17 American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) ISSN (Print) 2313-4410, ISSN (Online) 2313-4402 © Global Society of Scientific Research and Researchers http://asrjetsjournal.org/ Theoretical Studies of the Chemical Reactivity of a Series of Coumarin Derivatives by the Density Functional Theory Lamoussa Ouattara a , Kafoumba Bamba b *, Mamadou Guy-Richard Kone c , Jean Stéphane N’dri d , Affoué Lucie Bede e , Kouakou Nobel N’guessan f , Doh Soro g a,b,c,d,fg Faculty of Fundamental and Applied Sciences (UFR SFA), Laboratoire de Thermodynamique et de Physico- Chimie du Milieu, University NanguiAbrogoua, Abidjan, Côte d'Ivoire e Faculty of Science of Structures of Matter and Technology (UFR SSMT), Laboratoire de Constitution et Réaction de la Matière (LCRM), University Félix Houphouët - Boigny, Abidjan-Cocody, Côte d'Ivoire Abstract The global descriptors of reactivity such as HOMO and LUMO energies, chemical hardness, electrophilicity, softness and dipole moment are theoretically determined for five coumarin derivatives in this paper. The analysis of the determined descriptors allows us to classify the studied molecules according to their reactivities. Thus, compound M3 is qualified to be the most reactive and the least stable with 3.933 eV as its gap energy ΔEgap. It is at the same time the softest, the best electron donor, the most electrophilic and the most polar molecule. The study of thermodynamic parameters shows that all the reactions of formation of studied coumarin derivatives are exothermic and spontaneous with less disorder. Furthermore, Hirschfield population analysis was carried out in order to locate the reactive sites, that are assumed to be the electrophilic and nucleophilic sites of the molecules. It appears that all the reactive sites are located on carbon atoms except those of molecule M3 which are located on oxygen atoms. Compounds M1 and M2 have the same electrophilic site (C15) and the same nucleophilic site (C13) thereby showing that the methyl group does not have any influence on the reactive site. The electrophilic site of the molecule M3 is located on both the identical oxygen atoms O33 and O34 while its nucleophilic site is located on the oxygen atoms O12. The electrophilic sites of compound M4 and M5 are the same and it is located on carbon atom(C11) while the nucleophilic site is located on carbon atom C23 for molecule M4. ------------------------------------------------------------------------ * Corresponding author. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 18 Concerning the nucleophilic sites of molecule M5 it is located on carbon atom C20. The difference nucleophilic reactive site may be due to the conjugation of activity of both fluorine atom and methyl group on the M5. Keywords: coumarin derivatives; global descriptors; DFT; reactivity. 1. Introduction Coumarins are heterocyclic compounds which possess crucial importance in life because they play an essential role in the metabolism of all living cells[1]. Coumarins are substances coming from plants and they have considerable therapeutic importance. They can exhibit potent biological and pharmacodynamic properties such as photosensitizing, anti-solar, antibiotic, anticoagulant (antivitamin) and antihemorrhagic properties[2]. The study of heterocyclic chemistry is a widespread and growing field of chemistry with applications in medicine, agriculture, photodiodes [3], cosmetology [4] and many other fields. Several heterocyclic derivatives containing sulfur and/or nitrogen atoms serve as a unique and versatile scaffold for the design of new drugs [5]. Coumarins are well known for their multiple biological activities including anticancer, anti-HIV, antitumor and antioxidant [6]. According to their biological