbering of the atoms of the rhodanine ring of molecules 2, 6 and 5.</figcaption></figure>

<table><caption>Table 3. Compound 2 reactivity descriptors calculated using Mulliken population analysis (MPA).</caption><thead><tr><th rowspan="2">Sites</th><th colspan="9">Local descriptors</th><th colspan="3">Dual descriptors</th></tr><tr><th>f-</th><th>f+</th><th>σ-</th><th>σ+</th><th>η-</th><th>η+</th><th>ω-</th><th>ω+</th><th>Δf</th><th>Δσ</th><th>Δω</th></tr></thead><tbody><tr><td>S1</td><td>0.107</td><td>0.075</td><td>0.065</td><td>0.045</td><td>0.177</td><td>0.124</td><td>0.575</td><td>0.403</td><td>-0.032</td><td>-0.019</td><td>-0.172</td></tr><tr><td>N2</td><td>0.008</td><td>-0.011</td><td>0.005</td><td>-0.007</td><td>0.014</td><td>-0.018</td><td>0.045</td><td>-0.058</td><td>-0.019</td><td>-0.012</td><td>-0.103</td></tr><tr><td>C3</td><td>-0.024</td><td>0.007</td><td>-0.015</td><td>0.004</td><td>-0.040</td><td>0.012</td><td>-0.131</td><td>0.039</td><td>0.032</td><td>0.019</td><td>0.170</td></tr><tr><td>C4</td><td><strong>0.018</strong></td><td><strong>0.060</strong></td><td><strong>0.011</strong></td><td><strong>0.036</strong></td><td><strong>0.029</strong></td><td><strong>0.099</strong></td><td><strong>0.095</strong></td><td><strong>0.323</strong></td><td><strong>0.043</strong></td><td><strong>0.026</strong></td><td><strong>0.229</strong></td></tr><tr><td>S5</td><td>0.182</td><td>0.209</td><td>0.110</td><td>0.127</td><td>0.301</td><td>0.345</td><td>0.981</td><td>1.125</td><td>0.027</td><td>0.016</td><td>0.143</td></tr><tr><td>O6</td><td>0.050</td><td>0.105</td><td>0.030</td><td>0.064</td><td>0.083</td><td>0.174</td><td>0.270</td><td>0.566</td><td>0.055</td><td>0.033</td><td>0.296</td></tr><tr><td>C7</td><td>0.016</td><td>0.016</td><td>0.010</td><td>0.010</td><td>0.027</td><td>0.026</td><td>0.088</td><td>0.086</td><td>0.000</td><td>0.000</td><td>-0.002</td></tr></tbody></table>

<table><caption>Table 4. Compound 6 reactivity descriptors calculated using Mulliken population analysis (MPA).</caption><thead><tr><th rowspan="2">Sites</th><th colspan="9">Local descriptors</th><th colspan="3">Dual descriptors</th></tr><tr><th>f-</th><th>f+</th><th>σ-</th><th>σ+</th><th>η-</th><th>η+</th><th>ω-</th><th>ω+</th><th>Δf</th><th>Δσ</th><th>Δω</th></tr></thead><tbody><tr><td>S1</td><td>0.070</td><td>0.081</td><td>0.046</td><td>0.054</td><td>0.105</td><td>0.122</td><td>0.358</td><td>0.418</td><td>0.012</td><td>0.008</td><td>0.060</td></tr><tr><td>C2</td><td>-0.015</td><td>0.009</td><td>-0.010</td><td>0.006</td><td>-0.023</td><td>0.013</td><td>-0.078</td><td>0.044</td><td>0.024</td><td>0.016</td><td>0.122</td></tr><tr><td>N4</td><td><strong>0.003</strong></td><td><strong>-0.010</strong></td><td><strong>0.002</strong></td><td><strong>-0.007</strong></td><td><strong>0.004</strong></td><td><strong>-0.016</strong></td><td><strong>0.014</strong></td><td><strong>-0.054</strong></td><td><strong>-0.013</strong></td><td><strong>-0.009</strong></td><td><strong>-0.068</strong></td></tr><tr><td>C5</td><td>0.008</td><td>0.063</td><td>0.006</td><td>0.042</td><td>0.013</td><td>0.095</td><td>0.043</td><td>0.323</td><td>0.055</td><td>0.036</td><td>0.281</td></tr><tr><td>S6</td><td><strong>0.090</strong></td><td><strong>0.217</strong></td><td><strong>0.060</strong></td><td><strong>0.145</strong></td><td><strong>0.135</strong></td><td><strong>0.327</strong></td><td><strong>0.462</strong></td><td><strong>1.117</strong></td><td><strong>0.128</strong></td><td><strong>0.085</strong></td><td><strong>0.656</strong></td></tr><tr><td>O7</td><td>0.021</td><td>0.107</td><td>0.014</td><td>0.071</td><td>0.032</td><td>0.161</td><td>0.110</td><td>0.552</td><td>0.086</td><td>0.057</td><td>0.442</td></tr><tr><td>C8</td><td>0.003</td><td>0.015</td><td>0.002</td><td>0.010</td><td>0.004</td><td>0.023</td><td>0.014</td><td>0.078</td><td>0.012</td><td>0.008</td><td>0.064</td></tr></tbody></table>

