Study of the Chemical Reactivity of a Series of Dihydrothiophenone Derivatives by the Density Functional Theory (DFT) Method

Study of the Chemical Reactivity of a Series of Dihydrothiophenone Derivatives by the Density Functional Theory


Introduction
Malaria is an acute febrile human disease caused by the Plasmodium parasite that is transmitted by the bites of infected female Anopheles mosquitoes.Two of the five species of malaria parasites that cause human malaria are particularly dangerous: P. falciparum, the parasite that causes the most deaths and is also the most widespread on the African continent, and P. vivax, the dominant species in most countries outside sub-Saharan Africa [1].Thus, Xu et al. [2] have synthesised a series of dihydrothiophenone derivatives against Plasmodium falciparum dihydroorotate dehydrogenase (PfDHODH)(Table 1).Nowadays, a number of these heterocyclic derivatives containing atoms such as sulphur are used as intermediates in the design of experimental drugs [3].Also, computational chemistry provides a lot of information about the electronic structures of molecules and contributes greatly to the development of traditional experimental chemistry [3][4][5].In this work, we predicted the reactivity and reactive sites on molecules through a computational study based on density functional theory (DFT/B3LYP) using a 6-31G (d, p) basis set.Descriptors have been tested and studied in the literature by several research groups and are considered very useful for rationalising reactivity models of molecular systems [7,8].
Geerlings et al. and Roy et al. have examined and tested the theoretical basis of these descriptors and their applications [9,10].A set of global and local descriptors for measuring the reactivity of molecular systems has emerged.Fukui indices have also been determined and discussed.
The general objective of this manuscript is to study the reactivity and stability of a series of dihydrothiophenone derivatives.Specifically, the reactivity of dihydrothiophenone will be determined theoretically and the nucleophilic/electrophilic attack sites will be identified by various quantum chemical methods.Ethyl 2-(anthracen-2-ylamino)-4-oxo-4,5-dihydrothiophene-3carboxylate

Level of Theory of Calculation
The geometries of the molecules were optimized at the DFT level with the B3LYP [6][7][8] in the 6-31G(d, p) basis using the Gaussian 09 software.[9] This Hybrid functional gives better energies and is in agreement with high level ab initio methods [10,11].As for the split-valence and doubledzeta basis (6-31G (d, p)), it is sufficiently broad and the consideration of polarisation functions are important for the explanation of the free doublets of heteroatoms.The geometries are kept constant for both cationic and anionic systems.The overall reactivity indices were obtained from the conceptual DFT model [12][13][14][15].The local chemical reactivity indices were determined using the electronic populations calculated with the Natural Population Analysis (NPA) [16].

Thermodynamic Formation Quantities
The thermodynamic quantities of the molecules were carried out from optimisation and calculation of frequencies at the level B3LYP/6-31G (d, p).The quantities such as entropy, enthalpy and free enthalpy of formation of DHs were determined via the following formulae proposed by Otchersky et al [9]. With: ∑ : Atomisation energy; : Total energy of the molecule; !: Zero-point energy of the molecule; 298 − 0 : Enthalpy corrections for atomic elements.These values are included in the Janaf table [17]; 298 − 0 = " ## − !: Enthalpy correction of the molecule; " ## : Thermal correction enthalpy.
: Number of atoms of X in the molecule.

Global Reactivity Descriptors
We determined several descriptors of overall reactivity using the conceptual density functional theory method.These descriptors have proven to be very effective in predicting reactivity patterns.Based on the study by Koopmans [18].These are: global hardness (η), global softness (S) energy gap ∆Egap.The global reactivity descriptors are calculated using the boundary energies, E HOMO , E LUMO molecular orbitals.These descriptors have been tested and studied in the literature by several research groups and are considered very useful for rationalising reactivity models of molecular systems [8,19].

Local Reactivity Descriptors
The local reactivity descriptor as the Fukui function indicates the preferred regions where a chemical (molecule) will change its density when the number of electrons is changed.It indicates the tendency of the electron density to deform at a given position when accepting or donating electrons [20,21].They are used to decide the relative reactivity of the different atoms in the molecule.The Fukui function [19,22] is one of the most widely used local density functional descriptors for modelling chemical reactivity and site selectivity.It is defined as the derivative of the electron density ρ(r) with respect to the total number of electrons N. In the system, these functions are calculated according to the procedure proposed by Yang and Mortier [22].This function describes the sensitivity of the chemical potential of a system to a local external potential.Using the left and right derivatives with respect to the number of electrons, one can define the electrophilic, nucleophilic and local softness Fukui function.To describe the site selectivity or reactivity of an atom in a molecule, it is necessary to condense the values of (() and (() around each atomic site into a single value that characterises the atom in a molecule.This can be achieved by an electronic population analysis.Thus, for an atom k in a molecule, depending on the type of electron transfer, we have three different types of condensed Fukui function of atom k.
, * -+ 1 : Electron population of atom k in the anionic molecule.
, * -− 1 : Electron population of atom k in the cationic molecule.

Thermodynamic Formation Quantities
The thermodynamic quantities of formation of Dihydrothiophenone derivatives, namely enthalpy, entropy and free enthalpy of formation were calculated at B3LYP/ 6-31 G(d, p).The values of these quantities are given in Table 3.

Code
∆ 0 1 2 (Kcal/mol.K) ∆ 0 3 The values of the different thermodynamic quantities are all negative.This result indicates that dihydrothiophenone derivatives can be formed spontaneously, exothermically with a decrease in disorder at the level of theory used.