activities’ usefulness, they have been considered as a subject of special attention. Regarding the harmful side effects of existing treatments for pathologies such as cancer and AIDS, access to new therapeutic molecules that are effective and free of adverse effects has become the backbone of chemists. Computational chemistry is therefore both an independent research area and a vital adjunct to experimental studies [7]. Density functional theory (DFT) is recognized as a popular approach for calculating the structural and energetic characteristics of molecules[8-10]. This popularity is due to the fact that it provides very precise information for the evaluation of molecular properties[10]. The general objective of this study is to determine theoretically the chemical reactivity sites of five coumarin derivatives by the DFT method. 2. Materials and Methods 2.1 Level of Calculation Theory All calculations were performed by using the DFT method at B3LYP level and 6-31G(d, p) was used as basis set. The calculations were performed with Gaussian 09 software developed by Frisch and his colleagues [11]. It is important to note that Becke's three-parameters hybrid function known as B3LYP correlation function is one of the most robust functions of the hybrid family [12,13]. The output files were visualized using the GAUSS VIEW 05 graphical interface [14]. All the calculations were performed over the optimized molecules characterized by the minimum of energy. Besides, this state is indicated by the absence of imaginary frequencies. Figure 1 displays the structures of the studied molecules. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 19 M1 4 3 5 2 6 1 9 11 O 8 10 O 12 13 S 14 15 N 19 N 16 18 N 17 20 25 21 24 22 23 26 27 31 28 30 29 CH3 7 M2 4 3 5 2 6 1 9 11 O 8 10 O 12 13 S 14 15 N 19 N 16 18 N 17 20 25 21 24 22 23 26 27 31 28 30 29 CH3 32 CH3 7 4-{[(4,5-Diphenyl-4H-1,2,4-triazol-3-yl) sulfanyl]methyl}-6- methyl-2H-chromen-2-one 6-Methyl-4-({[4-phenyl-5-(4-methylphenyl)-4H-1,2,4- triazol-3-yl]sulfanyl}methyl)-2H-chromen-2-one M3 4 3 5 2 6 1 9 11 O 8 10 O 12 13 S 14 15 N 19 N 16 18 N 17 20 25 21 24 22 23 26 27 31 28 30 29 N + 32 O - 34 O 33 CH3 7 M4 4 3 5 2 6 1 9 11 O 8 10 O 12 13 S 14 15 N 19 N 16 18 N 17 20 25 21 24 22 23 26 27 31 28 30 29 F 32 CH3 7 6-Methyl-4-({[5-(4-nitrophenyl)-4-phenyl-4H-1,2,4- triazol-3- yl]thio}sulfanyl)-2H-chromen-2-one 4-({[4-(4-Fluorophenyl)-5-(phenyl)-4H-1,2,4-triazol-3- yl]sulfanyl} methyl)-6-methyl-2H-chromen-2-one M5 4 3 5 2 6 1 9 11 O 8 10 O 12 13 S 14 15 N 19 N 16 18 N 17 20 25 21 24 22 23 26 27 31 28 30 29 F 32 CH3 33 CH3 7 4-({[4-(4-Fluorophenyl)-5-(4-methylphenyl)-4H-1,2,4-triazol3-yl] sulfanyl}methyl)-6-methyl-2H-chromen-2-one Figure 1: Structures of studied coumarin molecules 2.2 Thermodynamic Parameters The knowledge of a molecule’s thermodynamic parameters is useful for understanding its behavior in terms of reactivity and disorder which can characterize a chemical component energetically. The thermodynamic parameters which have been considered in this study are enthalpy of formation ( , free enthalpy of formation ) and entropy of formation . These parameters are calculated according to Ochtersky [15] by using the following relationships: American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 20 ∑ (1) corresponds to Hcorr (thermal correction to enthalpy) in Gaussian’s output of the molecule, corresponds to its ZPE (Zero Point Energy) and ∑ ∑ (2) are given in JANAF table [16]. And energy of atomization denoted D0 which is the amount of energy changes when a compound's bonds are broken and the component atoms are reduced to individual atoms. ∑ ∑ (3) To calculate these quantities, we need a few component pieces first. In the abovementioned descriptions, we use: M to stand for the