<table><caption>Table 5. Compound 5 reactivity descriptors calculated using Mulliken population analysis (MPA).</caption><thead><tr><th rowspan="2">Sites</th><th colspan="9">Local descriptors</th><th colspan="3">Dual descriptors</th></tr><tr><th>f-</th><th>f+</th><th>σ-</th><th>σ+</th><th>η-</th><th>η+</th><th>ω-</th><th>ω+</th><th>Δf</th><th>Δσ</th><th>Δω</th></tr></thead><tbody><tr><td>S1</td><td>0.070</td><td>0.081</td><td>0.046</td><td>0.054</td><td>0.105</td><td>0.122</td><td>0.358</td><td>0.418</td><td>0.012</td><td>0.008</td><td>0.060</td></tr><tr><td>C2</td><td>-0.015</td><td>0.009</td><td>-0.010</td><td>0.006</td><td>-0.023</td><td>0.013</td><td>-0.078</td><td>0.044</td><td>0.024</td><td>0.016</td><td>0.122</td></tr><tr><td>N3</td><td><strong>0.003</strong></td><td><strong>-0.010</strong></td><td><strong>0.002</strong></td><td><strong>-0.007</strong></td><td><strong>0.004</strong></td><td><strong>-0.016</strong></td><td><strong>0.014</strong></td><td><strong>-0.054</strong></td><td><strong>-0.013</strong></td><td><strong>-0.009</strong></td><td><strong>-0.068</strong></td></tr><tr><td>C4</td><td>0.008</td><td>0.063</td><td>0.006</td><td>0.042</td><td>0.013</td><td>0.095</td><td>0.043</td><td>0.323</td><td>0.055</td><td>0.036</td><td>0.281</td></tr><tr><td>S6</td><td><strong>0.090</strong></td><td><strong>0.217</strong></td><td><strong>0.060</strong></td><td><strong>0.145</strong></td><td><strong>0.135</strong></td><td><strong>0.327</strong></td><td><strong>0.462</strong></td><td><strong>1.117</strong></td><td><strong>0.128</strong></td><td><strong>0.085</strong></td><td><strong>0.656</strong></td></tr><tr><td>O6</td><td>0.021</td><td>0.107</td><td>0.014</td><td>0.071</td><td>0.032</td><td>0.161</td><td>0.110</td><td>0.552</td><td>0.086</td><td>0.057</td><td>0.442</td></tr><tr><td>C7</td><td>0.003</td><td>0.015</td><td>0.002</td><td>0.010</td><td>0.004</td><td>0.023</td><td>0.014</td><td>0.078</td><td>0.012</td><td>0.008</td><td>0.064</td></tr></tbody></table>
**Table 4** summarizes the results of local index calculations and dual reactivity descriptors, using the MPA population analysis at computational level B3LYP/6-31G (d). It follows that an electrophilic attack probably occurs on the N14 heteroatom. However, the sulfur heteroatom in an sp2 (S6) hybridization state is the most favorable site for nucleophilic attack.

The results in **Table 4** predict that the N3 site is the most favored against electrophilic attacks. As regards the nucleophilic attack, it occurs preferentially on the sulfur heteroatom in a sp2 (S6) hybridization state.