Overall Reactivity Indices
The study of the global reactivity of molecules is based on the calculation of global indices deduced from the electronic properties.Global hardness (η), global softness (S) and global reactivity descriptors are very effective in predicting reactivity trends based on the Koopman study [18].The overall indices of the reactivity of the investigated HDs are shown in Table 4.According to the theoretical calculations made, it was found that the DH1 molecule has the lowest value of energy gap (3.4051ev).This lower gap allows it to be the most reactive (soft) and least stable molecule.Also we find that it has the lowest hardness (η = 1.7026 eV), but the highest softness (0.2937 ev).This indicates that this molecule is the most reactive of all the compounds.
Thus, the following sequence can be established in order of increasing reactivity: ∆E: DH 1>DH > 2> DH 3> DH4 > DH5> DH 6>DH7> DH8 >DH 9> DH10.This DH1 compound is therefore more polarisable and is associated with high chemical reactivity, low kinetic stability and is also called a "soft molecule".This indicates that it is the most electrophilic of all the compounds.
On the other hand, the same calculations reveal that the DH10 molecule with the highest energy gap (4.6168 eV) the highest hardness (2.3084 eV) and the lowest softness (0.2166 eV) is the least reactive compound.Therefore, the most nucleophilic compound.

Local Reactivity
In the context of the isodensity map study, a site is likely to be nucleophilic or electrophilic if it belongs to a larger lobe.The isodensity maps showing the likely nucleophilic and electrophilic attack sites using the bulky lobes of the ten (10) compounds studied are shown in Figures.Analysis of the maps through HOMO indicates that the largest lobe containing the entire S5 atoms would be the likely nucleophilic sites of the DH1 series.With regard to the electrophilic attack sites obtained from the LUMO; the C23 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.The analysis of the maps through HOMO indicates that the largest lobe entirely containing atoms S7, C4 would be the likely nucleophilic sites of the DH2; DH3; DH4 series of compounds.With regard to the electrophilic attack sites obtained from LUMO; the 1N, C4 atoms present the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.The analysis of the maps through HOMO indicates that the largest lobe containing the entire O7, C3 atoms would be the likely nucleophilic sites of the DH5 series.With regard to the electrophilic attack sites obtained from LUMO; the 1N, C3 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.Analysis of the maps through HOMO indicates that the largest lobe containing all C1 atoms would be the likely nucleophilic sites of the DH6 series.With regard to the electrophilic attack sites obtained from LUMO, the C6 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.Analysis of the maps through HOMO indicates that the larger lobe containing the entire S7, C4 atoms would be the likely nucleophilic sites of the compound series.DH7.With regard to the electrophilic attack sites obtained from LUMO; the 1N, C4 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.Analysis of the maps through HOMO indicates that the largest lobe containing the entire C24 atoms would be the likely nucleophilic sites of the DH8 series.With regard to the electrophilic attack sites obtained from LUMO; the C11 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.Analysis of the maps through HOMO indicates that the largest lobe containing all C1 atoms would be the likely nucleophilic sites of the DH9 series.With regard to the electrophilic attack sites obtained from LUMO, the C6 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.The analysis of the maps through HOMO indicates that the largest lobe containing the entire O7, C3 atoms would be the likely nucleophilic sites of the DH10 series.With regard to the electrophilic attack sites obtained from LUMO; the 1N, C3 atoms show the largest lobes.These would appear to be the likely electrophilic sites for the DH series studied.The analysis of the local descriptors in Table DH6 and DH9 shows that the 1C carbon atom is the most reactive site for nucleophilic attack and the 6C carbon atom is the most reactive site for electrophilic attack.
Also, that of table DH8 illustrates that the 24C atom is the most reactive site for nucleophilic attacks and the 11C is the most reactive site for electrophilic attacks.On the other hand, those of tables DH5 and DH10 show that the oxygen atom 7O is the most reactive site for nucleophilic attacks and the nitrogen atom 1N is the most reactive site for electrophilic attacks.The values of the local descriptors in Table DH2, DH7 and DH4 show that the 5S sulphur atom is the nucleophilic attack site and the 1N nitrogen atom is the electrophilic attack site.Also, Table DH1 shows that the 5S sulphur atom is the nucleophilic attack site and the 23C carbon atom is the electrophilic attack site.Table DH3 shows that the 5S sulphur atom is the nucleophilic attack site and the 28C carbon atom is the electrophilic attack site.

Conclusion
The methods of Quantum Chemistry and Molecular Modelling were employed on ten (10) molecules of the dihydrothiophenone family to study their chemical stability and reactivity.This theoretical study was carried out by exploiting the density functional method (DFT) with the B3LYP/6-31G (d, p) level.
The analysis of the global descriptors revealed that the DH1 molecule has the lowest energy gap value (3.4051ev).This lower gap allows it to be the most reactive (soft) and least stable molecule.This indicates that it is the most electrophilic of all the compounds.In the future, we intend to carry out molecular docking in order to evaluate the interaction sites between these molecules and the plasmodim.

Table 1 .
Structures and nomenclature of the studied dihydrothiophenones and their codes.
Study of the Chemical Reactivity of a Series of Dihydrothiophenone Derivatives by the Density Functional Theory (DFT) Method 4,5dihydrothiophene-3-carboxamide DH10 Fandia Konate et al.:

Table 12 .
Fukui descriptors of compound DH 8. Study of the Chemical Reactivity of a Series of Dihydrothiophenone Derivatives by the Density Functional Theory (DFT) Method