molecule, X to represent each element that makes up M, x is the number of X atoms in M. stands for total energy. Regarding the enthalpies of formation, its calculation requires two steps processes. The first step is to calculate the enthalpies of formation (∆fH°(0K)) of the species at 0k involved in the reaction. The second step is to calculate the enthalpies of formation of the species at 298K. The entropy of formation is calculated according to the following formula ∑ (4) Corresponds to the entropy of the molecule M at 298K. corresponds to the value of entropy given by Gaussian output in thermochemistry section. Corresponds to the entropy of the atom X given in JANAF table. The free enthalpy of Gibbs will be calculated by using the following relation (5) American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 21 2.3 Global and Local Indices Derived from the Conceptual DFT Frontier Molecular Orbital theory (FMO) is used to characterize the overall reactivity of a compound [17]. This theory predicts the excitation properties of a molecule. Therefore, it constitutes quantum parameters for the determination of molecular reactivity [18][19]. The lower the energetic gap between HOMO and LUMO orbitals, the more reactive the molecule is. The functions of Fukui are obtained by using the procedure based on the finite difference method [20][21][22]. They allow to highlight the electrophilic and nucleophilic sites values. The different values of the local descriptors are calculated from equations (6) and (7) below. (6) (7) : electron population of the atom k in the neutral molecule. : electron population of the atom k in the anionic molecule. : electron population of the atom k in the cationic molecule. The function f(r) reflects the ability for a molecular site to accept or to donate electrons. High values of f(r) are related to high reactivity at that site [23]. Besides, Dual descriptors are good tool to predict reactivity because they give information about the ability for a site to give or to gain electron density. They also permit to understand the problem of regioselectivity. Indeed, a dual positive descriptor corresponds to a site which can receive electron density thereby becoming the most electrophilic. Conversely, dual negative descriptor corresponds to a site which is capable to yield electron density. Thus, it is the most nucleophilic site. A site with a value of the dual descriptor close to zero corresponds to a site whose capacity to receive and to liberate electron density are equal. The different values of the local descriptors are calculated from the following relationship [24] (8) The chemical potential μ measures the tendency of electron cloud to escape from the molecule. This reactivity parameter can be expressed as a function of ionization potential PI and the electronic affinity AE. It corresponds to the opposite of the electronegativity χ as defined by Pauling and Mulliken[25,26]. (9) (10) and are respectively the energies of the HOMO and LUMO frontier molecular orbitals. The hardness ɳ, the softness S and the electrophile index ω can be expressed as a function of the ionization American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 22 potentials (PI) and the electron affinity (AE) [27][28]. (11) (12) 3. Results and Discussion 3.1 Thermodynamic descriptors The thermodynamic parameters that were determined in this study are standard enthalpy of formation, standard free enthalpy of formation and standard entropy of formation. All values are summarized in Table 1. Table 1: The standard thermodynamic parameters of formation of studied compounds. Molecules ΔfH 0 298 (kcal/mol) ΔfG 0 298 (kcal/mol) ΔfS 0 298 (kcal/mol- K) M1 -1375.949 -894.735 -1.614 M2 -1428.322 -950.388 -1.603 M3 -1575.789 -1099.047 -1.599 M4 -1423.329 -943.606 -1.609 M5 -1475.769 -999.623 -1.597 It is noted that any variation in enthalpy and free enthalpy reflects respectively the thermicity of a chemical reaction and the spontaneity with which a chemical reaction takes place. As far as entropy is concerned, it provides relative information on the level of disorder in each chemical system. All the calculated values of thermodynamic parameters in this study are negative. These negative values of enthalpy and free enthalpy mean respectively that the reactions are exothermic and spontaneous under the required conditions for the study. Furthermore, compound M3 is discovered as the most spontaneous and exothermic molecule during the synthesis. Regarding the entropy, its negative value is assumed to increase the order during the syntheses of coumarin molecules. Thus, the formation of all studied compounds is spontaneous, exothermic and reduces the order. According to overmentioned statement, it can be assumed that all these compounds exist and are thermodynamically stable. 3.2 Global Reactivity Descriptors Global reactivity parameters are necessary for the classification of compounds according to their chemical reactivity. These descriptors are calculated from HOMO (Highest Occupied Molecular Orbital) and LUMO (Lowest unoccupied Molecular Orbital) energies and they are grouped in Table 2. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 23 Table2: Global Reactivity Descriptors from Frontier Molecular Orbitals (FMOs) Molecules EHOMO(eV) ELUMO(eV) ΔEgap(eV) ω (eV) ɳ, (eV) S (eV -1 )  (eV) µ(D) M1 -6.214 -1.868 4.346 3.757 2.174 0.460 -4.041 6.600 M2 -6.162 -1.845 4.317 3.713 2.160 0.463 -4.003 6.563 M3 -6.371 -2.653 3.718 5.475 1.859 0.538 -4.512 9.363 M4 -6.254 -1.920 4.334 3.854 2.169 0.461 -4.087 5.200 M5 -6.233 -1.893 4.339 3.804 2.169 0.461 -4.063 5.233 Table 2 shows that the compound M3 has the smallest value of the gap energy (ΔEgap = 3.718 eV), which allows to qualify it as the most reactive and the least kinetically stable among all the studied molecules. Conversely, the compound M1 is the least reactive with the highest value of the gap energy (ΔEgap= 4.346 eV) thereby appearing as the most stable compound, i.e. the least reactive molecule. The analysis of the other global reactivity indices, such as global softness (S) reveals that compound M3 displays the highest value (S = 0.538 eV). It is therefore admitted as the softest studied molecule. Moreover, this compound M3 also has the lowest value of electronegativity (χ = - 4.512 eV) assuming it to be the best electron donor of the studied compounds. In addition, the electrophilic index value of compound M3 (ω = 5.475 eV) indicates that it is the most electrophilic molecule. Other parameter such as the solubility which is studied by the mean of the dipole moment of the five studied compounds was also considered. It varies from 5.200 to 9.363 Debye and the highest value of the dipole moment belongs to the compound M3. Therefore, M3 is assumed to be the most polar compound. This can be explained by the presence of the nitro group (-NO2) as a substituent. At the end of this analysis, we retain that M3 is the most reactive, the least stable, the softest, the best electron donor, the most electrophilic and the most polar compound. 