## 4. Conclusion

In conclusion, based on the B3LYP/6-31G (d) functional density method, global and local descriptors were used to study the reactivity of different nucleophilic, electrophilic and radical sites and the influence of these on molecular interaction qualitatively and quantitatively. The descriptors obtained could also provide more information and contribute to a better understanding of the electronic structure of rhodanine derivatives. Electrostatic potential maps have shown that areas of high electron density are located around oxygen and sulfur heteroatoms in a hybridization (sp3) state of the rhodanine ring. In particular, the oxygen atom represents an electrophilic attack site on the rhodanine nucleus. Of all these compounds, compound 6 has the highest chemical reactivity and the lowest kinetic stability with respect to the other molecules studied. In addition, this compound 6 is the softest molecule of all and the best electron donor. In addition, the local descriptors of reactivity of the rhodanine derivatives obtained by the Mulliken population analysis method indicate that the sulfur heteroatom of the rhodanine ring is the preferred site of electrophilic attack in a hybridization state sp3 and also the privileged site of nucleophilic attack in a sp2 hybridization state. Therefore, the sulfur heteroatoms contained in the rhodanine ring can be used as precursors for the synthesis of new rhodanine derivatives. Finally, we hope that these results will be useful in the search for experimental and theoretical proofs of new rhodanine compounds across molecular bonds.

## Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

## References

[1] Souness, E., Aldous, D. and Sargent, C. (2004) Immunosuppressive and Anti-Inflammatory Effects of Cyclic AMP Phosphodiesterase (PDE) Type 4 Inhibitors. *Immunopharmacology*, **47**, 127-162.
https://doi.org/10.1016/S0162-3109(00)00185-5

[2] Achson, A. (2009) An Introduction to the Chemistry of Heterocyclic Compounds. 3rd Edition, Wiley, Hoboken.

[3] Dua, R., Shrivastava, S., Sonwane, S.K. and Srivastava, S.K. (2011) Pharmacological
Significance of Synthetic Heterocycles Scaffold: A Review. *Adv. Biol. Res.* (Rennes), **5**, 120-144.

[4] Coulibaly, W.K. (2012) Conception, synthèse de bis-(5-arylidène-imidazolinone) et de bis-(5-arylidène thiazolidinone) dérivés du modèle de la pentamidine (pour la malaria), et leurs évaluations biologiques. Thèse de Doctorat, No. 4549, 1-236.

[5] Jain, A.K., Vaidya, A., Ravichandran, V., Kasshaw, S.K. and Agrawal, R.K. (2012) Recent Developments and Biological Activities of Thiazolidinone Derivatives: A Review. *Bioorganic & Medicinal Chemistry*, **20**, 3378-3395.
https://doi.org/10.1016/j.bmc.2012.03.069

[6] Kaur Manjal, S., et al. (2017) Synthetic and Medicinal Perspective of Thiazolidinones: A Review. *Bioorganic Chemistry*, **75**, 406-423.
https://doi.org/10.1016/j.bioorg.2017.10.014

[7] Foye, W.O. and Tovivich, P.J. (1977) N-Glucopyranosyl-5-Aralkylidenerhodanines: Synthesis and Antibacterial and Antiviral Activities. *Journal of Pharmaceutical Sciences*, **66**, 1607-1611. https://doi.org/10.1002/jps.2600661126

[8] Alegaon, S.G., Alagawadi, K.R., Sonkusare, P.V., Chaudhary, S.M., Dadwe, D.H. and Shah, A.S. (2012) Novel Imidazo [2,1-b] [1,3,4] Thiadiazole Carring Rhodanine-3-Acetic Acid as Potential Antitubercular Agents. *Bioorganic & Medicinal Chemistry Letters*, **22**, 1917-1921.
https://doi.org/10.1016/j.bmcl.2012.01.052

[9] Radi, M., Botta, L., Casaluce, G., Bernardini, M. and Botta, M. (2010) Practical One-Pot Two-Step Protocol for the Microwave-Assisted Synthesis of Highly Functionalized Rhodanine Derivatives. *Journal of Combinatorial Chemistry*, **12**, 200-205.
https://doi.org/10.1021/cc9001789

[10] Benson, S.W. and Buss, J.H. (1958) Additivity Rules for the Estimation of Molecular Properties. Thermodynamic Properties. *The Journal of Chemical Physics*, **29**, 546-572. https://doi.org/10.1063/1.1744539

