Abstract

The study of the reactivity and stability of the five (05) compounds of Thiazine was carried out using the density functional theory at the level B3LYP/6-31+ G (d, p). The determination of the dual descriptor as well as the analysis of the map of the molecular electrostatic potential (MEP) made it possible to show that the sulfur and nitrogen atoms of the Thiazine cycle are respectively the electrophilic and nucleophilic sites. The study of the chemical reactivity of our compounds was carried out from the analysis of the frontier molecular orbitals (HOMO and LUMO), the energy gap (ΔE), the chemical hardness (η), the electrophilicity index (ω) and electronegativity (χ). Thus, the Thz3 compound is the least reactive, the least electron donor and the most stable of all our compounds.

1. Introduction

Heterocycles are defined as chemical species whose carbon chain contains one or more carbon atoms are substituted by heteroatoms such as nitrogen, sulfur, oxygen, phosphorus, etc. ^{1, 2}. Heterocycles possess structural variety and are used in several fields. Heterocyclic compounds comprising nitrogen and sulfur atoms are widely used in coordination chemistry for the development of new bioactive molecules ^{3, 4, 5}. In the case of our study, we are interested in Thiazine derivatives which are six-membered ring systems containing endocyclic sulfur and nitrogen atoms ⁶. In addition to their biological activity, Thiazines are used in the dye and insecticide industries ⁷. Nowadays one of the methods allowing to give a lot of information on the molecular electronic structures and contributes to the evolution experimental chemistry is the computational chemistry ^{8, 9}, thus, it makes it possible to reduce the number of experiments, often long, dangerous and costly in time and money ^{10, 11}. The stability is a theoretical study that predicts the global and local reactivity sites of a molecule ¹². The general objective of this work is to theoretically determine the reactivity, to identify the nucleophilic/electrophilic attack sites by different methods of quantum chemistry.

2. Materials and Methods

The theoretical study of chemical reactivity has been conducted based on three theoretical approaches. The first one concerns the analysis of electrostatic potential maps. The second approach is concerned with the local indices of reactivity and the dual descriptors. The last approach is related to the boundary molecular orbitals. The geometries of the molecules have been optimized at the DFT level with the B3LYP ^{13, 14} in the 6-31+G(d,p) basis using the Gaussian 09 software ¹⁵. This Hybrid functional gives better energies and is in agreement with high level ab initio methods ^{16, 17}. The geometries are held constant for both cationic and anionic systems. The global reactivity indices were obtained from the conceptual DFT model ^{18, 19}.

The analysis of the surface of the electrostatic potential makes it possible to highlight the zones capable of being nucleophilic or electrophilic attack sites. The analysis of this surface is based on the colors. The potential increases in the order red < orange < yellow < green < cyan < blue ^{20, 21}. In the electrostatic potential surface, areas that have zero potential are represented by the color green, negative areas (red and yellow) are electrophilic attack sites, and positive areas (cyan and blue) are electrophilic attack sites. nucleophilic attack.

To predict the chemical reactivity, some theoretical descriptors related to the conceptual DFT have been determined. In particular, the energy of the lowest vacant molecular orbital (MO) (E_LUMO), the energy of the highest occupied molecular orbital (MO) (E_HOMO), the electronegativity (χ), the global softness (σ) and the global electrophilicity index (ω). These descriptors are all determined from the optimized molecules. It should be noted that, the descriptors related to the boundary molecular orbitals were calculated in a very simple way within the Koopmans approximation ²². The 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. The electronegativity(χ) is the parameter which translates the aptitude of a molecule not to let escape its electrons. The overall softness (σ) expresses the resistance of a system to the change of its number of electrons. The global electrophilicity index characterizes the electrophilic power of the molecule. These different parameters are calculated from equations (1-6):

(1)

(2)

(3)

(4)

(5)

(6)