3.3 Functions of Fukui Thanks to Hirschfeld parameters that were calculated from the optimized structures. Fukui indices were determined to highlight the electrophilic and nucleophilic attack sites. The calculated Fukui indices are shown in Tables 3 and 4. The nucleus which is concerned by this study is the coumarin nucleus, the triazol ring and the two benzenic cycles which are connected to the triazol ring. American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 24 Table 3: Fukui Indices and dual descriptors of M1, M2 and M3 using Hirshfeld Population Analysis (HPA). Molecule M1 Molecule M2 Molecule M3 atom F+ F- atom F+ F- atom F+ F- C1 0.042 0.047 -0.005 C1 0.042 0.046 -0.004 C1 0.045 0.072 -0.027 C2 0.040 0.043 -0.003 C2 0.040 0.042 -0.002 C2 0.030 0.051 -0.020 C3 0.004 0.004 0.000 C3 0.005 0.004 0.001 C3 0.009 0.046 -0.037 C4 -0.004 -0.007 0.003 C4 -0.004 -0.007 0.003 C4 0.002 0.037 -0.035 C5 0.015 0.014 0.002 C5 0.015 0.013 0.002 C5 0.021 0.034 -0.013 C6 0.014 0.016 -0.002 C6 0.015 0.016 -0.001 C6 0.014 0.051 -0.037 C7 0.031 0.034 -0.004 C7 0.031 0.034 -0.003 C7 0.029 0.073 -0.043 O8 0.023 0.025 -0.003 O8 0.023 0.025 -0.002 O8 0.017 0.038 -0.02 C9 0.039 0.022 0.017 C9 0.04 0.022 0.018 C9 0.031 0.013 0.018 C10 0.032 0.028 0.004 C10 0.032 0.027 0.005 C10 0.019 0.021 -0.002 C11 0.063 0.103 -0.04 C11 0.064 0.102 -0.038 C11 0.041 0.049 -0.008 O12 0.059 0.070 -0.011 O12 0.059 0.069 -0.010 O12 0.034 0.077 -0.043 C13 0.111 0.218 -0.107 C13 0.113 0.216 -0.103 C13 0.036 0.03 0.006 S14 0.150 0.154 -0.005 S14 0.151 0.152 -0.001 S14 0.054 0.060 -0.006 C15 0.024 -0.008 0.032 C15 0.023 -0.008 0.031 C15 0.017 0.018 0.000 N16 0.048 0.026 0.022 N16 0.046 0.026 0.020 N16 0.018 0.020 -0.002 N17 0.026 0.025 0.001 N17 0.023 0.024 -0.001 N17 0.024 0.033 -0.009 C18 0.040 0.023 0.017 C18 0.039 0.022 0.017 C18 0.012 0.024 -0.012 N19 0.017 0.007 0.010 N19 0.018 0.007 0.011 N19 0.013 0.007 0.006 C20 0.001 -0.001 0.002 C20 -0.001 0.000 -0.001 C20 0.039 0.010 0.028 C21 0.014 0.010 0.004 C21 0.032 0.023 0.009 C21 0.042 0.022 0.020 C22 0.033 0.026 0.007 C22 0.008 -0.006 0.014 C22 0.050 0.025 0.025 C23 0.046 0.036 0.010 C23 0.026 0.022 0.004 C23 0.027 0.029 -0.003 C24 0.026 0.020 0.006 C24 0.023 0.019 0.004 C24 0.049 0.028 0.021 C25 0.027 0.016 0.011 C25 0.027 0.023 0.004 C25 0.041 0.023 0.018 C26 -0.008 -0.009 0.001 C26 0.006 0.003 0.003 C26 -0.009 -0.009 0.000 C27 0.008 -0.006 0.014 C27 -0.007 -0.009 0.002 C27 0.008 0.006 0.003 C28 0.021 0.012 0.009 C28 0.001 0.001 0.000 C28 0.024 0.024 0.000 C29 0.030 0.025 0.005 C29 0.027 0.023 0.004 C29 0.028 0.027 0.001 C30 0.027 0.023 0.004 C30 0.030 0.025 0.005 C30 0.016 0.016 -0.001 C31 0.000 0.002 -0.001 C31 0.020 0.012 0.008 C31 -0.007 -0.006 -0.001 C32 0.034 0.030 0.004 N32 0.051 0.005 0.046 O33 0.088 0.024 0.064 O34 0.088 0.024 0.064 The analysis of these data shows that the smallest and the highest values of Δf are obtained for C13 and C15 carbon atoms, respectively. These atoms represent respectively the nucleophilic and electrophilic sites. These American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 25 reactive sites are the same for compounds M1 and M2 however their structures are different from a methyl group on M2 specially localized on carbon C23. Table 4: Fukui Indices and dual descriptors of M4 et M5 using Hirshfeld Population Analysis (HPA). Molecule M4 Molecule M5 Atom F + F - Atom F + F - C1 0.076 0.063 0.013 C1 0.076 0.057 0.019 C2 0.051 0.045 0.006 C2 0.052 0.041 0.010 C3 0.017 0.039 -0.021 C3 0.017 0.034 -0.017 C4 0.007 0.029 -0.022 C4 0.008 0.025 -0.017 C5 0.042 0.028 0.014 C5 0.042 0.025 0.018 C6 0.023 0.045 -0.022 C6 0.023 0.040 -0.017 C7 0.046 0.064 -0.017 C7 0.046 0.058 -0.011 O8 0.031 0.033 -0.002 O8 0.031 0.030 0.001 C9 0.063 0.010 0.053 C9 0.063 0.008 0.055 C10 0.039 0.017 0.022 C10 0.039 0.015 0.024 C11 0.091 0.038 0.053 C11 0.091 0.032 0.06 O12 0.066 0.064 0.002 12 0.066 0.056 0.010 C13 0.050 0.030 0.020 C13 0.049 0.029 0.020 S14 0.075 0.054 0.021 C14 0.074 0.051 0.023 C15 0.007 0.026 -0.019 C15 0.006 0.028 -0.022 N16 0.016 0.027 -0.010 N16 0.016 0.028 -0.012 N17 0.019 0.039 -0.019 N17 0.019 0.039 -0.021 C18 0.022 0.023 -0.001 C18 0.022 0.021 0.001 N19 0.011 0.009 0.002 N19 0.011 0.009 0.002 C20 0.006 0.027 -0.021 