[11] Kumar, V., Khandare, D.G., Chatterjee, A. and Banerjee, M. (2013) Protic Ionic Liquids as Recyclable Solvents for the Acid Catalysed Synthesis of Diphenylmethyl Thioethers. *Tetrahedron Letters*, **54**, 5505-5509.
https://doi.org/10.1016/j.tetlet.2013.07.147

[12] Deohate, P.P., Deohate, J.P. and Berad, B.N. (2004) Synthesis of Some Novel 1,2,4-Dithiazolidines and Their Antibacterial and Antifungal Activity. *Asian Journal of Chemistry*, **16**, 255-260.

[13] Rao, V.J., Reddy, T.N., Ravinder, M., Bagul, P., Ravikanti, K., Bagul, C., Nanubolu, J.B., Srinivas, K. and Banerjee, S.K. (2014) Synthesis and Biological Evaluation of New Epalrestat Analogues as Aldose Reductase Inhibitors (ARIs). *European Journal of Medicinal Chemistry*, **71**, 53-66. https://doi.org/10.1016/j.ejmech.2013.10.043

[14] Sha, X., Zhang, H. and Huang, W. (2009) Design and Synthesis of Thiazolidinedione Derivatives as Selective PPARγ Modulators. *Letters in Drug Design & Discovery*, **6**, 224-227. https://doi.org/10.2174/157018009787847819

[15] Bozdag, D.O., Verspohl, E.J., Das, E., Kaup, R.M., Bauer, K., Sarikaya, M., Evi, B. and Ertan, R. (2008) Synthesis and Biological Activity of Some New Flavonyl-2,4-Thiazolidinediones. *Bioorganic & Medicinal Chemistry*, **16**, 6747-6751.
https://doi.org/10.1016/j.bmc.2008.05.059

[16] Rao, B.A., Rajpoot, R.S., Naidu, V.G.M., Srinivas, K., Ramakrishna, S. and Rao, V.J. (2011) Synthesis and *in Vitro* Antitumor Activity of New Nicotinyl-Rhodanine Derivatives. *International Journal of Pharma and Bio Sciences*, **2**, 191-202.
[17] Patel, N.B. and Shaikh, F.M. (2010) New 4-Thiazolidinones of Nicotinic Acid with 2-Amino-6-Methylbenzothiazole and Their Biological Activity. *Scientia Pharmaneutica*, **78**, 753-765. https://doi.org/10.3797/scipharm.1009-15

[18] Foresman, J.B. and Frisch, A. (1996) Exploring Chemistry with Electronic Structure Methods. Gaussian Inc., Pittsburgh.

[19] Kurt, M., Sertbakan, T.R. and Ozduran, M. (2008) Spectrochim: An Experimental and Theoretical Study of Molecular Structure and Vibrational Spectra of 3- and 4-Pyridineboronic Acid Molecules by Density Functional Theory Calculations. *Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy*, **70**, 664-673. https://doi.org/10.1016/j.saa.2007.08.019

[20] Abdel-Rahman, L.H., El-Khatib, R.M., Nassr, L.A.E., Abu-Dief, A.M., Ismael, M. and Seleem, A.A. (2014) Metal Based Pharmacologically Active Agents: Synthesis, Structural Characterization, Molecular Modeling, CT-DNA Binding Studies and in Vitro Antimicrobial Screening of Iron (II) Bromosalicylidene Amino Acid Chelates. *Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy*, **117**, 366-378. https://doi.org/10.1016/j.saa.2013.07.056

[21] Abdel-Rahman, L.H., Abu-Dief, A.M., Adam, M.S.S. and Hamdan, S.K. (2016) Some New Nano-Sized Mononuclear Cu(II) Schiff Base Complexes: Design, Characterization, Molecular Modeling and Catalytic Potentials in Benzyl Alcohol Oxidation. *Catalysis Letters*, **146**, 1373-1396. https://doi.org/10.1007/s10562-016-1755-0