The Fukui numbers of a molecule give information about the local reactivity in a molecule. The atom with the largest Fukui number is more reactive than the other atoms in the molecule ²³. These indices represent the qualitative description of the reactivity of atoms in the molecule. The Fukui function successfully predicts the relative reactivity for most chemical systems. The determination of Fukui indices for the selectivity of electrophilic and nucleophilic atoms in chalcone-derived compounds has been done. Ayers and Parr ²⁴. Explained that molecules tend to react where the Fukui function is largest when attacked by soft reagents and in places where the Fukui function is smallest when attacked by hard reagents. Using the Natural Atomic Population charges of the optimized ground state compounds, the Fukui function , local softness and local indices of electrophilia ²⁵. have been determined. The Fukui functions are calculated using equations (7) and (8):

(7)

(8)

for nucleophilic attack

for electrophilic attack

: Electronic population of atom k in the neutral molecule.

: Electronic population of atom k in the anionic molecule.

: Electronic population of atom k in the cationic molecule.

The values of the dual descriptors ²⁶ are obtained from equation (9)

(9)

The calculation of natural atomic charge plays an important role in the study of molecular systems in quantum chemistry. For the quantitative description of a molecular charge distribution, the molecule is dissected into well-defined atomic fragments. A general and natural choice is to share the charge density at each point between the different atoms in proportion to their free atom densities at the corresponding distances of the nuclei ¹. In this work, the atomic charge values were obtained by the Natural population analysis.

3. Results and Discussion

In order to have a general idea about the sites of reactivity of the compounds, we analyzed the potential energy surface of each of these compounds. Images of these maps are shown in Figure 1.

The surface of electrostatic potential, areas that have zero potential are represented by the color green, negative areas (red and yellow) are electrophilic etch sites, and positive areas (cyan and blue) are etch sites nucleophiles. The analysis of these maps indicates that the sulfur atoms (s) are the sites of electrophilic attacks because a neighborhood of negative potential is observed around these atoms. As for nucleophilic attack sites in this study, nitrogen atoms are the most available.

The determination of the dual descriptor allows us to locate the nucleophilic and electrophilic sites of the five (05) compounds derived from Thiazines. In this study we calculated the Fukui indices (f+, f-) and the dual descriptor (Δf(r)) and the results shown in Table 2 to Table 6.

The different results obtained from the calculation of the dual descriptor show that the sulfur (S) atoms of the Thiazine nucleus indicate the greatest values of the dual descriptor. which from them the electrophilic sites. As for the Nitrogen (N) atoms of the Thiazine ring. they display the lowest values of the dual descriptor. These low values show that these nitrogen atoms are the nucleophilic sites of the Thiazine derivatives studied.

The study of the global reactivity of molecules is based on the calculation of global indices deduced from the electronic properties. The values of the energies related to the molecular frontier orbitals are given in Table 7. In view of these values we note the largest value of the energy gap for the compound Thz3 (ΔE= 5.915 eV). which allows us to say that it is less reactive of our compounds. However, the compound Thz5 would be more reactive because it has the smallest value of the energy gap (ΔE= 5.442 eV). of this series studied. Thus. the compounds are classified in the following descending order of stability:

Table 8 shows the overall reactivity indices of the Thiazine derivatives studied.

In view of the results of Table 8, the compound Thz3 presents the smallest electronegativity value (χ=3.370 eV) of all our compounds. It is therefore the compound capable of giving up its electrons the fastest. The Thz5 compound has the smallest chemical hardness (η = 2.721 eV) which makes it the softest of all the compounds studied. With a low value of the electrophilic index (ω = 1.920 eV), the compound Thz3 is the one that receives the least electrons.

4. Conclusion

The theoretical study carried out on the five (05) compounds of the Thiazine family. using the methods of Quantum Chemistry and Molecular Modeling. made it possible to show that the compound Thz3 is the most stable and the one which yields with difficulty the electrons through the use of global reactivity descriptors. The Fukui indices and the dual descriptors made it possible to precisely determine attack sites. The latter showed that the sulfur atoms of the Thiazine ring are the electrophilic sites and those of nitrogen of the nucleus of Thiazine are the nucleophilic sites. For the rest of this work, we plan to study the stability of these compounds in solvents and then do an NBO study.

References