C20 0.004 0.034 -0.030 C21 0.017 0.034 -0.018 C21 0.015 0.037 -0.022 C22 0.031 0.041 -0.010 C22 0.027 0.044 -0.017 C23 0.049 0.073 -0.024 C23 0.025 0.047 -0.022 C24 0.029 0.046 -0.017 C24 0.025 0.049 -0.023 C25 0.020 0.035 -0.015 C25 0.019 0.039 -0.020 C26 -0.004 -0.010 0.006 C26 -0.003 -0.010 0.007 C27 0.011 0.006 0.005 C27 0.011 0.006 0.004 C28 0.030 0.025 0.005 C28 0.030 0.024 0.006 C29 0.018 0.014 0.005 C29 0.018 0.013 0.005 C30 0.02 0.017 0.003 C30 0.02 0.017 0.003 C31 0.002 -0.006 0.008 C31 0.003 -0.006 0.009 F32 0.018 0.016 0.002 C32 0.018 0.016 0.002 C33 0.037 0.064 -0.027 Through this difference regarding the structures and yet the reactive sites are the same, we can assume that the American Scientific Research Journal for Engineering, Technology, and Sciences (ASRJETS) (2021) Volume 75, No 1, pp 17-28 26 methyl donor group has no influence on the coumarine molecules. Regarding the molecule M3, a nitro group has substituted the methyl group. Here, the lowest value of Δf is found on oxygen atoms O12 and the highest value is attributed to both oxygen atoms O33 and O34 which are in the same environment. This finding allows to understand that O33 and O34 is the electrophilic sites where it will happen nucleophilic attack. This molecule must be bidentate during the electrophilic attacks as both O33 and O34 and the same. Besides O12 is the nucleophilic site where it will happen electrophilic attack. The presence of nitro group at carbon C23 influences seriously the sites of reactivity because they are no longer carried by carbon atoms but by oxygen ones. Hirshfeld population study of molecule M4 shows that C11 atom is the electrophilic site where it will happen nucleophilic attack due to the fact it displays the highest value of Δf. On the other hand, the carbon atom C23 has the lowest value of the same parameter, which makes it the nucleophilic site. Thus, we can assume that the presence of electronegative atom favors the displacement of reactivity sites. Concerning molecule M5, plus the fluorine atom on C29, the methyl group has been maintained on C23 comparatively to M4. It appears that the electrophilic site remains C11. However, the nucleophilic site has shifted from C23 to C20 regarding Δf values. The fact that the nucleophilic site moves from C23 to C20 can be explained by the conjugation of activity of both the electo-donnor (-CH3) and the electro-attractor (F) groups. It can be underlined that the fact of adding methyl group to carbon C23 of the molecule containing fluorine atom influences only the nucleophilic site. 4. Conclusion At the end of our study carried out by the DFT method at B3LYP/6-31G (d, p) level, we determined the most reactive molecule from the values of the global descriptors of chemical reactivity. The analysis of the results showed, on one hand that compound M3 is the most polar because, it has the highest chemical reactivity and has both the lowest kinetic stability and the smallest energy gap of the studied molecules. On the other hand, compound M1 is discovered as the least polar, with the lowest chemical reactivity and the highest kinetic stability. Besides, Hirshfeld's population analysis method allowed to highlight the sites of reactivity that are the sites of electrophilic and nucleophilic attacks. These sites are all located on carbon atoms except for molecule M3 in which they are located on oxygen atoms. This displacement is explained by the presence of nitro group. This work can help to understand the reactivity of coumarin derivatives and may be useful in the synthesis of new coumarin precursors. References [1]. D. Arora, Pragi; Arora, Varun; Lamba, H. S.; Wadhwa, “Importance of Heterocyclic Chemistry:,” Int. J. Pharm. Sci. 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