[22] Abdel Rahman, L.H., Abu-Dief, A.M., Moustafa, H. and Hamdan, S.K. (2017) Ni(II) and Cu(II) Complexes with ONNO Asymmetric Tetradentate Schiff Base Ligand: Synthesis, Spectroscopic Characterization, Theoretical Calculations, DNA Interaction and Antimicrobial Studies. *Applied Organometallic Chemistry*, **31**, e3555. https://doi.org/10.1002/aoc.3555

[23] Ravikumar, C., Joe, I.H. and Jayakumar, V.S. (2008) Charge Transfer Interactions and Nonlinear Optical Properties of Push-Pull Chromophore Benzaldehyde Phenylhydrazone: A Vibrational Approach. *Chemical Physics Letters*, **460**, 552-558. https://doi.org/10.1016/j.cplett.2008.06.047

[24] Parr, R.G. and Yang, W. (1995) Density-Functional Theory of the Electronic Structure of Molecules. *Annual Review of Physical Chemistry*, **46**, 701-728. https://doi.org/10.1146/annurev.pc.46.100195.003413

[25] Parr, R.G. and Yang, W. (1989) Density Functional Theory of Atoms and Molecules. Oxford University Press, Oxford.

[26] Fukui, K., Yonezawa, Y. and Shingu, H. (1952) A Molecular Orbital Theory of Reactivity in Aromatic Hydrocarbons. *The Journal of Chemical Physics*, **20**, 722-725. https://doi.org/10.1063/1.1700523

[27] Parr, R.G. and Yang, W. (1984) Density Functional Approach to the Frontier-Electron Theory of Chemical Reactivity. *Journal of the American Chemical Society*, **106**, 4049-4050. https://doi.org/10.1021/ja00326a036

[28] Ayers, P.W. and Levy, M. (2000) Density Functional Approach to the. Frontier-Electron Theory of Chemical Reactivity. *Theoretical Chemistry Accounts*, **103**, 353-360. https://doi.org/10.1007/s002149900093

[29] Lee, W.Y. and Parr, R.G. (1988) Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. *Physical Review B*, **37**, 785-789. https://doi.org/10.1103/PhysRevB.37.785

[30] Becke, A.D. (1993) Density-Functional Thermochemistry. III. The Role of Exact
Exchange. *The Journal of Chemical Physics*, **98**, 5648-5652.
https://doi.org/10.1063/1.464913

[31] Frisch, M.J., Trucks, G.W., Schlegel, H.B. and Scuseria, G.E. (2009) Gaussian 09, Revision A 02. Gaussian, Inc., Wallingford.

[32] Kapp, J., Remko, M. and Schleyer, P.V.R. (1996) H₂ XO and (CH₃)₂ XO Compounds (X = C, Si, Ge, Sn, Pb): Double Bonds vs. Carbene-Like Structures Can the Metal Compounds Exist at All? *Journal of the American Chemical Society*, **118**, 5745-5751. https://doi.org/10.1021/ja953846p

[33] Johnson, B.G., Gill, P.M. and Pople, J.A. (1993) The Performance of a Family of Density Functional Methods. *The Journal of Chemical Physics*, **98**, 5612-5626.
https://doi.org/10.1063/1.464906

[34] XLSTAT Version 2014.5.03 Copyright Addinsoft 1995-2014 (2014) XLSTAT and Addinsoft Are Registered Trademarks of Addinsoft. https://www.xlstat.com

[35] Mulliken, R.S. (1962) Criteria for the Construction of Good Self-Consistent-Field Molecular Orbital Wave Functions, and the Significance of LCAO-MO Population Analysis. *The Journal of Chemical Physics*, **36**, 3428-3439.
https://doi.org/10.1063/1.1732476

[36] Koopmans, T. (1934) Über die Zuordnung von Wellenfunktiomen und Eigenwerten zu den einzelnen Elektronen eines Atoms. *Physica*, **1**, 104-113.
https://doi.org/10.1016/S0031-8914(34)90011-2

[37] Yang, W., Parr, R.G. and Pucci, R. (1984) Electron Density, Kohn-Sham Frontier Orbitals, and Fukui Functions. *The Journal of Chemical Physics*, **81**, 2862-2863.
https://doi.org/10.1063/1.447964

[38] Yang, W. and Mortier, W. (1986) The Use of Global and Local Molecular Parameters for the Analysis of the Gas-Phase Basicity of Amines. *Journal of the American Chemical Society*, **108**, 5708-5711. https://doi.org/10.1021/ja00279a008

[39] Yang, W. and Parr, R.G. (1985) Chemistry. Hardness, Softness, and the Fukui Function in the Electronic Theory of Metals and Catalysis. *Proceedings of the National Academy of Sciences of the United States of America*, **82**, 6723-6726.
https://doi.org/10.1073/pnas.82.20.6723

[40] Chattaraj, P.K., Maiti, B. and Sarkar, U. (2003) Philicity: A Unified Treatment of Chemical Reactivity and Selectivity. *The Journal of Physical Chemistry*, **107**, 4973-4975. https://doi.org/10.1021/jp034707u

[41] Fuentealba, P. and Contreras, R. (2002) Fukui Function in Chemistry. In: Sen, K.D., Ed., *Reviews in Modern Quantum Chemistry: A Celebration of the Contributions of Robert G Parr*, World Scientific, River Edge, 1013-1052.
https://doi.org/10.1142/9789812775702_0034

[42] Padmanabhan, J., Parthasarathi, R., Elango, M., Subramanian, V., Krishnamoorthy, B.S., Gutierrez-Oliva, S., Toro-Labbe, A., Roy, D.R. and Chattaraj, P.K. (2007) Multiphilic Descriptor for Chemical Reactivity and Selectivity. *The Journal of Physical Chemistry*, **111**, 9130-9138. https://doi.org/10.1021/jp0718909

[43] Morell, C., Grand, A. and Toro-Labbé, A. (2005) New Dual Descriptor for Chemical Reactivity. *The Journal of Physical Chemistry*, **109**, 205-212.
https://doi.org/10.1021/jp046577a

[44] Morell, C., Grand, A. and Toro-Labbé, A. (2006) Theoretical Support for Using the Delta f(r). Descriptor. *Chemical Physics Letters*, **425**, 342-346.
https://doi.org/10.1016/j.cplett.2006.05.003

[45] Abdel-Baset, H.M., Hanan, G.E., El-Okr, M.M. and Ibrahim, M.A. (2015) Electros-
tatic Potential Maps of Fullerene C60 and Some of Its Specific Derivatives: Density Functional Theory Approach. *Journal of Nanomaterials Molecular Nanotechnology*, **4**, 2.

[46] Hong, L.X., Ling, C.H., Zhou, Z.R. and Zhou, Z.X. (2015) Molecular and Biomolecular Spectroscopy. *Spectrochimica Acta Part A*, **137**, 321-327.
https://doi.org/10.1016/j.saa.2014.08.036

[47] Woodward, R.B. and Hoffmann, R. (1970) The Conservation of Orbital Symmetry. Chemie, Weinheim. https://doi.org/10.1016/B978-1-4832-3290-4.50006-4

[48] Gece, G. (2008) The Use of Quantum Chemical Methods in Corrosion Inhibitor Studies. *Corrosion Science*, **50**, 2981-2992.
https://doi.org/10.1016/j.corsci.2008.08.043

[49] Lewis, D.F.V., Ioannides, C. and Parke, D.V. (1994) Interaction of a Series of Nitriles with the Alcohol-Inducible Isoform of P450: Computer Analysis of Structure-Activity Relationships. *Xenobiotica*, **24**, 401-408.
https://doi.org/10.3109/00498259409043243

[50] Uesugi, Y., Mizuno, M., Shimojima, A. and Takahashi, H. (1997) Transient Resonance Raman and Ab-Initio Mo Calculation Studies of the Structures and Vibrational Assignments of the t1 State and the Anion Radical of Coumarin and Its Isotopically Substituted Analogues. *The Journal of Physical Chemistry*, **101**, 268-274.
https://doi.org/10.1021/jp9626881

[51] Sinha, L., Prasad, O., Narayan, V., Shukla, S. and Raman, R. (2011) FT-IR Spectroscopic Analysis and First-Order Hyperpolarisability of 3-benzoyl-5-chlorouracil by First Principles. *Molecular Simulation*, **37**, 153-163.
https://doi.org/10.1080/08927022.2010.533273

[52] Pearson, R.G. (1963) Hard and Soft Acids and Bases. *Journal of the American Chemical Society*, **85**, 3533-3539. https://doi.org/10.1021/ja00905a001